LMFDB - Embedded newform 225.2.q.a.106.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			106.21
Character	$\chi$	$=$	225.106
Dual form			225.2.q.a.121.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.48808 + 0.316302i) q^{2} +(-0.689391 - 1.58894i) q^{3} +(0.287254 + 0.127894i) q^{4} +(-0.209129 - 2.22627i) q^{5} +(-0.523285 - 2.58254i) q^{6} +(0.255551 - 0.442627i) q^{7} +(-2.07456 - 1.50725i) q^{8} +(-2.04948 + 2.19081i) q^{9} +O(q^{10})$	\(q+(1.48808 + 0.316302i) q^{2} +(-0.689391 - 1.58894i) q^{3} +(0.287254 + 0.127894i) q^{4} +(-0.209129 - 2.22627i) q^{5} +(-0.523285 - 2.58254i) q^{6} +(0.255551 - 0.442627i) q^{7} +(-2.07456 - 1.50725i) q^{8} +(-2.04948 + 2.19081i) q^{9} +(0.392972 - 3.37902i) q^{10} +(0.818173 + 0.173908i) q^{11} +(0.00518556 - 0.544598i) q^{12} +(2.86246 - 0.608435i) q^{13} +(0.520284 - 0.577834i) q^{14} +(-3.39324 + 1.86706i) q^{15} +(-3.03117 - 3.36645i) q^{16} +(2.78774 + 2.02541i) q^{17} +(-3.74275 + 2.61185i) q^{18} +(4.87884 + 3.54469i) q^{19} +(0.224652 - 0.666250i) q^{20} +(-0.879483 - 0.100913i) q^{21} +(1.16250 + 0.517580i) q^{22} +(3.89542 - 4.32630i) q^{23} +(-0.964759 + 4.33544i) q^{24} +(-4.91253 + 0.931153i) q^{25} +4.45203 q^{26} +(4.89396 + 1.74619i) q^{27} +(0.130017 - 0.0944629i) q^{28} +(-0.0623933 - 0.593632i) q^{29} +(-5.63998 + 1.70505i) q^{30} +(0.0928139 - 0.883066i) q^{31} +(-0.881520 - 1.52684i) q^{32} +(-0.287711 - 1.41992i) q^{33} +(3.50774 + 3.89575i) q^{34} +(-1.03885 - 0.476358i) q^{35} +(-0.868911 + 0.367202i) q^{36} +(-2.62260 + 8.07154i) q^{37} +(6.13893 + 6.81797i) q^{38} +(-2.94012 - 4.12884i) q^{39} +(-2.92170 + 4.93372i) q^{40} +(-8.80767 + 1.87213i) q^{41} +(-1.27682 - 0.428348i) q^{42} +(-1.06736 + 1.84872i) q^{43} +(0.212782 + 0.154595i) q^{44} +(5.30592 + 4.10453i) q^{45} +(7.16513 - 5.20577i) q^{46} +(-0.760356 - 7.23431i) q^{47} +(-3.25944 + 7.13715i) q^{48} +(3.36939 + 5.83595i) q^{49} +(-7.60478 - 0.168210i) q^{50} +(1.29642 - 5.82586i) q^{51} +(0.900067 + 0.191315i) q^{52} +(7.16056 - 5.20245i) q^{53} +(6.73030 + 4.14644i) q^{54} +(0.216062 - 1.85784i) q^{55} +(-1.19730 + 0.533074i) q^{56} +(2.26888 - 10.1959i) q^{57} +(0.0949206 - 0.903110i) q^{58} +(-7.87309 + 1.67348i) q^{59} +(-1.21351 + 0.102347i) q^{60} +(-2.68489 - 0.570692i) q^{61} +(0.417430 - 1.28472i) q^{62} +(0.445963 + 1.46702i) q^{63} +(1.97086 + 6.06570i) q^{64} +(-1.95316 - 6.24536i) q^{65} +(0.0209857 - 2.20397i) q^{66} +(0.160059 - 1.52286i) q^{67} +(0.541751 + 0.938340i) q^{68} +(-9.55972 - 3.20709i) q^{69} +(-1.39522 - 1.03745i) q^{70} +(4.04843 - 2.94135i) q^{71} +(7.55386 - 1.45586i) q^{72} +(3.39778 + 10.4573i) q^{73} +(-6.45569 + 11.1816i) q^{74} +(4.86620 + 7.16380i) q^{75} +(0.948122 + 1.64220i) q^{76} +(0.286061 - 0.317703i) q^{77} +(-3.06919 - 7.07402i) q^{78} +(-0.788634 - 7.50335i) q^{79} +(-6.86071 + 7.45220i) q^{80} +(-0.599260 - 8.98003i) q^{81} -13.6987 q^{82} +(0.410770 - 0.182886i) q^{83} +(-0.239729 - 0.141468i) q^{84} +(3.92611 - 6.62982i) q^{85} +(-2.17308 + 2.41345i) q^{86} +(-0.900235 + 0.508384i) q^{87} +(-1.43522 - 1.59398i) q^{88} +(-5.39621 - 16.6078i) q^{89} +(6.59739 + 7.78616i) q^{90} +(0.462194 - 1.42249i) q^{91} +(1.67228 - 0.744547i) q^{92} +(-1.46713 + 0.461301i) q^{93} +(1.15675 - 11.0058i) q^{94} +(6.87111 - 11.6029i) q^{95} +(-1.81835 + 2.45327i) q^{96} +(1.76921 + 16.8329i) q^{97} +(3.16801 + 9.75012i) q^{98} +(-2.05783 + 1.43604i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	1.48808	+	0.316302i	1.05223	+	0.223659i	0.701392	−	0.712776i	$-0.252562\pi$
$2$	1.48808	+	0.316302i	1.05223	+	0.223659i	0.350842	+	0.936435i	$0.385896\pi$
$3$	−0.689391	−	1.58894i	−0.398020	−	0.917377i
$3$	−0.689391	−	1.58894i	−0.398020	−	0.917377i
$4$	0.287254	+	0.127894i	0.143627	+	0.0639468i
$5$	−0.209129	−	2.22627i	−0.0935252	−	0.995617i
$5$	−0.209129	−	2.22627i	−0.0935252	−	0.995617i
$6$	−0.523285	−	2.58254i	−0.213630	−	1.05432i
$7$	0.255551	−	0.442627i	0.0965891	−	0.167297i	−0.813682	−	0.581311i	$-0.802540\pi$
$7$	0.255551	−	0.442627i	0.0965891	−	0.167297i	0.910271	+	0.414014i	$0.135873\pi$
$8$	−2.07456	−	1.50725i	−0.733466	−	0.532894i
$9$	−2.04948	+	2.19081i	−0.683160	+	0.730269i
$10$	0.392972	−	3.37902i	0.124269	−	1.06854i
$11$	0.818173	+	0.173908i	0.246689	+	0.0524353i	0.329596	−	0.944122i	$-0.393087\pi$
$11$	0.818173	+	0.173908i	0.246689	+	0.0524353i	−0.0829078	+	0.996557i	$0.526421\pi$
$12$	0.00518556	−	0.544598i	0.00149694	−	0.157212i
$13$	2.86246	−	0.608435i	0.793904	−	0.168749i	0.206930	−	0.978356i	$-0.433653\pi$
$13$	2.86246	−	0.608435i	0.793904	−	0.168749i	0.586973	+	0.809606i	$0.300319\pi$
$14$	0.520284	−	0.577834i	0.139052	−	0.154433i
$15$	−3.39324	+	1.86706i	−0.876131	+	0.482073i
$16$	−3.03117	−	3.36645i	−0.757791	−	0.841612i
$17$	2.78774	+	2.02541i	0.676126	+	0.491234i	0.872070	−	0.489381i	$-0.162777\pi$
$17$	2.78774	+	2.02541i	0.676126	+	0.491234i	−0.195944	+	0.980615i	$0.562777\pi$
$18$	−3.74275	+	2.61185i	−0.882175	+	0.615618i
$19$	4.87884	+	3.54469i	1.11928	+	0.813207i	0.984100	−	0.177614i	$-0.0568379\pi$
$19$	4.87884	+	3.54469i	1.11928	+	0.813207i	0.135183	+	0.990821i	$0.456838\pi$
$20$	0.224652	−	0.666250i	0.0502338	−	0.148978i
$21$	−0.879483	−	0.100913i	−0.191919	−	0.0220209i
$22$	1.16250	+	0.517580i	0.247846	+	0.110348i
$23$	3.89542	−	4.32630i	0.812252	−	0.902097i	−0.184484	−	0.982836i	$-0.559061\pi$
$23$	3.89542	−	4.32630i	0.812252	−	0.902097i	0.996735	+	0.0807387i	$0.0257279\pi$
$24$	−0.964759	+	4.33544i	−0.196931	+	0.884967i
$25$	−4.91253	+	0.931153i	−0.982506	+	0.186231i
$26$	4.45203			0.873115
$27$	4.89396	+	1.74619i	0.941843	+	0.336054i
$28$	0.130017	−	0.0944629i	0.0245709	−	0.0178518i
$29$	−0.0623933	−	0.593632i	−0.0115861	−	0.110235i	0.987200	−	0.159485i	$-0.0509834\pi$
$29$	−0.0623933	−	0.593632i	−0.0115861	−	0.110235i	−0.998786	+	0.0492504i	$0.984317\pi$
$30$	−5.63998	+	1.70505i	−1.02971	+	0.311299i
$31$	0.0928139	−	0.883066i	0.0166699	−	0.158603i	−0.983020	−	0.183497i	$-0.941258\pi$
$31$	0.0928139	−	0.883066i	0.0166699	−	0.158603i	0.999690	+	0.0248940i	$0.00792483\pi$
$32$	−0.881520	−	1.52684i	−0.155832	−	0.269909i
$33$	−0.287711	−	1.41992i	−0.0500841	−	0.247177i
$34$	3.50774	+	3.89575i	0.601573	+	0.668115i
$35$	−1.03885	−	0.476358i	−0.175597	−	0.0805192i
$36$	−0.868911	+	0.367202i	−0.144818	+	0.0612003i
$37$	−2.62260	+	8.07154i	−0.431153	+	1.32695i	0.465825	+	0.884877i	$0.345758\pi$
$37$	−2.62260	+	8.07154i	−0.431153	+	1.32695i	−0.896978	+	0.442075i	$0.854242\pi$
$38$	6.13893	+	6.81797i	0.995866	+	1.10602i
$39$	−2.94012	−	4.12884i	−0.470796	−	0.661143i
$40$	−2.92170	+	4.93372i	−0.461961	+	0.780090i
$41$	−8.80767	+	1.87213i	−1.37553	+	0.292377i	−0.835602	−	0.549335i	$-0.814881\pi$
$41$	−8.80767	+	1.87213i	−1.37553	+	0.292377i	−0.539926	+	0.841713i	$0.681548\pi$
$42$	−1.27682	−	0.428348i	−0.197018	−	0.0660956i
$43$	−1.06736	+	1.84872i	−0.162771	+	0.281928i	−0.935862	−	0.352368i	$-0.885377\pi$
$43$	−1.06736	+	1.84872i	−0.162771	+	0.281928i	0.773090	+	0.634296i	$0.218710\pi$
$44$	0.212782	+	0.154595i	0.0320780	+	0.0233061i
$45$	5.30592	+	4.10453i	0.790960	+	0.611867i
$46$	7.16513	−	5.20577i	1.05644	−	0.767549i
$47$	−0.760356	−	7.23431i	−0.110909	−	1.05523i	−0.898482	−	0.439010i	$-0.855329\pi$
$47$	−0.760356	−	7.23431i	−0.110909	−	1.05523i	0.787573	−	0.616222i	$-0.211338\pi$
$48$	−3.25944	+	7.13715i	−0.470460	+	1.03016i
$49$	3.36939	+	5.83595i	0.481341	+	0.833707i
$50$	−7.60478	−	0.168210i	−1.07548	−	0.0237885i
$51$	1.29642	−	5.82586i	0.181535	−	0.815783i
$52$	0.900067	+	0.191315i	0.124817	+	0.0265307i
$53$	7.16056	−	5.20245i	0.983578	−	0.714612i	0.0250729	−	0.999686i	$-0.492018\pi$
$53$	7.16056	−	5.20245i	0.983578	−	0.714612i	0.958505	+	0.285074i	$0.0920182\pi$
$54$	6.73030	+	4.14644i	0.915877	+	0.564259i
$55$	0.216062	−	1.85784i	0.0291339	−	0.250511i
$56$	−1.19730	+	0.533074i	−0.159997	+	0.0712350i
$57$	2.26888	−	10.1959i	0.300520	−	1.35048i
$58$	0.0949206	−	0.903110i	0.0124637	−	0.118584i
$59$	−7.87309	+	1.67348i	−1.02499	+	0.217868i	−0.689584	−	0.724206i	$-0.742207\pi$
$59$	−7.87309	+	1.67348i	−1.02499	+	0.217868i	−0.335405	+	0.942074i	$0.608873\pi$
$60$	−1.21351	+	0.102347i	−0.156663	+	0.0132129i
$61$	−2.68489	−	0.570692i	−0.343765	−	0.0730696i	0.0327938	−	0.999462i	$-0.489560\pi$
$61$	−2.68489	−	0.570692i	−0.343765	−	0.0730696i	−0.376559	+	0.926393i	$0.622893\pi$
$62$	0.417430	−	1.28472i	0.0530137	−	0.163159i
$63$	0.445963	+	1.46702i	0.0561861	+	0.184827i
$64$	1.97086	+	6.06570i	0.246358	+	0.758212i
$65$	−1.95316	−	6.24536i	−0.242260	−	0.774642i
$66$	0.0209857	−	2.20397i	0.00258316	−	0.271289i
$67$	0.160059	−	1.52286i	0.0195543	−	0.186047i	−0.980385	−	0.197094i	$-0.936850\pi$
$67$	0.160059	−	1.52286i	0.0195543	−	0.186047i	0.999939	+	0.0110468i	$0.00351636\pi$
$68$	0.541751	+	0.938340i	0.0656970	+	0.113790i
$69$	−9.55972	−	3.20709i	−1.15086	−	0.386088i
$70$	−1.39522	−	1.03745i	−0.166761	−	0.123999i
$71$	4.04843	−	2.94135i	0.480460	−	0.349075i	−0.321044	−	0.947064i	$-0.604034\pi$
$71$	4.04843	−	2.94135i	0.480460	−	0.349075i	0.801504	+	0.597990i	$0.204034\pi$
$72$	7.55386	−	1.45586i	0.890231	−	0.171575i
$73$	3.39778	+	10.4573i	0.397680	+	1.22393i	0.926855	+	0.375419i	$0.122501\pi$
$73$	3.39778	+	10.4573i	0.397680	+	1.22393i	−0.529175	+	0.848512i	$0.677499\pi$
$74$	−6.45569	+	11.1816i	−0.750459	+	1.29983i
$75$	4.86620	+	7.16380i	0.561901	+	0.827205i
$76$	0.948122	+	1.64220i	0.108757	+	0.188373i
$77$	0.286061	−	0.317703i	0.0325997	−	0.0362056i
$78$	−3.06919	−	7.07402i	−0.347517	−	0.800975i
$79$	−0.788634	−	7.50335i	−0.0887283	−	0.844193i	−0.944869	−	0.327450i	$-0.893811\pi$
$79$	−0.788634	−	7.50335i	−0.0887283	−	0.844193i	0.856140	−	0.516744i	$-0.172856\pi$
$80$	−6.86071	+	7.45220i	−0.767051	+	0.833182i
$81$	−0.599260	−	8.98003i	−0.0665844	−	0.997781i
$82$	−13.6987			−1.51277
$83$	0.410770	−	0.182886i	0.0450878	−	0.0200744i	−0.384069	−	0.923304i	$-0.625477\pi$
$83$	0.410770	−	0.182886i	0.0450878	−	0.0200744i	0.429157	+	0.903230i	$0.358811\pi$
$84$	−0.239729	−	0.141468i	−0.0261565	−	0.0154354i
$85$	3.92611	−	6.62982i	0.425846	−	0.719105i
$86$	−2.17308	+	2.41345i	−0.234329	+	0.260249i
$87$	−0.900235	+	0.508384i	−0.0965153	+	0.0545045i
$88$	−1.43522	−	1.59398i	−0.152995	−	0.169918i
$89$	−5.39621	−	16.6078i	−0.571997	−	1.76043i	−0.646184	−	0.763181i	$-0.723636\pi$
$89$	−5.39621	−	16.6078i	−0.571997	−	1.76043i	0.0741872	−	0.997244i	$-0.476364\pi$
$90$	6.59739	+	7.78616i	0.695425	+	0.820733i
$91$	0.462194	−	1.42249i	0.0484511	−	0.149117i
$92$	1.67228	−	0.744547i	0.174347	−	0.0776244i
$93$	−1.46713	+	0.461301i	−0.152134	+	0.0478347i
$94$	1.15675	−	11.0058i	0.119310	−	1.13516i
$95$	6.87111	−	11.6029i	0.704961	−	1.19043i
$96$	−1.81835	+	2.45327i	−0.185584	+	0.250386i
$97$	1.76921	+	16.8329i	0.179636	+	1.70912i	0.598542	+	0.801091i	$0.295747\pi$
$97$	1.76921	+	16.8329i	0.179636	+	1.70912i	−0.418906	+	0.908030i	$0.637586\pi$
$98$	3.16801	+	9.75012i	0.320017	+	0.984911i
$99$	−2.05783	+	1.43604i	−0.206820	+	0.144327i
$100$	−1.53023	−	0.360804i	−0.153023	−	0.0360804i
$101$	−8.66842	+	15.0141i	−0.862540	+	1.49396i	0.00692858	+	0.999976i	$0.497795\pi$
$101$	−8.66842	+	15.0141i	−0.862540	+	1.49396i	−0.869469	+	0.493988i	$0.835539\pi$
$102$	3.77191	−	8.25930i	0.373475	−	0.817792i
$103$	7.65661	+	3.40894i	0.754428	+	0.335893i	0.747658	−	0.664084i	$-0.231178\pi$
$103$	7.65661	+	3.40894i	0.754428	+	0.335893i	0.00676999	+	0.999977i	$0.497845\pi$
$104$	−6.85540	−	3.05222i	−0.672227	−	0.299295i
$105$	−0.0407334	+	1.97907i	−0.00397517	+	0.193137i
$106$	12.3011	−	5.47678i	1.19478	−	0.531952i
$107$	12.3203			1.19105			0.595524	−	0.803338i	$-0.296945\pi$
$107$	12.3203			1.19105			0.595524	+	0.803338i	$0.296945\pi$
$108$	1.18248	+	1.12750i	0.113784	+	0.108494i
$109$	−4.53429	+	13.9551i	−0.434306	+	1.33666i	0.459490	+	0.888183i	$0.348032\pi$
$109$	−4.53429	+	13.9551i	−0.434306	+	1.33666i	−0.893796	+	0.448474i	$0.851968\pi$
$110$	0.909158	−	2.69628i	0.0866848	−	0.257080i
$111$	14.6332	−	1.39728i	1.38892	−	0.132624i
$112$	−2.26470	+	0.481376i	−0.213994	+	0.0454858i
$113$	12.1591	−	2.58450i	1.14384	−	0.243130i	0.403249	−	0.915090i	$-0.367881\pi$
$113$	12.1591	−	2.58450i	1.14384	−	0.243130i	0.740587	+	0.671961i	$0.234548\pi$
$114$	6.60125	−	14.4547i	0.618264	−	1.35380i
$115$	−10.4462	−	7.76750i	−0.974109	−	0.724323i
$116$	0.0579991	−	0.178503i	0.00538508	−	0.0165736i
$117$	−4.53360	+	7.51807i	−0.419131	+	0.695046i
$118$	−12.2451			−1.12726
$119$	1.60891	−	0.716332i	0.147488	−	0.0656661i
$120$	9.85360	+	1.24115i	0.899507	+	0.113301i
$121$	−9.40984	−	4.18953i	−0.855440	−	0.380866i
$122$	−3.81483	−	1.69847i	−0.345379	−	0.153773i
$123$	9.04664	+	12.7043i	0.815708	+	1.14550i
$124$	0.139600	−	0.241794i	0.0125364	−	0.0217137i
$125$	3.10035	+	10.7419i	0.277303	+	0.960782i
$126$	0.199610	+	2.32410i	0.0177827	+	0.207047i
$127$	−4.71456	−	14.5099i	−0.418349	−	1.28755i	−0.909221	−	0.416315i	$-0.863321\pi$
$127$	−4.71456	−	14.5099i	−0.418349	−	1.28755i	0.490871	−	0.871232i	$-0.336679\pi$
$128$	1.38279	+	13.1564i	0.122223	+	1.16287i
$129$	3.67335	+	0.421483i	0.323420	+	0.0371095i
$130$	−0.931047	−	9.91141i	−0.0816582	−	0.869288i
$131$	−0.964208	+	9.17382i	−0.0842432	+	0.801521i	0.868079	+	0.496426i	$0.165355\pi$
$131$	−0.964208	+	9.17382i	−0.0842432	+	0.801521i	−0.952322	+	0.305094i	$0.901312\pi$
$132$	0.0989528	−	0.444674i	0.00861273	−	0.0387039i
$133$	2.81576	−	1.25366i	0.244158	−	0.108706i
$134$	0.719864	−	2.21551i	0.0621868	−	0.191391i
$135$	2.86401	−	11.2604i	0.246495	−	0.969144i
$136$	−2.73051	−	8.40365i	−0.234139	−	0.720607i
$137$	−6.23387	−	6.92342i	−0.532596	−	0.591507i	0.415460	−	0.909611i	$-0.363621\pi$
$137$	−6.23387	−	6.92342i	−0.532596	−	0.591507i	−0.948056	+	0.318104i	$0.896954\pi$
$138$	−13.2113	−	7.79617i	−1.12462	−	0.663654i
$139$	3.90039	−	4.33183i	0.330827	−	0.367421i	−0.554666	−	0.832073i	$-0.687154\pi$
$139$	3.90039	−	4.33183i	0.330827	−	0.367421i	0.885493	+	0.464652i	$0.153821\pi$
$140$	−0.237490	−	0.269698i	−0.0200716	−	0.0227936i
$141$	−10.9707	+	6.19543i	−0.923901	+	0.521749i
$142$	6.95475	−	3.09646i	0.583630	−	0.259849i
$143$	2.44780			0.204695
$144$	13.5876	+	0.258779i	1.13230	+	0.0215650i
$145$	−1.30854	+	0.263050i	−0.108668	+	0.0218451i
$146$	1.74852	+	16.6360i	0.144708	+	1.37681i
$147$	6.95017	−	9.37702i	0.573240	−	0.773403i
$148$	−1.78565	+	1.98316i	−0.146779	+	0.163015i
$149$	−0.938800	−	1.62605i	−0.0769095	−	0.133211i	0.825006	−	0.565125i	$-0.191172\pi$
$149$	−0.938800	−	1.62605i	−0.0769095	−	0.133211i	−0.901915	+	0.431913i	$0.857839\pi$
$150$	4.97539	+	12.1995i	0.406239	+	0.996087i
$151$	−1.02623	+	1.77749i	−0.0835138	+	0.144650i	−0.904757	−	0.425928i	$-0.859948\pi$
$151$	−1.02623	+	1.77749i	−0.0835138	+	0.144650i	0.821243	+	0.570578i	$0.193281\pi$
$152$	−4.77869	−	14.7073i	−0.387603	−	1.19292i
$153$	−10.1507	+	1.95635i	−0.820635	+	0.158162i
$154$	0.526173	−	0.382287i	0.0424002	−	0.0308056i
$155$	−1.98535	−	0.0219543i	−0.159467	−	0.00176341i
$156$	−0.316509	−	1.56205i	−0.0253410	−	0.125064i
$157$	−2.99334	−	5.18462i	−0.238895	−	0.413778i	0.721503	−	0.692412i	$-0.243452\pi$
$157$	−2.99334	−	5.18462i	−0.238895	−	0.413778i	−0.960397	+	0.278634i	$0.910118\pi$
$158$	1.19977	−	11.4151i	0.0954487	−	0.908134i
$159$	−13.2028	−	7.79120i	−1.04705	−	0.617882i
$160$	−3.21480	+	2.28180i	−0.254152	+	0.180392i
$161$	−0.919460	−	2.82981i	−0.0724636	−	0.223020i
$162$	1.94865	−	13.5526i	0.153100	−	1.06479i
$163$	5.22667	−	16.0860i	0.409385	−	1.25996i	−0.507793	−	0.861479i	$-0.669539\pi$
$163$	5.22667	−	16.0860i	0.409385	−	1.25996i	0.917178	−	0.398478i	$-0.130461\pi$
$164$	−2.76947	−	0.588669i	−0.216259	−	0.0459673i
$165$	−3.10096	+	0.937468i	−0.241409	+	0.0729818i
$166$	0.669107	−	0.142223i	0.0519328	−	0.0110387i
$167$	−2.23209	+	21.2370i	−0.172725	+	1.64337i	0.473916	+	0.880570i	$0.342840\pi$
$167$	−2.23209	+	21.2370i	−0.172725	+	1.64337i	−0.646640	+	0.762795i	$0.723827\pi$
$168$	1.67244	+	1.53495i	0.129031	+	0.118424i
$169$	−4.05260	+	1.80433i	−0.311738	+	0.138795i
$170$	7.93940	−	8.62389i	0.608924	−	0.661422i
$171$	−17.7648	+	3.42383i	−1.35851	+	0.261827i
$172$	−0.543043	+	0.394544i	−0.0414067	+	0.0300837i
$173$	−3.24371	−	0.689471i	−0.246614	−	0.0524195i	0.0829458	−	0.996554i	$-0.473567\pi$
$173$	−3.24371	−	0.689471i	−0.246614	−	0.0524195i	−0.329560	+	0.944135i	$0.606900\pi$
$174$	−1.50043	+	0.471772i	−0.113747	+	0.0357649i
$175$	−0.843247	+	2.41237i	−0.0637435	+	0.182358i
$176$	−1.89457	−	3.28148i	−0.142808	−	0.247351i
$177$	8.08670	+	11.3562i	0.607834	+	0.853586i
$178$	−2.77692	−	26.4207i	−0.208139	−	1.98031i
$179$	−2.64332	+	1.92048i	−0.197571	+	0.143543i	−0.682172	−	0.731191i	$-0.738965\pi$
$179$	−2.64332	+	1.92048i	−0.197571	+	0.143543i	0.484602	+	0.874735i	$0.338965\pi$
$180$	0.999203	+	1.85764i	0.0744762	+	0.138460i
$181$	−5.08500	−	3.69447i	−0.377965	−	0.274607i	0.382541	−	0.923938i	$-0.375049\pi$
$181$	−5.08500	−	3.69447i	−0.377965	−	0.274607i	−0.760506	+	0.649331i	$0.775049\pi$
$182$	1.13772	−	1.97059i	0.0843333	−	0.146070i
$183$	0.944145	+	4.65957i	0.0697932	+	0.344446i
$184$	−14.6021	+	3.10377i	−1.07648	+	0.228813i
$185$	18.5179	+	4.15062i	1.36146	+	0.305160i
$186$	−2.32912	+	0.222400i	−0.170779	+	0.0163072i
$187$	1.92862	+	2.14195i	0.141034	+	0.156635i
$188$	0.706806	−	2.17533i	0.0515491	−	0.158652i
$189$	2.02356	−	1.71996i	0.147193	−	0.125109i
$190$	13.8948	−	15.0927i	1.00803	−	1.09494i
$191$	7.42126	+	8.24214i	0.536983	+	0.596380i	0.949188	−	0.314711i	$-0.101908\pi$
$191$	7.42126	+	8.24214i	0.536983	+	0.596380i	−0.412204	+	0.911091i	$0.635241\pi$
$192$	8.27935	−	7.31323i	0.597511	−	0.527787i
$193$	−4.50515	−	7.80315i	−0.324288	−	0.561683i	0.657080	−	0.753821i	$-0.271791\pi$
$193$	−4.50515	−	7.80315i	−0.324288	−	0.561683i	−0.981368	+	0.192138i	$0.938458\pi$
$194$	−2.69155	+	25.6083i	−0.193242	+	1.83857i
$195$	−8.57703	+	7.40896i	−0.614214	+	0.530566i
$196$	0.221488	+	2.10732i	0.0158206	+	0.150523i
$197$	−21.9807	+	15.9699i	−1.56606	+	1.13781i	−0.635253	+	0.772304i	$0.719104\pi$
$197$	−21.9807	+	15.9699i	−1.56606	+	1.13781i	−0.930809	+	0.365506i	$0.880896\pi$
$198$	−3.51644	+	1.48605i	−0.249903	+	0.105609i
$199$	15.6745			1.11114			0.555569	−	0.831471i	$-0.312501\pi$
$199$	15.6745			1.11114			0.555569	+	0.831471i	$0.312501\pi$
$200$	11.5948	+	5.47270i	0.819876	+	0.386978i
$201$	−2.53008	+	0.795521i	−0.178458	+	0.0561117i
$202$	−17.6483	+	19.6005i	−1.24173	+	1.37908i
$203$	−0.278702	−	0.124086i	−0.0195611	−	0.00870914i
$204$	1.11749	−	1.50769i	0.0782400	−	0.105560i
$205$	6.00980	+	19.2167i	0.419742	+	1.34215i
$206$	10.3154	+	7.49459i	0.718709	+	0.522173i
$207$	1.49450	+	17.4008i	0.103875	+	1.20944i
$208$	−10.7249	−	7.79207i	−0.743635	−	0.540283i
$209$	3.37529	+	3.74864i	0.233474	+	0.259299i
$210$	−0.686597	+	2.93213i	−0.0473797	+	0.202336i
$211$	−11.2118	+	12.4519i	−0.771850	+	0.857226i	−0.993012	−	0.118011i	$-0.962348\pi$
$211$	−11.2118	+	12.4519i	−0.771850	+	0.857226i	0.221162	+	0.975237i	$0.429015\pi$
$212$	2.72226	−	0.578634i	0.186965	−	0.0397407i
$213$	−7.46459	−	4.40498i	−0.511466	−	0.301824i
$214$	18.3336	+	3.89693i	1.25326	+	0.266389i
$215$	4.33897	+	1.98961i	0.295915	+	0.135690i
$216$	−7.52085	−	10.9990i	−0.511729	−	0.748387i
$217$	−0.367150	−	0.266750i	−0.0249237	−	0.0181082i
$218$	−11.1614	+	19.3322i	−0.755947	+	1.30934i
$219$	14.2736	−	12.6080i	0.964522	−	0.851971i
$220$	0.299671	−	0.506039i	0.0202038	−	0.0341171i
$221$	9.21212	+	4.10150i	0.619674	+	0.275897i
$222$	22.2174	+	2.54924i	1.49113	+	0.171094i
$223$	−10.0324	−	2.13246i	−0.671821	−	0.142800i	−0.140643	−	0.990060i	$-0.544917\pi$
$223$	−10.0324	−	2.13246i	−0.671821	−	0.142800i	−0.531178	+	0.847260i	$0.678250\pi$
$224$	−0.901091			−0.0602067
$225$	8.02816	−	12.6708i	0.535211	−	0.844719i
$226$	18.9113			1.25796
$227$	5.76078	+	1.22449i	0.382356	+	0.0812723i	0.395080	−	0.918647i	$-0.370717\pi$
$227$	5.76078	+	1.22449i	0.382356	+	0.0812723i	−0.0127238	+	0.999919i	$0.504050\pi$
$228$	1.95573	−	2.63863i	0.129521	−	0.174747i
$229$	12.9894	+	5.78325i	0.858363	+	0.382168i	0.788238	−	0.615370i	$-0.210993\pi$
$229$	12.9894	+	5.78325i	0.858363	+	0.382168i	0.0701252	+	0.997538i	$0.477660\pi$
$230$	−13.0879	−	14.8628i	−0.862989	−	0.980025i
$231$	−0.702020	−	0.235513i	−0.0461895	−	0.0154956i
$232$	−0.765316	+	1.32557i	−0.0502454	+	0.0870277i
$233$	4.13877	+	3.00699i	0.271140	+	0.196995i	0.715044	−	0.699080i	$-0.246407\pi$
$233$	4.13877	+	3.00699i	0.271140	+	0.196995i	−0.443904	+	0.896074i	$0.646407\pi$
$234$	−9.12435	+	9.75353i	−0.596477	+	0.637608i
$235$	−15.9465	+	3.20566i	−1.04023	+	0.209114i
$236$	−2.47560	−	0.526205i	−0.161148	−	0.0342531i
$237$	−11.3787	+	6.42584i	−0.739128	+	0.417403i
$238$	2.62077	−	0.557061i	0.169879	−	0.0361089i
$239$	−3.73001	+	4.14260i	−0.241274	+	0.267962i	−0.851605	−	0.524185i	$-0.824370\pi$
$239$	−3.73001	+	4.14260i	−0.241274	+	0.267962i	0.610330	+	0.792147i	$0.291037\pi$
$240$	16.5708	+	5.76380i	1.06964	+	0.372052i
$241$	15.5919	+	17.3165i	1.00436	+	1.11545i	0.993306	+	0.115516i	$0.0368521\pi$
$241$	15.5919	+	17.3165i	1.00436	+	1.11545i	0.0110544	+	0.999939i	$0.496481\pi$
$242$	−12.6775	−	9.21072i	−0.814938	−	0.592087i
$243$	−13.8556	+	7.14294i	−0.888839	+	0.458220i
$244$	−0.698258	−	0.507314i	−0.0447014	−	0.0324775i
$245$	12.2877	−	8.72162i	0.785036	−	0.557204i
$246$	9.44376	+	21.7665i	0.602112	+	1.38778i
$247$	16.1222	+	7.17807i	1.02583	+	0.456729i
$248$	−1.52355	+	1.69207i	−0.0967456	+	0.107447i
$249$	−0.573777	−	0.526610i	−0.0363616	−	0.0333725i
$250$	1.21590	+	16.9654i	0.0769001	+	1.07299i
$251$	−22.9704			−1.44988			−0.724941	−	0.688811i	$-0.758133\pi$
$251$	−22.9704			−1.44988			−0.724941	+	0.688811i	$0.758133\pi$
$252$	−0.0595175	+	0.478442i	−0.00374925	+	0.0301390i
$253$	3.93951	−	2.86222i	0.247675	−	0.179946i
$254$	−2.42614	−	23.0832i	−0.152230	−	1.44837i
$255$	−13.2410	−	1.66782i	−0.829185	−	0.104443i
$256$	−0.770350	+	7.32939i	−0.0481469	+	0.458087i
$257$	0.0155867	+	0.0269970i	0.000972274	+	0.00168403i	0.866511	−	0.499158i	$-0.166357\pi$
$257$	0.0155867	+	0.0269970i	0.000972274	+	0.00168403i	−0.865539	+	0.500842i	$0.833024\pi$
$258$	5.33293	+	1.78909i	0.332014	+	0.111384i
$259$	2.90247	+	3.22352i	0.180351	+	0.200300i
$260$	0.237689	−	2.04380i	0.0147408	−	0.126751i
$261$	1.42841	+	1.07995i	0.0884162	+	0.0668470i
$262$	−4.33652	+	13.3464i	−0.267911	+	0.824545i
$263$	−15.6163	−	17.3437i	−0.962944	−	1.06946i	−0.997543	−	0.0700559i	$-0.977682\pi$
$263$	−15.6163	−	17.3437i	−0.962944	−	1.06946i	0.0345995	−	0.999401i	$-0.488984\pi$
$264$	−1.54331	+	3.37936i	−0.0949841	+	0.207985i
$265$	−13.0795	−	14.8533i	−0.803469	−	0.912433i
$266$	4.58662	−	0.974917i	0.281224	−	0.0597760i
$267$	−22.6688	+	20.0236i	−1.38731	+	1.22542i
$268$	0.240741	−	0.416976i	0.0147056	−	0.0254709i
$269$	13.1174	+	9.53037i	0.799784	+	0.581077i	0.910851	−	0.412736i	$-0.135427\pi$
$269$	13.1174	+	9.53037i	0.799784	+	0.581077i	−0.111067	+	0.993813i	$0.535427\pi$
$270$	7.82358	−	15.8506i	0.476128	−	0.964635i
$271$	8.23042	−	5.97975i	0.499962	−	0.363244i	−0.309040	−	0.951049i	$-0.600008\pi$
$271$	8.23042	−	5.97975i	0.499962	−	0.363244i	0.809003	+	0.587805i	$0.200008\pi$
$272$	−1.63165	−	15.5241i	−0.0989334	−	0.941289i
$273$	−2.57888	+	0.246250i	−0.156081	+	0.0149037i
$274$	−7.08663	−	12.2744i	−0.428119	−	0.741524i
$275$	−4.18124	−	0.0924847i	−0.252138	−	0.00557704i
$276$	−2.33590	−	2.14388i	−0.140605	−	0.129046i
$277$	−6.73241	−	1.43102i	−0.404511	−	0.0859815i	0.00116276	−	0.999999i	$-0.499630\pi$
$277$	−6.73241	−	1.43102i	−0.404511	−	0.0859815i	−0.405674	+	0.914018i	$0.632963\pi$
$278$	7.17427	−	5.21241i	0.430284	−	0.312620i
$279$	1.74440	+	2.01316i	0.104435	+	0.120525i
$280$	1.43716	+	2.55404i	0.0858865	+	0.152633i
$281$	−14.7368	+	6.56124i	−0.879122	+	0.391411i	−0.796120	−	0.605139i	$-0.793118\pi$
$281$	−14.7368	+	6.56124i	−0.879122	+	0.391411i	−0.0830025	+	0.996549i	$0.526451\pi$
$282$	−18.2850	+	5.74925i	−1.08885	+	0.342363i
$283$	−1.75231	+	16.6721i	−0.104164	+	0.991054i	0.810198	+	0.586156i	$0.199359\pi$
$283$	−1.75231	+	16.6721i	−0.104164	+	0.991054i	−0.914362	+	0.404898i	$0.867307\pi$
$284$	1.53911	−	0.327147i	0.0913291	−	0.0194126i
$285$	−23.1732	−	2.91887i	−1.37266	−	0.172899i
$286$	3.64253	+	0.774244i	0.215387	+	0.0457820i
$287$	−1.42215	+	4.37693i	−0.0839470	+	0.258362i
$288$	5.15166	+	1.19798i	0.303564	+	0.0705919i
$289$	−1.58409	−	4.87534i	−0.0931819	−	0.286785i
$290$	−2.03041	−	0.0224526i	−0.119230	−	0.00131846i
$291$	25.5268	−	14.4156i	1.49641	−	0.845058i
$292$	−0.361395	+	3.43845i	−0.0211491	+	0.201220i
$293$	−11.7345	−	20.3247i	−0.685536	−	1.18738i	−0.973268	−	0.229672i	$-0.926235\pi$
$293$	−11.7345	−	20.3247i	−0.685536	−	1.18738i	0.287732	−	0.957711i	$-0.407099\pi$
$294$	13.3084	−	11.7554i	0.776161	−	0.685591i
$295$	5.37210	+	17.1776i	0.312776	+	1.00012i
$296$	17.6066	−	12.7919i	1.02336	−	0.743516i
$297$	3.70043	+	2.27978i	0.214721	+	0.132286i
$298$	−0.882691	−	2.71664i	−0.0511329	−	0.157371i
$299$	8.51822	−	14.7540i	0.492621	−	0.853245i
$300$	0.481630	+	2.68018i	0.0278069	+	0.154741i
$301$	0.545530	+	0.944885i	0.0314438	+	0.0544623i
$302$	−2.08935	+	2.32045i	−0.120228	+	0.133527i
$303$	29.8326	+	3.42301i	1.71384	+	0.196647i
$304$	−2.85557	−	27.1689i	−0.163778	−	1.55824i
$305$	−0.709024	+	6.09664i	−0.0405986	+	0.349093i
$306$	−15.7239	−	0.299466i	−0.898874	−	0.0171194i
$307$	−8.91785			−0.508969			−0.254484	−	0.967077i	$-0.581906\pi$
$307$	−8.91785			−0.508969			−0.254484	+	0.967077i	$0.581906\pi$
$308$	0.122804	−	0.0546760i	0.00699742	−	0.00311545i
$309$	0.138219	−	14.5160i	0.00786298	−	0.825787i
$310$	−2.94742	−	0.660640i	−0.167402	−	0.0375218i
$311$	13.6761	−	15.1889i	0.775503	−	0.861283i	−0.217899	−	0.975971i	$-0.569920\pi$
$311$	13.6761	−	15.1889i	0.775503	−	0.861283i	0.993402	+	0.114688i	$0.0365869\pi$
$312$	−0.123755	+	12.9970i	−0.00700625	+	0.735811i
$313$	−15.4871	−	17.2002i	−0.875384	−	0.972212i	0.124416	−	0.992230i	$-0.460294\pi$
$313$	−15.4871	−	17.2002i	−0.875384	−	0.972212i	−0.999800	+	0.0200179i	$0.993628\pi$
$314$	−2.81444	−	8.66194i	−0.158828	−	0.488822i
$315$	3.17271	−	1.29963i	0.178762	−	0.0732257i
$316$	0.733093	−	2.25623i	0.0412397	−	0.126923i
$317$	9.78492	−	4.35653i	0.549576	−	0.244687i	−0.113112	−	0.993582i	$-0.536082\pi$
$317$	9.78492	−	4.35653i	0.549576	−	0.244687i	0.662688	+	0.748895i	$0.269415\pi$
$318$	−17.1825	−	15.7700i	−0.963548	−	0.884339i
$319$	0.0521890	−	0.496545i	0.00292202	−	0.0278012i
$320$	13.0917	−	5.65618i	0.731848	−	0.316190i
$321$	−8.49350	−	19.5762i	−0.474061	−	1.09264i
$322$	−0.473160	−	4.50182i	−0.0263682	−	0.250876i
$323$	6.42149	+	19.7633i	0.357301	+	1.09966i
$324$	0.976348	−	2.65619i	0.0542416	−	0.147566i
$325$	−13.4954	+	5.65434i	−0.748589	+	0.313647i
$326$	12.8658	−	22.2842i	0.712569	−	1.23421i
$327$	25.2998	−	2.41580i	1.39908	−	0.133594i
$328$	21.0938	+	9.39156i	1.16471	+	0.518562i
$329$	−3.39641	−	1.51218i	−0.187250	−	0.0833690i
$330$	−4.91100	+	0.414192i	−0.270342	+	0.0228005i
$331$	21.4732	−	9.56048i	1.18027	−	0.525491i	0.279654	−	0.960101i	$-0.409780\pi$
$331$	21.4732	−	9.56048i	1.18027	−	0.525491i	0.900619	+	0.434610i	$0.143114\pi$
$332$	0.141385			0.00775952
$333$	−12.3082	−	22.2881i	−0.674485	−	1.22138i
$334$	−10.0388	+	30.8963i	−0.549300	+	1.69057i
$335$	−3.42376	−	0.0378605i	−0.187060	−	0.00206854i
$336$	2.32614	+	3.26662i	0.126901	+	0.178209i
$337$	1.21798	−	0.258889i	0.0663475	−	0.0141026i	−0.174618	−	0.984636i	$-0.555869\pi$
$337$	1.21798	−	0.258889i	0.0663475	−	0.0141026i	0.240966	+	0.970534i	$0.422536\pi$
$338$	−6.60132	+	1.40315i	−0.359064	+	0.0763215i
$339$	−12.4890	−	17.5384i	−0.678311	−	0.952558i
$340$	1.97570	−	1.40232i	0.107147	−	0.0760513i
$341$	0.229510	−	0.706360i	0.0124287	−	0.0382515i
$342$	−27.5185	−	0.524098i	−1.48803	−	0.0283400i
$343$	7.02190			0.379147
$344$	5.00079	−	2.22650i	0.269625	−	0.120045i
$345$	−5.14063	+	21.9532i	−0.276762	+	1.18192i
$346$	−4.60882	−	2.05198i	−0.247772	−	0.110315i
$347$	−30.2288	−	13.4587i	−1.62276	−	0.722501i	−0.624479	−	0.781041i	$-0.714689\pi$
$347$	−30.2288	−	13.4587i	−1.62276	−	0.722501i	−0.998285	+	0.0585399i	$0.981355\pi$
$348$	−0.323615	+	0.0309010i	−0.0173476	+	0.00165647i
$349$	−7.71967	+	13.3709i	−0.413224	+	0.715726i	−0.995240	−	0.0974517i	$-0.968931\pi$
$349$	−7.71967	+	13.3709i	−0.413224	+	0.715726i	0.582016	+	0.813177i	$0.302264\pi$
$350$	−2.01786	+	3.32309i	−0.107859	+	0.177627i
$351$	15.0712	+	2.02074i	0.804442	+	0.107859i
$352$	−0.455707	−	1.40252i	−0.0242892	−	0.0747546i
$353$	−2.62236	−	24.9501i	−0.139574	−	1.32796i	−0.810195	−	0.586160i	$-0.800639\pi$
$353$	−2.62236	−	24.9501i	−0.139574	−	1.32796i	0.670621	−	0.741800i	$-0.266028\pi$
$354$	8.44169	+	19.4568i	0.448671	+	1.03412i
$355$	−7.39488	−	8.39776i	−0.392480	−	0.445707i
$356$	0.573953	−	5.46080i	0.0304195	−	0.289422i
$357$	−2.24738	−	2.06263i	−0.118944	−	0.109166i
$358$	−4.54092	+	2.02175i	−0.239995	+	0.106853i
$359$	0.624628	−	1.92241i	0.0329666	−	0.101461i	−0.933219	−	0.359307i	$-0.883013\pi$
$359$	0.624628	−	1.92241i	0.0329666	−	0.101461i	0.966186	+	0.257847i	$0.0830130\pi$
$360$	−4.82087	−	16.5124i	−0.254082	−	0.870282i
$361$	5.36697	+	16.5178i	0.282472	+	0.869360i
$362$	−6.39833	−	7.10607i	−0.336289	−	0.373487i
$363$	−0.169868	+	17.8399i	−0.00891577	+	0.936353i
$364$	0.314694	−	0.349503i	0.0164944	−	0.0183189i
$365$	22.5701	−	9.75127i	1.18137	−	0.510405i
$366$	−0.0688661	+	7.23247i	−0.00359969	+	0.378047i
$367$	32.0015	−	14.2480i	1.67046	−	0.743738i	0.670465	−	0.741941i	$-0.266095\pi$
$367$	32.0015	−	14.2480i	1.67046	−	0.743738i	0.999998	−	0.00179673i	$-0.000571917\pi$
$368$	−26.3720			−1.37473
$369$	13.9497	−	23.1328i	0.726192	−	1.20425i
$370$	26.2433	+	12.0337i	1.36432	+	0.625602i
$371$	−0.472858	−	4.49894i	−0.0245496	−	0.233574i
$372$	−0.480435	−	0.0551255i	−0.0249094	−	0.00285812i
$373$	9.18980	−	10.2063i	0.475830	−	0.528463i	−0.456668	−	0.889637i	$-0.650957\pi$
$373$	9.18980	−	10.2063i	0.475830	−	0.528463i	0.932498	+	0.361174i	$0.117624\pi$
$374$	2.19244	+	3.79742i	0.113368	+	0.196360i
$375$	14.9309	−	12.3316i	0.771027	−	0.636802i
$376$	−9.32653	+	16.1540i	−0.480979	+	0.833080i
$377$	−0.539785	−	1.66129i	−0.0278003	−	0.0855607i
$378$	3.55526	−	1.91938i	0.182863	−	0.0987224i
$379$	20.8462	−	15.1457i	1.07080	−	0.777980i	0.0947423	−	0.995502i	$-0.469797\pi$
$379$	20.8462	−	15.1457i	1.07080	−	0.777980i	0.976055	+	0.217522i	$0.0697973\pi$
$380$	3.45769	−	2.45420i	0.177376	−	0.125898i
$381$	−19.8053	+	17.4942i	−1.01465	+	0.896253i
$382$	8.43644	+	14.6123i	0.431646	+	0.747633i
$383$	−1.72911	+	16.4514i	−0.0883535	+	0.840627i	0.857161	+	0.515048i	$0.172226\pi$
$383$	−1.72911	+	16.4514i	−0.0883535	+	0.840627i	−0.945515	+	0.325579i	$0.894441\pi$
$384$	19.9515	−	11.2671i	1.01815	−	0.574971i
$385$	−0.767115	−	0.570408i	−0.0390958	−	0.0290707i
$386$	−4.23589	−	13.0367i	−0.215601	−	0.663552i
$387$	−1.86266	−	6.12730i	−0.0946843	−	0.311468i
$388$	−1.64461	+	5.06158i	−0.0834923	+	0.256963i
$389$	15.2360	+	3.23851i	0.772496	+	0.164199i	0.577264	−	0.816558i	$-0.304120\pi$
$389$	15.2360	+	3.23851i	0.772496	+	0.164199i	0.195233	+	0.980757i	$0.437454\pi$
$390$	−15.1068	+	8.31221i	−0.764963	+	0.420905i
$391$	19.6220	−	4.17078i	0.992325	−	0.210925i
$392$	1.80627	−	17.1855i	0.0912305	−	0.868000i
$393$	15.2414	−	4.79228i	0.768827	−	0.241738i
$394$	−37.7605	+	16.8120i	−1.90234	+	0.846978i
$395$	−16.5395	+	3.32488i	−0.832195	+	0.167293i
$396$	−0.774779	+	0.149324i	−0.0389341	+	0.00750381i
$397$	2.54039	−	1.84570i	0.127498	−	0.0926330i	−0.522208	−	0.852818i	$-0.674892\pi$
$397$	2.54039	−	1.84570i	0.127498	−	0.0926330i	0.649707	+	0.760185i	$0.274892\pi$
$398$	23.3250	+	4.95788i	1.16918	+	0.248516i
$399$	−3.93315	−	3.60983i	−0.196904	−	0.180717i
$400$	18.0254	+	13.7153i	0.901268	+	0.685766i
$401$	1.03308	+	1.78934i	0.0515894	+	0.0893554i	0.890667	−	0.454656i	$-0.150238\pi$
$401$	1.03308	+	1.78934i	0.0515894	+	0.0893554i	−0.839077	+	0.544012i	$0.816905\pi$
$402$	−4.01659	+	0.383532i	−0.200330	+	0.0191288i
$403$	−0.271612	−	2.58421i	−0.0135299	−	0.128729i
$404$	−4.41025	+	3.20423i	−0.219418	+	0.159417i
$405$	−19.8666	+	3.21209i	−0.987180	+	0.159610i
$406$	−0.375483	−	0.272805i	−0.0186349	−	0.0135391i
$407$	−3.54945	+	6.14782i	−0.175940	+	0.304736i
$408$	−11.4705	+	10.1320i	−0.567876	+	0.501610i
$409$	29.6718	−	6.30694i	1.46718	−	0.311858i	0.596063	−	0.802938i	$-0.296731\pi$
$409$	29.6718	−	6.30694i	1.46718	−	0.311858i	0.871115	+	0.491080i	$0.163398\pi$
$410$	2.86479	+	30.4970i	0.141482	+	1.50614i
$411$	−6.70334	+	14.6782i	−0.330651	+	0.724023i
$412$	1.76341	+	1.95846i	0.0868768	+	0.0964865i
$413$	−1.27125	+	3.91250i	−0.0625540	+	0.192521i
$414$	−3.27996	+	26.3665i	−0.161201	+	1.29584i
$415$	−0.493058	−	0.876236i	−0.0242033	−	0.0430128i
$416$	−3.45230	−	3.83416i	−0.169263	−	0.187985i
$417$	−9.57192	−	3.21118i	−0.468739	−	0.157252i
$418$	3.83701	+	6.64589i	0.187674	+	0.325061i
$419$	−2.48466	+	23.6399i	−0.121384	+	1.15489i	0.749020	+	0.662548i	$0.230525\pi$
$419$	−2.48466	+	23.6399i	−0.121384	+	1.15489i	−0.870403	+	0.492339i	$0.836142\pi$
$420$	−0.264811	+	0.563285i	−0.0129214	+	0.0274855i
$421$	−1.13469	−	10.7958i	−0.0553013	−	0.526157i	−0.986746	−	0.162274i	$-0.948117\pi$
$421$	−1.13469	−	10.7958i	−0.0553013	−	0.526157i	0.931444	−	0.363884i	$-0.118549\pi$
$422$	−20.6226	+	14.9832i	−1.00389	+	0.729371i
$423$	17.4073	+	13.1608i	0.846372	+	0.639899i
$424$	−22.6964			−1.10223
$425$	−15.5808	−	7.35408i	−0.755780	−	0.356725i
$426$	−9.71463	−	8.91604i	−0.470676	−	0.431983i
$427$	−0.938730	+	1.04257i	−0.0454283	+	0.0504533i
$428$	3.53905	+	1.57569i	0.171066	+	0.0761637i
$429$	−1.68749	−	3.88942i	−0.0814729	−	0.187783i
$430$	5.82743	+	4.33313i	0.281024	+	0.208962i
$431$	−6.07997	−	4.41736i	−0.292862	−	0.212777i	0.431646	−	0.902043i	$-0.357933\pi$
$431$	−6.07997	−	4.41736i	−0.292862	−	0.212777i	−0.724508	+	0.689266i	$0.757933\pi$
$432$	−8.95595	−	21.7682i	−0.430893	−	1.04733i
$433$	−3.91359	−	2.84339i	−0.188075	−	0.136644i	0.489763	−	0.871855i	$-0.337083\pi$
$433$	−3.91359	−	2.84339i	−0.188075	−	0.136644i	−0.677838	+	0.735211i	$0.737083\pi$
$434$	−0.461976	−	0.513076i	−0.0221755	−	0.0246284i
$435$	1.32006	+	1.89785i	0.0632922	+	0.0909947i
$436$	−3.08726	+	3.42875i	−0.147853	+	0.164207i
$437$	34.3405	−	7.29931i	1.64273	−	0.349173i
$438$	25.2283	−	14.2470i	1.20545	−	0.680749i
$439$	−31.2320	−	6.63857i	−1.49062	−	0.316841i	−0.610663	−	0.791891i	$-0.709097\pi$
$439$	−31.2320	−	6.63857i	−1.49062	−	0.316841i	−0.879959	+	0.475049i	$0.842430\pi$
$440$	−3.24847	+	3.52854i	−0.154865	+	0.168216i
$441$	−19.6909	−	4.57899i	−0.937663	−	0.218047i
$442$	12.4111	+	9.01718i	0.590335	+	0.428904i
$443$	4.66178	−	8.07443i	0.221488	−	0.383628i	−0.733772	−	0.679396i	$-0.762242\pi$
$443$	4.66178	−	8.07443i	0.221488	−	0.383628i	0.955260	+	0.295768i	$0.0955754\pi$
$444$	4.38215	+	1.47012i	0.207967	+	0.0697688i
$445$	−35.8449	+	15.4866i	−1.69921	+	0.734134i
$446$	−14.2546	−	6.34655i	−0.674975	−	0.300518i
$447$	−1.93650	+	2.61268i	−0.0915933	+	0.123576i
$448$	3.18849	+	0.677735i	0.150642	+	0.0320200i
$449$	−25.4208			−1.19968			−0.599840	−	0.800120i	$-0.704769\pi$
$449$	−25.4208			−1.19968			−0.599840	+	0.800120i	$0.704769\pi$
$450$	15.9544	−	16.3159i	0.752096	−	0.769137i
$451$	−7.53178			−0.354658
$452$	3.82330	+	0.812667i	0.179833	+	0.0382247i
$453$	3.53181	+	0.405243i	0.165939	+	0.0190400i
$454$	8.18521	+	3.64429i	0.384151	+	0.171035i
$455$	−3.26350	−	0.731485i	−0.152995	−	0.0342925i
$456$	−20.0747	+	17.7321i	−0.940082	+	0.830384i
$457$	15.2755	−	26.4579i	0.714557	−	1.23765i	−0.248573	−	0.968613i	$-0.579962\pi$
$457$	15.2755	−	26.4579i	0.714557	−	1.23765i	0.963130	−	0.269036i	$-0.0867050\pi$
$458$	17.5000	+	12.7145i	0.817724	+	0.594111i
$459$	10.1063	+	14.7802i	0.471723	+	0.689880i
$460$	−2.00728	−	3.56724i	−0.0935901	−	0.166323i
$461$	14.2840	+	3.03616i	0.665272	+	0.141408i	0.528156	−	0.849147i	$-0.322884\pi$
$461$	14.2840	+	3.03616i	0.665272	+	0.141408i	0.137116	+	0.990555i	$0.456217\pi$
$462$	−0.970171	−	0.572513i	−0.0451364	−	0.0266357i
$463$	−10.6503	+	2.26379i	−0.494962	+	0.105207i	−0.448628	−	0.893719i	$-0.648087\pi$
$463$	−10.6503	+	2.26379i	−0.494962	+	0.105207i	−0.0463337	+	0.998926i	$0.514754\pi$
$464$	−1.80931	+	2.00944i	−0.0839951	+	0.0932860i
$465$	1.33380	+	3.16974i	0.0618534	+	0.146993i
$466$	5.20772	+	5.78375i	0.241243	+	0.267927i
$467$	0.134914	+	0.0980206i	0.00624307	+	0.00453585i	0.590902	−	0.806743i	$-0.298772\pi$
$467$	0.134914	+	0.0980206i	0.00624307	+	0.00453585i	−0.584659	+	0.811279i	$0.698772\pi$
$468$	−2.26381	+	1.57978i	−0.104644	+	0.0730252i
$469$	−0.633155	−	0.460014i	−0.0292364	−	0.0212415i
$470$	−24.7437	−	0.273619i	−1.14134	−	0.0126211i
$471$	−6.17448	+	8.33048i	−0.284505	+	0.383848i
$472$	18.8555	+	8.39502i	0.867896	+	0.386412i
$473$	−1.19479	+	1.32695i	−0.0549367	+	0.0610134i
$474$	−18.9650	+	5.96307i	−0.871091	+	0.273893i
$475$	−27.2681	−	12.8704i	−1.25115	−	0.590536i
$476$	0.553779			0.0253824
$477$	−3.27787	+	26.3497i	−0.150083	+	1.20647i
$478$	−6.86088	+	4.98472i	−0.313809	+	0.227996i
$479$	3.05781	+	29.0931i	0.139715	+	1.32930i	0.809665	+	0.586892i	$0.199649\pi$
$479$	3.05781	+	29.0931i	0.139715	+	1.32930i	−0.669950	+	0.742406i	$0.733684\pi$
$480$	5.84191	+	3.53507i	0.266645	+	0.161353i
$481$	−2.59609	+	24.7001i	−0.118371	+	1.12623i
$482$	17.7247	+	30.7001i	0.807340	+	1.39835i
$483$	−3.86254	+	3.41181i	−0.175751	+	0.155243i
$484$	−2.16720	−	2.40692i	−0.0985089	−	0.109405i
$485$	37.1045	−	7.45897i	1.68483	−	0.338694i
$486$	−22.8777	+	6.24672i	−1.03775	+	0.283357i
$487$	10.0050	−	30.7921i	0.453369	−	1.39532i	−0.419671	−	0.907676i	$-0.637855\pi$
$487$	10.0050	−	30.7921i	0.453369	−	1.39532i	0.873040	−	0.487649i	$-0.162145\pi$
$488$	4.70979	+	5.23075i	0.213202	+	0.236785i
$489$	−29.1630	+	2.78469i	−1.31880	+	0.125928i
$490$	21.0439	−	9.09186i	0.950665	−	0.410728i
$491$	−3.26774	+	0.694580i	−0.147471	+	0.0313459i	−0.281056	−	0.959691i	$-0.590685\pi$
$491$	−3.26774	+	0.694580i	−0.147471	+	0.0313459i	0.133585	+	0.991037i	$0.457351\pi$
$492$	0.973886	+	4.80635i	0.0439062	+	0.216687i
$493$	1.02841	−	1.78126i	0.0463174	−	0.0802241i
$494$	21.7207	+	15.7810i	0.977262	+	0.710023i
$495$	3.62735	+	4.28096i	0.163037	+	0.192415i
$496$	−3.25413	+	2.36426i	−0.146115	+	0.106159i
$497$	−0.267344	−	2.54361i	−0.0119920	−	0.114096i
$498$	−0.687261	−	0.965125i	−0.0307969	−	0.0432483i
$499$	−13.0016	−	22.5194i	−0.582030	−	1.00811i	−0.995239	−	0.0974695i	$-0.968925\pi$
$499$	−13.0016	−	22.5194i	−0.582030	−	1.00811i	0.413208	−	0.910637i	$-0.364408\pi$
$500$	−0.483231	+	3.48216i	−0.0216108	+	0.155727i
$501$	35.2831	−	11.0939i	1.57633	−	0.495639i
$502$	−34.1819	−	7.26559i	−1.52561	−	0.324279i
$503$	−11.9885	+	8.71019i	−0.534543	+	0.388368i	−0.822054	−	0.569409i	$-0.807172\pi$
$503$	−11.9885	+	8.71019i	−0.534543	+	0.388368i	0.287512	+	0.957777i	$0.407172\pi$
$504$	1.28599	−	3.71559i	0.0572825	−	0.165505i
$505$	35.2383	+	16.1583i	1.56808	+	0.719037i
$506$	6.76764	−	3.01315i	0.300859	−	0.133951i
$507$	5.66081	+	5.19546i	0.251405	+	0.230738i
$508$	0.501451	−	4.77099i	0.0222483	−	0.211678i
$509$	37.7857	−	8.03160i	1.67482	−	0.355994i	0.729966	−	0.683483i	$-0.239536\pi$
$509$	37.7857	−	8.03160i	1.67482	−	0.355994i	0.944855	+	0.327489i	$0.106202\pi$
$510$	−19.1762	−	6.67002i	−0.849137	−	0.295354i
$511$	5.49697	+	1.16842i	0.243172	+	0.0516878i
$512$	4.71125	−	14.4997i	0.208210	−	0.640804i
$513$	17.6872	+	25.8669i	0.780907	+	1.14205i
$514$	0.0146551	+	0.0451039i	0.000646411	+	0.00198945i
$515$	5.98800	−	17.7586i	0.263863	−	0.782536i
$516$	1.00128	+	0.590870i	0.0440788	+	0.0260116i
$517$	0.636001	−	6.05115i	0.0279713	−	0.266129i
$518$	3.29951	+	5.71492i	0.144972	+	0.251099i
$519$	1.14065	+	5.62938i	0.0500690	+	0.247102i
$520$	−5.36140	+	15.9003i	−0.235113	+	0.697272i
$521$	−7.88351	+	5.72771i	−0.345383	+	0.250935i	−0.746929	−	0.664903i	$-0.768473\pi$
$521$	−7.88351	+	5.72771i	−0.345383	+	0.250935i	0.401547	+	0.915839i	$0.368473\pi$
$522$	1.78400	+	2.05886i	0.0780835	+	0.0901138i
$523$	9.64807	+	29.6937i	0.421881	+	1.29842i	0.905950	+	0.423386i	$0.139158\pi$
$523$	9.64807	+	29.6937i	0.421881	+	1.29842i	−0.484069	+	0.875030i	$0.660842\pi$
$524$	−1.45025	+	2.51190i	−0.0633543	+	0.109733i
$525$	4.41445	−	0.323196i	0.192662	−	0.0141054i
$526$	−17.7525	−	30.7483i	−0.774048	−	1.34069i
$527$	2.04731	−	2.27377i	0.0891823	−	0.0990469i
$528$	−3.90800	+	5.27258i	−0.170074	+	0.229460i
$529$	−1.13844	−	10.8316i	−0.0494975	−	0.470937i
$530$	−14.7653	−	26.2401i	−0.641363	−	1.13980i
$531$	12.4695	−	20.6782i	0.541130	−	0.897356i
$532$	0.969173			0.0420190
$533$	−24.0726	+	10.7178i	−1.04270	+	0.464239i
$534$	−40.0665	+	22.6265i	−1.73385	+	0.979146i
$535$	−2.57653	−	27.4283i	−0.111393	−	1.18583i
$536$	−2.62739	+	2.91801i	−0.113486	+	0.126039i
$537$	4.87381	+	2.87612i	0.210321	+	0.124114i
$538$	16.5054	+	18.3311i	0.711596	+	0.790308i
$539$	1.74182	+	5.36078i	0.0750257	+	0.230905i
$540$	2.26284	−	2.86831i	0.0973769	−	0.123433i
$541$	−3.37778	+	10.3957i	−0.145222	+	0.446948i	−0.997039	−	0.0768912i	$-0.975501\pi$
$541$	−3.37778	+	10.3957i	−0.145222	+	0.446948i	0.851817	+	0.523839i	$0.175501\pi$
$542$	14.1390	−	6.29507i	0.607320	−	0.270396i
$543$	−2.36475	+	10.6267i	−0.101481	+	0.456035i
$544$	0.635025	−	6.04186i	0.0272265	−	0.259043i
$545$	32.0160	+	7.17613i	1.37142	+	0.307391i
$546$	−3.91548	−	0.449266i	−0.167567	−	0.0192268i
$547$	−1.60294	−	15.2510i	−0.0685367	−	0.652084i	−0.973827	−	0.227290i	$-0.927013\pi$
$547$	−1.60294	−	15.2510i	−0.0685367	−	0.652084i	0.905290	−	0.424793i	$-0.139653\pi$
$548$	−0.905242	−	2.78605i	−0.0386700	−	0.119014i
$549$	6.75291	−	4.71246i	0.288207	−	0.201123i
$550$	−6.19277	−	1.46016i	−0.264061	−	0.0622613i
$551$	1.79983	−	3.11740i	0.0766755	−	0.132806i
$552$	14.9983	+	21.0622i	0.638369	+	0.896467i
$553$	−3.52272	−	1.56842i	−0.149801	−	0.0666958i
$554$	−9.56575	−	4.25895i	−0.406410	−	0.180945i
$555$	−6.17094	−	32.2852i	−0.261942	−	1.37043i
$556$	1.67442	−	0.745498i	0.0710110	−	0.0316161i
$557$	22.3912			0.948745			0.474373	−	0.880324i	$-0.342675\pi$
$557$	22.3912			0.948745			0.474373	+	0.880324i	$0.342675\pi$
$558$	1.95905	+	3.54751i	0.0829333	+	0.150178i
$559$	−1.93045	+	5.94132i	−0.0816494	+	0.251291i
$560$	1.54528	+	4.94115i	0.0653002	+	0.208802i
$561$	2.07386	−	4.54110i	0.0875585	−	0.191725i
$562$	−24.0049	+	5.10240i	−1.01258	+	0.215232i
$563$	−13.1274	+	2.79031i	−0.553253	+	0.117598i	−0.476051	−	0.879418i	$-0.657932\pi$
$563$	−13.1274	+	2.79031i	−0.553253	+	0.117598i	−0.0772026	+	0.997015i	$0.524599\pi$
$564$	−3.94373	+	0.376575i	−0.166061	+	0.0158567i
$565$	−8.29662	−	26.5290i	−0.349041	−	1.11608i
$566$	−7.88100	+	24.2552i	−0.331263	+	1.01952i
$567$	−4.12794	−	2.02960i	−0.173357	−	0.0852353i
$568$	−12.8321			−0.538421
$569$	−10.6775	+	4.75393i	−0.447624	+	0.199295i	−0.618153	−	0.786057i	$-0.712119\pi$
$569$	−10.6775	+	4.75393i	−0.447624	+	0.199295i	0.170529	+	0.985353i	$0.445452\pi$
$570$	−33.5604	−	11.6733i	−1.40569	−	0.488939i
$571$	−35.4134	−	15.7671i	−1.48201	−	0.659831i	−0.503116	−	0.864219i	$-0.667813\pi$
$571$	−35.4134	−	15.7671i	−1.48201	−	0.659831i	−0.978890	+	0.204388i	$0.934480\pi$
$572$	0.703140	+	0.313058i	0.0293998	+	0.0130896i
$573$	7.98015	−	17.4740i	0.333375	−	0.729987i
$574$	−3.50071	+	6.06341i	−0.146117	+	0.253082i
$575$	−15.1079	+	24.8803i	−0.630044	+	1.03758i
$576$	−17.3280	−	8.11374i	−0.722000	−	0.338073i
$577$	−10.4483	−	32.1567i	−0.434970	−	1.33870i	−0.893118	−	0.449823i	$-0.851487\pi$
$577$	−10.4483	−	32.1567i	−0.434970	−	1.33870i	0.458148	−	0.888876i	$-0.348513\pi$
$578$	−0.815184	−	7.75596i	−0.0339072	−	0.322605i
$579$	−9.29296	+	12.5379i	−0.386202	+	0.521055i
$580$	−0.409524	−	0.0917914i	−0.0170046	−	0.00381143i
$581$	0.0240220	−	0.228554i	0.000996602	−	0.00948203i
$582$	42.5457	−	13.3774i	1.76358	−	0.554513i
$583$	6.76333	−	3.01123i	0.280108	−	0.124712i
$584$	8.71289	−	26.8155i	0.360542	−	1.10963i
$585$	17.6853	+	8.52075i	0.731199	+	0.352290i
$586$	−11.0331	−	33.9565i	−0.455775	−	1.40273i
$587$	9.89923	+	10.9942i	0.408585	+	0.453780i	0.911954	−	0.410292i	$-0.134573\pi$
$587$	9.89923	+	10.9942i	0.408585	+	0.453780i	−0.503369	+	0.864071i	$0.667906\pi$
$588$	3.19572	−	1.80470i	0.131789	−	0.0744246i
$589$	3.58301	−	3.97934i	0.147636	−	0.163966i
$590$	2.56081	+	27.2610i	0.105427	+	1.12232i
$591$	40.5286	+	23.9166i	1.66712	+	0.983797i
$592$	35.1220	−	15.6373i	1.44350	−	0.642689i
$593$	2.30607			0.0946989			0.0473495	−	0.998878i	$-0.484923\pi$
$593$	2.30607			0.0946989			0.0473495	+	0.998878i	$0.484923\pi$
$594$	4.78545	+	4.56296i	0.196349	+	0.187220i
$595$	−1.93122	−	3.43205i	−0.0791721	−	0.140701i
$596$	−0.0617125	−	0.587155i	−0.00252784	−	0.0240508i
$597$	−10.8059	−	24.9059i	−0.442255	−	1.01933i
$598$	17.3425	−	19.2608i	0.709189	−	0.787634i
$599$	−4.41108	−	7.64022i	−0.180232	−	0.312171i	0.761727	−	0.647898i	$-0.224352\pi$
$599$	−4.41108	−	7.64022i	−0.180232	−	0.312171i	−0.941959	+	0.335727i	$0.891018\pi$
$600$	0.702456	−	22.1963i	0.0286777	−	0.906160i
$601$	−15.5663	+	26.9616i	−0.634961	+	1.09978i	0.351562	+	0.936165i	$0.385651\pi$
$601$	−15.5663	+	26.9616i	−0.634961	+	1.09978i	−0.986523	+	0.163620i	$0.947683\pi$
$602$	0.512925	+	1.57862i	0.0209052	+	0.0643397i
$603$	3.00825	+	3.47173i	0.122505	+	0.141380i
$604$	−0.522119	+	0.379342i	−0.0212447	+	0.0154352i
$605$	−7.35914	+	21.8250i	−0.299192	+	0.887311i
$606$	43.3106	+	14.5298i	1.75937	+	0.590234i
$607$	−3.13347	−	5.42734i	−0.127184	−	0.220289i	0.795401	−	0.606084i	$-0.207260\pi$
$607$	−3.13347	−	5.42734i	−0.127184	−	0.220289i	−0.922584	+	0.385795i	$0.873927\pi$
$608$	1.11136	−	10.5739i	0.0450717	−	0.428828i
$609$	−0.00503119	+	0.528386i	−0.000203874	+	0.0214113i
$610$	−2.98347	+	8.84804i	−0.120797	+	0.358247i
$611$	−6.57809	−	20.2453i	−0.266121	−	0.819037i
$612$	−3.16603	−	0.736239i	−0.127979	−	0.0297607i
$613$	−8.53626	+	26.2719i	−0.344776	+	1.06111i	0.616927	+	0.787020i	$0.288377\pi$
$613$	−8.53626	+	26.2719i	−0.344776	+	1.06111i	−0.961704	+	0.274092i	$0.911623\pi$
$614$	−13.2705	−	2.82073i	−0.535554	−	0.113835i
$615$	26.3912	−	22.7971i	1.06419	−	0.919266i
$616$	−1.07231	+	0.227926i	−0.0432045	+	0.00918341i
$617$	−0.346515	+	3.29687i	−0.0139501	+	0.132727i	−0.999280	−	0.0379321i	$-0.987923\pi$
$617$	−0.346515	+	3.29687i	−0.0139501	+	0.132727i	0.985330	+	0.170659i	$0.0545896\pi$
$618$	4.79712	−	21.5573i	0.192968	−	0.867162i
$619$	−23.7757	+	10.5856i	−0.955626	+	0.425472i	−0.824480	−	0.565891i	$-0.808532\pi$
$619$	−23.7757	+	10.5856i	−0.955626	+	0.425472i	−0.131146	+	0.991363i	$0.541866\pi$
$620$	−0.567491	−	0.260220i	−0.0227910	−	0.0104507i
$621$	26.6186	−	14.3706i	1.06817	−	0.576673i
$622$	25.1555	−	18.2766i	1.00864	−	0.732823i
$623$	−8.73007	−	1.85563i	−0.349763	−	0.0743444i
$624$	−4.98753	+	22.4130i	−0.199661	+	0.897237i
$625$	23.2659	−	9.14863i	0.930636	−	0.365945i
$626$	−17.6057	−	30.4939i	−0.703664	−	1.21878i
$627$	3.62948	−	7.94742i	0.144947	−	0.317389i
$628$	−0.196769	−	1.87213i	−0.00785193	−	0.0747061i
$629$	−23.6593	+	17.1895i	−0.943358	+	0.685390i
$630$	5.13233	−	0.930421i	0.204477	−	0.0370689i
$631$	−17.6953	−	12.8564i	−0.704439	−	0.511805i	0.176936	−	0.984222i	$-0.443381\pi$
$631$	−17.6953	−	12.8564i	−0.704439	−	0.511805i	−0.881375	+	0.472417i	$0.843381\pi$
$632$	−9.67339	+	16.7548i	−0.384787	+	0.666470i
$633$	27.5147	+	9.23062i	1.09361	+	0.366884i
$634$	15.9388	−	3.38789i	0.633009	−	0.134550i
$635$	−31.3170	+	13.5303i	−1.24278	+	0.536934i
$636$	−2.79612	−	3.92661i	−0.110873	−	0.155700i
$637$	13.1955	+	14.6551i	0.522826	+	0.580657i
$638$	0.234720	−	0.722393i	0.00929264	−	0.0285998i
$639$	−1.85324	+	14.8976i	−0.0733129	+	0.589339i
$640$	29.0005	−	5.82985i	1.14635	−	0.230445i
$641$	−21.3213	−	23.6797i	−0.842142	−	0.935294i	0.156485	−	0.987680i	$-0.449984\pi$
$641$	−21.3213	−	23.6797i	−0.842142	−	0.935294i	−0.998627	+	0.0523866i	$0.983317\pi$
$642$	−6.44703	−	31.8176i	−0.254444	−	1.25574i
$643$	6.74775	+	11.6875i	0.266105	+	0.460908i	0.967853	−	0.251518i	$-0.0809297\pi$
$643$	6.74775	+	11.6875i	0.266105	+	0.460908i	−0.701747	+	0.712426i	$0.747596\pi$
$644$	0.0977959	−	0.930466i	0.00385370	−	0.0366655i
$645$	0.170132	−	8.26599i	0.00669892	−	0.325473i
$646$	3.30454	+	31.4406i	0.130015	+	1.23701i
$647$	−20.1643	+	14.6502i	−0.792741	+	0.575960i	−0.908776	−	0.417285i	$-0.862982\pi$
$647$	−20.1643	+	14.6502i	−0.792741	+	0.575960i	0.116035	+	0.993245i	$0.462982\pi$
$648$	−12.2920	+	19.5328i	−0.482874	+	0.767321i
$649$	−6.73259			−0.264277
$650$	−21.8707	+	4.14552i	−0.857841	+	0.162601i
$651$	−0.170741	+	0.767275i	−0.00669186	+	0.0300719i
$652$	3.55868	−	3.95232i	0.139369	−	0.154785i
$653$	26.1658	+	11.6498i	1.02395	+	0.455891i	0.848835	−	0.528657i	$-0.177304\pi$
$653$	26.1658	+	11.6498i	1.02395	+	0.455891i	0.175113	+	0.984548i	$0.443971\pi$
$654$	38.4123	+	4.40746i	1.50204	+	0.172345i
$655$	20.6250	+	0.228074i	0.805886	+	0.00891160i
$656$	32.9999	+	23.9759i	1.28843	+	0.936100i
$657$	−29.8735	−	13.9881i	−1.16548	−	0.545729i
$658$	−4.57583	−	3.32454i	−0.178384	−	0.129604i
$659$	5.81444	+	6.45759i	0.226498	+	0.251552i	0.845673	−	0.533701i	$-0.179199\pi$
$659$	5.81444	+	6.45759i	0.226498	+	0.251552i	−0.619175	+	0.785253i	$0.712533\pi$
$660$	−1.01066	−	0.127301i	−0.0393398	−	0.00495519i
$661$	−20.5678	+	22.8429i	−0.799996	+	0.888486i	−0.995743	−	0.0921684i	$-0.970620\pi$
$661$	−20.5678	+	22.8429i	−0.799996	+	0.888486i	0.195747	+	0.980654i	$0.437287\pi$
$662$	34.9779	−	7.43478i	1.35945	−	0.288961i
$663$	0.166299	−	17.4651i	0.00645852	−	0.678287i
$664$	−1.12782	−	0.239726i	−0.0437679	−	0.00930316i
$665$	−3.37984	−	6.00646i	−0.131064	−	0.232921i
$666$	−11.2659	−	37.0596i	−0.436543	−	1.43603i
$667$	−2.81128	−	2.04252i	−0.108853	−	0.0790866i
$668$	−3.35725	+	5.81492i	−0.129896	+	0.224986i
$669$	3.52791	+	17.4111i	0.136397	+	0.673151i
$670$	−5.08287	−	1.13928i	−0.196368	−	0.0440143i
$671$	−2.09746	−	0.933850i	−0.0809716	−	0.0360509i
$672$	0.621204	+	1.43178i	0.0239635	+	0.0552322i
$673$	24.2630	+	5.15726i	0.935271	+	0.198798i	0.650247	−	0.759723i	$-0.274665\pi$
$673$	24.2630	+	5.15726i	0.935271	+	0.198798i	0.285023	+	0.958521i	$0.407999\pi$
$674$	1.89434			0.0729673
$675$	−25.6677	−	4.02117i	−0.987950	−	0.154775i
$676$	−1.39489			−0.0536495
$677$	7.10383	+	1.50996i	0.273022	+	0.0580327i	0.342388	−	0.939559i	$-0.388764\pi$
$677$	7.10383	+	1.50996i	0.273022	+	0.0580327i	−0.0693658	+	0.997591i	$0.522098\pi$
$678$	−13.0373	−	30.0490i	−0.500693	−	1.15402i
$679$	7.90281	+	3.51856i	0.303282	+	0.135030i
$680$	−18.1377	+	7.83629i	−0.695551	+	0.300508i
$681$	−2.02578	−	9.99770i	−0.0776281	−	0.383113i
$682$	0.564953	−	0.978527i	0.0216332	−	0.0374697i
$683$	−38.6994	−	28.1168i	−1.48079	−	1.07586i	−0.977301	−	0.211857i	$-0.932049\pi$
$683$	−38.6994	−	28.1168i	−1.48079	−	1.07586i	−0.503491	−	0.864001i	$-0.667951\pi$
$684$	−5.54089	−	1.28850i	−0.211861	−	0.0492669i
$685$	−14.1097	+	15.3262i	−0.539104	+	0.585582i
$686$	10.4492	+	2.22104i	0.398951	+	0.0847998i
$687$	0.234487	−	24.6263i	0.00894624	−	0.939553i
$688$	9.45898	−	2.01057i	0.360620	−	0.0766522i
$689$	17.3315	−	19.2485i	0.660276	−	0.733311i
$690$	−14.5935	+	31.0422i	−0.555565	+	1.18176i
$691$	−26.9874	−	29.9725i	−1.02665	−	1.14021i	−0.990027	−	0.140880i	$-0.955007\pi$
$691$	−26.9874	−	29.9725i	−1.02665	−	1.14021i	−0.0366223	−	0.999329i	$-0.511660\pi$
$692$	−0.843588	−	0.612902i	−0.0320684	−	0.0232991i
$693$	0.109749	+	1.27783i	0.00416902	+	0.0485408i
$694$	−40.7259	−	29.5891i	−1.54593	−	1.12319i
$695$	−10.4595	−	7.77741i	−0.396751	−	0.295014i
$696$	2.63385	+	0.302210i	0.0998359	+	0.0114553i
$697$	−28.3453	−	12.6201i	−1.07366	−	0.478022i
$698$	−15.7167	+	17.4552i	−0.594887	+	0.660689i
$699$	1.92471	−	8.64926i	0.0727992	−	0.327145i
$700$	−0.550753	+	0.585117i	−0.0208165	+	0.0221154i
$701$	−6.65878			−0.251498			−0.125749	−	0.992062i	$-0.540133\pi$
$701$	−6.65878			−0.251498			−0.125749	+	0.992062i	$0.540133\pi$
$702$	21.7880	+	7.77407i	0.822337	+	0.293413i
$703$	−41.4063	+	30.0834i	−1.56167	+	1.13462i
$704$	0.557635	+	5.30554i	0.0210167	+	0.199960i
$705$	16.0870	+	23.1281i	0.605870	+	0.871055i
$706$	3.98947	−	37.9573i	0.150146	−	1.42854i
$707$	4.43044	+	7.67375i	0.166624	+	0.288601i
$708$	0.870547	+	4.29635i	0.0327172	+	0.161467i
$709$	15.0114	+	16.6718i	0.563763	+	0.626123i	0.955867	−	0.293798i	$-0.0949194\pi$
$709$	15.0114	+	16.6718i	0.563763	+	0.626123i	−0.392104	+	0.919921i	$0.628253\pi$
$710$	−8.34797	−	14.8356i	−0.313294	−	0.556769i
$711$	18.0547	+	13.6502i	0.677104	+	0.511924i
$712$	−13.8375	+	42.5873i	−0.518581	+	1.59603i
$713$	−3.45886	−	3.84145i	−0.129535	−	0.143864i
$714$	−2.69187	−	3.78022i	−0.100741	−	0.141471i
$715$	−0.511905	−	5.44946i	−0.0191442	−	0.203798i
$716$	−1.00492	+	0.213602i	−0.0375556	+	0.00798269i
$717$	9.15378	+	3.07091i	0.341854	+	0.114685i
$718$	1.53756	−	2.66313i	0.0573812	−	0.0993871i
$719$	1.49516	+	1.08630i	0.0557602	+	0.0405122i	0.615316	−	0.788280i	$-0.289028\pi$
$719$	1.49516	+	1.08630i	0.0557602	+	0.0405122i	−0.559556	+	0.828793i	$0.689028\pi$
$720$	−2.26543	−	30.3036i	−0.0844278	−	1.12935i
$721$	3.46554	−	2.51786i	0.129063	−	0.0937700i
$722$	2.76188	+	26.2775i	0.102786	+	0.977947i
$723$	16.7661	−	36.7124i	0.623537	−	1.36535i
$724$	−0.988185	−	1.71159i	−0.0367256	−	0.0636106i
$725$	0.859271	+	2.85814i	0.0319125	+	0.106149i
$726$	−5.89558	+	26.4936i	−0.218805	+	0.983268i
$727$	2.49549	+	0.530433i	0.0925527	+	0.0196727i	0.253955	−	0.967216i	$-0.418268\pi$
$727$	2.49549	+	0.530433i	0.0925527	+	0.0196727i	−0.161403	+	0.986889i	$0.551602\pi$
$728$	−3.10290	+	2.25439i	−0.115001	+	0.0835531i
$729$	20.9017	+	17.0915i	0.774136	+	0.633020i
$730$	36.6706	−	7.37173i	1.35724	−	0.272840i
$731$	−6.71995	+	2.99191i	−0.248546	+	0.110660i
$732$	−0.324721	+	1.45923i	−0.0120020	+	0.0539347i
$733$	1.19718	−	11.3904i	0.0442187	−	0.420713i	−0.949911	−	0.312520i	$-0.898827\pi$
$733$	1.19718	−	11.3904i	0.0442187	−	0.420713i	0.994130	−	0.108193i	$-0.0345065\pi$
$734$	52.1275	−	11.0800i	1.92406	−	0.408972i
$735$	−22.3292	−	13.5119i	−0.823626	−	0.498395i
$736$	−10.0395	−	2.13395i	−0.370059	−	0.0786585i
$737$	0.395794	−	1.21813i	0.0145792	−	0.0448703i
$738$	28.0752	−	30.0112i	1.03346	−	1.10473i
$739$	14.8777	+	45.7888i	0.547285	+	1.68437i	0.715495	+	0.698618i	$0.246201\pi$
$739$	14.8777	+	45.7888i	0.547285	+	1.68437i	−0.168210	+	0.985751i	$0.553799\pi$
$740$	4.78848	+	3.56060i	0.176028	+	0.130890i
$741$	0.291041	−	30.5658i	0.0106917	−	1.12286i
$742$	0.719372	−	6.84437i	0.0264090	−	0.251265i
$743$	3.67273	+	6.36135i	0.134739	+	0.233375i	0.925498	−	0.378753i	$-0.123647\pi$
$743$	3.67273	+	6.36135i	0.134739	+	0.233375i	−0.790759	+	0.612128i	$0.790314\pi$
$744$	3.73893	+	1.25433i	0.137076	+	0.0459861i
$745$	−3.42369	+	2.43007i	−0.125434	+	0.0890310i
$746$	16.9035	−	12.2811i	0.618880	−	0.449642i
$747$	−0.441196	+	1.27474i	−0.0161425	+	0.0466403i
$748$	0.280061	+	0.861940i	0.0102401	+	0.0315156i
$749$	3.14846	−	5.45329i	0.115042	−	0.199259i
$750$	26.1189	−	13.6278i	0.953727	−	0.497617i
$751$	7.69305	+	13.3248i	0.280724	+	0.486227i	0.971563	−	0.236781i	$-0.0760923\pi$
$751$	7.69305	+	13.3248i	0.280724	+	0.486227i	−0.690840	+	0.723008i	$0.742759\pi$
$752$	−22.0492	+	24.4881i	−0.804050	+	0.892988i
$753$	15.8356	+	36.4987i	0.577082	+	1.33009i
$754$	−0.277777	−	2.64287i	−0.0101160	−	0.0962476i
$755$	4.17178	+	1.91295i	0.151827	+	0.0696193i
$756$	0.801247	−	0.235263i	0.0291411	−	0.00855645i
$757$	−28.4272			−1.03320			−0.516602	−	0.856226i	$-0.672803\pi$
$757$	−28.4272			−1.03320			−0.516602	+	0.856226i	$0.672803\pi$
$758$	35.8115	−	15.9443i	1.30073	−	0.579123i
$759$	−7.26377	−	4.28647i	−0.263658	−	0.155589i
$760$	−31.7430	+	13.7144i	−1.15144	+	0.497472i
$761$	−23.0186	+	25.5648i	−0.834425	+	0.926723i	−0.998212	−	0.0597727i	$-0.980962\pi$
$761$	−23.0186	+	25.5648i	−0.834425	+	0.926723i	0.163787	+	0.986496i	$0.447629\pi$
$762$	−35.0053	+	19.7683i	−1.26811	+	0.716131i
$763$	5.01816	+	5.57323i	0.181670	+	0.201765i
$764$	1.07767	+	3.31672i	0.0389886	+	0.119995i
$765$	6.47817	+	22.1890i	0.234219	+	0.802246i
$766$	−7.77667	+	23.9341i	−0.280983	+	0.864775i
$767$	−21.5182	+	9.58053i	−0.776978	+	0.345933i
$768$	12.1771	−	3.82877i	0.439402	−	0.138159i
$769$	−0.452849	+	4.30857i	−0.0163302	+	0.155371i	−0.999648	−	0.0265235i	$-0.991556\pi$
$769$	−0.452849	+	4.30857i	−0.0163302	+	0.155371i	0.983318	+	0.181895i	$0.0582230\pi$
$770$	−0.961110	−	1.09145i	−0.0346360	−	0.0393333i
$771$	0.0321514	−	0.0433779i	0.00115790	−	0.00156222i
$772$	−0.296149	−	2.81766i	−0.0106586	−	0.101410i
$773$	−8.09794	−	24.9229i	−0.291263	−	0.896414i	−0.984451	−	0.175658i	$-0.943795\pi$
$773$	−8.09794	−	24.9229i	−0.291263	−	0.896414i	0.693189	−	0.720756i	$-0.256205\pi$
$774$	−0.833714	−	9.70710i	−0.0299672	−	0.348915i
$775$	0.366318	+	4.42451i	0.0131585	+	0.158933i
$776$	21.7011	−	37.5874i	0.779024	−	1.34931i
$777$	3.12105	−	6.83412i	0.111967	−	0.245173i
$778$	21.6481	+	9.63835i	0.776122	+	0.345552i
$779$	−49.6073	−	22.0866i	−1.77737	−	0.791335i
$780$	−3.41134	+	1.03130i	−0.122146	+	0.0369266i
$781$	3.82384	−	1.70248i	0.136828	−	0.0609197i
$782$	30.5183			1.09133
$783$	0.731243	−	3.01416i	0.0261325	−	0.107717i
$784$	9.43327	−	29.0326i	0.336902	−	1.03688i
$785$	−10.9164	+	7.74823i	−0.389621	+	0.276546i
$786$	24.1963	−	2.31043i	0.863052	−	0.0824102i
$787$	38.3846	−	8.15889i	1.36826	−	0.290833i	0.535534	−	0.844514i	$-0.320111\pi$
$787$	38.3846	−	8.15889i	1.36826	−	0.290833i	0.832729	+	0.553681i	$0.186777\pi$
$788$	−8.35650	+	1.77623i	−0.297688	+	0.0632755i
$789$	−16.7924	+	36.7700i	−0.597824	+	1.30905i
$790$	−25.6639	−	0.283795i	−0.913080	−	0.0100970i
$791$	1.96330	−	6.04243i	0.0698071	−	0.214844i
$792$	6.43355	+	0.122529i	0.228606	+	0.00435388i
$793$	−8.03263			−0.285247
$794$	4.36410	−	1.94302i	0.154876	−	0.0689554i
$795$	−14.5842	+	31.0224i	−0.517248	+	1.10025i
$796$	4.50256	+	2.00467i	0.159589	+	0.0710537i
$797$	−26.5409	−	11.8167i	−0.940125	−	0.418571i	−0.121301	−	0.992616i	$-0.538707\pi$
$797$	−26.5409	−	11.8167i	−0.940125	−	0.418571i	−0.818824	+	0.574045i	$0.805373\pi$
$798$	−4.71106	−	6.61579i	−0.166770	−	0.234196i
$799$	12.5328	−	21.7074i	0.443377	−	0.767952i
$800$	5.75221	+	6.67980i	0.203371	+	0.236167i
$801$	47.4439	+	22.2154i	1.67635	+	0.784941i
$802$	0.971332	+	2.98945i	0.0342989	+	0.105561i
$803$	0.961364	+	9.14677i	0.0339258	+	0.322782i
$804$	−0.828517	−	0.0950647i	−0.0292195	−	0.00335267i
$805$	−6.10762	+	2.63876i	−0.215265	+	0.0930040i
$806$	0.413210	−	3.93143i	0.0145547	−	0.138479i
$807$	6.10018	−	27.4130i	0.214737	−	0.964983i
$808$	40.6132	−	18.0822i	1.42877	−	0.636129i
$809$	2.52965	−	7.78546i	0.0889378	−	0.273722i	−0.896689	−	0.442662i	$-0.854034\pi$
$809$	2.52965	−	7.78546i	0.0889378	−	0.273722i	0.985626	+	0.168939i	$0.0540342\pi$
$810$	−30.5792	−	1.50399i	−1.07444	−	0.0528447i
$811$	−10.9116	−	33.5823i	−0.383157	−	1.17923i	−0.937809	−	0.347152i	$-0.887149\pi$
$811$	−10.9116	−	33.5823i	−0.383157	−	1.17923i	0.554652	−	0.832082i	$-0.312851\pi$
$812$	−0.0641884	−	0.0712884i	−0.00225257	−	0.00250173i
$813$	−15.1755	−	8.95529i	−0.532227	−	0.314076i
$814$	−7.22644	+	8.02578i	−0.253287	+	0.281303i
$815$	−36.9049	−	8.27192i	−1.29272	−	0.289753i
$816$	−23.5421	+	13.2948i	−0.824139	+	0.465411i
$817$	−11.7606	+	5.23617i	−0.411452	+	0.183190i
$818$	46.1490			1.61356
$819$	2.16914	+	3.92794i	0.0757957	+	0.137253i
$820$	−0.731359	+	6.28869i	−0.0255402	+	0.219611i
$821$	−2.71382	−	25.8203i	−0.0947131	−	0.901135i	−0.933958	−	0.357382i	$-0.883669\pi$
$821$	−2.71382	−	25.8203i	−0.0947131	−	0.901135i	0.839245	−	0.543753i	$-0.182997\pi$
$822$	−14.6179	+	19.7221i	−0.509857	+	0.687888i
$823$	−25.2114	+	28.0001i	−0.878814	+	0.976022i	−0.999862	−	0.0166249i	$-0.994708\pi$
$823$	−25.2114	+	28.0001i	−0.878814	+	0.976022i	0.121048	+	0.992647i	$0.461375\pi$
$824$	−10.7459	−	18.6125i	−0.374352	−	0.648396i
$825$	2.73555	+	6.70751i	0.0952397	+	0.233525i
$826$	−3.12925	+	5.42003i	−0.108881	+	0.188587i
$827$	5.57826	+	17.1681i	0.193975	+	0.596994i	0.999987	+	0.00509483i	$0.00162174\pi$
$827$	5.57826	+	17.1681i	0.193975	+	0.596994i	−0.806012	+	0.591899i	$0.798378\pi$
$828$	−1.79615	+	5.18958i	−0.0624205	+	0.180350i
$829$	38.5194	−	27.9860i	1.33783	−	0.971993i	0.338313	−	0.941034i	$-0.390144\pi$
$829$	38.5194	−	27.9860i	1.33783	−	0.971993i	0.999521	−	0.0309591i	$-0.00985618\pi$
$830$	−0.456556	−	1.45987i	−0.0158473	−	0.0506727i
$831$	2.36746	+	11.6839i	0.0821261	+	0.405312i
$832$	9.33210	+	16.1637i	0.323532	+	0.560375i
$833$	−2.42722	+	23.0935i	−0.0840983	+	0.800142i
$834$	−13.2281	−	7.80612i	−0.458052	−	0.270304i
$835$	47.7459	+	0.527981i	1.65232	+	0.0182715i
$836$	0.490137	+	1.50849i	0.0169518	+	0.0521721i
$837$	1.99622	−	4.15962i	0.0689996	−	0.143777i
$838$	−11.1747	+	34.3923i	−0.386025	+	1.18806i
$839$	29.4734	+	6.26476i	1.01753	+	0.216284i	0.686342	−	0.727279i	$-0.259215\pi$
$839$	29.4734	+	6.26476i	1.01753	+	0.216284i	0.331193	+	0.943563i	$0.392549\pi$
$840$	3.06746	−	4.04429i	0.105837	−	0.139541i
$841$	28.0178	−	5.95536i	0.966130	−	0.205357i
$842$	1.72623	−	16.4240i	0.0594899	−	0.566009i
$843$	20.5848	+	18.8926i	0.708979	+	0.650697i
$844$	−4.81314	+	2.14295i	−0.165675	+	0.0737634i
$845$	4.86444	+	8.64483i	0.167342	+	0.297391i
$846$	21.7407	+	25.0903i	0.747462	+	0.862622i
$847$	−4.25909	+	3.09441i	−0.146344	+	0.106325i
$848$	−39.2186	−	8.33618i	−1.34677	−	0.286265i
$849$	27.6990	−	8.70928i	0.950629	−	0.298902i
$850$	−20.8594	−	15.8717i	−0.715473	−	0.544396i
$851$	24.7038	+	42.7882i	0.846835	+	1.46676i
$852$	−1.58086	−	2.22002i	−0.0541595	−	0.0760566i
$853$	0.726124	+	6.90861i	0.0248620	+	0.236546i	0.999895	+	0.0144865i	$0.00461135\pi$
$853$	0.726124	+	6.90861i	0.0248620	+	0.236546i	−0.975033	+	0.222060i	$0.928722\pi$
$854$	−1.72667	+	1.25450i	−0.0590855	+	0.0429282i
$855$	11.3375	+	38.8332i	0.387734	+	1.32807i
$856$	−25.5591	−	18.5698i	−0.873593	−	0.634702i
$857$	−16.5062	+	28.5897i	−0.563843	+	0.976604i	0.433314	+	0.901243i	$0.357344\pi$
$857$	−16.5062	+	28.5897i	−0.563843	+	0.976604i	−0.997156	+	0.0753610i	$0.975989\pi$
$858$	−1.28090	−	6.32153i	−0.0437292	−	0.215814i
$859$	−23.6619	+	5.02948i	−0.807332	+	0.171604i	−0.593047	−	0.805167i	$-0.702075\pi$
$859$	−23.6619	+	5.02948i	−0.807332	+	0.171604i	−0.214285	+	0.976771i	$0.568742\pi$
$860$	0.991926	+	1.12645i	0.0338244	+	0.0384116i
$861$	7.93512	−	0.757700i	0.270428	−	0.0258223i
$862$	−7.65029	−	8.49650i	−0.260570	−	0.289392i
$863$	10.3560	−	31.8723i	0.352521	−	1.08495i	−0.604912	−	0.796292i	$-0.706792\pi$
$863$	10.3560	−	31.8723i	0.352521	−	1.08495i	0.957433	−	0.288655i	$-0.0932081\pi$
$864$	−1.64798	−	9.01157i	−0.0560654	−	0.306580i
$865$	−0.856595	+	7.36555i	−0.0291251	+	0.250436i
$866$	−4.92437	−	5.46907i	−0.167337	−	0.185847i
$867$	−6.65457	+	5.87805i	−0.226001	+	0.199629i
$868$	−0.0713495	−	0.123581i	−0.00242176	−	0.00419461i
$869$	0.659655	−	6.27620i	0.0223773	−	0.212905i
$870$	1.36407	+	3.24169i	0.0462464	+	0.109904i
$871$	−0.468398	−	4.45651i	−0.0158711	−	0.151003i
$872$	30.4405	−	22.1163i	1.03085	−	0.748953i
$873$	−40.5035	−	30.6227i	−1.37084	−	1.03642i
$874$	53.4103			1.80663
$875$	5.54693	+	1.37280i	0.187521	+	0.0464090i
$876$	5.71264	−	1.79620i	0.193012	−	0.0606879i
$877$	−28.8513	+	32.0426i	−0.974240	+	1.08200i	0.0223712	+	0.999750i	$0.492878\pi$
$877$	−28.8513	+	32.0426i	−0.974240	+	1.08200i	−0.996611	+	0.0822537i	$0.973788\pi$
$878$	−44.3760	−	19.7575i	−1.49762	−	0.666782i
$879$	−24.2052	+	32.6571i	−0.816420	+	1.10150i
$880$	−6.90925	+	4.90406i	−0.232911	+	0.165316i
$881$	1.01683	+	0.738771i	0.0342579	+	0.0248898i	0.604782	−	0.796391i	$-0.293260\pi$
$881$	1.01683	+	0.738771i	0.0342579	+	0.0248898i	−0.570525	+	0.821281i	$0.693260\pi$
$882$	−27.8534	−	13.0422i	−0.937873	−	0.439154i
$883$	10.5261	+	7.64764i	0.354231	+	0.257364i	0.750642	−	0.660709i	$-0.229744\pi$
$883$	10.5261	+	7.64764i	0.354231	+	0.257364i	−0.396411	+	0.918073i	$0.629744\pi$
$884$	2.12166	+	2.35634i	0.0713592	+	0.0792524i
$885$	23.5908	−	20.3781i	0.792996	−	0.685001i
$886$	9.49107	−	10.5409i	0.318859	−	0.354129i
$887$	29.7052	−	6.31405i	0.997405	−	0.212005i	0.319843	−	0.947471i	$-0.396370\pi$
$887$	29.7052	−	6.31405i	0.997405	−	0.212005i	0.677562	+	0.735466i	$0.263037\pi$
$888$	−32.4635	−	19.1572i	−1.08940	−	0.642874i
$889$	−7.62728	−	1.62123i	−0.255811	−	0.0543743i
$890$	−58.2387	+	11.7075i	−1.95217	+	0.392436i
$891$	1.07140	−	7.45144i	0.0358933	−	0.249632i
$892$	−2.60913	−	1.89564i	−0.0873600	−	0.0634707i
$893$	21.9337	−	37.9903i	0.733983	−	1.27130i
$894$	−3.70807	+	3.27537i	−0.124016	+	0.109545i
$895$	4.82830	+	5.48310i	0.161392	+	0.183280i
$896$	6.17675	+	2.75007i	0.206351	+	0.0918733i
$897$	−29.3156	−	3.36370i	−0.978820	−	0.112311i
$898$	−37.8282	−	8.04063i	−1.26234	−	0.268319i
$899$	−0.530007			−0.0176767
$900$	3.92663	−	2.61298i	0.130888	−	0.0870993i
$901$	30.4989			1.01606
$902$	−11.2079	−	2.38232i	−0.373183	−	0.0793225i
$903$	1.12529	−	1.51821i	0.0374472	−	0.0505229i
$904$	−29.1203	−	12.9652i	−0.968527	−	0.431216i
$905$	−7.16145	+	12.0932i	−0.238055	+	0.401991i
$906$	5.12744	+	1.72015i	0.170348	+	0.0571482i
$907$	−19.2588	+	33.3572i	−0.639477	+	1.10761i	0.346071	+	0.938208i	$0.387516\pi$
$907$	−19.2588	+	33.3572i	−0.639477	+	1.10761i	−0.985548	+	0.169398i	$0.945818\pi$
$908$	1.49820	+	1.08851i	0.0497195	+	0.0361233i
$909$	−15.1273	−	49.7620i	−0.501742	−	1.65050i
$910$	−4.62498	−	2.12076i	−0.153317	−	0.0703025i
$911$	19.3060	+	4.10363i	0.639638	+	0.135959i	0.516303	−	0.856406i	$-0.327308\pi$
$911$	19.3060	+	4.10363i	0.639638	+	0.135959i	0.123335	+	0.992365i	$0.460641\pi$
$912$	−41.2012	+	23.2673i	−1.36431	+	0.770458i
$913$	0.367886	−	0.0781967i	0.0121753	−	0.00258793i
$914$	31.0999	−	34.5399i	1.02869	−	1.14248i
$915$	10.1760	−	3.07637i	0.336408	−	0.101702i
$916$	2.99161	+	3.32252i	0.0988456	+	0.109779i
$917$	3.81417	+	2.77116i	0.125955	+	0.0915118i
$918$	10.3641	+	25.1908i	0.342065	+	0.831420i
$919$	−17.8319	−	12.9556i	−0.588219	−	0.427366i	0.253459	−	0.967346i	$-0.418432\pi$
$919$	−17.8319	−	12.9556i	−0.588219	−	0.427366i	−0.841678	+	0.539980i	$0.818432\pi$
$920$	9.96355	+	31.8591i	0.328488	+	1.05036i
$921$	6.14788	+	14.1700i	0.202580	+	0.466916i
$922$	20.2954	+	9.03611i	0.668394	+	0.297588i
$923$	9.79884	−	10.8827i	0.322533	−	0.358209i
$924$	−0.171537	−	0.157436i	−0.00564316	−	0.00517926i
$925$	5.36778	−	42.0937i	0.176491	−	1.38403i
$926$	−16.5646			−0.544346
$927$	−23.1604	+	9.78758i	−0.760687	+	0.321466i
$928$	−0.851379	+	0.618563i	−0.0279479	+	0.0203053i
$929$	1.65981	+	15.7920i	0.0544566	+	0.518120i	0.987417	+	0.158140i	$0.0505498\pi$
$929$	1.65981	+	15.7920i	0.0544566	+	0.518120i	−0.932960	+	0.359980i	$0.882784\pi$
$930$	0.982207	+	5.13872i	0.0322078	+	0.168505i
$931$	−4.24790	+	40.4161i	−0.139219	+	1.32458i
$932$	0.804302	+	1.39309i	0.0263458	+	0.0456322i
$933$	−33.5625	−	11.2595i	−1.09879	−	0.368620i
$934$	0.169759	+	0.188536i	0.00555468	+	0.00616910i
$935$	4.36522	−	4.74156i	0.142758	−	0.155066i
$936$	20.7368	−	8.76338i	0.677805	−	0.286440i
$937$	10.7106	−	32.9639i	0.349901	−	1.07688i	−0.609007	−	0.793165i	$-0.708432\pi$
$937$	10.7106	−	32.9639i	0.349901	−	1.07688i	0.958908	−	0.283718i	$-0.0915681\pi$
$938$	−0.796684	−	0.884807i	−0.0260127	−	0.0288900i
$939$	−16.6534	+	36.4658i	−0.543465	+	1.19002i
$940$	−4.99067	−	1.11862i	−0.162778	−	0.0364852i
$941$	7.95616	−	1.69114i	0.259364	−	0.0551294i	−0.0763946	−	0.997078i	$-0.524341\pi$
$941$	7.95616	−	1.69114i	0.259364	−	0.0551294i	0.335758	+	0.941948i	$0.391008\pi$
$942$	−11.8231	+	10.4434i	−0.385217	+	0.340266i
$943$	−26.2102	+	45.3974i	−0.853522	+	1.47834i
$944$	29.4983	+	21.4318i	0.960089	+	0.697545i
$945$	−4.25227	−	4.14530i	−0.138326	−	0.134847i
$946$	−2.19767	+	1.59670i	−0.0714525	+	0.0519133i
$947$	3.93506	+	37.4396i	0.127872	+	1.21662i	0.850721	+	0.525617i	$0.176166\pi$
$947$	3.93506	+	37.4396i	0.127872	+	1.21662i	−0.722849	+	0.691006i	$0.757168\pi$
$948$	−4.09040	+	0.390580i	−0.132850	+	0.0126854i
$949$	16.0886	+	27.8662i	0.522257	+	0.904576i
$950$	−36.5063	−	27.7772i	−1.18442	−	0.901212i
$951$	−13.6679	−	12.5443i	−0.443212	−	0.406778i
$952$	−4.41746	−	0.938961i	−0.143171	−	0.0304319i
$953$	−5.31982	+	3.86508i	−0.172326	+	0.125202i	−0.670605	−	0.741814i	$-0.733965\pi$
$953$	−5.31982	+	3.86508i	−0.172326	+	0.125202i	0.498279	+	0.867017i	$0.333965\pi$
$954$	−13.2122	+	38.1738i	−0.427761	+	1.23592i
$955$	16.7972	−	18.2454i	0.543545	−	0.590406i
$956$	−1.60127	+	0.712932i	−0.0517888	+	0.0230579i
$957$	−0.824960	+	0.259388i	−0.0266672	+	0.00838483i
$958$	−4.65193	+	44.2602i	−0.150297	+	1.42998i
$959$	−4.65756	+	0.989995i	−0.150400	+	0.0319686i
$960$	−18.0126	−	16.9026i	−0.581356	−	0.545530i
$961$	29.5514	+	6.28134i	0.953270	+	0.202624i
$962$	−11.6759	+	35.9347i	−0.376446	+	1.15858i
$963$	−25.2502	+	26.9914i	−0.813676	+	0.869785i
$964$	2.26415	+	6.96833i	0.0729233	+	0.224435i
$965$	−16.4297	+	11.6615i	−0.528892	+	0.375398i
$966$	−6.82694	+	3.85533i	−0.219653	+	0.124043i
$967$	−1.90493	+	18.1242i	−0.0612586	+	0.582836i	0.920238	+	0.391358i	$0.127995\pi$
$967$	−1.90493	+	18.1242i	−0.0612586	+	0.582836i	−0.981497	+	0.191478i	$0.938672\pi$
$968$	13.2065	+	22.8744i	0.424475	+	0.735212i
$969$	26.9759	−	23.8280i	0.866589	−	0.765466i
$970$	57.5739	+	0.636660i	1.84859	+	0.0204419i
$971$	−9.06609	+	6.58690i	−0.290945	+	0.211384i	−0.723677	−	0.690139i	$-0.757550\pi$
$971$	−9.06609	+	6.58690i	−0.290945	+	0.211384i	0.432732	+	0.901522i	$0.357550\pi$
$972$	−4.89362	+	0.279789i	−0.156963	+	0.00897425i
$973$	−0.920633	−	2.83342i	−0.0295142	−	0.0908352i
$974$	24.6278	−	42.6567i	0.789127	−	1.36681i
$975$	18.2880	+	17.5453i	0.585685	+	0.561901i
$976$	6.21715	+	10.7684i	0.199006	+	0.344689i
$977$	6.98766	−	7.76058i	0.223555	−	0.248283i	−0.620925	−	0.783870i	$-0.713243\pi$
$977$	6.98766	−	7.76058i	0.223555	−	0.248283i	0.844480	+	0.535587i	$0.179910\pi$
$978$	−44.2778	−	5.08048i	−1.41585	−	0.162456i
$979$	−1.52680	−	14.5265i	−0.0487967	−	0.464270i
$980$	4.64514	−	0.933794i	0.148384	−	0.0298289i
$981$	−21.2800	−	38.5345i	−0.679418	−	1.23031i
$982$	−5.08237			−0.162185
$983$	1.23032	−	0.547772i	0.0392410	−	0.0174712i	−0.387022	−	0.922070i	$-0.626496\pi$
$983$	1.23032	−	0.547772i	0.0392410	−	0.0174712i	0.426263	+	0.904599i	$0.359830\pi$
$984$	0.380789	−	39.9913i	0.0121391	−	1.27488i
$985$	40.1501	+	45.5952i	1.27929	+	1.45278i
$986$	2.09378	−	2.32538i	0.0666796	−	0.0740552i
$987$	−0.0613126	+	6.43918i	−0.00195160	+	0.204961i
$988$	3.71313	+	4.12385i	0.118131	+	0.131197i
$989$	3.84032	+	11.8193i	0.122115	+	0.375832i
$990$	4.04373	+	7.51776i	0.128518	+	0.238930i
$991$	3.33798	−	10.2732i	0.106034	−	0.326340i	−0.883937	−	0.467605i	$-0.845117\pi$
$991$	3.33798	−	10.2732i	0.106034	−	0.326340i	0.989972	+	0.141265i	$0.0451169\pi$
$992$	−1.43011	+	0.636728i	−0.0454062	+	0.0202161i
$993$	−29.9945	−	27.5288i	−0.951846	−	0.873599i
$994$	0.406718	−	3.86966i	0.0129003	−	0.122738i
$995$	−3.27799	−	34.8957i	−0.103919	−	1.10627i
$996$	−0.0974696	−	0.224653i	−0.00308844	−	0.00711840i
$997$	−1.97292	−	18.7710i	−0.0624829	−	0.594485i	−0.980305	−	0.197492i	$-0.936720\pi$
$997$	−1.97292	−	18.7710i	−0.0624829	−	0.594485i	0.917822	−	0.396993i	$-0.129946\pi$
$998$	−12.2245	−	37.6231i	−0.386960	−	1.19094i
$999$	−26.9293	+	34.9222i	−0.852006	+	1.10489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.106.21	yes	224
3.2	odd	2		675.2.r.a.181.8		224
9.4	even	3	inner	225.2.q.a.31.8	✓	224
9.5	odd	6		675.2.r.a.631.21		224
25.21	even	5	inner	225.2.q.a.196.8	yes	224
75.71	odd	10		675.2.r.a.46.21		224
225.121	even	15	inner	225.2.q.a.121.21	yes	224
225.221	odd	30		675.2.r.a.496.8		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.8	✓	224	9.4	even	3	inner
225.2.q.a.106.21	yes	224	1.1	even	1	trivial
225.2.q.a.121.21	yes	224	225.121	even	15	inner
225.2.q.a.196.8	yes	224	25.21	even	5	inner
675.2.r.a.46.21		224	75.71	odd	10
675.2.r.a.181.8		224	3.2	odd	2
675.2.r.a.496.8		224	225.221	odd	30
675.2.r.a.631.21		224	9.5	odd	6

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.48808 + 0.316302i) q^{2} +(-0.689391 - 1.58894i) q^{3} +(0.287254 + 0.127894i) q^{4} +(-0.209129 - 2.22627i) q^{5} +(-0.523285 - 2.58254i) q^{6} +(0.255551 - 0.442627i) q^{7} +(-2.07456 - 1.50725i) q^{8} +(-2.04948 + 2.19081i) q^{9} +O(q^{10})\)	\(q+(1.48808 + 0.316302i) q^{2} +(-0.689391 - 1.58894i) q^{3} +(0.287254 + 0.127894i) q^{4} +(-0.209129 - 2.22627i) q^{5} +(-0.523285 - 2.58254i) q^{6} +(0.255551 - 0.442627i) q^{7} +(-2.07456 - 1.50725i) q^{8} +(-2.04948 + 2.19081i) q^{9} +(0.392972 - 3.37902i) q^{10} +(0.818173 + 0.173908i) q^{11} +(0.00518556 - 0.544598i) q^{12} +(2.86246 - 0.608435i) q^{13} +(0.520284 - 0.577834i) q^{14} +(-3.39324 + 1.86706i) q^{15} +(-3.03117 - 3.36645i) q^{16} +(2.78774 + 2.02541i) q^{17} +(-3.74275 + 2.61185i) q^{18} +(4.87884 + 3.54469i) q^{19} +(0.224652 - 0.666250i) q^{20} +(-0.879483 - 0.100913i) q^{21} +(1.16250 + 0.517580i) q^{22} +(3.89542 - 4.32630i) q^{23} +(-0.964759 + 4.33544i) q^{24} +(-4.91253 + 0.931153i) q^{25} +4.45203 q^{26} +(4.89396 + 1.74619i) q^{27} +(0.130017 - 0.0944629i) q^{28} +(-0.0623933 - 0.593632i) q^{29} +(-5.63998 + 1.70505i) q^{30} +(0.0928139 - 0.883066i) q^{31} +(-0.881520 - 1.52684i) q^{32} +(-0.287711 - 1.41992i) q^{33} +(3.50774 + 3.89575i) q^{34} +(-1.03885 - 0.476358i) q^{35} +(-0.868911 + 0.367202i) q^{36} +(-2.62260 + 8.07154i) q^{37} +(6.13893 + 6.81797i) q^{38} +(-2.94012 - 4.12884i) q^{39} +(-2.92170 + 4.93372i) q^{40} +(-8.80767 + 1.87213i) q^{41} +(-1.27682 - 0.428348i) q^{42} +(-1.06736 + 1.84872i) q^{43} +(0.212782 + 0.154595i) q^{44} +(5.30592 + 4.10453i) q^{45} +(7.16513 - 5.20577i) q^{46} +(-0.760356 - 7.23431i) q^{47} +(-3.25944 + 7.13715i) q^{48} +(3.36939 + 5.83595i) q^{49} +(-7.60478 - 0.168210i) q^{50} +(1.29642 - 5.82586i) q^{51} +(0.900067 + 0.191315i) q^{52} +(7.16056 - 5.20245i) q^{53} +(6.73030 + 4.14644i) q^{54} +(0.216062 - 1.85784i) q^{55} +(-1.19730 + 0.533074i) q^{56} +(2.26888 - 10.1959i) q^{57} +(0.0949206 - 0.903110i) q^{58} +(-7.87309 + 1.67348i) q^{59} +(-1.21351 + 0.102347i) q^{60} +(-2.68489 - 0.570692i) q^{61} +(0.417430 - 1.28472i) q^{62} +(0.445963 + 1.46702i) q^{63} +(1.97086 + 6.06570i) q^{64} +(-1.95316 - 6.24536i) q^{65} +(0.0209857 - 2.20397i) q^{66} +(0.160059 - 1.52286i) q^{67} +(0.541751 + 0.938340i) q^{68} +(-9.55972 - 3.20709i) q^{69} +(-1.39522 - 1.03745i) q^{70} +(4.04843 - 2.94135i) q^{71} +(7.55386 - 1.45586i) q^{72} +(3.39778 + 10.4573i) q^{73} +(-6.45569 + 11.1816i) q^{74} +(4.86620 + 7.16380i) q^{75} +(0.948122 + 1.64220i) q^{76} +(0.286061 - 0.317703i) q^{77} +(-3.06919 - 7.07402i) q^{78} +(-0.788634 - 7.50335i) q^{79} +(-6.86071 + 7.45220i) q^{80} +(-0.599260 - 8.98003i) q^{81} -13.6987 q^{82} +(0.410770 - 0.182886i) q^{83} +(-0.239729 - 0.141468i) q^{84} +(3.92611 - 6.62982i) q^{85} +(-2.17308 + 2.41345i) q^{86} +(-0.900235 + 0.508384i) q^{87} +(-1.43522 - 1.59398i) q^{88} +(-5.39621 - 16.6078i) q^{89} +(6.59739 + 7.78616i) q^{90} +(0.462194 - 1.42249i) q^{91} +(1.67228 - 0.744547i) q^{92} +(-1.46713 + 0.461301i) q^{93} +(1.15675 - 11.0058i) q^{94} +(6.87111 - 11.6029i) q^{95} +(-1.81835 + 2.45327i) q^{96} +(1.76921 + 16.8329i) q^{97} +(3.16801 + 9.75012i) q^{98} +(-2.05783 + 1.43604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

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