LMFDB - Embedded newform 77.2.m.a.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,2,Mod(4,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, 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("77.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.m (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:	$0.614848095564$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			25.1
Root			$0.669131 - 0.743145i$ of defining polynomial
Character	$\chi$	$=$	77.25
Dual form			77.2.m.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.564602 - 0.251377i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-1.08268 - 1.20243i) q^{4} +(0.233733 - 2.22382i) q^{5} +(0.500000 + 0.363271i) q^{6} +(1.59618 - 2.11002i) q^{7} +(0.690983 + 2.12663i) q^{8} +(-1.82709 - 0.813473i) q^{9} +O(q^{10})$	\(q+(-0.564602 - 0.251377i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-1.08268 - 1.20243i) q^{4} +(0.233733 - 2.22382i) q^{5} +(0.500000 + 0.363271i) q^{6} +(1.59618 - 2.11002i) q^{7} +(0.690983 + 2.12663i) q^{8} +(-1.82709 - 0.813473i) q^{9} +(-0.690983 + 1.19682i) q^{10} +(2.04732 + 2.60931i) q^{11} +(0.809017 + 1.40126i) q^{12} +(-0.690983 + 0.502029i) q^{13} +(-1.43162 + 0.790081i) q^{14} +(-0.690983 + 2.12663i) q^{15} +(-0.193806 + 1.84395i) q^{16} +(-1.12920 + 0.502754i) q^{17} +(0.827091 + 0.918578i) q^{18} +(5.25542 - 5.83674i) q^{19} +(-2.92705 + 2.12663i) q^{20} +(-2.00000 + 1.73205i) q^{21} +(-0.500000 - 1.98787i) q^{22} +(3.11803 + 5.40059i) q^{23} +(-0.233733 - 2.22382i) q^{24} +(0.516329 - 0.109749i) q^{26} +(4.04508 + 2.93893i) q^{27} +(-4.26531 + 0.365171i) q^{28} +(-0.354102 + 1.08981i) q^{29} +(0.924716 - 1.02700i) q^{30} +(-0.691773 - 6.58178i) q^{31} +(2.80902 - 4.86536i) q^{32} +(-1.46007 - 2.97795i) q^{33} +0.763932 q^{34} +(-4.31923 - 4.04280i) q^{35} +(1.00000 + 3.07768i) q^{36} +(-4.97894 + 1.05831i) q^{37} +(-4.43444 + 1.97434i) q^{38} +(0.780261 - 0.347395i) q^{39} +(4.89074 - 1.03956i) q^{40} +(-1.42705 - 4.39201i) q^{41} +(1.56460 - 0.475165i) q^{42} +6.85410 q^{43} +(0.920937 - 5.28680i) q^{44} +(-2.23607 + 3.87298i) q^{45} +(-0.402863 - 3.83299i) q^{46} +(-5.66897 + 6.29602i) q^{47} +(0.572949 - 1.76336i) q^{48} +(-1.90441 - 6.73597i) q^{49} +(1.20906 - 0.256993i) q^{51} +(1.35177 + 0.287327i) q^{52} +(0.532068 + 5.06229i) q^{53} +(-1.54508 - 2.67617i) q^{54} +(6.28115 - 3.94298i) q^{55} +(5.59017 + 1.93649i) q^{56} +(-6.35410 + 4.61653i) q^{57} +(0.473881 - 0.526298i) q^{58} +(2.48127 + 2.75573i) q^{59} +(3.30524 - 1.47159i) q^{60} +(-0.725874 + 6.90623i) q^{61} +(-1.26393 + 3.88998i) q^{62} +(-4.63282 + 2.55676i) q^{63} +(0.190983 - 0.138757i) q^{64} +(0.954915 + 1.65396i) q^{65} +(0.0757724 + 2.04839i) q^{66} +(-5.30902 + 9.19549i) q^{67} +(1.82709 + 0.813473i) q^{68} +(-1.92705 - 5.93085i) q^{69} +(1.42238 + 3.36833i) q^{70} +(-4.23607 - 3.07768i) q^{71} +(0.467465 - 4.44764i) q^{72} +(2.77415 + 3.08100i) q^{73} +(3.07715 + 0.654069i) q^{74} -12.7082 q^{76} +(8.77360 - 0.154962i) q^{77} -0.527864 q^{78} +(0.646976 + 0.288052i) q^{79} +(4.05530 + 0.861981i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-0.298335 + 2.83847i) q^{82} +(7.28115 + 5.29007i) q^{83} +(4.24803 + 0.529617i) q^{84} +(0.854102 + 2.62866i) q^{85} +(-3.86984 - 1.72296i) q^{86} +(0.572949 - 0.992377i) q^{87} +(-4.13436 + 6.15687i) q^{88} +(-5.23607 - 9.06914i) q^{89} +(2.23607 - 1.62460i) q^{90} +(-0.0436417 + 2.25932i) q^{91} +(3.11803 - 9.59632i) q^{92} +(-0.691773 + 6.58178i) q^{93} +(4.78339 - 2.12970i) q^{94} +(-11.7515 - 13.0513i) q^{95} +(-3.75920 + 4.17501i) q^{96} +(-2.30902 + 1.67760i) q^{97} +(-0.618034 + 4.28187i) q^{98} +(-1.61803 - 6.43288i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + q^{3} + 2 q^{4} - 5 q^{5} + 4 q^{6} - 5 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + q^3 + 2 * q^4 - 5 * q^5 + 4 * q^6 - 5 * q^7 + 10 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + q^{3} + 2 q^{4} - 5 q^{5} + 4 q^{6} - 5 q^{7} + 10 q^{8} - 2 q^{9} - 10 q^{10} + 4 q^{11} + 2 q^{12} - 10 q^{13} + 3 q^{14} - 10 q^{15} + 6 q^{16} - 4 q^{17} - 6 q^{18} - 3 q^{19} - 10 q^{20} - 16 q^{21} - 4 q^{22} + 16 q^{23} + 5 q^{24} - 15 q^{26} + 10 q^{27} - 12 q^{28} + 24 q^{29} + 5 q^{30} + 8 q^{31} + 18 q^{32} - 11 q^{33} + 24 q^{34} - 5 q^{35} + 8 q^{36} - 13 q^{37} - 9 q^{38} + 5 q^{39} - 5 q^{40} + 2 q^{41} + 10 q^{42} + 28 q^{43} - 12 q^{44} + 8 q^{46} + 6 q^{47} + 18 q^{48} - 11 q^{49} + 6 q^{51} - 5 q^{52} - 12 q^{53} + 10 q^{54} + 10 q^{55} - 24 q^{57} - 21 q^{58} - 18 q^{59} + 5 q^{60} + 18 q^{61} - 28 q^{62} - 2 q^{63} + 6 q^{64} + 30 q^{65} + 2 q^{66} - 38 q^{67} + 2 q^{68} - 2 q^{69} + 20 q^{70} - 16 q^{71} - 10 q^{72} + 15 q^{73} - 14 q^{74} - 48 q^{76} - 4 q^{77} - 40 q^{78} + 9 q^{79} - 15 q^{80} + q^{81} + 7 q^{82} + 18 q^{83} + 2 q^{84} - 20 q^{85} - 7 q^{86} + 18 q^{87} - 5 q^{88} - 24 q^{89} + 50 q^{91} + 16 q^{92} + 8 q^{93} + 8 q^{94} + 15 q^{95} - 2 q^{96} - 14 q^{97} + 4 q^{98} - 4 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + q^3 + 2 * q^4 - 5 * q^5 + 4 * q^6 - 5 * q^7 + 10 * q^8 - 2 * q^9 - 10 * q^10 + 4 * q^11 + 2 * q^12 - 10 * q^13 + 3 * q^14 - 10 * q^15 + 6 * q^16 - 4 * q^17 - 6 * q^18 - 3 * q^19 - 10 * q^20 - 16 * q^21 - 4 * q^22 + 16 * q^23 + 5 * q^24 - 15 * q^26 + 10 * q^27 - 12 * q^28 + 24 * q^29 + 5 * q^30 + 8 * q^31 + 18 * q^32 - 11 * q^33 + 24 * q^34 - 5 * q^35 + 8 * q^36 - 13 * q^37 - 9 * q^38 + 5 * q^39 - 5 * q^40 + 2 * q^41 + 10 * q^42 + 28 * q^43 - 12 * q^44 + 8 * q^46 + 6 * q^47 + 18 * q^48 - 11 * q^49 + 6 * q^51 - 5 * q^52 - 12 * q^53 + 10 * q^54 + 10 * q^55 - 24 * q^57 - 21 * q^58 - 18 * q^59 + 5 * q^60 + 18 * q^61 - 28 * q^62 - 2 * q^63 + 6 * q^64 + 30 * q^65 + 2 * q^66 - 38 * q^67 + 2 * q^68 - 2 * q^69 + 20 * q^70 - 16 * q^71 - 10 * q^72 + 15 * q^73 - 14 * q^74 - 48 * q^76 - 4 * q^77 - 40 * q^78 + 9 * q^79 - 15 * q^80 + q^81 + 7 * q^82 + 18 * q^83 + 2 * q^84 - 20 * q^85 - 7 * q^86 + 18 * q^87 - 5 * q^88 - 24 * q^89 + 50 * q^91 + 16 * q^92 + 8 * q^93 + 8 * q^94 + 15 * q^95 - 2 * q^96 - 14 * q^97 + 4 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.564602	−	0.251377i	−0.399234	−	0.177750i	0.197291	−	0.980345i	$-0.436786\pi$
$2$	−0.564602	−	0.251377i	−0.399234	−	0.177750i	−0.596525	+	0.802595i	$0.703452\pi$
$3$	−0.978148	−	0.207912i	−0.564734	−	0.120038i	−0.0833066	−	0.996524i	$-0.526548\pi$
$3$	−0.978148	−	0.207912i	−0.564734	−	0.120038i	−0.481427	+	0.876486i	$0.659881\pi$
$4$	−1.08268	−	1.20243i	−0.541338	−	0.601217i
$5$	0.233733	−	2.22382i	0.104528	−	0.994522i	−0.809017	−	0.587785i	$-0.800000\pi$
$5$	0.233733	−	2.22382i	0.104528	−	0.994522i	0.913545	−	0.406737i	$-0.133333\pi$
$6$	0.500000	+	0.363271i	0.204124	+	0.148305i
$7$	1.59618	−	2.11002i	0.603300	−	0.797514i
$7$	1.59618	−	2.11002i	0.603300	−	0.797514i
$8$	0.690983	+	2.12663i	0.244299	+	0.751876i
$9$	−1.82709	−	0.813473i	−0.609030	−	0.271158i
$10$	−0.690983	+	1.19682i	−0.218508	+	0.378467i
$11$	2.04732	+	2.60931i	0.617290	+	0.786736i
$11$	2.04732	+	2.60931i	0.617290	+	0.786736i
$12$	0.809017	+	1.40126i	0.233543	+	0.404508i
$13$	−0.690983	+	0.502029i	−0.191644	+	0.139238i	−0.679470	−	0.733703i	$-0.737790\pi$
$13$	−0.690983	+	0.502029i	−0.191644	+	0.139238i	0.487826	+	0.872941i	$0.337790\pi$
$14$	−1.43162	+	0.790081i	−0.382616	+	0.211158i
$15$	−0.690983	+	2.12663i	−0.178411	+	0.549093i
$16$	−0.193806	+	1.84395i	−0.0484516	+	0.460986i
$17$	−1.12920	+	0.502754i	−0.273872	+	0.121936i	−0.539077	−	0.842256i	$-0.681227\pi$
$17$	−1.12920	+	0.502754i	−0.273872	+	0.121936i	0.265205	+	0.964192i	$0.414560\pi$
$18$	0.827091	+	0.918578i	0.194947	+	0.216511i
$19$	5.25542	−	5.83674i	1.20568	−	1.33904i	0.280335	−	0.959902i	$-0.409554\pi$
$19$	5.25542	−	5.83674i	1.20568	−	1.33904i	0.925341	−	0.379137i	$-0.123779\pi$
$20$	−2.92705	+	2.12663i	−0.654508	+	0.475528i
$21$	−2.00000	+	1.73205i	−0.436436	+	0.377964i
$22$	−0.500000	−	1.98787i	−0.106600	−	0.423815i
$23$	3.11803	+	5.40059i	0.650155	+	1.12610i	0.983085	+	0.183150i	$0.0586294\pi$
$23$	3.11803	+	5.40059i	0.650155	+	1.12610i	−0.332930	+	0.942952i	$0.608037\pi$
$24$	−0.233733	−	2.22382i	−0.0477105	−	0.453935i
$25$		0			0
$26$	0.516329	−	0.109749i	0.101260	−	0.0215236i
$27$	4.04508	+	2.93893i	0.778477	+	0.565597i
$28$	−4.26531	+	0.365171i	−0.806068	+	0.0690108i
$29$	−0.354102	+	1.08981i	−0.0657551	+	0.202373i	−0.978536	−	0.206076i	$-0.933930\pi$
$29$	−0.354102	+	1.08981i	−0.0657551	+	0.202373i	0.912781	+	0.408450i	$0.133930\pi$
$30$	0.924716	−	1.02700i	0.168829	−	0.187504i
$31$	−0.691773	−	6.58178i	−0.124246	−	1.18212i	−0.861948	−	0.506996i	$-0.830756\pi$
$31$	−0.691773	−	6.58178i	−0.124246	−	1.18212i	0.737702	−	0.675126i	$-0.235911\pi$
$32$	2.80902	−	4.86536i	0.496569	−	0.860082i
$33$	−1.46007	−	2.97795i	−0.254166	−	0.518395i
$34$	0.763932			0.131013
$35$	−4.31923	−	4.04280i	−0.730084	−	0.683358i
$36$	1.00000	+	3.07768i	0.166667	+	0.512947i
$37$	−4.97894	+	1.05831i	−0.818532	+	0.173984i	−0.598104	−	0.801419i	$-0.704079\pi$
$37$	−4.97894	+	1.05831i	−0.818532	+	0.173984i	−0.220429	+	0.975403i	$0.570746\pi$
$38$	−4.43444	+	1.97434i	−0.719362	+	0.320280i
$39$	0.780261	−	0.347395i	0.124942	−	0.0556277i
$40$	4.89074	−	1.03956i	0.773294	−	0.164369i
$41$	−1.42705	−	4.39201i	−0.222868	−	0.685917i	−0.998501	−	0.0547329i	$-0.982569\pi$
$41$	−1.42705	−	4.39201i	−0.222868	−	0.685917i	0.775633	−	0.631184i	$-0.217431\pi$
$42$	1.56460	−	0.475165i	0.241423	−	0.0733196i
$43$	6.85410			1.04524			0.522620	−	0.852566i	$-0.324955\pi$
$43$	6.85410			1.04524			0.522620	+	0.852566i	$0.324955\pi$
$44$	0.920937	−	5.28680i	0.138837	−	0.797015i
$45$	−2.23607	+	3.87298i	−0.333333	+	0.577350i
$46$	−0.402863	−	3.83299i	−0.0593990	−	0.565143i
$47$	−5.66897	+	6.29602i	−0.826904	+	0.918369i	−0.997758	−	0.0669268i	$-0.978681\pi$
$47$	−5.66897	+	6.29602i	−0.826904	+	0.918369i	0.170854	+	0.985296i	$0.445347\pi$
$48$	0.572949	−	1.76336i	0.0826981	−	0.254518i
$49$	−1.90441	−	6.73597i	−0.272058	−	0.962281i
$50$		0			0
$51$	1.20906	−	0.256993i	0.169302	−	0.0359862i
$52$	1.35177	+	0.287327i	0.187456	+	0.0398451i
$53$	0.532068	+	5.06229i	0.0730851	+	0.695358i	0.968311	+	0.249746i	$0.0803472\pi$
$53$	0.532068	+	5.06229i	0.0730851	+	0.695358i	−0.895226	+	0.445612i	$0.852986\pi$
$54$	−1.54508	−	2.67617i	−0.210259	−	0.364180i
$55$	6.28115	−	3.94298i	0.846950	−	0.531672i
$56$	5.59017	+	1.93649i	0.747018	+	0.258775i
$57$	−6.35410	+	4.61653i	−0.841621	+	0.611474i
$58$	0.473881	−	0.526298i	0.0622236	−	0.0691063i
$59$	2.48127	+	2.75573i	0.323034	+	0.358766i	0.882687	−	0.469961i	$-0.155732\pi$
$59$	2.48127	+	2.75573i	0.323034	+	0.358766i	−0.559653	+	0.828727i	$0.689065\pi$
$60$	3.30524	−	1.47159i	0.426704	−	0.189981i
$61$	−0.725874	+	6.90623i	−0.0929387	+	0.884252i	0.844372	+	0.535757i	$0.179974\pi$
$61$	−0.725874	+	6.90623i	−0.0929387	+	0.884252i	−0.937311	+	0.348495i	$0.886693\pi$
$62$	−1.26393	+	3.88998i	−0.160520	+	0.494028i
$63$	−4.63282	+	2.55676i	−0.583680	+	0.322121i
$64$	0.190983	−	0.138757i	0.0238729	−	0.0173447i
$65$	0.954915	+	1.65396i	0.118443	+	0.205149i
$66$	0.0757724	+	2.04839i	0.00932694	+	0.252139i
$67$	−5.30902	+	9.19549i	−0.648600	+	1.12341i	0.334858	+	0.942269i	$0.391312\pi$
$67$	−5.30902	+	9.19549i	−0.648600	+	1.12341i	−0.983458	+	0.181139i	$0.942022\pi$
$68$	1.82709	+	0.813473i	0.221567	+	0.0986481i
$69$	−1.92705	−	5.93085i	−0.231990	−	0.713991i
$70$	1.42238	+	3.36833i	0.170007	+	0.402592i
$71$	−4.23607	−	3.07768i	−0.502729	−	0.365254i	0.307330	−	0.951603i	$-0.400565\pi$
$71$	−4.23607	−	3.07768i	−0.502729	−	0.365254i	−0.810058	+	0.586349i	$0.800565\pi$
$72$	0.467465	−	4.44764i	0.0550913	−	0.524159i
$73$	2.77415	+	3.08100i	0.324689	+	0.360604i	0.883285	−	0.468836i	$-0.155326\pi$
$73$	2.77415	+	3.08100i	0.324689	+	0.360604i	−0.558596	+	0.829440i	$0.688660\pi$
$74$	3.07715	+	0.654069i	0.357712	+	0.0760340i
$75$		0			0
$76$	−12.7082			−1.45773
$77$	8.77360	−	0.154962i	0.999844	−	0.0176596i
$78$	−0.527864			−0.0597688
$79$	0.646976	+	0.288052i	0.0727905	+	0.0324084i	0.442809	−	0.896616i	$-0.353982\pi$
$79$	0.646976	+	0.288052i	0.0727905	+	0.0324084i	−0.370018	+	0.929024i	$0.620649\pi$
$80$	4.05530	+	0.861981i	0.453396	+	0.0963724i
$81$	0.669131	+	0.743145i	0.0743478	+	0.0825716i
$82$	−0.298335	+	2.83847i	−0.0329456	+	0.313456i
$83$	7.28115	+	5.29007i	0.799210	+	0.580660i	0.910682	−	0.413107i	$-0.135557\pi$
$83$	7.28115	+	5.29007i	0.799210	+	0.580660i	−0.111472	+	0.993768i	$0.535557\pi$
$84$	4.24803	+	0.529617i	0.463498	+	0.0577860i
$85$	0.854102	+	2.62866i	0.0926404	+	0.285118i
$86$	−3.86984	−	1.72296i	−0.417296	−	0.185792i
$87$	0.572949	−	0.992377i	0.0614266	−	0.106394i
$88$	−4.13436	+	6.15687i	−0.440725	+	0.656325i
$89$	−5.23607	−	9.06914i	−0.555022	−	0.961326i	−0.997902	−	0.0647454i	$-0.979376\pi$
$89$	−5.23607	−	9.06914i	−0.555022	−	0.961326i	0.442880	−	0.896581i	$-0.353957\pi$
$90$	2.23607	−	1.62460i	0.235702	−	0.171248i
$91$	−0.0436417	+	2.25932i	−0.00457490	+	0.236841i
$92$	3.11803	−	9.59632i	0.325078	−	1.00049i
$93$	−0.691773	+	6.58178i	−0.0717335	+	0.682499i
$94$	4.78339	−	2.12970i	0.493369	−	0.219662i
$95$	−11.7515	−	13.0513i	−1.20568	−	1.33904i
$96$	−3.75920	+	4.17501i	−0.383672	+	0.426110i
$97$	−2.30902	+	1.67760i	−0.234445	+	0.170334i	−0.698805	−	0.715312i	$-0.746284\pi$
$97$	−2.30902	+	1.67760i	−0.234445	+	0.170334i	0.464360	+	0.885647i	$0.346284\pi$
$98$	−0.618034	+	4.28187i	−0.0624309	+	0.432534i
$99$	−1.61803	−	6.43288i	−0.162619	−	0.646529i
$100$		0			0
$101$	0.408689	+	3.88841i	0.0406660	+	0.386911i	0.995858	+	0.0909239i	$0.0289820\pi$
$101$	0.408689	+	3.88841i	0.0406660	+	0.386911i	−0.955192	+	0.295987i	$0.904351\pi$
$102$	−0.747238	−	0.158830i	−0.0739876	−	0.0157266i
$103$	−5.86889	+	1.24747i	−0.578278	+	0.122917i	−0.487760	−	0.872978i	$-0.662186\pi$
$103$	−5.86889	+	1.24747i	−0.578278	+	0.122917i	−0.0905187	+	0.995895i	$0.528852\pi$
$104$	−1.54508	−	1.12257i	−0.151508	−	0.110077i
$105$	3.38430	+	4.85247i	0.330274	+	0.473553i
$106$	0.972136	−	2.99193i	0.0944222	−	0.290602i
$107$	7.48111	−	8.30861i	0.723226	−	0.803224i	−0.263665	−	0.964614i	$-0.584931\pi$
$107$	7.48111	−	8.30861i	0.723226	−	0.803224i	0.986891	+	0.161391i	$0.0515979\pi$
$108$	−0.845653	−	8.04585i	−0.0813730	−	0.774212i
$109$	3.42705	−	5.93583i	0.328252	−	0.568549i	−0.653913	−	0.756570i	$-0.726874\pi$
$109$	3.42705	−	5.93583i	0.328252	−	0.568549i	0.982165	+	0.188021i	$0.0602072\pi$
$110$	−4.53753	+	0.647279i	−0.432636	+	0.0617156i
$111$	5.09017			0.483138
$112$	3.58142	+	3.35221i	0.338412	+	0.316754i
$113$	−2.80902	−	8.64527i	−0.264250	−	0.813278i	−0.991865	−	0.127293i	$-0.959371\pi$
$113$	−2.80902	−	8.64527i	−0.264250	−	0.813278i	0.727615	−	0.685986i	$-0.240629\pi$
$114$	4.74803	−	1.00922i	0.444694	−	0.0945225i
$115$	12.7387	−	5.67165i	1.18789	−	0.528884i
$116$	1.69381	−	0.754131i	0.157266	−	0.0700193i
$117$	1.67088	−	0.355156i	0.154473	−	0.0328341i
$118$	−0.708204	−	2.17963i	−0.0651955	−	0.200651i
$119$	−0.741591	+	3.18514i	−0.0679816	+	0.291981i
$120$	−5.00000			−0.456435
$121$	−2.61698	+	10.6842i	−0.237907	+	0.971288i
$122$	2.14590	−	3.71680i	0.194280	−	0.336504i
$123$	0.482716	+	4.59274i	0.0435250	+	0.414113i
$124$	−7.16519	+	7.95775i	−0.643453	+	0.714627i
$125$	3.45492	−	10.6331i	0.309017	−	0.951057i
$126$	3.25841	−	0.278966i	0.290282	−	0.0248522i
$127$	−3.42705	−	2.48990i	−0.304102	−	0.220943i	0.425260	−	0.905071i	$-0.360183\pi$
$127$	−3.42705	−	2.48990i	−0.304102	−	0.220943i	−0.729361	+	0.684129i	$0.760183\pi$
$128$	−11.1332	+	2.36644i	−0.984049	+	0.209166i
$129$	−6.70432	−	1.42505i	−0.590283	−	0.125468i
$130$	−0.123379	−	1.17387i	−0.0108211	−	0.102956i
$131$	4.66312	+	8.07676i	0.407419	+	0.705670i	0.994600	−	0.103786i	$-0.0330957\pi$
$131$	4.66312	+	8.07676i	0.407419	+	0.705670i	−0.587181	+	0.809456i	$0.699762\pi$
$132$	−2.00000	+	4.97980i	−0.174078	+	0.433436i
$133$	−3.92705	−	20.4056i	−0.340519	−	1.76939i
$134$	5.30902	−	3.85723i	0.458629	−	0.333214i
$135$	7.48111	−	8.30861i	0.643871	−	0.715091i
$136$	−1.84943	−	2.05400i	−0.158587	−	0.176129i
$137$	−14.0012	+	6.23374i	−1.19620	+	0.532585i	−0.905548	−	0.424243i	$-0.860540\pi$
$137$	−14.0012	+	6.23374i	−1.19620	+	0.532585i	−0.290656	+	0.956828i	$0.593874\pi$
$138$	−0.402863	+	3.83299i	−0.0342940	+	0.326286i
$139$	−6.92705	+	21.3193i	−0.587545	+	1.80828i	0.00125662	+	0.999999i	$0.499600\pi$
$139$	−6.92705	+	21.3193i	−0.587545	+	1.80828i	−0.588801	+	0.808278i	$0.700400\pi$
$140$	−0.184869	+	9.57063i	−0.0156243	+	0.808866i
$141$	6.85410	−	4.97980i	0.577220	−	0.419375i
$142$	1.61803	+	2.80252i	0.135782	+	0.235182i
$143$	−2.72461	−	0.775175i	−0.227843	−	0.0648234i
$144$	1.85410	−	3.21140i	0.154508	−	0.267617i
$145$	2.34078	+	1.04218i	0.194391	+	0.0865486i
$146$	−0.791796	−	2.43690i	−0.0655295	−	0.201679i
$147$	0.462307	+	6.98472i	0.0381304	+	0.576090i
$148$	6.66312	+	4.84104i	0.547705	+	0.397931i
$149$	1.82994	−	17.4107i	0.149914	−	1.42634i	−0.618198	−	0.786023i	$-0.712137\pi$
$149$	1.82994	−	17.4107i	0.149914	−	1.42634i	0.768112	−	0.640316i	$-0.221196\pi$
$150$		0			0
$151$	2.32991	+	0.495239i	0.189606	+	0.0403019i	0.301736	−	0.953392i	$-0.402434\pi$
$151$	2.32991	+	0.495239i	0.189606	+	0.0403019i	−0.112130	+	0.993694i	$0.535767\pi$
$152$	16.0440	+	7.14323i	1.30134	+	0.579393i
$153$	2.47214			0.199860
$154$	−4.99255	−	2.11799i	−0.402311	−	0.170672i
$155$	−14.7984			−1.18863
$156$	−1.26249	−	0.562096i	−0.101080	−	0.0450037i
$157$	15.8813	+	3.37567i	1.26746	+	0.269408i	0.792105	−	0.610385i	$-0.208985\pi$
$157$	15.8813	+	3.37567i	1.26746	+	0.269408i	0.475358	+	0.879792i	$0.342318\pi$
$158$	−0.292875	−	0.325270i	−0.0232998	−	0.0258771i
$159$	0.532068	−	5.06229i	0.0421957	−	0.401465i
$160$	−10.1631	−	7.38394i	−0.803465	−	0.583752i
$161$	16.3723	+	2.04120i	1.29032	+	0.160869i
$162$	−0.190983	−	0.587785i	−0.0150050	−	0.0461808i
$163$	13.4875	+	6.00503i	1.05642	+	0.470350i	0.860067	−	0.510182i	$-0.170422\pi$
$163$	13.4875	+	6.00503i	1.05642	+	0.470350i	0.196358	+	0.980532i	$0.437089\pi$
$164$	−3.73607	+	6.47106i	−0.291738	+	0.505305i
$165$	−6.96369	+	2.55089i	−0.542122	+	0.198587i
$166$	−2.78115	−	4.81710i	−0.215859	−	0.373879i
$167$	−2.38197	+	1.73060i	−0.184322	+	0.133918i	−0.676120	−	0.736792i	$-0.736340\pi$
$167$	−2.38197	+	1.73060i	−0.184322	+	0.133918i	0.491798	+	0.870709i	$0.336340\pi$
$168$	−5.06539	−	3.05644i	−0.390803	−	0.235809i
$169$	−3.79180	+	11.6699i	−0.291677	+	0.897688i
$170$	0.178556	−	1.69885i	0.0136946	−	0.130296i
$171$	−14.3502	+	6.38910i	−1.09738	+	0.488587i
$172$	−7.42077	−	8.24160i	−0.565829	−	0.628416i
$173$	−13.0294	+	14.4706i	−0.990607	+	1.10018i	0.00436121	+	0.999990i	$0.498612\pi$
$173$	−13.0294	+	14.4706i	−0.990607	+	1.10018i	−0.994968	+	0.100190i	$0.968055\pi$
$174$	−0.572949	+	0.416272i	−0.0434352	+	0.0315575i
$175$		0			0
$176$	−5.20820	+	3.26944i	−0.392583	+	0.246443i
$177$	−1.85410	−	3.21140i	−0.139363	−	0.241384i
$178$	0.676522	+	6.43668i	0.0507075	+	0.482450i
$179$	17.1240	+	3.63982i	1.27991	+	0.272053i	0.797193	−	0.603724i	$-0.206317\pi$
$179$	17.1240	+	3.63982i	1.27991	+	0.272053i	0.482716	+	0.875777i	$0.339650\pi$
$180$	7.07794	−	1.50446i	0.527559	−	0.112136i
$181$	−0.954915	−	0.693786i	−0.0709783	−	0.0515687i	0.551730	−	0.834023i	$-0.313968\pi$
$181$	−0.954915	−	0.693786i	−0.0709783	−	0.0515687i	−0.622709	+	0.782454i	$0.713968\pi$
$182$	0.592581	−	1.26465i	0.0439251	−	0.0937418i
$183$	2.14590	−	6.60440i	0.158629	−	0.488211i
$184$	−9.33054	+	10.3626i	−0.687856	+	0.763942i
$185$	1.18974	+	11.3196i	0.0874714	+	0.832235i
$186$	2.04508	−	3.54219i	0.149953	−	0.259726i
$187$	−3.62368	−	1.91714i	−0.264990	−	0.140195i
$188$	13.7082			0.999774
$189$	12.6579	−	3.84417i	0.920727	−	0.279622i
$190$	3.35410	+	10.3229i	0.243332	+	0.748899i
$191$	−9.55057	+	2.03004i	−0.691055	+	0.146888i	−0.540035	−	0.841643i	$-0.681589\pi$
$191$	−9.55057	+	2.03004i	−0.691055	+	0.146888i	−0.151020	+	0.988531i	$0.548256\pi$
$192$	−0.215659	+	0.0960175i	−0.0155638	+	0.00692947i
$193$	3.81893	−	1.70030i	0.274893	−	0.122390i	−0.264660	−	0.964342i	$-0.585260\pi$
$193$	3.81893	−	1.70030i	0.274893	−	0.122390i	0.539553	+	0.841952i	$0.318593\pi$
$194$	1.72539	−	0.366742i	0.123875	−	0.0263305i
$195$	−0.590170	−	1.81636i	−0.0422629	−	0.130072i
$196$	−6.03769	+	9.58279i	−0.431264	+	0.684485i
$197$	4.61803			0.329021			0.164511	−	0.986375i	$-0.447396\pi$
$197$	4.61803			0.329021			0.164511	+	0.986375i	$0.447396\pi$
$198$	−0.703533	+	4.03876i	−0.0499979	+	0.287022i
$199$	−0.718847	+	1.24508i	−0.0509577	+	0.0882614i	−0.890379	−	0.455220i	$-0.849561\pi$
$199$	−0.718847	+	1.24508i	−0.0509577	+	0.0882614i	0.839421	+	0.543481i	$0.182894\pi$
$200$		0			0
$201$	7.10485	−	7.89074i	0.501138	−	0.556570i
$202$	0.746711	−	2.29814i	0.0525384	−	0.161697i
$203$	1.73432	+	2.48670i	0.121726	+	0.174532i
$204$	−1.61803	−	1.17557i	−0.113285	−	0.0823064i
$205$	−10.1006	+	2.14695i	−0.705455	+	0.149949i
$206$	3.62717	+	0.770979i	0.252717	+	0.0537166i
$207$	−1.30369	−	12.4038i	−0.0906129	−	0.862125i
$208$	−0.791796	−	1.37143i	−0.0549012	−	0.0950916i
$209$	25.9894	+	1.76336i	1.79772	+	0.121974i
$210$	−0.690983	−	3.59045i	−0.0476824	−	0.247765i
$211$	7.28115	−	5.29007i	0.501255	−	0.364183i	−0.308241	−	0.951308i	$-0.599740\pi$
$211$	7.28115	−	5.29007i	0.501255	−	0.364183i	0.809496	+	0.587125i	$0.199740\pi$
$212$	5.51101	−	6.12059i	0.378497	−	0.420364i
$213$	3.50361	+	3.89116i	0.240064	+	0.266618i
$214$	−6.31244	+	2.81048i	−0.431510	+	0.192121i
$215$	1.60203	−	15.2423i	0.109257	−	1.03951i
$216$	−3.45492	+	10.6331i	−0.235077	+	0.723493i
$217$	−14.9919	−	9.04606i	−1.01772	−	0.614086i
$218$	−3.42705	+	2.48990i	−0.232109	+	0.168637i
$219$	−2.07295	−	3.59045i	−0.140077	−	0.242620i
$220$	−11.5416	−	3.28370i	−0.778137	−	0.221387i
$221$	0.527864	−	0.914287i	0.0355080	−	0.0615016i
$222$	−2.87392	−	1.27955i	−0.192885	−	0.0858779i
$223$	−7.98936	−	24.5887i	−0.535007	−	1.64658i	−0.743634	−	0.668587i	$-0.766900\pi$
$223$	−7.98936	−	24.5887i	−0.535007	−	1.64658i	0.208627	−	0.977995i	$-0.433100\pi$
$224$	−5.78233	−	13.6931i	−0.386348	−	0.914908i
$225$		0			0
$226$	−0.587244	+	5.58726i	−0.0390629	+	0.371659i
$227$	−12.9921	−	14.4292i	−0.862317	−	0.957700i	0.137143	−	0.990551i	$-0.456208\pi$
$227$	−12.9921	−	14.4292i	−0.862317	−	0.957700i	−0.999460	+	0.0328514i	$0.989541\pi$
$228$	12.4305	+	2.64218i	0.823230	+	0.174983i
$229$	−0.780261	−	0.347395i	−0.0515611	−	0.0229565i	0.380794	−	0.924660i	$-0.375651\pi$
$229$	−0.780261	−	0.347395i	−0.0515611	−	0.0229565i	−0.432355	+	0.901703i	$0.642317\pi$
$230$	−8.61803			−0.568256
$231$	−8.61409	−	1.67256i	−0.566766	−	0.110046i
$232$	−2.56231			−0.168224
$233$	7.39074	+	3.29057i	0.484183	+	0.215572i	0.634287	−	0.773098i	$-0.281294\pi$
$233$	7.39074	+	3.29057i	0.484183	+	0.215572i	−0.150103	+	0.988670i	$0.547961\pi$
$234$	−1.03266	−	0.219498i	−0.0675070	−	0.0143490i
$235$	12.6762	+	14.0783i	0.826904	+	0.918369i
$236$	0.627171	−	5.96713i	0.0408253	−	0.388427i
$237$	−0.572949	−	0.416272i	−0.0372170	−	0.0270398i
$238$	1.21937	−	1.61192i	0.0790403	−	0.104485i
$239$	−0.218847	−	0.673542i	−0.0141560	−	0.0435678i	0.943729	−	0.330720i	$-0.107292\pi$
$239$	−0.218847	−	0.673542i	−0.0141560	−	0.0435678i	−0.957885	+	0.287152i	$0.907292\pi$
$240$	−3.78747	−	1.68629i	−0.244480	−	0.108849i
$241$	14.2082	−	24.6093i	0.915231	−	1.58523i	0.108668	−	0.994078i	$-0.465341\pi$
$241$	14.2082	−	24.6093i	0.915231	−	1.58523i	0.806563	−	0.591148i	$-0.201325\pi$
$242$	4.16331	−	5.37446i	0.267627	−	0.345483i
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$	9.09017	−	6.60440i	0.581938	−	0.422803i
$245$	−15.4247	+	2.66064i	−0.985447	+	0.169982i
$246$	0.881966	−	2.71441i	0.0562321	−	0.173065i
$247$	−0.701198	+	6.67146i	−0.0446162	+	0.424495i
$248$	13.5190	−	6.01904i	0.858457	−	0.382209i
$249$	−6.02218	−	6.68830i	−0.381640	−	0.423854i
$250$	−4.62358	+	5.13500i	−0.292421	+	0.324766i
$251$	−14.0172	+	10.1841i	−0.884759	+	0.642815i	−0.934506	−	0.355947i	$-0.884158\pi$
$251$	−14.0172	+	10.1841i	−0.884759	+	0.642815i	0.0497471	+	0.998762i	$0.484158\pi$
$252$	8.09017	+	2.80252i	0.509633	+	0.176542i
$253$	−7.70820	+	19.1926i	−0.484611	+	1.20663i
$254$	1.30902	+	2.26728i	0.0821350	+	0.142262i
$255$	−0.288910	−	2.74879i	−0.0180922	−	0.172136i
$256$	6.41890	+	1.36438i	0.401181	+	0.0852738i
$257$	−5.81438	+	1.23588i	−0.362691	+	0.0770923i	−0.385653	−	0.922644i	$-0.626024\pi$
$257$	−5.81438	+	1.23588i	−0.362691	+	0.0770923i	0.0229619	+	0.999736i	$0.492690\pi$
$258$	3.42705	+	2.48990i	0.213359	+	0.155014i
$259$	−5.71424	+	12.1949i	−0.355065	+	0.757756i
$260$	0.954915	−	2.93893i	0.0592213	−	0.182264i
$261$	1.53351	−	1.70314i	0.0949219	−	0.105421i
$262$	−0.602495	−	5.73236i	−0.0372223	−	0.354146i
$263$	−6.00000	+	10.3923i	−0.369976	+	0.640817i	−0.989561	−	0.144112i	$-0.953967\pi$
$263$	−6.00000	+	10.3923i	−0.369976	+	0.640817i	0.619586	+	0.784929i	$0.287301\pi$
$264$	5.32410	−	5.16274i	0.327676	−	0.317745i
$265$	11.3820			0.699189
$266$	−2.91227	+	12.5082i	−0.178563	+	0.766926i
$267$	3.23607	+	9.95959i	0.198044	+	0.609517i
$268$	16.8049	−	3.57199i	1.02652	−	0.218194i
$269$	−20.7764	+	9.25027i	−1.26676	+	0.563999i	−0.926487	−	0.376327i	$-0.877187\pi$
$269$	−20.7764	+	9.25027i	−1.26676	+	0.563999i	−0.340275	+	0.940326i	$0.610520\pi$
$270$	−6.31244	+	2.81048i	−0.384163	+	0.171040i
$271$	24.5756	−	5.22370i	1.49286	−	0.317317i	0.612062	−	0.790810i	$-0.290340\pi$
$271$	24.5756	−	5.22370i	1.49286	−	0.317317i	0.880798	+	0.473492i	$0.157007\pi$
$272$	−0.708204	−	2.17963i	−0.0429412	−	0.132159i
$273$	0.512427	−	2.20087i	0.0310135	−	0.133203i
$274$	9.47214			0.572233
$275$		0			0
$276$	−5.04508	+	8.73834i	−0.303678	+	0.525986i
$277$	1.32837	+	12.6386i	0.0798140	+	0.759379i	0.959097	+	0.283079i	$0.0913558\pi$
$277$	1.32837	+	12.6386i	0.0798140	+	0.759379i	−0.879283	+	0.476300i	$0.841978\pi$
$278$	9.27020	−	10.2956i	0.555990	−	0.617489i
$279$	−4.09017	+	12.5882i	−0.244872	+	0.753639i
$280$	5.61301	−	11.9789i	0.335442	−	0.715876i
$281$	21.5623	+	15.6659i	1.28630	+	0.934551i	0.999724	−	0.0235065i	$-0.00748303\pi$
$281$	21.5623	+	15.6659i	1.28630	+	0.934551i	0.286576	+	0.958058i	$0.407483\pi$
$282$	−5.12165	+	1.08864i	−0.304990	+	0.0648276i
$283$	−6.27619	−	1.33405i	−0.373081	−	0.0793008i	0.0175553	−	0.999846i	$-0.494412\pi$
$283$	−6.27619	−	1.33405i	−0.373081	−	0.0793008i	−0.390636	+	0.920545i	$0.627745\pi$
$284$	0.885579	+	8.42572i	0.0525495	+	0.499975i
$285$	8.78115	+	15.2094i	0.520151	+	0.900927i
$286$	1.34346	+	1.12257i	0.0794404	+	0.0663790i
$287$	−11.5451	−	3.99933i	−0.681485	−	0.236073i
$288$	−9.09017	+	6.60440i	−0.535643	+	0.389168i
$289$	−10.3529	+	11.4980i	−0.608993	+	0.676355i
$290$	−1.05963	−	1.17684i	−0.0622236	−	0.0691063i
$291$	2.60735	−	1.16087i	0.152846	−	0.0680513i
$292$	0.701198	−	6.67146i	0.0410345	−	0.390417i
$293$	−1.09017	+	3.35520i	−0.0636884	+	0.196013i	−0.977837	−	0.209365i	$-0.932860\pi$
$293$	−1.09017	+	3.35520i	−0.0636884	+	0.196013i	0.914149	+	0.405378i	$0.132860\pi$
$294$	1.49478	−	4.05980i	0.0871772	−	0.236772i
$295$	6.70820	−	4.87380i	0.390567	−	0.283763i
$296$	−5.69098	−	9.85707i	−0.330782	−	0.572931i
$297$	0.613012	+	16.5718i	0.0355706	+	0.961593i
$298$	−5.40983	+	9.37010i	−0.313383	+	0.542795i
$299$	−4.86576	−	2.16638i	−0.281394	−	0.125285i
$300$		0			0
$301$	10.9404	−	14.4623i	0.630594	−	0.833595i
$302$	−1.19098	−	0.865300i	−0.0685334	−	0.0497924i
$303$	0.408689	−	3.88841i	0.0234785	−	0.223383i
$304$	9.74408	+	10.8219i	0.558862	+	0.620679i
$305$	15.1885	+	3.22842i	0.869693	+	0.184859i
$306$	−1.39577	−	0.621438i	−0.0797910	−	0.0355253i
$307$	−24.5066			−1.39866			−0.699332	−	0.714797i	$-0.746519\pi$
$307$	−24.5066			−1.39866			−0.699332	+	0.714797i	$0.746519\pi$
$308$	−9.68529	−	10.3819i	−0.551871	−	0.591563i
$309$	6.00000			0.341328
$310$	8.35519	+	3.71997i	0.474543	+	0.211280i
$311$	−30.6754	−	6.52025i	−1.73944	−	0.369730i	−0.774577	−	0.632480i	$-0.782037\pi$
$311$	−30.6754	−	6.52025i	−1.73944	−	0.369730i	−0.964864	+	0.262750i	$0.915371\pi$
$312$	1.27793	+	1.41928i	0.0723483	+	0.0803509i
$313$	1.14399	−	10.8843i	0.0646620	−	0.615218i	−0.913423	−	0.407012i	$-0.866571\pi$
$313$	1.14399	−	10.8843i	0.0646620	−	0.615218i	0.978085	−	0.208206i	$-0.0667625\pi$
$314$	−8.11803	−	5.89810i	−0.458127	−	0.332849i
$315$	4.60292	+	10.9001i	0.259345	+	0.614154i
$316$	−0.354102	−	1.08981i	−0.0199198	−	0.0613068i
$317$	−2.39169	−	1.06485i	−0.134331	−	0.0598080i	0.338470	−	0.940977i	$-0.390090\pi$
$317$	−2.39169	−	1.06485i	−0.134331	−	0.0598080i	−0.472801	+	0.881169i	$0.656757\pi$
$318$	−1.57295	+	2.72443i	−0.0882066	+	0.152778i
$319$	−3.56862	+	1.30723i	−0.199804	+	0.0731911i
$320$	−0.263932	−	0.457144i	−0.0147542	−	0.0255551i
$321$	−9.04508	+	6.57164i	−0.504847	+	0.366793i
$322$	−8.73074	−	5.26809i	−0.486545	−	0.293579i
$323$	−3.00000	+	9.23305i	−0.166924	+	0.513741i
$324$	0.169131	−	1.60917i	0.00939614	−	0.0893983i
$325$		0			0
$326$	−6.10556	−	6.78091i	−0.338156	−	0.375560i
$327$	−4.58629	+	5.09359i	−0.253622	+	0.281676i
$328$	8.35410	−	6.06961i	0.461278	−	0.335138i
$329$	4.23607	+	22.0113i	0.233542	+	1.21352i
$330$	4.57295	+	0.310271i	0.251733	+	0.0170798i
$331$	7.35410	+	12.7377i	0.404218	+	0.700126i	0.994230	−	0.107268i	$-0.0342104\pi$
$331$	7.35410	+	12.7377i	0.404218	+	0.700126i	−0.590012	+	0.807394i	$0.700877\pi$
$332$	−1.52218	−	14.4825i	−0.0835402	−	0.794832i
$333$	9.95788	+	2.11661i	0.545688	+	0.115990i
$334$	1.77990	−	0.378329i	0.0973916	−	0.0207012i
$335$	19.2082	+	13.9556i	1.04946	+	0.762475i
$336$	−2.80619	−	4.02357i	−0.153090	−	0.219504i
$337$	0.399187	−	1.22857i	0.0217451	−	0.0669245i	−0.939595	−	0.342288i	$-0.888798\pi$
$337$	0.399187	−	1.22857i	0.0217451	−	0.0669245i	0.961340	+	0.275363i	$0.0887982\pi$
$338$	5.07441	−	5.63571i	0.276012	−	0.306542i
$339$	0.950181	+	9.04037i	0.0516068	+	0.491006i
$340$	2.23607	−	3.87298i	0.121268	−	0.210042i
$341$	15.7576	−	15.2800i	0.853323	−	0.827461i
$342$	9.70820			0.524960
$343$	−17.2528	−	6.73347i	−0.931566	−	0.363573i
$344$	4.73607	+	14.5761i	0.255352	+	0.785892i
$345$	−13.6396	+	2.89918i	−0.734329	+	0.156086i
$346$	10.9940	−	4.89485i	0.591042	−	0.263149i
$347$	18.5375	−	8.25342i	0.995144	−	0.443067i	0.156460	−	0.987684i	$-0.449992\pi$
$347$	18.5375	−	8.25342i	0.995144	−	0.443067i	0.838684	+	0.544618i	$0.183325\pi$
$348$	−1.81359	+	0.385489i	−0.0972184	+	0.0206644i
$349$	−3.93769	−	12.1190i	−0.210780	−	0.648714i	−0.999426	−	0.0338669i	$-0.989218\pi$
$349$	−3.93769	−	12.1190i	−0.210780	−	0.648714i	0.788646	−	0.614847i	$-0.210782\pi$
$350$		0			0
$351$	−4.27051			−0.227943
$352$	18.4462	−	2.63135i	0.983184	−	0.140251i
$353$	2.23607	−	3.87298i	0.119014	−	0.206138i	−0.800363	−	0.599515i	$-0.795360\pi$
$353$	2.23607	−	3.87298i	0.119014	−	0.206138i	0.919377	+	0.393377i	$0.128693\pi$
$354$	0.239558	+	2.27924i	0.0127324	+	0.121140i
$355$	−7.83432	+	8.70089i	−0.415802	+	0.461795i
$356$	−5.23607	+	16.1150i	−0.277511	+	0.854091i
$357$	1.38761	−	2.96135i	0.0734403	−	0.156731i
$358$	−8.75329	−	6.35964i	−0.462626	−	0.336117i
$359$	−6.18799	+	1.31530i	−0.326590	+	0.0694188i	−0.368289	−	0.929711i	$-0.620056\pi$
$359$	−6.18799	+	1.31530i	−0.326590	+	0.0694188i	0.0416990	+	0.999130i	$0.486723\pi$
$360$	−9.78148	−	2.07912i	−0.515529	−	0.109579i
$361$	−4.46200	−	42.4531i	−0.234842	−	2.23437i
$362$	0.364745	+	0.631757i	0.0191706	+	0.0332044i
$363$	4.78115	−	9.90659i	0.250945	−	0.519961i
$364$	2.76393	−	2.39364i	0.144869	−	0.125461i
$365$	7.50000	−	5.44907i	0.392568	−	0.285217i
$366$	−2.87177	+	3.18943i	−0.150110	+	0.166714i
$367$	−4.19579	−	4.65990i	−0.219018	−	0.243245i	0.623616	−	0.781731i	$-0.285663\pi$
$367$	−4.19579	−	4.65990i	−0.219018	−	0.243245i	−0.842634	+	0.538486i	$0.818996\pi$
$368$	−10.5627	+	4.70281i	−0.550618	+	0.245151i
$369$	−0.965432	+	9.18547i	−0.0502584	+	0.478177i
$370$	2.17376	−	6.69015i	0.113009	−	0.347804i
$371$	11.5308	+	6.95765i	0.598651	+	0.361223i
$372$	8.66312	−	6.29412i	0.449162	−	0.326335i
$373$	−12.7984	−	22.1674i	−0.662675	−	1.14779i	−0.979910	−	0.199439i	$-0.936088\pi$
$373$	−12.7984	−	22.1674i	−0.662675	−	1.14779i	0.317235	−	0.948347i	$-0.397245\pi$
$374$	1.56401	+	1.99333i	0.0808731	+	0.103073i
$375$	−5.59017	+	9.68246i	−0.288675	+	0.500000i
$376$	−17.3065	−	7.70533i	−0.892512	−	0.397372i
$377$	−0.302439	−	0.930812i	−0.0155764	−	0.0479393i
$378$	−8.11301	−	1.01148i	−0.417288	−	0.0520249i
$379$	−6.70820	−	4.87380i	−0.344577	−	0.250350i	0.402013	−	0.915634i	$-0.368311\pi$
$379$	−6.70820	−	4.87380i	−0.344577	−	0.250350i	−0.746591	+	0.665284i	$0.768311\pi$
$380$	−2.97032	+	28.2607i	−0.152374	+	1.44975i
$381$	2.83448	+	3.14801i	0.145215	+	0.161278i
$382$	5.90257	+	1.25463i	0.302002	+	0.0641925i
$383$	1.64290	+	0.731465i	0.0839481	+	0.0373761i	0.448281	−	0.893893i	$-0.352036\pi$
$383$	1.64290	+	0.731465i	0.0839481	+	0.0373761i	−0.364333	+	0.931269i	$0.618703\pi$
$384$	11.3820			0.580834
$385$	1.70607	−	19.5471i	0.0869493	−	0.996213i
$386$	−2.58359			−0.131501
$387$	−12.5231	−	5.57563i	−0.636583	−	0.283425i
$388$	4.51712	+	0.960143i	0.229322	+	0.0487439i
$389$	−21.7281	−	24.1315i	−1.10166	−	1.22352i	−0.972749	−	0.231859i	$-0.925519\pi$
$389$	−21.7281	−	24.1315i	−1.10166	−	1.22352i	−0.128909	−	0.991656i	$-0.541148\pi$
$390$	−0.123379	+	1.17387i	−0.00624754	+	0.0594414i
$391$	−6.23607	−	4.53077i	−0.315372	−	0.229131i
$392$	13.0090	−	8.70440i	0.657052	−	0.439639i
$393$	−2.88197	−	8.86978i	−0.145376	−	0.447421i
$394$	−2.60735	−	1.16087i	−0.131356	−	0.0584837i
$395$	0.791796	−	1.37143i	0.0398396	−	0.0690042i
$396$	−5.98331	+	8.91031i	−0.300672	+	0.447760i
$397$	12.8435	+	22.2455i	0.644595	+	1.11647i	0.984395	+	0.175973i	$0.0563072\pi$
$397$	12.8435	+	22.2455i	0.644595	+	1.11647i	−0.339800	+	0.940498i	$0.610359\pi$
$398$	0.718847	−	0.522273i	0.0360325	−	0.0261792i
$399$	−0.401318	+	20.7761i	−0.0200910	+	1.04011i
$400$		0			0
$401$	0.00582517	−	0.0554228i	0.000290895	−	0.00276768i	−0.994375	−	0.105912i	$-0.966224\pi$
$401$	0.00582517	−	0.0554228i	0.000290895	−	0.00276768i	0.994666	+	0.103145i	$0.0328904\pi$
$402$	−5.99496	+	2.66913i	−0.299002	+	0.133124i
$403$	3.78224	+	4.20061i	0.188407	+	0.209247i
$404$	4.23308	−	4.70131i	0.210604	−	0.233899i
$405$	1.80902	−	1.31433i	0.0898908	−	0.0653095i
$406$	−0.354102	−	1.83997i	−0.0175738	−	0.0913161i
$407$	−12.9549	−	10.8249i	−0.642151	−	0.536570i
$408$	1.38197	+	2.39364i	0.0684175	+	0.118503i
$409$	0.294735	+	2.80421i	0.0145737	+	0.138659i	0.999389	−	0.0349444i	$-0.0111254\pi$
$409$	0.294735	+	2.80421i	0.0145737	+	0.138659i	−0.984816	+	0.173604i	$0.944459\pi$
$410$	6.24250	+	1.32689i	0.308295	+	0.0655302i
$411$	14.9913	−	3.18650i	0.739467	−	0.157179i
$412$	7.85410	+	5.70634i	0.386944	+	0.281131i
$413$	9.77523	−	0.836897i	0.481007	−	0.0411810i
$414$	−2.38197	+	7.33094i	−0.117067	+	0.360296i
$415$	13.4660	−	14.9555i	0.661020	−	0.734137i
$416$	0.501567	+	4.77209i	0.0245913	+	0.233971i
$417$	11.2082	−	19.4132i	0.548868	−	0.950667i
$418$	−14.2304	−	7.52872i	−0.696031	−	0.368242i
$419$	0.819660			0.0400430			0.0200215	−	0.999800i	$-0.493627\pi$
$419$	0.819660			0.0400430			0.0200215	+	0.999800i	$0.493627\pi$
$420$	2.17068	−	9.32306i	0.105918	−	0.454919i
$421$	−4.41641	−	13.5923i	−0.215243	−	0.662448i	−0.999136	−	0.0415534i	$-0.986769\pi$
$421$	−4.41641	−	13.5923i	−0.215243	−	0.662448i	0.783894	−	0.620895i	$-0.213231\pi$
$422$	−5.44076	+	1.15647i	−0.264852	+	0.0562960i
$423$	15.4794	−	6.89186i	0.752632	−	0.335094i
$424$	−10.3979	+	4.62946i	−0.504969	+	0.224827i
$425$		0			0
$426$	−1.00000	−	3.07768i	−0.0484502	−	0.149114i
$427$	13.4137	+	12.5552i	0.649134	+	0.607589i
$428$	−18.0902			−0.874421
$429$	2.50390	+	1.32471i	0.120890	+	0.0639578i
$430$	−4.73607	+	8.20311i	−0.228393	+	0.395589i
$431$	−1.86986	−	17.7905i	−0.0900681	−	0.856941i	−0.942523	−	0.334140i	$-0.891554\pi$
$431$	−1.86986	−	17.7905i	−0.0900681	−	0.856941i	0.852455	−	0.522800i	$-0.175113\pi$
$432$	−6.20318	+	6.88933i	−0.298451	+	0.331463i
$433$	3.83688	−	11.8087i	0.184389	−	0.567490i	−0.815549	−	0.578689i	$-0.803565\pi$
$433$	3.83688	−	11.8087i	0.184389	−	0.567490i	0.999937	+	0.0111985i	$0.00356466\pi$
$434$	6.19049	+	8.87605i	0.297153	+	0.426064i
$435$	−2.07295	−	1.50609i	−0.0993903	−	0.0722113i
$436$	−10.8478	+	2.30578i	−0.519517	+	0.110427i
$437$	47.9084	+	10.1832i	2.29177	+	0.487131i
$438$	0.267834	+	2.54827i	0.0127976	+	0.121761i
$439$	15.0902	+	26.1369i	0.720215	+	1.24745i	0.960914	+	0.276848i	$0.0892900\pi$
$439$	15.0902	+	26.1369i	0.720215	+	1.24745i	−0.240699	+	0.970600i	$0.577377\pi$
$440$	12.7254	+	10.6331i	0.606661	+	0.506915i
$441$	−2.00000	+	13.8564i	−0.0952381	+	0.659829i
$442$	−0.527864	+	0.383516i	−0.0251079	+	0.0182420i
$443$	6.53335	−	7.25602i	0.310409	−	0.344744i	−0.567673	−	0.823254i	$-0.692156\pi$
$443$	6.53335	−	7.25602i	0.310409	−	0.344744i	0.878082	+	0.478510i	$0.158823\pi$
$444$	−5.51101	−	6.12059i	−0.261541	−	0.290470i
$445$	−21.3920	+	9.52431i	−1.01408	+	0.451496i
$446$	−1.67023	+	15.8912i	−0.0790877	+	0.752469i
$447$	−5.40983	+	16.6497i	−0.255876	+	0.787506i
$448$	0.0120623	−	0.624461i	0.000569889	−	0.0295030i
$449$	−26.0795	+	18.9479i	−1.23077	+	0.894206i	−0.996948	−	0.0780736i	$-0.975123\pi$
$449$	−26.0795	+	18.9479i	−1.23077	+	0.894206i	−0.233821	+	0.972280i	$0.575123\pi$
$450$		0			0
$451$	8.53848	−	12.7155i	0.402061	−	0.598748i
$452$	−7.35410	+	12.7377i	−0.345908	+	0.599130i
$453$	−2.17603	−	0.968833i	−0.102239	−	0.0455197i
$454$	3.70820	+	11.4127i	0.174035	+	0.535624i
$455$	5.01412	+	0.625128i	0.235065	+	0.0293065i
$456$	−14.2082	−	10.3229i	−0.665360	−	0.483412i
$457$	−1.44815	+	13.7782i	−0.0677415	+	0.644517i	0.906992	+	0.421147i	$0.138372\pi$
$457$	−1.44815	+	13.7782i	−0.0677415	+	0.644517i	−0.974734	+	0.223370i	$0.928294\pi$
$458$	0.353210	+	0.392279i	0.0165044	+	0.0183300i
$459$	−6.04528	−	1.28496i	−0.282170	−	0.0599770i
$460$	−20.6117	−	9.17692i	−0.961025	−	0.427876i
$461$	−19.0902			−0.889118			−0.444559	−	0.895750i	$-0.646640\pi$
$461$	−19.0902			−0.889118			−0.444559	+	0.895750i	$0.646640\pi$
$462$	4.44309	+	3.10971i	0.206711	+	0.144677i
$463$	10.5967			0.492473			0.246236	−	0.969210i	$-0.420806\pi$
$463$	10.5967			0.492473			0.246236	+	0.969210i	$0.420806\pi$
$464$	−1.94093	−	0.864157i	−0.0901054	−	0.0401175i
$465$	14.4750	+	3.07675i	0.671262	+	0.142681i
$466$	−3.34565	−	3.71572i	−0.154984	−	0.172128i
$467$	1.19916	−	11.4093i	0.0554907	−	0.527959i	−0.931102	−	0.364758i	$-0.881152\pi$
$467$	1.19916	−	11.4093i	0.0554907	−	0.527959i	0.986593	−	0.163201i	$-0.0521818\pi$
$468$	−2.23607	−	1.62460i	−0.103362	−	0.0750971i
$469$	10.9286	+	25.8798i	0.504634	+	1.19502i
$470$	−3.61803	−	11.1352i	−0.166887	−	0.513627i
$471$	−14.8324	−	6.60380i	−0.683440	−	0.304287i
$472$	−4.14590	+	7.18091i	−0.190830	+	0.330528i
$473$	14.0325	+	17.8845i	0.645216	+	0.822329i
$474$	0.218847	+	0.379054i	0.0100520	+	0.0174105i
$475$		0			0
$476$	4.63282	−	2.55676i	0.212345	−	0.117189i
$477$	3.14590	−	9.68208i	0.144041	−	0.443312i
$478$	−0.0457515	+	0.435296i	−0.00209262	+	0.0199100i
$479$	−15.1813	+	6.75916i	−0.693653	+	0.308834i	−0.723111	−	0.690732i	$-0.757288\pi$
$479$	−15.1813	+	6.75916i	−0.693653	+	0.308834i	0.0294582	+	0.999566i	$0.490622\pi$
$480$	8.40582	+	9.33561i	0.383672	+	0.426110i
$481$	2.90906	−	3.23084i	0.132642	−	0.147314i
$482$	−14.2082	+	10.3229i	−0.647166	+	0.470194i
$483$	−15.5902	−	5.40059i	−0.709377	−	0.245736i
$484$	15.6803	−	8.42075i	0.712743	−	0.382761i
$485$	3.19098	+	5.52694i	0.144895	+	0.250966i
$486$	1.03363	+	9.83437i	0.0468866	+	0.446096i
$487$	−0.461819	−	0.0981626i	−0.0209270	−	0.00444817i	0.197436	−	0.980316i	$-0.436738\pi$
$487$	−0.461819	−	0.0981626i	−0.0209270	−	0.00444817i	−0.218363	+	0.975868i	$0.570072\pi$
$488$	−15.1885	+	3.22842i	−0.687553	+	0.146144i
$489$	−11.9443	−	8.67802i	−0.540139	−	0.392434i
$490$	9.37764	+	2.37521i	0.423638	+	0.107301i
$491$	10.0623	−	30.9686i	0.454106	−	1.39759i	−0.418077	−	0.908412i	$-0.637296\pi$
$491$	10.0623	−	30.9686i	0.454106	−	1.39759i	0.872182	−	0.489181i	$-0.162704\pi$
$492$	4.99983	−	5.55288i	0.225410	−	0.250343i
$493$	−0.148055	−	1.40865i	−0.00666806	−	0.0634423i
$494$	2.07295	−	3.59045i	0.0932664	−	0.161542i
$495$	−14.6837	+	2.09464i	−0.659985	+	0.0941470i
$496$	12.2705			0.550962
$497$	−13.2555	+	4.02567i	−0.594591	+	0.180576i
$498$	1.71885	+	5.29007i	0.0770234	+	0.237054i
$499$	29.7517	−	6.32393i	1.33187	−	0.283098i	0.513649	−	0.858001i	$-0.328293\pi$
$499$	29.7517	−	6.32393i	1.33187	−	0.283098i	0.818222	+	0.574903i	$0.194960\pi$
$500$	−16.5262	+	7.35793i	−0.739074	+	0.329057i
$501$	2.68973	−	1.19754i	0.120168	−	0.0535023i
$502$	10.4742	−	2.22636i	0.467487	−	0.0993673i
$503$	−3.10739	−	9.56357i	−0.138552	−	0.426418i	0.857574	−	0.514361i	$-0.171971\pi$
$503$	−3.10739	−	9.56357i	−0.138552	−	0.426418i	−0.996126	+	0.0879426i	$0.971971\pi$
$504$	−8.63846	−	8.08560i	−0.384788	−	0.360161i
$505$	8.74265			0.389043
$506$	9.17666	−	8.89854i	0.407952	−	0.395588i
$507$	6.13525	−	10.6266i	0.272476	−	0.471943i
$508$	0.716449	+	6.81655i	0.0317873	+	0.302436i
$509$	−22.2623	+	24.7248i	−0.986760	+	1.09591i	0.00862681	+	0.999963i	$0.497254\pi$
$509$	−22.2623	+	24.7248i	−0.986760	+	1.09591i	−0.995387	+	0.0959450i	$0.969413\pi$
$510$	−0.527864	+	1.62460i	−0.0233742	+	0.0719384i
$511$	10.9290	−	0.935680i	0.483472	−	0.0413920i
$512$	15.1353	+	10.9964i	0.668890	+	0.485977i
$513$	38.4124	−	8.16480i	1.69595	−	0.360485i
$514$	3.59348	+	0.763818i	0.158502	+	0.0336906i
$515$	1.40240	+	13.3429i	0.0617970	+	0.587959i
$516$	5.54508	+	9.60437i	0.244109	+	0.422809i
$517$	−28.0344	−	1.90211i	−1.23295	−	0.0836548i
$518$	6.29180	−	5.44886i	0.276446	−	0.239409i
$519$	15.7533	−	11.4454i	0.691493	−	0.502399i
$520$	−2.85753	+	3.17361i	−0.125311	+	0.139172i
$521$	10.0139	+	11.1216i	0.438717	+	0.487245i	0.921436	−	0.388531i	$-0.127017\pi$
$521$	10.0139	+	11.1216i	0.438717	+	0.487245i	−0.482718	+	0.875776i	$0.660351\pi$
$522$	−1.29395	+	0.576105i	−0.0566348	+	0.0252154i
$523$	−1.85461	+	17.6454i	−0.0810965	+	0.771582i	0.876097	+	0.482134i	$0.160138\pi$
$523$	−1.85461	+	17.6454i	−0.0810965	+	0.771582i	−0.957194	+	0.289447i	$0.906528\pi$
$524$	4.66312	−	14.3516i	0.203709	−	0.626953i
$525$		0			0
$526$	6.00000	−	4.35926i	0.261612	−	0.190073i
$527$	4.09017	+	7.08438i	0.178171	+	0.308601i
$528$	5.77415	−	2.11515i	0.251288	−	0.0920501i
$529$	−7.94427	+	13.7599i	−0.345403	+	0.598256i
$530$	−6.42628	−	2.86117i	−0.279140	−	0.124281i
$531$	−2.29180	−	7.05342i	−0.0994555	−	0.306092i
$532$	−20.2846	+	26.8146i	−0.879449	+	1.16256i
$533$	3.19098	+	2.31838i	0.138217	+	0.100420i
$534$	0.676522	−	6.43668i	0.0292760	−	0.278542i
$535$	−16.7283	−	18.5786i	−0.723226	−	0.803224i
$536$	−23.2238	−	4.93637i	−1.00312	−	0.213219i
$537$	−15.9931	−	7.12057i	−0.690151	−	0.307275i
$538$	14.0557			0.605985
$539$	13.6773	−	18.7599i	0.589122	−	0.808044i
$540$	−18.0902			−0.778477
$541$	−27.0380	−	12.0381i	−1.16245	−	0.517558i	−0.267430	−	0.963577i	$-0.586174\pi$
$541$	−27.0380	−	12.0381i	−1.16245	−	0.517558i	−0.895023	+	0.446020i	$0.852841\pi$
$542$	−15.1885	−	3.22842i	−0.652404	−	0.138673i
$543$	0.789802	+	0.877163i	0.0338936	+	0.0376427i
$544$	−0.725874	+	6.90623i	−0.0311216	+	0.296102i
$545$	−12.3992	−	9.00854i	−0.531123	−	0.385883i
$546$	−0.842567	+	1.11381i	−0.0360585	+	0.0476665i
$547$	10.5557	+	32.4872i	0.451330	+	1.38905i	0.875390	+	0.483418i	$0.160605\pi$
$547$	10.5557	+	32.4872i	0.451330	+	1.38905i	−0.424060	+	0.905634i	$0.639395\pi$
$548$	22.6544	+	10.0864i	0.967750	+	0.430870i
$549$	6.94427	−	12.0278i	0.296374	−	0.513335i
$550$		0			0
$551$	4.50000	+	7.79423i	0.191706	+	0.332045i
$552$	11.2812	−	8.19624i	0.480158	−	0.348855i
$553$	1.64049	−	0.905352i	0.0697607	−	0.0384995i
$554$	2.42705	−	7.46969i	0.103116	−	0.317357i
$555$	1.18974	−	11.3196i	0.0505016	−	0.480491i
$556$	33.1348	−	14.7525i	1.40523	−	0.625647i
$557$	−7.22552	−	8.02476i	−0.306155	−	0.340020i	0.570359	−	0.821395i	$-0.306804\pi$
$557$	−7.22552	−	8.02476i	−0.306155	−	0.340020i	−0.876514	+	0.481376i	$0.840137\pi$
$558$	5.47372	−	6.07918i	0.231721	−	0.257352i
$559$	−4.73607	+	3.44095i	−0.200314	+	0.145537i
$560$	8.29180	−	7.18091i	0.350392	−	0.303449i
$561$	3.14590	+	2.62866i	0.132820	+	0.110982i
$562$	−8.23607	−	14.2653i	−0.347418	−	0.601745i
$563$	−1.30369	−	12.4038i	−0.0549441	−	0.522758i	−0.987032	−	0.160525i	$-0.948681\pi$
$563$	−1.30369	−	12.4038i	−0.0549441	−	0.522758i	0.932088	−	0.362233i	$-0.117986\pi$
$564$	−13.4086	−	2.85010i	−0.564606	−	0.120011i
$565$	−19.8821	+	4.22606i	−0.836445	+	0.177792i
$566$	3.20820	+	2.33090i	0.134851	+	0.0979749i
$567$	2.63611	−	0.225688i	0.110706	−	0.00947801i
$568$	3.61803	−	11.1352i	0.151809	−	0.467221i
$569$	−9.11224	+	10.1202i	−0.382005	+	0.424260i	−0.903228	−	0.429161i	$-0.858809\pi$
$569$	−9.11224	+	10.1202i	−0.382005	+	0.424260i	0.521223	+	0.853421i	$0.325476\pi$
$570$	−1.13456	−	10.7946i	−0.0475216	−	0.452138i
$571$	−6.28115	+	10.8793i	−0.262858	+	0.455284i	−0.967000	−	0.254775i	$-0.917998\pi$
$571$	−6.28115	+	10.8793i	−0.262858	+	0.455284i	0.704142	+	0.710059i	$0.251332\pi$
$572$	2.01777	+	4.11543i	0.0843673	+	0.172075i
$573$	9.76393			0.407894
$574$	5.51304	+	5.16020i	0.230110	+	0.215383i
$575$		0			0
$576$	−0.461819	+	0.0981626i	−0.0192424	+	0.00409011i
$577$	−8.62176	+	3.83866i	−0.358929	+	0.159805i	−0.578275	−	0.815842i	$-0.696274\pi$
$577$	−8.62176	+	3.83866i	−0.358929	+	0.159805i	0.219347	+	0.975647i	$0.429607\pi$
$578$	8.73560	−	3.88934i	0.363353	−	0.161775i
$579$	−4.08899	+	0.869142i	−0.169933	+	0.0361203i
$580$	−1.28115	−	3.94298i	−0.0531970	−	0.163723i
$581$	22.7842	−	6.91950i	0.945249	−	0.287069i
$582$	−1.76393			−0.0731173
$583$	−12.1198	+	11.7524i	−0.501949	+	0.486736i
$584$	−4.63525	+	8.02850i	−0.191808	+	0.332222i
$585$	−0.399263	−	3.79874i	−0.0165075	−	0.157058i
$586$	1.45893	−	1.62031i	0.0602679	−	0.0669343i
$587$	2.57953	−	7.93897i	0.106468	−	0.327676i	−0.883604	−	0.468235i	$-0.844890\pi$
$587$	2.57953	−	7.93897i	0.106468	−	0.327676i	0.990072	+	0.140559i	$0.0448900\pi$
$588$	7.89813	−	8.11808i	0.325713	−	0.334784i
$589$	−42.0517	−	30.5523i	−1.73271	−	1.25889i
$590$	−5.01263	+	1.06547i	−0.206367	+	0.0438646i
$591$	−4.51712	−	0.960143i	−0.185809	−	0.0394950i
$592$	−0.986508	−	9.38599i	−0.0405452	−	0.385762i
$593$	−19.0344	−	32.9686i	−0.781651	−	1.35386i	−0.930980	−	0.365071i	$-0.881045\pi$
$593$	−19.0344	−	32.9686i	−0.781651	−	1.35386i	0.149329	−	0.988788i	$-0.452289\pi$
$594$	3.81966	−	9.51057i	0.156723	−	0.390223i
$595$	6.90983	+	2.39364i	0.283275	+	0.0981295i
$596$	−22.9164	+	16.6497i	−0.938693	+	0.682000i
$597$	0.962005	−	1.06841i	0.0393722	−	0.0437273i
$598$	2.20264	+	2.44628i	0.0900727	+	0.100036i
$599$	42.4859	−	18.9159i	1.73593	−	0.772884i	0.741088	−	0.671408i	$-0.234310\pi$
$599$	42.4859	−	18.9159i	1.73593	−	0.772884i	0.994838	−	0.101476i	$-0.0323564\pi$
$600$		0			0
$601$	−7.98936	+	24.5887i	−0.325893	+	1.00299i	0.645143	+	0.764062i	$0.276798\pi$
$601$	−7.98936	+	24.5887i	−0.325893	+	1.00299i	−0.971036	+	0.238933i	$0.923202\pi$
$602$	−9.81247	+	5.41530i	−0.399926	+	0.220711i
$603$	17.1803	−	12.4822i	0.699638	−	0.508316i
$604$	−1.92705	−	3.33775i	−0.0784106	−	0.135811i
$605$	23.1480	+	8.31692i	0.941099	+	0.338131i
$606$	−1.20820	+	2.09267i	−0.0490799	+	0.0850089i
$607$	24.9129	+	11.0919i	1.01118	+	0.450207i	0.844358	−	0.535780i	$-0.179982\pi$
$607$	24.9129	+	11.0919i	1.01118	+	0.450207i	0.166824	+	0.985987i	$0.446649\pi$
$608$	−13.6353	−	41.9650i	−0.552983	−	1.70191i
$609$	−1.17941	−	2.79295i	−0.0477921	−	0.113176i
$610$	−7.76393	−	5.64083i	−0.314352	−	0.228390i
$611$	0.756375	−	7.19643i	0.0305997	−	0.291136i
$612$	−2.67652	−	2.97258i	−0.108192	−	0.120159i
$613$	−15.1340	−	3.21684i	−0.611258	−	0.129927i	−0.108127	−	0.994137i	$-0.534485\pi$
$613$	−15.1340	−	3.21684i	−0.611258	−	0.129927i	−0.503131	+	0.864210i	$0.667819\pi$
$614$	13.8365	+	6.16039i	0.558394	+	0.248613i
$615$	10.3262			0.416394
$616$	6.39195	+	18.5511i	0.257539	+	0.747445i
$617$	25.4721			1.02547			0.512735	−	0.858547i	$-0.328632\pi$
$617$	25.4721			1.02547			0.512735	+	0.858547i	$0.328632\pi$
$618$	−3.38761	−	1.50826i	−0.136270	−	0.0606712i
$619$	13.3878	+	2.84567i	0.538102	+	0.114377i	0.468943	−	0.883228i	$-0.344635\pi$
$619$	13.3878	+	2.84567i	0.538102	+	0.114377i	0.0691593	+	0.997606i	$0.477968\pi$
$620$	16.0218	+	17.7941i	0.643453	+	0.714627i
$621$	−3.25923	+	31.0095i	−0.130789	+	1.24437i
$622$	15.6803	+	11.3924i	0.628724	+	0.456795i
$623$	−27.4938	−	3.42775i	−1.10152	−	0.137330i
$624$	0.489357	+	1.50609i	0.0195900	+	0.0602917i
$625$	−22.8386	−	10.1684i	−0.913545	−	0.406737i
$626$	−3.38197	+	5.85774i	−0.135171	+	0.234122i
$627$	−25.0548	−	7.12831i	−1.00059	−	0.284677i
$628$	−13.1353	−	22.7509i	−0.524154	−	0.907861i
$629$	5.09017	−	3.69822i	0.202958	−	0.147458i
$630$	0.141228	−	7.31131i	0.00562664	−	0.291290i
$631$	−5.04508	+	15.5272i	−0.200842	+	0.618127i	0.799017	+	0.601309i	$0.205354\pi$
$631$	−5.04508	+	15.5272i	−0.200842	+	0.618127i	−0.999859	+	0.0168185i	$0.994646\pi$
$632$	−0.165530	+	1.57492i	−0.00658445	+	0.0626468i
$633$	−8.22191	+	3.66063i	−0.326792	+	0.145497i
$634$	1.08268	+	1.20243i	0.0429986	+	0.0477547i
$635$	−6.33810	+	7.03917i	−0.251520	+	0.279341i
$636$	−6.66312	+	4.84104i	−0.264210	+	0.191960i
$637$	4.69756	+	3.69837i	0.186124	+	0.146535i
$638$	2.34346	+	0.159002i	0.0927784	+	0.00629494i
$639$	5.23607	+	9.06914i	0.207136	+	0.358769i
$640$	2.66034	+	25.3114i	0.105159	+	1.00052i
$641$	−3.19904	−	0.679977i	−0.126355	−	0.0268575i	0.144300	−	0.989534i	$-0.453907\pi$
$641$	−3.19904	−	0.679977i	−0.126355	−	0.0268575i	−0.270655	+	0.962676i	$0.587240\pi$
$642$	6.75883	−	1.43663i	0.266750	−	0.0566994i
$643$	15.3713	+	11.1679i	0.606186	+	0.440420i	0.848069	−	0.529886i	$-0.177765\pi$
$643$	15.3713	+	11.1679i	0.606186	+	0.440420i	−0.241883	+	0.970305i	$0.577765\pi$
$644$	−15.2715	−	21.8966i	−0.601783	−	0.862847i
$645$	−4.73607	+	14.5761i	−0.186482	+	0.573934i
$646$	4.01478	−	4.45887i	0.157960	−	0.175432i
$647$	1.17449	+	11.1745i	0.0461739	+	0.439316i	0.993048	+	0.117711i	$0.0375556\pi$
$647$	1.17449	+	11.1745i	0.0461739	+	0.439316i	−0.946874	+	0.321605i	$0.895778\pi$
$648$	−1.11803	+	1.93649i	−0.0439205	+	0.0760726i
$649$	−2.11060	+	12.1163i	−0.0828483	+	0.475605i
$650$		0			0
$651$	12.7835	+	11.9654i	0.501026	+	0.468960i
$652$	−7.38197	−	22.7194i	−0.289100	−	0.889759i
$653$	0.957327	−	0.203486i	0.0374631	−	0.00796302i	−0.189142	−	0.981950i	$-0.560571\pi$
$653$	0.957327	−	0.203486i	0.0374631	−	0.00796302i	0.226605	+	0.973987i	$0.427237\pi$
$654$	3.86984	−	1.72296i	0.151323	−	0.0673732i
$655$	19.0512	−	8.48213i	0.744391	−	0.331424i
$656$	8.37520	−	1.78020i	0.326997	−	0.0695053i
$657$	−2.56231	−	7.88597i	−0.0999651	−	0.307661i
$658$	3.14143	−	13.4925i	0.122466	−	0.525991i
$659$	5.56231			0.216677			0.108338	−	0.994114i	$-0.465447\pi$
$659$	5.56231			0.216677			0.108338	+	0.994114i	$0.465447\pi$
$660$	10.6067	+	5.61158i	0.412865	+	0.218430i
$661$	5.78115	−	10.0133i	0.224861	−	0.389470i	−0.731417	−	0.681931i	$-0.761141\pi$
$661$	5.78115	−	10.0133i	0.224861	−	0.389470i	0.956278	+	0.292460i	$0.0944739\pi$
$662$	−0.950181	−	9.04037i	−0.0369299	−	0.351364i
$663$	−0.706420	+	0.784559i	−0.0274351	+	0.0304697i
$664$	−6.21885	+	19.1396i	−0.241338	+	0.742762i
$665$	−46.2961	+	3.96360i	−1.79529	+	0.153702i
$666$	−5.09017	−	3.69822i	−0.197240	−	0.143303i
$667$	−6.98974	+	1.48572i	−0.270644	+	0.0575271i
$668$	4.65983	+	0.990477i	0.180294	+	0.0383227i
$669$	2.70249	+	25.7125i	0.104484	+	0.994102i
$670$	−7.33688	−	12.7079i	−0.283448	−	0.490947i
$671$	−19.5066	+	12.2452i	−0.753043	+	0.472722i
$672$	2.80902	+	14.5961i	0.108360	+	0.563056i
$673$	−27.8435	+	20.2295i	−1.07329	+	0.779788i	−0.976500	−	0.215517i	$-0.930856\pi$
$673$	−27.8435	+	20.2295i	−1.07329	+	0.779788i	−0.0967864	+	0.995305i	$0.530856\pi$
$674$	−0.534216	+	0.593307i	−0.0205772	+	0.0228533i
$675$		0			0
$676$	18.1376	−	8.07539i	0.697601	−	0.310592i
$677$	3.68317	−	35.0430i	0.141556	−	1.34681i	−0.661067	−	0.750327i	$-0.729896\pi$
$677$	3.68317	−	35.0430i	0.141556	−	1.34681i	0.802623	−	0.596487i	$-0.203437\pi$
$678$	1.73607	−	5.34307i	0.0666733	−	0.205199i
$679$	−0.145835	+	7.54984i	−0.00559663	+	0.289736i
$680$	−5.00000	+	3.63271i	−0.191741	+	0.139308i
$681$	9.70820	+	16.8151i	0.372019	+	0.644356i
$682$	−12.7378	+	4.66604i	−0.487757	+	0.178672i
$683$	−4.40983	+	7.63805i	−0.168737	+	0.292262i	−0.937976	−	0.346700i	$-0.887302\pi$
$683$	−4.40983	+	7.63805i	−0.168737	+	0.292262i	0.769239	+	0.638961i	$0.220636\pi$
$684$	23.2190	+	10.3378i	0.887802	+	0.395275i
$685$	10.5902	+	32.5932i	0.404630	+	1.24532i
$686$	8.04835	+	8.13870i	0.307287	+	0.310737i
$687$	0.690983	+	0.502029i	0.0263626	+	0.0191536i
$688$	−1.32837	+	12.6386i	−0.0506436	+	0.481842i
$689$	−2.90906	−	3.23084i	−0.110826	−	0.123085i
$690$	8.42971	+	1.79179i	0.320914	+	0.0682123i
$691$	10.8098	+	4.81284i	0.411225	+	0.183089i	0.601913	−	0.798562i	$-0.294405\pi$
$691$	10.8098	+	4.81284i	0.411225	+	0.183089i	−0.190688	+	0.981651i	$0.561072\pi$
$692$	31.5066			1.19770
$693$	−16.1562	−	6.85396i	−0.613724	−	0.260360i
$694$	−12.5410			−0.476051
$695$	45.7911	+	20.3875i	1.73696	+	0.773343i
$696$	2.50631	+	0.532733i	0.0950016	+	0.0201932i
$697$	3.81953	+	4.24202i	0.144675	+	0.160678i
$698$	−0.823202	+	7.83225i	−0.0311587	+	0.296455i
$699$	−6.54508	−	4.75528i	−0.247558	−	0.179861i
$700$		0			0
$701$	−0.437694	−	1.34708i	−0.0165315	−	0.0508787i	0.942450	−	0.334346i	$-0.108515\pi$
$701$	−0.437694	−	1.34708i	−0.0165315	−	0.0508787i	−0.958982	+	0.283467i	$0.908515\pi$
$702$	2.41114	+	1.07351i	0.0910026	+	0.0405170i
$703$	−19.9894	+	34.6226i	−0.753913	+	1.30582i
$704$	0.753063	+	0.214253i	0.0283821	+	0.00807497i
$705$	−9.47214	−	16.4062i	−0.356741	−	0.617894i
$706$	−2.23607	+	1.62460i	−0.0841555	+	0.0611426i
$707$	8.85699	+	5.34427i	0.333101	+	0.200992i
$708$	−1.85410	+	5.70634i	−0.0696814	+	0.214457i
$709$	−0.378188	+	3.59821i	−0.0142031	+	0.135134i	−0.999326	−	0.0367201i	$-0.988309\pi$
$709$	−0.378188	+	3.59821i	−0.0142031	+	0.135134i	0.985122	+	0.171854i	$0.0549757\pi$
$710$	6.61048	−	2.94317i	0.248087	−	0.110455i
$711$	−0.947762	−	1.05260i	−0.0355438	−	0.0394754i
$712$	15.6686	−	17.4018i	0.587207	−	0.652159i
$713$	33.3885	−	24.2582i	1.25041	−	0.908477i
$714$	−1.52786	+	1.32317i	−0.0571789	+	0.0495184i
$715$	−2.36068	+	5.87785i	−0.0882844	+	0.219819i
$716$	−14.1631	−	24.5312i	−0.529301	−	0.916776i
$717$	0.0740275	+	0.704324i	0.00276461	+	0.0263035i
$718$	3.82439	+	0.812899i	0.142725	+	0.0303371i
$719$	16.8049	−	3.57199i	0.626717	−	0.133213i	0.116405	−	0.993202i	$-0.462863\pi$
$719$	16.8049	−	3.57199i	0.626717	−	0.133213i	0.510313	+	0.859989i	$0.329530\pi$
$720$	−6.70820	−	4.87380i	−0.250000	−	0.181636i
$721$	−6.73561	+	14.3747i	−0.250847	+	0.535341i
$722$	−8.15248	+	25.0907i	−0.303404	+	0.933781i
$723$	−19.0143	+	21.1175i	−0.707149	+	0.785369i
$724$	0.199632	+	1.89937i	0.00741925	+	0.0705894i
$725$		0			0
$726$	−5.18974	+	4.39141i	−0.192609	+	0.162981i
$727$	−28.4164			−1.05391			−0.526953	−	0.849894i	$-0.676666\pi$
$727$	−28.4164			−1.05391			−0.526953	+	0.849894i	$0.676666\pi$
$728$	−4.83489	+	1.46834i	−0.179193	+	0.0544204i
$729$	4.01722	+	12.3637i	0.148786	+	0.457916i
$730$	−5.60429	+	1.19123i	−0.207424	+	0.0440893i
$731$	−7.73968	+	3.44593i	−0.286262	+	0.127452i
$732$	−10.2647	+	4.57012i	−0.379393	+	0.168917i
$733$	−6.96892	+	1.48129i	−0.257403	+	0.0547127i	−0.334806	−	0.942287i	$-0.608671\pi$
$733$	−6.96892	+	1.48129i	−0.257403	+	0.0547127i	0.0774026	+	0.997000i	$0.475337\pi$
$734$	1.19756	+	3.68571i	0.0442028	+	0.136042i
$735$	15.6408	+	0.604471i	0.576920	+	0.0222962i
$736$	35.0344			1.29139
$737$	−34.8631	+	4.97323i	−1.28420	+	0.183191i
$738$	2.85410	−	4.94345i	0.105061	−	0.181971i
$739$	−2.47818	−	23.5783i	−0.0911614	−	0.867343i	−0.940568	−	0.339604i	$-0.889707\pi$
$739$	−2.47818	−	23.5783i	−0.0911614	−	0.867343i	0.849407	−	0.527738i	$-0.176960\pi$
$740$	12.3230	−	13.6861i	0.453002	−	0.503110i
$741$	2.07295	−	6.37988i	0.0761517	−	0.234371i
$742$	−4.76133	−	6.82689i	−0.174794	−	0.250623i
$743$	25.5066	+	18.5316i	0.935746	+	0.679859i	0.947393	−	0.320073i	$-0.103708\pi$
$743$	25.5066	+	18.5316i	0.935746	+	0.679859i	−0.0116472	+	0.999932i	$0.503708\pi$
$744$	−14.4750	+	3.07675i	−0.530679	+	0.112799i
$745$	−38.2905	−	8.13889i	−1.40285	−	0.298186i
$746$	1.65360	+	15.7330i	0.0605428	+	0.576026i
$747$	−9.00000	−	15.5885i	−0.329293	−	0.570352i
$748$	1.61803	+	6.43288i	0.0591612	+	0.235209i
$749$	−5.59017	−	29.0474i	−0.204260	−	1.06137i
$750$	5.59017	−	4.06150i	0.204124	−	0.148305i
$751$	26.7510	−	29.7100i	0.976157	−	1.08413i	−0.0202800	−	0.999794i	$-0.506456\pi$
$751$	26.7510	−	29.7100i	0.976157	−	1.08413i	0.996437	−	0.0843380i	$-0.0268776\pi$
$752$	−10.5108	−	11.6735i	−0.383291	−	0.425688i
$753$	15.8283	−	7.04722i	0.576816	−	0.256815i
$754$	−0.0632270	+	0.601565i	−0.00230259	+	0.0219077i
$755$	1.64590	−	5.06555i	0.0599004	−	0.184354i
$756$	−18.3268	−	11.0583i	−0.666538	−	0.402186i
$757$	−13.2533	+	9.62908i	−0.481699	+	0.349975i	−0.801983	−	0.597347i	$-0.796222\pi$
$757$	−13.2533	+	9.62908i	−0.481699	+	0.349975i	0.320284	+	0.947322i	$0.396222\pi$
$758$	2.56231	+	4.43804i	0.0930671	+	0.161197i
$759$	11.5301	−	17.1706i	0.418517	−	0.623254i
$760$	19.6353	−	34.0093i	0.712246	−	1.23365i
$761$	27.3360	+	12.1708i	0.990930	+	0.441190i	0.837185	−	0.546920i	$-0.184200\pi$
$761$	27.3360	+	12.1708i	0.990930	+	0.441190i	0.153745	+	0.988111i	$0.450867\pi$
$762$	−0.809017	−	2.48990i	−0.0293076	−	0.0901995i
$763$	−7.05454	−	16.7058i	−0.255392	−	0.604791i
$764$	12.7812	+	9.28605i	0.462406	+	0.335958i
$765$	0.577819	−	5.49758i	0.0208911	−	0.198765i
$766$	−0.743709	−	0.825973i	−0.0268713	−	0.0298436i
$767$	−3.09797	−	0.658495i	−0.111861	−	0.0237769i
$768$	−5.99496	−	2.66913i	−0.216325	−	0.0963139i
$769$	−3.52786			−0.127218			−0.0636090	−	0.997975i	$-0.520261\pi$
$769$	−3.52786			−0.127218			−0.0636090	+	0.997975i	$0.520261\pi$
$770$	−5.87694	+	10.6075i	−0.211790	+	0.382267i
$771$	5.94427			0.214078
$772$	−6.17916	−	2.75114i	−0.222393	−	0.0990157i
$773$	−4.31990	−	0.918223i	−0.155376	−	0.0330262i	0.129567	−	0.991571i	$-0.458641\pi$
$773$	−4.31990	−	0.918223i	−0.155376	−	0.0330262i	−0.284943	+	0.958545i	$0.591975\pi$
$774$	5.66897	+	6.29602i	0.203767	+	0.226306i
$775$		0			0
$776$	−5.16312	−	3.75123i	−0.185345	−	0.134661i
$777$	8.12484	−	10.7404i	0.291477	−	0.385309i
$778$	6.20163	+	19.0866i	0.222339	+	0.684289i
$779$	−33.1348	−	14.7525i	−1.18718	−	0.528565i
$780$	−1.54508	+	2.67617i	−0.0553229	+	0.0958221i
$781$	−0.641954	−	17.3542i	−0.0229709	−	0.620982i
$782$	2.38197	+	4.12569i	0.0851789	+	0.147534i
$783$	−4.63525	+	3.36771i	−0.165650	+	0.120352i
$784$	12.7898	−	2.20615i	0.456780	−	0.0787911i
$785$	11.2188	−	34.5281i	0.400418	−	1.23236i
$786$	−0.602495	+	5.73236i	−0.0214903	+	0.204466i
$787$	−28.3199	+	12.6088i	−1.00950	+	0.449456i	−0.843764	−	0.536714i	$-0.819665\pi$
$787$	−28.3199	+	12.6088i	−1.00950	+	0.449456i	−0.165732	+	0.986171i	$0.552999\pi$
$788$	−4.99983	−	5.55288i	−0.178112	−	0.197813i
$789$	8.02957	−	8.91774i	0.285860	−	0.317480i
$790$	−0.791796	+	0.575274i	−0.0281708	+	0.0204673i
$791$	−22.7254	−	7.87232i	−0.808023	−	0.279907i
$792$	12.5623	−	7.88597i	0.446382	−	0.280216i
$793$	−2.96556	−	5.13650i	−0.105310	−	0.182402i
$794$	−1.65943	−	15.7884i	−0.0588910	−	0.560310i
$795$	−11.1332	−	2.36644i	−0.394855	−	0.0839291i
$796$	2.27540	−	0.483652i	0.0806496	−	0.0171426i
$797$	−12.0902	−	8.78402i	−0.428256	−	0.311146i	0.352695	−	0.935738i	$-0.385265\pi$
$797$	−12.0902	−	8.78402i	−0.428256	−	0.311146i	−0.780951	+	0.624592i	$0.785265\pi$
$798$	5.44923	−	11.6294i	0.192901	−	0.411675i
$799$	3.23607	−	9.95959i	0.114484	−	0.352345i
$800$		0			0
$801$	2.18927	+	20.8295i	0.0773541	+	0.735976i
$802$	−0.0172209	+	0.0298275i	−0.000608092	+	0.00105325i
$803$	−2.35972	+	13.5464i	−0.0832728	+	0.478042i
$804$	−17.1803			−0.605904
$805$	8.36601	−	35.9320i	0.294863	−	1.26644i
$806$	−1.07953	−	3.32244i	−0.0380247	−	0.117028i
$807$	22.2457	−	4.72846i	0.783084	−	0.166450i
$808$	−7.98680	+	3.55595i	−0.280975	+	0.125098i
$809$	−18.1376	+	8.07539i	−0.637685	+	0.283916i	−0.700002	−	0.714141i	$-0.746818\pi$
$809$	−18.1376	+	8.07539i	−0.637685	+	0.283916i	0.0623172	+	0.998056i	$0.480151\pi$
$810$	−1.35177	+	0.287327i	−0.0474962	+	0.0100956i
$811$	12.0517	+	37.0912i	0.423191	+	1.30245i	0.904716	+	0.426016i	$0.140083\pi$
$811$	12.0517	+	37.0912i	0.423191	+	1.30245i	−0.481525	+	0.876433i	$0.659917\pi$
$812$	1.11239	−	4.77770i	0.0390371	−	0.167665i
$813$	−25.1246			−0.881159
$814$	4.59324	+	9.36833i	0.160993	+	0.328360i
$815$	16.5066	−	28.5902i	0.578200	−	1.00147i
$816$	0.239558	+	2.27924i	0.00838620	+	0.0797894i
$817$	36.0212	−	40.0056i	1.26022	−	1.39962i
$818$	0.538507	−	1.65735i	0.0188285	−	0.0579480i
$819$	1.91763	−	4.09248i	0.0670075	−	0.143003i
$820$	13.5172	+	9.82084i	0.472042	+	0.342958i
$821$	1.46079	−	0.310500i	0.0509818	−	0.0108365i	−0.182350	−	0.983234i	$-0.558370\pi$
$821$	1.46079	−	0.310500i	0.0509818	−	0.0108365i	0.233332	+	0.972397i	$0.425037\pi$
$822$	−9.26515	−	1.96937i	−0.323159	−	0.0686896i
$823$	3.38844	+	32.2388i	0.118113	+	1.12377i	0.879640	+	0.475641i	$0.157784\pi$
$823$	3.38844	+	32.2388i	0.118113	+	1.12377i	−0.761526	+	0.648134i	$0.775550\pi$
$824$	−6.70820	−	11.6190i	−0.233691	−	0.404765i
$825$		0			0
$826$	−5.72949	−	1.98475i	−0.199354	−	0.0690584i
$827$	22.9164	−	16.6497i	0.796882	−	0.578968i	−0.113116	−	0.993582i	$-0.536083\pi$
$827$	22.9164	−	16.6497i	0.796882	−	0.578968i	0.909998	+	0.414613i	$0.136083\pi$
$828$	−13.5033	+	14.9969i	−0.469272	+	0.521179i
$829$	−11.2776	−	12.5250i	−0.391687	−	0.435013i	0.514758	−	0.857335i	$-0.327882\pi$
$829$	−11.2776	−	12.5250i	−0.391687	−	0.435013i	−0.906446	+	0.422323i	$0.861215\pi$
$830$	−11.3624	+	5.05887i	−0.394395	+	0.175596i
$831$	1.32837	−	12.6386i	0.0460806	−	0.438428i
$832$	−0.0623059	+	0.191758i	−0.00216007	+	0.00664801i
$833$	5.53700	+	6.64883i	0.191846	+	0.230368i
$834$	−11.2082	+	8.14324i	−0.388108	+	0.281977i
$835$	3.29180	+	5.70156i	0.113917	+	0.197311i
$836$	−26.0177	−	33.1596i	−0.899842	−	1.14685i
$837$	16.5451	−	28.6569i	0.571882	−	0.990528i
$838$	−0.462782	−	0.206044i	−0.0159865	−	0.00711766i
$839$	16.4828	+	50.7288i	0.569049	+	1.75135i	0.655604	+	0.755105i	$0.272414\pi$
$839$	16.4828	+	50.7288i	0.569049	+	1.75135i	−0.0865553	+	0.996247i	$0.527586\pi$
$840$	−7.98091	+	10.5501i	−0.275367	+	0.364014i
$841$	22.3992	+	16.2740i	0.772386	+	0.561171i
$842$	−0.923281	+	8.78443i	−0.0318184	+	0.302731i
$843$	−17.8340	−	19.8066i	−0.614235	−	0.682177i
$844$	−14.2441	−	3.02767i	−0.490302	−	0.104217i
$845$	25.0656	+	11.1599i	0.862282	+	0.383913i
$846$	−10.4721			−0.360039
$847$	18.3667	+	22.5758i	0.631087	+	0.775712i
$848$	−9.43769			−0.324092
$849$	5.86168	+	2.60979i	0.201172	+	0.0895677i
$850$		0			0
$851$	−21.2400	−	23.5894i	−0.728097	−	0.808634i
$852$	0.885579	−	8.42572i	0.0303394	−	0.288661i
$853$	27.3262	+	19.8537i	0.935633	+	0.679777i	0.947365	−	0.320154i	$-0.103735\pi$
$853$	27.3262	+	19.8537i	0.935633	+	0.679777i	−0.0117328	+	0.999931i	$0.503735\pi$
$854$	−4.41731	−	10.4606i	−0.151157	−	0.357954i
$855$	10.8541	+	33.4055i	0.371202	+	1.14244i
$856$	22.8386	+	10.1684i	0.780609	+	0.347549i
$857$	1.26393	−	2.18919i	0.0431751	−	0.0747815i	−0.843630	−	0.536924i	$-0.819586\pi$
$857$	1.26393	−	2.18919i	0.0431751	−	0.0747815i	0.886805	+	0.462143i	$0.152919\pi$
$858$	−1.08071	−	1.37736i	−0.0368947	−	0.0470223i
$859$	−10.8541	−	18.7999i	−0.370337	−	0.641443i	0.619280	−	0.785170i	$-0.287425\pi$
$859$	−10.8541	−	18.7999i	−0.370337	−	0.641443i	−0.989617	+	0.143727i	$0.954091\pi$
$860$	−20.0623	+	14.5761i	−0.684119	+	0.497042i
$861$	10.4613	+	6.31230i	0.356520	+	0.215123i
$862$	−3.41641	+	10.5146i	−0.116363	+	0.358129i
$863$	0.171356	−	1.63034i	0.00583301	−	0.0554974i	−0.991218	−	0.132236i	$-0.957784\pi$
$863$	0.171356	−	1.63034i	0.00583301	−	0.0554974i	0.997051	+	0.0767391i	$0.0244508\pi$
$864$	25.6616	−	11.4253i	0.873027	−	0.388697i
$865$	29.1346	+	32.3573i	0.990607	+	1.10018i
$866$	−5.13475	+	5.70272i	−0.174486	+	0.193786i
$867$	12.5172	−	9.09429i	0.425107	−	0.308858i
$868$	5.35410	+	27.8207i	0.181730	+	0.944297i
$869$	0.572949	+	2.27790i	0.0194360	+	0.0772723i
$870$	0.791796	+	1.37143i	0.0268444	+	0.0464959i
$871$	−0.947956	−	9.01920i	−0.0321203	−	0.305604i
$872$	14.9913	+	3.18650i	0.507670	+	0.107909i
$873$	5.58347	−	1.18680i	0.188972	−	0.0401672i
$874$	−24.4894	−	17.7926i	−0.828365	−	0.601842i
$875$	−16.9215	−	24.2624i	−0.572051	−	0.820218i
$876$	−2.07295	+	6.37988i	−0.0700385	+	0.215556i
$877$	−29.1116	+	32.3317i	−0.983028	+	1.09176i	0.0127450	+	0.999919i	$0.495943\pi$
$877$	−29.1116	+	32.3317i	−0.983028	+	1.09176i	−0.995773	+	0.0918448i	$0.970724\pi$
$878$	−1.94971	−	18.5503i	−0.0657997	−	0.626042i
$879$	1.76393	−	3.05522i	0.0594960	−	0.103050i
$880$	6.05332	+	12.3463i	0.204057	+	0.416193i
$881$	−30.6525			−1.03271			−0.516354	−	0.856375i	$-0.672711\pi$
$881$	−30.6525			−1.03271			−0.516354	+	0.856375i	$0.672711\pi$
$882$	4.61239	−	7.32060i	0.155307	−	0.246498i
$883$	−9.36475	−	28.8217i	−0.315149	−	0.969928i	−0.975693	−	0.219141i	$-0.929674\pi$
$883$	−9.36475	−	28.8217i	−0.315149	−	0.969928i	0.660544	−	0.750787i	$-0.270326\pi$
$884$	−1.67088	+	0.355156i	−0.0561976	+	0.0119452i
$885$	−7.57493	+	3.37258i	−0.254629	+	0.113368i
$886$	−5.51274	+	2.45443i	−0.185204	+	0.0824581i
$887$	−11.5406	+	2.45302i	−0.387494	+	0.0823643i	−0.397539	−	0.917585i	$-0.630136\pi$
$887$	−11.5406	+	2.45302i	−0.387494	+	0.0823643i	0.0100454	+	0.999950i	$0.496802\pi$
$888$	3.51722	+	10.8249i	0.118030	+	0.363260i
$889$	−10.7239	+	3.25683i	−0.359669	+	0.109231i
$890$	14.4721			0.485107
$891$	−0.569171	+	3.26742i	−0.0190679	+	0.109463i
$892$	−20.9164	+	36.2283i	−0.700333	+	1.21301i
$893$	6.95543	+	66.1765i	0.232755	+	2.21451i
$894$	7.23977	−	8.04057i	0.242134	−	0.268917i
$895$	12.0967	−	37.2300i	0.404350	−	1.24446i
$896$	−12.7774	+	27.2687i	−0.426864	+	0.910983i
$897$	4.30902	+	3.13068i	0.143874	+	0.104530i
$898$	19.4876	−	4.14222i	0.650310	−	0.138228i
$899$	7.41787	+	1.57672i	0.247400	+	0.0525865i
$900$		0			0
$901$	−3.14590	−	5.44886i	−0.104805	−	0.181528i
$902$	−8.01722	+	5.03280i	−0.266944	+	0.167574i
$903$	−13.7082	+	11.8717i	−0.456180	+	0.395064i
$904$	16.4443	−	11.9475i	0.546928	−	0.397367i
$905$	−1.76605	+	1.96140i	−0.0587055	+	0.0651990i
$906$	0.985051	+	1.09401i	0.0327261	+	0.0363461i
$907$	−4.58717	+	2.04234i	−0.152315	+	0.0678148i	−0.481478	−	0.876458i	$-0.659900\pi$
$907$	−4.58717	+	2.04234i	−0.152315	+	0.0678148i	0.329164	+	0.944273i	$0.393233\pi$
$908$	−3.28391	+	31.2443i	−0.108980	+	1.03688i
$909$	2.41641	−	7.43694i	0.0801472	−	0.246668i
$910$	−2.67384	−	1.61338i	−0.0886369	−	0.0534831i
$911$	−11.1180	+	8.07772i	−0.368357	+	0.267627i	−0.756529	−	0.653960i	$-0.773107\pi$
$911$	−11.1180	+	8.07772i	−0.368357	+	0.267627i	0.388172	+	0.921587i	$0.373107\pi$
$912$	−7.28115	−	12.6113i	−0.241103	−	0.417603i
$913$	1.10342	+	29.8292i	0.0365179	+	0.987203i
$914$	4.28115	−	7.41517i	0.141608	−	0.245272i
$915$	−14.1854	−	6.31575i	−0.468955	−	0.208792i
$916$	0.427051	+	1.31433i	0.0141102	+	0.0434266i
$917$	24.4853	+	3.05268i	0.808577	+	0.100808i
$918$	3.09017	+	2.24514i	0.101991	+	0.0741007i
$919$	4.99989	−	47.5708i	0.164931	−	1.56922i	−0.528652	−	0.848839i	$-0.677302\pi$
$919$	4.99989	−	47.5708i	0.164931	−	1.56922i	0.693583	−	0.720377i	$-0.256031\pi$
$920$	20.8637	+	23.1715i	0.687856	+	0.763942i
$921$	23.9711	+	5.09520i	0.789873	+	0.167893i
$922$	10.7784	+	4.79883i	0.354966	+	0.158041i
$923$	4.47214			0.147202
$924$	7.31513	+	12.1687i	0.240650	+	0.400321i
$925$		0			0
$926$	−5.98295	−	2.66378i	−0.196612	−	0.0875372i
$927$	11.7378	+	2.49494i	0.385519	+	0.0819446i
$928$	4.30766	+	4.78414i	0.141406	+	0.157047i
$929$	6.35294	−	60.4441i	0.208433	−	1.98311i	0.0274414	−	0.999623i	$-0.491264\pi$
$929$	6.35294	−	60.4441i	0.208433	−	1.98311i	0.180992	−	0.983485i	$-0.442069\pi$
$930$	−7.39919	−	5.37582i	−0.242629	−	0.176280i
$931$	−49.3245	−	24.2848i	−1.61655	−	0.795902i
$932$	−4.04508	−	12.4495i	−0.132501	−	0.407797i
$933$	28.6494	+	12.7555i	0.937939	+	0.417598i
$934$	−3.54508	+	6.14027i	−0.115999	+	0.200916i
$935$	−5.11035	+	7.61031i	−0.167126	+	0.248884i
$936$	1.90983	+	3.30792i	0.0624247	+	0.108123i
$937$	7.73607	−	5.62058i	0.252726	−	0.183616i	−0.454208	−	0.890896i	$-0.650078\pi$
$937$	7.73607	−	5.62058i	0.252726	−	0.183616i	0.706934	+	0.707279i	$0.250078\pi$
$938$	0.335312	−	17.3590i	0.0109483	−	0.566791i
$939$	−3.38197	+	10.4086i	−0.110366	+	0.339673i
$940$	3.20406	−	30.4846i	0.104505	−	0.994297i
$941$	11.6919	−	5.20557i	0.381145	−	0.169697i	−0.207216	−	0.978295i	$-0.566440\pi$
$941$	11.6919	−	5.20557i	0.381145	−	0.169697i	0.588361	+	0.808599i	$0.299774\pi$
$942$	6.71435	+	7.45704i	0.218765	+	0.242964i
$943$	19.2699	−	21.4014i	0.627513	−	0.696924i
$944$	−5.56231	+	4.04125i	−0.181038	+	0.131532i
$945$	−5.59017	−	29.0474i	−0.181848	−	0.944911i
$946$	−3.42705	−	13.6251i	−0.111423	−	0.442989i
$947$	3.44427	+	5.96565i	0.111924	+	0.193858i	0.916546	−	0.399930i	$-0.130965\pi$
$947$	3.44427	+	5.96565i	0.111924	+	0.193858i	−0.804622	+	0.593787i	$0.797632\pi$
$948$	0.119779	+	1.13962i	0.00389024	+	0.0370132i
$949$	−3.46364	−	0.736219i	−0.112435	−	0.0238987i
$950$		0			0
$951$	2.11803	+	1.53884i	0.0686820	+	0.0499004i
$952$	−7.28602	+	0.623786i	−0.236141	+	0.0202170i
$953$	−13.3992	+	41.2385i	−0.434042	+	1.33584i	0.460023	+	0.887907i	$0.347841\pi$
$953$	−13.3992	+	41.2385i	−0.434042	+	1.33584i	−0.894065	+	0.447937i	$0.852159\pi$
$954$	−4.21003	+	4.67572i	−0.136305	+	0.151382i
$955$	2.28215	+	21.7132i	0.0738487	+	0.702623i
$956$	−0.572949	+	0.992377i	−0.0185305	+	0.0320958i
$957$	3.76243	−	0.536711i	0.121622	−	0.0173494i
$958$	10.2705			0.331825
$959$	−9.19513	+	39.4931i	−0.296926	+	1.27530i
$960$	0.163119	+	0.502029i	0.00526464	+	0.0162029i
$961$	−12.5187	+	2.66093i	−0.403829	+	0.0858365i
$962$	−2.45462	+	1.09287i	−0.0791402	+	0.0352355i
$963$	−20.4275	+	9.09491i	−0.658267	+	0.293079i
$964$	−44.9740	+	9.55951i	−1.44851	+	0.307891i
$965$	−2.88854	−	8.89002i	−0.0929855	−	0.286180i
$966$	7.44466	+	6.96820i	0.239528	+	0.224198i
$967$	−38.9787			−1.25347			−0.626735	−	0.779232i	$-0.715609\pi$
$967$	−38.9787			−1.25347			−0.626735	+	0.779232i	$0.715609\pi$
$968$	−24.5295	+	1.81724i	−0.788409	+	0.0584084i
$969$	4.85410	−	8.40755i	0.155936	−	0.270089i
$970$	−0.412289	−	3.92266i	−0.0132378	−	0.125949i
$971$	−12.0444	+	13.3766i	−0.386522	+	0.429276i	−0.904735	−	0.425976i	$-0.859931\pi$
$971$	−12.0444	+	13.3766i	−0.386522	+	0.429276i	0.518213	+	0.855252i	$0.326597\pi$
$972$	−8.00000	+	24.6215i	−0.256600	+	0.789734i
$973$	33.9274	+	48.6457i	1.08766	+	1.55951i
$974$	0.236068	+	0.171513i	0.00756411	+	0.00549564i
$975$		0			0
$976$	−12.5940	−	2.67694i	−0.403125	−	0.0856869i
$977$	−4.49250	−	42.7433i	−0.143728	−	1.36748i	−0.794065	−	0.607833i	$-0.792039\pi$
$977$	−4.49250	−	42.7433i	−0.143728	−	1.36748i	0.650337	−	0.759646i	$-0.274628\pi$
$978$	4.56231	+	7.90215i	0.145886	+	0.252683i
$979$	12.9443	−	32.2299i	0.413701	−	1.03007i
$980$	19.8992	+	15.6665i	0.635656	+	0.500449i
$981$	−11.0902	+	8.05748i	−0.354082	+	0.257256i
$982$	−13.4660	+	14.9555i	−0.429717	+	0.477249i
$983$	29.7434	+	33.0334i	0.948668	+	1.05360i	0.998495	+	0.0548446i	$0.0174663\pi$
$983$	29.7434	+	33.0334i	0.948668	+	1.05360i	−0.0498270	+	0.998758i	$0.515867\pi$
$984$	−9.43349	+	4.20006i	−0.300729	+	0.133893i
$985$	1.07939	−	10.2697i	0.0343921	−	0.327219i
$986$	−0.270510	+	0.832544i	−0.00861479	+	0.0265136i
$987$	0.432897	−	22.4110i	0.0137793	−	0.713349i
$988$	8.78115	−	6.37988i	0.279366	−	0.202971i
$989$	21.3713	+	37.0162i	0.679569	+	1.17705i
$990$	8.81702	+	2.50852i	0.280223	+	0.0797260i
$991$	11.5172	−	19.9484i	0.365857	−	0.633682i	−0.623057	−	0.782177i	$-0.714109\pi$
$991$	11.5172	−	19.9484i	0.365857	−	0.633682i	0.988913	+	0.148495i	$0.0474427\pi$
$992$	−33.9659	−	15.1226i	−1.07842	−	0.480143i
$993$	−4.54508	−	13.9883i	−0.144234	−	0.443906i
$994$	8.49606	+	1.05923i	0.269479	+	0.0335969i
$995$	2.60081	+	1.88960i	0.0824513	+	0.0599044i
$996$	−1.52218	+	14.4825i	−0.0482320	+	0.458897i
$997$	−1.89552	−	2.10519i	−0.0600318	−	0.0666721i	0.712381	−	0.701793i	$-0.247617\pi$
$997$	−1.89552	−	2.10519i	−0.0600318	−	0.0666721i	−0.772413	+	0.635121i	$0.780950\pi$
$998$	−18.3876	−	3.90840i	−0.582049	−	0.123718i
$999$	−23.2505	−	10.3518i	−0.735614	−	0.327516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.m.a.25.1	yes	8
3.2	odd	2		693.2.by.a.487.1		8
7.2	even	3	inner	77.2.m.a.58.1	yes	8
7.3	odd	6		539.2.f.b.344.1		4
7.4	even	3		539.2.f.a.344.1		4
7.5	odd	6		539.2.q.a.520.1		8
7.6	odd	2		539.2.q.a.410.1		8
11.2	odd	10		847.2.e.b.606.1		4
11.3	even	5		847.2.n.c.753.1		8
11.4	even	5	inner	77.2.m.a.4.1	✓	8
11.5	even	5		847.2.n.c.130.1		8
11.6	odd	10		847.2.n.a.130.1		8
11.7	odd	10		847.2.n.b.81.1		8
11.8	odd	10		847.2.n.a.753.1		8
11.9	even	5		847.2.e.a.606.2		4
11.10	odd	2		847.2.n.b.487.1		8
21.2	odd	6		693.2.by.a.289.1		8
33.26	odd	10		693.2.by.a.235.1		8
77.2	odd	30		847.2.e.b.485.1		4
77.4	even	15		539.2.f.a.246.1		4
77.9	even	15		847.2.e.a.485.2		4
77.16	even	15		847.2.n.c.9.1		8
77.24	even	30		5929.2.a.j.1.2		2
77.26	odd	30		539.2.q.a.422.1		8
77.30	odd	30		847.2.n.a.632.1		8
77.31	odd	30		5929.2.a.o.1.1		2
77.37	even	15	inner	77.2.m.a.37.1	yes	8
77.46	odd	30		5929.2.a.l.1.2		2
77.48	odd	10		539.2.q.a.312.1		8
77.51	odd	30		847.2.n.b.807.1		8
77.53	even	15		5929.2.a.q.1.1		2
77.58	even	15		847.2.n.c.632.1		8
77.59	odd	30		539.2.f.b.246.1		4
77.65	odd	6		847.2.n.b.366.1		8
77.72	odd	30		847.2.n.a.9.1		8
231.191	odd	30		693.2.by.a.37.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.a.4.1	✓	8	11.4	even	5	inner
77.2.m.a.25.1	yes	8	1.1	even	1	trivial
77.2.m.a.37.1	yes	8	77.37	even	15	inner
77.2.m.a.58.1	yes	8	7.2	even	3	inner
539.2.f.a.246.1		4	77.4	even	15
539.2.f.a.344.1		4	7.4	even	3
539.2.f.b.246.1		4	77.59	odd	30
539.2.f.b.344.1		4	7.3	odd	6
539.2.q.a.312.1		8	77.48	odd	10
539.2.q.a.410.1		8	7.6	odd	2
539.2.q.a.422.1		8	77.26	odd	30
539.2.q.a.520.1		8	7.5	odd	6
693.2.by.a.37.1		8	231.191	odd	30
693.2.by.a.235.1		8	33.26	odd	10
693.2.by.a.289.1		8	21.2	odd	6
693.2.by.a.487.1		8	3.2	odd	2
847.2.e.a.485.2		4	77.9	even	15
847.2.e.a.606.2		4	11.9	even	5
847.2.e.b.485.1		4	77.2	odd	30
847.2.e.b.606.1		4	11.2	odd	10
847.2.n.a.9.1		8	77.72	odd	30
847.2.n.a.130.1		8	11.6	odd	10
847.2.n.a.632.1		8	77.30	odd	30
847.2.n.a.753.1		8	11.8	odd	10
847.2.n.b.81.1		8	11.7	odd	10
847.2.n.b.366.1		8	77.65	odd	6
847.2.n.b.487.1		8	11.10	odd	2
847.2.n.b.807.1		8	77.51	odd	30
847.2.n.c.9.1		8	77.16	even	15
847.2.n.c.130.1		8	11.5	even	5
847.2.n.c.632.1		8	77.58	even	15
847.2.n.c.753.1		8	11.3	even	5
5929.2.a.j.1.2		2	77.24	even	30
5929.2.a.l.1.2		2	77.46	odd	30
5929.2.a.o.1.1		2	77.31	odd	30
5929.2.a.q.1.1		2	77.53	even	15

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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.564602 - 0.251377i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-1.08268 - 1.20243i) q^{4} +(0.233733 - 2.22382i) q^{5} +(0.500000 + 0.363271i) q^{6} +(1.59618 - 2.11002i) q^{7} +(0.690983 + 2.12663i) q^{8} +(-1.82709 - 0.813473i) q^{9} +O(q^{10})\)	\(q+(-0.564602 - 0.251377i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-1.08268 - 1.20243i) q^{4} +(0.233733 - 2.22382i) q^{5} +(0.500000 + 0.363271i) q^{6} +(1.59618 - 2.11002i) q^{7} +(0.690983 + 2.12663i) q^{8} +(-1.82709 - 0.813473i) q^{9} +(-0.690983 + 1.19682i) q^{10} +(2.04732 + 2.60931i) q^{11} +(0.809017 + 1.40126i) q^{12} +(-0.690983 + 0.502029i) q^{13} +(-1.43162 + 0.790081i) q^{14} +(-0.690983 + 2.12663i) q^{15} +(-0.193806 + 1.84395i) q^{16} +(-1.12920 + 0.502754i) q^{17} +(0.827091 + 0.918578i) q^{18} +(5.25542 - 5.83674i) q^{19} +(-2.92705 + 2.12663i) q^{20} +(-2.00000 + 1.73205i) q^{21} +(-0.500000 - 1.98787i) q^{22} +(3.11803 + 5.40059i) q^{23} +(-0.233733 - 2.22382i) q^{24} +(0.516329 - 0.109749i) q^{26} +(4.04508 + 2.93893i) q^{27} +(-4.26531 + 0.365171i) q^{28} +(-0.354102 + 1.08981i) q^{29} +(0.924716 - 1.02700i) q^{30} +(-0.691773 - 6.58178i) q^{31} +(2.80902 - 4.86536i) q^{32} +(-1.46007 - 2.97795i) q^{33} +0.763932 q^{34} +(-4.31923 - 4.04280i) q^{35} +(1.00000 + 3.07768i) q^{36} +(-4.97894 + 1.05831i) q^{37} +(-4.43444 + 1.97434i) q^{38} +(0.780261 - 0.347395i) q^{39} +(4.89074 - 1.03956i) q^{40} +(-1.42705 - 4.39201i) q^{41} +(1.56460 - 0.475165i) q^{42} +6.85410 q^{43} +(0.920937 - 5.28680i) q^{44} +(-2.23607 + 3.87298i) q^{45} +(-0.402863 - 3.83299i) q^{46} +(-5.66897 + 6.29602i) q^{47} +(0.572949 - 1.76336i) q^{48} +(-1.90441 - 6.73597i) q^{49} +(1.20906 - 0.256993i) q^{51} +(1.35177 + 0.287327i) q^{52} +(0.532068 + 5.06229i) q^{53} +(-1.54508 - 2.67617i) q^{54} +(6.28115 - 3.94298i) q^{55} +(5.59017 + 1.93649i) q^{56} +(-6.35410 + 4.61653i) q^{57} +(0.473881 - 0.526298i) q^{58} +(2.48127 + 2.75573i) q^{59} +(3.30524 - 1.47159i) q^{60} +(-0.725874 + 6.90623i) q^{61} +(-1.26393 + 3.88998i) q^{62} +(-4.63282 + 2.55676i) q^{63} +(0.190983 - 0.138757i) q^{64} +(0.954915 + 1.65396i) q^{65} +(0.0757724 + 2.04839i) q^{66} +(-5.30902 + 9.19549i) q^{67} +(1.82709 + 0.813473i) q^{68} +(-1.92705 - 5.93085i) q^{69} +(1.42238 + 3.36833i) q^{70} +(-4.23607 - 3.07768i) q^{71} +(0.467465 - 4.44764i) q^{72} +(2.77415 + 3.08100i) q^{73} +(3.07715 + 0.654069i) q^{74} -12.7082 q^{76} +(8.77360 - 0.154962i) q^{77} -0.527864 q^{78} +(0.646976 + 0.288052i) q^{79} +(4.05530 + 0.861981i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-0.298335 + 2.83847i) q^{82} +(7.28115 + 5.29007i) q^{83} +(4.24803 + 0.529617i) q^{84} +(0.854102 + 2.62866i) q^{85} +(-3.86984 - 1.72296i) q^{86} +(0.572949 - 0.992377i) q^{87} +(-4.13436 + 6.15687i) q^{88} +(-5.23607 - 9.06914i) q^{89} +(2.23607 - 1.62460i) q^{90} +(-0.0436417 + 2.25932i) q^{91} +(3.11803 - 9.59632i) q^{92} +(-0.691773 + 6.58178i) q^{93} +(4.78339 - 2.12970i) q^{94} +(-11.7515 - 13.0513i) q^{95} +(-3.75920 + 4.17501i) q^{96} +(-2.30902 + 1.67760i) q^{97} +(-0.618034 + 4.28187i) q^{98} +(-1.61803 - 6.43288i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + q^{3} + 2 q^{4} - 5 q^{5} + 4 q^{6} - 5 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + q^3 + 2 * q^4 - 5 * q^5 + 4 * q^6 - 5 * q^7 + 10 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + q^{3} + 2 q^{4} - 5 q^{5} + 4 q^{6} - 5 q^{7} + 10 q^{8} - 2 q^{9} - 10 q^{10} + 4 q^{11} + 2 q^{12} - 10 q^{13} + 3 q^{14} - 10 q^{15} + 6 q^{16} - 4 q^{17} - 6 q^{18} - 3 q^{19} - 10 q^{20} - 16 q^{21} - 4 q^{22} + 16 q^{23} + 5 q^{24} - 15 q^{26} + 10 q^{27} - 12 q^{28} + 24 q^{29} + 5 q^{30} + 8 q^{31} + 18 q^{32} - 11 q^{33} + 24 q^{34} - 5 q^{35} + 8 q^{36} - 13 q^{37} - 9 q^{38} + 5 q^{39} - 5 q^{40} + 2 q^{41} + 10 q^{42} + 28 q^{43} - 12 q^{44} + 8 q^{46} + 6 q^{47} + 18 q^{48} - 11 q^{49} + 6 q^{51} - 5 q^{52} - 12 q^{53} + 10 q^{54} + 10 q^{55} - 24 q^{57} - 21 q^{58} - 18 q^{59} + 5 q^{60} + 18 q^{61} - 28 q^{62} - 2 q^{63} + 6 q^{64} + 30 q^{65} + 2 q^{66} - 38 q^{67} + 2 q^{68} - 2 q^{69} + 20 q^{70} - 16 q^{71} - 10 q^{72} + 15 q^{73} - 14 q^{74} - 48 q^{76} - 4 q^{77} - 40 q^{78} + 9 q^{79} - 15 q^{80} + q^{81} + 7 q^{82} + 18 q^{83} + 2 q^{84} - 20 q^{85} - 7 q^{86} + 18 q^{87} - 5 q^{88} - 24 q^{89} + 50 q^{91} + 16 q^{92} + 8 q^{93} + 8 q^{94} + 15 q^{95} - 2 q^{96} - 14 q^{97} + 4 q^{98} - 4 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + q^3 + 2 * q^4 - 5 * q^5 + 4 * q^6 - 5 * q^7 + 10 * q^8 - 2 * q^9 - 10 * q^10 + 4 * q^11 + 2 * q^12 - 10 * q^13 + 3 * q^14 - 10 * q^15 + 6 * q^16 - 4 * q^17 - 6 * q^18 - 3 * q^19 - 10 * q^20 - 16 * q^21 - 4 * q^22 + 16 * q^23 + 5 * q^24 - 15 * q^26 + 10 * q^27 - 12 * q^28 + 24 * q^29 + 5 * q^30 + 8 * q^31 + 18 * q^32 - 11 * q^33 + 24 * q^34 - 5 * q^35 + 8 * q^36 - 13 * q^37 - 9 * q^38 + 5 * q^39 - 5 * q^40 + 2 * q^41 + 10 * q^42 + 28 * q^43 - 12 * q^44 + 8 * q^46 + 6 * q^47 + 18 * q^48 - 11 * q^49 + 6 * q^51 - 5 * q^52 - 12 * q^53 + 10 * q^54 + 10 * q^55 - 24 * q^57 - 21 * q^58 - 18 * q^59 + 5 * q^60 + 18 * q^61 - 28 * q^62 - 2 * q^63 + 6 * q^64 + 30 * q^65 + 2 * q^66 - 38 * q^67 + 2 * q^68 - 2 * q^69 + 20 * q^70 - 16 * q^71 - 10 * q^72 + 15 * q^73 - 14 * q^74 - 48 * q^76 - 4 * q^77 - 40 * q^78 + 9 * q^79 - 15 * q^80 + q^81 + 7 * q^82 + 18 * q^83 + 2 * q^84 - 20 * q^85 - 7 * q^86 + 18 * q^87 - 5 * q^88 - 24 * q^89 + 50 * q^91 + 16 * q^92 + 8 * q^93 + 8 * q^94 + 15 * q^95 - 2 * q^96 - 14 * q^97 + 4 * q^98 - 4 * q^99

Introduction

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