LMFDB - Embedded newform 315.2.bf.a.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(109,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("315.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bf (of order $6$, 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:	$2.51528766367$
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			109.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	315.109
Dual form			315.2.bf.a.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} +(2.59808 - 0.500000i) q^{7} -3.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} +(2.59808 - 0.500000i) q^{7} -3.00000i q^{8} +(-1.86603 + 1.23205i) q^{10} -2.00000i q^{13} +(-2.00000 + 1.73205i) q^{14} +(0.500000 + 0.866025i) q^{16} +(1.73205 + 1.00000i) q^{17} +(3.00000 + 5.19615i) q^{19} +(-1.00000 + 2.00000i) q^{20} +(-2.59808 + 1.50000i) q^{23} +(4.96410 - 0.598076i) q^{25} +(1.00000 + 1.73205i) q^{26} +(-0.866025 + 2.50000i) q^{28} +7.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(4.33013 + 2.50000i) q^{32} -2.00000 q^{34} +(5.73205 - 1.46410i) q^{35} +(-6.92820 + 4.00000i) q^{37} +(-5.19615 - 3.00000i) q^{38} +(-0.401924 - 6.69615i) q^{40} -5.00000 q^{41} -7.00000i q^{43} +(1.50000 - 2.59808i) q^{46} +(6.50000 - 2.59808i) q^{49} +(-4.00000 + 3.00000i) q^{50} +(1.73205 + 1.00000i) q^{52} +(-5.19615 - 3.00000i) q^{53} +(-1.50000 - 7.79423i) q^{56} +(-6.06218 + 3.50000i) q^{58} +(-5.00000 + 8.66025i) q^{59} +(-3.50000 - 6.06218i) q^{61} -2.00000i q^{62} -7.00000 q^{64} +(-0.267949 - 4.46410i) q^{65} +(4.33013 + 2.50000i) q^{67} +(-1.73205 + 1.00000i) q^{68} +(-4.23205 + 4.13397i) q^{70} +2.00000 q^{71} +(-5.19615 - 3.00000i) q^{73} +(4.00000 - 6.92820i) q^{74} -6.00000 q^{76} +(-1.00000 - 1.73205i) q^{79} +(1.23205 + 1.86603i) q^{80} +(4.33013 - 2.50000i) q^{82} -11.0000i q^{83} +(4.00000 + 2.00000i) q^{85} +(3.50000 + 6.06218i) q^{86} +(-4.50000 - 7.79423i) q^{89} +(-1.00000 - 5.19615i) q^{91} -3.00000i q^{92} +(7.39230 + 11.1962i) q^{95} -16.0000i q^{97} +(-4.33013 + 5.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{4} + 2 q^{5}+O(q^{10}) $ 4 * q - 2 * q^4 + 2 * q^5	$ 4 q - 2 q^{4} + 2 q^{5} - 4 q^{10} - 8 q^{14} + 2 q^{16} + 12 q^{19} - 4 q^{20} + 6 q^{25} + 4 q^{26} + 28 q^{29} - 4 q^{31} - 8 q^{34} + 16 q^{35} - 12 q^{40} - 20 q^{41} + 6 q^{46} + 26 q^{49} - 16 q^{50} - 6 q^{56} - 20 q^{59} - 14 q^{61} - 28 q^{64} - 8 q^{65} - 10 q^{70} + 8 q^{71} + 16 q^{74} - 24 q^{76} - 4 q^{79} - 2 q^{80} + 16 q^{85} + 14 q^{86} - 18 q^{89} - 4 q^{91} - 12 q^{95}+O(q^{100}) $ 4 * q - 2 * q^4 + 2 * q^5 - 4 * q^10 - 8 * q^14 + 2 * q^16 + 12 * q^19 - 4 * q^20 + 6 * q^25 + 4 * q^26 + 28 * q^29 - 4 * q^31 - 8 * q^34 + 16 * q^35 - 12 * q^40 - 20 * q^41 + 6 * q^46 + 26 * q^49 - 16 * q^50 - 6 * q^56 - 20 * q^59 - 14 * q^61 - 28 * q^64 - 8 * q^65 - 10 * q^70 + 8 * q^71 + 16 * q^74 - 24 * q^76 - 4 * q^79 - 2 * q^80 + 16 * q^85 + 14 * q^86 - 18 * q^89 - 4 * q^91 - 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

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			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.23205	−	0.133975i	0.998203	−	0.0599153i
$5$	2.23205	−	0.133975i	0.998203	−	0.0599153i
$6$		0			0
$7$	2.59808	−	0.500000i	0.981981	−	0.188982i
$7$	2.59808	−	0.500000i	0.981981	−	0.188982i
$8$		−	3.00000i		−	1.06066i
$9$		0			0
$10$	−1.86603	+	1.23205i	−0.590089	+	0.389609i
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$		0			0
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$	−2.00000	+	1.73205i	−0.534522	+	0.462910i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	0.695113	−	0.718900i	$-0.255354\pi$
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	−0.275029	+	0.961436i	$0.588688\pi$
$18$		0			0
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	0.972404	+	0.233301i	$0.0749529\pi$
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	−0.284157	+	0.958778i	$0.591714\pi$
$20$	−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	$0.434591\pi$
$24$		0			0
$25$	4.96410	−	0.598076i	0.992820	−	0.119615i
$26$	1.00000	+	1.73205i	0.196116	+	0.339683i
$27$		0			0
$28$	−0.866025	+	2.50000i	−0.163663	+	0.472456i
$29$	7.00000			1.29987			0.649934	−	0.759991i	$-0.274797\pi$
$29$	7.00000			1.29987			0.649934	+	0.759991i	$0.274797\pi$
$30$		0			0
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	−0.941745	−	0.336327i	$-0.890815\pi$
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	0.762140	+	0.647412i	$0.224149\pi$
$32$	4.33013	+	2.50000i	0.765466	+	0.441942i
$33$		0			0
$34$	−2.00000			−0.342997
$35$	5.73205	−	1.46410i	0.968893	−	0.247478i
$36$		0			0
$37$	−6.92820	+	4.00000i	−1.13899	+	0.657596i	−0.946180	−	0.323640i	$-0.895093\pi$
$37$	−6.92820	+	4.00000i	−1.13899	+	0.657596i	−0.192809	+	0.981236i	$0.561760\pi$
$38$	−5.19615	−	3.00000i	−0.842927	−	0.486664i
$39$		0			0
$40$	−0.401924	−	6.69615i	−0.0635497	−	1.05875i
$41$	−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	$-0.820784\pi$
$43$		−	7.00000i		−	1.06749i	0.845645	−	0.533745i	$-0.179216\pi$
$44$		0			0
$45$		0			0
$46$	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	$0.333333\pi$
$48$		0			0
$49$	6.50000	−	2.59808i	0.928571	−	0.371154i
$50$	−4.00000	+	3.00000i	−0.565685	+	0.424264i
$51$		0			0
$52$	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	$0.801865\pi$
$54$		0			0
$55$		0			0
$56$	−1.50000	−	7.79423i	−0.200446	−	1.04155i
$57$		0			0
$58$	−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			0
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	0.550135	−	0.835076i	$-0.314576\pi$
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	−0.998264	+	0.0588933i	$0.981243\pi$
$62$		−	2.00000i		−	0.254000i
$63$		0			0
$64$	−7.00000			−0.875000
$65$	−0.267949	−	4.46410i	−0.0332350	−	0.553704i
$66$		0			0
$67$	4.33013	+	2.50000i	0.529009	+	0.305424i	0.740613	−	0.671932i	$-0.234535\pi$
$67$	4.33013	+	2.50000i	0.529009	+	0.305424i	−0.211604	+	0.977356i	$0.567869\pi$
$68$	−1.73205	+	1.00000i	−0.210042	+	0.121268i
$69$		0			0
$70$	−4.23205	+	4.13397i	−0.505827	+	0.494104i
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$		0			0
$73$	−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			0
$76$	−6.00000			−0.688247
$77$		0			0
$78$		0			0
$79$	−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	$0.869222\pi$
$80$	1.23205	+	1.86603i	0.137747	+	0.208628i
$81$		0			0
$82$	4.33013	−	2.50000i	0.478183	−	0.276079i
$83$		−	11.0000i		−	1.20741i	−0.797209	−	0.603703i	$-0.793691\pi$
$83$		−	11.0000i		−	1.20741i	0.797209	−	0.603703i	$-0.206309\pi$
$84$		0			0
$85$	4.00000	+	2.00000i	0.433861	+	0.216930i
$86$	3.50000	+	6.06218i	0.377415	+	0.653701i
$87$		0			0
$88$		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	$0.991609\pi$
$90$		0			0
$91$	−1.00000	−	5.19615i	−0.104828	−	0.544705i
$92$		−	3.00000i		−	0.312772i
$93$		0			0
$94$		0			0
$95$	7.39230	+	11.1962i	0.758434	+	1.14870i
$96$		0			0
$97$		−	16.0000i		−	1.62455i	−0.583272	−	0.812277i	$-0.698228\pi$
$97$		−	16.0000i		−	1.62455i	0.583272	−	0.812277i	$-0.301772\pi$
$98$	−4.33013	+	5.50000i	−0.437409	+	0.555584i
$99$		0			0
$100$	−1.96410	+	4.59808i	−0.196410	+	0.459808i
$101$	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	$0.0188862\pi$
$102$		0			0
$103$	−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	$0.511782\pi$
$108$		0			0
$109$	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
$111$		0			0
$112$	1.73205	+	2.00000i	0.163663	+	0.188982i
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$		0			0
$115$	−5.59808	+	3.69615i	−0.522023	+	0.344668i
$116$	−3.50000	+	6.06218i	−0.324967	+	0.562859i
$117$		0			0
$118$		−	10.0000i		−	0.920575i
$119$	5.00000	+	1.73205i	0.458349	+	0.158777i
$120$		0			0
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	6.06218	+	3.50000i	0.548844	+	0.316875i
$123$		0			0
$124$	−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	$0.251253\pi$
$127$			16.0000i			1.41977i	−0.704317	+	0.709885i	$0.748747\pi$
$128$	−2.59808	+	1.50000i	−0.229640	+	0.132583i
$129$		0			0
$130$	2.46410	+	3.73205i	0.216116	+	0.327323i
$131$	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
$133$	10.3923	+	12.0000i	0.901127	+	1.04053i
$134$	−5.00000			−0.431934
$135$		0			0
$136$	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	$0.666667\pi$
$138$		0			0
$139$	−8.00000			−0.678551			−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000			−0.678551			−0.339276	+	0.940687i	$0.610182\pi$
$140$	−1.59808	+	5.69615i	−0.135062	+	0.481413i
$141$		0			0
$142$	−1.73205	+	1.00000i	−0.145350	+	0.0839181i
$143$		0			0
$144$		0			0
$145$	15.6244	−	0.937822i	1.29753	−	0.0778819i
$146$	6.00000			0.496564
$147$		0			0
$148$		−	8.00000i		−	0.657596i
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	0.844818	−	0.535054i	$-0.179709\pi$
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	−0.885779	+	0.464107i	$0.846375\pi$
$150$		0			0
$151$	−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
$153$		0			0
$154$		0			0
$155$	−2.00000	+	4.00000i	−0.160644	+	0.321288i
$156$		0			0
$157$	−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
$159$		0			0
$160$	10.0000	+	5.00000i	0.790569	+	0.395285i
$161$	−6.00000	+	5.19615i	−0.472866	+	0.409514i
$162$		0			0
$163$	3.46410	−	2.00000i	0.271329	−	0.156652i	−0.358162	−	0.933659i	$-0.616597\pi$
$163$	3.46410	−	2.00000i	0.271329	−	0.156652i	0.629492	+	0.777007i	$0.283263\pi$
$164$	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	$0.0370308\pi$
$167$			3.00000i			0.232147i	−0.993241	+	0.116073i	$0.962969\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$	−4.46410	+	0.267949i	−0.342381	+	0.0205508i
$171$		0			0
$172$	6.06218	+	3.50000i	0.462237	+	0.266872i
$173$	−10.3923	+	6.00000i	−0.790112	+	0.456172i	−0.840002	−	0.542583i	$-0.817446\pi$
$173$	−10.3923	+	6.00000i	−0.790112	+	0.456172i	0.0498898	+	0.998755i	$0.484113\pi$
$174$		0			0
$175$	12.5981	−	4.03590i	0.952325	−	0.305085i
$176$		0			0
$177$		0			0
$178$	7.79423	+	4.50000i	0.584202	+	0.337289i
$179$	1.00000	−	1.73205i	0.0747435	−	0.129460i	−0.826231	−	0.563331i	$-0.809520\pi$
$179$	1.00000	−	1.73205i	0.0747435	−	0.129460i	0.900975	+	0.433872i	$0.142853\pi$
$180$		0			0
$181$	−3.00000			−0.222988			−0.111494	−	0.993765i	$-0.535564\pi$
$181$	−3.00000			−0.222988			−0.111494	+	0.993765i	$0.535564\pi$
$182$	3.46410	+	4.00000i	0.256776	+	0.296500i
$183$		0			0
$184$	4.50000	+	7.79423i	0.331744	+	0.574598i
$185$	−14.9282	+	9.85641i	−1.09754	+	0.724657i
$186$		0			0
$187$		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	0.997225	−	0.0744412i	$-0.0237173\pi$
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	−0.563081	+	0.826402i	$0.690384\pi$
$192$		0			0
$193$	−3.46410	−	2.00000i	−0.249351	−	0.143963i	0.370116	−	0.928986i	$-0.379318\pi$
$193$	−3.46410	−	2.00000i	−0.249351	−	0.143963i	−0.619467	+	0.785022i	$0.712651\pi$
$194$	8.00000	+	13.8564i	0.574367	+	0.994832i
$195$		0			0
$196$	−1.00000	+	6.92820i	−0.0714286	+	0.494872i
$197$			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	−0.928166	−	0.372168i	$-0.878615\pi$
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	0.786389	+	0.617731i	$0.211948\pi$
$200$	−1.79423	−	14.8923i	−0.126871	−	1.05304i
$201$		0			0
$202$			9.00000i			0.633238i
$203$	18.1865	−	3.50000i	1.27644	−	0.245652i
$204$		0			0
$205$	−11.1603	+	0.669873i	−0.779466	+	0.0467860i
$206$	3.50000	−	6.06218i	0.243857	−	0.422372i
$207$		0			0
$208$	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
$213$		0			0
$214$	5.50000	−	9.52628i	0.375972	−	0.651203i
$215$	−0.937822	−	15.6244i	−0.0639589	−	1.06557i
$216$		0			0
$217$	−1.73205	+	5.00000i	−0.117579	+	0.339422i
$218$			5.00000i			0.338643i
$219$		0			0
$220$		0			0
$221$	2.00000	−	3.46410i	0.134535	−	0.233021i
$222$		0			0
$223$		0			0		1.00000			$0$
$223$		0			0		−1.00000			$\pi$
$224$	12.5000	+	4.33013i	0.835191	+	0.289319i
$225$		0			0
$226$	3.00000	+	5.19615i	0.199557	+	0.345643i
$227$	−17.3205	−	10.0000i	−1.14960	−	0.663723i	−0.200812	−	0.979630i	$-0.564358\pi$
$227$	−17.3205	−	10.0000i	−1.14960	−	0.663723i	−0.948790	+	0.315906i	$0.897691\pi$
$228$		0			0
$229$	−11.0000	−	19.0526i	−0.726900	−	1.25903i	−0.958187	−	0.286143i	$-0.907627\pi$
$229$	−11.0000	−	19.0526i	−0.726900	−	1.25903i	0.231287	−	0.972886i	$-0.425707\pi$
$230$	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	$0.181690\pi$
$234$		0			0
$235$		0			0
$236$	−5.00000	−	8.66025i	−0.325472	−	0.563735i
$237$		0			0
$238$	−5.19615	+	1.00000i	−0.336817	+	0.0648204i
$239$	−18.0000			−1.16432			−0.582162	−	0.813073i	$-0.697793\pi$
$239$	−18.0000			−1.16432			−0.582162	+	0.813073i	$0.697793\pi$
$240$		0			0
$241$	7.00000	−	12.1244i	0.450910	−	0.780998i	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	7.00000	−	12.1244i	0.450910	−	0.780998i	0.998443	+	0.0557856i	$0.0177663\pi$
$242$	−9.52628	−	5.50000i	−0.612372	−	0.353553i
$243$		0			0
$244$	7.00000			0.448129
$245$	14.1603	−	6.66987i	0.904665	−	0.426123i
$246$		0			0
$247$	10.3923	−	6.00000i	0.661247	−	0.381771i
$248$	5.19615	+	3.00000i	0.329956	+	0.190500i
$249$		0			0
$250$	−8.52628	+	7.23205i	−0.539249	+	0.457395i
$251$	−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
$255$		0			0
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−17.3205	+	10.0000i	−1.08042	+	0.623783i	−0.931011	−	0.364992i	$-0.881072\pi$
$257$	−17.3205	+	10.0000i	−1.08042	+	0.623783i	−0.149413	+	0.988775i	$0.547738\pi$
$258$		0			0
$259$	−16.0000	+	13.8564i	−0.994192	+	0.860995i
$260$	4.00000	+	2.00000i	0.248069	+	0.124035i
$261$		0			0
$262$	−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
$266$	−15.0000	−	5.19615i	−0.919709	−	0.318597i
$267$		0			0
$268$	−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	$0.0578152\pi$
$270$		0			0
$271$	1.00000	+	1.73205i	0.0607457	+	0.105215i	0.894799	−	0.446469i	$-0.147319\pi$
$271$	1.00000	+	1.73205i	0.0607457	+	0.105215i	−0.834053	+	0.551684i	$0.813985\pi$
$272$			2.00000i			0.121268i
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−8.66025	−	5.00000i	−0.520344	−	0.300421i	0.216731	−	0.976231i	$-0.430460\pi$
$277$	−8.66025	−	5.00000i	−0.520344	−	0.300421i	−0.737075	+	0.675810i	$0.763794\pi$
$278$	6.92820	−	4.00000i	0.415526	−	0.239904i
$279$		0			0
$280$	−4.39230	−	17.1962i	−0.262490	−	1.02767i
$281$	14.0000			0.835170			0.417585	−	0.908638i	$-0.362877\pi$
$281$	14.0000			0.835170			0.417585	+	0.908638i	$0.362877\pi$
$282$		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
$285$		0			0
$286$		0			0
$287$	−12.9904	+	2.50000i	−0.766798	+	0.147570i
$288$		0			0
$289$	−6.50000	−	11.2583i	−0.382353	−	0.662255i
$290$	−13.0622	+	8.62436i	−0.767037	+	0.506440i
$291$		0			0
$292$	5.19615	−	3.00000i	0.304082	−	0.175562i
$293$			24.0000i			1.40209i	0.713115	+	0.701047i	$0.247284\pi$
$293$			24.0000i			1.40209i	−0.713115	+	0.701047i	$0.752716\pi$
$294$		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
$300$		0			0
$301$	−3.50000	−	18.1865i	−0.201737	−	1.04825i
$302$		−	14.0000i		−	0.805609i
$303$		0			0
$304$	−3.00000	+	5.19615i	−0.172062	+	0.298020i
$305$	−8.62436	−	13.0622i	−0.493829	−	0.747938i
$306$		0			0
$307$			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
$309$		0			0
$310$	−0.267949	−	4.46410i	−0.0152185	−	0.253544i
$311$	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	$-0.157077\pi$
$312$		0			0
$313$	−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	$0.279442\pi$
$318$		0			0
$319$		0			0
$320$	−15.6244	+	0.937822i	−0.873428	+	0.0524259i
$321$		0			0
$322$	2.59808	−	7.50000i	0.144785	−	0.417959i
$323$			12.0000i			0.667698i
$324$		0			0
$325$	−1.19615	−	9.92820i	−0.0663506	−	0.550718i
$326$	−2.00000	+	3.46410i	−0.110770	+	0.191859i
$327$		0			0
$328$			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
$333$		0			0
$334$	−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	$0.163099\pi$
$337$			18.0000i			0.980522i	−0.871576	+	0.490261i	$0.836901\pi$
$338$	−7.79423	+	4.50000i	−0.423950	+	0.244768i
$339$		0			0
$340$	−3.73205	+	2.46410i	−0.202399	+	0.133635i
$341$		0			0
$342$		0			0
$343$	15.5885	−	10.0000i	0.841698	−	0.539949i
$344$	−21.0000			−1.13224
$345$		0			0
$346$	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	$0.534766\pi$
$348$		0			0
$349$	17.0000			0.909989			0.454995	−	0.890494i	$-0.349641\pi$
$349$	17.0000			0.909989			0.454995	+	0.890494i	$0.349641\pi$
$350$	−8.89230	+	9.79423i	−0.475314	+	0.523524i
$351$		0			0
$352$		0			0
$353$	22.5167	+	13.0000i	1.19844	+	0.691920i	0.960207	−	0.279288i	$-0.0900983\pi$
$353$	22.5167	+	13.0000i	1.19844	+	0.691920i	0.238233	+	0.971208i	$0.423432\pi$
$354$		0			0
$355$	4.46410	−	0.267949i	0.236930	−	0.0142213i
$356$	9.00000			0.476999
$357$		0			0
$358$			2.00000i			0.105703i
$359$	−5.00000	−	8.66025i	−0.263890	−	0.457071i	0.703382	−	0.710812i	$-0.251672\pi$
$359$	−5.00000	−	8.66025i	−0.263890	−	0.457071i	−0.967272	+	0.253741i	$0.918339\pi$
$360$		0			0
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	2.59808	−	1.50000i	0.136552	−	0.0788382i
$363$		0			0
$364$	5.00000	+	1.73205i	0.262071	+	0.0907841i
$365$	−12.0000	−	6.00000i	−0.628109	−	0.314054i
$366$		0			0
$367$	−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
$369$		0			0
$370$	8.00000	−	16.0000i	0.415900	−	0.831800i
$371$	−15.0000	−	5.19615i	−0.778761	−	0.269771i
$372$		0			0
$373$	20.7846	−	12.0000i	1.07619	−	0.621336i	0.146321	−	0.989237i	$-0.453257\pi$
$373$	20.7846	−	12.0000i	1.07619	−	0.621336i	0.929865	+	0.367901i	$0.119923\pi$
$374$		0			0
$375$		0			0
$376$		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	$0.417321\pi$
$380$	−13.3923	+	0.803848i	−0.687011	+	0.0412365i
$381$		0			0
$382$	−10.3923	−	6.00000i	−0.531717	−	0.306987i
$383$	4.33013	−	2.50000i	0.221259	−	0.127744i	−0.385274	−	0.922802i	$-0.625893\pi$
$383$	4.33013	−	2.50000i	0.221259	−	0.127744i	0.606533	+	0.795058i	$0.292560\pi$
$384$		0			0
$385$		0			0
$386$	4.00000			0.203595
$387$		0			0
$388$	13.8564	+	8.00000i	0.703452	+	0.406138i
$389$	−7.00000	+	12.1244i	−0.354914	+	0.614729i	−0.987103	−	0.160085i	$-0.948823\pi$
$389$	−7.00000	+	12.1244i	−0.354914	+	0.614729i	0.632189	+	0.774814i	$0.282157\pi$
$390$		0			0
$391$	−6.00000			−0.303433
$392$	−7.79423	−	19.5000i	−0.393668	−	0.984899i
$393$		0			0
$394$	−4.00000	−	6.92820i	−0.201517	−	0.349038i
$395$	−2.46410	−	3.73205i	−0.123982	−	0.187780i
$396$		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	0.901046	−	0.433724i	$-0.142801\pi$
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	−0.826139	+	0.563466i	$0.809468\pi$
$402$		0			0
$403$	3.46410	+	2.00000i	0.172559	+	0.0996271i
$404$	4.50000	+	7.79423i	0.223883	+	0.387777i
$405$		0			0
$406$	−14.0000	+	12.1244i	−0.694808	+	0.601722i
$407$		0			0
$408$		0			0
$409$	−12.5000	+	21.6506i	−0.618085	+	1.07056i	0.371750	+	0.928333i	$0.378758\pi$
$409$	−12.5000	+	21.6506i	−0.618085	+	1.07056i	−0.989835	+	0.142222i	$0.954575\pi$
$410$	9.33013	−	6.16025i	0.460782	−	0.304233i
$411$		0			0
$412$		−	7.00000i		−	0.344865i
$413$	−8.66025	+	25.0000i	−0.426143	+	1.23017i
$414$		0			0
$415$	−1.47372	−	24.5526i	−0.0723421	−	1.20524i
$416$	5.00000	−	8.66025i	0.245145	−	0.424604i
$417$		0			0
$418$		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
$425$	9.19615	+	3.92820i	0.446079	+	0.190546i
$426$		0			0
$427$	−12.1244	−	14.0000i	−0.586739	−	0.677507i
$428$		−	11.0000i		−	0.531705i
$429$		0			0
$430$	8.62436	+	13.0622i	0.415903	+	0.629914i
$431$	−16.0000	+	27.7128i	−0.770693	+	1.33488i	0.166491	+	0.986043i	$0.446756\pi$
$431$	−16.0000	+	27.7128i	−0.770693	+	1.33488i	−0.937184	+	0.348836i	$0.886577\pi$
$432$		0			0
$433$			2.00000i			0.0961139i	0.998845	+	0.0480569i	$0.0153029\pi$
$433$			2.00000i			0.0961139i	−0.998845	+	0.0480569i	$0.984697\pi$
$434$	−1.00000	−	5.19615i	−0.0480015	−	0.249423i
$435$		0			0
$436$	2.50000	+	4.33013i	0.119728	+	0.207375i
$437$	−15.5885	−	9.00000i	−0.745697	−	0.430528i
$438$		0			0
$439$	12.0000	+	20.7846i	0.572729	+	0.991995i	0.996284	+	0.0861252i	$0.0274485\pi$
$439$	12.0000	+	20.7846i	0.572729	+	0.991995i	−0.423556	+	0.905870i	$0.639218\pi$
$440$		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	$0.0698447\pi$
$444$		0			0
$445$	−11.0885	−	16.7942i	−0.525643	−	0.796123i
$446$		0			0
$447$		0			0
$448$	−18.1865	+	3.50000i	−0.859233	+	0.165359i
$449$	31.0000			1.46298			0.731490	−	0.681852i	$-0.238825\pi$
$449$	31.0000			1.46298			0.731490	+	0.681852i	$0.238825\pi$
$450$		0			0
$451$		0			0
$452$	5.19615	+	3.00000i	0.244406	+	0.141108i
$453$		0			0
$454$	20.0000			0.938647
$455$	−2.92820	−	11.4641i	−0.137276	−	0.537445i
$456$		0			0
$457$	27.7128	−	16.0000i	1.29635	−	0.748448i	0.316579	−	0.948566i	$-0.397466\pi$
$457$	27.7128	−	16.0000i	1.29635	−	0.748448i	0.979772	+	0.200118i	$0.0641325\pi$
$458$	19.0526	+	11.0000i	0.890268	+	0.513996i
$459$		0			0
$460$	−0.401924	−	6.69615i	−0.0187398	−	0.312210i
$461$	−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	$-0.977792\pi$
$463$		−	3.00000i		−	0.139422i	0.997567	−	0.0697109i	$-0.0222077\pi$
$464$	3.50000	+	6.06218i	0.162483	+	0.281430i
$465$		0			0
$466$	−7.00000	+	12.1244i	−0.324269	+	0.561650i
$467$	−2.59808	+	1.50000i	−0.120225	+	0.0694117i	−0.558906	−	0.829231i	$-0.688779\pi$
$467$	−2.59808	+	1.50000i	−0.120225	+	0.0694117i	0.438682	+	0.898642i	$0.355446\pi$
$468$		0			0
$469$	12.5000	+	4.33013i	0.577196	+	0.199947i
$470$		0			0
$471$		0			0
$472$	25.9808	+	15.0000i	1.19586	+	0.690431i
$473$		0			0
$474$		0			0
$475$	18.0000	+	24.0000i	0.825897	+	1.10120i
$476$	−4.00000	+	3.46410i	−0.183340	+	0.158777i
$477$		0			0
$478$	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	$0.757551\pi$
$480$		0			0
$481$	8.00000	+	13.8564i	0.364769	+	0.631798i
$482$			14.0000i			0.637683i
$483$		0			0
$484$	−11.0000			−0.500000
$485$	−2.14359	−	35.7128i	−0.0973356	−	1.62164i
$486$		0			0
$487$	10.3923	+	6.00000i	0.470920	+	0.271886i	0.716625	−	0.697459i	$-0.245686\pi$
$487$	10.3923	+	6.00000i	0.470920	+	0.271886i	−0.245705	+	0.969345i	$0.579019\pi$
$488$	−18.1865	+	10.5000i	−0.823266	+	0.475313i
$489$		0			0
$490$	−8.92820	+	12.8564i	−0.403335	+	0.580793i
$491$	26.0000			1.17336			0.586682	−	0.809818i	$-0.300434\pi$
$491$	26.0000			1.17336			0.586682	+	0.809818i	$0.300434\pi$
$492$		0			0
$493$	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
$497$	5.19615	−	1.00000i	0.233079	−	0.0448561i
$498$		0			0
$499$	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	$0.716748\pi$
$500$	−3.76795	+	10.5263i	−0.168508	+	0.470750i
$501$		0			0
$502$	25.9808	−	15.0000i	1.15958	−	0.669483i
$503$		−	15.0000i		−	0.668817i	−0.942428	−	0.334408i	$-0.891463\pi$
$503$		−	15.0000i		−	0.668817i	0.942428	−	0.334408i	$-0.108537\pi$
$504$		0			0
$505$	9.00000	−	18.0000i	0.400495	−	0.800989i
$506$		0			0
$507$		0			0
$508$	−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	$-0.370854\pi$
$510$		0			0
$511$	−15.0000	−	5.19615i	−0.663561	−	0.229864i
$512$			11.0000i			0.486136i
$513$		0			0
$514$	10.0000	−	17.3205i	0.441081	−	0.763975i
$515$	−13.0622	+	8.62436i	−0.575588	+	0.380035i
$516$		0			0
$517$		0			0
$518$	6.92820	−	20.0000i	0.304408	−	0.878750i
$519$		0			0
$520$	−13.3923	+	0.803848i	−0.587291	+	0.0352510i
$521$	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	$0.0674500\pi$
$522$		0			0
$523$	−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
$530$	13.3923	−	0.803848i	0.581725	−	0.0349169i
$531$		0			0
$532$	−15.5885	+	3.00000i	−0.675845	+	0.130066i
$533$			10.0000i			0.433148i
$534$		0			0
$535$	−20.5263	+	13.5526i	−0.887428	+	0.585928i
$536$	7.50000	−	12.9904i	0.323951	−	0.561099i
$537$		0			0
$538$			11.0000i			0.474244i
$539$		0			0
$540$		0			0
$541$	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
$543$		0			0
$544$	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	$-0.881604\pi$
$547$		−	17.0000i		−	0.726868i	0.931620	−	0.363434i	$-0.118396\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	21.0000	+	36.3731i	0.894630	+	1.54954i
$552$		0			0
$553$	−3.46410	−	4.00000i	−0.147309	−	0.170097i
$554$	10.0000			0.424859
$555$		0			0
$556$	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	$-0.715420\pi$
$558$		0			0
$559$	−14.0000			−0.592137
$560$	4.13397	+	4.23205i	0.174692	+	0.178837i
$561$		0			0
$562$	−12.1244	+	7.00000i	−0.511435	+	0.295277i
$563$	−28.5788	−	16.5000i	−1.20445	−	0.695392i	−0.242912	−	0.970048i	$-0.578103\pi$
$563$	−28.5788	−	16.5000i	−1.20445	−	0.695392i	−0.961542	+	0.274656i	$0.911436\pi$
$564$		0			0
$565$	−0.803848	−	13.3923i	−0.0338181	−	0.563418i
$566$	−16.0000			−0.672530
$567$		0			0
$568$		−	6.00000i		−	0.251754i
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	0.990668	−	0.136295i	$-0.0435194\pi$
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	−0.613369	+	0.789797i	$0.710186\pi$
$570$		0			0
$571$	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
$573$		0			0
$574$	10.0000	−	8.66025i	0.417392	−	0.361472i
$575$	−12.0000	+	9.00000i	−0.500435	+	0.375326i
$576$		0			0
$577$	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
$579$		0			0
$580$	−7.00000	+	14.0000i	−0.290659	+	0.581318i
$581$	−5.50000	−	28.5788i	−0.228178	−	1.18565i
$582$		0			0
$583$		0			0
$584$	−9.00000	+	15.5885i	−0.372423	+	0.645055i
$585$		0			0
$586$	−12.0000	−	20.7846i	−0.495715	−	0.858604i
$587$			36.0000i			1.48588i	0.669359	+	0.742940i	$0.266569\pi$
$587$			36.0000i			1.48588i	−0.669359	+	0.742940i	$0.733431\pi$
$588$		0			0
$589$	−12.0000			−0.494451
$590$	−1.33975	−	22.3205i	−0.0551565	−	0.918921i
$591$		0			0
$592$	−6.92820	−	4.00000i	−0.284747	−	0.164399i
$593$	19.0526	−	11.0000i	0.782395	−	0.451716i	−0.0548835	−	0.998493i	$-0.517479\pi$
$593$	19.0526	−	11.0000i	0.782395	−	0.451716i	0.837278	+	0.546777i	$0.184145\pi$
$594$		0			0
$595$	11.3923	+	3.19615i	0.467039	+	0.131029i
$596$	1.00000			0.0409616
$597$		0			0
$598$	−5.19615	−	3.00000i	−0.212486	−	0.122679i
$599$	22.0000	−	38.1051i	0.898896	−	1.55693i	0.0699877	−	0.997548i	$-0.477704\pi$
$599$	22.0000	−	38.1051i	0.898896	−	1.55693i	0.828908	−	0.559385i	$-0.188963\pi$
$600$		0			0
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$	12.1244	+	14.0000i	0.494152	+	0.570597i
$603$		0			0
$604$	−7.00000	−	12.1244i	−0.284826	−	0.493333i
$605$	13.5526	+	20.5263i	0.550990	+	0.834512i
$606$		0			0
$607$	−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
$612$		0			0
$613$	−29.4449	−	17.0000i	−1.18927	−	0.686624i	−0.231127	−	0.972924i	$-0.574241\pi$
$613$	−29.4449	−	17.0000i	−1.18927	−	0.686624i	−0.958140	+	0.286300i	$0.907575\pi$
$614$	−11.5000	−	19.9186i	−0.464102	−	0.803849i
$615$		0			0
$616$		0			0
$617$			4.00000i			0.161034i	0.996753	+	0.0805170i	$0.0256571\pi$
$617$			4.00000i			0.161034i	−0.996753	+	0.0805170i	$0.974343\pi$
$618$		0			0
$619$	14.0000	−	24.2487i	0.562708	−	0.974638i	−0.434551	−	0.900647i	$-0.643093\pi$
$619$	14.0000	−	24.2487i	0.562708	−	0.974638i	0.997259	−	0.0739910i	$-0.0235736\pi$
$620$	−2.46410	−	3.73205i	−0.0989607	−	0.149883i
$621$		0			0
$622$			30.0000i			1.20289i
$623$	−15.5885	−	18.0000i	−0.624538	−	0.721155i
$624$		0			0
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$	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
$633$		0			0
$634$	−3.00000	+	5.19615i	−0.119145	+	0.206366i
$635$	2.14359	+	35.7128i	0.0850659	+	1.41722i
$636$		0			0
$637$	−5.19615	−	13.0000i	−0.205879	−	0.515079i
$638$		0			0
$639$		0			0
$640$	−5.59808	+	3.69615i	−0.221283	+	0.146103i
$641$	−5.50000	+	9.52628i	−0.217237	+	0.376265i	−0.953962	−	0.299927i	$-0.903038\pi$
$641$	−5.50000	+	9.52628i	−0.217237	+	0.376265i	0.736725	+	0.676192i	$0.236371\pi$
$642$		0			0
$643$			4.00000i			0.157745i	0.996885	+	0.0788723i	$0.0251319\pi$
$643$			4.00000i			0.157745i	−0.996885	+	0.0788723i	$0.974868\pi$
$644$	−1.50000	−	7.79423i	−0.0591083	−	0.307136i
$645$		0			0
$646$	−6.00000	−	10.3923i	−0.236067	−	0.408880i
$647$	40.7032	+	23.5000i	1.60021	+	0.923880i	0.991445	+	0.130528i	$0.0416673\pi$
$647$	40.7032	+	23.5000i	1.60021	+	0.923880i	0.608763	+	0.793352i	$0.291666\pi$
$648$		0			0
$649$		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	$0.503218\pi$
$654$		0			0
$655$	4.92820	+	7.46410i	0.192561	+	0.291647i
$656$	−2.50000	−	4.33013i	−0.0976086	−	0.169063i
$657$		0			0
$658$		0			0
$659$	6.00000			0.233727			0.116863	−	0.993148i	$-0.462716\pi$
$659$	6.00000			0.233727			0.116863	+	0.993148i	$0.462716\pi$
$660$		0			0
$661$	4.50000	−	7.79423i	0.175030	−	0.303160i	−0.765142	−	0.643862i	$-0.777331\pi$
$661$	4.50000	−	7.79423i	0.175030	−	0.303160i	0.940172	+	0.340701i	$0.110665\pi$
$662$	5.19615	+	3.00000i	0.201954	+	0.116598i
$663$		0			0
$664$	−33.0000			−1.28065
$665$	24.8038	+	25.3923i	0.961852	+	0.984671i
$666$		0			0
$667$	−18.1865	+	10.5000i	−0.704185	+	0.406562i
$668$	−2.59808	−	1.50000i	−0.100523	−	0.0580367i
$669$		0			0
$670$	−11.1603	+	0.669873i	−0.431158	+	0.0258795i
$671$		0			0
$672$		0			0
$673$			36.0000i			1.38770i	0.720121	+	0.693849i	$0.244086\pi$
$673$			36.0000i			1.38770i	−0.720121	+	0.693849i	$0.755914\pi$
$674$	−9.00000	−	15.5885i	−0.346667	−	0.600445i
$675$		0			0
$676$	−4.50000	+	7.79423i	−0.173077	+	0.299778i
$677$	12.1244	−	7.00000i	0.465977	−	0.269032i	−0.248577	−	0.968612i	$-0.579963\pi$
$677$	12.1244	−	7.00000i	0.465977	−	0.269032i	0.714554	+	0.699580i	$0.246630\pi$
$678$		0			0
$679$	−8.00000	−	41.5692i	−0.307012	−	1.59528i
$680$	6.00000	−	12.0000i	0.230089	−	0.460179i
$681$		0			0
$682$		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	$0.900209\pi$
$684$		0			0
$685$		0			0
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$		0			0
$688$	6.06218	−	3.50000i	0.231118	−	0.133436i
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$		0			0
$691$	10.0000	+	17.3205i	0.380418	+	0.658903i	0.991122	−	0.132956i	$-0.0424468\pi$
$691$	10.0000	+	17.3205i	0.380418	+	0.658903i	−0.610704	+	0.791859i	$0.709113\pi$
$692$		−	12.0000i		−	0.456172i
$693$		0			0
$694$	−15.0000			−0.569392
$695$	−17.8564	+	1.07180i	−0.677332	+	0.0406556i
$696$		0			0
$697$	−8.66025	−	5.00000i	−0.328031	−	0.189389i
$698$	−14.7224	+	8.50000i	−0.557252	+	0.321730i
$699$		0			0
$700$	−2.80385	+	12.9282i	−0.105975	+	0.488640i
$701$	1.00000			0.0377695			0.0188847	−	0.999822i	$-0.493988\pi$
$701$	1.00000			0.0377695			0.0188847	+	0.999822i	$0.493988\pi$
$702$		0			0
$703$	−41.5692	−	24.0000i	−1.56781	−	0.905177i
$704$		0			0
$705$		0			0
$706$	−26.0000			−0.978523
$707$	7.79423	−	22.5000i	0.293132	−	0.846200i
$708$		0			0
$709$	−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	$-0.538573\pi$
$710$	−3.73205	+	2.46410i	−0.140061	+	0.0924761i
$711$		0			0
$712$	−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
$717$		0			0
$718$	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	$-0.400925\pi$
$720$		0			0
$721$	−14.0000	+	12.1244i	−0.521387	+	0.451535i
$722$		−	17.0000i		−	0.632674i
$723$		0			0
$724$	1.50000	−	2.59808i	0.0557471	−	0.0965567i
$725$	34.7487	−	4.18653i	1.29053	−	0.155484i
$726$		0			0
$727$		−	47.0000i		−	1.74313i	−0.490277	−	0.871567i	$-0.663104\pi$
$727$		−	47.0000i		−	1.74313i	0.490277	−	0.871567i	$-0.336896\pi$
$728$	−15.5885	+	3.00000i	−0.577747	+	0.111187i
$729$		0			0
$730$	13.3923	−	0.803848i	0.495671	−	0.0297517i
$731$	7.00000	−	12.1244i	0.258904	−	0.448435i
$732$		0			0
$733$	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
$738$		0			0
$739$	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	$0.0715853\pi$
$740$	−1.07180	−	17.8564i	−0.0394000	−	0.656415i
$741$		0			0
$742$	15.5885	−	3.00000i	0.572270	−	0.110133i
$743$		−	49.0000i		−	1.79764i	−0.438322	−	0.898818i	$-0.644427\pi$
$743$		−	49.0000i		−	1.79764i	0.438322	−	0.898818i	$-0.355573\pi$
$744$		0			0
$745$	−1.23205	−	1.86603i	−0.0451388	−	0.0683659i
$746$	−12.0000	+	20.7846i	−0.439351	+	0.760979i
$747$		0			0
$748$		0			0
$749$	−22.0000	+	19.0526i	−0.803863	+	0.696165i
$750$		0			0
$751$	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
$753$		0			0
$754$	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	$0.130921\pi$
$757$			22.0000i			0.799604i	−0.916602	+	0.399802i	$0.869079\pi$
$758$	−8.66025	+	5.00000i	−0.314555	+	0.181608i
$759$		0			0
$760$	33.5885	−	22.1769i	1.21838	−	0.804441i
$761$	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	$0.751669\pi$
$762$		0			0
$763$	4.33013	−	12.5000i	0.156761	−	0.452530i
$764$	−12.0000			−0.434145
$765$		0			0
$766$	−2.50000	+	4.33013i	−0.0903287	+	0.156454i
$767$	17.3205	+	10.0000i	0.625407	+	0.361079i
$768$		0			0
$769$	30.0000			1.08183			0.540914	−	0.841078i	$-0.318079\pi$
$769$	30.0000			1.08183			0.540914	+	0.841078i	$0.318079\pi$
$770$		0			0
$771$		0			0
$772$	3.46410	−	2.00000i	0.124676	−	0.0719816i
$773$	−15.5885	−	9.00000i	−0.560678	−	0.323708i	0.192740	−	0.981250i	$-0.438263\pi$
$773$	−15.5885	−	9.00000i	−0.560678	−	0.323708i	−0.753418	+	0.657542i	$0.771596\pi$
$774$		0			0
$775$	−3.92820	+	9.19615i	−0.141105	+	0.330336i
$776$	−48.0000			−1.72310
$777$		0			0
$778$		−	14.0000i		−	0.501924i
$779$	−15.0000	−	25.9808i	−0.537431	−	0.930857i
$780$		0			0
$781$		0			0
$782$	5.19615	−	3.00000i	0.185814	−	0.107280i
$783$		0			0
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$	−24.0000	−	12.0000i	−0.856597	−	0.428298i
$786$		0			0
$787$	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
$789$		0			0
$790$	4.00000	+	2.00000i	0.142314	+	0.0711568i
$791$	−3.00000	−	15.5885i	−0.106668	−	0.554262i
$792$		0			0
$793$	−12.1244	+	7.00000i	−0.430548	+	0.248577i
$794$	8.00000	−	13.8564i	0.283909	−	0.491745i
$795$		0			0
$796$	−2.00000	−	3.46410i	−0.0708881	−	0.122782i
$797$		−	40.0000i		−	1.41687i	−0.705775	−	0.708436i	$-0.749401\pi$
$797$		−	40.0000i		−	1.41687i	0.705775	−	0.708436i	$-0.250599\pi$
$798$		0			0
$799$		0			0
$800$	22.9904	+	9.82051i	0.812833	+	0.347207i
$801$		0			0
$802$	−2.59808	−	1.50000i	−0.0917413	−	0.0529668i
$803$		0			0
$804$		0			0
$805$	−12.6962	+	12.4019i	−0.447481	+	0.437110i
$806$	−4.00000			−0.140894
$807$		0			0
$808$	−23.3827	−	13.5000i	−0.822600	−	0.474928i
$809$	−4.50000	+	7.79423i	−0.158212	+	0.274030i	−0.934224	−	0.356687i	$-0.883906\pi$
$809$	−4.50000	+	7.79423i	−0.158212	+	0.274030i	0.776012	+	0.630718i	$0.217239\pi$
$810$		0			0
$811$	−2.00000			−0.0702295			−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000			−0.0702295			−0.0351147	+	0.999383i	$0.511180\pi$
$812$	−6.06218	+	17.5000i	−0.212741	+	0.614130i
$813$		0			0
$814$		0			0
$815$	7.46410	−	4.92820i	0.261456	−	0.172627i
$816$		0			0
$817$	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	0.991616	−	0.129217i	$-0.0412465\pi$
$821$	11.0000	+	19.0526i	0.383903	+	0.664939i	−0.607714	+	0.794156i	$0.707913\pi$
$822$		0			0
$823$	21.6506	+	12.5000i	0.754694	+	0.435723i	0.827387	−	0.561632i	$-0.189826\pi$
$823$	21.6506	+	12.5000i	0.754694	+	0.435723i	−0.0726937	+	0.997354i	$0.523160\pi$
$824$	10.5000	+	18.1865i	0.365785	+	0.633558i
$825$		0			0
$826$	−5.00000	−	25.9808i	−0.173972	−	0.903986i
$827$			39.0000i			1.35616i	0.734987	+	0.678081i	$0.237188\pi$
$827$			39.0000i			1.35616i	−0.734987	+	0.678081i	$0.762812\pi$
$828$		0			0
$829$	−15.0000	+	25.9808i	−0.520972	+	0.902349i	0.478731	+	0.877962i	$0.341097\pi$
$829$	−15.0000	+	25.9808i	−0.520972	+	0.902349i	−0.999703	+	0.0243876i	$0.992236\pi$
$830$	13.5526	+	20.5263i	0.470416	+	0.712478i
$831$		0			0
$832$			14.0000i			0.485363i
$833$	13.8564	+	2.00000i	0.480096	+	0.0692959i
$834$		0			0
$835$	0.401924	+	6.69615i	0.0139091	+	0.231730i
$836$		0			0
$837$		0			0
$838$	−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
$843$		0			0
$844$	5.00000	−	8.66025i	0.172107	−	0.298098i
$845$	20.0885	−	1.20577i	0.691064	−	0.0414798i
$846$		0			0
$847$	19.0526	+	22.0000i	0.654654	+	0.755929i
$848$		−	6.00000i		−	0.206041i
$849$		0			0
$850$	−9.92820	+	1.19615i	−0.340535	+	0.0410277i
$851$	12.0000	−	20.7846i	0.411355	−	0.712487i
$852$		0			0
$853$			6.00000i			0.205436i	0.994711	+	0.102718i	$0.0327539\pi$
$853$			6.00000i			0.205436i	−0.994711	+	0.102718i	$0.967246\pi$
$854$	17.5000	+	6.06218i	0.598838	+	0.207443i
$855$		0			0
$856$	16.5000	+	28.5788i	0.563958	+	0.976805i
$857$	−10.3923	−	6.00000i	−0.354994	−	0.204956i	0.311888	−	0.950119i	$-0.399038\pi$
$857$	−10.3923	−	6.00000i	−0.354994	−	0.204956i	−0.666883	+	0.745163i	$0.732372\pi$
$858$		0			0
$859$	−16.0000	−	27.7128i	−0.545913	−	0.945549i	−0.998549	−	0.0538535i	$-0.982850\pi$
$859$	−16.0000	−	27.7128i	−0.545913	−	0.945549i	0.452636	−	0.891695i	$-0.350484\pi$
$860$	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	$0.382285\pi$
$864$		0			0
$865$	−22.3923	+	14.7846i	−0.761361	+	0.502692i
$866$	−1.00000	−	1.73205i	−0.0339814	−	0.0588575i
$867$		0			0
$868$	−3.46410	−	4.00000i	−0.117579	−	0.135769i
$869$		0			0
$870$		0			0
$871$	5.00000	−	8.66025i	0.169419	−	0.293442i
$872$	−12.9904	−	7.50000i	−0.439910	−	0.253982i
$873$		0			0
$874$	18.0000			0.608859
$875$	27.5788	−	10.6962i	0.932335	−	0.361596i
$876$		0			0
$877$	−1.73205	+	1.00000i	−0.0584872	+	0.0337676i	−0.528958	−	0.848648i	$-0.677417\pi$
$877$	−1.73205	+	1.00000i	−0.0584872	+	0.0337676i	0.470471	+	0.882415i	$0.344084\pi$
$878$	−20.7846	−	12.0000i	−0.701447	−	0.404980i
$879$		0			0
$880$		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	$-0.792874\pi$
$883$		−	36.0000i		−	1.21150i	0.795656	−	0.605748i	$-0.207126\pi$
$884$	2.00000	+	3.46410i	0.0672673	+	0.116510i
$885$		0			0
$886$	−15.5000	+	26.8468i	−0.520733	+	0.901935i
$887$	−37.2391	+	21.5000i	−1.25037	+	0.721899i	−0.971182	−	0.238338i	$-0.923397\pi$
$887$	−37.2391	+	21.5000i	−1.25037	+	0.721899i	−0.279184	+	0.960238i	$0.590064\pi$
$888$		0			0
$889$	8.00000	+	41.5692i	0.268311	+	1.39419i
$890$	18.0000	+	9.00000i	0.603361	+	0.301681i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	2.00000	−	4.00000i	0.0668526	−	0.133705i
$896$	−6.00000	+	5.19615i	−0.200446	+	0.173591i
$897$		0			0
$898$	−26.8468	+	15.5000i	−0.895889	+	0.517242i
$899$	−7.00000	+	12.1244i	−0.233463	+	0.404370i
$900$		0			0
$901$	−6.00000	−	10.3923i	−0.199889	−	0.346218i
$902$		0			0
$903$		0			0
$904$	−18.0000			−0.598671
$905$	−6.69615	+	0.401924i	−0.222588	+	0.0133604i
$906$		0			0
$907$	16.4545	+	9.50000i	0.546362	+	0.315442i	0.747653	−	0.664089i	$-0.231180\pi$
$907$	16.4545	+	9.50000i	0.546362	+	0.315442i	−0.201291	+	0.979531i	$0.564514\pi$
$908$	17.3205	−	10.0000i	0.574801	−	0.331862i
$909$		0			0
$910$	8.26795	+	8.46410i	0.274080	+	0.280582i
$911$	−24.0000			−0.795155			−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000			−0.795155			−0.397578	+	0.917568i	$0.630149\pi$
$912$		0			0
$913$		0			0
$914$	−16.0000	+	27.7128i	−0.529233	+	0.916658i
$915$		0			0
$916$	22.0000			0.726900
$917$	6.92820	+	8.00000i	0.228789	+	0.264183i
$918$		0			0
$919$	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	$0.643835\pi$
$920$	11.0885	+	16.7942i	0.365576	+	0.553689i
$921$		0			0
$922$	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
$927$		0			0
$928$	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	$0.675517\pi$
$930$		0			0
$931$	33.0000	+	25.9808i	1.08153	+	0.851485i
$932$			14.0000i			0.458585i
$933$		0			0
$934$	1.50000	−	2.59808i	0.0490815	−	0.0850117i
$935$		0			0
$936$		0			0
$937$		−	8.00000i		−	0.261349i	−0.991425	−	0.130674i	$-0.958286\pi$
$937$		−	8.00000i		−	0.261349i	0.991425	−	0.130674i	$-0.0417142\pi$
$938$	−12.9904	+	2.50000i	−0.424151	+	0.0816279i
$939$		0			0
$940$		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	$0.261451\pi$
$942$		0			0
$943$	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	$-0.0435483\pi$
$948$		0			0
$949$	−6.00000	+	10.3923i	−0.194768	+	0.337348i
$950$	−27.5885	−	11.7846i	−0.895088	−	0.382343i
$951$		0			0
$952$	5.19615	−	15.0000i	0.168408	−	0.486153i
$953$			60.0000i			1.94359i	0.235826	+	0.971795i	$0.424220\pi$
$953$			60.0000i			1.94359i	−0.235826	+	0.971795i	$0.575780\pi$
$954$		0			0
$955$	14.7846	+	22.3923i	0.478419	+	0.724598i
$956$	9.00000	−	15.5885i	0.291081	−	0.504167i
$957$		0			0
$958$		−	42.0000i		−	1.35696i
$959$		0			0
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	−13.8564	−	8.00000i	−0.446748	−	0.257930i
$963$		0			0
$964$	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	$-0.932971\pi$
$967$		−	13.0000i		−	0.418052i	0.977910	−	0.209026i	$-0.0670293\pi$
$968$	28.5788	−	16.5000i	0.918559	−	0.530330i
$969$		0			0
$970$	19.7128	+	29.8564i	0.632940	+	0.958631i
$971$	−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	$-0.338305\pi$
$972$		0			0
$973$	−20.7846	+	4.00000i	−0.666324	+	0.128234i
$974$	−12.0000			−0.384505
$975$		0			0
$976$	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	$0.257245\pi$
$978$		0			0
$979$		0			0
$980$	−1.30385	+	15.5981i	−0.0416499	+	0.498262i
$981$		0			0
$982$	−22.5167	+	13.0000i	−0.718536	+	0.414847i
$983$	−2.59808	−	1.50000i	−0.0828658	−	0.0478426i	0.457995	−	0.888955i	$-0.348568\pi$
$983$	−2.59808	−	1.50000i	−0.0828658	−	0.0478426i	−0.540860	+	0.841112i	$0.681901\pi$
$984$		0			0
$985$	1.07180	+	17.8564i	0.0341503	+	0.568952i
$986$	−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
$993$		0			0
$994$	−4.00000	+	3.46410i	−0.126872	+	0.109875i
$995$	−4.00000	+	8.00000i	−0.126809	+	0.253617i
$996$		0			0
$997$	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
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bf.a.109.1		4
3.2	odd	2		35.2.j.a.4.2	yes	4
5.4	even	2	inner	315.2.bf.a.109.2		4
7.2	even	3	inner	315.2.bf.a.289.2		4
7.3	odd	6		2205.2.d.e.1324.1		2
7.4	even	3		2205.2.d.d.1324.1		2
12.11	even	2		560.2.bw.b.529.2		4
15.2	even	4		175.2.e.b.151.1		2
15.8	even	4		175.2.e.a.151.1		2
15.14	odd	2		35.2.j.a.4.1	✓	4
21.2	odd	6		35.2.j.a.9.1	yes	4
21.5	even	6		245.2.j.c.79.1		4
21.11	odd	6		245.2.b.c.99.2		2
21.17	even	6		245.2.b.b.99.2		2
21.20	even	2		245.2.j.c.214.2		4
35.4	even	6		2205.2.d.d.1324.2		2
35.9	even	6	inner	315.2.bf.a.289.1		4
35.24	odd	6		2205.2.d.e.1324.2		2
60.59	even	2		560.2.bw.b.529.1		4
84.23	even	6		560.2.bw.b.289.1		4
105.2	even	12		175.2.e.b.51.1		2
105.17	odd	12		1225.2.a.b.1.1		1
105.23	even	12		175.2.e.a.51.1		2
105.32	even	12		1225.2.a.d.1.1		1
105.38	odd	12		1225.2.a.g.1.1		1
105.44	odd	6		35.2.j.a.9.2	yes	4
105.53	even	12		1225.2.a.f.1.1		1
105.59	even	6		245.2.b.b.99.1		2
105.74	odd	6		245.2.b.c.99.1		2
105.89	even	6		245.2.j.c.79.2		4
105.104	even	2		245.2.j.c.214.1		4
420.359	even	6		560.2.bw.b.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.j.a.4.1	✓	4	15.14	odd	2
35.2.j.a.4.2	yes	4	3.2	odd	2
35.2.j.a.9.1	yes	4	21.2	odd	6
35.2.j.a.9.2	yes	4	105.44	odd	6
175.2.e.a.51.1		2	105.23	even	12
175.2.e.a.151.1		2	15.8	even	4
175.2.e.b.51.1		2	105.2	even	12
175.2.e.b.151.1		2	15.2	even	4
245.2.b.b.99.1		2	105.59	even	6
245.2.b.b.99.2		2	21.17	even	6
245.2.b.c.99.1		2	105.74	odd	6
245.2.b.c.99.2		2	21.11	odd	6
245.2.j.c.79.1		4	21.5	even	6
245.2.j.c.79.2		4	105.89	even	6
245.2.j.c.214.1		4	105.104	even	2
245.2.j.c.214.2		4	21.20	even	2
315.2.bf.a.109.1		4	1.1	even	1	trivial
315.2.bf.a.109.2		4	5.4	even	2	inner
315.2.bf.a.289.1		4	35.9	even	6	inner
315.2.bf.a.289.2		4	7.2	even	3	inner
560.2.bw.b.289.1		4	84.23	even	6
560.2.bw.b.289.2		4	420.359	even	6
560.2.bw.b.529.1		4	60.59	even	2
560.2.bw.b.529.2		4	12.11	even	2
1225.2.a.b.1.1		1	105.17	odd	12
1225.2.a.d.1.1		1	105.32	even	12
1225.2.a.f.1.1		1	105.53	even	12
1225.2.a.g.1.1		1	105.38	odd	12
2205.2.d.d.1324.1		2	7.4	even	3
2205.2.d.d.1324.2		2	35.4	even	6
2205.2.d.e.1324.1		2	7.3	odd	6
2205.2.d.e.1324.2		2	35.24	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} +(2.59808 - 0.500000i) q^{7} -3.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} +(2.59808 - 0.500000i) q^{7} -3.00000i q^{8} +(-1.86603 + 1.23205i) q^{10} -2.00000i q^{13} +(-2.00000 + 1.73205i) q^{14} +(0.500000 + 0.866025i) q^{16} +(1.73205 + 1.00000i) q^{17} +(3.00000 + 5.19615i) q^{19} +(-1.00000 + 2.00000i) q^{20} +(-2.59808 + 1.50000i) q^{23} +(4.96410 - 0.598076i) q^{25} +(1.00000 + 1.73205i) q^{26} +(-0.866025 + 2.50000i) q^{28} +7.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(4.33013 + 2.50000i) q^{32} -2.00000 q^{34} +(5.73205 - 1.46410i) q^{35} +(-6.92820 + 4.00000i) q^{37} +(-5.19615 - 3.00000i) q^{38} +(-0.401924 - 6.69615i) q^{40} -5.00000 q^{41} -7.00000i q^{43} +(1.50000 - 2.59808i) q^{46} +(6.50000 - 2.59808i) q^{49} +(-4.00000 + 3.00000i) q^{50} +(1.73205 + 1.00000i) q^{52} +(-5.19615 - 3.00000i) q^{53} +(-1.50000 - 7.79423i) q^{56} +(-6.06218 + 3.50000i) q^{58} +(-5.00000 + 8.66025i) q^{59} +(-3.50000 - 6.06218i) q^{61} -2.00000i q^{62} -7.00000 q^{64} +(-0.267949 - 4.46410i) q^{65} +(4.33013 + 2.50000i) q^{67} +(-1.73205 + 1.00000i) q^{68} +(-4.23205 + 4.13397i) q^{70} +2.00000 q^{71} +(-5.19615 - 3.00000i) q^{73} +(4.00000 - 6.92820i) q^{74} -6.00000 q^{76} +(-1.00000 - 1.73205i) q^{79} +(1.23205 + 1.86603i) q^{80} +(4.33013 - 2.50000i) q^{82} -11.0000i q^{83} +(4.00000 + 2.00000i) q^{85} +(3.50000 + 6.06218i) q^{86} +(-4.50000 - 7.79423i) q^{89} +(-1.00000 - 5.19615i) q^{91} -3.00000i q^{92} +(7.39230 + 11.1962i) q^{95} -16.0000i q^{97} +(-4.33013 + 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{4} + 2 q^{5}+O(q^{10}) \) 4 * q - 2 * q^4 + 2 * q^5	\( 4 q - 2 q^{4} + 2 q^{5} - 4 q^{10} - 8 q^{14} + 2 q^{16} + 12 q^{19} - 4 q^{20} + 6 q^{25} + 4 q^{26} + 28 q^{29} - 4 q^{31} - 8 q^{34} + 16 q^{35} - 12 q^{40} - 20 q^{41} + 6 q^{46} + 26 q^{49} - 16 q^{50} - 6 q^{56} - 20 q^{59} - 14 q^{61} - 28 q^{64} - 8 q^{65} - 10 q^{70} + 8 q^{71} + 16 q^{74} - 24 q^{76} - 4 q^{79} - 2 q^{80} + 16 q^{85} + 14 q^{86} - 18 q^{89} - 4 q^{91} - 12 q^{95}+O(q^{100}) \) 4 * q - 2 * q^4 + 2 * q^5 - 4 * q^10 - 8 * q^14 + 2 * q^16 + 12 * q^19 - 4 * q^20 + 6 * q^25 + 4 * q^26 + 28 * q^29 - 4 * q^31 - 8 * q^34 + 16 * q^35 - 12 * q^40 - 20 * q^41 + 6 * q^46 + 26 * q^49 - 16 * q^50 - 6 * q^56 - 20 * q^59 - 14 * q^61 - 28 * q^64 - 8 * q^65 - 10 * q^70 + 8 * q^71 + 16 * q^74 - 24 * q^76 - 4 * q^79 - 2 * q^80 + 16 * q^85 + 14 * q^86 - 18 * q^89 - 4 * q^91 - 12 * q^95

Introduction

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