LMFDB - Embedded newform 1520.2.q.o.881.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1520,2,Mod(881,1520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1520, 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("1520.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1520 = 2^{4} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1520.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.1372611072$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.4601315889.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 $ x^8 - x^7 + 6x^6 - 3x^5 + 26x^4 - 14x^3 + 31x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			881.1
Root			$1.07988 + 1.87040i$ of defining polynomial
Character	$\chi$	$=$	1520.881
Dual form			1520.2.q.o.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.579878 - 1.00438i) q^{3} +(-0.500000 - 0.866025i) q^{5} +2.43525 q^{7} +(0.827483 - 1.43324i) q^{9} +O(q^{10})$	\(q+(-0.579878 - 1.00438i) q^{3} +(-0.500000 - 0.866025i) q^{5} +2.43525 q^{7} +(0.827483 - 1.43324i) q^{9} +5.75477 q^{11} +(0.797505 - 1.38132i) q^{13} +(-0.579878 + 1.00438i) q^{15} +(2.99203 + 5.18234i) q^{17} +(-0.149412 + 4.35634i) q^{19} +(-1.41215 - 2.44592i) q^{21} +(-0.470022 + 0.814102i) q^{23} +(-0.500000 + 0.866025i) q^{25} -5.39862 q^{27} +(-1.30917 + 2.26755i) q^{29} +5.26913 q^{31} +(-3.33706 - 5.77996i) q^{33} +(-1.21763 - 2.10899i) q^{35} -2.89384 q^{37} -1.84982 q^{39} +(3.15767 + 5.46925i) q^{41} +(2.26961 + 3.93108i) q^{43} -1.65497 q^{45} +(4.47718 - 7.75471i) q^{47} -1.06953 q^{49} +(3.47002 - 6.01025i) q^{51} +(1.09819 - 1.90213i) q^{53} +(-2.87738 - 4.98377i) q^{55} +(4.46205 - 2.37608i) q^{57} +(-5.39939 - 9.35202i) q^{59} +(5.26434 - 9.11811i) q^{61} +(2.01513 - 3.49031i) q^{63} -1.59501 q^{65} +(0.504789 - 0.874320i) q^{67} +1.09022 q^{69} +(4.41694 + 7.65036i) q^{71} +(5.12499 + 8.87674i) q^{73} +1.15976 q^{75} +14.0143 q^{77} +(3.80229 + 6.58577i) q^{79} +(0.648093 + 1.12253i) q^{81} -3.11355 q^{83} +(2.99203 - 5.18234i) q^{85} +3.03663 q^{87} +(5.55706 - 9.62511i) q^{89} +(1.94213 - 3.36387i) q^{91} +(-3.05545 - 5.29220i) q^{93} +(3.84741 - 2.04877i) q^{95} +(-2.02888 - 3.51412i) q^{97} +(4.76197 - 8.24798i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{3} - 4 q^{5} + 8 q^{7} - q^{9}+O(q^{10}) $ 8 * q + 3 * q^3 - 4 * q^5 + 8 * q^7 - q^9	$ 8 q + 3 q^{3} - 4 q^{5} + 8 q^{7} - q^{9} + 4 q^{11} - 7 q^{13} + 3 q^{15} + q^{17} - 5 q^{19} + 4 q^{21} + 2 q^{23} - 4 q^{25} - 24 q^{27} + q^{29} - 19 q^{33} - 4 q^{35} - 4 q^{37} - 30 q^{39} + 8 q^{41} + q^{43} + 2 q^{45} - 12 q^{47} - 20 q^{49} + 22 q^{51} + 5 q^{53} - 2 q^{55} + 7 q^{57} - 5 q^{59} - 3 q^{63} + 14 q^{65} + 4 q^{67} - 18 q^{69} + 20 q^{71} + 20 q^{73} - 6 q^{75} + 28 q^{77} + 17 q^{79} - 12 q^{81} - 2 q^{83} + q^{85} + 32 q^{87} - 11 q^{89} + 6 q^{91} + 8 q^{93} + 4 q^{95} - q^{97} + 38 q^{99}+O(q^{100}) $ 8 * q + 3 * q^3 - 4 * q^5 + 8 * q^7 - q^9 + 4 * q^11 - 7 * q^13 + 3 * q^15 + q^17 - 5 * q^19 + 4 * q^21 + 2 * q^23 - 4 * q^25 - 24 * q^27 + q^29 - 19 * q^33 - 4 * q^35 - 4 * q^37 - 30 * q^39 + 8 * q^41 + q^43 + 2 * q^45 - 12 * q^47 - 20 * q^49 + 22 * q^51 + 5 * q^53 - 2 * q^55 + 7 * q^57 - 5 * q^59 - 3 * q^63 + 14 * q^65 + 4 * q^67 - 18 * q^69 + 20 * q^71 + 20 * q^73 - 6 * q^75 + 28 * q^77 + 17 * q^79 - 12 * q^81 - 2 * q^83 + q^85 + 32 * q^87 - 11 * q^89 + 6 * q^91 + 8 * q^93 + 4 * q^95 - q^97 + 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times$.

$n$	$191$	$401$	$1141$	$1217$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.579878	−	1.00438i	−0.334793	−	0.579878i	0.648652	−	0.761085i	$-0.275333\pi$
$3$	−0.579878	−	1.00438i	−0.334793	−	0.579878i	−0.983445	+	0.181207i	$0.942000\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	2.43525			0.920440			0.460220	−	0.887805i	$-0.347771\pi$
$7$	2.43525			0.920440			0.460220	+	0.887805i	$0.347771\pi$
$8$		0			0
$9$	0.827483	−	1.43324i	0.275828	−	0.477748i
$10$		0			0
$11$	5.75477			1.73513			0.867564	−	0.497326i	$-0.165685\pi$
$11$	5.75477			1.73513			0.867564	+	0.497326i	$0.165685\pi$
$12$		0			0
$13$	0.797505	−	1.38132i	0.221188	−	0.383109i	−0.733981	−	0.679170i	$-0.762340\pi$
$13$	0.797505	−	1.38132i	0.221188	−	0.383109i	0.955169	+	0.296061i	$0.0956732\pi$
$14$		0			0
$15$	−0.579878	+	1.00438i	−0.149724	+	0.259329i
$16$		0			0
$17$	2.99203	+	5.18234i	0.725673	+	1.25690i	0.958696	+	0.284432i	$0.0918050\pi$
$17$	2.99203	+	5.18234i	0.725673	+	1.25690i	−0.233023	+	0.972471i	$0.574862\pi$
$18$		0			0
$19$	−0.149412	+	4.35634i	−0.0342775	+	0.999412i
$19$	−0.149412	+	4.35634i	−0.0342775	+	0.999412i
$20$		0			0
$21$	−1.41215	−	2.44592i	−0.308156	−	0.533743i
$22$		0			0
$23$	−0.470022	+	0.814102i	−0.0980064	+	0.169752i	−0.910859	−	0.412717i	$-0.864580\pi$
$23$	−0.470022	+	0.814102i	−0.0980064	+	0.169752i	0.812853	+	0.582469i	$0.197913\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−5.39862			−1.03897
$28$		0			0
$29$	−1.30917	+	2.26755i	−0.243106	+	0.421073i	−0.961598	−	0.274463i	$-0.911500\pi$
$29$	−1.30917	+	2.26755i	−0.243106	+	0.421073i	0.718491	+	0.695536i	$0.244833\pi$
$30$		0			0
$31$	5.26913			0.946364			0.473182	−	0.880965i	$-0.343105\pi$
$31$	5.26913			0.946364			0.473182	+	0.880965i	$0.343105\pi$
$32$		0			0
$33$	−3.33706	−	5.77996i	−0.580908	−	1.00616i
$34$		0			0
$35$	−1.21763	−	2.10899i	−0.205817	−	0.356485i
$36$		0			0
$37$	−2.89384			−0.475744			−0.237872	−	0.971297i	$-0.576450\pi$
$37$	−2.89384			−0.475744			−0.237872	+	0.971297i	$0.576450\pi$
$38$		0			0
$39$	−1.84982			−0.296209
$40$		0			0
$41$	3.15767	+	5.46925i	0.493145	+	0.854153i	0.999969	−	0.00789701i	$-0.00251372\pi$
$41$	3.15767	+	5.46925i	0.493145	+	0.854153i	−0.506823	+	0.862050i	$0.669180\pi$
$42$		0			0
$43$	2.26961	+	3.93108i	0.346113	+	0.599485i	0.985555	−	0.169354i	$-0.0541682\pi$
$43$	2.26961	+	3.93108i	0.346113	+	0.599485i	−0.639443	+	0.768839i	$0.720835\pi$
$44$		0			0
$45$	−1.65497			−0.246708
$46$		0			0
$47$	4.47718	−	7.75471i	0.653064	−	1.13114i	−0.329311	−	0.944221i	$-0.606816\pi$
$47$	4.47718	−	7.75471i	0.653064	−	1.13114i	0.982375	−	0.186919i	$-0.0598502\pi$
$48$		0			0
$49$	−1.06953			−0.152791
$50$		0			0
$51$	3.47002	−	6.01025i	0.485900	−	0.841604i
$52$		0			0
$53$	1.09819	−	1.90213i	0.150848	−	0.261277i	−0.780691	−	0.624917i	$-0.785133\pi$
$53$	1.09819	−	1.90213i	0.150848	−	0.261277i	0.931540	+	0.363640i	$0.118466\pi$
$54$		0			0
$55$	−2.87738	−	4.98377i	−0.387986	−	0.672012i
$56$		0			0
$57$	4.46205	−	2.37608i	0.591013	−	0.314719i
$58$		0			0
$59$	−5.39939	−	9.35202i	−0.702941	−	1.21753i	−0.967430	−	0.253140i	$-0.918537\pi$
$59$	−5.39939	−	9.35202i	−0.702941	−	1.21753i	0.264489	−	0.964389i	$-0.414797\pi$
$60$		0			0
$61$	5.26434	−	9.11811i	0.674030	−	1.16745i	−0.302721	−	0.953079i	$-0.597895\pi$
$61$	5.26434	−	9.11811i	0.674030	−	1.16745i	0.976751	−	0.214375i	$-0.0687716\pi$
$62$		0			0
$63$	2.01513	−	3.49031i	0.253883	−	0.439738i
$64$		0			0
$65$	−1.59501			−0.197837
$66$		0			0
$67$	0.504789	−	0.874320i	0.0616698	−	0.106815i	−0.833542	−	0.552456i	$-0.813691\pi$
$67$	0.504789	−	0.874320i	0.0616698	−	0.106815i	0.895212	+	0.445641i	$0.147024\pi$
$68$		0			0
$69$	1.09022			0.131247
$70$		0			0
$71$	4.41694	+	7.65036i	0.524194	+	0.907931i	0.999603	+	0.0281662i	$0.00896677\pi$
$71$	4.41694	+	7.65036i	0.524194	+	0.907931i	−0.475409	+	0.879765i	$0.657700\pi$
$72$		0			0
$73$	5.12499	+	8.87674i	0.599835	+	1.03894i	0.992845	+	0.119410i	$0.0381003\pi$
$73$	5.12499	+	8.87674i	0.599835	+	1.03894i	−0.393011	+	0.919534i	$0.628566\pi$
$74$		0			0
$75$	1.15976			0.133917
$76$		0			0
$77$	14.0143			1.59708
$78$		0			0
$79$	3.80229	+	6.58577i	0.427792	+	0.740957i	0.996677	−	0.0814604i	$-0.0259584\pi$
$79$	3.80229	+	6.58577i	0.427792	+	0.740957i	−0.568885	+	0.822417i	$0.692625\pi$
$80$		0			0
$81$	0.648093	+	1.12253i	0.0720103	+	0.124726i
$82$		0			0
$83$	−3.11355			−0.341756			−0.170878	−	0.985292i	$-0.554660\pi$
$83$	−3.11355			−0.341756			−0.170878	+	0.985292i	$0.554660\pi$
$84$		0			0
$85$	2.99203	−	5.18234i	0.324531	−	0.562104i
$86$		0			0
$87$	3.03663			0.325561
$88$		0			0
$89$	5.55706	−	9.62511i	0.589047	−	1.02026i	−0.405310	−	0.914179i	$-0.632837\pi$
$89$	5.55706	−	9.62511i	0.589047	−	1.02026i	0.994358	−	0.106081i	$-0.0338302\pi$
$90$		0			0
$91$	1.94213	−	3.36387i	0.203590	−	0.352629i
$92$		0			0
$93$	−3.05545	−	5.29220i	−0.316836	−	0.548776i
$94$		0			0
$95$	3.84741	−	2.04877i	0.394735	−	0.210200i
$96$		0			0
$97$	−2.02888	−	3.51412i	−0.206002	−	0.356805i	0.744450	−	0.667678i	$-0.232712\pi$
$97$	−2.02888	−	3.51412i	−0.206002	−	0.356805i	−0.950451	+	0.310873i	$0.899379\pi$
$98$		0			0
$99$	4.76197	−	8.24798i	0.478596	−	0.828953i
$100$		0			0
$101$	5.56503	−	9.63892i	0.553741	−	0.959108i	−0.444259	−	0.895898i	$-0.646533\pi$
$101$	5.56503	−	9.63892i	0.553741	−	0.959108i	0.998000	−	0.0632098i	$-0.0201337\pi$
$102$		0			0
$103$	−11.5791			−1.14092			−0.570460	−	0.821326i	$-0.693235\pi$
$103$	−11.5791			−1.14092			−0.570460	+	0.821326i	$0.693235\pi$
$104$		0			0
$105$	−1.41215	+	2.44592i	−0.137812	+	0.238697i
$106$		0			0
$107$	−17.9177			−1.73217			−0.866086	−	0.499894i	$-0.833372\pi$
$107$	−17.9177			−1.73217			−0.866086	+	0.499894i	$0.833372\pi$
$108$		0			0
$109$	−2.81235	−	4.87113i	−0.269374	−	0.466570i	0.699326	−	0.714803i	$-0.253484\pi$
$109$	−2.81235	−	4.87113i	−0.269374	−	0.466570i	−0.968700	+	0.248233i	$0.920150\pi$
$110$		0			0
$111$	1.67807	+	2.90650i	0.159275	+	0.275873i
$112$		0			0
$113$	−15.6789			−1.47494			−0.737472	−	0.675378i	$-0.763981\pi$
$113$	−15.6789			−1.47494			−0.737472	+	0.675378i	$0.763981\pi$
$114$		0			0
$115$	0.940044			0.0876595
$116$		0			0
$117$	−1.31984	−	2.28604i	−0.122020	−	0.211344i
$118$		0			0
$119$	7.28635	+	12.6203i	0.667939	+	1.15690i
$120$		0			0
$121$	22.1173			2.01067
$122$		0			0
$123$	3.66213	−	6.34299i	0.330203	−	0.571928i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	3.05996	−	5.30000i	0.271527	−	0.470299i	−0.697726	−	0.716365i	$-0.745805\pi$
$127$	3.05996	−	5.30000i	0.271527	−	0.470299i	0.969253	+	0.246066i	$0.0791380\pi$
$128$		0			0
$129$	2.63220	−	4.55910i	0.231752	−	0.401406i
$130$		0			0
$131$	−7.44055	−	12.8874i	−0.650084	−	1.12598i	−0.983102	−	0.183058i	$-0.941400\pi$
$131$	−7.44055	−	12.8874i	−0.650084	−	1.12598i	0.333018	−	0.942920i	$-0.391933\pi$
$132$		0			0
$133$	−0.363857	+	10.6088i	−0.0315504	+	0.919899i
$134$		0			0
$135$	2.69931	+	4.67535i	0.232320	+	0.402390i
$136$		0			0
$137$	−8.67518	+	15.0258i	−0.741170	+	1.28374i	0.210793	+	0.977531i	$0.432396\pi$
$137$	−8.67518	+	15.0258i	−0.741170	+	1.28374i	−0.951963	+	0.306214i	$0.900938\pi$
$138$		0			0
$139$	−3.35267	+	5.80700i	−0.284370	+	0.492543i	−0.972456	−	0.233086i	$-0.925118\pi$
$139$	−3.35267	+	5.80700i	−0.284370	+	0.492543i	0.688086	+	0.725629i	$0.258451\pi$
$140$		0			0
$141$	−10.3849			−0.874564
$142$		0			0
$143$	4.58946	−	7.94917i	0.383790	−	0.664743i
$144$		0			0
$145$	2.61834			0.217441
$146$		0			0
$147$	0.620199	+	1.07422i	0.0511532	+	0.0885999i
$148$		0			0
$149$	−7.19642	−	12.4646i	−0.589553	−	1.02114i	−0.994291	−	0.106704i	$-0.965970\pi$
$149$	−7.19642	−	12.4646i	−0.589553	−	1.02114i	0.404737	−	0.914433i	$-0.367363\pi$
$150$		0			0
$151$	−12.7219			−1.03529			−0.517645	−	0.855595i	$-0.673191\pi$
$151$	−12.7219			−1.03529			−0.517645	+	0.855595i	$0.673191\pi$
$152$		0			0
$153$	9.90341			0.800644
$154$		0			0
$155$	−2.63457	−	4.56320i	−0.211614	−	0.366525i
$156$		0			0
$157$	1.68765	+	2.92309i	0.134689	+	0.233288i	0.925479	−	0.378800i	$-0.123663\pi$
$157$	1.68765	+	2.92309i	0.134689	+	0.233288i	−0.790790	+	0.612088i	$0.790330\pi$
$158$		0			0
$159$	−2.54727			−0.202012
$160$		0			0
$161$	−1.14462	+	1.98255i	−0.0902089	+	0.156246i
$162$		0			0
$163$	−0.307960			−0.0241213			−0.0120607	−	0.999927i	$-0.503839\pi$
$163$	−0.307960			−0.0241213			−0.0120607	+	0.999927i	$0.503839\pi$
$164$		0			0
$165$	−3.33706	+	5.77996i	−0.259790	+	0.449969i
$166$		0			0
$167$	7.13215	−	12.3532i	0.551902	−	0.955923i	−0.446235	−	0.894916i	$-0.647235\pi$
$167$	7.13215	−	12.3532i	0.551902	−	0.955923i	0.998137	−	0.0610070i	$-0.0194312\pi$
$168$		0			0
$169$	5.22797	+	9.05511i	0.402152	+	0.696547i
$170$		0			0
$171$	6.12005	+	3.81894i	0.468012	+	0.292042i
$172$		0			0
$173$	−6.67357	−	11.5590i	−0.507382	−	0.878811i	−0.999963	−	0.00854514i	$-0.997280\pi$
$173$	−6.67357	−	11.5590i	−0.507382	−	0.878811i	0.492581	−	0.870266i	$-0.336053\pi$
$174$		0			0
$175$	−1.21763	+	2.10899i	−0.0920440	+	0.159425i
$176$		0			0
$177$	−6.26197	+	10.8461i	−0.470679	+	0.815239i
$178$		0			0
$179$	14.2207			1.06291			0.531454	−	0.847087i	$-0.321646\pi$
$179$	14.2207			1.06291			0.531454	+	0.847087i	$0.321646\pi$
$180$		0			0
$181$	−4.94132	+	8.55861i	−0.367285	+	0.636157i	−0.989140	−	0.146976i	$-0.953046\pi$
$181$	−4.94132	+	8.55861i	−0.367285	+	0.636157i	0.621855	+	0.783133i	$0.286379\pi$
$182$		0			0
$183$	−12.2107			−0.902641
$184$		0			0
$185$	1.44692	+	2.50613i	0.106379	+	0.184255i
$186$		0			0
$187$	17.2184	+	29.8232i	1.25914	+	2.18089i
$188$		0			0
$189$	−13.1470			−0.956305
$190$		0			0
$191$	12.9942			0.940228			0.470114	−	0.882606i	$-0.344213\pi$
$191$	12.9942			0.940228			0.470114	+	0.882606i	$0.344213\pi$
$192$		0			0
$193$	−7.25795	−	12.5711i	−0.522439	−	0.904890i	−0.999659	−	0.0261066i	$-0.991689\pi$
$193$	−7.25795	−	12.5711i	−0.522439	−	0.904890i	0.477221	−	0.878784i	$-0.341644\pi$
$194$		0			0
$195$	0.924911	+	1.60199i	0.0662343	+	0.114721i
$196$		0			0
$197$	−25.0010			−1.78125			−0.890624	−	0.454740i	$-0.849732\pi$
$197$	−25.0010			−1.78125			−0.890624	+	0.454740i	$0.849732\pi$
$198$		0			0
$199$	−1.12769	+	1.95322i	−0.0799401	+	0.138460i	−0.903224	−	0.429170i	$-0.858806\pi$
$199$	−1.12769	+	1.95322i	−0.0799401	+	0.138460i	0.823284	+	0.567630i	$0.192140\pi$
$200$		0			0
$201$	−1.17086			−0.0825864
$202$		0			0
$203$	−3.18816	+	5.52205i	−0.223765	+	0.387572i
$204$		0			0
$205$	3.15767	−	5.46925i	0.220541	−	0.381989i
$206$		0			0
$207$	0.777871	+	1.34731i	0.0540657	+	0.0936446i
$208$		0			0
$209$	−0.859833	+	25.0697i	−0.0594759	+	1.73411i
$210$		0			0
$211$	11.1081	+	19.2397i	0.764710	+	1.32452i	0.940400	+	0.340071i	$0.110451\pi$
$211$	11.1081	+	19.2397i	0.764710	+	1.32452i	−0.175689	+	0.984446i	$0.556215\pi$
$212$		0			0
$213$	5.12257	−	8.87255i	0.350993	−	0.607937i
$214$		0			0
$215$	2.26961	−	3.93108i	0.154786	−	0.268098i
$216$		0			0
$217$	12.8317			0.871071
$218$		0			0
$219$	5.94373	−	10.2949i	0.401640	−	0.695662i
$220$		0			0
$221$	9.54463			0.642041
$222$		0			0
$223$	5.10799	+	8.84730i	0.342056	+	0.592459i	0.984814	−	0.173610i	$-0.0555432\pi$
$223$	5.10799	+	8.84730i	0.342056	+	0.592459i	−0.642758	+	0.766069i	$0.722210\pi$
$224$		0			0
$225$	0.827483	+	1.43324i	0.0551656	+	0.0955495i
$226$		0			0
$227$	−4.15180			−0.275565			−0.137782	−	0.990463i	$-0.543997\pi$
$227$	−4.15180			−0.275565			−0.137782	+	0.990463i	$0.543997\pi$
$228$		0			0
$229$	6.53286			0.431703			0.215852	−	0.976426i	$-0.430747\pi$
$229$	6.53286			0.431703			0.215852	+	0.976426i	$0.430747\pi$
$230$		0			0
$231$	−8.12660	−	14.0757i	−0.534691	−	0.926111i
$232$		0			0
$233$	−2.57410	−	4.45848i	−0.168635	−	0.292084i	0.769305	−	0.638882i	$-0.220603\pi$
$233$	−2.57410	−	4.45848i	−0.168635	−	0.292084i	−0.937940	+	0.346797i	$0.887269\pi$
$234$		0			0
$235$	−8.95437			−0.584118
$236$		0			0
$237$	4.40973	−	7.63788i	0.286443	−	0.496134i
$238$		0			0
$239$	−13.9962			−0.905338			−0.452669	−	0.891679i	$-0.649528\pi$
$239$	−13.9962			−0.905338			−0.452669	+	0.891679i	$0.649528\pi$
$240$		0			0
$241$	−7.61285	+	13.1858i	−0.490387	+	0.849375i	−0.999939	−	0.0110652i	$-0.996478\pi$
$241$	−7.61285	+	13.1858i	−0.490387	+	0.849375i	0.509552	+	0.860440i	$0.329811\pi$
$242$		0			0
$243$	−7.34631	+	12.7242i	−0.471266	+	0.816256i
$244$		0			0
$245$	0.534767	+	0.926244i	0.0341650	+	0.0591756i
$246$		0			0
$247$	5.89834	+	3.68059i	0.375302	+	0.234190i
$248$		0			0
$249$	1.80548	+	3.12718i	0.114417	+	0.198177i
$250$		0			0
$251$	−3.05630	+	5.29366i	−0.192912	+	0.334133i	−0.946214	−	0.323542i	$-0.895126\pi$
$251$	−3.05630	+	5.29366i	−0.192912	+	0.334133i	0.753302	+	0.657674i	$0.228460\pi$
$252$		0			0
$253$	−2.70487	+	4.68497i	−0.170053	+	0.294541i
$254$		0			0
$255$	−6.94004			−0.434602
$256$		0			0
$257$	−0.0613414	+	0.106246i	−0.00382637	+	0.00662747i	−0.867932	−	0.496683i	$-0.834551\pi$
$257$	−0.0613414	+	0.106246i	−0.00382637	+	0.00662747i	0.864106	+	0.503310i	$0.167885\pi$
$258$		0			0
$259$	−7.04723			−0.437893
$260$		0			0
$261$	2.16663	+	3.75271i	0.134111	+	0.232287i
$262$		0			0
$263$	−5.03027	−	8.71267i	−0.310179	−	0.537247i	0.668222	−	0.743962i	$-0.267056\pi$
$263$	−5.03027	−	8.71267i	−0.310179	−	0.537247i	−0.978401	+	0.206716i	$0.933722\pi$
$264$		0			0
$265$	−2.19639			−0.134923
$266$		0			0
$267$	−12.8897			−0.788835
$268$		0			0
$269$	−2.85614	−	4.94698i	−0.174142	−	0.301623i	0.765722	−	0.643172i	$-0.222382\pi$
$269$	−2.85614	−	4.94698i	−0.174142	−	0.301623i	−0.939864	+	0.341549i	$0.889049\pi$
$270$		0			0
$271$	−6.35560	−	11.0082i	−0.386075	−	0.668702i	0.605843	−	0.795585i	$-0.292836\pi$
$271$	−6.35560	−	11.0082i	−0.386075	−	0.668702i	−0.991918	+	0.126883i	$0.959503\pi$
$272$		0			0
$273$	−4.50479			−0.272642
$274$		0			0
$275$	−2.87738	+	4.98377i	−0.173513	+	0.300533i
$276$		0			0
$277$	17.6019			1.05760			0.528799	−	0.848747i	$-0.322642\pi$
$277$	17.6019			1.05760			0.528799	+	0.848747i	$0.322642\pi$
$278$		0			0
$279$	4.36012	−	7.55195i	0.261034	−	0.452123i
$280$		0			0
$281$	10.2502	−	17.7539i	0.611476	−	1.05911i	−0.379516	−	0.925185i	$-0.623910\pi$
$281$	10.2502	−	17.7539i	0.611476	−	1.05911i	0.990992	−	0.133922i	$-0.0427571\pi$
$282$		0			0
$283$	−5.92805	−	10.2677i	−0.352386	−	0.610350i	0.634281	−	0.773103i	$-0.281296\pi$
$283$	−5.92805	−	10.2677i	−0.352386	−	0.610350i	−0.986667	+	0.162752i	$0.947963\pi$
$284$		0			0
$285$	−4.28877	−	2.67621i	−0.254045	−	0.158525i
$286$		0			0
$287$	7.68973	+	13.3190i	0.453911	+	0.786196i
$288$		0			0
$289$	−9.40447	+	16.2890i	−0.553204	+	0.958177i
$290$		0			0
$291$	−2.35301	+	4.07552i	−0.137936	+	0.238911i
$292$		0			0
$293$	−24.9814			−1.45943			−0.729715	−	0.683751i	$-0.760347\pi$
$293$	−24.9814			−1.45943			−0.729715	+	0.683751i	$0.760347\pi$
$294$		0			0
$295$	−5.39939	+	9.35202i	−0.314365	+	0.544495i
$296$		0			0
$297$	−31.0678			−1.80274
$298$		0			0
$299$	0.749690	+	1.29850i	0.0433557	+	0.0750943i
$300$		0			0
$301$	5.52708	+	9.57319i	0.318576	+	0.551789i
$302$		0			0
$303$	−12.9082			−0.741554
$304$		0			0
$305$	−10.5287			−0.602871
$306$		0			0
$307$	8.45997	+	14.6531i	0.482836	+	0.836296i	0.999806	−	0.0197074i	$-0.00627348\pi$
$307$	8.45997	+	14.6531i	0.482836	+	0.836296i	−0.516970	+	0.856003i	$0.672940\pi$
$308$		0			0
$309$	6.71444	+	11.6298i	0.381971	+	0.661594i
$310$		0			0
$311$	15.2133			0.862670			0.431335	−	0.902192i	$-0.358043\pi$
$311$	15.2133			0.862670			0.431335	+	0.902192i	$0.358043\pi$
$312$		0			0
$313$	−12.4637	+	21.5877i	−0.704488	+	1.22021i	0.262389	+	0.964962i	$0.415490\pi$
$313$	−12.4637	+	21.5877i	−0.704488	+	1.22021i	−0.966876	+	0.255246i	$0.917844\pi$
$314$		0			0
$315$	−4.03027			−0.227080
$316$		0			0
$317$	12.6152	−	21.8502i	0.708541	−	1.22723i	−0.256857	−	0.966449i	$-0.582687\pi$
$317$	12.6152	−	21.8502i	0.708541	−	1.22723i	0.965398	−	0.260780i	$-0.0839798\pi$
$318$		0			0
$319$	−7.53396	+	13.0492i	−0.421821	+	0.730615i
$320$		0			0
$321$	10.3901	+	17.9962i	0.579919	+	1.00445i
$322$		0			0
$323$	−23.0231	+	12.2600i	−1.28104	+	0.682163i
$324$		0			0
$325$	0.797505	+	1.38132i	0.0442376	+	0.0766218i
$326$		0			0
$327$	−3.26164	+	5.64933i	−0.180369	+	0.312408i
$328$		0			0
$329$	10.9031	−	18.8847i	0.601106	−	1.04115i
$330$		0			0
$331$	20.2063			1.11064			0.555320	−	0.831637i	$-0.312596\pi$
$331$	20.2063			1.11064			0.555320	+	0.831637i	$0.312596\pi$
$332$		0			0
$333$	−2.39460	+	4.14757i	−0.131223	+	0.227285i
$334$		0			0
$335$	−1.00958			−0.0551592
$336$		0			0
$337$	15.9123	+	27.5610i	0.866800	+	1.50134i	0.865249	+	0.501342i	$0.167160\pi$
$337$	15.9123	+	27.5610i	0.866800	+	1.50134i	0.00155051	+	0.999999i	$0.499506\pi$
$338$		0			0
$339$	9.09183	+	15.7475i	0.493800	+	0.855287i
$340$		0			0
$341$	30.3226			1.64206
$342$		0			0
$343$	−19.6514			−1.06107
$344$		0			0
$345$	−0.545111	−	0.944159i	−0.0293478	−	0.0508318i
$346$		0			0
$347$	−1.65128	−	2.86009i	−0.0886451	−	0.153538i	0.818294	−	0.574801i	$-0.194920\pi$
$347$	−1.65128	−	2.86009i	−0.0886451	−	0.153538i	−0.906939	+	0.421263i	$0.861587\pi$
$348$		0			0
$349$	17.8486			0.955416			0.477708	−	0.878519i	$-0.341468\pi$
$349$	17.8486			0.955416			0.477708	+	0.878519i	$0.341468\pi$
$350$		0			0
$351$	−4.30543	+	7.45723i	−0.229807	+	0.398037i
$352$		0			0
$353$	−8.29523			−0.441511			−0.220755	−	0.975329i	$-0.570852\pi$
$353$	−8.29523			−0.441511			−0.220755	+	0.975329i	$0.570852\pi$
$354$		0			0
$355$	4.41694	−	7.65036i	0.234427	−	0.406039i
$356$		0			0
$357$	8.45039	−	14.6365i	0.447242	−	0.774646i
$358$		0			0
$359$	4.17511	+	7.23150i	0.220354	+	0.381664i	0.954915	−	0.296878i	$-0.0959455\pi$
$359$	4.17511	+	7.23150i	0.220354	+	0.381664i	−0.734562	+	0.678542i	$0.762612\pi$
$360$		0			0
$361$	−18.9554	−	1.30178i	−0.997650	−	0.0685148i
$362$		0			0
$363$	−12.8254	−	22.2142i	−0.673156	−	1.16594i
$364$		0			0
$365$	5.12499	−	8.87674i	0.268254	−	0.464630i
$366$		0			0
$367$	7.20988	−	12.4879i	0.376353	−	0.651862i	−0.614176	−	0.789169i	$-0.710511\pi$
$367$	7.20988	−	12.4879i	0.376353	−	0.651862i	0.990528	+	0.137307i	$0.0438448\pi$
$368$		0			0
$369$	10.4517			0.544093
$370$		0			0
$371$	2.67438	−	4.63216i	0.138847	−	0.240490i
$372$		0			0
$373$	−24.1157			−1.24866			−0.624332	−	0.781159i	$-0.714629\pi$
$373$	−24.1157			−1.24866			−0.624332	+	0.781159i	$0.714629\pi$
$374$		0			0
$375$	−0.579878	−	1.00438i	−0.0299448	−	0.0518659i
$376$		0			0
$377$	2.08814	+	3.61676i	0.107545	+	0.186273i
$378$		0			0
$379$	−16.6757			−0.856571			−0.428285	−	0.903644i	$-0.640882\pi$
$379$	−16.6757			−0.856571			−0.428285	+	0.903644i	$0.640882\pi$
$380$		0			0
$381$	−7.09760			−0.363621
$382$		0			0
$383$	−5.43895	−	9.42053i	−0.277917	−	0.481367i	0.692950	−	0.720986i	$-0.256311\pi$
$383$	−5.43895	−	9.42053i	−0.277917	−	0.481367i	−0.970867	+	0.239619i	$0.922977\pi$
$384$		0			0
$385$	−7.00716	−	12.1368i	−0.357118	−	0.618546i
$386$		0			0
$387$	7.51226			0.381870
$388$		0			0
$389$	−18.2272	+	31.5704i	−0.924154	+	1.60068i	−0.131237	+	0.991351i	$0.541895\pi$
$389$	−18.2272	+	31.5704i	−0.924154	+	1.60068i	−0.792917	+	0.609330i	$0.791438\pi$
$390$		0			0
$391$	−5.62528			−0.284482
$392$		0			0
$393$	−8.62922	+	14.9463i	−0.435287	+	0.753939i
$394$		0			0
$395$	3.80229	−	6.58577i	0.191314	−	0.331366i
$396$		0			0
$397$	−4.29191	−	7.43380i	−0.215405	−	0.373092i	0.737993	−	0.674808i	$-0.235774\pi$
$397$	−4.29191	−	7.43380i	−0.215405	−	0.373092i	−0.953398	+	0.301717i	$0.902440\pi$
$398$		0			0
$399$	10.8662	−	5.78635i	0.543992	−	0.289680i
$400$		0			0
$401$	8.52785	+	14.7707i	0.425860	+	0.737612i	0.996500	−	0.0835885i	$-0.0266381\pi$
$401$	8.52785	+	14.7707i	0.425860	+	0.737612i	−0.570640	+	0.821200i	$0.693305\pi$
$402$		0			0
$403$	4.20216	−	7.27836i	0.209325	−	0.362561i
$404$		0			0
$405$	0.648093	−	1.12253i	0.0322040	−	0.0557790i
$406$		0			0
$407$	−16.6533			−0.825476
$408$		0			0
$409$	5.89702	−	10.2139i	0.291589	−	0.505047i	−0.682597	−	0.730795i	$-0.739149\pi$
$409$	5.89702	−	10.2139i	0.291589	−	0.505047i	0.974186	+	0.225749i	$0.0724828\pi$
$410$		0			0
$411$	20.1222			0.992553
$412$		0			0
$413$	−13.1489	−	22.7745i	−0.647015	−	1.12066i
$414$		0			0
$415$	1.55677	+	2.69641i	0.0764190	+	0.132362i
$416$		0			0
$417$	7.77656			0.380820
$418$		0			0
$419$	−1.14280			−0.0558292			−0.0279146	−	0.999610i	$-0.508887\pi$
$419$	−1.14280			−0.0558292			−0.0279146	+	0.999610i	$0.508887\pi$
$420$		0			0
$421$	−9.75944	−	16.9039i	−0.475646	−	0.823843i	0.523965	−	0.851740i	$-0.324452\pi$
$421$	−9.75944	−	16.9039i	−0.475646	−	0.823843i	−0.999611	+	0.0278967i	$0.991119\pi$
$422$		0			0
$423$	−7.40959	−	12.8338i	−0.360266	−	0.624000i
$424$		0			0
$425$	−5.98406			−0.290269
$426$		0			0
$427$	12.8200	−	22.2049i	0.620404	−	1.07457i
$428$		0			0
$429$	−10.6453			−0.513960
$430$		0			0
$431$	−18.4392	+	31.9377i	−0.888187	+	1.53838i	−0.0461694	+	0.998934i	$0.514701\pi$
$431$	−18.4392	+	31.9377i	−0.888187	+	1.53838i	−0.842017	+	0.539451i	$0.818632\pi$
$432$		0			0
$433$	−0.184467	+	0.319506i	−0.00886490	+	0.0153545i	−0.870424	−	0.492303i	$-0.836155\pi$
$433$	−0.184467	+	0.319506i	−0.00886490	+	0.0153545i	0.861559	+	0.507658i	$0.169488\pi$
$434$		0			0
$435$	−1.51832	−	2.62980i	−0.0727976	−	0.126089i
$436$		0			0
$437$	−3.47628	−	2.16921i	−0.166293	−	0.103767i
$438$		0			0
$439$	−1.13220	−	1.96102i	−0.0540367	−	0.0935944i	0.837742	−	0.546067i	$-0.183875\pi$
$439$	−1.13220	−	1.96102i	−0.0540367	−	0.0935944i	−0.891778	+	0.452472i	$0.850542\pi$
$440$		0			0
$441$	−0.885022	+	1.53290i	−0.0421439	+	0.0729954i
$442$		0			0
$443$	−8.23137	+	14.2572i	−0.391084	+	0.677378i	−0.992593	−	0.121488i	$-0.961233\pi$
$443$	−8.23137	+	14.2572i	−0.391084	+	0.677378i	0.601508	+	0.798866i	$0.294567\pi$
$444$		0			0
$445$	−11.1141			−0.526860
$446$		0			0
$447$	−8.34609	+	14.4558i	−0.394756	+	0.683738i
$448$		0			0
$449$	14.1613			0.668315			0.334158	−	0.942517i	$-0.391548\pi$
$449$	14.1613			0.668315			0.334158	+	0.942517i	$0.391548\pi$
$450$		0			0
$451$	18.1717	+	31.4742i	0.855670	+	1.48206i
$452$		0			0
$453$	7.37713	+	12.7776i	0.346608	+	0.600342i
$454$		0			0
$455$	−3.88426			−0.182097
$456$		0			0
$457$	1.22073			0.0571033			0.0285516	−	0.999592i	$-0.490910\pi$
$457$	1.22073			0.0571033			0.0285516	+	0.999592i	$0.490910\pi$
$458$		0			0
$459$	−16.1528	−	27.9775i	−0.753950	−	1.30588i
$460$		0			0
$461$	4.34580	+	7.52714i	0.202404	+	0.350574i	0.949303	−	0.314364i	$-0.101791\pi$
$461$	4.34580	+	7.52714i	0.202404	+	0.350574i	−0.746898	+	0.664938i	$0.768458\pi$
$462$		0			0
$463$	19.7149			0.916229			0.458114	−	0.888893i	$-0.348525\pi$
$463$	19.7149			0.916229			0.458114	+	0.888893i	$0.348525\pi$
$464$		0			0
$465$	−3.05545	+	5.29220i	−0.141693	+	0.245420i
$466$		0			0
$467$	11.4795			0.531207			0.265604	−	0.964082i	$-0.414429\pi$
$467$	11.4795			0.531207			0.265604	+	0.964082i	$0.414429\pi$
$468$		0			0
$469$	1.22929	−	2.12919i	0.0567633	−	0.0983170i
$470$		0			0
$471$	1.95726	−	3.39008i	0.0901858	−	0.156206i
$472$		0			0
$473$	13.0611	+	22.6225i	0.600549	+	1.04018i
$474$		0			0
$475$	−3.69799	−	2.30756i	−0.169676	−	0.105878i
$476$		0			0
$477$	−1.81747	−	3.14796i	−0.0832164	−	0.144135i
$478$		0			0
$479$	19.6316	−	34.0029i	0.896989	−	1.55363i	0.0656652	−	0.997842i	$-0.479083\pi$
$479$	19.6316	−	34.0029i	0.896989	−	1.55363i	0.831324	−	0.555789i	$-0.187584\pi$
$480$		0			0
$481$	−2.30785	+	3.99731i	−0.105229	+	0.182262i
$482$		0			0
$483$	2.65497			0.120805
$484$		0			0
$485$	−2.02888	+	3.51412i	−0.0921267	+	0.159568i
$486$		0			0
$487$	−31.5943			−1.43168			−0.715838	−	0.698266i	$-0.753955\pi$
$487$	−31.5943			−1.43168			−0.715838	+	0.698266i	$0.753955\pi$
$488$		0			0
$489$	0.178579	+	0.309309i	0.00807564	+	0.0139874i
$490$		0			0
$491$	−5.53187	−	9.58148i	−0.249650	−	0.432406i	0.713779	−	0.700371i	$-0.246982\pi$
$491$	−5.53187	−	9.58148i	−0.249650	−	0.432406i	−0.963429	+	0.267965i	$0.913649\pi$
$492$		0			0
$493$	−15.6683			−0.705663
$494$		0			0
$495$	−9.52395			−0.428070
$496$		0			0
$497$	10.7564	+	18.6306i	0.482489	+	0.835696i
$498$		0			0
$499$	−10.1868	−	17.6440i	−0.456023	−	0.789854i	0.542724	−	0.839911i	$-0.317393\pi$
$499$	−10.1868	−	17.6440i	−0.456023	−	0.789854i	−0.998746	+	0.0500570i	$0.984060\pi$
$500$		0			0
$501$	−16.5431			−0.739091
$502$		0			0
$503$	−6.83622	+	11.8407i	−0.304812	+	0.527950i	−0.977219	−	0.212231i	$-0.931927\pi$
$503$	−6.83622	+	11.8407i	−0.304812	+	0.527950i	0.672407	+	0.740181i	$0.265260\pi$
$504$		0			0
$505$	−11.1301			−0.495281
$506$		0			0
$507$	6.06317	−	10.5017i	0.269275	−	0.466398i
$508$		0			0
$509$	3.86196	−	6.68912i	0.171179	−	0.296490i	−0.767654	−	0.640865i	$-0.778576\pi$
$509$	3.86196	−	6.68912i	0.171179	−	0.296490i	0.938832	+	0.344375i	$0.111909\pi$
$510$		0			0
$511$	12.4807	+	21.6171i	0.552112	+	0.956285i
$512$		0			0
$513$	0.806621	−	23.5182i	0.0356132	−	1.03836i
$514$		0			0
$515$	5.78953	+	10.0278i	0.255117	+	0.441876i
$516$		0			0
$517$	25.7651	−	44.6265i	1.13315	−	1.96267i
$518$		0			0
$519$	−7.73971	+	13.4056i	−0.339736	+	0.588439i
$520$		0			0
$521$	−2.16876			−0.0950151			−0.0475075	−	0.998871i	$-0.515128\pi$
$521$	−2.16876			−0.0950151			−0.0475075	+	0.998871i	$0.515128\pi$
$522$		0			0
$523$	−11.9466	+	20.6921i	−0.522389	+	0.904804i	0.477272	+	0.878756i	$0.341626\pi$
$523$	−11.9466	+	20.6921i	−0.522389	+	0.904804i	−0.999661	+	0.0260485i	$0.991708\pi$
$524$		0			0
$525$	2.82430			0.123263
$526$		0			0
$527$	15.7654	+	27.3065i	0.686751	+	1.18949i
$528$		0			0
$529$	11.0582	+	19.1533i	0.480790	+	0.832752i
$530$		0			0
$531$	−17.8716			−0.775562
$532$		0			0
$533$	10.0730			0.436312
$534$		0			0
$535$	8.95887	+	15.5172i	0.387326	+	0.670868i
$536$		0			0
$537$	−8.24629	−	14.2830i	−0.355854	−	0.616356i
$538$		0			0
$539$	−6.15492			−0.265111
$540$		0			0
$541$	−21.2275	+	36.7671i	−0.912641	+	1.58074i	−0.102323	+	0.994751i	$0.532627\pi$
$541$	−21.2275	+	36.7671i	−0.912641	+	1.58074i	−0.810319	+	0.585990i	$0.800706\pi$
$542$		0			0
$543$	11.4614			0.491858
$544$		0			0
$545$	−2.81235	+	4.87113i	−0.120468	+	0.208656i
$546$		0			0
$547$	6.01535	−	10.4189i	0.257198	−	0.445480i	−0.708292	−	0.705919i	$-0.750534\pi$
$547$	6.01535	−	10.4189i	0.257198	−	0.445480i	0.965490	+	0.260439i	$0.0838674\pi$
$548$		0			0
$549$	−8.71231	−	15.0902i	−0.371833	−	0.644033i
$550$		0			0
$551$	−9.68259	−	6.04198i	−0.412492	−	0.257397i
$552$		0			0
$553$	9.25956	+	16.0380i	0.393756	+	0.682006i
$554$		0			0
$555$	1.67807	−	2.90650i	0.0712301	−	0.123374i
$556$		0			0
$557$	4.37635	−	7.58006i	0.185432	−	0.321178i	−0.758290	−	0.651917i	$-0.773965\pi$
$557$	4.37635	−	7.58006i	0.185432	−	0.321178i	0.943722	+	0.330740i	$0.107298\pi$
$558$		0			0
$559$	7.24011			0.306224
$560$		0			0
$561$	19.9692	−	34.5876i	0.843099	−	1.46029i
$562$		0			0
$563$	35.9707			1.51598			0.757991	−	0.652265i	$-0.226181\pi$
$563$	35.9707			1.51598			0.757991	+	0.652265i	$0.226181\pi$
$564$		0			0
$565$	7.83943	+	13.5783i	0.329807	+	0.571243i
$566$		0			0
$567$	1.57827	+	2.73365i	0.0662812	+	0.114802i
$568$		0			0
$569$	−20.3125			−0.851543			−0.425772	−	0.904831i	$-0.639997\pi$
$569$	−20.3125			−0.851543			−0.425772	+	0.904831i	$0.639997\pi$
$570$		0			0
$571$	−10.1773			−0.425906			−0.212953	−	0.977062i	$-0.568308\pi$
$571$	−10.1773			−0.425906			−0.212953	+	0.977062i	$0.568308\pi$
$572$		0			0
$573$	−7.53505	−	13.0511i	−0.314781	−	0.545217i
$574$		0			0
$575$	−0.470022	−	0.814102i	−0.0196013	−	0.0339504i
$576$		0			0
$577$	−32.7441			−1.36316			−0.681578	−	0.731745i	$-0.738706\pi$
$577$	−32.7441			−1.36316			−0.681578	+	0.731745i	$0.738706\pi$
$578$		0			0
$579$	−8.41745	+	14.5794i	−0.349817	+	0.605901i
$580$		0			0
$581$	−7.58228			−0.314566
$582$		0			0
$583$	6.31984	−	10.9463i	0.261741	−	0.453349i
$584$		0			0
$585$	−1.31984	+	2.28604i	−0.0545689	+	0.0945160i
$586$		0			0
$587$	4.38663	+	7.59786i	0.181056	+	0.313597i	0.942240	−	0.334938i	$-0.108715\pi$
$587$	4.38663	+	7.59786i	0.181056	+	0.313597i	−0.761185	+	0.648535i	$0.775382\pi$
$588$		0			0
$589$	−0.787274	+	22.9541i	−0.0324390	+	0.945808i
$590$		0			0
$591$	14.4975	+	25.1105i	0.596349	+	1.03291i
$592$		0			0
$593$	16.1603	−	27.9905i	0.663625	−	1.14943i	−0.316031	−	0.948749i	$-0.602350\pi$
$593$	16.1603	−	27.9905i	0.663625	−	1.14943i	0.979656	−	0.200684i	$-0.0643163\pi$
$594$		0			0
$595$	7.28635	−	12.6203i	0.298711	−	0.517383i
$596$		0			0
$597$	2.61570			0.107053
$598$		0			0
$599$	−9.77520	+	16.9311i	−0.399404	+	0.691787i	−0.993652	−	0.112494i	$-0.964116\pi$
$599$	−9.77520	+	16.9311i	−0.399404	+	0.691787i	0.594249	+	0.804281i	$0.297449\pi$
$600$		0			0
$601$	−0.401837			−0.0163913			−0.00819564	−	0.999966i	$-0.502609\pi$
$601$	−0.401837			−0.0163913			−0.00819564	+	0.999966i	$0.502609\pi$
$602$		0			0
$603$	−0.835409	−	1.44697i	−0.0340205	−	0.0589252i
$604$		0			0
$605$	−11.0587	−	19.1542i	−0.449599	−	0.778728i
$606$		0			0
$607$	−13.4453			−0.545727			−0.272863	−	0.962053i	$-0.587971\pi$
$607$	−13.4453			−0.545727			−0.272863	+	0.962053i	$0.587971\pi$
$608$		0			0
$609$	7.39497			0.299659
$610$		0			0
$611$	−7.14115	−	12.3688i	−0.288900	−	0.500390i
$612$		0			0
$613$	10.3527	+	17.9313i	0.418140	+	0.724239i	0.995752	−	0.0920716i	$-0.0293489\pi$
$613$	10.3527	+	17.9313i	0.418140	+	0.724239i	−0.577613	+	0.816311i	$0.696016\pi$
$614$		0			0
$615$	−7.32425			−0.295342
$616$		0			0
$617$	4.63936	−	8.03560i	0.186773	−	0.323501i	−0.757399	−	0.652952i	$-0.773530\pi$
$617$	4.63936	−	8.03560i	0.186773	−	0.323501i	0.944173	+	0.329451i	$0.106864\pi$
$618$		0			0
$619$	2.89129			0.116211			0.0581053	−	0.998310i	$-0.481494\pi$
$619$	2.89129			0.116211			0.0581053	+	0.998310i	$0.481494\pi$
$620$		0			0
$621$	2.53747	−	4.39503i	0.101825	−	0.176366i
$622$		0			0
$623$	13.5329	−	23.4396i	0.542183	−	0.939088i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	25.6781	−	13.6738i	1.02548	−	0.546078i
$628$		0			0
$629$	−8.65844	−	14.9969i	−0.345234	−	0.597964i
$630$		0			0
$631$	15.2270	−	26.3740i	0.606178	−	1.04993i	−0.385686	−	0.922630i	$-0.626035\pi$
$631$	15.2270	−	26.3740i	0.606178	−	1.04993i	0.991864	−	0.127301i	$-0.0406314\pi$
$632$		0			0
$633$	12.8826	−	22.3134i	0.512039	−	0.886877i
$634$		0			0
$635$	−6.11991			−0.242861
$636$		0			0
$637$	−0.852959	+	1.47737i	−0.0337955	+	0.0585355i
$638$		0			0
$639$	14.6198			0.578349
$640$		0			0
$641$	10.0369	+	17.3845i	0.396434	+	0.686645i	0.993283	−	0.115709i	$-0.0369141\pi$
$641$	10.0369	+	17.3845i	0.396434	+	0.686645i	−0.596849	+	0.802354i	$0.703581\pi$
$642$		0			0
$643$	−1.04457	−	1.80924i	−0.0411937	−	0.0713496i	0.844693	−	0.535250i	$-0.179783\pi$
$643$	−1.04457	−	1.80924i	−0.0411937	−	0.0713496i	−0.885887	+	0.463901i	$0.846449\pi$
$644$		0			0
$645$	−5.26439			−0.207285
$646$		0			0
$647$	2.10623			0.0828043			0.0414021	−	0.999143i	$-0.486818\pi$
$647$	2.10623			0.0828043			0.0414021	+	0.999143i	$0.486818\pi$
$648$		0			0
$649$	−31.0722	−	53.8187i	−1.21969	−	2.11257i
$650$		0			0
$651$	−7.44081	−	12.8879i	−0.291628	−	0.505115i
$652$		0			0
$653$	1.83067			0.0716395			0.0358197	−	0.999358i	$-0.488596\pi$
$653$	1.83067			0.0716395			0.0358197	+	0.999358i	$0.488596\pi$
$654$		0			0
$655$	−7.44055	+	12.8874i	−0.290726	+	0.503553i
$656$		0			0
$657$	16.9634			0.661804
$658$		0			0
$659$	12.0268	−	20.8310i	0.468497	−	0.811460i	−0.530855	−	0.847463i	$-0.678129\pi$
$659$	12.0268	−	20.8310i	0.468497	−	0.811460i	0.999352	+	0.0360024i	$0.0114624\pi$
$660$		0			0
$661$	8.72110	−	15.1054i	0.339211	−	0.587531i	−0.645073	−	0.764121i	$-0.723173\pi$
$661$	8.72110	−	15.1054i	0.339211	−	0.587531i	0.984285	+	0.176589i	$0.0565065\pi$
$662$		0			0
$663$	−5.53472	−	9.58642i	−0.214951	−	0.372306i
$664$		0			0
$665$	9.36941	−	4.98929i	0.363330	−	0.193476i
$666$		0			0
$667$	−1.23068	−	2.13159i	−0.0476519	−	0.0825356i
$668$		0			0
$669$	5.92402	−	10.2607i	0.229036	−	0.396702i
$670$		0			0
$671$	30.2951	−	52.4726i	1.16953	−	2.02568i
$672$		0			0
$673$	47.5187			1.83171			0.915856	−	0.401506i	$-0.131513\pi$
$673$	47.5187			1.83171			0.915856	+	0.401506i	$0.131513\pi$
$674$		0			0
$675$	2.69931	−	4.67535i	0.103897	−	0.179954i
$676$		0			0
$677$	14.5531			0.559321			0.279661	−	0.960099i	$-0.409778\pi$
$677$	14.5531			0.559321			0.279661	+	0.960099i	$0.409778\pi$
$678$		0			0
$679$	−4.94084	−	8.55778i	−0.189612	−	0.328418i
$680$		0			0
$681$	2.40754	+	4.16998i	0.0922570	+	0.159794i
$682$		0			0
$683$	−3.33714			−0.127692			−0.0638460	−	0.997960i	$-0.520337\pi$
$683$	−3.33714			−0.127692			−0.0638460	+	0.997960i	$0.520337\pi$
$684$		0			0
$685$	17.3504			0.662923
$686$		0			0
$687$	−3.78826	−	6.56146i	−0.144531	−	0.250335i
$688$		0			0
$689$	−1.75163	−	3.03391i	−0.0667318	−	0.115583i
$690$		0			0
$691$	19.3318			0.735415			0.367708	−	0.929941i	$-0.380143\pi$
$691$	19.3318			0.735415			0.367708	+	0.929941i	$0.380143\pi$
$692$		0			0
$693$	11.5966	−	20.0859i	0.440519	−	0.763001i
$694$		0			0
$695$	6.70534			0.254348
$696$		0			0
$697$	−18.8957	+	32.7283i	−0.715725	+	1.23967i
$698$		0			0
$699$	−2.98533	+	5.17074i	−0.112916	+	0.195575i
$700$		0			0
$701$	−4.96892	−	8.60643i	−0.187674	−	0.325060i	0.756801	−	0.653646i	$-0.226761\pi$
$701$	−4.96892	−	8.60643i	−0.187674	−	0.325060i	−0.944474	+	0.328586i	$0.893428\pi$
$702$		0			0
$703$	0.432375	−	12.6065i	0.0163073	−	0.475464i
$704$		0			0
$705$	5.19244	+	8.99357i	0.195559	+	0.338717i
$706$		0			0
$707$	13.5523	−	23.4732i	0.509686	−	0.882801i
$708$		0			0
$709$	−18.6059	+	32.2264i	−0.698760	+	1.21029i	0.270136	+	0.962822i	$0.412931\pi$
$709$	−18.6059	+	32.2264i	−0.698760	+	1.21029i	−0.968897	+	0.247466i	$0.920402\pi$
$710$		0			0
$711$	12.5853			0.471987
$712$		0			0
$713$	−2.47661	+	4.28961i	−0.0927497	+	0.160647i
$714$		0			0
$715$	−9.17891			−0.343272
$716$		0			0
$717$	8.11608	+	14.0575i	0.303100	+	0.524985i
$718$		0			0
$719$	−1.32109	−	2.28819i	−0.0492683	−	0.0853351i	0.840340	−	0.542060i	$-0.182356\pi$
$719$	−1.32109	−	2.28819i	−0.0492683	−	0.0853351i	−0.889608	+	0.456725i	$0.849022\pi$
$720$		0			0
$721$	−28.1980			−1.05015
$722$		0			0
$723$	17.6581			0.656711
$724$		0			0
$725$	−1.30917	−	2.26755i	−0.0486213	−	0.0842145i
$726$		0			0
$727$	−5.08653	−	8.81013i	−0.188649	−	0.326750i	0.756151	−	0.654397i	$-0.227077\pi$
$727$	−5.08653	−	8.81013i	−0.188649	−	0.326750i	−0.944800	+	0.327647i	$0.893744\pi$
$728$		0			0
$729$	20.9284			0.775126
$730$		0			0
$731$	−13.5815	+	23.5238i	−0.502329	+	0.870060i
$732$		0			0
$733$	14.8222			0.547472			0.273736	−	0.961805i	$-0.411741\pi$
$733$	14.8222			0.547472			0.273736	+	0.961805i	$0.411741\pi$
$734$		0			0
$735$	0.620199	−	1.07422i	0.0228764	−	0.0396231i
$736$		0			0
$737$	2.90494	−	5.03151i	0.107005	−	0.185338i
$738$		0			0
$739$	17.7433	+	30.7323i	0.652697	+	1.13050i	0.982466	+	0.186443i	$0.0596959\pi$
$739$	17.7433	+	30.7323i	0.652697	+	1.13050i	−0.329769	+	0.944062i	$0.606971\pi$
$740$		0			0
$741$	0.276386	−	8.05845i	0.0101533	−	0.296035i
$742$		0			0
$743$	−4.36941	−	7.56804i	−0.160298	−	0.277645i	0.774677	−	0.632357i	$-0.217912\pi$
$743$	−4.36941	−	7.56804i	−0.160298	−	0.277645i	−0.934976	+	0.354712i	$0.884579\pi$
$744$		0			0
$745$	−7.19642	+	12.4646i	−0.263656	+	0.456666i
$746$		0			0
$747$	−2.57641	+	4.46247i	−0.0942658	+	0.163273i
$748$		0			0
$749$	−43.6342			−1.59436
$750$		0			0
$751$	6.54957	−	11.3442i	0.238997	−	0.413955i	−0.721430	−	0.692488i	$-0.756515\pi$
$751$	6.54957	−	11.3442i	0.238997	−	0.413955i	0.960427	+	0.278533i	$0.0898480\pi$
$752$		0			0
$753$	7.08911			0.258342
$754$		0			0
$755$	6.36093	+	11.0175i	0.231498	+	0.400966i
$756$		0			0
$757$	8.21901	+	14.2357i	0.298725	+	0.517407i	0.975845	−	0.218466i	$-0.0701053\pi$
$757$	8.21901	+	14.2357i	0.298725	+	0.517407i	−0.677119	+	0.735873i	$0.736772\pi$
$758$		0			0
$759$	6.27397			0.227731
$760$		0			0
$761$	16.3918			0.594203			0.297101	−	0.954846i	$-0.403980\pi$
$761$	16.3918			0.594203			0.297101	+	0.954846i	$0.403980\pi$
$762$		0			0
$763$	−6.84879	−	11.8625i	−0.247943	−	0.429450i
$764$		0			0
$765$	−4.95171	−	8.57661i	−0.179029	−	0.310088i
$766$		0			0
$767$	−17.2242			−0.621929
$768$		0			0
$769$	25.0210	−	43.3377i	0.902282	−	1.56280i	0.0777564	−	0.996972i	$-0.475224\pi$
$769$	25.0210	−	43.3377i	0.902282	−	1.56280i	0.824525	−	0.565825i	$-0.191442\pi$
$770$		0			0
$771$	0.142282			0.00512416
$772$		0			0
$773$	−24.3436	+	42.1644i	−0.875580	+	1.51655i	−0.0194356	+	0.999811i	$0.506187\pi$
$773$	−24.3436	+	42.1644i	−0.875580	+	1.51655i	−0.856144	+	0.516737i	$0.827146\pi$
$774$		0			0
$775$	−2.63457	+	4.56320i	−0.0946364	+	0.163915i
$776$		0			0
$777$	4.08653	+	7.07808i	0.146603	+	0.253925i
$778$		0			0
$779$	−24.2977	+	12.9387i	−0.870555	+	0.463577i
$780$		0			0
$781$	25.4185	+	44.0261i	0.909544	+	1.57538i
$782$		0			0
$783$	7.06771	−	12.2416i	0.252579	−	0.437480i
$784$		0			0
$785$	1.68765	−	2.92309i	0.0602348	−	0.104330i
$786$		0			0
$787$	−6.51678			−0.232298			−0.116149	−	0.993232i	$-0.537055\pi$
$787$	−6.51678			−0.232298			−0.116149	+	0.993232i	$0.537055\pi$
$788$		0			0
$789$	−5.83388	+	10.1046i	−0.207692	+	0.359732i
$790$		0			0
$791$	−38.1820			−1.35760
$792$		0			0
$793$	−8.39668	−	14.5435i	−0.298175	−	0.516454i
$794$		0			0
$795$	1.27364	+	2.20600i	0.0451712	+	0.0782388i
$796$		0			0
$797$	38.3796			1.35947			0.679737	−	0.733456i	$-0.262094\pi$
$797$	38.3796			1.35947			0.679737	+	0.733456i	$0.262094\pi$
$798$		0			0
$799$	53.5834			1.89565
$800$		0			0
$801$	−9.19675	−	15.9292i	−0.324951	−	0.562832i
$802$		0			0
$803$	29.4931	+	51.0836i	1.04079	+	1.80270i
$804$		0			0
$805$	2.28925			0.0806853
$806$		0			0
$807$	−3.31243	+	5.73729i	−0.116603	+	0.201962i
$808$		0			0
$809$	25.1409			0.883906			0.441953	−	0.897038i	$-0.354286\pi$
$809$	25.1409			0.883906			0.441953	+	0.897038i	$0.354286\pi$
$810$		0			0
$811$	−23.5053	+	40.7124i	−0.825383	+	1.42961i	0.0762426	+	0.997089i	$0.475708\pi$
$811$	−23.5053	+	40.7124i	−0.825383	+	1.42961i	−0.901626	+	0.432517i	$0.857626\pi$
$812$		0			0
$813$	−7.37094	+	12.7668i	−0.258510	+	0.447753i
$814$		0			0
$815$	0.153980	+	0.266702i	0.00539369	+	0.00934215i
$816$		0			0
$817$	−17.4642	+	9.29984i	−0.610996	+	0.325360i
$818$		0			0
$819$	−3.21416	−	5.56708i	−0.112312	−	0.194530i
$820$		0			0
$821$	9.91021	−	17.1650i	0.345869	−	0.599062i	−0.639642	−	0.768673i	$-0.720918\pi$
$821$	9.91021	−	17.1650i	0.345869	−	0.599062i	0.985511	+	0.169610i	$0.0542509\pi$
$822$		0			0
$823$	−19.6084	+	33.9627i	−0.683505	+	1.18387i	0.290399	+	0.956906i	$0.406212\pi$
$823$	−19.6084	+	33.9627i	−0.683505	+	1.18387i	−0.973904	+	0.226960i	$0.927121\pi$
$824$		0			0
$825$	6.67412			0.232363
$826$		0			0
$827$	−5.92176	+	10.2568i	−0.205920	+	0.356663i	−0.950425	−	0.310953i	$-0.899352\pi$
$827$	−5.92176	+	10.2568i	−0.205920	+	0.356663i	0.744506	+	0.667616i	$0.232685\pi$
$828$		0			0
$829$	46.9321			1.63002			0.815010	−	0.579447i	$-0.196731\pi$
$829$	46.9321			1.63002			0.815010	+	0.579447i	$0.196731\pi$
$830$		0			0
$831$	−10.2070	−	17.6790i	−0.354076	−	0.613278i
$832$		0			0
$833$	−3.20008	−	5.54270i	−0.110876	−	0.192043i
$834$		0			0
$835$	−14.2643			−0.493636
$836$		0			0
$837$	−28.4461			−0.983240
$838$		0			0
$839$	−26.5669	−	46.0153i	−0.917192	−	1.58862i	−0.803660	−	0.595089i	$-0.797117\pi$
$839$	−26.5669	−	46.0153i	−0.917192	−	1.58862i	−0.113532	−	0.993534i	$-0.536217\pi$
$840$		0			0
$841$	11.0722	+	19.1775i	0.381799	+	0.661294i
$842$		0			0
$843$	−23.7755			−0.818870
$844$		0			0
$845$	5.22797	−	9.05511i	0.179848	−	0.311505i
$846$		0			0
$847$	53.8613			1.85070
$848$		0			0
$849$	−6.87509	+	11.9080i	−0.235952	+	0.408682i
$850$		0			0
$851$	1.36017	−	2.35588i	0.0466259	−	0.0807584i
$852$		0			0
$853$	−21.1499	−	36.6327i	−0.724159	−	1.25428i	−0.959319	−	0.282324i	$-0.908895\pi$
$853$	−21.1499	−	36.6327i	−0.724159	−	1.25428i	0.235160	−	0.971957i	$-0.424438\pi$
$854$		0			0
$855$	0.247272	−	7.20959i	0.00845654	−	0.246563i
$856$		0			0
$857$	−11.7692	−	20.3849i	−0.402028	−	0.696333i	0.591942	−	0.805980i	$-0.298361\pi$
$857$	−11.7692	−	20.3849i	−0.402028	−	0.696333i	−0.993971	+	0.109647i	$0.965028\pi$
$858$		0			0
$859$	4.74062	−	8.21099i	0.161748	−	0.280156i	−0.773748	−	0.633494i	$-0.781620\pi$
$859$	4.74062	−	8.21099i	0.161748	−	0.280156i	0.935496	+	0.353338i	$0.114954\pi$
$860$		0			0
$861$	8.91821	−	15.4468i	0.303932	−	0.526425i
$862$		0			0
$863$	−22.8204			−0.776816			−0.388408	−	0.921487i	$-0.626975\pi$
$863$	−22.8204			−0.776816			−0.388408	+	0.921487i	$0.626975\pi$
$864$		0			0
$865$	−6.67357	+	11.5590i	−0.226908	+	0.393016i
$866$		0			0
$867$	21.8138			0.740834
$868$		0			0
$869$	21.8813	+	37.8996i	0.742273	+	1.28565i
$870$		0			0
$871$	−0.805144	−	1.39455i	−0.0272813	−	0.0472525i
$872$		0			0
$873$	−6.71546			−0.227284
$874$		0			0
$875$	2.43525			0.0823266
$876$		0			0
$877$	12.6471	+	21.9054i	0.427062	+	0.739693i	0.996611	−	0.0822647i	$-0.0262153\pi$
$877$	12.6471	+	21.9054i	0.427062	+	0.739693i	−0.569549	+	0.821958i	$0.692882\pi$
$878$		0			0
$879$	14.4862	+	25.0908i	0.488606	+	0.846291i
$880$		0			0
$881$	−33.2871			−1.12147			−0.560736	−	0.827995i	$-0.689482\pi$
$881$	−33.2871			−1.12147			−0.560736	+	0.827995i	$0.689482\pi$
$882$		0			0
$883$	−7.65544	+	13.2596i	−0.257626	+	0.446222i	−0.965606	−	0.260011i	$-0.916274\pi$
$883$	−7.65544	+	13.2596i	−0.257626	+	0.446222i	0.707979	+	0.706233i	$0.249607\pi$
$884$		0			0
$885$	12.5239			0.420988
$886$		0			0
$887$	21.6027	−	37.4171i	0.725349	−	1.25634i	−0.233481	−	0.972361i	$-0.575012\pi$
$887$	21.6027	−	37.4171i	0.725349	−	1.25634i	0.958830	−	0.283980i	$-0.0916550\pi$
$888$		0			0
$889$	7.45177	−	12.9068i	0.249924	−	0.432882i
$890$		0			0
$891$	3.72962	+	6.45990i	0.124947	+	0.216415i
$892$		0			0
$893$	33.1132	+	20.6628i	1.10809	+	0.691453i
$894$		0			0
$895$	−7.11036	−	12.3155i	−0.237673	−	0.411662i
$896$		0			0
$897$	0.869457	−	1.50594i	0.0290303	−	0.0502820i
$898$		0			0
$899$	−6.89818	+	11.9480i	−0.230067	+	0.398488i
$900$		0			0
$901$	13.1433			0.437867
$902$		0			0
$903$	6.41007	−	11.1026i	0.213314	−	0.369470i
$904$		0			0
$905$	9.88263			0.328510
$906$		0			0
$907$	7.16392	+	12.4083i	0.237874	+	0.412010i	0.960104	−	0.279643i	$-0.0902161\pi$
$907$	7.16392	+	12.4083i	0.237874	+	0.412010i	−0.722230	+	0.691653i	$0.756883\pi$
$908$		0			0
$909$	−9.20994	−	15.9521i	−0.305475	−	0.529097i
$910$		0			0
$911$	4.61162			0.152790			0.0763949	−	0.997078i	$-0.475659\pi$
$911$	4.61162			0.152790			0.0763949	+	0.997078i	$0.475659\pi$
$912$		0			0
$913$	−17.9177			−0.592990
$914$		0			0
$915$	6.10535	+	10.5748i	0.201837	+	0.349592i
$916$		0			0
$917$	−18.1196	−	31.3841i	−0.598363	−	1.03640i
$918$		0			0
$919$	−26.4921			−0.873892			−0.436946	−	0.899488i	$-0.643940\pi$
$919$	−26.4921			−0.873892			−0.436946	+	0.899488i	$0.643940\pi$
$920$		0			0
$921$	9.81149	−	16.9940i	0.323300	−	0.559972i
$922$		0			0
$923$	14.0901			0.463782
$924$		0			0
$925$	1.44692	−	2.50613i	0.0475744	−	0.0824012i
$926$		0			0
$927$	−9.58148	+	16.5956i	−0.314697	+	0.545072i
$928$		0			0
$929$	2.37863	+	4.11990i	0.0780402	+	0.135170i	0.902404	−	0.430890i	$-0.141800\pi$
$929$	2.37863	+	4.11990i	0.0780402	+	0.135170i	−0.824364	+	0.566060i	$0.808467\pi$
$930$		0			0
$931$	0.159802	−	4.65925i	0.00523729	−	0.152701i
$932$		0			0
$933$	−8.82188	−	15.2799i	−0.288815	−	0.500243i
$934$		0			0
$935$	17.2184	−	29.8232i	0.563103	−	0.975322i
$936$		0			0
$937$	5.96833	−	10.3375i	0.194977	−	0.337710i	−0.751916	−	0.659259i	$-0.770870\pi$
$937$	5.96833	−	10.3375i	0.194977	−	0.337710i	0.946893	+	0.321549i	$0.104203\pi$
$938$		0			0
$939$	28.9096			0.943429
$940$		0			0
$941$	8.99715	−	15.5835i	0.293299	−	0.508008i	−0.681289	−	0.732015i	$-0.738580\pi$
$941$	8.99715	−	15.5835i	0.293299	−	0.508008i	0.974588	+	0.224006i	$0.0719136\pi$
$942$		0			0
$943$	−5.93670			−0.193326
$944$		0			0
$945$	6.57351	+	11.3857i	0.213836	+	0.370375i
$946$		0			0
$947$	−12.6096	−	21.8404i	−0.409755	−	0.709717i	0.585107	−	0.810956i	$-0.301053\pi$
$947$	−12.6096	−	21.8404i	−0.409755	−	0.709717i	−0.994862	+	0.101239i	$0.967719\pi$
$948$		0			0
$949$	16.3488			0.530705
$950$		0			0
$951$	−29.2611			−0.948858
$952$		0			0
$953$	−21.1589	−	36.6484i	−0.685405	−	1.18716i	−0.973309	−	0.229498i	$-0.926292\pi$
$953$	−21.1589	−	36.6484i	−0.685405	−	1.18716i	0.287904	−	0.957659i	$-0.407042\pi$
$954$		0			0
$955$	−6.49710	−	11.2533i	−0.210241	−	0.364149i
$956$		0			0
$957$	17.4751			0.564890
$958$		0			0
$959$	−21.1263	+	36.5918i	−0.682203	+	1.18161i
$960$		0			0
$961$	−3.23623			−0.104395
$962$		0			0
$963$	−14.8266	+	25.6805i	−0.477781	+	0.827542i
$964$		0			0
$965$	−7.25795	+	12.5711i	−0.233642	+	0.404679i
$966$		0			0
$967$	−6.84820	−	11.8614i	−0.220223	−	0.381438i	0.734652	−	0.678444i	$-0.237345\pi$
$967$	−6.84820	−	11.8614i	−0.220223	−	0.381438i	−0.954876	+	0.297006i	$0.904012\pi$
$968$		0			0
$969$	25.6642	+	16.0146i	0.824454	+	0.514463i
$970$		0			0
$971$	−19.2906	−	33.4123i	−0.619065	−	1.07225i	−0.989657	−	0.143457i	$-0.954178\pi$
$971$	−19.2906	−	33.4123i	−0.619065	−	1.07225i	0.370591	−	0.928796i	$-0.379155\pi$
$972$		0			0
$973$	−8.16461	+	14.1415i	−0.261745	+	0.453356i
$974$		0			0
$975$	0.924911	−	1.60199i	0.0296209	−	0.0513048i
$976$		0			0
$977$	−17.4592			−0.558568			−0.279284	−	0.960209i	$-0.590097\pi$
$977$	−17.4592			−0.558568			−0.279284	+	0.960209i	$0.590097\pi$
$978$		0			0
$979$	31.9796	−	55.3903i	1.02207	−	1.77028i
$980$		0			0
$981$	−9.30869			−0.297204
$982$		0			0
$983$	21.9581	+	38.0325i	0.700353	+	1.21305i	0.968342	+	0.249625i	$0.0803075\pi$
$983$	21.9581	+	38.0325i	0.700353	+	1.21305i	−0.267989	+	0.963422i	$0.586359\pi$
$984$		0			0
$985$	12.5005	+	21.6515i	0.398299	+	0.689875i
$986$		0			0
$987$	−25.2898			−0.804984
$988$		0			0
$989$	−4.26707			−0.135685
$990$		0			0
$991$	23.1731	+	40.1370i	0.736118	+	1.27499i	0.954231	+	0.299071i	$0.0966767\pi$
$991$	23.1731	+	40.1370i	0.736118	+	1.27499i	−0.218112	+	0.975924i	$0.569990\pi$
$992$		0			0
$993$	−11.7172	−	20.2948i	−0.371834	−	0.644035i
$994$		0			0
$995$	2.25539			0.0715006
$996$		0			0
$997$	−5.86857	+	10.1647i	−0.185859	+	0.321918i	−0.943866	−	0.330329i	$-0.892840\pi$
$997$	−5.86857	+	10.1647i	−0.185859	+	0.321918i	0.758006	+	0.652247i	$0.226174\pi$
$998$		0			0
$999$	15.6227			0.494281

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1520.2.q.o.881.1		8
4.3	odd	2		95.2.e.c.26.4	yes	8
12.11	even	2		855.2.k.h.406.1		8
19.11	even	3	inner	1520.2.q.o.961.1		8
20.3	even	4		475.2.j.c.349.7		16
20.7	even	4		475.2.j.c.349.2		16
20.19	odd	2		475.2.e.e.26.1		8
76.7	odd	6		1805.2.a.o.1.1		4
76.11	odd	6		95.2.e.c.11.4	✓	8
76.31	even	6		1805.2.a.i.1.4		4
228.11	even	6		855.2.k.h.676.1		8
380.87	even	12		475.2.j.c.49.7		16
380.159	odd	6		9025.2.a.bg.1.4		4
380.163	even	12		475.2.j.c.49.2		16
380.239	odd	6		475.2.e.e.201.1		8
380.259	even	6		9025.2.a.bp.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.c.11.4	✓	8	76.11	odd	6
95.2.e.c.26.4	yes	8	4.3	odd	2
475.2.e.e.26.1		8	20.19	odd	2
475.2.e.e.201.1		8	380.239	odd	6
475.2.j.c.49.2		16	380.163	even	12
475.2.j.c.49.7		16	380.87	even	12
475.2.j.c.349.2		16	20.7	even	4
475.2.j.c.349.7		16	20.3	even	4
855.2.k.h.406.1		8	12.11	even	2
855.2.k.h.676.1		8	228.11	even	6
1520.2.q.o.881.1		8	1.1	even	1	trivial
1520.2.q.o.961.1		8	19.11	even	3	inner
1805.2.a.i.1.4		4	76.31	even	6
1805.2.a.o.1.1		4	76.7	odd	6
9025.2.a.bg.1.4		4	380.159	odd	6
9025.2.a.bp.1.1		4	380.259	even	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:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1520.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.579878 - 1.00438i) q^{3} +(-0.500000 - 0.866025i) q^{5} +2.43525 q^{7} +(0.827483 - 1.43324i) q^{9} +O(q^{10})\)	\(q+(-0.579878 - 1.00438i) q^{3} +(-0.500000 - 0.866025i) q^{5} +2.43525 q^{7} +(0.827483 - 1.43324i) q^{9} +5.75477 q^{11} +(0.797505 - 1.38132i) q^{13} +(-0.579878 + 1.00438i) q^{15} +(2.99203 + 5.18234i) q^{17} +(-0.149412 + 4.35634i) q^{19} +(-1.41215 - 2.44592i) q^{21} +(-0.470022 + 0.814102i) q^{23} +(-0.500000 + 0.866025i) q^{25} -5.39862 q^{27} +(-1.30917 + 2.26755i) q^{29} +5.26913 q^{31} +(-3.33706 - 5.77996i) q^{33} +(-1.21763 - 2.10899i) q^{35} -2.89384 q^{37} -1.84982 q^{39} +(3.15767 + 5.46925i) q^{41} +(2.26961 + 3.93108i) q^{43} -1.65497 q^{45} +(4.47718 - 7.75471i) q^{47} -1.06953 q^{49} +(3.47002 - 6.01025i) q^{51} +(1.09819 - 1.90213i) q^{53} +(-2.87738 - 4.98377i) q^{55} +(4.46205 - 2.37608i) q^{57} +(-5.39939 - 9.35202i) q^{59} +(5.26434 - 9.11811i) q^{61} +(2.01513 - 3.49031i) q^{63} -1.59501 q^{65} +(0.504789 - 0.874320i) q^{67} +1.09022 q^{69} +(4.41694 + 7.65036i) q^{71} +(5.12499 + 8.87674i) q^{73} +1.15976 q^{75} +14.0143 q^{77} +(3.80229 + 6.58577i) q^{79} +(0.648093 + 1.12253i) q^{81} -3.11355 q^{83} +(2.99203 - 5.18234i) q^{85} +3.03663 q^{87} +(5.55706 - 9.62511i) q^{89} +(1.94213 - 3.36387i) q^{91} +(-3.05545 - 5.29220i) q^{93} +(3.84741 - 2.04877i) q^{95} +(-2.02888 - 3.51412i) q^{97} +(4.76197 - 8.24798i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{3} - 4 q^{5} + 8 q^{7} - q^{9}+O(q^{10}) \) 8 * q + 3 * q^3 - 4 * q^5 + 8 * q^7 - q^9	\( 8 q + 3 q^{3} - 4 q^{5} + 8 q^{7} - q^{9} + 4 q^{11} - 7 q^{13} + 3 q^{15} + q^{17} - 5 q^{19} + 4 q^{21} + 2 q^{23} - 4 q^{25} - 24 q^{27} + q^{29} - 19 q^{33} - 4 q^{35} - 4 q^{37} - 30 q^{39} + 8 q^{41} + q^{43} + 2 q^{45} - 12 q^{47} - 20 q^{49} + 22 q^{51} + 5 q^{53} - 2 q^{55} + 7 q^{57} - 5 q^{59} - 3 q^{63} + 14 q^{65} + 4 q^{67} - 18 q^{69} + 20 q^{71} + 20 q^{73} - 6 q^{75} + 28 q^{77} + 17 q^{79} - 12 q^{81} - 2 q^{83} + q^{85} + 32 q^{87} - 11 q^{89} + 6 q^{91} + 8 q^{93} + 4 q^{95} - q^{97} + 38 q^{99}+O(q^{100}) \) 8 * q + 3 * q^3 - 4 * q^5 + 8 * q^7 - q^9 + 4 * q^11 - 7 * q^13 + 3 * q^15 + q^17 - 5 * q^19 + 4 * q^21 + 2 * q^23 - 4 * q^25 - 24 * q^27 + q^29 - 19 * q^33 - 4 * q^35 - 4 * q^37 - 30 * q^39 + 8 * q^41 + q^43 + 2 * q^45 - 12 * q^47 - 20 * q^49 + 22 * q^51 + 5 * q^53 - 2 * q^55 + 7 * q^57 - 5 * q^59 - 3 * q^63 + 14 * q^65 + 4 * q^67 - 18 * q^69 + 20 * q^71 + 20 * q^73 - 6 * q^75 + 28 * q^77 + 17 * q^79 - 12 * q^81 - 2 * q^83 + q^85 + 32 * q^87 - 11 * q^89 + 6 * q^91 + 8 * q^93 + 4 * q^95 - q^97 + 38 * q^99

Introduction

L-functions

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