LMFDB - Embedded newform 650.2.e.k.451.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(451,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("650.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.591408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 4x^{4} + x^{3} + 10x^{2} - 3x + 1 $ x^6 - x^5 + 4x^4 + x^3 + 10x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.2
Root			$1.08504 - 1.87935i$ of defining polynomial
Character	$\chi$	$=$	650.451
Dual form			650.2.e.k.601.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.269594 + 0.466951i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.269594 + 0.466951i) q^{6} +(0.354638 + 0.614250i) q^{7} -1.00000 q^{8} +(1.35464 + 2.34630i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.269594 + 0.466951i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.269594 + 0.466951i) q^{6} +(0.354638 + 0.614250i) q^{7} -1.00000 q^{8} +(1.35464 + 2.34630i) q^{9} +(2.25513 - 3.90600i) q^{11} +0.539189 q^{12} +(1.30878 + 3.35963i) q^{13} +0.709275 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.58504 + 2.74538i) q^{17} +2.70928 q^{18} +(0.0603191 + 0.104476i) q^{19} -0.382433 q^{21} +(-2.25513 - 3.90600i) q^{22} +(2.48554 - 4.30507i) q^{23} +(0.269594 - 0.466951i) q^{24} +(3.56391 + 0.546373i) q^{26} -3.07838 q^{27} +(0.354638 - 0.614250i) q^{28} +(3.63090 - 6.28890i) q^{29} +9.66701 q^{31} +(0.500000 + 0.866025i) q^{32} +(1.21594 + 2.10607i) q^{33} +3.17009 q^{34} +(1.35464 - 2.34630i) q^{36} +(-3.47887 + 6.02558i) q^{37} +0.120638 q^{38} +(-1.92162 - 0.294598i) q^{39} +(-0.223740 + 0.387529i) q^{41} +(-0.191217 + 0.331197i) q^{42} +(1.00000 + 1.73205i) q^{43} -4.51026 q^{44} +(-2.48554 - 4.30507i) q^{46} +4.70928 q^{47} +(-0.269594 - 0.466951i) q^{48} +(3.24846 - 5.62651i) q^{49} -1.70928 q^{51} +(2.25513 - 2.81325i) q^{52} -9.58864 q^{53} +(-1.53919 + 2.66595i) q^{54} +(-0.354638 - 0.614250i) q^{56} -0.0650468 q^{57} +(-3.63090 - 6.28890i) q^{58} +(2.87936 + 4.98720i) q^{59} +(-3.53139 - 6.11655i) q^{61} +(4.83351 - 8.37188i) q^{62} +(-0.960811 + 1.66417i) q^{63} +1.00000 q^{64} +2.43188 q^{66} +(-1.46081 + 2.53020i) q^{67} +(1.58504 - 2.74538i) q^{68} +(1.34017 + 2.32125i) q^{69} +(4.09171 + 7.08705i) q^{71} +(-1.35464 - 2.34630i) q^{72} -6.74539 q^{73} +(3.47887 + 6.02558i) q^{74} +(0.0603191 - 0.104476i) q^{76} +3.19902 q^{77} +(-1.21594 + 1.51687i) q^{78} -16.0072 q^{79} +(-3.23400 + 5.60145i) q^{81} +(0.223740 + 0.387529i) q^{82} +0.355771 q^{83} +(0.191217 + 0.331197i) q^{84} +2.00000 q^{86} +(1.95774 + 3.39090i) q^{87} +(-2.25513 + 3.90600i) q^{88} +(-1.81545 + 3.14445i) q^{89} +(-1.59951 + 1.99537i) q^{91} -4.97107 q^{92} +(-2.60617 + 4.51402i) q^{93} +(2.35464 - 4.07835i) q^{94} -0.539189 q^{96} +(-3.95415 - 6.84878i) q^{97} +(-3.24846 - 5.62651i) q^{98} +12.2195 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} - 5 q^{7} - 6 q^{8} + q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 - 5 * q^7 - 6 * q^8 + q^9	$ 6 q + 3 q^{2} - 3 q^{4} - 5 q^{7} - 6 q^{8} + q^{9} - 3 q^{11} + 3 q^{13} - 10 q^{14} - 3 q^{16} + 4 q^{17} + 2 q^{18} + 13 q^{19} - 12 q^{21} + 3 q^{22} - 12 q^{27} - 5 q^{28} + 14 q^{29} + 12 q^{31} + 3 q^{32} - 6 q^{33} + 8 q^{34} + q^{36} - 5 q^{37} + 26 q^{38} - 18 q^{39} - 2 q^{41} - 6 q^{42} + 6 q^{43} + 6 q^{44} + 14 q^{47} + 2 q^{49} + 4 q^{51} - 3 q^{52} - 18 q^{53} - 6 q^{54} + 5 q^{56} + 8 q^{57} - 14 q^{58} - 8 q^{59} - 4 q^{61} + 6 q^{62} - 9 q^{63} + 6 q^{64} - 12 q^{66} - 12 q^{67} + 4 q^{68} - 14 q^{69} + 20 q^{71} - q^{72} + 12 q^{73} + 5 q^{74} + 13 q^{76} + 38 q^{77} + 6 q^{78} - 28 q^{79} + 13 q^{81} + 2 q^{82} + 8 q^{83} + 6 q^{84} + 12 q^{86} - 20 q^{87} + 3 q^{88} - 7 q^{89} - 19 q^{91} - 26 q^{93} + 7 q^{94} - 26 q^{97} - 2 q^{98} + 26 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 - 5 * q^7 - 6 * q^8 + q^9 - 3 * q^11 + 3 * q^13 - 10 * q^14 - 3 * q^16 + 4 * q^17 + 2 * q^18 + 13 * q^19 - 12 * q^21 + 3 * q^22 - 12 * q^27 - 5 * q^28 + 14 * q^29 + 12 * q^31 + 3 * q^32 - 6 * q^33 + 8 * q^34 + q^36 - 5 * q^37 + 26 * q^38 - 18 * q^39 - 2 * q^41 - 6 * q^42 + 6 * q^43 + 6 * q^44 + 14 * q^47 + 2 * q^49 + 4 * q^51 - 3 * q^52 - 18 * q^53 - 6 * q^54 + 5 * q^56 + 8 * q^57 - 14 * q^58 - 8 * q^59 - 4 * q^61 + 6 * q^62 - 9 * q^63 + 6 * q^64 - 12 * q^66 - 12 * q^67 + 4 * q^68 - 14 * q^69 + 20 * q^71 - q^72 + 12 * q^73 + 5 * q^74 + 13 * q^76 + 38 * q^77 + 6 * q^78 - 28 * q^79 + 13 * q^81 + 2 * q^82 + 8 * q^83 + 6 * q^84 + 12 * q^86 - 20 * q^87 + 3 * q^88 - 7 * q^89 - 19 * q^91 - 26 * q^93 + 7 * q^94 - 26 * q^97 - 2 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.269594	+	0.466951i	−0.155650	+	0.269594i	−0.933296	−	0.359109i	$-0.883081\pi$
$3$	−0.269594	+	0.466951i	−0.155650	+	0.269594i	0.777645	+	0.628703i	$0.216414\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.269594	+	0.466951i	0.110061	+	0.190632i
$7$	0.354638	+	0.614250i	0.134040	+	0.232165i	0.925230	−	0.379406i	$-0.123871\pi$
$7$	0.354638	+	0.614250i	0.134040	+	0.232165i	−0.791190	+	0.611570i	$0.790538\pi$
$8$	−1.00000			−0.353553
$9$	1.35464	+	2.34630i	0.451546	+	0.782100i
$10$		0			0
$11$	2.25513	−	3.90600i	0.679947	−	1.17770i	−0.295049	−	0.955482i	$-0.595336\pi$
$11$	2.25513	−	3.90600i	0.679947	−	1.17770i	0.974996	−	0.222221i	$-0.0713306\pi$
$12$	0.539189			0.155650
$13$	1.30878	+	3.35963i	0.362991	+	0.931793i
$13$	1.30878	+	3.35963i	0.362991	+	0.931793i
$14$	0.709275			0.189562
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.58504	+	2.74538i	0.384429	+	0.665851i	0.991690	−	0.128652i	$-0.0410649\pi$
$17$	1.58504	+	2.74538i	0.384429	+	0.665851i	−0.607260	+	0.794503i	$0.707732\pi$
$18$	2.70928			0.638582
$19$	0.0603191	+	0.104476i	0.0138381	+	0.0239684i	0.872862	−	0.487968i	$-0.162262\pi$
$19$	0.0603191	+	0.104476i	0.0138381	+	0.0239684i	−0.859023	+	0.511936i	$0.828928\pi$
$20$		0			0
$21$	−0.382433			−0.0834538
$22$	−2.25513	−	3.90600i	−0.480795	−	0.832762i
$23$	2.48554	−	4.30507i	0.518270	−	0.897670i	−0.481505	−	0.876443i	$-0.659910\pi$
$23$	2.48554	−	4.30507i	0.518270	−	0.897670i	0.999775	−	0.0212264i	$-0.00675708\pi$
$24$	0.269594	−	0.466951i	0.0550307	−	0.0953160i
$25$		0			0
$26$	3.56391	+	0.546373i	0.698941	+	0.107153i
$27$	−3.07838			−0.592434
$28$	0.354638	−	0.614250i	0.0670202	−	0.116082i
$29$	3.63090	−	6.28890i	0.674241	−	1.16782i	−0.302449	−	0.953165i	$-0.597804\pi$
$29$	3.63090	−	6.28890i	0.674241	−	1.16782i	0.976690	−	0.214654i	$-0.0688623\pi$
$30$		0			0
$31$	9.66701			1.73625			0.868124	−	0.496348i	$-0.165326\pi$
$31$	9.66701			1.73625			0.868124	+	0.496348i	$0.165326\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.21594	+	2.10607i	0.211668	+	0.366620i
$34$	3.17009			0.543665
$35$		0			0
$36$	1.35464	−	2.34630i	0.225773	−	0.391050i
$37$	−3.47887	+	6.02558i	−0.571923	+	0.990599i	0.424446	+	0.905453i	$0.360469\pi$
$37$	−3.47887	+	6.02558i	−0.571923	+	0.990599i	−0.996369	+	0.0851458i	$0.972864\pi$
$38$	0.120638			0.0195701
$39$	−1.92162	−	0.294598i	−0.307706	−	0.0471735i
$40$		0			0
$41$	−0.223740	+	0.387529i	−0.0349423	+	0.0605219i	−0.882968	−	0.469434i	$-0.844458\pi$
$41$	−0.223740	+	0.387529i	−0.0349423	+	0.0605219i	0.848025	+	0.529956i	$0.177791\pi$
$42$	−0.191217	+	0.331197i	−0.0295054	+	0.0511048i
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	0.932145	−	0.362084i	$-0.117935\pi$
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	−0.779647	+	0.626219i	$0.784601\pi$
$44$	−4.51026			−0.679947
$45$		0			0
$46$	−2.48554	−	4.30507i	−0.366472	−	0.634748i
$47$	4.70928			0.686918			0.343459	−	0.939168i	$-0.388401\pi$
$47$	4.70928			0.686918			0.343459	+	0.939168i	$0.388401\pi$
$48$	−0.269594	−	0.466951i	−0.0389126	−	0.0673986i
$49$	3.24846	−	5.62651i	0.464066	−	0.803786i
$50$		0			0
$51$	−1.70928			−0.239346
$52$	2.25513	−	2.81325i	0.312730	−	0.390128i
$53$	−9.58864			−1.31710			−0.658550	−	0.752537i	$-0.728830\pi$
$53$	−9.58864			−1.31710			−0.658550	+	0.752537i	$0.728830\pi$
$54$	−1.53919	+	2.66595i	−0.209457	+	0.362790i
$55$		0			0
$56$	−0.354638	−	0.614250i	−0.0473905	−	0.0820827i
$57$	−0.0650468			−0.00861565
$58$	−3.63090	−	6.28890i	−0.476760	−	0.825773i
$59$	2.87936	+	4.98720i	0.374861	+	0.649278i	0.990306	−	0.138901i	$-0.0443571\pi$
$59$	2.87936	+	4.98720i	0.374861	+	0.649278i	−0.615445	+	0.788180i	$0.711024\pi$
$60$		0			0
$61$	−3.53139	−	6.11655i	−0.452148	−	0.783144i	0.546371	−	0.837543i	$-0.316009\pi$
$61$	−3.53139	−	6.11655i	−0.452148	−	0.783144i	−0.998519	+	0.0543997i	$0.982675\pi$
$62$	4.83351	−	8.37188i	0.613856	−	1.06323i
$63$	−0.960811	+	1.66417i	−0.121051	+	0.209666i
$64$	1.00000			0.125000
$65$		0			0
$66$	2.43188			0.299344
$67$	−1.46081	+	2.53020i	−0.178466	+	0.309113i	−0.941355	−	0.337416i	$-0.890447\pi$
$67$	−1.46081	+	2.53020i	−0.178466	+	0.309113i	0.762889	+	0.646530i	$0.223780\pi$
$68$	1.58504	−	2.74538i	0.192215	−	0.332926i
$69$	1.34017	+	2.32125i	0.161338	+	0.279445i
$70$		0			0
$71$	4.09171	+	7.08705i	0.485596	+	0.841078i	0.999863	−	0.0165526i	$-0.00526911\pi$
$71$	4.09171	+	7.08705i	0.485596	+	0.841078i	−0.514267	+	0.857630i	$0.671936\pi$
$72$	−1.35464	−	2.34630i	−0.159646	−	0.276514i
$73$	−6.74539			−0.789488			−0.394744	−	0.918791i	$-0.629167\pi$
$73$	−6.74539			−0.789488			−0.394744	+	0.918791i	$0.629167\pi$
$74$	3.47887	+	6.02558i	0.404410	+	0.700459i
$75$		0			0
$76$	0.0603191	−	0.104476i	0.00691907	−	0.0119842i
$77$	3.19902			0.364562
$78$	−1.21594	+	1.51687i	−0.137678	+	0.171752i
$79$	−16.0072			−1.80095			−0.900475	−	0.434908i	$-0.856781\pi$
$79$	−16.0072			−1.80095			−0.900475	+	0.434908i	$0.856781\pi$
$80$		0			0
$81$	−3.23400	+	5.60145i	−0.359333	+	0.622383i
$82$	0.223740	+	0.387529i	0.0247080	+	0.0427954i
$83$	0.355771			0.0390510			0.0195255	−	0.999809i	$-0.493784\pi$
$83$	0.355771			0.0390510			0.0195255	+	0.999809i	$0.493784\pi$
$84$	0.191217	+	0.331197i	0.0208635	+	0.0361366i
$85$		0			0
$86$	2.00000			0.215666
$87$	1.95774	+	3.39090i	0.209892	+	0.363543i
$88$	−2.25513	+	3.90600i	−0.240398	+	0.416381i
$89$	−1.81545	+	3.14445i	−0.192437	+	0.333311i	−0.946057	−	0.323999i	$-0.894973\pi$
$89$	−1.81545	+	3.14445i	−0.192437	+	0.333311i	0.753620	+	0.657310i	$0.228306\pi$
$90$		0			0
$91$	−1.59951	+	1.99537i	−0.167674	+	0.209172i
$92$	−4.97107			−0.518270
$93$	−2.60617	+	4.51402i	−0.270248	+	0.468083i
$94$	2.35464	−	4.07835i	0.242862	−	0.420650i
$95$		0			0
$96$	−0.539189			−0.0550307
$97$	−3.95415	−	6.84878i	−0.401483	−	0.695388i	0.592422	−	0.805627i	$-0.298172\pi$
$97$	−3.95415	−	6.84878i	−0.401483	−	0.695388i	−0.993905	+	0.110239i	$0.964838\pi$
$98$	−3.24846	−	5.62651i	−0.328144	−	0.568363i
$99$	12.2195			1.22811
$100$		0			0
$101$	−3.07058	+	5.31840i	−0.305534	+	0.529200i	−0.977380	−	0.211490i	$-0.932168\pi$
$101$	−3.07058	+	5.31840i	−0.305534	+	0.529200i	0.671846	+	0.740691i	$0.265502\pi$
$102$	−0.854638	+	1.48028i	−0.0846217	+	0.146569i
$103$	17.6803			1.74210			0.871048	−	0.491198i	$-0.163441\pi$
$103$	17.6803			1.74210			0.871048	+	0.491198i	$0.163441\pi$
$104$	−1.30878	−	3.35963i	−0.128337	−	0.329438i
$105$		0			0
$106$	−4.79432	+	8.30400i	−0.465665	+	0.806556i
$107$	0.269594	−	0.466951i	0.0260627	−	0.0451419i	−0.852700	−	0.522401i	$-0.825036\pi$
$107$	0.269594	−	0.466951i	0.0260627	−	0.0451419i	0.878763	+	0.477259i	$0.158370\pi$
$108$	1.53919	+	2.66595i	0.148109	+	0.256531i
$109$	−11.0205			−1.05557			−0.527787	−	0.849377i	$-0.676978\pi$
$109$	−11.0205			−1.05557			−0.527787	+	0.849377i	$0.676978\pi$
$110$		0			0
$111$	−1.87577	−	3.24893i	−0.178040	−	0.308374i
$112$	−0.709275			−0.0670202
$113$	−7.00000	−	12.1244i	−0.658505	−	1.14056i	−0.981003	−	0.193993i	$-0.937856\pi$
$113$	−7.00000	−	12.1244i	−0.658505	−	1.14056i	0.322498	−	0.946570i	$-0.395477\pi$
$114$	−0.0325234	+	0.0563321i	−0.00304609	+	0.00527599i
$115$		0			0
$116$	−7.26180			−0.674241
$117$	−6.10977	+	7.62188i	−0.564848	+	0.704643i
$118$	5.75872			0.530133
$119$	−1.12423	+	1.94723i	−0.103058	+	0.178502i
$120$		0			0
$121$	−4.67122	−	8.09079i	−0.424656	−	0.735526i
$122$	−7.06278			−0.639434
$123$	−0.120638	−	0.208951i	−0.0108776	−	0.0188405i
$124$	−4.83351	−	8.37188i	−0.434062	−	0.751817i
$125$		0			0
$126$	0.960811	+	1.66417i	0.0855959	+	0.148256i
$127$	−6.08864	+	10.5458i	−0.540279	+	0.935791i	0.458609	+	0.888638i	$0.348348\pi$
$127$	−6.08864	+	10.5458i	−0.540279	+	0.935791i	−0.998888	+	0.0471526i	$0.984985\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−1.07838			−0.0949459
$130$		0			0
$131$	−17.4547			−1.52502			−0.762511	−	0.646976i	$-0.776034\pi$
$131$	−17.4547			−1.52502			−0.762511	+	0.646976i	$0.776034\pi$
$132$	1.21594	−	2.10607i	0.105834	−	0.183310i
$133$	−0.0427828	+	0.0741020i	−0.00370974	+	0.00642546i
$134$	1.46081	+	2.53020i	0.126195	+	0.218576i
$135$		0			0
$136$	−1.58504	−	2.74538i	−0.135916	−	0.235414i
$137$	−4.67675	−	8.10037i	−0.399562	−	0.692061i	0.594110	−	0.804384i	$-0.297504\pi$
$137$	−4.67675	−	8.10037i	−0.399562	−	0.692061i	−0.993672	+	0.112322i	$0.964171\pi$
$138$	2.68035			0.228166
$139$	1.32211	+	2.28997i	0.112140	+	0.194233i	0.916633	−	0.399730i	$-0.130896\pi$
$139$	1.32211	+	2.28997i	0.112140	+	0.194233i	−0.804493	+	0.593963i	$0.797563\pi$
$140$		0			0
$141$	−1.26959	+	2.19900i	−0.106919	+	0.185189i
$142$	8.18342			0.686737
$143$	16.0742	+	2.46429i	1.34419	+	0.206074i
$144$	−2.70928			−0.225773
$145$		0			0
$146$	−3.37270	+	5.84168i	−0.279126	+	0.483461i
$147$	1.75154	+	3.03375i	0.144464	+	0.250219i
$148$	6.95774			0.571923
$149$	4.61757	+	7.99786i	0.378286	+	0.655210i	0.990813	−	0.135239i	$-0.0431803\pi$
$149$	4.61757	+	7.99786i	0.378286	+	0.655210i	−0.612527	+	0.790450i	$0.709847\pi$
$150$		0			0
$151$	−9.42574			−0.767056			−0.383528	−	0.923529i	$-0.625291\pi$
$151$	−9.42574			−0.767056			−0.383528	+	0.923529i	$0.625291\pi$
$152$	−0.0603191	−	0.104476i	−0.00489252	−	0.00847410i
$153$	−4.29432	+	7.43798i	−0.347175	+	0.601325i
$154$	1.59951	−	2.77043i	0.128892	−	0.223248i
$155$		0			0
$156$	0.705681	+	1.81147i	0.0564997	+	0.145034i
$157$	5.77205			0.460660			0.230330	−	0.973113i	$-0.426019\pi$
$157$	5.77205			0.460660			0.230330	+	0.973113i	$0.426019\pi$
$158$	−8.00359	+	13.8626i	−0.636732	+	1.10285i
$159$	2.58504	−	4.47743i	0.205007	−	0.355083i
$160$		0			0
$161$	3.52586			0.277877
$162$	3.23400	+	5.60145i	0.254087	+	0.440092i
$163$	−8.41075	−	14.5678i	−0.658781	−	1.14104i	−0.980932	−	0.194354i	$-0.937739\pi$
$163$	−8.41075	−	14.5678i	−0.658781	−	1.14104i	0.322151	−	0.946688i	$-0.395594\pi$
$164$	0.447480			0.0349423
$165$		0			0
$166$	0.177886	−	0.308107i	0.0138066	−	0.0239137i
$167$	9.05971	−	15.6919i	0.701061	−	1.21427i	−0.267033	−	0.963687i	$-0.586043\pi$
$167$	9.05971	−	15.6919i	0.701061	−	1.21427i	0.968094	−	0.250586i	$-0.0806234\pi$
$168$	0.382433			0.0295054
$169$	−9.57417	+	8.79404i	−0.736475	+	0.676465i
$170$		0			0
$171$	−0.163421	+	0.283053i	−0.0124971	+	0.0216456i
$172$	1.00000	−	1.73205i	0.0762493	−	0.132068i
$173$	5.15203	+	8.92357i	0.391701	+	0.678447i	0.992674	−	0.120823i	$-0.0385533\pi$
$173$	5.15203	+	8.92357i	0.391701	+	0.678447i	−0.600973	+	0.799270i	$0.705220\pi$
$174$	3.91548			0.296832
$175$		0			0
$176$	2.25513	+	3.90600i	0.169987	+	0.294426i
$177$	−3.10504			−0.233389
$178$	1.81545	+	3.14445i	0.136074	+	0.235686i
$179$	−0.630898	+	1.09275i	−0.0471555	+	0.0816757i	−0.888640	−	0.458606i	$-0.848349\pi$
$179$	−0.630898	+	1.09275i	−0.0471555	+	0.0816757i	0.841484	+	0.540282i	$0.181682\pi$
$180$		0			0
$181$	2.38243			0.177085			0.0885424	−	0.996072i	$-0.471779\pi$
$181$	2.38243			0.177085			0.0885424	+	0.996072i	$0.471779\pi$
$182$	0.928288	+	2.38290i	0.0688093	+	0.176632i
$183$	3.80817			0.281508
$184$	−2.48554	+	4.30507i	−0.183236	+	0.317374i
$185$		0			0
$186$	2.60617	+	4.51402i	0.191094	+	0.330984i
$187$	14.2979			1.04557
$188$	−2.35464	−	4.07835i	−0.171730	−	0.297444i
$189$	−1.09171	−	1.89090i	−0.0794101	−	0.137542i
$190$		0			0
$191$	5.54278	+	9.60038i	0.401062	+	0.694659i	0.993854	−	0.110696i	$-0.0353080\pi$
$191$	5.54278	+	9.60038i	0.401062	+	0.694659i	−0.592793	+	0.805355i	$0.701975\pi$
$192$	−0.269594	+	0.466951i	−0.0194563	+	0.0336993i
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	0.496119	+	0.868255i	$0.334758\pi$
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$	−7.90829			−0.567782
$195$		0			0
$196$	−6.49693			−0.464066
$197$	−4.34684	+	7.52895i	−0.309699	+	0.536415i	−0.978297	−	0.207210i	$-0.933562\pi$
$197$	−4.34684	+	7.52895i	−0.309699	+	0.536415i	0.668597	+	0.743625i	$0.266895\pi$
$198$	6.10977	−	10.5824i	0.434202	−	0.752060i
$199$	−10.7587	−	18.6347i	−0.762666	−	1.32098i	−0.941472	−	0.337091i	$-0.890557\pi$
$199$	−10.7587	−	18.6347i	−0.762666	−	1.32098i	0.178806	−	0.983884i	$-0.442776\pi$
$200$		0			0
$201$	−0.787653	−	1.36426i	−0.0555568	−	0.0962271i
$202$	3.07058	+	5.31840i	0.216045	+	0.374201i
$203$	5.15061			0.361502
$204$	0.854638	+	1.48028i	0.0598366	+	0.103640i
$205$		0			0
$206$	8.84017	−	15.3116i	0.615924	−	1.06681i
$207$	13.4680			0.936091
$208$	−3.56391	−	0.546373i	−0.247113	−	0.0378842i
$209$	0.544109			0.0376368
$210$		0			0
$211$	2.79432	−	4.83990i	0.192369	−	0.333193i	−0.753666	−	0.657258i	$-0.771716\pi$
$211$	2.79432	−	4.83990i	0.192369	−	0.333193i	0.946035	+	0.324065i	$0.105050\pi$
$212$	4.79432	+	8.30400i	0.329275	+	0.570321i
$213$	−4.41241			−0.302333
$214$	−0.269594	−	0.466951i	−0.0184291	−	0.0319201i
$215$		0			0
$216$	3.07838			0.209457
$217$	3.42829	+	5.93797i	0.232727	+	0.403096i
$218$	−5.51026	+	9.54405i	−0.373202	+	0.646405i
$219$	1.81852	−	3.14977i	0.122884	−	0.212842i
$220$		0			0
$221$	−7.14896	+	8.91825i	−0.480891	+	0.599907i
$222$	−3.75154			−0.251787
$223$	−12.3546	+	21.3989i	−0.827328	+	1.43297i	0.0727995	+	0.997347i	$0.476807\pi$
$223$	−12.3546	+	21.3989i	−0.827328	+	1.43297i	−0.900127	+	0.435627i	$0.856527\pi$
$224$	−0.354638	+	0.614250i	−0.0236952	+	0.0410413i
$225$		0			0
$226$	−14.0000			−0.931266
$227$	−14.3474	−	24.8504i	−0.952268	−	1.64938i	−0.740500	−	0.672056i	$-0.765411\pi$
$227$	−14.3474	−	24.8504i	−0.952268	−	1.64938i	−0.211768	−	0.977320i	$-0.567922\pi$
$228$	0.0325234	+	0.0563321i	0.00215391	+	0.00373069i
$229$	−1.89988			−0.125548			−0.0627738	−	0.998028i	$-0.519995\pi$
$229$	−1.89988			−0.125548			−0.0627738	+	0.998028i	$0.519995\pi$
$230$		0			0
$231$	−0.862437	+	1.49378i	−0.0567442	+	0.0982838i
$232$	−3.63090	+	6.28890i	−0.238380	+	0.412886i
$233$	22.2485			1.45755			0.728773	−	0.684756i	$-0.240091\pi$
$233$	22.2485			1.45755			0.728773	+	0.684756i	$0.240091\pi$
$234$	3.54585	+	9.10215i	0.231800	+	0.595026i
$235$		0			0
$236$	2.87936	−	4.98720i	0.187430	−	0.324639i
$237$	4.31545	−	7.47458i	0.280319	−	0.485526i
$238$	1.12423	+	1.94723i	0.0728731	+	0.126220i
$239$	24.8710			1.60877			0.804384	−	0.594110i	$-0.202495\pi$
$239$	24.8710			1.60877			0.804384	+	0.594110i	$0.202495\pi$
$240$		0			0
$241$	1.47528	+	2.55525i	0.0950309	+	0.164598i	0.909621	−	0.415438i	$-0.136372\pi$
$241$	1.47528	+	2.55525i	0.0950309	+	0.164598i	−0.814591	+	0.580036i	$0.803038\pi$
$242$	−9.34244			−0.600555
$243$	−6.36130	−	11.0181i	−0.408078	−	0.706811i
$244$	−3.53139	+	6.11655i	−0.226074	+	0.391572i
$245$		0			0
$246$	−0.241276			−0.0153832
$247$	−0.272055	+	0.339386i	−0.0173104	+	0.0215946i
$248$	−9.66701			−0.613856
$249$	−0.0959140	+	0.166128i	−0.00607830	+	0.0105279i
$250$		0			0
$251$	−8.27985	−	14.3411i	−0.522620	−	0.905204i	−0.999654	−	0.0263190i	$-0.991621\pi$
$251$	−8.27985	−	14.3411i	−0.522620	−	0.905204i	0.477034	−	0.878885i	$-0.341712\pi$
$252$	1.92162			0.121051
$253$	−11.2104	−	19.4170i	−0.704792	−	1.22074i
$254$	6.08864	+	10.5458i	0.382035	+	0.661704i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.261795	−	0.453443i	0.0163303	−	0.0282850i	−0.857745	−	0.514076i	$-0.828135\pi$
$257$	0.261795	−	0.453443i	0.0163303	−	0.0282850i	0.874075	+	0.485791i	$0.161468\pi$
$258$	−0.539189	+	0.933903i	−0.0335684	+	0.0581422i
$259$	−4.93495			−0.306643
$260$		0			0
$261$	19.6742			1.21780
$262$	−8.72733	+	15.1162i	−0.539176	+	0.933881i
$263$	14.3908	−	24.9255i	0.887372	−	1.53697i	0.0444013	−	0.999014i	$-0.485862\pi$
$263$	14.3908	−	24.9255i	0.887372	−	1.53697i	0.842971	−	0.537960i	$-0.180805\pi$
$264$	−1.21594	−	2.10607i	−0.0748360	−	0.129620i
$265$		0			0
$266$	0.0427828	+	0.0741020i	0.00262318	+	0.00454349i
$267$	−0.978870	−	1.69545i	−0.0599059	−	0.103760i
$268$	2.92162			0.178466
$269$	−5.02832	−	8.70930i	−0.306582	−	0.531016i	0.671030	−	0.741430i	$-0.265852\pi$
$269$	−5.02832	−	8.70930i	−0.306582	−	0.531016i	−0.977612	+	0.210414i	$0.932519\pi$
$270$		0			0
$271$	−9.06278	+	15.6972i	−0.550525	+	0.953537i	0.447712	+	0.894178i	$0.352239\pi$
$271$	−9.06278	+	15.6972i	−0.550525	+	0.953537i	−0.998237	+	0.0593589i	$0.981094\pi$
$272$	−3.17009			−0.192215
$273$	−0.500522	−	1.28483i	−0.0302930	−	0.0777616i
$274$	−9.35350			−0.565066
$275$		0			0
$276$	1.34017	−	2.32125i	0.0806689	−	0.139723i
$277$	−12.3582	−	21.4051i	−0.742534	−	1.28611i	−0.951338	−	0.308149i	$-0.900290\pi$
$277$	−12.3582	−	21.4051i	−0.742534	−	1.28611i	0.208804	−	0.977958i	$-0.433043\pi$
$278$	2.64423			0.158590
$279$	13.0953	+	22.6817i	0.783995	+	1.35792i
$280$		0			0
$281$	22.9854			1.37120			0.685598	−	0.727980i	$-0.259541\pi$
$281$	22.9854			1.37120			0.685598	+	0.727980i	$0.259541\pi$
$282$	1.26959	+	2.19900i	0.0756032	+	0.130949i
$283$	9.04945	−	15.6741i	0.537934	−	0.931729i	−0.461081	−	0.887358i	$-0.652538\pi$
$283$	9.04945	−	15.6741i	0.537934	−	0.931729i	0.999015	−	0.0443709i	$-0.0141283\pi$
$284$	4.09171	−	7.08705i	0.242798	−	0.420539i
$285$		0			0
$286$	10.1712	−	12.6885i	0.601437	−	0.750287i
$287$	−0.317387			−0.0187347
$288$	−1.35464	+	2.34630i	−0.0798228	+	0.138257i
$289$	3.47528	−	6.01935i	0.204428	−	0.354080i
$290$		0			0
$291$	4.26406			0.249964
$292$	3.37270	+	5.84168i	0.197372	+	0.341859i
$293$	8.92214	+	15.4536i	0.521237	+	0.902809i	0.999695	+	0.0246988i	$0.00786267\pi$
$293$	8.92214	+	15.4536i	0.521237	+	0.902809i	−0.478458	+	0.878111i	$0.658804\pi$
$294$	3.50307			0.204303
$295$		0			0
$296$	3.47887	−	6.02558i	0.202205	−	0.350230i
$297$	−6.94214	+	12.0241i	−0.402824	+	0.697711i
$298$	9.23513			0.534977
$299$	17.7165	+	2.71606i	1.02457	+	0.157074i
$300$		0			0
$301$	−0.709275	+	1.22850i	−0.0408820	+	0.0708096i
$302$	−4.71287	+	8.16293i	−0.271195	+	0.469724i
$303$	−1.65562	−	2.86762i	−0.0951130	−	0.164741i
$304$	−0.120638			−0.00691907
$305$		0			0
$306$	4.29432	+	7.43798i	0.245490	+	0.425201i
$307$	−3.44521			−0.196629			−0.0983143	−	0.995155i	$-0.531345\pi$
$307$	−3.44521			−0.196629			−0.0983143	+	0.995155i	$0.531345\pi$
$308$	−1.59951	−	2.77043i	−0.0911404	−	0.157860i
$309$	−4.76652	+	8.25586i	−0.271158	+	0.469659i
$310$		0			0
$311$	17.8238			1.01069			0.505347	−	0.862916i	$-0.331365\pi$
$311$	17.8238			1.01069			0.505347	+	0.862916i	$0.331365\pi$
$312$	1.92162	+	0.294598i	0.108790	+	0.0166784i
$313$	−32.2245			−1.82143			−0.910717	−	0.413031i	$-0.864470\pi$
$313$	−32.2245			−1.82143			−0.910717	+	0.413031i	$0.864470\pi$
$314$	2.88603	−	4.99875i	0.162868	−	0.282096i
$315$		0			0
$316$	8.00359	+	13.8626i	0.450237	+	0.779834i
$317$	−1.90602			−0.107053			−0.0535265	−	0.998566i	$-0.517046\pi$
$317$	−1.90602			−0.107053			−0.0535265	+	0.998566i	$0.517046\pi$
$318$	−2.58504	−	4.47743i	−0.144962	−	0.251082i
$319$	−16.3763	−	28.3646i	−0.916896	−	1.58811i
$320$		0			0
$321$	0.145362	+	0.251775i	0.00811333	+	0.0140527i
$322$	1.76293	−	3.05348i	0.0982442	−	0.170164i
$323$	−0.191217	+	0.331197i	−0.0106396	+	0.0184283i
$324$	6.46800			0.359333
$325$		0			0
$326$	−16.8215			−0.931657
$327$	2.97107	−	5.14605i	0.164301	−	0.284577i
$328$	0.223740	−	0.387529i	0.0123540	−	0.0213977i
$329$	1.67009	+	2.89267i	0.0920748	+	0.159478i
$330$		0			0
$331$	0.355771	+	0.616214i	0.0195550	+	0.0338702i	0.875637	−	0.482969i	$-0.160442\pi$
$331$	0.355771	+	0.616214i	0.0195550	+	0.0338702i	−0.856082	+	0.516839i	$0.827108\pi$
$332$	−0.177886	−	0.308107i	−0.00976275	−	0.0169096i
$333$	−18.8504			−1.03300
$334$	−9.05971	−	15.6919i	−0.495725	−	0.858621i
$335$		0			0
$336$	0.191217	−	0.331197i	0.0104317	−	0.0180683i
$337$	−9.85043			−0.536587			−0.268294	−	0.963337i	$-0.586460\pi$
$337$	−9.85043			−0.536587			−0.268294	+	0.963337i	$0.586460\pi$
$338$	2.82878	+	12.6885i	0.153865	+	0.690163i
$339$	7.54864			0.409986
$340$		0			0
$341$	21.8004	−	37.7594i	1.18056	−	2.04478i
$342$	0.163421	+	0.283053i	0.00883680	+	0.0153058i
$343$	9.57304			0.516896
$344$	−1.00000	−	1.73205i	−0.0539164	−	0.0933859i
$345$		0			0
$346$	10.3041			0.553949
$347$	−12.7665	−	22.1123i	−0.685343	−	1.18705i	−0.973329	−	0.229414i	$-0.926319\pi$
$347$	−12.7665	−	22.1123i	−0.685343	−	1.18705i	0.287986	−	0.957635i	$-0.407014\pi$
$348$	1.95774	−	3.39090i	0.104946	−	0.181772i
$349$	9.02832	−	15.6375i	0.483275	−	0.837056i	−0.516541	−	0.856263i	$-0.672781\pi$
$349$	9.02832	−	15.6375i	0.483275	−	0.837056i	0.999816	+	0.0192061i	$0.00611387\pi$
$350$		0			0
$351$	−4.02893	−	10.3422i	−0.215048	−	0.552026i
$352$	4.51026			0.240398
$353$	−7.32325	+	12.6842i	−0.389777	+	0.675114i	−0.992419	−	0.122898i	$-0.960781\pi$
$353$	−7.32325	+	12.6842i	−0.389777	+	0.675114i	0.602642	+	0.798012i	$0.294115\pi$
$354$	−1.55252	+	2.68904i	−0.0825155	+	0.142921i
$355$		0			0
$356$	3.63090			0.192437
$357$	−0.606173	−	1.04992i	−0.0320821	−	0.0555678i
$358$	0.630898	+	1.09275i	0.0333440	+	0.0577535i
$359$	−13.4186			−0.708204			−0.354102	−	0.935207i	$-0.615213\pi$
$359$	−13.4186			−0.708204			−0.354102	+	0.935207i	$0.615213\pi$
$360$		0			0
$361$	9.49272	−	16.4419i	0.499617	−	0.865362i
$362$	1.19122	−	2.06325i	0.0626090	−	0.108442i
$363$	5.03734			0.264392
$364$	2.52780	+	0.387529i	0.132492	+	0.0203120i
$365$		0			0
$366$	1.90409	−	3.29797i	0.0995282	−	0.172388i
$367$	10.7721	−	18.6577i	0.562297	−	0.973926i	−0.434999	−	0.900431i	$-0.643251\pi$
$367$	10.7721	−	18.6577i	0.562297	−	0.973926i	0.997296	−	0.0734954i	$-0.0234154\pi$
$368$	2.48554	+	4.30507i	0.129567	+	0.224417i
$369$	−1.21235			−0.0631123
$370$		0			0
$371$	−3.40049	−	5.88983i	−0.176545	−	0.305784i
$372$	5.21235			0.270248
$373$	−10.6670	−	18.4758i	−0.552317	−	0.956641i	−0.998107	−	0.0615036i	$-0.980410\pi$
$373$	−10.6670	−	18.4758i	−0.552317	−	0.956641i	0.445790	−	0.895138i	$-0.352923\pi$
$374$	7.14896	−	12.3824i	0.369664	−	0.640276i
$375$		0			0
$376$	−4.70928			−0.242862
$377$	25.8804	+	3.96765i	1.33291	+	0.204344i
$378$	−2.18342			−0.112303
$379$	−4.05611	+	7.02540i	−0.208349	+	0.360870i	−0.951194	−	0.308592i	$-0.900142\pi$
$379$	−4.05611	+	7.02540i	−0.208349	+	0.360870i	0.742846	+	0.669462i	$0.233476\pi$
$380$		0			0
$381$	−3.28293	−	5.68619i	−0.168189	−	0.291313i
$382$	11.0856			0.567187
$383$	−12.4699	−	21.5986i	−0.637184	−	1.10364i	−0.986048	−	0.166462i	$-0.946766\pi$
$383$	−12.4699	−	21.5986i	−0.637184	−	1.10364i	0.348864	−	0.937173i	$-0.386568\pi$
$384$	0.269594	+	0.466951i	0.0137577	+	0.0238290i
$385$		0			0
$386$	7.00000	+	12.1244i	0.356291	+	0.617113i
$387$	−2.70928	+	4.69260i	−0.137720	+	0.238538i
$388$	−3.95415	+	6.84878i	−0.200741	+	0.347694i
$389$	13.5330			0.686153			0.343076	−	0.939308i	$-0.388531\pi$
$389$	13.5330			0.686153			0.343076	+	0.939308i	$0.388531\pi$
$390$		0			0
$391$	15.7587			0.796953
$392$	−3.24846	+	5.62651i	−0.164072	+	0.284181i
$393$	4.70568	−	8.15048i	0.237370	−	0.411137i
$394$	4.34684	+	7.52895i	0.218991	+	0.379303i
$395$		0			0
$396$	−6.10977	−	10.5824i	−0.307027	−	0.531787i
$397$	2.29739	+	3.97920i	0.115303	+	0.199710i	0.917901	−	0.396810i	$-0.129883\pi$
$397$	2.29739	+	3.97920i	0.115303	+	0.199710i	−0.802598	+	0.596520i	$0.796550\pi$
$398$	−21.5174			−1.07857
$399$	−0.0230680	−	0.0399550i	−0.00115485	−	0.00200025i
$400$		0			0
$401$	−14.8516	+	25.7237i	−0.741652	+	1.28458i	0.210091	+	0.977682i	$0.432624\pi$
$401$	−14.8516	+	25.7237i	−0.741652	+	1.28458i	−0.951743	+	0.306897i	$0.900709\pi$
$402$	−1.57531			−0.0785691
$403$	12.6520	+	32.4776i	0.630242	+	1.61782i
$404$	6.14116			0.305534
$405$		0			0
$406$	2.57531	−	4.46056i	0.127810	−	0.221374i
$407$	15.6906	+	27.1769i	0.777754	+	1.34711i
$408$	1.70928			0.0846217
$409$	5.15562	+	8.92980i	0.254929	+	0.441550i	0.964876	−	0.262705i	$-0.0846145\pi$
$409$	5.15562	+	8.92980i	0.254929	+	0.441550i	−0.709947	+	0.704255i	$0.751281\pi$
$410$		0			0
$411$	5.04331			0.248768
$412$	−8.84017	−	15.3116i	−0.435524	−	0.754350i
$413$	−2.04226	+	3.53730i	−0.100493	+	0.174059i
$414$	6.73400	−	11.6636i	0.330958	−	0.573236i
$415$		0			0
$416$	−2.25513	+	2.81325i	−0.110567	+	0.137931i
$417$	−1.42574			−0.0698187
$418$	0.272055	−	0.471213i	0.0133066	−	0.0230478i
$419$	−19.0452	+	32.9873i	−0.930421	+	1.61154i	−0.147819	+	0.989014i	$0.547225\pi$
$419$	−19.0452	+	32.9873i	−0.930421	+	1.61154i	−0.782602	+	0.622522i	$0.786108\pi$
$420$		0			0
$421$	−26.7103			−1.30178			−0.650891	−	0.759171i	$-0.725604\pi$
$421$	−26.7103			−1.30178			−0.650891	+	0.759171i	$0.725604\pi$
$422$	−2.79432	−	4.83990i	−0.136025	−	0.235603i
$423$	6.37936	+	11.0494i	0.310175	+	0.537239i
$424$	9.58864			0.465665
$425$		0			0
$426$	−2.20620	+	3.82126i	−0.106891	+	0.185141i
$427$	2.50473	−	4.33832i	0.121212	−	0.209946i
$428$	−0.539189			−0.0260627
$429$	−5.48421	+	6.84150i	−0.264780	+	0.330311i
$430$		0			0
$431$	10.3594	−	17.9429i	0.498993	−	0.864281i	−0.501006	−	0.865444i	$-0.667037\pi$
$431$	10.3594	−	17.9429i	0.498993	−	0.864281i	0.999999	+	0.00116231i	$0.000369975\pi$
$432$	1.53919	−	2.66595i	0.0740543	−	0.128266i
$433$	7.92881	+	13.7331i	0.381034	+	0.659971i	0.991210	−	0.132295i	$-0.0422346\pi$
$433$	7.92881	+	13.7331i	0.381034	+	0.659971i	−0.610176	+	0.792266i	$0.708901\pi$
$434$	6.85658			0.329126
$435$		0			0
$436$	5.51026	+	9.54405i	0.263894	+	0.457077i
$437$	0.599701			0.0286876
$438$	−1.81852	−	3.14977i	−0.0868923	−	0.150502i
$439$	4.86962	−	8.43444i	0.232415	−	0.402554i	−0.726104	−	0.687585i	$-0.758671\pi$
$439$	4.86962	−	8.43444i	0.232415	−	0.402554i	0.958518	+	0.285032i	$0.0920041\pi$
$440$		0			0
$441$	17.6020			0.838189
$442$	4.14896	+	10.6503i	0.197346	+	0.506583i
$443$	9.23060			0.438559			0.219279	−	0.975662i	$-0.429629\pi$
$443$	9.23060			0.438559			0.219279	+	0.975662i	$0.429629\pi$
$444$	−1.87577	+	3.24893i	−0.0890200	+	0.154187i
$445$		0			0
$446$	12.3546	+	21.3989i	0.585009	+	1.01327i
$447$	−4.97948			−0.235521
$448$	0.354638	+	0.614250i	0.0167551	+	0.0290206i
$449$	1.46194	+	2.53216i	0.0689934	+	0.119500i	0.898458	−	0.439058i	$-0.144688\pi$
$449$	1.46194	+	2.53216i	0.0689934	+	0.119500i	−0.829465	+	0.558559i	$0.811355\pi$
$450$		0			0
$451$	1.00913	+	1.74786i	0.0475179	+	0.0823034i
$452$	−7.00000	+	12.1244i	−0.329252	+	0.570282i
$453$	2.54113	−	4.40136i	0.119393	−	0.206794i
$454$	−28.6947			−1.34671
$455$		0			0
$456$	0.0650468			0.00304609
$457$	−5.82632	+	10.0915i	−0.272544	+	0.472060i	−0.969512	−	0.245042i	$-0.921198\pi$
$457$	−5.82632	+	10.0915i	−0.272544	+	0.472060i	0.696969	+	0.717101i	$0.254532\pi$
$458$	−0.949940	+	1.64535i	−0.0443878	+	0.0768819i
$459$	−4.87936	−	8.45130i	−0.227749	−	0.394473i
$460$		0			0
$461$	15.1490	+	26.2388i	0.705557	+	1.22206i	0.966490	+	0.256704i	$0.0826366\pi$
$461$	15.1490	+	26.2388i	0.705557	+	1.22206i	−0.260933	+	0.965357i	$0.584030\pi$
$462$	0.862437	+	1.49378i	0.0401242	+	0.0694971i
$463$	7.04331			0.327330			0.163665	−	0.986516i	$-0.447668\pi$
$463$	7.04331			0.327330			0.163665	+	0.986516i	$0.447668\pi$
$464$	3.63090	+	6.28890i	0.168560	+	0.291955i
$465$		0			0
$466$	11.1242	−	19.2677i	0.515320	−	0.892561i
$467$	3.90110			0.180522			0.0902608	−	0.995918i	$-0.471230\pi$
$467$	3.90110			0.180522			0.0902608	+	0.995918i	$0.471230\pi$
$468$	9.65562	+	1.48028i	0.446331	+	0.0684258i
$469$	−2.07223			−0.0956869
$470$		0			0
$471$	−1.55611	+	2.69527i	−0.0717019	+	0.124191i
$472$	−2.87936	−	4.98720i	−0.132533	−	0.229555i
$473$	9.02052			0.414764
$474$	−4.31545	−	7.47458i	−0.198215	−	0.343319i
$475$		0			0
$476$	2.24846			0.103058
$477$	−12.9891	−	22.4978i	−0.594731	−	1.03010i
$478$	12.4355	−	21.5389i	0.568785	−	0.985165i
$479$	−8.75513	+	15.1643i	−0.400032	+	0.692876i	−0.993729	−	0.111813i	$-0.964334\pi$
$479$	−8.75513	+	15.1643i	−0.400032	+	0.692876i	0.593697	+	0.804689i	$0.297668\pi$
$480$		0			0
$481$	−24.7968	−	3.80152i	−1.13064	−	0.173335i
$482$	2.95055			0.134394
$483$	−0.950552	+	1.64640i	−0.0432516	+	0.0749140i
$484$	−4.67122	+	8.09079i	−0.212328	+	0.367763i
$485$		0			0
$486$	−12.7226			−0.577109
$487$	19.2659	+	33.3695i	0.873022	+	1.51212i	0.858855	+	0.512218i	$0.171176\pi$
$487$	19.2659	+	33.3695i	0.873022	+	1.51212i	0.0141666	+	0.999900i	$0.495490\pi$
$488$	3.53139	+	6.11655i	0.159858	+	0.276883i
$489$	9.06997			0.410158
$490$		0			0
$491$	−3.41189	+	5.90956i	−0.153976	+	0.266695i	−0.932686	−	0.360690i	$-0.882541\pi$
$491$	−3.41189	+	5.90956i	−0.153976	+	0.266695i	0.778710	+	0.627385i	$0.215875\pi$
$492$	−0.120638	+	0.208951i	−0.00543879	+	0.00942026i
$493$	23.0205			1.03679
$494$	0.157889	+	0.405299i	0.00710377	+	0.0182353i
$495$		0			0
$496$	−4.83351	+	8.37188i	−0.217031	+	0.375909i
$497$	−2.90215	+	5.02667i	−0.130179	+	0.225477i
$498$	0.0959140	+	0.166128i	0.00429801	+	0.00744437i
$499$	9.57918			0.428823			0.214412	−	0.976743i	$-0.431217\pi$
$499$	9.57918			0.428823			0.214412	+	0.976743i	$0.431217\pi$
$500$		0			0
$501$	4.88489	+	8.46088i	0.218241	+	0.378004i
$502$	−16.5597			−0.739096
$503$	8.33710	+	14.4403i	0.371733	+	0.643860i	0.989832	−	0.142240i	$-0.0454304\pi$
$503$	8.33710	+	14.4403i	0.371733	+	0.643860i	−0.618099	+	0.786100i	$0.712097\pi$
$504$	0.960811	−	1.66417i	0.0427979	−	0.0741282i
$505$		0			0
$506$	−22.4208			−0.996727
$507$	−1.52525	−	6.84150i	−0.0677386	−	0.303842i
$508$	12.1773			0.540279
$509$	11.8299	−	20.4900i	0.524352	−	0.908204i	−0.475246	−	0.879853i	$-0.657641\pi$
$509$	11.8299	−	20.4900i	0.524352	−	0.908204i	0.999598	−	0.0283510i	$-0.00902561\pi$
$510$		0			0
$511$	−2.39217	−	4.14336i	−0.105823	−	0.183291i
$512$	−1.00000			−0.0441942
$513$	−0.185685	−	0.321616i	−0.00819819	−	0.0141997i
$514$	−0.261795	−	0.453443i	−0.0115473	−	0.0200005i
$515$		0			0
$516$	0.539189	+	0.933903i	0.0237365	+	0.0411128i
$517$	10.6200	−	18.3944i	0.467068	−	0.808986i
$518$	−2.46748	+	4.27379i	−0.108415	+	0.187780i
$519$	−5.55583			−0.243874
$520$		0			0
$521$	−24.0472			−1.05353			−0.526763	−	0.850012i	$-0.676594\pi$
$521$	−24.0472			−1.05353			−0.526763	+	0.850012i	$0.676594\pi$
$522$	9.83710	−	17.0384i	0.430558	−	0.745749i
$523$	11.6670	−	20.2079i	0.510163	−	0.883628i	−0.489768	−	0.871853i	$-0.662918\pi$
$523$	11.6670	−	20.2079i	0.510163	−	0.883628i	0.999931	−	0.0117752i	$-0.00374824\pi$
$524$	8.72733	+	15.1162i	0.381255	+	0.660354i
$525$		0			0
$526$	−14.3908	−	24.9255i	−0.627467	−	1.08680i
$527$	15.3226	+	26.5396i	0.667465	+	1.15608i
$528$	−2.43188			−0.105834
$529$	−0.855771	−	1.48224i	−0.0372075	−	0.0644452i
$530$		0			0
$531$	−7.80098	+	13.5117i	−0.338534	+	0.586358i
$532$	0.0855657			0.00370974
$533$	−1.59478	−	0.244491i	−0.0690776	−	0.0105901i
$534$	−1.95774			−0.0847197
$535$		0			0
$536$	1.46081	−	2.53020i	0.0630974	−	0.109288i
$537$	−0.340173	−	0.589197i	−0.0146795	−	0.0254257i
$538$	−10.0566			−0.433572
$539$	−14.6514	−	25.3770i	−0.631081	−	1.09306i
$540$		0			0
$541$	−33.1494			−1.42520			−0.712602	−	0.701569i	$-0.752483\pi$
$541$	−33.1494			−1.42520			−0.712602	+	0.701569i	$0.752483\pi$
$542$	9.06278	+	15.6972i	0.389280	+	0.674252i
$543$	−0.642291	+	1.11248i	−0.0275633	+	0.0477411i
$544$	−1.58504	+	2.74538i	−0.0679582	+	0.117707i
$545$		0			0
$546$	−1.36296	−	0.208951i	−0.0583293	−	0.00894229i
$547$	−43.6742			−1.86737			−0.933687	−	0.358090i	$-0.883428\pi$
$547$	−43.6742			−1.86737			−0.933687	+	0.358090i	$0.883428\pi$
$548$	−4.67675	+	8.10037i	−0.199781	+	0.346031i
$549$	9.56751	−	16.5714i	0.408331	−	0.707250i
$550$		0			0
$551$	0.876050			0.0373210
$552$	−1.34017	−	2.32125i	−0.0570415	−	0.0987989i
$553$	−5.67675	−	9.83242i	−0.241400	−	0.418117i
$554$	−24.7165			−1.05010
$555$		0			0
$556$	1.32211	−	2.28997i	0.0560701	−	0.0971163i
$557$	−11.1995	+	19.3982i	−0.474540	+	0.821927i	−0.999575	−	0.0291537i	$-0.990719\pi$
$557$	−11.1995	+	19.3982i	−0.474540	+	0.821927i	0.525035	+	0.851080i	$0.324052\pi$
$558$	26.1906			1.10874
$559$	−4.51026	+	5.62651i	−0.190764	+	0.237976i
$560$		0			0
$561$	−3.85464	+	6.67643i	−0.162743	+	0.281879i
$562$	11.4927	−	19.9060i	0.484791	−	0.839683i
$563$	0.120638	+	0.208951i	0.00508429	+	0.00880625i	0.868556	−	0.495590i	$-0.165048\pi$
$563$	0.120638	+	0.208951i	0.00508429	+	0.00880625i	−0.863472	+	0.504397i	$0.831715\pi$
$564$	2.53919			0.106919
$565$		0			0
$566$	−9.04945	−	15.6741i	−0.380377	−	0.658832i
$567$	−4.58759			−0.192661
$568$	−4.09171	−	7.08705i	−0.171684	−	0.297366i
$569$	−13.5856	+	23.5309i	−0.569537	+	0.986466i	0.427075	+	0.904216i	$0.359544\pi$
$569$	−13.5856	+	23.5309i	−0.569537	+	0.986466i	−0.996612	+	0.0822501i	$0.973789\pi$
$570$		0			0
$571$	2.25461			0.0943524			0.0471762	−	0.998887i	$-0.484978\pi$
$571$	2.25461			0.0943524			0.0471762	+	0.998887i	$0.484978\pi$
$572$	−5.90295	−	15.1528i	−0.246815	−	0.633570i
$573$	−5.97721			−0.249702
$574$	−0.158693	+	0.274865i	−0.00662373	+	0.0114726i
$575$		0			0
$576$	1.35464	+	2.34630i	0.0564432	+	0.0977626i
$577$	−7.86481			−0.327416			−0.163708	−	0.986509i	$-0.552346\pi$
$577$	−7.86481			−0.327416			−0.163708	+	0.986509i	$0.552346\pi$
$578$	−3.47528	−	6.01935i	−0.144552	−	0.250372i
$579$	−3.77432	−	6.53732i	−0.156855	−	0.271682i
$580$		0			0
$581$	0.126170	+	0.218533i	0.00523441	+	0.00906627i
$582$	2.13203	−	3.69279i	0.0883755	−	0.153071i
$583$	−21.6236	+	37.4532i	−0.895559	+	1.55115i
$584$	6.74539			0.279126
$585$		0			0
$586$	17.8443			0.737141
$587$	−5.60197	+	9.70289i	−0.231218	+	0.400481i	−0.958167	−	0.286210i	$-0.907604\pi$
$587$	−5.60197	+	9.70289i	−0.231218	+	0.400481i	0.726949	+	0.686692i	$0.240938\pi$
$588$	1.75154	−	3.03375i	0.0722321	−	0.125110i
$589$	0.583105	+	1.00997i	0.0240264	+	0.0416150i
$590$		0			0
$591$	−2.34377	−	4.05952i	−0.0964097	−	0.166986i
$592$	−3.47887	−	6.02558i	−0.142981	−	0.247650i
$593$	−13.4186			−0.551034			−0.275517	−	0.961296i	$-0.588849\pi$
$593$	−13.4186			−0.551034			−0.275517	+	0.961296i	$0.588849\pi$
$594$	6.94214	+	12.0241i	0.284840	+	0.493356i
$595$		0			0
$596$	4.61757	−	7.99786i	0.189143	−	0.327605i
$597$	11.6020			0.474837
$598$	11.2104	−	13.9849i	0.458428	−	0.571884i
$599$	29.5753			1.20841			0.604207	−	0.796827i	$-0.293490\pi$
$599$	29.5753			1.20841			0.604207	+	0.796827i	$0.293490\pi$
$600$		0			0
$601$	−12.4916	+	21.6361i	−0.509543	+	0.882554i	0.490396	+	0.871500i	$0.336852\pi$
$601$	−12.4916	+	21.6361i	−0.509543	+	0.882554i	−0.999939	+	0.0110541i	$0.996481\pi$
$602$	0.709275	+	1.22850i	0.0289079	+	0.0500700i
$603$	−7.91548			−0.322343
$604$	4.71287	+	8.16293i	0.191764	+	0.332145i
$605$		0			0
$606$	−3.31124			−0.134510
$607$	5.19594	+	8.99964i	0.210897	+	0.365284i	0.951995	−	0.306112i	$-0.0990282\pi$
$607$	5.19594	+	8.99964i	0.210897	+	0.365284i	−0.741099	+	0.671396i	$0.765695\pi$
$608$	−0.0603191	+	0.104476i	−0.00244626	+	0.00423705i
$609$	−1.38858	+	2.40508i	−0.0562680	+	0.0974590i
$610$		0			0
$611$	6.16342	+	15.8214i	0.249345	+	0.640065i
$612$	8.58864			0.347175
$613$	−15.2643	+	26.4385i	−0.616517	+	1.06784i	0.373599	+	0.927590i	$0.378124\pi$
$613$	−15.2643	+	26.4385i	−0.616517	+	1.06784i	−0.990116	+	0.140249i	$0.955210\pi$
$614$	−1.72261	+	2.98364i	−0.0695187	+	0.120410i
$615$		0			0
$616$	−3.19902			−0.128892
$617$	3.65142	+	6.32444i	0.147000	+	0.254612i	0.930118	−	0.367262i	$-0.119705\pi$
$617$	3.65142	+	6.32444i	0.147000	+	0.254612i	−0.783117	+	0.621874i	$0.786371\pi$
$618$	4.76652	+	8.25586i	0.191738	+	0.332099i
$619$	−24.5103			−0.985151			−0.492575	−	0.870270i	$-0.663944\pi$
$619$	−24.5103			−0.985151			−0.492575	+	0.870270i	$0.663944\pi$
$620$		0			0
$621$	−7.65142	+	13.2526i	−0.307041	+	0.531810i
$622$	8.91189	−	15.4358i	0.357334	−	0.618921i
$623$	−2.57531			−0.103177
$624$	1.21594	−	1.51687i	0.0486766	−	0.0607236i
$625$		0			0
$626$	−16.1122	+	27.9072i	−0.643974	+	1.11540i
$627$	−0.146689	+	0.254073i	−0.00585819	+	0.0101467i
$628$	−2.88603	−	4.99875i	−0.115165	−	0.199472i
$629$	−22.0566			−0.879456
$630$		0			0
$631$	1.53919	+	2.66595i	0.0612741	+	0.106130i	0.895035	−	0.445996i	$-0.147150\pi$
$631$	1.53919	+	2.66595i	0.0612741	+	0.106130i	−0.833761	+	0.552125i	$0.813817\pi$
$632$	16.0072			0.636732
$633$	1.50667	+	2.60962i	0.0598846	+	0.103723i
$634$	−0.953012	+	1.65067i	−0.0378489	+	0.0655563i
$635$		0			0
$636$	−5.17009			−0.205007
$637$	23.1545	+	3.54975i	0.917414	+	0.140646i
$638$	−32.7526			−1.29669
$639$	−11.0856	+	19.2008i	−0.438538	+	0.759570i
$640$		0			0
$641$	1.23400	+	2.13735i	0.0487401	+	0.0844202i	0.889366	−	0.457196i	$-0.151146\pi$
$641$	1.23400	+	2.13735i	0.0487401	+	0.0844202i	−0.840626	+	0.541616i	$0.817813\pi$
$642$	0.290725			0.0114740
$643$	−9.41075	−	16.2999i	−0.371124	−	0.642805i	0.618615	−	0.785694i	$-0.287694\pi$
$643$	−9.41075	−	16.2999i	−0.371124	−	0.642805i	−0.989739	+	0.142889i	$0.954361\pi$
$644$	−1.76293	−	3.05348i	−0.0694691	−	0.120324i
$645$		0			0
$646$	0.191217	+	0.331197i	0.00752332	+	0.0130308i
$647$	−5.85157	+	10.1352i	−0.230049	+	0.398456i	−0.957822	−	0.287361i	$-0.907222\pi$
$647$	−5.85157	+	10.1352i	−0.230049	+	0.398456i	0.727773	+	0.685818i	$0.240555\pi$
$648$	3.23400	−	5.60145i	0.127043	−	0.220046i
$649$	25.9733			1.01954
$650$		0			0
$651$	−3.69699			−0.144896
$652$	−8.41075	+	14.5678i	−0.329390	+	0.570521i
$653$	7.34684	−	12.7251i	0.287504	−	0.497972i	−0.685709	−	0.727875i	$-0.740508\pi$
$653$	7.34684	−	12.7251i	0.287504	−	0.497972i	0.973213	+	0.229904i	$0.0738412\pi$
$654$	−2.97107	−	5.14605i	−0.116178	−	0.201226i
$655$		0			0
$656$	−0.223740	−	0.387529i	−0.00873558	−	0.0151305i
$657$	−9.13756	−	15.8267i	−0.356490	−	0.617459i
$658$	3.34017			0.130213
$659$	−9.39383	−	16.2706i	−0.365932	−	0.633812i	0.622994	−	0.782227i	$-0.285916\pi$
$659$	−9.39383	−	16.2706i	−0.365932	−	0.633812i	−0.988925	+	0.148415i	$0.952583\pi$
$660$		0			0
$661$	2.92101	−	5.05934i	0.113614	−	0.196785i	−0.803611	−	0.595155i	$-0.797091\pi$
$661$	2.92101	−	5.05934i	0.113614	−	0.196785i	0.917225	+	0.398370i	$0.130424\pi$
$662$	0.711543			0.0276549
$663$	−2.23707	−	5.74253i	−0.0868806	−	0.223021i
$664$	−0.355771			−0.0138066
$665$		0			0
$666$	−9.42522	+	16.3250i	−0.365220	+	0.632579i
$667$	−18.0494	−	31.2626i	−0.698877	−	1.21049i
$668$	−18.1194			−0.701061
$669$	−6.66148	−	11.5380i	−0.257548	−	0.446086i
$670$		0			0
$671$	−31.8550			−1.22975
$672$	−0.191217	−	0.331197i	−0.00737634	−	0.0127762i
$673$	−20.4463	+	35.4140i	−0.788145	+	1.36511i	0.138957	+	0.990298i	$0.455625\pi$
$673$	−20.4463	+	35.4140i	−0.788145	+	1.36511i	−0.927102	+	0.374809i	$0.877708\pi$
$674$	−4.92522	+	8.53072i	−0.189712	+	0.328591i
$675$		0			0
$676$	12.4030	+	3.89445i	0.477037	+	0.149787i
$677$	28.2700			1.08651			0.543253	−	0.839569i	$-0.317193\pi$
$677$	28.2700			1.08651			0.543253	+	0.839569i	$0.317193\pi$
$678$	3.77432	−	6.53732i	0.144952	−	0.251064i
$679$	2.80458	−	4.85767i	0.107630	−	0.186420i
$680$		0			0
$681$	15.4719			0.592884
$682$	−21.8004	−	37.7594i	−0.834779	−	1.44588i
$683$	−20.7526	−	35.9445i	−0.794075	−	1.37538i	−0.923425	−	0.383780i	$-0.874622\pi$
$683$	−20.7526	−	35.9445i	−0.794075	−	1.37538i	0.129349	−	0.991599i	$-0.458711\pi$
$684$	0.326842			0.0124971
$685$		0			0
$686$	4.78652	−	8.29049i	0.182750	−	0.316533i
$687$	0.512197	−	0.887152i	0.0195415	−	0.0338469i
$688$	−2.00000			−0.0762493
$689$	−12.5494	−	32.2142i	−0.478096	−	1.22726i
$690$		0			0
$691$	12.0542	−	20.8784i	0.458562	−	0.794253i	−0.540323	−	0.841458i	$-0.681698\pi$
$691$	12.0542	−	20.8784i	0.458562	−	0.794253i	0.998885	+	0.0472043i	$0.0150312\pi$
$692$	5.15203	−	8.92357i	0.195851	−	0.339223i
$693$	4.33351	+	7.50586i	0.164616	+	0.285124i
$694$	−25.5330			−0.969221
$695$		0			0
$696$	−1.95774	−	3.39090i	−0.0742079	−	0.128532i
$697$	−1.41855			−0.0537314
$698$	−9.02832	−	15.6375i	−0.341727	−	0.591888i
$699$	−5.99806	+	10.3889i	−0.226868	+	0.392946i
$700$		0			0
$701$	−14.1822			−0.535654			−0.267827	−	0.963467i	$-0.586306\pi$
$701$	−14.1822			−0.535654			−0.267827	+	0.963467i	$0.586306\pi$
$702$	−10.9711	−	1.68194i	−0.414076	−	0.0634809i
$703$	−0.839369			−0.0316574
$704$	2.25513	−	3.90600i	0.0849934	−	0.147213i
$705$		0			0
$706$	7.32325	+	12.6842i	0.275614	+	0.477378i
$707$	−4.35577			−0.163816
$708$	1.55252	+	2.68904i	0.0583473	+	0.101060i
$709$	23.2479	+	40.2665i	0.873091	+	1.51224i	0.858782	+	0.512341i	$0.171222\pi$
$709$	23.2479	+	40.2665i	0.873091	+	1.51224i	0.0143094	+	0.999898i	$0.495445\pi$
$710$		0			0
$711$	−21.6839	−	37.5577i	−0.813211	−	1.40852i
$712$	1.81545	−	3.14445i	0.0680368	−	0.117843i
$713$	24.0277	−	41.6172i	0.899845	−	1.55858i
$714$	−1.21235			−0.0453709
$715$		0			0
$716$	1.26180			0.0471555
$717$	−6.70507	+	11.6135i	−0.250405	+	0.433715i
$718$	−6.70928	+	11.6208i	−0.250388	+	0.433685i
$719$	6.36069	+	11.0170i	0.237214	+	0.410866i	0.959914	−	0.280296i	$-0.0904325\pi$
$719$	6.36069	+	11.0170i	0.237214	+	0.410866i	−0.722700	+	0.691162i	$0.757099\pi$
$720$		0			0
$721$	6.27012	+	10.8602i	0.233511	+	0.404454i
$722$	−9.49272	−	16.4419i	−0.353283	−	0.611903i
$723$	−1.59090			−0.0591664
$724$	−1.19122	−	2.06325i	−0.0442712	−	0.0766800i
$725$		0			0
$726$	2.51867	−	4.36246i	0.0934766	−	0.161906i
$727$	13.2595			0.491769			0.245884	−	0.969299i	$-0.420922\pi$
$727$	13.2595			0.491769			0.245884	+	0.969299i	$0.420922\pi$
$728$	1.59951	−	1.99537i	0.0592817	−	0.0739534i
$729$	−12.5441			−0.464597
$730$		0			0
$731$	−3.17009	+	5.49075i	−0.117250	+	0.203083i
$732$	−1.90409	−	3.29797i	−0.0703770	−	0.121897i
$733$	31.5848			1.16661			0.583305	−	0.812253i	$-0.301759\pi$
$733$	31.5848			1.16661			0.583305	+	0.812253i	$0.301759\pi$
$734$	−10.7721	−	18.6577i	−0.397604	−	0.688670i
$735$		0			0
$736$	4.97107			0.183236
$737$	6.58864	+	11.4119i	0.242696	+	0.420361i
$738$	−0.606173	+	1.04992i	−0.0223136	+	0.0386482i
$739$	−1.41609	+	2.45274i	−0.0520917	+	0.0902255i	−0.890895	−	0.454208i	$-0.849922\pi$
$739$	−1.41609	+	2.45274i	−0.0520917	+	0.0902255i	0.838804	+	0.544434i	$0.183255\pi$
$740$		0			0
$741$	−0.0851321	−	0.218533i	−0.00312741	−	0.00802800i
$742$	−6.80098			−0.249672
$743$	−10.4010	+	18.0151i	−0.381576	+	0.660909i	−0.991288	−	0.131714i	$-0.957952\pi$
$743$	−10.4010	+	18.0151i	−0.381576	+	0.660909i	0.609712	+	0.792623i	$0.291285\pi$
$744$	2.60617	−	4.51402i	0.0955470	−	0.165492i
$745$		0			0
$746$	−21.3340			−0.781094
$747$	0.481941	+	0.834747i	0.0176333	+	0.0305418i
$748$	−7.14896	−	12.3824i	−0.261392	−	0.452744i
$749$	0.382433			0.0139738
$750$		0			0
$751$	−18.1412	+	31.4214i	−0.661980	+	1.14658i	0.318114	+	0.948052i	$0.396950\pi$
$751$	−18.1412	+	31.4214i	−0.661980	+	1.14658i	−0.980095	+	0.198531i	$0.936383\pi$
$752$	−2.35464	+	4.07835i	−0.0858648	+	0.148722i
$753$	8.92881			0.325384
$754$	16.3763	−	20.4293i	0.596389	−	0.743990i
$755$		0			0
$756$	−1.09171	+	1.89090i	−0.0397051	+	0.0687712i
$757$	−20.4343	+	35.3933i	−0.742699	+	1.28639i	0.208563	+	0.978009i	$0.433121\pi$
$757$	−20.4343	+	35.3933i	−0.742699	+	1.28639i	−0.951262	+	0.308383i	$0.900212\pi$
$758$	4.05611	+	7.02540i	0.147325	+	0.255174i
$759$	12.0891			0.438805
$760$		0			0
$761$	−17.8112	−	30.8500i	−0.645657	−	1.11831i	−0.984149	−	0.177342i	$-0.943250\pi$
$761$	−17.8112	−	30.8500i	−0.645657	−	1.11831i	0.338492	−	0.940969i	$-0.390083\pi$
$762$	−6.56585			−0.237856
$763$	−3.90829	−	6.76936i	−0.141490	−	0.245067i
$764$	5.54278	−	9.60038i	0.200531	−	0.347330i
$765$		0			0
$766$	−24.9399			−0.901114
$767$	−12.9867	+	16.2007i	−0.468921	+	0.584975i
$768$	0.539189			0.0194563
$769$	−1.68455	+	2.91773i	−0.0607465	+	0.105216i	−0.894799	−	0.446469i	$-0.852681\pi$
$769$	−1.68455	+	2.91773i	−0.0607465	+	0.105216i	0.834053	+	0.551685i	$0.186015\pi$
$770$		0			0
$771$	0.141157	+	0.244491i	0.00508365	+	0.00880514i
$772$	14.0000			0.503871
$773$	5.53971	+	9.59506i	0.199250	+	0.345110i	0.948285	−	0.317419i	$-0.102816\pi$
$773$	5.53971	+	9.59506i	0.199250	+	0.345110i	−0.749036	+	0.662530i	$0.769483\pi$
$774$	2.70928	+	4.69260i	0.0973829	+	0.168672i
$775$		0			0
$776$	3.95415	+	6.84878i	0.141946	+	0.245857i
$777$	1.33044	−	2.30438i	0.0477291	−	0.0826693i
$778$	6.76652	−	11.7200i	0.242592	−	0.420181i
$779$	−0.0539832			−0.00193415
$780$		0			0
$781$	36.9093			1.32072
$782$	7.87936	−	13.6475i	0.281765	−	0.488032i
$783$	−11.1773	+	19.3596i	−0.399443	+	0.691856i
$784$	3.24846	+	5.62651i	0.116017	+	0.200947i
$785$		0			0
$786$	−4.70568	−	8.15048i	−0.167846	−	0.290718i
$787$	2.83545	+	4.91114i	0.101073	+	0.175063i	0.912127	−	0.409908i	$-0.134439\pi$
$787$	2.83545	+	4.91114i	0.101073	+	0.175063i	−0.811054	+	0.584971i	$0.801106\pi$
$788$	8.69368			0.309699
$789$	7.75933	+	13.4396i	0.276240	+	0.478461i
$790$		0			0
$791$	4.96493	−	8.59951i	0.176532	−	0.305763i
$792$	−12.2195			−0.434202
$793$	15.9275	−	19.8694i	0.565602	−	0.705582i
$794$	4.59478			0.163063
$795$		0			0
$796$	−10.7587	+	18.6347i	−0.381333	+	0.660488i
$797$	13.6712	+	23.6792i	0.484259	+	0.838762i	0.999837	−	0.0180812i	$-0.00575574\pi$
$797$	13.6712	+	23.6792i	0.484259	+	0.838762i	−0.515577	+	0.856843i	$0.672422\pi$
$798$	−0.0461361			−0.00163320
$799$	7.46441	+	12.9287i	0.264072	+	0.457386i
$800$		0			0
$801$	−9.83710			−0.347577
$802$	14.8516	+	25.7237i	0.524427	+	0.908334i
$803$	−15.2117	+	26.3475i	−0.536810	+	0.929783i
$804$	−0.787653	+	1.36426i	−0.0277784	+	0.0481136i
$805$		0			0
$806$	34.4524	+	5.28180i	1.21353	+	0.186043i
$807$	5.42243			0.190878
$808$	3.07058	−	5.31840i	0.108023	−	0.187101i
$809$	2.51446	−	4.35518i	0.0884039	−	0.153120i	−0.818433	−	0.574602i	$-0.805157\pi$
$809$	2.51446	−	4.35518i	0.0884039	−	0.153120i	0.906837	+	0.421482i	$0.138490\pi$
$810$		0			0
$811$	47.3390			1.66230			0.831148	−	0.556052i	$-0.187684\pi$
$811$	47.3390			1.66230			0.831148	+	0.556052i	$0.187684\pi$
$812$	−2.57531	−	4.46056i	−0.0903755	−	0.156535i
$813$	−4.88655	−	8.46375i	−0.171379	−	0.296837i
$814$	31.3812			1.09991
$815$		0			0
$816$	0.854638	−	1.48028i	0.0299183	−	0.0518200i
$817$	−0.120638	+	0.208951i	−0.00422059	+	0.00731028i
$818$	10.3112			0.360524
$819$	−6.84849	−	1.04992i	−0.239306	−	0.0366873i
$820$		0			0
$821$	10.3408	−	17.9108i	0.360896	−	0.625090i	−0.627213	−	0.778848i	$-0.715804\pi$
$821$	10.3408	−	17.9108i	0.360896	−	0.625090i	0.988109	+	0.153758i	$0.0491376\pi$
$822$	2.52165	−	4.36763i	0.0879527	−	0.152339i
$823$	−9.91855	−	17.1794i	−0.345739	−	0.598837i	0.639749	−	0.768584i	$-0.279038\pi$
$823$	−9.91855	−	17.1794i	−0.345739	−	0.598837i	−0.985488	+	0.169747i	$0.945705\pi$
$824$	−17.6803			−0.615924
$825$		0			0
$826$	2.04226	+	3.53730i	0.0710593	+	0.123078i
$827$	−39.6730			−1.37956			−0.689782	−	0.724017i	$-0.742294\pi$
$827$	−39.6730			−1.37956			−0.689782	+	0.724017i	$0.742294\pi$
$828$	−6.73400	−	11.6636i	−0.234023	−	0.405339i
$829$	12.6937	−	21.9861i	0.440870	−	0.763609i	−0.556885	−	0.830590i	$-0.688003\pi$
$829$	12.6937	−	21.9861i	0.440870	−	0.763609i	0.997754	+	0.0669813i	$0.0213368\pi$
$830$		0			0
$831$	13.3268			0.462303
$832$	1.30878	+	3.35963i	0.0453739	+	0.116474i
$833$	20.5958			0.713603
$834$	−0.712869	+	1.23473i	−0.0246846	+	0.0427551i
$835$		0			0
$836$	−0.272055	−	0.471213i	−0.00940921	−	0.0162972i
$837$	−29.7587			−1.02861
$838$	19.0452	+	32.9873i	0.657907	+	1.13953i
$839$	11.5139	+	19.9426i	0.397502	+	0.688494i	0.993417	−	0.114553i	$-0.0365437\pi$
$839$	11.5139	+	19.9426i	0.397502	+	0.688494i	−0.595915	+	0.803048i	$0.703210\pi$
$840$		0			0
$841$	−11.8668	−	20.5540i	−0.409201	−	0.708757i
$842$	−13.3552	+	23.1318i	−0.460249	+	0.797175i
$843$	−6.19675	+	10.7331i	−0.213427	+	0.369667i
$844$	−5.58864			−0.192369
$845$		0			0
$846$	12.7587			0.438654
$847$	3.31318	−	5.73860i	0.113842	−	0.197181i
$848$	4.79432	−	8.30400i	0.164638	−	0.285161i
$849$	4.87936	+	8.45130i	0.167459	+	0.290048i
$850$		0			0
$851$	17.2937	+	29.9536i	0.592821	+	1.02680i
$852$	2.20620	+	3.82126i	0.0755833	+	0.130914i
$853$	13.7047			0.469241			0.234621	−	0.972087i	$-0.424615\pi$
$853$	13.7047			0.469241			0.234621	+	0.972087i	$0.424615\pi$
$854$	−2.50473	−	4.33832i	−0.0857100	−	0.148454i
$855$		0			0
$856$	−0.269594	+	0.466951i	−0.00921455	+	0.0159601i
$857$	17.8648			0.610250			0.305125	−	0.952312i	$-0.401302\pi$
$857$	17.8648			0.610250			0.305125	+	0.952312i	$0.401302\pi$
$858$	3.18281	+	8.17021i	0.108659	+	0.278926i
$859$	13.7187			0.468077			0.234039	−	0.972227i	$-0.424806\pi$
$859$	13.7187			0.468077			0.234039	+	0.972227i	$0.424806\pi$
$860$		0			0
$861$	0.0855657	−	0.148204i	0.00291607	−	0.00505078i
$862$	−10.3594	−	17.9429i	−0.352841	−	0.611139i
$863$	19.9383			0.678706			0.339353	−	0.940659i	$-0.389792\pi$
$863$	19.9383			0.678706			0.339353	+	0.940659i	$0.389792\pi$
$864$	−1.53919	−	2.66595i	−0.0523643	−	0.0906976i
$865$		0			0
$866$	15.8576			0.538864
$867$	1.87383	+	3.24557i	0.0636386	+	0.110225i
$868$	3.42829	−	5.93797i	0.116364	−	0.201548i
$869$	−36.0983	+	62.5241i	−1.22455	+	2.12098i
$870$		0			0
$871$	−10.4124	−	1.59630i	−0.352811	−	0.0540884i
$872$	11.0205			0.373202
$873$	10.7129	−	18.5552i	0.362576	−	0.628000i
$874$	0.299850	−	0.519356i	0.0101426	−	0.0175675i
$875$		0			0
$876$	−3.63704			−0.122884
$877$	−10.8082	−	18.7203i	−0.364966	−	0.632140i	0.623805	−	0.781580i	$-0.285586\pi$
$877$	−10.8082	−	18.7203i	−0.364966	−	0.632140i	−0.988771	+	0.149441i	$0.952253\pi$
$878$	−4.86962	−	8.43444i	−0.164342	−	0.284648i
$879$	−9.62144			−0.324523
$880$		0			0
$881$	3.99693	−	6.92288i	0.134660	−	0.233238i	−0.790808	−	0.612065i	$-0.790339\pi$
$881$	3.99693	−	6.92288i	0.134660	−	0.233238i	0.925468	+	0.378827i	$0.123672\pi$
$882$	8.80098	−	15.2438i	0.296345	−	0.513284i
$883$	−26.2713			−0.884098			−0.442049	−	0.896991i	$-0.645748\pi$
$883$	−26.2713			−0.884098			−0.442049	+	0.896991i	$0.645748\pi$
$884$	11.2979	+	1.73205i	0.379990	+	0.0582552i
$885$		0			0
$886$	4.61530	−	7.99393i	0.155054	−	0.268561i
$887$	8.58136	−	14.8634i	0.288134	−	0.499063i	−0.685230	−	0.728326i	$-0.740299\pi$
$887$	8.58136	−	14.8634i	0.288134	−	0.499063i	0.973364	+	0.229264i	$0.0736318\pi$
$888$	1.87577	+	3.24893i	0.0629466	+	0.109027i
$889$	−8.63704			−0.289677
$890$		0			0
$891$	14.5862	+	25.2640i	0.488655	+	0.846376i
$892$	24.7093			0.827328
$893$	0.284059	+	0.492005i	0.00950568	+	0.0164643i
$894$	−2.48974	+	4.31236i	−0.0832694	+	0.144227i
$895$		0			0
$896$	0.709275			0.0236952
$897$	−6.04453	+	7.54049i	−0.201821	+	0.251770i
$898$	2.92389			0.0975715
$899$	35.0999	−	60.7949i	1.17065	−	2.02762i
$900$		0			0
$901$	−15.1984	−	26.3244i	−0.506332	−	0.876993i
$902$	2.01825			0.0672004
$903$	−0.382433	−	0.662394i	−0.0127266	−	0.0220431i
$904$	7.00000	+	12.1244i	0.232817	+	0.403250i
$905$		0			0
$906$	−2.54113	−	4.40136i	−0.0844233	−	0.146225i
$907$	8.20682	−	14.2146i	0.272503	−	0.471989i	−0.696999	−	0.717072i	$-0.745482\pi$
$907$	8.20682	−	14.2146i	0.272503	−	0.471989i	0.969502	+	0.245083i	$0.0788153\pi$
$908$	−14.3474	+	24.8504i	−0.476134	+	0.824688i
$909$	−16.6381			−0.551850
$910$		0			0
$911$	−4.52359			−0.149873			−0.0749366	−	0.997188i	$-0.523875\pi$
$911$	−4.52359			−0.149873			−0.0749366	+	0.997188i	$0.523875\pi$
$912$	0.0325234	−	0.0563321i	0.00107696	−	0.00186534i
$913$	0.802311	−	1.38964i	0.0265526	−	0.0459905i
$914$	5.82632	+	10.0915i	0.192718	+	0.333797i
$915$		0			0
$916$	0.949940	+	1.64535i	0.0313869	+	0.0543637i
$917$	−6.19008	−	10.7215i	−0.204415	−	0.354056i
$918$	−9.75872			−0.322086
$919$	3.82150	+	6.61904i	0.126060	+	0.218342i	0.922147	−	0.386840i	$-0.126434\pi$
$919$	3.82150	+	6.61904i	0.126060	+	0.218342i	−0.796087	+	0.605182i	$0.793100\pi$
$920$		0			0
$921$	0.928810	−	1.60875i	0.0306053	−	0.0530100i
$922$	30.2979			0.997809
$923$	−18.4547	+	23.0220i	−0.607443	+	0.757779i
$924$	1.72487			0.0567442
$925$		0			0
$926$	3.52165	−	6.09968i	0.115729	−	0.200448i
$927$	23.9505	+	41.4834i	0.786636	+	1.36249i
$928$	7.26180			0.238380
$929$	−29.6647	−	51.3808i	−0.973269	−	1.68575i	−0.685534	−	0.728041i	$-0.740431\pi$
$929$	−29.6647	−	51.3808i	−0.973269	−	1.68575i	−0.287735	−	0.957710i	$-0.592902\pi$
$930$		0			0
$931$	0.783777			0.0256873
$932$	−11.1242	−	19.2677i	−0.364386	−	0.631136i
$933$	−4.80519	+	8.32283i	−0.157315	+	0.272477i
$934$	1.95055	−	3.37845i	0.0638240	−	0.110546i
$935$		0			0
$936$	6.10977	−	7.62188i	0.199704	−	0.249129i
$937$	−1.75872			−0.0574550			−0.0287275	−	0.999587i	$-0.509146\pi$
$937$	−1.75872			−0.0574550			−0.0287275	+	0.999587i	$0.509146\pi$
$938$	−1.03612	+	1.79461i	−0.0338304	+	0.0585960i
$939$	8.68753	−	15.0473i	0.283507	−	0.491048i
$940$		0			0
$941$	42.2967			1.37883			0.689416	−	0.724365i	$-0.257867\pi$
$941$	42.2967			1.37883			0.689416	+	0.724365i	$0.257867\pi$
$942$	1.55611	+	2.69527i	0.0507009	+	0.0878166i
$943$	1.11223	+	1.92643i	0.0362191	+	0.0627333i
$944$	−5.75872			−0.187430
$945$		0			0
$946$	4.51026	−	7.81200i	0.146641	−	0.253990i
$947$	2.41916	−	4.19011i	0.0786122	−	0.136160i	−0.824039	−	0.566533i	$-0.808284\pi$
$947$	2.41916	−	4.19011i	0.0786122	−	0.136160i	0.902651	+	0.430372i	$0.141618\pi$
$948$	−8.63090			−0.280319
$949$	−8.82826	−	22.6620i	−0.286577	−	0.735640i
$950$		0			0
$951$	0.513853	−	0.890020i	0.0166628	−	0.0288609i
$952$	1.12423	−	1.94723i	0.0364366	−	0.0631100i
$953$	12.9769	+	22.4767i	0.420364	+	0.728092i	0.995975	−	0.0896318i	$-0.0285690\pi$
$953$	12.9769	+	22.4767i	0.420364	+	0.728092i	−0.575611	+	0.817724i	$0.695236\pi$
$954$	−25.9783			−0.841077
$955$		0			0
$956$	−12.4355	−	21.5389i	−0.402192	−	0.696617i
$957$	17.6598			0.570861
$958$	8.75513	+	15.1643i	0.282865	+	0.489937i
$959$	3.31710	−	5.74539i	0.107115	−	0.185528i
$960$		0			0
$961$	62.4512			2.01455
$962$	−15.6906	+	19.5739i	−0.505885	+	0.631087i
$963$	1.46081			0.0470740
$964$	1.47528	−	2.55525i	0.0475154	−	0.0822991i
$965$		0			0
$966$	0.950552	+	1.64640i	0.0305835	+	0.0529722i
$967$	29.9939			0.964537			0.482269	−	0.876023i	$-0.339813\pi$
$967$	29.9939			0.964537			0.482269	+	0.876023i	$0.339813\pi$
$968$	4.67122	+	8.09079i	0.150139	+	0.260048i
$969$	−0.103102	−	0.178578i	−0.00331211	−	0.00573674i
$970$		0			0
$971$	−7.86429	−	13.6213i	−0.252377	−	0.437130i	0.711803	−	0.702379i	$-0.247879\pi$
$971$	−7.86429	−	13.6213i	−0.252377	−	0.437130i	−0.964180	+	0.265250i	$0.914546\pi$
$972$	−6.36130	+	11.0181i	−0.204039	+	0.353406i
$973$	−0.937743	+	1.62422i	−0.0300627	+	0.0520701i
$974$	38.5318			1.23464
$975$		0			0
$976$	7.06278			0.226074
$977$	13.7721	−	23.8539i	0.440607	−	0.763154i	−0.557128	−	0.830427i	$-0.688097\pi$
$977$	13.7721	−	23.8539i	0.440607	−	0.763154i	0.997735	+	0.0672731i	$0.0214299\pi$
$978$	4.53498	−	7.85482i	0.145013	−	0.251170i
$979$	8.18815	+	14.1823i	0.261694	+	0.453268i
$980$		0			0
$981$	−14.9288	−	25.8575i	−0.476640	−	0.825565i
$982$	3.41189	+	5.90956i	0.108878	+	0.188582i
$983$	18.0289			0.575034			0.287517	−	0.957776i	$-0.407170\pi$
$983$	18.0289			0.575034			0.287517	+	0.957776i	$0.407170\pi$
$984$	0.120638	+	0.208951i	0.00384580	+	0.00666113i
$985$		0			0
$986$	11.5103	−	19.9364i	0.366561	−	0.634903i
$987$	−1.80098			−0.0573260
$988$	0.429944	+	0.0659135i	0.0136783	+	0.00209699i
$989$	9.94214			0.316142
$990$		0			0
$991$	−5.81658	+	10.0746i	−0.184770	+	0.320031i	−0.943499	−	0.331376i	$-0.892487\pi$
$991$	−5.81658	+	10.0746i	−0.184770	+	0.320031i	0.758729	+	0.651406i	$0.225821\pi$
$992$	4.83351	+	8.37188i	0.153464	+	0.265807i
$993$	−0.383656			−0.0121750
$994$	2.90215	+	5.02667i	0.0920506	+	0.159436i
$995$		0			0
$996$	0.191828			0.00607830
$997$	14.4324	+	24.9977i	0.457079	+	0.791684i	0.998805	−	0.0488712i	$-0.0155624\pi$
$997$	14.4324	+	24.9977i	0.457079	+	0.791684i	−0.541726	+	0.840555i	$0.682229\pi$
$998$	4.78959	−	8.29581i	0.151612	−	0.262599i
$999$	10.7093	−	18.5490i	0.338826	−	0.586865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.e.k.451.2		6
5.2	odd	4		130.2.n.a.9.5	yes	12
5.3	odd	4		130.2.n.a.9.2	✓	12
5.4	even	2		650.2.e.j.451.2		6
13.3	even	3	inner	650.2.e.k.601.2		6
13.4	even	6		8450.2.a.ca.1.2		3
13.9	even	3		8450.2.a.bu.1.2		3
15.2	even	4		1170.2.bp.h.919.2		12
15.8	even	4		1170.2.bp.h.919.5		12
20.3	even	4		1040.2.dh.b.529.4		12
20.7	even	4		1040.2.dh.b.529.3		12
65.3	odd	12		130.2.n.a.29.5	yes	12
65.4	even	6		8450.2.a.bt.1.2		3
65.7	even	12		1690.2.c.c.1689.3		6
65.9	even	6		8450.2.a.cb.1.2		3
65.17	odd	12		1690.2.b.b.339.5		6
65.22	odd	12		1690.2.b.c.339.2		6
65.29	even	6		650.2.e.j.601.2		6
65.32	even	12		1690.2.c.b.1689.3		6
65.33	even	12		1690.2.c.b.1689.4		6
65.42	odd	12		130.2.n.a.29.2	yes	12
65.43	odd	12		1690.2.b.b.339.2		6
65.48	odd	12		1690.2.b.c.339.5		6
65.58	even	12		1690.2.c.c.1689.4		6
195.68	even	12		1170.2.bp.h.289.2		12
195.107	even	12		1170.2.bp.h.289.5		12
260.3	even	12		1040.2.dh.b.289.3		12
260.107	even	12		1040.2.dh.b.289.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.n.a.9.2	✓	12	5.3	odd	4
130.2.n.a.9.5	yes	12	5.2	odd	4
130.2.n.a.29.2	yes	12	65.42	odd	12
130.2.n.a.29.5	yes	12	65.3	odd	12
650.2.e.j.451.2		6	5.4	even	2
650.2.e.j.601.2		6	65.29	even	6
650.2.e.k.451.2		6	1.1	even	1	trivial
650.2.e.k.601.2		6	13.3	even	3	inner
1040.2.dh.b.289.3		12	260.3	even	12
1040.2.dh.b.289.4		12	260.107	even	12
1040.2.dh.b.529.3		12	20.7	even	4
1040.2.dh.b.529.4		12	20.3	even	4
1170.2.bp.h.289.2		12	195.68	even	12
1170.2.bp.h.289.5		12	195.107	even	12
1170.2.bp.h.919.2		12	15.2	even	4
1170.2.bp.h.919.5		12	15.8	even	4
1690.2.b.b.339.2		6	65.43	odd	12
1690.2.b.b.339.5		6	65.17	odd	12
1690.2.b.c.339.2		6	65.22	odd	12
1690.2.b.c.339.5		6	65.48	odd	12
1690.2.c.b.1689.3		6	65.32	even	12
1690.2.c.b.1689.4		6	65.33	even	12
1690.2.c.c.1689.3		6	65.7	even	12
1690.2.c.c.1689.4		6	65.58	even	12
8450.2.a.bt.1.2		3	65.4	even	6
8450.2.a.bu.1.2		3	13.9	even	3
8450.2.a.ca.1.2		3	13.4	even	6
8450.2.a.cb.1.2		3	65.9	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.269594 + 0.466951i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.269594 + 0.466951i) q^{6} +(0.354638 + 0.614250i) q^{7} -1.00000 q^{8} +(1.35464 + 2.34630i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.269594 + 0.466951i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.269594 + 0.466951i) q^{6} +(0.354638 + 0.614250i) q^{7} -1.00000 q^{8} +(1.35464 + 2.34630i) q^{9} +(2.25513 - 3.90600i) q^{11} +0.539189 q^{12} +(1.30878 + 3.35963i) q^{13} +0.709275 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.58504 + 2.74538i) q^{17} +2.70928 q^{18} +(0.0603191 + 0.104476i) q^{19} -0.382433 q^{21} +(-2.25513 - 3.90600i) q^{22} +(2.48554 - 4.30507i) q^{23} +(0.269594 - 0.466951i) q^{24} +(3.56391 + 0.546373i) q^{26} -3.07838 q^{27} +(0.354638 - 0.614250i) q^{28} +(3.63090 - 6.28890i) q^{29} +9.66701 q^{31} +(0.500000 + 0.866025i) q^{32} +(1.21594 + 2.10607i) q^{33} +3.17009 q^{34} +(1.35464 - 2.34630i) q^{36} +(-3.47887 + 6.02558i) q^{37} +0.120638 q^{38} +(-1.92162 - 0.294598i) q^{39} +(-0.223740 + 0.387529i) q^{41} +(-0.191217 + 0.331197i) q^{42} +(1.00000 + 1.73205i) q^{43} -4.51026 q^{44} +(-2.48554 - 4.30507i) q^{46} +4.70928 q^{47} +(-0.269594 - 0.466951i) q^{48} +(3.24846 - 5.62651i) q^{49} -1.70928 q^{51} +(2.25513 - 2.81325i) q^{52} -9.58864 q^{53} +(-1.53919 + 2.66595i) q^{54} +(-0.354638 - 0.614250i) q^{56} -0.0650468 q^{57} +(-3.63090 - 6.28890i) q^{58} +(2.87936 + 4.98720i) q^{59} +(-3.53139 - 6.11655i) q^{61} +(4.83351 - 8.37188i) q^{62} +(-0.960811 + 1.66417i) q^{63} +1.00000 q^{64} +2.43188 q^{66} +(-1.46081 + 2.53020i) q^{67} +(1.58504 - 2.74538i) q^{68} +(1.34017 + 2.32125i) q^{69} +(4.09171 + 7.08705i) q^{71} +(-1.35464 - 2.34630i) q^{72} -6.74539 q^{73} +(3.47887 + 6.02558i) q^{74} +(0.0603191 - 0.104476i) q^{76} +3.19902 q^{77} +(-1.21594 + 1.51687i) q^{78} -16.0072 q^{79} +(-3.23400 + 5.60145i) q^{81} +(0.223740 + 0.387529i) q^{82} +0.355771 q^{83} +(0.191217 + 0.331197i) q^{84} +2.00000 q^{86} +(1.95774 + 3.39090i) q^{87} +(-2.25513 + 3.90600i) q^{88} +(-1.81545 + 3.14445i) q^{89} +(-1.59951 + 1.99537i) q^{91} -4.97107 q^{92} +(-2.60617 + 4.51402i) q^{93} +(2.35464 - 4.07835i) q^{94} -0.539189 q^{96} +(-3.95415 - 6.84878i) q^{97} +(-3.24846 - 5.62651i) q^{98} +12.2195 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 5 q^{7} - 6 q^{8} + q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 - 5 * q^7 - 6 * q^8 + q^9	\( 6 q + 3 q^{2} - 3 q^{4} - 5 q^{7} - 6 q^{8} + q^{9} - 3 q^{11} + 3 q^{13} - 10 q^{14} - 3 q^{16} + 4 q^{17} + 2 q^{18} + 13 q^{19} - 12 q^{21} + 3 q^{22} - 12 q^{27} - 5 q^{28} + 14 q^{29} + 12 q^{31} + 3 q^{32} - 6 q^{33} + 8 q^{34} + q^{36} - 5 q^{37} + 26 q^{38} - 18 q^{39} - 2 q^{41} - 6 q^{42} + 6 q^{43} + 6 q^{44} + 14 q^{47} + 2 q^{49} + 4 q^{51} - 3 q^{52} - 18 q^{53} - 6 q^{54} + 5 q^{56} + 8 q^{57} - 14 q^{58} - 8 q^{59} - 4 q^{61} + 6 q^{62} - 9 q^{63} + 6 q^{64} - 12 q^{66} - 12 q^{67} + 4 q^{68} - 14 q^{69} + 20 q^{71} - q^{72} + 12 q^{73} + 5 q^{74} + 13 q^{76} + 38 q^{77} + 6 q^{78} - 28 q^{79} + 13 q^{81} + 2 q^{82} + 8 q^{83} + 6 q^{84} + 12 q^{86} - 20 q^{87} + 3 q^{88} - 7 q^{89} - 19 q^{91} - 26 q^{93} + 7 q^{94} - 26 q^{97} - 2 q^{98} + 26 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 - 5 * q^7 - 6 * q^8 + q^9 - 3 * q^11 + 3 * q^13 - 10 * q^14 - 3 * q^16 + 4 * q^17 + 2 * q^18 + 13 * q^19 - 12 * q^21 + 3 * q^22 - 12 * q^27 - 5 * q^28 + 14 * q^29 + 12 * q^31 + 3 * q^32 - 6 * q^33 + 8 * q^34 + q^36 - 5 * q^37 + 26 * q^38 - 18 * q^39 - 2 * q^41 - 6 * q^42 + 6 * q^43 + 6 * q^44 + 14 * q^47 + 2 * q^49 + 4 * q^51 - 3 * q^52 - 18 * q^53 - 6 * q^54 + 5 * q^56 + 8 * q^57 - 14 * q^58 - 8 * q^59 - 4 * q^61 + 6 * q^62 - 9 * q^63 + 6 * q^64 - 12 * q^66 - 12 * q^67 + 4 * q^68 - 14 * q^69 + 20 * q^71 - q^72 + 12 * q^73 + 5 * q^74 + 13 * q^76 + 38 * q^77 + 6 * q^78 - 28 * q^79 + 13 * q^81 + 2 * q^82 + 8 * q^83 + 6 * q^84 + 12 * q^86 - 20 * q^87 + 3 * q^88 - 7 * q^89 - 19 * q^91 - 26 * q^93 + 7 * q^94 - 26 * q^97 - 2 * q^98 + 26 * q^99

Introduction

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