LMFDB - Embedded newform 1950.2.y.h.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(49,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("1950.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.y (of order $6$, degree $2$, not 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:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.49
Dual form			1950.2.y.h.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(2.36603 - 4.09808i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(2.36603 - 4.09808i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(4.09808 - 2.36603i) q^{11} +1.00000i q^{12} +(-0.232051 + 3.59808i) q^{13} +4.73205 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.50000 - 2.59808i) q^{17} +1.00000 q^{18} +(-1.09808 - 0.633975i) q^{19} -4.73205i q^{21} +(4.09808 + 2.36603i) q^{22} +(1.90192 - 1.09808i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-3.23205 + 1.59808i) q^{26} -1.00000i q^{27} +(2.36603 + 4.09808i) q^{28} +(-1.50000 - 2.59808i) q^{29} -2.53590i q^{31} +(0.500000 - 0.866025i) q^{32} +(2.36603 - 4.09808i) q^{33} -5.19615i q^{34} +(0.500000 + 0.866025i) q^{36} +(1.50000 + 2.59808i) q^{37} -1.26795i q^{38} +(1.59808 + 3.23205i) q^{39} +(0.401924 - 0.232051i) q^{41} +(4.09808 - 2.36603i) q^{42} +(-5.36603 - 3.09808i) q^{43} +4.73205i q^{44} +(1.90192 + 1.09808i) q^{46} +1.26795 q^{47} +(-0.866025 - 0.500000i) q^{48} +(-7.69615 - 13.3301i) q^{49} -5.19615 q^{51} +(-3.00000 - 2.00000i) q^{52} -3.00000i q^{53} +(0.866025 - 0.500000i) q^{54} +(-2.36603 + 4.09808i) q^{56} -1.26795 q^{57} +(1.50000 - 2.59808i) q^{58} +(12.0000 + 6.92820i) q^{59} +(-2.40192 + 4.16025i) q^{61} +(2.19615 - 1.26795i) q^{62} +(-2.36603 - 4.09808i) q^{63} +1.00000 q^{64} +4.73205 q^{66} +(-5.36603 - 9.29423i) q^{67} +(4.50000 - 2.59808i) q^{68} +(1.09808 - 1.90192i) q^{69} +(7.09808 + 4.09808i) q^{71} +(-0.500000 + 0.866025i) q^{72} -12.1244 q^{73} +(-1.50000 + 2.59808i) q^{74} +(1.09808 - 0.633975i) q^{76} -22.3923i q^{77} +(-2.00000 + 3.00000i) q^{78} +12.3923 q^{79} +(-0.500000 - 0.866025i) q^{81} +(0.401924 + 0.232051i) q^{82} +11.6603 q^{83} +(4.09808 + 2.36603i) q^{84} -6.19615i q^{86} +(-2.59808 - 1.50000i) q^{87} +(-4.09808 + 2.36603i) q^{88} +(-2.19615 + 1.26795i) q^{89} +(14.1962 + 9.46410i) q^{91} +2.19615i q^{92} +(-1.26795 - 2.19615i) q^{93} +(0.633975 + 1.09808i) q^{94} -1.00000i q^{96} +(-3.00000 + 5.19615i) q^{97} +(7.69615 - 13.3301i) q^{98} -4.73205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 6 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 6 * q^7 - 4 * q^8 + 2 * q^9	$ 4 q + 2 q^{2} - 2 q^{4} + 6 q^{7} - 4 q^{8} + 2 q^{9} + 6 q^{11} + 6 q^{13} + 12 q^{14} - 2 q^{16} - 18 q^{17} + 4 q^{18} + 6 q^{19} + 6 q^{22} + 18 q^{23} - 6 q^{26} + 6 q^{28} - 6 q^{29} + 2 q^{32} + 6 q^{33} + 2 q^{36} + 6 q^{37} - 4 q^{39} + 12 q^{41} + 6 q^{42} - 18 q^{43} + 18 q^{46} + 12 q^{47} - 10 q^{49} - 12 q^{52} - 6 q^{56} - 12 q^{57} + 6 q^{58} + 48 q^{59} - 20 q^{61} - 12 q^{62} - 6 q^{63} + 4 q^{64} + 12 q^{66} - 18 q^{67} + 18 q^{68} - 6 q^{69} + 18 q^{71} - 2 q^{72} - 6 q^{74} - 6 q^{76} - 8 q^{78} + 8 q^{79} - 2 q^{81} + 12 q^{82} + 12 q^{83} + 6 q^{84} - 6 q^{88} + 12 q^{89} + 36 q^{91} - 12 q^{93} + 6 q^{94} - 12 q^{97} + 10 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 6 * q^7 - 4 * q^8 + 2 * q^9 + 6 * q^11 + 6 * q^13 + 12 * q^14 - 2 * q^16 - 18 * q^17 + 4 * q^18 + 6 * q^19 + 6 * q^22 + 18 * q^23 - 6 * q^26 + 6 * q^28 - 6 * q^29 + 2 * q^32 + 6 * q^33 + 2 * q^36 + 6 * q^37 - 4 * q^39 + 12 * q^41 + 6 * q^42 - 18 * q^43 + 18 * q^46 + 12 * q^47 - 10 * q^49 - 12 * q^52 - 6 * q^56 - 12 * q^57 + 6 * q^58 + 48 * q^59 - 20 * q^61 - 12 * q^62 - 6 * q^63 + 4 * q^64 + 12 * q^66 - 18 * q^67 + 18 * q^68 - 6 * q^69 + 18 * q^71 - 2 * q^72 - 6 * q^74 - 6 * q^76 - 8 * q^78 + 8 * q^79 - 2 * q^81 + 12 * q^82 + 12 * q^83 + 6 * q^84 - 6 * q^88 + 12 * q^89 + 36 * q^91 - 12 * q^93 + 6 * q^94 - 12 * q^97 + 10 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	2.36603	−	4.09808i	0.894274	−	1.54893i	0.0595724	−	0.998224i	$-0.481026\pi$
$7$	2.36603	−	4.09808i	0.894274	−	1.54893i	0.834701	−	0.550703i	$-0.185640\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	4.09808	−	2.36603i	1.23562	−	0.713384i	0.267421	−	0.963580i	$-0.413828\pi$
$11$	4.09808	−	2.36603i	1.23562	−	0.713384i	0.968195	+	0.250196i	$0.0804951\pi$
$12$			1.00000i			0.288675i
$13$	−0.232051	+	3.59808i	−0.0643593	+	0.997927i
$13$	−0.232051	+	3.59808i	−0.0643593	+	0.997927i
$14$	4.73205			1.26469
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−4.50000	−	2.59808i	−1.09141	−	0.630126i	−0.157459	−	0.987526i	$-0.550330\pi$
$17$	−4.50000	−	2.59808i	−1.09141	−	0.630126i	−0.933952	+	0.357400i	$0.883663\pi$
$18$	1.00000			0.235702
$19$	−1.09808	−	0.633975i	−0.251916	−	0.145444i	0.368725	−	0.929538i	$-0.379794\pi$
$19$	−1.09808	−	0.633975i	−0.251916	−	0.145444i	−0.620641	+	0.784095i	$0.713128\pi$
$20$		0			0
$21$		−	4.73205i		−	1.03262i
$22$	4.09808	+	2.36603i	0.873713	+	0.504438i
$23$	1.90192	−	1.09808i	0.396579	−	0.228965i	−0.288428	−	0.957502i	$-0.593133\pi$
$23$	1.90192	−	1.09808i	0.396579	−	0.228965i	0.685007	+	0.728537i	$0.259799\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$		0			0
$26$	−3.23205	+	1.59808i	−0.633857	+	0.313409i
$27$		−	1.00000i		−	0.192450i
$28$	2.36603	+	4.09808i	0.447137	+	0.774464i
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		0			0
$31$		−	2.53590i		−	0.455461i	−0.973724	−	0.227730i	$-0.926870\pi$
$31$		−	2.53590i		−	0.455461i	0.973724	−	0.227730i	$-0.0731305\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.36603	−	4.09808i	0.411872	−	0.713384i
$34$		−	5.19615i		−	0.891133i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	1.50000	+	2.59808i	0.246598	+	0.427121i	0.962580	−	0.270998i	$-0.0873538\pi$
$37$	1.50000	+	2.59808i	0.246598	+	0.427121i	−0.715981	+	0.698119i	$0.754020\pi$
$38$		−	1.26795i		−	0.205689i
$39$	1.59808	+	3.23205i	0.255897	+	0.517542i
$40$		0			0
$41$	0.401924	−	0.232051i	0.0627700	−	0.0362402i	−0.468287	−	0.883577i	$-0.655129\pi$
$41$	0.401924	−	0.232051i	0.0627700	−	0.0362402i	0.531057	+	0.847336i	$0.321795\pi$
$42$	4.09808	−	2.36603i	0.632347	−	0.365086i
$43$	−5.36603	−	3.09808i	−0.818311	−	0.472452i	0.0315225	−	0.999503i	$-0.489964\pi$
$43$	−5.36603	−	3.09808i	−0.818311	−	0.472452i	−0.849834	+	0.527051i	$0.823298\pi$
$44$			4.73205i			0.713384i
$45$		0			0
$46$	1.90192	+	1.09808i	0.280423	+	0.161903i
$47$	1.26795			0.184949			0.0924747	−	0.995715i	$-0.470522\pi$
$47$	1.26795			0.184949			0.0924747	+	0.995715i	$0.470522\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−7.69615	−	13.3301i	−1.09945	−	1.90430i
$50$		0			0
$51$	−5.19615			−0.727607
$52$	−3.00000	−	2.00000i	−0.416025	−	0.277350i
$53$		−	3.00000i		−	0.412082i	−0.978543	−	0.206041i	$-0.933942\pi$
$53$		−	3.00000i		−	0.412082i	0.978543	−	0.206041i	$-0.0660580\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$		0			0
$56$	−2.36603	+	4.09808i	−0.316173	+	0.547628i
$57$	−1.26795			−0.167944
$58$	1.50000	−	2.59808i	0.196960	−	0.341144i
$59$	12.0000	+	6.92820i	1.56227	+	0.901975i	0.997027	+	0.0770484i	$0.0245496\pi$
$59$	12.0000	+	6.92820i	1.56227	+	0.901975i	0.565240	+	0.824927i	$0.308784\pi$
$60$		0			0
$61$	−2.40192	+	4.16025i	−0.307535	+	0.532666i	−0.977822	−	0.209435i	$-0.932837\pi$
$61$	−2.40192	+	4.16025i	−0.307535	+	0.532666i	0.670288	+	0.742101i	$0.266171\pi$
$62$	2.19615	−	1.26795i	0.278912	−	0.161030i
$63$	−2.36603	−	4.09808i	−0.298091	−	0.516309i
$64$	1.00000			0.125000
$65$		0			0
$66$	4.73205			0.582475
$67$	−5.36603	−	9.29423i	−0.655564	−	1.13547i	−0.981752	−	0.190166i	$-0.939097\pi$
$67$	−5.36603	−	9.29423i	−0.655564	−	1.13547i	0.326188	−	0.945305i	$-0.394236\pi$
$68$	4.50000	−	2.59808i	0.545705	−	0.315063i
$69$	1.09808	−	1.90192i	0.132193	−	0.228965i
$70$		0			0
$71$	7.09808	+	4.09808i	0.842387	+	0.486352i	0.858075	−	0.513525i	$-0.171661\pi$
$71$	7.09808	+	4.09808i	0.842387	+	0.486352i	−0.0156881	+	0.999877i	$0.504994\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−12.1244			−1.41905			−0.709524	−	0.704681i	$-0.751090\pi$
$73$	−12.1244			−1.41905			−0.709524	+	0.704681i	$0.751090\pi$
$74$	−1.50000	+	2.59808i	−0.174371	+	0.302020i
$75$		0			0
$76$	1.09808	−	0.633975i	0.125958	−	0.0727219i
$77$		−	22.3923i		−	2.55184i
$78$	−2.00000	+	3.00000i	−0.226455	+	0.339683i
$79$	12.3923			1.39424			0.697122	−	0.716953i	$-0.254464\pi$
$79$	12.3923			1.39424			0.697122	+	0.716953i	$0.254464\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.401924	+	0.232051i	0.0443851	+	0.0256257i
$83$	11.6603			1.27988			0.639940	−	0.768425i	$-0.278959\pi$
$83$	11.6603			1.27988			0.639940	+	0.768425i	$0.278959\pi$
$84$	4.09808	+	2.36603i	0.447137	+	0.258155i
$85$		0			0
$86$		−	6.19615i		−	0.668148i
$87$	−2.59808	−	1.50000i	−0.278543	−	0.160817i
$88$	−4.09808	+	2.36603i	−0.436856	+	0.252219i
$89$	−2.19615	+	1.26795i	−0.232792	+	0.134402i	−0.611859	−	0.790967i	$-0.709578\pi$
$89$	−2.19615	+	1.26795i	−0.232792	+	0.134402i	0.379068	+	0.925369i	$0.376245\pi$
$90$		0			0
$91$	14.1962	+	9.46410i	1.48816	+	0.992107i
$92$			2.19615i			0.228965i
$93$	−1.26795	−	2.19615i	−0.131480	−	0.227730i
$94$	0.633975	+	1.09808i	0.0653895	+	0.113258i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	−3.00000	+	5.19615i	−0.304604	+	0.527589i	−0.977173	−	0.212445i	$-0.931857\pi$
$97$	−3.00000	+	5.19615i	−0.304604	+	0.527589i	0.672569	+	0.740034i	$0.265191\pi$
$98$	7.69615	−	13.3301i	0.777429	−	1.34655i
$99$		−	4.73205i		−	0.475589i
$100$		0			0
$101$	−0.696152	−	1.20577i	−0.0692698	−	0.119979i	0.829310	−	0.558788i	$-0.188734\pi$
$101$	−0.696152	−	1.20577i	−0.0692698	−	0.119979i	−0.898580	+	0.438810i	$0.855400\pi$
$102$	−2.59808	−	4.50000i	−0.257248	−	0.445566i
$103$		−	4.19615i		−	0.413459i	−0.978398	−	0.206730i	$-0.933718\pi$
$103$		−	4.19615i		−	0.413459i	0.978398	−	0.206730i	$-0.0662820\pi$
$104$	0.232051	−	3.59808i	0.0227545	−	0.352820i
$105$		0			0
$106$	2.59808	−	1.50000i	0.252347	−	0.145693i
$107$	7.09808	−	4.09808i	0.686197	−	0.396176i	−0.115989	−	0.993251i	$-0.537004\pi$
$107$	7.09808	−	4.09808i	0.686197	−	0.396176i	0.802186	+	0.597075i	$0.203670\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$			16.3923i			1.57010i	0.619434	+	0.785049i	$0.287362\pi$
$109$			16.3923i			1.57010i	−0.619434	+	0.785049i	$0.712638\pi$
$110$		0			0
$111$	2.59808	+	1.50000i	0.246598	+	0.142374i
$112$	−4.73205			−0.447137
$113$	9.69615	+	5.59808i	0.912137	+	0.526623i	0.881118	−	0.472896i	$-0.156791\pi$
$113$	9.69615	+	5.59808i	0.912137	+	0.526623i	0.0310191	+	0.999519i	$0.490125\pi$
$114$	−0.633975	−	1.09808i	−0.0593772	−	0.102844i
$115$		0			0
$116$	3.00000			0.278543
$117$	3.00000	+	2.00000i	0.277350	+	0.184900i
$118$			13.8564i			1.27559i
$119$	−21.2942	+	12.2942i	−1.95204	+	1.12701i
$120$		0			0
$121$	5.69615	−	9.86603i	0.517832	−	0.896911i
$122$	−4.80385			−0.434920
$123$	0.232051	−	0.401924i	0.0209233	−	0.0362402i
$124$	2.19615	+	1.26795i	0.197220	+	0.113865i
$125$		0			0
$126$	2.36603	−	4.09808i	0.210782	−	0.365086i
$127$	3.46410	−	2.00000i	0.307389	−	0.177471i	−0.338368	−	0.941014i	$-0.609875\pi$
$127$	3.46410	−	2.00000i	0.307389	−	0.177471i	0.645758	+	0.763542i	$0.276542\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−6.19615			−0.545541
$130$		0			0
$131$	16.3923			1.43220			0.716101	−	0.697997i	$-0.245925\pi$
$131$	16.3923			1.43220			0.716101	+	0.697997i	$0.245925\pi$
$132$	2.36603	+	4.09808i	0.205936	+	0.356692i
$133$	−5.19615	+	3.00000i	−0.450564	+	0.260133i
$134$	5.36603	−	9.29423i	0.463554	−	0.802899i
$135$		0			0
$136$	4.50000	+	2.59808i	0.385872	+	0.222783i
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	−0.991694	−	0.128618i	$-0.958946\pi$
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	0.607233	+	0.794524i	$0.292279\pi$
$138$	2.19615			0.186949
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	−0.938293	−	0.345843i	$-0.887593\pi$
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	0.768655	+	0.639664i	$0.220926\pi$
$140$		0			0
$141$	1.09808	−	0.633975i	0.0924747	−	0.0533903i
$142$			8.19615i			0.687806i
$143$	7.56218	+	15.2942i	0.632381	+	1.27897i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	−6.06218	−	10.5000i	−0.501709	−	0.868986i
$147$	−13.3301	−	7.69615i	−1.09945	−	0.634768i
$148$	−3.00000			−0.246598
$149$	15.6962	+	9.06218i	1.28588	+	0.742403i	0.977916	−	0.208996i	$-0.0670196\pi$
$149$	15.6962	+	9.06218i	1.28588	+	0.742403i	0.307962	+	0.951399i	$0.400353\pi$
$150$		0			0
$151$			7.26795i			0.591457i	0.955272	+	0.295729i	$0.0955624\pi$
$151$			7.26795i			0.591457i	−0.955272	+	0.295729i	$0.904438\pi$
$152$	1.09808	+	0.633975i	0.0890657	+	0.0514221i
$153$	−4.50000	+	2.59808i	−0.363803	+	0.210042i
$154$	19.3923	−	11.1962i	1.56268	−	0.902212i
$155$		0			0
$156$	−3.59808	−	0.232051i	−0.288077	−	0.0185789i
$157$		−	3.19615i		−	0.255081i	−0.991833	−	0.127540i	$-0.959292\pi$
$157$		−	3.19615i		−	0.255081i	0.991833	−	0.127540i	$-0.0407082\pi$
$158$	6.19615	+	10.7321i	0.492939	+	0.853796i
$159$	−1.50000	−	2.59808i	−0.118958	−	0.206041i
$160$		0			0
$161$		−	10.3923i		−	0.819028i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	−4.73205	+	8.19615i	−0.370643	+	0.641972i	−0.989665	−	0.143402i	$-0.954196\pi$
$163$	−4.73205	+	8.19615i	−0.370643	+	0.641972i	0.619022	+	0.785374i	$0.287529\pi$
$164$			0.464102i			0.0362402i
$165$		0			0
$166$	5.83013	+	10.0981i	0.452506	+	0.783763i
$167$	−1.26795	−	2.19615i	−0.0981169	−	0.169943i	0.812788	−	0.582559i	$-0.197949\pi$
$167$	−1.26795	−	2.19615i	−0.0981169	−	0.169943i	−0.910905	+	0.412616i	$0.864615\pi$
$168$			4.73205i			0.365086i
$169$	−12.8923	−	1.66987i	−0.991716	−	0.128452i
$170$		0			0
$171$	−1.09808	+	0.633975i	−0.0839720	+	0.0484812i
$172$	5.36603	−	3.09808i	0.409156	−	0.236226i
$173$	−14.1962	−	8.19615i	−1.07931	−	0.623142i	−0.148602	−	0.988897i	$-0.547477\pi$
$173$	−14.1962	−	8.19615i	−1.07931	−	0.623142i	−0.930711	+	0.365755i	$0.880811\pi$
$174$		−	3.00000i		−	0.227429i
$175$		0			0
$176$	−4.09808	−	2.36603i	−0.308904	−	0.178346i
$177$	13.8564			1.04151
$178$	−2.19615	−	1.26795i	−0.164609	−	0.0950368i
$179$	4.09808	+	7.09808i	0.306305	+	0.530535i	0.977551	−	0.210699i	$-0.0675741\pi$
$179$	4.09808	+	7.09808i	0.306305	+	0.530535i	−0.671246	+	0.741234i	$0.734241\pi$
$180$		0			0
$181$	11.5885			0.861363			0.430682	−	0.902504i	$-0.358273\pi$
$181$	11.5885			0.861363			0.430682	+	0.902504i	$0.358273\pi$
$182$	−1.09808	+	17.0263i	−0.0813948	+	1.26207i
$183$			4.80385i			0.355111i
$184$	−1.90192	+	1.09808i	−0.140212	+	0.0809513i
$185$		0			0
$186$	1.26795	−	2.19615i	0.0929705	−	0.161030i
$187$	−24.5885			−1.79809
$188$	−0.633975	+	1.09808i	−0.0462373	+	0.0800854i
$189$	−4.09808	−	2.36603i	−0.298091	−	0.172103i
$190$		0			0
$191$	−10.3923	+	18.0000i	−0.751961	+	1.30243i	0.194910	+	0.980821i	$0.437558\pi$
$191$	−10.3923	+	18.0000i	−0.751961	+	1.30243i	−0.946871	+	0.321613i	$0.895775\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	6.40192	+	11.0885i	0.460821	+	0.798165i	0.999002	−	0.0446644i	$-0.0142218\pi$
$193$	6.40192	+	11.0885i	0.460821	+	0.798165i	−0.538181	+	0.842829i	$0.680889\pi$
$194$	−6.00000			−0.430775
$195$		0			0
$196$	15.3923			1.09945
$197$	−3.46410	−	6.00000i	−0.246807	−	0.427482i	0.715831	−	0.698273i	$-0.246048\pi$
$197$	−3.46410	−	6.00000i	−0.246807	−	0.427482i	−0.962638	+	0.270791i	$0.912715\pi$
$198$	4.09808	−	2.36603i	0.291238	−	0.168146i
$199$	−4.29423	+	7.43782i	−0.304410	+	0.527253i	−0.977130	−	0.212644i	$-0.931793\pi$
$199$	−4.29423	+	7.43782i	−0.304410	+	0.527253i	0.672720	+	0.739897i	$0.265126\pi$
$200$		0			0
$201$	−9.29423	−	5.36603i	−0.655564	−	0.378490i
$202$	0.696152	−	1.20577i	0.0489811	−	0.0848378i
$203$	−14.1962			−0.996375
$204$	2.59808	−	4.50000i	0.181902	−	0.315063i
$205$		0			0
$206$	3.63397	−	2.09808i	0.253191	−	0.146180i
$207$		−	2.19615i		−	0.152643i
$208$	3.23205	−	1.59808i	0.224102	−	0.110807i
$209$	−6.00000			−0.415029
$210$		0			0
$211$	1.80385	+	3.12436i	0.124182	+	0.215090i	0.921413	−	0.388585i	$-0.127036\pi$
$211$	1.80385	+	3.12436i	0.124182	+	0.215090i	−0.797231	+	0.603674i	$0.793703\pi$
$212$	2.59808	+	1.50000i	0.178437	+	0.103020i
$213$	8.19615			0.561591
$214$	7.09808	+	4.09808i	0.485215	+	0.280139i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	−10.3923	−	6.00000i	−0.705476	−	0.407307i
$218$	−14.1962	+	8.19615i	−0.961485	+	0.555113i
$219$	−10.5000	+	6.06218i	−0.709524	+	0.409644i
$220$		0			0
$221$	10.3923	−	15.5885i	0.699062	−	1.04859i
$222$			3.00000i			0.201347i
$223$	−9.46410	−	16.3923i	−0.633763	−	1.09771i	−0.986776	−	0.162091i	$-0.948176\pi$
$223$	−9.46410	−	16.3923i	−0.633763	−	1.09771i	0.353013	−	0.935619i	$-0.385157\pi$
$224$	−2.36603	−	4.09808i	−0.158087	−	0.273814i
$225$		0			0
$226$			11.1962i			0.744757i
$227$	4.90192	−	8.49038i	0.325352	−	0.563526i	−0.656231	−	0.754560i	$-0.727851\pi$
$227$	4.90192	−	8.49038i	0.325352	−	0.563526i	0.981584	+	0.191033i	$0.0611838\pi$
$228$	0.633975	−	1.09808i	0.0419860	−	0.0727219i
$229$		−	19.8564i		−	1.31215i	−0.754696	−	0.656074i	$-0.772216\pi$
$229$		−	19.8564i		−	1.31215i	0.754696	−	0.656074i	$-0.227784\pi$
$230$		0			0
$231$	−11.1962	−	19.3923i	−0.736653	−	1.27592i
$232$	1.50000	+	2.59808i	0.0984798	+	0.170572i
$233$		−	18.0000i		−	1.17922i	−0.807688	−	0.589610i	$-0.799282\pi$
$233$		−	18.0000i		−	1.17922i	0.807688	−	0.589610i	$-0.200718\pi$
$234$	−0.232051	+	3.59808i	−0.0151696	+	0.235214i
$235$		0			0
$236$	−12.0000	+	6.92820i	−0.781133	+	0.450988i
$237$	10.7321	−	6.19615i	0.697122	−	0.402483i
$238$	−21.2942	−	12.2942i	−1.38030	−	0.796916i
$239$		−	24.5885i		−	1.59050i	−0.606285	−	0.795248i	$-0.707341\pi$
$239$		−	24.5885i		−	1.59050i	0.606285	−	0.795248i	$-0.292659\pi$
$240$		0			0
$241$	−0.696152	−	0.401924i	−0.0448431	−	0.0258902i	0.477411	−	0.878680i	$-0.341575\pi$
$241$	−0.696152	−	0.401924i	−0.0448431	−	0.0258902i	−0.522254	+	0.852790i	$0.674909\pi$
$242$	11.3923			0.732325
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−2.40192	−	4.16025i	−0.153767	−	0.266333i
$245$		0			0
$246$	0.464102			0.0295900
$247$	2.53590	−	3.80385i	0.161355	−	0.242033i
$248$			2.53590i			0.161030i
$249$	10.0981	−	5.83013i	0.639940	−	0.369469i
$250$		0			0
$251$	−2.19615	+	3.80385i	−0.138620	+	0.240097i	−0.926974	−	0.375124i	$-0.877600\pi$
$251$	−2.19615	+	3.80385i	−0.138620	+	0.240097i	0.788355	+	0.615221i	$0.210933\pi$
$252$	4.73205			0.298091
$253$	5.19615	−	9.00000i	0.326679	−	0.565825i
$254$	3.46410	+	2.00000i	0.217357	+	0.125491i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.0885	+	6.40192i	−0.691679	+	0.399341i	−0.804241	−	0.594304i	$-0.797428\pi$
$257$	−11.0885	+	6.40192i	−0.691679	+	0.399341i	0.112562	+	0.993645i	$0.464094\pi$
$258$	−3.09808	−	5.36603i	−0.192878	−	0.334074i
$259$	14.1962			0.882106
$260$		0			0
$261$	−3.00000			−0.185695
$262$	8.19615	+	14.1962i	0.506360	+	0.877041i
$263$	1.90192	−	1.09808i	0.117278	−	0.0677103i	−0.440214	−	0.897893i	$-0.645097\pi$
$263$	1.90192	−	1.09808i	0.117278	−	0.0677103i	0.557491	+	0.830183i	$0.311764\pi$
$264$	−2.36603	+	4.09808i	−0.145619	+	0.252219i
$265$		0			0
$266$	−5.19615	−	3.00000i	−0.318597	−	0.183942i
$267$	−1.26795	+	2.19615i	−0.0775972	+	0.134402i
$268$	10.7321			0.655564
$269$	−14.1962	+	24.5885i	−0.865555	+	1.49918i	0.000940662		1.00000i	$0.499701\pi$
$269$	−14.1962	+	24.5885i	−0.865555	+	1.49918i	−0.866495	+	0.499185i	$0.833633\pi$
$270$		0			0
$271$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$271$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$272$			5.19615i			0.315063i
$273$	17.0263	+	1.09808i	1.03048	+	0.0664586i
$274$	−9.00000			−0.543710
$275$		0			0
$276$	1.09808	+	1.90192i	0.0660964	+	0.114482i
$277$	13.1603	+	7.59808i	0.790723	+	0.456524i	0.840217	−	0.542250i	$-0.182428\pi$
$277$	13.1603	+	7.59808i	0.790723	+	0.456524i	−0.0494940	+	0.998774i	$0.515761\pi$
$278$	−4.00000			−0.239904
$279$	−2.19615	−	1.26795i	−0.131480	−	0.0759101i
$280$		0			0
$281$			24.4641i			1.45941i	0.683764	+	0.729703i	$0.260342\pi$
$281$			24.4641i			1.45941i	−0.683764	+	0.729703i	$0.739658\pi$
$282$	1.09808	+	0.633975i	0.0653895	+	0.0377526i
$283$	−26.1506	+	15.0981i	−1.55449	+	0.897487i	−0.556727	+	0.830696i	$0.687943\pi$
$283$	−26.1506	+	15.0981i	−1.55449	+	0.897487i	−0.997767	+	0.0667919i	$0.978724\pi$
$284$	−7.09808	+	4.09808i	−0.421193	+	0.243176i
$285$		0			0
$286$	−9.46410	+	14.1962i	−0.559624	+	0.839436i
$287$		−	2.19615i		−	0.129635i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	5.00000	+	8.66025i	0.294118	+	0.509427i
$290$		0			0
$291$			6.00000i			0.351726i
$292$	6.06218	−	10.5000i	0.354762	−	0.614466i
$293$	7.33013	−	12.6962i	0.428231	−	0.741717i	−0.568485	−	0.822693i	$-0.692470\pi$
$293$	7.33013	−	12.6962i	0.428231	−	0.741717i	0.996716	+	0.0809762i	$0.0258038\pi$
$294$		−	15.3923i		−	0.897697i
$295$		0			0
$296$	−1.50000	−	2.59808i	−0.0871857	−	0.151010i
$297$	−2.36603	−	4.09808i	−0.137291	−	0.237795i
$298$			18.1244i			1.04992i
$299$	3.50962	+	7.09808i	0.202967	+	0.410492i
$300$		0			0
$301$	−25.3923	+	14.6603i	−1.46359	+	0.845003i
$302$	−6.29423	+	3.63397i	−0.362192	+	0.209112i
$303$	−1.20577	−	0.696152i	−0.0692698	−	0.0399929i
$304$			1.26795i			0.0727219i
$305$		0			0
$306$	−4.50000	−	2.59808i	−0.257248	−	0.148522i
$307$	−10.7321			−0.612510			−0.306255	−	0.951949i	$-0.599076\pi$
$307$	−10.7321			−0.612510			−0.306255	+	0.951949i	$0.599076\pi$
$308$	19.3923	+	11.1962i	1.10498	+	0.637960i
$309$	−2.09808	−	3.63397i	−0.119355	−	0.206730i
$310$		0			0
$311$	−2.19615			−0.124532			−0.0622662	−	0.998060i	$-0.519833\pi$
$311$	−2.19615			−0.124532			−0.0622662	+	0.998060i	$0.519833\pi$
$312$	−1.59808	−	3.23205i	−0.0904732	−	0.182979i
$313$			24.3923i			1.37873i	0.724412	+	0.689367i	$0.242111\pi$
$313$			24.3923i			1.37873i	−0.724412	+	0.689367i	$0.757889\pi$
$314$	2.76795	−	1.59808i	0.156204	−	0.0901847i
$315$		0			0
$316$	−6.19615	+	10.7321i	−0.348561	+	0.603725i
$317$	6.12436			0.343978			0.171989	−	0.985099i	$-0.444981\pi$
$317$	6.12436			0.343978			0.171989	+	0.985099i	$0.444981\pi$
$318$	1.50000	−	2.59808i	0.0841158	−	0.145693i
$319$	−12.2942	−	7.09808i	−0.688345	−	0.397416i
$320$		0			0
$321$	4.09808	−	7.09808i	0.228732	−	0.396176i
$322$	9.00000	−	5.19615i	0.501550	−	0.289570i
$323$	3.29423	+	5.70577i	0.183296	+	0.317478i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−9.46410			−0.524168
$327$	8.19615	+	14.1962i	0.453248	+	0.785049i
$328$	−0.401924	+	0.232051i	−0.0221925	+	0.0128129i
$329$	3.00000	−	5.19615i	0.165395	−	0.286473i
$330$		0			0
$331$	10.3923	+	6.00000i	0.571213	+	0.329790i	0.757634	−	0.652680i	$-0.226355\pi$
$331$	10.3923	+	6.00000i	0.571213	+	0.329790i	−0.186421	+	0.982470i	$0.559689\pi$
$332$	−5.83013	+	10.0981i	−0.319970	+	0.554204i
$333$	3.00000			0.164399
$334$	1.26795	−	2.19615i	0.0693791	−	0.120168i
$335$		0			0
$336$	−4.09808	+	2.36603i	−0.223568	+	0.129077i
$337$			31.0000i			1.68868i	0.535810	+	0.844339i	$0.320006\pi$
$337$			31.0000i			1.68868i	−0.535810	+	0.844339i	$0.679994\pi$
$338$	−5.00000	−	12.0000i	−0.271964	−	0.652714i
$339$	11.1962			0.608092
$340$		0			0
$341$	−6.00000	−	10.3923i	−0.324918	−	0.562775i
$342$	−1.09808	−	0.633975i	−0.0593772	−	0.0342814i
$343$	−39.7128			−2.14429
$344$	5.36603	+	3.09808i	0.289317	+	0.167037i
$345$		0			0
$346$		−	16.3923i		−	0.881256i
$347$	10.9019	+	6.29423i	0.585246	+	0.337892i	0.763215	−	0.646144i	$-0.223620\pi$
$347$	10.9019	+	6.29423i	0.585246	+	0.337892i	−0.177969	+	0.984036i	$0.556953\pi$
$348$	2.59808	−	1.50000i	0.139272	−	0.0804084i
$349$	−2.19615	+	1.26795i	−0.117557	+	0.0678718i	−0.557626	−	0.830093i	$-0.688288\pi$
$349$	−2.19615	+	1.26795i	−0.117557	+	0.0678718i	0.440068	+	0.897964i	$0.354954\pi$
$350$		0			0
$351$	3.59808	+	0.232051i	0.192051	+	0.0123860i
$352$		−	4.73205i		−	0.252219i
$353$	2.89230	+	5.00962i	0.153942	+	0.266635i	0.932673	−	0.360722i	$-0.117470\pi$
$353$	2.89230	+	5.00962i	0.153942	+	0.266635i	−0.778731	+	0.627358i	$0.784136\pi$
$354$	6.92820	+	12.0000i	0.368230	+	0.637793i
$355$		0			0
$356$		−	2.53590i		−	0.134402i
$357$	−12.2942	+	21.2942i	−0.650680	+	1.12701i
$358$	−4.09808	+	7.09808i	−0.216590	+	0.375145i
$359$		−	22.0526i		−	1.16389i	−0.813228	−	0.581945i	$-0.802292\pi$
$359$		−	22.0526i		−	1.16389i	0.813228	−	0.581945i	$-0.197708\pi$
$360$		0			0
$361$	−8.69615	−	15.0622i	−0.457692	−	0.792746i
$362$	5.79423	+	10.0359i	0.304538	+	0.527475i
$363$		−	11.3923i		−	0.597941i
$364$	−15.2942	+	7.56218i	−0.801635	+	0.396366i
$365$		0			0
$366$	−4.16025	+	2.40192i	−0.217460	+	0.125551i
$367$	−20.9545	+	12.0981i	−1.09382	+	0.631514i	−0.934590	−	0.355728i	$-0.884233\pi$
$367$	−20.9545	+	12.0981i	−1.09382	+	0.631514i	−0.159225	+	0.987242i	$0.550900\pi$
$368$	−1.90192	−	1.09808i	−0.0991446	−	0.0572412i
$369$		−	0.464102i		−	0.0241602i
$370$		0			0
$371$	−12.2942	−	7.09808i	−0.638285	−	0.368514i
$372$	2.53590			0.131480
$373$	20.7679	+	11.9904i	1.07532	+	0.620838i	0.929631	−	0.368492i	$-0.120126\pi$
$373$	20.7679	+	11.9904i	1.07532	+	0.620838i	0.145693	+	0.989330i	$0.453459\pi$
$374$	−12.2942	−	21.2942i	−0.635719	−	1.10110i
$375$		0			0
$376$	−1.26795			−0.0653895
$377$	9.69615	−	4.79423i	0.499377	−	0.246915i
$378$		−	4.73205i		−	0.243390i
$379$	−15.8038	+	9.12436i	−0.811789	+	0.468687i	−0.847577	−	0.530673i	$-0.821939\pi$
$379$	−15.8038	+	9.12436i	−0.811789	+	0.468687i	0.0357877	+	0.999359i	$0.488606\pi$
$380$		0			0
$381$	2.00000	−	3.46410i	0.102463	−	0.177471i
$382$	−20.7846			−1.06343
$383$	5.66025	−	9.80385i	0.289225	−	0.500953i	−0.684400	−	0.729107i	$-0.739936\pi$
$383$	5.66025	−	9.80385i	0.289225	−	0.500953i	0.973625	+	0.228154i	$0.0732689\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$		0			0
$386$	−6.40192	+	11.0885i	−0.325849	+	0.564388i
$387$	−5.36603	+	3.09808i	−0.272770	+	0.157484i
$388$	−3.00000	−	5.19615i	−0.152302	−	0.263795i
$389$	−13.3923			−0.679017			−0.339508	−	0.940603i	$-0.610261\pi$
$389$	−13.3923			−0.679017			−0.339508	+	0.940603i	$0.610261\pi$
$390$		0			0
$391$	−11.4115			−0.577107
$392$	7.69615	+	13.3301i	0.388714	+	0.673273i
$393$	14.1962	−	8.19615i	0.716101	−	0.413441i
$394$	3.46410	−	6.00000i	0.174519	−	0.302276i
$395$		0			0
$396$	4.09808	+	2.36603i	0.205936	+	0.118897i
$397$	−8.19615	+	14.1962i	−0.411353	+	0.712484i	−0.995038	−	0.0994958i	$-0.968277\pi$
$397$	−8.19615	+	14.1962i	−0.411353	+	0.712484i	0.583685	+	0.811980i	$0.301610\pi$
$398$	−8.58846			−0.430500
$399$	−3.00000	+	5.19615i	−0.150188	+	0.260133i
$400$		0			0
$401$	18.1865	−	10.5000i	0.908192	−	0.524345i	0.0283431	−	0.999598i	$-0.490977\pi$
$401$	18.1865	−	10.5000i	0.908192	−	0.524345i	0.879849	+	0.475253i	$0.157644\pi$
$402$		−	10.7321i		−	0.535266i
$403$	9.12436	+	0.588457i	0.454517	+	0.0293131i
$404$	1.39230			0.0692698
$405$		0			0
$406$	−7.09808	−	12.2942i	−0.352272	−	0.610152i
$407$	12.2942	+	7.09808i	0.609402	+	0.351839i
$408$	5.19615			0.257248
$409$	2.89230	+	1.66987i	0.143015	+	0.0825699i	0.569800	−	0.821783i	$-0.307021\pi$
$409$	2.89230	+	1.66987i	0.143015	+	0.0825699i	−0.426785	+	0.904353i	$0.640354\pi$
$410$		0			0
$411$			9.00000i			0.443937i
$412$	3.63397	+	2.09808i	0.179033	+	0.103365i
$413$	56.7846	−	32.7846i	2.79419	−	1.61323i
$414$	1.90192	−	1.09808i	0.0934745	−	0.0539675i
$415$		0			0
$416$	3.00000	+	2.00000i	0.147087	+	0.0980581i
$417$			4.00000i			0.195881i
$418$	−3.00000	−	5.19615i	−0.146735	−	0.254152i
$419$	8.19615	+	14.1962i	0.400408	+	0.693527i	0.993775	−	0.111405i	$-0.0355350\pi$
$419$	8.19615	+	14.1962i	0.400408	+	0.693527i	−0.593367	+	0.804932i	$0.702202\pi$
$420$		0			0
$421$		−	0.464102i		−	0.0226189i	−0.999936	−	0.0113095i	$-0.996400\pi$
$421$		−	0.464102i		−	0.0226189i	0.999936	−	0.0113095i	$-0.00359999\pi$
$422$	−1.80385	+	3.12436i	−0.0878099	+	0.152091i
$423$	0.633975	−	1.09808i	0.0308249	−	0.0533903i
$424$			3.00000i			0.145693i
$425$		0			0
$426$	4.09808	+	7.09808i	0.198552	+	0.343903i
$427$	11.3660	+	19.6865i	0.550041	+	0.952698i
$428$			8.19615i			0.396176i
$429$	14.1962	+	9.46410i	0.685397	+	0.456931i
$430$		0			0
$431$	−24.0788	+	13.9019i	−1.15984	+	0.669632i	−0.951265	−	0.308375i	$-0.900215\pi$
$431$	−24.0788	+	13.9019i	−1.15984	+	0.669632i	−0.208572	+	0.978007i	$0.566882\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	29.2583	+	16.8923i	1.40607	+	0.811792i	0.995006	−	0.0998161i	$-0.0318254\pi$
$433$	29.2583	+	16.8923i	1.40607	+	0.811792i	0.411060	+	0.911608i	$0.365159\pi$
$434$		−	12.0000i		−	0.576018i
$435$		0			0
$436$	−14.1962	−	8.19615i	−0.679872	−	0.392525i
$437$	−2.78461			−0.133206
$438$	−10.5000	−	6.06218i	−0.501709	−	0.289662i
$439$	−8.29423	−	14.3660i	−0.395862	−	0.685653i	0.597349	−	0.801982i	$-0.296221\pi$
$439$	−8.29423	−	14.3660i	−0.395862	−	0.685653i	−0.993211	+	0.116329i	$0.962887\pi$
$440$		0			0
$441$	−15.3923			−0.732967
$442$	18.6962	+	1.20577i	0.889285	+	0.0573527i
$443$			4.39230i			0.208685i	0.994541	+	0.104342i	$0.0332738\pi$
$443$			4.39230i			0.208685i	−0.994541	+	0.104342i	$0.966726\pi$
$444$	−2.59808	+	1.50000i	−0.123299	+	0.0711868i
$445$		0			0
$446$	9.46410	−	16.3923i	0.448138	−	0.776198i
$447$	18.1244			0.857253
$448$	2.36603	−	4.09808i	0.111784	−	0.193616i
$449$	28.9808	+	16.7321i	1.36769	+	0.789634i	0.990632	−	0.136557i	$-0.0436036\pi$
$449$	28.9808	+	16.7321i	1.36769	+	0.789634i	0.377054	+	0.926191i	$0.376937\pi$
$450$		0			0
$451$	1.09808	−	1.90192i	0.0517064	−	0.0895581i
$452$	−9.69615	+	5.59808i	−0.456069	+	0.263311i
$453$	3.63397	+	6.29423i	0.170739	+	0.295729i
$454$	9.80385			0.460117
$455$		0			0
$456$	1.26795			0.0593772
$457$	−9.99038	−	17.3038i	−0.467330	−	0.809440i	0.531973	−	0.846761i	$-0.321451\pi$
$457$	−9.99038	−	17.3038i	−0.467330	−	0.809440i	−0.999303	+	0.0373215i	$0.988117\pi$
$458$	17.1962	−	9.92820i	0.803523	−	0.463914i
$459$	−2.59808	+	4.50000i	−0.121268	+	0.210042i
$460$		0			0
$461$	−17.3038	−	9.99038i	−0.805921	−	0.465298i	0.0396167	−	0.999215i	$-0.487386\pi$
$461$	−17.3038	−	9.99038i	−0.805921	−	0.465298i	−0.845537	+	0.533917i	$0.820720\pi$
$462$	11.1962	−	19.3923i	0.520892	−	0.902212i
$463$	−26.1962			−1.21744			−0.608719	−	0.793386i	$-0.708316\pi$
$463$	−26.1962			−1.21744			−0.608719	+	0.793386i	$0.708316\pi$
$464$	−1.50000	+	2.59808i	−0.0696358	+	0.120613i
$465$		0			0
$466$	15.5885	−	9.00000i	0.722121	−	0.416917i
$467$		−	36.5885i		−	1.69311i	−0.532300	−	0.846556i	$-0.678672\pi$
$467$		−	36.5885i		−	1.69311i	0.532300	−	0.846556i	$-0.321328\pi$
$468$	−3.23205	+	1.59808i	−0.149402	+	0.0738711i
$469$	−50.7846			−2.34502
$470$		0			0
$471$	−1.59808	−	2.76795i	−0.0736355	−	0.127540i
$472$	−12.0000	−	6.92820i	−0.552345	−	0.318896i
$473$	−29.3205			−1.34816
$474$	10.7321	+	6.19615i	0.492939	+	0.284599i
$475$		0			0
$476$		−	24.5885i		−	1.12701i
$477$	−2.59808	−	1.50000i	−0.118958	−	0.0686803i
$478$	21.2942	−	12.2942i	0.973975	−	0.562325i
$479$	30.5885	−	17.6603i	1.39762	−	0.806918i	0.403479	−	0.914989i	$-0.367801\pi$
$479$	30.5885	−	17.6603i	1.39762	−	0.806918i	0.994143	+	0.108071i	$0.0344675\pi$
$480$		0			0
$481$	−9.69615	+	4.79423i	−0.442106	+	0.218598i
$482$		−	0.803848i		−	0.0366143i
$483$	−5.19615	−	9.00000i	−0.236433	−	0.409514i
$484$	5.69615	+	9.86603i	0.258916	+	0.448456i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	−4.56218	+	7.90192i	−0.206732	+	0.358070i	−0.950683	−	0.310164i	$-0.899616\pi$
$487$	−4.56218	+	7.90192i	−0.206732	+	0.358070i	0.743951	+	0.668234i	$0.232949\pi$
$488$	2.40192	−	4.16025i	0.108730	−	0.188326i
$489$			9.46410i			0.427981i
$490$		0			0
$491$	0.294229	+	0.509619i	0.0132784	+	0.0229988i	0.872588	−	0.488457i	$-0.162440\pi$
$491$	0.294229	+	0.509619i	0.0132784	+	0.0229988i	−0.859310	+	0.511455i	$0.829107\pi$
$492$	0.232051	+	0.401924i	0.0104617	+	0.0181201i
$493$			15.5885i			0.702069i
$494$	4.56218	+	0.294229i	0.205262	+	0.0132380i
$495$		0			0
$496$	−2.19615	+	1.26795i	−0.0986102	+	0.0569326i
$497$	33.5885	−	19.3923i	1.50665	−	0.869864i
$498$	10.0981	+	5.83013i	0.452506	+	0.261254i
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$		0			0
$501$	−2.19615	−	1.26795i	−0.0981169	−	0.0566478i
$502$	−4.39230			−0.196038
$503$	−16.0981	−	9.29423i	−0.717778	−	0.414409i	0.0961565	−	0.995366i	$-0.469345\pi$
$503$	−16.0981	−	9.29423i	−0.717778	−	0.414409i	−0.813934	+	0.580957i	$0.802678\pi$
$504$	2.36603	+	4.09808i	0.105391	+	0.182543i
$505$		0			0
$506$	10.3923			0.461994
$507$	−12.0000	+	5.00000i	−0.532939	+	0.222058i
$508$			4.00000i			0.177471i
$509$	8.08846	−	4.66987i	0.358515	−	0.206988i	−0.309914	−	0.950764i	$-0.600300\pi$
$509$	8.08846	−	4.66987i	0.358515	−	0.206988i	0.668429	+	0.743776i	$0.266967\pi$
$510$		0			0
$511$	−28.6865	+	49.6865i	−1.26902	+	2.19800i
$512$	−1.00000			−0.0441942
$513$	−0.633975	+	1.09808i	−0.0279907	+	0.0484812i
$514$	−11.0885	−	6.40192i	−0.489091	−	0.282377i
$515$		0			0
$516$	3.09808	−	5.36603i	0.136385	−	0.236226i
$517$	5.19615	−	3.00000i	0.228527	−	0.131940i
$518$	7.09808	+	12.2942i	0.311872	+	0.540177i
$519$	−16.3923			−0.719542
$520$		0			0
$521$	−18.8038			−0.823812			−0.411906	−	0.911226i	$-0.635137\pi$
$521$	−18.8038			−0.823812			−0.411906	+	0.911226i	$0.635137\pi$
$522$	−1.50000	−	2.59808i	−0.0656532	−	0.113715i
$523$	−1.22243	+	0.705771i	−0.0534532	+	0.0308612i	−0.526488	−	0.850182i	$-0.676492\pi$
$523$	−1.22243	+	0.705771i	−0.0534532	+	0.0308612i	0.473035	+	0.881044i	$0.343158\pi$
$524$	−8.19615	+	14.1962i	−0.358051	+	0.620162i
$525$		0			0
$526$	1.90192	+	1.09808i	0.0829278	+	0.0478784i
$527$	−6.58846	+	11.4115i	−0.286998	+	0.497095i
$528$	−4.73205			−0.205936
$529$	−9.08846	+	15.7417i	−0.395150	+	0.684420i
$530$		0			0
$531$	12.0000	−	6.92820i	0.520756	−	0.300658i
$532$		−	6.00000i		−	0.260133i
$533$	0.741670	+	1.50000i	0.0321253	+	0.0649722i
$534$	−2.53590			−0.109739
$535$		0			0
$536$	5.36603	+	9.29423i	0.231777	+	0.401450i
$537$	7.09808	+	4.09808i	0.306305	+	0.176845i
$538$	−28.3923			−1.22408
$539$	−63.0788	−	36.4186i	−2.71700	−	1.56866i
$540$		0			0
$541$			16.8564i			0.724714i	0.932039	+	0.362357i	$0.118028\pi$
$541$			16.8564i			0.724714i	−0.932039	+	0.362357i	$0.881972\pi$
$542$		0			0
$543$	10.0359	−	5.79423i	0.430682	−	0.248654i
$544$	−4.50000	+	2.59808i	−0.192936	+	0.111392i
$545$		0			0
$546$	7.56218	+	15.2942i	0.323631	+	0.654533i
$547$		−	6.19615i		−	0.264928i	−0.991188	−	0.132464i	$-0.957711\pi$
$547$		−	6.19615i		−	0.264928i	0.991188	−	0.132464i	$-0.0422889\pi$
$548$	−4.50000	−	7.79423i	−0.192230	−	0.332953i
$549$	2.40192	+	4.16025i	0.102512	+	0.177555i
$550$		0			0
$551$			3.80385i			0.162049i
$552$	−1.09808	+	1.90192i	−0.0467372	+	0.0809513i
$553$	29.3205	−	50.7846i	1.24683	−	2.15958i
$554$			15.1962i			0.645623i
$555$		0			0
$556$	−2.00000	−	3.46410i	−0.0848189	−	0.146911i
$557$	11.1340	+	19.2846i	0.471762	+	0.817115i	0.999478	−	0.0323055i	$-0.0102849\pi$
$557$	11.1340	+	19.2846i	0.471762	+	0.817115i	−0.527716	+	0.849421i	$0.676952\pi$
$558$		−	2.53590i		−	0.107353i
$559$	12.3923	−	18.5885i	0.524139	−	0.786208i
$560$		0			0
$561$	−21.2942	+	12.2942i	−0.899043	+	0.519063i
$562$	−21.1865	+	12.2321i	−0.893700	+	0.515978i
$563$	−7.60770	−	4.39230i	−0.320626	−	0.185114i	0.331046	−	0.943615i	$-0.392599\pi$
$563$	−7.60770	−	4.39230i	−0.320626	−	0.185114i	−0.651672	+	0.758501i	$0.725932\pi$
$564$			1.26795i			0.0533903i
$565$		0			0
$566$	−26.1506	−	15.0981i	−1.09919	−	0.634619i
$567$	−4.73205			−0.198727
$568$	−7.09808	−	4.09808i	−0.297829	−	0.171951i
$569$	16.3923	+	28.3923i	0.687201	+	1.19027i	0.972740	+	0.231900i	$0.0744942\pi$
$569$	16.3923	+	28.3923i	0.687201	+	1.19027i	−0.285538	+	0.958367i	$0.592172\pi$
$570$		0			0
$571$	13.8038			0.577673			0.288837	−	0.957378i	$-0.406732\pi$
$571$	13.8038			0.577673			0.288837	+	0.957378i	$0.406732\pi$
$572$	−17.0263	−	1.09808i	−0.711905	−	0.0459129i
$573$			20.7846i			0.868290i
$574$	1.90192	−	1.09808i	0.0793848	−	0.0458328i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−16.2679			−0.677244			−0.338622	−	0.940923i	$-0.609961\pi$
$577$	−16.2679			−0.677244			−0.338622	+	0.940923i	$0.609961\pi$
$578$	−5.00000	+	8.66025i	−0.207973	+	0.360219i
$579$	11.0885	+	6.40192i	0.460821	+	0.266055i
$580$		0			0
$581$	27.5885	−	47.7846i	1.14456	−	1.98244i
$582$	−5.19615	+	3.00000i	−0.215387	+	0.124354i
$583$	−7.09808	−	12.2942i	−0.293972	−	0.509175i
$584$	12.1244			0.501709
$585$		0			0
$586$	14.6603			0.605610
$587$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$587$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$588$	13.3301	−	7.69615i	0.549725	−	0.317384i
$589$	−1.60770	+	2.78461i	−0.0662439	+	0.114738i
$590$		0			0
$591$	−6.00000	−	3.46410i	−0.246807	−	0.142494i
$592$	1.50000	−	2.59808i	0.0616496	−	0.106780i
$593$	−46.8564			−1.92416			−0.962081	−	0.272764i	$-0.912062\pi$
$593$	−46.8564			−1.92416			−0.962081	+	0.272764i	$0.912062\pi$
$594$	2.36603	−	4.09808i	0.0970792	−	0.168146i
$595$		0			0
$596$	−15.6962	+	9.06218i	−0.642939	+	0.371201i
$597$			8.58846i			0.351502i
$598$	−4.39230	+	6.58846i	−0.179615	+	0.269422i
$599$	4.39230			0.179465			0.0897324	−	0.995966i	$-0.471399\pi$
$599$	4.39230			0.179465			0.0897324	+	0.995966i	$0.471399\pi$
$600$		0			0
$601$	−10.8923	−	18.8660i	−0.444306	−	0.769561i	0.553697	−	0.832718i	$-0.313216\pi$
$601$	−10.8923	−	18.8660i	−0.444306	−	0.769561i	−0.998004	+	0.0631568i	$0.979883\pi$
$602$	−25.3923	−	14.6603i	−1.03491	−	0.597507i
$603$	−10.7321			−0.437043
$604$	−6.29423	−	3.63397i	−0.256109	−	0.147864i
$605$		0			0
$606$		−	1.39230i		−	0.0565585i
$607$	42.2487	+	24.3923i	1.71482	+	0.990053i	0.927758	+	0.373182i	$0.121733\pi$
$607$	42.2487	+	24.3923i	1.71482	+	0.990053i	0.787064	+	0.616871i	$0.211600\pi$
$608$	−1.09808	+	0.633975i	−0.0445329	+	0.0257111i
$609$	−12.2942	+	7.09808i	−0.498187	+	0.287629i
$610$		0			0
$611$	−0.294229	+	4.56218i	−0.0119032	+	0.184566i
$612$		−	5.19615i		−	0.210042i
$613$	−20.4282	−	35.3827i	−0.825087	−	1.42909i	−0.901853	−	0.432044i	$-0.857793\pi$
$613$	−20.4282	−	35.3827i	−0.825087	−	1.42909i	0.0767652	−	0.997049i	$-0.475541\pi$
$614$	−5.36603	−	9.29423i	−0.216555	−	0.375085i
$615$		0			0
$616$			22.3923i			0.902212i
$617$	−5.30385	+	9.18653i	−0.213525	+	0.369836i	−0.952815	−	0.303551i	$-0.901828\pi$
$617$	−5.30385	+	9.18653i	−0.213525	+	0.369836i	0.739290	+	0.673387i	$0.235161\pi$
$618$	2.09808	−	3.63397i	0.0843970	−	0.146180i
$619$			7.60770i			0.305779i	0.988243	+	0.152890i	$0.0488579\pi$
$619$			7.60770i			0.305779i	−0.988243	+	0.152890i	$0.951142\pi$
$620$		0			0
$621$	−1.09808	−	1.90192i	−0.0440643	−	0.0763216i
$622$	−1.09808	−	1.90192i	−0.0440288	−	0.0762602i
$623$			12.0000i			0.480770i
$624$	2.00000	−	3.00000i	0.0800641	−	0.120096i
$625$		0			0
$626$	−21.1244	+	12.1962i	−0.844299	+	0.487456i
$627$	−5.19615	+	3.00000i	−0.207514	+	0.119808i
$628$	2.76795	+	1.59808i	0.110453	+	0.0637702i
$629$		−	15.5885i		−	0.621552i
$630$		0			0
$631$	−22.3923	−	12.9282i	−0.891424	−	0.514664i	−0.0170157	−	0.999855i	$-0.505417\pi$
$631$	−22.3923	−	12.9282i	−0.891424	−	0.514664i	−0.874408	+	0.485192i	$0.838750\pi$
$632$	−12.3923			−0.492939
$633$	3.12436	+	1.80385i	0.124182	+	0.0716965i
$634$	3.06218	+	5.30385i	0.121615	+	0.210643i
$635$		0			0
$636$	3.00000			0.118958
$637$	49.7487	−	24.5981i	1.97112	−	0.974611i
$638$		−	14.1962i		−	0.562031i
$639$	7.09808	−	4.09808i	0.280796	−	0.162117i
$640$		0			0
$641$	−15.4019	+	26.6769i	−0.608339	+	1.05367i	0.383175	+	0.923676i	$0.374831\pi$
$641$	−15.4019	+	26.6769i	−0.608339	+	1.05367i	−0.991514	+	0.129999i	$0.958503\pi$
$642$	8.19615			0.323476
$643$	−13.8564	+	24.0000i	−0.546443	+	0.946468i	0.452071	+	0.891982i	$0.350685\pi$
$643$	−13.8564	+	24.0000i	−0.546443	+	0.946468i	−0.998515	+	0.0544858i	$0.982648\pi$
$644$	9.00000	+	5.19615i	0.354650	+	0.204757i
$645$		0			0
$646$	−3.29423	+	5.70577i	−0.129610	+	0.224491i
$647$	−11.4115	+	6.58846i	−0.448634	+	0.259019i	−0.707253	−	0.706960i	$-0.750066\pi$
$647$	−11.4115	+	6.58846i	−0.448634	+	0.259019i	0.258619	+	0.965979i	$0.416733\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	65.5692			2.57382
$650$		0			0
$651$	−12.0000			−0.470317
$652$	−4.73205	−	8.19615i	−0.185321	−	0.320986i
$653$	42.5885	−	24.5885i	1.66662	−	0.962221i	0.697172	−	0.716904i	$-0.254441\pi$
$653$	42.5885	−	24.5885i	1.66662	−	0.962221i	0.969443	−	0.245317i	$-0.0788920\pi$
$654$	−8.19615	+	14.1962i	−0.320495	+	0.555113i
$655$		0			0
$656$	−0.401924	−	0.232051i	−0.0156925	−	0.00906006i
$657$	−6.06218	+	10.5000i	−0.236508	+	0.409644i
$658$	6.00000			0.233904
$659$	12.5885	−	21.8038i	0.490377	−	0.849357i	−0.509562	−	0.860434i	$-0.670193\pi$
$659$	12.5885	−	21.8038i	0.490377	−	0.849357i	0.999939	+	0.0110766i	$0.00352588\pi$
$660$		0			0
$661$	7.79423	−	4.50000i	0.303160	−	0.175030i	−0.340701	−	0.940172i	$-0.610665\pi$
$661$	7.79423	−	4.50000i	0.303160	−	0.175030i	0.643862	+	0.765142i	$0.277331\pi$
$662$			12.0000i			0.466393i
$663$	1.20577	−	18.6962i	0.0468283	−	0.726098i
$664$	−11.6603			−0.452506
$665$		0			0
$666$	1.50000	+	2.59808i	0.0581238	+	0.100673i
$667$	−5.70577	−	3.29423i	−0.220928	−	0.127553i
$668$	2.53590			0.0981169
$669$	−16.3923	−	9.46410i	−0.633763	−	0.365903i
$670$		0			0
$671$			22.7321i			0.877561i
$672$	−4.09808	−	2.36603i	−0.158087	−	0.0912714i
$673$	0.866025	−	0.500000i	0.0333828	−	0.0192736i	−0.483216	−	0.875501i	$-0.660531\pi$
$673$	0.866025	−	0.500000i	0.0333828	−	0.0192736i	0.516599	+	0.856228i	$0.327198\pi$
$674$	−26.8468	+	15.5000i	−1.03410	+	0.597038i
$675$		0			0
$676$	7.89230	−	10.3301i	0.303550	−	0.397313i
$677$			4.39230i			0.168810i	0.996432	+	0.0844050i	$0.0268989\pi$
$677$			4.39230i			0.168810i	−0.996432	+	0.0844050i	$0.973101\pi$
$678$	5.59808	+	9.69615i	0.214993	+	0.372378i
$679$	14.1962	+	24.5885i	0.544798	+	0.943618i
$680$		0			0
$681$		−	9.80385i		−	0.375684i
$682$	6.00000	−	10.3923i	0.229752	−	0.397942i
$683$	−13.8564	+	24.0000i	−0.530201	+	0.918334i	0.469179	+	0.883103i	$0.344550\pi$
$683$	−13.8564	+	24.0000i	−0.530201	+	0.918334i	−0.999379	+	0.0352311i	$0.988783\pi$
$684$		−	1.26795i		−	0.0484812i
$685$		0			0
$686$	−19.8564	−	34.3923i	−0.758121	−	1.31310i
$687$	−9.92820	−	17.1962i	−0.378785	−	0.656074i
$688$			6.19615i			0.236226i
$689$	10.7942	+	0.696152i	0.411227	+	0.0265213i
$690$		0			0
$691$	16.9019	−	9.75833i	0.642979	−	0.371224i	−0.142782	−	0.989754i	$-0.545605\pi$
$691$	16.9019	−	9.75833i	0.642979	−	0.371224i	0.785761	+	0.618530i	$0.212271\pi$
$692$	14.1962	−	8.19615i	0.539657	−	0.311571i
$693$	−19.3923	−	11.1962i	−0.736653	−	0.425307i
$694$			12.5885i			0.477851i
$695$		0			0
$696$	2.59808	+	1.50000i	0.0984798	+	0.0568574i
$697$	−2.41154			−0.0913437
$698$	−2.19615	−	1.26795i	−0.0831256	−	0.0479926i
$699$	−9.00000	−	15.5885i	−0.340411	−	0.589610i
$700$		0			0
$701$	−4.39230			−0.165895			−0.0829475	−	0.996554i	$-0.526433\pi$
$701$	−4.39230			−0.165895			−0.0829475	+	0.996554i	$0.526433\pi$
$702$	1.59808	+	3.23205i	0.0603155	+	0.121986i
$703$		−	3.80385i		−	0.143465i
$704$	4.09808	−	2.36603i	0.154452	−	0.0891729i
$705$		0			0
$706$	−2.89230	+	5.00962i	−0.108853	+	0.188539i
$707$	−6.58846			−0.247784
$708$	−6.92820	+	12.0000i	−0.260378	+	0.450988i
$709$	2.81347	+	1.62436i	0.105662	+	0.0610040i	0.551900	−	0.833910i	$-0.313903\pi$
$709$	2.81347	+	1.62436i	0.105662	+	0.0610040i	−0.446238	+	0.894914i	$0.647236\pi$
$710$		0			0
$711$	6.19615	−	10.7321i	0.232374	−	0.402483i
$712$	2.19615	−	1.26795i	0.0823043	−	0.0475184i
$713$	−2.78461	−	4.82309i	−0.104284	−	0.180626i
$714$	−24.5885			−0.920200
$715$		0			0
$716$	−8.19615			−0.306305
$717$	−12.2942	−	21.2942i	−0.459136	−	0.795248i
$718$	19.0981	−	11.0263i	0.712734	−	0.411497i
$719$	−26.1962	+	45.3731i	−0.976952	+	1.69213i	−0.303613	+	0.952795i	$0.598193\pi$
$719$	−26.1962	+	45.3731i	−0.976952	+	1.69213i	−0.673338	+	0.739335i	$0.735140\pi$
$720$		0			0
$721$	−17.1962	−	9.92820i	−0.640418	−	0.369746i
$722$	8.69615	−	15.0622i	0.323637	−	0.560556i
$723$	−0.803848			−0.0298954
$724$	−5.79423	+	10.0359i	−0.215341	+	0.372981i
$725$		0			0
$726$	9.86603	−	5.69615i	0.366163	−	0.211404i
$727$			24.1962i			0.897386i	0.893686	+	0.448693i	$0.148110\pi$
$727$			24.1962i			0.897386i	−0.893686	+	0.448693i	$0.851890\pi$
$728$	−14.1962	−	9.46410i	−0.526144	−	0.350763i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	16.0981	+	27.8827i	0.595409	+	1.03128i
$732$	−4.16025	−	2.40192i	−0.153767	−	0.0887777i
$733$	14.3205			0.528940			0.264470	−	0.964394i	$-0.414803\pi$
$733$	14.3205			0.528940			0.264470	+	0.964394i	$0.414803\pi$
$734$	−20.9545	−	12.0981i	−0.773444	−	0.446548i
$735$		0			0
$736$		−	2.19615i		−	0.0809513i
$737$	−43.9808	−	25.3923i	−1.62005	−	0.935338i
$738$	0.401924	−	0.232051i	0.0147950	−	0.00854191i
$739$	16.3923	−	9.46410i	0.603001	−	0.348143i	−0.167220	−	0.985920i	$-0.553479\pi$
$739$	16.3923	−	9.46410i	0.603001	−	0.348143i	0.770221	+	0.637777i	$0.220146\pi$
$740$		0			0
$741$	0.294229	−	4.56218i	0.0108088	−	0.167596i
$742$		−	14.1962i		−	0.521157i
$743$	2.19615	+	3.80385i	0.0805690	+	0.139550i	0.903494	−	0.428600i	$-0.140993\pi$
$743$	2.19615	+	3.80385i	0.0805690	+	0.139550i	−0.822925	+	0.568149i	$0.807660\pi$
$744$	1.26795	+	2.19615i	0.0464853	+	0.0805149i
$745$		0			0
$746$			23.9808i			0.877998i
$747$	5.83013	−	10.0981i	0.213313	−	0.369469i
$748$	12.2942	−	21.2942i	0.449522	−	0.778594i
$749$		−	38.7846i		−	1.41716i
$750$		0			0
$751$	−12.4904	−	21.6340i	−0.455780	−	0.789435i	0.542952	−	0.839764i	$-0.317306\pi$
$751$	−12.4904	−	21.6340i	−0.455780	−	0.789435i	−0.998733	+	0.0503286i	$0.983973\pi$
$752$	−0.633975	−	1.09808i	−0.0231187	−	0.0400427i
$753$			4.39230i			0.160064i
$754$	9.00000	+	6.00000i	0.327761	+	0.218507i
$755$		0			0
$756$	4.09808	−	2.36603i	0.149046	−	0.0860515i
$757$	16.2679	−	9.39230i	0.591269	−	0.341369i	−0.174330	−	0.984687i	$-0.555776\pi$
$757$	16.2679	−	9.39230i	0.591269	−	0.341369i	0.765599	+	0.643318i	$0.222443\pi$
$758$	−15.8038	−	9.12436i	−0.574022	−	0.331412i
$759$		−	10.3923i		−	0.377217i
$760$		0			0
$761$	3.80385	+	2.19615i	0.137889	+	0.0796105i	0.567358	−	0.823471i	$-0.307966\pi$
$761$	3.80385	+	2.19615i	0.137889	+	0.0796105i	−0.429468	+	0.903082i	$0.641299\pi$
$762$	4.00000			0.144905
$763$	67.1769	+	38.7846i	2.43197	+	1.40410i
$764$	−10.3923	−	18.0000i	−0.375980	−	0.651217i
$765$		0			0
$766$	11.3205			0.409027
$767$	−27.7128	+	41.5692i	−1.00065	+	1.50098i
$768$			1.00000i			0.0360844i
$769$	29.1962	−	16.8564i	1.05284	−	0.607858i	0.129397	−	0.991593i	$-0.458696\pi$
$769$	29.1962	−	16.8564i	1.05284	−	0.607858i	0.923443	+	0.383735i	$0.125362\pi$
$770$		0			0
$771$	−6.40192	+	11.0885i	−0.230560	+	0.399341i
$772$	−12.8038			−0.460821
$773$	−25.3923	+	43.9808i	−0.913298	+	1.58188i	−0.103923	+	0.994585i	$0.533140\pi$
$773$	−25.3923	+	43.9808i	−0.913298	+	1.58188i	−0.809375	+	0.587293i	$0.800194\pi$
$774$	−5.36603	−	3.09808i	−0.192878	−	0.111358i
$775$		0			0
$776$	3.00000	−	5.19615i	0.107694	−	0.186531i
$777$	12.2942	−	7.09808i	0.441053	−	0.254642i
$778$	−6.69615	−	11.5981i	−0.240069	−	0.415811i
$779$	−0.588457			−0.0210837
$780$		0			0
$781$	38.7846			1.38782
$782$	−5.70577	−	9.88269i	−0.204038	−	0.353404i
$783$	−2.59808	+	1.50000i	−0.0928477	+	0.0536056i
$784$	−7.69615	+	13.3301i	−0.274863	+	0.476076i
$785$		0			0
$786$	14.1962	+	8.19615i	0.506360	+	0.292347i
$787$	−7.26795	+	12.5885i	−0.259074	+	0.448730i	−0.965994	−	0.258564i	$-0.916751\pi$
$787$	−7.26795	+	12.5885i	−0.259074	+	0.448730i	0.706920	+	0.707294i	$0.250084\pi$
$788$	6.92820			0.246807
$789$	1.09808	−	1.90192i	0.0390925	−	0.0677103i
$790$		0			0
$791$	45.8827	−	26.4904i	1.63140	−	0.941890i
$792$			4.73205i			0.168146i
$793$	−14.4115	−	9.60770i	−0.511769	−	0.341179i
$794$	−16.3923			−0.581741
$795$		0			0
$796$	−4.29423	−	7.43782i	−0.152205	−	0.263627i
$797$	5.19615	+	3.00000i	0.184057	+	0.106265i	0.589197	−	0.807989i	$-0.299444\pi$
$797$	5.19615	+	3.00000i	0.184057	+	0.106265i	−0.405140	+	0.914255i	$0.632777\pi$
$798$	−6.00000			−0.212398
$799$	−5.70577	−	3.29423i	−0.201856	−	0.116541i
$800$		0			0
$801$			2.53590i			0.0896016i
$802$	18.1865	+	10.5000i	0.642189	+	0.370768i
$803$	−49.6865	+	28.6865i	−1.75340	+	1.01233i
$804$	9.29423	−	5.36603i	0.327782	−	0.189245i
$805$		0			0
$806$	4.05256	+	8.19615i	0.142745	+	0.288697i
$807$			28.3923i			0.999456i
$808$	0.696152	+	1.20577i	0.0244906	+	0.0424189i
$809$	−23.5981	−	40.8731i	−0.829664	−	1.43702i	−0.898302	−	0.439379i	$-0.855199\pi$
$809$	−23.5981	−	40.8731i	−0.829664	−	1.43702i	0.0686377	−	0.997642i	$-0.478135\pi$
$810$		0			0
$811$		−	4.39230i		−	0.154235i	−0.997022	−	0.0771173i	$-0.975428\pi$
$811$		−	4.39230i		−	0.154235i	0.997022	−	0.0771173i	$-0.0245716\pi$
$812$	7.09808	−	12.2942i	0.249094	−	0.431443i
$813$		0			0
$814$			14.1962i			0.497575i
$815$		0			0
$816$	2.59808	+	4.50000i	0.0909509	+	0.157532i
$817$	3.92820	+	6.80385i	0.137430	+	0.238036i
$818$			3.33975i			0.116771i
$819$	15.2942	−	7.56218i	0.534424	−	0.264244i
$820$		0			0
$821$	35.1962	−	20.3205i	1.22835	−	0.709191i	0.261669	−	0.965158i	$-0.415727\pi$
$821$	35.1962	−	20.3205i	1.22835	−	0.709191i	0.966685	+	0.255967i	$0.0823939\pi$
$822$	−7.79423	+	4.50000i	−0.271855	+	0.156956i
$823$	27.7128	+	16.0000i	0.966008	+	0.557725i	0.898017	−	0.439961i	$-0.145008\pi$
$823$	27.7128	+	16.0000i	0.966008	+	0.557725i	0.0679910	+	0.997686i	$0.478341\pi$
$824$			4.19615i			0.146180i
$825$		0			0
$826$	56.7846	+	32.7846i	1.97579	+	1.14072i
$827$	32.1051			1.11640			0.558202	−	0.829705i	$-0.311491\pi$
$827$	32.1051			1.11640			0.558202	+	0.829705i	$0.311491\pi$
$828$	1.90192	+	1.09808i	0.0660964	+	0.0381608i
$829$	5.99038	+	10.3756i	0.208055	+	0.360361i	0.951102	−	0.308878i	$-0.0999535\pi$
$829$	5.99038	+	10.3756i	0.208055	+	0.360361i	−0.743047	+	0.669239i	$0.766620\pi$
$830$		0			0
$831$	15.1962			0.527149
$832$	−0.232051	+	3.59808i	−0.00804491	+	0.124741i
$833$			79.9808i			2.77117i
$834$	−3.46410	+	2.00000i	−0.119952	+	0.0692543i
$835$		0			0
$836$	3.00000	−	5.19615i	0.103757	−	0.179713i
$837$	−2.53590			−0.0876535
$838$	−8.19615	+	14.1962i	−0.283131	+	0.490398i
$839$	−10.3923	−	6.00000i	−0.358782	−	0.207143i	0.309764	−	0.950813i	$-0.399750\pi$
$839$	−10.3923	−	6.00000i	−0.358782	−	0.207143i	−0.668546	+	0.743670i	$0.733083\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	0.401924	−	0.232051i	0.0138512	−	0.00799700i
$843$	12.2321	+	21.1865i	0.421294	+	0.729703i
$844$	−3.60770			−0.124182
$845$		0			0
$846$	1.26795			0.0435930
$847$	−26.9545	−	46.6865i	−0.926167	−	1.60417i
$848$	−2.59808	+	1.50000i	−0.0892183	+	0.0515102i
$849$	−15.0981	+	26.1506i	−0.518165	+	0.897487i
$850$		0			0
$851$	5.70577	+	3.29423i	0.195591	+	0.112925i
$852$	−4.09808	+	7.09808i	−0.140398	+	0.243176i
$853$	9.00000			0.308154			0.154077	−	0.988059i	$-0.450760\pi$
$853$	9.00000			0.308154			0.154077	+	0.988059i	$0.450760\pi$
$854$	−11.3660	+	19.6865i	−0.388937	+	0.673659i
$855$		0			0
$856$	−7.09808	+	4.09808i	−0.242607	+	0.140069i
$857$			54.3731i			1.85735i	0.370896	+	0.928674i	$0.379051\pi$
$857$			54.3731i			1.85735i	−0.370896	+	0.928674i	$0.620949\pi$
$858$	−1.09808	+	17.0263i	−0.0374877	+	0.581268i
$859$	−10.5885			−0.361273			−0.180637	−	0.983550i	$-0.557816\pi$
$859$	−10.5885			−0.361273			−0.180637	+	0.983550i	$0.557816\pi$
$860$		0			0
$861$	−1.09808	−	1.90192i	−0.0374223	−	0.0648174i
$862$	−24.0788	−	13.9019i	−0.820128	−	0.473501i
$863$	−4.48334			−0.152615			−0.0763073	−	0.997084i	$-0.524313\pi$
$863$	−4.48334			−0.152615			−0.0763073	+	0.997084i	$0.524313\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$		0			0
$866$			33.7846i			1.14805i
$867$	8.66025	+	5.00000i	0.294118	+	0.169809i
$868$	10.3923	−	6.00000i	0.352738	−	0.203653i
$869$	50.7846	−	29.3205i	1.72275	−	0.994630i
$870$		0			0
$871$	34.6865	−	17.1506i	1.17531	−	0.581127i
$872$		−	16.3923i		−	0.555113i
$873$	3.00000	+	5.19615i	0.101535	+	0.175863i
$874$	−1.39230	−	2.41154i	−0.0470954	−	0.0815716i
$875$		0			0
$876$		−	12.1244i		−	0.409644i
$877$	−21.6962	+	37.5788i	−0.732627	+	1.26895i	0.223130	+	0.974789i	$0.428373\pi$
$877$	−21.6962	+	37.5788i	−0.732627	+	1.26895i	−0.955757	+	0.294158i	$0.904961\pi$
$878$	8.29423	−	14.3660i	0.279917	−	0.484830i
$879$		−	14.6603i		−	0.494478i
$880$		0			0
$881$	18.9904	+	32.8923i	0.639802	+	1.10817i	0.985476	+	0.169815i	$0.0543171\pi$
$881$	18.9904	+	32.8923i	0.639802	+	1.10817i	−0.345674	+	0.938355i	$0.612350\pi$
$882$	−7.69615	−	13.3301i	−0.259143	−	0.448849i
$883$		−	24.7846i		−	0.834069i	−0.908891	−	0.417034i	$-0.863070\pi$
$883$		−	24.7846i		−	0.834069i	0.908891	−	0.417034i	$-0.136930\pi$
$884$	8.30385	+	16.7942i	0.279289	+	0.564851i
$885$		0			0
$886$	−3.80385	+	2.19615i	−0.127793	+	0.0737812i
$887$	41.5692	−	24.0000i	1.39576	−	0.805841i	0.401813	−	0.915722i	$-0.368380\pi$
$887$	41.5692	−	24.0000i	1.39576	−	0.805841i	0.993945	+	0.109881i	$0.0350469\pi$
$888$	−2.59808	−	1.50000i	−0.0871857	−	0.0503367i
$889$		−	18.9282i		−	0.634832i
$890$		0			0
$891$	−4.09808	−	2.36603i	−0.137291	−	0.0792648i
$892$	18.9282			0.633763
$893$	−1.39230	−	0.803848i	−0.0465917	−	0.0268997i
$894$	9.06218	+	15.6962i	0.303085	+	0.524958i
$895$		0			0
$896$	4.73205			0.158087
$897$	6.58846	+	4.39230i	0.219982	+	0.146655i
$898$			33.4641i			1.11671i
$899$	−6.58846	+	3.80385i	−0.219737	+	0.126865i
$900$		0			0
$901$	−7.79423	+	13.5000i	−0.259663	+	0.449750i
$902$	2.19615			0.0731239
$903$	−14.6603	+	25.3923i	−0.487863	+	0.845003i
$904$	−9.69615	−	5.59808i	−0.322489	−	0.186189i
$905$		0			0
$906$	−3.63397	+	6.29423i	−0.120731	+	0.209112i
$907$	35.6603	−	20.5885i	1.18408	−	0.683629i	0.227125	−	0.973866i	$-0.427068\pi$
$907$	35.6603	−	20.5885i	1.18408	−	0.683629i	0.956955	+	0.290237i	$0.0937342\pi$
$908$	4.90192	+	8.49038i	0.162676	+	0.281763i
$909$	−1.39230			−0.0461798
$910$		0			0
$911$	37.1769			1.23173			0.615863	−	0.787853i	$-0.288807\pi$
$911$	37.1769			1.23173			0.615863	+	0.787853i	$0.288807\pi$
$912$	0.633975	+	1.09808i	0.0209930	+	0.0363609i
$913$	47.7846	−	27.5885i	1.58144	−	0.913045i
$914$	9.99038	−	17.3038i	0.330452	−	0.572360i
$915$		0			0
$916$	17.1962	+	9.92820i	0.568177	+	0.328037i
$917$	38.7846	−	67.1769i	1.28078	−	2.21838i
$918$	−5.19615			−0.171499
$919$	16.1962	−	28.0526i	0.534262	−	0.925369i	−0.464937	−	0.885344i	$-0.653923\pi$
$919$	16.1962	−	28.0526i	0.534262	−	0.925369i	0.999199	−	0.0400247i	$-0.0127437\pi$
$920$		0			0
$921$	−9.29423	+	5.36603i	−0.306255	+	0.176817i
$922$		−	19.9808i		−	0.658031i
$923$	−16.3923	+	24.5885i	−0.539559	+	0.809339i
$924$	22.3923			0.736653
$925$		0			0
$926$	−13.0981	−	22.6865i	−0.430429	−	0.745526i
$927$	−3.63397	−	2.09808i	−0.119355	−	0.0689099i
$928$	−3.00000			−0.0984798
$929$	29.9711	+	17.3038i	0.983321	+	0.567721i	0.903271	−	0.429070i	$-0.141159\pi$
$929$	29.9711	+	17.3038i	0.983321	+	0.567721i	0.0800501	+	0.996791i	$0.474492\pi$
$930$		0			0
$931$			19.5167i			0.639633i
$932$	15.5885	+	9.00000i	0.510617	+	0.294805i
$933$	−1.90192	+	1.09808i	−0.0622662	+	0.0359494i
$934$	31.6865	−	18.2942i	1.03682	−	0.598605i
$935$		0			0
$936$	−3.00000	−	2.00000i	−0.0980581	−	0.0653720i
$937$			5.39230i			0.176159i	0.996113	+	0.0880795i	$0.0280729\pi$
$937$			5.39230i			0.176159i	−0.996113	+	0.0880795i	$0.971927\pi$
$938$	−25.3923	−	43.9808i	−0.829088	−	1.43602i
$939$	12.1962	+	21.1244i	0.398006	+	0.689367i
$940$		0			0
$941$		−	2.78461i		−	0.0907757i	−0.998969	−	0.0453878i	$-0.985548\pi$
$941$		−	2.78461i		−	0.0907757i	0.998969	−	0.0453878i	$-0.0144524\pi$
$942$	1.59808	−	2.76795i	0.0520681	−	0.0901847i
$943$	0.509619	−	0.882686i	0.0165955	−	0.0287442i
$944$		−	13.8564i		−	0.450988i
$945$		0			0
$946$	−14.6603	−	25.3923i	−0.476646	−	0.825575i
$947$	−21.4641	−	37.1769i	−0.697490	−	1.20809i	−0.969334	−	0.245746i	$-0.920967\pi$
$947$	−21.4641	−	37.1769i	−0.697490	−	1.20809i	0.271845	−	0.962341i	$-0.412366\pi$
$948$			12.3923i			0.402483i
$949$	2.81347	−	43.6244i	0.0913290	−	1.41611i
$950$		0			0
$951$	5.30385	−	3.06218i	0.171989	−	0.0992979i
$952$	21.2942	−	12.2942i	0.690150	−	0.398458i
$953$	20.7846	+	12.0000i	0.673280	+	0.388718i	0.797318	−	0.603559i	$-0.206251\pi$
$953$	20.7846	+	12.0000i	0.673280	+	0.388718i	−0.124039	+	0.992277i	$0.539585\pi$
$954$		−	3.00000i		−	0.0971286i
$955$		0			0
$956$	21.2942	+	12.2942i	0.688705	+	0.397624i
$957$	−14.1962			−0.458896
$958$	30.5885	+	17.6603i	0.988268	+	0.570577i
$959$	21.2942	+	36.8827i	0.687627	+	1.19100i
$960$		0			0
$961$	24.5692			0.792555
$962$	−9.00000	−	6.00000i	−0.290172	−	0.193448i
$963$		−	8.19615i		−	0.264117i
$964$	0.696152	−	0.401924i	0.0224216	−	0.0129451i
$965$		0			0
$966$	5.19615	−	9.00000i	0.167183	−	0.289570i
$967$	−14.8756			−0.478368			−0.239184	−	0.970974i	$-0.576880\pi$
$967$	−14.8756			−0.478368			−0.239184	+	0.970974i	$0.576880\pi$
$968$	−5.69615	+	9.86603i	−0.183081	+	0.317106i
$969$	5.70577	+	3.29423i	0.183296	+	0.105826i
$970$		0			0
$971$	6.58846	−	11.4115i	0.211434	−	0.366214i	−0.740730	−	0.671803i	$-0.765520\pi$
$971$	6.58846	−	11.4115i	0.211434	−	0.366214i	0.952163	+	0.305589i	$0.0988534\pi$
$972$	0.866025	−	0.500000i	0.0277778	−	0.0160375i
$973$	9.46410	+	16.3923i	0.303405	+	0.525513i
$974$	−9.12436			−0.292363
$975$		0			0
$976$	4.80385			0.153767
$977$	8.42820	+	14.5981i	0.269642	+	0.467034i	0.968769	−	0.247963i	$-0.0797613\pi$
$977$	8.42820	+	14.5981i	0.269642	+	0.467034i	−0.699127	+	0.714997i	$0.746428\pi$
$978$	−8.19615	+	4.73205i	−0.262084	+	0.151314i
$979$	−6.00000	+	10.3923i	−0.191761	+	0.332140i
$980$		0			0
$981$	14.1962	+	8.19615i	0.453248	+	0.261683i
$982$	−0.294229	+	0.509619i	−0.00938921	+	0.0162626i
$983$	−20.7846			−0.662926			−0.331463	−	0.943468i	$-0.607542\pi$
$983$	−20.7846			−0.662926			−0.331463	+	0.943468i	$0.607542\pi$
$984$	−0.232051	+	0.401924i	−0.00739751	+	0.0128129i
$985$		0			0
$986$	−13.5000	+	7.79423i	−0.429928	+	0.248219i
$987$		−	6.00000i		−	0.190982i
$988$	2.02628	+	4.09808i	0.0644645	+	0.130377i
$989$	−13.6077			−0.432700
$990$		0			0
$991$	−14.6865	−	25.4378i	−0.466533	−	0.808059i	0.532736	−	0.846281i	$-0.321164\pi$
$991$	−14.6865	−	25.4378i	−0.466533	−	0.808059i	−0.999269	+	0.0382223i	$0.987830\pi$
$992$	−2.19615	−	1.26795i	−0.0697279	−	0.0402574i
$993$	12.0000			0.380808
$994$	33.5885	+	19.3923i	1.06536	+	0.615087i
$995$		0			0
$996$			11.6603i			0.369469i
$997$	−11.4282	−	6.59808i	−0.361935	−	0.208963i	0.307994	−	0.951388i	$-0.400342\pi$
$997$	−11.4282	−	6.59808i	−0.361935	−	0.208963i	−0.669929	+	0.742425i	$0.733676\pi$
$998$		0			0
$999$	2.59808	−	1.50000i	0.0821995	−	0.0474579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.y.h.49.2		4
5.2	odd	4		1950.2.bc.c.751.1		4
5.3	odd	4		78.2.i.b.49.2	yes	4
5.4	even	2		1950.2.y.a.49.1		4
13.4	even	6		1950.2.y.a.199.1		4
15.8	even	4		234.2.l.a.127.1		4
20.3	even	4		624.2.bv.d.49.2		4
60.23	odd	4		1872.2.by.k.1297.2		4
65.3	odd	12		1014.2.b.d.337.4		4
65.4	even	6	inner	1950.2.y.h.199.2		4
65.8	even	4		1014.2.e.j.991.1		4
65.17	odd	12		1950.2.bc.c.901.1		4
65.18	even	4		1014.2.e.h.991.2		4
65.23	odd	12		1014.2.b.d.337.1		4
65.28	even	12		1014.2.a.j.1.2		2
65.33	even	12		1014.2.e.j.529.1		4
65.38	odd	4		1014.2.i.f.361.1		4
65.43	odd	12		78.2.i.b.43.2	✓	4
65.48	odd	12		1014.2.i.f.823.1		4
65.58	even	12		1014.2.e.h.529.2		4
65.63	even	12		1014.2.a.h.1.1		2
195.23	even	12		3042.2.b.l.1351.4		4
195.68	even	12		3042.2.b.l.1351.1		4
195.128	odd	12		3042.2.a.v.1.2		2
195.158	odd	12		3042.2.a.s.1.1		2
195.173	even	12		234.2.l.a.199.1		4
260.43	even	12		624.2.bv.d.433.2		4
260.63	odd	12		8112.2.a.bq.1.1		2
260.223	odd	12		8112.2.a.bx.1.2		2
780.563	odd	12		1872.2.by.k.433.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.b.43.2	✓	4	65.43	odd	12
78.2.i.b.49.2	yes	4	5.3	odd	4
234.2.l.a.127.1		4	15.8	even	4
234.2.l.a.199.1		4	195.173	even	12
624.2.bv.d.49.2		4	20.3	even	4
624.2.bv.d.433.2		4	260.43	even	12
1014.2.a.h.1.1		2	65.63	even	12
1014.2.a.j.1.2		2	65.28	even	12
1014.2.b.d.337.1		4	65.23	odd	12
1014.2.b.d.337.4		4	65.3	odd	12
1014.2.e.h.529.2		4	65.58	even	12
1014.2.e.h.991.2		4	65.18	even	4
1014.2.e.j.529.1		4	65.33	even	12
1014.2.e.j.991.1		4	65.8	even	4
1014.2.i.f.361.1		4	65.38	odd	4
1014.2.i.f.823.1		4	65.48	odd	12
1872.2.by.k.433.2		4	780.563	odd	12
1872.2.by.k.1297.2		4	60.23	odd	4
1950.2.y.a.49.1		4	5.4	even	2
1950.2.y.a.199.1		4	13.4	even	6
1950.2.y.h.49.2		4	1.1	even	1	trivial
1950.2.y.h.199.2		4	65.4	even	6	inner
1950.2.bc.c.751.1		4	5.2	odd	4
1950.2.bc.c.901.1		4	65.17	odd	12
3042.2.a.s.1.1		2	195.158	odd	12
3042.2.a.v.1.2		2	195.128	odd	12
3042.2.b.l.1351.1		4	195.68	even	12
3042.2.b.l.1351.4		4	195.23	even	12
8112.2.a.bq.1.1		2	260.63	odd	12
8112.2.a.bx.1.2		2	260.223	odd	12

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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.y (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(2.36603 - 4.09808i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(2.36603 - 4.09808i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(4.09808 - 2.36603i) q^{11} +1.00000i q^{12} +(-0.232051 + 3.59808i) q^{13} +4.73205 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.50000 - 2.59808i) q^{17} +1.00000 q^{18} +(-1.09808 - 0.633975i) q^{19} -4.73205i q^{21} +(4.09808 + 2.36603i) q^{22} +(1.90192 - 1.09808i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-3.23205 + 1.59808i) q^{26} -1.00000i q^{27} +(2.36603 + 4.09808i) q^{28} +(-1.50000 - 2.59808i) q^{29} -2.53590i q^{31} +(0.500000 - 0.866025i) q^{32} +(2.36603 - 4.09808i) q^{33} -5.19615i q^{34} +(0.500000 + 0.866025i) q^{36} +(1.50000 + 2.59808i) q^{37} -1.26795i q^{38} +(1.59808 + 3.23205i) q^{39} +(0.401924 - 0.232051i) q^{41} +(4.09808 - 2.36603i) q^{42} +(-5.36603 - 3.09808i) q^{43} +4.73205i q^{44} +(1.90192 + 1.09808i) q^{46} +1.26795 q^{47} +(-0.866025 - 0.500000i) q^{48} +(-7.69615 - 13.3301i) q^{49} -5.19615 q^{51} +(-3.00000 - 2.00000i) q^{52} -3.00000i q^{53} +(0.866025 - 0.500000i) q^{54} +(-2.36603 + 4.09808i) q^{56} -1.26795 q^{57} +(1.50000 - 2.59808i) q^{58} +(12.0000 + 6.92820i) q^{59} +(-2.40192 + 4.16025i) q^{61} +(2.19615 - 1.26795i) q^{62} +(-2.36603 - 4.09808i) q^{63} +1.00000 q^{64} +4.73205 q^{66} +(-5.36603 - 9.29423i) q^{67} +(4.50000 - 2.59808i) q^{68} +(1.09808 - 1.90192i) q^{69} +(7.09808 + 4.09808i) q^{71} +(-0.500000 + 0.866025i) q^{72} -12.1244 q^{73} +(-1.50000 + 2.59808i) q^{74} +(1.09808 - 0.633975i) q^{76} -22.3923i q^{77} +(-2.00000 + 3.00000i) q^{78} +12.3923 q^{79} +(-0.500000 - 0.866025i) q^{81} +(0.401924 + 0.232051i) q^{82} +11.6603 q^{83} +(4.09808 + 2.36603i) q^{84} -6.19615i q^{86} +(-2.59808 - 1.50000i) q^{87} +(-4.09808 + 2.36603i) q^{88} +(-2.19615 + 1.26795i) q^{89} +(14.1962 + 9.46410i) q^{91} +2.19615i q^{92} +(-1.26795 - 2.19615i) q^{93} +(0.633975 + 1.09808i) q^{94} -1.00000i q^{96} +(-3.00000 + 5.19615i) q^{97} +(7.69615 - 13.3301i) q^{98} -4.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 6 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 6 * q^7 - 4 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{4} + 6 q^{7} - 4 q^{8} + 2 q^{9} + 6 q^{11} + 6 q^{13} + 12 q^{14} - 2 q^{16} - 18 q^{17} + 4 q^{18} + 6 q^{19} + 6 q^{22} + 18 q^{23} - 6 q^{26} + 6 q^{28} - 6 q^{29} + 2 q^{32} + 6 q^{33} + 2 q^{36} + 6 q^{37} - 4 q^{39} + 12 q^{41} + 6 q^{42} - 18 q^{43} + 18 q^{46} + 12 q^{47} - 10 q^{49} - 12 q^{52} - 6 q^{56} - 12 q^{57} + 6 q^{58} + 48 q^{59} - 20 q^{61} - 12 q^{62} - 6 q^{63} + 4 q^{64} + 12 q^{66} - 18 q^{67} + 18 q^{68} - 6 q^{69} + 18 q^{71} - 2 q^{72} - 6 q^{74} - 6 q^{76} - 8 q^{78} + 8 q^{79} - 2 q^{81} + 12 q^{82} + 12 q^{83} + 6 q^{84} - 6 q^{88} + 12 q^{89} + 36 q^{91} - 12 q^{93} + 6 q^{94} - 12 q^{97} + 10 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 6 * q^7 - 4 * q^8 + 2 * q^9 + 6 * q^11 + 6 * q^13 + 12 * q^14 - 2 * q^16 - 18 * q^17 + 4 * q^18 + 6 * q^19 + 6 * q^22 + 18 * q^23 - 6 * q^26 + 6 * q^28 - 6 * q^29 + 2 * q^32 + 6 * q^33 + 2 * q^36 + 6 * q^37 - 4 * q^39 + 12 * q^41 + 6 * q^42 - 18 * q^43 + 18 * q^46 + 12 * q^47 - 10 * q^49 - 12 * q^52 - 6 * q^56 - 12 * q^57 + 6 * q^58 + 48 * q^59 - 20 * q^61 - 12 * q^62 - 6 * q^63 + 4 * q^64 + 12 * q^66 - 18 * q^67 + 18 * q^68 - 6 * q^69 + 18 * q^71 - 2 * q^72 - 6 * q^74 - 6 * q^76 - 8 * q^78 + 8 * q^79 - 2 * q^81 + 12 * q^82 + 12 * q^83 + 6 * q^84 - 6 * q^88 + 12 * q^89 + 36 * q^91 - 12 * q^93 + 6 * q^94 - 12 * q^97 + 10 * q^98

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