LMFDB - Embedded newform 245.2.j.c.214.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,2,Mod(79,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(6))

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("245.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.95633484952$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			214.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	245.214
Dual form			245.2.j.c.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.23205 + 1.86603i) q^{5} +1.00000 q^{6} -3.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.23205 + 1.86603i) q^{5} +1.00000 q^{6} -3.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} +(0.133975 - 2.23205i) q^{10} +(0.866025 - 0.500000i) q^{12} -2.00000i q^{13} +(2.00000 - 1.00000i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.73205 - 1.00000i) q^{17} +(1.73205 + 1.00000i) q^{18} +(-3.00000 - 5.19615i) q^{19} +(-1.00000 - 2.00000i) q^{20} +(-2.59808 + 1.50000i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(-1.96410 - 4.59808i) q^{25} +(1.00000 + 1.73205i) q^{26} +5.00000i q^{27} -7.00000 q^{29} +(-1.23205 + 1.86603i) q^{30} +(1.00000 - 1.73205i) q^{31} +(4.33013 + 2.50000i) q^{32} +2.00000 q^{34} +2.00000 q^{36} +(6.92820 - 4.00000i) q^{37} +(5.19615 + 3.00000i) q^{38} +(-1.00000 + 1.73205i) q^{39} +(5.59808 + 3.69615i) q^{40} -5.00000 q^{41} +7.00000i q^{43} +(4.46410 + 0.267949i) q^{45} +(1.50000 - 2.59808i) q^{46} -1.00000i q^{48} +(4.00000 + 3.00000i) q^{50} +(1.00000 + 1.73205i) q^{51} +(1.73205 + 1.00000i) q^{52} +(-5.19615 - 3.00000i) q^{53} +(-2.50000 - 4.33013i) q^{54} +6.00000i q^{57} +(6.06218 - 3.50000i) q^{58} +(-5.00000 + 8.66025i) q^{59} +(-0.133975 + 2.23205i) q^{60} +(3.50000 + 6.06218i) q^{61} +2.00000i q^{62} -7.00000 q^{64} +(3.73205 + 2.46410i) q^{65} +(-4.33013 - 2.50000i) q^{67} +(1.73205 - 1.00000i) q^{68} +3.00000 q^{69} -2.00000 q^{71} +(-5.19615 + 3.00000i) q^{72} +(-5.19615 - 3.00000i) q^{73} +(-4.00000 + 6.92820i) q^{74} +(-0.598076 + 4.96410i) q^{75} +6.00000 q^{76} -2.00000i q^{78} +(-1.00000 - 1.73205i) q^{79} +(-2.23205 - 0.133975i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.33013 - 2.50000i) q^{82} +11.0000i q^{83} +(4.00000 - 2.00000i) q^{85} +(-3.50000 - 6.06218i) q^{86} +(6.06218 + 3.50000i) q^{87} +(-4.50000 - 7.79423i) q^{89} +(-4.00000 + 2.00000i) q^{90} -3.00000i q^{92} +(-1.73205 + 1.00000i) q^{93} +(13.3923 + 0.803848i) q^{95} +(-2.50000 - 4.33013i) q^{96} -16.0000i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{4} + 2 q^{5} + 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^4 + 2 * q^5 + 4 * q^6 - 4 * q^9	$ 4 q - 2 q^{4} + 2 q^{5} + 4 q^{6} - 4 q^{9} + 4 q^{10} + 8 q^{15} + 2 q^{16} - 12 q^{19} - 4 q^{20} - 6 q^{24} + 6 q^{25} + 4 q^{26} - 28 q^{29} + 2 q^{30} + 4 q^{31} + 8 q^{34} + 8 q^{36} - 4 q^{39} + 12 q^{40} - 20 q^{41} + 4 q^{45} + 6 q^{46} + 16 q^{50} + 4 q^{51} - 10 q^{54} - 20 q^{59} - 4 q^{60} + 14 q^{61} - 28 q^{64} + 8 q^{65} + 12 q^{69} - 8 q^{71} - 16 q^{74} + 8 q^{75} + 24 q^{76} - 4 q^{79} - 2 q^{80} - 2 q^{81} + 16 q^{85} - 14 q^{86} - 18 q^{89} - 16 q^{90} + 12 q^{95} - 10 q^{96}+O(q^{100}) $ 4 * q - 2 * q^4 + 2 * q^5 + 4 * q^6 - 4 * q^9 + 4 * q^10 + 8 * q^15 + 2 * q^16 - 12 * q^19 - 4 * q^20 - 6 * q^24 + 6 * q^25 + 4 * q^26 - 28 * q^29 + 2 * q^30 + 4 * q^31 + 8 * q^34 + 8 * q^36 - 4 * q^39 + 12 * q^40 - 20 * q^41 + 4 * q^45 + 6 * q^46 + 16 * q^50 + 4 * q^51 - 10 * q^54 - 20 * q^59 - 4 * q^60 + 14 * q^61 - 28 * q^64 + 8 * q^65 + 12 * q^69 - 8 * q^71 - 16 * q^74 + 8 * q^75 + 24 * q^76 - 4 * q^79 - 2 * q^80 - 2 * q^81 + 16 * q^85 - 14 * q^86 - 18 * q^89 - 16 * q^90 + 12 * q^95 - 10 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i	−0.773893	−	0.633316i	$-0.781693\pi$
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i	0.161521	+	0.986869i	$0.448360\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i	0.228714	−	0.973494i	$-0.426548\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i	−0.728714	+	0.684819i	$0.759881\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.23205	+	1.86603i	−0.550990	+	0.834512i
$5$	−1.23205	+	1.86603i	−0.550990	+	0.834512i
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$		−	3.00000i		−	1.06066i
$9$	−1.00000	−	1.73205i	−0.333333	−	0.577350i
$10$	0.133975	−	2.23205i	0.0423665	−	0.705836i
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$		0			0
$15$	2.00000	−	1.00000i	0.516398	−	0.258199i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	0.275029	−	0.961436i	$-0.411312\pi$
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	−0.695113	+	0.718900i	$0.744646\pi$
$18$	1.73205	+	1.00000i	0.408248	+	0.235702i
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	−0.972404	−	0.233301i	$-0.925047\pi$
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	0.284157	−	0.958778i	$-0.408286\pi$
$20$	−1.00000	−	2.00000i	−0.223607	−	0.447214i
$21$		0			0
$22$		0			0
$23$	−2.59808	+	1.50000i	−0.541736	+	0.312772i	−0.745782	−	0.666190i	$-0.767924\pi$
$23$	−2.59808	+	1.50000i	−0.541736	+	0.312772i	0.204046	+	0.978961i	$0.434591\pi$
$24$	−1.50000	+	2.59808i	−0.306186	+	0.530330i
$25$	−1.96410	−	4.59808i	−0.392820	−	0.919615i
$26$	1.00000	+	1.73205i	0.196116	+	0.339683i
$27$			5.00000i			0.962250i
$28$		0			0
$29$	−7.00000			−1.29987			−0.649934	−	0.759991i	$-0.725203\pi$
$29$	−7.00000			−1.29987			−0.649934	+	0.759991i	$0.725203\pi$
$30$	−1.23205	+	1.86603i	−0.224941	+	0.340688i
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	−0.762140	−	0.647412i	$-0.775851\pi$
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	0.941745	+	0.336327i	$0.109185\pi$
$32$	4.33013	+	2.50000i	0.765466	+	0.441942i
$33$		0			0
$34$	2.00000			0.342997
$35$		0			0
$36$	2.00000			0.333333
$37$	6.92820	−	4.00000i	1.13899	−	0.657596i	0.192809	−	0.981236i	$-0.438240\pi$
$37$	6.92820	−	4.00000i	1.13899	−	0.657596i	0.946180	+	0.323640i	$0.104907\pi$
$38$	5.19615	+	3.00000i	0.842927	+	0.486664i
$39$	−1.00000	+	1.73205i	−0.160128	+	0.277350i
$40$	5.59808	+	3.69615i	0.885134	+	0.584413i
$41$	−5.00000			−0.780869			−0.390434	−	0.920631i	$-0.627675\pi$
$41$	−5.00000			−0.780869			−0.390434	+	0.920631i	$0.627675\pi$
$42$		0			0
$43$			7.00000i			1.06749i	0.845645	+	0.533745i	$0.179216\pi$
$43$			7.00000i			1.06749i	−0.845645	+	0.533745i	$0.820784\pi$
$44$		0			0
$45$	4.46410	+	0.267949i	0.665469	+	0.0399435i
$46$	1.50000	−	2.59808i	0.221163	−	0.383065i
$47$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$47$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$48$		−	1.00000i		−	0.144338i
$49$		0			0
$50$	4.00000	+	3.00000i	0.565685	+	0.424264i
$51$	1.00000	+	1.73205i	0.140028	+	0.242536i
$52$	1.73205	+	1.00000i	0.240192	+	0.138675i
$53$	−5.19615	−	3.00000i	−0.713746	−	0.412082i	0.0987002	−	0.995117i	$-0.468532\pi$
$53$	−5.19615	−	3.00000i	−0.713746	−	0.412082i	−0.812447	+	0.583036i	$0.801865\pi$
$54$	−2.50000	−	4.33013i	−0.340207	−	0.589256i
$55$		0			0
$56$		0			0
$57$			6.00000i			0.794719i
$58$	6.06218	−	3.50000i	0.796003	−	0.459573i
$59$	−5.00000	+	8.66025i	−0.650945	+	1.12747i	0.331949	+	0.943297i	$0.392294\pi$
$59$	−5.00000	+	8.66025i	−0.650945	+	1.12747i	−0.982894	+	0.184172i	$0.941040\pi$
$60$	−0.133975	+	2.23205i	−0.0172960	+	0.288157i
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	0.998264	−	0.0588933i	$-0.0187572\pi$
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	−0.550135	+	0.835076i	$0.685424\pi$
$62$			2.00000i			0.254000i
$63$		0			0
$64$	−7.00000			−0.875000
$65$	3.73205	+	2.46410i	0.462904	+	0.305634i
$66$		0			0
$67$	−4.33013	−	2.50000i	−0.529009	−	0.305424i	0.211604	−	0.977356i	$-0.432131\pi$
$67$	−4.33013	−	2.50000i	−0.529009	−	0.305424i	−0.740613	+	0.671932i	$0.765465\pi$
$68$	1.73205	−	1.00000i	0.210042	−	0.121268i
$69$	3.00000			0.361158
$70$		0			0
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$	−5.19615	+	3.00000i	−0.612372	+	0.353553i
$73$	−5.19615	−	3.00000i	−0.608164	−	0.351123i	0.164083	−	0.986447i	$-0.447534\pi$
$73$	−5.19615	−	3.00000i	−0.608164	−	0.351123i	−0.772246	+	0.635323i	$0.780867\pi$
$74$	−4.00000	+	6.92820i	−0.464991	+	0.805387i
$75$	−0.598076	+	4.96410i	−0.0690599	+	0.573205i
$76$	6.00000			0.688247
$77$		0			0
$78$		−	2.00000i		−	0.226455i
$79$	−1.00000	−	1.73205i	−0.112509	−	0.194871i	0.804272	−	0.594261i	$-0.202555\pi$
$79$	−1.00000	−	1.73205i	−0.112509	−	0.194871i	−0.916781	+	0.399390i	$0.869222\pi$
$80$	−2.23205	−	0.133975i	−0.249551	−	0.0149788i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.33013	−	2.50000i	0.478183	−	0.276079i
$83$			11.0000i			1.20741i	0.797209	+	0.603703i	$0.206309\pi$
$83$			11.0000i			1.20741i	−0.797209	+	0.603703i	$0.793691\pi$
$84$		0			0
$85$	4.00000	−	2.00000i	0.433861	−	0.216930i
$86$	−3.50000	−	6.06218i	−0.377415	−	0.653701i
$87$	6.06218	+	3.50000i	0.649934	+	0.375239i
$88$		0			0
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	0.522654	−	0.852545i	$-0.324942\pi$
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	−0.999653	+	0.0263586i	$0.991609\pi$
$90$	−4.00000	+	2.00000i	−0.421637	+	0.210819i
$91$		0			0
$92$		−	3.00000i		−	0.312772i
$93$	−1.73205	+	1.00000i	−0.179605	+	0.103695i
$94$		0			0
$95$	13.3923	+	0.803848i	1.37402	+	0.0824730i
$96$	−2.50000	−	4.33013i	−0.255155	−	0.441942i
$97$		−	16.0000i		−	1.62455i	−0.583272	−	0.812277i	$-0.698228\pi$
$97$		−	16.0000i		−	1.62455i	0.583272	−	0.812277i	$-0.301772\pi$
$98$		0			0
$99$		0			0
$100$	4.96410	+	0.598076i	0.496410	+	0.0598076i
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	−0.550474	−	0.834853i	$-0.685553\pi$
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	0.998240	+	0.0592978i	$0.0188862\pi$
$102$	−1.73205	−	1.00000i	−0.171499	−	0.0990148i
$103$	−6.06218	+	3.50000i	−0.597324	+	0.344865i	−0.767988	−	0.640464i	$-0.778742\pi$
$103$	−6.06218	+	3.50000i	−0.597324	+	0.344865i	0.170664	+	0.985329i	$0.445409\pi$
$104$	−6.00000			−0.588348
$105$		0			0
$106$	6.00000			0.582772
$107$	−9.52628	+	5.50000i	−0.920940	+	0.531705i	−0.883935	−	0.467610i	$-0.845115\pi$
$107$	−9.52628	+	5.50000i	−0.920940	+	0.531705i	−0.0370053	+	0.999315i	$0.511782\pi$
$108$	−4.33013	−	2.50000i	−0.416667	−	0.240563i
$109$	2.50000	−	4.33013i	0.239457	−	0.414751i	−0.721102	−	0.692829i	$-0.756364\pi$
$109$	2.50000	−	4.33013i	0.239457	−	0.414751i	0.960558	+	0.278078i	$0.0896974\pi$
$110$		0			0
$111$	−8.00000			−0.759326
$112$		0			0
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$	−3.00000	−	5.19615i	−0.280976	−	0.486664i
$115$	0.401924	−	6.69615i	0.0374796	−	0.624419i
$116$	3.50000	−	6.06218i	0.324967	−	0.562859i
$117$	−3.46410	+	2.00000i	−0.320256	+	0.184900i
$118$		−	10.0000i		−	0.920575i
$119$		0			0
$120$	−3.00000	−	6.00000i	−0.273861	−	0.547723i
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	−6.06218	−	3.50000i	−0.548844	−	0.316875i
$123$	4.33013	+	2.50000i	0.390434	+	0.225417i
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$		0			0
$127$		−	16.0000i		−	1.41977i	−0.704317	−	0.709885i	$-0.748747\pi$
$127$		−	16.0000i		−	1.41977i	0.704317	−	0.709885i	$-0.251253\pi$
$128$	−2.59808	+	1.50000i	−0.229640	+	0.132583i
$129$	3.50000	−	6.06218i	0.308158	−	0.533745i
$130$	−4.46410	−	0.267949i	−0.391528	−	0.0235007i
$131$	2.00000	+	3.46410i	0.174741	+	0.302660i	0.940072	−	0.340977i	$-0.110758\pi$
$131$	2.00000	+	3.46410i	0.174741	+	0.302660i	−0.765331	+	0.643637i	$0.777425\pi$
$132$		0			0
$133$		0			0
$134$	5.00000			0.431934
$135$	−9.33013	−	6.16025i	−0.803009	−	0.530190i
$136$	−3.00000	+	5.19615i	−0.257248	+	0.445566i
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$	−2.59808	+	1.50000i	−0.221163	+	0.127688i
$139$	8.00000			0.678551			0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000			0.678551			0.339276	+	0.940687i	$0.389818\pi$
$140$		0			0
$141$		0			0
$142$	1.73205	−	1.00000i	0.145350	−	0.0839181i
$143$		0			0
$144$	1.00000	−	1.73205i	0.0833333	−	0.144338i
$145$	8.62436	−	13.0622i	0.716214	−	1.08475i
$146$	6.00000			0.496564
$147$		0			0
$148$			8.00000i			0.657596i
$149$	0.500000	+	0.866025i	0.0409616	+	0.0709476i	0.885779	−	0.464107i	$-0.153625\pi$
$149$	0.500000	+	0.866025i	0.0409616	+	0.0709476i	−0.844818	+	0.535054i	$0.820291\pi$
$150$	−1.96410	−	4.59808i	−0.160368	−	0.375431i
$151$	−7.00000	+	12.1244i	−0.569652	+	0.986666i	0.426948	+	0.904276i	$0.359589\pi$
$151$	−7.00000	+	12.1244i	−0.569652	+	0.986666i	−0.996600	+	0.0823900i	$0.973745\pi$
$152$	−15.5885	+	9.00000i	−1.26439	+	0.729996i
$153$			4.00000i			0.323381i
$154$		0			0
$155$	2.00000	+	4.00000i	0.160644	+	0.321288i
$156$	−1.00000	−	1.73205i	−0.0800641	−	0.138675i
$157$	−10.3923	−	6.00000i	−0.829396	−	0.478852i	0.0242497	−	0.999706i	$-0.492280\pi$
$157$	−10.3923	−	6.00000i	−0.829396	−	0.478852i	−0.853646	+	0.520854i	$0.825614\pi$
$158$	1.73205	+	1.00000i	0.137795	+	0.0795557i
$159$	3.00000	+	5.19615i	0.237915	+	0.412082i
$160$	−10.0000	+	5.00000i	−0.790569	+	0.395285i
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$	−3.46410	+	2.00000i	−0.271329	+	0.156652i	−0.629492	−	0.777007i	$-0.716737\pi$
$163$	−3.46410	+	2.00000i	−0.271329	+	0.156652i	0.358162	+	0.933659i	$0.383403\pi$
$164$	2.50000	−	4.33013i	0.195217	−	0.338126i
$165$		0			0
$166$	−5.50000	−	9.52628i	−0.426883	−	0.739383i
$167$		−	3.00000i		−	0.232147i	−0.993241	−	0.116073i	$-0.962969\pi$
$167$		−	3.00000i		−	0.232147i	0.993241	−	0.116073i	$-0.0370308\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$	−2.46410	+	3.73205i	−0.188988	+	0.286235i
$171$	−6.00000	+	10.3923i	−0.458831	+	0.794719i
$172$	−6.06218	−	3.50000i	−0.462237	−	0.266872i
$173$	10.3923	−	6.00000i	0.790112	−	0.456172i	−0.0498898	−	0.998755i	$-0.515887\pi$
$173$	10.3923	−	6.00000i	0.790112	−	0.456172i	0.840002	+	0.542583i	$0.182554\pi$
$174$	−7.00000			−0.530669
$175$		0			0
$176$		0			0
$177$	8.66025	−	5.00000i	0.650945	−	0.375823i
$178$	7.79423	+	4.50000i	0.584202	+	0.337289i
$179$	−1.00000	+	1.73205i	−0.0747435	+	0.129460i	−0.900975	−	0.433872i	$-0.857147\pi$
$179$	−1.00000	+	1.73205i	−0.0747435	+	0.129460i	0.826231	+	0.563331i	$0.190480\pi$
$180$	−2.46410	+	3.73205i	−0.183663	+	0.278171i
$181$	3.00000			0.222988			0.111494	−	0.993765i	$-0.464436\pi$
$181$	3.00000			0.222988			0.111494	+	0.993765i	$0.464436\pi$
$182$		0			0
$183$		−	7.00000i		−	0.517455i
$184$	4.50000	+	7.79423i	0.331744	+	0.574598i
$185$	−1.07180	+	17.8564i	−0.0788001	+	1.31283i
$186$	1.00000	−	1.73205i	0.0733236	−	0.127000i
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−12.0000	+	6.00000i	−0.870572	+	0.435286i
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	0.563081	−	0.826402i	$-0.309616\pi$
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	−0.997225	+	0.0744412i	$0.976283\pi$
$192$	6.06218	+	3.50000i	0.437500	+	0.252591i
$193$	3.46410	+	2.00000i	0.249351	+	0.143963i	0.619467	−	0.785022i	$-0.287349\pi$
$193$	3.46410	+	2.00000i	0.249351	+	0.143963i	−0.370116	+	0.928986i	$0.620682\pi$
$194$	8.00000	+	13.8564i	0.574367	+	0.994832i
$195$	−2.00000	−	4.00000i	−0.143223	−	0.286446i
$196$		0			0
$197$			8.00000i			0.569976i	0.958531	+	0.284988i	$0.0919897\pi$
$197$			8.00000i			0.569976i	−0.958531	+	0.284988i	$0.908010\pi$
$198$		0			0
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	−0.786389	−	0.617731i	$-0.788052\pi$
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	0.928166	+	0.372168i	$0.121385\pi$
$200$	−13.7942	+	5.89230i	−0.975399	+	0.416649i
$201$	2.50000	+	4.33013i	0.176336	+	0.305424i
$202$			9.00000i			0.633238i
$203$		0			0
$204$	−2.00000			−0.140028
$205$	6.16025	−	9.33013i	0.430251	−	0.651644i
$206$	3.50000	−	6.06218i	0.243857	−	0.422372i
$207$	5.19615	+	3.00000i	0.361158	+	0.208514i
$208$	1.73205	−	1.00000i	0.120096	−	0.0693375i
$209$		0			0
$210$		0			0
$211$	−10.0000			−0.688428			−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000			−0.688428			−0.344214	+	0.938891i	$0.611855\pi$
$212$	5.19615	−	3.00000i	0.356873	−	0.206041i
$213$	1.73205	+	1.00000i	0.118678	+	0.0685189i
$214$	5.50000	−	9.52628i	0.375972	−	0.651203i
$215$	−13.0622	−	8.62436i	−0.890833	−	0.588176i
$216$	15.0000			1.02062
$217$		0			0
$218$			5.00000i			0.338643i
$219$	3.00000	+	5.19615i	0.202721	+	0.351123i
$220$		0			0
$221$	−2.00000	+	3.46410i	−0.134535	+	0.233021i
$222$	6.92820	−	4.00000i	0.464991	−	0.268462i
$223$		0			0		1.00000			$0$
$223$		0			0		−1.00000			$\pi$
$224$		0			0
$225$	−6.00000	+	8.00000i	−0.400000	+	0.533333i
$226$	3.00000	+	5.19615i	0.199557	+	0.345643i
$227$	17.3205	+	10.0000i	1.14960	+	0.663723i	0.948790	−	0.315906i	$-0.102309\pi$
$227$	17.3205	+	10.0000i	1.14960	+	0.663723i	0.200812	+	0.979630i	$0.435642\pi$
$228$	−5.19615	−	3.00000i	−0.344124	−	0.198680i
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	0.958187	+	0.286143i	$0.0923732\pi$
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	−0.231287	+	0.972886i	$0.574293\pi$
$230$	3.00000	+	6.00000i	0.197814	+	0.395628i
$231$		0			0
$232$			21.0000i			1.37872i
$233$	12.1244	−	7.00000i	0.794293	−	0.458585i	−0.0471787	−	0.998886i	$-0.515023\pi$
$233$	12.1244	−	7.00000i	0.794293	−	0.458585i	0.841472	+	0.540301i	$0.181690\pi$
$234$	2.00000	−	3.46410i	0.130744	−	0.226455i
$235$		0			0
$236$	−5.00000	−	8.66025i	−0.325472	−	0.563735i
$237$			2.00000i			0.129914i
$238$		0			0
$239$	18.0000			1.16432			0.582162	−	0.813073i	$-0.302207\pi$
$239$	18.0000			1.16432			0.582162	+	0.813073i	$0.302207\pi$
$240$	1.86603	+	1.23205i	0.120451	+	0.0795285i
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	0.547533	+	0.836784i	$0.315567\pi$
$242$	−9.52628	−	5.50000i	−0.612372	−	0.353553i
$243$	13.8564	−	8.00000i	0.888889	−	0.513200i
$244$	−7.00000			−0.448129
$245$		0			0
$246$	−5.00000			−0.318788
$247$	−10.3923	+	6.00000i	−0.661247	+	0.381771i
$248$	−5.19615	−	3.00000i	−0.329956	−	0.190500i
$249$	5.50000	−	9.52628i	0.348548	−	0.603703i
$250$	−10.5263	+	3.76795i	−0.665740	+	0.238306i
$251$	−30.0000			−1.89358			−0.946792	−	0.321847i	$-0.895696\pi$
$251$	−30.0000			−1.89358			−0.946792	+	0.321847i	$0.895696\pi$
$252$		0			0
$253$		0			0
$254$	8.00000	+	13.8564i	0.501965	+	0.869428i
$255$	−4.46410	−	0.267949i	−0.279553	−	0.0167796i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	17.3205	−	10.0000i	1.08042	−	0.623783i	0.149413	−	0.988775i	$-0.452262\pi$
$257$	17.3205	−	10.0000i	1.08042	−	0.623783i	0.931011	+	0.364992i	$0.118928\pi$
$258$			7.00000i			0.435801i
$259$		0			0
$260$	−4.00000	+	2.00000i	−0.248069	+	0.124035i
$261$	7.00000	+	12.1244i	0.433289	+	0.750479i
$262$	−3.46410	−	2.00000i	−0.214013	−	0.123560i
$263$	7.79423	+	4.50000i	0.480613	+	0.277482i	0.720672	−	0.693276i	$-0.243833\pi$
$263$	7.79423	+	4.50000i	0.480613	+	0.277482i	−0.240059	+	0.970758i	$0.577167\pi$
$264$		0			0
$265$	12.0000	−	6.00000i	0.737154	−	0.368577i
$266$		0			0
$267$			9.00000i			0.550791i
$268$	4.33013	−	2.50000i	0.264505	−	0.152712i
$269$	5.50000	−	9.52628i	0.335341	−	0.580828i	−0.648209	−	0.761462i	$-0.724482\pi$
$269$	5.50000	−	9.52628i	0.335341	−	0.580828i	0.983550	+	0.180635i	$0.0578152\pi$
$270$	11.1603	+	0.669873i	0.679191	+	0.0407672i
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	0.834053	−	0.551684i	$-0.186015\pi$
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	−0.894799	+	0.446469i	$0.852681\pi$
$272$		−	2.00000i		−	0.121268i
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−1.50000	+	2.59808i	−0.0902894	+	0.156386i
$277$	8.66025	+	5.00000i	0.520344	+	0.300421i	0.737075	−	0.675810i	$-0.236206\pi$
$277$	8.66025	+	5.00000i	0.520344	+	0.300421i	−0.216731	+	0.976231i	$0.569540\pi$
$278$	−6.92820	+	4.00000i	−0.415526	+	0.239904i
$279$	−4.00000			−0.239474
$280$		0			0
$281$	−14.0000			−0.835170			−0.417585	−	0.908638i	$-0.637123\pi$
$281$	−14.0000			−0.835170			−0.417585	+	0.908638i	$0.637123\pi$
$282$		0			0
$283$	13.8564	+	8.00000i	0.823678	+	0.475551i	0.851683	−	0.524057i	$-0.175582\pi$
$283$	13.8564	+	8.00000i	0.823678	+	0.475551i	−0.0280052	+	0.999608i	$0.508916\pi$
$284$	1.00000	−	1.73205i	0.0593391	−	0.102778i
$285$	−11.1962	−	7.39230i	−0.663203	−	0.437882i
$286$		0			0
$287$		0			0
$288$		−	10.0000i		−	0.589256i
$289$	−6.50000	−	11.2583i	−0.382353	−	0.662255i
$290$	−0.937822	+	15.6244i	−0.0550708	+	0.917494i
$291$	−8.00000	+	13.8564i	−0.468968	+	0.812277i
$292$	5.19615	−	3.00000i	0.304082	−	0.175562i
$293$		−	24.0000i		−	1.40209i	−0.713115	−	0.701047i	$-0.752716\pi$
$293$		−	24.0000i		−	1.40209i	0.713115	−	0.701047i	$-0.247284\pi$
$294$		0			0
$295$	−10.0000	−	20.0000i	−0.582223	−	1.16445i
$296$	−12.0000	−	20.7846i	−0.697486	−	1.20808i
$297$		0			0
$298$	−0.866025	−	0.500000i	−0.0501675	−	0.0289642i
$299$	3.00000	+	5.19615i	0.173494	+	0.300501i
$300$	−4.00000	−	3.00000i	−0.230940	−	0.173205i
$301$		0			0
$302$		−	14.0000i		−	0.805609i
$303$	−7.79423	+	4.50000i	−0.447767	+	0.258518i
$304$	3.00000	−	5.19615i	0.172062	−	0.298020i
$305$	−15.6244	−	0.937822i	−0.894648	−	0.0536995i
$306$	−2.00000	−	3.46410i	−0.114332	−	0.198030i
$307$			23.0000i			1.31268i	0.754466	+	0.656340i	$0.227896\pi$
$307$			23.0000i			1.31268i	−0.754466	+	0.656340i	$0.772104\pi$
$308$		0			0
$309$	7.00000			0.398216
$310$	−3.73205	−	2.46410i	−0.211966	−	0.139952i
$311$	15.0000	−	25.9808i	0.850572	−	1.47323i	−0.0301210	−	0.999546i	$-0.509589\pi$
$311$	15.0000	−	25.9808i	0.850572	−	1.47323i	0.880693	−	0.473688i	$-0.157077\pi$
$312$	5.19615	+	3.00000i	0.294174	+	0.169842i
$313$	−20.7846	+	12.0000i	−1.17482	+	0.678280i	−0.954810	−	0.297218i	$-0.903941\pi$
$313$	−20.7846	+	12.0000i	−1.17482	+	0.678280i	−0.220006	+	0.975499i	$0.570608\pi$
$314$	12.0000			0.677199
$315$		0			0
$316$	2.00000			0.112509
$317$	5.19615	−	3.00000i	0.291845	−	0.168497i	−0.346929	−	0.937892i	$-0.612775\pi$
$317$	5.19615	−	3.00000i	0.291845	−	0.168497i	0.638774	+	0.769395i	$0.279442\pi$
$318$	−5.19615	−	3.00000i	−0.291386	−	0.168232i
$319$		0			0
$320$	8.62436	−	13.0622i	0.482116	−	0.730198i
$321$	11.0000			0.613960
$322$		0			0
$323$			12.0000i			0.667698i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−9.19615	+	3.92820i	−0.510111	+	0.217898i
$326$	2.00000	−	3.46410i	0.110770	−	0.191859i
$327$	−4.33013	+	2.50000i	−0.239457	+	0.138250i
$328$			15.0000i			0.828236i
$329$		0			0
$330$		0			0
$331$	−3.00000	−	5.19615i	−0.164895	−	0.285606i	0.771723	−	0.635959i	$-0.219395\pi$
$331$	−3.00000	−	5.19615i	−0.164895	−	0.285606i	−0.936618	+	0.350352i	$0.886062\pi$
$332$	−9.52628	−	5.50000i	−0.522823	−	0.301852i
$333$	−13.8564	−	8.00000i	−0.759326	−	0.438397i
$334$	1.50000	+	2.59808i	0.0820763	+	0.142160i
$335$	10.0000	−	5.00000i	0.546358	−	0.273179i
$336$		0			0
$337$		−	18.0000i		−	0.980522i	−0.871576	−	0.490261i	$-0.836901\pi$
$337$		−	18.0000i		−	0.980522i	0.871576	−	0.490261i	$-0.163099\pi$
$338$	−7.79423	+	4.50000i	−0.423950	+	0.244768i
$339$	−3.00000	+	5.19615i	−0.162938	+	0.282216i
$340$	−0.267949	+	4.46410i	−0.0145316	+	0.242100i
$341$		0			0
$342$		−	12.0000i		−	0.648886i
$343$		0			0
$344$	21.0000			1.13224
$345$	−3.69615	+	5.59808i	−0.198994	+	0.301390i
$346$	−6.00000	+	10.3923i	−0.322562	+	0.558694i
$347$	12.9904	+	7.50000i	0.697360	+	0.402621i	0.806363	−	0.591420i	$-0.201433\pi$
$347$	12.9904	+	7.50000i	0.697360	+	0.402621i	−0.109003	+	0.994041i	$0.534766\pi$
$348$	−6.06218	+	3.50000i	−0.324967	+	0.187620i
$349$	−17.0000			−0.909989			−0.454995	−	0.890494i	$-0.650359\pi$
$349$	−17.0000			−0.909989			−0.454995	+	0.890494i	$0.650359\pi$
$350$		0			0
$351$	10.0000			0.533761
$352$		0			0
$353$	−22.5167	−	13.0000i	−1.19844	−	0.691920i	−0.238233	−	0.971208i	$-0.576568\pi$
$353$	−22.5167	−	13.0000i	−1.19844	−	0.691920i	−0.960207	+	0.279288i	$0.909902\pi$
$354$	−5.00000	+	8.66025i	−0.265747	+	0.460287i
$355$	2.46410	−	3.73205i	0.130781	−	0.198077i
$356$	9.00000			0.476999
$357$		0			0
$358$		−	2.00000i		−	0.105703i
$359$	5.00000	+	8.66025i	0.263890	+	0.457071i	0.967272	−	0.253741i	$-0.0816611\pi$
$359$	5.00000	+	8.66025i	0.263890	+	0.457071i	−0.703382	+	0.710812i	$0.748328\pi$
$360$	0.803848	−	13.3923i	0.0423665	−	0.705836i
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	−2.59808	+	1.50000i	−0.136552	+	0.0788382i
$363$		−	11.0000i		−	0.577350i
$364$		0			0
$365$	12.0000	−	6.00000i	0.628109	−	0.314054i
$366$	3.50000	+	6.06218i	0.182948	+	0.316875i
$367$	−23.3827	−	13.5000i	−1.22057	−	0.704694i	−0.255528	−	0.966802i	$-0.582249\pi$
$367$	−23.3827	−	13.5000i	−1.22057	−	0.704694i	−0.965039	+	0.262108i	$0.915582\pi$
$368$	−2.59808	−	1.50000i	−0.135434	−	0.0781929i
$369$	5.00000	+	8.66025i	0.260290	+	0.450835i
$370$	−8.00000	−	16.0000i	−0.415900	−	0.831800i
$371$		0			0
$372$		−	2.00000i		−	0.103695i
$373$	−20.7846	+	12.0000i	−1.07619	+	0.621336i	−0.929865	−	0.367901i	$-0.880077\pi$
$373$	−20.7846	+	12.0000i	−1.07619	+	0.621336i	−0.146321	+	0.989237i	$0.546743\pi$
$374$		0			0
$375$	−8.52628	−	7.23205i	−0.440295	−	0.373461i
$376$		0			0
$377$			14.0000i			0.721037i
$378$		0			0
$379$	10.0000			0.513665			0.256833	−	0.966456i	$-0.417321\pi$
$379$	10.0000			0.513665			0.256833	+	0.966456i	$0.417321\pi$
$380$	−7.39230	+	11.1962i	−0.379217	+	0.574351i
$381$	−8.00000	+	13.8564i	−0.409852	+	0.709885i
$382$	10.3923	+	6.00000i	0.531717	+	0.306987i
$383$	−4.33013	+	2.50000i	−0.221259	+	0.127744i	−0.606533	−	0.795058i	$-0.707440\pi$
$383$	−4.33013	+	2.50000i	−0.221259	+	0.127744i	0.385274	+	0.922802i	$0.374107\pi$
$384$	3.00000			0.153093
$385$		0			0
$386$	−4.00000			−0.203595
$387$	12.1244	−	7.00000i	0.616316	−	0.355830i
$388$	13.8564	+	8.00000i	0.703452	+	0.406138i
$389$	7.00000	−	12.1244i	0.354914	−	0.614729i	−0.632189	−	0.774814i	$-0.717843\pi$
$389$	7.00000	−	12.1244i	0.354914	−	0.614729i	0.987103	+	0.160085i	$0.0511768\pi$
$390$	3.73205	+	2.46410i	0.188980	+	0.124775i
$391$	6.00000			0.303433
$392$		0			0
$393$		−	4.00000i		−	0.201773i
$394$	−4.00000	−	6.92820i	−0.201517	−	0.349038i
$395$	4.46410	+	0.267949i	0.224613	+	0.0134820i
$396$		0			0
$397$	−13.8564	+	8.00000i	−0.695433	+	0.401508i	−0.805644	−	0.592400i	$-0.798181\pi$
$397$	−13.8564	+	8.00000i	−0.695433	+	0.401508i	0.110211	+	0.993908i	$0.464847\pi$
$398$			4.00000i			0.200502i
$399$		0			0
$400$	3.00000	−	4.00000i	0.150000	−	0.200000i
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	0.826139	−	0.563466i	$-0.190532\pi$
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$402$	−4.33013	−	2.50000i	−0.215967	−	0.124689i
$403$	−3.46410	−	2.00000i	−0.172559	−	0.0996271i
$404$	4.50000	+	7.79423i	0.223883	+	0.387777i
$405$	−1.00000	−	2.00000i	−0.0496904	−	0.0993808i
$406$		0			0
$407$		0			0
$408$	5.19615	−	3.00000i	0.257248	−	0.148522i
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	−0.371750	−	0.928333i	$-0.621242\pi$
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	0.989835	−	0.142222i	$-0.0454247\pi$
$410$	−0.669873	+	11.1603i	−0.0330827	+	0.551166i
$411$		0			0
$412$		−	7.00000i		−	0.344865i
$413$		0			0
$414$	−6.00000			−0.294884
$415$	−20.5263	−	13.5526i	−1.00760	−	0.665269i
$416$	5.00000	−	8.66025i	0.245145	−	0.424604i
$417$	−6.92820	−	4.00000i	−0.339276	−	0.195881i
$418$		0			0
$419$	24.0000			1.17248			0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000			1.17248			0.586238	+	0.810139i	$0.300608\pi$
$420$		0			0
$421$	15.0000			0.731055			0.365528	−	0.930800i	$-0.380889\pi$
$421$	15.0000			0.731055			0.365528	+	0.930800i	$0.380889\pi$
$422$	8.66025	−	5.00000i	0.421575	−	0.243396i
$423$		0			0
$424$	−9.00000	+	15.5885i	−0.437079	+	0.757042i
$425$	−1.19615	+	9.92820i	−0.0580219	+	0.481589i
$426$	−2.00000			−0.0969003
$427$		0			0
$428$		−	11.0000i		−	0.531705i
$429$		0			0
$430$	15.6244	+	0.937822i	0.753473	+	0.0452258i
$431$	16.0000	−	27.7128i	0.770693	−	1.33488i	−0.166491	−	0.986043i	$-0.553244\pi$
$431$	16.0000	−	27.7128i	0.770693	−	1.33488i	0.937184	−	0.348836i	$-0.113423\pi$
$432$	−4.33013	+	2.50000i	−0.208333	+	0.120281i
$433$			2.00000i			0.0961139i	0.998845	+	0.0480569i	$0.0153029\pi$
$433$			2.00000i			0.0961139i	−0.998845	+	0.0480569i	$0.984697\pi$
$434$		0			0
$435$	−14.0000	+	7.00000i	−0.671249	+	0.335624i
$436$	2.50000	+	4.33013i	0.119728	+	0.207375i
$437$	15.5885	+	9.00000i	0.745697	+	0.430528i
$438$	−5.19615	−	3.00000i	−0.248282	−	0.143346i
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	−0.996284	−	0.0861252i	$-0.972552\pi$
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	0.423556	−	0.905870i	$-0.360782\pi$
$440$		0			0
$441$		0			0
$442$		−	4.00000i		−	0.190261i
$443$	26.8468	−	15.5000i	1.27553	−	0.736427i	0.299506	−	0.954094i	$-0.403178\pi$
$443$	26.8468	−	15.5000i	1.27553	−	0.736427i	0.976023	+	0.217667i	$0.0698447\pi$
$444$	4.00000	−	6.92820i	0.189832	−	0.328798i
$445$	20.0885	+	1.20577i	0.952284	+	0.0571590i
$446$		0			0
$447$		−	1.00000i		−	0.0472984i
$448$		0			0
$449$	−31.0000			−1.46298			−0.731490	−	0.681852i	$-0.761175\pi$
$449$	−31.0000			−1.46298			−0.731490	+	0.681852i	$0.761175\pi$
$450$	1.19615	−	9.92820i	0.0563872	−	0.468020i
$451$		0			0
$452$	5.19615	+	3.00000i	0.244406	+	0.141108i
$453$	12.1244	−	7.00000i	0.569652	−	0.328889i
$454$	−20.0000			−0.938647
$455$		0			0
$456$	18.0000			0.842927
$457$	−27.7128	+	16.0000i	−1.29635	+	0.748448i	−0.979772	−	0.200118i	$-0.935868\pi$
$457$	−27.7128	+	16.0000i	−1.29635	+	0.748448i	−0.316579	+	0.948566i	$0.602534\pi$
$458$	−19.0526	−	11.0000i	−0.890268	−	0.513996i
$459$	5.00000	−	8.66025i	0.233380	−	0.404226i
$460$	5.59808	+	3.69615i	0.261012	+	0.172334i
$461$	−18.0000			−0.838344			−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000			−0.838344			−0.419172	+	0.907907i	$0.637680\pi$
$462$		0			0
$463$			3.00000i			0.139422i	0.997567	+	0.0697109i	$0.0222077\pi$
$463$			3.00000i			0.139422i	−0.997567	+	0.0697109i	$0.977792\pi$
$464$	−3.50000	−	6.06218i	−0.162483	−	0.281430i
$465$	0.267949	−	4.46410i	0.0124258	−	0.207018i
$466$	−7.00000	+	12.1244i	−0.324269	+	0.561650i
$467$	2.59808	−	1.50000i	0.120225	−	0.0694117i	−0.438682	−	0.898642i	$-0.644554\pi$
$467$	2.59808	−	1.50000i	0.120225	−	0.0694117i	0.558906	+	0.829231i	$0.311221\pi$
$468$		−	4.00000i		−	0.184900i
$469$		0			0
$470$		0			0
$471$	6.00000	+	10.3923i	0.276465	+	0.478852i
$472$	25.9808	+	15.0000i	1.19586	+	0.690431i
$473$		0			0
$474$	−1.00000	−	1.73205i	−0.0459315	−	0.0795557i
$475$	−18.0000	+	24.0000i	−0.825897	+	1.10120i
$476$		0			0
$477$			12.0000i			0.549442i
$478$	−15.5885	+	9.00000i	−0.712999	+	0.411650i
$479$	−21.0000	+	36.3731i	−0.959514	+	1.66193i	−0.235833	+	0.971794i	$0.575782\pi$
$479$	−21.0000	+	36.3731i	−0.959514	+	1.66193i	−0.723681	+	0.690134i	$0.757551\pi$
$480$	11.1603	+	0.669873i	0.509394	+	0.0305754i
$481$	−8.00000	−	13.8564i	−0.364769	−	0.631798i
$482$		−	14.0000i		−	0.637683i
$483$		0			0
$484$	−11.0000			−0.500000
$485$	29.8564	+	19.7128i	1.35571	+	0.895113i
$486$	−8.00000	+	13.8564i	−0.362887	+	0.628539i
$487$	−10.3923	−	6.00000i	−0.470920	−	0.271886i	0.245705	−	0.969345i	$-0.420981\pi$
$487$	−10.3923	−	6.00000i	−0.470920	−	0.271886i	−0.716625	+	0.697459i	$0.754314\pi$
$488$	18.1865	−	10.5000i	0.823266	−	0.475313i
$489$	4.00000			0.180886
$490$		0			0
$491$	−26.0000			−1.17336			−0.586682	−	0.809818i	$-0.699566\pi$
$491$	−26.0000			−1.17336			−0.586682	+	0.809818i	$0.699566\pi$
$492$	−4.33013	+	2.50000i	−0.195217	+	0.112709i
$493$	12.1244	+	7.00000i	0.546054	+	0.315264i
$494$	6.00000	−	10.3923i	0.269953	−	0.467572i
$495$		0			0
$496$	2.00000			0.0898027
$497$		0			0
$498$			11.0000i			0.492922i
$499$	8.00000	+	13.8564i	0.358129	+	0.620298i	0.987648	−	0.156687i	$-0.0500814\pi$
$499$	8.00000	+	13.8564i	0.358129	+	0.620298i	−0.629519	+	0.776985i	$0.716748\pi$
$500$	−7.23205	+	8.52628i	−0.323427	+	0.381307i
$501$	−1.50000	+	2.59808i	−0.0670151	+	0.116073i
$502$	25.9808	−	15.0000i	1.15958	−	0.669483i
$503$			15.0000i			0.668817i	0.942428	+	0.334408i	$0.108537\pi$
$503$			15.0000i			0.668817i	−0.942428	+	0.334408i	$0.891463\pi$
$504$		0			0
$505$	9.00000	+	18.0000i	0.400495	+	0.800989i
$506$		0			0
$507$	−7.79423	−	4.50000i	−0.346154	−	0.199852i
$508$	13.8564	+	8.00000i	0.614779	+	0.354943i
$509$	−13.5000	−	23.3827i	−0.598377	−	1.03642i	−0.993061	−	0.117602i	$-0.962479\pi$
$509$	−13.5000	−	23.3827i	−0.598377	−	1.03642i	0.394684	−	0.918817i	$-0.370854\pi$
$510$	4.00000	−	2.00000i	0.177123	−	0.0885615i
$511$		0			0
$512$			11.0000i			0.486136i
$513$	25.9808	−	15.0000i	1.14708	−	0.662266i
$514$	−10.0000	+	17.3205i	−0.441081	+	0.763975i
$515$	0.937822	−	15.6244i	0.0413254	−	0.688491i
$516$	3.50000	+	6.06218i	0.154079	+	0.266872i
$517$		0			0
$518$		0			0
$519$	−12.0000			−0.526742
$520$	7.39230	−	11.1962i	0.324174	−	0.490984i
$521$	7.00000	−	12.1244i	0.306676	−	0.531178i	−0.670957	−	0.741496i	$-0.734117\pi$
$521$	7.00000	−	12.1244i	0.306676	−	0.531178i	0.977633	+	0.210318i	$0.0674500\pi$
$522$	−12.1244	−	7.00000i	−0.530669	−	0.306382i
$523$	−3.46410	+	2.00000i	−0.151475	+	0.0874539i	−0.573822	−	0.818980i	$-0.694540\pi$
$523$	−3.46410	+	2.00000i	−0.151475	+	0.0874539i	0.422347	+	0.906434i	$0.361206\pi$
$524$	−4.00000			−0.174741
$525$		0			0
$526$	−9.00000			−0.392419
$527$	−3.46410	+	2.00000i	−0.150899	+	0.0871214i
$528$		0			0
$529$	−7.00000	+	12.1244i	−0.304348	+	0.527146i
$530$	−7.39230	+	11.1962i	−0.321101	+	0.486330i
$531$	20.0000			0.867926
$532$		0			0
$533$			10.0000i			0.433148i
$534$	−4.50000	−	7.79423i	−0.194734	−	0.337289i
$535$	1.47372	−	24.5526i	0.0637145	−	1.06150i
$536$	−7.50000	+	12.9904i	−0.323951	+	0.561099i
$537$	1.73205	−	1.00000i	0.0747435	−	0.0431532i
$538$			11.0000i			0.474244i
$539$		0			0
$540$	10.0000	−	5.00000i	0.430331	−	0.215166i
$541$	1.50000	+	2.59808i	0.0644900	+	0.111700i	0.896468	−	0.443109i	$-0.146125\pi$
$541$	1.50000	+	2.59808i	0.0644900	+	0.111700i	−0.831978	+	0.554809i	$0.812791\pi$
$542$	1.73205	+	1.00000i	0.0743980	+	0.0429537i
$543$	−2.59808	−	1.50000i	−0.111494	−	0.0643712i
$544$	−5.00000	−	8.66025i	−0.214373	−	0.371305i
$545$	5.00000	+	10.0000i	0.214176	+	0.428353i
$546$		0			0
$547$			17.0000i			0.726868i	0.931620	+	0.363434i	$0.118396\pi$
$547$			17.0000i			0.726868i	−0.931620	+	0.363434i	$0.881604\pi$
$548$		0			0
$549$	7.00000	−	12.1244i	0.298753	−	0.517455i
$550$		0			0
$551$	21.0000	+	36.3731i	0.894630	+	1.54954i
$552$		−	9.00000i		−	0.383065i
$553$		0			0
$554$	−10.0000			−0.424859
$555$	9.85641	−	14.9282i	0.418381	−	0.633667i
$556$	−4.00000	+	6.92820i	−0.169638	+	0.293821i
$557$	−38.1051	−	22.0000i	−1.61457	−	0.932170i	−0.988293	−	0.152566i	$-0.951246\pi$
$557$	−38.1051	−	22.0000i	−1.61457	−	0.932170i	−0.626272	−	0.779604i	$-0.715420\pi$
$558$	3.46410	−	2.00000i	0.146647	−	0.0846668i
$559$	14.0000			0.592137
$560$		0			0
$561$		0			0
$562$	12.1244	−	7.00000i	0.511435	−	0.295277i
$563$	28.5788	+	16.5000i	1.20445	+	0.695392i	0.961542	−	0.274656i	$-0.0885641\pi$
$563$	28.5788	+	16.5000i	1.20445	+	0.695392i	0.242912	+	0.970048i	$0.421897\pi$
$564$		0			0
$565$	11.1962	+	7.39230i	0.471026	+	0.310997i
$566$	−16.0000			−0.672530
$567$		0			0
$568$			6.00000i			0.251754i
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	0.613369	−	0.789797i	$-0.289814\pi$
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	−0.990668	+	0.136295i	$0.956481\pi$
$570$	13.3923	+	0.803848i	0.560942	+	0.0336695i
$571$	9.00000	−	15.5885i	0.376638	−	0.652357i	−0.613933	−	0.789359i	$-0.710413\pi$
$571$	9.00000	−	15.5885i	0.376638	−	0.652357i	0.990571	+	0.137002i	$0.0437466\pi$
$572$		0			0
$573$			12.0000i			0.501307i
$574$		0			0
$575$	12.0000	+	9.00000i	0.500435	+	0.375326i
$576$	7.00000	+	12.1244i	0.291667	+	0.505181i
$577$	27.7128	+	16.0000i	1.15370	+	0.666089i	0.949786	−	0.312900i	$-0.101301\pi$
$577$	27.7128	+	16.0000i	1.15370	+	0.666089i	0.203913	+	0.978989i	$0.434634\pi$
$578$	11.2583	+	6.50000i	0.468285	+	0.270364i
$579$	−2.00000	−	3.46410i	−0.0831172	−	0.143963i
$580$	7.00000	+	14.0000i	0.290659	+	0.581318i
$581$		0			0
$582$		−	16.0000i		−	0.663221i
$583$		0			0
$584$	−9.00000	+	15.5885i	−0.372423	+	0.645055i
$585$	0.535898	−	8.92820i	0.0221567	−	0.369136i
$586$	12.0000	+	20.7846i	0.495715	+	0.858604i
$587$		−	36.0000i		−	1.48588i	−0.669359	−	0.742940i	$-0.733431\pi$
$587$		−	36.0000i		−	1.48588i	0.669359	−	0.742940i	$-0.266569\pi$
$588$		0			0
$589$	−12.0000			−0.494451
$590$	18.6603	+	12.3205i	0.768231	+	0.507227i
$591$	4.00000	−	6.92820i	0.164538	−	0.284988i
$592$	6.92820	+	4.00000i	0.284747	+	0.164399i
$593$	−19.0526	+	11.0000i	−0.782395	+	0.451716i	−0.837278	−	0.546777i	$-0.815855\pi$
$593$	−19.0526	+	11.0000i	−0.782395	+	0.451716i	0.0548835	+	0.998493i	$0.482521\pi$
$594$		0			0
$595$		0			0
$596$	−1.00000			−0.0409616
$597$	−3.46410	+	2.00000i	−0.141776	+	0.0818546i
$598$	−5.19615	−	3.00000i	−0.212486	−	0.122679i
$599$	−22.0000	+	38.1051i	−0.898896	+	1.55693i	−0.0699877	+	0.997548i	$0.522296\pi$
$599$	−22.0000	+	38.1051i	−0.898896	+	1.55693i	−0.828908	+	0.559385i	$0.811037\pi$
$600$	14.8923	+	1.79423i	0.607976	+	0.0732491i
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$		0			0
$603$			10.0000i			0.407231i
$604$	−7.00000	−	12.1244i	−0.284826	−	0.493333i
$605$	−24.5526	−	1.47372i	−0.998203	−	0.0599153i
$606$	4.50000	−	7.79423i	0.182800	−	0.316619i
$607$	−28.5788	+	16.5000i	−1.15998	+	0.669714i	−0.951299	−	0.308270i	$-0.900250\pi$
$607$	−28.5788	+	16.5000i	−1.15998	+	0.669714i	−0.208680	+	0.977984i	$0.566917\pi$
$608$		−	30.0000i		−	1.21666i
$609$		0			0
$610$	14.0000	−	7.00000i	0.566843	−	0.283422i
$611$		0			0
$612$	−3.46410	−	2.00000i	−0.140028	−	0.0808452i
$613$	29.4449	+	17.0000i	1.18927	+	0.686624i	0.958140	−	0.286300i	$-0.0924254\pi$
$613$	29.4449	+	17.0000i	1.18927	+	0.686624i	0.231127	+	0.972924i	$0.425759\pi$
$614$	−11.5000	−	19.9186i	−0.464102	−	0.803849i
$615$	−10.0000	+	5.00000i	−0.403239	+	0.201619i
$616$		0			0
$617$			4.00000i			0.161034i	0.996753	+	0.0805170i	$0.0256571\pi$
$617$			4.00000i			0.161034i	−0.996753	+	0.0805170i	$0.974343\pi$
$618$	−6.06218	+	3.50000i	−0.243857	+	0.140791i
$619$	−14.0000	+	24.2487i	−0.562708	+	0.974638i	0.434551	+	0.900647i	$0.356907\pi$
$619$	−14.0000	+	24.2487i	−0.562708	+	0.974638i	−0.997259	+	0.0739910i	$0.976426\pi$
$620$	−4.46410	−	0.267949i	−0.179283	−	0.0107611i
$621$	−7.50000	−	12.9904i	−0.300965	−	0.521286i
$622$			30.0000i			1.20289i
$623$		0			0
$624$	−2.00000			−0.0800641
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$	12.0000	−	20.7846i	0.479616	−	0.830720i
$627$		0			0
$628$	10.3923	−	6.00000i	0.414698	−	0.239426i
$629$	−16.0000			−0.637962
$630$		0			0
$631$	40.0000			1.59237			0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000			1.59237			0.796187	+	0.605050i	$0.206847\pi$
$632$	−5.19615	+	3.00000i	−0.206692	+	0.119334i
$633$	8.66025	+	5.00000i	0.344214	+	0.198732i
$634$	−3.00000	+	5.19615i	−0.119145	+	0.206366i
$635$	29.8564	+	19.7128i	1.18482	+	0.782279i
$636$	−6.00000			−0.237915
$637$		0			0
$638$		0			0
$639$	2.00000	+	3.46410i	0.0791188	+	0.137038i
$640$	0.401924	−	6.69615i	0.0158874	−	0.264689i
$641$	5.50000	−	9.52628i	0.217237	−	0.376265i	−0.736725	−	0.676192i	$-0.763629\pi$
$641$	5.50000	−	9.52628i	0.217237	−	0.376265i	0.953962	+	0.299927i	$0.0969622\pi$
$642$	−9.52628	+	5.50000i	−0.375972	+	0.217068i
$643$			4.00000i			0.157745i	0.996885	+	0.0788723i	$0.0251319\pi$
$643$			4.00000i			0.157745i	−0.996885	+	0.0788723i	$0.974868\pi$
$644$		0			0
$645$	7.00000	+	14.0000i	0.275625	+	0.551249i
$646$	−6.00000	−	10.3923i	−0.236067	−	0.408880i
$647$	−40.7032	−	23.5000i	−1.60021	−	0.923880i	−0.991445	−	0.130528i	$-0.958333\pi$
$647$	−40.7032	−	23.5000i	−1.60021	−	0.923880i	−0.608763	−	0.793352i	$-0.708334\pi$
$648$	2.59808	+	1.50000i	0.102062	+	0.0589256i
$649$		0			0
$650$	6.00000	−	8.00000i	0.235339	−	0.313786i
$651$		0			0
$652$		−	4.00000i		−	0.156652i
$653$	−22.5167	+	13.0000i	−0.881145	+	0.508729i	−0.871036	−	0.491220i	$-0.836551\pi$
$653$	−22.5167	+	13.0000i	−0.881145	+	0.508729i	−0.0101092	+	0.999949i	$0.503218\pi$
$654$	2.50000	−	4.33013i	0.0977577	−	0.169321i
$655$	−8.92820	−	0.535898i	−0.348854	−	0.0209393i
$656$	−2.50000	−	4.33013i	−0.0976086	−	0.169063i
$657$			12.0000i			0.468165i
$658$		0			0
$659$	−6.00000			−0.233727			−0.116863	−	0.993148i	$-0.537284\pi$
$659$	−6.00000			−0.233727			−0.116863	+	0.993148i	$0.537284\pi$
$660$		0			0
$661$	−4.50000	+	7.79423i	−0.175030	+	0.303160i	−0.940172	−	0.340701i	$-0.889335\pi$
$661$	−4.50000	+	7.79423i	−0.175030	+	0.303160i	0.765142	+	0.643862i	$0.222669\pi$
$662$	5.19615	+	3.00000i	0.201954	+	0.116598i
$663$	3.46410	−	2.00000i	0.134535	−	0.0776736i
$664$	33.0000			1.28065
$665$		0			0
$666$	16.0000			0.619987
$667$	18.1865	−	10.5000i	0.704185	−	0.406562i
$668$	2.59808	+	1.50000i	0.100523	+	0.0580367i
$669$		0			0
$670$	−6.16025	+	9.33013i	−0.237991	+	0.360454i
$671$		0			0
$672$		0			0
$673$		−	36.0000i		−	1.38770i	−0.720121	−	0.693849i	$-0.755914\pi$
$673$		−	36.0000i		−	1.38770i	0.720121	−	0.693849i	$-0.244086\pi$
$674$	9.00000	+	15.5885i	0.346667	+	0.600445i
$675$	22.9904	−	9.82051i	0.884900	−	0.377992i
$676$	−4.50000	+	7.79423i	−0.173077	+	0.299778i
$677$	−12.1244	+	7.00000i	−0.465977	+	0.269032i	−0.714554	−	0.699580i	$-0.753370\pi$
$677$	−12.1244	+	7.00000i	−0.465977	+	0.269032i	0.248577	+	0.968612i	$0.420037\pi$
$678$		−	6.00000i		−	0.230429i
$679$		0			0
$680$	−6.00000	−	12.0000i	−0.230089	−	0.460179i
$681$	−10.0000	−	17.3205i	−0.383201	−	0.663723i
$682$		0			0
$683$	−30.3109	−	17.5000i	−1.15981	−	0.669619i	−0.208555	−	0.978011i	$-0.566876\pi$
$683$	−30.3109	−	17.5000i	−1.15981	−	0.669619i	−0.951259	+	0.308392i	$0.900209\pi$
$684$	−6.00000	−	10.3923i	−0.229416	−	0.397360i
$685$		0			0
$686$		0			0
$687$		−	22.0000i		−	0.839352i
$688$	−6.06218	+	3.50000i	−0.231118	+	0.133436i
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$	0.401924	−	6.69615i	0.0153010	−	0.254918i
$691$	−10.0000	−	17.3205i	−0.380418	−	0.658903i	0.610704	−	0.791859i	$-0.290887\pi$
$691$	−10.0000	−	17.3205i	−0.380418	−	0.658903i	−0.991122	+	0.132956i	$0.957553\pi$
$692$			12.0000i			0.456172i
$693$		0			0
$694$	−15.0000			−0.569392
$695$	−9.85641	+	14.9282i	−0.373875	+	0.566259i
$696$	10.5000	−	18.1865i	0.398001	−	0.689359i
$697$	8.66025	+	5.00000i	0.328031	+	0.189389i
$698$	14.7224	−	8.50000i	0.557252	−	0.321730i
$699$	−14.0000			−0.529529
$700$		0			0
$701$	−1.00000			−0.0377695			−0.0188847	−	0.999822i	$-0.506012\pi$
$701$	−1.00000			−0.0377695			−0.0188847	+	0.999822i	$0.506012\pi$
$702$	−8.66025	+	5.00000i	−0.326860	+	0.188713i
$703$	−41.5692	−	24.0000i	−1.56781	−	0.905177i
$704$		0			0
$705$		0			0
$706$	26.0000			0.978523
$707$		0			0
$708$			10.0000i			0.375823i
$709$	−24.5000	−	42.4352i	−0.920117	−	1.59369i	−0.799232	−	0.601023i	$-0.794760\pi$
$709$	−24.5000	−	42.4352i	−0.920117	−	1.59369i	−0.120885	−	0.992667i	$-0.538573\pi$
$710$	−0.267949	+	4.46410i	−0.0100560	+	0.167535i
$711$	−2.00000	+	3.46410i	−0.0750059	+	0.129914i
$712$	−23.3827	+	13.5000i	−0.876303	+	0.505934i
$713$			6.00000i			0.224702i
$714$		0			0
$715$		0			0
$716$	−1.00000	−	1.73205i	−0.0373718	−	0.0647298i
$717$	−15.5885	−	9.00000i	−0.582162	−	0.336111i
$718$	−8.66025	−	5.00000i	−0.323198	−	0.186598i
$719$	−18.0000	−	31.1769i	−0.671287	−	1.16270i	−0.977539	−	0.210752i	$-0.932409\pi$
$719$	−18.0000	−	31.1769i	−0.671287	−	1.16270i	0.306253	−	0.951950i	$-0.400925\pi$
$720$	2.00000	+	4.00000i	0.0745356	+	0.149071i
$721$		0			0
$722$		−	17.0000i		−	0.632674i
$723$	12.1244	−	7.00000i	0.450910	−	0.260333i
$724$	−1.50000	+	2.59808i	−0.0557471	+	0.0965567i
$725$	13.7487	+	32.1865i	0.510614	+	1.19538i
$726$	5.50000	+	9.52628i	0.204124	+	0.353553i
$727$		−	47.0000i		−	1.74313i	−0.490277	−	0.871567i	$-0.663104\pi$
$727$		−	47.0000i		−	1.74313i	0.490277	−	0.871567i	$-0.336896\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$	−7.39230	+	11.1962i	−0.273601	+	0.414388i
$731$	7.00000	−	12.1244i	0.258904	−	0.448435i
$732$	6.06218	+	3.50000i	0.224065	+	0.129364i
$733$	13.8564	−	8.00000i	0.511798	−	0.295487i	−0.221774	−	0.975098i	$-0.571185\pi$
$733$	13.8564	−	8.00000i	0.511798	−	0.295487i	0.733572	+	0.679611i	$0.237852\pi$
$734$	27.0000			0.996588
$735$		0			0
$736$	−15.0000			−0.552907
$737$		0			0
$738$	−8.66025	−	5.00000i	−0.318788	−	0.184053i
$739$	8.00000	−	13.8564i	0.294285	−	0.509716i	−0.680534	−	0.732717i	$-0.738252\pi$
$739$	8.00000	−	13.8564i	0.294285	−	0.509716i	0.974818	+	0.223001i	$0.0715853\pi$
$740$	−14.9282	−	9.85641i	−0.548772	−	0.362329i
$741$	12.0000			0.440831
$742$		0			0
$743$		−	49.0000i		−	1.79764i	−0.438322	−	0.898818i	$-0.644427\pi$
$743$		−	49.0000i		−	1.79764i	0.438322	−	0.898818i	$-0.355573\pi$
$744$	3.00000	+	5.19615i	0.109985	+	0.190500i
$745$	−2.23205	−	0.133975i	−0.0817760	−	0.00490845i
$746$	12.0000	−	20.7846i	0.439351	−	0.760979i
$747$	19.0526	−	11.0000i	0.697097	−	0.402469i
$748$		0			0
$749$		0			0
$750$	11.0000	+	2.00000i	0.401663	+	0.0730297i
$751$	6.00000	+	10.3923i	0.218943	+	0.379221i	0.954485	−	0.298259i	$-0.0964058\pi$
$751$	6.00000	+	10.3923i	0.218943	+	0.379221i	−0.735542	+	0.677479i	$0.763072\pi$
$752$		0			0
$753$	25.9808	+	15.0000i	0.946792	+	0.546630i
$754$	−7.00000	−	12.1244i	−0.254925	−	0.441543i
$755$	−14.0000	−	28.0000i	−0.509512	−	1.01902i
$756$		0			0
$757$		−	22.0000i		−	0.799604i	−0.916602	−	0.399802i	$-0.869079\pi$
$757$		−	22.0000i		−	0.799604i	0.916602	−	0.399802i	$-0.130921\pi$
$758$	−8.66025	+	5.00000i	−0.314555	+	0.181608i
$759$		0			0
$760$	2.41154	−	40.1769i	0.0874758	−	1.45737i
$761$	7.00000	+	12.1244i	0.253750	+	0.439508i	0.964555	−	0.263881i	$-0.0850027\pi$
$761$	7.00000	+	12.1244i	0.253750	+	0.439508i	−0.710805	+	0.703389i	$0.751669\pi$
$762$		−	16.0000i		−	0.579619i
$763$		0			0
$764$	12.0000			0.434145
$765$	−7.46410	−	4.92820i	−0.269865	−	0.178180i
$766$	2.50000	−	4.33013i	0.0903287	−	0.156454i
$767$	17.3205	+	10.0000i	0.625407	+	0.361079i
$768$	−14.7224	+	8.50000i	−0.531250	+	0.306717i
$769$	−30.0000			−1.08183			−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000			−1.08183			−0.540914	+	0.841078i	$0.681921\pi$
$770$		0			0
$771$	−20.0000			−0.720282
$772$	−3.46410	+	2.00000i	−0.124676	+	0.0719816i
$773$	15.5885	+	9.00000i	0.560678	+	0.323708i	0.753418	−	0.657542i	$-0.228404\pi$
$773$	15.5885	+	9.00000i	0.560678	+	0.323708i	−0.192740	+	0.981250i	$0.561737\pi$
$774$	−7.00000	+	12.1244i	−0.251610	+	0.435801i
$775$	−9.92820	−	1.19615i	−0.356632	−	0.0429671i
$776$	−48.0000			−1.72310
$777$		0			0
$778$			14.0000i			0.501924i
$779$	15.0000	+	25.9808i	0.537431	+	0.930857i
$780$	4.46410	+	0.267949i	0.159840	+	0.00959412i
$781$		0			0
$782$	−5.19615	+	3.00000i	−0.185814	+	0.107280i
$783$		−	35.0000i		−	1.25080i
$784$		0			0
$785$	24.0000	−	12.0000i	0.856597	−	0.428298i
$786$	2.00000	+	3.46410i	0.0713376	+	0.123560i
$787$	14.7224	+	8.50000i	0.524798	+	0.302992i	0.738896	−	0.673820i	$-0.235348\pi$
$787$	14.7224	+	8.50000i	0.524798	+	0.302992i	−0.214097	+	0.976812i	$0.568681\pi$
$788$	−6.92820	−	4.00000i	−0.246807	−	0.142494i
$789$	−4.50000	−	7.79423i	−0.160204	−	0.277482i
$790$	−4.00000	+	2.00000i	−0.142314	+	0.0711568i
$791$		0			0
$792$		0			0
$793$	12.1244	−	7.00000i	0.430548	−	0.248577i
$794$	8.00000	−	13.8564i	0.283909	−	0.491745i
$795$	−13.3923	−	0.803848i	−0.474976	−	0.0285095i
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$			40.0000i			1.41687i	0.705775	+	0.708436i	$0.250599\pi$
$797$			40.0000i			1.41687i	−0.705775	+	0.708436i	$0.749401\pi$
$798$		0			0
$799$		0			0
$800$	2.99038	−	24.8205i	0.105726	−	0.877537i
$801$	−9.00000	+	15.5885i	−0.317999	+	0.550791i
$802$	2.59808	+	1.50000i	0.0917413	+	0.0529668i
$803$		0			0
$804$	−5.00000			−0.176336
$805$		0			0
$806$	4.00000			0.140894
$807$	−9.52628	+	5.50000i	−0.335341	+	0.193609i
$808$	−23.3827	−	13.5000i	−0.822600	−	0.474928i
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	−0.776012	−	0.630718i	$-0.782761\pi$
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	0.934224	+	0.356687i	$0.116094\pi$
$810$	1.86603	+	1.23205i	0.0655654	+	0.0432899i
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$		0			0
$813$			2.00000i			0.0701431i
$814$		0			0
$815$	0.535898	−	8.92820i	0.0187717	−	0.312741i
$816$	−1.00000	+	1.73205i	−0.0350070	+	0.0606339i
$817$	36.3731	−	21.0000i	1.27253	−	0.734697i
$818$			25.0000i			0.874105i
$819$		0			0
$820$	5.00000	+	10.0000i	0.174608	+	0.349215i
$821$	−11.0000	−	19.0526i	−0.383903	−	0.664939i	0.607714	−	0.794156i	$-0.292087\pi$
$821$	−11.0000	−	19.0526i	−0.383903	−	0.664939i	−0.991616	+	0.129217i	$0.958754\pi$
$822$		0			0
$823$	−21.6506	−	12.5000i	−0.754694	−	0.435723i	0.0726937	−	0.997354i	$-0.476840\pi$
$823$	−21.6506	−	12.5000i	−0.754694	−	0.435723i	−0.827387	+	0.561632i	$0.810174\pi$
$824$	10.5000	+	18.1865i	0.365785	+	0.633558i
$825$		0			0
$826$		0			0
$827$			39.0000i			1.35616i	0.734987	+	0.678081i	$0.237188\pi$
$827$			39.0000i			1.35616i	−0.734987	+	0.678081i	$0.762812\pi$
$828$	−5.19615	+	3.00000i	−0.180579	+	0.104257i
$829$	15.0000	−	25.9808i	0.520972	−	0.902349i	−0.478731	−	0.877962i	$-0.658903\pi$
$829$	15.0000	−	25.9808i	0.520972	−	0.902349i	0.999703	−	0.0243876i	$-0.00776357\pi$
$830$	24.5526	+	1.47372i	0.852232	+	0.0511536i
$831$	−5.00000	−	8.66025i	−0.173448	−	0.300421i
$832$			14.0000i			0.485363i
$833$		0			0
$834$	8.00000			0.277017
$835$	5.59808	+	3.69615i	0.193729	+	0.127911i
$836$		0			0
$837$	8.66025	+	5.00000i	0.299342	+	0.172825i
$838$	−20.7846	+	12.0000i	−0.717992	+	0.414533i
$839$	48.0000			1.65714			0.828572	−	0.559883i	$-0.189154\pi$
$839$	48.0000			1.65714			0.828572	+	0.559883i	$0.189154\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$	−12.9904	+	7.50000i	−0.447678	+	0.258467i
$843$	12.1244	+	7.00000i	0.417585	+	0.241093i
$844$	5.00000	−	8.66025i	0.172107	−	0.298098i
$845$	−11.0885	+	16.7942i	−0.381455	+	0.577739i
$846$		0			0
$847$		0			0
$848$		−	6.00000i		−	0.206041i
$849$	−8.00000	−	13.8564i	−0.274559	−	0.475551i
$850$	−3.92820	−	9.19615i	−0.134736	−	0.315425i
$851$	−12.0000	+	20.7846i	−0.411355	+	0.712487i
$852$	−1.73205	+	1.00000i	−0.0593391	+	0.0342594i
$853$			6.00000i			0.205436i	0.994711	+	0.102718i	$0.0327539\pi$
$853$			6.00000i			0.205436i	−0.994711	+	0.102718i	$0.967246\pi$
$854$		0			0
$855$	−12.0000	−	24.0000i	−0.410391	−	0.820783i
$856$	16.5000	+	28.5788i	0.563958	+	0.976805i
$857$	10.3923	+	6.00000i	0.354994	+	0.204956i	0.666883	−	0.745163i	$-0.267628\pi$
$857$	10.3923	+	6.00000i	0.354994	+	0.204956i	−0.311888	+	0.950119i	$0.600962\pi$
$858$		0			0
$859$	16.0000	+	27.7128i	0.545913	+	0.945549i	0.998549	+	0.0538535i	$0.0171504\pi$
$859$	16.0000	+	27.7128i	0.545913	+	0.945549i	−0.452636	+	0.891695i	$0.649516\pi$
$860$	14.0000	−	7.00000i	0.477396	−	0.238698i
$861$		0			0
$862$			32.0000i			1.08992i
$863$	−7.79423	+	4.50000i	−0.265319	+	0.153182i	−0.626758	−	0.779214i	$-0.715619\pi$
$863$	−7.79423	+	4.50000i	−0.265319	+	0.153182i	0.361440	+	0.932395i	$0.382285\pi$
$864$	−12.5000	+	21.6506i	−0.425259	+	0.736570i
$865$	−1.60770	+	26.7846i	−0.0546633	+	0.910704i
$866$	−1.00000	−	1.73205i	−0.0339814	−	0.0588575i
$867$			13.0000i			0.441503i
$868$		0			0
$869$		0			0
$870$	8.62436	−	13.0622i	0.292393	−	0.442849i
$871$	−5.00000	+	8.66025i	−0.169419	+	0.293442i
$872$	−12.9904	−	7.50000i	−0.439910	−	0.253982i
$873$	−27.7128	+	16.0000i	−0.937937	+	0.541518i
$874$	−18.0000			−0.608859
$875$		0			0
$876$	−6.00000			−0.202721
$877$	1.73205	−	1.00000i	0.0584872	−	0.0337676i	−0.470471	−	0.882415i	$-0.655916\pi$
$877$	1.73205	−	1.00000i	0.0584872	−	0.0337676i	0.528958	+	0.848648i	$0.322583\pi$
$878$	20.7846	+	12.0000i	0.701447	+	0.404980i
$879$	−12.0000	+	20.7846i	−0.404750	+	0.701047i
$880$		0			0
$881$	43.0000			1.44871			0.724353	−	0.689429i	$-0.242138\pi$
$881$	43.0000			1.44871			0.724353	+	0.689429i	$0.242138\pi$
$882$		0			0
$883$			36.0000i			1.21150i	0.795656	+	0.605748i	$0.207126\pi$
$883$			36.0000i			1.21150i	−0.795656	+	0.605748i	$0.792874\pi$
$884$	−2.00000	−	3.46410i	−0.0672673	−	0.116510i
$885$	−1.33975	+	22.3205i	−0.0450351	+	0.750296i
$886$	−15.5000	+	26.8468i	−0.520733	+	0.901935i
$887$	37.2391	−	21.5000i	1.25037	−	0.721899i	0.279184	−	0.960238i	$-0.409936\pi$
$887$	37.2391	−	21.5000i	1.25037	−	0.721899i	0.971182	+	0.238338i	$0.0766027\pi$
$888$			24.0000i			0.805387i
$889$		0			0
$890$	−18.0000	+	9.00000i	−0.603361	+	0.301681i
$891$		0			0
$892$		0			0
$893$		0			0
$894$	0.500000	+	0.866025i	0.0167225	+	0.0289642i
$895$	−2.00000	−	4.00000i	−0.0668526	−	0.133705i
$896$		0			0
$897$		−	6.00000i		−	0.200334i
$898$	26.8468	−	15.5000i	0.895889	−	0.517242i
$899$	−7.00000	+	12.1244i	−0.233463	+	0.404370i
$900$	−3.92820	−	9.19615i	−0.130940	−	0.306538i
$901$	6.00000	+	10.3923i	0.199889	+	0.346218i
$902$		0			0
$903$		0			0
$904$	−18.0000			−0.598671
$905$	−3.69615	+	5.59808i	−0.122864	+	0.186086i
$906$	−7.00000	+	12.1244i	−0.232559	+	0.402805i
$907$	−16.4545	−	9.50000i	−0.546362	−	0.315442i	0.201291	−	0.979531i	$-0.435486\pi$
$907$	−16.4545	−	9.50000i	−0.546362	−	0.315442i	−0.747653	+	0.664089i	$0.768820\pi$
$908$	−17.3205	+	10.0000i	−0.574801	+	0.331862i
$909$	−18.0000			−0.597022
$910$		0			0
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$	−5.19615	+	3.00000i	−0.172062	+	0.0993399i
$913$		0			0
$914$	16.0000	−	27.7128i	0.529233	−	0.916658i
$915$	13.0622	+	8.62436i	0.431822	+	0.285112i
$916$	−22.0000			−0.726900
$917$		0			0
$918$			10.0000i			0.330049i
$919$	17.0000	+	29.4449i	0.560778	+	0.971296i	0.997429	+	0.0716652i	$0.0228313\pi$
$919$	17.0000	+	29.4449i	0.560778	+	0.971296i	−0.436650	+	0.899631i	$0.643835\pi$
$920$	−20.0885	−	1.20577i	−0.662297	−	0.0397531i
$921$	11.5000	−	19.9186i	0.378938	−	0.656340i
$922$	15.5885	−	9.00000i	0.513378	−	0.296399i
$923$			4.00000i			0.131662i
$924$		0			0
$925$	−32.0000	−	24.0000i	−1.05215	−	0.789115i
$926$	−1.50000	−	2.59808i	−0.0492931	−	0.0853781i
$927$	12.1244	+	7.00000i	0.398216	+	0.229910i
$928$	−30.3109	−	17.5000i	−0.995004	−	0.574466i
$929$	14.5000	+	25.1147i	0.475730	+	0.823988i	0.999613	−	0.0278019i	$-0.00885076\pi$
$929$	14.5000	+	25.1147i	0.475730	+	0.823988i	−0.523884	+	0.851790i	$0.675517\pi$
$930$	2.00000	+	4.00000i	0.0655826	+	0.131165i
$931$		0			0
$932$			14.0000i			0.458585i
$933$	−25.9808	+	15.0000i	−0.850572	+	0.491078i
$934$	−1.50000	+	2.59808i	−0.0490815	+	0.0850117i
$935$		0			0
$936$	6.00000	+	10.3923i	0.196116	+	0.339683i
$937$		−	8.00000i		−	0.261349i	−0.991425	−	0.130674i	$-0.958286\pi$
$937$		−	8.00000i		−	0.261349i	0.991425	−	0.130674i	$-0.0417142\pi$
$938$		0			0
$939$	24.0000			0.783210
$940$		0			0
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	−0.974609	−	0.223912i	$-0.928117\pi$
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	0.681218	+	0.732081i	$0.261451\pi$
$942$	−10.3923	−	6.00000i	−0.338600	−	0.195491i
$943$	12.9904	−	7.50000i	0.423025	−	0.244234i
$944$	−10.0000			−0.325472
$945$		0			0
$946$		0			0
$947$	49.3634	−	28.5000i	1.60410	−	0.926126i	0.613441	−	0.789741i	$-0.289785\pi$
$947$	49.3634	−	28.5000i	1.60410	−	0.926126i	0.990656	−	0.136385i	$-0.0435483\pi$
$948$	−1.73205	−	1.00000i	−0.0562544	−	0.0324785i
$949$	−6.00000	+	10.3923i	−0.194768	+	0.337348i
$950$	3.58846	−	29.7846i	0.116425	−	0.966340i
$951$	−6.00000			−0.194563
$952$		0			0
$953$			60.0000i			1.94359i	0.235826	+	0.971795i	$0.424220\pi$
$953$			60.0000i			1.94359i	−0.235826	+	0.971795i	$0.575780\pi$
$954$	−6.00000	−	10.3923i	−0.194257	−	0.336463i
$955$	26.7846	+	1.60770i	0.866730	+	0.0520238i
$956$	−9.00000	+	15.5885i	−0.291081	+	0.504167i
$957$		0			0
$958$		−	42.0000i		−	1.35696i
$959$		0			0
$960$	−14.0000	+	7.00000i	−0.451848	+	0.225924i
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	13.8564	+	8.00000i	0.446748	+	0.257930i
$963$	19.0526	+	11.0000i	0.613960	+	0.354470i
$964$	−7.00000	−	12.1244i	−0.225455	−	0.390499i
$965$	−8.00000	+	4.00000i	−0.257529	+	0.128765i
$966$		0			0
$967$			13.0000i			0.418052i	0.977910	+	0.209026i	$0.0670293\pi$
$967$			13.0000i			0.418052i	−0.977910	+	0.209026i	$0.932971\pi$
$968$	28.5788	−	16.5000i	0.918559	−	0.530330i
$969$	6.00000	−	10.3923i	0.192748	−	0.333849i
$970$	−35.7128	−	2.14359i	−1.14667	−	0.0688266i
$971$	−16.0000	−	27.7128i	−0.513464	−	0.889346i	−0.999878	−	0.0156178i	$-0.995028\pi$
$971$	−16.0000	−	27.7128i	−0.513464	−	0.889346i	0.486414	−	0.873729i	$-0.338305\pi$
$972$			16.0000i			0.513200i
$973$		0			0
$974$	12.0000			0.384505
$975$	9.92820	+	1.19615i	0.317957	+	0.0383075i
$976$	−3.50000	+	6.06218i	−0.112032	+	0.194046i
$977$	51.9615	+	30.0000i	1.66240	+	0.959785i	0.971566	+	0.236768i	$0.0760881\pi$
$977$	51.9615	+	30.0000i	1.66240	+	0.959785i	0.690830	+	0.723017i	$0.257245\pi$
$978$	−3.46410	+	2.00000i	−0.110770	+	0.0639529i
$979$		0			0
$980$		0			0
$981$	−10.0000			−0.319275
$982$	22.5167	−	13.0000i	0.718536	−	0.414847i
$983$	2.59808	+	1.50000i	0.0828658	+	0.0478426i	0.540860	−	0.841112i	$-0.318099\pi$
$983$	2.59808	+	1.50000i	0.0828658	+	0.0478426i	−0.457995	+	0.888955i	$0.651432\pi$
$984$	7.50000	−	12.9904i	0.239091	−	0.414118i
$985$	−14.9282	−	9.85641i	−0.475652	−	0.314051i
$986$	−14.0000			−0.445851
$987$		0			0
$988$		−	12.0000i		−	0.381771i
$989$	−10.5000	−	18.1865i	−0.333881	−	0.578298i
$990$		0			0
$991$	25.0000	−	43.3013i	0.794151	−	1.37551i	−0.129226	−	0.991615i	$-0.541249\pi$
$991$	25.0000	−	43.3013i	0.794151	−	1.37551i	0.923377	−	0.383895i	$-0.125418\pi$
$992$	8.66025	−	5.00000i	0.274963	−	0.158750i
$993$			6.00000i			0.190404i
$994$		0			0
$995$	4.00000	+	8.00000i	0.126809	+	0.253617i
$996$	5.50000	+	9.52628i	0.174274	+	0.301852i
$997$	1.73205	+	1.00000i	0.0548546	+	0.0316703i	0.527176	−	0.849756i	$-0.323251\pi$
$997$	1.73205	+	1.00000i	0.0548546	+	0.0316703i	−0.472322	+	0.881426i	$0.656584\pi$
$998$	−13.8564	−	8.00000i	−0.438617	−	0.253236i
$999$	20.0000	+	34.6410i	0.632772	+	1.09599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.j.c.214.1		4
5.4	even	2	inner	245.2.j.c.214.2		4
7.2	even	3	inner	245.2.j.c.79.2		4
7.3	odd	6		245.2.b.c.99.1		2
7.4	even	3		245.2.b.b.99.1		2
7.5	odd	6		35.2.j.a.9.2	yes	4
7.6	odd	2		35.2.j.a.4.1	✓	4
21.5	even	6		315.2.bf.a.289.1		4
21.11	odd	6		2205.2.d.e.1324.2		2
21.17	even	6		2205.2.d.d.1324.2		2
21.20	even	2		315.2.bf.a.109.2		4
28.19	even	6		560.2.bw.b.289.2		4
28.27	even	2		560.2.bw.b.529.1		4
35.3	even	12		1225.2.a.d.1.1		1
35.4	even	6		245.2.b.b.99.2		2
35.9	even	6	inner	245.2.j.c.79.1		4
35.12	even	12		175.2.e.a.51.1		2
35.13	even	4		175.2.e.b.151.1		2
35.17	even	12		1225.2.a.f.1.1		1
35.18	odd	12		1225.2.a.b.1.1		1
35.19	odd	6		35.2.j.a.9.1	yes	4
35.24	odd	6		245.2.b.c.99.2		2
35.27	even	4		175.2.e.a.151.1		2
35.32	odd	12		1225.2.a.g.1.1		1
35.33	even	12		175.2.e.b.51.1		2
35.34	odd	2		35.2.j.a.4.2	yes	4
105.59	even	6		2205.2.d.d.1324.1		2
105.74	odd	6		2205.2.d.e.1324.1		2
105.89	even	6		315.2.bf.a.289.2		4
105.104	even	2		315.2.bf.a.109.1		4
140.19	even	6		560.2.bw.b.289.1		4
140.139	even	2		560.2.bw.b.529.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.j.a.4.1	✓	4	7.6	odd	2
35.2.j.a.4.2	yes	4	35.34	odd	2
35.2.j.a.9.1	yes	4	35.19	odd	6
35.2.j.a.9.2	yes	4	7.5	odd	6
175.2.e.a.51.1		2	35.12	even	12
175.2.e.a.151.1		2	35.27	even	4
175.2.e.b.51.1		2	35.33	even	12
175.2.e.b.151.1		2	35.13	even	4
245.2.b.b.99.1		2	7.4	even	3
245.2.b.b.99.2		2	35.4	even	6
245.2.b.c.99.1		2	7.3	odd	6
245.2.b.c.99.2		2	35.24	odd	6
245.2.j.c.79.1		4	35.9	even	6	inner
245.2.j.c.79.2		4	7.2	even	3	inner
245.2.j.c.214.1		4	1.1	even	1	trivial
245.2.j.c.214.2		4	5.4	even	2	inner
315.2.bf.a.109.1		4	105.104	even	2
315.2.bf.a.109.2		4	21.20	even	2
315.2.bf.a.289.1		4	21.5	even	6
315.2.bf.a.289.2		4	105.89	even	6
560.2.bw.b.289.1		4	140.19	even	6
560.2.bw.b.289.2		4	28.19	even	6
560.2.bw.b.529.1		4	28.27	even	2
560.2.bw.b.529.2		4	140.139	even	2
1225.2.a.b.1.1		1	35.18	odd	12
1225.2.a.d.1.1		1	35.3	even	12
1225.2.a.f.1.1		1	35.17	even	12
1225.2.a.g.1.1		1	35.32	odd	12
2205.2.d.d.1324.1		2	105.59	even	6
2205.2.d.d.1324.2		2	21.17	even	6
2205.2.d.e.1324.1		2	105.74	odd	6
2205.2.d.e.1324.2		2	21.11	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.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.23205 + 1.86603i) q^{5} +1.00000 q^{6} -3.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.23205 + 1.86603i) q^{5} +1.00000 q^{6} -3.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} +(0.133975 - 2.23205i) q^{10} +(0.866025 - 0.500000i) q^{12} -2.00000i q^{13} +(2.00000 - 1.00000i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.73205 - 1.00000i) q^{17} +(1.73205 + 1.00000i) q^{18} +(-3.00000 - 5.19615i) q^{19} +(-1.00000 - 2.00000i) q^{20} +(-2.59808 + 1.50000i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(-1.96410 - 4.59808i) q^{25} +(1.00000 + 1.73205i) q^{26} +5.00000i q^{27} -7.00000 q^{29} +(-1.23205 + 1.86603i) q^{30} +(1.00000 - 1.73205i) q^{31} +(4.33013 + 2.50000i) q^{32} +2.00000 q^{34} +2.00000 q^{36} +(6.92820 - 4.00000i) q^{37} +(5.19615 + 3.00000i) q^{38} +(-1.00000 + 1.73205i) q^{39} +(5.59808 + 3.69615i) q^{40} -5.00000 q^{41} +7.00000i q^{43} +(4.46410 + 0.267949i) q^{45} +(1.50000 - 2.59808i) q^{46} -1.00000i q^{48} +(4.00000 + 3.00000i) q^{50} +(1.00000 + 1.73205i) q^{51} +(1.73205 + 1.00000i) q^{52} +(-5.19615 - 3.00000i) q^{53} +(-2.50000 - 4.33013i) q^{54} +6.00000i q^{57} +(6.06218 - 3.50000i) q^{58} +(-5.00000 + 8.66025i) q^{59} +(-0.133975 + 2.23205i) q^{60} +(3.50000 + 6.06218i) q^{61} +2.00000i q^{62} -7.00000 q^{64} +(3.73205 + 2.46410i) q^{65} +(-4.33013 - 2.50000i) q^{67} +(1.73205 - 1.00000i) q^{68} +3.00000 q^{69} -2.00000 q^{71} +(-5.19615 + 3.00000i) q^{72} +(-5.19615 - 3.00000i) q^{73} +(-4.00000 + 6.92820i) q^{74} +(-0.598076 + 4.96410i) q^{75} +6.00000 q^{76} -2.00000i q^{78} +(-1.00000 - 1.73205i) q^{79} +(-2.23205 - 0.133975i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.33013 - 2.50000i) q^{82} +11.0000i q^{83} +(4.00000 - 2.00000i) q^{85} +(-3.50000 - 6.06218i) q^{86} +(6.06218 + 3.50000i) q^{87} +(-4.50000 - 7.79423i) q^{89} +(-4.00000 + 2.00000i) q^{90} -3.00000i q^{92} +(-1.73205 + 1.00000i) q^{93} +(13.3923 + 0.803848i) q^{95} +(-2.50000 - 4.33013i) q^{96} -16.0000i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{4} + 2 q^{5} + 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^4 + 2 * q^5 + 4 * q^6 - 4 * q^9	\( 4 q - 2 q^{4} + 2 q^{5} + 4 q^{6} - 4 q^{9} + 4 q^{10} + 8 q^{15} + 2 q^{16} - 12 q^{19} - 4 q^{20} - 6 q^{24} + 6 q^{25} + 4 q^{26} - 28 q^{29} + 2 q^{30} + 4 q^{31} + 8 q^{34} + 8 q^{36} - 4 q^{39} + 12 q^{40} - 20 q^{41} + 4 q^{45} + 6 q^{46} + 16 q^{50} + 4 q^{51} - 10 q^{54} - 20 q^{59} - 4 q^{60} + 14 q^{61} - 28 q^{64} + 8 q^{65} + 12 q^{69} - 8 q^{71} - 16 q^{74} + 8 q^{75} + 24 q^{76} - 4 q^{79} - 2 q^{80} - 2 q^{81} + 16 q^{85} - 14 q^{86} - 18 q^{89} - 16 q^{90} + 12 q^{95} - 10 q^{96}+O(q^{100}) \) 4 * q - 2 * q^4 + 2 * q^5 + 4 * q^6 - 4 * q^9 + 4 * q^10 + 8 * q^15 + 2 * q^16 - 12 * q^19 - 4 * q^20 - 6 * q^24 + 6 * q^25 + 4 * q^26 - 28 * q^29 + 2 * q^30 + 4 * q^31 + 8 * q^34 + 8 * q^36 - 4 * q^39 + 12 * q^40 - 20 * q^41 + 4 * q^45 + 6 * q^46 + 16 * q^50 + 4 * q^51 - 10 * q^54 - 20 * q^59 - 4 * q^60 + 14 * q^61 - 28 * q^64 + 8 * q^65 + 12 * q^69 - 8 * q^71 - 16 * q^74 + 8 * q^75 + 24 * q^76 - 4 * q^79 - 2 * q^80 - 2 * q^81 + 16 * q^85 - 14 * q^86 - 18 * q^89 - 16 * q^90 + 12 * q^95 - 10 * q^96

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