LMFDB - Embedded newform 525.2.bo.a.319.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(4,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 3, 20]))

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

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

chi := DirichletCharacter("525.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bo (of order $30$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$40$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			319.8
Character	$\chi$	$=$	525.319
Dual form			525.2.bo.a.79.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41954 - 1.27816i) q^{2} +(-0.994522 + 0.104528i) q^{3} +(0.172344 + 1.63974i) q^{4} +(-2.15797 - 0.585803i) q^{5} +(1.54537 + 1.12277i) q^{6} +(2.41699 - 1.07617i) q^{7} +(-0.394346 + 0.542771i) q^{8} +(0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(-1.41954 - 1.27816i) q^{2} +(-0.994522 + 0.104528i) q^{3} +(0.172344 + 1.63974i) q^{4} +(-2.15797 - 0.585803i) q^{5} +(1.54537 + 1.12277i) q^{6} +(2.41699 - 1.07617i) q^{7} +(-0.394346 + 0.542771i) q^{8} +(0.978148 - 0.207912i) q^{9} +(2.31457 + 3.58980i) q^{10} +(3.83448 + 0.815044i) q^{11} +(-0.342800 - 1.61275i) q^{12} +(1.04619 + 0.339929i) q^{13} +(-4.80653 - 1.56163i) q^{14} +(2.20738 + 0.357024i) q^{15} +(4.47903 - 0.952047i) q^{16} +(0.815798 + 1.83231i) q^{17} +(-1.65426 - 0.955088i) q^{18} +(-0.0467088 + 0.444405i) q^{19} +(0.588653 - 3.63948i) q^{20} +(-2.29126 + 1.32292i) q^{21} +(-4.40144 - 6.05806i) q^{22} +(-6.01927 - 5.41977i) q^{23} +(0.335451 - 0.581018i) q^{24} +(4.31367 + 2.52829i) q^{25} +(-1.05063 - 1.81974i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(2.18120 + 3.77777i) q^{28} +(3.29586 - 2.39458i) q^{29} +(-2.67713 - 3.32819i) q^{30} +(1.88694 - 0.840120i) q^{31} +(-6.41298 - 3.70253i) q^{32} +(-3.89867 - 0.409767i) q^{33} +(1.18393 - 3.64375i) q^{34} +(-5.84622 + 0.906469i) q^{35} +(0.509500 + 1.56808i) q^{36} +(-1.72286 - 8.10541i) q^{37} +(0.634325 - 0.571148i) q^{38} +(-1.07599 - 0.228710i) q^{39} +(1.16894 - 0.940274i) q^{40} +(0.178401 - 0.549063i) q^{41} +(4.94344 + 1.05066i) q^{42} -5.19818i q^{43} +(-0.675613 + 6.42803i) q^{44} +(-2.23261 - 0.124334i) q^{45} +(1.61725 + 15.3871i) q^{46} +(1.48114 - 3.32669i) q^{47} +(-4.35497 + 1.41502i) q^{48} +(4.68370 - 5.20220i) q^{49} +(-2.89187 - 9.10255i) q^{50} +(-1.00286 - 1.73700i) q^{51} +(-0.377091 + 1.77407i) q^{52} +(-2.11372 + 0.222161i) q^{53} +(1.74503 + 0.776939i) q^{54} +(-7.79724 - 4.00509i) q^{55} +(-0.369016 + 1.73626i) q^{56} -0.446853i q^{57} +(-7.73924 - 0.813427i) q^{58} +(-1.77026 - 1.96607i) q^{59} +(-0.204999 + 3.68107i) q^{60} +(-7.57664 + 8.41471i) q^{61} +(-3.75239 - 1.21922i) q^{62} +(2.14043 - 1.55518i) q^{63} +(1.54101 + 4.74274i) q^{64} +(-2.05852 - 1.34642i) q^{65} +(5.01056 + 5.56480i) q^{66} +(1.36794 + 3.07243i) q^{67} +(-2.86392 + 1.65349i) q^{68} +(6.55281 + 4.76090i) q^{69} +(9.45754 + 6.18563i) q^{70} +(12.4920 - 9.07597i) q^{71} +(-0.272880 + 0.612899i) q^{72} +(1.02355 - 4.81544i) q^{73} +(-7.91433 + 13.7080i) q^{74} +(-4.55432 - 2.06354i) q^{75} -0.736760 q^{76} +(10.1450 - 2.15661i) q^{77} +(1.23509 + 1.69995i) q^{78} +(-1.56360 - 0.696161i) q^{79} +(-10.2233 - 0.569338i) q^{80} +(0.913545 - 0.406737i) q^{81} +(-0.955036 + 0.551391i) q^{82} +(-6.60368 + 9.08918i) q^{83} +(-2.56414 - 3.52908i) q^{84} +(-0.687094 - 4.43197i) q^{85} +(-6.64410 + 7.37902i) q^{86} +(-3.02750 + 2.72597i) q^{87} +(-1.95449 + 1.75983i) q^{88} +(-1.49410 + 1.65937i) q^{89} +(3.01035 + 3.03012i) q^{90} +(2.89446 - 0.304280i) q^{91} +(7.84965 - 10.8041i) q^{92} +(-1.78879 + 1.03276i) q^{93} +(-6.35457 + 2.82924i) q^{94} +(0.361130 - 0.931650i) q^{95} +(6.76487 + 3.01191i) q^{96} +(1.09334 + 1.50486i) q^{97} +(-13.2979 + 1.39821i) q^{98} +3.92015 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9}+O(q^{10}) $ 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9	$ 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9} + 4 q^{10} - 6 q^{11} + 12 q^{14} + 4 q^{15} + 40 q^{16} - 20 q^{17} + 16 q^{19} + 8 q^{20} + 40 q^{22} - 60 q^{23} - 48 q^{24} + 4 q^{25} - 30 q^{28} + 24 q^{29} - 48 q^{30} - 30 q^{31} - 80 q^{36} + 30 q^{38} - 32 q^{40} + 36 q^{41} + 10 q^{42} - 16 q^{44} + 2 q^{45} + 32 q^{46} + 16 q^{49} - 140 q^{50} + 190 q^{52} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 60 q^{58} + 24 q^{59} - 46 q^{60} - 20 q^{61} + 120 q^{62} + 10 q^{63} - 4 q^{64} - 30 q^{65} - 16 q^{66} - 60 q^{67} - 32 q^{69} - 76 q^{70} + 32 q^{71} - 30 q^{72} - 40 q^{73} - 12 q^{74} - 8 q^{75} - 344 q^{76} + 4 q^{79} - 52 q^{80} + 40 q^{81} - 80 q^{83} + 48 q^{84} - 76 q^{85} + 24 q^{86} - 200 q^{88} - 52 q^{90} + 26 q^{91} + 180 q^{92} + 16 q^{94} - 38 q^{95} - 58 q^{96} - 140 q^{97} + 360 q^{98} + 8 q^{99}+O(q^{100}) $ 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9 + 4 * q^10 - 6 * q^11 + 12 * q^14 + 4 * q^15 + 40 * q^16 - 20 * q^17 + 16 * q^19 + 8 * q^20 + 40 * q^22 - 60 * q^23 - 48 * q^24 + 4 * q^25 - 30 * q^28 + 24 * q^29 - 48 * q^30 - 30 * q^31 - 80 * q^36 + 30 * q^38 - 32 * q^40 + 36 * q^41 + 10 * q^42 - 16 * q^44 + 2 * q^45 + 32 * q^46 + 16 * q^49 - 140 * q^50 + 190 * q^52 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 60 * q^58 + 24 * q^59 - 46 * q^60 - 20 * q^61 + 120 * q^62 + 10 * q^63 - 4 * q^64 - 30 * q^65 - 16 * q^66 - 60 * q^67 - 32 * q^69 - 76 * q^70 + 32 * q^71 - 30 * q^72 - 40 * q^73 - 12 * q^74 - 8 * q^75 - 344 * q^76 + 4 * q^79 - 52 * q^80 + 40 * q^81 - 80 * q^83 + 48 * q^84 - 76 * q^85 + 24 * q^86 - 200 * q^88 - 52 * q^90 + 26 * q^91 + 180 * q^92 + 16 * q^94 - 38 * q^95 - 58 * q^96 - 140 * q^97 + 360 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.41954	−	1.27816i	−1.00376	−	0.903794i	−0.00840006	−	0.999965i	$-0.502674\pi$
$2$	−1.41954	−	1.27816i	−1.00376	−	0.903794i	−0.995365	+	0.0961707i	$0.969341\pi$
$3$	−0.994522	+	0.104528i	−0.574187	+	0.0603495i
$3$	−0.994522	+	0.104528i	−0.574187	+	0.0603495i
$4$	0.172344	+	1.63974i	0.0861720	+	0.819872i
$5$	−2.15797	−	0.585803i	−0.965074	−	0.261979i
$5$	−2.15797	−	0.585803i	−0.965074	−	0.261979i
$6$	1.54537	+	1.12277i	0.630893	+	0.458370i
$7$	2.41699	−	1.07617i	0.913537	−	0.406755i
$7$	2.41699	−	1.07617i	0.913537	−	0.406755i
$8$	−0.394346	+	0.542771i	−0.139422	+	0.191898i
$9$	0.978148	−	0.207912i	0.326049	−	0.0693039i
$10$	2.31457	+	3.58980i	0.731932	+	1.13519i
$11$	3.83448	+	0.815044i	1.15614	+	0.245745i	0.745789	−	0.666183i	$-0.232073\pi$
$11$	3.83448	+	0.815044i	1.15614	+	0.245745i	0.410351	+	0.911928i	$0.365406\pi$
$12$	−0.342800	−	1.61275i	−0.0989577	−	0.465560i
$13$	1.04619	+	0.339929i	0.290162	+	0.0942793i	0.450481	−	0.892786i	$-0.351252\pi$
$13$	1.04619	+	0.339929i	0.290162	+	0.0942793i	−0.160319	+	0.987065i	$0.551252\pi$
$14$	−4.80653	−	1.56163i	−1.28460	−	0.417363i
$15$	2.20738	+	0.357024i	0.569943	+	0.0921833i
$16$	4.47903	−	0.952047i	1.11976	−	0.238012i
$17$	0.815798	+	1.83231i	0.197860	+	0.444401i	0.985041	−	0.172322i	$-0.0551268\pi$
$17$	0.815798	+	1.83231i	0.197860	+	0.444401i	−0.787181	+	0.616722i	$0.788460\pi$
$18$	−1.65426	−	0.955088i	−0.389913	−	0.225116i
$19$	−0.0467088	+	0.444405i	−0.0107157	+	0.101953i	−0.998572	−	0.0534143i	$-0.982990\pi$
$19$	−0.0467088	+	0.444405i	−0.0107157	+	0.101953i	0.987857	+	0.155368i	$0.0496563\pi$
$20$	0.588653	−	3.63948i	0.131627	−	0.813812i
$21$	−2.29126	+	1.32292i	−0.499994	+	0.288685i
$22$	−4.40144	−	6.05806i	−0.938389	−	1.29158i
$23$	−6.01927	−	5.41977i	−1.25510	−	1.13010i	−0.985957	−	0.167002i	$-0.946591\pi$
$23$	−6.01927	−	5.41977i	−1.25510	−	1.13010i	−0.269148	−	0.963099i	$-0.586742\pi$
$24$	0.335451	−	0.581018i	0.0684736	−	0.118600i
$25$	4.31367	+	2.52829i	0.862734	+	0.505658i
$26$	−1.05063	−	1.81974i	−0.206045	−	0.356881i
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	2.18120	+	3.77777i	0.412208	+	0.713932i
$29$	3.29586	−	2.39458i	0.612025	−	0.444662i	−0.238102	−	0.971240i	$-0.576525\pi$
$29$	3.29586	−	2.39458i	0.612025	−	0.444662i	0.850127	+	0.526578i	$0.176525\pi$
$30$	−2.67713	−	3.32819i	−0.488775	−	0.607642i
$31$	1.88694	−	0.840120i	0.338904	−	0.150890i	−0.230226	−	0.973137i	$-0.573947\pi$
$31$	1.88694	−	0.840120i	0.338904	−	0.150890i	0.569130	+	0.822247i	$0.307280\pi$
$32$	−6.41298	−	3.70253i	−1.13367	−	0.654522i
$33$	−3.89867	−	0.409767i	−0.678672	−	0.0713312i
$34$	1.18393	−	3.64375i	0.203042	−	0.624899i
$35$	−5.84622	+	0.906469i	−0.988192	+	0.153221i
$36$	0.509500	+	1.56808i	0.0849166	+	0.261346i
$37$	−1.72286	−	8.10541i	−0.283236	−	1.33252i	−0.857767	−	0.514039i	$-0.828149\pi$
$37$	−1.72286	−	8.10541i	−0.283236	−	1.33252i	0.574531	−	0.818483i	$-0.305185\pi$
$38$	0.634325	−	0.571148i	0.102901	−	0.0926525i
$39$	−1.07599	−	0.228710i	−0.172297	−	0.0366229i
$40$	1.16894	−	0.940274i	0.184826	−	0.148670i
$41$	0.178401	−	0.549063i	0.0278616	−	0.0857492i	−0.936159	−	0.351577i	$-0.885645\pi$
$41$	0.178401	−	0.549063i	0.0278616	−	0.0857492i	0.964020	+	0.265828i	$0.0856454\pi$
$42$	4.94344	+	1.05066i	0.762789	+	0.162120i
$43$		−	5.19818i		−	0.792715i	−0.918096	−	0.396358i	$-0.870274\pi$
$43$		−	5.19818i		−	0.792715i	0.918096	−	0.396358i	$-0.129726\pi$
$44$	−0.675613	+	6.42803i	−0.101853	+	0.969062i
$45$	−2.23261	−	0.124334i	−0.332818	−	0.0185346i
$46$	1.61725	+	15.3871i	0.238451	+	2.26871i
$47$	1.48114	−	3.32669i	0.216046	−	0.485248i	−0.772715	−	0.634754i	$-0.781102\pi$
$47$	1.48114	−	3.32669i	0.216046	−	0.485248i	0.988761	+	0.149506i	$0.0477682\pi$
$48$	−4.35497	+	1.41502i	−0.628586	+	0.204240i
$49$	4.68370	−	5.20220i	0.669101	−	0.743172i
$50$	−2.89187	−	9.10255i	−0.408972	−	1.28730i
$51$	−1.00286	−	1.73700i	−0.140428	−	0.243229i
$52$	−0.377091	+	1.77407i	−0.0522931	+	0.246020i
$53$	−2.11372	+	0.222161i	−0.290342	+	0.0305162i	−0.248580	−	0.968611i	$-0.579964\pi$
$53$	−2.11372	+	0.222161i	−0.290342	+	0.0305162i	−0.0417623	+	0.999128i	$0.513297\pi$
$54$	1.74503	+	0.776939i	0.237469	+	0.105728i
$55$	−7.79724	−	4.00509i	−1.05138	−	0.540046i
$56$	−0.369016	+	1.73626i	−0.0493119	+	0.232017i
$57$		−	0.446853i		−	0.0591871i
$58$	−7.73924	−	0.813427i	−1.01621	−	0.106808i
$59$	−1.77026	−	1.96607i	−0.230468	−	0.255961i	0.616808	−	0.787114i	$-0.288426\pi$
$59$	−1.77026	−	1.96607i	−0.230468	−	0.255961i	−0.847276	+	0.531153i	$0.821759\pi$
$60$	−0.204999	+	3.68107i	−0.0264653	+	0.475224i
$61$	−7.57664	+	8.41471i	−0.970090	+	1.07739i	0.0268827	+	0.999639i	$0.491442\pi$
$61$	−7.57664	+	8.41471i	−0.970090	+	1.07739i	−0.996972	+	0.0777552i	$0.975225\pi$
$62$	−3.75239	−	1.21922i	−0.476554	−	0.154842i
$63$	2.14043	−	1.55518i	0.269668	−	0.195934i
$64$	1.54101	+	4.74274i	0.192626	+	0.592842i
$65$	−2.05852	−	1.34642i	−0.255328	−	0.167003i
$66$	5.01056	+	5.56480i	0.616758	+	0.684979i
$67$	1.36794	+	3.07243i	0.167120	+	0.375358i	0.977619	−	0.210382i	$-0.0674708\pi$
$67$	1.36794	+	3.07243i	0.167120	+	0.375358i	−0.810499	+	0.585740i	$0.800804\pi$
$68$	−2.86392	+	1.65349i	−0.347302	+	0.200515i
$69$	6.55281	+	4.76090i	0.788866	+	0.573145i
$70$	9.45754	+	6.18563i	1.13039	+	0.739324i
$71$	12.4920	−	9.07597i	1.48253	−	1.07712i	0.505796	−	0.862653i	$-0.331199\pi$
$71$	12.4920	−	9.07597i	1.48253	−	1.07712i	0.976731	−	0.214466i	$-0.0688012\pi$
$72$	−0.272880	+	0.612899i	−0.0321592	+	0.0722308i
$73$	1.02355	−	4.81544i	0.119798	−	0.563605i	−0.876776	−	0.480899i	$-0.840310\pi$
$73$	1.02355	−	4.81544i	0.119798	−	0.563605i	0.996574	−	0.0827060i	$-0.0263563\pi$
$74$	−7.91433	+	13.7080i	−0.920023	+	1.59353i
$75$	−4.55432	−	2.06354i	−0.525887	−	0.238277i
$76$	−0.736760			−0.0845122
$77$	10.1450	−	2.15661i	1.15613	−	0.245768i
$78$	1.23509	+	1.69995i	0.139846	+	0.192482i
$79$	−1.56360	−	0.696161i	−0.175919	−	0.0783242i	0.316887	−	0.948463i	$-0.397362\pi$
$79$	−1.56360	−	0.696161i	−0.175919	−	0.0783242i	−0.492806	+	0.870139i	$0.664029\pi$
$80$	−10.2233	−	0.569338i	−1.14300	−	0.0636539i
$81$	0.913545	−	0.406737i	0.101505	−	0.0451930i
$82$	−0.955036	+	0.551391i	−0.105466	+	0.0608909i
$83$	−6.60368	+	9.08918i	−0.724848	+	0.997667i	0.274501	+	0.961587i	$0.411487\pi$
$83$	−6.60368	+	9.08918i	−0.724848	+	0.997667i	−0.999349	+	0.0360803i	$0.988513\pi$
$84$	−2.56414	−	3.52908i	−0.279770	−	0.385054i
$85$	−0.687094	−	4.43197i	−0.0745258	−	0.480715i
$86$	−6.64410	+	7.37902i	−0.716451	+	0.795700i
$87$	−3.02750	+	2.72597i	−0.324582	+	0.292255i
$88$	−1.95449	+	1.75983i	−0.208350	+	0.187599i
$89$	−1.49410	+	1.65937i	−0.158375	+	0.175893i	−0.817110	−	0.576482i	$-0.804425\pi$
$89$	−1.49410	+	1.65937i	−0.158375	+	0.175893i	0.658735	+	0.752375i	$0.271092\pi$
$90$	3.01035	+	3.03012i	0.317319	+	0.319403i
$91$	2.89446	−	0.304280i	0.303422	−	0.0318972i
$92$	7.84965	−	10.8041i	0.818383	−	1.12641i
$93$	−1.78879	+	1.03276i	−0.185488	+	0.107092i
$94$	−6.35457	+	2.82924i	−0.655424	+	0.291814i
$95$	0.361130	−	0.931650i	0.0370511	−	0.0955853i
$96$	6.76487	+	3.01191i	0.690436	+	0.307402i
$97$	1.09334	+	1.50486i	0.111012	+	0.152795i	0.860908	−	0.508761i	$-0.169896\pi$
$97$	1.09334	+	1.50486i	0.111012	+	0.152795i	−0.749896	+	0.661556i	$0.769896\pi$
$98$	−13.2979	+	1.39821i	−1.34329	+	0.141241i
$99$	3.92015			0.393989
$100$	−3.40231	+	7.50905i	−0.340231	+	0.750905i
$101$	9.60153	−	16.6303i	0.955387	−	1.65478i	0.221909	−	0.975067i	$-0.428771\pi$
$101$	9.60153	−	16.6303i	0.955387	−	1.65478i	0.733479	−	0.679712i	$-0.237895\pi$
$102$	−0.796566	+	3.74755i	−0.0788718	+	0.371062i
$103$	2.66247	−	5.98000i	0.262341	−	0.589227i	−0.733565	−	0.679619i	$-0.762145\pi$
$103$	2.66247	−	5.98000i	0.262341	−	0.589227i	0.995906	+	0.0903915i	$0.0288118\pi$
$104$	−0.597066	+	0.433794i	−0.0585471	+	0.0425370i
$105$	5.71944	−	1.51260i	0.558161	−	0.147615i
$106$	3.28447	+	2.38631i	0.319016	+	0.231778i
$107$	13.3490	−	7.70704i	1.29049	−	0.745067i	0.311753	−	0.950163i	$-0.399084\pi$
$107$	13.3490	−	7.70704i	1.29049	−	0.745067i	0.978742	+	0.205096i	$0.0657506\pi$
$108$	−0.670617	−	1.50623i	−0.0645302	−	0.144937i
$109$	−3.54703	−	3.93938i	−0.339744	−	0.377324i	0.548926	−	0.835871i	$-0.315037\pi$
$109$	−3.54703	−	3.93938i	−0.339744	−	0.377324i	−0.888670	+	0.458547i	$0.848370\pi$
$110$	5.94934	+	15.6515i	0.567248	+	1.49231i
$111$	2.56067	+	7.88092i	0.243048	+	0.748024i
$112$	9.80121	−	7.12130i	0.926127	−	0.672899i
$113$	14.3026	+	4.64719i	1.34547	+	0.437171i	0.891167	−	0.453675i	$-0.149887\pi$
$113$	14.3026	+	4.64719i	1.34547	+	0.437171i	0.454306	+	0.890846i	$0.349887\pi$
$114$	−0.571148	+	0.634325i	−0.0534930	+	0.0594099i
$115$	9.81448	+	15.2218i	0.915205	+	1.41944i
$116$	4.49451	+	4.99166i	0.417305	+	0.463464i
$117$	1.09401	+	0.114985i	0.101141	+	0.0106303i
$118$			5.05358i			0.465220i
$119$	3.94366	+	3.55074i	0.361515	+	0.325496i
$120$	−1.06425	+	1.05731i	−0.0971527	+	0.0965188i
$121$	3.98995	+	1.77644i	0.362723	+	0.161495i
$122$	21.5107	−	2.26086i	1.94748	−	0.204689i
$123$	−0.120031	+	0.564703i	−0.0108229	+	0.0509176i
$124$	1.70278	+	2.94931i	0.152914	+	0.264856i
$125$	−7.82769	−	7.98293i	−0.700130	−	0.714015i
$126$	−5.02618	−	0.528170i	−0.447768	−	0.0470531i
$127$	3.28705	−	1.06803i	0.291678	−	0.0947720i	−0.159523	−	0.987194i	$-0.550996\pi$
$127$	3.28705	−	1.06803i	0.291678	−	0.0947720i	0.451201	+	0.892422i	$0.350996\pi$
$128$	−2.14938	+	4.82759i	−0.189980	+	0.426702i
$129$	0.543358	+	5.16971i	0.0478400	+	0.455167i
$130$	1.20122	+	4.54241i	0.105354	+	0.398396i
$131$	0.303265	−	2.88537i	0.0264964	−	0.252096i	−0.973254	−	0.229734i	$-0.926214\pi$
$131$	0.303265	−	2.88537i	0.0264964	−	0.252096i	0.999750	−	0.0223627i	$-0.00711885\pi$
$132$		−	6.46344i		−	0.562570i
$133$	0.365362	+	1.12439i	0.0316809	+	0.0974970i
$134$	1.98522	−	6.10987i	0.171497	−	0.527813i
$135$	2.23337	−	0.109718i	0.192218	−	0.00944303i
$136$	−1.31623	−	0.279774i	−0.112866	−	0.0239904i
$137$	14.9005	−	13.4165i	1.27304	−	1.14625i	0.291174	−	0.956670i	$-0.405954\pi$
$137$	14.9005	−	13.4165i	1.27304	−	1.14625i	0.981865	−	0.189580i	$-0.0607126\pi$
$138$	−3.21679	−	15.1338i	−0.273831	−	1.28828i
$139$	6.43828	+	19.8150i	0.546088	+	1.68069i	0.718389	+	0.695641i	$0.244880\pi$
$139$	6.43828	+	19.8150i	0.546088	+	1.68069i	−0.172301	+	0.985044i	$0.555120\pi$
$140$	−2.49394	−	9.43008i	−0.210776	−	0.796987i
$141$	−1.12529	+	3.46329i	−0.0947666	+	0.291662i
$142$	−29.3334	−	3.08306i	−2.46160	−	0.258725i
$143$	3.73455	+	2.15615i	0.312299	+	0.180306i
$144$	4.18321	−	1.86248i	0.348601	−	0.155207i
$145$	−8.51511	+	3.23671i	−0.707141	+	0.268794i
$146$	−7.60787	+	5.52744i	−0.629632	+	0.457454i
$147$	−4.11427	+	5.66329i	−0.339339	+	0.467100i
$148$	12.9939	−	4.22196i	1.06809	−	0.347043i
$149$	2.82960	+	4.90101i	0.231810	+	0.401506i	0.958341	−	0.285627i	$-0.0922020\pi$
$149$	2.82960	+	4.90101i	0.231810	+	0.401506i	−0.726531	+	0.687134i	$0.758869\pi$
$150$	3.82750	+	8.75041i	0.312514	+	0.714468i
$151$	3.09946	−	5.36843i	0.252231	−	0.436876i	−0.711909	−	0.702272i	$-0.752169\pi$
$151$	3.09946	−	5.36843i	0.252231	−	0.436876i	0.964140	+	0.265395i	$0.0855025\pi$
$152$	−0.222791	−	0.200602i	−0.0180707	−	0.0162709i
$153$	1.17893	+	1.62266i	0.0953108	+	0.131184i
$154$	−17.1578	−	9.90557i	−1.38261	−	0.798214i
$155$	−4.56410	+	0.707579i	−0.366598	+	0.0568341i
$156$	0.189584	−	1.80377i	0.0151789	−	0.144417i
$157$	−1.03000	−	0.594670i	−0.0822028	−	0.0474598i	0.458335	−	0.888779i	$-0.348446\pi$
$157$	−1.03000	−	0.594670i	−0.0822028	−	0.0474598i	−0.540538	+	0.841320i	$0.681779\pi$
$158$	1.32979	+	2.98676i	0.105792	+	0.237614i
$159$	2.07892	−	0.441889i	0.164869	−	0.0350440i
$160$	11.6701	+	11.7467i	0.922599	+	0.928658i
$161$	−20.3811	−	6.62178i	−1.60626	−	0.521869i
$162$	−1.81669	−	0.590277i	−0.142732	−	0.0463765i
$163$	4.01236	+	18.8767i	0.314272	+	1.47853i	0.797649	+	0.603122i	$0.206077\pi$
$163$	4.01236	+	18.8767i	0.314272	+	1.47853i	−0.483377	+	0.875412i	$0.660590\pi$
$164$	0.931068	+	0.197905i	0.0727042	+	0.0154538i
$165$	8.17317	+	3.16812i	0.636281	+	0.246638i
$166$	20.9916	−	4.46190i	1.62926	−	0.346310i
$167$	−10.6387	+	14.6429i	−0.823244	+	1.13310i	0.165899	+	0.986143i	$0.446947\pi$
$167$	−10.6387	+	14.6429i	−0.823244	+	1.13310i	−0.989143	+	0.146956i	$0.953053\pi$
$168$	0.185506	−	1.76532i	0.0143121	−	0.136197i
$169$	−9.53825	−	6.92995i	−0.733712	−	0.533073i
$170$	−4.68940	+	7.16956i	−0.359661	+	0.549880i
$171$	0.0467088	+	0.444405i	0.00357191	+	0.0339845i
$172$	8.52368	−	0.895875i	0.649925	−	0.0683098i
$173$	−10.5422	−	9.49221i	−0.801506	−	0.721680i	0.162745	−	0.986668i	$-0.447965\pi$
$173$	−10.5422	−	9.49221i	−0.801506	−	0.721680i	−0.964252	+	0.264989i	$0.914632\pi$
$174$	7.78187			0.589942
$175$	13.1470	+	1.46860i	0.993819	+	0.111016i
$176$	17.9507			1.35309
$177$	1.96607	+	1.77026i	0.147779	+	0.133061i
$178$	4.24187	−	0.445839i	0.317942	−	0.0334170i
$179$	1.24185	+	11.8154i	0.0928202	+	0.883125i	0.937531	+	0.347902i	$0.113106\pi$
$179$	1.24185	+	11.8154i	0.0928202	+	0.883125i	−0.844711	+	0.535223i	$0.820228\pi$
$180$	−0.180900	−	3.68233i	−0.0134835	−	0.274465i
$181$	−17.9503	−	13.0417i	−1.33424	−	0.969379i	−0.999635	−	0.0270192i	$-0.991398\pi$
$181$	−17.9503	−	13.0417i	−1.33424	−	0.969379i	−0.334601	−	0.942360i	$-0.608602\pi$
$182$	−4.49772	−	3.26765i	−0.333393	−	0.242214i
$183$	6.65556	−	9.16059i	0.491993	−	0.677171i
$184$	5.31537	−	1.12982i	0.391854	−	0.0832912i
$185$	−1.03029	+	18.5005i	−0.0757487	+	1.36018i
$186$	3.85927	+	0.820314i	0.282976	+	0.0601484i
$187$	1.63475	+	7.69088i	0.119544	+	0.562413i
$188$	5.71019	+	1.85535i	0.416458	+	0.135315i
$189$	−1.96614	+	1.77039i	−0.143016	+	0.128777i
$190$	−1.70343	+	0.860932i	−0.123580	+	0.0624586i
$191$	18.2529	−	3.87978i	1.32073	−	0.280731i	0.506989	−	0.861953i	$-0.330759\pi$
$191$	18.2529	−	3.87978i	1.32073	−	0.280731i	0.813745	+	0.581222i	$0.197425\pi$
$192$	−2.02832	−	4.55568i	−0.146381	−	0.328778i
$193$	−21.7993	−	12.5858i	−1.56915	−	0.905949i	−0.996268	−	0.0863102i	$-0.972492\pi$
$193$	−21.7993	−	12.5858i	−1.56915	−	0.905949i	−0.572881	−	0.819639i	$-0.694174\pi$
$194$	0.371403	−	3.53367i	0.0266652	−	0.253702i
$195$	2.18799	+	1.12387i	0.156685	+	0.0804820i
$196$	9.33748	+	6.78350i	0.666963	+	0.484536i
$197$	9.56075	+	13.1592i	0.681175	+	0.937557i	0.999947	−	0.0102742i	$-0.00327042\pi$
$197$	9.56075	+	13.1592i	0.681175	+	0.937557i	−0.318772	+	0.947831i	$0.603270\pi$
$198$	−5.56480	−	5.01056i	−0.395473	−	0.356085i
$199$	3.80524	−	6.59086i	0.269746	−	0.467214i	−0.699050	−	0.715073i	$-0.746394\pi$
$199$	3.80524	−	6.59086i	0.269746	−	0.467214i	0.968796	+	0.247859i	$0.0797269\pi$
$200$	−3.07336	+	1.34431i	−0.217319	+	0.0950573i
$201$	−1.68160	−	2.91261i	−0.118611	−	0.205440i
$202$	−34.8859	+	11.3351i	−2.45456	+	0.797536i
$203$	5.38908	−	9.33459i	0.378239	−	0.655160i
$204$	2.67540	−	1.94379i	0.187315	−	0.136092i
$205$	−0.706627	+	1.08035i	−0.0493530	+	0.0754551i
$206$	−11.4229	+	5.08579i	−0.795869	+	0.354344i
$207$	−7.01457	−	4.04986i	−0.487546	−	0.281485i
$208$	5.00956	+	0.526526i	0.347350	+	0.0365080i
$209$	−0.541314	+	1.66599i	−0.0374435	+	0.115239i
$210$	−10.0523	−	5.16316i	−0.693675	−	0.356292i
$211$	−5.68863	−	17.5078i	−0.391621	−	1.20529i	−0.931562	−	0.363583i	$-0.881553\pi$
$211$	−5.68863	−	17.5078i	−0.391621	−	1.20529i	0.539941	−	0.841703i	$-0.318447\pi$
$212$	−0.728575	−	3.42767i	−0.0500387	−	0.235414i
$213$	−11.4749	+	10.3320i	−0.786245	+	0.707938i
$214$	−28.8002	−	6.12167i	−1.96874	−	0.418469i
$215$	−3.04511	+	11.2175i	−0.207675	+	0.765029i
$216$	0.207320	−	0.638065i	0.0141063	−	0.0434148i
$217$	3.65660	−	4.06124i	0.248226	−	0.275695i
$218$			10.1258i			0.685803i
$219$	−0.514596	+	4.89605i	−0.0347732	+	0.330845i
$220$	5.22351	−	13.4757i	0.352169	−	0.908533i
$221$	0.230627	+	2.19427i	0.0155136	+	0.147602i
$222$	6.43810	−	14.4602i	0.432097	−	0.970505i
$223$	20.1442	−	6.54526i	1.34896	−	0.438303i	0.456616	−	0.889664i	$-0.349061\pi$
$223$	20.1442	−	6.54526i	1.34896	−	0.438303i	0.892341	+	0.451361i	$0.149061\pi$
$224$	−19.4847	−	2.04752i	−1.30188	−	0.136806i
$225$	4.74507	+	1.57618i	0.316338	+	0.105078i
$226$	−14.3632	−	24.8778i	−0.955427	−	1.65485i
$227$	0.761225	−	3.58128i	0.0505243	−	0.237698i	−0.945638	−	0.325220i	$-0.894562\pi$
$227$	0.761225	−	3.58128i	0.0505243	−	0.237698i	0.996163	+	0.0875222i	$0.0278949\pi$
$228$	0.732724	−	0.0770124i	0.0485258	−	0.00510027i
$229$	−9.62020	−	4.28319i	−0.635721	−	0.283041i	0.0634619	−	0.997984i	$-0.479786\pi$
$229$	−9.62020	−	4.28319i	−0.635721	−	0.283041i	−0.699183	+	0.714943i	$0.746453\pi$
$230$	5.52384	−	34.1524i	0.364232	−	2.25194i
$231$	−9.86404	+	3.20524i	−0.649006	+	0.210889i
$232$			2.73319i			0.179442i
$233$	−2.40807	−	0.253099i	−0.157758	−	0.0165811i	0.0253201	−	0.999679i	$-0.491940\pi$
$233$	−2.40807	−	0.253099i	−0.157758	−	0.0165811i	−0.183078	+	0.983098i	$0.558606\pi$
$234$	−1.40602	−	1.56154i	−0.0919141	−	0.102081i
$235$	−5.14504	+	6.31125i	−0.335625	+	0.411700i
$236$	2.91876	−	3.24161i	0.189995	−	0.211011i
$237$	1.62781	+	0.528906i	0.105737	+	0.0343561i
$238$	−1.05977	−	10.0810i	−0.0686944	−	0.653456i
$239$	5.18733	+	15.9650i	0.335540	+	1.03269i	0.966455	+	0.256835i	$0.0826797\pi$
$239$	5.18733	+	15.9650i	0.335540	+	1.03269i	−0.630915	+	0.775852i	$0.717320\pi$
$240$	10.2268	−	0.502409i	0.660139	−	0.0324304i
$241$	−15.1325	−	16.8064i	−0.974772	−	1.08259i	−0.996564	−	0.0828310i	$-0.973604\pi$
$241$	−15.1325	−	16.8064i	−0.974772	−	1.08259i	0.0217920	−	0.999763i	$-0.493063\pi$
$242$	−3.39331	−	7.62151i	−0.218131	−	0.489929i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−15.1038	−	10.9735i	−0.966919	−	0.702508i
$245$	−13.1548	+	8.48247i	−0.840427	+	0.541925i
$246$	0.892169	−	0.648198i	0.0568826	−	0.0413276i
$247$	−0.199933	+	0.449056i	−0.0127214	+	0.0285727i
$248$	−0.288115	+	1.35547i	−0.0182953	+	0.0860726i
$249$	5.61742	−	9.72966i	0.355990	−	0.616592i
$250$	0.908263	+	21.3371i	0.0574436	+	1.34948i
$251$	−27.5962			−1.74186			−0.870929	−	0.491409i	$-0.836482\pi$
$251$	−27.5962			−1.74186			−0.870929	+	0.491409i	$0.836482\pi$
$252$	2.91898	+	3.24172i	0.183878	+	0.204209i
$253$	−18.6634	−	25.6880i	−1.17336	−	1.61499i
$254$	−6.03119	−	2.68526i	−0.378431	−	0.168488i
$255$	1.14660	+	4.33587i	0.0718027	+	0.271523i
$256$	18.3329	−	8.16233i	1.14581	−	0.510146i
$257$	2.25355	−	1.30109i	0.140573	−	0.0811597i	−0.428064	−	0.903748i	$-0.640804\pi$
$257$	2.25355	−	1.30109i	0.140573	−	0.0811597i	0.568637	+	0.822589i	$0.307471\pi$
$258$	5.83638	−	8.03309i	0.363357	−	0.500118i
$259$	−12.8870	−	17.7366i	−0.800757	−	1.10210i
$260$	1.85301	−	3.60750i	0.114919	−	0.223727i
$261$	2.72597	−	3.02750i	0.168733	−	0.187397i
$262$	−4.11846	+	3.70828i	−0.254439	+	0.229098i
$263$	−16.2514	+	14.6329i	−1.00211	+	0.902300i	−0.995218	−	0.0976761i	$-0.968859\pi$
$263$	−16.2514	+	14.6329i	−1.00211	+	0.902300i	−0.00688764	+	0.999976i	$0.502192\pi$
$264$	1.75983	−	1.95449i	0.108310	−	0.120291i
$265$	4.69149	+	0.758807i	0.288196	+	0.0466132i
$266$	0.918503	−	2.06310i	0.0563170	−	0.126497i
$267$	1.31247	−	1.80646i	0.0803217	−	0.110553i
$268$	−4.80225	+	2.77258i	−0.293344	+	0.169362i
$269$	−25.4087	+	11.3127i	−1.54920	+	0.689747i	−0.990230	−	0.139444i	$-0.955469\pi$
$269$	−25.4087	+	11.3127i	−1.54920	+	0.689747i	−0.558966	+	0.829190i	$0.688802\pi$
$270$	−3.31060	−	2.69886i	−0.201477	−	0.164247i
$271$	11.4604	+	5.10251i	0.696171	+	0.309955i	0.724139	−	0.689654i	$-0.242237\pi$
$271$	11.4604	+	5.10251i	0.696171	+	0.309955i	−0.0279686	+	0.999609i	$0.508904\pi$
$272$	5.39843	+	7.43029i	0.327328	+	0.450528i
$273$	−2.84680	+	0.605167i	−0.172296	+	0.0366264i
$274$	−38.3003			−2.31381
$275$	14.4800	+	13.2105i	0.873178	+	0.796624i
$276$	−6.67731	+	11.5654i	−0.401927	+	0.696158i
$277$	−4.33783	+	20.4079i	−0.260635	+	1.22619i	0.631842	+	0.775097i	$0.282299\pi$
$277$	−4.33783	+	20.4079i	−0.260635	+	1.22619i	−0.892477	+	0.451093i	$0.851034\pi$
$278$	16.1873	−	36.3573i	0.970850	−	2.18056i
$279$	1.67103	−	1.21408i	0.100042	−	0.0726849i
$280$	1.81343	−	3.53062i	0.108373	−	0.210995i
$281$	0.612277	+	0.444845i	0.0365254	+	0.0265372i	0.605898	−	0.795542i	$-0.292814\pi$
$281$	0.612277	+	0.444845i	0.0365254	+	0.0265372i	−0.569373	+	0.822079i	$0.692814\pi$
$282$	6.02402	−	3.47797i	0.358725	−	0.207110i
$283$	7.05418	+	15.8440i	0.419328	+	0.941825i	0.992483	+	0.122379i	$0.0390523\pi$
$283$	7.05418	+	15.8440i	0.419328	+	0.941825i	−0.573156	+	0.819446i	$0.694281\pi$
$284$	17.0352	+	18.9195i	1.01085	+	1.12266i
$285$	−0.261768	+	0.964295i	−0.0155058	+	0.0571199i
$286$	−2.54545	−	7.83408i	−0.150515	−	0.463239i
$287$	−0.159692	−	1.51907i	−0.00942632	−	0.0896680i
$288$	−7.04264	−	2.28829i	−0.414992	−	0.134839i
$289$	8.68338	−	9.64387i	0.510787	−	0.567287i
$290$	16.2245	+	6.28902i	0.952738	+	0.369304i
$291$	−1.24465	−	1.38233i	−0.0729629	−	0.0810335i
$292$	8.07249	+	0.848453i	0.472407	+	0.0496520i
$293$		−	6.35894i		−	0.371493i	−0.982598	−	0.185747i	$-0.940530\pi$
$293$		−	6.35894i		−	0.371493i	0.982598	−	0.185747i	$-0.0594704\pi$
$294$	13.0789	−	2.78057i	0.762779	−	0.162166i
$295$	2.66843	+	5.27974i	0.155362	+	0.307398i
$296$	5.07878	+	2.26122i	0.295198	+	0.131431i
$297$	−3.89867	+	0.409767i	−0.226224	+	0.0237771i
$298$	2.24754	−	10.5738i	0.130196	−	0.612526i
$299$	−4.45498	−	7.71626i	−0.257638	−	0.446243i
$300$	2.59876	−	7.82355i	0.150040	−	0.451693i
$301$	−5.59414	−	12.5640i	−0.322441	−	0.724175i
$302$	−11.2615	+	3.65908i	−0.648026	+	0.210557i
$303$	−7.81058	+	17.5429i	−0.448706	+	1.00781i
$304$	0.213884	+	2.03497i	0.0122671	+	0.116714i
$305$	21.2795	−	13.7203i	1.21846	−	0.785621i
$306$	0.400477	−	3.81028i	0.0228937	−	0.217819i
$307$			14.5271i			0.829105i	0.910025	+	0.414553i	$0.136062\pi$
$307$			14.5271i			0.829105i	−0.910025	+	0.414553i	$0.863938\pi$
$308$	5.28472	+	16.2636i	0.301125	+	0.926704i
$309$	−2.02280	+	6.22555i	−0.115073	+	0.354159i
$310$	7.38331	+	4.82921i	0.419344	+	0.274281i
$311$	8.54750	+	1.81683i	0.484685	+	0.103023i	0.443772	−	0.896140i	$-0.353640\pi$
$311$	8.54750	+	1.81683i	0.484685	+	0.103023i	0.0409128	+	0.999163i	$0.486973\pi$
$312$	0.548451	−	0.493828i	0.0310499	−	0.0279575i
$313$	3.99574	+	18.7985i	0.225852	+	1.06255i	0.934217	+	0.356706i	$0.116100\pi$
$313$	3.99574	+	18.7985i	0.225852	+	1.06255i	−0.708364	+	0.705847i	$0.750567\pi$
$314$	0.702040	+	2.16066i	0.0396184	+	0.121933i
$315$	−5.53000	+	2.10216i	−0.311580	+	0.118443i
$316$	0.872047	−	2.68388i	0.0490565	−	0.150980i
$317$	2.97772	+	0.312971i	0.167245	+	0.0175782i	0.187781	−	0.982211i	$-0.439870\pi$
$317$	2.97772	+	0.312971i	0.167245	+	0.0175782i	−0.0205356	+	0.999789i	$0.506537\pi$
$318$	−3.51591	−	2.02991i	−0.197163	−	0.113832i
$319$	14.5896	−	6.49570i	0.816860	−	0.363689i
$320$	−0.547143	−	11.1374i	−0.0305862	−	0.622600i
$321$	−12.4702	+	9.06017i	−0.696021	+	0.505689i
$322$	20.4681	+	35.4502i	1.14064	+	1.97556i
$323$	−0.852393	+	0.276959i	−0.0474284	+	0.0154104i
$324$	0.824388	+	1.42788i	0.0457993	+	0.0793267i
$325$	3.65350	+	4.11142i	0.202659	+	0.228061i
$326$	18.4317	−	31.9246i	1.02084	−	1.76814i
$327$	3.93938	+	3.54703i	0.217848	+	0.196151i
$328$	0.227663	+	0.313352i	0.0125706	+	0.0173020i
$329$	−0.000194970	−	9.63455i	−1.07490e−5	−	0.531170i
$330$	−7.55278	−	14.9439i	−0.415767	−	0.822633i
$331$	−0.517010	+	4.91902i	−0.0284174	+	0.270374i	0.971082	+	0.238745i	$0.0767361\pi$
$331$	−0.517010	+	4.91902i	−0.0284174	+	0.270374i	−0.999500	+	0.0316286i	$0.989931\pi$
$332$	−16.0420	−	9.26187i	−0.880420	−	0.508311i
$333$	−3.37042	−	7.57009i	−0.184698	−	0.414838i
$334$	33.8179	−	7.18821i	1.85043	−	0.393321i
$335$	−1.15212	−	7.43156i	−0.0629473	−	0.406030i
$336$	−9.00314	+	8.10679i	−0.491161	+	0.442262i
$337$	−18.2453	−	5.92827i	−0.993887	−	0.322934i	−0.233467	−	0.972365i	$-0.575007\pi$
$337$	−18.2453	−	5.92827i	−0.993887	−	0.322934i	−0.760420	+	0.649431i	$0.775007\pi$
$338$	4.68235	+	22.0287i	0.254686	+	1.19820i
$339$	−14.7100	−	3.12671i	−0.798937	−	0.169819i
$340$	7.14888	−	1.89048i	0.387702	−	0.102526i
$341$	7.92017	−	1.68348i	0.428901	−	0.0911658i
$342$	0.501715	−	0.690551i	0.0271296	−	0.0373407i
$343$	5.72201	−	17.6142i	0.308959	−	0.951075i
$344$	2.82142	+	2.04988i	0.152121	+	0.110522i
$345$	−11.3518	−	14.1125i	−0.611162	−	0.759793i
$346$	2.83247	+	26.9491i	0.152274	+	1.44879i
$347$	21.1624	−	2.22426i	1.13606	−	0.119405i	0.482228	−	0.876046i	$-0.339828\pi$
$347$	21.1624	−	2.22426i	1.13606	−	0.119405i	0.653831	+	0.756641i	$0.273161\pi$
$348$	−4.99166	−	4.49451i	−0.267581	−	0.240931i
$349$	31.1803			1.66904			0.834522	−	0.550974i	$-0.185744\pi$
$349$	31.1803			1.66904			0.834522	+	0.550974i	$0.185744\pi$
$350$	−16.7855	−	18.8887i	−0.897225	−	1.00964i
$351$	−1.10003			−0.0587154
$352$	−21.5727	−	19.4242i	−1.14983	−	1.03531i
$353$	28.8718	−	3.03455i	1.53669	−	0.161513i	0.701979	−	0.712198i	$-0.252300\pi$
$353$	28.8718	−	3.03455i	1.53669	−	0.161513i	0.834713	+	0.550685i	$0.185634\pi$
$354$	−0.528243	−	5.02590i	−0.0280758	−	0.267123i
$355$	−32.2741	+	12.2678i	−1.71293	+	0.651108i
$356$	−2.97844	−	2.16396i	−0.157857	−	0.114690i
$357$	−4.29321	−	3.11907i	−0.227221	−	0.165079i
$358$	13.3391	−	18.3597i	0.704993	−	0.970340i
$359$	−21.8711	+	4.64884i	−1.15431	+	0.245356i	−0.745017	−	0.667046i	$-0.767559\pi$
$359$	−21.8711	+	4.64884i	−1.15431	+	0.245356i	−0.409295	+	0.912402i	$0.634225\pi$
$360$	0.947905	−	1.16276i	0.0499590	−	0.0612830i
$361$	18.3895	+	3.90881i	0.967868	+	0.205727i
$362$	8.81184	+	41.4565i	0.463140	+	2.17890i
$363$	−4.15378	−	1.34965i	−0.218017	−	0.0708380i
$364$	0.997784	+	4.69374i	0.0522981	+	0.246019i
$365$	−5.02970	+	9.79198i	−0.263266	+	0.512536i
$366$	−21.1565	+	4.49695i	−1.10587	+	0.235060i
$367$	3.89150	+	8.74045i	0.203135	+	0.456248i	0.986172	−	0.165727i	$-0.0529972\pi$
$367$	3.89150	+	8.74045i	0.203135	+	0.456248i	−0.783037	+	0.621975i	$0.786331\pi$
$368$	−32.1203	−	18.5447i	−1.67439	−	0.966709i
$369$	0.0603463	−	0.574156i	0.00314150	−	0.0298894i
$370$	25.1091	−	24.9453i	1.30536	−	1.29684i
$371$	−4.86977	+	2.81169i	−0.252826	+	0.145976i
$372$	−2.00174	−	2.75516i	−0.103785	−	0.142848i
$373$	−2.93813	−	2.64551i	−0.152131	−	0.136979i	0.589551	−	0.807731i	$-0.299305\pi$
$373$	−2.93813	−	2.64551i	−0.152131	−	0.136979i	−0.741682	+	0.670752i	$0.765971\pi$
$374$	7.50957	−	13.0070i	0.388311	−	0.672574i
$375$	8.61926	+	7.12098i	0.445097	+	0.367726i
$376$	1.22155	+	2.11579i	0.0629966	+	0.109113i
$377$	4.26209	−	1.38484i	0.219509	−	0.0713227i
$378$	5.05385		0.000102272i	0.259942		5.26032e-6i
$379$	−27.4089	+	19.9137i	−1.40790	+	1.02290i	−0.414276	+	0.910151i	$0.635965\pi$
$379$	−27.4089	+	19.9137i	−1.40790	+	1.02290i	−0.993624	+	0.112748i	$0.964035\pi$
$380$	1.58991	+	0.431596i	0.0815605	+	0.0221404i
$381$	−3.15740	+	1.40577i	−0.161759	+	0.0720195i
$382$	−30.8697	−	17.8226i	−1.57943	−	0.911884i
$383$	31.3451	+	3.29450i	1.60166	+	0.168341i	0.862809	−	0.505531i	$-0.168703\pi$
$383$	31.3451	+	3.29450i	1.60166	+	0.168341i	0.738849	+	0.673871i	$0.235370\pi$
$384$	1.63298	−	5.02581i	0.0833329	−	0.256472i
$385$	−23.1560	−	1.28909i	−1.18014	−	0.0656982i
$386$	14.8583	+	45.7290i	0.756266	+	2.32755i
$387$	−1.08076	−	5.08459i	−0.0549383	−	0.258464i
$388$	−2.27915	+	2.05215i	−0.115706	+	0.104182i
$389$	10.9790	+	2.33367i	0.556660	+	0.118322i	0.477647	−	0.878552i	$-0.341490\pi$
$389$	10.9790	+	2.33367i	0.556660	+	0.118322i	0.0790129	+	0.996874i	$0.474823\pi$
$390$	−1.66945	−	4.39197i	−0.0845357	−	0.222396i
$391$	5.02021	−	15.4506i	0.253883	−	0.781371i
$392$	0.976604	+	4.59365i	0.0493259	+	0.232014i
$393$			2.90127i			0.146350i
$394$	3.24774	−	30.9002i	0.163619	−	1.55673i
$395$	2.96639	+	2.41826i	0.149255	+	0.121676i
$396$	0.675613	+	6.42803i	0.0339508	+	0.323021i
$397$	−4.08091	+	9.16587i	−0.204815	+	0.460022i	−0.986523	−	0.163623i	$-0.947682\pi$
$397$	−4.08091	+	9.16587i	−0.204815	+	0.460022i	0.781708	+	0.623644i	$0.214349\pi$
$398$	−13.8258	+	4.49229i	−0.693027	+	0.225178i
$399$	−0.480891	−	1.08004i	−0.0240747	−	0.0540696i
$400$	21.7281	+	7.21746i	1.08640	+	0.360873i
$401$	−12.4160	−	21.5052i	−0.620028	−	1.07392i	−0.989480	−	0.144670i	$-0.953788\pi$
$401$	−12.4160	−	21.5052i	−0.620028	−	1.07392i	0.369452	−	0.929250i	$-0.379545\pi$
$402$	−1.33569	+	6.28391i	−0.0666180	+	0.313413i
$403$	2.25968	−	0.237502i	0.112563	−	0.0118308i
$404$	28.9242	+	12.8779i	1.43903	+	0.640699i
$405$	−2.20967	+	0.342568i	−0.109799	+	0.0170224i
$406$	−19.5811	+	6.36271i	−0.971792	+	0.315776i
$407$		−	32.4843i		−	1.61019i
$408$	1.33827	+	0.140657i	0.0662540	+	0.00696358i
$409$	14.9419	+	16.5947i	0.738830	+	0.820554i	0.989042	−	0.147638i	$-0.0471669\pi$
$409$	14.9419	+	16.5947i	0.738830	+	0.820554i	−0.250212	+	0.968191i	$0.580500\pi$
$410$	2.38395	−	0.630422i	0.117735	−	0.0311343i
$411$	−13.4165	+	14.9005i	−0.661788	+	0.734990i
$412$	10.2645	+	3.33515i	0.505697	+	0.164311i
$413$	−6.39453	−	2.84687i	−0.314654	−	0.140085i
$414$	4.78108	+	14.7147i	0.234977	+	0.723186i
$415$	19.5750	−	15.7457i	0.960899	−	0.772927i
$416$	−5.45062	−	6.05353i	−0.267239	−	0.296798i
$417$	−8.47424	−	19.0335i	−0.414985	−	0.932072i
$418$	2.89782	−	1.67306i	0.141737	−	0.0818318i
$419$	26.7340	+	19.4234i	1.30604	+	0.948894i	0.999995	−	0.00312304i	$-0.000994097\pi$
$419$	26.7340	+	19.4234i	1.30604	+	0.948894i	0.306045	+	0.952017i	$0.400994\pi$
$420$	3.46599	+	9.11773i	0.169123	+	0.444900i
$421$	−13.2532	+	9.62903i	−0.645922	+	0.469290i	−0.861880	−	0.507113i	$-0.830713\pi$
$421$	−13.2532	+	9.62903i	−0.645922	+	0.469290i	0.215957	+	0.976403i	$0.430713\pi$
$422$	−14.3025	+	32.1239i	−0.696235	+	1.56377i
$423$	0.757114	−	3.56194i	0.0368122	−	0.173188i
$424$	0.712956	−	1.23488i	0.0346242	−	0.0599709i
$425$	−1.11353	+	9.96656i	−0.0540142	+	0.483449i
$426$	29.4950			1.42904
$427$	−9.25700	+	28.4921i	−0.447978	+	1.37883i
$428$	14.9382	+	20.5606i	0.722064	+	0.993836i
$429$	−3.93947	−	1.75397i	−0.190200	−	0.0846823i
$430$	18.6604	−	12.0316i	0.899885	−	0.580214i
$431$	−26.3711	+	11.7412i	−1.27025	+	0.565552i	−0.927482	−	0.373868i	$-0.878031\pi$
$431$	−26.3711	+	11.7412i	−1.27025	+	0.565552i	−0.342768	+	0.939420i	$0.611365\pi$
$432$	−3.96561	+	2.28955i	−0.190795	+	0.110156i
$433$	0.0254359	−	0.0350095i	0.00122237	−	0.00168245i	−0.808405	−	0.588626i	$-0.799669\pi$
$433$	0.0254359	−	0.0350095i	0.00122237	−	0.00168245i	0.809628	+	0.586944i	$0.199669\pi$
$434$	−10.3816	+	1.09136i	−0.498332	+	0.0523870i
$435$	8.13013	−	4.10905i	0.389810	−	0.197014i
$436$	5.84826	−	6.49515i	0.280081	−	0.311061i
$437$	2.68973	−	2.42184i	0.128667	−	0.115852i
$438$	6.98842	−	6.29240i	0.333919	−	0.300662i
$439$	14.7263	−	16.3553i	0.702850	−	0.780594i	−0.280977	−	0.959715i	$-0.590658\pi$
$439$	14.7263	−	16.3553i	0.702850	−	0.780594i	0.983827	+	0.179120i	$0.0573251\pi$
$440$	5.24866	−	2.65272i	0.250220	−	0.126464i
$441$	3.49975	−	6.06232i	0.166655	−	0.288682i
$442$	2.47723	−	3.40962i	0.117830	−	0.162179i
$443$	14.2681	−	8.23771i	0.677899	−	0.391385i	−0.121164	−	0.992633i	$-0.538663\pi$
$443$	14.2681	−	8.23771i	0.677899	−	0.391385i	0.799063	+	0.601247i	$0.205329\pi$
$444$	−12.4814	+	5.55707i	−0.592340	+	0.263727i
$445$	4.19630	−	2.70562i	0.198923	−	0.128259i
$446$	−36.9614	−	16.4563i	−1.75017	−	0.779227i
$447$	−3.32639	−	4.57839i	−0.157333	−	0.216550i
$448$	8.82861	+	9.80477i	0.417113	+	0.463232i
$449$	−35.8664			−1.69264			−0.846321	−	0.532674i	$-0.821187\pi$
$449$	−35.8664			−1.69264			−0.846321	+	0.532674i	$0.821187\pi$
$450$	−4.72120	−	8.30239i	−0.222560	−	0.391378i
$451$	1.13159	−	1.95997i	0.0532844	−	0.0922912i
$452$	−5.15524	+	24.2535i	−0.242482	+	1.14079i
$453$	−2.52133	+	5.66300i	−0.118462	+	0.266071i
$454$	−5.65803	+	4.11080i	−0.265545	+	0.192929i
$455$	−6.42442	−	1.03896i	−0.301181	−	0.0487071i
$456$	0.242539	+	0.176215i	0.0113579	+	0.00825201i
$457$	7.35734	−	4.24776i	0.344162	−	0.198702i	−0.317949	−	0.948108i	$-0.602994\pi$
$457$	7.35734	−	4.24776i	0.344162	−	0.198702i	0.662111	+	0.749406i	$0.269661\pi$
$458$	8.18165	+	18.3763i	0.382303	+	0.858667i
$459$	−1.34209	−	1.49054i	−0.0626432	−	0.0695723i
$460$	−23.2684	+	18.7166i	−1.08489	+	0.872667i
$461$	5.41594	+	16.6685i	0.252245	+	0.776331i	0.994360	+	0.106058i	$0.0338230\pi$
$461$	5.41594	+	16.6685i	0.252245	+	0.776331i	−0.742115	+	0.670273i	$0.766177\pi$
$462$	18.0992	+	8.05783i	0.842050	+	0.374884i
$463$	24.5660	+	7.98198i	1.14168	+	0.370954i	0.818003	−	0.575214i	$-0.195081\pi$
$463$	24.5660	+	7.98198i	1.14168	+	0.370954i	0.323676	+	0.946168i	$0.395081\pi$
$464$	12.4825	−	13.8632i	0.579484	−	0.643582i
$465$	4.46514	−	1.18078i	0.207066	−	0.0547574i
$466$	3.09485	+	3.43718i	0.143366	+	0.159224i
$467$	9.46947	+	0.995282i	0.438195	+	0.0460561i	0.321058	−	0.947060i	$-0.395962\pi$
$467$	9.46947	+	0.995282i	0.438195	+	0.0460561i	0.117137	+	0.993116i	$0.462628\pi$
$468$			1.81371i			0.0838386i
$469$	6.61276	+	5.95391i	0.305349	+	0.274926i
$470$	15.3703	−	2.38289i	0.708981	−	0.109914i
$471$	1.08652	+	0.483748i	0.0500640	+	0.0222899i
$472$	1.76522	−	0.185532i	0.0812508	−	0.00853980i
$473$	4.23675	−	19.9323i	0.194806	−	0.916490i
$474$	−1.63471	−	2.83139i	−0.0750845	−	0.130050i
$475$	−1.32507	+	1.79892i	−0.0607984	+	0.0825403i
$476$	−5.14264	+	7.07854i	−0.235713	+	0.324444i
$477$	−2.02134	+	0.656774i	−0.0925510	+	0.0300716i
$478$	13.0421	−	29.2931i	0.596533	−	1.33983i
$479$	−4.28910	−	40.8081i	−0.195974	−	1.86457i	−0.444282	−	0.895887i	$-0.646541\pi$
$479$	−4.28910	−	40.8081i	−0.195974	−	1.86457i	0.248309	−	0.968681i	$-0.420125\pi$
$480$	−12.8340	−	10.4625i	−0.585789	−	0.477545i
$481$	0.952820	−	9.06548i	0.0434449	−	0.413350i
$482$			43.1990i			1.96766i
$483$	20.9617	+	4.45509i	0.953788	+	0.202714i
$484$	−2.22526	+	6.84865i	−0.101148	+	0.311302i
$485$	−1.47785	−	3.88792i	−0.0671058	−	0.176541i
$486$	1.86843	+	0.397148i	0.0847539	+	0.0180150i
$487$	−25.0937	+	22.5945i	−1.13710	+	1.02385i	−0.137661	+	0.990479i	$0.543958\pi$
$487$	−25.0937	+	22.5945i	−1.13710	+	1.02385i	−0.999443	+	0.0333734i	$0.989375\pi$
$488$	−1.57944	−	7.43069i	−0.0714980	−	0.336371i
$489$	−5.96353	−	18.3538i	−0.269680	−	0.829990i
$490$	29.5156	+	4.77266i	1.33338	+	0.215607i
$491$	−1.27380	+	3.92036i	−0.0574858	+	0.176923i	−0.975676	−	0.219216i	$-0.929650\pi$
$491$	−1.27380	+	3.92036i	−0.0574858	+	0.176923i	0.918191	+	0.396139i	$0.129650\pi$
$492$	−0.946655	−	0.0994974i	−0.0426785	−	0.00448569i
$493$	7.07637	+	4.08554i	0.318703	+	0.184004i
$494$	0.857776	−	0.381907i	0.0385932	−	0.0171828i
$495$	−8.45956	−	2.29643i	−0.380229	−	0.103217i
$496$	7.65182	−	5.55937i	0.343577	−	0.249623i
$497$	20.4258	−	35.3801i	0.916220	−	1.58701i
$498$	−20.4102	+	6.63167i	−0.914602	+	0.297172i
$499$	12.1780	+	21.0929i	0.545162	+	0.944249i	0.998597	+	0.0529591i	$0.0168653\pi$
$499$	12.1780	+	21.0929i	0.545162	+	0.944249i	−0.453434	+	0.891290i	$0.649801\pi$
$500$	11.7409	−	14.2112i	0.525069	−	0.635545i
$501$	9.04978	−	15.6747i	0.404315	−	0.700293i
$502$	39.1739	+	35.2723i	1.74842	+	1.57428i
$503$	6.13377	+	8.44242i	0.273491	+	0.376429i	0.923565	−	0.383443i	$-0.125262\pi$
$503$	6.13377	+	8.44242i	0.273491	+	0.376429i	−0.650073	+	0.759872i	$0.725262\pi$
$504$	3.59206e−5		1.77504i	1.60003e−6		0.0790665i
$505$	−30.4619	+	30.2632i	−1.35554	+	1.34669i
$506$	−6.33987	+	60.3199i	−0.281842	+	2.68154i
$507$	10.2104	+	5.89496i	0.453459	+	0.261805i
$508$	2.31779	+	5.20584i	0.102835	+	0.230972i
$509$	−8.68040	+	1.84508i	−0.384752	+	0.0817816i	−0.396227	−	0.918153i	$-0.629681\pi$
$509$	−8.68040	+	1.84508i	−0.384752	+	0.0817816i	0.0114749	+	0.999934i	$0.496347\pi$
$510$	3.91429	−	7.62046i	0.173328	−	0.337440i
$511$	−2.70833	−	12.7404i	−0.119809	−	0.563602i
$512$	−26.4054	−	8.57962i	−1.16696	−	0.379169i
$513$	−0.0929059	−	0.437088i	−0.00410190	−	0.0192979i
$514$	−4.86200	−	1.03345i	−0.214454	−	0.0455835i
$515$	−9.24863	+	11.3450i	−0.407543	+	0.499920i
$516$	−8.38335	+	1.78194i	−0.369056	+	0.0784453i
$517$	8.39080	−	11.5489i	0.369027	−	0.507922i
$518$	−4.37667	+	41.6494i	−0.192300	+	1.82997i
$519$	11.4766	+	8.33826i	0.503768	+	0.366009i
$520$	1.54257	−	0.586351i	0.0676461	−	0.0257132i
$521$	1.00352	+	9.54786i	0.0439650	+	0.418299i	0.994263	+	0.106959i	$0.0341113\pi$
$521$	1.00352	+	9.54786i	0.0439650	+	0.418299i	−0.950298	+	0.311341i	$0.899222\pi$
$522$	−7.73924	+	0.813427i	−0.338737	+	0.0356027i
$523$	9.01842	+	8.12022i	0.394348	+	0.355072i	0.842322	−	0.538974i	$-0.181188\pi$
$523$	9.01842	+	8.12022i	0.394348	+	0.355072i	−0.447975	+	0.894046i	$0.647855\pi$
$524$	4.78354			0.208970
$525$	−13.2285	−	0.0863206i	−0.577338	−	0.00376734i
$526$	41.7726			1.82137
$527$	3.07872	+	2.77209i	0.134111	+	0.120754i
$528$	−17.8524	+	1.87636i	−0.776925	+	0.0816581i
$529$	4.45349	+	42.3721i	0.193630	+	1.84227i
$530$	−5.68988	−	7.07363i	−0.247153	−	0.307259i
$531$	−2.14034	−	1.55505i	−0.0928829	−	0.0674834i
$532$	−1.78074	+	0.792881i	−0.0772050	+	0.0343758i
$533$	0.373285	−	0.513782i	0.0161688	−	0.0222544i
$534$	−4.17203	+	0.886793i	−0.180542	+	0.0383753i
$535$	−33.3215	+	8.81169i	−1.44061	+	0.380963i
$536$	−2.20707	−	0.469127i	−0.0953308	−	0.0202632i
$537$	−2.47009	−	11.6209i	−0.106592	−	0.501478i
$538$	50.5280	+	16.4176i	2.17842	+	0.707811i
$539$	22.1996	−	16.1303i	0.956204	−	0.694782i
$540$	0.564818	+	3.64325i	0.0243059	+	0.156781i
$541$	−4.18059	+	0.888613i	−0.179738	+	0.0382044i	−0.296901	−	0.954908i	$-0.595953\pi$
$541$	−4.18059	+	0.888613i	−0.179738	+	0.0382044i	0.117163	+	0.993113i	$0.462620\pi$
$542$	−9.74669	−	21.8914i	−0.418656	−	0.940317i
$543$	19.2152	+	11.0939i	0.824603	+	0.476085i
$544$	1.55250	−	14.7711i	0.0665631	−	0.633305i
$545$	5.34669	+	10.5789i	0.229027	+	0.453151i
$546$	4.81464	+	2.77961i	0.206048	+	0.118956i
$547$	20.8611	+	28.7128i	0.891955	+	1.22767i	0.972964	+	0.230957i	$0.0741856\pi$
$547$	20.8611	+	28.7128i	0.891955	+	1.22767i	−0.0810095	+	0.996713i	$0.525814\pi$
$548$	24.5677	+	22.1208i	1.04948	+	0.944954i
$549$	−5.66156	+	9.80611i	−0.241629	+	0.418514i
$550$	−3.66983	−	37.2606i	−0.156482	−	1.58880i
$551$	0.910217	+	1.57654i	0.0387766	+	0.0671630i
$552$	−5.16815	+	1.67923i	−0.219971	+	0.0714730i
$553$	−4.52840		9.16390e-5i	−0.192567		3.89689e-6i
$554$	32.2422	−	23.4253i	1.36984	−	0.995247i
$555$	−0.909178	−	18.5068i	−0.0385925	−	0.785572i
$556$	−31.3819	+	13.9721i	−1.33089	+	0.592550i
$557$	−18.2010	−	10.5084i	−0.771203	−	0.445254i	0.0621008	−	0.998070i	$-0.480220\pi$
$557$	−18.2010	−	10.5084i	−0.771203	−	0.445254i	−0.833303	+	0.552816i	$0.813553\pi$
$558$	−3.92388	−	0.412416i	−0.166111	−	0.0174590i
$559$	1.76701	−	5.43831i	0.0747367	−	0.230016i
$560$	−25.3224	+	9.62597i	−1.07007	+	0.406772i
$561$	−2.42971	−	7.47787i	−0.102582	−	0.315716i
$562$	−0.300568	−	1.41406i	−0.0126787	−	0.0596486i
$563$	−8.68484	+	7.81987i	−0.366023	+	0.329568i	−0.831534	−	0.555474i	$-0.812537\pi$
$563$	−8.68484	+	7.81987i	−0.366023	+	0.329568i	0.465512	+	0.885042i	$0.345870\pi$
$564$	−5.87284	−	1.24831i	−0.247291	−	0.0525634i
$565$	−28.1422	−	18.4070i	−1.18395	−	0.774388i
$566$	10.2374	−	31.5074i	0.430310	−	1.32436i
$567$	1.77031	−	1.96621i	0.0743462	−	0.0825732i
$568$			10.3594i			0.434669i
$569$	−2.17488	+	20.6926i	−0.0911758	+	0.867480i	0.849367	+	0.527803i	$0.176984\pi$
$569$	−2.17488	+	20.6926i	−0.0911758	+	0.867480i	−0.940542	+	0.339676i	$0.889682\pi$
$570$	1.60411	−	1.03427i	0.0671888	−	0.0433209i
$571$	−4.06153	−	38.6429i	−0.169970	−	1.61715i	−0.664017	−	0.747718i	$-0.731150\pi$
$571$	−4.06153	−	38.6429i	−0.169970	−	1.61715i	0.494047	−	0.869435i	$-0.335517\pi$
$572$	−2.89190	+	6.49531i	−0.120916	+	0.271582i
$573$	−17.7474	+	5.76647i	−0.741407	+	0.240898i
$574$	−1.71492	+	2.36049i	−0.0715795	+	0.0985250i
$575$	−12.2624	−	38.5976i	−0.511377	−	1.60963i
$576$	2.49341	+	4.31870i	0.103892	+	0.179946i
$577$	8.81886	−	41.4895i	0.367134	−	1.72723i	−0.275719	−	0.961238i	$-0.588916\pi$
$577$	8.81886	−	41.4895i	0.367134	−	1.72723i	0.642852	−	0.765990i	$-0.277751\pi$
$578$	−24.6528	+	2.59111i	−1.02542	+	0.107776i
$579$	22.9955	+	10.2382i	0.955659	+	0.425487i
$580$	−6.77490	−	13.4048i	−0.281312	−	0.556602i
$581$	−6.17950	+	29.0752i	−0.256369	+	1.20624i
$582$			3.55313i			0.147282i
$583$	−8.28610	−	0.870905i	−0.343175	−	0.0360692i
$584$	2.21005	+	2.45451i	0.0914524	+	0.101568i
$585$	−2.29348	−	0.889006i	−0.0948236	−	0.0367559i
$586$	−8.12773	+	9.02676i	−0.335754	+	0.372892i
$587$	−38.0834	−	12.3741i	−1.57187	−	0.510732i	−0.611925	−	0.790916i	$-0.709605\pi$
$587$	−38.0834	−	12.3741i	−1.57187	−	0.510732i	−0.959946	+	0.280184i	$0.909605\pi$
$588$	−9.99540	−	5.77031i	−0.412203	−	0.237964i
$589$	0.285217	+	0.877806i	0.0117521	+	0.0361694i
$590$	2.96040	−	10.9055i	0.121878	−	0.448971i
$591$	−10.8839	−	12.0878i	−0.447703	−	0.497225i
$592$	−15.4335	−	34.6641i	−0.634311	−	1.42469i
$593$	−13.9622	+	8.06107i	−0.573358	+	0.331029i	−0.758490	−	0.651685i	$-0.774062\pi$
$593$	−13.9622	+	8.06107i	−0.573358	+	0.331029i	0.185131	+	0.982714i	$0.440729\pi$
$594$	6.05806	+	4.40144i	0.248565	+	0.180593i
$595$	−6.43027	−	9.97261i	−0.263615	−	0.408837i
$596$	−7.54873	+	5.48447i	−0.309208	+	0.224653i
$597$	−3.09546	+	6.95251i	−0.126689	+	0.284547i
$598$	−3.53858	+	16.6477i	−0.144703	+	0.680775i
$599$	−3.80118	+	6.58384i	−0.155312	+	0.269008i	−0.933173	−	0.359429i	$-0.882972\pi$
$599$	−3.80118	+	6.58384i	−0.155312	+	0.269008i	0.777861	+	0.628437i	$0.216305\pi$
$600$	2.91600	−	1.65820i	0.119045	−	0.0676958i
$601$	1.24900			0.0509477			0.0254738	−	0.999675i	$-0.491891\pi$
$601$	1.24900			0.0509477			0.0254738	+	0.999675i	$0.491891\pi$
$602$	−8.11763	+	24.9852i	−0.330850	+	1.01832i
$603$	1.97684	+	2.72088i	0.0805031	+	0.110803i
$604$	9.33701	+	4.15711i	0.379918	+	0.169150i
$605$	−7.56955	−	6.17083i	−0.307746	−	0.250880i
$606$	33.5100	−	14.9196i	1.36125	−	0.606067i
$607$	−9.92851	+	5.73223i	−0.402986	+	0.232664i	−0.687771	−	0.725927i	$-0.741411\pi$
$607$	−9.92851	+	5.73223i	−0.402986	+	0.232664i	0.284786	+	0.958591i	$0.408078\pi$
$608$	1.94497	−	2.67702i	0.0788789	−	0.108567i
$609$	−4.38382	+	9.84677i	−0.177641	+	0.399011i
$610$	−47.7438	−	7.72213i	−1.93309	−	0.312660i
$611$	2.68040	−	2.97688i	0.108437	−	0.120432i
$612$	−2.45756	+	2.21280i	−0.0993410	+	0.0894470i
$613$	−13.8986	+	12.5143i	−0.561358	+	0.505449i	−0.900248	−	0.435377i	$-0.856615\pi$
$613$	−13.8986	+	12.5143i	−0.561358	+	0.505449i	0.338890	+	0.940826i	$0.389949\pi$
$614$	18.5679	−	20.6218i	0.749340	−	0.832227i
$615$	0.589829	−	1.14830i	0.0237842	−	0.0463038i
$616$	−2.83011	+	6.35688i	−0.114028	+	0.256126i
$617$	8.03455	−	11.0586i	0.323459	−	0.445203i	−0.616060	−	0.787699i	$-0.711272\pi$
$617$	8.03455	−	11.0586i	0.323459	−	0.445203i	0.939519	+	0.342496i	$0.111272\pi$
$618$	10.8287	−	6.25194i	0.435593	−	0.251490i
$619$	8.17905	−	3.64155i	0.328744	−	0.146366i	−0.235727	−	0.971819i	$-0.575747\pi$
$619$	8.17905	−	3.64155i	0.328744	−	0.146366i	0.564471	+	0.825453i	$0.309080\pi$
$620$	−1.94684	−	7.36201i	−0.0781871	−	0.295665i
$621$	7.39947	+	3.29445i	0.296930	+	0.132202i
$622$	−9.81131	−	13.5041i	−0.393398	−	0.541466i
$623$	−1.82547	+	5.61860i	−0.0731358	+	0.225104i
$624$	−5.03715			−0.201647
$625$	12.2155	+	21.8124i	0.488620	+	0.872497i
$626$	18.3553	−	31.7923i	0.733626	−	1.27068i
$627$	0.364205	−	1.71345i	0.0145449	−	0.0684286i
$628$	0.797592	−	1.79142i	0.0318274	−	0.0714855i
$629$	13.4461	−	9.76919i	0.536133	−	0.389523i
$630$	10.5369	+	4.08412i	0.419802	+	0.162715i
$631$	−11.3286	−	8.23071i	−0.450984	−	0.327659i	0.339000	−	0.940786i	$-0.389911\pi$
$631$	−11.3286	−	8.23071i	−0.450984	−	0.327659i	−0.789984	+	0.613127i	$0.789911\pi$
$632$	0.994456	−	0.574149i	0.0395573	−	0.0228384i
$633$	7.48753	+	16.8173i	0.297602	+	0.668426i
$634$	−3.82696	−	4.25027i	−0.151988	−	0.168800i
$635$	−7.71900	+	0.379208i	−0.306319	+	0.0150484i
$636$	1.08287	+	3.33274i	0.0429387	+	0.132152i
$637$	6.66844	−	3.85039i	0.264213	−	0.152558i
$638$	−29.0130	−	9.42689i	−1.14864	−	0.373214i
$639$	10.3320	−	11.4749i	0.408728	−	0.453939i
$640$	7.46631	−	9.15867i	0.295132	−	0.362028i
$641$	12.5444	+	13.9319i	0.495473	+	0.550278i	0.938072	−	0.346442i	$-0.112610\pi$
$641$	12.5444	+	13.9319i	0.495473	+	0.550278i	−0.442599	+	0.896720i	$0.645943\pi$
$642$	29.2823	+	3.07769i	1.15568	+	0.121467i
$643$			37.4405i			1.47651i	0.674523	+	0.738254i	$0.264349\pi$
$643$			37.4405i			1.47651i	−0.674523	+	0.738254i	$0.735651\pi$
$644$	7.34545	−	34.5611i	0.289451	−	1.36190i
$645$	1.85588	−	11.4744i	0.0730751	−	0.451803i
$646$	1.56400	+	0.696339i	0.0615349	+	0.0273971i
$647$	17.1768	−	1.80535i	0.675289	−	0.0709758i	0.239325	−	0.970940i	$-0.423074\pi$
$647$	17.1768	−	1.80535i	0.675289	−	0.0709758i	0.435965	+	0.899964i	$0.356407\pi$
$648$	−0.139488	+	0.656241i	−0.00547962	+	0.0257796i
$649$	−5.18559	−	8.98170i	−0.203552	−	0.352562i
$650$	0.0687685	−	10.5061i	0.00269732	−	0.412082i
$651$	−3.21206	+	4.42121i	−0.125890	+	0.173281i
$652$	−30.2614	+	9.83252i	−1.18513	+	0.385071i
$653$	−13.0773	+	29.3721i	−0.511754	+	1.14942i	0.454246	+	0.890876i	$0.349909\pi$
$653$	−13.0773	+	29.3721i	−0.511754	+	1.14942i	−0.966000	+	0.258542i	$0.916758\pi$
$654$	−1.05843	−	10.0703i	−0.0413879	−	0.393780i
$655$	−2.34470	+	6.04890i	−0.0916149	+	0.236350i
$656$	0.276331	−	2.62911i	0.0107889	−	0.102650i
$657$		−	4.92302i		−	0.192065i
$658$	−12.3142	+	13.6769i	−0.480057	+	0.533180i
$659$	−1.40453	+	4.32270i	−0.0547127	+	0.168388i	−0.974679	−	0.223610i	$-0.928216\pi$
$659$	−1.40453	+	4.32270i	−0.0547127	+	0.168388i	0.919966	+	0.391998i	$0.128216\pi$
$660$	−3.78630	+	13.9479i	−0.147382	+	0.542922i
$661$	−14.7702	−	3.13950i	−0.574494	−	0.122112i	−0.0885024	−	0.996076i	$-0.528208\pi$
$661$	−14.7702	−	3.13950i	−0.574494	−	0.122112i	−0.485992	+	0.873963i	$0.661541\pi$
$662$	7.02120	−	6.32192i	0.272887	−	0.245708i
$663$	−0.458726	−	2.15814i	−0.0178155	−	0.0838151i
$664$	−2.32921	−	7.16856i	−0.0903908	−	0.278194i
$665$	−0.129769	−	2.64043i	−0.00503222	−	0.102391i
$666$	−4.89133	+	15.0540i	−0.189535	+	0.583329i
$667$	−32.8167	−	3.44918i	−1.27067	−	0.133553i
$668$	−25.8440	−	14.9211i	−0.999936	−	0.577313i
$669$	−19.3497	+	8.61505i	−0.748103	+	0.333077i
$670$	−7.86322	+	12.0220i	−0.303783	+	0.464450i
$671$	−35.9109	+	26.0908i	−1.38632	+	1.00722i
$672$	19.5920		0.000396473i	0.755777		1.52943e-5i
$673$	37.7806	−	12.2757i	1.45633	−	0.473192i	0.529386	−	0.848381i	$-0.322422\pi$
$673$	37.7806	−	12.2757i	1.45633	−	0.473192i	0.926948	+	0.375189i	$0.122422\pi$
$674$	18.3227	+	31.7358i	0.705764	+	1.22242i
$675$	−4.88383	−	1.07155i	−0.187979	−	0.0412439i
$676$	9.71947	−	16.8346i	0.373826	−	0.647485i
$677$	27.7175	+	24.9569i	1.06527	+	0.959173i	0.999253	−	0.0386458i	$-0.0123044\pi$
$677$	27.7175	+	24.9569i	1.06527	+	0.959173i	0.0660162	+	0.997819i	$0.478971\pi$
$678$	16.8850	+	23.2402i	0.648463	+	0.892533i
$679$	4.26209	+	2.46060i	0.163564	+	0.0944292i
$680$	2.67650	+	1.37480i	0.102639	+	0.0527210i
$681$	−0.382709	+	3.64123i	−0.0146654	+	0.139532i
$682$	−13.3947	−	7.73346i	−0.512911	−	0.296129i
$683$	−19.5184	−	43.8391i	−0.746852	−	1.67746i	−0.735502	−	0.677522i	$-0.763054\pi$
$683$	−19.5184	−	43.8391i	−0.746852	−	1.67746i	−0.0113503	−	0.999936i	$-0.503613\pi$
$684$	−0.720660	+	0.153181i	−0.0275551	+	0.00585702i
$685$	−40.0144	+	20.2237i	−1.52887	+	0.772706i
$686$	−30.6363	+	17.6903i	−1.16970	+	0.675420i
$687$	10.0152	+	3.25414i	0.382104	+	0.124153i
$688$	−4.94891	−	23.2828i	−0.188675	−	0.887648i
$689$	−2.28688	−	0.486092i	−0.0871233	−	0.0185186i
$690$	−1.92369	+	34.5427i	−0.0732335	+	1.31502i
$691$	−24.6465	+	5.23877i	−0.937597	+	0.199292i	−0.651276	−	0.758841i	$-0.725766\pi$
$691$	−24.6465	+	5.23877i	−0.937597	+	0.199292i	−0.286321	+	0.958134i	$0.592432\pi$
$692$	13.7479	−	18.9224i	0.522617	−	0.719321i
$693$	9.47496	−	4.21875i	0.359924	−	0.160257i
$694$	−32.8838	−	23.8915i	−1.24825	−	0.906909i
$695$	−2.28594	−	46.5317i	−0.0867108	−	1.76505i
$696$	−0.285696	−	2.71821i	−0.0108293	−	0.103034i
$697$	1.15159	−	0.121037i	0.0436197	−	0.00458462i
$698$	−44.2616	−	39.8534i	−1.67533	−	1.50847i
$699$	2.42134			0.0915834
$700$	−0.142323	+	21.8108i	−0.00537931	+	0.824370i
$701$	21.5902			0.815451			0.407726	−	0.913105i	$-0.366322\pi$
$701$	21.5902			0.815451			0.407726	+	0.913105i	$0.366322\pi$
$702$	1.56154	+	1.40602i	0.0589365	+	0.0530666i
$703$	3.68256	−	0.387052i	0.138890	−	0.0145980i
$704$	2.04343	+	19.4419i	0.0770146	+	0.732745i
$705$	4.45715	−	6.81448i	0.167866	−	0.256648i
$706$	−44.8633	−	32.5951i	−1.68845	−	1.22673i
$707$	5.30970	−	50.5283i	0.199692	−	1.90031i
$708$	−2.56393	+	3.52894i	−0.0963583	+	0.132626i
$709$	6.67239	−	1.41826i	0.250587	−	0.0532639i	−0.0809055	−	0.996722i	$-0.525781\pi$
$709$	6.67239	−	1.41826i	0.250587	−	0.0532639i	0.331492	+	0.943458i	$0.392448\pi$
$710$	61.4945	+	23.8367i	2.30785	+	0.894577i
$711$	−1.67417	−	0.355857i	−0.0627864	−	0.0133457i
$712$	−0.311464	−	1.46532i	−0.0116726	−	0.0549153i
$713$	−15.9113	−	5.16988i	−0.595881	−	0.193613i
$714$	2.10772	+	9.91503i	0.0788793	+	0.371061i
$715$	−6.79598	−	6.84061i	−0.254155	−	0.255824i
$716$	−19.1602	+	4.07263i	−0.716051	+	0.152201i
$717$	−6.82770	−	15.3353i	−0.254985	−	0.572706i
$718$	36.9888	+	21.3555i	1.38041	+	0.796979i
$719$	−1.86193	+	17.7151i	−0.0694382	+	0.660660i	0.903341	+	0.428924i	$0.141107\pi$
$719$	−1.86193	+	17.7151i	−0.0694382	+	0.660660i	−0.972779	+	0.231736i	$0.925559\pi$
$720$	−10.1183	+	1.56865i	−0.377086	+	0.0584602i
$721$	−0.000350474	−	17.3189i	−1.30523e−5	−	0.644990i
$722$	−21.1085	−	29.0534i	−0.785577	−	1.08125i
$723$	16.8064	+	15.1325i	0.625036	+	0.562785i
$724$	18.2913	−	31.6815i	0.679793	−	1.17744i
$725$	20.2714	−	1.99655i	0.752862	−	0.0741500i
$726$	4.17139	+	7.22506i	0.154815	+	0.268147i
$727$	13.9274	−	4.52529i	0.516539	−	0.167834i	−0.0391349	−	0.999234i	$-0.512460\pi$
$727$	13.9274	−	4.52529i	0.516539	−	0.167834i	0.555674	+	0.831400i	$0.312460\pi$
$728$	−0.976266	+	1.69102i	−0.0361828	+	0.0626734i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	19.6555	−	7.47134i	0.727484	−	0.276527i
$731$	9.52469	−	4.24067i	0.352283	−	0.156847i
$732$	16.1681	+	9.33464i	0.597589	+	0.345018i
$733$	−47.2590	−	4.96713i	−1.74555	−	0.183465i	−0.822663	−	0.568529i	$-0.807513\pi$
$733$	−47.2590	−	4.96713i	−1.74555	−	0.183465i	−0.922890	+	0.385064i	$0.874179\pi$
$734$	5.64754	−	17.3813i	0.208455	−	0.641557i
$735$	12.1960	−	9.81105i	0.449857	−	0.361886i
$736$	18.5345	+	57.0434i	0.683192	+	2.10265i
$737$	2.74115	+	12.8961i	0.100972	+	0.475035i
$738$	−0.819526	+	0.737905i	−0.0301672	+	0.0271626i
$739$	−6.17539	−	1.31262i	−0.227166	−	0.0482855i	0.0929224	−	0.995673i	$-0.470379\pi$
$739$	−6.17539	−	1.31262i	−0.227166	−	0.0482855i	−0.320088	+	0.947388i	$0.603712\pi$
$740$	−30.5136	+	1.49903i	−1.12170	+	0.0551054i
$741$	0.151898	−	0.467495i	0.00558012	−	0.0171738i
$742$	10.5066	+	2.23303i	0.385710	+	0.0819770i
$743$			7.00529i			0.256999i	0.991710	+	0.128500i	$0.0410161\pi$
$743$			7.00529i			0.256999i	−0.991710	+	0.128500i	$0.958984\pi$
$744$	0.144851	−	1.37816i	0.00531049	−	0.0505259i
$745$	−3.23517	−	12.2338i	−0.118527	−	0.448212i
$746$	0.789416	+	7.51079i	0.0289026	+	0.274990i
$747$	−4.56962	+	10.2635i	−0.167194	+	0.375523i
$748$	−12.3293	+	4.00604i	−0.450805	+	0.146475i
$749$	23.9703	−	32.9937i	0.875855	−	1.20556i
$750$	−3.13362	−	21.1253i	−0.114424	−	0.771386i
$751$	7.57107	+	13.1135i	0.276272	+	0.478518i	0.970455	−	0.241281i	$-0.0775675\pi$
$751$	7.57107	+	13.1135i	0.276272	+	0.478518i	−0.694183	+	0.719798i	$0.744234\pi$
$752$	3.46689	−	16.3105i	0.126425	−	0.594781i
$753$	27.4451	−	2.88459i	1.00015	−	0.105120i
$754$	−7.82024	−	3.48179i	−0.284796	−	0.126799i
$755$	−9.83338	+	9.76923i	−0.357874	+	0.355539i
$756$	−3.24184	−	2.91885i	−0.117905	−	0.106158i
$757$		−	2.61744i		−	0.0951326i	−0.998868	−	0.0475663i	$-0.984853\pi$
$757$		−	2.61744i		−	0.0951326i	0.998868	−	0.0475663i	$-0.0151465\pi$
$758$	64.3608	+	6.76460i	2.33769	+	0.245701i
$759$	21.2463	+	23.5964i	0.771192	+	0.856495i
$760$	0.363262	+	0.563403i	0.0131769	+	0.0204368i
$761$	19.6354	−	21.8073i	0.711781	−	0.790513i	−0.273423	−	0.961894i	$-0.588156\pi$
$761$	19.6354	−	21.8073i	0.711781	−	0.790513i	0.985205	+	0.171380i	$0.0548227\pi$
$762$	6.27884	+	2.04012i	0.227458	+	0.0739057i
$763$	−12.8126	−	5.70423i	−0.463847	−	0.206507i
$764$	9.50761	+	29.2614i	0.343973	+	1.05864i
$765$	−1.59354	−	4.19227i	−0.0576145	−	0.151572i
$766$	−40.2846	−	44.7406i	−1.45554	−	1.61654i
$767$	−1.18371	−	2.65865i	−0.0427412	−	0.0959983i
$768$	−17.3793	+	10.0339i	−0.627120	+	0.362068i
$769$	22.5790	+	16.4046i	0.814219	+	0.591565i	0.915051	−	0.403339i	$-0.132150\pi$
$769$	22.5790	+	16.4046i	0.814219	+	0.591565i	−0.100832	+	0.994904i	$0.532150\pi$
$770$	31.2232	+	31.4270i	1.12521	+	1.13255i
$771$	−2.10521	+	1.52952i	−0.0758171	+	0.0550844i
$772$	16.8806	−	37.9144i	0.607545	−	1.36457i
$773$	1.49721	−	7.04383i	0.0538510	−	0.253349i	−0.942985	−	0.332835i	$-0.891995\pi$
$773$	1.49721	−	7.04383i	0.0538510	−	0.253349i	0.996836	+	0.0794864i	$0.0253280\pi$
$774$	−4.96472	+	8.59915i	−0.178453	+	0.309090i
$775$	10.2637	+	1.14673i	0.368683	+	0.0411917i
$776$	−1.24795			−0.0447987
$777$	14.6703	+	16.2924i	0.526296	+	0.584487i
$778$	−12.6024	−	17.3457i	−0.451817	−	0.621873i
$779$	0.235673	+	0.104929i	0.00844387	+	0.00375945i
$780$	−1.46577	+	3.78143i	−0.0524830	+	0.135397i
$781$	55.2976	−	24.6201i	1.97871	−	0.880976i
$782$	−26.8747	+	15.5161i	−0.961037	+	0.554855i
$783$	−2.39458	+	3.29586i	−0.0855753	+	0.117784i
$784$	16.0257	−	27.7599i	0.572346	−	0.991425i
$785$	1.87435	+	1.88666i	0.0668983	+	0.0673376i
$786$	3.70828	−	4.11846i	0.132270	−	0.146901i
$787$	5.38188	−	4.84586i	0.191843	−	0.172736i	−0.567612	−	0.823296i	$-0.692132\pi$
$787$	5.38188	−	4.84586i	0.191843	−	0.172736i	0.759455	+	0.650560i	$0.225466\pi$
$788$	−19.9300	+	17.9451i	−0.709978	+	0.639267i
$789$	14.6329	−	16.2514i	0.520943	−	0.578566i
$790$	−1.12000	−	7.22433i	−0.0398477	−	0.257030i
$791$	39.5704	−	4.15983i	1.40696	−	0.147906i
$792$	−1.54589	+	2.12774i	−0.0549309	+	0.0756060i
$793$	−10.7870	+	6.22790i	−0.383059	+	0.221159i
$794$	17.5084	−	7.79525i	0.621351	−	0.276643i
$795$	−4.74511	−	0.264256i	−0.168292	−	0.00937218i
$796$	11.4631	+	5.10372i	0.406300	+	0.180896i
$797$	−8.44016	−	11.6169i	−0.298966	−	0.411491i	0.632935	−	0.774205i	$-0.281850\pi$
$797$	−8.44016	−	11.6169i	−0.298966	−	0.411491i	−0.931900	+	0.362714i	$0.881850\pi$
$798$	−0.697818	+	2.14781i	−0.0247025	+	0.0760317i
$799$	7.30385			0.258392
$800$	−18.3024	−	32.1854i	−0.647087	−	1.13793i
$801$	−1.11645	+	1.93375i	−0.0394479	+	0.0683257i
$802$	−9.86201	+	46.3971i	−0.348240	+	1.63834i
$803$	7.84960	−	17.6305i	0.277006	−	0.622166i
$804$	4.48613	−	3.25936i	0.158213	−	0.114949i
$805$	40.1028	+	26.2289i	1.41344	+	0.924448i
$806$	−3.51127	−	2.55109i	−0.123679	−	0.0898583i
$807$	24.0870	−	13.9066i	0.847903	−	0.489537i
$808$	5.24013	+	11.7695i	0.184347	+	0.414051i
$809$	19.9489	+	22.1555i	0.701365	+	0.778944i	0.983593	−	0.180403i	$-0.0577402\pi$
$809$	19.9489	+	22.1555i	0.701365	+	0.778944i	−0.282228	+	0.959347i	$0.591074\pi$
$810$	3.57457	+	2.33802i	0.125598	+	0.0821496i
$811$	13.8858	+	42.7361i	0.487597	+	1.50067i	0.828184	+	0.560456i	$0.189374\pi$
$811$	13.8858	+	42.7361i	0.487597	+	1.50067i	−0.340587	+	0.940213i	$0.610626\pi$
$812$	16.2351	+	7.22794i	0.569740	+	0.253651i
$813$	−11.9310	−	3.87662i	−0.418438	−	0.135959i
$814$	−41.5200	+	46.1126i	−1.45528	+	1.61625i
$815$	2.39945	−	43.0857i	0.0840490	−	1.50923i
$816$	−6.14553	−	6.82530i	−0.215137	−	0.238933i
$817$	2.31010	+	0.242801i	0.0808201	+	0.00849453i
$818$		−	42.6549i		−	1.49139i
$819$	2.76795	−	0.899423i	0.0967200	−	0.0314284i
$820$	−1.89328	−	0.972495i	−0.0661164	−	0.0339610i
$821$	22.3472	+	9.94963i	0.779924	+	0.347245i	0.757780	−	0.652510i	$-0.226284\pi$
$821$	22.3472	+	9.94963i	0.779924	+	0.347245i	0.0221442	+	0.999755i	$0.492951\pi$
$822$	38.0905	−	4.00347i	1.32856	−	0.139637i
$823$	−3.03166	+	14.2628i	−0.105677	+	0.497171i	0.893194	+	0.449671i	$0.148459\pi$
$823$	−3.03166	+	14.2628i	−0.105677	+	0.497171i	−0.998871	+	0.0475003i	$0.984875\pi$
$824$	2.19584	+	3.80330i	0.0764956	+	0.132494i
$825$	−15.7816	−	11.6246i	−0.549444	−	0.404715i
$826$	5.43853	+	12.2145i	0.189230	+	0.424996i
$827$	−34.0493	+	11.0633i	−1.18401	+	0.384709i	−0.833856	−	0.551983i	$-0.813871\pi$
$827$	−34.0493	+	11.0633i	−1.18401	+	0.384709i	−0.350156	+	0.936691i	$0.613871\pi$
$828$	5.43181	−	12.2001i	0.188769	−	0.423981i
$829$	1.14550	+	10.8987i	0.0397849	+	0.378528i	0.996239	+	0.0866459i	$0.0276149\pi$
$829$	1.14550	+	10.8987i	0.0397849	+	0.378528i	−0.956454	+	0.291882i	$0.905718\pi$
$830$	−47.9130	−	2.66828i	−1.66308	−	0.0926173i
$831$	2.18086	−	20.7495i	0.0756532	−	0.719792i
$832$			5.48566i			0.190181i
$833$	13.3530	+	4.33806i	0.462654	+	0.150305i
$834$	−12.2983	+	37.8501i	−0.425854	+	1.31064i
$835$	31.5357	−	25.3667i	1.09134	−	0.877851i
$836$	−2.82509	−	0.600492i	−0.0977079	−	0.0207684i
$837$	−1.53497	+	1.38210i	−0.0530565	+	0.0477723i
$838$	−13.1238	−	61.7425i	−0.453353	−	2.13286i
$839$	−9.65518	−	29.7156i	−0.333334	−	1.02590i	−0.967537	−	0.252730i	$-0.918672\pi$
$839$	−9.65518	−	29.7156i	−0.333334	−	1.02590i	0.634203	−	0.773167i	$-0.281328\pi$
$840$	−1.43445	+	3.70083i	−0.0494931	+	0.127691i
$841$	−3.83284	+	11.7963i	−0.132167	+	0.406768i
$842$	31.1209	+	3.27093i	1.07250	+	0.112724i
$843$	−0.655422	−	0.378408i	−0.0225739	−	0.0130331i
$844$	27.7279	−	12.3452i	0.954433	−	0.424941i
$845$	16.5237	+	20.5421i	0.568432	+	0.706671i
$846$	−5.62748	+	4.08860i	−0.193477	+	0.140569i
$847$	11.5554		0.000233842i	0.397049		8.03489e-6i
$848$	−9.25592	+	3.00743i	−0.317849	+	0.103276i
$849$	−8.67168	−	15.0198i	−0.297611	−	0.515478i
$850$	14.3195	−	12.7246i	0.491156	−	0.436452i
$851$	−33.5592	+	58.1262i	−1.15039	+	1.99254i
$852$	−18.9195	−	17.0352i	−0.648171	−	0.583616i
$853$	−5.37287	−	7.39512i	−0.183963	−	0.253204i	0.707068	−	0.707146i	$-0.250017\pi$
$853$	−5.37287	−	7.39512i	−0.183963	−	0.253204i	−0.891031	+	0.453942i	$0.850017\pi$
$854$	49.5580	−	28.6137i	1.69584	−	0.979140i
$855$	0.159537	−	0.986375i	0.00545606	−	0.0337333i
$856$	−1.08096	+	10.2847i	−0.0369465	+	0.351523i
$857$	−37.1871	−	21.4700i	−1.27029	−	0.733401i	−0.295246	−	0.955421i	$-0.595402\pi$
$857$	−37.1871	−	21.4700i	−1.27029	−	0.733401i	−0.975042	+	0.222020i	$0.928735\pi$
$858$	3.35039	+	7.52509i	0.114380	+	0.256902i
$859$	−25.7047	+	5.46371i	−0.877034	+	0.186419i	−0.624364	−	0.781133i	$-0.714642\pi$
$859$	−25.7047	+	5.46371i	−0.877034	+	0.186419i	−0.252670	+	0.967553i	$0.581309\pi$
$860$	−18.9187	−	3.05992i	−0.645121	−	0.104343i
$861$	0.317603	+	1.49406i	0.0108239	+	0.0509173i
$862$	52.4418	+	17.0394i	1.78617	+	0.580363i
$863$	−7.19906	−	33.8689i	−0.245059	−	1.15291i	−0.912765	−	0.408486i	$-0.866057\pi$
$863$	−7.19906	−	33.8689i	−0.245059	−	1.15291i	0.667706	−	0.744425i	$-0.267276\pi$
$864$	7.24325	+	1.53960i	0.246420	+	0.0523783i
$865$	17.1891	+	26.6595i	0.584448	+	0.906452i
$866$	−0.0808548	+	0.0171862i	−0.00274756	+	0.000584012i
$867$	−7.62775	+	10.4987i	−0.259052	+	0.356555i
$868$	7.28958	+	5.29596i	0.247424	+	0.179757i
$869$	−5.42820	−	3.94382i	−0.184139	−	0.133785i
$870$	−16.7930	−	4.55864i	−0.569338	−	0.154552i
$871$	0.386716	+	3.67936i	0.0131034	+	0.124670i
$872$	3.53694	−	0.371747i	0.119776	−	0.0125889i
$873$	1.38233	+	1.24465i	0.0467847	+	0.0421251i
$874$	−6.91366			−0.233858
$875$	−27.5105	−	10.8707i	−0.930024	−	0.367498i
$876$	−8.11696			−0.274247
$877$	−18.4335	−	16.5976i	−0.622455	−	0.560461i	0.296397	−	0.955065i	$-0.404215\pi$
$877$	−18.4335	−	16.5976i	−0.622455	−	0.560461i	−0.918851	+	0.394604i	$0.870882\pi$
$878$	−41.8092	+	4.39433i	−1.41099	+	0.148301i
$879$	0.664691	+	6.32411i	0.0224195	+	0.213307i
$880$	−38.7371	−	10.5156i	−1.30583	−	0.354480i
$881$	−7.00323	−	5.08814i	−0.235945	−	0.171424i	0.463530	−	0.886081i	$-0.346583\pi$
$881$	−7.00323	−	5.08814i	−0.235945	−	0.171424i	−0.699475	+	0.714657i	$0.746583\pi$
$882$	−12.7166	+	4.13245i	−0.428191	+	0.139147i
$883$	3.81922	−	5.25671i	0.128527	−	0.176902i	−0.739904	−	0.672713i	$-0.765129\pi$
$883$	3.81922	−	5.25671i	0.128527	−	0.176902i	0.868431	+	0.495811i	$0.165129\pi$
$884$	−3.55828	+	0.756337i	−0.119678	+	0.0254384i
$885$	−3.20570	−	4.97189i	−0.107758	−	0.167128i
$886$	−30.7832	−	6.54318i	−1.03418	−	0.219822i
$887$	4.61161	+	21.6959i	0.154843	+	0.728478i	0.985222	+	0.171280i	$0.0547902\pi$
$887$	4.61161	+	21.6959i	0.154843	+	0.728478i	−0.830380	+	0.557198i	$0.811876\pi$
$888$	−5.28732	−	1.71796i	−0.177431	−	0.0576508i
$889$	6.79539	−	6.11884i	0.227910	−	0.205219i
$890$	−9.41501	−	1.52279i	−0.315592	−	0.0510442i
$891$	3.83448	−	0.815044i	0.128460	−	0.0273050i
$892$	14.2043	+	31.9033i	0.475594	+	1.06820i
$893$	1.40922	+	0.813611i	0.0471576	+	0.0272265i
$894$	−1.12996	+	10.7509i	−0.0377915	+	0.359562i
$895$	4.24162	−	26.2248i	0.141782	−	0.876598i
$896$	0.000282933		13.9813i	9.45214e−6		0.467084i
$897$	5.23715	+	7.20831i	0.174863	+	0.240679i
$898$	50.9138	+	45.8430i	1.69901	+	1.52980i
$899$	4.20735	−	7.28734i	0.140323	−	0.243046i
$900$	−1.76674	+	8.05234i	−0.0588914	+	0.268411i
$901$	−2.13144	−	3.69176i	−0.0710085	−	0.122990i
$902$	−4.11148	+	1.33590i	−0.136897	+	0.0444806i
$903$	6.87679	+	11.9104i	0.228845	+	0.396353i
$904$	−8.16252	+	5.93042i	−0.271482	+	0.197243i
$905$	31.0964	+	38.6589i	1.03368	+	1.28506i
$906$	10.8173	−	4.81619i	0.359382	−	0.160007i
$907$	11.6573	+	6.73034i	0.387074	+	0.223477i	0.680891	−	0.732384i	$-0.261593\pi$
$907$	11.6573	+	6.73034i	0.387074	+	0.223477i	−0.293818	+	0.955861i	$0.594926\pi$
$908$	6.00357	+	0.631001i	0.199236	+	0.0209405i
$909$	5.93407	−	18.2632i	0.196821	−	0.605752i
$910$	7.79175	+	9.68626i	0.258294	+	0.321096i
$911$	2.17280	+	6.68718i	0.0719880	+	0.221556i	0.980577	−	0.196135i	$-0.0628392\pi$
$911$	2.17280	+	6.68718i	0.0719880	+	0.221556i	−0.908589	+	0.417692i	$0.862839\pi$
$912$	−0.425425	−	2.00147i	−0.0140872	−	0.0662752i
$913$	−32.7298	+	29.4700i	−1.08320	+	0.975315i
$914$	−15.8733	−	3.37398i	−0.525043	−	0.111601i
$915$	−19.7288	+	15.8694i	−0.652214	+	0.524628i
$916$	5.36535	−	16.5128i	0.177276	−	0.545599i
$917$	−2.37217	−	7.30029i	−0.0783360	−	0.241077i
$918$			3.83127i			0.126451i
$919$	−0.560623	+	5.33397i	−0.0184932	+	0.175951i	−0.999870	−	0.0161429i	$-0.994861\pi$
$919$	−0.560623	+	5.33397i	−0.0184932	+	0.175951i	0.981376	+	0.192094i	$0.0615280\pi$
$920$	−12.1323	−	0.675646i	−0.399989	−	0.0222754i
$921$	−1.51849	−	14.4475i	−0.0500361	−	0.476062i
$922$	13.6169	−	30.5840i	0.448448	−	1.00723i
$923$	16.1542	−	5.24883i	0.531723	−	0.172767i
$924$	−6.95578	−	15.6221i	−0.228828	−	0.513929i
$925$	13.0610	−	39.3200i	0.429442	−	1.29283i
$926$	−24.6702	−	42.7300i	−0.810712	−	1.40419i
$927$	1.36098	−	6.40289i	0.0447003	−	0.210298i
$928$	−30.0023	+	3.15336i	−0.984872	+	0.103514i
$929$	−46.0539	−	20.5045i	−1.51098	−	0.672731i	−0.526814	−	0.849981i	$-0.676613\pi$
$929$	−46.0539	−	20.5045i	−1.51098	−	0.672731i	−0.984166	+	0.177249i	$0.943280\pi$
$930$	−7.84766	−	4.03099i	−0.257335	−	0.132181i
$931$	2.09311	+	2.32445i	0.0685991	+	0.0761808i
$932$		−	3.99224i		−	0.130770i
$933$	−8.69059	−	0.913418i	−0.284517	−	0.0299040i
$934$	−12.1701	−	13.5163i	−0.398219	−	0.442267i
$935$	0.977602	−	17.5543i	0.0319710	−	0.574088i
$936$	−0.493828	+	0.548451i	−0.0161413	+	0.0179267i
$937$	−28.8439	−	9.37195i	−0.942289	−	0.306168i	−0.202711	−	0.979239i	$-0.564975\pi$
$937$	−28.8439	−	9.37195i	−0.942289	−	0.306168i	−0.739579	+	0.673070i	$0.764975\pi$
$938$	−1.77702	−	16.9040i	−0.0580219	−	0.551934i
$939$	−5.93882	−	18.2778i	−0.193806	−	0.596474i
$940$	−11.2355	−	7.34884i	−0.366463	−	0.239693i
$941$	−0.718642	−	0.798133i	−0.0234271	−	0.0260184i	0.731317	−	0.682037i	$-0.238906\pi$
$941$	−0.718642	−	0.798133i	−0.0234271	−	0.0260184i	−0.754744	+	0.656019i	$0.772239\pi$
$942$	−0.924044	−	2.07544i	−0.0301070	−	0.0676214i
$943$	−4.04964	+	2.33806i	−0.131874	+	0.0761378i
$944$	−9.80082	−	7.12071i	−0.318990	−	0.231759i
$945$	5.27997	−	2.66868i	0.171758	−	0.0868123i
$946$	−31.4909	+	22.8795i	−1.02386	+	0.743876i
$947$	−9.97306	+	22.3999i	−0.324081	+	0.727898i	−0.999958	−	0.00911619i	$-0.997098\pi$
$947$	−9.97306	+	22.3999i	−0.324081	+	0.727898i	0.675877	+	0.737014i	$0.263765\pi$
$948$	−0.586728	+	2.76034i	−0.0190560	+	0.0896515i
$949$	2.70774	−	4.68995i	0.0878971	−	0.152242i
$950$	4.18030	−	0.859990i	0.135627	−	0.0279018i
$951$	−2.99412			−0.0970911
$952$	−3.48241	+	0.740282i	−0.112865	+	0.0239927i
$953$	16.0725	+	22.1219i	0.520639	+	0.716599i	0.985668	−	0.168697i	$-0.0539559\pi$
$953$	16.0725	+	22.1219i	0.520639	+	0.716599i	−0.465028	+	0.885296i	$0.653956\pi$
$954$	3.70884	+	1.65128i	0.120078	+	0.0534622i
$955$	−41.6620	−	2.32016i	−1.34815	−	0.0750787i
$956$	−25.2844	+	11.2573i	−0.817756	+	0.364089i
$957$	−13.8307	+	7.98514i	−0.447082	+	0.258123i
$958$	−46.0706	+	63.4107i	−1.48847	+	2.04871i
$959$	21.5760	−	48.4632i	0.696726	−	1.56496i
$960$	1.70832	+	11.0192i	0.0551359	+	0.355644i
$961$	−17.8883	+	19.8670i	−0.577042	+	0.640870i
$962$	−12.9397	+	11.6509i	−0.417192	+	0.375641i
$963$	11.4549	−	10.3140i	0.369129	−	0.332365i
$964$	24.9501	−	27.7099i	0.803590	−	0.892477i
$965$	39.6695	+	39.9300i	1.27701	+	1.28539i
$966$	−24.0615	−	33.1165i	−0.774168	−	1.06550i
$967$	−4.70829	+	6.48040i	−0.151408	+	0.208396i	−0.877983	−	0.478692i	$-0.841111\pi$
$967$	−4.70829	+	6.48040i	−0.151408	+	0.208396i	0.726575	+	0.687087i	$0.241111\pi$
$968$	−2.53762	+	1.46510i	−0.0815622	+	0.0470900i
$969$	0.818774	−	0.364542i	0.0263028	−	0.0117108i
$970$	−2.87151	+	7.40798i	−0.0921985	+	0.237856i
$971$	−2.88070	−	1.28257i	−0.0924462	−	0.0411597i	0.359993	−	0.932955i	$-0.382779\pi$
$971$	−2.88070	−	1.28257i	−0.0924462	−	0.0411597i	−0.452439	+	0.891795i	$0.649446\pi$
$972$	−0.969126	−	1.33389i	−0.0310847	−	0.0427844i
$973$	36.8856	+	40.9640i	1.18250	+	1.31324i
$974$	64.5007			2.06674
$975$	−4.06324	−	3.70700i	−0.130128	−	0.118719i
$976$	−25.9248	+	44.9030i	−0.829832	+	1.43731i
$977$	−11.2209	+	52.7902i	−0.358988	+	1.68891i	0.314136	+	0.949378i	$0.398285\pi$
$977$	−11.2209	+	52.7902i	−0.358988	+	1.68891i	−0.673124	+	0.739529i	$0.735048\pi$
$978$	−14.9937	+	33.6763i	−0.479444	+	1.07685i
$979$	−7.08157	+	5.14506i	−0.226328	+	0.164437i
$980$	−16.1762	−	20.1085i	−0.516730	−	0.642343i
$981$	−4.28856	−	3.11582i	−0.136923	−	0.0994806i
$982$	6.81904	−	3.93698i	0.217604	−	0.125634i
$983$	−12.9862	−	29.1675i	−0.414196	−	0.930300i	−0.993356	−	0.115085i	$-0.963286\pi$
$983$	−12.9862	−	29.1675i	−0.414196	−	0.930300i	0.579160	−	0.815214i	$-0.303381\pi$
$984$	−0.259170	−	0.287838i	−0.00826205	−	0.00917594i
$985$	−12.9231	−	33.9980i	−0.411764	−	1.08327i
$986$	−4.82320	−	14.8443i	−0.153602	−	0.472739i
$987$	1.00728	+	9.58175i	0.0320620	+	0.304991i
$988$	−0.770794	−	0.250446i	−0.0245222	−	0.00796775i
$989$	−28.1730	+	31.2893i	−0.895848	+	0.994940i
$990$	9.07346	+	14.0725i	0.288374	+	0.447254i
$991$	−8.03251	−	8.92101i	−0.255161	−	0.283385i	0.601931	−	0.798548i	$-0.294398\pi$
$991$	−8.03251	−	8.92101i	−0.255161	−	0.283385i	−0.857092	+	0.515163i	$0.827731\pi$
$992$	−15.2115	−	1.59879i	−0.482965	−	0.0507616i
$993$		−	4.94611i		−	0.156960i
$994$	−74.2165	+	24.1161i	−2.35400	+	0.764915i
$995$	−12.0725	+	11.9938i	−0.382725	+	0.380228i
$996$	16.9223	+	7.53428i	0.536203	+	0.238733i
$997$	19.8985	−	2.09142i	0.630193	−	0.0662360i	0.215953	−	0.976404i	$-0.430714\pi$
$997$	19.8985	−	2.09142i	0.630193	−	0.0662360i	0.414240	+	0.910168i	$0.364047\pi$
$998$	9.67294	−	45.5076i	0.306192	−	1.44052i
$999$	4.14325	+	7.17631i	0.131087	+	0.227049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bo.a.319.8	yes	320
7.2	even	3	inner	525.2.bo.a.394.8	yes	320
25.4	even	10	inner	525.2.bo.a.4.8	✓	320
175.79	even	30	inner	525.2.bo.a.79.8	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bo.a.4.8	✓	320	25.4	even	10	inner
525.2.bo.a.79.8	yes	320	175.79	even	30	inner
525.2.bo.a.319.8	yes	320	1.1	even	1	trivial
525.2.bo.a.394.8	yes	320	7.2	even	3	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bo (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41954 - 1.27816i) q^{2} +(-0.994522 + 0.104528i) q^{3} +(0.172344 + 1.63974i) q^{4} +(-2.15797 - 0.585803i) q^{5} +(1.54537 + 1.12277i) q^{6} +(2.41699 - 1.07617i) q^{7} +(-0.394346 + 0.542771i) q^{8} +(0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(-1.41954 - 1.27816i) q^{2} +(-0.994522 + 0.104528i) q^{3} +(0.172344 + 1.63974i) q^{4} +(-2.15797 - 0.585803i) q^{5} +(1.54537 + 1.12277i) q^{6} +(2.41699 - 1.07617i) q^{7} +(-0.394346 + 0.542771i) q^{8} +(0.978148 - 0.207912i) q^{9} +(2.31457 + 3.58980i) q^{10} +(3.83448 + 0.815044i) q^{11} +(-0.342800 - 1.61275i) q^{12} +(1.04619 + 0.339929i) q^{13} +(-4.80653 - 1.56163i) q^{14} +(2.20738 + 0.357024i) q^{15} +(4.47903 - 0.952047i) q^{16} +(0.815798 + 1.83231i) q^{17} +(-1.65426 - 0.955088i) q^{18} +(-0.0467088 + 0.444405i) q^{19} +(0.588653 - 3.63948i) q^{20} +(-2.29126 + 1.32292i) q^{21} +(-4.40144 - 6.05806i) q^{22} +(-6.01927 - 5.41977i) q^{23} +(0.335451 - 0.581018i) q^{24} +(4.31367 + 2.52829i) q^{25} +(-1.05063 - 1.81974i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(2.18120 + 3.77777i) q^{28} +(3.29586 - 2.39458i) q^{29} +(-2.67713 - 3.32819i) q^{30} +(1.88694 - 0.840120i) q^{31} +(-6.41298 - 3.70253i) q^{32} +(-3.89867 - 0.409767i) q^{33} +(1.18393 - 3.64375i) q^{34} +(-5.84622 + 0.906469i) q^{35} +(0.509500 + 1.56808i) q^{36} +(-1.72286 - 8.10541i) q^{37} +(0.634325 - 0.571148i) q^{38} +(-1.07599 - 0.228710i) q^{39} +(1.16894 - 0.940274i) q^{40} +(0.178401 - 0.549063i) q^{41} +(4.94344 + 1.05066i) q^{42} -5.19818i q^{43} +(-0.675613 + 6.42803i) q^{44} +(-2.23261 - 0.124334i) q^{45} +(1.61725 + 15.3871i) q^{46} +(1.48114 - 3.32669i) q^{47} +(-4.35497 + 1.41502i) q^{48} +(4.68370 - 5.20220i) q^{49} +(-2.89187 - 9.10255i) q^{50} +(-1.00286 - 1.73700i) q^{51} +(-0.377091 + 1.77407i) q^{52} +(-2.11372 + 0.222161i) q^{53} +(1.74503 + 0.776939i) q^{54} +(-7.79724 - 4.00509i) q^{55} +(-0.369016 + 1.73626i) q^{56} -0.446853i q^{57} +(-7.73924 - 0.813427i) q^{58} +(-1.77026 - 1.96607i) q^{59} +(-0.204999 + 3.68107i) q^{60} +(-7.57664 + 8.41471i) q^{61} +(-3.75239 - 1.21922i) q^{62} +(2.14043 - 1.55518i) q^{63} +(1.54101 + 4.74274i) q^{64} +(-2.05852 - 1.34642i) q^{65} +(5.01056 + 5.56480i) q^{66} +(1.36794 + 3.07243i) q^{67} +(-2.86392 + 1.65349i) q^{68} +(6.55281 + 4.76090i) q^{69} +(9.45754 + 6.18563i) q^{70} +(12.4920 - 9.07597i) q^{71} +(-0.272880 + 0.612899i) q^{72} +(1.02355 - 4.81544i) q^{73} +(-7.91433 + 13.7080i) q^{74} +(-4.55432 - 2.06354i) q^{75} -0.736760 q^{76} +(10.1450 - 2.15661i) q^{77} +(1.23509 + 1.69995i) q^{78} +(-1.56360 - 0.696161i) q^{79} +(-10.2233 - 0.569338i) q^{80} +(0.913545 - 0.406737i) q^{81} +(-0.955036 + 0.551391i) q^{82} +(-6.60368 + 9.08918i) q^{83} +(-2.56414 - 3.52908i) q^{84} +(-0.687094 - 4.43197i) q^{85} +(-6.64410 + 7.37902i) q^{86} +(-3.02750 + 2.72597i) q^{87} +(-1.95449 + 1.75983i) q^{88} +(-1.49410 + 1.65937i) q^{89} +(3.01035 + 3.03012i) q^{90} +(2.89446 - 0.304280i) q^{91} +(7.84965 - 10.8041i) q^{92} +(-1.78879 + 1.03276i) q^{93} +(-6.35457 + 2.82924i) q^{94} +(0.361130 - 0.931650i) q^{95} +(6.76487 + 3.01191i) q^{96} +(1.09334 + 1.50486i) q^{97} +(-13.2979 + 1.39821i) q^{98} +3.92015 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9}+O(q^{10}) \) 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9	\( 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9} + 4 q^{10} - 6 q^{11} + 12 q^{14} + 4 q^{15} + 40 q^{16} - 20 q^{17} + 16 q^{19} + 8 q^{20} + 40 q^{22} - 60 q^{23} - 48 q^{24} + 4 q^{25} - 30 q^{28} + 24 q^{29} - 48 q^{30} - 30 q^{31} - 80 q^{36} + 30 q^{38} - 32 q^{40} + 36 q^{41} + 10 q^{42} - 16 q^{44} + 2 q^{45} + 32 q^{46} + 16 q^{49} - 140 q^{50} + 190 q^{52} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 60 q^{58} + 24 q^{59} - 46 q^{60} - 20 q^{61} + 120 q^{62} + 10 q^{63} - 4 q^{64} - 30 q^{65} - 16 q^{66} - 60 q^{67} - 32 q^{69} - 76 q^{70} + 32 q^{71} - 30 q^{72} - 40 q^{73} - 12 q^{74} - 8 q^{75} - 344 q^{76} + 4 q^{79} - 52 q^{80} + 40 q^{81} - 80 q^{83} + 48 q^{84} - 76 q^{85} + 24 q^{86} - 200 q^{88} - 52 q^{90} + 26 q^{91} + 180 q^{92} + 16 q^{94} - 38 q^{95} - 58 q^{96} - 140 q^{97} + 360 q^{98} + 8 q^{99}+O(q^{100}) \) 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9 + 4 * q^10 - 6 * q^11 + 12 * q^14 + 4 * q^15 + 40 * q^16 - 20 * q^17 + 16 * q^19 + 8 * q^20 + 40 * q^22 - 60 * q^23 - 48 * q^24 + 4 * q^25 - 30 * q^28 + 24 * q^29 - 48 * q^30 - 30 * q^31 - 80 * q^36 + 30 * q^38 - 32 * q^40 + 36 * q^41 + 10 * q^42 - 16 * q^44 + 2 * q^45 + 32 * q^46 + 16 * q^49 - 140 * q^50 + 190 * q^52 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 60 * q^58 + 24 * q^59 - 46 * q^60 - 20 * q^61 + 120 * q^62 + 10 * q^63 - 4 * q^64 - 30 * q^65 - 16 * q^66 - 60 * q^67 - 32 * q^69 - 76 * q^70 + 32 * q^71 - 30 * q^72 - 40 * q^73 - 12 * q^74 - 8 * q^75 - 344 * q^76 + 4 * q^79 - 52 * q^80 + 40 * q^81 - 80 * q^83 + 48 * q^84 - 76 * q^85 + 24 * q^86 - 200 * q^88 - 52 * q^90 + 26 * q^91 + 180 * q^92 + 16 * q^94 - 38 * q^95 - 58 * q^96 - 140 * q^97 + 360 * q^98 + 8 * q^99

Introduction

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