LMFDB - Embedded newform 4020.2.q.j.3781.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4020,2,Mod(841,4020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4020, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4020.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$32.0998616126$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 30 x^{10} - 53 x^{9} + 798 x^{8} - 1096 x^{7} + 4060 x^{6} - 915 x^{5} + 10392 x^{4} + \cdots + 81 $ x^12 - x^11 + 30x^10 - 53x^9 + 798x^8 - 1096x^7 + 4060x^6 - 915x^5 + 10392x^4 - 7038x^3 + 4869x^2 - 675x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3781.6
Root			$2.33000 + 4.03568i$ of defining polynomial
Character	$\chi$	$=$	4020.3781
Dual form			4020.2.q.j.841.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} -1.00000 q^{5} +(2.37984 + 4.12200i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} -1.00000 q^{5} +(2.37984 + 4.12200i) q^{7} +1.00000 q^{9} +(2.09011 + 3.62018i) q^{11} +(0.500000 - 0.866025i) q^{13} -1.00000 q^{15} +(-1.68241 + 2.91403i) q^{17} +(2.14970 - 3.72339i) q^{19} +(2.37984 + 4.12200i) q^{21} +(-0.737700 + 1.27773i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(2.87246 + 4.97524i) q^{29} +(1.32025 + 2.28674i) q^{31} +(2.09011 + 3.62018i) q^{33} +(-2.37984 - 4.12200i) q^{35} +(5.02524 - 8.70397i) q^{37} +(0.500000 - 0.866025i) q^{39} +(-0.0825512 - 0.142983i) q^{41} -7.29940 q^{43} -1.00000 q^{45} +(2.73280 + 4.73335i) q^{47} +(-7.82727 + 13.5572i) q^{49} +(-1.68241 + 2.91403i) q^{51} +1.64050 q^{53} +(-2.09011 - 3.62018i) q^{55} +(2.14970 - 3.72339i) q^{57} -8.85112 q^{59} +(3.86271 - 6.69041i) q^{61} +(2.37984 + 4.12200i) q^{63} +(-0.500000 + 0.866025i) q^{65} +(3.11483 - 7.56954i) q^{67} +(-0.737700 + 1.27773i) q^{69} +(6.87027 + 11.8997i) q^{71} +(-6.88057 + 11.9175i) q^{73} +1.00000 q^{75} +(-9.94827 + 17.2309i) q^{77} +(-2.08037 - 3.60330i) q^{79} +1.00000 q^{81} +(7.24720 - 12.5525i) q^{83} +(1.68241 - 2.91403i) q^{85} +(2.87246 + 4.97524i) q^{87} -9.17586 q^{89} +4.75968 q^{91} +(1.32025 + 2.28674i) q^{93} +(-2.14970 + 3.72339i) q^{95} +(-7.67804 + 13.2988i) q^{97} +(2.09011 + 3.62018i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{3} - 12 q^{5} + 2 q^{7} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^3 - 12 * q^5 + 2 * q^7 + 12 * q^9	$ 12 q + 12 q^{3} - 12 q^{5} + 2 q^{7} + 12 q^{9} - 5 q^{11} + 6 q^{13} - 12 q^{15} + 9 q^{17} - 11 q^{19} + 2 q^{21} + 19 q^{23} + 12 q^{25} + 12 q^{27} + 8 q^{29} - 4 q^{31} - 5 q^{33} - 2 q^{35} + 5 q^{37} + 6 q^{39} - 9 q^{41} - 14 q^{43} - 12 q^{45} - 6 q^{47} - 46 q^{49} + 9 q^{51} - 20 q^{53} + 5 q^{55} - 11 q^{57} + 6 q^{59} + 27 q^{61} + 2 q^{63} - 6 q^{65} + 3 q^{67} + 19 q^{69} + 25 q^{71} - 8 q^{73} + 12 q^{75} + 10 q^{77} - 2 q^{79} + 12 q^{81} + 20 q^{83} - 9 q^{85} + 8 q^{87} + 12 q^{89} + 4 q^{91} - 4 q^{93} + 11 q^{95} - q^{97} - 5 q^{99}+O(q^{100}) $ 12 * q + 12 * q^3 - 12 * q^5 + 2 * q^7 + 12 * q^9 - 5 * q^11 + 6 * q^13 - 12 * q^15 + 9 * q^17 - 11 * q^19 + 2 * q^21 + 19 * q^23 + 12 * q^25 + 12 * q^27 + 8 * q^29 - 4 * q^31 - 5 * q^33 - 2 * q^35 + 5 * q^37 + 6 * q^39 - 9 * q^41 - 14 * q^43 - 12 * q^45 - 6 * q^47 - 46 * q^49 + 9 * q^51 - 20 * q^53 + 5 * q^55 - 11 * q^57 + 6 * q^59 + 27 * q^61 + 2 * q^63 - 6 * q^65 + 3 * q^67 + 19 * q^69 + 25 * q^71 - 8 * q^73 + 12 * q^75 + 10 * q^77 - 2 * q^79 + 12 * q^81 + 20 * q^83 - 9 * q^85 + 8 * q^87 + 12 * q^89 + 4 * q^91 - 4 * q^93 + 11 * q^95 - q^97 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times$.

$n$	$1141$	$2011$	$2681$	$3217$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	2.37984	+	4.12200i	0.899495	+	1.55797i	0.828142	+	0.560519i	$0.189398\pi$
$7$	2.37984	+	4.12200i	0.899495	+	1.55797i	0.0713530	+	0.997451i	$0.477268\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	2.09011	+	3.62018i	0.630193	+	1.09153i	0.987512	+	0.157544i	$0.0503576\pi$
$11$	2.09011	+	3.62018i	0.630193	+	1.09153i	−0.357319	+	0.933982i	$0.616309\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	−0.788320	−	0.615265i	$-0.789049\pi$
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	0.926995	+	0.375073i	$0.122382\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	−1.68241	+	2.91403i	−0.408045	+	0.706755i	−0.994671	−	0.103103i	$-0.967123\pi$
$17$	−1.68241	+	2.91403i	−0.408045	+	0.706755i	0.586625	+	0.809858i	$0.300456\pi$
$18$		0			0
$19$	2.14970	−	3.72339i	0.493175	−	0.854205i	−0.506794	−	0.862067i	$-0.669169\pi$
$19$	2.14970	−	3.72339i	0.493175	−	0.854205i	0.999969	+	0.00786249i	$0.00250273\pi$
$20$		0			0
$21$	2.37984	+	4.12200i	0.519323	+	0.899495i
$22$		0			0
$23$	−0.737700	+	1.27773i	−0.153821	+	0.266426i	−0.932629	−	0.360836i	$-0.882491\pi$
$23$	−0.737700	+	1.27773i	−0.153821	+	0.266426i	0.778808	+	0.627262i	$0.215825\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	2.87246	+	4.97524i	0.533402	+	0.923880i	0.999239	+	0.0390090i	$0.0124201\pi$
$29$	2.87246	+	4.97524i	0.533402	+	0.923880i	−0.465837	+	0.884871i	$0.654247\pi$
$30$		0			0
$31$	1.32025	+	2.28674i	0.237124	+	0.410711i	0.959888	−	0.280384i	$-0.0904619\pi$
$31$	1.32025	+	2.28674i	0.237124	+	0.410711i	−0.722764	+	0.691095i	$0.757129\pi$
$32$		0			0
$33$	2.09011	+	3.62018i	0.363842	+	0.630193i
$34$		0			0
$35$	−2.37984	−	4.12200i	−0.402266	−	0.696745i
$36$		0			0
$37$	5.02524	−	8.70397i	0.826144	−	1.43092i	−0.0748976	−	0.997191i	$-0.523863\pi$
$37$	5.02524	−	8.70397i	0.826144	−	1.43092i	0.901042	−	0.433732i	$-0.142804\pi$
$38$		0			0
$39$	0.500000	−	0.866025i	0.0800641	−	0.138675i
$40$		0			0
$41$	−0.0825512	−	0.142983i	−0.0128923	−	0.0223302i	0.859507	−	0.511124i	$-0.170771\pi$
$41$	−0.0825512	−	0.142983i	−0.0128923	−	0.0223302i	−0.872400	+	0.488793i	$0.837437\pi$
$42$		0			0
$43$	−7.29940			−1.11315			−0.556574	−	0.830798i	$-0.687885\pi$
$43$	−7.29940			−1.11315			−0.556574	+	0.830798i	$0.687885\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	2.73280	+	4.73335i	0.398620	+	0.690430i	0.993556	−	0.113343i	$-0.0361559\pi$
$47$	2.73280	+	4.73335i	0.398620	+	0.690430i	−0.594936	+	0.803773i	$0.702823\pi$
$48$		0			0
$49$	−7.82727	+	13.5572i	−1.11818	+	1.93675i
$50$		0			0
$51$	−1.68241	+	2.91403i	−0.235585	+	0.408045i
$52$		0			0
$53$	1.64050			0.225340			0.112670	−	0.993632i	$-0.464060\pi$
$53$	1.64050			0.225340			0.112670	+	0.993632i	$0.464060\pi$
$54$		0			0
$55$	−2.09011	−	3.62018i	−0.281831	−	0.488145i
$56$		0			0
$57$	2.14970	−	3.72339i	0.284735	−	0.493175i
$58$		0			0
$59$	−8.85112			−1.15232			−0.576159	−	0.817338i	$-0.695449\pi$
$59$	−8.85112			−1.15232			−0.576159	+	0.817338i	$0.695449\pi$
$60$		0			0
$61$	3.86271	−	6.69041i	0.494569	−	0.856619i	−0.505411	−	0.862879i	$-0.668659\pi$
$61$	3.86271	−	6.69041i	0.494569	−	0.856619i	0.999980	+	0.00625940i	$0.00199244\pi$
$62$		0			0
$63$	2.37984	+	4.12200i	0.299832	+	0.519323i
$64$		0			0
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$		0			0
$67$	3.11483	−	7.56954i	0.380537	−	0.924766i
$67$	3.11483	−	7.56954i	0.380537	−	0.924766i
$68$		0			0
$69$	−0.737700	+	1.27773i	−0.0888086	+	0.153821i
$70$		0			0
$71$	6.87027	+	11.8997i	0.815351	+	1.41223i	0.909075	+	0.416632i	$0.136790\pi$
$71$	6.87027	+	11.8997i	0.815351	+	1.41223i	−0.0937239	+	0.995598i	$0.529877\pi$
$72$		0			0
$73$	−6.88057	+	11.9175i	−0.805310	+	1.39484i	0.110772	+	0.993846i	$0.464668\pi$
$73$	−6.88057	+	11.9175i	−0.805310	+	1.39484i	−0.916082	+	0.400992i	$0.868666\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	−9.94827	+	17.2309i	−1.13371	+	1.96364i
$78$		0			0
$79$	−2.08037	−	3.60330i	−0.234059	−	0.405403i	0.724940	−	0.688813i	$-0.241868\pi$
$79$	−2.08037	−	3.60330i	−0.234059	−	0.405403i	−0.958999	+	0.283410i	$0.908534\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	7.24720	−	12.5525i	0.795483	−	1.37782i	−0.127049	−	0.991896i	$-0.540551\pi$
$83$	7.24720	−	12.5525i	0.795483	−	1.37782i	0.922532	−	0.385921i	$-0.126116\pi$
$84$		0			0
$85$	1.68241	−	2.91403i	0.182483	−	0.316070i
$86$		0			0
$87$	2.87246	+	4.97524i	0.307960	+	0.533402i
$88$		0			0
$89$	−9.17586			−0.972639			−0.486319	−	0.873781i	$-0.661661\pi$
$89$	−9.17586			−0.972639			−0.486319	+	0.873781i	$0.661661\pi$
$90$		0			0
$91$	4.75968			0.498950
$92$		0			0
$93$	1.32025	+	2.28674i	0.136904	+	0.237124i
$94$		0			0
$95$	−2.14970	+	3.72339i	−0.220555	+	0.382012i
$96$		0			0
$97$	−7.67804	+	13.2988i	−0.779587	+	1.35028i	0.152593	+	0.988289i	$0.451238\pi$
$97$	−7.67804	+	13.2988i	−0.779587	+	1.35028i	−0.932180	+	0.361995i	$0.882096\pi$
$98$		0			0
$99$	2.09011	+	3.62018i	0.210064	+	0.363842i
$100$		0			0
$101$	0.495102	+	0.857541i	0.0492644	+	0.0853285i	0.889606	−	0.456729i	$-0.150979\pi$
$101$	0.495102	+	0.857541i	0.0492644	+	0.0853285i	−0.840342	+	0.542057i	$0.817646\pi$
$102$		0			0
$103$	−8.62783	−	14.9438i	−0.850126	−	1.47246i	−0.881094	−	0.472941i	$-0.843192\pi$
$103$	−8.62783	−	14.9438i	−0.850126	−	1.47246i	0.0309685	−	0.999520i	$-0.490141\pi$
$104$		0			0
$105$	−2.37984	−	4.12200i	−0.232248	−	0.402266i
$106$		0			0
$107$	12.0259			1.16259			0.581295	−	0.813693i	$-0.302546\pi$
$107$	12.0259			1.16259			0.581295	+	0.813693i	$0.302546\pi$
$108$		0			0
$109$	−17.3958			−1.66622			−0.833108	−	0.553110i	$-0.813441\pi$
$109$	−17.3958			−1.66622			−0.833108	+	0.553110i	$0.813441\pi$
$110$		0			0
$111$	5.02524	−	8.70397i	0.476975	−	0.826144i
$112$		0			0
$113$	2.32025	+	4.01879i	0.218271	+	0.378056i	0.954279	−	0.298916i	$-0.0966251\pi$
$113$	2.32025	+	4.01879i	0.218271	+	0.378056i	−0.736009	+	0.676972i	$0.763292\pi$
$114$		0			0
$115$	0.737700	−	1.27773i	0.0687908	−	0.119149i
$116$		0			0
$117$	0.500000	−	0.866025i	0.0462250	−	0.0800641i
$118$		0			0
$119$	−16.0155			−1.46814
$120$		0			0
$121$	−3.23715	+	5.60691i	−0.294287	+	0.509719i
$122$		0			0
$123$	−0.0825512	−	0.142983i	−0.00744339	−	0.0128923i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−7.04294	−	12.1987i	−0.624960	−	1.08246i	−0.988549	−	0.150902i	$-0.951782\pi$
$127$	−7.04294	−	12.1987i	−0.624960	−	1.08246i	0.363589	−	0.931559i	$-0.381551\pi$
$128$		0			0
$129$	−7.29940			−0.642677
$130$		0			0
$131$	5.52373			0.482610			0.241305	−	0.970449i	$-0.422425\pi$
$131$	5.52373			0.482610			0.241305	+	0.970449i	$0.422425\pi$
$132$		0			0
$133$	20.4638			1.77443
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	17.8550			1.52545			0.762727	−	0.646720i	$-0.223860\pi$
$137$	17.8550			1.52545			0.762727	+	0.646720i	$0.223860\pi$
$138$		0			0
$139$	−13.2254			−1.12177			−0.560883	−	0.827895i	$-0.689538\pi$
$139$	−13.2254			−1.12177			−0.560883	+	0.827895i	$0.689538\pi$
$140$		0			0
$141$	2.73280	+	4.73335i	0.230143	+	0.398620i
$142$		0			0
$143$	4.18023			0.349568
$144$		0			0
$145$	−2.87246	−	4.97524i	−0.238545	−	0.413172i
$146$		0			0
$147$	−7.82727	+	13.5572i	−0.645582	+	1.11818i
$148$		0			0
$149$	8.55580			0.700919			0.350459	−	0.936578i	$-0.386025\pi$
$149$	8.55580			0.700919			0.350459	+	0.936578i	$0.386025\pi$
$150$		0			0
$151$	−10.3253	+	17.8839i	−0.840258	+	1.45537i	0.0494190	+	0.998778i	$0.484263\pi$
$151$	−10.3253	+	17.8839i	−0.840258	+	1.45537i	−0.889677	+	0.456591i	$0.849070\pi$
$152$		0			0
$153$	−1.68241	+	2.91403i	−0.136015	+	0.235585i
$154$		0			0
$155$	−1.32025	−	2.28674i	−0.106045	−	0.183675i
$156$		0			0
$157$	−5.92713	+	10.2661i	−0.473036	+	0.819323i	−0.999524	−	0.0308600i	$-0.990175\pi$
$157$	−5.92713	+	10.2661i	−0.473036	+	0.819323i	0.526487	+	0.850183i	$0.323509\pi$
$158$		0			0
$159$	1.64050			0.130100
$160$		0			0
$161$	−7.02242			−0.553445
$162$		0			0
$163$	−6.41720	−	11.1149i	−0.502634	−	0.870587i	−0.999995	−	0.00304373i	$-0.999031\pi$
$163$	−6.41720	−	11.1149i	−0.502634	−	0.870587i	0.497362	−	0.867543i	$-0.334302\pi$
$164$		0			0
$165$	−2.09011	−	3.62018i	−0.162715	−	0.281831i
$166$		0			0
$167$	−1.50686	−	2.60995i	−0.116604	−	0.201964i	0.801816	−	0.597571i	$-0.203867\pi$
$167$	−1.50686	−	2.60995i	−0.116604	−	0.201964i	−0.918420	+	0.395607i	$0.870534\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$		0			0
$171$	2.14970	−	3.72339i	0.164392	−	0.284735i
$172$		0			0
$173$	−8.85464	+	15.3367i	−0.673206	+	1.16603i	0.303784	+	0.952741i	$0.401750\pi$
$173$	−8.85464	+	15.3367i	−0.673206	+	1.16603i	−0.976990	+	0.213286i	$0.931583\pi$
$174$		0			0
$175$	2.37984	+	4.12200i	0.179899	+	0.311594i
$176$		0			0
$177$	−8.85112			−0.665291
$178$		0			0
$179$	4.57826			0.342195			0.171097	−	0.985254i	$-0.445269\pi$
$179$	4.57826			0.342195			0.171097	+	0.985254i	$0.445269\pi$
$180$		0			0
$181$	−3.07453	−	5.32524i	−0.228528	−	0.395822i	0.728844	−	0.684680i	$-0.240058\pi$
$181$	−3.07453	−	5.32524i	−0.228528	−	0.395822i	−0.957372	+	0.288858i	$0.906725\pi$
$182$		0			0
$183$	3.86271	−	6.69041i	0.285540	−	0.494569i
$184$		0			0
$185$	−5.02524	+	8.70397i	−0.369463	+	0.639929i
$186$		0			0
$187$	−14.0657			−1.02859
$188$		0			0
$189$	2.37984	+	4.12200i	0.173108	+	0.299832i
$190$		0			0
$191$	−1.02453	+	1.77454i	−0.0741325	+	0.128401i	−0.900709	−	0.434424i	$-0.856952\pi$
$191$	−1.02453	+	1.77454i	−0.0741325	+	0.128401i	0.826576	+	0.562825i	$0.190285\pi$
$192$		0			0
$193$	23.4218			1.68594			0.842970	−	0.537961i	$-0.180805\pi$
$193$	23.4218			1.68594			0.842970	+	0.537961i	$0.180805\pi$
$194$		0			0
$195$	−0.500000	+	0.866025i	−0.0358057	+	0.0620174i
$196$		0			0
$197$	9.38680	+	16.2584i	0.668782	+	1.15836i	0.978245	+	0.207453i	$0.0665174\pi$
$197$	9.38680	+	16.2584i	0.668782	+	1.15836i	−0.309463	+	0.950912i	$0.600149\pi$
$198$		0			0
$199$	6.28243	−	10.8815i	0.445350	−	0.771369i	−0.552727	−	0.833363i	$-0.686413\pi$
$199$	6.28243	−	10.8815i	0.445350	−	0.771369i	0.998077	+	0.0619939i	$0.0197459\pi$
$200$		0			0
$201$	3.11483	−	7.56954i	0.219703	−	0.533914i
$202$		0			0
$203$	−13.6720	+	23.6806i	−0.959585	+	1.66205i
$204$		0			0
$205$	0.0825512	+	0.142983i	0.00576563	+	0.00998636i
$206$		0			0
$207$	−0.737700	+	1.27773i	−0.0512737	+	0.0888086i
$208$		0			0
$209$	17.9725			1.24318
$210$		0			0
$211$	−4.05487	+	7.02324i	−0.279149	+	0.483500i	−0.971173	−	0.238374i	$-0.923386\pi$
$211$	−4.05487	+	7.02324i	−0.279149	+	0.483500i	0.692025	+	0.721874i	$0.256719\pi$
$212$		0			0
$213$	6.87027	+	11.8997i	0.470743	+	0.815351i
$214$		0			0
$215$	7.29940			0.497815
$216$		0			0
$217$	−6.28397	+	10.8842i	−0.426584	+	0.738864i
$218$		0			0
$219$	−6.88057	+	11.9175i	−0.464946	+	0.805310i
$220$		0			0
$221$	1.68241	+	2.91403i	0.113171	+	0.196019i
$222$		0			0
$223$	1.57513			0.105478			0.0527391	−	0.998608i	$-0.483205\pi$
$223$	1.57513			0.105478			0.0527391	+	0.998608i	$0.483205\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	13.2481	+	22.9463i	0.879305	+	1.52300i	0.852105	+	0.523370i	$0.175326\pi$
$227$	13.2481	+	22.9463i	0.879305	+	1.52300i	0.0271993	+	0.999630i	$0.491341\pi$
$228$		0			0
$229$	12.1723	−	21.0830i	0.804368	−	1.39321i	−0.112349	−	0.993669i	$-0.535837\pi$
$229$	12.1723	−	21.0830i	0.804368	−	1.39321i	0.916717	−	0.399538i	$-0.130829\pi$
$230$		0			0
$231$	−9.94827	+	17.2309i	−0.654548	+	1.13371i
$232$		0			0
$233$	−3.45772	−	5.98895i	−0.226523	−	0.392349i	0.730252	−	0.683178i	$-0.239402\pi$
$233$	−3.45772	−	5.98895i	−0.226523	−	0.392349i	−0.956775	+	0.290828i	$0.906069\pi$
$234$		0			0
$235$	−2.73280	−	4.73335i	−0.178268	−	0.308770i
$236$		0			0
$237$	−2.08037	−	3.60330i	−0.135134	−	0.234059i
$238$		0			0
$239$	−4.25531	−	7.37041i	−0.275253	−	0.476752i	0.694946	−	0.719062i	$-0.255428\pi$
$239$	−4.25531	−	7.37041i	−0.275253	−	0.476752i	−0.970199	+	0.242310i	$0.922095\pi$
$240$		0			0
$241$	13.8854			0.894436			0.447218	−	0.894425i	$-0.352415\pi$
$241$	13.8854			0.894436			0.447218	+	0.894425i	$0.352415\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	7.82727	−	13.5572i	0.500066	−	0.866139i
$246$		0			0
$247$	−2.14970	−	3.72339i	−0.136782	−	0.236914i
$248$		0			0
$249$	7.24720	−	12.5525i	0.459272	−	0.795483i
$250$		0			0
$251$	1.00722	−	1.74456i	0.0635752	−	0.110115i	−0.832486	−	0.554046i	$-0.813083\pi$
$251$	1.00722	−	1.74456i	0.0635752	−	0.110115i	0.896061	+	0.443931i	$0.146416\pi$
$252$		0			0
$253$	−6.16750			−0.387748
$254$		0			0
$255$	1.68241	−	2.91403i	0.105357	−	0.182483i
$256$		0			0
$257$	7.98982	+	13.8388i	0.498391	+	0.863239i	0.999998	−	0.00185682i	$-0.000591045\pi$
$257$	7.98982	+	13.8388i	0.498391	+	0.863239i	−0.501607	+	0.865095i	$0.667258\pi$
$258$		0			0
$259$	47.8370			2.97245
$260$		0			0
$261$	2.87246	+	4.97524i	0.177801	+	0.307960i
$262$		0			0
$263$	22.5143			1.38829			0.694144	−	0.719836i	$-0.255783\pi$
$263$	22.5143			1.38829			0.694144	+	0.719836i	$0.255783\pi$
$264$		0			0
$265$	−1.64050			−0.100775
$266$		0			0
$267$	−9.17586			−0.561553
$268$		0			0
$269$	−22.8898			−1.39562			−0.697808	−	0.716285i	$-0.745841\pi$
$269$	−22.8898			−1.39562			−0.697808	+	0.716285i	$0.745841\pi$
$270$		0			0
$271$	16.4504			0.999293			0.499646	−	0.866229i	$-0.333463\pi$
$271$	16.4504			0.999293			0.499646	+	0.866229i	$0.333463\pi$
$272$		0			0
$273$	4.75968			0.288069
$274$		0			0
$275$	2.09011	+	3.62018i	0.126039	+	0.218305i
$276$		0			0
$277$	−14.2683			−0.857298			−0.428649	−	0.903471i	$-0.641010\pi$
$277$	−14.2683			−0.857298			−0.428649	+	0.903471i	$0.641010\pi$
$278$		0			0
$279$	1.32025	+	2.28674i	0.0790413	+	0.136904i
$280$		0			0
$281$	−5.96740	+	10.3358i	−0.355985	+	0.616584i	−0.987286	−	0.158954i	$-0.949188\pi$
$281$	−5.96740	+	10.3358i	−0.355985	+	0.616584i	0.631301	+	0.775538i	$0.282521\pi$
$282$		0			0
$283$	24.1591			1.43611			0.718055	−	0.695986i	$-0.245032\pi$
$283$	24.1591			1.43611			0.718055	+	0.695986i	$0.245032\pi$
$284$		0			0
$285$	−2.14970	+	3.72339i	−0.127337	+	0.220555i
$286$		0			0
$287$	0.392917	−	0.680553i	0.0231932	−	0.0401718i
$288$		0			0
$289$	2.83897	+	4.91724i	0.166998	+	0.289249i
$290$		0			0
$291$	−7.67804	+	13.2988i	−0.450095	+	0.779587i
$292$		0			0
$293$	−25.6256			−1.49706			−0.748530	−	0.663100i	$-0.769240\pi$
$293$	−25.6256			−1.49706			−0.748530	+	0.663100i	$0.769240\pi$
$294$		0			0
$295$	8.85112			0.515332
$296$		0			0
$297$	2.09011	+	3.62018i	0.121281	+	0.210064i
$298$		0			0
$299$	0.737700	+	1.27773i	0.0426623	+	0.0738932i
$300$		0			0
$301$	−17.3714	−	30.0882i	−1.00127	−	1.73425i
$302$		0			0
$303$	0.495102	+	0.857541i	0.0284428	+	0.0492644i
$304$		0			0
$305$	−3.86271	+	6.69041i	−0.221178	+	0.383092i
$306$		0			0
$307$	−3.79669	+	6.57606i	−0.216689	+	0.375316i	−0.953794	−	0.300463i	$-0.902859\pi$
$307$	−3.79669	+	6.57606i	−0.216689	+	0.375316i	0.737105	+	0.675778i	$0.236192\pi$
$308$		0			0
$309$	−8.62783	−	14.9438i	−0.490820	−	0.850126i
$310$		0			0
$311$	−30.1269			−1.70834			−0.854169	−	0.519995i	$-0.825934\pi$
$311$	−30.1269			−1.70834			−0.854169	+	0.519995i	$0.825934\pi$
$312$		0			0
$313$	9.75311			0.551279			0.275639	−	0.961261i	$-0.411110\pi$
$313$	9.75311			0.551279			0.275639	+	0.961261i	$0.411110\pi$
$314$		0			0
$315$	−2.37984	−	4.12200i	−0.134089	−	0.232248i
$316$		0			0
$317$	8.81690	−	15.2713i	0.495206	−	0.857722i	−0.504778	−	0.863249i	$-0.668426\pi$
$317$	8.81690	−	15.2713i	0.495206	−	0.857722i	0.999985	+	0.00552649i	$0.00175914\pi$
$318$		0			0
$319$	−12.0075	+	20.7977i	−0.672293	+	1.16445i
$320$		0			0
$321$	12.0259			0.671221
$322$		0			0
$323$	7.23337	+	12.5286i	0.402476	+	0.697108i
$324$		0			0
$325$	0.500000	−	0.866025i	0.0277350	−	0.0480384i
$326$		0			0
$327$	−17.3958			−0.961990
$328$		0			0
$329$	−13.0073	+	22.5292i	−0.717113	+	1.24208i
$330$		0			0
$331$	3.03476	+	5.25636i	0.166805	+	0.288915i	0.937295	−	0.348537i	$-0.113322\pi$
$331$	3.03476	+	5.25636i	0.166805	+	0.288915i	−0.770490	+	0.637453i	$0.779988\pi$
$332$		0			0
$333$	5.02524	−	8.70397i	0.275381	−	0.476975i
$334$		0			0
$335$	−3.11483	+	7.56954i	−0.170181	+	0.413568i
$336$		0			0
$337$	7.20173	−	12.4738i	0.392303	−	0.679489i	−0.600450	−	0.799662i	$-0.705012\pi$
$337$	7.20173	−	12.4738i	0.392303	−	0.679489i	0.992753	+	0.120174i	$0.0383451\pi$
$338$		0			0
$339$	2.32025	+	4.01879i	0.126019	+	0.218271i
$340$		0			0
$341$	−5.51895	+	9.55910i	−0.298868	+	0.517654i
$342$		0			0
$343$	−41.1928			−2.22420
$344$		0			0
$345$	0.737700	−	1.27773i	0.0397164	−	0.0687908i
$346$		0			0
$347$	−8.30032	−	14.3766i	−0.445584	−	0.771775i	0.552508	−	0.833507i	$-0.313671\pi$
$347$	−8.30032	−	14.3766i	−0.445584	−	0.771775i	−0.998093	+	0.0617326i	$0.980337\pi$
$348$		0			0
$349$	23.7268			1.27007			0.635034	−	0.772484i	$-0.280986\pi$
$349$	23.7268			1.27007			0.635034	+	0.772484i	$0.280986\pi$
$350$		0			0
$351$	0.500000	−	0.866025i	0.0266880	−	0.0462250i
$352$		0			0
$353$	17.7981	−	30.8272i	0.947296	−	1.64077i	0.196210	−	0.980562i	$-0.437137\pi$
$353$	17.7981	−	30.8272i	0.947296	−	1.64077i	0.751087	−	0.660203i	$-0.229530\pi$
$354$		0			0
$355$	−6.87027	−	11.8997i	−0.364636	−	0.631568i
$356$		0			0
$357$	−16.0155			−0.847630
$358$		0			0
$359$	−15.8601			−0.837063			−0.418532	−	0.908202i	$-0.637455\pi$
$359$	−15.8601			−0.837063			−0.418532	+	0.908202i	$0.637455\pi$
$360$		0			0
$361$	0.257564	+	0.446113i	0.0135560	+	0.0234797i
$362$		0			0
$363$	−3.23715	+	5.60691i	−0.169906	+	0.294287i
$364$		0			0
$365$	6.88057	−	11.9175i	0.360145	−	0.623790i
$366$		0			0
$367$	3.83216	+	6.63750i	0.200037	+	0.346475i	0.948540	−	0.316657i	$-0.102560\pi$
$367$	3.83216	+	6.63750i	0.200037	+	0.346475i	−0.748503	+	0.663131i	$0.769227\pi$
$368$		0			0
$369$	−0.0825512	−	0.142983i	−0.00429745	−	0.00744339i
$370$		0			0
$371$	3.90413	+	6.76215i	0.202692	+	0.351073i
$372$		0			0
$373$	−1.53394	−	2.65685i	−0.0794242	−	0.137567i	0.823577	−	0.567204i	$-0.191975\pi$
$373$	−1.53394	−	2.65685i	−0.0794242	−	0.137567i	−0.903002	+	0.429637i	$0.858641\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	5.74492			0.295878
$378$		0			0
$379$	−7.73354	+	13.3949i	−0.397245	+	0.688049i	−0.993385	−	0.114832i	$-0.963367\pi$
$379$	−7.73354	+	13.3949i	−0.397245	+	0.688049i	0.596140	+	0.802881i	$0.296701\pi$
$380$		0			0
$381$	−7.04294	−	12.1987i	−0.360821	−	0.624960i
$382$		0			0
$383$	11.0084	−	19.0671i	0.562502	−	0.974282i	−0.434775	−	0.900539i	$-0.643172\pi$
$383$	11.0084	−	19.0671i	0.562502	−	0.974282i	0.997277	−	0.0737432i	$-0.0234945\pi$
$384$		0			0
$385$	9.94827	−	17.2309i	0.507011	−	0.878168i
$386$		0			0
$387$	−7.29940			−0.371050
$388$		0			0
$389$	−0.582458	+	1.00885i	−0.0295318	+	0.0511506i	−0.880414	−	0.474207i	$-0.842735\pi$
$389$	−0.582458	+	1.00885i	−0.0295318	+	0.0511506i	0.850882	+	0.525357i	$0.176068\pi$
$390$		0			0
$391$	−2.48223	−	4.29935i	−0.125532	−	0.217427i
$392$		0			0
$393$	5.52373			0.278635
$394$		0			0
$395$	2.08037	+	3.60330i	0.104675	+	0.181302i
$396$		0			0
$397$	29.7246			1.49183			0.745916	−	0.666040i	$-0.232012\pi$
$397$	29.7246			1.49183			0.745916	+	0.666040i	$0.232012\pi$
$398$		0			0
$399$	20.4638			1.02447
$400$		0			0
$401$	24.7299			1.23495			0.617476	−	0.786590i	$-0.288155\pi$
$401$	24.7299			1.23495			0.617476	+	0.786590i	$0.288155\pi$
$402$		0			0
$403$	2.64050			0.131533
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	42.0133			2.08252
$408$		0			0
$409$	8.02136	+	13.8934i	0.396631	+	0.686985i	0.993308	−	0.115497i	$-0.0368460\pi$
$409$	8.02136	+	13.8934i	0.396631	+	0.686985i	−0.596677	+	0.802481i	$0.703513\pi$
$410$		0			0
$411$	17.8550			0.880721
$412$		0			0
$413$	−21.0642	−	36.4843i	−1.03650	−	1.79528i
$414$		0			0
$415$	−7.24720	+	12.5525i	−0.355751	+	0.616179i
$416$		0			0
$417$	−13.2254			−0.647652
$418$		0			0
$419$	−7.83738	+	13.5747i	−0.382881	+	0.663169i	−0.991473	−	0.130314i	$-0.958401\pi$
$419$	−7.83738	+	13.5747i	−0.382881	+	0.663169i	0.608592	+	0.793483i	$0.291735\pi$
$420$		0			0
$421$	5.19572	−	8.99925i	0.253224	−	0.438596i	−0.711188	−	0.703002i	$-0.751842\pi$
$421$	5.19572	−	8.99925i	0.253224	−	0.438596i	0.964412	+	0.264406i	$0.0851758\pi$
$422$		0			0
$423$	2.73280	+	4.73335i	0.132873	+	0.230143i
$424$		0			0
$425$	−1.68241	+	2.91403i	−0.0816090	+	0.141351i
$426$		0			0
$427$	36.7705			1.77945
$428$		0			0
$429$	4.18023			0.201823
$430$		0			0
$431$	−13.8276	−	23.9500i	−0.666050	−	1.15363i	−0.978999	−	0.203863i	$-0.934650\pi$
$431$	−13.8276	−	23.9500i	−0.666050	−	1.15363i	0.312949	−	0.949770i	$-0.398683\pi$
$432$		0			0
$433$	−18.7804	−	32.5286i	−0.902528	−	1.56322i	−0.824202	−	0.566296i	$-0.808376\pi$
$433$	−18.7804	−	32.5286i	−0.902528	−	1.56322i	−0.0783256	−	0.996928i	$-0.524957\pi$
$434$		0			0
$435$	−2.87246	−	4.97524i	−0.137724	−	0.238545i
$436$		0			0
$437$	3.17167	+	5.49349i	0.151721	+	0.262789i
$438$		0			0
$439$	−0.0704578	+	0.122037i	−0.00336277	+	0.00582449i	−0.867702	−	0.497085i	$-0.834404\pi$
$439$	−0.0704578	+	0.122037i	−0.00336277	+	0.00582449i	0.864339	+	0.502909i	$0.167737\pi$
$440$		0			0
$441$	−7.82727	+	13.5572i	−0.372727	+	0.645582i
$442$		0			0
$443$	10.6504	+	18.4471i	0.506016	+	0.876446i	0.999976	+	0.00696104i	$0.00221579\pi$
$443$	10.6504	+	18.4471i	0.506016	+	0.876446i	−0.493959	+	0.869485i	$0.664451\pi$
$444$		0			0
$445$	9.17586			0.434977
$446$		0			0
$447$	8.55580			0.404676
$448$		0			0
$449$	−13.1422	−	22.7629i	−0.620217	−	1.07425i	−0.989445	−	0.144908i	$-0.953711\pi$
$449$	−13.1422	−	22.7629i	−0.620217	−	1.07425i	0.369228	−	0.929339i	$-0.379622\pi$
$450$		0			0
$451$	0.345083	−	0.597701i	0.0162493	−	0.0281447i
$452$		0			0
$453$	−10.3253	+	17.8839i	−0.485123	+	0.840258i
$454$		0			0
$455$	−4.75968			−0.223137
$456$		0			0
$457$	−15.9722	−	27.6646i	−0.747146	−	1.29409i	−0.949185	−	0.314718i	$-0.898090\pi$
$457$	−15.9722	−	27.6646i	−0.747146	−	1.29409i	0.202039	−	0.979377i	$-0.435243\pi$
$458$		0			0
$459$	−1.68241	+	2.91403i	−0.0785283	+	0.136015i
$460$		0			0
$461$	−16.9942			−0.791497			−0.395749	−	0.918359i	$-0.629515\pi$
$461$	−16.9942			−0.791497			−0.395749	+	0.918359i	$0.629515\pi$
$462$		0			0
$463$	6.34997	−	10.9985i	0.295108	−	0.511143i	−0.679902	−	0.733303i	$-0.737978\pi$
$463$	6.34997	−	10.9985i	0.295108	−	0.511143i	0.975010	+	0.222161i	$0.0713109\pi$
$464$		0			0
$465$	−1.32025	−	2.28674i	−0.0612252	−	0.106045i
$466$		0			0
$467$	−11.1079	+	19.2395i	−0.514013	+	0.890297i	0.485854	+	0.874040i	$0.338509\pi$
$467$	−11.1079	+	19.2395i	−0.514013	+	0.890297i	−0.999868	+	0.0162576i	$0.994825\pi$
$468$		0			0
$469$	38.6144	−	5.17496i	1.78305	−	0.238957i
$470$		0			0
$471$	−5.92713	+	10.2661i	−0.273108	+	0.473036i
$472$		0			0
$473$	−15.2566	−	26.4252i	−0.701499	−	1.21503i
$474$		0			0
$475$	2.14970	−	3.72339i	0.0986351	−	0.170841i
$476$		0			0
$477$	1.64050			0.0751134
$478$		0			0
$479$	−2.32237	+	4.02246i	−0.106112	+	0.183791i	−0.914192	−	0.405282i	$-0.867173\pi$
$479$	−2.32237	+	4.02246i	−0.106112	+	0.183791i	0.808080	+	0.589072i	$0.200507\pi$
$480$		0			0
$481$	−5.02524	−	8.70397i	−0.229131	−	0.396867i
$482$		0			0
$483$	−7.02242			−0.319531
$484$		0			0
$485$	7.67804	−	13.2988i	0.348642	−	0.603866i
$486$		0			0
$487$	−3.12363	+	5.41028i	−0.141545	+	0.245163i	−0.928079	−	0.372384i	$-0.878540\pi$
$487$	−3.12363	+	5.41028i	−0.141545	+	0.245163i	0.786534	+	0.617547i	$0.211874\pi$
$488$		0			0
$489$	−6.41720	−	11.1149i	−0.290196	−	0.502634i
$490$		0			0
$491$	−31.5224			−1.42258			−0.711292	−	0.702897i	$-0.751890\pi$
$491$	−31.5224			−1.42258			−0.711292	+	0.702897i	$0.751890\pi$
$492$		0			0
$493$	−19.3307			−0.870609
$494$		0			0
$495$	−2.09011	−	3.62018i	−0.0939436	−	0.162715i
$496$		0			0
$497$	−32.7003	+	56.6386i	−1.46681	+	2.54059i
$498$		0			0
$499$	13.3739	−	23.1643i	0.598700	−	1.03698i	−0.394314	−	0.918976i	$-0.629018\pi$
$499$	13.3739	−	23.1643i	0.598700	−	1.03698i	0.993013	−	0.118002i	$-0.0376490\pi$
$500$		0			0
$501$	−1.50686	−	2.60995i	−0.0673213	−	0.116604i
$502$		0			0
$503$	−16.2605	−	28.1640i	−0.725021	−	1.25577i	−0.958965	−	0.283523i	$-0.908497\pi$
$503$	−16.2605	−	28.1640i	−0.725021	−	1.25577i	0.233945	−	0.972250i	$-0.424837\pi$
$504$		0			0
$505$	−0.495102	−	0.857541i	−0.0220317	−	0.0381601i
$506$		0			0
$507$	6.00000	+	10.3923i	0.266469	+	0.461538i
$508$		0			0
$509$	16.5835			0.735053			0.367526	−	0.930013i	$-0.380205\pi$
$509$	16.5835			0.735053			0.367526	+	0.930013i	$0.380205\pi$
$510$		0			0
$511$	−65.4986			−2.89749
$512$		0			0
$513$	2.14970	−	3.72339i	0.0949117	−	0.164392i
$514$		0			0
$515$	8.62783	+	14.9438i	0.380188	+	0.658505i
$516$		0			0
$517$	−11.4237	+	19.7865i	−0.502415	+	0.870208i
$518$		0			0
$519$	−8.85464	+	15.3367i	−0.388676	+	0.673206i
$520$		0			0
$521$	−21.5696			−0.944980			−0.472490	−	0.881336i	$-0.656645\pi$
$521$	−21.5696			−0.944980			−0.472490	+	0.881336i	$0.656645\pi$
$522$		0			0
$523$	9.42836	−	16.3304i	0.412273	−	0.714078i	−0.582865	−	0.812569i	$-0.698068\pi$
$523$	9.42836	−	16.3304i	0.412273	−	0.714078i	0.995138	+	0.0984910i	$0.0314016\pi$
$524$		0			0
$525$	2.37984	+	4.12200i	0.103865	+	0.179899i
$526$		0			0
$527$	−8.88483			−0.387029
$528$		0			0
$529$	10.4116	+	18.0334i	0.452678	+	0.784062i
$530$		0			0
$531$	−8.85112			−0.384106
$532$		0			0
$533$	−0.165102			−0.00715138
$534$		0			0
$535$	−12.0259			−0.519926
$536$		0			0
$537$	4.57826			0.197566
$538$		0			0
$539$	−65.4395			−2.81868
$540$		0			0
$541$	34.0366			1.46335			0.731675	−	0.681654i	$-0.238739\pi$
$541$	34.0366			1.46335			0.731675	+	0.681654i	$0.238739\pi$
$542$		0			0
$543$	−3.07453	−	5.32524i	−0.131941	−	0.228528i
$544$		0			0
$545$	17.3958			0.745155
$546$		0			0
$547$	−3.82050	−	6.61731i	−0.163353	−	0.282936i	0.772716	−	0.634752i	$-0.218898\pi$
$547$	−3.82050	−	6.61731i	−0.163353	−	0.282936i	−0.936069	+	0.351816i	$0.885564\pi$
$548$		0			0
$549$	3.86271	−	6.69041i	0.164856	−	0.285540i
$550$		0			0
$551$	24.6997			1.05224
$552$		0			0
$553$	9.90187	−	17.1505i	0.421070	−	0.729315i
$554$		0			0
$555$	−5.02524	+	8.70397i	−0.213310	+	0.369463i
$556$		0			0
$557$	−22.3554	−	38.7206i	−0.947227	−	1.64064i	−0.751230	−	0.660040i	$-0.770539\pi$
$557$	−22.3554	−	38.7206i	−0.947227	−	1.64064i	−0.195996	−	0.980605i	$-0.562794\pi$
$558$		0			0
$559$	−3.64970	+	6.32147i	−0.154366	+	0.267370i
$560$		0			0
$561$	−14.0657			−0.593856
$562$		0			0
$563$	16.5230			0.696359			0.348180	−	0.937428i	$-0.386800\pi$
$563$	16.5230			0.696359			0.348180	+	0.937428i	$0.386800\pi$
$564$		0			0
$565$	−2.32025	−	4.01879i	−0.0976137	−	0.169072i
$566$		0			0
$567$	2.37984	+	4.12200i	0.0999438	+	0.173108i
$568$		0			0
$569$	0.995243	+	1.72381i	0.0417228	+	0.0722659i	0.886133	−	0.463432i	$-0.153382\pi$
$569$	0.995243	+	1.72381i	0.0417228	+	0.0722659i	−0.844410	+	0.535698i	$0.820049\pi$
$570$		0			0
$571$	7.49896	+	12.9886i	0.313822	+	0.543555i	0.979186	−	0.202963i	$-0.0650573\pi$
$571$	7.49896	+	12.9886i	0.313822	+	0.543555i	−0.665365	+	0.746519i	$0.731724\pi$
$572$		0			0
$573$	−1.02453	+	1.77454i	−0.0428004	+	0.0741325i
$574$		0			0
$575$	−0.737700	+	1.27773i	−0.0307642	+	0.0532852i
$576$		0			0
$577$	−9.99157	−	17.3059i	−0.415954	−	0.720454i	0.579574	−	0.814920i	$-0.303219\pi$
$577$	−9.99157	−	17.3059i	−0.415954	−	0.720454i	−0.995528	+	0.0944658i	$0.969886\pi$
$578$		0			0
$579$	23.4218			0.973378
$580$		0			0
$581$	68.9886			2.86213
$582$		0			0
$583$	3.42883	+	5.93892i	0.142008	+	0.245965i
$584$		0			0
$585$	−0.500000	+	0.866025i	−0.0206725	+	0.0358057i
$586$		0			0
$587$	−0.973887	+	1.68682i	−0.0401966	+	0.0696226i	−0.885424	−	0.464785i	$-0.846132\pi$
$587$	−0.973887	+	1.68682i	−0.0401966	+	0.0696226i	0.845227	+	0.534407i	$0.179465\pi$
$588$		0			0
$589$	11.3526			0.467775
$590$		0			0
$591$	9.38680	+	16.2584i	0.386122	+	0.668782i
$592$		0			0
$593$	4.11496	−	7.12732i	0.168981	−	0.292684i	−0.769081	−	0.639152i	$-0.779286\pi$
$593$	4.11496	−	7.12732i	0.168981	−	0.292684i	0.938062	+	0.346468i	$0.112619\pi$
$594$		0			0
$595$	16.0155			0.656571
$596$		0			0
$597$	6.28243	−	10.8815i	0.257123	−	0.445350i
$598$		0			0
$599$	7.01255	+	12.1461i	0.286525	+	0.496276i	0.972978	−	0.230899i	$-0.0741666\pi$
$599$	7.01255	+	12.1461i	0.286525	+	0.496276i	−0.686453	+	0.727174i	$0.740833\pi$
$600$		0			0
$601$	0.0927989	−	0.160732i	0.00378534	−	0.00655641i	−0.864127	−	0.503275i	$-0.832128\pi$
$601$	0.0927989	−	0.160732i	0.00378534	−	0.00655641i	0.867912	+	0.496718i	$0.165462\pi$
$602$		0			0
$603$	3.11483	−	7.56954i	0.126846	−	0.308255i
$604$		0			0
$605$	3.23715	−	5.60691i	0.131609	−	0.227953i
$606$		0			0
$607$	−3.63638	−	6.29840i	−0.147596	−	0.255644i	0.782742	−	0.622346i	$-0.213820\pi$
$607$	−3.63638	−	6.29840i	−0.147596	−	0.255644i	−0.930339	+	0.366702i	$0.880487\pi$
$608$		0			0
$609$	−13.6720	+	23.6806i	−0.554017	+	0.959585i
$610$		0			0
$611$	5.46560			0.221115
$612$		0			0
$613$	6.58148	−	11.3995i	0.265824	−	0.460420i	−0.701955	−	0.712221i	$-0.747689\pi$
$613$	6.58148	−	11.3995i	0.265824	−	0.460420i	0.967779	+	0.251801i	$0.0810228\pi$
$614$		0			0
$615$	0.0825512	+	0.142983i	0.00332879	+	0.00576563i
$616$		0			0
$617$	13.7706			0.554382			0.277191	−	0.960815i	$-0.410596\pi$
$617$	13.7706			0.554382			0.277191	+	0.960815i	$0.410596\pi$
$618$		0			0
$619$	11.5226	−	19.9578i	0.463134	−	0.802172i	−0.535981	−	0.844230i	$-0.680058\pi$
$619$	11.5226	−	19.9578i	0.463134	−	0.802172i	0.999115	+	0.0420584i	$0.0133915\pi$
$620$		0			0
$621$	−0.737700	+	1.27773i	−0.0296029	+	0.0512737i
$622$		0			0
$623$	−21.8371	−	37.8229i	−0.874883	−	1.51534i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	17.9725			0.717752
$628$		0			0
$629$	16.9091	+	29.2873i	0.674208	+	1.16776i
$630$		0			0
$631$	−13.9125	+	24.0972i	−0.553849	+	0.959294i	0.444143	+	0.895956i	$0.353508\pi$
$631$	−13.9125	+	24.0972i	−0.553849	+	0.959294i	−0.997992	+	0.0633384i	$0.979825\pi$
$632$		0			0
$633$	−4.05487	+	7.02324i	−0.161167	+	0.279149i
$634$		0			0
$635$	7.04294	+	12.1987i	0.279490	+	0.484092i
$636$		0			0
$637$	7.82727	+	13.5572i	0.310128	+	0.537157i
$638$		0			0
$639$	6.87027	+	11.8997i	0.271784	+	0.470743i
$640$		0			0
$641$	−0.347927	−	0.602628i	−0.0137423	−	0.0238024i	0.859072	−	0.511854i	$-0.171041\pi$
$641$	−0.347927	−	0.602628i	−0.0137423	−	0.0238024i	−0.872815	+	0.488052i	$0.837708\pi$
$642$		0			0
$643$	−0.154256			−0.00608325			−0.00304163	−	0.999995i	$-0.500968\pi$
$643$	−0.154256			−0.00608325			−0.00304163	+	0.999995i	$0.500968\pi$
$644$		0			0
$645$	7.29940			0.287414
$646$		0			0
$647$	−20.2371	+	35.0517i	−0.795602	+	1.37802i	0.126854	+	0.991921i	$0.459512\pi$
$647$	−20.2371	+	35.0517i	−0.795602	+	1.37802i	−0.922456	+	0.386102i	$0.873821\pi$
$648$		0			0
$649$	−18.4998	−	32.0427i	−0.726182	−	1.25778i
$650$		0			0
$651$	−6.28397	+	10.8842i	−0.246288	+	0.426584i
$652$		0			0
$653$	9.68089	−	16.7678i	0.378842	−	0.656174i	−0.612052	−	0.790818i	$-0.709656\pi$
$653$	9.68089	−	16.7678i	0.378842	−	0.656174i	0.990894	+	0.134644i	$0.0429889\pi$
$654$		0			0
$655$	−5.52373			−0.215830
$656$		0			0
$657$	−6.88057	+	11.9175i	−0.268437	+	0.464946i
$658$		0			0
$659$	−5.54663	−	9.60704i	−0.216066	−	0.374237i	0.737536	−	0.675308i	$-0.235989\pi$
$659$	−5.54663	−	9.60704i	−0.216066	−	0.374237i	−0.953602	+	0.301071i	$0.902656\pi$
$660$		0			0
$661$	−11.0676			−0.430480			−0.215240	−	0.976561i	$-0.569053\pi$
$661$	−11.0676			−0.430480			−0.215240	+	0.976561i	$0.569053\pi$
$662$		0			0
$663$	1.68241	+	2.91403i	0.0653395	+	0.113171i
$664$		0			0
$665$	−20.4638			−0.793551
$666$		0			0
$667$	−8.47605			−0.328194
$668$		0			0
$669$	1.57513			0.0608979
$670$		0			0
$671$	32.2940			1.24670
$672$		0			0
$673$	9.29659			0.358357			0.179179	−	0.983817i	$-0.442656\pi$
$673$	9.29659			0.358357			0.179179	+	0.983817i	$0.442656\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$		0			0
$677$	−14.4619	−	25.0487i	−0.555815	−	0.962699i	−0.997840	−	0.0656964i	$-0.979073\pi$
$677$	−14.4619	−	25.0487i	−0.555815	−	0.962699i	0.442025	−	0.897003i	$-0.354260\pi$
$678$		0			0
$679$	−73.0900			−2.80494
$680$		0			0
$681$	13.2481	+	22.9463i	0.507667	+	0.879305i
$682$		0			0
$683$	−13.6605	+	23.6606i	−0.522704	+	0.905349i	0.476947	+	0.878932i	$0.341743\pi$
$683$	−13.6605	+	23.6606i	−0.522704	+	0.905349i	−0.999651	+	0.0264173i	$0.991590\pi$
$684$		0			0
$685$	−17.8550			−0.682204
$686$		0			0
$687$	12.1723	−	21.0830i	0.464402	−	0.804368i
$688$		0			0
$689$	0.820251	−	1.42072i	0.0312491	−	0.0541250i
$690$		0			0
$691$	4.33577	+	7.50978i	0.164941	+	0.285686i	0.936634	−	0.350309i	$-0.113923\pi$
$691$	4.33577	+	7.50978i	0.164941	+	0.285686i	−0.771694	+	0.635995i	$0.780590\pi$
$692$		0			0
$693$	−9.94827	+	17.2309i	−0.377903	+	0.654548i
$694$		0			0
$695$	13.2254			0.501669
$696$		0			0
$697$	0.555541			0.0210426
$698$		0			0
$699$	−3.45772	−	5.98895i	−0.130783	−	0.226523i
$700$		0			0
$701$	−1.91040	−	3.30891i	−0.0721548	−	0.124976i	0.827691	−	0.561185i	$-0.189654\pi$
$701$	−1.91040	−	3.30891i	−0.0721548	−	0.124976i	−0.899845	+	0.436209i	$0.856321\pi$
$702$		0			0
$703$	−21.6055	−	37.4219i	−0.814868	−	1.41139i
$704$		0			0
$705$	−2.73280	−	4.73335i	−0.102923	−	0.178268i
$706$		0			0
$707$	−2.35652	+	4.08162i	−0.0886262	+	0.153505i
$708$		0			0
$709$	10.3083	−	17.8545i	0.387136	−	0.670539i	−0.604927	−	0.796281i	$-0.706798\pi$
$709$	10.3083	−	17.8545i	0.387136	−	0.670539i	0.992063	+	0.125742i	$0.0401310\pi$
$710$		0			0
$711$	−2.08037	−	3.60330i	−0.0780198	−	0.135134i
$712$		0			0
$713$	−3.89579			−0.145899
$714$		0			0
$715$	−4.18023			−0.156332
$716$		0			0
$717$	−4.25531	−	7.37041i	−0.158917	−	0.275253i
$718$		0			0
$719$	−4.49936	+	7.79312i	−0.167798	+	0.290634i	−0.937645	−	0.347593i	$-0.886999\pi$
$719$	−4.49936	+	7.79312i	−0.167798	+	0.290634i	0.769847	+	0.638228i	$0.220332\pi$
$720$		0			0
$721$	41.0657	−	71.1279i	1.52937	−	2.64894i
$722$		0			0
$723$	13.8854			0.516403
$724$		0			0
$725$	2.87246	+	4.97524i	0.106680	+	0.184776i
$726$		0			0
$727$	−6.74353	+	11.6801i	−0.250104	+	0.433193i	−0.963554	−	0.267513i	$-0.913798\pi$
$727$	−6.74353	+	11.6801i	−0.250104	+	0.433193i	0.713450	+	0.700706i	$0.247131\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	12.2806	−	21.2706i	0.454215	−	0.786723i
$732$		0			0
$733$	21.5363	+	37.3019i	0.795461	+	1.37778i	0.922546	+	0.385887i	$0.126104\pi$
$733$	21.5363	+	37.3019i	0.795461	+	1.37778i	−0.127085	+	0.991892i	$0.540562\pi$
$734$		0			0
$735$	7.82727	−	13.5572i	0.288713	−	0.500066i
$736$		0			0
$737$	33.9134	−	4.54495i	1.24922	−	0.167415i
$738$		0			0
$739$	3.41568	−	5.91613i	0.125648	−	0.217628i	−0.796338	−	0.604852i	$-0.793232\pi$
$739$	3.41568	−	5.91613i	0.125648	−	0.217628i	0.921986	+	0.387223i	$0.126566\pi$
$740$		0			0
$741$	−2.14970	−	3.72339i	−0.0789713	−	0.136782i
$742$		0			0
$743$	20.1047	−	34.8223i	0.737570	−	1.27751i	−0.216017	−	0.976390i	$-0.569307\pi$
$743$	20.1047	−	34.8223i	0.737570	−	1.27751i	0.953587	−	0.301118i	$-0.0973599\pi$
$744$		0			0
$745$	−8.55580			−0.313460
$746$		0			0
$747$	7.24720	−	12.5525i	0.265161	−	0.459272i
$748$		0			0
$749$	28.6198	+	49.5709i	1.04574	+	1.81128i
$750$		0			0
$751$	−35.0195			−1.27788			−0.638941	−	0.769256i	$-0.720627\pi$
$751$	−35.0195			−1.27788			−0.638941	+	0.769256i	$0.720627\pi$
$752$		0			0
$753$	1.00722	−	1.74456i	0.0367052	−	0.0635752i
$754$		0			0
$755$	10.3253	−	17.8839i	0.375775	−	0.650861i
$756$		0			0
$757$	6.47460	+	11.2143i	0.235323	+	0.407592i	0.959367	−	0.282163i	$-0.0910518\pi$
$757$	6.47460	+	11.2143i	0.235323	+	0.407592i	−0.724043	+	0.689755i	$0.757718\pi$
$758$		0			0
$759$	−6.16750			−0.223866
$760$		0			0
$761$	−24.0939			−0.873403			−0.436701	−	0.899607i	$-0.643853\pi$
$761$	−24.0939			−0.873403			−0.436701	+	0.899607i	$0.643853\pi$
$762$		0			0
$763$	−41.3992	−	71.7055i	−1.49875	−	2.59592i
$764$		0			0
$765$	1.68241	−	2.91403i	0.0608278	−	0.105357i
$766$		0			0
$767$	−4.42556	+	7.66529i	−0.159798	+	0.276778i
$768$		0			0
$769$	15.5293	+	26.8975i	0.560000	+	0.969948i	0.997496	+	0.0707275i	$0.0225321\pi$
$769$	15.5293	+	26.8975i	0.560000	+	0.969948i	−0.437496	+	0.899220i	$0.644135\pi$
$770$		0			0
$771$	7.98982	+	13.8388i	0.287746	+	0.498391i
$772$		0			0
$773$	−27.3293	−	47.3358i	−0.982968	−	1.70255i	−0.650641	−	0.759386i	$-0.725500\pi$
$773$	−27.3293	−	47.3358i	−0.982968	−	1.70255i	−0.332327	−	0.943164i	$-0.607834\pi$
$774$		0			0
$775$	1.32025	+	2.28674i	0.0474248	+	0.0821422i
$776$		0			0
$777$	47.8370			1.71614
$778$		0			0
$779$	−0.709842			−0.0254327
$780$		0			0
$781$	−28.7193	+	49.7433i	−1.02766	+	1.77996i
$782$		0			0
$783$	2.87246	+	4.97524i	0.102653	+	0.177801i
$784$		0			0
$785$	5.92713	−	10.2661i	0.211548	−	0.366412i
$786$		0			0
$787$	3.62025	−	6.27046i	0.129048	−	0.223518i	−0.794260	−	0.607578i	$-0.792141\pi$
$787$	3.62025	−	6.27046i	0.129048	−	0.223518i	0.923308	+	0.384060i	$0.125475\pi$
$788$		0			0
$789$	22.5143			0.801529
$790$		0			0
$791$	−11.0436	+	19.1282i	−0.392667	+	0.680119i
$792$		0			0
$793$	−3.86271	−	6.69041i	−0.137169	−	0.237583i
$794$		0			0
$795$	−1.64050			−0.0581826
$796$		0			0
$797$	13.8520	+	23.9924i	0.490663	+	0.849853i	0.999942	−	0.0107482i	$-0.00342132\pi$
$797$	13.8520	+	23.9924i	0.490663	+	0.849853i	−0.509279	+	0.860601i	$0.670088\pi$
$798$		0			0
$799$	−18.3908			−0.650620
$800$		0			0
$801$	−9.17586			−0.324213
$802$		0			0
$803$	−57.5247			−2.03000
$804$		0			0
$805$	7.02242			0.247508
$806$		0			0
$807$	−22.8898			−0.805759
$808$		0			0
$809$	41.0156			1.44203			0.721016	−	0.692918i	$-0.243675\pi$
$809$	41.0156			1.44203			0.721016	+	0.692918i	$0.243675\pi$
$810$		0			0
$811$	9.72130	+	16.8378i	0.341361	+	0.591255i	0.984686	−	0.174339i	$-0.0557788\pi$
$811$	9.72130	+	16.8378i	0.341361	+	0.591255i	−0.643325	+	0.765593i	$0.722445\pi$
$812$		0			0
$813$	16.4504			0.576942
$814$		0			0
$815$	6.41720	+	11.1149i	0.224785	+	0.389338i
$816$		0			0
$817$	−15.6915	+	27.1785i	−0.548978	+	0.950857i
$818$		0			0
$819$	4.75968			0.166317
$820$		0			0
$821$	5.17982	−	8.97171i	0.180777	−	0.313115i	−0.761368	−	0.648320i	$-0.775472\pi$
$821$	5.17982	−	8.97171i	0.180777	−	0.313115i	0.942145	+	0.335205i	$0.108805\pi$
$822$		0			0
$823$	0.398838	−	0.690808i	0.0139026	−	0.0240801i	−0.858990	−	0.511992i	$-0.828908\pi$
$823$	0.398838	−	0.690808i	0.0139026	−	0.0240801i	0.872893	+	0.487912i	$0.162241\pi$
$824$		0			0
$825$	2.09011	+	3.62018i	0.0727684	+	0.126039i
$826$		0			0
$827$	1.77393	−	3.07254i	0.0616856	−	0.106843i	−0.833533	−	0.552469i	$-0.813686\pi$
$827$	1.77393	−	3.07254i	0.0616856	−	0.106843i	0.895219	+	0.445626i	$0.147019\pi$
$828$		0			0
$829$	11.5893			0.402511			0.201256	−	0.979539i	$-0.435498\pi$
$829$	11.5893			0.402511			0.201256	+	0.979539i	$0.435498\pi$
$830$		0			0
$831$	−14.2683			−0.494961
$832$		0			0
$833$	−26.3374	−	45.6177i	−0.912537	−	1.58056i
$834$		0			0
$835$	1.50686	+	2.60995i	0.0521469	+	0.0903210i
$836$		0			0
$837$	1.32025	+	2.28674i	0.0456345	+	0.0790413i
$838$		0			0
$839$	13.3569	+	23.1349i	0.461133	+	0.798705i	0.999018	−	0.0443129i	$-0.0141098\pi$
$839$	13.3569	+	23.1349i	0.461133	+	0.798705i	−0.537885	+	0.843018i	$0.680777\pi$
$840$		0			0
$841$	−2.00204	+	3.46763i	−0.0690359	+	0.119574i
$842$		0			0
$843$	−5.96740	+	10.3358i	−0.205528	+	0.355985i
$844$		0			0
$845$	−6.00000	−	10.3923i	−0.206406	−	0.357506i
$846$		0			0
$847$	−30.8156			−1.05884
$848$		0			0
$849$	24.1591			0.829139
$850$		0			0
$851$	7.41423	+	12.8418i	0.254157	+	0.440212i
$852$		0			0
$853$	−7.26560	+	12.5844i	−0.248769	+	0.430881i	−0.963185	−	0.268841i	$-0.913359\pi$
$853$	−7.26560	+	12.5844i	−0.248769	+	0.430881i	0.714415	+	0.699722i	$0.246693\pi$
$854$		0			0
$855$	−2.14970	+	3.72339i	−0.0735183	+	0.127337i
$856$		0			0
$857$	−15.3070			−0.522878			−0.261439	−	0.965220i	$-0.584197\pi$
$857$	−15.3070			−0.522878			−0.261439	+	0.965220i	$0.584197\pi$
$858$		0			0
$859$	−12.0840	−	20.9302i	−0.412302	−	0.714128i	0.582839	−	0.812587i	$-0.301942\pi$
$859$	−12.0840	−	20.9302i	−0.412302	−	0.714128i	−0.995141	+	0.0984599i	$0.968608\pi$
$860$		0			0
$861$	0.392917	−	0.680553i	0.0133906	−	0.0231932i
$862$		0			0
$863$	−4.49398			−0.152977			−0.0764884	−	0.997070i	$-0.524371\pi$
$863$	−4.49398			−0.152977			−0.0764884	+	0.997070i	$0.524371\pi$
$864$		0			0
$865$	8.85464	−	15.3367i	0.301067	−	0.521463i
$866$		0			0
$867$	2.83897	+	4.91724i	0.0964165	+	0.166998i
$868$		0			0
$869$	8.69640	−	15.0626i	0.295005	−	0.510964i
$870$		0			0
$871$	−4.99800	−	6.48229i	−0.169351	−	0.219644i
$872$		0			0
$873$	−7.67804	+	13.2988i	−0.259862	+	0.450095i
$874$		0			0
$875$	−2.37984	−	4.12200i	−0.0804532	−	0.139349i
$876$		0			0
$877$	21.1460	−	36.6259i	0.714049	−	1.23677i	−0.249276	−	0.968433i	$-0.580193\pi$
$877$	21.1460	−	36.6259i	0.714049	−	1.23677i	0.963325	−	0.268337i	$-0.0864741\pi$
$878$		0			0
$879$	−25.6256			−0.864329
$880$		0			0
$881$	−14.2266	+	24.6413i	−0.479308	+	0.830185i	−0.999718	−	0.0237308i	$-0.992446\pi$
$881$	−14.2266	+	24.6413i	−0.479308	+	0.830185i	0.520411	+	0.853916i	$0.325779\pi$
$882$		0			0
$883$	6.07395	+	10.5204i	0.204405	+	0.354040i	0.949943	−	0.312423i	$-0.101141\pi$
$883$	6.07395	+	10.5204i	0.204405	+	0.354040i	−0.745538	+	0.666463i	$0.767807\pi$
$884$		0			0
$885$	8.85112			0.297527
$886$		0			0
$887$	18.3334	−	31.7543i	0.615574	−	1.06621i	−0.374709	−	0.927142i	$-0.622257\pi$
$887$	18.3334	−	31.7543i	0.615574	−	1.06621i	0.990283	−	0.139064i	$-0.0444092\pi$
$888$		0			0
$889$	33.5221	−	58.0620i	1.12430	−	1.94734i
$890$		0			0
$891$	2.09011	+	3.62018i	0.0700214	+	0.121281i
$892$		0			0
$893$	23.4988			0.786358
$894$		0			0
$895$	−4.57826			−0.153034
$896$		0			0
$897$	0.737700	+	1.27773i	0.0246311	+	0.0426623i
$898$		0			0
$899$	−7.58473	+	13.1371i	−0.252965	+	0.438148i
$900$		0			0
$901$	−2.76000	+	4.78046i	−0.0919490	+	0.159260i
$902$		0			0
$903$	−17.3714	−	30.0882i	−0.578084	−	1.00127i
$904$		0			0
$905$	3.07453	+	5.32524i	0.102201	+	0.177017i
$906$		0			0
$907$	−23.0942	−	40.0003i	−0.766830	−	1.32819i	−0.939274	−	0.343169i	$-0.888500\pi$
$907$	−23.0942	−	40.0003i	−0.766830	−	1.32819i	0.172444	−	0.985019i	$-0.444834\pi$
$908$		0			0
$909$	0.495102	+	0.857541i	0.0164215	+	0.0284428i
$910$		0			0
$911$	0.0532440			0.00176405			0.000882026	−	1.00000i	$-0.499719\pi$
$911$	0.0532440			0.00176405			0.000882026		1.00000i	$0.499719\pi$
$912$		0			0
$913$	60.5899			2.00523
$914$		0			0
$915$	−3.86271	+	6.69041i	−0.127697	+	0.221178i
$916$		0			0
$917$	13.1456	+	22.7688i	0.434105	+	0.751892i
$918$		0			0
$919$	22.1909	−	38.4358i	0.732011	−	1.26788i	−0.224012	−	0.974586i	$-0.571915\pi$
$919$	22.1909	−	38.4358i	0.732011	−	1.26788i	0.956023	−	0.293293i	$-0.0947512\pi$
$920$		0			0
$921$	−3.79669	+	6.57606i	−0.125105	+	0.216689i
$922$		0			0
$923$	13.7405			0.452276
$924$		0			0
$925$	5.02524	−	8.70397i	0.165229	−	0.286185i
$926$		0			0
$927$	−8.62783	−	14.9438i	−0.283375	−	0.490820i
$928$		0			0
$929$	9.01781			0.295865			0.147932	−	0.988997i	$-0.452738\pi$
$929$	9.01781			0.295865			0.147932	+	0.988997i	$0.452738\pi$
$930$		0			0
$931$	33.6526	+	58.2880i	1.10292	+	1.91031i
$932$		0			0
$933$	−30.1269			−0.986310
$934$		0			0
$935$	14.0657			0.459999
$936$		0			0
$937$	36.5780			1.19495			0.597476	−	0.801887i	$-0.296170\pi$
$937$	36.5780			1.19495			0.597476	+	0.801887i	$0.296170\pi$
$938$		0			0
$939$	9.75311			0.318281
$940$		0			0
$941$	−0.383115			−0.0124892			−0.00624460	−	0.999981i	$-0.501988\pi$
$941$	−0.383115			−0.0124892			−0.00624460	+	0.999981i	$0.501988\pi$
$942$		0			0
$943$	0.243592			0.00793245
$944$		0			0
$945$	−2.37984	−	4.12200i	−0.0774162	−	0.134089i
$946$		0			0
$947$	51.5386			1.67478			0.837389	−	0.546607i	$-0.184081\pi$
$947$	51.5386			1.67478			0.837389	+	0.546607i	$0.184081\pi$
$948$		0			0
$949$	6.88057	+	11.9175i	0.223353	+	0.386858i
$950$		0			0
$951$	8.81690	−	15.2713i	0.285907	−	0.495206i
$952$		0			0
$953$	37.9346			1.22882			0.614411	−	0.788986i	$-0.289394\pi$
$953$	37.9346			1.22882			0.614411	+	0.788986i	$0.289394\pi$
$954$		0			0
$955$	1.02453	−	1.77454i	0.0331531	−	0.0574228i
$956$		0			0
$957$	−12.0075	+	20.7977i	−0.388148	+	0.672293i
$958$		0			0
$959$	42.4920	+	73.5983i	1.37214	+	2.37661i
$960$		0			0
$961$	12.0139	−	20.8086i	0.387544	−	0.671247i
$962$		0			0
$963$	12.0259			0.387530
$964$		0			0
$965$	−23.4218			−0.753975
$966$		0			0
$967$	−24.0439	−	41.6452i	−0.773199	−	1.33922i	−0.935801	−	0.352528i	$-0.885322\pi$
$967$	−24.0439	−	41.6452i	−0.773199	−	1.33922i	0.162603	−	0.986692i	$-0.448011\pi$
$968$		0			0
$969$	7.23337	+	12.5286i	0.232369	+	0.402476i
$970$		0			0
$971$	−0.670821	−	1.16190i	−0.0215277	−	0.0372870i	0.855061	−	0.518528i	$-0.173520\pi$
$971$	−0.670821	−	1.16190i	−0.0215277	−	0.0372870i	−0.876589	+	0.481241i	$0.840186\pi$
$972$		0			0
$973$	−31.4744	−	54.5152i	−1.00902	−	1.74768i
$974$		0			0
$975$	0.500000	−	0.866025i	0.0160128	−	0.0277350i
$976$		0			0
$977$	−22.2826	+	38.5946i	−0.712883	+	1.23475i	0.250887	+	0.968016i	$0.419278\pi$
$977$	−22.2826	+	38.5946i	−0.712883	+	1.23475i	−0.963770	+	0.266734i	$0.914056\pi$
$978$		0			0
$979$	−19.1786	−	33.2183i	−0.612950	−	1.06166i
$980$		0			0
$981$	−17.3958			−0.555405
$982$		0			0
$983$	−40.0240			−1.27657			−0.638284	−	0.769801i	$-0.720356\pi$
$983$	−40.0240			−1.27657			−0.638284	+	0.769801i	$0.720356\pi$
$984$		0			0
$985$	−9.38680	−	16.2584i	−0.299088	−	0.518036i
$986$		0			0
$987$	−13.0073	+	22.5292i	−0.414025	+	0.717113i
$988$		0			0
$989$	5.38477	−	9.32669i	0.171226	−	0.296571i
$990$		0			0
$991$	−8.09980			−0.257299			−0.128649	−	0.991690i	$-0.541064\pi$
$991$	−8.09980			−0.257299			−0.128649	+	0.991690i	$0.541064\pi$
$992$		0			0
$993$	3.03476	+	5.25636i	0.0963051	+	0.166805i
$994$		0			0
$995$	−6.28243	+	10.8815i	−0.199167	+	0.344967i
$996$		0			0
$997$	37.3062			1.18150			0.590750	−	0.806855i	$-0.298832\pi$
$997$	37.3062			1.18150			0.590750	+	0.806855i	$0.298832\pi$
$998$		0			0
$999$	5.02524	−	8.70397i	0.158992	−	0.275381i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.j.3781.6	yes	12
67.37	even	3	inner	4020.2.q.j.841.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.j.841.6	✓	12	67.37	even	3	inner
4020.2.q.j.3781.6	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4020.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} -1.00000 q^{5} +(2.37984 + 4.12200i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} -1.00000 q^{5} +(2.37984 + 4.12200i) q^{7} +1.00000 q^{9} +(2.09011 + 3.62018i) q^{11} +(0.500000 - 0.866025i) q^{13} -1.00000 q^{15} +(-1.68241 + 2.91403i) q^{17} +(2.14970 - 3.72339i) q^{19} +(2.37984 + 4.12200i) q^{21} +(-0.737700 + 1.27773i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(2.87246 + 4.97524i) q^{29} +(1.32025 + 2.28674i) q^{31} +(2.09011 + 3.62018i) q^{33} +(-2.37984 - 4.12200i) q^{35} +(5.02524 - 8.70397i) q^{37} +(0.500000 - 0.866025i) q^{39} +(-0.0825512 - 0.142983i) q^{41} -7.29940 q^{43} -1.00000 q^{45} +(2.73280 + 4.73335i) q^{47} +(-7.82727 + 13.5572i) q^{49} +(-1.68241 + 2.91403i) q^{51} +1.64050 q^{53} +(-2.09011 - 3.62018i) q^{55} +(2.14970 - 3.72339i) q^{57} -8.85112 q^{59} +(3.86271 - 6.69041i) q^{61} +(2.37984 + 4.12200i) q^{63} +(-0.500000 + 0.866025i) q^{65} +(3.11483 - 7.56954i) q^{67} +(-0.737700 + 1.27773i) q^{69} +(6.87027 + 11.8997i) q^{71} +(-6.88057 + 11.9175i) q^{73} +1.00000 q^{75} +(-9.94827 + 17.2309i) q^{77} +(-2.08037 - 3.60330i) q^{79} +1.00000 q^{81} +(7.24720 - 12.5525i) q^{83} +(1.68241 - 2.91403i) q^{85} +(2.87246 + 4.97524i) q^{87} -9.17586 q^{89} +4.75968 q^{91} +(1.32025 + 2.28674i) q^{93} +(-2.14970 + 3.72339i) q^{95} +(-7.67804 + 13.2988i) q^{97} +(2.09011 + 3.62018i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{3} - 12 q^{5} + 2 q^{7} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^3 - 12 * q^5 + 2 * q^7 + 12 * q^9	\( 12 q + 12 q^{3} - 12 q^{5} + 2 q^{7} + 12 q^{9} - 5 q^{11} + 6 q^{13} - 12 q^{15} + 9 q^{17} - 11 q^{19} + 2 q^{21} + 19 q^{23} + 12 q^{25} + 12 q^{27} + 8 q^{29} - 4 q^{31} - 5 q^{33} - 2 q^{35} + 5 q^{37} + 6 q^{39} - 9 q^{41} - 14 q^{43} - 12 q^{45} - 6 q^{47} - 46 q^{49} + 9 q^{51} - 20 q^{53} + 5 q^{55} - 11 q^{57} + 6 q^{59} + 27 q^{61} + 2 q^{63} - 6 q^{65} + 3 q^{67} + 19 q^{69} + 25 q^{71} - 8 q^{73} + 12 q^{75} + 10 q^{77} - 2 q^{79} + 12 q^{81} + 20 q^{83} - 9 q^{85} + 8 q^{87} + 12 q^{89} + 4 q^{91} - 4 q^{93} + 11 q^{95} - q^{97} - 5 q^{99}+O(q^{100}) \) 12 * q + 12 * q^3 - 12 * q^5 + 2 * q^7 + 12 * q^9 - 5 * q^11 + 6 * q^13 - 12 * q^15 + 9 * q^17 - 11 * q^19 + 2 * q^21 + 19 * q^23 + 12 * q^25 + 12 * q^27 + 8 * q^29 - 4 * q^31 - 5 * q^33 - 2 * q^35 + 5 * q^37 + 6 * q^39 - 9 * q^41 - 14 * q^43 - 12 * q^45 - 6 * q^47 - 46 * q^49 + 9 * q^51 - 20 * q^53 + 5 * q^55 - 11 * q^57 + 6 * q^59 + 27 * q^61 + 2 * q^63 - 6 * q^65 + 3 * q^67 + 19 * q^69 + 25 * q^71 - 8 * q^73 + 12 * q^75 + 10 * q^77 - 2 * q^79 + 12 * q^81 + 20 * q^83 - 9 * q^85 + 8 * q^87 + 12 * q^89 + 4 * q^91 - 4 * q^93 + 11 * q^95 - q^97 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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