LMFDB - Embedded newform 507.2.t.a.4.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(4,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

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

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

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

chi := DirichletCharacter("507.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, degree $24$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$14$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			4.14
Character	$\chi$	$=$	507.4
Dual form			507.2.t.a.127.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.69937 + 0.108781i) q^{2} +(0.278217 - 0.960518i) q^{3} +(5.28123 + 0.426345i) q^{4} +(-2.66969 - 1.01248i) q^{5} +(0.855497 - 2.56253i) q^{6} +(-1.46999 - 3.45019i) q^{7} +(8.84587 + 1.07408i) q^{8} +(-0.845190 - 0.534466i) q^{9} +O(q^{10})$	\(q+(2.69937 + 0.108781i) q^{2} +(0.278217 - 0.960518i) q^{3} +(5.28123 + 0.426345i) q^{4} +(-2.66969 - 1.01248i) q^{5} +(0.855497 - 2.56253i) q^{6} +(-1.46999 - 3.45019i) q^{7} +(8.84587 + 1.07408i) q^{8} +(-0.845190 - 0.534466i) q^{9} +(-7.09634 - 3.02347i) q^{10} +(3.02709 + 4.78696i) q^{11} +(1.87884 - 4.95410i) q^{12} +(3.60555 - 0.00206402i) q^{13} +(-3.59272 - 9.47323i) q^{14} +(-1.71526 + 2.28260i) q^{15} +(13.3018 + 2.16175i) q^{16} +(-5.50825 + 2.34685i) q^{17} +(-2.22334 - 1.53466i) q^{18} +(0.00817830 - 0.00472175i) q^{19} +(-13.6676 - 6.48536i) q^{20} +(-3.72294 + 0.452047i) q^{21} +(7.65049 + 13.2510i) q^{22} +(1.35072 - 2.33952i) q^{23} +(3.49275 - 8.19779i) q^{24} +(2.35960 + 2.09042i) q^{25} +(9.73293 + 0.386643i) q^{26} +(-0.748511 + 0.663123i) q^{27} +(-6.29237 - 18.8480i) q^{28} +(-0.299524 + 7.43261i) q^{29} +(-4.87842 + 5.97499i) q^{30} +(-1.24388 - 1.40406i) q^{31} +(18.2098 + 3.71755i) q^{32} +(5.44015 - 1.57576i) q^{33} +(-15.1241 + 5.73580i) q^{34} +(0.431166 + 10.6993i) q^{35} +(-4.23578 - 3.18298i) q^{36} +(-6.01898 + 1.22878i) q^{37} +(0.0225899 - 0.0118561i) q^{38} +(1.00114 - 3.46377i) q^{39} +(-22.5283 - 11.8238i) q^{40} +(1.74960 + 0.506779i) q^{41} +(-10.0988 + 0.815257i) q^{42} +(-1.32061 + 6.46876i) q^{43} +(13.9459 + 26.5716i) q^{44} +(1.71526 + 2.28260i) q^{45} +(3.90059 - 6.16829i) q^{46} +(-0.101185 + 0.0698431i) q^{47} +(5.77720 - 12.1752i) q^{48} +(-4.89387 + 5.09505i) q^{49} +(6.14202 + 5.89949i) q^{50} +(0.721696 + 5.94370i) q^{51} +(19.0426 + 1.52631i) q^{52} +(0.313785 - 2.58425i) q^{53} +(-2.09264 + 1.70859i) q^{54} +(-3.23470 - 15.8446i) q^{55} +(-9.29753 - 32.0988i) q^{56} +(-0.00225998 - 0.00916908i) q^{57} +(-1.61705 + 20.0307i) q^{58} +(1.44574 + 8.89598i) q^{59} +(-10.0319 + 11.3236i) q^{60} +(-0.731047 + 0.549346i) q^{61} +(-3.20497 - 3.92537i) q^{62} +(-0.601589 + 3.70172i) q^{63} +(22.5810 + 5.56572i) q^{64} +(-9.62781 - 3.64504i) q^{65} +(14.8564 - 3.66176i) q^{66} +(0.151649 + 1.87851i) q^{67} +(-30.0909 + 10.0458i) q^{68} +(-1.87136 - 1.94829i) q^{69} +28.9282i q^{70} +(5.83813 - 5.60760i) q^{71} +(-6.90238 - 5.63562i) q^{72} +(1.18988 - 2.26713i) q^{73} +(-16.3811 + 2.66219i) q^{74} +(2.66437 - 1.68484i) q^{75} +(0.0452046 - 0.0214498i) q^{76} +(12.0661 - 17.4808i) q^{77} +(3.07925 - 9.24108i) q^{78} +(-8.75708 - 12.6868i) q^{79} +(-33.3230 - 19.2391i) q^{80} +(0.428693 + 0.903450i) q^{81} +(4.66769 + 1.55831i) q^{82} +(3.44923 - 13.9941i) q^{83} +(-19.8545 + 0.800107i) q^{84} +(17.0815 - 0.688360i) q^{85} +(-4.26848 + 17.3179i) q^{86} +(7.05582 + 2.35558i) q^{87} +(21.6356 + 45.5962i) q^{88} +(-1.82645 - 1.05450i) q^{89} +(4.38182 + 6.34816i) q^{90} +(-5.30724 - 12.4368i) q^{91} +(8.13091 - 11.7797i) q^{92} +(-1.69469 + 0.804141i) q^{93} +(-0.280733 + 0.177525i) q^{94} +(-0.0266143 + 0.00432524i) q^{95} +(8.63705 - 16.4565i) q^{96} +(-8.25578 - 6.74064i) q^{97} +(-13.7646 + 13.2211i) q^{98} -5.66376i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9}+O(q^{10}) $ 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9	$ 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9} + 4 q^{10} + 24 q^{12} + 26 q^{13} + 4 q^{14} + 8 q^{16} + 4 q^{17} + 72 q^{22} - 48 q^{23} + 68 q^{25} + 39 q^{26} - 28 q^{27} - 45 q^{29} + 4 q^{30} + 26 q^{31} + 65 q^{32} - 13 q^{33} + 65 q^{34} - 82 q^{35} - 12 q^{36} - 73 q^{38} + 24 q^{40} - 132 q^{42} - 72 q^{43} + 39 q^{44} + 8 q^{48} + 68 q^{49} + 52 q^{50} - 8 q^{51} - 65 q^{52} + 37 q^{53} - 53 q^{55} + 14 q^{56} - 26 q^{57} + 26 q^{58} - 208 q^{59} + 78 q^{60} - 12 q^{61} - 49 q^{62} + 14 q^{64} + 52 q^{65} + 64 q^{66} - 26 q^{67} - 33 q^{68} + 4 q^{69} - 78 q^{71} + 52 q^{73} + 205 q^{74} - 8 q^{75} - 26 q^{76} - 114 q^{77} - 65 q^{78} + 28 q^{79} - 468 q^{80} + 14 q^{81} - 45 q^{82} - 78 q^{83} + 13 q^{85} + 13 q^{86} + 46 q^{87} + 26 q^{88} - 8 q^{90} - 260 q^{91} + 8 q^{92} - 25 q^{94} - 90 q^{95} - 65 q^{96} - 26 q^{97} + 104 q^{98}+O(q^{100}) $ 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9 + 4 * q^10 + 24 * q^12 + 26 * q^13 + 4 * q^14 + 8 * q^16 + 4 * q^17 + 72 * q^22 - 48 * q^23 + 68 * q^25 + 39 * q^26 - 28 * q^27 - 45 * q^29 + 4 * q^30 + 26 * q^31 + 65 * q^32 - 13 * q^33 + 65 * q^34 - 82 * q^35 - 12 * q^36 - 73 * q^38 + 24 * q^40 - 132 * q^42 - 72 * q^43 + 39 * q^44 + 8 * q^48 + 68 * q^49 + 52 * q^50 - 8 * q^51 - 65 * q^52 + 37 * q^53 - 53 * q^55 + 14 * q^56 - 26 * q^57 + 26 * q^58 - 208 * q^59 + 78 * q^60 - 12 * q^61 - 49 * q^62 + 14 * q^64 + 52 * q^65 + 64 * q^66 - 26 * q^67 - 33 * q^68 + 4 * q^69 - 78 * q^71 + 52 * q^73 + 205 * q^74 - 8 * q^75 - 26 * q^76 - 114 * q^77 - 65 * q^78 + 28 * q^79 - 468 * q^80 + 14 * q^81 - 45 * q^82 - 78 * q^83 + 13 * q^85 + 13 * q^86 + 46 * q^87 + 26 * q^88 - 8 * q^90 - 260 * q^91 + 8 * q^92 - 25 * q^94 - 90 * q^95 - 65 * q^96 - 26 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{78}\right)$

Coefficient data

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

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

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

$2$	2.69937	+	0.108781i	1.90874	+	0.0769196i	0.966294	−	0.257440i	$-0.0828789\pi$
$2$	2.69937	+	0.108781i	1.90874	+	0.0769196i	0.942446	+	0.334359i	$0.108520\pi$
$3$	0.278217	−	0.960518i	0.160629	−	0.554555i
$3$	0.278217	−	0.960518i	0.160629	−	0.554555i
$4$	5.28123	+	0.426345i	2.64061	+	0.213172i
$5$	−2.66969	−	1.01248i	−1.19392	−	0.452796i	−0.324036	−	0.946045i	$-0.605040\pi$
$5$	−2.66969	−	1.01248i	−1.19392	−	0.452796i	−0.869888	+	0.493249i	$0.835809\pi$
$6$	0.855497	−	2.56253i	0.349255	−	1.04615i
$7$	−1.46999	−	3.45019i	−0.555603	−	1.30405i	−0.926821	−	0.375503i	$-0.877470\pi$
$7$	−1.46999	−	3.45019i	−0.555603	−	1.30405i	0.371218	−	0.928546i	$-0.378940\pi$
$8$	8.84587	+	1.07408i	3.12749	+	0.379746i
$9$	−0.845190	−	0.534466i	−0.281730	−	0.178155i
$10$	−7.09634	−	3.02347i	−2.24406	−	0.956105i
$11$	3.02709	+	4.78696i	0.912702	+	1.44332i	0.896296	+	0.443457i	$0.146248\pi$
$11$	3.02709	+	4.78696i	0.912702	+	1.44332i	0.0164058	+	0.999865i	$0.494778\pi$
$12$	1.87884	−	4.95410i	0.542375	−	1.43013i
$13$	3.60555	−	0.00206402i	1.00000	−	0.000572457i
$13$	3.60555	−	0.00206402i	1.00000	−	0.000572457i
$14$	−3.59272	−	9.47323i	−0.960195	−	2.53183i
$15$	−1.71526	+	2.28260i	−0.442879	+	0.589365i
$16$	13.3018	+	2.16175i	3.32545	+	0.540439i
$17$	−5.50825	+	2.34685i	−1.33595	+	0.569194i	−0.937496	−	0.347996i	$-0.886862\pi$
$17$	−5.50825	+	2.34685i	−1.33595	+	0.569194i	−0.398450	+	0.917190i	$0.630452\pi$
$18$	−2.22334	−	1.53466i	−0.524046	−	0.361723i
$19$	0.00817830	−	0.00472175i	0.00187623	−	0.00108324i	−0.499062	−	0.866567i	$-0.666322\pi$
$19$	0.00817830	−	0.00472175i	0.00187623	−	0.00108324i	0.500938	+	0.865483i	$0.332989\pi$
$20$	−13.6676	−	6.48536i	−3.05617	−	1.45017i
$21$	−3.72294	+	0.452047i	−0.812413	+	0.0986448i
$22$	7.65049	+	13.2510i	1.63109	+	2.82513i
$23$	1.35072	−	2.33952i	0.281645	−	0.487824i	−0.690145	−	0.723671i	$-0.742453\pi$
$23$	1.35072	−	2.33952i	0.281645	−	0.487824i	0.971790	+	0.235848i	$0.0757866\pi$
$24$	3.49275	−	8.19779i	0.712955	−	1.67337i
$25$	2.35960	+	2.09042i	0.471919	+	0.418084i
$26$	9.73293	+	0.386643i	1.90878	+	0.0758269i
$27$	−0.748511	+	0.663123i	−0.144051	+	0.127618i
$28$	−6.29237	−	18.8480i	−1.18915	−	3.56193i
$29$	−0.299524	+	7.43261i	−0.0556202	+	1.38020i	0.694783	+	0.719220i	$0.255501\pi$
$29$	−0.299524	+	7.43261i	−0.0556202	+	1.38020i	−0.750403	+	0.660981i	$0.770140\pi$
$30$	−4.87842	+	5.97499i	−0.890674	+	1.09088i
$31$	−1.24388	−	1.40406i	−0.223408	−	0.252176i	0.626110	−	0.779735i	$-0.284646\pi$
$31$	−1.24388	−	1.40406i	−0.223408	−	0.252176i	−0.849519	+	0.527559i	$0.823108\pi$
$32$	18.2098	+	3.71755i	3.21906	+	0.657177i
$33$	5.44015	−	1.57576i	0.947008	−	0.274304i
$34$	−15.1241	+	5.73580i	−2.59376	+	0.983682i
$35$	0.431166	+	10.6993i	0.0728804	+	1.80851i
$36$	−4.23578	−	3.18298i	−0.705963	−	0.530496i
$37$	−6.01898	+	1.22878i	−0.989514	+	0.202011i	−0.667407	−	0.744693i	$-0.732596\pi$
$37$	−6.01898	+	1.22878i	−0.989514	+	0.202011i	−0.322106	+	0.946704i	$0.604391\pi$
$38$	0.0225899	−	0.0118561i	0.00366456	−	0.00192331i
$39$	1.00114	−	3.46377i	0.160311	−	0.554647i
$40$	−22.5283	−	11.8238i	−3.56203	−	1.86950i
$41$	1.74960	+	0.506779i	0.273242	+	0.0791456i	0.412010	−	0.911179i	$-0.364827\pi$
$41$	1.74960	+	0.506779i	0.273242	+	0.0791456i	−0.138768	+	0.990325i	$0.544314\pi$
$42$	−10.0988	+	0.815257i	−1.55827	+	0.125797i
$43$	−1.32061	+	6.46876i	−0.201391	+	0.986477i	0.745889	+	0.666070i	$0.232025\pi$
$43$	−1.32061	+	6.46876i	−0.201391	+	0.986477i	−0.947280	+	0.320407i	$0.896180\pi$
$44$	13.9459	+	26.5716i	2.10242	+	4.00582i
$45$	1.71526	+	2.28260i	0.255696	+	0.340270i
$46$	3.90059	−	6.16829i	0.575110	−	0.909464i
$47$	−0.101185	+	0.0698431i	−0.0147594	+	0.0101877i	−0.575422	−	0.817857i	$-0.695162\pi$
$47$	−0.101185	+	0.0698431i	−0.0147594	+	0.0101877i	0.560662	+	0.828045i	$0.310547\pi$
$48$	5.77720	−	12.1752i	0.833867	−	1.75734i
$49$	−4.89387	+	5.09505i	−0.699124	+	0.727865i
$50$	6.14202	+	5.89949i	0.868613	+	0.834314i
$51$	0.721696	+	5.94370i	0.101058	+	0.832285i
$52$	19.0426	+	1.52631i	2.64074	+	0.211661i
$53$	0.313785	−	2.58425i	0.0431017	−	0.354975i	−0.955163	−	0.296082i	$-0.904320\pi$
$53$	0.313785	−	2.58425i	0.0431017	−	0.354975i	0.998264	−	0.0588928i	$-0.0187570\pi$
$54$	−2.09264	+	1.70859i	−0.284772	+	0.232509i
$55$	−3.23470	−	15.8446i	−0.436166	−	2.13648i
$56$	−9.29753	−	32.0988i	−1.24244	−	4.28938i
$57$	−0.00225998	−	0.00916908i	−0.000299341	−	0.00121447i
$58$	−1.61705	+	20.0307i	−0.212329	+	2.63017i
$59$	1.44574	+	8.89598i	0.188219	+	1.15816i	0.893444	+	0.449174i	$0.148282\pi$
$59$	1.44574	+	8.89598i	0.188219	+	1.15816i	−0.705225	+	0.708983i	$0.749154\pi$
$60$	−10.0319	+	11.3236i	−1.29511	+	1.46188i
$61$	−0.731047	+	0.549346i	−0.0936010	+	0.0703366i	−0.646512	−	0.762903i	$-0.723773\pi$
$61$	−0.731047	+	0.549346i	−0.0936010	+	0.0703366i	0.552911	+	0.833240i	$0.313517\pi$
$62$	−3.20497	−	3.92537i	−0.407031	−	0.498523i
$63$	−0.601589	+	3.70172i	−0.0757930	+	0.466373i
$64$	22.5810	+	5.56572i	2.82262	+	0.695715i
$65$	−9.62781	−	3.64504i	−1.19418	−	0.452112i
$66$	14.8564	−	3.66176i	1.82869	−	0.450732i
$67$	0.151649	+	1.87851i	0.0185269	+	0.229497i	0.999394	+	0.0348169i	$0.0110848\pi$
$67$	0.151649	+	1.87851i	0.0185269	+	0.229497i	−0.980867	+	0.194680i	$0.937633\pi$
$68$	−30.0909	+	10.0458i	−3.64906	+	1.21823i
$69$	−1.87136	−	1.94829i	−0.225285	−	0.234546i
$70$			28.9282i			3.45758i
$71$	5.83813	−	5.60760i	0.692858	−	0.665499i	−0.261144	−	0.965300i	$-0.584100\pi$
$71$	5.83813	−	5.60760i	0.692858	−	0.665499i	0.954002	+	0.299801i	$0.0969201\pi$
$72$	−6.90238	−	5.63562i	−0.813453	−	0.664164i
$73$	1.18988	−	2.26713i	0.139265	−	0.265347i	−0.805828	−	0.592150i	$-0.798279\pi$
$73$	1.18988	−	2.26713i	0.139265	−	0.265347i	0.945092	+	0.326803i	$0.105971\pi$
$74$	−16.3811	+	2.66219i	−1.90426	+	0.309473i
$75$	2.66437	−	1.68484i	0.307655	−	0.194549i
$76$	0.0452046	−	0.0214498i	0.00518532	−	0.00246047i
$77$	12.0661	−	17.4808i	1.37506	−	1.99212i
$78$	3.07925	−	9.24108i	0.348656	−	1.04635i
$79$	−8.75708	−	12.6868i	−0.985248	−	1.42738i	−0.902441	−	0.430813i	$-0.858227\pi$
$79$	−8.75708	−	12.6868i	−0.985248	−	1.42738i	−0.0828072	−	0.996566i	$-0.526389\pi$
$80$	−33.3230	−	19.2391i	−3.72563	−	2.15099i
$81$	0.428693	+	0.903450i	0.0476325	+	0.100383i
$82$	4.66769	+	1.55831i	0.515461	+	0.172086i
$83$	3.44923	−	13.9941i	0.378602	−	1.53605i	−0.404726	−	0.914438i	$-0.632633\pi$
$83$	3.44923	−	13.9941i	0.378602	−	1.53605i	0.783328	−	0.621609i	$-0.213521\pi$
$84$	−19.8545	+	0.800107i	−2.16630	+	0.0872988i
$85$	17.0815	−	0.688360i	1.85275	−	0.0746631i
$86$	−4.26848	+	17.3179i	−0.460282	+	1.86744i
$87$	7.05582	+	2.35558i	0.756463	+	0.252545i
$88$	21.6356	+	45.5962i	2.30637	+	4.86057i
$89$	−1.82645	−	1.05450i	−0.193603	−	0.111777i	0.400065	−	0.916487i	$-0.368988\pi$
$89$	−1.82645	−	1.05450i	−0.193603	−	0.111777i	−0.593668	+	0.804710i	$0.702321\pi$
$90$	4.38182	+	6.34816i	0.461884	+	0.669155i
$91$	−5.30724	−	12.4368i	−0.556350	−	1.30373i
$92$	8.13091	−	11.7797i	0.847706	−	1.22811i
$93$	−1.69469	+	0.804141i	−0.175731	+	0.0833856i
$94$	−0.280733	+	0.177525i	−0.0289554	+	0.0183103i
$95$	−0.0266143	+	0.00432524i	−0.00273056	+	0.000443760i
$96$	8.63705	−	16.4565i	0.881516	−	1.67959i
$97$	−8.25578	−	6.74064i	−0.838248	−	0.684408i	0.112744	−	0.993624i	$-0.464036\pi$
$97$	−8.25578	−	6.74064i	−0.838248	−	0.684408i	−0.950992	+	0.309216i	$0.899933\pi$
$98$	−13.7646	+	13.2211i	−1.39043	+	1.33553i
$99$		−	5.66376i		−	0.569230i
$100$	11.5703	+	12.0460i	1.15703	+	1.20460i
$101$	1.37272	−	0.458281i	0.136591	−	0.0456007i	−0.247551	−	0.968875i	$-0.579626\pi$
$101$	1.37272	−	0.458281i	0.136591	−	0.0456007i	0.384141	+	0.923274i	$0.374497\pi$
$102$	1.30156	+	16.1227i	0.128874	+	1.59639i
$103$	9.66946	−	2.38331i	0.952760	−	0.234834i	0.267849	−	0.963461i	$-0.413687\pi$
$103$	9.66946	−	2.38331i	0.952760	−	0.234834i	0.684911	+	0.728627i	$0.259841\pi$
$104$	31.8965	+	3.85440i	3.12770	+	0.377955i
$105$	10.3968	+	2.56258i	1.01463	+	0.250083i
$106$	1.12814	−	6.94171i	0.109574	−	0.674239i
$107$	5.90986	+	7.23826i	0.571327	+	0.699749i	0.976750	−	0.214380i	$-0.0687732\pi$
$107$	5.90986	+	7.23826i	0.571327	+	0.699749i	−0.405423	+	0.914129i	$0.632876\pi$
$108$	−4.23578	+	3.18298i	−0.407588	+	0.306282i
$109$	9.66797	−	10.9129i	0.926024	−	1.04526i	−0.0728273	−	0.997345i	$-0.523202\pi$
$109$	9.66797	−	10.9129i	0.926024	−	1.04526i	0.998851	−	0.0479203i	$-0.0152594\pi$
$110$	−7.00804	−	43.1222i	−0.668191	−	4.11154i
$111$	−0.494316	+	6.12320i	−0.0469184	+	0.581189i
$112$	−12.0950	−	49.0715i	−1.14287	−	4.63682i
$113$	−4.53979	−	15.6732i	−0.427067	−	1.47441i	−0.829266	−	0.558855i	$-0.811241\pi$
$113$	−4.53979	−	15.6732i	−0.427067	−	1.47441i	0.402198	−	0.915553i	$-0.368246\pi$
$114$	−0.00510308	−	0.0249965i	−0.000477947	−	0.00234114i
$115$	−5.97474	+	4.87822i	−0.557147	+	0.454896i
$116$	−4.75071	+	39.1256i	−0.441092	+	3.63272i
$117$	−3.04848	−	1.92530i	−0.281832	−	0.177994i
$118$	2.93486	+	24.1708i	0.270176	+	2.22510i
$119$	16.1941	+	15.5547i	1.48451	+	1.42589i
$120$	−17.6247	+	18.3493i	−1.60891	+	1.67505i
$121$	−9.03608	+	19.0431i	−0.821462	+	1.73119i
$122$	−2.03312	+	1.40336i	−0.184070	+	0.127055i
$123$	0.973541	−	1.53953i	0.0877812	−	0.138815i
$124$	−5.97063	−	7.94546i	−0.536178	−	0.713524i
$125$	2.45159	+	4.67111i	0.219277	+	0.417797i
$126$	−2.02658	+	9.92686i	−0.180542	+	0.884355i
$127$	−17.7531	+	1.43318i	−1.57533	+	0.127174i	−0.836977	−	0.547238i	$-0.815679\pi$
$127$	−17.7531	+	1.43318i	−1.57533	+	0.127174i	−0.738355	+	0.674412i	$0.764397\pi$
$128$	24.6458	+	7.13873i	2.17840	+	0.630981i
$129$	5.84594	+	3.06819i	0.514707	+	0.270139i
$130$	−25.5925	−	10.8866i	−2.24461	−	0.954820i
$131$	−17.8355	+	9.36079i	−1.55829	+	0.817856i	−0.999931	−	0.0117407i	$-0.996263\pi$
$131$	−17.8355	+	9.36079i	−1.55829	+	0.817856i	−0.558363	+	0.829597i	$0.688570\pi$
$132$	29.4025	−	6.00256i	2.55916	−	0.522456i
$133$	−0.0283129	−	0.0212758i	−0.00245504	−	0.00184484i
$134$	0.205011	+	5.08729i	0.0177102	+	0.439475i
$135$	2.66969	−	1.01248i	0.229771	−	0.0871405i
$136$	−51.2460	+	14.8436i	−4.39430	+	1.27283i
$137$	2.40328	+	0.490633i	0.205326	+	0.0419176i	0.301588	−	0.953438i	$-0.402483\pi$
$137$	2.40328	+	0.490633i	0.205326	+	0.0419176i	−0.0962616	+	0.995356i	$0.530689\pi$
$138$	−4.83954	−	5.46271i	−0.411969	−	0.465017i
$139$	1.71989	−	2.10649i	0.145879	−	0.178670i	−0.696497	−	0.717560i	$-0.745259\pi$
$139$	1.71989	−	2.10649i	0.145879	−	0.178670i	0.842376	+	0.538890i	$0.181156\pi$
$140$	−2.28450	+	56.6892i	−0.193075	+	4.79111i
$141$	0.0389341	+	0.116622i	0.00327884	+	0.00982132i
$142$	16.3692	−	14.5019i	1.37368	−	1.21697i
$143$	10.9242	+	17.2534i	0.913528	+	1.44280i
$144$	−10.0872	−	8.93646i	−0.840598	−	0.744705i
$145$	8.32502	−	19.5395i	0.691355	−	1.62267i
$146$	3.45854	−	5.99037i	0.286231	−	0.495766i
$147$	3.53233	+	6.11818i	0.291342	+	0.504619i
$148$	−32.3115	+	3.92332i	−2.65599	+	0.322495i
$149$	−6.41286	−	3.04294i	−0.525362	−	0.249287i	0.147491	−	0.989063i	$-0.452880\pi$
$149$	−6.41286	−	3.04294i	−0.525362	−	0.249287i	−0.672853	+	0.739776i	$0.734931\pi$
$150$	7.37538	−	4.25818i	0.602198	−	0.347679i
$151$	9.49092	+	6.55111i	0.772360	+	0.533121i	0.887820	−	0.460191i	$-0.152219\pi$
$151$	9.49092	+	6.55111i	0.772360	+	0.533121i	−0.115460	+	0.993312i	$0.536834\pi$
$152$	0.0774158	−	0.0329838i	0.00627925	−	0.00267534i
$153$	5.90982	+	0.960440i	0.477781	+	0.0776470i
$154$	34.4725	−	45.8745i	2.77787	−	3.69667i
$155$	1.89921	+	5.00781i	0.152548	+	0.402237i
$156$	6.76403	−	17.8661i	0.541556	−	1.43044i
$157$	0.768458	−	2.02626i	0.0613296	−	0.161713i	−0.900849	−	0.434133i	$-0.857055\pi$
$157$	0.768458	−	2.02626i	0.0613296	−	0.161713i	0.962178	+	0.272420i	$0.0878240\pi$
$158$	−22.2585	−	35.1990i	−1.77079	−	2.80028i
$159$	−2.39492	−	1.02038i	−0.189930	−	0.0809215i
$160$	−44.8506	−	28.3618i	−3.54575	−	2.24220i
$161$	−10.0573	−	1.22118i	−0.792629	−	0.0962425i
$162$	1.05892	+	2.48538i	0.0831966	+	0.195270i
$163$	1.88593	−	5.64906i	0.147718	−	0.442469i	−0.848517	−	0.529169i	$-0.822504\pi$
$163$	1.88593	−	5.64906i	0.147718	−	0.442469i	0.996234	+	0.0866999i	$0.0276321\pi$
$164$	9.02400	+	3.42235i	0.704656	+	0.267241i
$165$	−16.1190	−	1.30126i	−1.25486	−	0.101303i
$166$	10.8330	−	37.3999i	0.840804	−	2.90279i
$167$	−3.01013	−	0.121304i	−0.232931	−	0.00938680i	−0.0764741	−	0.997072i	$-0.524366\pi$
$167$	−3.01013	−	0.121304i	−0.232931	−	0.00938680i	−0.156457	+	0.987685i	$0.550007\pi$
$168$	−33.4182			−2.57827
$169$	13.0000	−	0.0148839i	0.999999	−	0.00114491i
$170$	46.1840			3.54215
$171$	−0.00943583		0.000380251i	−0.000721576		2.90785e-5i
$172$	−9.73235	+	33.6000i	−0.742085	+	2.56197i
$173$	−7.75850	−	0.626331i	−0.589868	−	0.0476191i	−0.218071	−	0.975933i	$-0.569976\pi$
$173$	−7.75850	−	0.626331i	−0.589868	−	0.0476191i	−0.371797	+	0.928314i	$0.621258\pi$
$174$	18.7900	+	7.12611i	1.42447	+	0.540229i
$175$	3.74377	−	11.2139i	0.283002	−	0.847695i
$176$	29.9175	+	70.2190i	2.25512	+	5.29296i
$177$	8.94698	+	1.08636i	0.672496	+	0.0816558i
$178$	−4.81555	−	3.04517i	−0.360941	−	0.228245i
$179$	11.3850	+	4.85070i	0.850956	+	0.362559i	0.773006	−	0.634399i	$-0.218752\pi$
$179$	11.3850	+	4.85070i	0.850956	+	0.362559i	0.0779503	+	0.996957i	$0.475162\pi$
$180$	8.08552	+	12.7862i	0.602659	+	0.953029i
$181$	−2.23423	+	5.89117i	−0.166069	+	0.437887i	−0.992055	−	0.125803i	$-0.959849\pi$
$181$	−2.23423	+	5.89117i	−0.166069	+	0.437887i	0.825987	+	0.563690i	$0.190619\pi$
$182$	−12.9733	−	34.1488i	−0.961644	−	2.53128i
$183$	0.324267	+	0.855022i	0.0239705	+	0.0632050i
$184$	14.4612	−	19.2443i	1.06609	−	1.41871i
$185$	17.3129	+	2.81363i	1.27287	+	0.206862i
$186$	−4.66207	+	1.98632i	−0.341839	+	0.145644i
$187$	−27.9082	−	19.2636i	−2.04085	−	1.40870i
$188$	−0.564159	+	0.325718i	−0.0411455	+	0.0237554i
$189$	3.38820	+	1.60772i	0.246455	+	0.116944i
$190$	−0.0723121	+	0.00878028i	−0.00524607	+	0.000636988i
$191$	2.71523	+	4.70291i	0.196467	+	0.340290i	0.947380	−	0.320110i	$-0.103720\pi$
$191$	2.71523	+	4.70291i	0.196467	+	0.340290i	−0.750914	+	0.660400i	$0.770387\pi$
$192$	11.6284	−	20.1410i	0.839207	−	1.45355i
$193$	4.55176	−	10.6834i	0.327643	−	0.769006i	−0.671953	−	0.740594i	$-0.734544\pi$
$193$	4.55176	−	10.6834i	0.327643	−	0.769006i	0.999596	−	0.0284129i	$-0.00904532\pi$
$194$	−21.5521	−	19.0935i	−1.54735	−	1.37083i
$195$	−6.17976	+	8.23357i	−0.442541	+	0.589618i
$196$	−28.0179	+	24.8217i	−2.00128	+	1.77298i
$197$	−5.35035	−	16.0263i	−0.381197	−	1.14182i	−0.948082	−	0.318026i	$-0.896980\pi$
$197$	−5.35035	−	16.0263i	−0.381197	−	1.14182i	0.566885	−	0.823797i	$-0.308148\pi$
$198$	0.616108	−	15.2886i	0.0437849	−	1.08651i
$199$	−7.46434	+	9.14215i	−0.529133	+	0.648070i	−0.968139	−	0.250414i	$-0.919433\pi$
$199$	−7.46434	+	9.14215i	−0.529133	+	0.648070i	0.439006	+	0.898484i	$0.355331\pi$
$200$	18.6274	+	21.0260i	1.31716	+	1.48676i
$201$	1.84654	+	0.376973i	0.130245	+	0.0265896i
$202$	3.75532	−	1.08774i	0.264224	−	0.0765333i
$203$	26.0842	−	9.89243i	1.83075	−	0.694312i
$204$	1.27738	+	31.6978i	0.0894342	+	2.21929i
$205$	−4.15781	−	3.12439i	−0.290394	−	0.218217i
$206$	26.3607	−	5.38157i	1.83663	−	0.374952i
$207$	−2.39201	+	1.25542i	−0.166256	+	0.0872580i
$208$	47.9648	+	7.76686i	3.32576	+	0.538535i
$209$	0.0473592	+	0.0248560i	0.00327591	+	0.00171933i
$210$	27.7861	+	8.04833i	1.91742	+	0.555387i
$211$	−18.6342	+	1.50430i	−1.28283	+	0.103561i	−0.703007	−	0.711183i	$-0.748160\pi$
$211$	−18.6342	+	1.50430i	−1.28283	+	0.103561i	−0.579822	+	0.814744i	$0.696878\pi$
$212$	2.75896	−	13.5143i	0.189486	−	0.928163i
$213$	−3.76193	−	7.16776i	−0.257763	−	0.491127i
$214$	15.1655	+	20.1816i	1.03669	+	1.37958i
$215$	10.0751	−	15.9325i	0.687117	−	1.08659i
$216$	−7.33348	+	5.06193i	−0.498980	+	0.344421i
$217$	−3.01576	+	6.35558i	−0.204723	+	0.431445i
$218$	27.2845	−	28.4062i	1.84794	−	1.92391i
$219$	−1.84657	−	1.77365i	−0.124780	−	0.119852i
$220$	−10.3279	−	85.0580i	−0.696307	−	5.73461i
$221$	−19.8554	+	8.47304i	−1.33562	+	0.569958i
$222$	−2.00043	+	16.4750i	−0.134260	+	1.10573i
$223$	8.22126	−	6.71245i	0.550537	−	0.449499i	−0.315896	−	0.948794i	$-0.602305\pi$
$223$	8.22126	−	6.71245i	0.550537	−	0.449499i	0.866432	+	0.499295i	$0.166408\pi$
$224$	−13.9419	−	68.2919i	−0.931532	−	4.56295i
$225$	−0.877050	−	3.02793i	−0.0584700	−	0.201862i
$226$	−10.5496	−	42.8014i	−0.701750	−	2.84711i
$227$	−1.40044	+	17.3476i	−0.0929505	+	1.15140i	0.767217	+	0.641387i	$0.221641\pi$
$227$	−1.40044	+	17.3476i	−0.0929505	+	1.15140i	−0.860168	+	0.510011i	$0.829641\pi$
$228$	−0.00802626	−	0.0493875i	−0.000531552	−	0.00327077i
$229$	8.87544	−	10.0183i	0.586506	−	0.662028i	−0.378088	−	0.925770i	$-0.623418\pi$
$229$	8.87544	−	10.0183i	0.586506	−	0.662028i	0.964593	+	0.263742i	$0.0849567\pi$
$230$	−16.6587	+	12.5182i	−1.09844	+	0.825424i
$231$	−13.4336	−	16.4532i	−0.883867	−	1.08254i
$232$	−10.6328	+	65.4262i	−0.698077	+	4.29544i
$233$	−5.71651	−	1.40899i	−0.374501	−	0.0923063i	0.0475724	−	0.998868i	$-0.484852\pi$
$233$	−5.71651	−	1.40899i	−0.374501	−	0.0923063i	−0.422074	+	0.906562i	$0.638698\pi$
$234$	−8.01952	−	5.52870i	−0.524253	−	0.361423i
$235$	0.340848	−	0.0840116i	0.0222345	−	0.00548031i
$236$	3.84251	+	47.5981i	0.250126	+	3.09837i
$237$	−14.6223	+	4.88164i	−0.949820	+	0.317096i
$238$	42.0218	+	43.7493i	2.72387	+	2.83585i
$239$			17.7950i			1.15106i	0.817779	+	0.575532i	$0.195205\pi$
$239$			17.7950i			1.15106i	−0.817779	+	0.575532i	$0.804795\pi$
$240$	−27.7505	+	26.6547i	−1.79129	+	1.72056i
$241$	−0.733315	−	0.598733i	−0.0472369	−	0.0385678i	0.608533	−	0.793529i	$-0.291758\pi$
$241$	−0.733315	−	0.598733i	−0.0472369	−	0.0385678i	−0.655770	+	0.754961i	$0.727656\pi$
$242$	−26.4632	+	50.4214i	−1.70112	+	3.24121i
$243$	0.987050	−	0.160411i	0.0633193	−	0.0102904i
$244$	−4.09504	+	2.58955i	−0.262158	+	0.165779i
$245$	18.2238	−	8.64729i	1.16427	−	0.552455i
$246$	2.79541	−	4.04986i	0.178229	−	0.258209i
$247$	0.0294775	−	0.0170414i	0.00187561	−	0.00108432i
$248$	−9.49517	−	13.7561i	−0.602944	−	0.873515i
$249$	−12.4819	−	7.20643i	−0.791009	−	0.456689i
$250$	6.10960	+	12.8757i	0.386405	+	0.814332i
$251$	−27.4746	−	9.17237i	−1.73418	−	0.578955i	−0.738711	−	0.674022i	$-0.764565\pi$
$251$	−27.4746	−	9.17237i	−1.73418	−	0.578955i	−0.995471	+	0.0950673i	$0.969693\pi$
$252$	−4.75534	+	19.2932i	−0.299558	+	1.21536i
$253$	15.2879	−	0.616083i	0.961144	−	0.0387328i
$254$	−48.0780	+	1.93748i	−3.01668	+	0.121568i
$255$	4.09118	−	16.5986i	0.256200	−	1.03944i
$256$	21.6315	+	7.22166i	1.35197	+	0.451354i
$257$	11.6185	+	24.4854i	0.724739	+	1.52736i	0.845090	+	0.534624i	$0.179547\pi$
$257$	11.6185	+	24.4854i	0.724739	+	1.52736i	−0.120351	+	0.992731i	$0.538402\pi$
$258$	15.4466	+	8.91809i	0.961662	+	0.555216i
$259$	13.0874	+	18.9603i	0.813209	+	1.17814i
$260$	−49.2926	−	23.3551i	−3.05700	−	1.44842i
$261$	4.22563	−	6.12188i	0.261560	−	0.378935i
$262$	−49.1628	+	23.3280i	−3.03729	+	1.44121i
$263$	2.39655	−	1.51549i	0.147778	−	0.0934489i	−0.458531	−	0.888679i	$-0.651624\pi$
$263$	2.39655	−	1.51549i	0.147778	−	0.0934489i	0.606308	+	0.795230i	$0.292650\pi$
$264$	49.8153	−	8.09578i	3.06592	−	0.498261i
$265$	−3.45422	+	6.58147i	−0.212191	+	0.404296i
$266$	−0.0741125	−	0.0605110i	−0.00454413	−	0.00371017i
$267$	−1.52102	+	1.46096i	−0.0930849	+	0.0894092i
$268$			9.98551i			0.609962i
$269$	7.55816	+	7.86887i	0.460829	+	0.479774i	0.910552	−	0.413394i	$-0.135657\pi$
$269$	7.55816	+	7.86887i	0.460829	+	0.479774i	−0.449723	+	0.893168i	$0.648477\pi$
$270$	7.31662	−	2.44265i	0.445275	−	0.148655i
$271$	0.178724	+	2.21389i	0.0108567	+	0.134484i	0.999915	−	0.0130411i	$-0.00415124\pi$
$271$	0.178724	+	2.21389i	0.0108567	+	0.134484i	−0.989058	+	0.147525i	$0.952869\pi$
$272$	−78.3430	+	19.3098i	−4.75024	+	1.17083i
$273$	−13.4223	+	1.63756i	−0.812357	+	0.0991099i
$274$	6.43396	+	1.58583i	0.388690	+	0.0958034i
$275$	−2.86405	+	17.6232i	−0.172708	+	1.06272i
$276$	−9.05242	−	11.0872i	−0.544891	−	0.667371i
$277$	23.6654	−	17.7834i	1.42192	−	1.06850i	0.436247	−	0.899827i	$-0.356307\pi$
$277$	23.6654	−	17.7834i	1.42192	−	1.06850i	0.985672	−	0.168675i	$-0.0539489\pi$
$278$	4.87176	−	5.49908i	0.292189	−	0.329813i
$279$	0.300899	+	1.85151i	0.0180144	+	0.110847i
$280$	−7.67788	+	95.1076i	−0.458841	+	5.68377i
$281$	5.23519	+	21.2400i	0.312305	+	1.26707i	0.891924	+	0.452184i	$0.149355\pi$
$281$	5.23519	+	21.2400i	0.312305	+	1.26707i	−0.579619	+	0.814887i	$0.696799\pi$
$282$	0.0924111	+	0.319040i	0.00550300	+	0.0189986i
$283$	2.37257	+	11.6216i	0.141035	+	0.690834i	0.987402	+	0.158234i	$0.0505799\pi$
$283$	2.37257	+	11.6216i	0.141035	+	0.690834i	−0.846367	+	0.532600i	$0.821215\pi$
$284$	33.2233	−	27.1259i	1.97144	−	1.60963i
$285$	−0.00325008	+	0.0267668i	−0.000192518	+	0.00158553i
$286$	27.6116	+	47.7615i	1.63271	+	2.82420i
$287$	−0.823414	−	6.78142i	−0.0486046	−	0.400295i
$288$	−13.4038	−	12.8745i	−0.789828	−	0.758640i
$289$	13.0568	−	13.5936i	0.768047	−	0.799622i
$290$	24.5978	−	51.8387i	1.44443	−	3.04408i
$291$	−8.77141	+	6.05447i	−0.514189	+	0.354919i
$292$	7.25060	−	11.4659i	0.424309	−	0.670992i
$293$	7.54954	+	10.0466i	0.441049	+	0.586929i	0.964155	−	0.265338i	$-0.0854835\pi$
$293$	7.54954	+	10.0466i	0.441049	+	0.586929i	−0.523107	+	0.852267i	$0.675227\pi$
$294$	8.86952	+	16.8995i	0.517281	+	0.985596i
$295$	5.14734	−	25.2133i	0.299690	−	1.46798i
$296$	−54.5629	+	4.40477i	−3.17140	+	0.256022i
$297$	−5.44015	−	1.57576i	−0.315669	−	0.0914348i
$298$	−16.9796	−	8.91160i	−0.983604	−	0.516235i
$299$	4.86527	−	8.43804i	0.281366	−	0.487985i
$300$	14.7895	−	7.76211i	0.853870	−	0.448146i
$301$	24.2597	−	4.95266i	1.39831	−	0.285466i
$302$	24.9068	+	18.7163i	1.43323	+	1.07700i
$303$	−0.0582728	−	1.44602i	−0.00334768	−	0.0830719i
$304$	0.118993	−	0.0451283i	0.00682474	−	0.00258828i
$305$	2.50788	−	0.726415i	0.143601	−	0.0415944i
$306$	15.8483	+	3.23545i	0.905987	+	0.184959i
$307$	6.87028	+	7.75494i	0.392108	+	0.442598i	0.911103	−	0.412179i	$-0.135232\pi$
$307$	6.87028	+	7.75494i	0.392108	+	0.442598i	−0.518995	+	0.854777i	$0.673694\pi$
$308$	71.1768	−	87.1758i	4.05567	−	4.96730i
$309$	0.401002	−	9.95077i	0.0228122	−	0.566079i
$310$	4.58192	+	13.7245i	0.260235	+	0.779500i
$311$	−11.3993	+	10.0989i	−0.646398	+	0.572658i	−0.921319	−	0.388809i	$-0.872887\pi$
$311$	−11.3993	+	10.0989i	−0.646398	+	0.572658i	0.274921	+	0.961467i	$0.411348\pi$
$312$	12.5764	−	29.5648i	0.711997	−	1.67377i
$313$	−6.48303	−	5.74346i	−0.366443	−	0.324640i	0.459728	−	0.888060i	$-0.347947\pi$
$313$	−6.48303	−	5.74346i	−0.366443	−	0.324640i	−0.826171	+	0.563420i	$0.809485\pi$
$314$	2.29477	−	5.38601i	0.129501	−	0.303950i
$315$	5.35399	−	9.27337i	0.301663	−	0.522495i
$316$	−40.8392	−	70.7355i	−2.29738	−	3.97918i
$317$	18.4334	−	2.23822i	1.03532	−	0.125711i	0.414811	−	0.909908i	$-0.363848\pi$
$317$	18.4334	−	2.23822i	1.03532	−	0.125711i	0.620512	+	0.784197i	$0.286925\pi$
$318$	−6.35377	−	3.01490i	−0.356302	−	0.169067i
$319$	−36.4863	+	21.0654i	−2.04284	+	1.17943i
$320$	−54.6492	−	37.7216i	−3.05498	−	2.10870i
$321$	8.59670	−	3.66271i	0.479821	−	0.204433i
$322$	−27.0156	−	4.39046i	−1.50552	−	0.244671i
$323$	−0.0339669	+	0.0452017i	−0.00188997	+	0.00251509i
$324$	1.87884	+	4.95410i	0.104380	+	0.275228i
$325$	8.51196	+	7.53225i	0.472159	+	0.417814i
$326$	5.70533	−	15.0437i	0.315989	−	0.833195i
$327$	−7.79223	−	12.3224i	−0.430911	−	0.681431i
$328$	14.9325	+	6.36212i	0.824507	+	0.351289i
$329$	0.389713	+	0.246439i	0.0214856	+	0.0135866i
$330$	−43.3694	−	5.26600i	−2.38741	−	0.289884i
$331$	−9.42126	−	22.1125i	−0.517839	−	1.21541i	−0.949611	−	0.313430i	$-0.898522\pi$
$331$	−9.42126	−	22.1125i	−0.517839	−	1.21541i	0.431772	−	0.901983i	$-0.357888\pi$
$332$	24.1824	−	72.4352i	1.32718	−	3.97540i
$333$	5.74392	+	2.17838i	0.314765	+	0.119375i
$334$	−8.11226	−	0.654889i	−0.443883	−	0.0358339i
$335$	1.49710	−	5.16860i	0.0817955	−	0.282391i
$336$	−50.4991	−	2.03504i	−2.75495	−	0.111021i
$337$	11.3905			0.620482			0.310241	−	0.950658i	$-0.399590\pi$
$337$	11.3905			0.620482			0.310241	+	0.950658i	$0.399590\pi$
$338$	35.0934	+	1.37397i	1.90883	+	0.0747342i
$339$	−16.3174			−0.886240
$340$	90.5047	+	3.64721i	4.90830	+	0.197798i
$341$	2.95581	−	10.2046i	0.160066	−	0.552611i
$342$	−0.0254294	−	0.00205287i	−0.00137506	−	0.000111007i
$343$	0.226753	+	0.0859961i	0.0122435	+	0.00464335i
$344$	−18.6299	+	55.8034i	−1.00446	+	3.00872i
$345$	3.02334	+	7.09605i	0.162771	+	0.382038i
$346$	−20.8749	−	2.53467i	−1.12224	−	0.136265i
$347$	−9.65901	−	6.10799i	−0.518523	−	0.327894i	0.249438	−	0.968391i	$-0.419754\pi$
$347$	−9.65901	−	6.10799i	−0.518523	−	0.327894i	−0.767961	+	0.640497i	$0.778728\pi$
$348$	36.2591	+	15.4486i	1.94369	+	0.828130i
$349$	−2.08354	−	3.29486i	−0.111530	−	0.176370i	0.784812	−	0.619734i	$-0.212759\pi$
$349$	−2.08354	−	3.29486i	−0.111530	−	0.176370i	−0.896342	+	0.443364i	$0.853785\pi$
$350$	11.3257	−	29.8633i	0.605382	−	1.59626i
$351$	−2.69742	+	2.39247i	−0.143978	+	0.127700i
$352$	37.3268	+	98.4228i	1.98953	+	5.24595i
$353$	15.0619	−	20.0437i	0.801663	−	1.06682i	−0.194637	−	0.980875i	$-0.562353\pi$
$353$	15.0619	−	20.0437i	0.801663	−	1.06682i	0.996300	−	0.0859442i	$-0.0273907\pi$
$354$	24.0330	+	3.90574i	1.27734	+	0.207588i
$355$	−21.2636	+	9.05958i	−1.12856	+	0.480832i
$356$	−9.19633	−	6.34777i	−0.487404	−	0.336431i
$357$	19.4460	−	11.2272i	1.02919	−	0.594204i
$358$	30.2047	+	14.3323i	1.59637	+	0.757485i
$359$	5.15275	−	0.625658i	0.271952	−	0.0330209i	0.0165754	−	0.999863i	$-0.494724\pi$
$359$	5.15275	−	0.625658i	0.271952	−	0.0330209i	0.255377	+	0.966842i	$0.417801\pi$
$360$	12.7213	+	22.0339i	0.670471	+	1.16129i
$361$	−9.49996	+	16.4544i	−0.499998	+	0.866021i
$362$	−6.67184	+	15.6594i	−0.350664	+	0.823039i
$363$	15.7773	+	13.9775i	0.828093	+	0.733626i
$364$	−22.7264	−	67.9443i	−1.19119	−	3.56125i
$365$	−5.47204	+	4.84780i	−0.286420	+	0.253746i
$366$	0.782306	+	2.34329i	0.0408918	+	0.122486i
$367$	0.919884	−	22.8267i	0.0480176	−	1.19154i	−0.778135	−	0.628097i	$-0.783834\pi$
$367$	0.919884	−	22.8267i	0.0480176	−	1.19154i	0.826153	−	0.563446i	$-0.190525\pi$
$368$	23.0245	−	28.1999i	1.20024	−	1.47002i
$369$	−1.20789	−	1.36343i	−0.0628804	−	0.0709772i
$370$	46.4279	+	9.47833i	2.41367	+	0.492755i
$371$	−9.37743	+	2.71620i	−0.486852	+	0.141018i
$372$	−9.29289	+	3.52433i	−0.481814	+	0.182728i
$373$	0.988783	+	24.5364i	0.0511972	+	1.27045i	0.796877	+	0.604142i	$0.206484\pi$
$373$	0.988783	+	24.5364i	0.0511972	+	1.27045i	−0.745680	+	0.666305i	$0.767875\pi$
$374$	−73.2389	−	55.0355i	−3.78710	−	2.84582i
$375$	5.16876	−	1.05521i	0.266914	−	0.0544908i
$376$	−0.970088	+	0.509142i	−0.0500285	+	0.0262570i
$377$	−1.06461	+	26.7993i	−0.0548301	+	1.38023i
$378$	8.97110	+	4.70840i	0.461424	+	0.242174i
$379$	15.4927	+	4.48751i	0.795806	+	0.230508i	0.651125	−	0.758970i	$-0.274297\pi$
$379$	15.4927	+	4.48751i	0.795806	+	0.230508i	0.144681	+	0.989478i	$0.453784\pi$
$380$	−0.142400	+	0.0114957i	−0.00730497	+	0.000589718i
$381$	−3.56263	+	17.4509i	−0.182519	+	0.894037i
$382$	6.81780	+	12.9902i	0.348829	+	0.664638i
$383$	−19.1095	−	25.4301i	−0.976448	−	1.29942i	−0.954044	−	0.299667i	$-0.903124\pi$
$383$	−19.1095	−	25.4301i	−0.976448	−	1.29942i	−0.0224037	−	0.999749i	$-0.507132\pi$
$384$	13.7138	−	21.6866i	0.699827	−	1.10669i
$385$	−49.9119	+	34.4517i	−2.54374	+	1.75582i
$386$	13.4490	−	28.3432i	0.684537	−	1.44263i
$387$	4.57349	−	4.76151i	0.232484	−	0.242041i
$388$	−40.7268	−	39.1187i	−2.06759	−	1.98595i
$389$	0.0396025	+	0.326156i	0.00200793	+	0.0165368i	0.993678	−	0.112264i	$-0.0358103\pi$
$389$	0.0396025	+	0.326156i	0.00200793	+	0.0165368i	−0.991670	+	0.128801i	$0.958887\pi$
$390$	−17.5771	+	21.5532i	−0.890050	+	1.09139i
$391$	−1.94962	+	16.0566i	−0.0985967	+	0.812017i
$392$	−48.7630	+	39.8138i	−2.46290	+	2.01090i
$393$	4.02906	+	19.7356i	0.203239	+	0.995532i
$394$	−12.6992	−	43.8427i	−0.639777	−	2.20876i
$395$	10.5336	+	42.7363i	0.530001	+	2.15030i
$396$	2.41472	−	29.9116i	0.121344	−	1.50312i
$397$	−0.0959515	−	0.590413i	−0.00481567	−	0.0296320i	0.984531	−	0.175209i	$-0.0560602\pi$
$397$	−0.0959515	−	0.590413i	−0.00481567	−	0.0296320i	−0.989347	+	0.145577i	$0.953496\pi$
$398$	−21.1435	+	23.8660i	−1.05983	+	1.19630i
$399$	−0.0283129	+	0.0212758i	−0.00141742	+	0.00106512i
$400$	26.8679	+	32.9072i	1.34340	+	1.64536i
$401$	0.880939	−	5.42064i	0.0439920	−	0.270694i	−0.955731	−	0.294243i	$-0.904933\pi$
$401$	0.880939	−	5.42064i	0.0439920	−	0.270694i	0.999723	+	0.0235492i	$0.00749664\pi$
$402$	4.94347	+	1.21846i	0.246558	+	0.0607711i
$403$	−4.48779	−	5.05983i	−0.223553	−	0.252048i
$404$	7.44503	−	1.83504i	0.370404	−	0.0912964i
$405$	−0.229751	−	2.84598i	−0.0114164	−	0.141418i
$406$	71.4869	−	23.8658i	3.54783	−	1.18444i
$407$	−24.1021	−	25.0929i	−1.19470	−	1.24381i
$408$			53.3524i			2.64134i
$409$	6.27828	−	6.03037i	0.310441	−	0.298182i	−0.521270	−	0.853392i	$-0.674541\pi$
$409$	6.27828	−	6.03037i	0.310441	−	0.298182i	0.831711	+	0.555210i	$0.187362\pi$
$410$	−10.8836	−	8.88616i	−0.537501	−	0.438856i
$411$	1.13990	−	2.17189i	0.0562269	−	0.107131i
$412$	52.0827	−	8.46427i	2.56593	−	0.417004i
$413$	28.5676	−	18.0650i	1.40572	−	0.888923i
$414$	−6.59348	+	3.12864i	−0.324052	+	0.153764i
$415$	−23.3771	+	33.8676i	−1.14754	+	1.66249i
$416$	65.6639	+	13.3662i	3.21944	+	0.655334i
$417$	−1.54481	−	2.23805i	−0.0756498	−	0.109598i
$418$	0.125136	+	0.0722473i	0.00612060	+	0.00353373i
$419$	6.25270	+	13.1773i	0.305464	+	0.643752i	0.996899	−	0.0786861i	$-0.0250725\pi$
$419$	6.25270	+	13.1773i	0.305464	+	0.643752i	−0.691435	+	0.722439i	$0.743021\pi$
$420$	53.8154	+	17.9662i	2.62592	+	0.876662i
$421$	3.61082	−	14.6497i	0.175981	−	0.713982i	−0.814941	−	0.579544i	$-0.803231\pi$
$421$	3.61082	−	14.6497i	0.175981	−	0.713982i	0.990922	−	0.134438i	$-0.0429230\pi$
$422$	−50.4641	+	2.03363i	−2.45655	+	0.0989957i
$423$	0.122849	−	0.00495066i	0.00597315	−	0.000240710i
$424$	5.55141	−	22.5229i	0.269600	−	1.09381i
$425$	−17.9031	−	5.97695i	−0.868430	−	0.289924i
$426$	−9.37511	−	19.7576i	−0.454226	−	0.957260i
$427$	2.96998	+	1.71472i	0.143727	+	0.0829810i
$428$	28.1253	+	40.7465i	1.35949	+	1.96956i
$429$	19.6115	−	5.69270i	0.946851	−	0.274846i
$430$	28.9296	−	41.9117i	1.39511	−	2.02116i
$431$	−32.7918	+	15.5599i	−1.57953	+	0.749495i	−0.997950	−	0.0639959i	$-0.979616\pi$
$431$	−32.7918	+	15.5599i	−1.57953	+	0.749495i	−0.581577	+	0.813491i	$0.697564\pi$
$432$	−11.3901	+	7.20264i	−0.548004	+	0.346537i
$433$	−1.65533	+	0.269017i	−0.0795500	+	0.0129281i	−0.200056	−	0.979784i	$-0.564112\pi$
$433$	−1.65533	+	0.269017i	−0.0795500	+	0.0129281i	0.120506	+	0.992713i	$0.461548\pi$
$434$	−8.83201	+	16.8280i	−0.423950	+	0.807769i
$435$	−16.4519	−	13.4326i	−0.788809	−	0.644042i
$436$	55.7114	−	53.5116i	2.66809	−	2.56274i
$437$		−	0.0255111i		−	0.00122036i
$438$	−4.79163	−	4.98861i	−0.228953	−	0.238365i
$439$	5.81121	−	1.94007i	0.277354	−	0.0925943i	−0.174588	−	0.984641i	$-0.555859\pi$
$439$	5.81121	−	1.94007i	0.277354	−	0.0925943i	0.451942	+	0.892047i	$0.350731\pi$
$440$	−11.5953	−	143.634i	−0.552784	−	6.84746i
$441$	6.85938	−	1.69069i	0.326637	−	0.0805088i
$442$	−54.5188	+	20.7119i	−2.59319	+	0.985167i
$443$	−25.8676	−	6.37578i	−1.22900	−	0.302923i	−0.429215	−	0.903202i	$-0.641210\pi$
$443$	−25.8676	−	6.37578i	−1.22900	−	0.302923i	−0.799790	+	0.600280i	$0.795056\pi$
$444$	−5.22119	+	32.1273i	−0.247787	+	1.52469i
$445$	3.80840	+	4.66445i	0.180536	+	0.221116i
$446$	22.9224	−	17.2251i	1.08541	−	0.815630i
$447$	−4.70697	+	5.31307i	−0.222632	+	0.251300i
$448$	−13.9910	−	86.0902i	−0.661014	−	4.06738i
$449$	2.31371	−	28.6604i	0.109191	−	1.35257i	−0.677637	−	0.735397i	$-0.736996\pi$
$449$	2.31371	−	28.6604i	0.109191	−	1.35257i	0.786828	−	0.617173i	$-0.211722\pi$
$450$	−2.03810	−	8.26889i	−0.0960769	−	0.389799i
$451$	2.87028	+	9.90935i	0.135156	+	0.466613i
$452$	−17.2935	−	84.7091i	−0.813417	−	3.98438i
$453$	8.93299	−	7.29356i	0.419709	−	0.342682i
$454$	−5.66738	+	46.6751i	−0.265983	+	2.19057i
$455$	1.57668	+	38.5759i	0.0739157	+	1.80847i
$456$	−0.0101431	−	0.0835359i	−0.000474994	−	0.00391193i
$457$	−3.83773	−	3.68619i	−0.179521	−	0.172433i	0.597577	−	0.801811i	$-0.296130\pi$
$457$	−3.83773	−	3.68619i	−0.179521	−	0.172433i	−0.777099	+	0.629379i	$0.783310\pi$
$458$	25.0479	−	26.0776i	1.17041	−	1.21853i
$459$	2.56674	−	5.40928i	0.119805	−	0.252484i
$460$	−33.6338	+	23.2157i	−1.56818	+	1.08244i
$461$	16.2783	−	25.7420i	0.758155	−	1.19893i	−0.216733	−	0.976231i	$-0.569540\pi$
$461$	16.2783	−	25.7420i	0.758155	−	1.19893i	0.974888	−	0.222695i	$-0.0714855\pi$
$462$	−34.4725	−	45.8745i	−1.60380	−	2.13428i
$463$	16.9850	+	32.3622i	0.789359	+	1.50400i	0.862152	+	0.506650i	$0.169116\pi$
$463$	16.9850	+	32.3622i	0.789359	+	1.50400i	−0.0727933	+	0.997347i	$0.523191\pi$
$464$	−20.0517	+	98.2196i	−0.930876	+	4.55973i
$465$	5.33849	−	0.430967i	0.247566	−	0.0199856i
$466$	−15.2777	−	4.42524i	−0.707726	−	0.204995i
$467$	10.9536	+	5.74891i	0.506874	+	0.266028i	0.698718	−	0.715397i	$-0.253754\pi$
$467$	10.9536	+	5.74891i	0.506874	+	0.266028i	−0.191844	+	0.981425i	$0.561447\pi$
$468$	−15.2789	−	11.4676i	−0.706266	−	0.530092i
$469$	6.25830	−	3.28461i	0.288982	−	0.151669i
$470$	0.929213	−	0.189700i	0.0428614	−	0.00875022i
$471$	−1.73246	−	1.30186i	−0.0798274	−	0.0599864i
$472$	3.23378	+	80.2455i	0.148847	+	3.69360i
$473$	−34.9633	+	13.2598i	−1.60761	+	0.609687i
$474$	−40.0019	+	11.5867i	−1.83735	+	0.532195i
$475$	0.0291679	+	0.00595468i	0.00133832	+	0.000273219i
$476$	78.8932	+	89.0520i	3.61606	+	4.08169i
$477$	−1.64640	+	2.01648i	−0.0753837	+	0.0923282i
$478$	−1.93576	+	48.0353i	−0.0885394	+	2.19708i
$479$	9.70757	+	29.0777i	0.443550	+	1.32859i	0.898850	+	0.438256i	$0.144404\pi$
$479$	9.70757	+	29.0777i	0.443550	+	1.32859i	−0.455300	+	0.890338i	$0.650468\pi$
$480$	−39.7202	+	35.1891i	−1.81297	+	1.60615i
$481$	−21.6992	+	4.44286i	−0.989398	+	0.202577i
$482$	−1.91435	−	1.69597i	−0.0871964	−	0.0772493i
$483$	−3.97109	+	9.32049i	−0.180691	+	0.424097i
$484$	−55.8405	+	96.7187i	−2.53821	+	4.39630i
$485$	15.2156	+	26.3543i	0.690907	+	1.19669i
$486$	2.68186	−	0.325637i	0.121652	−	0.0147712i
$487$	34.5337	+	16.3865i	1.56487	+	0.742541i	0.996762	−	0.0804115i	$-0.0256234\pi$
$487$	34.5337	+	16.3865i	1.56487	+	0.742541i	0.568110	+	0.822952i	$0.307675\pi$
$488$	−7.05679	+	4.07424i	−0.319446	+	0.184432i
$489$	−4.90133	−	3.38314i	−0.221646	−	0.152991i
$490$	50.1333	−	21.3598i	2.26479	−	0.964937i
$491$	12.0392	+	1.95656i	0.543322	+	0.0882984i	0.425877	−	0.904781i	$-0.359966\pi$
$491$	12.0392	+	1.95656i	0.543322	+	0.0882984i	0.117445	+	0.993079i	$0.462530\pi$
$492$	5.79786	−	7.71556i	0.261388	−	0.347844i
$493$	−15.7933	−	41.6436i	−0.711296	−	1.87553i
$494$	0.0814244	−	0.0427943i	0.00366346	−	0.00192541i
$495$	−5.73446	+	15.1205i	−0.257745	+	0.679617i
$496$	−13.5107	−	21.3655i	−0.606648	−	0.959337i
$497$	−27.9292	−	11.8995i	−1.25280	−	0.533767i
$498$	−32.9093	−	20.8106i	−1.47470	−	0.932545i
$499$	−12.4303	−	1.50932i	−0.556459	−	0.0675663i	−0.162524	−	0.986705i	$-0.551963\pi$
$499$	−12.4303	−	1.50932i	−0.556459	−	0.0675663i	−0.393935	+	0.919138i	$0.628886\pi$
$500$	10.9559	+	25.7144i	0.489962	+	1.14998i
$501$	−0.953987	+	2.85754i	−0.0426210	+	0.127665i
$502$	−73.1662	−	27.7483i	−3.26557	−	1.23847i
$503$	−28.1391	−	2.27163i	−1.25466	−	0.101287i	−0.564800	−	0.825228i	$-0.691047\pi$
$503$	−28.1391	−	2.27163i	−1.25466	−	0.101287i	−0.689862	+	0.723941i	$0.742329\pi$
$504$	−9.29753	+	32.0988i	−0.414145	+	1.42979i
$505$	−4.12874	−	0.166383i	−0.183727	−	0.00740393i
$506$	41.3348			1.83755
$507$	3.60253	−	12.4909i	0.159994	−	0.554739i
$508$	−94.3692			−4.18696
$509$	34.5982	+	1.39426i	1.53354	+	0.0617994i	0.792586	−	0.609760i	$-0.208734\pi$
$509$	34.5982	+	1.39426i	1.53354	+	0.0617994i	0.740951	+	0.671559i	$0.234375\pi$
$510$	12.8492	−	44.3606i	0.568972	−	1.96432i
$511$	−9.57112	−	0.772661i	−0.423401	−	0.0341805i
$512$	9.62299	+	3.64952i	0.425280	+	0.161287i
$513$	−0.00299045	+	0.00895749i	−0.000132032	+	0.000395483i
$514$	28.6989	+	67.3588i	1.26585	+	2.97107i
$515$	−28.2276	−	3.42745i	−1.24385	−	0.151031i
$516$	29.5657	+	18.6962i	1.30156	+	0.823054i
$517$	−0.640632	−	0.272948i	−0.0281750	−	0.0120042i
$518$	33.2650	+	52.6045i	1.46158	+	2.31131i
$519$	−2.76015	+	7.27793i	−0.121157	+	0.319465i
$520$	−81.2513	−	42.5847i	−3.56310	−	1.86746i
$521$	−1.14233	−	3.01208i	−0.0500465	−	0.131962i	0.907662	−	0.419702i	$-0.137865\pi$
$521$	−1.14233	−	3.01208i	−0.0500465	−	0.131962i	−0.957709	+	0.287740i	$0.907096\pi$
$522$	12.0725	−	16.0655i	0.528397	−	0.703169i
$523$	22.0635	+	3.58567i	0.964771	+	0.156791i	0.622335	−	0.782751i	$-0.286184\pi$
$523$	22.0635	+	3.58567i	0.964771	+	0.156791i	0.342436	+	0.939541i	$0.388748\pi$
$524$	−98.1842	+	41.8324i	−4.28920	+	1.82746i
$525$	−9.72962	−	6.71587i	−0.424635	−	0.293105i
$526$	6.63402	−	3.83016i	0.289257	−	0.167003i
$527$	10.1467	+	4.81468i	0.441998	+	0.209731i
$528$	75.7702	−	9.20017i	3.29748	−	0.400386i
$529$	7.85110	+	13.5985i	0.341352	+	0.591239i
$530$	−10.0401	+	17.3900i	−0.436116	+	0.755375i
$531$	3.53267	−	8.29149i	0.153305	−	0.359820i
$532$	−0.140456	−	0.124433i	−0.00608955	−	0.00539487i
$533$	6.30933	+	1.82361i	0.273288	+	0.0789892i
$534$	−4.26471	+	3.77820i	−0.184552	+	0.163499i
$535$	−8.44891	−	25.3076i	−0.365278	−	1.09414i
$536$	−0.676210	+	16.7800i	−0.0292078	+	0.724784i
$537$	7.82670	−	9.58597i	0.337747	−	0.413665i
$538$	19.5462	+	22.0632i	0.842699	+	0.951210i
$539$	−39.2040	−	8.00355i	−1.68863	−	0.344737i
$540$	14.5309	−	4.20894i	0.625312	−	0.181124i
$541$	9.09419	−	3.44897i	0.390990	−	0.148283i	−0.151272	−	0.988492i	$-0.548337\pi$
$541$	9.09419	−	3.44897i	0.390990	−	0.148283i	0.542262	+	0.840209i	$0.317568\pi$
$542$	0.241612	+	5.99554i	0.0103781	+	0.257531i
$543$	5.03697	+	3.78504i	0.216157	+	0.162432i
$544$	−109.028	+	22.2583i	−4.67456	+	0.954318i
$545$	−36.8596	+	19.3454i	−1.57889	+	0.828667i
$546$	−36.4099	+	2.96029i	−1.55820	+	0.126689i
$547$	−38.9890	−	20.4630i	−1.66705	−	0.874935i	−0.990336	−	0.138688i	$-0.955711\pi$
$547$	−38.9890	−	20.4630i	−1.66705	−	0.874935i	−0.676713	−	0.736247i	$-0.736596\pi$
$548$	12.4831	+	3.61577i	0.533251	+	0.154458i
$549$	0.911481	−	0.0735823i	0.0389011	−	0.00314042i
$550$	−9.64817	+	47.2599i	−0.411399	+	2.01517i
$551$	0.0326453	+	0.0622004i	0.00139074	+	0.00264983i
$552$	−14.4612	−	19.2443i	−0.615508	−	0.819092i
$553$	−30.8991	+	48.8630i	−1.31396	+	2.07787i
$554$	65.8162	−	45.4296i	2.79626	−	1.93012i
$555$	7.51931	−	15.8466i	0.319177	−	0.672651i
$556$	9.98123	−	10.3916i	0.423299	−	0.440700i
$557$	−10.9874	−	10.5536i	−0.465552	−	0.447168i	0.422874	−	0.906188i	$-0.361021\pi$
$557$	−10.9874	−	10.5536i	−0.465552	−	0.447168i	−0.888426	+	0.459020i	$0.848201\pi$
$558$	0.610829	+	5.03063i	0.0258585	+	0.212964i
$559$	−4.74816	+	23.3262i	−0.200826	+	0.986592i
$560$	−17.3939	+	143.252i	−0.735028	+	6.05350i
$561$	−26.2676	+	21.4469i	−1.10902	+	0.905487i
$562$	11.8212	+	57.9040i	0.498647	+	2.44253i
$563$	5.15846	+	17.8091i	0.217403	+	0.750563i	0.992873	+	0.119178i	$0.0380260\pi$
$563$	5.15846	+	17.8091i	0.217403	+	0.750563i	−0.775470	+	0.631385i	$0.782487\pi$
$564$	0.155899	+	0.632506i	0.00656452	+	0.0266333i
$565$	−3.74895	+	46.4390i	−0.157719	+	1.95370i
$566$	5.14023	+	31.6291i	0.216060	+	1.32947i
$567$	2.48690	−	2.80713i	0.104440	−	0.117888i
$568$	57.6663	−	43.3334i	2.41963	−	1.81823i
$569$	−29.5027	−	36.1342i	−1.23682	−	1.51482i	−0.780703	−	0.624902i	$-0.785139\pi$
$569$	−29.5027	−	36.1342i	−1.23682	−	1.51482i	−0.456112	−	0.889922i	$-0.650758\pi$
$570$	−0.0116849	+	0.0718999i	−0.000489425	+	0.00301156i
$571$	15.8752	+	3.91288i	0.664355	+	0.163749i	0.557052	−	0.830478i	$-0.311932\pi$
$571$	15.8752	+	3.91288i	0.664355	+	0.163749i	0.107303	+	0.994226i	$0.465779\pi$
$572$	50.3373	+	95.7765i	2.10471	+	4.00462i
$573$	5.27265	−	1.29959i	0.220268	−	0.0542912i
$574$	−1.48501	−	18.3951i	−0.0619830	−	0.767797i
$575$	8.07774	−	2.69675i	0.336865	−	0.112462i
$576$	−16.1106	−	16.7729i	−0.671273	−	0.698869i
$577$		−	5.37769i		−	0.223876i	−0.993715	−	0.111938i	$-0.964294\pi$
$577$		−	5.37769i		−	0.223876i	0.993715	−	0.111938i	$-0.0357058\pi$
$578$	36.7238	−	35.2737i	1.52751	−	1.46719i
$579$	−8.99520	−	7.34435i	−0.373828	−	0.305221i
$580$	52.2969	−	99.6434i	2.17151	−	4.13747i
$581$	−53.3525	+	8.67062i	−2.21343	+	0.359718i
$582$	−24.3358	+	15.3891i	−1.00875	+	0.637897i
$583$	13.3206	−	6.32069i	0.551682	−	0.261776i
$584$	12.9606	−	18.7767i	0.536313	−	0.776984i
$585$	6.18918	+	8.22649i	0.255891	+	0.340123i
$586$	19.2861	+	27.9407i	0.796701	+	1.15422i
$587$	−11.3158	−	6.53317i	−0.467052	−	0.269653i	0.247953	−	0.968772i	$-0.420242\pi$
$587$	−11.3158	−	6.53317i	−0.467052	−	0.269653i	−0.715005	+	0.699119i	$0.753576\pi$
$588$	16.0466	+	33.8175i	0.661751	+	1.39461i
$589$	−0.0168025	−	0.00560949i	−0.000692333	−	0.000231135i
$590$	16.6373	−	67.5001i	0.684946	−	2.77893i
$591$	−16.8821	+	0.680324i	−0.694435	+	0.0279848i
$592$	−82.7196	+	3.33349i	−3.39975	+	0.137005i
$593$	1.57078	−	6.37290i	0.0645041	−	0.261703i	−0.929832	−	0.367984i	$-0.880048\pi$
$593$	1.57078	−	6.37290i	0.0645041	−	0.261703i	0.994336	+	0.106281i	$0.0338942\pi$
$594$	−14.5135	−	4.84533i	−0.595498	−	0.198806i
$595$	−27.4845	−	57.9224i	−1.12676	−	2.37459i
$596$	−32.5704	−	18.8045i	−1.33414	−	0.770264i
$597$	6.70449	+	9.71314i	0.274397	+	0.397532i
$598$	14.0510	−	22.2481i	0.574590	−	0.909793i
$599$	−5.07380	+	7.35066i	−0.207310	+	0.300340i	−0.912822	−	0.408358i	$-0.866102\pi$
$599$	−5.07380	+	7.35066i	−0.207310	+	0.300340i	0.705512	+	0.708698i	$0.250717\pi$
$600$	25.3783	−	12.0422i	1.03607	−	0.491619i
$601$	28.8908	−	18.2695i	1.17848	−	0.745227i	0.206079	−	0.978535i	$-0.433929\pi$
$601$	28.8908	−	18.2695i	1.17848	−	0.745227i	0.972403	+	0.233308i	$0.0749551\pi$
$602$	66.0246	−	10.7300i	2.69096	−	0.437324i
$603$	0.875829	−	1.66875i	0.0356665	−	0.0679568i
$604$	47.3307	+	38.6443i	1.92586	+	1.57241i
$605$	43.4044	−	41.6905i	1.76464	−	1.69496i
$606$		−	3.90969i		−	0.158820i
$607$	−19.4369	−	20.2360i	−0.788920	−	0.821353i	0.198396	−	0.980122i	$-0.436427\pi$
$607$	−19.4369	−	20.2360i	−0.788920	−	0.821353i	−0.987316	+	0.158769i	$0.949247\pi$
$608$	0.166478	−	0.0555787i	0.00675159	−	0.00225401i
$609$	−2.24478	−	27.8066i	−0.0909631	−	1.12678i
$610$	6.84870	−	1.68805i	0.277296	−	0.0683472i
$611$	−0.364684	+	0.252032i	−0.0147535	+	0.0101961i
$612$	30.8017	+	7.59193i	1.24508	+	0.306885i
$613$	0.0485373	−	0.298662i	0.00196040	−	0.0120628i	−0.986052	−	0.166440i	$-0.946773\pi$
$613$	0.0485373	−	0.298662i	0.00196040	−	0.0120628i	0.988012	+	0.154377i	$0.0493370\pi$
$614$	17.7018	+	21.6808i	0.714387	+	0.874965i
$615$	−4.15781	+	3.12439i	−0.167659	+	0.125987i
$616$	125.511	−	141.673i	5.05699	−	5.70816i
$617$	4.62403	+	28.4528i	0.186157	+	1.14547i	0.896971	+	0.442088i	$0.145762\pi$
$617$	4.62403	+	28.4528i	0.186157	+	1.14547i	−0.710815	+	0.703379i	$0.751674\pi$
$618$	2.16490	−	26.8171i	0.0870852	−	1.07874i
$619$	3.93946	+	15.9830i	0.158340	+	0.642412i	0.995442	+	0.0953652i	$0.0304019\pi$
$619$	3.93946	+	15.9830i	0.158340	+	0.642412i	−0.837102	+	0.547047i	$0.815752\pi$
$620$	7.89512	+	27.2571i	0.317076	+	1.09467i
$621$	0.540358	+	2.64685i	0.0216838	+	0.106214i
$622$	−31.8696	+	26.0207i	−1.27785	+	1.04334i
$623$	−0.953370	+	7.85171i	−0.0381960	+	0.314572i
$624$	20.8049	−	43.9102i	0.832861	−	1.75781i
$625$	−3.71547	−	30.5996i	−0.148619	−	1.22399i
$626$	−16.8753	−	16.2089i	−0.674472	−	0.647839i
$627$	0.0370509	−	0.0385740i	0.00147967	−	0.00154050i
$628$	4.92229	−	10.3735i	0.196421	−	0.413948i
$629$	30.2702	−	20.8940i	1.20695	−	0.833100i
$630$	15.4611	−	24.4498i	0.615986	−	0.974104i
$631$	19.0050	+	25.2911i	0.756579	+	1.00682i	0.999325	+	0.0367336i	$0.0116953\pi$
$631$	19.0050	+	25.2911i	0.756579	+	1.00682i	−0.242746	+	0.970090i	$0.578048\pi$
$632$	−63.8373	−	121.632i	−2.53931	−	4.83825i
$633$	−3.73944	+	18.3170i	−0.148629	+	0.728034i
$634$	50.0020	−	4.03658i	1.98583	−	0.160313i
$635$	48.8464	+	14.1485i	1.93841	+	0.561468i
$636$	−12.2131	−	6.40993i	−0.484281	−	0.254170i
$637$	−17.6346	+	18.3806i	−0.698707	+	0.728265i
$638$	−100.781	+	52.8941i	−3.98997	+	2.09410i
$639$	−7.93140	+	1.61921i	−0.313761	+	0.0640548i
$640$	−58.5688	−	44.0116i	−2.31514	−	1.73971i
$641$	1.20677	+	29.9457i	0.0476646	+	1.18278i	0.829210	+	0.558937i	$0.188790\pi$
$641$	1.20677	+	29.9457i	0.0476646	+	1.18278i	−0.781546	+	0.623848i	$0.785569\pi$
$642$	23.6041	−	8.95185i	0.931579	−	0.353301i
$643$	10.6067	−	3.07226i	0.418286	−	0.121158i	−0.0623990	−	0.998051i	$-0.519875\pi$
$643$	10.6067	−	3.07226i	0.418286	−	0.121158i	0.480685	+	0.876893i	$0.340388\pi$
$644$	−52.5944	−	10.7372i	−2.07251	−	0.423106i
$645$	−12.5004	−	14.1100i	−0.492203	−	0.555582i
$646$	−0.0966062	+	0.118321i	−0.00380092	+	0.00465528i
$647$	0.828462	−	20.5581i	0.0325702	−	0.808221i	−0.897538	−	0.440937i	$-0.854646\pi$
$647$	0.828462	−	20.5581i	0.0325702	−	0.808221i	0.930108	−	0.367285i	$-0.119713\pi$
$648$	2.82178	+	8.45226i	0.110850	+	0.332036i
$649$	−38.2083	+	33.8496i	−1.49981	+	1.32871i
$650$	22.1575	+	21.2582i	0.869090	+	0.833816i
$651$	5.26561	+	4.66493i	0.206376	+	0.182833i
$652$	12.3685	−	29.0299i	0.484388	−	1.13690i
$653$	3.58263	−	6.20531i	0.140199	−	0.242832i	−0.787372	−	0.616478i	$-0.788559\pi$
$653$	3.58263	−	6.20531i	0.140199	−	0.242832i	0.927572	+	0.373645i	$0.121892\pi$
$654$	−19.6936	−	34.1104i	−0.770082	−	1.33382i
$655$	57.0930	−	6.93234i	2.23081	−	0.270869i
$656$	22.1774	+	10.5233i	0.865881	+	0.410866i
$657$	−2.21738	+	1.28020i	−0.0865080	+	0.0499454i
$658$	1.02517	+	0.707624i	0.0399653	+	0.0275860i
$659$	26.8291	−	11.4308i	1.04511	−	0.445282i	0.199960	−	0.979804i	$-0.435919\pi$
$659$	26.8291	−	11.4308i	1.04511	−	0.445282i	0.845154	+	0.534522i	$0.179508\pi$
$660$	−84.5731	−	13.7445i	−3.29200	−	0.535003i
$661$	−5.09184	+	6.77601i	−0.198050	+	0.263556i	−0.887532	−	0.460747i	$-0.847582\pi$
$661$	−5.09184	+	6.77601i	−0.198050	+	0.263556i	0.689482	+	0.724303i	$0.257838\pi$
$662$	−23.0260	−	60.7146i	−0.894931	−	2.35974i
$663$	2.61438	+	21.4288i	0.101534	+	0.832227i
$664$	45.5422	−	120.085i	1.76738	−	4.66020i
$665$	0.0540455	+	0.0854661i	0.00209580	+	0.00331423i
$666$	15.2680	+	6.50508i	0.591622	+	0.252067i
$667$	16.9842	+	10.7401i	0.657629	+	0.415859i
$668$	−15.8455	−	1.92399i	−0.613080	−	0.0744414i
$669$	−4.16013	−	9.76419i	−0.160840	−	0.377506i
$670$	4.60347	−	13.7891i	0.177848	−	0.532719i
$671$	−4.84264	−	1.83657i	−0.186948	−	0.0709001i
$672$	−69.4745	−	5.60856i	−2.68004	−	0.216355i
$673$	4.34896	−	15.0144i	0.167640	−	0.578761i	−0.832070	−	0.554671i	$-0.812844\pi$
$673$	4.34896	−	15.0144i	0.167640	−	0.578761i	0.999710	−	0.0240899i	$-0.00766881\pi$
$674$	30.7472	+	1.23907i	1.18434	+	0.0477272i
$675$	−3.15239			−0.121336
$676$	68.6623	+	5.46387i	2.64086	+	0.210149i
$677$	24.5474			0.943432			0.471716	−	0.881751i	$-0.343635\pi$
$677$	24.5474			0.943432			0.471716	+	0.881751i	$0.343635\pi$
$678$	−44.0467	−	1.77502i	−1.69160	−	0.0681692i
$679$	−11.1206	+	38.3927i	−0.426768	+	1.47338i
$680$	151.840	+	12.2578i	5.82279	+	0.470065i
$681$	16.2730	+	6.17154i	0.623584	+	0.236494i
$682$	9.08887	−	27.2245i	0.348031	−	1.04248i
$683$	2.58788	+	6.07398i	0.0990225	+	0.232414i	0.962122	−	0.272620i	$-0.0878901\pi$
$683$	2.58788	+	6.07398i	0.0990225	+	0.232414i	−0.863099	+	0.505034i	$0.831480\pi$
$684$	−0.0496707	−	0.00603111i	−0.00189921	−	0.000230605i
$685$	−5.91927	−	3.74312i	−0.226164	−	0.143017i
$686$	0.602735	+	0.256801i	0.0230125	+	0.00980472i
$687$	−7.15346	−	11.3123i	−0.272921	−	0.431591i
$688$	−31.5503	+	83.1914i	−1.20284	+	3.17164i
$689$	1.12603	−	9.31831i	0.0428985	−	0.354999i
$690$	7.38920	+	19.4837i	0.281302	+	0.741732i
$691$	−23.7878	+	31.6558i	−0.904929	+	1.20424i	0.0734245	+	0.997301i	$0.476607\pi$
$691$	−23.7878	+	31.6558i	−0.904929	+	1.20424i	−0.978353	+	0.206941i	$0.933649\pi$
$692$	−40.7074	−	6.61560i	−1.54746	−	0.251487i
$693$	−19.5411	+	8.32567i	−0.742303	+	0.316266i
$694$	−25.4088	−	17.5384i	−0.964504	−	0.665749i
$695$	−6.72437	+	3.88231i	−0.255070	+	0.147265i
$696$	59.8848	+	28.4157i	2.26993	+	1.07709i
$697$	−10.8266	+	1.31459i	−0.410086	+	0.0497935i
$698$	−5.26583	−	9.12069i	−0.199315	−	0.345223i
$699$	−2.94380	+	5.09881i	−0.111345	+	0.192855i
$700$	24.5527	−	57.6273i	0.928005	−	2.17811i
$701$	−14.4236	−	12.7782i	−0.544770	−	0.482624i	0.345272	−	0.938503i	$-0.387787\pi$
$701$	−14.4236	−	12.7782i	−0.544770	−	0.482624i	−0.890042	+	0.455879i	$0.849325\pi$
$702$	−7.54159	+	6.16472i	−0.284639	+	0.232672i
$703$	−0.0434230	+	0.0384694i	−0.00163773	+	0.00145090i
$704$	41.7118	+	124.942i	1.57207	+	4.70894i
$705$	0.0141353	−	0.350765i	0.000532367	−	0.0132106i
$706$	42.8379	−	52.4669i	1.61223	−	1.97462i
$707$	−3.59904	−	4.06247i	−0.135356	−	0.152785i
$708$	46.7879	+	9.55181i	1.75840	+	0.358979i
$709$	25.2232	−	7.30599i	0.947277	−	0.274382i	0.231598	−	0.972811i	$-0.425604\pi$
$709$	25.2232	−	7.30599i	0.947277	−	0.274382i	0.715679	+	0.698429i	$0.246117\pi$
$710$	−58.3838	+	22.1420i	−2.19110	+	0.830976i
$711$	0.620725	+	15.4031i	0.0232790	+	0.577663i
$712$	−15.0239	−	11.2898i	−0.563046	−	0.423101i
$713$	−4.96496	+	1.01360i	−0.185939	+	0.0379598i
$714$	53.7132	−	28.1909i	2.01017	−	1.05502i
$715$	−11.6956	−	57.1218i	−0.437389	−	2.13623i
$716$	58.0588	+	30.4716i	2.16976	+	1.13878i
$717$	17.0924	+	4.95089i	0.638329	+	0.184894i
$718$	13.9772	−	1.12836i	0.521625	−	0.0421100i
$719$	−7.44514	+	36.4687i	−0.277657	+	1.36005i	0.566547	+	0.824030i	$0.308279\pi$
$719$	−7.44514	+	36.4687i	−0.277657	+	1.36005i	−0.844203	+	0.536023i	$0.819926\pi$
$720$	17.8817	+	34.0707i	0.666411	+	1.26974i
$721$	−22.4368	−	29.8580i	−0.835592	−	1.11197i
$722$	−27.4338	+	43.3830i	−1.02098	+	1.61455i
$723$	−0.779115	+	0.537784i	−0.0289756	+	0.0200004i
$724$	−14.3111	+	30.1601i	−0.531869	+	1.12089i
$725$	−16.2440	+	16.9118i	−0.603288	+	0.628089i
$726$	41.0682	+	39.4465i	1.52418	+	1.46400i
$727$	3.03711	+	25.0128i	0.112640	+	0.927675i	0.934002	+	0.357268i	$0.116292\pi$
$727$	3.03711	+	25.0128i	0.112640	+	0.927675i	−0.821362	+	0.570407i	$0.806785\pi$
$728$	−33.5890	−	115.715i	−1.24489	−	4.28867i
$729$	0.120537	−	0.992709i	0.00446432	−	0.0367670i
$730$	−15.2984	+	12.4907i	−0.566218	+	0.462303i
$731$	−7.90695	−	38.7308i	−0.292449	−	1.43251i
$732$	1.34799	+	4.65382i	0.0498233	+	0.172010i
$733$	7.27388	+	29.5113i	0.268667	+	1.09002i	0.937882	+	0.346955i	$0.112784\pi$
$733$	7.27388	+	29.5113i	0.268667	+	1.09002i	−0.669215	+	0.743069i	$0.733370\pi$
$734$	4.96621	−	61.5175i	0.183306	−	2.27065i
$735$	−3.23571	−	19.9101i	−0.119351	−	0.734395i
$736$	33.2936	−	37.5807i	1.22722	−	1.38524i
$737$	−8.53331	+	6.41236i	−0.314328	+	0.236202i
$738$	−3.11223	−	3.81179i	−0.114563	−	0.140314i
$739$	0.962435	−	5.92210i	0.0354037	−	0.217848i	−0.963320	−	0.268356i	$-0.913520\pi$
$739$	0.962435	−	5.92210i	0.0354037	−	0.217848i	0.998724	+	0.0505076i	$0.0160839\pi$
$740$	90.2341	+	22.2407i	3.31707	+	0.817584i
$741$	−0.00816738	−	0.0330549i	−0.000300036	−	0.00121430i
$742$	−25.6086	+	6.31195i	−0.940120	+	0.231719i
$743$	0.0168630	+	0.208885i	0.000618642	+	0.00766326i	0.997059	−	0.0766343i	$-0.0244174\pi$
$743$	0.0168630	+	0.208885i	0.000618642	+	0.00766326i	−0.996441	+	0.0842976i	$0.973135\pi$
$744$	−15.8547	+	5.29309i	−0.581263	+	0.194054i
$745$	14.0395	+	14.6166i	0.514366	+	0.535512i
$746$			66.3403i			2.42889i
$747$	−10.3946	+	9.98414i	−0.380318	+	0.365301i
$748$	−139.177	−	113.634i	−5.08880	−	4.15488i
$749$	16.2859	−	31.0303i	0.595075	−	1.13382i
$750$	14.0672	−	2.28614i	0.513660	−	0.0834779i
$751$	22.2689	−	14.0820i	0.812602	−	0.513858i	−0.0623579	−	0.998054i	$-0.519862\pi$
$751$	22.2689	−	14.0820i	0.812602	−	0.513858i	0.874960	+	0.484196i	$0.160888\pi$
$752$	−1.49693	+	0.710302i	−0.0545874	+	0.0259020i
$753$	−16.4541	+	23.8379i	−0.599622	+	0.868703i
$754$	−5.78901	+	72.2252i	−0.210823	+	2.63029i
$755$	−18.7050	−	27.0988i	−0.680744	−	0.986227i
$756$	17.2084	+	9.93528i	0.625864	+	0.361343i
$757$	−10.3234	−	21.7562i	−0.375212	−	0.790743i	−0.999951	−	0.00990883i	$-0.996846\pi$
$757$	−10.3234	−	21.7562i	−0.375212	−	0.790743i	0.624739	−	0.780834i	$-0.285205\pi$
$758$	41.3323	+	13.7988i	1.50126	+	0.501193i
$759$	3.66161	−	14.8557i	0.132908	−	0.539229i
$760$	−0.240072	+	0.00967457i	−0.00870832	+	0.000350933i
$761$	39.0685	−	1.57441i	1.41623	−	0.0570722i	0.679708	−	0.733483i	$-0.262106\pi$
$761$	39.0685	−	1.57441i	1.41623	−	0.0570722i	0.736525	+	0.676410i	$0.236465\pi$
$762$	−11.5152	+	46.7188i	−0.417150	+	1.69244i
$763$	−51.8633	−	17.3145i	−1.87758	−	0.626828i
$764$	12.3347	+	25.9948i	0.446252	+	0.940457i
$765$	−14.8050	−	8.54767i	−0.535276	−	0.309042i
$766$	−48.8171	−	70.7238i	−1.76383	−	2.55535i
$767$	5.23104	+	32.0719i	0.188882	+	1.15805i
$768$	12.9548	−	18.7683i	0.467466	−	0.677242i
$769$	4.39058	−	2.08336i	0.158328	−	0.0751277i	−0.347879	−	0.937539i	$-0.613098\pi$
$769$	4.39058	−	2.08336i	0.158328	−	0.0751277i	0.506208	+	0.862412i	$0.331047\pi$
$770$	−138.478	+	87.5682i	−4.99040	+	3.15574i
$771$	26.7511	−	4.34748i	0.963417	−	0.156571i
$772$	28.5937	−	54.4807i	1.02911	−	1.96080i
$773$	11.9891	+	9.78879i	0.431218	+	0.352078i	0.823060	−	0.567954i	$-0.192265\pi$
$773$	11.9891	+	9.78879i	0.431218	+	0.352078i	−0.391843	+	0.920032i	$0.628162\pi$
$774$	12.8635	−	12.3556i	0.462369	−	0.444111i
$775$		−	5.91325i		−	0.212410i
$776$	−65.7896	−	68.4942i	−2.36171	−	2.45880i
$777$	21.8528	−	7.29555i	0.783967	−	0.261726i
$778$	0.0714222	+	0.884723i	0.00256061	+	0.0317188i
$779$	0.0167017	−	0.00411659i	0.000598400	−	0.000147492i
$780$	−36.1470	+	40.8487i	−1.29427	+	1.46262i
$781$	44.5159	+	10.9722i	1.59290	+	0.392615i
$782$	−7.00939	+	43.1305i	−0.250655	+	1.54234i
$783$	−4.70453	−	5.76201i	−0.168126	−	0.205917i
$784$	−76.1115	+	57.1941i	−2.71827	+	2.04265i
$785$	−4.10310	+	4.63144i	−0.146446	+	0.165303i
$786$	8.72905	+	53.7120i	0.311355	+	1.91584i
$787$	−2.07283	+	25.6766i	−0.0738883	+	0.915271i	0.848547	+	0.529120i	$0.177478\pi$
$787$	−2.07283	+	25.6766i	−0.0738883	+	0.915271i	−0.922435	+	0.386151i	$0.873804\pi$
$788$	−21.4237	−	86.9194i	−0.763188	−	3.09637i
$789$	−0.788890	−	2.72357i	−0.0280852	−	0.0969615i
$790$	23.7850	+	116.507i	0.846234	+	4.14513i
$791$	−47.4019	+	38.7025i	−1.68542	+	1.37610i
$792$	6.08335	−	50.1009i	0.216163	−	1.78026i
$793$	−2.63469	+	1.98221i	−0.0935607	+	0.0703902i
$794$	−0.194783	−	1.60418i	−0.00691258	−	0.0569302i
$795$	5.36060	+	5.14892i	0.190121	+	0.182613i
$796$	−43.3186	+	45.0994i	−1.53539	+	1.59851i
$797$	−8.81581	+	18.5789i	−0.312272	+	0.658099i	−0.997533	−	0.0701984i	$-0.977637\pi$
$797$	−8.81581	+	18.5789i	−0.312272	+	0.658099i	0.685261	+	0.728297i	$0.259688\pi$
$798$	−0.0787413	+	0.0543512i	−0.00278741	+	0.00192401i
$799$	0.393442	−	0.622179i	0.0139190	−	0.0220111i
$800$	35.1965	+	46.8380i	1.24438	+	1.65597i
$801$	0.980103	+	1.86743i	0.0346302	+	0.0659824i
$802$	2.96764	−	14.5365i	0.104791	−	0.513300i
$803$	14.4545	−	1.16689i	0.510088	−	0.0411786i
$804$	9.59127	+	2.77814i	0.338258	+	0.0979776i
$805$	25.6136	+	13.4430i	0.902760	+	0.473805i
$806$	−11.5638	−	14.1465i	−0.407316	−	0.498290i
$807$	9.66101	−	5.07049i	0.340084	−	0.178490i
$808$	12.6351	−	2.57948i	0.444502	−	0.0907458i
$809$	−12.7517	−	9.58227i	−0.448326	−	0.336895i	0.352480	−	0.935819i	$-0.385339\pi$
$809$	−12.7517	−	9.58227i	−0.448326	−	0.336895i	−0.800805	+	0.598925i	$0.795595\pi$
$810$	−0.310595	−	7.70733i	−0.0109132	−	0.270808i
$811$	12.9141	−	4.89766i	0.453474	−	0.171980i	−0.117284	−	0.993098i	$-0.537419\pi$
$811$	12.9141	−	4.89766i	0.453474	−	0.171980i	0.570758	+	0.821118i	$0.306649\pi$
$812$	141.974	−	41.1233i	4.98232	−	1.44315i
$813$	2.17621	+	0.444276i	0.0763229	+	0.0155814i
$814$	−62.3308	−	70.3569i	−2.18469	−	2.46601i
$815$	−10.7544	+	13.1718i	−0.376712	+	0.461388i
$816$	−3.24896	+	80.6222i	−0.113736	+	2.82234i
$817$	0.0197435	+	0.0591390i	0.000690738	+	0.00206901i
$818$	17.6034	−	15.5952i	0.615487	−	0.545274i
$819$	−2.16142	+	13.3480i	−0.0755260	+	0.466417i
$820$	−20.6263	−	18.2733i	−0.720300	−	0.638130i
$821$	13.8942	−	32.6110i	0.484912	−	1.13813i	−0.480404	−	0.877047i	$-0.659510\pi$
$821$	13.8942	−	32.6110i	0.484912	−	1.13813i	0.965316	−	0.261084i	$-0.0840798\pi$
$822$	3.31326	−	5.73873i	0.115563	−	0.200161i
$823$	27.9207	+	48.3602i	0.973256	+	1.68573i	0.685574	+	0.728003i	$0.259551\pi$
$823$	27.9207	+	48.3602i	0.973256	+	1.68573i	0.287682	+	0.957726i	$0.407115\pi$
$824$	88.0946	−	10.6966i	3.06892	−	0.372635i
$825$	16.1306	+	7.65404i	0.561594	+	0.266480i
$826$	79.0795	−	45.6566i	2.75153	−	1.58860i
$827$	−10.7382	−	7.41206i	−0.373404	−	0.257742i	0.366552	−	0.930398i	$-0.380538\pi$
$827$	−10.7382	−	7.41206i	−0.373404	−	0.257742i	−0.739956	+	0.672655i	$0.765154\pi$
$828$	−13.1680	+	5.61036i	−0.457619	+	0.194973i
$829$	−13.2515	−	2.15358i	−0.460244	−	0.0747970i	−0.0741313	−	0.997248i	$-0.523618\pi$
$829$	−13.2515	−	2.15358i	−0.460244	−	0.0747970i	−0.386113	+	0.922452i	$0.626182\pi$
$830$	−66.7875	+	88.8780i	−2.31823	+	3.08500i
$831$	−10.4972	−	27.6787i	−0.364143	−	0.960165i
$832$	81.4284	+	20.0209i	2.82302	+	0.694099i
$833$	14.9993	−	39.5500i	0.519696	−	1.37032i
$834$	−3.92656	−	6.20936i	−0.135966	−	0.215012i
$835$	7.91332	+	3.37155i	0.273852	+	0.116677i
$836$	0.239518	+	0.151462i	0.00828389	+	0.00523842i
$837$	1.86212	+	0.226103i	0.0643644	+	0.00781525i
$838$	15.4449	+	36.2505i	0.533535	+	1.25225i
$839$	16.8132	−	50.3617i	0.580456	−	1.73868i	−0.0892065	−	0.996013i	$-0.528433\pi$
$839$	16.8132	−	50.3617i	0.580456	−	1.73868i	0.669663	−	0.742665i	$-0.266439\pi$
$840$	89.2165	+	33.8353i	3.07826	+	1.16743i
$841$	−26.2480	−	2.11895i	−0.905102	−	0.0730674i
$842$	11.3405	−	39.1521i	0.390821	−	1.34927i
$843$	21.8579	+	0.880844i	0.752827	+	0.0303379i
$844$	−99.0526			−3.40953
$845$	−34.7211	−	13.1225i	−1.19444	−	0.451428i
$846$	0.332154			0.0114197
$847$	78.9853	+	3.18300i	2.71397	+	0.109369i
$848$	9.76044	−	33.6969i	0.335175	−	1.15716i
$849$	11.8229	+	0.954441i	0.405760	+	0.0327563i
$850$	−47.6769	−	18.0815i	−1.63531	−	0.620190i
$851$	−5.25520	+	15.7413i	−0.180146	+	0.539603i
$852$	−16.8117	−	39.4585i	−0.575958	−	1.35182i
$853$	−24.3255	−	2.95365i	−0.832890	−	0.101131i	−0.307027	−	0.951701i	$-0.599334\pi$
$853$	−24.3255	−	2.95365i	−0.832890	−	0.101131i	−0.525862	+	0.850570i	$0.676257\pi$
$854$	7.83053	+	4.95173i	0.267955	+	0.169445i
$855$	0.0248058	+	0.0105688i	0.000848340	+	0.000361444i
$856$	44.5033	+	70.3764i	1.52109	+	2.40542i
$857$	−0.686483	+	1.81011i	−0.0234498	+	0.0618321i	−0.946230	−	0.323495i	$-0.895142\pi$
$857$	−0.686483	+	1.81011i	−0.0234498	+	0.0618321i	0.922780	+	0.385327i	$0.125911\pi$
$858$	53.5578	−	13.2333i	1.82843	−	0.451779i
$859$	3.63948	+	9.59652i	0.124177	+	0.327429i	0.982661	−	0.185412i	$-0.0593621\pi$
$859$	3.63948	+	9.59652i	0.124177	+	0.327429i	−0.858483	+	0.512841i	$0.828593\pi$
$860$	60.0017	−	79.8478i	2.04604	−	2.72279i
$861$	−6.74277	−	1.09581i	−0.229793	−	0.0373450i
$862$	−90.2098	+	38.4348i	−3.07256	+	1.30909i
$863$	−32.9502	−	22.7439i	−1.12164	−	0.774210i	−0.145069	−	0.989422i	$-0.546340\pi$
$863$	−32.9502	−	22.7439i	−1.12164	−	0.774210i	−0.976567	+	0.215212i	$0.930956\pi$
$864$	−16.0954	+	9.29269i	−0.547577	+	0.316144i
$865$	20.0787	+	9.52745i	0.682696	+	0.323943i
$866$	−4.49760	+	0.546108i	−0.152835	+	0.0185575i
$867$	−9.42424	−	16.3233i	−0.320064	−	0.554367i
$868$	−18.6366	+	32.2795i	−0.632567	+	1.09564i
$869$	34.2228	−	80.3239i	1.16093	−	2.72480i
$870$	−42.9485	−	38.0491i	−1.45609	−	1.28998i
$871$	0.550656	+	6.77276i	0.0186583	+	0.229486i
$872$	97.2430	−	86.1498i	3.29306	−	2.91740i
$873$	3.37506	+	10.1096i	0.114229	+	0.342157i
$874$	0.00277511	−	0.0688637i	9.38696e−5	−	0.00232935i
$875$	12.5124	−	15.3249i	0.422996	−	0.518076i
$876$	−8.99597	−	10.1543i	−0.303946	−	0.343084i
$877$	−12.7591	−	2.60479i	−0.430845	−	0.0879576i	−0.0202912	−	0.999794i	$-0.506459\pi$
$877$	−12.7591	−	2.60479i	−0.430845	−	0.0879576i	−0.410553	+	0.911837i	$0.634664\pi$
$878$	15.8976	−	4.60480i	0.536519	−	0.155405i
$879$	11.7504	−	4.45632i	0.396330	−	0.150308i
$880$	−8.77520	−	217.754i	−0.295812	−	7.34050i
$881$	2.00613	+	1.50751i	0.0675882	+	0.0507893i	0.633999	−	0.773334i	$-0.281412\pi$
$881$	2.00613	+	1.50751i	0.0675882	+	0.0507893i	−0.566411	+	0.824123i	$0.691669\pi$
$882$	18.6999	−	3.81761i	0.629658	−	0.128546i
$883$	38.0796	−	19.9857i	1.28148	−	0.672572i	0.319992	−	0.947420i	$-0.396320\pi$
$883$	38.0796	−	19.9857i	1.28148	−	0.672572i	0.961488	+	0.274848i	$0.0886276\pi$
$884$	−108.473	+	36.2828i	−3.64836	+	1.22032i
$885$	−22.7858	−	11.9589i	−0.765936	−	0.401994i
$886$	−69.1324	−	20.0245i	−2.32255	−	0.672735i
$887$	8.15654	−	0.658464i	0.273870	−	0.0221091i	0.0572313	−	0.998361i	$-0.481773\pi$
$887$	8.15654	−	0.658464i	0.273870	−	0.0221091i	0.216638	+	0.976252i	$0.430491\pi$
$888$	−10.9495	+	53.6341i	−0.367441	+	1.79984i
$889$	31.0416	+	59.1448i	1.04110	+	1.98365i
$890$	9.77287	+	13.0053i	0.327587	+	0.435940i
$891$	−3.02709	+	4.78696i	−0.101411	+	0.160369i
$892$	46.2802	−	31.9449i	1.54958	−	1.06959i
$893$	−0.000497742		0.00104897i	−1.66563e−5		3.51024e-5i
$894$	−13.2838	+	13.8299i	−0.444276	+	0.462541i
$895$	−25.4833	−	24.4770i	−0.851812	−	0.818177i
$896$	−11.5990	−	95.5264i	−0.387495	−	3.19131i
$897$	−6.75129	−	7.02079i	−0.225419	−	0.234417i
$898$	9.36325	−	77.1133i	0.312456	−	2.57330i
$899$	10.8084	−	8.82476i	0.360479	−	0.294322i
$900$	−3.34096	−	16.3651i	−0.111365	−	0.545503i
$901$	4.33644	+	14.9711i	0.144468	+	0.498760i
$902$	6.66998	+	27.0612i	0.222086	+	0.901039i
$903$	1.99236	−	24.6798i	0.0663016	−	0.821293i
$904$	−23.3241	−	143.519i	−0.775748	−	4.77337i
$905$	11.9294	−	13.4655i	0.396547	−	0.447609i
$906$	24.9068	−	18.7163i	0.827474	−	0.621806i
$907$	9.56722	+	11.7177i	0.317674	+	0.389080i	0.908615	−	0.417635i	$-0.137141\pi$
$907$	9.56722	+	11.7177i	0.317674	+	0.389080i	−0.590941	+	0.806715i	$0.701243\pi$
$908$	−14.7921	+	91.0194i	−0.490893	+	3.02058i
$909$	−1.40514	−	0.346337i	−0.0466057	−	0.0114873i
$910$	0.0597084	+	104.302i	0.00197931	+	3.45758i
$911$	1.39834	−	0.344659i	0.0463290	−	0.0114191i	−0.216083	−	0.976375i	$-0.569328\pi$
$911$	1.39834	−	0.344659i	0.0463290	−	0.0114191i	0.262412	+	0.964956i	$0.415482\pi$
$912$	−0.0102405	−	0.126851i	−0.000339096	−	0.00420045i
$913$	77.4301	−	25.8500i	2.56256	−	0.855509i
$914$	−9.95845	−	10.3678i	−0.329396	−	0.342938i
$915$		−	2.61096i		−	0.0863157i
$916$	51.1445	−	49.1249i	1.68986	−	1.62313i
$917$	58.5144	+	47.7756i	1.93232	+	1.57769i
$918$	7.51699	−	14.3224i	0.248098	−	0.472710i
$919$	−12.0334	+	1.95562i	−0.396946	+	0.0645100i	−0.355608	−	0.934635i	$-0.615726\pi$
$919$	−12.0334	+	1.95562i	−0.396946	+	0.0645100i	−0.0413381	+	0.999145i	$0.513162\pi$
$920$	−58.0914	+	36.7348i	−1.91522	+	1.21111i
$921$	9.36020	−	4.44147i	0.308429	−	0.146351i
$922$	46.7413	−	67.7164i	1.53934	−	2.23012i
$923$	21.0381	−	20.2305i	0.692477	−	0.665896i
$924$	−63.9313	−	92.6204i	−2.10318	−	3.04699i
$925$	−16.7710	−	9.68276i	−0.551428	−	0.318367i
$926$	42.3283	+	89.2049i	1.39099	+	2.93146i
$927$	−9.44633	−	3.15365i	−0.310258	−	0.103579i
$928$	−33.0854	+	134.233i	−1.08608	+	4.40640i
$929$	−20.6240	+	0.831119i	−0.676652	+	0.0272681i	−0.376213	−	0.926533i	$-0.622774\pi$
$929$	−20.6240	+	0.831119i	−0.676652	+	0.0272681i	−0.300439	+	0.953801i	$0.597133\pi$
$930$	14.4574	−	0.582614i	0.474077	−	0.0191047i
$931$	−0.0159660	+	0.0647765i	−0.000523263	+	0.00212296i
$932$	−29.5895	−	9.87843i	−0.969236	−	0.323579i
$933$	6.52872	+	13.7590i	0.213741	+	0.450449i
$934$	28.9425	+	16.7100i	0.947028	+	0.546767i
$935$	55.0023	+	79.6846i	1.79877	+	2.60596i
$936$	−24.8985	−	20.3053i	−0.813834	−	0.663698i
$937$	−8.18896	+	11.8638i	−0.267522	+	0.387572i	−0.933604	−	0.358306i	$-0.883354\pi$
$937$	−8.18896	+	11.8638i	−0.267522	+	0.387572i	0.666083	+	0.745878i	$0.267970\pi$
$938$	17.2508	−	8.18558i	0.563257	−	0.267269i
$939$	−7.32039	+	4.62914i	−0.238892	+	0.151066i
$940$	1.83592	−	0.298365i	0.0598810	−	0.00973161i
$941$	3.75041	−	7.14580i	0.122260	−	0.232946i	−0.816632	−	0.577158i	$-0.804162\pi$
$941$	3.75041	−	7.14580i	0.122260	−	0.232946i	0.938892	+	0.344212i	$0.111854\pi$
$942$	−4.53492	−	3.70265i	−0.147756	−	0.120639i
$943$	3.54885	−	3.40872i	0.115566	−	0.111003i
$944$			121.458i			3.95312i
$945$	−7.41767	−	7.72261i	−0.241297	−	0.251217i
$946$	−95.8211	+	31.9898i	−3.11541	+	1.04008i
$947$	−1.16506	−	14.4319i	−0.0378594	−	0.468973i	−0.987713	−	0.156278i	$-0.950050\pi$
$947$	−1.16506	−	14.4319i	−0.0378594	−	0.468973i	0.949854	−	0.312695i	$-0.101232\pi$
$948$	−79.3049	+	19.5469i	−2.57570	+	0.634854i
$949$	4.28549	−	8.17669i	0.139113	−	0.265427i
$950$	0.0780872	+	0.0192468i	0.00253348	+	0.000624447i
$951$	2.97864	−	18.3283i	0.0965892	−	0.594337i
$952$	126.544	+	154.988i	4.10132	+	5.02320i
$953$	−19.4684	+	14.6295i	−0.630642	+	0.473897i	−0.867360	−	0.497682i	$-0.834185\pi$
$953$	−19.4684	+	14.6295i	−0.630642	+	0.473897i	0.236718	+	0.971578i	$0.423928\pi$
$954$	−4.66360	+	5.26412i	−0.150990	+	0.170432i
$955$	−2.48721	−	15.3044i	−0.0804844	−	0.495240i
$956$	−7.58682	+	93.9796i	−0.245375	+	3.03952i
$957$	10.0825	+	40.9065i	0.325922	+	1.32232i
$958$	23.0412	+	79.5474i	0.744427	+	2.57006i
$959$	−1.84002	−	9.01299i	−0.0594172	−	0.291045i
$960$	−51.4367	+	41.9967i	−1.66011	+	1.35544i
$961$	3.31251	−	27.2810i	0.106855	−	0.880032i
$962$	−59.0573	+	9.63246i	−1.90409	+	0.310563i
$963$	−1.12635	−	9.27632i	−0.0362961	−	0.298925i
$964$	−3.61754	−	3.47469i	−0.116513	−	0.111912i
$965$	−22.9685	+	23.9128i	−0.739384	+	0.769780i
$966$	−11.7333	+	24.7274i	−0.377513	+	0.795592i
$967$	11.9250	−	8.23123i	0.383482	−	0.264698i	−0.360691	−	0.932685i	$-0.617459\pi$
$967$	11.9250	−	8.23123i	0.383482	−	0.264698i	0.744173	+	0.667987i	$0.232844\pi$
$968$	−100.386	+	158.748i	−3.22653	+	5.10234i
$969$	0.0339669	+	0.0452017i	0.00109117	+	0.00145209i
$970$	38.2058	+	72.7950i	1.22671	+	2.33731i
$971$	4.33389	−	21.2288i	0.139081	−	0.681265i	−0.849132	−	0.528181i	$-0.822874\pi$
$971$	4.33389	−	21.2288i	0.139081	−	0.681265i	0.988213	−	0.153084i	$-0.0489205\pi$
$972$	5.28123	−	0.426345i	0.169395	−	0.0136750i
$973$	−9.79599	−	2.83744i	−0.314045	−	0.0909643i
$974$	91.4366	+	47.9896i	2.92982	+	1.53769i
$975$	9.60304	−	6.08029i	0.307543	−	0.194725i
$976$	−10.9118	+	5.72696i	−0.349278	+	0.183315i
$977$	−29.4680	+	6.01594i	−0.942766	+	0.192467i	−0.646738	−	0.762712i	$-0.723867\pi$
$977$	−29.4680	+	6.01594i	−0.942766	+	0.192467i	−0.296028	+	0.955179i	$0.595662\pi$
$978$	−12.8625	−	9.66550i	−0.411296	−	0.309069i
$979$	−0.480973	−	11.9352i	−0.0153720	−	0.381451i
$980$	99.9306	−	37.8987i	3.19217	−	1.21063i
$981$	−14.0038	+	4.05626i	−0.447108	+	0.129506i
$982$	32.2854	+	6.59111i	1.03027	+	0.210331i
$983$	−7.86818	−	8.88134i	−0.250956	−	0.283271i	0.609510	−	0.792778i	$-0.291366\pi$
$983$	−7.86818	−	8.88134i	−0.250956	−	0.283271i	−0.860466	+	0.509507i	$0.829828\pi$
$984$	10.2654	−	12.5728i	0.327249	−	0.400807i
$985$	−1.94249	+	48.2023i	−0.0618928	+	1.53585i
$986$	−38.1019	−	114.129i	−1.21341	−	3.63462i
$987$	0.345134	−	0.305762i	0.0109858	−	0.00973253i
$988$	0.162943	−	0.0774318i	0.00518391	−	0.00246343i
$989$	13.3500	+	11.8271i	0.424506	+	0.376079i
$990$	−17.1242	+	40.1920i	−0.544243	+	1.27739i
$991$	−19.0940	+	33.0718i	−0.606542	+	1.05056i	0.385264	+	0.922806i	$0.374110\pi$
$991$	−19.0940	+	33.0718i	−0.606542	+	1.05056i	−0.991806	+	0.127755i	$0.959223\pi$
$992$	−17.4312	−	30.1918i	−0.553442	−	0.958589i
$993$	−23.8606	+	2.89720i	−0.757194	+	0.0919400i
$994$	−74.0968	−	35.1594i	−2.35021	−	1.11519i
$995$	29.1838	−	16.8493i	0.925187	−	0.534157i
$996$	−62.8474	−	43.3804i	−1.99140	−	1.37456i
$997$	−6.92576	+	2.95079i	−0.219341	+	0.0934525i	−0.498842	−	0.866693i	$-0.666241\pi$
$997$	−6.92576	+	2.95079i	−0.219341	+	0.0934525i	0.279501	+	0.960145i	$0.409831\pi$
$998$	−33.3899	−	5.42638i	−1.05694	−	0.171769i
$999$	3.69043	−	4.91108i	0.116760	−	0.155380i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.a.4.14	✓	336
169.127	even	78	inner	507.2.t.a.127.14	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.a.4.14	✓	336	1.1	even	1	trivial
507.2.t.a.127.14	yes	336	169.127	even	78	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(2.69937 + 0.108781i) q^{2} +(0.278217 - 0.960518i) q^{3} +(5.28123 + 0.426345i) q^{4} +(-2.66969 - 1.01248i) q^{5} +(0.855497 - 2.56253i) q^{6} +(-1.46999 - 3.45019i) q^{7} +(8.84587 + 1.07408i) q^{8} +(-0.845190 - 0.534466i) q^{9} +O(q^{10})\)	\(q+(2.69937 + 0.108781i) q^{2} +(0.278217 - 0.960518i) q^{3} +(5.28123 + 0.426345i) q^{4} +(-2.66969 - 1.01248i) q^{5} +(0.855497 - 2.56253i) q^{6} +(-1.46999 - 3.45019i) q^{7} +(8.84587 + 1.07408i) q^{8} +(-0.845190 - 0.534466i) q^{9} +(-7.09634 - 3.02347i) q^{10} +(3.02709 + 4.78696i) q^{11} +(1.87884 - 4.95410i) q^{12} +(3.60555 - 0.00206402i) q^{13} +(-3.59272 - 9.47323i) q^{14} +(-1.71526 + 2.28260i) q^{15} +(13.3018 + 2.16175i) q^{16} +(-5.50825 + 2.34685i) q^{17} +(-2.22334 - 1.53466i) q^{18} +(0.00817830 - 0.00472175i) q^{19} +(-13.6676 - 6.48536i) q^{20} +(-3.72294 + 0.452047i) q^{21} +(7.65049 + 13.2510i) q^{22} +(1.35072 - 2.33952i) q^{23} +(3.49275 - 8.19779i) q^{24} +(2.35960 + 2.09042i) q^{25} +(9.73293 + 0.386643i) q^{26} +(-0.748511 + 0.663123i) q^{27} +(-6.29237 - 18.8480i) q^{28} +(-0.299524 + 7.43261i) q^{29} +(-4.87842 + 5.97499i) q^{30} +(-1.24388 - 1.40406i) q^{31} +(18.2098 + 3.71755i) q^{32} +(5.44015 - 1.57576i) q^{33} +(-15.1241 + 5.73580i) q^{34} +(0.431166 + 10.6993i) q^{35} +(-4.23578 - 3.18298i) q^{36} +(-6.01898 + 1.22878i) q^{37} +(0.0225899 - 0.0118561i) q^{38} +(1.00114 - 3.46377i) q^{39} +(-22.5283 - 11.8238i) q^{40} +(1.74960 + 0.506779i) q^{41} +(-10.0988 + 0.815257i) q^{42} +(-1.32061 + 6.46876i) q^{43} +(13.9459 + 26.5716i) q^{44} +(1.71526 + 2.28260i) q^{45} +(3.90059 - 6.16829i) q^{46} +(-0.101185 + 0.0698431i) q^{47} +(5.77720 - 12.1752i) q^{48} +(-4.89387 + 5.09505i) q^{49} +(6.14202 + 5.89949i) q^{50} +(0.721696 + 5.94370i) q^{51} +(19.0426 + 1.52631i) q^{52} +(0.313785 - 2.58425i) q^{53} +(-2.09264 + 1.70859i) q^{54} +(-3.23470 - 15.8446i) q^{55} +(-9.29753 - 32.0988i) q^{56} +(-0.00225998 - 0.00916908i) q^{57} +(-1.61705 + 20.0307i) q^{58} +(1.44574 + 8.89598i) q^{59} +(-10.0319 + 11.3236i) q^{60} +(-0.731047 + 0.549346i) q^{61} +(-3.20497 - 3.92537i) q^{62} +(-0.601589 + 3.70172i) q^{63} +(22.5810 + 5.56572i) q^{64} +(-9.62781 - 3.64504i) q^{65} +(14.8564 - 3.66176i) q^{66} +(0.151649 + 1.87851i) q^{67} +(-30.0909 + 10.0458i) q^{68} +(-1.87136 - 1.94829i) q^{69} +28.9282i q^{70} +(5.83813 - 5.60760i) q^{71} +(-6.90238 - 5.63562i) q^{72} +(1.18988 - 2.26713i) q^{73} +(-16.3811 + 2.66219i) q^{74} +(2.66437 - 1.68484i) q^{75} +(0.0452046 - 0.0214498i) q^{76} +(12.0661 - 17.4808i) q^{77} +(3.07925 - 9.24108i) q^{78} +(-8.75708 - 12.6868i) q^{79} +(-33.3230 - 19.2391i) q^{80} +(0.428693 + 0.903450i) q^{81} +(4.66769 + 1.55831i) q^{82} +(3.44923 - 13.9941i) q^{83} +(-19.8545 + 0.800107i) q^{84} +(17.0815 - 0.688360i) q^{85} +(-4.26848 + 17.3179i) q^{86} +(7.05582 + 2.35558i) q^{87} +(21.6356 + 45.5962i) q^{88} +(-1.82645 - 1.05450i) q^{89} +(4.38182 + 6.34816i) q^{90} +(-5.30724 - 12.4368i) q^{91} +(8.13091 - 11.7797i) q^{92} +(-1.69469 + 0.804141i) q^{93} +(-0.280733 + 0.177525i) q^{94} +(-0.0266143 + 0.00432524i) q^{95} +(8.63705 - 16.4565i) q^{96} +(-8.25578 - 6.74064i) q^{97} +(-13.7646 + 13.2211i) q^{98} -5.66376i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9}+O(q^{10}) \) 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9	\( 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9} + 4 q^{10} + 24 q^{12} + 26 q^{13} + 4 q^{14} + 8 q^{16} + 4 q^{17} + 72 q^{22} - 48 q^{23} + 68 q^{25} + 39 q^{26} - 28 q^{27} - 45 q^{29} + 4 q^{30} + 26 q^{31} + 65 q^{32} - 13 q^{33} + 65 q^{34} - 82 q^{35} - 12 q^{36} - 73 q^{38} + 24 q^{40} - 132 q^{42} - 72 q^{43} + 39 q^{44} + 8 q^{48} + 68 q^{49} + 52 q^{50} - 8 q^{51} - 65 q^{52} + 37 q^{53} - 53 q^{55} + 14 q^{56} - 26 q^{57} + 26 q^{58} - 208 q^{59} + 78 q^{60} - 12 q^{61} - 49 q^{62} + 14 q^{64} + 52 q^{65} + 64 q^{66} - 26 q^{67} - 33 q^{68} + 4 q^{69} - 78 q^{71} + 52 q^{73} + 205 q^{74} - 8 q^{75} - 26 q^{76} - 114 q^{77} - 65 q^{78} + 28 q^{79} - 468 q^{80} + 14 q^{81} - 45 q^{82} - 78 q^{83} + 13 q^{85} + 13 q^{86} + 46 q^{87} + 26 q^{88} - 8 q^{90} - 260 q^{91} + 8 q^{92} - 25 q^{94} - 90 q^{95} - 65 q^{96} - 26 q^{97} + 104 q^{98}+O(q^{100}) \) 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9 + 4 * q^10 + 24 * q^12 + 26 * q^13 + 4 * q^14 + 8 * q^16 + 4 * q^17 + 72 * q^22 - 48 * q^23 + 68 * q^25 + 39 * q^26 - 28 * q^27 - 45 * q^29 + 4 * q^30 + 26 * q^31 + 65 * q^32 - 13 * q^33 + 65 * q^34 - 82 * q^35 - 12 * q^36 - 73 * q^38 + 24 * q^40 - 132 * q^42 - 72 * q^43 + 39 * q^44 + 8 * q^48 + 68 * q^49 + 52 * q^50 - 8 * q^51 - 65 * q^52 + 37 * q^53 - 53 * q^55 + 14 * q^56 - 26 * q^57 + 26 * q^58 - 208 * q^59 + 78 * q^60 - 12 * q^61 - 49 * q^62 + 14 * q^64 + 52 * q^65 + 64 * q^66 - 26 * q^67 - 33 * q^68 + 4 * q^69 - 78 * q^71 + 52 * q^73 + 205 * q^74 - 8 * q^75 - 26 * q^76 - 114 * q^77 - 65 * q^78 + 28 * q^79 - 468 * q^80 + 14 * q^81 - 45 * q^82 - 78 * q^83 + 13 * q^85 + 13 * q^86 + 46 * q^87 + 26 * q^88 - 8 * q^90 - 260 * q^91 + 8 * q^92 - 25 * q^94 - 90 * q^95 - 65 * q^96 - 26 * q^97 + 104 * q^98

Introduction

L-functions

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