LMFDB - Embedded newform 975.2.i.j.451.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(451,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("975.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.i (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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
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:	$ 3 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	975.451
Dual form			975.2.i.j.601.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 - 0.633975i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.732051 + 1.26795i) q^{4} +(-0.366025 - 0.633975i) q^{6} +(-0.866025 - 1.50000i) q^{7} +2.53590 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.366025 - 0.633975i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.732051 + 1.26795i) q^{4} +(-0.366025 - 0.633975i) q^{6} +(-0.866025 - 1.50000i) q^{7} +2.53590 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} +1.46410 q^{12} +(1.59808 - 3.23205i) q^{13} -1.26795 q^{14} +(-0.535898 + 0.928203i) q^{16} +(0.366025 + 0.633975i) q^{17} -0.732051 q^{18} +(0.267949 + 0.464102i) q^{19} -1.73205 q^{21} +(-0.732051 - 1.26795i) q^{22} +(1.00000 - 1.73205i) q^{23} +(1.26795 - 2.19615i) q^{24} +(-1.46410 - 2.19615i) q^{26} -1.00000 q^{27} +(1.26795 - 2.19615i) q^{28} +(1.63397 - 2.83013i) q^{29} +4.46410 q^{31} +(2.92820 + 5.07180i) q^{32} +(-1.00000 - 1.73205i) q^{33} +0.535898 q^{34} +(0.732051 - 1.26795i) q^{36} +(-5.19615 + 9.00000i) q^{37} +0.392305 q^{38} +(-2.00000 - 3.00000i) q^{39} +(5.36603 - 9.29423i) q^{41} +(-0.633975 + 1.09808i) q^{42} +(-4.59808 - 7.96410i) q^{43} +2.92820 q^{44} +(-0.732051 - 1.26795i) q^{46} -0.196152 q^{47} +(0.535898 + 0.928203i) q^{48} +(2.00000 - 3.46410i) q^{49} +0.732051 q^{51} +(5.26795 - 0.339746i) q^{52} +9.46410 q^{53} +(-0.366025 + 0.633975i) q^{54} +(-2.19615 - 3.80385i) q^{56} +0.535898 q^{57} +(-1.19615 - 2.07180i) q^{58} +(5.83013 + 10.0981i) q^{59} +(-2.69615 - 4.66987i) q^{61} +(1.63397 - 2.83013i) q^{62} +(-0.866025 + 1.50000i) q^{63} +2.14359 q^{64} -1.46410 q^{66} +(-4.59808 + 7.96410i) q^{67} +(-0.535898 + 0.928203i) q^{68} +(-1.00000 - 1.73205i) q^{69} +(2.36603 + 4.09808i) q^{71} +(-1.26795 - 2.19615i) q^{72} -1.73205 q^{73} +(3.80385 + 6.58846i) q^{74} +(-0.392305 + 0.679492i) q^{76} -3.46410 q^{77} +(-2.63397 + 0.169873i) q^{78} -11.0000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-3.92820 - 6.80385i) q^{82} -2.92820 q^{83} +(-1.26795 - 2.19615i) q^{84} -6.73205 q^{86} +(-1.63397 - 2.83013i) q^{87} +(2.53590 - 4.39230i) q^{88} +(-2.63397 + 4.56218i) q^{89} +(-6.23205 + 0.401924i) q^{91} +2.92820 q^{92} +(2.23205 - 3.86603i) q^{93} +(-0.0717968 + 0.124356i) q^{94} +5.85641 q^{96} +(2.59808 + 4.50000i) q^{97} +(-1.46410 - 2.53590i) q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 4 q^{4} + 2 q^{6} + 24 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 4 * q^4 + 2 * q^6 + 24 * q^8 - 2 * q^9	$ 4 q - 2 q^{2} + 2 q^{3} - 4 q^{4} + 2 q^{6} + 24 q^{8} - 2 q^{9} + 4 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{16} - 2 q^{17} + 4 q^{18} + 8 q^{19} + 4 q^{22} + 4 q^{23} + 12 q^{24} + 8 q^{26} - 4 q^{27} + 12 q^{28} + 10 q^{29} + 4 q^{31} - 16 q^{32} - 4 q^{33} + 16 q^{34} - 4 q^{36} - 40 q^{38} - 8 q^{39} + 18 q^{41} - 6 q^{42} - 8 q^{43} - 16 q^{44} + 4 q^{46} + 20 q^{47} + 16 q^{48} + 8 q^{49} - 4 q^{51} + 28 q^{52} + 24 q^{53} + 2 q^{54} + 12 q^{56} + 16 q^{57} + 16 q^{58} + 6 q^{59} + 10 q^{61} + 10 q^{62} + 64 q^{64} + 8 q^{66} - 8 q^{67} - 16 q^{68} - 4 q^{69} + 6 q^{71} - 12 q^{72} + 36 q^{74} + 40 q^{76} - 14 q^{78} - 44 q^{79} - 2 q^{81} + 12 q^{82} + 16 q^{83} - 12 q^{84} - 20 q^{86} - 10 q^{87} + 24 q^{88} - 14 q^{89} - 18 q^{91} - 16 q^{92} + 2 q^{93} - 28 q^{94} - 32 q^{96} + 8 q^{98} - 8 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 - 4 * q^4 + 2 * q^6 + 24 * q^8 - 2 * q^9 + 4 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^16 - 2 * q^17 + 4 * q^18 + 8 * q^19 + 4 * q^22 + 4 * q^23 + 12 * q^24 + 8 * q^26 - 4 * q^27 + 12 * q^28 + 10 * q^29 + 4 * q^31 - 16 * q^32 - 4 * q^33 + 16 * q^34 - 4 * q^36 - 40 * q^38 - 8 * q^39 + 18 * q^41 - 6 * q^42 - 8 * q^43 - 16 * q^44 + 4 * q^46 + 20 * q^47 + 16 * q^48 + 8 * q^49 - 4 * q^51 + 28 * q^52 + 24 * q^53 + 2 * q^54 + 12 * q^56 + 16 * q^57 + 16 * q^58 + 6 * q^59 + 10 * q^61 + 10 * q^62 + 64 * q^64 + 8 * q^66 - 8 * q^67 - 16 * q^68 - 4 * q^69 + 6 * q^71 - 12 * q^72 + 36 * q^74 + 40 * q^76 - 14 * q^78 - 44 * q^79 - 2 * q^81 + 12 * q^82 + 16 * q^83 - 12 * q^84 - 20 * q^86 - 10 * q^87 + 24 * q^88 - 14 * q^89 - 18 * q^91 - 16 * q^92 + 2 * q^93 - 28 * q^94 - 32 * q^96 + 8 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	0.366025	−	0.633975i	0.258819	−	0.448288i	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	0.366025	−	0.633975i	0.258819	−	0.448288i	0.965926	+	0.258819i	$0.0833333\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.732051	+	1.26795i	0.366025	+	0.633975i
$5$		0			0
$5$		0			0
$6$	−0.366025	−	0.633975i	−0.149429	−	0.258819i
$7$	−0.866025	−	1.50000i	−0.327327	−	0.566947i	0.654654	−	0.755929i	$-0.272814\pi$
$7$	−0.866025	−	1.50000i	−0.327327	−	0.566947i	−0.981981	+	0.188982i	$0.939481\pi$
$8$	2.53590			0.896575
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$	1.46410			0.422650
$13$	1.59808	−	3.23205i	0.443227	−	0.896410i
$13$	1.59808	−	3.23205i	0.443227	−	0.896410i
$14$	−1.26795			−0.338874
$15$		0			0
$16$	−0.535898	+	0.928203i	−0.133975	+	0.232051i
$17$	0.366025	+	0.633975i	0.0887742	+	0.153761i	0.906993	−	0.421145i	$-0.138372\pi$
$17$	0.366025	+	0.633975i	0.0887742	+	0.153761i	−0.818219	+	0.574907i	$0.805038\pi$
$18$	−0.732051			−0.172546
$19$	0.267949	+	0.464102i	0.0614718	+	0.106472i	0.895123	−	0.445818i	$-0.147087\pi$
$19$	0.267949	+	0.464102i	0.0614718	+	0.106472i	−0.833652	+	0.552291i	$0.813754\pi$
$20$		0			0
$21$	−1.73205			−0.377964
$22$	−0.732051	−	1.26795i	−0.156074	−	0.270328i
$23$	1.00000	−	1.73205i	0.208514	−	0.361158i	−0.742732	−	0.669588i	$-0.766471\pi$
$23$	1.00000	−	1.73205i	0.208514	−	0.361158i	0.951247	+	0.308431i	$0.0998038\pi$
$24$	1.26795	−	2.19615i	0.258819	−	0.448288i
$25$		0			0
$26$	−1.46410	−	2.19615i	−0.287134	−	0.430701i
$27$	−1.00000			−0.192450
$28$	1.26795	−	2.19615i	0.239620	−	0.415034i
$29$	1.63397	−	2.83013i	0.303421	−	0.525541i	−0.673487	−	0.739199i	$-0.735204\pi$
$29$	1.63397	−	2.83013i	0.303421	−	0.525541i	0.976909	+	0.213658i	$0.0685377\pi$
$30$		0			0
$31$	4.46410			0.801776			0.400888	−	0.916127i	$-0.368702\pi$
$31$	4.46410			0.801776			0.400888	+	0.916127i	$0.368702\pi$
$32$	2.92820	+	5.07180i	0.517638	+	0.896575i
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$	0.535898			0.0919058
$35$		0			0
$36$	0.732051	−	1.26795i	0.122008	−	0.211325i
$37$	−5.19615	+	9.00000i	−0.854242	+	1.47959i	0.0231041	+	0.999733i	$0.492645\pi$
$37$	−5.19615	+	9.00000i	−0.854242	+	1.47959i	−0.877346	+	0.479858i	$0.840688\pi$
$38$	0.392305			0.0636402
$39$	−2.00000	−	3.00000i	−0.320256	−	0.480384i
$40$		0			0
$41$	5.36603	−	9.29423i	0.838032	−	1.45151i	−0.0535050	−	0.998568i	$-0.517039\pi$
$41$	5.36603	−	9.29423i	0.838032	−	1.45151i	0.891537	−	0.452947i	$-0.149627\pi$
$42$	−0.633975	+	1.09808i	−0.0978244	+	0.169437i
$43$	−4.59808	−	7.96410i	−0.701200	−	1.21451i	−0.968045	−	0.250775i	$-0.919315\pi$
$43$	−4.59808	−	7.96410i	−0.701200	−	1.21451i	0.266845	−	0.963739i	$-0.414019\pi$
$44$	2.92820			0.441443
$45$		0			0
$46$	−0.732051	−	1.26795i	−0.107935	−	0.186949i
$47$	−0.196152			−0.0286118			−0.0143059	−	0.999898i	$-0.504554\pi$
$47$	−0.196152			−0.0286118			−0.0143059	+	0.999898i	$0.504554\pi$
$48$	0.535898	+	0.928203i	0.0773503	+	0.133975i
$49$	2.00000	−	3.46410i	0.285714	−	0.494872i
$50$		0			0
$51$	0.732051			0.102508
$52$	5.26795	−	0.339746i	0.730533	−	0.0471143i
$53$	9.46410			1.29999			0.649997	−	0.759937i	$-0.274770\pi$
$53$	9.46410			1.29999			0.649997	+	0.759937i	$0.274770\pi$
$54$	−0.366025	+	0.633975i	−0.0498097	+	0.0862730i
$55$		0			0
$56$	−2.19615	−	3.80385i	−0.293473	−	0.508311i
$57$	0.535898			0.0709815
$58$	−1.19615	−	2.07180i	−0.157063	−	0.272040i
$59$	5.83013	+	10.0981i	0.759018	+	1.31466i	0.943352	+	0.331794i	$0.107654\pi$
$59$	5.83013	+	10.0981i	0.759018	+	1.31466i	−0.184334	+	0.982864i	$0.559013\pi$
$60$		0			0
$61$	−2.69615	−	4.66987i	−0.345207	−	0.597916i	0.640184	−	0.768221i	$-0.278858\pi$
$61$	−2.69615	−	4.66987i	−0.345207	−	0.597916i	−0.985391	+	0.170305i	$0.945525\pi$
$62$	1.63397	−	2.83013i	0.207515	−	0.359426i
$63$	−0.866025	+	1.50000i	−0.109109	+	0.188982i
$64$	2.14359			0.267949
$65$		0			0
$66$	−1.46410			−0.180218
$67$	−4.59808	+	7.96410i	−0.561744	+	0.972970i	0.435600	+	0.900140i	$0.356536\pi$
$67$	−4.59808	+	7.96410i	−0.561744	+	0.972970i	−0.997344	+	0.0728295i	$0.976797\pi$
$68$	−0.535898	+	0.928203i	−0.0649872	+	0.112561i
$69$	−1.00000	−	1.73205i	−0.120386	−	0.208514i
$70$		0			0
$71$	2.36603	+	4.09808i	0.280796	+	0.486352i	0.971581	−	0.236708i	$-0.0760684\pi$
$71$	2.36603	+	4.09808i	0.280796	+	0.486352i	−0.690785	+	0.723060i	$0.742735\pi$
$72$	−1.26795	−	2.19615i	−0.149429	−	0.258819i
$73$	−1.73205			−0.202721			−0.101361	−	0.994850i	$-0.532320\pi$
$73$	−1.73205			−0.202721			−0.101361	+	0.994850i	$0.532320\pi$
$74$	3.80385	+	6.58846i	0.442188	+	0.765893i
$75$		0			0
$76$	−0.392305	+	0.679492i	−0.0450005	+	0.0779431i
$77$	−3.46410			−0.394771
$78$	−2.63397	+	0.169873i	−0.298239	+	0.0192343i
$79$	−11.0000			−1.23760			−0.618798	−	0.785550i	$-0.712380\pi$
$79$	−11.0000			−1.23760			−0.618798	+	0.785550i	$0.712380\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.92820	−	6.80385i	−0.433797	−	0.751359i
$83$	−2.92820			−0.321412			−0.160706	−	0.987002i	$-0.551377\pi$
$83$	−2.92820			−0.321412			−0.160706	+	0.987002i	$0.551377\pi$
$84$	−1.26795	−	2.19615i	−0.138345	−	0.239620i
$85$		0			0
$86$	−6.73205			−0.725936
$87$	−1.63397	−	2.83013i	−0.175180	−	0.303421i
$88$	2.53590	−	4.39230i	0.270328	−	0.468221i
$89$	−2.63397	+	4.56218i	−0.279201	+	0.483590i	−0.971186	−	0.238321i	$-0.923403\pi$
$89$	−2.63397	+	4.56218i	−0.279201	+	0.483590i	0.691986	+	0.721911i	$0.256736\pi$
$90$		0			0
$91$	−6.23205	+	0.401924i	−0.653296	+	0.0421331i
$92$	2.92820			0.305286
$93$	2.23205	−	3.86603i	0.231453	−	0.400888i
$94$	−0.0717968	+	0.124356i	−0.00740527	+	0.0128263i
$95$		0			0
$96$	5.85641			0.597717
$97$	2.59808	+	4.50000i	0.263795	+	0.456906i	0.967247	−	0.253837i	$-0.0816925\pi$
$97$	2.59808	+	4.50000i	0.263795	+	0.456906i	−0.703452	+	0.710742i	$0.748359\pi$
$98$	−1.46410	−	2.53590i	−0.147897	−	0.256164i
$99$	−2.00000			−0.201008
$100$		0			0
$101$	−5.19615	+	9.00000i	−0.517036	+	0.895533i	0.482768	+	0.875748i	$0.339632\pi$
$101$	−5.19615	+	9.00000i	−0.517036	+	0.895533i	−0.999804	+	0.0197851i	$0.993702\pi$
$102$	0.267949	−	0.464102i	0.0265309	−	0.0459529i
$103$	−5.73205			−0.564796			−0.282398	−	0.959297i	$-0.591130\pi$
$103$	−5.73205			−0.564796			−0.282398	+	0.959297i	$0.591130\pi$
$104$	4.05256	−	8.19615i	0.397386	−	0.803699i
$105$		0			0
$106$	3.46410	−	6.00000i	0.336463	−	0.582772i
$107$	4.09808	−	7.09808i	0.396176	−	0.686197i	−0.597075	−	0.802186i	$-0.703670\pi$
$107$	4.09808	−	7.09808i	0.396176	−	0.686197i	0.993251	+	0.115989i	$0.0370037\pi$
$108$	−0.732051	−	1.26795i	−0.0704416	−	0.122008i
$109$	−15.3923			−1.47432			−0.737158	−	0.675721i	$-0.763833\pi$
$109$	−15.3923			−1.47432			−0.737158	+	0.675721i	$0.763833\pi$
$110$		0			0
$111$	5.19615	+	9.00000i	0.493197	+	0.854242i
$112$	1.85641			0.175414
$113$	9.19615	+	15.9282i	0.865101	+	1.49840i	0.866947	+	0.498401i	$0.166079\pi$
$113$	9.19615	+	15.9282i	0.865101	+	1.49840i	−0.00184536	+	0.999998i	$0.500587\pi$
$114$	0.196152	−	0.339746i	0.0183714	−	0.0318201i
$115$		0			0
$116$	4.78461			0.444240
$117$	−3.59808	+	0.232051i	−0.332642	+	0.0214531i
$118$	8.53590			0.785793
$119$	0.633975	−	1.09808i	0.0581164	−	0.100660i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−3.94744			−0.357385
$123$	−5.36603	−	9.29423i	−0.483838	−	0.838032i
$124$	3.26795	+	5.66025i	0.293471	+	0.508306i
$125$		0			0
$126$	0.633975	+	1.09808i	0.0564789	+	0.0978244i
$127$	−0.330127	+	0.571797i	−0.0292940	+	0.0507388i	−0.880301	−	0.474416i	$-0.842659\pi$
$127$	−0.330127	+	0.571797i	−0.0292940	+	0.0507388i	0.851007	+	0.525155i	$0.175993\pi$
$128$	−5.07180	+	8.78461i	−0.448288	+	0.776457i
$129$	−9.19615			−0.809676
$130$		0			0
$131$	−2.19615			−0.191879			−0.0959394	−	0.995387i	$-0.530585\pi$
$131$	−2.19615			−0.191879			−0.0959394	+	0.995387i	$0.530585\pi$
$132$	1.46410	−	2.53590i	0.127434	−	0.220722i
$133$	0.464102	−	0.803848i	0.0402427	−	0.0697024i
$134$	3.36603	+	5.83013i	0.290780	+	0.503646i
$135$		0			0
$136$	0.928203	+	1.60770i	0.0795928	+	0.137859i
$137$	−5.83013	−	10.0981i	−0.498101	−	0.862737i	0.501896	−	0.864928i	$-0.332636\pi$
$137$	−5.83013	−	10.0981i	−0.498101	−	0.862737i	−0.999998	+	0.00219097i	$0.999303\pi$
$138$	−1.46410			−0.124633
$139$	−9.96410	−	17.2583i	−0.845144	−	1.46383i	−0.885496	−	0.464647i	$-0.846181\pi$
$139$	−9.96410	−	17.2583i	−0.845144	−	1.46383i	0.0403520	−	0.999186i	$-0.487152\pi$
$140$		0			0
$141$	−0.0980762	+	0.169873i	−0.00825951	+	0.0143059i
$142$	3.46410			0.290701
$143$	−4.00000	−	6.00000i	−0.334497	−	0.501745i
$144$	1.07180			0.0893164
$145$		0			0
$146$	−0.633975	+	1.09808i	−0.0524681	+	0.0908774i
$147$	−2.00000	−	3.46410i	−0.164957	−	0.285714i
$148$	−15.2154			−1.25070
$149$	2.92820	+	5.07180i	0.239888	+	0.415498i	0.960682	−	0.277651i	$-0.0895560\pi$
$149$	2.92820	+	5.07180i	0.239888	+	0.415498i	−0.720794	+	0.693149i	$0.756223\pi$
$150$		0			0
$151$	−0.928203			−0.0755361			−0.0377681	−	0.999287i	$-0.512025\pi$
$151$	−0.928203			−0.0755361			−0.0377681	+	0.999287i	$0.512025\pi$
$152$	0.679492	+	1.17691i	0.0551141	+	0.0954604i
$153$	0.366025	−	0.633975i	0.0295914	−	0.0512538i
$154$	−1.26795	+	2.19615i	−0.102174	+	0.176971i
$155$		0			0
$156$	2.33975	−	4.73205i	0.187330	−	0.378867i
$157$	3.73205			0.297850			0.148925	−	0.988848i	$-0.452419\pi$
$157$	3.73205			0.297850			0.148925	+	0.988848i	$0.452419\pi$
$158$	−4.02628	+	6.97372i	−0.320314	+	0.554799i
$159$	4.73205	−	8.19615i	0.375276	−	0.649997i
$160$		0			0
$161$	−3.46410			−0.273009
$162$	0.366025	+	0.633975i	0.0287577	+	0.0498097i
$163$	10.5981	+	18.3564i	0.830105	+	1.43778i	0.897954	+	0.440089i	$0.145053\pi$
$163$	10.5981	+	18.3564i	0.830105	+	1.43778i	−0.0678487	+	0.997696i	$0.521614\pi$
$164$	15.7128			1.22696
$165$		0			0
$166$	−1.07180	+	1.85641i	−0.0831876	+	0.144085i
$167$	−10.9282	+	18.9282i	−0.845650	+	1.46471i	0.0394060	+	0.999223i	$0.487453\pi$
$167$	−10.9282	+	18.9282i	−0.845650	+	1.46471i	−0.885056	+	0.465485i	$0.845880\pi$
$168$	−4.39230			−0.338874
$169$	−7.89230	−	10.3301i	−0.607100	−	0.794625i
$170$		0			0
$171$	0.267949	−	0.464102i	0.0204906	−	0.0354907i
$172$	6.73205	−	11.6603i	0.513314	−	0.889086i
$173$	6.09808	+	10.5622i	0.463628	+	0.803028i	0.999138	−	0.0415012i	$-0.0132140\pi$
$173$	6.09808	+	10.5622i	0.463628	+	0.803028i	−0.535510	+	0.844529i	$0.679881\pi$
$174$	−2.39230			−0.181360
$175$		0			0
$176$	1.07180	+	1.85641i	0.0807897	+	0.139932i
$177$	11.6603			0.876438
$178$	1.92820	+	3.33975i	0.144525	+	0.250325i
$179$	−8.83013	+	15.2942i	−0.659995	+	1.14314i	0.320622	+	0.947207i	$0.396108\pi$
$179$	−8.83013	+	15.2942i	−0.659995	+	1.14314i	−0.980616	+	0.195937i	$0.937225\pi$
$180$		0			0
$181$	8.39230			0.623795			0.311898	−	0.950116i	$-0.399035\pi$
$181$	8.39230			0.623795			0.311898	+	0.950116i	$0.399035\pi$
$182$	−2.02628	+	4.09808i	−0.150198	+	0.303770i
$183$	−5.39230			−0.398611
$184$	2.53590	−	4.39230i	0.186949	−	0.323805i
$185$		0			0
$186$	−1.63397	−	2.83013i	−0.119809	−	0.207515i
$187$	1.46410			0.107066
$188$	−0.143594	−	0.248711i	−0.0104726	−	0.0181391i
$189$	0.866025	+	1.50000i	0.0629941	+	0.109109i
$190$		0			0
$191$	−11.2942	−	19.5622i	−0.817222	−	1.41547i	−0.907722	−	0.419573i	$-0.862180\pi$
$191$	−11.2942	−	19.5622i	−0.817222	−	1.41547i	0.0904999	−	0.995896i	$-0.471154\pi$
$192$	1.07180	−	1.85641i	0.0773503	−	0.133975i
$193$	−9.59808	+	16.6244i	−0.690885	+	1.19665i	0.280664	+	0.959806i	$0.409445\pi$
$193$	−9.59808	+	16.6244i	−0.690885	+	1.19665i	−0.971548	+	0.236841i	$0.923888\pi$
$194$	3.80385			0.273100
$195$		0			0
$196$	5.85641			0.418315
$197$	8.19615	−	14.1962i	0.583952	−	1.01143i	−0.411054	−	0.911611i	$-0.634839\pi$
$197$	8.19615	−	14.1962i	0.583952	−	1.01143i	0.995005	−	0.0998228i	$-0.0318276\pi$
$198$	−0.732051	+	1.26795i	−0.0520246	+	0.0901092i
$199$	12.4282	+	21.5263i	0.881012	+	1.52596i	0.850217	+	0.526432i	$0.176470\pi$
$199$	12.4282	+	21.5263i	0.881012	+	1.52596i	0.0307946	+	0.999526i	$0.490196\pi$
$200$		0			0
$201$	4.59808	+	7.96410i	0.324323	+	0.561744i
$202$	3.80385	+	6.58846i	0.267638	+	0.463562i
$203$	−5.66025			−0.397272
$204$	0.535898	+	0.928203i	0.0375204	+	0.0649872i
$205$		0			0
$206$	−2.09808	+	3.63397i	−0.146180	+	0.253191i
$207$	−2.00000			−0.139010
$208$	2.14359	+	3.21539i	0.148631	+	0.222947i
$209$	1.07180			0.0741377
$210$		0			0
$211$	−11.1603	+	19.3301i	−0.768304	+	1.33074i	0.170179	+	0.985413i	$0.445566\pi$
$211$	−11.1603	+	19.3301i	−0.768304	+	1.33074i	−0.938482	+	0.345328i	$0.887768\pi$
$212$	6.92820	+	12.0000i	0.475831	+	0.824163i
$213$	4.73205			0.324235
$214$	−3.00000	−	5.19615i	−0.205076	−	0.355202i
$215$		0			0
$216$	−2.53590			−0.172546
$217$	−3.86603	−	6.69615i	−0.262443	−	0.454564i
$218$	−5.63397	+	9.75833i	−0.381581	+	0.660918i
$219$	−0.866025	+	1.50000i	−0.0585206	+	0.101361i
$220$		0			0
$221$	2.63397	−	0.169873i	0.177180	−	0.0114269i
$222$	7.60770			0.510595
$223$	0.928203	−	1.60770i	0.0621571	−	0.107659i	−0.833272	−	0.552863i	$-0.813535\pi$
$223$	0.928203	−	1.60770i	0.0621571	−	0.107659i	0.895429	+	0.445204i	$0.146869\pi$
$224$	5.07180	−	8.78461i	0.338874	−	0.586946i
$225$		0			0
$226$	13.4641			0.895619
$227$	−2.36603	−	4.09808i	−0.157039	−	0.271999i	0.776761	−	0.629796i	$-0.216861\pi$
$227$	−2.36603	−	4.09808i	−0.157039	−	0.271999i	−0.933799	+	0.357797i	$0.883528\pi$
$228$	0.392305	+	0.679492i	0.0259810	+	0.0450005i
$229$	12.7846			0.844831			0.422415	−	0.906402i	$-0.361182\pi$
$229$	12.7846			0.844831			0.422415	+	0.906402i	$0.361182\pi$
$230$		0			0
$231$	−1.73205	+	3.00000i	−0.113961	+	0.197386i
$232$	4.14359	−	7.17691i	0.272040	−	0.471188i
$233$	28.2487			1.85063			0.925317	−	0.379194i	$-0.123799\pi$
$233$	28.2487			1.85063			0.925317	+	0.379194i	$0.123799\pi$
$234$	−1.16987	+	2.36603i	−0.0764770	+	0.154672i
$235$		0			0
$236$	−8.53590	+	14.7846i	−0.555640	+	0.962396i
$237$	−5.50000	+	9.52628i	−0.357263	+	0.618798i
$238$	−0.464102	−	0.803848i	−0.0300832	−	0.0521057i
$239$	−13.8564			−0.896296			−0.448148	−	0.893959i	$-0.647916\pi$
$239$	−13.8564			−0.896296			−0.448148	+	0.893959i	$0.647916\pi$
$240$		0			0
$241$	−2.00000	−	3.46410i	−0.128831	−	0.223142i	0.794393	−	0.607404i	$-0.207789\pi$
$241$	−2.00000	−	3.46410i	−0.128831	−	0.223142i	−0.923224	+	0.384262i	$0.874456\pi$
$242$	5.12436			0.329406
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	3.94744	−	6.83717i	0.252709	−	0.437705i
$245$		0			0
$246$	−7.85641			−0.500906
$247$	1.92820	−	0.124356i	0.122689	−	0.00791256i
$248$	11.3205			0.718853
$249$	−1.46410	+	2.53590i	−0.0927837	+	0.160706i
$250$		0			0
$251$	3.26795	+	5.66025i	0.206271	+	0.357272i	0.950537	−	0.310611i	$-0.100534\pi$
$251$	3.26795	+	5.66025i	0.206271	+	0.357272i	−0.744266	+	0.667883i	$0.767200\pi$
$252$	−2.53590			−0.159747
$253$	−2.00000	−	3.46410i	−0.125739	−	0.217786i
$254$	0.241670	+	0.418584i	0.0151637	+	0.0262643i
$255$		0			0
$256$	5.85641	+	10.1436i	0.366025	+	0.633975i
$257$	−1.09808	+	1.90192i	−0.0684961	+	0.118639i	−0.898239	−	0.439506i	$-0.855153\pi$
$257$	−1.09808	+	1.90192i	−0.0684961	+	0.118639i	0.829743	+	0.558145i	$0.188487\pi$
$258$	−3.36603	+	5.83013i	−0.209560	+	0.362968i
$259$	18.0000			1.11847
$260$		0			0
$261$	−3.26795			−0.202281
$262$	−0.803848	+	1.39230i	−0.0496619	+	0.0860169i
$263$	1.43782	−	2.49038i	0.0886599	−	0.153563i	−0.818285	−	0.574813i	$-0.805075\pi$
$263$	1.43782	−	2.49038i	0.0886599	−	0.153563i	0.906945	+	0.421249i	$0.138408\pi$
$264$	−2.53590	−	4.39230i	−0.156074	−	0.270328i
$265$		0			0
$266$	−0.339746	−	0.588457i	−0.0208312	−	0.0360806i
$267$	2.63397	+	4.56218i	0.161197	+	0.279201i
$268$	−13.4641			−0.822451
$269$	14.2942	+	24.7583i	0.871535	+	1.50954i	0.860409	+	0.509604i	$0.170208\pi$
$269$	14.2942	+	24.7583i	0.871535	+	1.50954i	0.0111254	+	0.999938i	$0.496459\pi$
$270$		0			0
$271$	−11.2321	+	19.4545i	−0.682298	+	1.18178i	0.291979	+	0.956425i	$0.405686\pi$
$271$	−11.2321	+	19.4545i	−0.682298	+	1.18178i	−0.974278	+	0.225351i	$0.927647\pi$
$272$	−0.784610			−0.0475740
$273$	−2.76795	+	5.59808i	−0.167524	+	0.338811i
$274$	−8.53590			−0.515672
$275$		0			0
$276$	1.46410	−	2.53590i	0.0881286	−	0.152643i
$277$	−13.1962	−	22.8564i	−0.792880	−	1.37331i	−0.924177	−	0.381965i	$-0.875247\pi$
$277$	−13.1962	−	22.8564i	−0.792880	−	1.37331i	0.131297	−	0.991343i	$-0.458086\pi$
$278$	−14.5885			−0.874958
$279$	−2.23205	−	3.86603i	−0.133629	−	0.231453i
$280$		0			0
$281$	−11.2679			−0.672189			−0.336095	−	0.941828i	$-0.609106\pi$
$281$	−11.2679			−0.672189			−0.336095	+	0.941828i	$0.609106\pi$
$282$	0.0717968	+	0.124356i	0.00427544	+	0.00740527i
$283$	8.06218	−	13.9641i	0.479247	−	0.830080i	−0.520470	−	0.853880i	$-0.674243\pi$
$283$	8.06218	−	13.9641i	0.479247	−	0.830080i	0.999717	+	0.0238003i	$0.00757658\pi$
$284$	−3.46410	+	6.00000i	−0.205557	+	0.356034i
$285$		0			0
$286$	−5.26795	+	0.339746i	−0.311500	+	0.0200896i
$287$	−18.5885			−1.09724
$288$	2.92820	−	5.07180i	0.172546	−	0.298858i
$289$	8.23205	−	14.2583i	0.484238	−	0.838725i
$290$		0			0
$291$	5.19615			0.304604
$292$	−1.26795	−	2.19615i	−0.0742011	−	0.128520i
$293$	4.09808	+	7.09808i	0.239412	+	0.414674i	0.960546	−	0.278122i	$-0.0897120\pi$
$293$	4.09808	+	7.09808i	0.239412	+	0.414674i	−0.721134	+	0.692796i	$0.756379\pi$
$294$	−2.92820			−0.170776
$295$		0			0
$296$	−13.1769	+	22.8231i	−0.765893	+	1.32656i
$297$	−1.00000	+	1.73205i	−0.0580259	+	0.100504i
$298$	4.28719			0.248350
$299$	−4.00000	−	6.00000i	−0.231326	−	0.346989i
$300$		0			0
$301$	−7.96410	+	13.7942i	−0.459043	+	0.795086i
$302$	−0.339746	+	0.588457i	−0.0195502	+	0.0338619i
$303$	5.19615	+	9.00000i	0.298511	+	0.517036i
$304$	−0.574374			−0.0329426
$305$		0			0
$306$	−0.267949	−	0.464102i	−0.0153176	−	0.0265309i
$307$	6.66025			0.380121			0.190060	−	0.981772i	$-0.439132\pi$
$307$	6.66025			0.380121			0.190060	+	0.981772i	$0.439132\pi$
$308$	−2.53590	−	4.39230i	−0.144496	−	0.250275i
$309$	−2.86603	+	4.96410i	−0.163042	+	0.282398i
$310$		0			0
$311$	12.5885			0.713826			0.356913	−	0.934138i	$-0.383829\pi$
$311$	12.5885			0.713826			0.356913	+	0.934138i	$0.383829\pi$
$312$	−5.07180	−	7.60770i	−0.287134	−	0.430701i
$313$	−19.1962			−1.08503			−0.542515	−	0.840046i	$-0.682528\pi$
$313$	−19.1962			−1.08503			−0.542515	+	0.840046i	$0.682528\pi$
$314$	1.36603	−	2.36603i	0.0770893	−	0.133523i
$315$		0			0
$316$	−8.05256	−	13.9474i	−0.452992	−	0.784605i
$317$	28.3923			1.59467			0.797335	−	0.603537i	$-0.206242\pi$
$317$	28.3923			1.59467			0.797335	+	0.603537i	$0.206242\pi$
$318$	−3.46410	−	6.00000i	−0.194257	−	0.336463i
$319$	−3.26795	−	5.66025i	−0.182970	−	0.316913i
$320$		0			0
$321$	−4.09808	−	7.09808i	−0.228732	−	0.396176i
$322$	−1.26795	+	2.19615i	−0.0706600	+	0.122387i
$323$	−0.196152	+	0.339746i	−0.0109142	+	0.0189040i
$324$	−1.46410			−0.0813390
$325$		0			0
$326$	15.5167			0.859388
$327$	−7.69615	+	13.3301i	−0.425598	+	0.737158i
$328$	13.6077	−	23.5692i	0.751359	−	1.30139i
$329$	0.169873	+	0.294229i	0.00936540	+	0.0162213i
$330$		0			0
$331$	−11.9641	−	20.7224i	−0.657606	−	1.13901i	−0.981234	−	0.192823i	$-0.938236\pi$
$331$	−11.9641	−	20.7224i	−0.657606	−	1.13901i	0.323627	−	0.946185i	$-0.395098\pi$
$332$	−2.14359	−	3.71281i	−0.117645	−	0.203767i
$333$	10.3923			0.569495
$334$	8.00000	+	13.8564i	0.437741	+	0.758189i
$335$		0			0
$336$	0.928203	−	1.60770i	0.0506376	−	0.0877070i
$337$	−25.5885			−1.39389			−0.696946	−	0.717124i	$-0.745458\pi$
$337$	−25.5885			−1.39389			−0.696946	+	0.717124i	$0.745458\pi$
$338$	−9.43782	+	1.22243i	−0.513350	+	0.0664915i
$339$	18.3923			0.998933
$340$		0			0
$341$	4.46410	−	7.73205i	0.241745	−	0.418714i
$342$	−0.196152	−	0.339746i	−0.0106067	−	0.0183714i
$343$	−19.0526			−1.02874
$344$	−11.6603	−	20.1962i	−0.628679	−	1.08890i
$345$		0			0
$346$	8.92820			0.479983
$347$	−0.732051	−	1.26795i	−0.0392985	−	0.0680671i	0.845707	−	0.533647i	$-0.179179\pi$
$347$	−0.732051	−	1.26795i	−0.0392985	−	0.0680671i	−0.885006	+	0.465580i	$0.845846\pi$
$348$	2.39230	−	4.14359i	0.128241	−	0.222120i
$349$	−15.4282	+	26.7224i	−0.825853	+	1.43042i	0.0754130	+	0.997152i	$0.475972\pi$
$349$	−15.4282	+	26.7224i	−0.825853	+	1.43042i	−0.901266	+	0.433267i	$0.857361\pi$
$350$		0			0
$351$	−1.59808	+	3.23205i	−0.0852990	+	0.172514i
$352$	11.7128			0.624295
$353$	−4.80385	+	8.32051i	−0.255683	+	0.442856i	−0.965081	−	0.261952i	$-0.915634\pi$
$353$	−4.80385	+	8.32051i	−0.255683	+	0.442856i	0.709398	+	0.704808i	$0.248967\pi$
$354$	4.26795	−	7.39230i	0.226839	−	0.392897i
$355$		0			0
$356$	−7.71281			−0.408778
$357$	−0.633975	−	1.09808i	−0.0335535	−	0.0581164i
$358$	6.46410	+	11.1962i	0.341638	+	0.591735i
$359$	0.196152			0.0103525			0.00517626	−	0.999987i	$-0.498352\pi$
$359$	0.196152			0.0103525			0.00517626	+	0.999987i	$0.498352\pi$
$360$		0			0
$361$	9.35641	−	16.2058i	0.492442	−	0.852935i
$362$	3.07180	−	5.32051i	0.161450	−	0.279640i
$363$	7.00000			0.367405
$364$	−5.07180	−	7.60770i	−0.265834	−	0.398752i
$365$		0			0
$366$	−1.97372	+	3.41858i	−0.103168	+	0.178692i
$367$	7.52628	−	13.0359i	0.392869	−	0.680468i	−0.599958	−	0.800031i	$-0.704816\pi$
$367$	7.52628	−	13.0359i	0.392869	−	0.680468i	0.992827	+	0.119563i	$0.0381494\pi$
$368$	1.07180	+	1.85641i	0.0558713	+	0.0967719i
$369$	−10.7321			−0.558688
$370$		0			0
$371$	−8.19615	−	14.1962i	−0.425523	−	0.737028i
$372$	6.53590			0.338871
$373$	3.66987	+	6.35641i	0.190019	+	0.329122i	0.945256	−	0.326329i	$-0.105812\pi$
$373$	3.66987	+	6.35641i	0.190019	+	0.329122i	−0.755237	+	0.655451i	$0.772478\pi$
$374$	0.535898	−	0.928203i	0.0277106	−	0.0479962i
$375$		0			0
$376$	−0.497423			−0.0256526
$377$	−6.53590	−	9.80385i	−0.336616	−	0.504924i
$378$	1.26795			0.0652163
$379$	−3.23205	+	5.59808i	−0.166019	+	0.287554i	−0.937017	−	0.349284i	$-0.886425\pi$
$379$	−3.23205	+	5.59808i	−0.166019	+	0.287554i	0.770997	+	0.636838i	$0.219758\pi$
$380$		0			0
$381$	0.330127	+	0.571797i	0.0169129	+	0.0292940i
$382$	−16.5359			−0.846050
$383$	−9.63397	−	16.6865i	−0.492273	−	0.852642i	0.507687	−	0.861541i	$-0.330501\pi$
$383$	−9.63397	−	16.6865i	−0.492273	−	0.852642i	−0.999960	+	0.00889939i	$0.997167\pi$
$384$	5.07180	+	8.78461i	0.258819	+	0.448288i
$385$		0			0
$386$	7.02628	+	12.1699i	0.357628	+	0.619430i
$387$	−4.59808	+	7.96410i	−0.233733	+	0.404838i
$388$	−3.80385	+	6.58846i	−0.193111	+	0.334478i
$389$	−14.5359			−0.736999			−0.368500	−	0.929628i	$-0.620128\pi$
$389$	−14.5359			−0.736999			−0.368500	+	0.929628i	$0.620128\pi$
$390$		0			0
$391$	1.46410			0.0740428
$392$	5.07180	−	8.78461i	0.256164	−	0.443690i
$393$	−1.09808	+	1.90192i	−0.0553906	+	0.0959394i
$394$	−6.00000	−	10.3923i	−0.302276	−	0.523557i
$395$		0			0
$396$	−1.46410	−	2.53590i	−0.0735739	−	0.127434i
$397$	4.86603	+	8.42820i	0.244219	+	0.422999i	0.961912	−	0.273360i	$-0.0881352\pi$
$397$	4.86603	+	8.42820i	0.244219	+	0.422999i	−0.717693	+	0.696360i	$0.754802\pi$
$398$	18.1962			0.912091
$399$	−0.464102	−	0.803848i	−0.0232341	−	0.0402427i
$400$		0			0
$401$	15.1244	−	26.1962i	0.755274	−	1.30817i	−0.189964	−	0.981791i	$-0.560837\pi$
$401$	15.1244	−	26.1962i	0.755274	−	1.30817i	0.945238	−	0.326382i	$-0.105830\pi$
$402$	6.73205			0.335764
$403$	7.13397	−	14.4282i	0.355369	−	0.718720i
$404$	−15.2154			−0.756994
$405$		0			0
$406$	−2.07180	+	3.58846i	−0.102822	+	0.178092i
$407$	10.3923	+	18.0000i	0.515127	+	0.892227i
$408$	1.85641			0.0919058
$409$	−3.16025	−	5.47372i	−0.156265	−	0.270658i	0.777254	−	0.629187i	$-0.216612\pi$
$409$	−3.16025	−	5.47372i	−0.156265	−	0.270658i	−0.933519	+	0.358529i	$0.883279\pi$
$410$		0			0
$411$	−11.6603			−0.575158
$412$	−4.19615	−	7.26795i	−0.206730	−	0.358066i
$413$	10.0981	−	17.4904i	0.496894	−	0.860645i
$414$	−0.732051	+	1.26795i	−0.0359783	+	0.0623163i
$415$		0			0
$416$	21.0718	−	1.35898i	1.03313	−	0.0666297i
$417$	−19.9282			−0.975888
$418$	0.392305	−	0.679492i	0.0191883	−	0.0332350i
$419$	19.9545	−	34.5622i	0.974840	−	1.68847i	0.294379	−	0.955689i	$-0.404887\pi$
$419$	19.9545	−	34.5622i	0.974840	−	1.68847i	0.680461	−	0.732784i	$-0.261780\pi$
$420$		0			0
$421$	12.8564			0.626583			0.313291	−	0.949657i	$-0.398568\pi$
$421$	12.8564			0.626583			0.313291	+	0.949657i	$0.398568\pi$
$422$	8.16987	+	14.1506i	0.397703	+	0.688842i
$423$	0.0980762	+	0.169873i	0.00476863	+	0.00825951i
$424$	24.0000			1.16554
$425$		0			0
$426$	1.73205	−	3.00000i	0.0839181	−	0.145350i
$427$	−4.66987	+	8.08846i	−0.225991	+	0.391428i
$428$	12.0000			0.580042
$429$	−7.19615	+	0.464102i	−0.347434	+	0.0224070i
$430$		0			0
$431$	10.5359	−	18.2487i	0.507496	−	0.879009i	−0.492466	−	0.870332i	$-0.663904\pi$
$431$	10.5359	−	18.2487i	0.507496	−	0.879009i	0.999962	−	0.00867780i	$-0.00276226\pi$
$432$	0.535898	−	0.928203i	0.0257834	−	0.0446582i
$433$	9.52628	+	16.5000i	0.457804	+	0.792939i	0.998845	−	0.0480569i	$-0.0153029\pi$
$433$	9.52628	+	16.5000i	0.457804	+	0.792939i	−0.541041	+	0.840996i	$0.681970\pi$
$434$	−5.66025			−0.271701
$435$		0			0
$436$	−11.2679	−	19.5167i	−0.539637	−	0.934679i
$437$	1.07180			0.0512710
$438$	0.633975	+	1.09808i	0.0302925	+	0.0524681i
$439$	9.69615	−	16.7942i	0.462772	−	0.801545i	−0.536326	−	0.844011i	$-0.680188\pi$
$439$	9.69615	−	16.7942i	0.462772	−	0.801545i	0.999098	+	0.0424662i	$0.0135215\pi$
$440$		0			0
$441$	−4.00000			−0.190476
$442$	0.856406	−	1.73205i	0.0407351	−	0.0823853i
$443$	−29.1244			−1.38374			−0.691870	−	0.722022i	$-0.743213\pi$
$443$	−29.1244			−1.38374			−0.691870	+	0.722022i	$0.743213\pi$
$444$	−7.60770	+	13.1769i	−0.361045	+	0.625349i
$445$		0			0
$446$	−0.679492	−	1.17691i	−0.0321749	−	0.0557285i
$447$	5.85641			0.276999
$448$	−1.85641	−	3.21539i	−0.0877070	−	0.151913i
$449$	−7.73205	−	13.3923i	−0.364898	−	0.632022i	0.623862	−	0.781535i	$-0.285563\pi$
$449$	−7.73205	−	13.3923i	−0.364898	−	0.632022i	−0.988760	+	0.149513i	$0.952229\pi$
$450$		0			0
$451$	−10.7321	−	18.5885i	−0.505353	−	0.875296i
$452$	−13.4641	+	23.3205i	−0.633298	+	1.09690i
$453$	−0.464102	+	0.803848i	−0.0218054	+	0.0377681i
$454$	−3.46410			−0.162578
$455$		0			0
$456$	1.35898			0.0636402
$457$	−7.25833	+	12.5718i	−0.339530	+	0.588084i	−0.984344	−	0.176256i	$-0.943601\pi$
$457$	−7.25833	+	12.5718i	−0.339530	+	0.588084i	0.644814	+	0.764339i	$0.276935\pi$
$458$	4.67949	−	8.10512i	0.218658	−	0.378727i
$459$	−0.366025	−	0.633975i	−0.0170846	−	0.0295914i
$460$		0			0
$461$	5.02628	+	8.70577i	0.234097	+	0.405468i	0.959010	−	0.283373i	$-0.0914533\pi$
$461$	5.02628	+	8.70577i	0.234097	+	0.405468i	−0.724913	+	0.688841i	$0.758120\pi$
$462$	1.26795	+	2.19615i	0.0589903	+	0.102174i
$463$	1.33975			0.0622633			0.0311316	−	0.999515i	$-0.490089\pi$
$463$	1.33975			0.0622633			0.0311316	+	0.999515i	$0.490089\pi$
$464$	1.75129	+	3.03332i	0.0813015	+	0.140818i
$465$		0			0
$466$	10.3397	−	17.9090i	0.478979	−	0.829617i
$467$	−10.3397			−0.478466			−0.239233	−	0.970962i	$-0.576896\pi$
$467$	−10.3397			−0.478466			−0.239233	+	0.970962i	$0.576896\pi$
$468$	−2.92820	−	4.39230i	−0.135356	−	0.203034i
$469$	15.9282			0.735496
$470$		0			0
$471$	1.86603	−	3.23205i	0.0859819	−	0.148925i
$472$	14.7846	+	25.6077i	0.680517	+	1.17869i
$473$	−18.3923			−0.845679
$474$	4.02628	+	6.97372i	0.184933	+	0.320314i
$475$		0			0
$476$	1.85641			0.0850883
$477$	−4.73205	−	8.19615i	−0.216666	−	0.375276i
$478$	−5.07180	+	8.78461i	−0.231979	+	0.401799i
$479$	−19.4186	+	33.6340i	−0.887258	+	1.53678i	−0.0441539	+	0.999025i	$0.514059\pi$
$479$	−19.4186	+	33.6340i	−0.887258	+	1.53678i	−0.843104	+	0.537751i	$0.819274\pi$
$480$		0			0
$481$	20.7846	+	31.1769i	0.947697	+	1.42154i
$482$	−2.92820			−0.133376
$483$	−1.73205	+	3.00000i	−0.0788110	+	0.136505i
$484$	−5.12436	+	8.87564i	−0.232925	+	0.403438i
$485$		0			0
$486$	0.732051			0.0332065
$487$	2.80385	+	4.85641i	0.127054	+	0.220065i	0.922534	−	0.385915i	$-0.126114\pi$
$487$	2.80385	+	4.85641i	0.127054	+	0.220065i	−0.795480	+	0.605980i	$0.792781\pi$
$488$	−6.83717	−	11.8423i	−0.309504	−	0.536077i
$489$	21.1962			0.958523
$490$		0			0
$491$	9.49038	−	16.4378i	0.428295	−	0.741829i	−0.568427	−	0.822734i	$-0.692448\pi$
$491$	9.49038	−	16.4378i	0.428295	−	0.741829i	0.996722	+	0.0809052i	$0.0257811\pi$
$492$	7.85641	−	13.6077i	0.354194	−	0.613482i
$493$	2.39230			0.107744
$494$	0.626933	−	1.26795i	0.0282071	−	0.0570477i
$495$		0			0
$496$	−2.39230	+	4.14359i	−0.107418	+	0.186053i
$497$	4.09808	−	7.09808i	0.183824	−	0.318392i
$498$	1.07180	+	1.85641i	0.0480284	+	0.0831876i
$499$	−25.3205			−1.13350			−0.566751	−	0.823889i	$-0.691800\pi$
$499$	−25.3205			−1.13350			−0.566751	+	0.823889i	$0.691800\pi$
$500$		0			0
$501$	10.9282	+	18.9282i	0.488236	+	0.845650i
$502$	4.78461			0.213548
$503$	−6.46410	−	11.1962i	−0.288220	−	0.499212i	0.685165	−	0.728388i	$-0.259730\pi$
$503$	−6.46410	−	11.1962i	−0.288220	−	0.499212i	−0.973385	+	0.229176i	$0.926397\pi$
$504$	−2.19615	+	3.80385i	−0.0978244	+	0.169437i
$505$		0			0
$506$	−2.92820			−0.130175
$507$	−12.8923	+	1.66987i	−0.572567	+	0.0741617i
$508$	−0.966679			−0.0428894
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	−0.594675	−	0.803966i	$-0.702719\pi$
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	0.993593	+	0.113020i	$0.0360525\pi$
$510$		0			0
$511$	1.50000	+	2.59808i	0.0663561	+	0.114932i
$512$	−11.7128			−0.517638
$513$	−0.267949	−	0.464102i	−0.0118302	−	0.0204906i
$514$	0.803848	+	1.39230i	0.0354562	+	0.0614119i
$515$		0			0
$516$	−6.73205	−	11.6603i	−0.296362	−	0.513314i
$517$	−0.196152	+	0.339746i	−0.00862677	+	0.0149420i
$518$	6.58846	−	11.4115i	0.289480	−	0.501394i
$519$	12.1962			0.535352
$520$		0			0
$521$	23.8038			1.04287			0.521433	−	0.853292i	$-0.325398\pi$
$521$	23.8038			1.04287			0.521433	+	0.853292i	$0.325398\pi$
$522$	−1.19615	+	2.07180i	−0.0523542	+	0.0906801i
$523$	14.5885	−	25.2679i	0.637909	−	1.10489i	−0.347982	−	0.937501i	$-0.613133\pi$
$523$	14.5885	−	25.2679i	0.637909	−	1.10489i	0.985891	−	0.167389i	$-0.0535336\pi$
$524$	−1.60770	−	2.78461i	−0.0702325	−	0.121646i
$525$		0			0
$526$	−1.05256	−	1.82309i	−0.0458937	−	0.0794903i
$527$	1.63397	+	2.83013i	0.0711771	+	0.123282i
$528$	2.14359			0.0932879
$529$	9.50000	+	16.4545i	0.413043	+	0.715412i
$530$		0			0
$531$	5.83013	−	10.0981i	0.253006	−	0.438219i
$532$	1.35898			0.0589194
$533$	−21.4641	−	32.1962i	−0.929713	−	1.39457i
$534$	3.85641			0.166883
$535$		0			0
$536$	−11.6603	+	20.1962i	−0.503646	+	0.872341i
$537$	8.83013	+	15.2942i	0.381048	+	0.659995i
$538$	20.9282			0.902279
$539$	−4.00000	−	6.92820i	−0.172292	−	0.298419i
$540$		0			0
$541$	11.2487			0.483620			0.241810	−	0.970324i	$-0.422259\pi$
$541$	11.2487			0.483620			0.241810	+	0.970324i	$0.422259\pi$
$542$	8.22243	+	14.2417i	0.353184	+	0.611732i
$543$	4.19615	−	7.26795i	0.180074	−	0.311898i
$544$	−2.14359	+	3.71281i	−0.0919058	+	0.159186i
$545$		0			0
$546$	2.53590	+	3.80385i	0.108526	+	0.162790i
$547$	31.9808			1.36740			0.683699	−	0.729764i	$-0.260370\pi$
$547$	31.9808			1.36740			0.683699	+	0.729764i	$0.260370\pi$
$548$	8.53590	−	14.7846i	0.364636	−	0.631567i
$549$	−2.69615	+	4.66987i	−0.115069	+	0.199305i
$550$		0			0
$551$	1.75129			0.0746074
$552$	−2.53590	−	4.39230i	−0.107935	−	0.186949i
$553$	9.52628	+	16.5000i	0.405099	+	0.701651i
$554$	−19.3205			−0.820850
$555$		0			0
$556$	14.5885	−	25.2679i	0.618688	−	1.07160i
$557$	4.73205	−	8.19615i	0.200503	−	0.347282i	−0.748187	−	0.663488i	$-0.769076\pi$
$557$	4.73205	−	8.19615i	0.200503	−	0.347282i	0.948691	+	0.316205i	$0.102409\pi$
$558$	−3.26795			−0.138343
$559$	−33.0885	+	2.13397i	−1.39949	+	0.0902575i
$560$		0			0
$561$	0.732051	−	1.26795i	0.0309072	−	0.0535329i
$562$	−4.12436	+	7.14359i	−0.173975	+	0.301334i
$563$	−17.3923	−	30.1244i	−0.732998	−	1.26959i	−0.955596	−	0.294680i	$-0.904787\pi$
$563$	−17.3923	−	30.1244i	−0.732998	−	1.26959i	0.222598	−	0.974910i	$-0.428546\pi$
$564$	−0.287187			−0.0120928
$565$		0			0
$566$	−5.90192	−	10.2224i	−0.248076	−	0.429681i
$567$	1.73205			0.0727393
$568$	6.00000	+	10.3923i	0.251754	+	0.436051i
$569$	9.49038	−	16.4378i	0.397857	−	0.689109i	−0.595604	−	0.803278i	$-0.703087\pi$
$569$	9.49038	−	16.4378i	0.397857	−	0.689109i	0.993461	+	0.114169i	$0.0364205\pi$
$570$		0			0
$571$	−42.7846			−1.79048			−0.895240	−	0.445584i	$-0.852996\pi$
$571$	−42.7846			−1.79048			−0.895240	+	0.445584i	$0.852996\pi$
$572$	4.67949	−	9.46410i	0.195659	−	0.395714i
$573$	−22.5885			−0.943646
$574$	−6.80385	+	11.7846i	−0.283987	+	0.491880i
$575$		0			0
$576$	−1.07180	−	1.85641i	−0.0446582	−	0.0773503i
$577$	8.53590			0.355354			0.177677	−	0.984089i	$-0.443142\pi$
$577$	8.53590			0.355354			0.177677	+	0.984089i	$0.443142\pi$
$578$	−6.02628	−	10.4378i	−0.250660	−	0.434156i
$579$	9.59808	+	16.6244i	0.398882	+	0.690885i
$580$		0			0
$581$	2.53590	+	4.39230i	0.105207	+	0.182224i
$582$	1.90192	−	3.29423i	0.0788373	−	0.136550i
$583$	9.46410	−	16.3923i	0.391963	−	0.678900i
$584$	−4.39230			−0.181755
$585$		0			0
$586$	6.00000			0.247858
$587$	14.4904	−	25.0981i	0.598082	−	1.03591i	−0.395022	−	0.918672i	$-0.629263\pi$
$587$	14.4904	−	25.0981i	0.598082	−	1.03591i	0.993104	−	0.117237i	$-0.0374036\pi$
$588$	2.92820	−	5.07180i	0.120757	−	0.209157i
$589$	1.19615	+	2.07180i	0.0492866	+	0.0853669i
$590$		0			0
$591$	−8.19615	−	14.1962i	−0.337145	−	0.583952i
$592$	−5.56922	−	9.64617i	−0.228894	−	0.396455i
$593$	15.4641			0.635035			0.317517	−	0.948252i	$-0.397151\pi$
$593$	15.4641			0.635035			0.317517	+	0.948252i	$0.397151\pi$
$594$	0.732051	+	1.26795i	0.0300364	+	0.0520246i
$595$		0			0
$596$	−4.28719	+	7.42563i	−0.175610	+	0.304165i
$597$	24.8564			1.01730
$598$	−5.26795	+	0.339746i	−0.215422	+	0.0138932i
$599$	−18.9808			−0.775533			−0.387766	−	0.921758i	$-0.626753\pi$
$599$	−18.9808			−0.775533			−0.387766	+	0.921758i	$0.626753\pi$
$600$		0			0
$601$	5.26795	−	9.12436i	0.214884	−	0.372190i	−0.738353	−	0.674415i	$-0.764396\pi$
$601$	5.26795	−	9.12436i	0.214884	−	0.372190i	0.953237	+	0.302225i	$0.0977293\pi$
$602$	5.83013	+	10.0981i	0.237618	+	0.411567i
$603$	9.19615			0.374496
$604$	−0.679492	−	1.17691i	−0.0276481	−	0.0478880i
$605$		0			0
$606$	7.60770			0.309041
$607$	9.19615	+	15.9282i	0.373260	+	0.646506i	0.990065	−	0.140610i	$-0.0449065\pi$
$607$	9.19615	+	15.9282i	0.373260	+	0.646506i	−0.616805	+	0.787116i	$0.711573\pi$
$608$	−1.56922	+	2.71797i	−0.0636402	+	0.110228i
$609$	−2.83013	+	4.90192i	−0.114683	+	0.198636i
$610$		0			0
$611$	−0.313467	+	0.633975i	−0.0126815	+	0.0256479i
$612$	1.07180			0.0433248
$613$	14.1340	−	24.4808i	0.570866	−	0.988769i	−0.425611	−	0.904906i	$-0.639941\pi$
$613$	14.1340	−	24.4808i	0.570866	−	0.988769i	0.996477	−	0.0838627i	$-0.0267257\pi$
$614$	2.43782	−	4.22243i	0.0983825	−	0.170403i
$615$		0			0
$616$	−8.78461			−0.353942
$617$	−17.0526	−	29.5359i	−0.686510	−	1.18907i	−0.972960	−	0.230975i	$-0.925808\pi$
$617$	−17.0526	−	29.5359i	−0.686510	−	1.18907i	0.286449	−	0.958095i	$-0.407525\pi$
$618$	2.09808	+	3.63397i	0.0843970	+	0.146180i
$619$	31.9282			1.28330			0.641651	−	0.766996i	$-0.278250\pi$
$619$	31.9282			1.28330			0.641651	+	0.766996i	$0.278250\pi$
$620$		0			0
$621$	−1.00000	+	1.73205i	−0.0401286	+	0.0695048i
$622$	4.60770	−	7.98076i	0.184752	−	0.319999i
$623$	9.12436			0.365560
$624$	3.85641	−	0.248711i	0.154380	−	0.00995642i
$625$		0			0
$626$	−7.02628	+	12.1699i	−0.280827	+	0.486406i
$627$	0.535898	−	0.928203i	0.0214017	−	0.0370689i
$628$	2.73205	+	4.73205i	0.109021	+	0.188829i
$629$	−7.60770			−0.303339
$630$		0			0
$631$	−12.6962	−	21.9904i	−0.505426	−	0.875423i	−0.999980	−	0.00627660i	$-0.998002\pi$
$631$	−12.6962	−	21.9904i	−0.505426	−	0.875423i	0.494554	−	0.869147i	$-0.335331\pi$
$632$	−27.8949			−1.10960
$633$	11.1603	+	19.3301i	0.443580	+	0.768304i
$634$	10.3923	−	18.0000i	0.412731	−	0.714871i
$635$		0			0
$636$	13.8564			0.549442
$637$	−8.00000	−	12.0000i	−0.316972	−	0.475457i
$638$	−4.78461			−0.189425
$639$	2.36603	−	4.09808i	0.0935985	−	0.162117i
$640$		0			0
$641$	1.73205	+	3.00000i	0.0684119	+	0.118493i	0.898202	−	0.439582i	$-0.144873\pi$
$641$	1.73205	+	3.00000i	0.0684119	+	0.118493i	−0.829790	+	0.558075i	$0.811540\pi$
$642$	−6.00000			−0.236801
$643$	6.79423	+	11.7679i	0.267938	+	0.464083i	0.968329	−	0.249677i	$-0.0803244\pi$
$643$	6.79423	+	11.7679i	0.267938	+	0.464083i	−0.700391	+	0.713759i	$0.746991\pi$
$644$	−2.53590	−	4.39230i	−0.0999284	−	0.173081i
$645$		0			0
$646$	0.143594	+	0.248711i	0.00564961	+	0.00978542i
$647$	−2.07180	+	3.58846i	−0.0814507	+	0.141077i	−0.903873	−	0.427800i	$-0.859289\pi$
$647$	−2.07180	+	3.58846i	−0.0814507	+	0.141077i	0.822423	+	0.568877i	$0.192622\pi$
$648$	−1.26795	+	2.19615i	−0.0498097	+	0.0862730i
$649$	23.3205			0.915410
$650$		0			0
$651$	−7.73205			−0.303043
$652$	−15.5167	+	26.8756i	−0.607679	+	1.05253i
$653$	6.75833	−	11.7058i	0.264474	−	0.458082i	−0.702952	−	0.711238i	$-0.748135\pi$
$653$	6.75833	−	11.7058i	0.264474	−	0.458082i	0.967426	+	0.253155i	$0.0814684\pi$
$654$	5.63397	+	9.75833i	0.220306	+	0.381581i
$655$		0			0
$656$	5.75129	+	9.96152i	0.224550	+	0.388932i
$657$	0.866025	+	1.50000i	0.0337869	+	0.0585206i
$658$	0.248711			0.00969578
$659$	9.12436	+	15.8038i	0.355434	+	0.615630i	0.987192	−	0.159535i	$-0.0509996\pi$
$659$	9.12436	+	15.8038i	0.355434	+	0.615630i	−0.631758	+	0.775166i	$0.717666\pi$
$660$		0			0
$661$	−18.0885	+	31.3301i	−0.703559	+	1.21860i	0.263649	+	0.964619i	$0.415074\pi$
$661$	−18.0885	+	31.3301i	−0.703559	+	1.21860i	−0.967209	+	0.253982i	$0.918260\pi$
$662$	−17.5167			−0.680804
$663$	1.16987	−	2.36603i	0.0454341	−	0.0918888i
$664$	−7.42563			−0.288170
$665$		0			0
$666$	3.80385	−	6.58846i	0.147396	−	0.255298i
$667$	−3.26795	−	5.66025i	−0.126535	−	0.219166i
$668$	−32.0000			−1.23812
$669$	−0.928203	−	1.60770i	−0.0358864	−	0.0621571i
$670$		0			0
$671$	−10.7846			−0.416335
$672$	−5.07180	−	8.78461i	−0.195649	−	0.338874i
$673$	−6.47372	+	11.2128i	−0.249544	+	0.432222i	−0.963399	−	0.268071i	$-0.913614\pi$
$673$	−6.47372	+	11.2128i	−0.249544	+	0.432222i	0.713856	+	0.700293i	$0.246947\pi$
$674$	−9.36603	+	16.2224i	−0.360766	+	0.624865i
$675$		0			0
$676$	7.32051	−	17.5692i	0.281558	−	0.675739i
$677$	−50.9282			−1.95733			−0.978665	−	0.205463i	$-0.934130\pi$
$677$	−50.9282			−1.95733			−0.978665	+	0.205463i	$0.934130\pi$
$678$	6.73205	−	11.6603i	0.258543	−	0.447809i
$679$	4.50000	−	7.79423i	0.172694	−	0.299115i
$680$		0			0
$681$	−4.73205			−0.181333
$682$	−3.26795	−	5.66025i	−0.125136	−	0.216742i
$683$	8.29423	+	14.3660i	0.317370	+	0.549701i	0.979938	−	0.199301i	$-0.0638670\pi$
$683$	8.29423	+	14.3660i	0.317370	+	0.549701i	−0.662569	+	0.749001i	$0.730534\pi$
$684$	0.784610			0.0300003
$685$		0			0
$686$	−6.97372	+	12.0788i	−0.266258	+	0.461172i
$687$	6.39230	−	11.0718i	0.243882	−	0.422415i
$688$	9.85641			0.375772
$689$	15.1244	−	30.5885i	0.576192	−	1.16533i
$690$		0			0
$691$	13.9641	−	24.1865i	0.531219	−	0.920099i	−0.468117	−	0.883667i	$-0.655067\pi$
$691$	13.9641	−	24.1865i	0.531219	−	0.920099i	0.999336	−	0.0364324i	$-0.0115994\pi$
$692$	−8.92820	+	15.4641i	−0.339399	+	0.587857i
$693$	1.73205	+	3.00000i	0.0657952	+	0.113961i
$694$	−1.07180			−0.0406848
$695$		0			0
$696$	−4.14359	−	7.17691i	−0.157063	−	0.272040i
$697$	7.85641			0.297583
$698$	11.2942	+	19.5622i	0.427493	+	0.740439i
$699$	14.1244	−	24.4641i	0.534232	−	0.925317i
$700$		0			0
$701$	−37.4641			−1.41500			−0.707500	−	0.706714i	$-0.750177\pi$
$701$	−37.4641			−1.41500			−0.707500	+	0.706714i	$0.750177\pi$
$702$	1.46410	+	2.19615i	0.0552590	+	0.0828884i
$703$	−5.56922			−0.210047
$704$	2.14359	−	3.71281i	0.0807897	−	0.139932i
$705$		0			0
$706$	3.51666	+	6.09103i	0.132351	+	0.229239i
$707$	18.0000			0.676960
$708$	8.53590	+	14.7846i	0.320799	+	0.555640i
$709$	18.6244	+	32.2583i	0.699452	+	1.21149i	0.968657	+	0.248404i	$0.0799060\pi$
$709$	18.6244	+	32.2583i	0.699452	+	1.21149i	−0.269204	+	0.963083i	$0.586761\pi$
$710$		0			0
$711$	5.50000	+	9.52628i	0.206266	+	0.357263i
$712$	−6.67949	+	11.5692i	−0.250325	+	0.433575i
$713$	4.46410	−	7.73205i	0.167182	−	0.289568i
$714$	−0.928203			−0.0347371
$715$		0			0
$716$	−25.8564			−0.966299
$717$	−6.92820	+	12.0000i	−0.258738	+	0.448148i
$718$	0.0717968	−	0.124356i	0.00267943	−	0.00464091i
$719$	−11.8301	−	20.4904i	−0.441189	−	0.764162i	0.556589	−	0.830788i	$-0.312110\pi$
$719$	−11.8301	−	20.4904i	−0.441189	−	0.764162i	−0.997778	+	0.0666259i	$0.978777\pi$
$720$		0			0
$721$	4.96410	+	8.59808i	0.184873	+	0.320209i
$722$	−6.84936	−	11.8634i	−0.254907	−	0.441512i
$723$	−4.00000			−0.148762
$724$	6.14359	+	10.6410i	0.228325	+	0.395470i
$725$		0			0
$726$	2.56218	−	4.43782i	0.0950913	−	0.164703i
$727$	2.66025			0.0986634			0.0493317	−	0.998782i	$-0.484291\pi$
$727$	2.66025			0.0986634			0.0493317	+	0.998782i	$0.484291\pi$
$728$	−15.8038	+	1.01924i	−0.585730	+	0.0377755i
$729$	1.00000			0.0370370
$730$		0			0
$731$	3.36603	−	5.83013i	0.124497	−	0.215635i
$732$	−3.94744	−	6.83717i	−0.145902	−	0.252709i
$733$	−13.9808			−0.516391			−0.258196	−	0.966093i	$-0.583128\pi$
$733$	−13.9808			−0.516391			−0.258196	+	0.966093i	$0.583128\pi$
$734$	−5.50962	−	9.54294i	−0.203364	−	0.352236i
$735$		0			0
$736$	11.7128			0.431740
$737$	9.19615	+	15.9282i	0.338745	+	0.586723i
$738$	−3.92820	+	6.80385i	−0.144599	+	0.250453i
$739$	−0.535898	+	0.928203i	−0.0197133	+	0.0341445i	−0.875714	−	0.482831i	$-0.839609\pi$
$739$	−0.535898	+	0.928203i	−0.0197133	+	0.0341445i	0.856000	+	0.516975i	$0.172942\pi$
$740$		0			0
$741$	0.856406	−	1.73205i	0.0314609	−	0.0636285i
$742$	−12.0000			−0.440534
$743$	−17.9545	+	31.0981i	−0.658686	+	1.14088i	0.322270	+	0.946648i	$0.395554\pi$
$743$	−17.9545	+	31.0981i	−0.658686	+	1.14088i	−0.980956	+	0.194230i	$0.937779\pi$
$744$	5.66025	−	9.80385i	0.207515	−	0.359426i
$745$		0			0
$746$	5.37307			0.196722
$747$	1.46410	+	2.53590i	0.0535687	+	0.0927837i
$748$	1.07180	+	1.85641i	0.0391888	+	0.0678769i
$749$	−14.1962			−0.518716
$750$		0			0
$751$	−5.19615	+	9.00000i	−0.189610	+	0.328415i	−0.945120	−	0.326722i	$-0.894056\pi$
$751$	−5.19615	+	9.00000i	−0.189610	+	0.328415i	0.755510	+	0.655137i	$0.227389\pi$
$752$	0.105118	−	0.182069i	0.00383325	−	0.00663938i
$753$	6.53590			0.238181
$754$	−8.60770	+	0.555136i	−0.313474	+	0.0202169i
$755$		0			0
$756$	−1.26795	+	2.19615i	−0.0461149	+	0.0798733i
$757$	−9.46410	+	16.3923i	−0.343979	+	0.595788i	−0.985168	−	0.171595i	$-0.945108\pi$
$757$	−9.46410	+	16.3923i	−0.343979	+	0.595788i	0.641189	+	0.767383i	$0.278441\pi$
$758$	2.36603	+	4.09808i	0.0859379	+	0.148849i
$759$	−4.00000			−0.145191
$760$		0			0
$761$	12.5359	+	21.7128i	0.454426	+	0.787089i	0.998655	−	0.0518478i	$-0.0165111\pi$
$761$	12.5359	+	21.7128i	0.454426	+	0.787089i	−0.544229	+	0.838937i	$0.683178\pi$
$762$	0.483340			0.0175095
$763$	13.3301	+	23.0885i	0.482583	+	0.835858i
$764$	16.5359	−	28.6410i	0.598248	−	1.03620i
$765$		0			0
$766$	−14.1051			−0.509639
$767$	41.9545	−	2.70577i	1.51489	−	0.0976997i
$768$	11.7128			0.422650
$769$	4.39230	−	7.60770i	0.158391	−	0.274341i	−0.775898	−	0.630859i	$-0.782703\pi$
$769$	4.39230	−	7.60770i	0.158391	−	0.274341i	0.934288	+	0.356518i	$0.116036\pi$
$770$		0			0
$771$	1.09808	+	1.90192i	0.0395462	+	0.0684961i
$772$	−28.1051			−1.01153
$773$	11.1962	+	19.3923i	0.402698	+	0.697493i	0.994050	−	0.108920i	$-0.0347393\pi$
$773$	11.1962	+	19.3923i	0.402698	+	0.697493i	−0.591353	+	0.806413i	$0.701406\pi$
$774$	3.36603	+	5.83013i	0.120989	+	0.209560i
$775$		0			0
$776$	6.58846	+	11.4115i	0.236512	+	0.409651i
$777$	9.00000	−	15.5885i	0.322873	−	0.559233i
$778$	−5.32051	+	9.21539i	−0.190749	+	0.330388i
$779$	5.75129			0.206061
$780$		0			0
$781$	9.46410			0.338652
$782$	0.535898	−	0.928203i	0.0191637	−	0.0331925i
$783$	−1.63397	+	2.83013i	−0.0583935	+	0.101140i
$784$	2.14359	+	3.71281i	0.0765569	+	0.132600i
$785$		0			0
$786$	0.803848	+	1.39230i	0.0286723	+	0.0496619i
$787$	22.0622	+	38.2128i	0.786432	+	1.36214i	0.928140	+	0.372231i	$0.121407\pi$
$787$	22.0622	+	38.2128i	0.786432	+	1.36214i	−0.141708	+	0.989908i	$0.545260\pi$
$788$	24.0000			0.854965
$789$	−1.43782	−	2.49038i	−0.0511878	−	0.0886599i
$790$		0			0
$791$	15.9282	−	27.5885i	0.566342	−	0.980933i
$792$	−5.07180			−0.180218
$793$	−19.4019	+	1.25129i	−0.688983	+	0.0444346i
$794$	7.12436			0.252834
$795$		0			0
$796$	−18.1962	+	31.5167i	−0.644946	+	1.11708i
$797$	−3.83013	−	6.63397i	−0.135670	−	0.234987i	0.790183	−	0.612871i	$-0.209985\pi$
$797$	−3.83013	−	6.63397i	−0.135670	−	0.234987i	−0.925853	+	0.377883i	$0.876652\pi$
$798$	−0.679492			−0.0240538
$799$	−0.0717968	−	0.124356i	−0.00253999	−	0.00439939i
$800$		0			0
$801$	5.26795			0.186134
$802$	−11.0718	−	19.1769i	−0.390959	−	0.677160i
$803$	−1.73205	+	3.00000i	−0.0611227	+	0.105868i
$804$	−6.73205	+	11.6603i	−0.237421	+	0.411225i
$805$		0			0
$806$	−6.53590	−	9.80385i	−0.230217	−	0.345326i
$807$	28.5885			1.00636
$808$	−13.1769	+	22.8231i	−0.463562	+	0.802913i
$809$	22.0526	−	38.1962i	0.775327	−	1.34291i	−0.159284	−	0.987233i	$-0.550919\pi$
$809$	22.0526	−	38.1962i	0.775327	−	1.34291i	0.934611	−	0.355672i	$-0.115748\pi$
$810$		0			0
$811$	−17.6410			−0.619460			−0.309730	−	0.950825i	$-0.600239\pi$
$811$	−17.6410			−0.619460			−0.309730	+	0.950825i	$0.600239\pi$
$812$	−4.14359	−	7.17691i	−0.145412	−	0.251860i
$813$	11.2321	+	19.4545i	0.393925	+	0.682298i
$814$	15.2154			0.533299
$815$		0			0
$816$	−0.392305	+	0.679492i	−0.0137334	+	0.0237870i
$817$	2.46410	−	4.26795i	0.0862080	−	0.149317i
$818$	−4.62693			−0.161777
$819$	3.46410	+	5.19615i	0.121046	+	0.181568i
$820$		0			0
$821$	−17.0000	+	29.4449i	−0.593304	+	1.02763i	0.400480	+	0.916306i	$0.368843\pi$
$821$	−17.0000	+	29.4449i	−0.593304	+	1.02763i	−0.993784	+	0.111327i	$0.964490\pi$
$822$	−4.26795	+	7.39230i	−0.148862	+	0.257836i
$823$	−6.33975	−	10.9808i	−0.220990	−	0.382765i	0.734119	−	0.679021i	$-0.237595\pi$
$823$	−6.33975	−	10.9808i	−0.220990	−	0.382765i	−0.955109	+	0.296255i	$0.904262\pi$
$824$	−14.5359			−0.506382
$825$		0			0
$826$	−7.39230	−	12.8038i	−0.257211	−	0.445503i
$827$	−11.6603			−0.405467			−0.202733	−	0.979234i	$-0.564982\pi$
$827$	−11.6603			−0.405467			−0.202733	+	0.979234i	$0.564982\pi$
$828$	−1.46410	−	2.53590i	−0.0508810	−	0.0881286i
$829$	−23.1603	+	40.1147i	−0.804389	+	1.39324i	0.112314	+	0.993673i	$0.464174\pi$
$829$	−23.1603	+	40.1147i	−0.804389	+	1.39324i	−0.916703	+	0.399570i	$0.869160\pi$
$830$		0			0
$831$	−26.3923			−0.915539
$832$	3.42563	−	6.92820i	0.118762	−	0.240192i
$833$	2.92820			0.101456
$834$	−7.29423	+	12.6340i	−0.252578	+	0.437479i
$835$		0			0
$836$	0.784610	+	1.35898i	0.0271363	+	0.0470014i
$837$	−4.46410			−0.154302
$838$	−14.6077	−	25.3013i	−0.504614	−	0.874018i
$839$	−19.1962	−	33.2487i	−0.662725	−	1.14787i	−0.979897	−	0.199505i	$-0.936067\pi$
$839$	−19.1962	−	33.2487i	−0.662725	−	1.14787i	0.317172	−	0.948368i	$-0.397267\pi$
$840$		0			0
$841$	9.16025	+	15.8660i	0.315871	+	0.547104i
$842$	4.70577	−	8.15064i	0.162172	−	0.280889i
$843$	−5.63397	+	9.75833i	−0.194044	+	0.336095i
$844$	−32.6795			−1.12487
$845$		0			0
$846$	0.143594			0.00493685
$847$	6.06218	−	10.5000i	0.208299	−	0.360784i
$848$	−5.07180	+	8.78461i	−0.174166	+	0.301665i
$849$	−8.06218	−	13.9641i	−0.276693	−	0.479247i
$850$		0			0
$851$	10.3923	+	18.0000i	0.356244	+	0.617032i
$852$	3.46410	+	6.00000i	0.118678	+	0.205557i
$853$	32.6603			1.11827			0.559133	−	0.829078i	$-0.311134\pi$
$853$	32.6603			1.11827			0.559133	+	0.829078i	$0.311134\pi$
$854$	3.41858	+	5.92116i	0.116982	+	0.202618i
$855$		0			0
$856$	10.3923	−	18.0000i	0.355202	−	0.615227i
$857$	47.8038			1.63295			0.816474	−	0.577382i	$-0.195926\pi$
$857$	47.8038			1.63295			0.816474	+	0.577382i	$0.195926\pi$
$858$	−2.33975	+	4.73205i	−0.0798776	+	0.161550i
$859$	11.9282			0.406985			0.203493	−	0.979077i	$-0.434771\pi$
$859$	11.9282			0.406985			0.203493	+	0.979077i	$0.434771\pi$
$860$		0			0
$861$	−9.29423	+	16.0981i	−0.316746	+	0.548621i
$862$	−7.71281	−	13.3590i	−0.262699	−	0.455009i
$863$	−47.9615			−1.63263			−0.816315	−	0.577607i	$-0.803986\pi$
$863$	−47.9615			−1.63263			−0.816315	+	0.577607i	$0.803986\pi$
$864$	−2.92820	−	5.07180i	−0.0996195	−	0.172546i
$865$		0			0
$866$	13.9474			0.473953
$867$	−8.23205	−	14.2583i	−0.279575	−	0.484238i
$868$	5.66025	−	9.80385i	0.192122	−	0.332764i
$869$	−11.0000	+	19.0526i	−0.373149	+	0.646314i
$870$		0			0
$871$	18.3923	+	27.5885i	0.623199	+	0.934799i
$872$	−39.0333			−1.32184
$873$	2.59808	−	4.50000i	0.0879316	−	0.152302i
$874$	0.392305	−	0.679492i	0.0132699	−	0.0229842i
$875$		0			0
$876$	−2.53590			−0.0856801
$877$	2.80385	+	4.85641i	0.0946792	+	0.163989i	0.909475	−	0.415759i	$-0.136484\pi$
$877$	2.80385	+	4.85641i	0.0946792	+	0.163989i	−0.814795	+	0.579749i	$0.803151\pi$
$878$	−7.09808	−	12.2942i	−0.239548	−	0.414910i
$879$	8.19615			0.276449
$880$		0			0
$881$	7.80385	−	13.5167i	0.262918	−	0.455388i	−0.704098	−	0.710103i	$-0.748648\pi$
$881$	7.80385	−	13.5167i	0.262918	−	0.455388i	0.967016	+	0.254715i	$0.0819817\pi$
$882$	−1.46410	+	2.53590i	−0.0492989	+	0.0853881i
$883$	−31.7321			−1.06787			−0.533934	−	0.845526i	$-0.679287\pi$
$883$	−31.7321			−1.06787			−0.533934	+	0.845526i	$0.679287\pi$
$884$	2.14359	+	3.21539i	0.0720969	+	0.108145i
$885$		0			0
$886$	−10.6603	+	18.4641i	−0.358138	+	0.620314i
$887$	18.6340	−	32.2750i	0.625668	−	1.08369i	−0.362744	−	0.931889i	$-0.618160\pi$
$887$	18.6340	−	32.2750i	0.625668	−	1.08369i	0.988411	−	0.151799i	$-0.0485067\pi$
$888$	13.1769	+	22.8231i	0.442188	+	0.765893i
$889$	1.14359			0.0383549
$890$		0			0
$891$	1.00000	+	1.73205i	0.0335013	+	0.0580259i
$892$	2.71797			0.0910043
$893$	−0.0525589	−	0.0910347i	−0.00175882	−	0.00304636i
$894$	2.14359	−	3.71281i	0.0716925	−	0.124175i
$895$		0			0
$896$	17.5692			0.586946
$897$	−7.19615	+	0.464102i	−0.240273	+	0.0154959i
$898$	−11.3205			−0.377770
$899$	7.29423	−	12.6340i	0.243276	−	0.421367i
$900$		0			0
$901$	3.46410	+	6.00000i	0.115406	+	0.199889i
$902$	−15.7128			−0.523179
$903$	7.96410	+	13.7942i	0.265029	+	0.459043i
$904$	23.3205	+	40.3923i	0.775629	+	1.34343i
$905$		0			0
$906$	0.339746	+	0.588457i	0.0112873	+	0.0195502i
$907$	28.1244	−	48.7128i	0.933854	−	1.61748i	0.157189	−	0.987569i	$-0.449757\pi$
$907$	28.1244	−	48.7128i	0.933854	−	1.61748i	0.776665	−	0.629914i	$-0.216910\pi$
$908$	3.46410	−	6.00000i	0.114960	−	0.199117i
$909$	10.3923			0.344691
$910$		0			0
$911$	−43.0333			−1.42576			−0.712879	−	0.701287i	$-0.752609\pi$
$911$	−43.0333			−1.42576			−0.712879	+	0.701287i	$0.752609\pi$
$912$	−0.287187	+	0.497423i	−0.00950971	+	0.0164713i
$913$	−2.92820	+	5.07180i	−0.0969094	+	0.167852i
$914$	5.31347	+	9.20319i	0.175754	+	0.304415i
$915$		0			0
$916$	9.35898	+	16.2102i	0.309230	+	0.535601i
$917$	1.90192	+	3.29423i	0.0628071	+	0.108785i
$918$	−0.535898			−0.0176873
$919$	−1.92820	−	3.33975i	−0.0636056	−	0.110168i	0.832469	−	0.554072i	$-0.186927\pi$
$919$	−1.92820	−	3.33975i	−0.0636056	−	0.110168i	−0.896075	+	0.443904i	$0.853593\pi$
$920$		0			0
$921$	3.33013	−	5.76795i	0.109731	−	0.190060i
$922$	7.35898			0.242355
$923$	17.0263	−	1.09808i	0.560427	−	0.0361436i
$924$	−5.07180			−0.166850
$925$		0			0
$926$	0.490381	−	0.849365i	0.0161149	−	0.0279119i
$927$	2.86603	+	4.96410i	0.0941326	+	0.163042i
$928$	19.1384			0.628250
$929$	20.5359	+	35.5692i	0.673761	+	1.16699i	0.976829	+	0.214019i	$0.0686556\pi$
$929$	20.5359	+	35.5692i	0.673761	+	1.16699i	−0.303068	+	0.952969i	$0.598011\pi$
$930$		0			0
$931$	2.14359			0.0702534
$932$	20.6795	+	35.8179i	0.677379	+	1.17326i
$933$	6.29423	−	10.9019i	0.206064	−	0.356913i
$934$	−3.78461	+	6.55514i	−0.123836	+	0.214491i
$935$		0			0
$936$	−9.12436	+	0.588457i	−0.298239	+	0.0192343i
$937$	12.5359			0.409530			0.204765	−	0.978811i	$-0.434357\pi$
$937$	12.5359			0.409530			0.204765	+	0.978811i	$0.434357\pi$
$938$	5.83013	−	10.0981i	0.190360	−	0.329714i
$939$	−9.59808	+	16.6244i	−0.313221	+	0.542515i
$940$		0			0
$941$	41.5167			1.35340			0.676702	−	0.736257i	$-0.263408\pi$
$941$	41.5167			1.35340			0.676702	+	0.736257i	$0.263408\pi$
$942$	−1.36603	−	2.36603i	−0.0445075	−	0.0770893i
$943$	−10.7321	−	18.5885i	−0.349484	−	0.605323i
$944$	−12.4974			−0.406756
$945$		0			0
$946$	−6.73205	+	11.6603i	−0.218878	+	0.379108i
$947$	−6.16987	+	10.6865i	−0.200494	+	0.347266i	−0.948688	−	0.316215i	$-0.897588\pi$
$947$	−6.16987	+	10.6865i	−0.200494	+	0.347266i	0.748194	+	0.663480i	$0.230921\pi$
$948$	−16.1051			−0.523070
$949$	−2.76795	+	5.59808i	−0.0898514	+	0.181721i
$950$		0			0
$951$	14.1962	−	24.5885i	0.460342	−	0.797335i
$952$	1.60770	−	2.78461i	0.0521057	−	0.0902497i
$953$	9.73205	+	16.8564i	0.315252	+	0.546033i	0.979491	−	0.201488i	$-0.0645776\pi$
$953$	9.73205	+	16.8564i	0.315252	+	0.546033i	−0.664239	+	0.747520i	$0.731244\pi$
$954$	−6.92820			−0.224309
$955$		0			0
$956$	−10.1436	−	17.5692i	−0.328067	−	0.568229i
$957$	−6.53590			−0.211276
$958$	14.2154	+	24.6218i	0.459278	+	0.795494i
$959$	−10.0981	+	17.4904i	−0.326084	+	0.564794i
$960$		0			0
$961$	−11.0718			−0.357155
$962$	27.3731	−	1.76537i	0.882543	−	0.0569179i
$963$	−8.19615			−0.264117
$964$	2.92820	−	5.07180i	0.0943111	−	0.163352i
$965$		0			0
$966$	1.26795	+	2.19615i	0.0407956	+	0.0706600i
$967$	−28.1051			−0.903800			−0.451900	−	0.892069i	$-0.649254\pi$
$967$	−28.1051			−0.903800			−0.451900	+	0.892069i	$0.649254\pi$
$968$	8.87564	+	15.3731i	0.285274	+	0.494109i
$969$	0.196152	+	0.339746i	0.00630132	+	0.0109142i
$970$		0			0
$971$	3.80385	+	6.58846i	0.122071	+	0.211434i	0.920584	−	0.390544i	$-0.127713\pi$
$971$	3.80385	+	6.58846i	0.122071	+	0.211434i	−0.798513	+	0.601977i	$0.794380\pi$
$972$	−0.732051	+	1.26795i	−0.0234805	+	0.0406695i
$973$	−17.2583	+	29.8923i	−0.553277	+	0.958303i
$974$	4.10512			0.131536
$975$		0			0
$976$	5.77945			0.184996
$977$	22.7321	−	39.3731i	0.727263	−	1.25966i	−0.230773	−	0.973008i	$-0.574126\pi$
$977$	22.7321	−	39.3731i	0.727263	−	1.25966i	0.958036	−	0.286648i	$-0.0925412\pi$
$978$	7.75833	−	13.4378i	0.248084	−	0.429694i
$979$	5.26795	+	9.12436i	0.168364	+	0.291616i
$980$		0			0
$981$	7.69615	+	13.3301i	0.245719	+	0.425598i
$982$	−6.94744	−	12.0333i	−0.221702	−	0.383999i
$983$	−13.6077			−0.434018			−0.217009	−	0.976170i	$-0.569630\pi$
$983$	−13.6077			−0.434018			−0.217009	+	0.976170i	$0.569630\pi$
$984$	−13.6077	−	23.5692i	−0.433797	−	0.751359i
$985$		0			0
$986$	0.875644	−	1.51666i	0.0278862	−	0.0483003i
$987$	0.339746			0.0108142
$988$	1.56922	+	2.35383i	0.0499235	+	0.0748853i
$989$	−18.3923			−0.584841
$990$		0			0
$991$	−0.464102	+	0.803848i	−0.0147427	+	0.0255351i	−0.873303	−	0.487178i	$-0.838026\pi$
$991$	−0.464102	+	0.803848i	−0.0147427	+	0.0255351i	0.858560	+	0.512713i	$0.171360\pi$
$992$	13.0718	+	22.6410i	0.415030	+	0.718853i
$993$	−23.9282			−0.759339
$994$	−3.00000	−	5.19615i	−0.0951542	−	0.164812i
$995$		0			0
$996$	−4.28719			−0.135845
$997$	0.598076	+	1.03590i	0.0189413	+	0.0328072i	0.875341	−	0.483507i	$-0.160637\pi$
$997$	0.598076	+	1.03590i	0.0189413	+	0.0328072i	−0.856399	+	0.516314i	$0.827304\pi$
$998$	−9.26795	+	16.0526i	−0.293372	+	0.508135i
$999$	5.19615	−	9.00000i	0.164399	−	0.284747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.i.j.451.2		4
5.2	odd	4		975.2.bb.h.724.1		4
5.3	odd	4		975.2.bb.a.724.2		4
5.4	even	2		195.2.i.c.61.1	yes	4
13.3	even	3	inner	975.2.i.j.601.2		4
15.14	odd	2		585.2.j.c.451.2		4
65.3	odd	12		975.2.bb.h.874.1		4
65.4	even	6		2535.2.a.r.1.1		2
65.9	even	6		2535.2.a.o.1.2		2
65.29	even	6		195.2.i.c.16.1	✓	4
65.42	odd	12		975.2.bb.a.874.2		4
195.29	odd	6		585.2.j.c.406.2		4
195.74	odd	6		7605.2.a.bj.1.1		2
195.134	odd	6		7605.2.a.z.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.c.16.1	✓	4	65.29	even	6
195.2.i.c.61.1	yes	4	5.4	even	2
585.2.j.c.406.2		4	195.29	odd	6
585.2.j.c.451.2		4	15.14	odd	2
975.2.i.j.451.2		4	1.1	even	1	trivial
975.2.i.j.601.2		4	13.3	even	3	inner
975.2.bb.a.724.2		4	5.3	odd	4
975.2.bb.a.874.2		4	65.42	odd	12
975.2.bb.h.724.1		4	5.2	odd	4
975.2.bb.h.874.1		4	65.3	odd	12
2535.2.a.o.1.2		2	65.9	even	6
2535.2.a.r.1.1		2	65.4	even	6
7605.2.a.z.1.2		2	195.134	odd	6
7605.2.a.bj.1.1		2	195.74	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 0.633975i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.732051 + 1.26795i) q^{4} +(-0.366025 - 0.633975i) q^{6} +(-0.866025 - 1.50000i) q^{7} +2.53590 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.366025 - 0.633975i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.732051 + 1.26795i) q^{4} +(-0.366025 - 0.633975i) q^{6} +(-0.866025 - 1.50000i) q^{7} +2.53590 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} +1.46410 q^{12} +(1.59808 - 3.23205i) q^{13} -1.26795 q^{14} +(-0.535898 + 0.928203i) q^{16} +(0.366025 + 0.633975i) q^{17} -0.732051 q^{18} +(0.267949 + 0.464102i) q^{19} -1.73205 q^{21} +(-0.732051 - 1.26795i) q^{22} +(1.00000 - 1.73205i) q^{23} +(1.26795 - 2.19615i) q^{24} +(-1.46410 - 2.19615i) q^{26} -1.00000 q^{27} +(1.26795 - 2.19615i) q^{28} +(1.63397 - 2.83013i) q^{29} +4.46410 q^{31} +(2.92820 + 5.07180i) q^{32} +(-1.00000 - 1.73205i) q^{33} +0.535898 q^{34} +(0.732051 - 1.26795i) q^{36} +(-5.19615 + 9.00000i) q^{37} +0.392305 q^{38} +(-2.00000 - 3.00000i) q^{39} +(5.36603 - 9.29423i) q^{41} +(-0.633975 + 1.09808i) q^{42} +(-4.59808 - 7.96410i) q^{43} +2.92820 q^{44} +(-0.732051 - 1.26795i) q^{46} -0.196152 q^{47} +(0.535898 + 0.928203i) q^{48} +(2.00000 - 3.46410i) q^{49} +0.732051 q^{51} +(5.26795 - 0.339746i) q^{52} +9.46410 q^{53} +(-0.366025 + 0.633975i) q^{54} +(-2.19615 - 3.80385i) q^{56} +0.535898 q^{57} +(-1.19615 - 2.07180i) q^{58} +(5.83013 + 10.0981i) q^{59} +(-2.69615 - 4.66987i) q^{61} +(1.63397 - 2.83013i) q^{62} +(-0.866025 + 1.50000i) q^{63} +2.14359 q^{64} -1.46410 q^{66} +(-4.59808 + 7.96410i) q^{67} +(-0.535898 + 0.928203i) q^{68} +(-1.00000 - 1.73205i) q^{69} +(2.36603 + 4.09808i) q^{71} +(-1.26795 - 2.19615i) q^{72} -1.73205 q^{73} +(3.80385 + 6.58846i) q^{74} +(-0.392305 + 0.679492i) q^{76} -3.46410 q^{77} +(-2.63397 + 0.169873i) q^{78} -11.0000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-3.92820 - 6.80385i) q^{82} -2.92820 q^{83} +(-1.26795 - 2.19615i) q^{84} -6.73205 q^{86} +(-1.63397 - 2.83013i) q^{87} +(2.53590 - 4.39230i) q^{88} +(-2.63397 + 4.56218i) q^{89} +(-6.23205 + 0.401924i) q^{91} +2.92820 q^{92} +(2.23205 - 3.86603i) q^{93} +(-0.0717968 + 0.124356i) q^{94} +5.85641 q^{96} +(2.59808 + 4.50000i) q^{97} +(-1.46410 - 2.53590i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 4 q^{4} + 2 q^{6} + 24 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 4 * q^4 + 2 * q^6 + 24 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 4 q^{4} + 2 q^{6} + 24 q^{8} - 2 q^{9} + 4 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{16} - 2 q^{17} + 4 q^{18} + 8 q^{19} + 4 q^{22} + 4 q^{23} + 12 q^{24} + 8 q^{26} - 4 q^{27} + 12 q^{28} + 10 q^{29} + 4 q^{31} - 16 q^{32} - 4 q^{33} + 16 q^{34} - 4 q^{36} - 40 q^{38} - 8 q^{39} + 18 q^{41} - 6 q^{42} - 8 q^{43} - 16 q^{44} + 4 q^{46} + 20 q^{47} + 16 q^{48} + 8 q^{49} - 4 q^{51} + 28 q^{52} + 24 q^{53} + 2 q^{54} + 12 q^{56} + 16 q^{57} + 16 q^{58} + 6 q^{59} + 10 q^{61} + 10 q^{62} + 64 q^{64} + 8 q^{66} - 8 q^{67} - 16 q^{68} - 4 q^{69} + 6 q^{71} - 12 q^{72} + 36 q^{74} + 40 q^{76} - 14 q^{78} - 44 q^{79} - 2 q^{81} + 12 q^{82} + 16 q^{83} - 12 q^{84} - 20 q^{86} - 10 q^{87} + 24 q^{88} - 14 q^{89} - 18 q^{91} - 16 q^{92} + 2 q^{93} - 28 q^{94} - 32 q^{96} + 8 q^{98} - 8 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 4 * q^4 + 2 * q^6 + 24 * q^8 - 2 * q^9 + 4 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^16 - 2 * q^17 + 4 * q^18 + 8 * q^19 + 4 * q^22 + 4 * q^23 + 12 * q^24 + 8 * q^26 - 4 * q^27 + 12 * q^28 + 10 * q^29 + 4 * q^31 - 16 * q^32 - 4 * q^33 + 16 * q^34 - 4 * q^36 - 40 * q^38 - 8 * q^39 + 18 * q^41 - 6 * q^42 - 8 * q^43 - 16 * q^44 + 4 * q^46 + 20 * q^47 + 16 * q^48 + 8 * q^49 - 4 * q^51 + 28 * q^52 + 24 * q^53 + 2 * q^54 + 12 * q^56 + 16 * q^57 + 16 * q^58 + 6 * q^59 + 10 * q^61 + 10 * q^62 + 64 * q^64 + 8 * q^66 - 8 * q^67 - 16 * q^68 - 4 * q^69 + 6 * q^71 - 12 * q^72 + 36 * q^74 + 40 * q^76 - 14 * q^78 - 44 * q^79 - 2 * q^81 + 12 * q^82 + 16 * q^83 - 12 * q^84 - 20 * q^86 - 10 * q^87 + 24 * q^88 - 14 * q^89 - 18 * q^91 - 16 * q^92 + 2 * q^93 - 28 * q^94 - 32 * q^96 + 8 * q^98 - 8 * q^99

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