LMFDB - Embedded newform 756.2.bo.a.169.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(85,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("756.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bo (of order $9$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			169.4
Character	$\chi$	$=$	756.169
Dual form			756.2.bo.a.85.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.576212 + 1.63340i) q^{3} +(0.746163 + 4.23170i) q^{5} +(0.766044 + 0.642788i) q^{7} +(-2.33596 - 1.88236i) q^{9} +O(q^{10})$	\(q+(-0.576212 + 1.63340i) q^{3} +(0.746163 + 4.23170i) q^{5} +(0.766044 + 0.642788i) q^{7} +(-2.33596 - 1.88236i) q^{9} +(-1.03318 + 5.85945i) q^{11} +(-1.51769 - 0.552392i) q^{13} +(-7.34199 - 1.21958i) q^{15} +(1.15541 + 2.00122i) q^{17} +(3.25715 - 5.64155i) q^{19} +(-1.49133 + 0.880871i) q^{21} +(4.79887 - 4.02673i) q^{23} +(-12.6521 + 4.60497i) q^{25} +(4.42065 - 2.73090i) q^{27} +(2.53931 - 0.924234i) q^{29} +(3.31963 - 2.78550i) q^{31} +(-8.97546 - 5.06387i) q^{33} +(-2.14849 + 3.72129i) q^{35} +(2.11243 + 3.65884i) q^{37} +(1.77678 - 2.16068i) q^{39} +(-1.36630 - 0.497294i) q^{41} +(-0.462038 + 2.62035i) q^{43} +(6.22260 - 11.2896i) q^{45} +(-5.85590 - 4.91368i) q^{47} +(0.173648 + 0.984808i) q^{49} +(-3.93455 + 0.734107i) q^{51} -10.4703 q^{53} -25.5663 q^{55} +(7.33808 + 8.57095i) q^{57} +(-0.550759 - 3.12351i) q^{59} +(0.329725 + 0.276672i) q^{61} +(-0.579488 - 2.94350i) q^{63} +(1.20512 - 6.83456i) q^{65} +(6.64079 + 2.41705i) q^{67} +(3.81208 + 10.1587i) q^{69} +(7.87452 + 13.6391i) q^{71} +(1.86339 - 3.22749i) q^{73} +(-0.231469 - 23.3193i) q^{75} +(-4.55784 + 3.82448i) q^{77} +(-14.1595 + 5.15363i) q^{79} +(1.91341 + 8.79425i) q^{81} +(14.0933 - 5.12954i) q^{83} +(-7.60646 + 6.38258i) q^{85} +(0.0464566 + 4.68025i) q^{87} +(-5.38115 + 9.32042i) q^{89} +(-0.807543 - 1.39871i) q^{91} +(2.63701 + 7.02731i) q^{93} +(26.3037 + 9.57378i) q^{95} +(-2.09832 + 11.9002i) q^{97} +(13.4431 - 11.7426i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9}+O(q^{10}) $ 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9	$ 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9} - 9 q^{13} + 3 q^{15} - 3 q^{21} - 45 q^{25} + 15 q^{27} + 6 q^{29} - 9 q^{31} + 6 q^{33} + 6 q^{35} + 30 q^{39} + 9 q^{41} + 9 q^{43} - 21 q^{45} - 27 q^{47} - 108 q^{51} - 84 q^{53} - 57 q^{57} - 66 q^{59} + 3 q^{63} + 30 q^{65} + 63 q^{67} + 42 q^{69} + 42 q^{71} + 3 q^{75} - 9 q^{77} + 36 q^{79} + 3 q^{81} + 12 q^{83} + 18 q^{85} + 39 q^{87} + 12 q^{89} + 21 q^{93} + 120 q^{95} + 18 q^{97} + 39 q^{99}+O(q^{100}) $ 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9 - 9 * q^13 + 3 * q^15 - 3 * q^21 - 45 * q^25 + 15 * q^27 + 6 * q^29 - 9 * q^31 + 6 * q^33 + 6 * q^35 + 30 * q^39 + 9 * q^41 + 9 * q^43 - 21 * q^45 - 27 * q^47 - 108 * q^51 - 84 * q^53 - 57 * q^57 - 66 * q^59 + 3 * q^63 + 30 * q^65 + 63 * q^67 + 42 * q^69 + 42 * q^71 + 3 * q^75 - 9 * q^77 + 36 * q^79 + 3 * q^81 + 12 * q^83 + 18 * q^85 + 39 * q^87 + 12 * q^89 + 21 * q^93 + 120 * q^95 + 18 * q^97 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$	$1$

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
$3$	−0.576212	+	1.63340i	−0.332676	+	0.943041i
$3$	−0.576212	+	1.63340i	−0.332676	+	0.943041i
$4$		0			0
$5$	0.746163	+	4.23170i	0.333694	+	1.89247i	0.439761	+	0.898115i	$0.355063\pi$
$5$	0.746163	+	4.23170i	0.333694	+	1.89247i	−0.106067	+	0.994359i	$0.533826\pi$
$6$		0			0
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$8$		0			0
$9$	−2.33596	−	1.88236i	−0.778653	−	0.627455i
$10$		0			0
$11$	−1.03318	+	5.85945i	−0.311515	+	1.76669i	0.279614	+	0.960113i	$0.409794\pi$
$11$	−1.03318	+	5.85945i	−0.311515	+	1.76669i	−0.591129	+	0.806577i	$0.701318\pi$
$12$		0			0
$13$	−1.51769	−	0.552392i	−0.420930	−	0.153206i	0.122866	−	0.992423i	$-0.460791\pi$
$13$	−1.51769	−	0.552392i	−0.420930	−	0.153206i	−0.543796	+	0.839217i	$0.683014\pi$
$14$		0			0
$15$	−7.34199	−	1.21958i	−1.89569	−	0.314894i
$16$		0			0
$17$	1.15541	+	2.00122i	0.280227	+	0.485368i	0.971441	−	0.237283i	$-0.0762568\pi$
$17$	1.15541	+	2.00122i	0.280227	+	0.485368i	−0.691213	+	0.722651i	$0.742923\pi$
$18$		0			0
$19$	3.25715	−	5.64155i	0.747242	−	1.29426i	−0.201898	−	0.979407i	$-0.564711\pi$
$19$	3.25715	−	5.64155i	0.747242	−	1.29426i	0.949140	−	0.314855i	$-0.101956\pi$
$20$		0			0
$21$	−1.49133	+	0.880871i	−0.325435	+	0.192222i
$22$		0			0
$23$	4.79887	−	4.02673i	1.00063	−	0.839632i	0.0135621	−	0.999908i	$-0.495683\pi$
$23$	4.79887	−	4.02673i	1.00063	−	0.839632i	0.987072	+	0.160276i	$0.0512385\pi$
$24$		0			0
$25$	−12.6521	+	4.60497i	−2.53041	+	0.920995i
$26$		0			0
$27$	4.42065	−	2.73090i	0.850755	−	0.525562i
$28$		0			0
$29$	2.53931	−	0.924234i	0.471538	−	0.171626i	−0.0953108	−	0.995448i	$-0.530384\pi$
$29$	2.53931	−	0.924234i	0.471538	−	0.171626i	0.566849	+	0.823822i	$0.308162\pi$
$30$		0			0
$31$	3.31963	−	2.78550i	0.596223	−	0.500291i	−0.294006	−	0.955804i	$-0.594989\pi$
$31$	3.31963	−	2.78550i	0.596223	−	0.500291i	0.890229	+	0.455513i	$0.150544\pi$
$32$		0			0
$33$	−8.97546	−	5.06387i	−1.56243	−	0.881507i
$34$		0			0
$35$	−2.14849	+	3.72129i	−0.363161	+	0.629014i
$36$		0			0
$37$	2.11243	+	3.65884i	0.347282	+	0.601510i	0.985766	−	0.168125i	$-0.0537714\pi$
$37$	2.11243	+	3.65884i	0.347282	+	0.601510i	−0.638484	+	0.769635i	$0.720438\pi$
$38$		0			0
$39$	1.77678	−	2.16068i	0.284513	−	0.345986i
$40$		0			0
$41$	−1.36630	−	0.497294i	−0.213381	−	0.0776643i	0.233118	−	0.972448i	$-0.425107\pi$
$41$	−1.36630	−	0.497294i	−0.213381	−	0.0776643i	−0.446499	+	0.894784i	$0.647329\pi$
$42$		0			0
$43$	−0.462038	+	2.62035i	−0.0704601	+	0.399599i	0.929097	+	0.369836i	$0.120586\pi$
$43$	−0.462038	+	2.62035i	−0.0704601	+	0.399599i	−0.999557	+	0.0297627i	$0.990525\pi$
$44$		0			0
$45$	6.22260	−	11.2896i	0.927610	−	1.68296i
$46$		0			0
$47$	−5.85590	−	4.91368i	−0.854171	−	0.716734i	0.106533	−	0.994309i	$-0.466025\pi$
$47$	−5.85590	−	4.91368i	−0.854171	−	0.716734i	−0.960704	+	0.277575i	$0.910469\pi$
$48$		0			0
$49$	0.173648	+	0.984808i	0.0248069	+	0.140687i
$50$		0			0
$51$	−3.93455	+	0.734107i	−0.550947	+	0.102796i
$52$		0			0
$53$	−10.4703			−1.43821			−0.719106	−	0.694901i	$-0.755448\pi$
$53$	−10.4703			−1.43821			−0.719106	+	0.694901i	$0.755448\pi$
$54$		0			0
$55$	−25.5663			−3.44736
$56$		0			0
$57$	7.33808	+	8.57095i	0.971952	+	1.13525i
$58$		0			0
$59$	−0.550759	−	3.12351i	−0.0717027	−	0.406646i	−0.999442	−	0.0334162i	$-0.989361\pi$
$59$	−0.550759	−	3.12351i	−0.0717027	−	0.406646i	0.927739	−	0.373230i	$-0.121750\pi$
$60$		0			0
$61$	0.329725	+	0.276672i	0.0422170	+	0.0354242i	0.663652	−	0.748041i	$-0.269006\pi$
$61$	0.329725	+	0.276672i	0.0422170	+	0.0354242i	−0.621435	+	0.783466i	$0.713450\pi$
$62$		0			0
$63$	−0.579488	−	2.94350i	−0.0730086	−	0.370846i
$64$		0			0
$65$	1.20512	−	6.83456i	0.149476	−	0.847723i
$66$		0			0
$67$	6.64079	+	2.41705i	0.811301	+	0.295290i	0.714161	−	0.699981i	$-0.246808\pi$
$67$	6.64079	+	2.41705i	0.811301	+	0.295290i	0.0971400	+	0.995271i	$0.469031\pi$
$68$		0			0
$69$	3.81208	+	10.1587i	0.458920	+	1.22296i
$70$		0			0
$71$	7.87452	+	13.6391i	0.934534	+	1.61866i	0.775464	+	0.631392i	$0.217516\pi$
$71$	7.87452	+	13.6391i	0.934534	+	1.61866i	0.159070	+	0.987267i	$0.449150\pi$
$72$		0			0
$73$	1.86339	−	3.22749i	0.218093	−	0.377749i	−0.736132	−	0.676838i	$-0.763350\pi$
$73$	1.86339	−	3.22749i	0.218093	−	0.377749i	0.954225	+	0.299089i	$0.0966829\pi$
$74$		0			0
$75$	−0.231469	−	23.3193i	−0.0267277	−	2.69268i
$76$		0			0
$77$	−4.55784	+	3.82448i	−0.519414	+	0.435840i
$78$		0			0
$79$	−14.1595	+	5.15363i	−1.59307	+	0.579829i	−0.977992	−	0.208641i	$-0.933096\pi$
$79$	−14.1595	+	5.15363i	−1.59307	+	0.579829i	−0.615074	+	0.788470i	$0.710874\pi$
$80$		0			0
$81$	1.91341	+	8.79425i	0.212601	+	0.977139i
$82$		0			0
$83$	14.0933	−	5.12954i	1.54694	−	0.563041i	0.579244	−	0.815154i	$-0.303348\pi$
$83$	14.0933	−	5.12954i	1.54694	−	0.563041i	0.967698	+	0.252114i	$0.0811257\pi$
$84$		0			0
$85$	−7.60646	+	6.38258i	−0.825036	+	0.692287i
$86$		0			0
$87$	0.0464566	+	4.68025i	0.00498067	+	0.501776i
$88$		0			0
$89$	−5.38115	+	9.32042i	−0.570401	+	0.987963i	0.426124	+	0.904665i	$0.359879\pi$
$89$	−5.38115	+	9.32042i	−0.570401	+	0.987963i	−0.996525	+	0.0832980i	$0.973455\pi$
$90$		0			0
$91$	−0.807543	−	1.39871i	−0.0846535	−	0.146624i
$92$		0			0
$93$	2.63701	+	7.02731i	0.273445	+	0.728698i
$94$		0			0
$95$	26.3037	+	9.57378i	2.69871	+	0.982249i
$96$		0			0
$97$	−2.09832	+	11.9002i	−0.213052	+	1.20828i	0.671202	+	0.741274i	$0.265778\pi$
$97$	−2.09832	+	11.9002i	−0.213052	+	1.20828i	−0.884255	+	0.467005i	$0.845333\pi$
$98$		0			0
$99$	13.4431	−	11.7426i	1.35108	−	1.18018i
$100$		0			0
$101$	4.81980	+	4.04429i	0.479588	+	0.402422i	0.850277	−	0.526335i	$-0.176434\pi$
$101$	4.81980	+	4.04429i	0.479588	+	0.402422i	−0.370690	+	0.928757i	$0.620879\pi$
$102$		0			0
$103$	−1.76037	−	9.98355i	−0.173454	−	0.983708i	−0.939913	−	0.341414i	$-0.889094\pi$
$103$	−1.76037	−	9.98355i	−0.173454	−	0.983708i	0.766459	−	0.642294i	$-0.222017\pi$
$104$		0			0
$105$	−4.84036	−	5.65359i	−0.472371	−	0.551734i
$106$		0			0
$107$	−2.94318			−0.284528			−0.142264	−	0.989829i	$-0.545438\pi$
$107$	−2.94318			−0.284528			−0.142264	+	0.989829i	$0.545438\pi$
$108$		0			0
$109$	3.87482			0.371140			0.185570	−	0.982631i	$-0.440587\pi$
$109$	3.87482			0.371140			0.185570	+	0.982631i	$0.440587\pi$
$110$		0			0
$111$	−7.19354	+	1.34217i	−0.682781	+	0.127393i
$112$		0			0
$113$	−0.339442	−	1.92507i	−0.0319320	−	0.181096i	0.964670	−	0.263460i	$-0.0848638\pi$
$113$	−0.339442	−	1.92507i	−0.0319320	−	0.181096i	−0.996602	+	0.0823648i	$0.973753\pi$
$114$		0			0
$115$	20.6207	+	17.3028i	1.92289	+	1.61349i
$116$		0			0
$117$	2.50545	+	4.14720i	0.231629	+	0.383409i
$118$		0			0
$119$	−0.401269	+	2.27571i	−0.0367842	+	0.208614i
$120$		0			0
$121$	−22.9290	−	8.34549i	−2.08446	−	0.758681i
$122$		0			0
$123$	1.59956	−	1.94517i	0.144227	−	0.175390i
$124$		0			0
$125$	−18.1849	−	31.4972i	−1.62651	−	2.81719i
$126$		0			0
$127$	4.87148	−	8.43764i	0.432274	−	0.748720i	−0.564795	−	0.825231i	$-0.691045\pi$
$127$	4.87148	−	8.43764i	0.432274	−	0.748720i	0.997069	+	0.0765114i	$0.0243782\pi$
$128$		0			0
$129$	−4.01383	−	2.26457i	−0.353398	−	0.199384i
$130$		0			0
$131$	15.1860	−	12.7425i	1.32680	−	1.11332i	0.341991	−	0.939703i	$-0.388899\pi$
$131$	15.1860	−	12.7425i	1.32680	−	1.11332i	0.984813	−	0.173618i	$-0.0555456\pi$
$132$		0			0
$133$	6.12145	−	2.22802i	0.530797	−	0.193194i
$134$		0			0
$135$	14.8549	+	16.6692i	1.27850	+	1.43465i
$136$		0			0
$137$	−5.13365	+	1.86849i	−0.438597	+	0.159636i	−0.551875	−	0.833927i	$-0.686087\pi$
$137$	−5.13365	+	1.86849i	−0.438597	+	0.159636i	0.113278	+	0.993563i	$0.463865\pi$
$138$		0			0
$139$	4.94296	−	4.14764i	0.419257	−	0.351798i	−0.408624	−	0.912703i	$-0.633991\pi$
$139$	4.94296	−	4.14764i	0.419257	−	0.351798i	0.827880	+	0.560905i	$0.189547\pi$
$140$		0			0
$141$	11.4002	−	6.73367i	0.960072	−	0.567078i
$142$		0			0
$143$	4.80475	−	8.32208i	0.401794	−	0.695927i
$144$		0			0
$145$	5.80582	+	10.0560i	0.482147	+	0.835103i
$146$		0			0
$147$	−1.70864	−	0.283822i	−0.140926	−	0.0234093i
$148$		0			0
$149$	15.1044	+	5.49754i	1.23740	+	0.450376i	0.876125	−	0.482085i	$-0.160120\pi$
$149$	15.1044	+	5.49754i	1.23740	+	0.450376i	0.361272	+	0.932460i	$0.382342\pi$
$150$		0			0
$151$	−1.23812	+	7.02174i	−0.100757	+	0.571421i	0.892074	+	0.451890i	$0.149250\pi$
$151$	−1.23812	+	7.02174i	−0.100757	+	0.571421i	−0.992831	+	0.119531i	$0.961861\pi$
$152$		0			0
$153$	1.06805	−	6.84967i	0.0863466	−	0.553763i
$154$		0			0
$155$	14.2644	+	11.9692i	1.14574	+	0.961393i
$156$		0			0
$157$	1.01778	+	5.77212i	0.0812277	+	0.460665i	0.998107	+	0.0615007i	$0.0195887\pi$
$157$	1.01778	+	5.77212i	0.0812277	+	0.460665i	−0.916879	+	0.399164i	$0.869300\pi$
$158$		0			0
$159$	6.03314	−	17.1022i	0.478459	−	1.35629i
$160$		0			0
$161$	6.26448			0.493711
$162$		0			0
$163$	1.96647			0.154026			0.0770129	−	0.997030i	$-0.475462\pi$
$163$	1.96647			0.154026			0.0770129	+	0.997030i	$0.475462\pi$
$164$		0			0
$165$	14.7316	−	41.7599i	1.14686	−	3.25101i
$166$		0			0
$167$	0.191500	+	1.08605i	0.0148187	+	0.0840413i	0.991320	−	0.131469i	$-0.0419695\pi$
$167$	0.191500	+	1.08605i	0.0148187	+	0.0840413i	−0.976501	+	0.215511i	$0.930858\pi$
$168$		0			0
$169$	−7.96035	−	6.67952i	−0.612334	−	0.513810i
$170$		0			0
$171$	−18.2280	+	7.04729i	−1.39393	+	0.538920i
$172$		0			0
$173$	−1.04938	+	5.95135i	−0.0797831	+	0.452473i	0.918578	+	0.395240i	$0.129339\pi$
$173$	−1.04938	+	5.95135i	−0.0797831	+	0.452473i	−0.998361	+	0.0572323i	$0.981772\pi$
$174$		0			0
$175$	−12.6521	−	4.60497i	−0.956406	−	0.348103i
$176$		0			0
$177$	5.41928	+	0.900197i	0.407338	+	0.0676630i
$178$		0			0
$179$	4.98023	+	8.62601i	0.372240	+	0.644738i	0.989910	−	0.141699i	$-0.0452566\pi$
$179$	4.98023	+	8.62601i	0.372240	+	0.644738i	−0.617670	+	0.786437i	$0.711923\pi$
$180$		0			0
$181$	−1.31158	+	2.27172i	−0.0974887	+	0.168855i	−0.910645	−	0.413191i	$-0.864414\pi$
$181$	−1.31158	+	2.27172i	−0.0974887	+	0.168855i	0.813156	+	0.582046i	$0.197748\pi$
$182$		0			0
$183$	−0.641907	+	0.379149i	−0.0474511	+	0.0280275i
$184$		0			0
$185$	−13.9069	+	11.6693i	−1.02246	+	0.857942i
$186$		0			0
$187$	−12.9198	+	4.70243i	−0.944790	+	0.343875i
$188$		0			0
$189$	5.14181	+	0.749548i	0.374011	+	0.0545216i
$190$		0			0
$191$	−6.42357	+	2.33799i	−0.464793	+	0.169171i	−0.563792	−	0.825917i	$-0.690658\pi$
$191$	−6.42357	+	2.33799i	−0.464793	+	0.169171i	0.0989991	+	0.995088i	$0.468436\pi$
$192$		0			0
$193$	3.09673	−	2.59847i	0.222908	−	0.187042i	−0.524494	−	0.851414i	$-0.675746\pi$
$193$	3.09673	−	2.59847i	0.222908	−	0.187042i	0.747402	+	0.664372i	$0.231301\pi$
$194$		0			0
$195$	10.4691	+	5.90659i	0.749710	+	0.422980i
$196$		0			0
$197$	0.622974	−	1.07902i	0.0443851	−	0.0768772i	−0.842979	−	0.537946i	$-0.819200\pi$
$197$	0.622974	−	1.07902i	0.0443851	−	0.0768772i	0.887364	+	0.461069i	$0.152534\pi$
$198$		0			0
$199$	8.38152	+	14.5172i	0.594150	+	1.02910i	0.993666	+	0.112372i	$0.0358450\pi$
$199$	8.38152	+	14.5172i	0.594150	+	1.02910i	−0.399516	+	0.916726i	$0.630822\pi$
$200$		0			0
$201$	−7.77450	+	9.45430i	−0.548371	+	0.666855i
$202$		0			0
$203$	2.53931	+	0.924234i	0.178225	+	0.0648685i
$204$		0			0
$205$	1.08491	−	6.15285i	0.0757736	−	0.429734i
$206$		0			0
$207$	−18.7897	+	0.373054i	−1.30598	+	0.0259291i
$208$		0			0
$209$	29.6912	+	24.9138i	2.05378	+	1.72333i
$210$		0			0
$211$	−1.17661	−	6.67290i	−0.0810013	−	0.459381i	−0.998148	−	0.0608316i	$-0.980625\pi$
$211$	−1.17661	−	6.67290i	−0.0810013	−	0.459381i	0.917147	−	0.398550i	$-0.130486\pi$
$212$		0			0
$213$	−26.8154	+	5.00320i	−1.83736	+	0.342814i
$214$		0			0
$215$	−11.4333			−0.779743
$216$		0			0
$217$	4.33347			0.294175
$218$		0			0
$219$	4.19806	+	4.90337i	0.283678	+	0.331339i
$220$		0			0
$221$	−0.648084	−	3.67547i	−0.0435948	−	0.247239i
$222$		0			0
$223$	−6.73612	−	5.65228i	−0.451084	−	0.378504i	0.388754	−	0.921342i	$-0.372906\pi$
$223$	−6.73612	−	5.65228i	−0.451084	−	0.378504i	−0.839838	+	0.542837i	$0.817350\pi$
$224$		0			0
$225$	38.2229	+	13.0588i	2.54820	+	0.870584i
$226$		0			0
$227$	−3.17896	+	18.0288i	−0.210995	+	1.19661i	0.676728	+	0.736233i	$0.263397\pi$
$227$	−3.17896	+	18.0288i	−0.210995	+	1.19661i	−0.887723	+	0.460379i	$0.847714\pi$
$228$		0			0
$229$	10.1588	+	3.69749i	0.671310	+	0.244337i	0.655112	−	0.755532i	$-0.272621\pi$
$229$	10.1588	+	3.69749i	0.671310	+	0.244337i	0.0161982	+	0.999869i	$0.494844\pi$
$230$		0			0
$231$	−3.62061	−	9.64847i	−0.238218	−	0.634823i
$232$		0			0
$233$	1.72993	+	2.99632i	0.113331	+	0.196296i	0.917112	−	0.398631i	$-0.130514\pi$
$233$	1.72993	+	2.99632i	0.113331	+	0.196296i	−0.803780	+	0.594926i	$0.797181\pi$
$234$		0			0
$235$	16.4238	−	28.4468i	1.07137	−	1.85567i
$236$		0			0
$237$	−0.259047	−	26.0976i	−0.0168269	−	1.69522i
$238$		0			0
$239$	18.1962	−	15.2684i	1.17701	−	0.987632i	0.177020	−	0.984207i	$-0.443354\pi$
$239$	18.1962	−	15.2684i	1.17701	−	0.987632i	0.999994	−	0.00342526i	$-0.00109030\pi$
$240$		0			0
$241$	19.0055	−	6.91743i	1.22425	−	0.445591i	0.352626	−	0.935764i	$-0.385289\pi$
$241$	19.0055	−	6.91743i	1.22425	−	0.445591i	0.871625	+	0.490174i	$0.163067\pi$
$242$		0			0
$243$	−15.4670	−	1.94200i	−0.992210	−	0.124580i
$244$		0			0
$245$	−4.03784	+	1.46965i	−0.257968	+	0.0938927i
$246$		0			0
$247$	−8.05968	+	6.76288i	−0.512825	+	0.430312i
$248$		0			0
$249$	0.257837	+	25.9756i	0.0163397	+	1.64614i
$250$		0			0
$251$	−1.56182	+	2.70516i	−0.0985814	+	0.170748i	−0.911098	−	0.412191i	$-0.864764\pi$
$251$	−1.56182	+	2.70516i	−0.0985814	+	0.170748i	0.812516	+	0.582938i	$0.198097\pi$
$252$		0			0
$253$	18.6363	+	32.2791i	1.17166	+	2.02937i
$254$		0			0
$255$	−6.04233	−	16.1021i	−0.378386	−	1.00835i
$256$		0			0
$257$	−23.4639	−	8.54017i	−1.46364	−	0.532721i	−0.517274	−	0.855820i	$-0.673053\pi$
$257$	−23.4639	−	8.54017i	−1.46364	−	0.532721i	−0.946365	+	0.323098i	$0.895276\pi$
$258$		0			0
$259$	−0.733640	+	4.16068i	−0.0455862	+	0.258532i
$260$		0			0
$261$	−7.67147	−	2.62094i	−0.474852	−	0.162232i
$262$		0			0
$263$	6.85306	+	5.75040i	0.422578	+	0.354585i	0.829143	−	0.559037i	$-0.188829\pi$
$263$	6.85306	+	5.75040i	0.422578	+	0.354585i	−0.406565	+	0.913622i	$0.633273\pi$
$264$		0			0
$265$	−7.81258	−	44.3073i	−0.479923	−	2.72178i
$266$		0			0
$267$	−12.1232	−	14.1601i	−0.741931	−	0.866583i
$268$		0			0
$269$	−0.747163			−0.0455553			−0.0227777	−	0.999741i	$-0.507251\pi$
$269$	−0.747163			−0.0455553			−0.0227777	+	0.999741i	$0.507251\pi$
$270$		0			0
$271$	14.1029			0.856691			0.428346	−	0.903615i	$-0.359097\pi$
$271$	14.1029			0.856691			0.428346	+	0.903615i	$0.359097\pi$
$272$		0			0
$273$	2.74996	−	0.513086i	0.166435	−	0.0310534i
$274$		0			0
$275$	−13.9108	−	78.8918i	−0.838850	−	4.75736i
$276$		0			0
$277$	7.22869	+	6.06559i	0.434330	+	0.364446i	0.833583	−	0.552395i	$-0.186286\pi$
$277$	7.22869	+	6.06559i	0.434330	+	0.364446i	−0.399253	+	0.916841i	$0.630730\pi$
$278$		0			0
$279$	−12.9978	+	0.258061i	−0.778161	+	0.0154497i
$280$		0			0
$281$	−2.84757	+	16.1494i	−0.169872	+	0.963392i	0.774026	+	0.633154i	$0.218240\pi$
$281$	−2.84757	+	16.1494i	−0.169872	+	0.963392i	−0.943898	+	0.330238i	$0.892871\pi$
$282$		0			0
$283$	−3.82892	−	1.39361i	−0.227606	−	0.0828416i	0.225700	−	0.974197i	$-0.427533\pi$
$283$	−3.82892	−	1.39361i	−0.227606	−	0.0828416i	−0.453305	+	0.891355i	$0.649755\pi$
$284$		0			0
$285$	−30.7943	+	37.4479i	−1.82410	+	2.21822i
$286$		0			0
$287$	−0.726995	−	1.25919i	−0.0429132	−	0.0743278i
$288$		0			0
$289$	5.83007	−	10.0980i	0.342945	−	0.593999i
$290$		0			0
$291$	−18.2286	−	10.2844i	−1.06858	−	0.602883i
$292$		0			0
$293$	−25.7341	+	21.5935i	−1.50340	+	1.26150i	−0.627898	+	0.778296i	$0.716084\pi$
$293$	−25.7341	+	21.5935i	−1.50340	+	1.26150i	−0.875505	+	0.483209i	$0.839471\pi$
$294$		0			0
$295$	12.8068	−	4.66129i	0.745641	−	0.271391i
$296$		0			0
$297$	11.4343	+	28.7241i	0.663483	+	1.66674i
$298$		0			0
$299$	−9.50751	+	3.46045i	−0.549834	+	0.200123i
$300$		0			0
$301$	−2.03827	+	1.71031i	−0.117484	+	0.0985806i
$302$		0			0
$303$	−9.38315	+	5.54227i	−0.539048	+	0.318395i
$304$		0			0
$305$	−0.924765	+	1.60174i	−0.0529519	+	0.0917154i
$306$		0			0
$307$	−6.11330	−	10.5885i	−0.348904	−	0.604320i	0.637151	−	0.770739i	$-0.280113\pi$
$307$	−6.11330	−	10.5885i	−0.348904	−	0.604320i	−0.986055	+	0.166419i	$0.946780\pi$
$308$		0			0
$309$	17.3214	+	2.87726i	0.985381	+	0.163682i
$310$		0			0
$311$	10.1123	+	3.68059i	0.573418	+	0.208707i	0.612421	−	0.790532i	$-0.290196\pi$
$311$	10.1123	+	3.68059i	0.573418	+	0.208707i	−0.0390026	+	0.999239i	$0.512418\pi$
$312$		0			0
$313$	4.14164	−	23.4884i	0.234099	−	1.32764i	−0.610403	−	0.792091i	$-0.708992\pi$
$313$	4.14164	−	23.4884i	0.234099	−	1.32764i	0.844502	−	0.535552i	$-0.179896\pi$
$314$		0			0
$315$	12.0236	−	4.64855i	0.677454	−	0.261916i
$316$		0			0
$317$	−9.36673	−	7.85962i	−0.526088	−	0.441440i	0.340660	−	0.940186i	$-0.389349\pi$
$317$	−9.36673	−	7.85962i	−0.526088	−	0.441440i	−0.866748	+	0.498746i	$0.833794\pi$
$318$		0			0
$319$	2.79194	+	15.8339i	0.156318	+	0.886526i
$320$		0			0
$321$	1.69590	−	4.80738i	0.0946557	−	0.268322i
$322$		0			0
$323$	15.0534			0.837591
$324$		0			0
$325$	21.7456			1.20623
$326$		0			0
$327$	−2.23272	+	6.32911i	−0.123470	+	0.350001i
$328$		0			0
$329$	−1.32742	−	7.52820i	−0.0731833	−	0.415043i
$330$		0			0
$331$	−17.9599	−	15.0701i	−0.987166	−	0.828330i	−0.00201066	−	0.999998i	$-0.500640\pi$
$331$	−17.9599	−	15.0701i	−0.987166	−	0.828330i	−0.985155	+	0.171668i	$0.945084\pi$
$332$		0			0
$333$	1.95272	−	12.5233i	0.107008	−	0.686271i
$334$		0			0
$335$	−5.27312	+	29.9053i	−0.288101	+	1.63390i
$336$		0			0
$337$	−21.0259	−	7.65280i	−1.14535	−	0.416874i	−0.301509	−	0.953463i	$-0.597490\pi$
$337$	−21.0259	−	7.65280i	−1.14535	−	0.416874i	−0.843844	+	0.536589i	$0.819713\pi$
$338$		0			0
$339$	3.34000	+	0.554807i	0.181404	+	0.0301330i
$340$		0			0
$341$	12.8917	+	22.3291i	0.698126	+	1.20919i
$342$		0			0
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$		0			0
$345$	−40.1442	+	23.7116i	−2.16129	+	1.27659i
$346$		0			0
$347$	−27.2722	+	22.8841i	−1.46405	+	1.22848i	−0.542598	+	0.839993i	$0.682559\pi$
$347$	−27.2722	+	22.8841i	−1.46405	+	1.22848i	−0.921452	+	0.388491i	$0.872996\pi$
$348$		0			0
$349$	−2.46532	+	0.897304i	−0.131966	+	0.0480316i	−0.407159	−	0.913357i	$-0.633480\pi$
$349$	−2.46532	+	0.897304i	−0.131966	+	0.0480316i	0.275193	+	0.961389i	$0.411258\pi$
$350$		0			0
$351$	−8.21769	+	1.70272i	−0.438628	+	0.0908842i
$352$		0			0
$353$	12.2293	−	4.45111i	0.650901	−	0.236909i	0.00459810	−	0.999989i	$-0.498536\pi$
$353$	12.2293	−	4.45111i	0.650901	−	0.236909i	0.646303	+	0.763081i	$0.276314\pi$
$354$		0			0
$355$	−51.8408	+	43.4996i	−2.75142	+	2.30872i
$356$		0			0
$357$	−3.48591	−	1.96672i	−0.184494	−	0.104090i
$358$		0			0
$359$	−0.586187	+	1.01530i	−0.0309377	+	0.0535857i	−0.881080	−	0.472968i	$-0.843183\pi$
$359$	−0.586187	+	1.01530i	−0.0309377	+	0.0535857i	0.850142	+	0.526554i	$0.176516\pi$
$360$		0			0
$361$	−11.7181	−	20.2963i	−0.616742	−	1.06823i
$362$		0			0
$363$	26.8435	−	32.6434i	1.40892	−	1.71333i
$364$		0			0
$365$	15.0482	+	5.47708i	0.787656	+	0.286684i
$366$		0			0
$367$	−4.05503	+	22.9972i	−0.211671	+	1.20045i	0.674920	+	0.737891i	$0.264178\pi$
$367$	−4.05503	+	22.9972i	−0.211671	+	1.20045i	−0.886591	+	0.462554i	$0.846933\pi$
$368$		0			0
$369$	2.25554	+	3.73354i	0.117419	+	0.194360i
$370$		0			0
$371$	−8.02074	−	6.73020i	−0.416416	−	0.349415i
$372$		0			0
$373$	2.94945	+	16.7271i	0.152717	+	0.866098i	0.960844	+	0.277091i	$0.0893702\pi$
$373$	2.94945	+	16.7271i	0.152717	+	0.866098i	−0.808127	+	0.589008i	$0.799519\pi$
$374$		0			0
$375$	61.9257	−	11.5541i	3.19783	−	0.596650i
$376$		0			0
$377$	−4.36442			−0.224779
$378$		0			0
$379$	2.67128			0.137214			0.0686071	−	0.997644i	$-0.478145\pi$
$379$	2.67128			0.137214			0.0686071	+	0.997644i	$0.478145\pi$
$380$		0			0
$381$	10.9750	+	12.8189i	0.562266	+	0.656733i
$382$		0			0
$383$	−1.38798	−	7.87161i	−0.0709223	−	0.402220i	−0.999516	−	0.0311213i	$-0.990092\pi$
$383$	−1.38798	−	7.87161i	−0.0709223	−	0.402220i	0.928593	−	0.371099i	$-0.121019\pi$
$384$		0			0
$385$	−19.5850	−	16.4337i	−0.998141	−	0.837540i
$386$		0			0
$387$	6.01175	−	5.25130i	0.305594	−	0.266939i
$388$		0			0
$389$	1.60841	−	9.12173i	0.0815495	−	0.462490i	−0.916498	−	0.400038i	$-0.868997\pi$
$389$	1.60841	−	9.12173i	0.0815495	−	0.462490i	0.998048	−	0.0624521i	$-0.0198921\pi$
$390$		0			0
$391$	13.6030	+	4.95110i	0.687936	+	0.250388i
$392$		0			0
$393$	12.0633	+	32.1471i	0.608511	+	1.62161i
$394$		0			0
$395$	−32.3739	−	56.0732i	−1.62891	−	2.82135i
$396$		0			0
$397$	12.4993	−	21.6494i	0.627322	−	1.08655i	−0.360765	−	0.932657i	$-0.617484\pi$
$397$	12.4993	−	21.6494i	0.627322	−	1.08655i	0.988087	−	0.153897i	$-0.0491824\pi$
$398$		0			0
$399$	0.111992	+	11.2826i	0.00560659	+	0.564834i
$400$		0			0
$401$	18.6747	−	15.6699i	0.932571	−	0.782520i	−0.0437065	−	0.999044i	$-0.513917\pi$
$401$	18.6747	−	15.6699i	0.932571	−	0.782520i	0.976277	+	0.216525i	$0.0694722\pi$
$402$		0			0
$403$	−6.57684	+	2.39377i	−0.327616	+	0.119242i
$404$		0			0
$405$	−35.7869	+	14.6589i	−1.77827	+	0.728407i
$406$		0			0
$407$	−23.6213	+	8.59745i	−1.17086	+	0.426160i
$408$		0			0
$409$	26.7337	−	22.4323i	1.32190	−	1.10920i	0.335999	−	0.941862i	$-0.390926\pi$
$409$	26.7337	−	22.4323i	1.32190	−	1.10920i	0.985899	−	0.167342i	$-0.0535185\pi$
$410$		0			0
$411$	−0.0939199	−	9.46192i	−0.00463273	−	0.466722i
$412$		0			0
$413$	1.58585	−	2.74677i	0.0780345	−	0.135160i
$414$		0			0
$415$	32.2226	+	55.8112i	1.58174	+	2.73966i
$416$		0			0
$417$	3.92654	+	10.4637i	0.192283	+	0.512411i
$418$		0			0
$419$	−12.4652	−	4.53696i	−0.608965	−	0.221645i	0.0190852	−	0.999818i	$-0.493925\pi$
$419$	−12.4652	−	4.53696i	−0.608965	−	0.221645i	−0.628050	+	0.778173i	$0.716147\pi$
$420$		0			0
$421$	−2.41781	+	13.7121i	−0.117837	+	0.668287i	0.867469	+	0.497491i	$0.165745\pi$
$421$	−2.41781	+	13.7121i	−0.117837	+	0.668287i	−0.985306	+	0.170796i	$0.945366\pi$
$422$		0			0
$423$	4.42980	+	22.5011i	0.215384	+	1.09404i
$424$		0			0
$425$	−23.8339	−	19.9990i	−1.15611	−	0.970093i
$426$		0			0
$427$	0.0747426	+	0.423886i	0.00361705	+	0.0205133i
$428$		0			0
$429$	10.8247	+	12.6433i	0.522620	+	0.610426i
$430$		0			0
$431$	−12.3509			−0.594923			−0.297461	−	0.954734i	$-0.596140\pi$
$431$	−12.3509			−0.594923			−0.297461	+	0.954734i	$0.596140\pi$
$432$		0			0
$433$	7.30667			0.351136			0.175568	−	0.984467i	$-0.443824\pi$
$433$	7.30667			0.351136			0.175568	+	0.984467i	$0.443824\pi$
$434$		0			0
$435$	−19.7708	+	3.68882i	−0.947936	+	0.176865i
$436$		0			0
$437$	−7.08637	−	40.1888i	−0.338987	−	1.92249i
$438$		0			0
$439$	18.4143	+	15.4515i	0.878868	+	0.737458i	0.965946	−	0.258743i	$-0.0833084\pi$
$439$	18.4143	+	15.4515i	0.878868	+	0.737458i	−0.0870777	+	0.996202i	$0.527753\pi$
$440$		0			0
$441$	1.44813	−	2.62734i	0.0689587	−	0.125111i
$442$		0			0
$443$	−3.58744	+	20.3454i	−0.170444	+	0.966638i	0.772827	+	0.634616i	$0.218842\pi$
$443$	−3.58744	+	20.3454i	−0.170444	+	0.966638i	−0.943272	+	0.332022i	$0.892269\pi$
$444$		0			0
$445$	−43.4564	−	15.8168i	−2.06003	−	0.749791i
$446$		0			0
$447$	−17.6830	+	21.5036i	−0.836375	+	1.01709i
$448$		0			0
$449$	−8.44135	−	14.6208i	−0.398372	−	0.690000i	0.595153	−	0.803612i	$-0.297091\pi$
$449$	−8.44135	−	14.6208i	−0.398372	−	0.690000i	−0.993525	+	0.113612i	$0.963758\pi$
$450$		0			0
$451$	4.32550	−	7.49199i	0.203680	−	0.352784i
$452$		0			0
$453$	−10.7559	−	6.06835i	−0.505354	−	0.285116i
$454$		0			0
$455$	5.31635	−	4.46094i	0.249234	−	0.209132i
$456$		0			0
$457$	4.46096	−	1.62366i	0.208675	−	0.0759514i	−0.235568	−	0.971858i	$-0.575695\pi$
$457$	4.46096	−	1.62366i	0.208675	−	0.0759514i	0.444243	+	0.895906i	$0.353473\pi$
$458$		0			0
$459$	10.5728	+	5.69141i	0.493496	+	0.265652i
$460$		0			0
$461$	3.78251	−	1.37672i	0.176169	−	0.0641203i	−0.252430	−	0.967615i	$-0.581230\pi$
$461$	3.78251	−	1.37672i	0.176169	−	0.0641203i	0.428599	+	0.903495i	$0.359007\pi$
$462$		0			0
$463$	−8.73275	+	7.32765i	−0.405845	+	0.340545i	−0.822748	−	0.568406i	$-0.807560\pi$
$463$	−8.73275	+	7.32765i	−0.405845	+	0.340545i	0.416902	+	0.908951i	$0.363116\pi$
$464$		0			0
$465$	−27.7698	+	16.4026i	−1.28779	+	0.760650i
$466$		0			0
$467$	16.2553	−	28.1550i	0.752206	−	1.30286i	−0.194545	−	0.980894i	$-0.562323\pi$
$467$	16.2553	−	28.1550i	0.752206	−	1.30286i	0.946751	−	0.321965i	$-0.104344\pi$
$468$		0			0
$469$	3.53349	+	6.12018i	0.163161	+	0.282604i
$470$		0			0
$471$	−10.0146	−	1.66353i	−0.461449	−	0.0766513i
$472$		0			0
$473$	−14.8764	−	5.41457i	−0.684018	−	0.248962i
$474$		0			0
$475$	−15.2305	+	86.3764i	−0.698823	+	3.96322i
$476$		0			0
$477$	24.4583	+	19.7090i	1.11987	+	0.902413i
$478$		0			0
$479$	−9.76186	−	8.19117i	−0.446031	−	0.374264i	0.391930	−	0.919995i	$-0.371808\pi$
$479$	−9.76186	−	8.19117i	−0.446031	−	0.374264i	−0.837960	+	0.545731i	$0.816252\pi$
$480$		0			0
$481$	−1.18489	−	6.71986i	−0.0540265	−	0.306399i
$482$		0			0
$483$	−3.60967	+	10.2324i	−0.164246	+	0.465589i
$484$		0			0
$485$	−51.9236			−2.35773
$486$		0			0
$487$	−24.6674			−1.11779			−0.558893	−	0.829240i	$-0.688774\pi$
$487$	−24.6674			−1.11779			−0.558893	+	0.829240i	$0.688774\pi$
$488$		0			0
$489$	−1.13310	+	3.21202i	−0.0512407	+	0.145253i
$490$		0			0
$491$	2.73026	+	15.4841i	0.123215	+	0.698788i	0.982352	+	0.187042i	$0.0598900\pi$
$491$	2.73026	+	15.4841i	0.123215	+	0.698788i	−0.859137	+	0.511746i	$0.828999\pi$
$492$		0			0
$493$	4.78354	+	4.01386i	0.215440	+	0.180775i
$494$		0			0
$495$	59.7219	+	48.1252i	2.68430	+	2.16307i
$496$		0			0
$497$	−2.73479	+	15.5098i	−0.122672	+	0.695709i
$498$		0			0
$499$	27.7556	+	10.1022i	1.24251	+	0.452236i	0.877864	−	0.478910i	$-0.158968\pi$
$499$	27.7556	+	10.1022i	1.24251	+	0.452236i	0.364645	+	0.931147i	$0.381190\pi$
$500$		0			0
$501$	−1.88430	−	0.313001i	−0.0841842	−	0.0139839i
$502$		0			0
$503$	−13.9961	−	24.2419i	−0.624055	−	1.08089i	−0.988723	−	0.149757i	$-0.952151\pi$
$503$	−13.9961	−	24.2419i	−0.624055	−	1.08089i	0.364668	−	0.931138i	$-0.381183\pi$
$504$		0			0
$505$	−13.5179	+	23.4136i	−0.601537	+	1.04189i
$506$		0			0
$507$	15.4972	−	9.15357i	0.688253	−	0.406524i
$508$		0			0
$509$	−2.38954	+	2.00507i	−0.105915	+	0.0888729i	−0.694207	−	0.719775i	$-0.744245\pi$
$509$	−2.38954	+	2.00507i	−0.105915	+	0.0888729i	0.588292	+	0.808648i	$0.299800\pi$
$510$		0			0
$511$	3.50203	−	1.27463i	0.154921	−	0.0563865i
$512$		0			0
$513$	−1.00779	−	33.8343i	−0.0444951	−	1.49382i
$514$		0			0
$515$	40.9338	−	14.8987i	1.80376	−	0.656515i
$516$		0			0
$517$	34.8416	−	29.2356i	1.53233	−	1.28578i
$518$		0			0
$519$	−9.11624	−	5.14330i	−0.400158	−	0.225766i
$520$		0			0
$521$	4.50675	−	7.80593i	0.197444	−	0.341984i	−0.750255	−	0.661149i	$-0.770069\pi$
$521$	4.50675	−	7.80593i	0.197444	−	0.341984i	0.947699	+	0.319165i	$0.103402\pi$
$522$		0			0
$523$	−11.0715	−	19.1765i	−0.484124	−	0.838528i	0.515709	−	0.856764i	$-0.327528\pi$
$523$	−11.0715	−	19.1765i	−0.484124	−	0.838528i	−0.999834	+	0.0182357i	$0.994195\pi$
$524$		0			0
$525$	14.8120	−	18.0124i	0.646449	−	0.786124i
$526$		0			0
$527$	9.40994	+	3.42494i	0.409903	+	0.149193i
$528$		0			0
$529$	2.82070	−	15.9970i	0.122639	−	0.695521i
$530$		0			0
$531$	−4.59303	+	8.33312i	−0.199321	+	0.361627i
$532$		0			0
$533$	1.79892	+	1.50947i	0.0779198	+	0.0653825i
$534$		0			0
$535$	−2.19609	−	12.4547i	−0.0949453	−	0.538462i
$536$		0			0
$537$	−16.9594	+	3.16427i	−0.731850	+	0.136548i
$538$		0			0
$539$	−5.94984			−0.256278
$540$		0			0
$541$	29.6884			1.27641			0.638203	−	0.769868i	$-0.279678\pi$
$541$	29.6884			1.27641			0.638203	+	0.769868i	$0.279678\pi$
$542$		0			0
$543$	−2.95487	−	3.45131i	−0.126805	−	0.148110i
$544$		0			0
$545$	2.89125	+	16.3971i	0.123847	+	0.702374i
$546$		0			0
$547$	−28.2258	−	23.6843i	−1.20685	−	1.01267i	−0.999408	−	0.0344183i	$-0.989042\pi$
$547$	−28.2258	−	23.6843i	−1.20685	−	1.01267i	−0.207441	−	0.978248i	$-0.566513\pi$
$548$		0			0
$549$	−0.249426	−	1.26696i	−0.0106453	−	0.0540724i
$550$		0			0
$551$	3.05681	−	17.3360i	0.130225	−	0.738540i
$552$		0			0
$553$	−14.1595	−	5.15363i	−0.602122	−	0.219155i
$554$		0			0
$555$	−11.0472	−	29.4394i	−0.468928	−	1.24963i
$556$		0			0
$557$	6.63788	+	11.4971i	0.281256	+	0.487150i	0.971694	−	0.236241i	$-0.0759156\pi$
$557$	6.63788	+	11.4971i	0.281256	+	0.487150i	−0.690438	+	0.723391i	$0.742582\pi$
$558$		0			0
$559$	2.14869	−	3.72163i	0.0908798	−	0.157408i
$560$		0			0
$561$	−0.236367	−	23.8127i	−0.00997944	−	1.00537i
$562$		0			0
$563$	−0.946305	+	0.794044i	−0.0398820	+	0.0334650i	−0.662511	−	0.749052i	$-0.730509\pi$
$563$	−0.946305	+	0.794044i	−0.0398820	+	0.0334650i	0.622629	+	0.782517i	$0.286065\pi$
$564$		0			0
$565$	7.89305	−	2.87284i	0.332063	−	0.120861i
$566$		0			0
$567$	−4.18708	+	7.96670i	−0.175841	+	0.334570i
$568$		0			0
$569$	−9.57856	+	3.48631i	−0.401554	+	0.146154i	−0.534899	−	0.844916i	$-0.679650\pi$
$569$	−9.57856	+	3.48631i	−0.401554	+	0.146154i	0.133345	+	0.991070i	$0.457428\pi$
$570$		0			0
$571$	23.9256	−	20.0759i	1.00125	−	0.840151i	0.0140958	−	0.999901i	$-0.495513\pi$
$571$	23.9256	−	20.0759i	1.00125	−	0.840151i	0.987158	+	0.159749i	$0.0510686\pi$
$572$		0			0
$573$	−0.117519	−	11.8394i	−0.00490943	−	0.494598i
$574$		0			0
$575$	−42.1726	+	73.0451i	−1.75872	+	3.04619i
$576$		0			0
$577$	−14.7350	−	25.5218i	−0.613427	−	1.06249i	−0.990658	−	0.136368i	$-0.956457\pi$
$577$	−14.7350	−	25.5218i	−0.613427	−	1.06249i	0.377231	−	0.926119i	$-0.376876\pi$
$578$		0			0
$579$	2.45995	+	6.55545i	0.102232	+	0.272435i
$580$		0			0
$581$	14.0933	+	5.12954i	0.584689	+	0.212809i
$582$		0			0
$583$	10.8177	−	61.3504i	0.448025	−	2.54087i
$584$		0			0
$585$	−15.6802	+	13.6968i	−0.648298	+	0.566292i
$586$		0			0
$587$	3.15113	+	2.64411i	0.130061	+	0.109134i	0.705498	−	0.708712i	$-0.250723\pi$
$587$	3.15113	+	2.64411i	0.130061	+	0.109134i	−0.575437	+	0.817846i	$0.695168\pi$
$588$		0			0
$589$	−4.90201	−	27.8007i	−0.201984	−	1.14551i
$590$		0			0
$591$	1.40351	+	1.63931i	0.0577325	+	0.0674322i
$592$		0			0
$593$	−11.5456			−0.474122			−0.237061	−	0.971495i	$-0.576184\pi$
$593$	−11.5456			−0.474122			−0.237061	+	0.971495i	$0.576184\pi$
$594$		0			0
$595$	−9.92952			−0.407071
$596$		0			0
$597$	−28.5419	+	5.32534i	−1.16814	+	0.217952i
$598$		0			0
$599$	−0.503425	−	2.85506i	−0.0205694	−	0.116655i	0.972794	−	0.231671i	$-0.0744192\pi$
$599$	−0.503425	−	2.85506i	−0.0205694	−	0.116655i	−0.993364	+	0.115016i	$0.963308\pi$
$600$		0			0
$601$	−4.45529	−	3.73844i	−0.181735	−	0.152494i	0.547382	−	0.836883i	$-0.315625\pi$
$601$	−4.45529	−	3.73844i	−0.181735	−	0.152494i	−0.729117	+	0.684389i	$0.760069\pi$
$602$		0			0
$603$	−10.9628	−	18.1465i	−0.446441	−	0.738983i
$604$		0			0
$605$	18.2068	−	103.256i	0.740212	−	4.19795i
$606$		0			0
$607$	10.2253	+	3.72170i	0.415032	+	0.151059i	0.541092	−	0.840963i	$-0.318011\pi$
$607$	10.2253	+	3.72170i	0.415032	+	0.151059i	−0.126060	+	0.992023i	$0.540233\pi$
$608$		0			0
$609$	−2.97282	+	3.61514i	−0.120465	+	0.146493i
$610$		0			0
$611$	6.17313	+	10.6922i	0.249738	+	0.432559i
$612$		0			0
$613$	−18.5809	+	32.1831i	−0.750476	+	1.29986i	0.197115	+	0.980380i	$0.436843\pi$
$613$	−18.5809	+	32.1831i	−0.750476	+	1.29986i	−0.947592	+	0.319483i	$0.896491\pi$
$614$		0			0
$615$	9.42489	+	5.31744i	0.380048	+	0.214420i
$616$		0			0
$617$	1.85060	−	1.55284i	0.0745023	−	0.0625148i	−0.604776	−	0.796396i	$-0.706737\pi$
$617$	1.85060	−	1.55284i	0.0745023	−	0.0625148i	0.679278	+	0.733881i	$0.262293\pi$
$618$		0			0
$619$	29.0884	−	10.5873i	1.16916	−	0.425540i	0.316800	−	0.948492i	$-0.397392\pi$
$619$	29.0884	−	10.5873i	1.16916	−	0.425540i	0.852362	+	0.522952i	$0.175169\pi$
$620$		0			0
$621$	10.2175	−	30.9060i	0.410016	−	1.24022i
$622$		0			0
$623$	−10.1132	+	3.68092i	−0.405179	+	0.147473i
$624$		0			0
$625$	68.1475	−	57.1825i	2.72590	−	2.28730i
$626$		0			0
$627$	−57.8026	+	34.1417i	−2.30841	+	1.36349i
$628$		0			0
$629$	−4.88144	+	8.45490i	−0.194636	+	0.337119i
$630$		0			0
$631$	−15.3271	−	26.5474i	−0.610164	−	1.05683i	−0.991212	−	0.132280i	$-0.957770\pi$
$631$	−15.3271	−	26.5474i	−0.610164	−	1.05683i	0.381049	−	0.924555i	$-0.375563\pi$
$632$		0			0
$633$	11.5775	+	1.92313i	0.460163	+	0.0764377i
$634$		0			0
$635$	39.3405	+	14.3188i	1.56118	+	0.568223i
$636$		0			0
$637$	0.280457	−	1.59055i	0.0111121	−	0.0630199i
$638$		0			0
$639$	7.27914	−	46.6830i	0.287958	−	1.84675i
$640$		0			0
$641$	13.6949	+	11.4914i	0.540915	+	0.453882i	0.871851	−	0.489772i	$-0.162920\pi$
$641$	13.6949	+	11.4914i	0.540915	+	0.453882i	−0.330936	+	0.943653i	$0.607364\pi$
$642$		0			0
$643$	−1.48923	−	8.44583i	−0.0587294	−	0.333071i	0.941260	−	0.337683i	$-0.109643\pi$
$643$	−1.48923	−	8.44583i	−0.0587294	−	0.333071i	−0.999989	+	0.00461178i	$0.998532\pi$
$644$		0			0
$645$	6.58799	−	18.6751i	0.259402	−	0.735330i
$646$		0			0
$647$	28.5878			1.12390			0.561951	−	0.827171i	$-0.310051\pi$
$647$	28.5878			1.12390			0.561951	+	0.827171i	$0.310051\pi$
$648$		0			0
$649$	18.8711			0.740754
$650$		0			0
$651$	−2.49700	+	7.07827i	−0.0978651	+	0.277419i
$652$		0			0
$653$	4.87999	+	27.6758i	0.190969	+	1.08304i	0.918044	+	0.396479i	$0.129768\pi$
$653$	4.87999	+	27.6758i	0.190969	+	1.08304i	−0.727075	+	0.686558i	$0.759121\pi$
$654$		0			0
$655$	65.2538	+	54.7544i	2.54968	+	2.13943i
$656$		0			0
$657$	−10.4281	+	4.03170i	−0.406840	+	0.157292i
$658$		0			0
$659$	−1.12611	+	6.38651i	−0.0438672	+	0.248783i	−0.998854	−	0.0478659i	$-0.984758\pi$
$659$	−1.12611	+	6.38651i	−0.0438672	+	0.248783i	0.954987	+	0.296649i	$0.0958691\pi$
$660$		0			0
$661$	25.3242	+	9.21727i	0.984998	+	0.358510i	0.783782	−	0.621037i	$-0.213288\pi$
$661$	25.3242	+	9.21727i	0.984998	+	0.358510i	0.201217	+	0.979547i	$0.435510\pi$
$662$		0			0
$663$	6.37692	+	1.05927i	0.247659	+	0.0411387i
$664$		0			0
$665$	13.9959	+	24.2417i	0.542739	+	0.940051i
$666$		0			0
$667$	8.46419	−	14.6604i	0.327735	−	0.567653i
$668$		0			0
$669$	13.1138	−	7.74584i	0.507010	−	0.299471i
$670$		0			0
$671$	−1.96181	+	1.64615i	−0.0757349	+	0.0635491i
$672$		0			0
$673$	13.0132	−	4.73641i	0.501621	−	0.182575i	−0.0788018	−	0.996890i	$-0.525109\pi$
$673$	13.0132	−	4.73641i	0.501621	−	0.182575i	0.580423	+	0.814315i	$0.302887\pi$
$674$		0			0
$675$	−43.3546	+	54.9085i	−1.66872	+	2.11343i
$676$		0			0
$677$	−12.9189	+	4.70209i	−0.496514	+	0.180716i	−0.578125	−	0.815948i	$-0.696215\pi$
$677$	−12.9189	+	4.70209i	−0.496514	+	0.180716i	0.0816117	+	0.996664i	$0.473993\pi$
$678$		0			0
$679$	−9.25669	+	7.76729i	−0.355239	+	0.298081i
$680$		0			0
$681$	−27.6164	−	15.5809i	−1.05826	−	0.597061i
$682$		0			0
$683$	11.2572	−	19.4981i	0.430745	−	0.746073i	−0.566192	−	0.824273i	$-0.691584\pi$
$683$	11.2572	−	19.4981i	0.430745	−	0.746073i	0.996938	+	0.0782004i	$0.0249174\pi$
$684$		0			0
$685$	−11.7374	−	20.3298i	−0.448465	−	0.776764i
$686$		0			0
$687$	−11.8931	+	14.4627i	−0.453749	+	0.551788i
$688$		0			0
$689$	15.8907	+	5.78373i	0.605387	+	0.220343i
$690$		0			0
$691$	−0.494088	+	2.80211i	−0.0187960	+	0.106597i	−0.992762	−	0.120095i	$-0.961680\pi$
$691$	−0.494088	+	2.80211i	−0.0187960	+	0.106597i	0.973966	+	0.226692i	$0.0727912\pi$
$692$		0			0
$693$	17.8460	−	0.354317i	0.677913	−	0.0134594i
$694$		0			0
$695$	21.2398	+	17.8223i	0.805672	+	0.676039i
$696$		0			0
$697$	−0.583441	−	3.30886i	−0.0220994	−	0.125332i
$698$		0			0
$699$	−5.89099	+	1.09914i	−0.222818	+	0.0415732i
$700$		0			0
$701$	−23.6761			−0.894236			−0.447118	−	0.894475i	$-0.647550\pi$
$701$	−23.6761			−0.894236			−0.447118	+	0.894475i	$0.647550\pi$
$702$		0			0
$703$	27.5221			1.03801
$704$		0			0
$705$	37.0013	+	43.2179i	1.39355	+	1.62768i
$706$		0			0
$707$	1.09256	+	6.19621i	0.0410899	+	0.233033i
$708$		0			0
$709$	26.9382	+	22.6038i	1.01168	+	0.848903i	0.988560	−	0.150829i	$-0.0481943\pi$
$709$	26.9382	+	22.6038i	1.01168	+	0.848903i	0.0231239	+	0.999733i	$0.492639\pi$
$710$		0			0
$711$	42.7770	+	14.6146i	1.60426	+	0.548092i
$712$		0			0
$713$	4.71402	−	26.7345i	0.176541	−	1.00122i
$714$		0			0
$715$	38.8016	+	14.1226i	1.45110	+	0.528157i
$716$		0			0
$717$	14.4545	+	38.5194i	0.539813	+	1.43853i
$718$		0			0
$719$	−4.29080	−	7.43188i	−0.160020	−	0.277162i	0.774856	−	0.632138i	$-0.217822\pi$
$719$	−4.29080	−	7.43188i	−0.160020	−	0.277162i	−0.934876	+	0.354976i	$0.884489\pi$
$720$		0			0
$721$	5.06878	−	8.77938i	0.188771	−	0.326961i
$722$		0			0
$723$	0.347705	+	35.0294i	0.0129313	+	1.30276i
$724$		0			0
$725$	−27.8714	+	23.3869i	−1.03512	+	0.868569i
$726$		0			0
$727$	3.87782	−	1.41141i	0.143821	−	0.0523464i	−0.269107	−	0.963110i	$-0.586729\pi$
$727$	3.87782	−	1.41141i	0.143821	−	0.0523464i	0.412927	+	0.910764i	$0.364506\pi$
$728$		0			0
$729$	12.0843	−	24.1447i	0.447568	−	0.894250i
$730$		0			0
$731$	−5.77774	+	2.10293i	−0.213698	+	0.0777795i
$732$		0			0
$733$	9.18425	−	7.70650i	0.339228	−	0.284646i	−0.457219	−	0.889354i	$-0.651155\pi$
$733$	9.18425	−	7.70650i	0.339228	−	0.284646i	0.796447	+	0.604708i	$0.206710\pi$
$734$		0			0
$735$	−0.0738722	−	7.44222i	−0.00272482	−	0.274510i
$736$		0			0
$737$	−21.0237	+	36.4141i	−0.774417	+	1.34133i
$738$		0			0
$739$	−23.0303	−	39.8896i	−0.847183	−	1.46736i	−0.883712	−	0.468031i	$-0.844964\pi$
$739$	−23.0303	−	39.8896i	−0.847183	−	1.46736i	0.0365293	−	0.999333i	$-0.488370\pi$
$740$		0			0
$741$	−6.40236	−	17.0615i	−0.235197	−	0.626770i
$742$		0			0
$743$	46.7214	+	17.0052i	1.71404	+	0.623860i	0.997297	−	0.0734753i	$-0.0234090\pi$
$743$	46.7214	+	17.0052i	1.71404	+	0.623860i	0.716745	+	0.697336i	$0.245631\pi$
$744$		0			0
$745$	−11.9936	+	68.0191i	−0.439412	+	2.49203i
$746$		0			0
$747$	−42.5771	−	14.5463i	−1.55781	−	0.532223i
$748$		0			0
$749$	−2.25461	−	1.89184i	−0.0823816	−	0.0691263i
$750$		0			0
$751$	3.62378	+	20.5515i	0.132234	+	0.749935i	0.976746	+	0.214399i	$0.0687792\pi$
$751$	3.62378	+	20.5515i	0.132234	+	0.749935i	−0.844513	+	0.535536i	$0.820110\pi$
$752$		0			0
$753$	−3.51865	−	4.10982i	−0.128227	−	0.149770i
$754$		0			0
$755$	−30.6377			−1.11502
$756$		0			0
$757$	41.1296			1.49488			0.747440	−	0.664329i	$-0.231283\pi$
$757$	41.1296			1.49488			0.747440	+	0.664329i	$0.231283\pi$
$758$		0			0
$759$	−63.4630	+	11.8409i	−2.30356	+	0.429797i
$760$		0			0
$761$	−6.67302	−	37.8446i	−0.241897	−	1.37186i	−0.827591	−	0.561332i	$-0.810289\pi$
$761$	−6.67302	−	37.8446i	−0.241897	−	1.37186i	0.585694	−	0.810532i	$-0.300822\pi$
$762$		0			0
$763$	2.96828	+	2.49069i	0.107459	+	0.0901689i
$764$		0			0
$765$	29.7827	−	0.591310i	1.07680	−	0.0213789i
$766$		0			0
$767$	−0.889524	+	5.04474i	−0.0321188	+	0.182155i
$768$		0			0
$769$	23.9736	+	8.72566i	0.864508	+	0.314655i	0.735941	−	0.677045i	$-0.236740\pi$
$769$	23.9736	+	8.72566i	0.864508	+	0.314655i	0.128567	+	0.991701i	$0.458962\pi$
$770$		0			0
$771$	27.4697	−	33.4049i	0.989296	−	1.20305i
$772$		0			0
$773$	−5.15298	−	8.92523i	−0.185340	−	0.321018i	0.758351	−	0.651846i	$-0.226005\pi$
$773$	−5.15298	−	8.92523i	−0.185340	−	0.321018i	−0.943691	+	0.330828i	$0.892672\pi$
$774$		0			0
$775$	−29.1730	+	50.5291i	−1.04793	+	1.81506i
$776$		0			0
$777$	−6.37330	−	3.59576i	−0.228641	−	0.128997i
$778$		0			0
$779$	−7.25577	+	6.08832i	−0.259965	+	0.218137i
$780$		0			0
$781$	−88.0532	+	32.0487i	−3.15079	+	1.14679i
$782$		0			0
$783$	8.70142	−	11.0203i	0.310963	−	0.393834i
$784$		0			0
$785$	−23.6664	+	8.61388i	−0.844692	+	0.307443i
$786$		0			0
$787$	−35.6426	+	29.9077i	−1.27052	+	1.06609i	−0.276043	+	0.961145i	$0.589023\pi$
$787$	−35.6426	+	29.9077i	−1.27052	+	1.06609i	−0.994478	+	0.104948i	$0.966532\pi$
$788$		0			0
$789$	−13.3415	+	7.88031i	−0.474970	+	0.280546i
$790$		0			0
$791$	0.977385	−	1.69288i	0.0347518	−	0.0601919i
$792$		0			0
$793$	−0.347587	−	0.602039i	−0.0123432	−	0.0213790i
$794$		0			0
$795$	76.8731	+	12.7694i	2.72641	+	0.452884i
$796$		0			0
$797$	19.7747	+	7.19740i	0.700455	+	0.254945i	0.667605	−	0.744515i	$-0.267319\pi$
$797$	19.7747	+	7.19740i	0.700455	+	0.254945i	0.0328500	+	0.999460i	$0.489542\pi$
$798$		0			0
$799$	3.06743	−	17.3963i	0.108518	−	0.615436i
$800$		0			0
$801$	30.1146	−	11.6428i	1.06405	−	0.411380i
$802$		0			0
$803$	16.9861	+	14.2530i	0.599426	+	0.502978i
$804$		0			0
$805$	4.67433	+	26.5094i	0.164748	+	0.934334i
$806$		0			0
$807$	0.430524	−	1.22041i	0.0151552	−	0.0429605i
$808$		0			0
$809$	46.7887			1.64500			0.822502	−	0.568763i	$-0.192578\pi$
$809$	46.7887			1.64500			0.822502	+	0.568763i	$0.192578\pi$
$810$		0			0
$811$	−11.8213			−0.415102			−0.207551	−	0.978224i	$-0.566549\pi$
$811$	−11.8213			−0.415102			−0.207551	+	0.978224i	$0.566549\pi$
$812$		0			0
$813$	−8.12627	+	23.0356i	−0.285001	+	0.807895i
$814$		0			0
$815$	1.46731	+	8.32151i	0.0513975	+	0.291490i
$816$		0			0
$817$	13.2779	+	11.1415i	0.464535	+	0.389791i
$818$		0			0
$819$	−0.746487	+	4.78741i	−0.0260844	+	0.167286i
$820$		0			0
$821$	−5.28672	+	29.9825i	−0.184508	+	1.04640i	0.742078	+	0.670314i	$0.233840\pi$
$821$	−5.28672	+	29.9825i	−0.184508	+	1.04640i	−0.926586	+	0.376083i	$0.877271\pi$
$822$		0			0
$823$	−43.3494	−	15.7779i	−1.51106	−	0.549982i	−0.552166	−	0.833734i	$-0.686199\pi$
$823$	−43.3494	−	15.7779i	−1.51106	−	0.549982i	−0.958898	+	0.283752i	$0.908421\pi$
$824$		0			0
$825$	136.877	+	22.7367i	4.76545	+	0.791589i
$826$		0			0
$827$	20.6275	+	35.7279i	0.717290	+	1.24238i	0.962070	+	0.272804i	$0.0879510\pi$
$827$	20.6275	+	35.7279i	0.717290	+	1.24238i	−0.244780	+	0.969579i	$0.578716\pi$
$828$		0			0
$829$	17.0709	−	29.5676i	0.592896	−	1.02693i	−0.400944	−	0.916103i	$-0.631318\pi$
$829$	17.0709	−	29.5676i	0.592896	−	1.02693i	0.993840	−	0.110824i	$-0.0353490\pi$
$830$		0			0
$831$	−14.0728	+	8.31224i	−0.488179	+	0.288349i
$832$		0			0
$833$	−1.77019	+	1.48536i	−0.0613333	+	0.0514648i
$834$		0			0
$835$	−4.45296	+	1.62074i	−0.154101	+	0.0560882i
$836$		0			0
$837$	7.06800	−	21.3793i	0.244306	−	0.738977i
$838$		0			0
$839$	46.3404	−	16.8665i	1.59985	−	0.582297i	0.620451	−	0.784245i	$-0.286949\pi$
$839$	46.3404	−	16.8665i	1.59985	−	0.582297i	0.979396	+	0.201948i	$0.0647272\pi$
$840$		0			0
$841$	−16.6214	+	13.9470i	−0.573152	+	0.480931i
$842$		0			0
$843$	−24.7375	−	13.9567i	−0.852006	−	0.480694i
$844$		0			0
$845$	22.3260	−	38.6698i	0.768039	−	1.33028i
$846$		0			0
$847$	−12.2003	−	21.1315i	−0.419207	−	0.726087i
$848$		0			0
$849$	4.48259	−	5.45112i	0.153842	−	0.187082i
$850$		0			0
$851$	24.8705	+	9.05211i	0.852549	+	0.310302i
$852$		0			0
$853$	5.83051	−	33.0665i	0.199633	−	1.13217i	−0.706032	−	0.708180i	$-0.749517\pi$
$853$	5.83051	−	33.0665i	0.199633	−	1.13217i	0.905665	−	0.423994i	$-0.139372\pi$
$854$		0			0
$855$	−43.4231	−	71.8772i	−1.48504	−	2.45815i
$856$		0			0
$857$	−42.3221	−	35.5125i	−1.44570	−	1.21308i	−0.935647	−	0.352936i	$-0.885183\pi$
$857$	−42.3221	−	35.5125i	−1.44570	−	1.21308i	−0.510048	−	0.860146i	$-0.670372\pi$
$858$		0			0
$859$	−7.24998	−	41.1167i	−0.247366	−	1.40288i	−0.814933	−	0.579555i	$-0.803226\pi$
$859$	−7.24998	−	41.1167i	−0.247366	−	1.40288i	0.567567	−	0.823327i	$-0.307885\pi$
$860$		0			0
$861$	2.47566	−	0.461908i	0.0843703	−	0.0157418i
$862$		0			0
$863$	−28.5145			−0.970646			−0.485323	−	0.874335i	$-0.661298\pi$
$863$	−28.5145			−0.970646			−0.485323	+	0.874335i	$0.661298\pi$
$864$		0			0
$865$	−25.9673			−0.882916
$866$		0			0
$867$	13.1346	+	15.3414i	0.446075	+	0.521021i
$868$		0			0
$869$	−15.5681	−	88.2913i	−0.528113	−	2.99508i
$870$		0			0
$871$	−8.74346	−	7.33664i	−0.296261	−	0.248592i
$872$		0			0
$873$	27.3021	−	23.8485i	0.924034	−	0.807150i
$874$		0			0
$875$	6.31555	−	35.8173i	0.213505	−	1.21084i
$876$		0			0
$877$	18.6037	+	6.77118i	0.628201	+	0.228646i	0.636448	−	0.771320i	$-0.280403\pi$
$877$	18.6037	+	6.77118i	0.628201	+	0.228646i	−0.00824727	+	0.999966i	$0.502625\pi$
$878$		0			0
$879$	−20.4424	−	54.4764i	−0.689504	−	1.83744i
$880$		0			0
$881$	19.6711	+	34.0714i	0.662738	+	1.14790i	0.979893	+	0.199522i	$0.0639390\pi$
$881$	19.6711	+	34.0714i	0.662738	+	1.14790i	−0.317155	+	0.948374i	$0.602728\pi$
$882$		0			0
$883$	3.36773	−	5.83308i	0.113333	−	0.196299i	−0.803779	−	0.594928i	$-0.797181\pi$
$883$	3.36773	−	5.83308i	0.113333	−	0.196299i	0.917112	+	0.398629i	$0.130514\pi$
$884$		0			0
$885$	0.234300	+	23.6045i	0.00787591	+	0.793455i
$886$		0			0
$887$	−13.5619	+	11.3797i	−0.455362	+	0.382094i	−0.841421	−	0.540380i	$-0.818281\pi$
$887$	−13.5619	+	11.3797i	−0.455362	+	0.382094i	0.386059	+	0.922474i	$0.373836\pi$
$888$		0			0
$889$	9.15538	−	3.33229i	0.307062	−	0.111761i
$890$		0			0
$891$	−53.5063	+	2.12548i	−1.79253	+	0.0712063i
$892$		0			0
$893$	−46.7944	+	17.0318i	−1.56591	+	0.569946i
$894$		0			0
$895$	−32.7866	+	27.5112i	−1.09594	+	0.919599i
$896$		0			0
$897$	−0.173940	−	17.5235i	−0.00580768	−	0.585092i
$898$		0			0
$899$	5.85512	−	10.1414i	0.195279	−	0.338234i
$900$		0			0
$901$	−12.0975	−	20.9535i	−0.403026	−	0.698062i
$902$		0			0
$903$	−1.61914	−	4.31480i	−0.0538815	−	0.143587i
$904$		0			0
$905$	−10.5919	−	3.85513i	−0.352086	−	0.128149i
$906$		0			0
$907$	8.82181	−	50.0310i	0.292923	−	1.66125i	−0.382601	−	0.923914i	$-0.624972\pi$
$907$	8.82181	−	50.0310i	0.292923	−	1.66125i	0.675524	−	0.737338i	$-0.263917\pi$
$908$		0			0
$909$	−3.64602	−	18.5199i	−0.120931	−	0.614267i
$910$		0			0
$911$	3.69890	+	3.10375i	0.122550	+	0.102832i	0.702003	−	0.712174i	$-0.252289\pi$
$911$	3.69890	+	3.10375i	0.122550	+	0.102832i	−0.579453	+	0.815006i	$0.696734\pi$
$912$		0			0
$913$	15.4954	+	87.8787i	0.512822	+	2.90836i
$914$		0			0
$915$	−2.08341	−	2.43345i	−0.0688755	−	0.0804473i
$916$		0			0
$917$	19.8239			0.654642
$918$		0			0
$919$	52.0821			1.71803			0.859014	−	0.511951i	$-0.171077\pi$
$919$	52.0821			1.71803			0.859014	+	0.511951i	$0.171077\pi$
$920$		0			0
$921$	20.8178	−	3.88418i	0.685971	−	0.127988i
$922$		0			0
$923$	−4.41693	−	25.0496i	−0.145385	−	0.824519i
$924$		0			0
$925$	−43.5755	−	36.5642i	−1.43275	−	1.20222i
$926$		0			0
$927$	−14.6805	+	26.6348i	−0.482172	+	0.874802i
$928$		0			0
$929$	2.64737	−	15.0140i	0.0868574	−	0.492593i	−0.910083	−	0.414426i	$-0.863982\pi$
$929$	2.64737	−	15.0140i	0.0868574	−	0.492593i	0.996940	−	0.0781667i	$-0.0249066\pi$
$930$		0			0
$931$	6.12145	+	2.22802i	0.200622	+	0.0730205i
$932$		0			0
$933$	−11.8387	+	14.3966i	−0.387582	+	0.471325i
$934$		0			0
$935$	−29.5395	−	51.1640i	−0.966046	−	1.67324i
$936$		0			0
$937$	−6.14164	+	10.6376i	−0.200638	+	0.347516i	−0.948734	−	0.316075i	$-0.897635\pi$
$937$	−6.14164	+	10.6376i	−0.200638	+	0.347516i	0.748096	+	0.663591i	$0.230968\pi$
$938$		0			0
$939$	35.9794	+	20.2992i	1.17414	+	0.662441i
$940$		0			0
$941$	−2.85568	+	2.39620i	−0.0930925	+	0.0781138i	−0.688146	−	0.725572i	$-0.741575\pi$
$941$	−2.85568	+	2.39620i	−0.0930925	+	0.0781138i	0.595054	+	0.803686i	$0.297131\pi$
$942$		0			0
$943$	−8.55919	+	3.11529i	−0.278726	+	0.101448i
$944$		0			0
$945$	0.664762	+	22.3179i	0.0216247	+	0.726000i
$946$		0			0
$947$	−4.38514	+	1.59606i	−0.142498	+	0.0518649i	−0.412284	−	0.911055i	$-0.635269\pi$
$947$	−4.38514	+	1.59606i	−0.142498	+	0.0518649i	0.269787	+	0.962920i	$0.413047\pi$
$948$		0			0
$949$	−4.61088	+	3.86899i	−0.149676	+	0.125593i
$950$		0			0
$951$	18.2351	−	10.7708i	0.591313	−	0.349266i
$952$		0			0
$953$	30.0341	−	52.0206i	0.972901	−	1.68511i	0.286206	−	0.958168i	$-0.407606\pi$
$953$	30.0341	−	52.0206i	0.972901	−	1.68511i	0.686695	−	0.726946i	$-0.259061\pi$
$954$		0			0
$955$	−14.6867	−	25.4381i	−0.475250	−	0.823157i
$956$		0			0
$957$	−27.4717	−	4.56333i	−0.888034	−	0.147511i
$958$		0			0
$959$	−5.13365	−	1.86849i	−0.165774	−	0.0603368i
$960$		0			0
$961$	−2.12216	+	12.0354i	−0.0684568	+	0.388238i
$962$		0			0
$963$	6.87515	+	5.54014i	0.221549	+	0.178528i
$964$		0			0
$965$	13.3066	+	11.1656i	0.428354	+	0.359432i
$966$		0			0
$967$	−0.275503	−	1.56246i	−0.00885959	−	0.0502452i	0.980057	−	0.198714i	$-0.0636766\pi$
$967$	−0.275503	−	1.56246i	−0.00885959	−	0.0502452i	−0.988917	+	0.148469i	$0.952565\pi$
$968$		0			0
$969$	−8.67393	+	24.5881i	−0.278647	+	0.789883i
$970$		0			0
$971$	38.9384			1.24959			0.624797	−	0.780788i	$-0.285182\pi$
$971$	38.9384			1.24959			0.624797	+	0.780788i	$0.285182\pi$
$972$		0			0
$973$	6.45258			0.206860
$974$		0			0
$975$	−12.5301	+	35.5191i	−0.401284	+	1.13752i
$976$		0			0
$977$	5.33962	+	30.2825i	0.170830	+	0.968823i	0.942848	+	0.333223i	$0.108136\pi$
$977$	5.33962	+	30.2825i	0.170830	+	0.968823i	−0.772018	+	0.635600i	$0.780753\pi$
$978$		0			0
$979$	−49.0528	−	41.1602i	−1.56774	−	1.31549i
$980$		0			0
$981$	−9.05142	−	7.29382i	−0.288990	−	0.232874i
$982$		0			0
$983$	−0.414038	+	2.34813i	−0.0132058	+	0.0748937i	−0.990698	−	0.136076i	$-0.956551\pi$
$983$	−0.414038	+	2.34813i	−0.0132058	+	0.0748937i	0.977493	+	0.210969i	$0.0676621\pi$
$984$		0			0
$985$	5.03094	+	1.83111i	0.160299	+	0.0583441i
$986$		0			0
$987$	13.0614	+	2.16963i	0.415749	+	0.0690601i
$988$		0			0
$989$	8.33417	+	14.4352i	0.265011	+	0.459013i
$990$		0			0
$991$	−24.3110	+	42.1079i	−0.772264	+	1.33760i	0.164056	+	0.986451i	$0.447542\pi$
$991$	−24.3110	+	42.1079i	−0.772264	+	1.33760i	−0.936320	+	0.351149i	$0.885791\pi$
$992$		0			0
$993$	34.9642	−	20.6520i	1.10956	−	0.655372i
$994$		0			0
$995$	−55.1786	+	46.3003i	−1.74928	+	1.46782i
$996$		0			0
$997$	−24.9880	+	9.09489i	−0.791378	+	0.288038i	−0.705909	−	0.708303i	$-0.749461\pi$
$997$	−24.9880	+	9.09489i	−0.791378	+	0.288038i	−0.0854693	+	0.996341i	$0.527239\pi$
$998$		0			0
$999$	19.3303	+	10.4056i	0.611583	+	0.329219i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bo.a.169.4	yes	54
27.4	even	9	inner	756.2.bo.a.85.4	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bo.a.85.4	✓	54	27.4	even	9	inner
756.2.bo.a.169.4	yes	54	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.576212 + 1.63340i) q^{3} +(0.746163 + 4.23170i) q^{5} +(0.766044 + 0.642788i) q^{7} +(-2.33596 - 1.88236i) q^{9} +O(q^{10})\)	\(q+(-0.576212 + 1.63340i) q^{3} +(0.746163 + 4.23170i) q^{5} +(0.766044 + 0.642788i) q^{7} +(-2.33596 - 1.88236i) q^{9} +(-1.03318 + 5.85945i) q^{11} +(-1.51769 - 0.552392i) q^{13} +(-7.34199 - 1.21958i) q^{15} +(1.15541 + 2.00122i) q^{17} +(3.25715 - 5.64155i) q^{19} +(-1.49133 + 0.880871i) q^{21} +(4.79887 - 4.02673i) q^{23} +(-12.6521 + 4.60497i) q^{25} +(4.42065 - 2.73090i) q^{27} +(2.53931 - 0.924234i) q^{29} +(3.31963 - 2.78550i) q^{31} +(-8.97546 - 5.06387i) q^{33} +(-2.14849 + 3.72129i) q^{35} +(2.11243 + 3.65884i) q^{37} +(1.77678 - 2.16068i) q^{39} +(-1.36630 - 0.497294i) q^{41} +(-0.462038 + 2.62035i) q^{43} +(6.22260 - 11.2896i) q^{45} +(-5.85590 - 4.91368i) q^{47} +(0.173648 + 0.984808i) q^{49} +(-3.93455 + 0.734107i) q^{51} -10.4703 q^{53} -25.5663 q^{55} +(7.33808 + 8.57095i) q^{57} +(-0.550759 - 3.12351i) q^{59} +(0.329725 + 0.276672i) q^{61} +(-0.579488 - 2.94350i) q^{63} +(1.20512 - 6.83456i) q^{65} +(6.64079 + 2.41705i) q^{67} +(3.81208 + 10.1587i) q^{69} +(7.87452 + 13.6391i) q^{71} +(1.86339 - 3.22749i) q^{73} +(-0.231469 - 23.3193i) q^{75} +(-4.55784 + 3.82448i) q^{77} +(-14.1595 + 5.15363i) q^{79} +(1.91341 + 8.79425i) q^{81} +(14.0933 - 5.12954i) q^{83} +(-7.60646 + 6.38258i) q^{85} +(0.0464566 + 4.68025i) q^{87} +(-5.38115 + 9.32042i) q^{89} +(-0.807543 - 1.39871i) q^{91} +(2.63701 + 7.02731i) q^{93} +(26.3037 + 9.57378i) q^{95} +(-2.09832 + 11.9002i) q^{97} +(13.4431 - 11.7426i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9}+O(q^{10}) \) 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9	\( 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9} - 9 q^{13} + 3 q^{15} - 3 q^{21} - 45 q^{25} + 15 q^{27} + 6 q^{29} - 9 q^{31} + 6 q^{33} + 6 q^{35} + 30 q^{39} + 9 q^{41} + 9 q^{43} - 21 q^{45} - 27 q^{47} - 108 q^{51} - 84 q^{53} - 57 q^{57} - 66 q^{59} + 3 q^{63} + 30 q^{65} + 63 q^{67} + 42 q^{69} + 42 q^{71} + 3 q^{75} - 9 q^{77} + 36 q^{79} + 3 q^{81} + 12 q^{83} + 18 q^{85} + 39 q^{87} + 12 q^{89} + 21 q^{93} + 120 q^{95} + 18 q^{97} + 39 q^{99}+O(q^{100}) \) 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9 - 9 * q^13 + 3 * q^15 - 3 * q^21 - 45 * q^25 + 15 * q^27 + 6 * q^29 - 9 * q^31 + 6 * q^33 + 6 * q^35 + 30 * q^39 + 9 * q^41 + 9 * q^43 - 21 * q^45 - 27 * q^47 - 108 * q^51 - 84 * q^53 - 57 * q^57 - 66 * q^59 + 3 * q^63 + 30 * q^65 + 63 * q^67 + 42 * q^69 + 42 * q^71 + 3 * q^75 - 9 * q^77 + 36 * q^79 + 3 * q^81 + 12 * q^83 + 18 * q^85 + 39 * q^87 + 12 * q^89 + 21 * q^93 + 120 * q^95 + 18 * q^97 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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