LMFDB - Embedded newform 1890.2.j.j.631.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(631,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1890.631");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.j (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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			631.2
Root			$-1.62241 - 0.606458i$ of defining polynomial
Character	$\chi$	$=$	1890.631
Dual form			1890.2.j.j.1261.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +1.00000 q^{10} +(-0.285997 - 0.495361i) q^{11} +(0.214003 - 0.370665i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} -5.67282 q^{17} -4.81681 q^{19} +(0.500000 + 0.866025i) q^{20} +(0.285997 - 0.495361i) q^{22} +(-3.88683 + 6.73218i) q^{23} +(-0.500000 - 0.866025i) q^{25} +0.428007 q^{26} +1.00000 q^{28} +(4.45882 + 7.72290i) q^{29} +(-4.24482 + 7.35224i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.83641 - 4.91281i) q^{34} -1.00000 q^{35} +5.95684 q^{37} +(-2.40841 - 4.17148i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(-5.63164 + 9.75429i) q^{41} +(-3.07199 - 5.32085i) q^{43} +0.571993 q^{44} -7.77365 q^{46} +(5.67282 + 9.82562i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.214003 + 0.370665i) q^{52} +5.10083 q^{53} -0.571993 q^{55} +(0.500000 + 0.866025i) q^{56} +(-4.45882 + 7.72290i) q^{58} +(3.16359 - 5.47950i) q^{59} +(2.12241 + 3.67612i) q^{61} -8.48963 q^{62} +1.00000 q^{64} +(-0.214003 - 0.370665i) q^{65} +(5.65322 - 9.79167i) q^{67} +(2.83641 - 4.91281i) q^{68} +(-0.500000 - 0.866025i) q^{70} -15.0224 q^{71} -6.34565 q^{73} +(2.97842 + 5.15878i) q^{74} +(2.40841 - 4.17148i) q^{76} +(-0.285997 + 0.495361i) q^{77} +(-3.67282 - 6.36152i) q^{79} -1.00000 q^{80} -11.2633 q^{82} +(5.10083 + 8.83490i) q^{83} +(-2.83641 + 4.91281i) q^{85} +(3.07199 - 5.32085i) q^{86} +(0.285997 + 0.495361i) q^{88} -8.28797 q^{89} -0.428007 q^{91} +(-3.88683 - 6.73218i) q^{92} +(-5.67282 + 9.82562i) q^{94} +(-2.40841 + 4.17148i) q^{95} +(-2.74482 - 4.75416i) q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 3 q^{7} - 6 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 3 * q^7 - 6 * q^8	$ 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 3 q^{7} - 6 q^{8} + 6 q^{10} - q^{11} + 2 q^{13} + 3 q^{14} - 3 q^{16} - 14 q^{17} - 6 q^{19} + 3 q^{20} + q^{22} - 4 q^{23} - 3 q^{25} + 4 q^{26} + 6 q^{28} + 6 q^{29} - 4 q^{31} + 3 q^{32} - 7 q^{34} - 6 q^{35} + 20 q^{37} - 3 q^{38} - 3 q^{40} + 7 q^{41} - 17 q^{43} + 2 q^{44} - 8 q^{46} + 14 q^{47} - 3 q^{49} + 3 q^{50} + 2 q^{52} + 12 q^{53} - 2 q^{55} + 3 q^{56} - 6 q^{58} + 29 q^{59} + 2 q^{61} - 8 q^{62} + 6 q^{64} - 2 q^{65} + q^{67} + 7 q^{68} - 3 q^{70} - 20 q^{71} + 2 q^{73} + 10 q^{74} + 3 q^{76} - q^{77} - 2 q^{79} - 6 q^{80} + 14 q^{82} + 12 q^{83} - 7 q^{85} + 17 q^{86} + q^{88} - 44 q^{89} - 4 q^{91} - 4 q^{92} - 14 q^{94} - 3 q^{95} + 5 q^{97} - 6 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 3 * q^7 - 6 * q^8 + 6 * q^10 - q^11 + 2 * q^13 + 3 * q^14 - 3 * q^16 - 14 * q^17 - 6 * q^19 + 3 * q^20 + q^22 - 4 * q^23 - 3 * q^25 + 4 * q^26 + 6 * q^28 + 6 * q^29 - 4 * q^31 + 3 * q^32 - 7 * q^34 - 6 * q^35 + 20 * q^37 - 3 * q^38 - 3 * q^40 + 7 * q^41 - 17 * q^43 + 2 * q^44 - 8 * q^46 + 14 * q^47 - 3 * q^49 + 3 * q^50 + 2 * q^52 + 12 * q^53 - 2 * q^55 + 3 * q^56 - 6 * q^58 + 29 * q^59 + 2 * q^61 - 8 * q^62 + 6 * q^64 - 2 * q^65 + q^67 + 7 * q^68 - 3 * q^70 - 20 * q^71 + 2 * q^73 + 10 * q^74 + 3 * q^76 - q^77 - 2 * q^79 - 6 * q^80 + 14 * q^82 + 12 * q^83 - 7 * q^85 + 17 * q^86 + q^88 - 44 * q^89 - 4 * q^91 - 4 * q^92 - 14 * q^94 - 3 * q^95 + 5 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.00000			0.316228
$11$	−0.285997	−	0.495361i	−0.0862312	−	0.149357i	0.819684	−	0.572816i	$-0.194149\pi$
$11$	−0.285997	−	0.495361i	−0.0862312	−	0.149357i	−0.905915	+	0.423459i	$0.860816\pi$
$12$		0			0
$13$	0.214003	−	0.370665i	0.0593539	−	0.102804i	−0.834822	−	0.550520i	$-0.814429\pi$
$13$	0.214003	−	0.370665i	0.0593539	−	0.102804i	0.894176	+	0.447717i	$0.147763\pi$
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.67282			−1.37586			−0.687931	−	0.725776i	$-0.741481\pi$
$17$	−5.67282			−1.37586			−0.687931	+	0.725776i	$0.741481\pi$
$18$		0			0
$19$	−4.81681			−1.10505			−0.552526	−	0.833496i	$-0.686336\pi$
$19$	−4.81681			−1.10505			−0.552526	+	0.833496i	$0.686336\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	0.285997	−	0.495361i	0.0609747	−	0.105611i
$23$	−3.88683	+	6.73218i	−0.810459	+	1.40376i	0.102083	+	0.994776i	$0.467449\pi$
$23$	−3.88683	+	6.73218i	−0.810459	+	1.40376i	−0.912543	+	0.408981i	$0.865884\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.428007			0.0839390
$27$		0			0
$28$	1.00000			0.188982
$29$	4.45882	+	7.72290i	0.827982	+	1.43411i	0.899619	+	0.436676i	$0.143845\pi$
$29$	4.45882	+	7.72290i	0.827982	+	1.43411i	−0.0716365	+	0.997431i	$0.522822\pi$
$30$		0			0
$31$	−4.24482	+	7.35224i	−0.762392	+	1.32050i	0.179223	+	0.983808i	$0.442642\pi$
$31$	−4.24482	+	7.35224i	−0.762392	+	1.32050i	−0.941615	+	0.336693i	$0.890692\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−2.83641	−	4.91281i	−0.486441	−	0.842540i
$35$	−1.00000			−0.169031
$36$		0			0
$37$	5.95684			0.979299			0.489650	−	0.871919i	$-0.337125\pi$
$37$	5.95684			0.979299			0.489650	+	0.871919i	$0.337125\pi$
$38$	−2.40841	−	4.17148i	−0.390695	−	0.676703i
$39$		0			0
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−5.63164	+	9.75429i	−0.879515	+	1.52336i	−0.0276411	+	0.999618i	$0.508800\pi$
$41$	−5.63164	+	9.75429i	−0.879515	+	1.52336i	−0.851874	+	0.523747i	$0.824534\pi$
$42$		0			0
$43$	−3.07199	−	5.32085i	−0.468475	−	0.811422i	0.530876	−	0.847449i	$-0.321863\pi$
$43$	−3.07199	−	5.32085i	−0.468475	−	0.811422i	−0.999351	+	0.0360276i	$0.988530\pi$
$44$	0.571993			0.0862312
$45$		0			0
$46$	−7.77365			−1.14616
$47$	5.67282	+	9.82562i	0.827466	+	1.43321i	0.900020	+	0.435849i	$0.143552\pi$
$47$	5.67282	+	9.82562i	0.827466	+	1.43321i	−0.0725533	+	0.997365i	$0.523115\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$		0			0
$52$	0.214003	+	0.370665i	0.0296769	+	0.0514019i
$53$	5.10083			0.700653			0.350326	−	0.936628i	$-0.386071\pi$
$53$	5.10083			0.700653			0.350326	+	0.936628i	$0.386071\pi$
$54$		0			0
$55$	−0.571993			−0.0771276
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$		0			0
$58$	−4.45882	+	7.72290i	−0.585472	+	1.01407i
$59$	3.16359	−	5.47950i	0.411864	−	0.713370i	−0.583230	−	0.812307i	$-0.698211\pi$
$59$	3.16359	−	5.47950i	0.411864	−	0.713370i	0.995094	+	0.0989379i	$0.0315445\pi$
$60$		0			0
$61$	2.12241	+	3.67612i	0.271747	+	0.470679i	0.969309	−	0.245845i	$-0.0790654\pi$
$61$	2.12241	+	3.67612i	0.271747	+	0.470679i	−0.697563	+	0.716524i	$0.745732\pi$
$62$	−8.48963			−1.07818
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.214003	−	0.370665i	−0.0265439	−	0.0459753i
$66$		0			0
$67$	5.65322	−	9.79167i	0.690651	−	1.19624i	−0.280974	−	0.959715i	$-0.590657\pi$
$67$	5.65322	−	9.79167i	0.690651	−	1.19624i	0.971625	−	0.236527i	$-0.0760092\pi$
$68$	2.83641	−	4.91281i	0.343965	−	0.595766i
$69$		0			0
$70$	−0.500000	−	0.866025i	−0.0597614	−	0.103510i
$71$	−15.0224			−1.78283			−0.891417	−	0.453184i	$-0.850288\pi$
$71$	−15.0224			−1.78283			−0.891417	+	0.453184i	$0.850288\pi$
$72$		0			0
$73$	−6.34565			−0.742702			−0.371351	−	0.928493i	$-0.621105\pi$
$73$	−6.34565			−0.742702			−0.371351	+	0.928493i	$0.621105\pi$
$74$	2.97842	+	5.15878i	0.346235	+	0.599696i
$75$		0			0
$76$	2.40841	−	4.17148i	0.276263	−	0.478502i
$77$	−0.285997	+	0.495361i	−0.0325923	+	0.0564516i
$78$		0			0
$79$	−3.67282	−	6.36152i	−0.413225	−	0.715727i	0.582015	−	0.813178i	$-0.302264\pi$
$79$	−3.67282	−	6.36152i	−0.413225	−	0.715727i	−0.995240	+	0.0974512i	$0.968931\pi$
$80$	−1.00000			−0.111803
$81$		0			0
$82$	−11.2633			−1.24382
$83$	5.10083	+	8.83490i	0.559889	+	0.969756i	0.997505	+	0.0705941i	$0.0224895\pi$
$83$	5.10083	+	8.83490i	0.559889	+	0.969756i	−0.437616	+	0.899162i	$0.644177\pi$
$84$		0			0
$85$	−2.83641	+	4.91281i	−0.307652	+	0.532869i
$86$	3.07199	−	5.32085i	0.331262	−	0.573762i
$87$		0			0
$88$	0.285997	+	0.495361i	0.0304873	+	0.0528056i
$89$	−8.28797			−0.878523			−0.439262	−	0.898359i	$-0.644760\pi$
$89$	−8.28797			−0.878523			−0.439262	+	0.898359i	$0.644760\pi$
$90$		0			0
$91$	−0.428007			−0.0448673
$92$	−3.88683	−	6.73218i	−0.405230	−	0.701878i
$93$		0			0
$94$	−5.67282	+	9.82562i	−0.585107	+	1.01344i
$95$	−2.40841	+	4.17148i	−0.247097	+	0.427985i
$96$		0			0
$97$	−2.74482	−	4.75416i	−0.278694	−	0.482712i	0.692366	−	0.721546i	$-0.256568\pi$
$97$	−2.74482	−	4.75416i	−0.278694	−	0.482712i	−0.971060	+	0.238834i	$0.923235\pi$
$98$	−1.00000			−0.101015
$99$		0			0
$100$	1.00000			0.100000
$101$	−1.71598	−	2.97216i	−0.170746	−	0.295741i	0.767935	−	0.640528i	$-0.221285\pi$
$101$	−1.71598	−	2.97216i	−0.170746	−	0.295741i	−0.938681	+	0.344787i	$0.887951\pi$
$102$		0			0
$103$	−4.36723	+	7.56426i	−0.430316	+	0.745328i	−0.996900	−	0.0786751i	$-0.974931\pi$
$103$	−4.36723	+	7.56426i	−0.430316	+	0.745328i	0.566585	+	0.824003i	$0.308264\pi$
$104$	−0.214003	+	0.370665i	−0.0209848	+	0.0363467i
$105$		0			0
$106$	2.55042	+	4.41745i	0.247718	+	0.429061i
$107$	−14.7305			−1.42405			−0.712025	−	0.702154i	$-0.752222\pi$
$107$	−14.7305			−1.42405			−0.712025	+	0.702154i	$0.752222\pi$
$108$		0			0
$109$	3.00395			0.287727			0.143863	−	0.989598i	$-0.454047\pi$
$109$	3.00395			0.287727			0.143863	+	0.989598i	$0.454047\pi$
$110$	−0.285997	−	0.495361i	−0.0272687	−	0.0472308i
$111$		0			0
$112$	−0.500000	+	0.866025i	−0.0472456	+	0.0818317i
$113$	−3.05239	+	5.28690i	−0.287145	+	0.497349i	−0.973127	−	0.230269i	$-0.926039\pi$
$113$	−3.05239	+	5.28690i	−0.287145	+	0.497349i	0.685982	+	0.727618i	$0.259373\pi$
$114$		0			0
$115$	3.88683	+	6.73218i	0.362448	+	0.627779i
$116$	−8.91764			−0.827982
$117$		0			0
$118$	6.32718			0.582464
$119$	2.83641	+	4.91281i	0.260013	+	0.450357i
$120$		0			0
$121$	5.33641	−	9.24294i	0.485128	−	0.840267i
$122$	−2.12241	+	3.67612i	−0.192154	+	0.332820i
$123$		0			0
$124$	−4.24482	−	7.35224i	−0.381196	−	0.660251i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	12.0616			1.07030			0.535148	−	0.844758i	$-0.320256\pi$
$127$	12.0616			1.07030			0.535148	+	0.844758i	$0.320256\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	0.214003	−	0.370665i	0.0187693	−	0.0325094i
$131$	−1.00924	+	1.74805i	−0.0881773	+	0.152728i	−0.906741	−	0.421689i	$-0.861438\pi$
$131$	−1.00924	+	1.74805i	−0.0881773	+	0.152728i	0.818563	+	0.574416i	$0.194771\pi$
$132$		0			0
$133$	2.40841	+	4.17148i	0.208835	+	0.361713i
$134$	11.3064			0.976728
$135$		0			0
$136$	5.67282			0.486441
$137$	−10.6801	−	18.4984i	−0.912461	−	1.58043i	−0.810577	−	0.585633i	$-0.800846\pi$
$137$	−10.6801	−	18.4984i	−0.912461	−	1.58043i	−0.101884	−	0.994796i	$-0.532487\pi$
$138$		0			0
$139$	6.41764	−	11.1157i	0.544337	−	0.942820i	−0.454311	−	0.890843i	$-0.650115\pi$
$139$	6.41764	−	11.1157i	0.544337	−	0.942820i	0.998648	−	0.0519766i	$-0.0165521\pi$
$140$	0.500000	−	0.866025i	0.0422577	−	0.0731925i
$141$		0			0
$142$	−7.51121	−	13.0098i	−0.630327	−	1.09176i
$143$	−0.244817			−0.0204726
$144$		0			0
$145$	8.91764			0.740570
$146$	−3.17282	−	5.49549i	−0.262585	−	0.454810i
$147$		0			0
$148$	−2.97842	+	5.15878i	−0.244825	+	0.424049i
$149$	2.10083	−	3.63875i	0.172107	−	0.298098i	−0.767049	−	0.641588i	$-0.778276\pi$
$149$	2.10083	−	3.63875i	0.172107	−	0.298098i	0.939156	+	0.343490i	$0.111609\pi$
$150$		0			0
$151$	−1.81681	−	3.14681i	−0.147850	−	0.256084i	0.782583	−	0.622547i	$-0.213902\pi$
$151$	−1.81681	−	3.14681i	−0.147850	−	0.256084i	−0.930433	+	0.366463i	$0.880569\pi$
$152$	4.81681			0.390695
$153$		0			0
$154$	−0.571993			−0.0460925
$155$	4.24482	+	7.35224i	0.340952	+	0.590546i
$156$		0			0
$157$	2.17480	−	3.76686i	0.173568	−	0.300629i	−0.766097	−	0.642725i	$-0.777804\pi$
$157$	2.17480	−	3.76686i	0.173568	−	0.300629i	0.939665	+	0.342097i	$0.111137\pi$
$158$	3.67282	−	6.36152i	0.292194	−	0.506095i
$159$		0			0
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	7.77365			0.612650
$162$		0			0
$163$	−10.1048			−0.791468			−0.395734	−	0.918365i	$-0.629510\pi$
$163$	−10.1048			−0.791468			−0.395734	+	0.918365i	$0.629510\pi$
$164$	−5.63164	−	9.75429i	−0.439758	−	0.761682i
$165$		0			0
$166$	−5.10083	+	8.83490i	−0.395901	+	0.685721i
$167$	3.69440	−	6.39889i	0.285881	−	0.495161i	−0.686941	−	0.726713i	$-0.741047\pi$
$167$	3.69440	−	6.39889i	0.285881	−	0.495161i	0.972823	+	0.231552i	$0.0743803\pi$
$168$		0			0
$169$	6.40841	+	11.0997i	0.492954	+	0.853822i
$170$	−5.67282			−0.435086
$171$		0			0
$172$	6.14399			0.468475
$173$	0.244817	+	0.424035i	0.0186131	+	0.0322388i	0.875182	−	0.483794i	$-0.160742\pi$
$173$	0.244817	+	0.424035i	0.0186131	+	0.0322388i	−0.856569	+	0.516033i	$0.827408\pi$
$174$		0			0
$175$	−0.500000	+	0.866025i	−0.0377964	+	0.0654654i
$176$	−0.285997	+	0.495361i	−0.0215578	+	0.0373392i
$177$		0			0
$178$	−4.14399	−	7.17760i	−0.310605	−	0.537984i
$179$	2.67282			0.199776			0.0998881	−	0.994999i	$-0.468152\pi$
$179$	2.67282			0.199776			0.0998881	+	0.994999i	$0.468152\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	−0.214003	−	0.370665i	−0.0158630	−	0.0274755i
$183$		0			0
$184$	3.88683	−	6.73218i	0.286541	−	0.496303i
$185$	2.97842	−	5.15878i	0.218978	−	0.379281i
$186$		0			0
$187$	1.62241	+	2.81009i	0.118642	+	0.205494i
$188$	−11.3456			−0.827466
$189$		0			0
$190$	−4.81681			−0.349448
$191$	5.42801	+	9.40158i	0.392757	+	0.680275i	0.992812	−	0.119684i	$-0.0381881\pi$
$191$	5.42801	+	9.40158i	0.392757	+	0.680275i	−0.600055	+	0.799959i	$0.704855\pi$
$192$		0			0
$193$	1.43922	−	2.49280i	0.103597	−	0.179436i	−0.809567	−	0.587027i	$-0.800298\pi$
$193$	1.43922	−	2.49280i	0.103597	−	0.179436i	0.913164	+	0.407592i	$0.133631\pi$
$194$	2.74482	−	4.75416i	0.197066	−	0.341329i
$195$		0			0
$196$	−0.500000	−	0.866025i	−0.0357143	−	0.0618590i
$197$	18.5697			1.32304			0.661519	−	0.749928i	$-0.269912\pi$
$197$	18.5697			1.32304			0.661519	+	0.749928i	$0.269912\pi$
$198$		0			0
$199$	−15.3210			−1.08607			−0.543037	−	0.839709i	$-0.682726\pi$
$199$	−15.3210			−1.08607			−0.543037	+	0.839709i	$0.682726\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$		0			0
$202$	1.71598	−	2.97216i	0.120736	−	0.209121i
$203$	4.45882	−	7.72290i	0.312948	−	0.542042i
$204$		0			0
$205$	5.63164	+	9.75429i	0.393331	+	0.681269i
$206$	−8.73445			−0.608558
$207$		0			0
$208$	−0.428007			−0.0296769
$209$	1.37759	+	2.38606i	0.0952900	+	0.165047i
$210$		0			0
$211$	−5.63362	+	9.75772i	−0.387834	+	0.671749i	−0.992158	−	0.124990i	$-0.960110\pi$
$211$	−5.63362	+	9.75772i	−0.387834	+	0.671749i	0.604324	+	0.796739i	$0.293443\pi$
$212$	−2.55042	+	4.41745i	−0.175163	+	0.303392i
$213$		0			0
$214$	−7.36525	−	12.7570i	−0.503478	−	0.872050i
$215$	−6.14399			−0.419016
$216$		0			0
$217$	8.48963			0.576314
$218$	1.50198	+	2.60150i	0.101727	+	0.176196i
$219$		0			0
$220$	0.285997	−	0.495361i	0.0192819	−	0.0333972i
$221$	−1.21400	+	2.10272i	−0.0816627	+	0.141444i
$222$		0			0
$223$	−3.22324	−	5.58281i	−0.215844	−	0.373853i	0.737689	−	0.675140i	$-0.235917\pi$
$223$	−3.22324	−	5.58281i	−0.215844	−	0.373853i	−0.953533	+	0.301288i	$0.902584\pi$
$224$	−1.00000			−0.0668153
$225$		0			0
$226$	−6.10478			−0.406084
$227$	−1.86723	−	3.23413i	−0.123932	−	0.214657i	0.797383	−	0.603474i	$-0.206217\pi$
$227$	−1.86723	−	3.23413i	−0.123932	−	0.214657i	−0.921315	+	0.388817i	$0.872884\pi$
$228$		0			0
$229$	−2.07925	+	3.60137i	−0.137401	+	0.237985i	−0.926512	−	0.376265i	$-0.877208\pi$
$229$	−2.07925	+	3.60137i	−0.137401	+	0.237985i	0.789111	+	0.614250i	$0.210542\pi$
$230$	−3.88683	+	6.73218i	−0.256290	+	0.443907i
$231$		0			0
$232$	−4.45882	−	7.72290i	−0.292736	−	0.507033i
$233$	20.0409			1.31292			0.656461	−	0.754360i	$-0.272053\pi$
$233$	20.0409			1.31292			0.656461	+	0.754360i	$0.272053\pi$
$234$		0			0
$235$	11.3456			0.740108
$236$	3.16359	+	5.47950i	0.205932	+	0.356685i
$237$		0			0
$238$	−2.83641	+	4.91281i	−0.183857	+	0.318450i
$239$	6.24482	−	10.8163i	0.403944	−	0.699651i	−0.590254	−	0.807217i	$-0.700973\pi$
$239$	6.24482	−	10.8163i	0.403944	−	0.699651i	0.994198	+	0.107566i	$0.0343059\pi$
$240$		0			0
$241$	1.19440	+	2.06876i	0.0769382	+	0.133261i	0.901927	−	0.431888i	$-0.142152\pi$
$241$	1.19440	+	2.06876i	0.0769382	+	0.133261i	−0.824989	+	0.565148i	$0.808819\pi$
$242$	10.6728			0.686075
$243$		0			0
$244$	−4.24482			−0.271747
$245$	0.500000	+	0.866025i	0.0319438	+	0.0553283i
$246$		0			0
$247$	−1.03081	+	1.78542i	−0.0655891	+	0.113604i
$248$	4.24482	−	7.35224i	0.269546	−	0.466868i
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−30.3826			−1.91773			−0.958866	−	0.283859i	$-0.908385\pi$
$251$	−30.3826			−1.91773			−0.958866	+	0.283859i	$0.908385\pi$
$252$		0			0
$253$	4.44648			0.279548
$254$	6.03081	+	10.4457i	0.378407	+	0.655420i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.12967	−	14.0810i	0.507115	−	0.878348i	−0.492851	−	0.870114i	$-0.664045\pi$
$257$	8.12967	−	14.0810i	0.507115	−	0.878348i	0.999966	−	0.00823496i	$-0.00262130\pi$
$258$		0			0
$259$	−2.97842	−	5.15878i	−0.185070	−	0.320551i
$260$	0.428007			0.0265439
$261$		0			0
$262$	−2.01847			−0.124702
$263$	1.45882	+	2.52675i	0.0899547	+	0.155806i	0.907492	−	0.420070i	$-0.137994\pi$
$263$	1.45882	+	2.52675i	0.0899547	+	0.155806i	−0.817537	+	0.575876i	$0.804661\pi$
$264$		0			0
$265$	2.55042	−	4.41745i	0.156671	−	0.271362i
$266$	−2.40841	+	4.17148i	−0.147669	+	0.255770i
$267$		0			0
$268$	5.65322	+	9.79167i	0.345326	+	0.598121i
$269$	−16.1664			−0.985683			−0.492842	−	0.870119i	$-0.664042\pi$
$269$	−16.1664			−0.985683			−0.492842	+	0.870119i	$0.664042\pi$
$270$		0			0
$271$	−3.37033			−0.204733			−0.102367	−	0.994747i	$-0.532641\pi$
$271$	−3.37033			−0.204733			−0.102367	+	0.994747i	$0.532641\pi$
$272$	2.83641	+	4.91281i	0.171983	+	0.297883i
$273$		0			0
$274$	10.6801	−	18.4984i	0.645207	−	1.11753i
$275$	−0.285997	+	0.495361i	−0.0172462	+	0.0298714i
$276$		0			0
$277$	−3.01847	−	5.22815i	−0.181362	−	0.314129i	0.760982	−	0.648773i	$-0.224717\pi$
$277$	−3.01847	−	5.22815i	−0.181362	−	0.314129i	−0.942345	+	0.334644i	$0.891384\pi$
$278$	12.8353			0.769809
$279$		0			0
$280$	1.00000			0.0597614
$281$	9.59970	+	16.6272i	0.572670	+	0.991894i	0.996290	+	0.0860539i	$0.0274257\pi$
$281$	9.59970	+	16.6272i	0.572670	+	0.991894i	−0.423620	+	0.905840i	$0.639241\pi$
$282$		0			0
$283$	−6.53279	+	11.3151i	−0.388334	+	0.672614i	−0.992226	−	0.124452i	$-0.960283\pi$
$283$	−6.53279	+	11.3151i	−0.388334	+	0.672614i	0.603892	+	0.797066i	$0.293616\pi$
$284$	7.51121	−	13.0098i	0.445708	−	0.771990i
$285$		0			0
$286$	−0.122408	−	0.212018i	−0.00723817	−	0.0125369i
$287$	11.2633			0.664851
$288$		0			0
$289$	15.1809			0.892996
$290$	4.45882	+	7.72290i	0.261831	+	0.453505i
$291$		0			0
$292$	3.17282	−	5.49549i	0.185675	−	0.321599i
$293$	11.2756	−	19.5300i	0.658729	−	1.14095i	−0.322215	−	0.946666i	$-0.604428\pi$
$293$	11.2756	−	19.5300i	0.658729	−	1.14095i	0.980945	−	0.194286i	$-0.0622391\pi$
$294$		0			0
$295$	−3.16359	−	5.47950i	−0.184191	−	0.319029i
$296$	−5.95684			−0.346235
$297$		0			0
$298$	4.20166			0.243396
$299$	1.66359	+	2.88142i	0.0962078	+	0.166637i
$300$		0			0
$301$	−3.07199	+	5.32085i	−0.177067	+	0.306689i
$302$	1.81681	−	3.14681i	0.104546	−	0.181078i
$303$		0			0
$304$	2.40841	+	4.17148i	0.138132	+	0.239251i
$305$	4.24482			0.243058
$306$		0			0
$307$	−12.4857			−0.712595			−0.356298	−	0.934372i	$-0.615961\pi$
$307$	−12.4857			−0.712595			−0.356298	+	0.934372i	$0.615961\pi$
$308$	−0.285997	−	0.495361i	−0.0162962	−	0.0282258i
$309$		0			0
$310$	−4.24482	+	7.35224i	−0.241089	+	0.417579i
$311$	−3.05767	+	5.29605i	−0.173385	+	0.300311i	−0.939601	−	0.342271i	$-0.888804\pi$
$311$	−3.05767	+	5.29605i	−0.173385	+	0.300311i	0.766216	+	0.642583i	$0.222137\pi$
$312$		0			0
$313$	14.8157	+	25.6615i	0.837432	+	1.45047i	0.892035	+	0.451966i	$0.149277\pi$
$313$	14.8157	+	25.6615i	0.837432	+	1.45047i	−0.0546033	+	0.998508i	$0.517389\pi$
$314$	4.34960			0.245462
$315$		0			0
$316$	7.34565			0.413225
$317$	8.41038	+	14.5672i	0.472374	+	0.818176i	0.999500	−	0.0316111i	$-0.0100638\pi$
$317$	8.41038	+	14.5672i	0.472374	+	0.818176i	−0.527126	+	0.849787i	$0.676730\pi$
$318$		0			0
$319$	2.55042	−	4.41745i	0.142796	−	0.247330i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$		0			0
$322$	3.88683	+	6.73218i	0.216604	+	0.375170i
$323$	27.3249			1.52040
$324$		0			0
$325$	−0.428007			−0.0237415
$326$	−5.05239	−	8.75100i	−0.279826	−	0.484673i
$327$		0			0
$328$	5.63164	−	9.75429i	0.310956	−	0.538591i
$329$	5.67282	−	9.82562i	0.312753	−	0.541704i
$330$		0			0
$331$	13.5905	+	23.5394i	0.746999	+	1.29384i	0.949255	+	0.314508i	$0.101840\pi$
$331$	13.5905	+	23.5394i	0.746999	+	1.29384i	−0.202255	+	0.979333i	$0.564827\pi$
$332$	−10.2017			−0.559889
$333$		0			0
$334$	7.38880			0.404297
$335$	−5.65322	−	9.79167i	−0.308869	−	0.534976i
$336$		0			0
$337$	7.25208	−	12.5610i	0.395046	−	0.684239i	−0.598061	−	0.801450i	$-0.704062\pi$
$337$	7.25208	−	12.5610i	0.395046	−	0.684239i	0.993107	+	0.117211i	$0.0373954\pi$
$338$	−6.40841	+	11.0997i	−0.348571	+	0.603743i
$339$		0			0
$340$	−2.83641	−	4.91281i	−0.153826	−	0.266435i
$341$	4.85601			0.262968
$342$		0			0
$343$	1.00000			0.0539949
$344$	3.07199	+	5.32085i	0.165631	+	0.286881i
$345$		0			0
$346$	−0.244817	+	0.424035i	−0.0131614	+	0.0227963i
$347$	3.32605	−	5.76088i	0.178551	−	0.309260i	−0.762833	−	0.646595i	$-0.776192\pi$
$347$	3.32605	−	5.76088i	0.178551	−	0.309260i	0.941385	+	0.337335i	$0.109526\pi$
$348$		0			0
$349$	−5.56889	−	9.64559i	−0.298096	−	0.516317i	0.677605	−	0.735426i	$-0.263018\pi$
$349$	−5.56889	−	9.64559i	−0.298096	−	0.516317i	−0.975700	+	0.219110i	$0.929685\pi$
$350$	−1.00000			−0.0534522
$351$		0			0
$352$	−0.571993			−0.0304873
$353$	12.6008	+	21.8253i	0.670675	+	1.16164i	0.977713	+	0.209945i	$0.0673286\pi$
$353$	12.6008	+	21.8253i	0.670675	+	1.16164i	−0.307039	+	0.951697i	$0.599338\pi$
$354$		0			0
$355$	−7.51121	+	13.0098i	−0.398654	+	0.690489i
$356$	4.14399	−	7.17760i	0.219631	−	0.380412i
$357$		0			0
$358$	1.33641	+	2.31473i	0.0706316	+	0.122337i
$359$	11.4257			0.603028			0.301514	−	0.953462i	$-0.402508\pi$
$359$	11.4257			0.603028			0.301514	+	0.953462i	$0.402508\pi$
$360$		0			0
$361$	4.20166			0.221140
$362$	−5.00000	−	8.66025i	−0.262794	−	0.455173i
$363$		0			0
$364$	0.214003	−	0.370665i	0.0112168	−	0.0194281i
$365$	−3.17282	+	5.49549i	−0.166073	+	0.287647i
$366$		0			0
$367$	−13.1801	−	22.8286i	−0.687995	−	1.19164i	−0.972486	−	0.232963i	$-0.925158\pi$
$367$	−13.1801	−	22.8286i	−0.687995	−	1.19164i	0.284491	−	0.958679i	$-0.408175\pi$
$368$	7.77365			0.405230
$369$		0			0
$370$	5.95684			0.309682
$371$	−2.55042	−	4.41745i	−0.132411	−	0.229343i
$372$		0			0
$373$	17.3025	−	29.9688i	0.895889	−	1.55173i	0.0631886	−	0.998002i	$-0.479873\pi$
$373$	17.3025	−	29.9688i	0.895889	−	1.55173i	0.832700	−	0.553724i	$-0.186794\pi$
$374$	−1.62241	+	2.81009i	−0.0838927	+	0.145306i
$375$		0			0
$376$	−5.67282	−	9.82562i	−0.292554	−	0.506718i
$377$	3.81681			0.196576
$378$		0			0
$379$	−15.0432			−0.772715			−0.386358	−	0.922349i	$-0.626267\pi$
$379$	−15.0432			−0.772715			−0.386358	+	0.922349i	$0.626267\pi$
$380$	−2.40841	−	4.17148i	−0.123549	−	0.213992i
$381$		0			0
$382$	−5.42801	+	9.40158i	−0.277721	+	0.481027i
$383$	−11.9176	+	20.6420i	−0.608963	+	1.05475i	0.382449	+	0.923977i	$0.375081\pi$
$383$	−11.9176	+	20.6420i	−0.608963	+	1.05475i	−0.991412	+	0.130778i	$0.958252\pi$
$384$		0			0
$385$	0.285997	+	0.495361i	0.0145757	+	0.0252459i
$386$	2.87844			0.146509
$387$		0			0
$388$	5.48963			0.278694
$389$	−3.81681	−	6.61091i	−0.193520	−	0.335186i	0.752894	−	0.658141i	$-0.228657\pi$
$389$	−3.81681	−	6.61091i	−0.193520	−	0.335186i	−0.946414	+	0.322955i	$0.895324\pi$
$390$		0			0
$391$	22.0493	−	38.1905i	1.11508	−	1.93138i
$392$	0.500000	−	0.866025i	0.0252538	−	0.0437409i
$393$		0			0
$394$	9.28487	+	16.0819i	0.467765	+	0.810192i
$395$	−7.34565			−0.369600
$396$		0			0
$397$	−10.7944			−0.541755			−0.270877	−	0.962614i	$-0.587314\pi$
$397$	−10.7944			−0.541755			−0.270877	+	0.962614i	$0.587314\pi$
$398$	−7.66048	−	13.2683i	−0.383985	−	0.665082i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−9.13362	+	15.8199i	−0.456111	+	0.790008i	−0.998751	−	0.0499575i	$-0.984091\pi$
$401$	−9.13362	+	15.8199i	−0.456111	+	0.790008i	0.542640	+	0.839965i	$0.317425\pi$
$402$		0			0
$403$	1.81681	+	3.14681i	0.0905018	+	0.156754i
$404$	3.43196			0.170746
$405$		0			0
$406$	8.91764			0.442575
$407$	−1.70364	−	2.95079i	−0.0844462	−	0.146265i
$408$		0			0
$409$	−2.95487	+	5.11798i	−0.146109	+	0.253068i	−0.929786	−	0.368100i	$-0.880008\pi$
$409$	−2.95487	+	5.11798i	−0.146109	+	0.253068i	0.783677	+	0.621168i	$0.213342\pi$
$410$	−5.63164	+	9.75429i	−0.278127	+	0.481730i
$411$		0			0
$412$	−4.36723	−	7.56426i	−0.215158	−	0.372664i
$413$	−6.32718			−0.311340
$414$		0			0
$415$	10.2017			0.500780
$416$	−0.214003	−	0.370665i	−0.0104924	−	0.0181733i
$417$		0			0
$418$	−1.37759	+	2.38606i	−0.0673802	+	0.116706i
$419$	4.99076	−	8.64426i	0.243815	−	0.422300i	−0.717983	−	0.696061i	$-0.754934\pi$
$419$	4.99076	−	8.64426i	0.243815	−	0.422300i	0.961798	+	0.273761i	$0.0882678\pi$
$420$		0			0
$421$	18.8661	+	32.6770i	0.919477	+	1.59258i	0.800211	+	0.599719i	$0.204721\pi$
$421$	18.8661	+	32.6770i	0.919477	+	1.59258i	0.119267	+	0.992862i	$0.461946\pi$
$422$	−11.2672			−0.548481
$423$		0			0
$424$	−5.10083			−0.247718
$425$	2.83641	+	4.91281i	0.137586	+	0.238306i
$426$		0			0
$427$	2.12241	−	3.67612i	0.102711	−	0.177900i
$428$	7.36525	−	12.7570i	0.356013	−	0.616632i
$429$		0			0
$430$	−3.07199	−	5.32085i	−0.148145	−	0.256594i
$431$	−14.2386			−0.685849			−0.342925	−	0.939363i	$-0.611418\pi$
$431$	−14.2386			−0.685849			−0.342925	+	0.939363i	$0.611418\pi$
$432$		0			0
$433$	17.2096			0.827039			0.413519	−	0.910495i	$-0.364299\pi$
$433$	17.2096			0.827039			0.413519	+	0.910495i	$0.364299\pi$
$434$	4.24482	+	7.35224i	0.203758	+	0.352919i
$435$		0			0
$436$	−1.50198	+	2.60150i	−0.0719316	+	0.124589i
$437$	18.7221	−	32.4276i	0.895600	−	1.55122i
$438$		0			0
$439$	20.0453	+	34.7195i	0.956711	+	1.65707i	0.730402	+	0.683017i	$0.239333\pi$
$439$	20.0453	+	34.7195i	0.956711	+	1.65707i	0.226309	+	0.974055i	$0.427334\pi$
$440$	0.571993			0.0272687
$441$		0			0
$442$	−2.42801			−0.115489
$443$	−4.25518	−	7.37019i	−0.202170	−	0.350168i	0.747057	−	0.664759i	$-0.231466\pi$
$443$	−4.25518	−	7.37019i	−0.202170	−	0.350168i	−0.949227	+	0.314591i	$0.898133\pi$
$444$		0			0
$445$	−4.14399	+	7.17760i	−0.196444	+	0.340251i
$446$	3.22324	−	5.58281i	0.152625	−	0.264354i
$447$		0			0
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	−13.0969			−0.618080			−0.309040	−	0.951049i	$-0.600008\pi$
$449$	−13.0969			−0.618080			−0.309040	+	0.951049i	$0.600008\pi$
$450$		0			0
$451$	6.44252			0.303367
$452$	−3.05239	−	5.28690i	−0.143572	−	0.248675i
$453$		0			0
$454$	1.86723	−	3.23413i	0.0876332	−	0.151785i
$455$	−0.214003	+	0.370665i	−0.0100326	+	0.0173770i
$456$		0			0
$457$	14.0165	+	24.2773i	0.655664	+	1.13564i	0.981727	+	0.190295i	$0.0609445\pi$
$457$	14.0165	+	24.2773i	0.655664	+	1.13564i	−0.326063	+	0.945348i	$0.605722\pi$
$458$	−4.15850			−0.194314
$459$		0			0
$460$	−7.77365			−0.362448
$461$	10.9784	+	19.0152i	0.511316	+	0.885625i	0.999914	+	0.0131164i	$0.00417519\pi$
$461$	10.9784	+	19.0152i	0.511316	+	0.885625i	−0.488598	+	0.872509i	$0.662491\pi$
$462$		0			0
$463$	−6.10083	+	10.5669i	−0.283530	+	0.491088i	−0.972252	−	0.233938i	$-0.924839\pi$
$463$	−6.10083	+	10.5669i	−0.283530	+	0.491088i	0.688722	+	0.725026i	$0.258172\pi$
$464$	4.45882	−	7.72290i	0.206996	−	0.358527i
$465$		0			0
$466$	10.0204	+	17.3559i	0.464188	+	0.803998i
$467$	26.4257			1.22284			0.611419	−	0.791307i	$-0.290599\pi$
$467$	26.4257			1.22284			0.611419	+	0.791307i	$0.290599\pi$
$468$		0			0
$469$	−11.3064			−0.522083
$470$	5.67282	+	9.82562i	0.261668	+	0.453222i
$471$		0			0
$472$	−3.16359	+	5.47950i	−0.145616	+	0.252214i
$473$	−1.75716	+	3.04349i	−0.0807943	+	0.139940i
$474$		0			0
$475$	2.40841	+	4.17148i	0.110505	+	0.191401i
$476$	−5.67282			−0.260013
$477$		0			0
$478$	12.4896			0.571263
$479$	−18.3949	−	31.8610i	−0.840486	−	1.45576i	−0.889484	−	0.456965i	$-0.848936\pi$
$479$	−18.3949	−	31.8610i	−0.840486	−	1.45576i	0.0489986	−	0.998799i	$-0.484397\pi$
$480$		0			0
$481$	1.27478	−	2.20799i	0.0581252	−	0.100676i
$482$	−1.19440	+	2.06876i	−0.0544035	+	0.0942296i
$483$		0			0
$484$	5.33641	+	9.24294i	0.242564	+	0.420133i
$485$	−5.48963			−0.249271
$486$		0			0
$487$	16.7776			0.760266			0.380133	−	0.924932i	$-0.375878\pi$
$487$	16.7776			0.760266			0.380133	+	0.924932i	$0.375878\pi$
$488$	−2.12241	−	3.67612i	−0.0960769	−	0.166410i
$489$		0			0
$490$	−0.500000	+	0.866025i	−0.0225877	+	0.0391230i
$491$	−11.6840	+	20.2373i	−0.527293	+	0.913299i	0.472201	+	0.881491i	$0.343460\pi$
$491$	−11.6840	+	20.2373i	−0.527293	+	0.913299i	−0.999494	+	0.0318075i	$0.989874\pi$
$492$		0			0
$493$	−25.2941	−	43.8107i	−1.13919	−	1.97313i
$494$	−2.06163			−0.0927570
$495$		0			0
$496$	8.48963			0.381196
$497$	7.51121	+	13.0098i	0.336924	+	0.583569i
$498$		0			0
$499$	−11.4053	+	19.7546i	−0.510571	+	0.884335i	0.489354	+	0.872085i	$0.337233\pi$
$499$	−11.4053	+	19.7546i	−0.510571	+	0.884335i	−0.999925	+	0.0122500i	$0.996101\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		0			0
$502$	−15.1913	−	26.3121i	−0.678021	−	1.17437i
$503$	−32.6129			−1.45414			−0.727068	−	0.686565i	$-0.759118\pi$
$503$	−32.6129			−1.45414			−0.727068	+	0.686565i	$0.759118\pi$
$504$		0			0
$505$	−3.43196			−0.152720
$506$	2.22324	+	3.85076i	0.0988350	+	0.171187i
$507$		0			0
$508$	−6.03081	+	10.4457i	−0.267574	+	0.463452i
$509$	−2.65520	+	4.59894i	−0.117690	+	0.203844i	−0.918852	−	0.394603i	$-0.870882\pi$
$509$	−2.65520	+	4.59894i	−0.117690	+	0.203844i	0.801162	+	0.598447i	$0.204215\pi$
$510$		0			0
$511$	3.17282	+	5.49549i	0.140357	+	0.243106i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	16.2593			0.717169
$515$	4.36723	+	7.56426i	0.192443	+	0.333321i
$516$		0			0
$517$	3.24482	−	5.62019i	0.142707	−	0.247176i
$518$	2.97842	−	5.15878i	0.130864	−	0.226664i
$519$		0			0
$520$	0.214003	+	0.370665i	0.00938467	+	0.0162547i
$521$	−11.5328			−0.505261			−0.252630	−	0.967563i	$-0.581296\pi$
$521$	−11.5328			−0.505261			−0.252630	+	0.967563i	$0.581296\pi$
$522$		0			0
$523$	21.1546			0.925024			0.462512	−	0.886613i	$-0.346948\pi$
$523$	21.1546			0.925024			0.462512	+	0.886613i	$0.346948\pi$
$524$	−1.00924	−	1.74805i	−0.0440887	−	0.0763638i
$525$		0			0
$526$	−1.45882	+	2.52675i	−0.0636076	+	0.110172i
$527$	24.0801	−	41.7080i	1.04895	−	1.81683i
$528$		0			0
$529$	−18.7148	−	32.4151i	−0.813689	−	1.40935i
$530$	5.10083			0.221566
$531$		0			0
$532$	−4.81681			−0.208835
$533$	2.41038	+	4.17490i	0.104405	+	0.180835i
$534$		0			0
$535$	−7.36525	+	12.7570i	−0.318427	+	0.551533i
$536$	−5.65322	+	9.79167i	−0.244182	+	0.422936i
$537$		0			0
$538$	−8.08321	−	14.0005i	−0.348492	−	0.603605i
$539$	0.571993			0.0246375
$540$		0			0
$541$	−34.0000			−1.46177			−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000			−1.46177			−0.730887	+	0.682498i	$0.760893\pi$
$542$	−1.68517	−	2.91879i	−0.0723841	−	0.125373i
$543$		0			0
$544$	−2.83641	+	4.91281i	−0.121610	+	0.210635i
$545$	1.50198	−	2.60150i	0.0643376	−	0.111436i
$546$		0			0
$547$	16.4216	+	28.4430i	0.702137	+	1.21614i	0.967715	+	0.252047i	$0.0811038\pi$
$547$	16.4216	+	28.4430i	0.702137	+	1.21614i	−0.265578	+	0.964089i	$0.585563\pi$
$548$	21.3602			0.912461
$549$		0			0
$550$	−0.571993			−0.0243899
$551$	−21.4773	−	37.1998i	−0.914963	−	1.58476i
$552$		0			0
$553$	−3.67282	+	6.36152i	−0.156184	+	0.270519i
$554$	3.01847	−	5.22815i	0.128243	−	0.222123i
$555$		0			0
$556$	6.41764	+	11.1157i	0.272169	+	0.471410i
$557$	15.9216			0.674620			0.337310	−	0.941394i	$-0.390483\pi$
$557$	15.9216			0.674620			0.337310	+	0.941394i	$0.390483\pi$
$558$		0			0
$559$	−2.62967			−0.111223
$560$	0.500000	+	0.866025i	0.0211289	+	0.0365963i
$561$		0			0
$562$	−9.59970	+	16.6272i	−0.404939	+	0.701375i
$563$	−0.810881	+	1.40449i	−0.0341746	+	0.0591921i	−0.882607	−	0.470112i	$-0.844214\pi$
$563$	−0.810881	+	1.40449i	−0.0341746	+	0.0591921i	0.848432	+	0.529304i	$0.177547\pi$
$564$		0			0
$565$	3.05239	+	5.28690i	0.128415	+	0.222421i
$566$	−13.0656			−0.549187
$567$		0			0
$568$	15.0224			0.630327
$569$	7.65717	+	13.2626i	0.321005	+	0.555998i	0.980696	−	0.195540i	$-0.0626459\pi$
$569$	7.65717	+	13.2626i	0.321005	+	0.555998i	−0.659690	+	0.751538i	$0.729313\pi$
$570$		0			0
$571$	2.42075	−	4.19286i	0.101305	−	0.175466i	−0.810917	−	0.585161i	$-0.801031\pi$
$571$	2.42075	−	4.19286i	0.101305	−	0.175466i	0.912223	+	0.409695i	$0.134365\pi$
$572$	0.122408	−	0.212018i	0.00511816	−	0.00886491i
$573$		0			0
$574$	5.63164	+	9.75429i	0.235060	+	0.407136i
$575$	7.77365			0.324184
$576$		0			0
$577$	28.2857			1.17755			0.588775	−	0.808297i	$-0.299610\pi$
$577$	28.2857			1.17755			0.588775	+	0.808297i	$0.299610\pi$
$578$	7.59046	+	13.1471i	0.315722	+	0.546846i
$579$		0			0
$580$	−4.45882	+	7.72290i	−0.185142	+	0.320676i
$581$	5.10083	−	8.83490i	0.211618	−	0.366533i
$582$		0			0
$583$	−1.45882	−	2.52675i	−0.0604182	−	0.104647i
$584$	6.34565			0.262585
$585$		0			0
$586$	22.5513			0.931584
$587$	−11.4093	−	19.7614i	−0.470910	−	0.815640i	0.528536	−	0.848911i	$-0.322741\pi$
$587$	−11.4093	−	19.7614i	−0.470910	−	0.815640i	−0.999446	+	0.0332704i	$0.989408\pi$
$588$		0			0
$589$	20.4465	−	35.4143i	0.842482	−	1.45922i
$590$	3.16359	−	5.47950i	0.130243	−	0.225587i
$591$		0			0
$592$	−2.97842	−	5.15878i	−0.122412	−	0.212024i
$593$	−25.8538			−1.06169			−0.530843	−	0.847470i	$-0.678125\pi$
$593$	−25.8538			−1.06169			−0.530843	+	0.847470i	$0.678125\pi$
$594$		0			0
$595$	5.67282			0.232563
$596$	2.10083	+	3.63875i	0.0860534	+	0.149049i
$597$		0			0
$598$	−1.66359	+	2.88142i	−0.0680292	+	0.117830i
$599$	−12.8745	+	22.2993i	−0.526037	+	0.911123i	0.473503	+	0.880792i	$0.342989\pi$
$599$	−12.8745	+	22.2993i	−0.526037	+	0.911123i	−0.999540	+	0.0303308i	$0.990344\pi$
$600$		0			0
$601$	5.94035	+	10.2890i	0.242312	+	0.419697i	0.961372	−	0.275251i	$-0.0887609\pi$
$601$	5.94035	+	10.2890i	0.242312	+	0.419697i	−0.719061	+	0.694947i	$0.755428\pi$
$602$	−6.14399			−0.250410
$603$		0			0
$604$	3.63362			0.147850
$605$	−5.33641	−	9.24294i	−0.216956	−	0.375779i
$606$		0			0
$607$	−0.287973	+	0.498784i	−0.0116885	+	0.0202450i	−0.871810	−	0.489843i	$-0.837054\pi$
$607$	−0.287973	+	0.498784i	−0.0116885	+	0.0202450i	0.860122	+	0.510088i	$0.170387\pi$
$608$	−2.40841	+	4.17148i	−0.0976737	+	0.169176i
$609$		0			0
$610$	2.12241	+	3.67612i	0.0859338	+	0.148842i
$611$	4.85601			0.196453
$612$		0			0
$613$	14.8639			0.600348			0.300174	−	0.953884i	$-0.402955\pi$
$613$	14.8639			0.600348			0.300174	+	0.953884i	$0.402955\pi$
$614$	−6.24284	−	10.8129i	−0.251941	−	0.436374i
$615$		0			0
$616$	0.285997	−	0.495361i	0.0115231	−	0.0199587i
$617$	14.3569	−	24.8668i	0.577985	−	1.00110i	−0.417725	−	0.908574i	$-0.637172\pi$
$617$	14.3569	−	24.8668i	0.577985	−	1.00110i	0.995710	−	0.0925265i	$-0.0294943\pi$
$618$		0			0
$619$	10.8417	+	18.7784i	0.435764	+	0.754766i	0.997358	−	0.0726472i	$-0.0231447\pi$
$619$	10.8417	+	18.7784i	0.435764	+	0.754766i	−0.561593	+	0.827413i	$0.689811\pi$
$620$	−8.48963			−0.340952
$621$		0			0
$622$	−6.11535			−0.245203
$623$	4.14399	+	7.17760i	0.166025	+	0.287564i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−14.8157	+	25.6615i	−0.592154	+	1.02564i
$627$		0			0
$628$	2.17480	+	3.76686i	0.0867840	+	0.150314i
$629$	−33.7921			−1.34738
$630$		0			0
$631$	−13.0224			−0.518415			−0.259207	−	0.965822i	$-0.583461\pi$
$631$	−13.0224			−0.518415			−0.259207	+	0.965822i	$0.583461\pi$
$632$	3.67282	+	6.36152i	0.146097	+	0.253048i
$633$		0			0
$634$	−8.41038	+	14.5672i	−0.334019	+	0.578538i
$635$	6.03081	−	10.4457i	0.239326	−	0.414524i
$636$		0			0
$637$	0.214003	+	0.370665i	0.00847912	+	0.0146863i
$638$	5.10083			0.201944
$639$		0			0
$640$	1.00000			0.0395285
$641$	−19.2252	−	33.2990i	−0.759350	−	1.31523i	−0.943182	−	0.332276i	$-0.892184\pi$
$641$	−19.2252	−	33.2990i	−0.759350	−	1.31523i	0.183832	−	0.982958i	$-0.441150\pi$
$642$		0			0
$643$	−15.0649	+	26.0932i	−0.594103	+	1.02902i	0.399570	+	0.916703i	$0.369160\pi$
$643$	−15.0649	+	26.0932i	−0.594103	+	1.02902i	−0.993673	+	0.112314i	$0.964174\pi$
$644$	−3.88683	+	6.73218i	−0.153162	+	0.265285i
$645$		0			0
$646$	13.6625	+	23.6641i	0.537542	+	0.931050i
$647$	22.4913			0.884225			0.442113	−	0.896960i	$-0.354229\pi$
$647$	22.4913			0.884225			0.442113	+	0.896960i	$0.354229\pi$
$648$		0			0
$649$	−3.61910			−0.142062
$650$	−0.214003	−	0.370665i	−0.00839390	−	0.0145387i
$651$		0			0
$652$	5.05239	−	8.75100i	0.197867	−	0.342716i
$653$	−7.85601	+	13.6070i	−0.307430	+	0.532484i	−0.977799	−	0.209544i	$-0.932802\pi$
$653$	−7.85601	+	13.6070i	−0.307430	+	0.532484i	0.670370	+	0.742027i	$0.266136\pi$
$654$		0			0
$655$	1.00924	+	1.74805i	0.0394341	+	0.0683019i
$656$	11.2633			0.439758
$657$		0			0
$658$	11.3456			0.442299
$659$	8.67282	+	15.0218i	0.337845	+	0.585165i	0.984027	−	0.178018i	$-0.0569686\pi$
$659$	8.67282	+	15.0218i	0.337845	+	0.585165i	−0.646182	+	0.763183i	$0.723635\pi$
$660$		0			0
$661$	−4.34960	+	7.53373i	−0.169180	+	0.293028i	−0.938132	−	0.346279i	$-0.887445\pi$
$661$	−4.34960	+	7.53373i	−0.169180	+	0.293028i	0.768952	+	0.639307i	$0.220779\pi$
$662$	−13.5905	+	23.5394i	−0.528208	+	0.914884i
$663$		0			0
$664$	−5.10083	−	8.83490i	−0.197951	−	0.342861i
$665$	4.81681			0.186788
$666$		0			0
$667$	−69.3227			−2.68418
$668$	3.69440	+	6.39889i	0.142941	+	0.247581i
$669$		0			0
$670$	5.65322	−	9.79167i	0.218403	−	0.378285i
$671$	1.21400	−	2.10272i	0.0468661	−	0.0811744i
$672$		0			0
$673$	0.284020	+	0.491937i	0.0109482	+	0.0189628i	0.871448	−	0.490489i	$-0.163182\pi$
$673$	0.284020	+	0.491937i	0.0109482	+	0.0189628i	−0.860499	+	0.509451i	$0.829848\pi$
$674$	14.5042			0.558679
$675$		0			0
$676$	−12.8168			−0.492954
$677$	18.4773	+	32.0036i	0.710140	+	1.23000i	0.964804	+	0.262969i	$0.0847017\pi$
$677$	18.4773	+	32.0036i	0.710140	+	1.23000i	−0.254664	+	0.967030i	$0.581965\pi$
$678$		0			0
$679$	−2.74482	+	4.75416i	−0.105336	+	0.182448i
$680$	2.83641	−	4.91281i	0.108771	−	0.188398i
$681$		0			0
$682$	2.42801	+	4.20543i	0.0929732	+	0.161034i
$683$	−32.7753			−1.25411			−0.627057	−	0.778973i	$-0.715741\pi$
$683$	−32.7753			−1.25411			−0.627057	+	0.778973i	$0.715741\pi$
$684$		0			0
$685$	−21.3602			−0.816130
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$		0			0
$688$	−3.07199	+	5.32085i	−0.117119	+	0.202855i
$689$	1.09159	−	1.89070i	0.0415865	−	0.0720298i
$690$		0			0
$691$	12.6913	+	21.9820i	0.482800	+	0.836233i	0.999805	−	0.0197487i	$-0.00628662\pi$
$691$	12.6913	+	21.9820i	0.482800	+	0.836233i	−0.517005	+	0.855982i	$0.672953\pi$
$692$	−0.489634			−0.0186131
$693$		0			0
$694$	6.65209			0.252510
$695$	−6.41764	−	11.1157i	−0.243435	−	0.421642i
$696$		0			0
$697$	31.9473	−	55.3344i	1.21009	−	2.09594i
$698$	5.56889	−	9.64559i	0.210785	−	0.365091i
$699$		0			0
$700$	−0.500000	−	0.866025i	−0.0188982	−	0.0327327i
$701$	47.9259			1.81014			0.905069	−	0.425265i	$-0.139819\pi$
$701$	47.9259			1.81014			0.905069	+	0.425265i	$0.139819\pi$
$702$		0			0
$703$	−28.6930			−1.08218
$704$	−0.285997	−	0.495361i	−0.0107789	−	0.0186696i
$705$		0			0
$706$	−12.6008	+	21.8253i	−0.474239	+	0.821405i
$707$	−1.71598	+	2.97216i	−0.0645361	+	0.111780i
$708$		0			0
$709$	16.1132	+	27.9088i	0.605143	+	1.04814i	0.992029	+	0.126011i	$0.0402174\pi$
$709$	16.1132	+	27.9088i	0.605143	+	1.04814i	−0.386886	+	0.922128i	$0.626449\pi$
$710$	−15.0224			−0.563782
$711$		0			0
$712$	8.28797			0.310605
$713$	−32.9977	−	57.1538i	−1.23578	−	2.14043i
$714$		0			0
$715$	−0.122408	+	0.212018i	−0.00457782	+	0.00792901i
$716$	−1.33641	+	2.31473i	−0.0499441	+	0.0865056i
$717$		0			0
$718$	5.71287	+	9.89499i	0.213203	+	0.369278i
$719$	−41.1562			−1.53487			−0.767434	−	0.641127i	$-0.778467\pi$
$719$	−41.1562			−1.53487			−0.767434	+	0.641127i	$0.778467\pi$
$720$		0			0
$721$	8.73445			0.325288
$722$	2.10083	+	3.63875i	0.0781848	+	0.135420i
$723$		0			0
$724$	5.00000	−	8.66025i	0.185824	−	0.321856i
$725$	4.45882	−	7.72290i	0.165596	−	0.286821i
$726$		0			0
$727$	−12.1409	−	21.0286i	−0.450280	−	0.779908i	0.548123	−	0.836398i	$-0.315343\pi$
$727$	−12.1409	−	21.0286i	−0.450280	−	0.779908i	−0.998403	+	0.0564894i	$0.982009\pi$
$728$	0.428007			0.0158630
$729$		0			0
$730$	−6.34565			−0.234863
$731$	17.4269	+	30.1842i	0.644556	+	1.11640i
$732$		0			0
$733$	7.90530	−	13.6924i	0.291989	−	0.505740i	−0.682291	−	0.731081i	$-0.739016\pi$
$733$	7.90530	−	13.6924i	0.291989	−	0.505740i	0.974280	+	0.225341i	$0.0723496\pi$
$734$	13.1801	−	22.8286i	0.486486	−	0.842618i
$735$		0			0
$736$	3.88683	+	6.73218i	0.143270	+	0.248152i
$737$	−6.46721			−0.238223
$738$		0			0
$739$	−39.3081			−1.44597			−0.722987	−	0.690862i	$-0.757231\pi$
$739$	−39.3081			−1.44597			−0.722987	+	0.690862i	$0.757231\pi$
$740$	2.97842	+	5.15878i	0.109489	+	0.189640i
$741$		0			0
$742$	2.55042	−	4.41745i	0.0936287	−	0.162170i
$743$	1.20166	−	2.08134i	0.0440847	−	0.0763569i	−0.843141	−	0.537692i	$-0.819296\pi$
$743$	1.20166	−	2.08134i	0.0440847	−	0.0763569i	0.887226	+	0.461335i	$0.152630\pi$
$744$		0			0
$745$	−2.10083	−	3.63875i	−0.0769685	−	0.133313i
$746$	34.6050			1.26698
$747$		0			0
$748$	−3.24482			−0.118642
$749$	7.36525	+	12.7570i	0.269120	+	0.466130i
$750$		0			0
$751$	−4.18008	+	7.24012i	−0.152533	+	0.264196i	−0.932158	−	0.362051i	$-0.882076\pi$
$751$	−4.18008	+	7.24012i	−0.152533	+	0.264196i	0.779625	+	0.626247i	$0.215410\pi$
$752$	5.67282	−	9.82562i	0.206867	−	0.358303i
$753$		0			0
$754$	1.90841	+	3.30545i	0.0695000	+	0.120378i
$755$	−3.63362			−0.132241
$756$		0			0
$757$	−28.8992			−1.05036			−0.525179	−	0.850992i	$-0.676002\pi$
$757$	−28.8992			−1.05036			−0.525179	+	0.850992i	$0.676002\pi$
$758$	−7.52158	−	13.0278i	−0.273196	−	0.473189i
$759$		0			0
$760$	2.40841	−	4.17148i	0.0873620	−	0.151315i
$761$	−14.2409	+	24.6659i	−0.516231	+	0.894138i	0.483592	+	0.875294i	$0.339332\pi$
$761$	−14.2409	+	24.6659i	−0.516231	+	0.894138i	−0.999822	+	0.0188444i	$0.994001\pi$
$762$		0			0
$763$	−1.50198	−	2.60150i	−0.0543752	−	0.0941806i
$764$	−10.8560			−0.392757
$765$		0			0
$766$	−23.8353			−0.861204
$767$	−1.35404	−	2.34526i	−0.0488914	−	0.0846825i
$768$		0			0
$769$	26.2148	−	45.4055i	0.945332	−	1.63736i	0.190246	−	0.981736i	$-0.439072\pi$
$769$	26.2148	−	45.4055i	0.945332	−	1.63736i	0.755086	−	0.655626i	$-0.227595\pi$
$770$	−0.285997	+	0.495361i	−0.0103066	+	0.0178516i
$771$		0			0
$772$	1.43922	+	2.49280i	0.0517986	+	0.0897178i
$773$	32.6376			1.17389			0.586946	−	0.809626i	$-0.300330\pi$
$773$	32.6376			1.17389			0.586946	+	0.809626i	$0.300330\pi$
$774$		0			0
$775$	8.48963			0.304957
$776$	2.74482	+	4.75416i	0.0985332	+	0.170664i
$777$		0			0
$778$	3.81681	−	6.61091i	0.136839	−	0.237013i
$779$	27.1266	−	46.9846i	0.971910	−	1.68340i
$780$		0			0
$781$	4.29636	+	7.44152i	0.153736	+	0.266278i
$782$	44.0986			1.57696
$783$		0			0
$784$	1.00000			0.0357143
$785$	−2.17480	−	3.76686i	−0.0776219	−	0.134445i
$786$		0			0
$787$	23.1378	−	40.0758i	0.824773	−	1.42855i	−0.0773205	−	0.997006i	$-0.524636\pi$
$787$	23.1378	−	40.0758i	0.824773	−	1.42855i	0.902093	−	0.431542i	$-0.142030\pi$
$788$	−9.28487	+	16.0819i	−0.330760	+	0.572893i
$789$		0			0
$790$	−3.67282	−	6.36152i	−0.130673	−	0.226333i
$791$	6.10478			0.217061
$792$		0			0
$793$	1.81681			0.0645168
$794$	−5.39719	−	9.34821i	−0.191539	−	0.331756i
$795$		0			0
$796$	7.66048	−	13.2683i	0.271519	−	0.470284i
$797$	−6.30249	+	10.9162i	−0.223246	+	0.386673i	−0.955792	−	0.294045i	$-0.904999\pi$
$797$	−6.30249	+	10.9162i	−0.223246	+	0.386673i	0.732546	+	0.680718i	$0.238332\pi$
$798$		0			0
$799$	−32.1809	−	55.7390i	−1.13848	−	1.97190i
$800$	−1.00000			−0.0353553
$801$		0			0
$802$	−18.2672			−0.645039
$803$	1.81483	+	3.14338i	0.0640441	+	0.110928i
$804$		0			0
$805$	3.88683	−	6.73218i	0.136993	−	0.237278i
$806$	−1.81681	+	3.14681i	−0.0639944	+	0.110842i
$807$		0			0
$808$	1.71598	+	2.97216i	0.0603680	+	0.104560i
$809$	12.7015			0.446560			0.223280	−	0.974754i	$-0.428324\pi$
$809$	12.7015			0.446560			0.223280	+	0.974754i	$0.428324\pi$
$810$		0			0
$811$	3.63136			0.127514			0.0637571	−	0.997965i	$-0.479692\pi$
$811$	3.63136			0.127514			0.0637571	+	0.997965i	$0.479692\pi$
$812$	4.45882	+	7.72290i	0.156474	+	0.271021i
$813$		0			0
$814$	1.70364	−	2.95079i	0.0597125	−	0.103425i
$815$	−5.05239	+	8.75100i	−0.176978	+	0.306534i
$816$		0			0
$817$	14.7972	+	25.6295i	0.517689	+	0.896663i
$818$	−5.90973			−0.206629
$819$		0			0
$820$	−11.2633			−0.393331
$821$	−0.584336	−	1.01210i	−0.0203935	−	0.0353225i	0.855649	−	0.517557i	$-0.173159\pi$
$821$	−0.584336	−	1.01210i	−0.0203935	−	0.0353225i	−0.876042	+	0.482235i	$0.839825\pi$
$822$		0			0
$823$	5.27958	−	9.14451i	0.184035	−	0.318757i	−0.759216	−	0.650839i	$-0.774417\pi$
$823$	5.27958	−	9.14451i	0.184035	−	0.318757i	0.943251	+	0.332081i	$0.107751\pi$
$824$	4.36723	−	7.56426i	0.152140	−	0.263513i
$825$		0			0
$826$	−3.16359	−	5.47950i	−0.110075	−	0.190656i
$827$	−0.220132			−0.00765474			−0.00382737	−	0.999993i	$-0.501218\pi$
$827$	−0.220132			−0.00765474			−0.00382737	+	0.999993i	$0.501218\pi$
$828$		0			0
$829$	9.02864			0.313578			0.156789	−	0.987632i	$-0.449886\pi$
$829$	9.02864			0.313578			0.156789	+	0.987632i	$0.449886\pi$
$830$	5.10083	+	8.83490i	0.177052	+	0.306664i
$831$		0			0
$832$	0.214003	−	0.370665i	0.00741923	−	0.0128505i
$833$	2.83641	−	4.91281i	0.0982758	−	0.170219i
$834$		0			0
$835$	−3.69440	−	6.39889i	−0.127850	−	0.221443i
$836$	−2.75518			−0.0952900
$837$		0			0
$838$	9.98153			0.344806
$839$	27.9445	+	48.4013i	0.964751	+	1.67100i	0.710282	+	0.703918i	$0.248568\pi$
$839$	27.9445	+	48.4013i	0.964751	+	1.67100i	0.254470	+	0.967081i	$0.418099\pi$
$840$		0			0
$841$	−25.2622	+	43.7553i	−0.871109	+	1.50880i
$842$	−18.8661	+	32.6770i	−0.650169	+	1.12612i
$843$		0			0
$844$	−5.63362	−	9.75772i	−0.193917	−	0.335874i
$845$	12.8168			0.440912
$846$		0			0
$847$	−10.6728			−0.366723
$848$	−2.55042	−	4.41745i	−0.0875816	−	0.151696i
$849$		0			0
$850$	−2.83641	+	4.91281i	−0.0972881	+	0.168508i
$851$	−23.1532	+	40.1026i	−0.793682	+	1.37470i
$852$		0			0
$853$	−19.8969	−	34.4625i	−0.681257	−	1.17997i	−0.974597	−	0.223964i	$-0.928100\pi$
$853$	−19.8969	−	34.4625i	−0.681257	−	1.17997i	0.293340	−	0.956008i	$-0.405233\pi$
$854$	4.24482			0.145255
$855$		0			0
$856$	14.7305			0.503478
$857$	23.5028	+	40.7081i	0.802841	+	1.39056i	0.917739	+	0.397184i	$0.130013\pi$
$857$	23.5028	+	40.7081i	0.802841	+	1.39056i	−0.114898	+	0.993377i	$0.536654\pi$
$858$		0			0
$859$	−10.1613	+	17.5999i	−0.346700	+	0.600502i	−0.985661	−	0.168737i	$-0.946031\pi$
$859$	−10.1613	+	17.5999i	−0.346700	+	0.600502i	0.638961	+	0.769239i	$0.279364\pi$
$860$	3.07199	−	5.32085i	0.104754	−	0.181439i
$861$		0			0
$862$	−7.11930	−	12.3310i	−0.242484	−	0.419995i
$863$	44.4033			1.51151			0.755753	−	0.654856i	$-0.227271\pi$
$863$	44.4033			1.51151			0.755753	+	0.654856i	$0.227271\pi$
$864$		0			0
$865$	0.489634			0.0166481
$866$	8.60478	+	14.9039i	0.292402	+	0.506456i
$867$		0			0
$868$	−4.24482	+	7.35224i	−0.144078	+	0.249551i
$869$	−2.10083	+	3.63875i	−0.0712658	+	0.123436i
$870$		0			0
$871$	−2.41962	−	4.19090i	−0.0819856	−	0.142003i
$872$	−3.00395			−0.101727
$873$		0			0
$874$	37.4442			1.26657
$875$	0.500000	+	0.866025i	0.0169031	+	0.0292770i
$876$		0			0
$877$	−9.30334	+	16.1139i	−0.314151	+	0.544126i	−0.979257	−	0.202623i	$-0.935053\pi$
$877$	−9.30334	+	16.1139i	−0.314151	+	0.544126i	0.665105	+	0.746750i	$0.268387\pi$
$878$	−20.0453	+	34.7195i	−0.676497	+	1.17173i
$879$		0			0
$880$	0.285997	+	0.495361i	0.00964094	+	0.0166986i
$881$	0.549569			0.0185155			0.00925773	−	0.999957i	$-0.497053\pi$
$881$	0.549569			0.0185155			0.00925773	+	0.999957i	$0.497053\pi$
$882$		0			0
$883$	21.6359			0.728105			0.364053	−	0.931378i	$-0.381393\pi$
$883$	21.6359			0.728105			0.364053	+	0.931378i	$0.381393\pi$
$884$	−1.21400	−	2.10272i	−0.0408314	−	0.0707220i
$885$		0			0
$886$	4.25518	−	7.37019i	0.142956	−	0.247606i
$887$	−4.52884	+	7.84418i	−0.152063	+	0.263382i	−0.931986	−	0.362495i	$-0.881925\pi$
$887$	−4.52884	+	7.84418i	−0.152063	+	0.263382i	0.779922	+	0.625876i	$0.215258\pi$
$888$		0			0
$889$	−6.03081	−	10.4457i	−0.202267	−	0.350337i
$890$	−8.28797			−0.277813
$891$		0			0
$892$	6.44648			0.215844
$893$	−27.3249	−	47.3281i	−0.914393	−	1.58378i
$894$		0			0
$895$	1.33641	−	2.31473i	0.0446713	−	0.0773730i
$896$	0.500000	−	0.866025i	0.0167038	−	0.0289319i
$897$		0			0
$898$	−6.54844	−	11.3422i	−0.218524	−	0.378495i
$899$	−75.7075			−2.52499
$900$		0			0
$901$	−28.9361			−0.964002
$902$	3.22126	+	5.57939i	0.107256	+	0.185773i
$903$		0			0
$904$	3.05239	−	5.28690i	0.101521	−	0.175840i
$905$	−5.00000	+	8.66025i	−0.166206	+	0.287877i
$906$		0			0
$907$	−17.7972	−	30.8257i	−0.590947	−	1.02355i	−0.994105	−	0.108419i	$-0.965421\pi$
$907$	−17.7972	−	30.8257i	−0.590947	−	1.02355i	0.403159	−	0.915130i	$-0.367912\pi$
$908$	3.73445			0.123932
$909$		0			0
$910$	−0.428007			−0.0141883
$911$	−12.8344	−	22.2299i	−0.425224	−	0.736509i	0.571217	−	0.820799i	$-0.306471\pi$
$911$	−12.8344	−	22.2299i	−0.425224	−	0.736509i	−0.996441	+	0.0842895i	$0.973138\pi$
$912$		0			0
$913$	2.91764	−	5.05350i	0.0965598	−	0.167247i
$914$	−14.0165	+	24.2773i	−0.463624	+	0.803021i
$915$		0			0
$916$	−2.07925	−	3.60137i	−0.0687004	−	0.118993i
$917$	2.01847			0.0666558
$918$		0			0
$919$	−11.7842			−0.388726			−0.194363	−	0.980930i	$-0.562264\pi$
$919$	−11.7842			−0.388726			−0.194363	+	0.980930i	$0.562264\pi$
$920$	−3.88683	−	6.73218i	−0.128145	−	0.221953i
$921$		0			0
$922$	−10.9784	+	19.0152i	−0.361555	+	0.626232i
$923$	−3.21485	+	5.56828i	−0.105818	+	0.183282i
$924$		0			0
$925$	−2.97842	−	5.15878i	−0.0979299	−	0.169620i
$926$	−12.2017			−0.400971
$927$		0			0
$928$	8.91764			0.292736
$929$	−11.4280	−	19.7939i	−0.374941	−	0.649416i	0.615377	−	0.788233i	$-0.289004\pi$
$929$	−11.4280	−	19.7939i	−0.374941	−	0.649416i	−0.990318	+	0.138816i	$0.955670\pi$
$930$		0			0
$931$	2.40841	−	4.17148i	0.0789323	−	0.136715i
$932$	−10.0204	+	17.3559i	−0.328231	+	0.568512i
$933$		0			0
$934$	13.2129	+	22.8854i	0.432338	+	0.748832i
$935$	3.24482			0.106117
$936$		0			0
$937$	−25.2073			−0.823487			−0.411743	−	0.911300i	$-0.635080\pi$
$937$	−25.2073			−0.823487			−0.411743	+	0.911300i	$0.635080\pi$
$938$	−5.65322	−	9.79167i	−0.184584	−	0.319709i
$939$		0			0
$940$	−5.67282	+	9.82562i	−0.185027	+	0.320476i
$941$	−6.73445	+	11.6644i	−0.219537	+	0.380249i	−0.954666	−	0.297678i	$-0.903788\pi$
$941$	−6.73445	+	11.6644i	−0.219537	+	0.380249i	0.735130	+	0.677927i	$0.237121\pi$
$942$		0			0
$943$	−43.7785	−	75.8265i	−1.42562	−	2.46925i
$944$	−6.32718			−0.205932
$945$		0			0
$946$	−3.51432			−0.114260
$947$	−24.4832	−	42.4062i	−0.795598	−	1.37802i	−0.922459	−	0.386095i	$-0.873824\pi$
$947$	−24.4832	−	42.4062i	−0.795598	−	1.37802i	0.126861	−	0.991920i	$-0.459510\pi$
$948$		0			0
$949$	−1.35799	+	2.35211i	−0.0440822	+	0.0763526i
$950$	−2.40841	+	4.17148i	−0.0781390	+	0.135341i
$951$		0			0
$952$	−2.83641	−	4.91281i	−0.0919286	−	0.159225i
$953$	−27.9546			−0.905538			−0.452769	−	0.891628i	$-0.649564\pi$
$953$	−27.9546			−0.905538			−0.452769	+	0.891628i	$0.649564\pi$
$954$		0			0
$955$	10.8560			0.351292
$956$	6.24482	+	10.8163i	0.201972	+	0.349825i
$957$		0			0
$958$	18.3949	−	31.8610i	0.594313	−	1.02938i
$959$	−10.6801	+	18.4984i	−0.344878	+	0.597346i
$960$		0			0
$961$	−20.5369	−	35.5710i	−0.662482	−	1.14745i
$962$	2.54957			0.0822014
$963$		0			0
$964$	−2.38880			−0.0769382
$965$	−1.43922	−	2.49280i	−0.0463301	−	0.0802461i
$966$		0			0
$967$	−18.6481	+	32.2995i	−0.599684	+	1.03868i	0.393184	+	0.919460i	$0.371374\pi$
$967$	−18.6481	+	32.2995i	−0.599684	+	1.03868i	−0.992868	+	0.119223i	$0.961960\pi$
$968$	−5.33641	+	9.24294i	−0.171519	+	0.297079i
$969$		0			0
$970$	−2.74482	−	4.75416i	−0.0881308	−	0.152647i
$971$	−20.0739			−0.644202			−0.322101	−	0.946705i	$-0.604389\pi$
$971$	−20.0739			−0.644202			−0.322101	+	0.946705i	$0.604389\pi$
$972$		0			0
$973$	−12.8353			−0.411480
$974$	8.38880	+	14.5298i	0.268795	+	0.465566i
$975$		0			0
$976$	2.12241	−	3.67612i	0.0679366	−	0.117670i
$977$	−4.21513	+	7.30083i	−0.134854	+	0.233574i	−0.925542	−	0.378646i	$-0.876390\pi$
$977$	−4.21513	+	7.30083i	−0.134854	+	0.233574i	0.790688	+	0.612220i	$0.209723\pi$
$978$		0			0
$979$	2.37033	+	4.10554i	0.0757562	+	0.131214i
$980$	−1.00000			−0.0319438
$981$		0			0
$982$	−23.3681			−0.745705
$983$	−18.4896	−	32.0250i	−0.589728	−	1.02144i	−0.994268	−	0.106918i	$-0.965902\pi$
$983$	−18.4896	−	32.0250i	−0.589728	−	1.02144i	0.404540	−	0.914520i	$-0.367432\pi$
$984$		0			0
$985$	9.28487	−	16.0819i	0.295840	−	0.512411i
$986$	25.2941	−	43.8107i	0.805528	−	1.39522i
$987$		0			0
$988$	−1.03081	−	1.78542i	−0.0327945	−	0.0568018i
$989$	47.7612			1.51872
$990$		0			0
$991$	−12.4482			−0.395429			−0.197715	−	0.980260i	$-0.563352\pi$
$991$	−12.4482			−0.395429			−0.197715	+	0.980260i	$0.563352\pi$
$992$	4.24482	+	7.35224i	0.134773	+	0.233434i
$993$		0			0
$994$	−7.51121	+	13.0098i	−0.238241	+	0.412646i
$995$	−7.66048	+	13.2683i	−0.242854	+	0.420635i
$996$		0			0
$997$	−1.30249	−	2.25598i	−0.0412503	−	0.0714476i	0.844663	−	0.535298i	$-0.179801\pi$
$997$	−1.30249	−	2.25598i	−0.0412503	−	0.0714476i	−0.885913	+	0.463851i	$0.846467\pi$
$998$	−22.8106			−0.722057
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.j.j.631.2		6
3.2	odd	2		630.2.j.k.211.1	✓	6
9.2	odd	6		630.2.j.k.421.1	yes	6
9.4	even	3		5670.2.a.bp.1.2		3
9.5	odd	6		5670.2.a.bt.1.2		3
9.7	even	3	inner	1890.2.j.j.1261.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.j.k.211.1	✓	6	3.2	odd	2
630.2.j.k.421.1	yes	6	9.2	odd	6
1890.2.j.j.631.2		6	1.1	even	1	trivial
1890.2.j.j.1261.2		6	9.7	even	3	inner
5670.2.a.bp.1.2		3	9.4	even	3
5670.2.a.bt.1.2		3	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.j (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +1.00000 q^{10} +(-0.285997 - 0.495361i) q^{11} +(0.214003 - 0.370665i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} -5.67282 q^{17} -4.81681 q^{19} +(0.500000 + 0.866025i) q^{20} +(0.285997 - 0.495361i) q^{22} +(-3.88683 + 6.73218i) q^{23} +(-0.500000 - 0.866025i) q^{25} +0.428007 q^{26} +1.00000 q^{28} +(4.45882 + 7.72290i) q^{29} +(-4.24482 + 7.35224i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.83641 - 4.91281i) q^{34} -1.00000 q^{35} +5.95684 q^{37} +(-2.40841 - 4.17148i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(-5.63164 + 9.75429i) q^{41} +(-3.07199 - 5.32085i) q^{43} +0.571993 q^{44} -7.77365 q^{46} +(5.67282 + 9.82562i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.214003 + 0.370665i) q^{52} +5.10083 q^{53} -0.571993 q^{55} +(0.500000 + 0.866025i) q^{56} +(-4.45882 + 7.72290i) q^{58} +(3.16359 - 5.47950i) q^{59} +(2.12241 + 3.67612i) q^{61} -8.48963 q^{62} +1.00000 q^{64} +(-0.214003 - 0.370665i) q^{65} +(5.65322 - 9.79167i) q^{67} +(2.83641 - 4.91281i) q^{68} +(-0.500000 - 0.866025i) q^{70} -15.0224 q^{71} -6.34565 q^{73} +(2.97842 + 5.15878i) q^{74} +(2.40841 - 4.17148i) q^{76} +(-0.285997 + 0.495361i) q^{77} +(-3.67282 - 6.36152i) q^{79} -1.00000 q^{80} -11.2633 q^{82} +(5.10083 + 8.83490i) q^{83} +(-2.83641 + 4.91281i) q^{85} +(3.07199 - 5.32085i) q^{86} +(0.285997 + 0.495361i) q^{88} -8.28797 q^{89} -0.428007 q^{91} +(-3.88683 - 6.73218i) q^{92} +(-5.67282 + 9.82562i) q^{94} +(-2.40841 + 4.17148i) q^{95} +(-2.74482 - 4.75416i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 3 q^{7} - 6 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 3 * q^7 - 6 * q^8	\( 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 3 q^{7} - 6 q^{8} + 6 q^{10} - q^{11} + 2 q^{13} + 3 q^{14} - 3 q^{16} - 14 q^{17} - 6 q^{19} + 3 q^{20} + q^{22} - 4 q^{23} - 3 q^{25} + 4 q^{26} + 6 q^{28} + 6 q^{29} - 4 q^{31} + 3 q^{32} - 7 q^{34} - 6 q^{35} + 20 q^{37} - 3 q^{38} - 3 q^{40} + 7 q^{41} - 17 q^{43} + 2 q^{44} - 8 q^{46} + 14 q^{47} - 3 q^{49} + 3 q^{50} + 2 q^{52} + 12 q^{53} - 2 q^{55} + 3 q^{56} - 6 q^{58} + 29 q^{59} + 2 q^{61} - 8 q^{62} + 6 q^{64} - 2 q^{65} + q^{67} + 7 q^{68} - 3 q^{70} - 20 q^{71} + 2 q^{73} + 10 q^{74} + 3 q^{76} - q^{77} - 2 q^{79} - 6 q^{80} + 14 q^{82} + 12 q^{83} - 7 q^{85} + 17 q^{86} + q^{88} - 44 q^{89} - 4 q^{91} - 4 q^{92} - 14 q^{94} - 3 q^{95} + 5 q^{97} - 6 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 3 * q^7 - 6 * q^8 + 6 * q^10 - q^11 + 2 * q^13 + 3 * q^14 - 3 * q^16 - 14 * q^17 - 6 * q^19 + 3 * q^20 + q^22 - 4 * q^23 - 3 * q^25 + 4 * q^26 + 6 * q^28 + 6 * q^29 - 4 * q^31 + 3 * q^32 - 7 * q^34 - 6 * q^35 + 20 * q^37 - 3 * q^38 - 3 * q^40 + 7 * q^41 - 17 * q^43 + 2 * q^44 - 8 * q^46 + 14 * q^47 - 3 * q^49 + 3 * q^50 + 2 * q^52 + 12 * q^53 - 2 * q^55 + 3 * q^56 - 6 * q^58 + 29 * q^59 + 2 * q^61 - 8 * q^62 + 6 * q^64 - 2 * q^65 + q^67 + 7 * q^68 - 3 * q^70 - 20 * q^71 + 2 * q^73 + 10 * q^74 + 3 * q^76 - q^77 - 2 * q^79 - 6 * q^80 + 14 * q^82 + 12 * q^83 - 7 * q^85 + 17 * q^86 + q^88 - 44 * q^89 - 4 * q^91 - 4 * q^92 - 14 * q^94 - 3 * q^95 + 5 * q^97 - 6 * q^98

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