LMFDB - Embedded newform 245.2.f.b.48.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,2,Mod(48,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("245.48");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.f (of order $4$, 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:	$1.95633484952$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			48.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	245.48
Dual form			245.2.f.b.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 + 0.366025i) q^{2} +(-0.366025 + 0.366025i) q^{3} +1.73205i q^{4} +(-2.00000 - 1.00000i) q^{5} -0.267949i q^{6} +(-1.36603 - 1.36603i) q^{8} +2.73205i q^{9} +O(q^{10})$	\(q+(-0.366025 + 0.366025i) q^{2} +(-0.366025 + 0.366025i) q^{3} +1.73205i q^{4} +(-2.00000 - 1.00000i) q^{5} -0.267949i q^{6} +(-1.36603 - 1.36603i) q^{8} +2.73205i q^{9} +(1.09808 - 0.366025i) q^{10} -2.73205 q^{11} +(-0.633975 - 0.633975i) q^{12} +(-2.00000 + 2.00000i) q^{13} +(1.09808 - 0.366025i) q^{15} -2.46410 q^{16} +(-2.73205 - 2.73205i) q^{17} +(-1.00000 - 1.00000i) q^{18} -0.732051 q^{19} +(1.73205 - 3.46410i) q^{20} +(1.00000 - 1.00000i) q^{22} +(0.0980762 + 0.0980762i) q^{23} +1.00000 q^{24} +(3.00000 + 4.00000i) q^{25} -1.46410i q^{26} +(-2.09808 - 2.09808i) q^{27} +3.00000i q^{29} +(-0.267949 + 0.535898i) q^{30} +7.46410i q^{31} +(3.63397 - 3.63397i) q^{32} +(1.00000 - 1.00000i) q^{33} +2.00000 q^{34} -4.73205 q^{36} +(3.46410 - 3.46410i) q^{37} +(0.267949 - 0.267949i) q^{38} -1.46410i q^{39} +(1.36603 + 4.09808i) q^{40} +6.46410i q^{41} +(2.83013 + 2.83013i) q^{43} -4.73205i q^{44} +(2.73205 - 5.46410i) q^{45} -0.0717968 q^{46} +(6.46410 + 6.46410i) q^{47} +(0.901924 - 0.901924i) q^{48} +(-2.56218 - 0.366025i) q^{50} +2.00000 q^{51} +(-3.46410 - 3.46410i) q^{52} +(-5.00000 - 5.00000i) q^{53} +1.53590 q^{54} +(5.46410 + 2.73205i) q^{55} +(0.267949 - 0.267949i) q^{57} +(-1.09808 - 1.09808i) q^{58} +8.19615 q^{59} +(0.633975 + 1.90192i) q^{60} +1.53590i q^{61} +(-2.73205 - 2.73205i) q^{62} -2.26795i q^{64} +(6.00000 - 2.00000i) q^{65} +0.732051i q^{66} +(7.83013 - 7.83013i) q^{67} +(4.73205 - 4.73205i) q^{68} -0.0717968 q^{69} +1.26795 q^{71} +(3.73205 - 3.73205i) q^{72} +(-9.46410 + 9.46410i) q^{73} +2.53590i q^{74} +(-2.56218 - 0.366025i) q^{75} -1.26795i q^{76} +(0.535898 + 0.535898i) q^{78} +3.26795i q^{79} +(4.92820 + 2.46410i) q^{80} -6.66025 q^{81} +(-2.36603 - 2.36603i) q^{82} +(-2.09808 + 2.09808i) q^{83} +(2.73205 + 8.19615i) q^{85} -2.07180 q^{86} +(-1.09808 - 1.09808i) q^{87} +(3.73205 + 3.73205i) q^{88} +0.660254 q^{89} +(1.00000 + 3.00000i) q^{90} +(-0.169873 + 0.169873i) q^{92} +(-2.73205 - 2.73205i) q^{93} -4.73205 q^{94} +(1.46410 + 0.732051i) q^{95} +2.66025i q^{96} +(-5.92820 - 5.92820i) q^{97} -7.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 8 q^{5} - 2 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 - 8 * q^5 - 2 * q^8	$ 4 q + 2 q^{2} + 2 q^{3} - 8 q^{5} - 2 q^{8} - 6 q^{10} - 4 q^{11} - 6 q^{12} - 8 q^{13} - 6 q^{15} + 4 q^{16} - 4 q^{17} - 4 q^{18} + 4 q^{19} + 4 q^{22} - 10 q^{23} + 4 q^{24} + 12 q^{25} + 2 q^{27} - 8 q^{30} + 18 q^{32} + 4 q^{33} + 8 q^{34} - 12 q^{36} + 8 q^{38} + 2 q^{40} - 6 q^{43} + 4 q^{45} - 28 q^{46} + 12 q^{47} + 14 q^{48} + 14 q^{50} + 8 q^{51} - 20 q^{53} + 20 q^{54} + 8 q^{55} + 8 q^{57} + 6 q^{58} + 12 q^{59} + 6 q^{60} - 4 q^{62} + 24 q^{65} + 14 q^{67} + 12 q^{68} - 28 q^{69} + 12 q^{71} + 8 q^{72} - 24 q^{73} + 14 q^{75} + 16 q^{78} - 8 q^{80} + 8 q^{81} - 6 q^{82} + 2 q^{83} + 4 q^{85} - 36 q^{86} + 6 q^{87} + 8 q^{88} - 32 q^{89} + 4 q^{90} - 18 q^{92} - 4 q^{93} - 12 q^{94} - 8 q^{95} + 4 q^{97}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 - 8 * q^5 - 2 * q^8 - 6 * q^10 - 4 * q^11 - 6 * q^12 - 8 * q^13 - 6 * q^15 + 4 * q^16 - 4 * q^17 - 4 * q^18 + 4 * q^19 + 4 * q^22 - 10 * q^23 + 4 * q^24 + 12 * q^25 + 2 * q^27 - 8 * q^30 + 18 * q^32 + 4 * q^33 + 8 * q^34 - 12 * q^36 + 8 * q^38 + 2 * q^40 - 6 * q^43 + 4 * q^45 - 28 * q^46 + 12 * q^47 + 14 * q^48 + 14 * q^50 + 8 * q^51 - 20 * q^53 + 20 * q^54 + 8 * q^55 + 8 * q^57 + 6 * q^58 + 12 * q^59 + 6 * q^60 - 4 * q^62 + 24 * q^65 + 14 * q^67 + 12 * q^68 - 28 * q^69 + 12 * q^71 + 8 * q^72 - 24 * q^73 + 14 * q^75 + 16 * q^78 - 8 * q^80 + 8 * q^81 - 6 * q^82 + 2 * q^83 + 4 * q^85 - 36 * q^86 + 6 * q^87 + 8 * q^88 - 32 * q^89 + 4 * q^90 - 18 * q^92 - 4 * q^93 - 12 * q^94 - 8 * q^95 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.366025	+	0.366025i	−0.258819	+	0.258819i	−0.824574	−	0.565755i	$-0.808585\pi$
$2$	−0.366025	+	0.366025i	−0.258819	+	0.258819i	0.565755	+	0.824574i	$0.308585\pi$
$3$	−0.366025	+	0.366025i	−0.211325	+	0.211325i	−0.804830	−	0.593505i	$-0.797744\pi$
$3$	−0.366025	+	0.366025i	−0.211325	+	0.211325i	0.593505	+	0.804830i	$0.297744\pi$
$4$			1.73205i			0.866025i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$		−	0.267949i		−	0.109390i
$7$		0			0
$7$		0			0
$8$	−1.36603	−	1.36603i	−0.482963	−	0.482963i
$9$			2.73205i			0.910684i
$10$	1.09808	−	0.366025i	0.347242	−	0.115747i
$11$	−2.73205			−0.823744			−0.411872	−	0.911242i	$-0.635125\pi$
$11$	−2.73205			−0.823744			−0.411872	+	0.911242i	$0.635125\pi$
$12$	−0.633975	−	0.633975i	−0.183013	−	0.183013i
$13$	−2.00000	+	2.00000i	−0.554700	+	0.554700i	−0.927794	−	0.373094i	$-0.878297\pi$
$13$	−2.00000	+	2.00000i	−0.554700	+	0.554700i	0.373094	+	0.927794i	$0.378297\pi$
$14$		0			0
$15$	1.09808	−	0.366025i	0.283522	−	0.0945074i
$16$	−2.46410			−0.616025
$17$	−2.73205	−	2.73205i	−0.662620	−	0.662620i	0.293377	−	0.955997i	$-0.405221\pi$
$17$	−2.73205	−	2.73205i	−0.662620	−	0.662620i	−0.955997	+	0.293377i	$0.905221\pi$
$18$	−1.00000	−	1.00000i	−0.235702	−	0.235702i
$19$	−0.732051			−0.167944			−0.0839720	−	0.996468i	$-0.526761\pi$
$19$	−0.732051			−0.167944			−0.0839720	+	0.996468i	$0.526761\pi$
$20$	1.73205	−	3.46410i	0.387298	−	0.774597i
$21$		0			0
$22$	1.00000	−	1.00000i	0.213201	−	0.213201i
$23$	0.0980762	+	0.0980762i	0.0204503	+	0.0204503i	0.717258	−	0.696808i	$-0.245397\pi$
$23$	0.0980762	+	0.0980762i	0.0204503	+	0.0204503i	−0.696808	+	0.717258i	$0.745397\pi$
$24$	1.00000			0.204124
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$		−	1.46410i		−	0.287134i
$27$	−2.09808	−	2.09808i	−0.403775	−	0.403775i
$28$		0			0
$29$			3.00000i			0.557086i	0.960424	+	0.278543i	$0.0898515\pi$
$29$			3.00000i			0.557086i	−0.960424	+	0.278543i	$0.910149\pi$
$30$	−0.267949	+	0.535898i	−0.0489206	+	0.0978412i
$31$			7.46410i			1.34059i	0.742094	+	0.670296i	$0.233833\pi$
$31$			7.46410i			1.34059i	−0.742094	+	0.670296i	$0.766167\pi$
$32$	3.63397	−	3.63397i	0.642402	−	0.642402i
$33$	1.00000	−	1.00000i	0.174078	−	0.174078i
$34$	2.00000			0.342997
$35$		0			0
$36$	−4.73205			−0.788675
$37$	3.46410	−	3.46410i	0.569495	−	0.569495i	−0.362492	−	0.931987i	$-0.618074\pi$
$37$	3.46410	−	3.46410i	0.569495	−	0.569495i	0.931987	+	0.362492i	$0.118074\pi$
$38$	0.267949	−	0.267949i	0.0434671	−	0.0434671i
$39$		−	1.46410i		−	0.234444i
$40$	1.36603	+	4.09808i	0.215988	+	0.647963i
$41$			6.46410i			1.00952i	0.863259	+	0.504762i	$0.168420\pi$
$41$			6.46410i			1.00952i	−0.863259	+	0.504762i	$0.831580\pi$
$42$		0			0
$43$	2.83013	+	2.83013i	0.431590	+	0.431590i	0.889169	−	0.457579i	$-0.151283\pi$
$43$	2.83013	+	2.83013i	0.431590	+	0.431590i	−0.457579	+	0.889169i	$0.651283\pi$
$44$		−	4.73205i		−	0.713384i
$45$	2.73205	−	5.46410i	0.407270	−	0.814540i
$46$	−0.0717968			−0.0105859
$47$	6.46410	+	6.46410i	0.942886	+	0.942886i	0.998455	−	0.0555687i	$-0.0176972\pi$
$47$	6.46410	+	6.46410i	0.942886	+	0.942886i	−0.0555687	+	0.998455i	$0.517697\pi$
$48$	0.901924	−	0.901924i	0.130181	−	0.130181i
$49$		0			0
$50$	−2.56218	−	0.366025i	−0.362347	−	0.0517638i
$51$	2.00000			0.280056
$52$	−3.46410	−	3.46410i	−0.480384	−	0.480384i
$53$	−5.00000	−	5.00000i	−0.686803	−	0.686803i	0.274721	−	0.961524i	$-0.411414\pi$
$53$	−5.00000	−	5.00000i	−0.686803	−	0.686803i	−0.961524	+	0.274721i	$0.911414\pi$
$54$	1.53590			0.209009
$55$	5.46410	+	2.73205i	0.736779	+	0.368390i
$56$		0			0
$57$	0.267949	−	0.267949i	0.0354907	−	0.0354907i
$58$	−1.09808	−	1.09808i	−0.144184	−	0.144184i
$59$	8.19615			1.06705			0.533524	−	0.845785i	$-0.320867\pi$
$59$	8.19615			1.06705			0.533524	+	0.845785i	$0.320867\pi$
$60$	0.633975	+	1.90192i	0.0818458	+	0.245537i
$61$			1.53590i			0.196652i	0.995154	+	0.0983258i	$0.0313487\pi$
$61$			1.53590i			0.196652i	−0.995154	+	0.0983258i	$0.968651\pi$
$62$	−2.73205	−	2.73205i	−0.346971	−	0.346971i
$63$		0			0
$64$		−	2.26795i		−	0.283494i
$65$	6.00000	−	2.00000i	0.744208	−	0.248069i
$66$			0.732051i			0.0901092i
$67$	7.83013	−	7.83013i	0.956602	−	0.956602i	−0.0424944	−	0.999097i	$-0.513530\pi$
$67$	7.83013	−	7.83013i	0.956602	−	0.956602i	0.999097	+	0.0424944i	$0.0135305\pi$
$68$	4.73205	−	4.73205i	0.573845	−	0.573845i
$69$	−0.0717968			−0.00864332
$70$		0			0
$71$	1.26795			0.150478			0.0752389	−	0.997166i	$-0.476028\pi$
$71$	1.26795			0.150478			0.0752389	+	0.997166i	$0.476028\pi$
$72$	3.73205	−	3.73205i	0.439826	−	0.439826i
$73$	−9.46410	+	9.46410i	−1.10769	+	1.10769i	−0.114236	+	0.993454i	$0.536442\pi$
$73$	−9.46410	+	9.46410i	−1.10769	+	1.10769i	−0.993454	+	0.114236i	$0.963558\pi$
$74$			2.53590i			0.294792i
$75$	−2.56218	−	0.366025i	−0.295855	−	0.0422650i
$76$		−	1.26795i		−	0.145444i
$77$		0			0
$78$	0.535898	+	0.535898i	0.0606785	+	0.0606785i
$79$			3.26795i			0.367673i	0.982957	+	0.183837i	$0.0588517\pi$
$79$			3.26795i			0.367673i	−0.982957	+	0.183837i	$0.941148\pi$
$80$	4.92820	+	2.46410i	0.550990	+	0.275495i
$81$	−6.66025			−0.740028
$82$	−2.36603	−	2.36603i	−0.261284	−	0.261284i
$83$	−2.09808	+	2.09808i	−0.230294	+	0.230294i	−0.812815	−	0.582522i	$-0.802066\pi$
$83$	−2.09808	+	2.09808i	−0.230294	+	0.230294i	0.582522	+	0.812815i	$0.302066\pi$
$84$		0			0
$85$	2.73205	+	8.19615i	0.296333	+	0.888998i
$86$	−2.07180			−0.223408
$87$	−1.09808	−	1.09808i	−0.117726	−	0.117726i
$88$	3.73205	+	3.73205i	0.397838	+	0.397838i
$89$	0.660254			0.0699868			0.0349934	−	0.999388i	$-0.488859\pi$
$89$	0.660254			0.0699868			0.0349934	+	0.999388i	$0.488859\pi$
$90$	1.00000	+	3.00000i	0.105409	+	0.316228i
$91$		0			0
$92$	−0.169873	+	0.169873i	−0.0177105	+	0.0177105i
$93$	−2.73205	−	2.73205i	−0.283300	−	0.283300i
$94$	−4.73205			−0.488074
$95$	1.46410	+	0.732051i	0.150214	+	0.0751068i
$96$			2.66025i			0.271511i
$97$	−5.92820	−	5.92820i	−0.601918	−	0.601918i	0.338903	−	0.940821i	$-0.389944\pi$
$97$	−5.92820	−	5.92820i	−0.601918	−	0.601918i	−0.940821	+	0.338903i	$0.889944\pi$
$98$		0			0
$99$		−	7.46410i		−	0.750170i
$100$	−6.92820	+	5.19615i	−0.692820	+	0.519615i
$101$		−	8.26795i		−	0.822692i	−0.911479	−	0.411346i	$-0.865059\pi$
$101$		−	8.26795i		−	0.822692i	0.911479	−	0.411346i	$-0.134941\pi$
$102$	−0.732051	+	0.732051i	−0.0724838	+	0.0724838i
$103$	−3.36603	+	3.36603i	−0.331664	+	0.331664i	−0.853218	−	0.521554i	$-0.825353\pi$
$103$	−3.36603	+	3.36603i	−0.331664	+	0.331664i	0.521554	+	0.853218i	$0.325353\pi$
$104$	5.46410			0.535799
$105$		0			0
$106$	3.66025			0.355515
$107$	−9.29423	+	9.29423i	−0.898507	+	0.898507i	−0.995304	−	0.0967971i	$-0.969140\pi$
$107$	−9.29423	+	9.29423i	−0.898507	+	0.898507i	0.0967971	+	0.995304i	$0.469140\pi$
$108$	3.63397	−	3.63397i	0.349679	−	0.349679i
$109$			10.1244i			0.969737i	0.874587	+	0.484869i	$0.161133\pi$
$109$			10.1244i			0.969737i	−0.874587	+	0.484869i	$0.838867\pi$
$110$	−3.00000	+	1.00000i	−0.286039	+	0.0953463i
$111$			2.53590i			0.240697i
$112$		0			0
$113$	−7.73205	−	7.73205i	−0.727370	−	0.727370i	0.242725	−	0.970095i	$-0.421959\pi$
$113$	−7.73205	−	7.73205i	−0.727370	−	0.727370i	−0.970095	+	0.242725i	$0.921959\pi$
$114$			0.196152i			0.0183714i
$115$	−0.0980762	−	0.294229i	−0.00914565	−	0.0274370i
$116$	−5.19615			−0.482451
$117$	−5.46410	−	5.46410i	−0.505156	−	0.505156i
$118$	−3.00000	+	3.00000i	−0.276172	+	0.276172i
$119$		0			0
$120$	−2.00000	−	1.00000i	−0.182574	−	0.0912871i
$121$	−3.53590			−0.321445
$122$	−0.562178	−	0.562178i	−0.0508972	−	0.0508972i
$123$	−2.36603	−	2.36603i	−0.213337	−	0.213337i
$124$	−12.9282			−1.16099
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$	0.464102	−	0.464102i	0.0411824	−	0.0411824i	−0.686216	−	0.727398i	$-0.740729\pi$
$127$	0.464102	−	0.464102i	0.0411824	−	0.0411824i	0.727398	+	0.686216i	$0.240729\pi$
$128$	8.09808	+	8.09808i	0.715776	+	0.715776i
$129$	−2.07180			−0.182412
$130$	−1.46410	+	2.92820i	−0.128410	+	0.256820i
$131$		−	15.4641i		−	1.35110i	−0.737312	−	0.675552i	$-0.763905\pi$
$131$		−	15.4641i		−	1.35110i	0.737312	−	0.675552i	$-0.236095\pi$
$132$	1.73205	+	1.73205i	0.150756	+	0.150756i
$133$		0			0
$134$			5.73205i			0.495174i
$135$	2.09808	+	6.29423i	0.180574	+	0.541721i
$136$			7.46410i			0.640041i
$137$	−9.66025	+	9.66025i	−0.825331	+	0.825331i	−0.986867	−	0.161536i	$-0.948355\pi$
$137$	−9.66025	+	9.66025i	−0.825331	+	0.825331i	0.161536	+	0.986867i	$0.448355\pi$
$138$	0.0262794	−	0.0262794i	0.00223705	−	0.00223705i
$139$	−5.66025			−0.480096			−0.240048	−	0.970761i	$-0.577163\pi$
$139$	−5.66025			−0.480096			−0.240048	+	0.970761i	$0.577163\pi$
$140$		0			0
$141$	−4.73205			−0.398511
$142$	−0.464102	+	0.464102i	−0.0389465	+	0.0389465i
$143$	5.46410	−	5.46410i	0.456931	−	0.456931i
$144$		−	6.73205i		−	0.561004i
$145$	3.00000	−	6.00000i	0.249136	−	0.498273i
$146$		−	6.92820i		−	0.573382i
$147$		0			0
$148$	6.00000	+	6.00000i	0.493197	+	0.493197i
$149$			0.803848i			0.0658538i	0.999458	+	0.0329269i	$0.0104828\pi$
$149$			0.803848i			0.0658538i	−0.999458	+	0.0329269i	$0.989517\pi$
$150$	1.07180	−	0.803848i	0.0875118	−	0.0656339i
$151$	13.8564			1.12762			0.563809	−	0.825905i	$-0.309335\pi$
$151$	13.8564			1.12762			0.563809	+	0.825905i	$0.309335\pi$
$152$	1.00000	+	1.00000i	0.0811107	+	0.0811107i
$153$	7.46410	−	7.46410i	0.603437	−	0.603437i
$154$		0			0
$155$	7.46410	−	14.9282i	0.599531	−	1.19906i
$156$	2.53590			0.203034
$157$	3.39230	+	3.39230i	0.270735	+	0.270735i	0.829396	−	0.558661i	$-0.188685\pi$
$157$	3.39230	+	3.39230i	0.270735	+	0.270735i	−0.558661	+	0.829396i	$0.688685\pi$
$158$	−1.19615	−	1.19615i	−0.0951608	−	0.0951608i
$159$	3.66025			0.290277
$160$	−10.9019	+	3.63397i	−0.861873	+	0.287291i
$161$		0			0
$162$	2.43782	−	2.43782i	0.191533	−	0.191533i
$163$	−9.92820	−	9.92820i	−0.777637	−	0.777637i	0.201792	−	0.979428i	$-0.435324\pi$
$163$	−9.92820	−	9.92820i	−0.777637	−	0.777637i	−0.979428	+	0.201792i	$0.935324\pi$
$164$	−11.1962			−0.874273
$165$	−3.00000	+	1.00000i	−0.233550	+	0.0778499i
$166$		−	1.53590i		−	0.119209i
$167$	11.7583	+	11.7583i	0.909887	+	0.909887i	0.996263	−	0.0863757i	$-0.0275285\pi$
$167$	11.7583	+	11.7583i	0.909887	+	0.909887i	−0.0863757	+	0.996263i	$0.527529\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$	−4.00000	−	2.00000i	−0.306786	−	0.153393i
$171$		−	2.00000i		−	0.152944i
$172$	−4.90192	+	4.90192i	−0.373768	+	0.373768i
$173$	−14.5885	+	14.5885i	−1.10914	+	1.10914i	−0.115876	+	0.993264i	$0.536968\pi$
$173$	−14.5885	+	14.5885i	−1.10914	+	1.10914i	−0.993264	+	0.115876i	$0.963032\pi$
$174$	0.803848			0.0609395
$175$		0			0
$176$	6.73205			0.507447
$177$	−3.00000	+	3.00000i	−0.225494	+	0.225494i
$178$	−0.241670	+	0.241670i	−0.0181139	+	0.0181139i
$179$		−	7.85641i		−	0.587215i	−0.955926	−	0.293608i	$-0.905144\pi$
$179$		−	7.85641i		−	0.587215i	0.955926	−	0.293608i	$-0.0948559\pi$
$180$	9.46410	+	4.73205i	0.705412	+	0.352706i
$181$			1.19615i			0.0889093i	0.999011	+	0.0444547i	$0.0141550\pi$
$181$			1.19615i			0.0889093i	−0.999011	+	0.0444547i	$0.985845\pi$
$182$		0			0
$183$	−0.562178	−	0.562178i	−0.0415574	−	0.0415574i
$184$		−	0.267949i		−	0.0197535i
$185$	−10.3923	+	3.46410i	−0.764057	+	0.254686i
$186$	2.00000			0.146647
$187$	7.46410	+	7.46410i	0.545829	+	0.545829i
$188$	−11.1962	+	11.1962i	−0.816563	+	0.816563i
$189$		0			0
$190$	−0.803848	+	0.267949i	−0.0583172	+	0.0194391i
$191$	13.2679			0.960035			0.480018	−	0.877259i	$-0.340630\pi$
$191$	13.2679			0.960035			0.480018	+	0.877259i	$0.340630\pi$
$192$	0.830127	+	0.830127i	0.0599093	+	0.0599093i
$193$	5.73205	+	5.73205i	0.412602	+	0.412602i	0.882644	−	0.470042i	$-0.155761\pi$
$193$	5.73205	+	5.73205i	0.412602	+	0.412602i	−0.470042	+	0.882644i	$0.655761\pi$
$194$	4.33975			0.311576
$195$	−1.46410	+	2.92820i	−0.104846	+	0.209693i
$196$		0			0
$197$	−10.1244	+	10.1244i	−0.721330	+	0.721330i	−0.968876	−	0.247546i	$-0.920376\pi$
$197$	−10.1244	+	10.1244i	−0.721330	+	0.721330i	0.247546	+	0.968876i	$0.420376\pi$
$198$	2.73205	+	2.73205i	0.194158	+	0.194158i
$199$	11.0718			0.784859			0.392429	−	0.919782i	$-0.371635\pi$
$199$	11.0718			0.784859			0.392429	+	0.919782i	$0.371635\pi$
$200$	1.36603	−	9.56218i	0.0965926	−	0.676148i
$201$			5.73205i			0.404308i
$202$	3.02628	+	3.02628i	0.212928	+	0.212928i
$203$		0			0
$204$			3.46410i			0.242536i
$205$	6.46410	−	12.9282i	0.451472	−	0.902945i
$206$		−	2.46410i		−	0.171682i
$207$	−0.267949	+	0.267949i	−0.0186238	+	0.0186238i
$208$	4.92820	−	4.92820i	0.341709	−	0.341709i
$209$	2.00000			0.138343
$210$		0			0
$211$	−0.196152			−0.0135037			−0.00675184	−	0.999977i	$-0.502149\pi$
$211$	−0.196152			−0.0135037			−0.00675184	+	0.999977i	$0.502149\pi$
$212$	8.66025	−	8.66025i	0.594789	−	0.594789i
$213$	−0.464102	+	0.464102i	−0.0317997	+	0.0317997i
$214$		−	6.80385i		−	0.465101i
$215$	−2.83013	−	8.49038i	−0.193013	−	0.579039i
$216$			5.73205i			0.390017i
$217$		0			0
$218$	−3.70577	−	3.70577i	−0.250987	−	0.250987i
$219$		−	6.92820i		−	0.468165i
$220$	−4.73205	+	9.46410i	−0.319035	+	0.638070i
$221$	10.9282			0.735111
$222$	−0.928203	−	0.928203i	−0.0622969	−	0.0622969i
$223$	18.1244	−	18.1244i	1.21370	−	1.21370i	0.243895	−	0.969802i	$-0.421575\pi$
$223$	18.1244	−	18.1244i	1.21370	−	1.21370i	0.969802	−	0.243895i	$-0.0784252\pi$
$224$		0			0
$225$	−10.9282	+	8.19615i	−0.728547	+	0.546410i
$226$	5.66025			0.376514
$227$	13.9282	+	13.9282i	0.924447	+	0.924447i	0.997340	−	0.0728925i	$-0.0232230\pi$
$227$	13.9282	+	13.9282i	0.924447	+	0.924447i	−0.0728925	+	0.997340i	$0.523223\pi$
$228$	0.464102	+	0.464102i	0.0307359	+	0.0307359i
$229$	18.3923			1.21540			0.607699	−	0.794168i	$-0.292093\pi$
$229$	18.3923			1.21540			0.607699	+	0.794168i	$0.292093\pi$
$230$	0.143594	+	0.0717968i	0.00946828	+	0.00473414i
$231$		0			0
$232$	4.09808	−	4.09808i	0.269052	−	0.269052i
$233$	−4.73205	−	4.73205i	−0.310007	−	0.310007i	0.534905	−	0.844912i	$-0.320347\pi$
$233$	−4.73205	−	4.73205i	−0.310007	−	0.310007i	−0.844912	+	0.534905i	$0.820347\pi$
$234$	4.00000			0.261488
$235$	−6.46410	−	19.3923i	−0.421671	−	1.26501i
$236$			14.1962i			0.924091i
$237$	−1.19615	−	1.19615i	−0.0776984	−	0.0776984i
$238$		0			0
$239$		−	2.39230i		−	0.154745i	−0.997002	−	0.0773727i	$-0.975347\pi$
$239$		−	2.39230i		−	0.154745i	0.997002	−	0.0773727i	$-0.0246531\pi$
$240$	−2.70577	+	0.901924i	−0.174657	+	0.0582189i
$241$		−	24.7846i		−	1.59652i	−0.602315	−	0.798259i	$-0.705755\pi$
$241$		−	24.7846i		−	1.59652i	0.602315	−	0.798259i	$-0.294245\pi$
$242$	1.29423	−	1.29423i	0.0831962	−	0.0831962i
$243$	8.73205	−	8.73205i	0.560161	−	0.560161i
$244$	−2.66025			−0.170305
$245$		0			0
$246$	1.73205			0.110432
$247$	1.46410	−	1.46410i	0.0931586	−	0.0931586i
$248$	10.1962	−	10.1962i	0.647456	−	0.647456i
$249$		−	1.53590i		−	0.0973336i
$250$	4.75833	+	3.29423i	0.300943	+	0.208345i
$251$		−	21.8564i		−	1.37956i	−0.724017	−	0.689782i	$-0.757706\pi$
$251$		−	21.8564i		−	1.37956i	0.724017	−	0.689782i	$-0.242294\pi$
$252$		0			0
$253$	−0.267949	−	0.267949i	−0.0168458	−	0.0168458i
$254$			0.339746i			0.0213176i
$255$	−4.00000	−	2.00000i	−0.250490	−	0.125245i
$256$	−1.39230			−0.0870191
$257$	−2.00000	−	2.00000i	−0.124757	−	0.124757i	0.641972	−	0.766728i	$-0.278117\pi$
$257$	−2.00000	−	2.00000i	−0.124757	−	0.124757i	−0.766728	+	0.641972i	$0.778117\pi$
$258$	0.758330	−	0.758330i	0.0472116	−	0.0472116i
$259$		0			0
$260$	3.46410	+	10.3923i	0.214834	+	0.644503i
$261$	−8.19615			−0.507329
$262$	5.66025	+	5.66025i	0.349692	+	0.349692i
$263$	11.0981	+	11.0981i	0.684337	+	0.684337i	0.960974	−	0.276638i	$-0.0892202\pi$
$263$	11.0981	+	11.0981i	0.684337	+	0.684337i	−0.276638	+	0.960974i	$0.589220\pi$
$264$	−2.73205			−0.168146
$265$	5.00000	+	15.0000i	0.307148	+	0.921443i
$266$		0			0
$267$	−0.241670	+	0.241670i	−0.0147899	+	0.0147899i
$268$	13.5622	+	13.5622i	0.828442	+	0.828442i
$269$	−22.8564			−1.39358			−0.696790	−	0.717275i	$-0.745389\pi$
$269$	−22.8564			−1.39358			−0.696790	+	0.717275i	$0.745389\pi$
$270$	−3.07180	−	1.53590i	−0.186944	−	0.0934718i
$271$			21.2679i			1.29194i	0.763365	+	0.645968i	$0.223546\pi$
$271$			21.2679i			1.29194i	−0.763365	+	0.645968i	$0.776454\pi$
$272$	6.73205	+	6.73205i	0.408191	+	0.408191i
$273$		0			0
$274$		−	7.07180i		−	0.427223i
$275$	−8.19615	−	10.9282i	−0.494247	−	0.658995i
$276$		−	0.124356i		−	0.00748533i
$277$	−3.80385	+	3.80385i	−0.228551	+	0.228551i	−0.812087	−	0.583536i	$-0.801669\pi$
$277$	−3.80385	+	3.80385i	−0.228551	+	0.228551i	0.583536	+	0.812087i	$0.301669\pi$
$278$	2.07180	−	2.07180i	0.124258	−	0.124258i
$279$	−20.3923			−1.22086
$280$		0			0
$281$	−0.928203			−0.0553720			−0.0276860	−	0.999617i	$-0.508814\pi$
$281$	−0.928203			−0.0553720			−0.0276860	+	0.999617i	$0.508814\pi$
$282$	1.73205	−	1.73205i	0.103142	−	0.103142i
$283$	−1.39230	+	1.39230i	−0.0827639	+	0.0827639i	−0.747277	−	0.664513i	$-0.768639\pi$
$283$	−1.39230	+	1.39230i	−0.0827639	+	0.0827639i	0.664513	+	0.747277i	$0.268639\pi$
$284$			2.19615i			0.130318i
$285$	−0.803848	+	0.267949i	−0.0476158	+	0.0158719i
$286$			4.00000i			0.236525i
$287$		0			0
$288$	9.92820	+	9.92820i	0.585025	+	0.585025i
$289$		−	2.07180i		−	0.121870i
$290$	1.09808	+	3.29423i	0.0644813	+	0.193444i
$291$	4.33975			0.254400
$292$	−16.3923	−	16.3923i	−0.959287	−	0.959287i
$293$	−2.39230	+	2.39230i	−0.139760	+	0.139760i	−0.773525	−	0.633765i	$-0.781508\pi$
$293$	−2.39230	+	2.39230i	−0.139760	+	0.139760i	0.633765	+	0.773525i	$0.281508\pi$
$294$		0			0
$295$	−16.3923	−	8.19615i	−0.954397	−	0.477198i
$296$	−9.46410			−0.550090
$297$	5.73205	+	5.73205i	0.332607	+	0.332607i
$298$	−0.294229	−	0.294229i	−0.0170442	−	0.0170442i
$299$	−0.392305			−0.0226876
$300$	0.633975	−	4.43782i	0.0366025	−	0.256218i
$301$		0			0
$302$	−5.07180	+	5.07180i	−0.291849	+	0.291849i
$303$	3.02628	+	3.02628i	0.173855	+	0.173855i
$304$	1.80385			0.103458
$305$	1.53590	−	3.07180i	0.0879453	−	0.175891i
$306$			5.46410i			0.312362i
$307$	6.29423	+	6.29423i	0.359231	+	0.359231i	0.863529	−	0.504299i	$-0.168249\pi$
$307$	6.29423	+	6.29423i	0.359231	+	0.359231i	−0.504299	+	0.863529i	$0.668249\pi$
$308$		0			0
$309$		−	2.46410i		−	0.140178i
$310$	2.73205	+	8.19615i	0.155170	+	0.465510i
$311$			15.2679i			0.865766i	0.901450	+	0.432883i	$0.142504\pi$
$311$			15.2679i			0.865766i	−0.901450	+	0.432883i	$0.857496\pi$
$312$	−2.00000	+	2.00000i	−0.113228	+	0.113228i
$313$	3.80385	−	3.80385i	0.215006	−	0.215006i	−0.591384	−	0.806390i	$-0.701418\pi$
$313$	3.80385	−	3.80385i	0.215006	−	0.215006i	0.806390	+	0.591384i	$0.201418\pi$
$314$	−2.48334			−0.140143
$315$		0			0
$316$	−5.66025			−0.318414
$317$	−6.73205	+	6.73205i	−0.378110	+	0.378110i	−0.870420	−	0.492310i	$-0.836153\pi$
$317$	−6.73205	+	6.73205i	−0.378110	+	0.378110i	0.492310	+	0.870420i	$0.336153\pi$
$318$	−1.33975	+	1.33975i	−0.0751292	+	0.0751292i
$319$		−	8.19615i		−	0.458896i
$320$	−2.26795	+	4.53590i	−0.126782	+	0.253564i
$321$		−	6.80385i		−	0.379754i
$322$		0			0
$323$	2.00000	+	2.00000i	0.111283	+	0.111283i
$324$		−	11.5359i		−	0.640883i
$325$	−14.0000	−	2.00000i	−0.776580	−	0.110940i
$326$	7.26795			0.402534
$327$	−3.70577	−	3.70577i	−0.204930	−	0.204930i
$328$	8.83013	−	8.83013i	0.487562	−	0.487562i
$329$		0			0
$330$	0.732051	−	1.46410i	0.0402981	−	0.0805961i
$331$	−1.85641			−0.102037			−0.0510187	−	0.998698i	$-0.516247\pi$
$331$	−1.85641			−0.102037			−0.0510187	+	0.998698i	$0.516247\pi$
$332$	−3.63397	−	3.63397i	−0.199440	−	0.199440i
$333$	9.46410	+	9.46410i	0.518630	+	0.518630i
$334$	−8.60770			−0.470992
$335$	−23.4904	+	7.83013i	−1.28342	+	0.427806i
$336$		0			0
$337$	9.53590	−	9.53590i	0.519453	−	0.519453i	−0.397953	−	0.917406i	$-0.630279\pi$
$337$	9.53590	−	9.53590i	0.519453	−	0.519453i	0.917406	+	0.397953i	$0.130279\pi$
$338$	−1.83013	−	1.83013i	−0.0995458	−	0.0995458i
$339$	5.66025			0.307423
$340$	−14.1962	+	4.73205i	−0.769894	+	0.256631i
$341$		−	20.3923i		−	1.10431i
$342$	0.732051	+	0.732051i	0.0395848	+	0.0395848i
$343$		0			0
$344$		−	7.73205i		−	0.416884i
$345$	0.143594	+	0.0717968i	0.00773082	+	0.00386541i
$346$		−	10.6795i		−	0.574133i
$347$	−21.2942	+	21.2942i	−1.14313	+	1.14313i	−0.155261	+	0.987874i	$0.549622\pi$
$347$	−21.2942	+	21.2942i	−1.14313	+	1.14313i	−0.987874	+	0.155261i	$0.950378\pi$
$348$	1.90192	−	1.90192i	0.101954	−	0.101954i
$349$	6.26795			0.335516			0.167758	−	0.985828i	$-0.446347\pi$
$349$	6.26795			0.335516			0.167758	+	0.985828i	$0.446347\pi$
$350$		0			0
$351$	8.39230			0.447948
$352$	−9.92820	+	9.92820i	−0.529175	+	0.529175i
$353$	9.92820	−	9.92820i	0.528425	−	0.528425i	−0.391678	−	0.920103i	$-0.628105\pi$
$353$	9.92820	−	9.92820i	0.528425	−	0.528425i	0.920103	+	0.391678i	$0.128105\pi$
$354$		−	2.19615i		−	0.116724i
$355$	−2.53590	−	1.26795i	−0.134592	−	0.0672958i
$356$			1.14359i			0.0606103i
$357$		0			0
$358$	2.87564	+	2.87564i	0.151983	+	0.151983i
$359$			34.2487i			1.80758i	0.427978	+	0.903789i	$0.359226\pi$
$359$			34.2487i			1.80758i	−0.427978	+	0.903789i	$0.640774\pi$
$360$	−11.1962	+	3.73205i	−0.590089	+	0.196696i
$361$	−18.4641			−0.971795
$362$	−0.437822	−	0.437822i	−0.0230114	−	0.0230114i
$363$	1.29423	−	1.29423i	0.0679294	−	0.0679294i
$364$		0			0
$365$	28.3923	−	9.46410i	1.48612	−	0.495374i
$366$	0.411543			0.0215117
$367$	−0.366025	−	0.366025i	−0.0191064	−	0.0191064i	0.697489	−	0.716595i	$-0.254301\pi$
$367$	−0.366025	−	0.366025i	−0.0191064	−	0.0191064i	−0.716595	+	0.697489i	$0.754301\pi$
$368$	−0.241670	−	0.241670i	−0.0125979	−	0.0125979i
$369$	−17.6603			−0.919356
$370$	2.53590	−	5.07180i	0.131835	−	0.263670i
$371$		0			0
$372$	4.73205	−	4.73205i	0.245345	−	0.245345i
$373$	5.66025	+	5.66025i	0.293077	+	0.293077i	0.838295	−	0.545218i	$-0.183553\pi$
$373$	5.66025	+	5.66025i	0.293077	+	0.293077i	−0.545218	+	0.838295i	$0.683553\pi$
$374$	−5.46410			−0.282542
$375$	4.75833	+	3.29423i	0.245719	+	0.170113i
$376$		−	17.6603i		−	0.910758i
$377$	−6.00000	−	6.00000i	−0.309016	−	0.309016i
$378$		0			0
$379$		−	2.33975i		−	0.120185i	−0.998193	−	0.0600923i	$-0.980860\pi$
$379$		−	2.33975i		−	0.120185i	0.998193	−	0.0600923i	$-0.0191395\pi$
$380$	−1.26795	+	2.53590i	−0.0650444	+	0.130089i
$381$			0.339746i			0.0174057i
$382$	−4.85641	+	4.85641i	−0.248475	+	0.248475i
$383$	−22.3660	+	22.3660i	−1.14285	+	1.14285i	−0.154924	+	0.987926i	$0.549513\pi$
$383$	−22.3660	+	22.3660i	−1.14285	+	1.14285i	−0.987926	+	0.154924i	$0.950487\pi$
$384$	−5.92820			−0.302522
$385$		0			0
$386$	−4.19615			−0.213579
$387$	−7.73205	+	7.73205i	−0.393042	+	0.393042i
$388$	10.2679	−	10.2679i	0.521276	−	0.521276i
$389$			4.92820i			0.249870i	0.992165	+	0.124935i	$0.0398722\pi$
$389$			4.92820i			0.249870i	−0.992165	+	0.124935i	$0.960128\pi$
$390$	−0.535898	−	1.60770i	−0.0271363	−	0.0814088i
$391$		−	0.535898i		−	0.0271015i
$392$		0			0
$393$	5.66025	+	5.66025i	0.285522	+	0.285522i
$394$		−	7.41154i		−	0.373388i
$395$	3.26795	−	6.53590i	0.164428	−	0.328857i
$396$	12.9282			0.649667
$397$	−2.66025	−	2.66025i	−0.133514	−	0.133514i	0.637191	−	0.770706i	$-0.280096\pi$
$397$	−2.66025	−	2.66025i	−0.133514	−	0.133514i	−0.770706	+	0.637191i	$0.780096\pi$
$398$	−4.05256	+	4.05256i	−0.203136	+	0.203136i
$399$		0			0
$400$	−7.39230	−	9.85641i	−0.369615	−	0.492820i
$401$	11.0000			0.549314			0.274657	−	0.961542i	$-0.411436\pi$
$401$	11.0000			0.549314			0.274657	+	0.961542i	$0.411436\pi$
$402$	−2.09808	−	2.09808i	−0.104643	−	0.104643i
$403$	−14.9282	−	14.9282i	−0.743627	−	0.743627i
$404$	14.3205			0.712472
$405$	13.3205	+	6.66025i	0.661901	+	0.330951i
$406$		0			0
$407$	−9.46410	+	9.46410i	−0.469118	+	0.469118i
$408$	−2.73205	−	2.73205i	−0.135257	−	0.135257i
$409$	20.8564			1.03128			0.515641	−	0.856804i	$-0.327554\pi$
$409$	20.8564			1.03128			0.515641	+	0.856804i	$0.327554\pi$
$410$	2.36603	+	7.09808i	0.116850	+	0.350549i
$411$		−	7.07180i		−	0.348826i
$412$	−5.83013	−	5.83013i	−0.287230	−	0.287230i
$413$		0			0
$414$		−	0.196152i		−	0.00964037i
$415$	6.29423	−	2.09808i	0.308972	−	0.102991i
$416$			14.5359i			0.712681i
$417$	2.07180	−	2.07180i	0.101456	−	0.101456i
$418$	−0.732051	+	0.732051i	−0.0358058	+	0.0358058i
$419$	23.8564			1.16546			0.582731	−	0.812665i	$-0.301984\pi$
$419$	23.8564			1.16546			0.582731	+	0.812665i	$0.301984\pi$
$420$		0			0
$421$	−17.3397			−0.845088			−0.422544	−	0.906343i	$-0.638863\pi$
$421$	−17.3397			−0.845088			−0.422544	+	0.906343i	$0.638863\pi$
$422$	0.0717968	−	0.0717968i	0.00349501	−	0.00349501i
$423$	−17.6603	+	17.6603i	−0.858671	+	0.858671i
$424$			13.6603i			0.663401i
$425$	2.73205	−	19.1244i	0.132524	−	0.927668i
$426$		−	0.339746i		−	0.0164607i
$427$		0			0
$428$	−16.0981	−	16.0981i	−0.778130	−	0.778130i
$429$			4.00000i			0.193122i
$430$	4.14359	+	2.07180i	0.199822	+	0.0999109i
$431$	6.19615			0.298458			0.149229	−	0.988803i	$-0.452321\pi$
$431$	6.19615			0.298458			0.149229	+	0.988803i	$0.452321\pi$
$432$	5.16987	+	5.16987i	0.248736	+	0.248736i
$433$	−17.5359	+	17.5359i	−0.842721	+	0.842721i	−0.989212	−	0.146491i	$-0.953202\pi$
$433$	−17.5359	+	17.5359i	−0.842721	+	0.842721i	0.146491	+	0.989212i	$0.453202\pi$
$434$		0			0
$435$	1.09808	+	3.29423i	0.0526487	+	0.157946i
$436$	−17.5359			−0.839817
$437$	−0.0717968	−	0.0717968i	−0.00343451	−	0.00343451i
$438$	2.53590	+	2.53590i	0.121170	+	0.121170i
$439$	−3.32051			−0.158479			−0.0792396	−	0.996856i	$-0.525249\pi$
$439$	−3.32051			−0.158479			−0.0792396	+	0.996856i	$0.525249\pi$
$440$	−3.73205	−	11.1962i	−0.177919	−	0.533756i
$441$		0			0
$442$	−4.00000	+	4.00000i	−0.190261	+	0.190261i
$443$	−9.56218	−	9.56218i	−0.454313	−	0.454313i	0.442470	−	0.896783i	$-0.354102\pi$
$443$	−9.56218	−	9.56218i	−0.454313	−	0.454313i	−0.896783	+	0.442470i	$0.854102\pi$
$444$	−4.39230			−0.208450
$445$	−1.32051	−	0.660254i	−0.0625981	−	0.0312990i
$446$			13.2679i			0.628256i
$447$	−0.294229	−	0.294229i	−0.0139165	−	0.0139165i
$448$		0			0
$449$			33.0526i			1.55985i	0.625875	+	0.779923i	$0.284742\pi$
$449$			33.0526i			1.55985i	−0.625875	+	0.779923i	$0.715258\pi$
$450$	1.00000	−	7.00000i	0.0471405	−	0.329983i
$451$		−	17.6603i		−	0.831589i
$452$	13.3923	−	13.3923i	0.629921	−	0.629921i
$453$	−5.07180	+	5.07180i	−0.238294	+	0.238294i
$454$	−10.1962			−0.478529
$455$		0			0
$456$	−0.732051			−0.0342814
$457$	8.58846	−	8.58846i	0.401751	−	0.401751i	−0.477099	−	0.878850i	$-0.658312\pi$
$457$	8.58846	−	8.58846i	0.401751	−	0.401751i	0.878850	+	0.477099i	$0.158312\pi$
$458$	−6.73205	+	6.73205i	−0.314568	+	0.314568i
$459$			11.4641i			0.535098i
$460$	0.509619	−	0.169873i	0.0237611	−	0.00792037i
$461$			5.60770i			0.261176i	0.991437	+	0.130588i	$0.0416866\pi$
$461$			5.60770i			0.261176i	−0.991437	+	0.130588i	$0.958313\pi$
$462$		0			0
$463$	−4.75833	−	4.75833i	−0.221138	−	0.221138i	0.587839	−	0.808978i	$-0.299979\pi$
$463$	−4.75833	−	4.75833i	−0.221138	−	0.221138i	−0.808978	+	0.587839i	$0.799979\pi$
$464$		−	7.39230i		−	0.343179i
$465$	2.73205	+	8.19615i	0.126696	+	0.380087i
$466$	3.46410			0.160471
$467$	9.95448	+	9.95448i	0.460639	+	0.460639i	0.898865	−	0.438226i	$-0.144393\pi$
$467$	9.95448	+	9.95448i	0.460639	+	0.460639i	−0.438226	+	0.898865i	$0.644393\pi$
$468$	9.46410	−	9.46410i	0.437478	−	0.437478i
$469$		0			0
$470$	9.46410	+	4.73205i	0.436546	+	0.218273i
$471$	−2.48334			−0.114426
$472$	−11.1962	−	11.1962i	−0.515345	−	0.515345i
$473$	−7.73205	−	7.73205i	−0.355520	−	0.355520i
$474$	0.875644			0.0402197
$475$	−2.19615	−	2.92820i	−0.100766	−	0.134355i
$476$		0			0
$477$	13.6603	−	13.6603i	0.625460	−	0.625460i
$478$	0.875644	+	0.875644i	0.0400510	+	0.0400510i
$479$	−13.0718			−0.597266			−0.298633	−	0.954368i	$-0.596531\pi$
$479$	−13.0718			−0.597266			−0.298633	+	0.954368i	$0.596531\pi$
$480$	2.66025	−	5.32051i	0.121423	−	0.242847i
$481$			13.8564i			0.631798i
$482$	9.07180	+	9.07180i	0.413209	+	0.413209i
$483$		0			0
$484$		−	6.12436i		−	0.278380i
$485$	5.92820	+	17.7846i	0.269186	+	0.807558i
$486$			6.39230i			0.289961i
$487$	19.9282	−	19.9282i	0.903033	−	0.903033i	−0.0926643	−	0.995697i	$-0.529538\pi$
$487$	19.9282	−	19.9282i	0.903033	−	0.903033i	0.995697	+	0.0926643i	$0.0295383\pi$
$488$	2.09808	−	2.09808i	0.0949754	−	0.0949754i
$489$	7.26795			0.328668
$490$		0			0
$491$	37.7128			1.70196			0.850978	−	0.525202i	$-0.176010\pi$
$491$	37.7128			1.70196			0.850978	+	0.525202i	$0.176010\pi$
$492$	4.09808	−	4.09808i	0.184756	−	0.184756i
$493$	8.19615	−	8.19615i	0.369136	−	0.369136i
$494$			1.07180i			0.0482224i
$495$	−7.46410	+	14.9282i	−0.335486	+	0.670973i
$496$		−	18.3923i		−	0.825839i
$497$		0			0
$498$	0.562178	+	0.562178i	0.0251918	+	0.0251918i
$499$		−	11.5167i		−	0.515557i	−0.966204	−	0.257778i	$-0.917010\pi$
$499$		−	11.5167i		−	0.515557i	0.966204	−	0.257778i	$-0.0829904\pi$
$500$	19.0526	−	3.46410i	0.852056	−	0.154919i
$501$	−8.60770			−0.384563
$502$	8.00000	+	8.00000i	0.357057	+	0.357057i
$503$	−17.6340	+	17.6340i	−0.786260	+	0.786260i	−0.980879	−	0.194619i	$-0.937653\pi$
$503$	−17.6340	+	17.6340i	−0.786260	+	0.786260i	0.194619	+	0.980879i	$0.437653\pi$
$504$		0			0
$505$	−8.26795	+	16.5359i	−0.367919	+	0.735838i
$506$	0.196152			0.00872004
$507$	−1.83013	−	1.83013i	−0.0812788	−	0.0812788i
$508$	0.803848	+	0.803848i	0.0356650	+	0.0356650i
$509$	38.9090			1.72461			0.862305	−	0.506390i	$-0.169020\pi$
$509$	38.9090			1.72461			0.862305	+	0.506390i	$0.169020\pi$
$510$	2.19615	−	0.732051i	0.0972473	−	0.0324158i
$511$		0			0
$512$	−15.6865	+	15.6865i	−0.693253	+	0.693253i
$513$	1.53590	+	1.53590i	0.0678116	+	0.0678116i
$514$	1.46410			0.0645788
$515$	10.0981	−	3.36603i	0.444974	−	0.148325i
$516$		−	3.58846i		−	0.157973i
$517$	−17.6603	−	17.6603i	−0.776697	−	0.776697i
$518$		0			0
$519$		−	10.6795i		−	0.468778i
$520$	−10.9282	−	5.46410i	−0.479233	−	0.239617i
$521$			23.8564i			1.04517i	0.852588	+	0.522584i	$0.175032\pi$
$521$			23.8564i			1.04517i	−0.852588	+	0.522584i	$0.824968\pi$
$522$	3.00000	−	3.00000i	0.131306	−	0.131306i
$523$	31.3923	−	31.3923i	1.37269	−	1.37269i	0.516254	−	0.856435i	$-0.327326\pi$
$523$	31.3923	−	31.3923i	1.37269	−	1.37269i	0.856435	−	0.516254i	$-0.172674\pi$
$524$	26.7846			1.17009
$525$		0			0
$526$	−8.12436			−0.354239
$527$	20.3923	−	20.3923i	0.888303	−	0.888303i
$528$	−2.46410	+	2.46410i	−0.107236	+	0.107236i
$529$		−	22.9808i		−	0.999164i
$530$	−7.32051	−	3.66025i	−0.317983	−	0.158991i
$531$			22.3923i			0.971743i
$532$		0			0
$533$	−12.9282	−	12.9282i	−0.559983	−	0.559983i
$534$		−	0.176915i		−	0.00765584i
$535$	27.8827	−	9.29423i	1.20547	−	0.401825i
$536$	−21.3923			−0.924007
$537$	2.87564	+	2.87564i	0.124093	+	0.124093i
$538$	8.36603	−	8.36603i	0.360685	−	0.360685i
$539$		0			0
$540$	−10.9019	+	3.63397i	−0.469144	+	0.156381i
$541$	36.7128			1.57841			0.789204	−	0.614132i	$-0.210494\pi$
$541$	36.7128			1.57841			0.789204	+	0.614132i	$0.210494\pi$
$542$	−7.78461	−	7.78461i	−0.334378	−	0.334378i
$543$	−0.437822	−	0.437822i	−0.0187887	−	0.0187887i
$544$	−19.8564			−0.851336
$545$	10.1244	−	20.2487i	0.433680	−	0.867359i
$546$		0			0
$547$	−16.7583	+	16.7583i	−0.716534	+	0.716534i	−0.967894	−	0.251359i	$-0.919122\pi$
$547$	−16.7583	+	16.7583i	−0.716534	+	0.716534i	0.251359	+	0.967894i	$0.419122\pi$
$548$	−16.7321	−	16.7321i	−0.714758	−	0.714758i
$549$	−4.19615			−0.179087
$550$	7.00000	+	1.00000i	0.298481	+	0.0426401i
$551$		−	2.19615i		−	0.0935592i
$552$	0.0980762	+	0.0980762i	0.00417440	+	0.00417440i
$553$		0			0
$554$		−	2.78461i		−	0.118307i
$555$	2.53590	−	5.07180i	0.107643	−	0.215286i
$556$		−	9.80385i		−	0.415776i
$557$	22.8564	−	22.8564i	0.968457	−	0.968457i	−0.0310605	−	0.999518i	$-0.509888\pi$
$557$	22.8564	−	22.8564i	0.968457	−	0.968457i	0.999518	+	0.0310605i	$0.00988845\pi$
$558$	7.46410	−	7.46410i	0.315981	−	0.315981i
$559$	−11.3205			−0.478806
$560$		0			0
$561$	−5.46410			−0.230695
$562$	0.339746	−	0.339746i	0.0143313	−	0.0143313i
$563$	−17.3660	+	17.3660i	−0.731891	+	0.731891i	−0.970994	−	0.239103i	$-0.923147\pi$
$563$	−17.3660	+	17.3660i	−0.731891	+	0.731891i	0.239103	+	0.970994i	$0.423147\pi$
$564$		−	8.19615i		−	0.345120i
$565$	7.73205	+	23.1962i	0.325290	+	0.975869i
$566$		−	1.01924i		−	0.0428418i
$567$		0			0
$568$	−1.73205	−	1.73205i	−0.0726752	−	0.0726752i
$569$		−	28.9282i		−	1.21273i	−0.795185	−	0.606367i	$-0.792626\pi$
$569$		−	28.9282i		−	1.21273i	0.795185	−	0.606367i	$-0.207374\pi$
$570$	0.196152	−	0.392305i	0.00821592	−	0.0164318i
$571$	−18.0526			−0.755476			−0.377738	−	0.925913i	$-0.623298\pi$
$571$	−18.0526			−0.755476			−0.377738	+	0.925913i	$0.623298\pi$
$572$	9.46410	+	9.46410i	0.395714	+	0.395714i
$573$	−4.85641	+	4.85641i	−0.202879	+	0.202879i
$574$		0			0
$575$	−0.0980762	+	0.686533i	−0.00409006	+	0.0286304i
$576$	6.19615			0.258173
$577$	−4.12436	−	4.12436i	−0.171699	−	0.171699i	0.616026	−	0.787726i	$-0.288741\pi$
$577$	−4.12436	−	4.12436i	−0.171699	−	0.171699i	−0.787726	+	0.616026i	$0.788741\pi$
$578$	0.758330	+	0.758330i	0.0315424	+	0.0315424i
$579$	−4.19615			−0.174386
$580$	10.3923	+	5.19615i	0.431517	+	0.215758i
$581$		0			0
$582$	−1.58846	+	1.58846i	−0.0658437	+	0.0658437i
$583$	13.6603	+	13.6603i	0.565750	+	0.565750i
$584$	25.8564			1.06995
$585$	5.46410	+	16.3923i	0.225913	+	0.677738i
$586$		−	1.75129i		−	0.0723451i
$587$	15.7846	+	15.7846i	0.651501	+	0.651501i	0.953354	−	0.301854i	$-0.0976054\pi$
$587$	15.7846	+	15.7846i	0.651501	+	0.651501i	−0.301854	+	0.953354i	$0.597605\pi$
$588$		0			0
$589$		−	5.46410i		−	0.225144i
$590$	9.00000	−	3.00000i	0.370524	−	0.123508i
$591$		−	7.41154i		−	0.304870i
$592$	−8.53590	+	8.53590i	−0.350823	+	0.350823i
$593$	−15.1962	+	15.1962i	−0.624031	+	0.624031i	−0.946560	−	0.322529i	$-0.895467\pi$
$593$	−15.1962	+	15.1962i	−0.624031	+	0.624031i	0.322529	+	0.946560i	$0.395467\pi$
$594$	−4.19615			−0.172170
$595$		0			0
$596$	−1.39230			−0.0570310
$597$	−4.05256	+	4.05256i	−0.165860	+	0.165860i
$598$	0.143594	−	0.143594i	0.00587198	−	0.00587198i
$599$			17.7128i			0.723726i	0.932231	+	0.361863i	$0.117859\pi$
$599$			17.7128i			0.723726i	−0.932231	+	0.361863i	$0.882141\pi$
$600$	3.00000	+	4.00000i	0.122474	+	0.163299i
$601$			41.1769i			1.67964i	0.542864	+	0.839821i	$0.317340\pi$
$601$			41.1769i			1.67964i	−0.542864	+	0.839821i	$0.682660\pi$
$602$		0			0
$603$	21.3923	+	21.3923i	0.871162	+	0.871162i
$604$			24.0000i			0.976546i
$605$	7.07180	+	3.53590i	0.287509	+	0.143755i
$606$	−2.21539			−0.0899941
$607$	9.29423	+	9.29423i	0.377241	+	0.377241i	0.870106	−	0.492865i	$-0.164050\pi$
$607$	9.29423	+	9.29423i	0.377241	+	0.377241i	−0.492865	+	0.870106i	$0.664050\pi$
$608$	−2.66025	+	2.66025i	−0.107888	+	0.107888i
$609$		0			0
$610$	0.562178	+	1.68653i	0.0227619	+	0.0682857i
$611$	−25.8564			−1.04604
$612$	12.9282	+	12.9282i	0.522592	+	0.522592i
$613$	−17.8564	−	17.8564i	−0.721213	−	0.721213i	0.247639	−	0.968852i	$-0.420345\pi$
$613$	−17.8564	−	17.8564i	−0.721213	−	0.721213i	−0.968852	+	0.247639i	$0.920345\pi$
$614$	−4.60770			−0.185951
$615$	2.36603	+	7.09808i	0.0954074	+	0.286222i
$616$		0			0
$617$	33.9090	−	33.9090i	1.36512	−	1.36512i	0.497874	−	0.867249i	$-0.334114\pi$
$617$	33.9090	−	33.9090i	1.36512	−	1.36512i	0.867249	−	0.497874i	$-0.165886\pi$
$618$	0.901924	+	0.901924i	0.0362807	+	0.0362807i
$619$	−10.1962			−0.409818			−0.204909	−	0.978781i	$-0.565690\pi$
$619$	−10.1962			−0.409818			−0.204909	+	0.978781i	$0.565690\pi$
$620$	25.8564	+	12.9282i	1.03842	+	0.519209i
$621$		−	0.411543i		−	0.0165146i
$622$	−5.58846	−	5.58846i	−0.224077	−	0.224077i
$623$		0			0
$624$			3.60770i			0.144423i
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$			2.78461i			0.111295i
$627$	−0.732051	+	0.732051i	−0.0292353	+	0.0292353i
$628$	−5.87564	+	5.87564i	−0.234464	+	0.234464i
$629$	−18.9282			−0.754717
$630$		0			0
$631$	−4.58846			−0.182664			−0.0913318	−	0.995821i	$-0.529112\pi$
$631$	−4.58846			−0.182664			−0.0913318	+	0.995821i	$0.529112\pi$
$632$	4.46410	−	4.46410i	0.177572	−	0.177572i
$633$	0.0717968	−	0.0717968i	0.00285367	−	0.00285367i
$634$		−	4.92820i		−	0.195724i
$635$	−1.39230	+	0.464102i	−0.0552519	+	0.0184173i
$636$			6.33975i			0.251387i
$637$		0			0
$638$	3.00000	+	3.00000i	0.118771	+	0.118771i
$639$			3.46410i			0.137038i
$640$	−8.09808	−	24.2942i	−0.320105	−	0.960314i
$641$	10.6603			0.421055			0.210527	−	0.977588i	$-0.432482\pi$
$641$	10.6603			0.421055			0.210527	+	0.977588i	$0.432482\pi$
$642$	2.49038	+	2.49038i	0.0982875	+	0.0982875i
$643$	17.5359	−	17.5359i	0.691548	−	0.691548i	−0.271024	−	0.962573i	$-0.587362\pi$
$643$	17.5359	−	17.5359i	0.691548	−	0.691548i	0.962573	+	0.271024i	$0.0873623\pi$
$644$		0			0
$645$	4.14359	+	2.07180i	0.163154	+	0.0815769i
$646$	−1.46410			−0.0576043
$647$	−28.9545	−	28.9545i	−1.13832	−	1.13832i	−0.988752	−	0.149567i	$-0.952212\pi$
$647$	−28.9545	−	28.9545i	−1.13832	−	1.13832i	−0.149567	−	0.988752i	$-0.547788\pi$
$648$	9.09808	+	9.09808i	0.357406	+	0.357406i
$649$	−22.3923			−0.878975
$650$	5.85641	−	4.39230i	0.229707	−	0.172280i
$651$		0			0
$652$	17.1962	−	17.1962i	0.673453	−	0.673453i
$653$	−14.3923	−	14.3923i	−0.563214	−	0.563214i	0.367005	−	0.930219i	$-0.380383\pi$
$653$	−14.3923	−	14.3923i	−0.563214	−	0.563214i	−0.930219	+	0.367005i	$0.880383\pi$
$654$	2.71281			0.106079
$655$	−15.4641	+	30.9282i	−0.604232	+	1.20846i
$656$		−	15.9282i		−	0.621892i
$657$	−25.8564	−	25.8564i	−1.00875	−	1.00875i
$658$		0			0
$659$			27.6603i			1.07749i	0.842469	+	0.538745i	$0.181101\pi$
$659$			27.6603i			1.07749i	−0.842469	+	0.538745i	$0.818899\pi$
$660$	−1.73205	−	5.19615i	−0.0674200	−	0.202260i
$661$			48.1769i			1.87386i	0.349511	+	0.936932i	$0.386348\pi$
$661$			48.1769i			1.87386i	−0.349511	+	0.936932i	$0.613652\pi$
$662$	0.679492	−	0.679492i	0.0264092	−	0.0264092i
$663$	−4.00000	+	4.00000i	−0.155347	+	0.155347i
$664$	5.73205			0.222447
$665$		0			0
$666$	−6.92820			−0.268462
$667$	−0.294229	+	0.294229i	−0.0113926	+	0.0113926i
$668$	−20.3660	+	20.3660i	−0.787985	+	0.787985i
$669$			13.2679i			0.512969i
$670$	5.73205	−	11.4641i	0.221448	−	0.442897i
$671$		−	4.19615i		−	0.161991i
$672$		0			0
$673$	4.39230	+	4.39230i	0.169311	+	0.169311i	0.786676	−	0.617366i	$-0.211800\pi$
$673$	4.39230	+	4.39230i	0.169311	+	0.169311i	−0.617366	+	0.786676i	$0.711800\pi$
$674$			6.98076i			0.268889i
$675$	2.09808	−	14.6865i	0.0807550	−	0.565285i
$676$	−8.66025			−0.333087
$677$	−18.9282	−	18.9282i	−0.727470	−	0.727470i	0.242645	−	0.970115i	$-0.421985\pi$
$677$	−18.9282	−	18.9282i	−0.727470	−	0.727470i	−0.970115	+	0.242645i	$0.921985\pi$
$678$	−2.07180	+	2.07180i	−0.0795669	+	0.0795669i
$679$		0			0
$680$	7.46410	−	14.9282i	0.286235	−	0.572470i
$681$	−10.1962			−0.390717
$682$	7.46410	+	7.46410i	0.285815	+	0.285815i
$683$	−12.4904	−	12.4904i	−0.477931	−	0.477931i	0.426538	−	0.904469i	$-0.359733\pi$
$683$	−12.4904	−	12.4904i	−0.477931	−	0.477931i	−0.904469	+	0.426538i	$0.859733\pi$
$684$	3.46410			0.132453
$685$	28.9808	−	9.66025i	1.10730	−	0.369099i
$686$		0			0
$687$	−6.73205	+	6.73205i	−0.256844	+	0.256844i
$688$	−6.97372	−	6.97372i	−0.265871	−	0.265871i
$689$	20.0000			0.761939
$690$	−0.0788383	+	0.0262794i	−0.00300132	+	0.00100044i
$691$		−	50.8372i		−	1.93394i	−0.254896	−	0.966969i	$-0.582041\pi$
$691$		−	50.8372i		−	1.93394i	0.254896	−	0.966969i	$-0.417959\pi$
$692$	−25.2679	−	25.2679i	−0.960543	−	0.960543i
$693$		0			0
$694$		−	15.5885i		−	0.591730i
$695$	11.3205	+	5.66025i	0.429411	+	0.214706i
$696$			3.00000i			0.113715i
$697$	17.6603	−	17.6603i	0.668930	−	0.668930i
$698$	−2.29423	+	2.29423i	−0.0868378	+	0.0868378i
$699$	3.46410			0.131024
$700$		0			0
$701$	−20.2679			−0.765510			−0.382755	−	0.923850i	$-0.625025\pi$
$701$	−20.2679			−0.765510			−0.382755	+	0.923850i	$0.625025\pi$
$702$	−3.07180	+	3.07180i	−0.115937	+	0.115937i
$703$	−2.53590	+	2.53590i	−0.0956432	+	0.0956432i
$704$			6.19615i			0.233526i
$705$	9.46410	+	4.73205i	0.356439	+	0.178219i
$706$			7.26795i			0.273533i
$707$		0			0
$708$	−5.19615	−	5.19615i	−0.195283	−	0.195283i
$709$			21.9282i			0.823531i	0.911290	+	0.411765i	$0.135088\pi$
$709$			21.9282i			0.823531i	−0.911290	+	0.411765i	$0.864912\pi$
$710$	1.39230	−	0.464102i	0.0522523	−	0.0174174i
$711$	−8.92820			−0.334834
$712$	−0.901924	−	0.901924i	−0.0338010	−	0.0338010i
$713$	−0.732051	+	0.732051i	−0.0274155	+	0.0274155i
$714$		0			0
$715$	−16.3923	+	5.46410i	−0.613037	+	0.204346i
$716$	13.6077			0.508543
$717$	0.875644	+	0.875644i	0.0327015	+	0.0327015i
$718$	−12.5359	−	12.5359i	−0.467836	−	0.467836i
$719$	−38.5885			−1.43911			−0.719553	−	0.694437i	$-0.755653\pi$
$719$	−38.5885			−1.43911			−0.719553	+	0.694437i	$0.755653\pi$
$720$	−6.73205	+	13.4641i	−0.250889	+	0.501777i
$721$		0			0
$722$	6.75833	−	6.75833i	0.251519	−	0.251519i
$723$	9.07180	+	9.07180i	0.337384	+	0.337384i
$724$	−2.07180			−0.0769977
$725$	−12.0000	+	9.00000i	−0.445669	+	0.334252i
$726$			0.947441i			0.0351628i
$727$	−10.0981	−	10.0981i	−0.374517	−	0.374517i	0.494602	−	0.869119i	$-0.335314\pi$
$727$	−10.0981	−	10.0981i	−0.374517	−	0.374517i	−0.869119	+	0.494602i	$0.835314\pi$
$728$		0			0
$729$		−	13.5885i		−	0.503276i
$730$	−6.92820	+	13.8564i	−0.256424	+	0.512849i
$731$		−	15.4641i		−	0.571960i
$732$	0.973721	−	0.973721i	0.0359897	−	0.0359897i
$733$	3.19615	−	3.19615i	0.118053	−	0.118053i	−0.645613	−	0.763665i	$-0.723398\pi$
$733$	3.19615	−	3.19615i	0.118053	−	0.118053i	0.763665	+	0.645613i	$0.223398\pi$
$734$	0.267949			0.00989019
$735$		0			0
$736$	0.712813			0.0262746
$737$	−21.3923	+	21.3923i	−0.787996	+	0.787996i
$738$	6.46410	−	6.46410i	0.237947	−	0.237947i
$739$			22.5885i			0.830930i	0.909609	+	0.415465i	$0.136381\pi$
$739$			22.5885i			0.830930i	−0.909609	+	0.415465i	$0.863619\pi$
$740$	−6.00000	−	18.0000i	−0.220564	−	0.661693i
$741$			1.07180i			0.0393734i
$742$		0			0
$743$	−6.16987	−	6.16987i	−0.226351	−	0.226351i	0.584816	−	0.811166i	$-0.301167\pi$
$743$	−6.16987	−	6.16987i	−0.226351	−	0.226351i	−0.811166	+	0.584816i	$0.801167\pi$
$744$			7.46410i			0.273647i
$745$	0.803848	−	1.60770i	0.0294507	−	0.0589014i
$746$	−4.14359			−0.151708
$747$	−5.73205	−	5.73205i	−0.209725	−	0.209725i
$748$	−12.9282	+	12.9282i	−0.472702	+	0.472702i
$749$		0			0
$750$	−2.94744	+	0.535898i	−0.107625	+	0.0195682i
$751$	−6.39230			−0.233259			−0.116629	−	0.993176i	$-0.537209\pi$
$751$	−6.39230			−0.233259			−0.116629	+	0.993176i	$0.537209\pi$
$752$	−15.9282	−	15.9282i	−0.580842	−	0.580842i
$753$	8.00000	+	8.00000i	0.291536	+	0.291536i
$754$	4.39230			0.159958
$755$	−27.7128	−	13.8564i	−1.00857	−	0.504286i
$756$		0			0
$757$	12.7321	−	12.7321i	0.462754	−	0.462754i	−0.436803	−	0.899557i	$-0.643889\pi$
$757$	12.7321	−	12.7321i	0.462754	−	0.462754i	0.899557	+	0.436803i	$0.143889\pi$
$758$	0.856406	+	0.856406i	0.0311061	+	0.0311061i
$759$	0.196152			0.00711988
$760$	−1.00000	−	3.00000i	−0.0362738	−	0.108821i
$761$			28.7846i			1.04344i	0.853116	+	0.521721i	$0.174710\pi$
$761$			28.7846i			1.04344i	−0.853116	+	0.521721i	$0.825290\pi$
$762$	−0.124356	−	0.124356i	−0.00450493	−	0.00450493i
$763$		0			0
$764$			22.9808i			0.831415i
$765$	−22.3923	+	7.46410i	−0.809595	+	0.269865i
$766$		−	16.3731i		−	0.591583i
$767$	−16.3923	+	16.3923i	−0.591892	+	0.591892i
$768$	0.509619	−	0.509619i	0.0183893	−	0.0183893i
$769$	15.1769			0.547294			0.273647	−	0.961830i	$-0.411770\pi$
$769$	15.1769			0.547294			0.273647	+	0.961830i	$0.411770\pi$
$770$		0			0
$771$	1.46410			0.0527283
$772$	−9.92820	+	9.92820i	−0.357324	+	0.357324i
$773$	11.1244	−	11.1244i	0.400115	−	0.400115i	−0.478158	−	0.878274i	$-0.658696\pi$
$773$	11.1244	−	11.1244i	0.400115	−	0.400115i	0.878274	+	0.478158i	$0.158696\pi$
$774$		−	5.66025i		−	0.203454i
$775$	−29.8564	+	22.3923i	−1.07247	+	0.804355i
$776$			16.1962i			0.581408i
$777$		0			0
$778$	−1.80385	−	1.80385i	−0.0646711	−	0.0646711i
$779$		−	4.73205i		−	0.169543i
$780$	−5.07180	−	2.53590i	−0.181599	−	0.0907997i
$781$	−3.46410			−0.123955
$782$	0.196152	+	0.196152i	0.00701440	+	0.00701440i
$783$	6.29423	−	6.29423i	0.224937	−	0.224937i
$784$		0			0
$785$	−3.39230	−	10.1769i	−0.121077	−	0.363230i
$786$	−4.14359			−0.147797
$787$	−22.8301	−	22.8301i	−0.813806	−	0.813806i	0.171396	−	0.985202i	$-0.445172\pi$
$787$	−22.8301	−	22.8301i	−0.813806	−	0.813806i	−0.985202	+	0.171396i	$0.945172\pi$
$788$	−17.5359	−	17.5359i	−0.624691	−	0.624691i
$789$	−8.12436			−0.289235
$790$	1.19615	+	3.58846i	0.0425572	+	0.127672i
$791$		0			0
$792$	−10.1962	+	10.1962i	−0.362305	+	0.362305i
$793$	−3.07180	−	3.07180i	−0.109083	−	0.109083i
$794$	1.94744			0.0691121
$795$	−7.32051	−	3.66025i	−0.259632	−	0.129816i
$796$			19.1769i			0.679708i
$797$	22.5359	+	22.5359i	0.798262	+	0.798262i	0.982821	−	0.184559i	$-0.0590857\pi$
$797$	22.5359	+	22.5359i	0.798262	+	0.798262i	−0.184559	+	0.982821i	$0.559086\pi$
$798$		0			0
$799$		−	35.3205i		−	1.24955i
$800$	25.4378	+	3.63397i	0.899363	+	0.128480i
$801$			1.80385i			0.0637358i
$802$	−4.02628	+	4.02628i	−0.142173	+	0.142173i
$803$	25.8564	−	25.8564i	0.912453	−	0.912453i
$804$	−9.92820			−0.350141
$805$		0			0
$806$	10.9282			0.384930
$807$	8.36603	−	8.36603i	0.294498	−	0.294498i
$808$	−11.2942	+	11.2942i	−0.397330	+	0.397330i
$809$			4.60770i			0.161998i	0.996714	+	0.0809990i	$0.0258110\pi$
$809$			4.60770i			0.161998i	−0.996714	+	0.0809990i	$0.974189\pi$
$810$	−7.31347	+	2.43782i	−0.256969	+	0.0856563i
$811$		−	42.9282i		−	1.50741i	−0.657211	−	0.753707i	$-0.728264\pi$
$811$		−	42.9282i		−	1.50741i	0.657211	−	0.753707i	$-0.271736\pi$
$812$		0			0
$813$	−7.78461	−	7.78461i	−0.273018	−	0.273018i
$814$		−	6.92820i		−	0.242833i
$815$	9.92820	+	29.7846i	0.347770	+	1.04331i
$816$	−4.92820			−0.172522
$817$	−2.07180	−	2.07180i	−0.0724830	−	0.0724830i
$818$	−7.63397	+	7.63397i	−0.266916	+	0.266916i
$819$		0			0
$820$	22.3923	+	11.1962i	0.781973	+	0.390987i
$821$	−49.3205			−1.72130			−0.860649	−	0.509199i	$-0.829942\pi$
$821$	−49.3205			−1.72130			−0.860649	+	0.509199i	$0.829942\pi$
$822$	2.58846	+	2.58846i	0.0902828	+	0.0902828i
$823$	39.0788	+	39.0788i	1.36220	+	1.36220i	0.871104	+	0.491099i	$0.163405\pi$
$823$	39.0788	+	39.0788i	1.36220	+	1.36220i	0.491099	+	0.871104i	$0.336595\pi$
$824$	9.19615			0.320363
$825$	7.00000	+	1.00000i	0.243709	+	0.0348155i
$826$		0			0
$827$	−33.2224	+	33.2224i	−1.15526	+	1.15526i	−0.169774	+	0.985483i	$0.554304\pi$
$827$	−33.2224	+	33.2224i	−1.15526	+	1.15526i	−0.985483	+	0.169774i	$0.945696\pi$
$828$	−0.464102	−	0.464102i	−0.0161286	−	0.0161286i
$829$	14.5359			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$829$	14.5359			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$830$	−1.53590	+	3.07180i	−0.0533118	+	0.106624i
$831$		−	2.78461i		−	0.0965970i
$832$	4.53590	+	4.53590i	0.157254	+	0.157254i
$833$		0			0
$834$			1.51666i			0.0525177i
$835$	−11.7583	−	35.2750i	−0.406914	−	1.22074i
$836$			3.46410i			0.119808i
$837$	15.6603	−	15.6603i	0.541298	−	0.541298i
$838$	−8.73205	+	8.73205i	−0.301644	+	0.301644i
$839$	6.87564			0.237374			0.118687	−	0.992932i	$-0.462132\pi$
$839$	6.87564			0.237374			0.118687	+	0.992932i	$0.462132\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$	6.34679	−	6.34679i	0.218725	−	0.218725i
$843$	0.339746	−	0.339746i	0.0117015	−	0.0117015i
$844$		−	0.339746i		−	0.0116945i
$845$	5.00000	−	10.0000i	0.172005	−	0.344010i
$846$		−	12.9282i		−	0.444481i
$847$		0			0
$848$	12.3205	+	12.3205i	0.423088	+	0.423088i
$849$		−	1.01924i		−	0.0349802i
$850$	6.00000	+	8.00000i	0.205798	+	0.274398i
$851$	0.679492			0.0232927
$852$	−0.803848	−	0.803848i	−0.0275394	−	0.0275394i
$853$	−18.1244	+	18.1244i	−0.620566	+	0.620566i	−0.945676	−	0.325110i	$-0.894599\pi$
$853$	−18.1244	+	18.1244i	−0.620566	+	0.620566i	0.325110	+	0.945676i	$0.394599\pi$
$854$		0			0
$855$	−2.00000	+	4.00000i	−0.0683986	+	0.136797i
$856$	25.3923			0.867891
$857$	8.12436	+	8.12436i	0.277523	+	0.277523i	0.832119	−	0.554597i	$-0.187127\pi$
$857$	8.12436	+	8.12436i	0.277523	+	0.277523i	−0.554597	+	0.832119i	$0.687127\pi$
$858$	−1.46410	−	1.46410i	−0.0499836	−	0.0499836i
$859$	34.9282			1.19173			0.595867	−	0.803083i	$-0.296808\pi$
$859$	34.9282			1.19173			0.595867	+	0.803083i	$0.296808\pi$
$860$	14.7058	−	4.90192i	0.501463	−	0.167154i
$861$		0			0
$862$	−2.26795	+	2.26795i	−0.0772467	+	0.0772467i
$863$	36.5622	+	36.5622i	1.24459	+	1.24459i	0.958076	+	0.286515i	$0.0924969\pi$
$863$	36.5622	+	36.5622i	1.24459	+	1.24459i	0.286515	+	0.958076i	$0.407503\pi$
$864$	−15.2487			−0.518772
$865$	43.7654	−	14.5885i	1.48807	−	0.496022i
$866$		−	12.8372i		−	0.436225i
$867$	0.758330	+	0.758330i	0.0257542	+	0.0257542i
$868$		0			0
$869$		−	8.92820i		−	0.302869i
$870$	−1.60770	−	0.803848i	−0.0545060	−	0.0272530i
$871$			31.3205i			1.06125i
$872$	13.8301	−	13.8301i	0.468347	−	0.468347i
$873$	16.1962	−	16.1962i	0.548157	−	0.548157i
$874$	0.0525589			0.00177783
$875$		0			0
$876$	12.0000			0.405442
$877$	28.6603	−	28.6603i	0.967788	−	0.967788i	−0.0317091	−	0.999497i	$-0.510095\pi$
$877$	28.6603	−	28.6603i	0.967788	−	0.967788i	0.999497	+	0.0317091i	$0.0100950\pi$
$878$	1.21539	−	1.21539i	0.0410174	−	0.0410174i
$879$		−	1.75129i		−	0.0590695i
$880$	−13.4641	−	6.73205i	−0.453875	−	0.226937i
$881$		−	25.1436i		−	0.847109i	−0.905871	−	0.423555i	$-0.860782\pi$
$881$		−	25.1436i		−	0.847109i	0.905871	−	0.423555i	$-0.139218\pi$
$882$		0			0
$883$	8.07180	+	8.07180i	0.271638	+	0.271638i	0.829759	−	0.558122i	$-0.188478\pi$
$883$	8.07180	+	8.07180i	0.271638	+	0.271638i	−0.558122	+	0.829759i	$0.688478\pi$
$884$			18.9282i			0.636624i
$885$	9.00000	−	3.00000i	0.302532	−	0.100844i
$886$	7.00000			0.235170
$887$	7.97372	+	7.97372i	0.267731	+	0.267731i	0.828185	−	0.560454i	$-0.189373\pi$
$887$	7.97372	+	7.97372i	0.267731	+	0.267731i	−0.560454	+	0.828185i	$0.689373\pi$
$888$	3.46410	−	3.46410i	0.116248	−	0.116248i
$889$		0			0
$890$	0.725009	−	0.241670i	0.0243024	−	0.00810079i
$891$	18.1962			0.609594
$892$	31.3923	+	31.3923i	1.05109	+	1.05109i
$893$	−4.73205	−	4.73205i	−0.158352	−	0.158352i
$894$	0.215390			0.00720373
$895$	−7.85641	+	15.7128i	−0.262611	+	0.525221i
$896$		0			0
$897$	0.143594	−	0.143594i	0.00479445	−	0.00479445i
$898$	−12.0981	−	12.0981i	−0.403718	−	0.403718i
$899$	−22.3923			−0.746825
$900$	−14.1962	−	18.9282i	−0.473205	−	0.630940i
$901$			27.3205i			0.910178i
$902$	6.46410	+	6.46410i	0.215231	+	0.215231i
$903$		0			0
$904$			21.1244i			0.702586i
$905$	1.19615	−	2.39230i	0.0397615	−	0.0795229i
$906$		−	3.71281i		−	0.123350i
$907$	−23.7583	+	23.7583i	−0.788882	+	0.788882i	−0.981311	−	0.192429i	$-0.938364\pi$
$907$	−23.7583	+	23.7583i	−0.788882	+	0.788882i	0.192429	+	0.981311i	$0.438364\pi$
$908$	−24.1244	+	24.1244i	−0.800595	+	0.800595i
$909$	22.5885			0.749212
$910$		0			0
$911$	−7.51666			−0.249038			−0.124519	−	0.992217i	$-0.539739\pi$
$911$	−7.51666			−0.249038			−0.124519	+	0.992217i	$0.539739\pi$
$912$	−0.660254	+	0.660254i	−0.0218632	+	0.0218632i
$913$	5.73205	−	5.73205i	0.189703	−	0.189703i
$914$			6.28719i			0.207962i
$915$	0.562178	+	1.68653i	0.0185850	+	0.0557551i
$916$			31.8564i			1.05257i
$917$		0			0
$918$	−4.19615	−	4.19615i	−0.138494	−	0.138494i
$919$		−	56.1962i		−	1.85374i	−0.375382	−	0.926870i	$-0.622489\pi$
$919$		−	56.1962i		−	1.85374i	0.375382	−	0.926870i	$-0.377511\pi$
$920$	−0.267949	+	0.535898i	−0.00883402	+	0.0176680i
$921$	−4.60770			−0.151829
$922$	−2.05256	−	2.05256i	−0.0675974	−	0.0675974i
$923$	−2.53590	+	2.53590i	−0.0834701	+	0.0834701i
$924$		0			0
$925$	24.2487	+	3.46410i	0.797293	+	0.113899i
$926$	3.48334			0.114470
$927$	−9.19615	−	9.19615i	−0.302041	−	0.302041i
$928$	10.9019	+	10.9019i	0.357873	+	0.357873i
$929$	36.3205			1.19164			0.595819	−	0.803119i	$-0.296828\pi$
$929$	36.3205			1.19164			0.595819	+	0.803119i	$0.296828\pi$
$930$	−4.00000	−	2.00000i	−0.131165	−	0.0655826i
$931$		0			0
$932$	8.19615	−	8.19615i	0.268474	−	0.268474i
$933$	−5.58846	−	5.58846i	−0.182958	−	0.182958i
$934$	−7.28719			−0.238444
$935$	−7.46410	−	22.3923i	−0.244102	−	0.732307i
$936$			14.9282i			0.487944i
$937$	17.0718	+	17.0718i	0.557711	+	0.557711i	0.928655	−	0.370944i	$-0.120966\pi$
$937$	17.0718	+	17.0718i	0.557711	+	0.557711i	−0.370944	+	0.928655i	$0.620966\pi$
$938$		0			0
$939$			2.78461i			0.0908723i
$940$	33.5885	−	11.1962i	1.09553	−	0.365178i
$941$		−	40.6410i		−	1.32486i	−0.749124	−	0.662430i	$-0.769525\pi$
$941$		−	40.6410i		−	1.32486i	0.749124	−	0.662430i	$-0.230475\pi$
$942$	0.908965	−	0.908965i	0.0296157	−	0.0296157i
$943$	−0.633975	+	0.633975i	−0.0206451	+	0.0206451i
$944$	−20.1962			−0.657329
$945$		0			0
$946$	5.66025			0.184031
$947$	0.954483	−	0.954483i	0.0310165	−	0.0310165i	−0.691428	−	0.722445i	$-0.743018\pi$
$947$	0.954483	−	0.954483i	0.0310165	−	0.0310165i	0.722445	+	0.691428i	$0.243018\pi$
$948$	2.07180	−	2.07180i	0.0672888	−	0.0672888i
$949$		−	37.8564i		−	1.22887i
$950$	1.87564	+	0.267949i	0.0608539	+	0.00869342i
$951$		−	4.92820i		−	0.159808i
$952$		0			0
$953$	−37.8564	−	37.8564i	−1.22629	−	1.22629i	−0.965357	−	0.260932i	$-0.915970\pi$
$953$	−37.8564	−	37.8564i	−1.22629	−	1.22629i	−0.260932	−	0.965357i	$-0.584030\pi$
$954$			10.0000i			0.323762i
$955$	−26.5359	−	13.2679i	−0.858682	−	0.429341i
$956$	4.14359			0.134013
$957$	3.00000	+	3.00000i	0.0969762	+	0.0969762i
$958$	4.78461	−	4.78461i	0.154584	−	0.154584i
$959$		0			0
$960$	−0.830127	−	2.49038i	−0.0267922	−	0.0803767i
$961$	−24.7128			−0.797188
$962$	−5.07180	−	5.07180i	−0.163521	−	0.163521i
$963$	−25.3923	−	25.3923i	−0.818256	−	0.818256i
$964$	42.9282			1.38262
$965$	−5.73205	−	17.1962i	−0.184521	−	0.553564i
$966$		0			0
$967$	−13.5622	+	13.5622i	−0.436130	+	0.436130i	−0.890707	−	0.454577i	$-0.849790\pi$
$967$	−13.5622	+	13.5622i	−0.436130	+	0.436130i	0.454577	+	0.890707i	$0.349790\pi$
$968$	4.83013	+	4.83013i	0.155246	+	0.155246i
$969$	−1.46410			−0.0470337
$970$	−8.67949	−	4.33975i	−0.278682	−	0.139341i
$971$			33.5692i			1.07729i	0.842534	+	0.538644i	$0.181063\pi$
$971$			33.5692i			1.07729i	−0.842534	+	0.538644i	$0.818937\pi$
$972$	15.1244	+	15.1244i	0.485114	+	0.485114i
$973$		0			0
$974$			14.5885i			0.467444i
$975$	5.85641	−	4.39230i	0.187555	−	0.140666i
$976$		−	3.78461i		−	0.121142i
$977$	−0.411543	+	0.411543i	−0.0131664	+	0.0131664i	−0.713659	−	0.700493i	$-0.752964\pi$
$977$	−0.411543	+	0.411543i	−0.0131664	+	0.0131664i	0.700493	+	0.713659i	$0.252964\pi$
$978$	−2.66025	+	2.66025i	−0.0850655	+	0.0850655i
$979$	−1.80385			−0.0576512
$980$		0			0
$981$	−27.6603			−0.883124
$982$	−13.8038	+	13.8038i	−0.440498	+	0.440498i
$983$	39.6147	−	39.6147i	1.26351	−	1.26351i	0.314136	−	0.949378i	$-0.398285\pi$
$983$	39.6147	−	39.6147i	1.26351	−	1.26351i	0.949378	−	0.314136i	$-0.101715\pi$
$984$			6.46410i			0.206068i
$985$	30.3731	−	10.1244i	0.967766	−	0.322589i
$986$			6.00000i			0.191079i
$987$		0			0
$988$	2.53590	+	2.53590i	0.0806777	+	0.0806777i
$989$			0.555136i			0.0176523i
$990$	−2.73205	−	8.19615i	−0.0868303	−	0.260491i
$991$	31.7128			1.00739			0.503695	−	0.863881i	$-0.331973\pi$
$991$	31.7128			1.00739			0.503695	+	0.863881i	$0.331973\pi$
$992$	27.1244	+	27.1244i	0.861199	+	0.861199i
$993$	0.679492	−	0.679492i	0.0215630	−	0.0215630i
$994$		0			0
$995$	−22.1436	−	11.0718i	−0.701999	−	0.351000i
$996$	2.66025			0.0842934
$997$	29.1962	+	29.1962i	0.924651	+	0.924651i	0.997354	−	0.0727023i	$-0.0231623\pi$
$997$	29.1962	+	29.1962i	0.924651	+	0.924651i	−0.0727023	+	0.997354i	$0.523162\pi$
$998$	4.21539	+	4.21539i	0.133436	+	0.133436i
$999$	−14.5359			−0.459895

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.f.b.48.1		4
5.2	odd	4		245.2.f.a.97.1		4
7.2	even	3		35.2.k.b.3.1	yes	4
7.3	odd	6		35.2.k.a.33.1	yes	4
7.4	even	3		245.2.l.a.68.1		4
7.5	odd	6		245.2.l.b.178.1		4
7.6	odd	2		245.2.f.a.48.1		4
21.2	odd	6		315.2.bz.a.73.1		4
21.17	even	6		315.2.bz.b.208.1		4
28.3	even	6		560.2.ci.a.33.1		4
28.23	odd	6		560.2.ci.b.353.1		4
35.2	odd	12		35.2.k.a.17.1	✓	4
35.3	even	12		175.2.o.a.82.1		4
35.9	even	6		175.2.o.a.143.1		4
35.12	even	12		245.2.l.a.227.1		4
35.17	even	12		35.2.k.b.12.1	yes	4
35.23	odd	12		175.2.o.b.157.1		4
35.24	odd	6		175.2.o.b.68.1		4
35.27	even	4	inner	245.2.f.b.97.1		4
35.32	odd	12		245.2.l.b.117.1		4
105.2	even	12		315.2.bz.b.262.1		4
105.17	odd	12		315.2.bz.a.82.1		4
140.87	odd	12		560.2.ci.b.257.1		4
140.107	even	12		560.2.ci.a.17.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.k.a.17.1	✓	4	35.2	odd	12
35.2.k.a.33.1	yes	4	7.3	odd	6
35.2.k.b.3.1	yes	4	7.2	even	3
35.2.k.b.12.1	yes	4	35.17	even	12
175.2.o.a.82.1		4	35.3	even	12
175.2.o.a.143.1		4	35.9	even	6
175.2.o.b.68.1		4	35.24	odd	6
175.2.o.b.157.1		4	35.23	odd	12
245.2.f.a.48.1		4	7.6	odd	2
245.2.f.a.97.1		4	5.2	odd	4
245.2.f.b.48.1		4	1.1	even	1	trivial
245.2.f.b.97.1		4	35.27	even	4	inner
245.2.l.a.68.1		4	7.4	even	3
245.2.l.a.227.1		4	35.12	even	12
245.2.l.b.117.1		4	35.32	odd	12
245.2.l.b.178.1		4	7.5	odd	6
315.2.bz.a.73.1		4	21.2	odd	6
315.2.bz.a.82.1		4	105.17	odd	12
315.2.bz.b.208.1		4	21.17	even	6
315.2.bz.b.262.1		4	105.2	even	12
560.2.ci.a.17.1		4	140.107	even	12
560.2.ci.a.33.1		4	28.3	even	6
560.2.ci.b.257.1		4	140.87	odd	12
560.2.ci.b.353.1		4	28.23	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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 + 0.366025i) q^{2} +(-0.366025 + 0.366025i) q^{3} +1.73205i q^{4} +(-2.00000 - 1.00000i) q^{5} -0.267949i q^{6} +(-1.36603 - 1.36603i) q^{8} +2.73205i q^{9} +O(q^{10})\)	\(q+(-0.366025 + 0.366025i) q^{2} +(-0.366025 + 0.366025i) q^{3} +1.73205i q^{4} +(-2.00000 - 1.00000i) q^{5} -0.267949i q^{6} +(-1.36603 - 1.36603i) q^{8} +2.73205i q^{9} +(1.09808 - 0.366025i) q^{10} -2.73205 q^{11} +(-0.633975 - 0.633975i) q^{12} +(-2.00000 + 2.00000i) q^{13} +(1.09808 - 0.366025i) q^{15} -2.46410 q^{16} +(-2.73205 - 2.73205i) q^{17} +(-1.00000 - 1.00000i) q^{18} -0.732051 q^{19} +(1.73205 - 3.46410i) q^{20} +(1.00000 - 1.00000i) q^{22} +(0.0980762 + 0.0980762i) q^{23} +1.00000 q^{24} +(3.00000 + 4.00000i) q^{25} -1.46410i q^{26} +(-2.09808 - 2.09808i) q^{27} +3.00000i q^{29} +(-0.267949 + 0.535898i) q^{30} +7.46410i q^{31} +(3.63397 - 3.63397i) q^{32} +(1.00000 - 1.00000i) q^{33} +2.00000 q^{34} -4.73205 q^{36} +(3.46410 - 3.46410i) q^{37} +(0.267949 - 0.267949i) q^{38} -1.46410i q^{39} +(1.36603 + 4.09808i) q^{40} +6.46410i q^{41} +(2.83013 + 2.83013i) q^{43} -4.73205i q^{44} +(2.73205 - 5.46410i) q^{45} -0.0717968 q^{46} +(6.46410 + 6.46410i) q^{47} +(0.901924 - 0.901924i) q^{48} +(-2.56218 - 0.366025i) q^{50} +2.00000 q^{51} +(-3.46410 - 3.46410i) q^{52} +(-5.00000 - 5.00000i) q^{53} +1.53590 q^{54} +(5.46410 + 2.73205i) q^{55} +(0.267949 - 0.267949i) q^{57} +(-1.09808 - 1.09808i) q^{58} +8.19615 q^{59} +(0.633975 + 1.90192i) q^{60} +1.53590i q^{61} +(-2.73205 - 2.73205i) q^{62} -2.26795i q^{64} +(6.00000 - 2.00000i) q^{65} +0.732051i q^{66} +(7.83013 - 7.83013i) q^{67} +(4.73205 - 4.73205i) q^{68} -0.0717968 q^{69} +1.26795 q^{71} +(3.73205 - 3.73205i) q^{72} +(-9.46410 + 9.46410i) q^{73} +2.53590i q^{74} +(-2.56218 - 0.366025i) q^{75} -1.26795i q^{76} +(0.535898 + 0.535898i) q^{78} +3.26795i q^{79} +(4.92820 + 2.46410i) q^{80} -6.66025 q^{81} +(-2.36603 - 2.36603i) q^{82} +(-2.09808 + 2.09808i) q^{83} +(2.73205 + 8.19615i) q^{85} -2.07180 q^{86} +(-1.09808 - 1.09808i) q^{87} +(3.73205 + 3.73205i) q^{88} +0.660254 q^{89} +(1.00000 + 3.00000i) q^{90} +(-0.169873 + 0.169873i) q^{92} +(-2.73205 - 2.73205i) q^{93} -4.73205 q^{94} +(1.46410 + 0.732051i) q^{95} +2.66025i q^{96} +(-5.92820 - 5.92820i) q^{97} -7.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 8 q^{5} - 2 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 - 8 * q^5 - 2 * q^8	\( 4 q + 2 q^{2} + 2 q^{3} - 8 q^{5} - 2 q^{8} - 6 q^{10} - 4 q^{11} - 6 q^{12} - 8 q^{13} - 6 q^{15} + 4 q^{16} - 4 q^{17} - 4 q^{18} + 4 q^{19} + 4 q^{22} - 10 q^{23} + 4 q^{24} + 12 q^{25} + 2 q^{27} - 8 q^{30} + 18 q^{32} + 4 q^{33} + 8 q^{34} - 12 q^{36} + 8 q^{38} + 2 q^{40} - 6 q^{43} + 4 q^{45} - 28 q^{46} + 12 q^{47} + 14 q^{48} + 14 q^{50} + 8 q^{51} - 20 q^{53} + 20 q^{54} + 8 q^{55} + 8 q^{57} + 6 q^{58} + 12 q^{59} + 6 q^{60} - 4 q^{62} + 24 q^{65} + 14 q^{67} + 12 q^{68} - 28 q^{69} + 12 q^{71} + 8 q^{72} - 24 q^{73} + 14 q^{75} + 16 q^{78} - 8 q^{80} + 8 q^{81} - 6 q^{82} + 2 q^{83} + 4 q^{85} - 36 q^{86} + 6 q^{87} + 8 q^{88} - 32 q^{89} + 4 q^{90} - 18 q^{92} - 4 q^{93} - 12 q^{94} - 8 q^{95} + 4 q^{97}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 8 * q^5 - 2 * q^8 - 6 * q^10 - 4 * q^11 - 6 * q^12 - 8 * q^13 - 6 * q^15 + 4 * q^16 - 4 * q^17 - 4 * q^18 + 4 * q^19 + 4 * q^22 - 10 * q^23 + 4 * q^24 + 12 * q^25 + 2 * q^27 - 8 * q^30 + 18 * q^32 + 4 * q^33 + 8 * q^34 - 12 * q^36 + 8 * q^38 + 2 * q^40 - 6 * q^43 + 4 * q^45 - 28 * q^46 + 12 * q^47 + 14 * q^48 + 14 * q^50 + 8 * q^51 - 20 * q^53 + 20 * q^54 + 8 * q^55 + 8 * q^57 + 6 * q^58 + 12 * q^59 + 6 * q^60 - 4 * q^62 + 24 * q^65 + 14 * q^67 + 12 * q^68 - 28 * q^69 + 12 * q^71 + 8 * q^72 - 24 * q^73 + 14 * q^75 + 16 * q^78 - 8 * q^80 + 8 * q^81 - 6 * q^82 + 2 * q^83 + 4 * q^85 - 36 * q^86 + 6 * q^87 + 8 * q^88 - 32 * q^89 + 4 * q^90 - 18 * q^92 - 4 * q^93 - 12 * q^94 - 8 * q^95 + 4 * q^97

Introduction

L-functions

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