LMFDB - Embedded newform 756.2.ba.a.71.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(71,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("756.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ba (of order $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.5
Character	$\chi$	$=$	756.71
Dual form			756.2.ba.a.575.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31979 + 0.508077i) q^{2} +(1.48372 - 1.34111i) q^{4} +(2.42137 + 1.39798i) q^{5} +(0.866025 - 0.500000i) q^{7} +(-1.27681 + 2.52384i) q^{8} +O(q^{10})$	\(q+(-1.31979 + 0.508077i) q^{2} +(1.48372 - 1.34111i) q^{4} +(2.42137 + 1.39798i) q^{5} +(0.866025 - 0.500000i) q^{7} +(-1.27681 + 2.52384i) q^{8} +(-3.90599 - 0.614803i) q^{10} +(-0.140963 - 0.244156i) q^{11} +(-2.43776 + 4.22232i) q^{13} +(-0.888937 + 1.09990i) q^{14} +(0.402825 - 3.97966i) q^{16} +5.66309i q^{17} +7.39353i q^{19} +(5.46748 - 1.17313i) q^{20} +(0.310093 + 0.250615i) q^{22} +(3.28934 - 5.69730i) q^{23} +(1.40869 + 2.43992i) q^{25} +(1.07208 - 6.81116i) q^{26} +(0.614378 - 1.90330i) q^{28} +(0.243350 - 0.140498i) q^{29} +(-8.09138 - 4.67156i) q^{31} +(1.49033 + 5.45701i) q^{32} +(-2.87728 - 7.47411i) q^{34} +2.79596 q^{35} +4.22211 q^{37} +(-3.75648 - 9.75794i) q^{38} +(-6.61990 + 4.32619i) q^{40} +(0.644767 + 0.372257i) q^{41} +(6.31743 - 3.64737i) q^{43} +(-0.536590 - 0.173210i) q^{44} +(-1.44658 + 9.19051i) q^{46} +(2.59024 + 4.48642i) q^{47} +(0.500000 - 0.866025i) q^{49} +(-3.09885 - 2.50448i) q^{50} +(2.04567 + 9.53403i) q^{52} +8.11915i q^{53} -0.788256i q^{55} +(0.156168 + 2.82411i) q^{56} +(-0.249788 + 0.309069i) q^{58} +(-0.215457 + 0.373183i) q^{59} +(2.95890 + 5.12497i) q^{61} +(13.0525 + 2.05446i) q^{62} +(-4.73951 - 6.44493i) q^{64} +(-11.8054 + 6.81586i) q^{65} +(2.11124 + 1.21893i) q^{67} +(7.59485 + 8.40241i) q^{68} +(-3.69009 + 1.42056i) q^{70} +2.47114 q^{71} +0.714758 q^{73} +(-5.57232 + 2.14516i) q^{74} +(9.91556 + 10.9699i) q^{76} +(-0.244156 - 0.140963i) q^{77} +(-2.15347 + 1.24331i) q^{79} +(6.53888 - 9.07310i) q^{80} +(-1.04010 - 0.163711i) q^{82} +(-4.10072 - 7.10266i) q^{83} +(-7.91688 + 13.7124i) q^{85} +(-6.48457 + 8.02353i) q^{86} +(0.796193 - 0.0440279i) q^{88} +0.354223i q^{89} +4.87551i q^{91} +(-2.76029 - 12.8646i) q^{92} +(-5.69802 - 4.60511i) q^{94} +(-10.3360 + 17.9025i) q^{95} +(-0.138992 - 0.240741i) q^{97} +(-0.219890 + 1.39701i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100}) $ 72 * q + 42 * q^20 + 36 * q^25 - 30 * q^32 - 12 * q^34 - 12 * q^40 + 60 * q^41 - 24 * q^46 + 36 * q^49 + 78 * q^50 - 18 * q^52 - 18 * q^58 - 60 * q^64 - 24 * q^65 - 78 * q^68 - 24 * q^73 + 12 * q^76 - 36 * q^82 - 30 * q^86 + 24 * q^88 + 114 * q^92 + 42 * q^94 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	−1.31979	+	0.508077i	−0.933236	+	0.359265i
$2$	−1.31979	+	0.508077i	−0.933236	+	0.359265i
$3$		0			0
$3$		0			0
$4$	1.48372	−	1.34111i	0.741858	−	0.670557i
$5$	2.42137	+	1.39798i	1.08287	+	0.625195i	0.931669	−	0.363308i	$-0.118353\pi$
$5$	2.42137	+	1.39798i	1.08287	+	0.625195i	0.151201	+	0.988503i	$0.451686\pi$
$6$		0			0
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$	−1.27681	+	2.52384i	−0.451421	+	0.892311i
$9$		0			0
$10$	−3.90599	−	0.614803i	−1.23518	−	0.194418i
$11$	−0.140963	−	0.244156i	−0.0425021	−	0.0736157i	0.843992	−	0.536356i	$-0.180200\pi$
$11$	−0.140963	−	0.244156i	−0.0425021	−	0.0736157i	−0.886494	+	0.462740i	$0.846866\pi$
$12$		0			0
$13$	−2.43776	+	4.22232i	−0.676112	+	1.17106i	0.300031	+	0.953930i	$0.403003\pi$
$13$	−2.43776	+	4.22232i	−0.676112	+	1.17106i	−0.976143	+	0.217131i	$0.930330\pi$
$14$	−0.888937	+	1.09990i	−0.237578	+	0.293962i
$15$		0			0
$16$	0.402825	−	3.97966i	0.100706	−	0.994916i
$17$			5.66309i			1.37350i	0.726894	+	0.686750i	$0.240963\pi$
$17$			5.66309i			1.37350i	−0.726894	+	0.686750i	$0.759037\pi$
$18$		0			0
$19$			7.39353i			1.69619i	0.529843	+	0.848096i	$0.322251\pi$
$19$			7.39353i			1.69619i	−0.529843	+	0.848096i	$0.677749\pi$
$20$	5.46748	−	1.17313i	1.22256	−	0.262320i
$21$		0			0
$22$	0.310093	+	0.250615i	0.0661120	+	0.0534314i
$23$	3.28934	−	5.69730i	0.685875	−	1.18797i	−0.287286	−	0.957845i	$-0.592753\pi$
$23$	3.28934	−	5.69730i	0.685875	−	1.18797i	0.973161	−	0.230125i	$-0.0739135\pi$
$24$		0			0
$25$	1.40869	+	2.43992i	0.281738	+	0.487985i
$26$	1.07208	−	6.81116i	0.210251	−	1.33578i
$27$		0			0
$28$	0.614378	−	1.90330i	0.116107	−	0.359689i
$29$	0.243350	−	0.140498i	0.0451889	−	0.0260898i	−0.477235	−	0.878776i	$-0.658361\pi$
$29$	0.243350	−	0.140498i	0.0451889	−	0.0260898i	0.522424	+	0.852686i	$0.325028\pi$
$30$		0			0
$31$	−8.09138	−	4.67156i	−1.45325	−	0.839037i	−0.454590	−	0.890701i	$-0.650214\pi$
$31$	−8.09138	−	4.67156i	−1.45325	−	0.839037i	−0.998665	+	0.0516641i	$0.983547\pi$
$32$	1.49033	+	5.45701i	0.263456	+	0.964672i
$33$		0			0
$34$	−2.87728	−	7.47411i	−0.493450	−	1.28180i
$35$	2.79596			0.472603
$36$		0			0
$37$	4.22211			0.694111			0.347056	−	0.937845i	$-0.387182\pi$
$37$	4.22211			0.694111			0.347056	+	0.937845i	$0.387182\pi$
$38$	−3.75648	−	9.75794i	−0.609382	−	1.58295i
$39$		0			0
$40$	−6.61990	+	4.32619i	−1.04670	+	0.684031i
$41$	0.644767	+	0.372257i	0.100696	+	0.0581367i	0.549502	−	0.835492i	$-0.314817\pi$
$41$	0.644767	+	0.372257i	0.100696	+	0.0581367i	−0.448806	+	0.893629i	$0.648151\pi$
$42$		0			0
$43$	6.31743	−	3.64737i	0.963400	−	0.556219i	0.0661820	−	0.997808i	$-0.478918\pi$
$43$	6.31743	−	3.64737i	0.963400	−	0.556219i	0.897218	+	0.441588i	$0.145585\pi$
$44$	−0.536590	−	0.173210i	−0.0808941	−	0.0261124i
$45$		0			0
$46$	−1.44658	+	9.19051i	−0.213287	+	1.35507i
$47$	2.59024	+	4.48642i	0.377825	+	0.654412i	0.990745	−	0.135733i	$-0.0433389\pi$
$47$	2.59024	+	4.48642i	0.377825	+	0.654412i	−0.612921	+	0.790144i	$0.710006\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	−3.09885	−	2.50448i	−0.438244	−	0.354186i
$51$		0			0
$52$	2.04567	+	9.53403i	0.283684	+	1.32213i
$53$			8.11915i			1.11525i	0.830093	+	0.557625i	$0.188287\pi$
$53$			8.11915i			1.11525i	−0.830093	+	0.557625i	$0.811713\pi$
$54$		0			0
$55$		−	0.788256i		−	0.106288i
$56$	0.156168	+	2.82411i	0.0208688	+	0.377388i
$57$		0			0
$58$	−0.249788	+	0.309069i	−0.0327988	+	0.0405828i
$59$	−0.215457	+	0.373183i	−0.0280501	+	0.0485843i	−0.879710	−	0.475511i	$-0.842263\pi$
$59$	−0.215457	+	0.373183i	−0.0280501	+	0.0485843i	0.851660	+	0.524095i	$0.175596\pi$
$60$		0			0
$61$	2.95890	+	5.12497i	0.378848	+	0.656185i	0.990895	−	0.134637i	$-0.0429869\pi$
$61$	2.95890	+	5.12497i	0.378848	+	0.656185i	−0.612047	+	0.790822i	$0.709654\pi$
$62$	13.0525	+	2.05446i	1.65767	+	0.260916i
$63$		0			0
$64$	−4.73951	−	6.44493i	−0.592438	−	0.805616i
$65$	−11.8054	+	6.81586i	−1.46428	+	0.845404i
$66$		0			0
$67$	2.11124	+	1.21893i	0.257930	+	0.148916i	0.623390	−	0.781911i	$-0.285755\pi$
$67$	2.11124	+	1.21893i	0.257930	+	0.148916i	−0.365460	+	0.930827i	$0.619088\pi$
$68$	7.59485	+	8.40241i	0.921010	+	1.01894i
$69$		0			0
$70$	−3.69009	+	1.42056i	−0.441050	+	0.169790i
$71$	2.47114			0.293270			0.146635	−	0.989191i	$-0.453156\pi$
$71$	2.47114			0.293270			0.146635	+	0.989191i	$0.453156\pi$
$72$		0			0
$73$	0.714758			0.0836560			0.0418280	−	0.999125i	$-0.486682\pi$
$73$	0.714758			0.0836560			0.0418280	+	0.999125i	$0.486682\pi$
$74$	−5.57232	+	2.14516i	−0.647769	+	0.249370i
$75$		0			0
$76$	9.91556	+	10.9699i	1.13739	+	1.25833i
$77$	−0.244156	−	0.140963i	−0.0278241	−	0.0160643i
$78$		0			0
$79$	−2.15347	+	1.24331i	−0.242285	+	0.139883i	−0.616226	−	0.787569i	$-0.711339\pi$
$79$	−2.15347	+	1.24331i	−0.242285	+	0.139883i	0.373942	+	0.927452i	$0.378006\pi$
$80$	6.53888	−	9.07310i	0.731069	−	1.01440i
$81$		0			0
$82$	−1.04010	−	0.163711i	−0.114859	−	0.0180788i
$83$	−4.10072	−	7.10266i	−0.450113	−	0.779618i	0.548280	−	0.836295i	$-0.315283\pi$
$83$	−4.10072	−	7.10266i	−0.450113	−	0.779618i	−0.998393	+	0.0566769i	$0.981950\pi$
$84$		0			0
$85$	−7.91688	+	13.7124i	−0.858706	+	1.48732i
$86$	−6.48457	+	8.02353i	−0.699249	+	0.865199i
$87$		0			0
$88$	0.796193	−	0.0440279i	0.0848745	−	0.00469339i
$89$			0.354223i			0.0375476i	0.999824	+	0.0187738i	$0.00597624\pi$
$89$			0.354223i			0.0375476i	−0.999824	+	0.0187738i	$0.994024\pi$
$90$		0			0
$91$			4.87551i			0.511093i
$92$	−2.76029	−	12.8646i	−0.287780	−	1.34122i
$93$		0			0
$94$	−5.69802	−	4.60511i	−0.587706	−	0.474981i
$95$	−10.3360	+	17.9025i	−1.06045	+	1.83675i
$96$		0			0
$97$	−0.138992	−	0.240741i	−0.0141125	−	0.0244435i	0.858883	−	0.512172i	$-0.171159\pi$
$97$	−0.138992	−	0.240741i	−0.0141125	−	0.0244435i	−0.872995	+	0.487728i	$0.837826\pi$
$98$	−0.219890	+	1.39701i	−0.0222122	+	0.141120i
$99$		0			0
$100$	5.36231	+	1.73094i	0.536231	+	0.173094i
$101$	−12.2098	+	7.04936i	−1.21493	+	0.701437i	−0.963828	−	0.266525i	$-0.914125\pi$
$101$	−12.2098	+	7.04936i	−1.21493	+	0.701437i	−0.251097	+	0.967962i	$0.580791\pi$
$102$		0			0
$103$	9.34581	+	5.39581i	0.920870	+	0.531665i	0.883913	−	0.467652i	$-0.154900\pi$
$103$	9.34581	+	5.39581i	0.920870	+	0.531665i	0.0369577	+	0.999317i	$0.488233\pi$
$104$	−7.54389	−	11.5436i	−0.739739	−	1.13194i
$105$		0			0
$106$	−4.12515	−	10.7156i	−0.400670	−	1.04079i
$107$	3.76330			0.363811			0.181906	−	0.983316i	$-0.441773\pi$
$107$	3.76330			0.363811			0.181906	+	0.983316i	$0.441773\pi$
$108$		0			0
$109$	6.11566			0.585774			0.292887	−	0.956147i	$-0.405384\pi$
$109$	6.11566			0.585774			0.292887	+	0.956147i	$0.405384\pi$
$110$	0.400494	+	1.04034i	0.0381856	+	0.0991921i
$111$		0			0
$112$	−1.64098	−	3.64790i	−0.155058	−	0.344694i
$113$	−1.77771	−	1.02636i	−0.167233	−	0.0965519i	0.414048	−	0.910255i	$-0.364115\pi$
$113$	−1.77771	−	1.02636i	−0.167233	−	0.0965519i	−0.581280	+	0.813703i	$0.697448\pi$
$114$		0			0
$115$	15.9294	−	9.19686i	1.48543	−	0.857611i
$116$	0.172638	−	0.534819i	0.0160290	−	0.0496567i
$117$		0			0
$118$	0.0947537	−	0.601993i	0.00872278	−	0.0554180i
$119$	2.83154	+	4.90438i	0.259567	+	0.449583i
$120$		0			0
$121$	5.46026	−	9.45745i	0.496387	−	0.859768i
$122$	−6.50902	−	5.26055i	−0.589299	−	0.476268i
$123$		0			0
$124$	−18.2704	+	3.92020i	−1.64073	+	0.352044i
$125$		−	6.10251i		−	0.545825i
$126$		0			0
$127$		−	12.5913i		−	1.11729i	−0.829406	−	0.558647i	$-0.811321\pi$
$127$		−	12.5913i		−	1.11729i	0.829406	−	0.558647i	$-0.188679\pi$
$128$	9.52969	+	6.09794i	0.842314	+	0.538987i
$129$		0			0
$130$	12.1178	−	14.9936i	1.06280	−	1.31503i
$131$	−4.13063	+	7.15447i	−0.360895	+	0.625089i	−0.988108	−	0.153759i	$-0.950862\pi$
$131$	−4.13063	+	7.15447i	−0.360895	+	0.625089i	0.627213	+	0.778848i	$0.284195\pi$
$132$		0			0
$133$	3.69676	+	6.40298i	0.320550	+	0.555209i
$134$	−3.40572	−	0.536060i	−0.294209	−	0.0463085i
$135$		0			0
$136$	−14.2927	−	7.23069i	−1.22559	−	0.620027i
$137$	14.5034	−	8.37353i	1.23911	−	0.715399i	0.270195	−	0.962806i	$-0.412912\pi$
$137$	14.5034	−	8.37353i	1.23911	−	0.715399i	0.968912	+	0.247407i	$0.0795784\pi$
$138$		0			0
$139$	−20.1639	−	11.6416i	−1.71028	−	0.987430i	−0.934169	−	0.356831i	$-0.883857\pi$
$139$	−20.1639	−	11.6416i	−1.71028	−	0.987430i	−0.776110	−	0.630598i	$-0.782810\pi$
$140$	4.14841	−	3.74970i	0.350604	−	0.316907i
$141$		0			0
$142$	−3.26140	+	1.25553i	−0.273690	+	0.105362i
$143$	1.37454			0.114945
$144$		0			0
$145$	0.785654			0.0652450
$146$	−0.943333	+	0.363152i	−0.0780708	+	0.0300547i
$147$		0			0
$148$	6.26442	−	5.66234i	0.514932	−	0.465441i
$149$	9.96222	+	5.75169i	0.816137	+	0.471197i	0.849083	−	0.528260i	$-0.177155\pi$
$149$	9.96222	+	5.75169i	0.816137	+	0.471197i	−0.0329454	+	0.999457i	$0.510489\pi$
$150$		0			0
$151$	4.20513	−	2.42783i	0.342209	−	0.197574i	−0.319040	−	0.947741i	$-0.603360\pi$
$151$	4.20513	−	2.42783i	0.342209	−	0.197574i	0.661248	+	0.750167i	$0.270027\pi$
$152$	−18.6601	−	9.44014i	−1.51353	−	0.765696i
$153$		0			0
$154$	0.393856	+	0.0619928i	0.0317378	+	0.00499553i
$155$	−13.0615	−	22.6232i	−1.04912	−	1.81714i
$156$		0			0
$157$	10.1032	−	17.4992i	0.806322	−	1.39659i	−0.109073	−	0.994034i	$-0.534788\pi$
$157$	10.1032	−	17.4992i	0.806322	−	1.39659i	0.915395	−	0.402557i	$-0.131878\pi$
$158$	2.21045	−	2.73504i	0.175854	−	0.217588i
$159$		0			0
$160$	−4.02014	+	15.2969i	−0.317820	+	1.20932i
$161$		−	6.57868i		−	0.518473i
$162$		0			0
$163$			16.5798i			1.29863i	0.760518	+	0.649317i	$0.224945\pi$
$163$			16.5798i			1.29863i	−0.760518	+	0.649317i	$0.775055\pi$
$164$	1.45589	−	0.312384i	0.113686	−	0.0243931i
$165$		0			0
$166$	9.02081	+	7.29057i	0.700150	+	0.565858i
$167$	−3.38550	+	5.86386i	−0.261978	+	0.453759i	−0.966768	−	0.255657i	$-0.917708\pi$
$167$	−3.38550	+	5.86386i	−0.261978	+	0.453759i	0.704789	+	0.709417i	$0.251042\pi$
$168$		0			0
$169$	−5.38531	−	9.32763i	−0.414255	−	0.717510i
$170$	3.48168	−	22.1200i	0.267033	−	1.69652i
$171$		0			0
$172$	4.48173	−	13.8841i	0.341729	−	1.05865i
$173$	8.38112	−	4.83884i	0.637204	−	0.367890i	−0.146332	−	0.989235i	$-0.546747\pi$
$173$	8.38112	−	4.83884i	0.637204	−	0.367890i	0.783537	+	0.621345i	$0.213414\pi$
$174$		0			0
$175$	2.43992	+	1.40869i	0.184441	+	0.106487i
$176$	−1.02844	+	0.462635i	−0.0775217	+	0.0348724i
$177$		0			0
$178$	−0.179973	−	0.467502i	−0.0134895	−	0.0350408i
$179$	−6.71304			−0.501756			−0.250878	−	0.968019i	$-0.580719\pi$
$179$	−6.71304			−0.501756			−0.250878	+	0.968019i	$0.580719\pi$
$180$		0			0
$181$	10.5763			0.786129			0.393065	−	0.919511i	$-0.371415\pi$
$181$	10.5763			0.786129			0.393065	+	0.919511i	$0.371415\pi$
$182$	−2.47713	−	6.43467i	−0.183617	−	0.476970i
$183$		0			0
$184$	10.1792	+	15.5761i	0.750421	+	1.14829i
$185$	10.2233	+	5.90243i	0.751632	+	0.433955i
$186$		0			0
$187$	1.38268	−	0.798288i	0.101111	−	0.0583766i
$188$	9.85997	+	3.18277i	0.719113	+	0.232127i
$189$		0			0
$190$	4.54556	−	28.8791i	0.329770	−	2.09511i
$191$	−4.68386	−	8.11268i	−0.338912	−	0.587013i	0.645316	−	0.763915i	$-0.276726\pi$
$191$	−4.68386	−	8.11268i	−0.338912	−	0.587013i	−0.984228	+	0.176903i	$0.943392\pi$
$192$		0			0
$193$	−0.439681	+	0.761550i	−0.0316489	+	0.0548176i	−0.881416	−	0.472341i	$-0.843409\pi$
$193$	−0.439681	+	0.761550i	−0.0316489	+	0.0548176i	0.849767	+	0.527158i	$0.176743\pi$
$194$	0.305756	+	0.247110i	0.0219520	+	0.0177415i
$195$		0			0
$196$	−0.419581	−	1.95549i	−0.0299701	−	0.139678i
$197$		−	14.4709i		−	1.03101i	−0.856887	−	0.515504i	$-0.827605\pi$
$197$		−	14.4709i		−	1.03101i	0.856887	−	0.515504i	$-0.172395\pi$
$198$		0			0
$199$		−	0.507764i		−	0.0359945i	−0.999838	−	0.0179972i	$-0.994271\pi$
$199$		−	0.507764i		−	0.0359945i	0.999838	−	0.0179972i	$-0.00572901\pi$
$200$	−7.95660	+	0.439984i	−0.562617	+	0.0311116i
$201$		0			0
$202$	12.5329	−	15.5072i	0.881810	−	1.09109i
$203$	0.140498	−	0.243350i	0.00986103	−	0.0170798i
$204$		0			0
$205$	1.04081	+	1.80274i	0.0726936	+	0.125909i
$206$	−15.0760	−	2.37297i	−1.05040	−	0.165332i
$207$		0			0
$208$	15.8214	+	11.4023i	1.09702	+	0.790608i
$209$	1.80517	−	1.04222i	0.124866	−	0.0720916i
$210$		0			0
$211$	−10.0333	−	5.79273i	−0.690721	−	0.398788i	0.113161	−	0.993577i	$-0.463902\pi$
$211$	−10.0333	−	5.79273i	−0.690721	−	0.398788i	−0.803882	+	0.594789i	$0.797236\pi$
$212$	10.8887	+	12.0465i	0.747839	+	0.827358i
$213$		0			0
$214$	−4.96678	+	1.91204i	−0.339522	+	0.130705i
$215$	20.3958			1.39098
$216$		0			0
$217$	−9.34312			−0.634252
$218$	−8.07142	+	3.10723i	−0.546665	+	0.210448i
$219$		0			0
$220$	−1.05714	−	1.16955i	−0.0712724	−	0.0788509i
$221$	−23.9113	−	13.8052i	−1.60845	−	0.928640i
$222$		0			0
$223$	−11.5096	+	6.64507i	−0.770739	+	0.444987i	−0.833138	−	0.553065i	$-0.813458\pi$
$223$	−11.5096	+	6.64507i	−0.770739	+	0.444987i	0.0623990	+	0.998051i	$0.480125\pi$
$224$	4.01917	+	3.98074i	0.268542	+	0.265974i
$225$		0			0
$226$	2.86768	+	0.451373i	0.190755	+	0.0300249i
$227$	4.25510	+	7.37006i	0.282421	+	0.489168i	0.971981	−	0.235061i	$-0.0755291\pi$
$227$	4.25510	+	7.37006i	0.282421	+	0.489168i	−0.689559	+	0.724229i	$0.742196\pi$
$228$		0			0
$229$	5.27466	−	9.13598i	0.348559	−	0.603722i	−0.637435	−	0.770505i	$-0.720004\pi$
$229$	5.27466	−	9.13598i	0.348559	−	0.603722i	0.985994	+	0.166782i	$0.0533377\pi$
$230$	−16.3509	+	20.2313i	−1.07814	+	1.33401i
$231$		0			0
$232$	0.0438826	+	0.793565i	0.00288103	+	0.0521001i
$233$		−	2.54006i		−	0.166405i	−0.996533	−	0.0832024i	$-0.973485\pi$
$233$		−	2.54006i		−	0.166405i	0.996533	−	0.0832024i	$-0.0265148\pi$
$234$		0			0
$235$			14.4844i			0.944857i
$236$	0.180804	+	0.842650i	0.0117693	+	0.0548518i
$237$		0			0
$238$	−6.22886	−	5.03413i	−0.403757	−	0.326314i
$239$	12.3345	−	21.3640i	0.797855	−	1.38193i	−0.123155	−	0.992387i	$-0.539301\pi$
$239$	12.3345	−	21.3640i	0.797855	−	1.38193i	0.921010	−	0.389538i	$-0.127365\pi$
$240$		0			0
$241$	−7.33435	−	12.7035i	−0.472447	−	0.818303i	0.527056	−	0.849831i	$-0.323296\pi$
$241$	−7.33435	−	12.7035i	−0.472447	−	0.818303i	−0.999503	+	0.0315281i	$0.989963\pi$
$242$	−2.40131	+	15.2561i	−0.154362	+	0.980700i
$243$		0			0
$244$	11.2633	+	3.63577i	0.721061	+	0.232756i
$245$	2.42137	−	1.39798i	0.154696	−	0.0893136i
$246$		0			0
$247$	−31.2178	−	18.0236i	−1.98634	−	1.14682i
$248$	22.1214	−	14.4566i	1.40471	−	0.917996i
$249$		0			0
$250$	3.10054	+	8.05406i	0.196096	+	0.509383i
$251$	15.0697			0.951191			0.475595	−	0.879664i	$-0.342233\pi$
$251$	15.0697			0.951191			0.475595	+	0.879664i	$0.342233\pi$
$252$		0			0
$253$	−1.85471			−0.116604
$254$	6.39733	+	16.6179i	0.401404	+	1.04270i
$255$		0			0
$256$	−15.6755	−	3.20622i	−0.979717	−	0.200389i
$257$	−3.71863	−	2.14695i	−0.231962	−	0.133923i	0.379515	−	0.925186i	$-0.376091\pi$
$257$	−3.71863	−	2.14695i	−0.231962	−	0.133923i	−0.611477	+	0.791262i	$0.709424\pi$
$258$		0			0
$259$	3.65646	−	2.11106i	0.227201	−	0.131175i
$260$	−8.37504	+	25.9452i	−0.519398	+	1.60905i
$261$		0			0
$262$	1.81657	−	11.5411i	0.112228	−	0.713012i
$263$	−4.80188	−	8.31711i	−0.296097	−	0.512855i	0.679143	−	0.734006i	$-0.262352\pi$
$263$	−4.80188	−	8.31711i	−0.296097	−	0.512855i	−0.975239	+	0.221152i	$0.929018\pi$
$264$		0			0
$265$	−11.3504	+	19.6595i	−0.697250	+	1.20767i
$266$	−8.13218	−	6.57238i	−0.498616	−	0.402979i
$267$		0			0
$268$	4.76721	−	1.02288i	0.291204	−	0.0624822i
$269$		−	21.0329i		−	1.28240i	−0.767375	−	0.641199i	$-0.778437\pi$
$269$		−	21.0329i		−	1.28240i	0.767375	−	0.641199i	$-0.221563\pi$
$270$		0			0
$271$			12.1109i			0.735682i	0.929889	+	0.367841i	$0.119903\pi$
$271$			12.1109i			0.735682i	−0.929889	+	0.367841i	$0.880097\pi$
$272$	22.5372	+	2.28123i	1.36652	+	0.138320i
$273$		0			0
$274$	−14.8871	+	18.4202i	−0.899361	+	1.11280i
$275$	0.397148	−	0.687880i	0.0239489	−	0.0414807i
$276$		0			0
$277$	1.37227	+	2.37683i	0.0824514	+	0.142810i	0.904302	−	0.426893i	$-0.140392\pi$
$277$	1.37227	+	2.37683i	0.0824514	+	0.142810i	−0.821851	+	0.569703i	$0.807058\pi$
$278$	32.5270	+	5.11975i	1.95084	+	0.307062i
$279$		0			0
$280$	−3.56991	+	7.05654i	−0.213343	+	0.421709i
$281$	−5.21831	+	3.01279i	−0.311298	+	0.179728i	−0.647507	−	0.762059i	$-0.724188\pi$
$281$	−5.21831	+	3.01279i	−0.311298	+	0.179728i	0.336209	+	0.941787i	$0.390855\pi$
$282$		0			0
$283$	24.0259	+	13.8713i	1.42819	+	0.824565i	0.996978	−	0.0776854i	$-0.0247530\pi$
$283$	24.0259	+	13.8713i	1.42819	+	0.824565i	0.431211	+	0.902251i	$0.358086\pi$
$284$	3.66647	−	3.31408i	0.217565	−	0.196655i
$285$		0			0
$286$	−1.81411	+	0.698371i	−0.107270	+	0.0412955i
$287$	0.744513			0.0439472
$288$		0			0
$289$	−15.0705			−0.886503
$290$	−1.03690	+	0.399172i	−0.0608889	+	0.0234402i
$291$		0			0
$292$	1.06050	−	0.958572i	0.0620609	−	0.0560962i
$293$	−10.8328	−	6.25434i	−0.632861	−	0.365383i	0.148998	−	0.988837i	$-0.452395\pi$
$293$	−10.8328	−	6.25434i	−0.632861	−	0.365383i	−0.781859	+	0.623455i	$0.785729\pi$
$294$		0			0
$295$	−1.04340	+	0.602409i	−0.0607493	+	0.0350736i
$296$	−5.39084	+	10.6559i	−0.313336	+	0.619363i
$297$		0			0
$298$	−16.0704	−	2.52948i	−0.930933	−	0.146529i
$299$	16.0372	+	27.7773i	0.927456	+	1.60640i
$300$		0			0
$301$	3.64737	−	6.31743i	0.210231	−	0.364131i
$302$	−4.31638	+	5.34077i	−0.248380	+	0.307327i
$303$		0			0
$304$	29.4238	+	2.97830i	1.68757	+	0.170817i
$305$			16.5459i			0.947417i
$306$		0			0
$307$			2.72302i			0.155411i	0.996976	+	0.0777054i	$0.0247594\pi$
$307$			2.72302i			0.155411i	−0.996976	+	0.0777054i	$0.975241\pi$
$308$	−0.551306	+	0.118291i	−0.0314136	+	0.00674027i
$309$		0			0
$310$	28.7328	+	23.2217i	1.63191	+	1.31890i
$311$	−4.22803	+	7.32317i	−0.239750	+	0.415259i	−0.960642	−	0.277788i	$-0.910399\pi$
$311$	−4.22803	+	7.32317i	−0.239750	+	0.415259i	0.720893	+	0.693047i	$0.243732\pi$
$312$		0			0
$313$	−13.8676	−	24.0195i	−0.783845	−	1.35766i	−0.929687	−	0.368352i	$-0.879922\pi$
$313$	−13.8676	−	24.0195i	−0.783845	−	1.35766i	0.145841	−	0.989308i	$-0.453411\pi$
$314$	−4.44318	+	28.2286i	−0.250743	+	1.59303i
$315$		0			0
$316$	−1.52772	+	4.73277i	−0.0859411	+	0.266239i
$317$	20.7198	−	11.9626i	1.16374	−	0.671886i	0.211544	−	0.977369i	$-0.432151\pi$
$317$	20.7198	−	11.9626i	1.16374	−	0.671886i	0.952198	+	0.305482i	$0.0988176\pi$
$318$		0			0
$319$	−0.0686069	−	0.0396102i	−0.00384125	−	0.00221774i
$320$	−2.46623	−	22.2313i	−0.137867	−	1.24277i
$321$		0			0
$322$	3.34247	+	8.68251i	0.186269	+	0.483857i
$323$	−41.8702			−2.32972
$324$		0			0
$325$	−13.7362			−0.761946
$326$	−8.42384	−	21.8820i	−0.466553	−	1.21193i
$327$		0			0
$328$	−1.76276	+	1.15199i	−0.0973322	+	0.0636078i
$329$	4.48642	+	2.59024i	0.247344	+	0.142804i
$330$		0			0
$331$	−24.6873	+	14.2532i	−1.35694	+	0.783427i	−0.989210	−	0.146506i	$-0.953197\pi$
$331$	−24.6873	+	14.2532i	−1.35694	+	0.783427i	−0.367727	+	0.929934i	$0.619864\pi$
$332$	−15.6098	−	5.03879i	−0.856698	−	0.276539i
$333$		0			0
$334$	1.48888	−	9.45919i	0.0814677	−	0.517584i
$335$	3.40807	+	5.90295i	0.186203	+	0.322513i
$336$		0			0
$337$	2.26282	−	3.91932i	0.123264	−	0.213499i	−0.797789	−	0.602937i	$-0.793997\pi$
$337$	2.26282	−	3.91932i	0.123264	−	0.213499i	0.921053	+	0.389437i	$0.127331\pi$
$338$	11.8467	+	9.57440i	0.644373	+	0.520779i
$339$		0			0
$340$	6.64354	+	30.9628i	0.360297	+	1.67919i
$341$			2.63408i			0.142643i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	1.13920	+	20.6012i	0.0614218	+	1.11074i
$345$		0			0
$346$	−8.60285	+	10.6445i	−0.462492	+	0.572253i
$347$	14.9377	−	25.8728i	0.801895	−	1.38892i	−0.116472	−	0.993194i	$-0.537159\pi$
$347$	14.9377	−	25.8728i	0.801895	−	1.38892i	0.918367	−	0.395729i	$-0.129508\pi$
$348$		0			0
$349$	−9.43250	−	16.3376i	−0.504910	−	0.874530i	−0.999984	−	0.00567921i	$-0.998192\pi$
$349$	−9.43250	−	16.3376i	−0.504910	−	0.874530i	0.495074	−	0.868851i	$-0.335141\pi$
$350$	−3.93592	−	0.619514i	−0.210384	−	0.0331144i
$351$		0			0
$352$	1.12228	−	1.13311i	0.0598176	−	0.0603950i
$353$	−26.5534	+	15.3306i	−1.41330	+	0.815967i	−0.995697	−	0.0926650i	$-0.970461\pi$
$353$	−26.5534	+	15.3306i	−1.41330	+	0.815967i	−0.417598	+	0.908632i	$0.637128\pi$
$354$		0			0
$355$	5.98355	+	3.45460i	0.317574	+	0.183351i
$356$	0.475054	+	0.525567i	0.0251778	+	0.0278550i
$357$		0			0
$358$	8.85983	−	3.41074i	0.468257	−	0.180263i
$359$	−18.8963			−0.997310			−0.498655	−	0.866801i	$-0.666172\pi$
$359$	−18.8963			−0.997310			−0.498655	+	0.866801i	$0.666172\pi$
$360$		0			0
$361$	−35.6642			−1.87706
$362$	−13.9585	+	5.37357i	−0.733644	+	0.282428i
$363$		0			0
$364$	6.53862	+	7.23387i	0.342717	+	0.379158i
$365$	1.73069	+	0.999216i	0.0905886	+	0.0523014i
$366$		0			0
$367$	4.63257	−	2.67462i	0.241818	−	0.139614i	−0.374194	−	0.927351i	$-0.622081\pi$
$367$	4.63257	−	2.67462i	0.241818	−	0.139614i	0.616012	+	0.787737i	$0.288747\pi$
$368$	−21.3483	−	15.3855i	−1.11286	−	0.802024i
$369$		0			0
$370$	−16.4915	−	2.59577i	−0.857355	−	0.134947i
$371$	4.05957	+	7.03139i	0.210763	+	0.365052i
$372$		0			0
$373$	−7.51238	+	13.0118i	−0.388976	+	0.673727i	−0.992312	−	0.123760i	$-0.960505\pi$
$373$	−7.51238	+	13.0118i	−0.388976	+	0.673727i	0.603336	+	0.797487i	$0.293838\pi$
$374$	−1.41926	+	1.75608i	−0.0733880	+	0.0908048i
$375$		0			0
$376$	−14.6302	+	0.809023i	−0.754497	+	0.0417222i
$377$			1.37000i			0.0705586i
$378$		0			0
$379$		−	3.97151i		−	0.204003i	−0.994784	−	0.102001i	$-0.967475\pi$
$379$		−	3.97151i		−	0.204003i	0.994784	−	0.102001i	$-0.0325246\pi$
$380$	8.67358	+	40.4239i	0.444945	+	2.07370i
$381$		0			0
$382$	10.3036	+	8.32731i	0.527178	+	0.426062i
$383$	−10.0601	+	17.4246i	−0.514047	+	0.890355i	0.485821	+	0.874059i	$0.338521\pi$
$383$	−10.0601	+	17.4246i	−0.514047	+	0.890355i	−0.999867	+	0.0162963i	$0.994812\pi$
$384$		0			0
$385$	−0.394128	−	0.682649i	−0.0200866	−	0.0347910i
$386$	0.193363	−	1.22848i	0.00984191	−	0.0625281i
$387$		0			0
$388$	−0.529086	−	0.170787i	−0.0268603	−	0.00867041i
$389$	30.9005	−	17.8404i	1.56672	−	0.904545i	0.570169	−	0.821527i	$-0.306878\pi$
$389$	30.9005	−	17.8404i	1.56672	−	0.904545i	0.996548	−	0.0830175i	$-0.0264558\pi$
$390$		0			0
$391$	32.2643	+	18.6278i	1.63168	+	0.942049i
$392$	1.54730	+	2.36767i	0.0781505	+	0.119585i
$393$		0			0
$394$	7.35232	+	19.0986i	0.370404	+	0.962173i
$395$	−6.95247			−0.349817
$396$		0			0
$397$	26.7209			1.34108			0.670541	−	0.741873i	$-0.266062\pi$
$397$	26.7209			1.34108			0.670541	+	0.741873i	$0.266062\pi$
$398$	0.257983	+	0.670145i	0.0129315	+	0.0335913i
$399$		0			0
$400$	10.2775	−	4.62326i	0.513877	−	0.231163i
$401$	−19.5104	−	11.2643i	−0.974302	−	0.562514i	−0.0737572	−	0.997276i	$-0.523499\pi$
$401$	−19.5104	−	11.2643i	−0.974302	−	0.562514i	−0.900545	+	0.434762i	$0.856832\pi$
$402$		0			0
$403$	39.4496	−	22.7762i	1.96513	−	1.13457i
$404$	−8.66195	+	26.8340i	−0.430948	+	1.33504i
$405$		0			0
$406$	−0.0617882	+	0.392556i	−0.00306650	+	0.0194822i
$407$	−0.595164	−	1.03085i	−0.0295012	−	0.0510975i
$408$		0			0
$409$	−7.38017	+	12.7828i	−0.364926	+	0.632070i	−0.988764	−	0.149483i	$-0.952239\pi$
$409$	−7.38017	+	12.7828i	−0.364926	+	0.632070i	0.623839	+	0.781553i	$0.285572\pi$
$410$	−2.28959	−	1.85044i	−0.113075	−	0.0913865i
$411$		0			0
$412$	21.1029	−	4.52796i	1.03967	−	0.223076i
$413$			0.430914i			0.0212039i
$414$		0			0
$415$		−	22.9309i		−	1.12563i
$416$	−26.6743	−	7.01021i	−1.30781	−	0.343704i
$417$		0			0
$418$	−1.85293	+	2.29268i	−0.0906298	+	0.112139i
$419$	15.0986	−	26.1515i	0.737614	−	1.27759i	−0.215953	−	0.976404i	$-0.569286\pi$
$419$	15.0986	−	26.1515i	0.737614	−	1.27759i	0.953567	−	0.301181i	$-0.0973810\pi$
$420$		0			0
$421$	12.0519	+	20.8744i	0.587372	+	1.01736i	0.994575	+	0.104021i	$0.0331708\pi$
$421$	12.0519	+	20.8744i	0.587372	+	1.01736i	−0.407203	+	0.913338i	$0.633496\pi$
$422$	16.1850	+	2.54752i	0.787875	+	0.124011i
$423$		0			0
$424$	−20.4914	−	10.3666i	−0.995151	−	0.503448i
$425$	−13.8175	+	7.97754i	−0.670247	+	0.386967i
$426$		0			0
$427$	5.12497	+	2.95890i	0.248014	+	0.143191i
$428$	5.58366	−	5.04701i	0.269896	−	0.243956i
$429$		0			0
$430$	−26.9183	+	10.3626i	−1.29811	+	0.499731i
$431$	26.8450			1.29308			0.646538	−	0.762882i	$-0.276216\pi$
$431$	26.8450			1.29308			0.646538	+	0.762882i	$0.276216\pi$
$432$		0			0
$433$	16.4401			0.790063			0.395031	−	0.918668i	$-0.370734\pi$
$433$	16.4401			0.790063			0.395031	+	0.918668i	$0.370734\pi$
$434$	12.3310	−	4.74702i	0.591907	−	0.227864i
$435$		0			0
$436$	9.07390	−	8.20180i	0.434561	−	0.392795i
$437$	42.1232	+	24.3198i	2.01502	+	1.16337i
$438$		0			0
$439$	10.2179	−	5.89931i	0.487674	−	0.281559i	−0.235935	−	0.971769i	$-0.575815\pi$
$439$	10.2179	−	5.89931i	0.487674	−	0.281559i	0.723609	+	0.690210i	$0.242482\pi$
$440$	1.98943	+	1.00645i	0.0948423	+	0.0479808i
$441$		0			0
$442$	38.5722	+	6.07126i	1.83469	+	0.288780i
$443$	−8.35739	−	14.4754i	−0.397071	−	0.687748i	0.596292	−	0.802768i	$-0.296640\pi$
$443$	−8.35739	−	14.4754i	−0.397071	−	0.687748i	−0.993363	+	0.115020i	$0.963307\pi$
$444$		0			0
$445$	−0.495197	+	0.857706i	−0.0234746	+	0.0406592i
$446$	11.8141	−	14.6179i	0.559414	−	0.692177i
$447$		0			0
$448$	−7.32700	−	3.21172i	−0.346168	−	0.151739i
$449$			36.4399i			1.71970i	0.510543	+	0.859852i	$0.329444\pi$
$449$			36.4399i			1.71970i	−0.510543	+	0.859852i	$0.670556\pi$
$450$		0			0
$451$		−	0.209898i		−	0.00988372i
$452$	−4.01408	+	0.861283i	−0.188807	+	0.0405114i
$453$		0			0
$454$	−9.36042	−	7.56504i	−0.439306	−	0.355045i
$455$	−6.81586	+	11.8054i	−0.319533	+	0.553447i
$456$		0			0
$457$	16.3554	+	28.3283i	0.765072	+	1.32514i	0.940208	+	0.340600i	$0.110630\pi$
$457$	16.3554	+	28.3283i	0.765072	+	1.32514i	−0.175136	+	0.984544i	$0.556036\pi$
$458$	−2.31969	+	14.7375i	−0.108392	+	0.688640i
$459$		0			0
$460$	11.3007	−	35.0087i	0.526898	−	1.63229i
$461$	23.5218	−	13.5803i	1.09552	−	0.632498i	0.160479	−	0.987039i	$-0.448696\pi$
$461$	23.5218	−	13.5803i	1.09552	−	0.632498i	0.935040	+	0.354541i	$0.115363\pi$
$462$		0			0
$463$	−15.5298	−	8.96612i	−0.721730	−	0.416691i	0.0936592	−	0.995604i	$-0.470144\pi$
$463$	−15.5298	−	8.96612i	−0.721730	−	0.416691i	−0.815389	+	0.578913i	$0.803477\pi$
$464$	−0.461108	−	1.02505i	−0.0214064	−	0.0475866i
$465$		0			0
$466$	1.29055	+	3.35236i	0.0597834	+	0.155295i
$467$	−24.3536			−1.12695			−0.563474	−	0.826134i	$-0.690536\pi$
$467$	−24.3536			−1.12695			−0.563474	+	0.826134i	$0.690536\pi$
$468$		0			0
$469$	2.43786			0.112570
$470$	−7.35918	−	19.1164i	−0.339454	−	0.881774i
$471$		0			0
$472$	−0.666754	−	1.02026i	−0.0306899	−	0.0469614i
$473$	−1.78105	−	1.02829i	−0.0818930	−	0.0472809i
$474$		0			0
$475$	−18.0396	+	10.4152i	−0.827716	+	0.477882i
$476$	10.7785	+	3.47928i	0.494033	+	0.159472i
$477$		0			0
$478$	−5.42448	+	34.4630i	−0.248110	+	1.57630i
$479$	8.74315	+	15.1436i	0.399485	+	0.691928i	0.993662	−	0.112406i	$-0.0358557\pi$
$479$	8.74315	+	15.1436i	0.399485	+	0.691928i	−0.594177	+	0.804334i	$0.702522\pi$
$480$		0			0
$481$	−10.2925	+	17.8271i	−0.469297	+	0.812846i
$482$	16.1342	+	13.0396i	0.734892	+	0.593936i
$483$		0			0
$484$	−4.58204	−	21.3550i	−0.208275	−	0.970681i
$485$		−	0.777231i		−	0.0352922i
$486$		0			0
$487$			5.76620i			0.261291i	0.991429	+	0.130646i	$0.0417050\pi$
$487$			5.76620i			0.261291i	−0.991429	+	0.130646i	$0.958295\pi$
$488$	−16.7125	+	0.924170i	−0.756541	+	0.0418352i
$489$		0			0
$490$	−2.48543	+	3.07529i	−0.112280	+	0.138927i
$491$	−16.6911	+	28.9099i	−0.753261	+	1.30469i	0.192973	+	0.981204i	$0.438187\pi$
$491$	−16.6911	+	28.9099i	−0.753261	+	1.30469i	−0.946234	+	0.323482i	$0.895146\pi$
$492$		0			0
$493$	0.795653	+	1.37811i	0.0358344	+	0.0620670i
$494$	50.3585	+	7.92642i	2.26574	+	0.356626i
$495$		0			0
$496$	−21.8506	+	30.3192i	−0.981123	+	1.36137i
$497$	2.14007	−	1.23557i	0.0959953	−	0.0554229i
$498$		0			0
$499$	−35.1612	−	20.3003i	−1.57403	−	0.908766i	−0.995667	−	0.0929863i	$-0.970359\pi$
$499$	−35.1612	−	20.3003i	−1.57403	−	0.908766i	−0.578362	−	0.815780i	$-0.696308\pi$
$500$	−8.18416	−	9.05439i	−0.366007	−	0.404925i
$501$		0			0
$502$	−19.8889	+	7.65656i	−0.887685	+	0.341729i
$503$	−16.0809			−0.717012			−0.358506	−	0.933528i	$-0.616714\pi$
$503$	−16.0809			−0.717012			−0.358506	+	0.933528i	$0.616714\pi$
$504$		0			0
$505$	−39.4194			−1.75414
$506$	2.44783	−	0.942333i	0.108819	−	0.0418918i
$507$		0			0
$508$	−16.8863	−	18.6818i	−0.749209	−	0.828873i
$509$	−0.457413	−	0.264088i	−0.0202745	−	0.0117055i	0.489829	−	0.871819i	$-0.337059\pi$
$509$	−0.457413	−	0.264088i	−0.0202745	−	0.0117055i	−0.510103	+	0.860113i	$0.670393\pi$
$510$		0			0
$511$	0.618998	−	0.357379i	0.0273829	−	0.0158095i
$512$	22.3174	−	3.73279i	0.986299	−	0.164968i
$513$		0			0
$514$	5.99864	+	0.944185i	0.264589	+	0.0416462i
$515$	15.0865	+	26.1305i	0.664788	+	1.15145i
$516$		0			0
$517$	0.730257	−	1.26484i	0.0321167	−	0.0556277i
$518$	−3.75319	+	4.64392i	−0.164906	+	0.204042i
$519$		0			0
$520$	−2.12884	−	38.4975i	−0.0933557	−	1.68823i
$521$		−	39.2616i		−	1.72008i	−0.510224	−	0.860042i	$-0.670437\pi$
$521$		−	39.2616i		−	1.72008i	0.510224	−	0.860042i	$-0.329563\pi$
$522$		0			0
$523$		−	12.1444i		−	0.531036i	−0.964106	−	0.265518i	$-0.914457\pi$
$523$		−	12.1444i		−	0.531036i	0.964106	−	0.265518i	$-0.0855430\pi$
$524$	3.46627	+	16.1548i	0.151425	+	0.705728i
$525$		0			0
$526$	10.5632	+	8.53715i	0.460579	+	0.372237i
$527$	26.4554	−	45.8222i	1.15242	−	1.99605i
$528$		0			0
$529$	−10.1395	−	17.5621i	−0.440848	−	0.763572i
$530$	4.99168	−	31.7133i	0.216825	−	1.37754i
$531$		0			0
$532$	14.0721	+	4.54242i	0.610102	+	0.196939i
$533$	−3.14357	+	1.81494i	−0.136163	+	0.0786138i
$534$		0			0
$535$	9.11233	+	5.26101i	0.393961	+	0.227453i
$536$	−5.77203	+	3.77210i	−0.249314	+	0.162930i
$537$		0			0
$538$	10.6863	+	27.7591i	0.460720	+	1.19678i
$539$	−0.281927			−0.0121434
$540$		0			0
$541$	−22.5265			−0.968490			−0.484245	−	0.874933i	$-0.660906\pi$
$541$	−22.5265			−0.968490			−0.484245	+	0.874933i	$0.660906\pi$
$542$	−6.15325	−	15.9838i	−0.264305	−	0.686565i
$543$		0			0
$544$	−30.9035	+	8.43987i	−1.32498	+	0.361856i
$545$	14.8083	+	8.54957i	0.634317	+	0.366223i
$546$		0			0
$547$	7.89651	−	4.55905i	0.337631	−	0.194931i	−0.321593	−	0.946878i	$-0.604218\pi$
$547$	7.89651	−	4.55905i	0.337631	−	0.194931i	0.659224	+	0.751947i	$0.270885\pi$
$548$	10.2890	−	31.8746i	0.439525	−	1.36162i
$549$		0			0
$550$	−0.174657	+	1.10964i	−0.00744742	+	0.0473153i
$551$	1.03878	+	1.79921i	0.0442534	+	0.0766491i
$552$		0			0
$553$	−1.24331	+	2.15347i	−0.0528708	+	0.0915750i
$554$	−3.01872	−	2.43972i	−0.128253	−	0.103654i
$555$		0			0
$556$	−45.5302	+	9.76921i	−1.93091	+	0.414307i
$557$		−	11.9979i		−	0.508369i	−0.967156	−	0.254184i	$-0.918193\pi$
$557$		−	11.9979i		−	0.508369i	0.967156	−	0.254184i	$-0.0818070\pi$
$558$		0			0
$559$			35.5656i			1.50427i
$560$	1.12628	−	11.1270i	0.0475941	−	0.470201i
$561$		0			0
$562$	5.35637	−	6.62757i	0.225945	−	0.279567i
$563$	9.48276	−	16.4246i	0.399651	−	0.692216i	−0.594032	−	0.804441i	$-0.702465\pi$
$563$	9.48276	−	16.4246i	0.399651	−	0.692216i	0.993683	+	0.112226i	$0.0357980\pi$
$564$		0			0
$565$	−2.86966	−	4.97040i	−0.120728	−	0.209106i
$566$	−38.7569	−	6.10033i	−1.62907	−	0.256416i
$567$		0			0
$568$	−3.15518	+	6.23676i	−0.132388	+	0.261688i
$569$	−20.5929	+	11.8893i	−0.863301	+	0.498427i	−0.865116	−	0.501571i	$-0.832756\pi$
$569$	−20.5929	+	11.8893i	−0.863301	+	0.498427i	0.00181529	+	0.999998i	$0.499422\pi$
$570$		0			0
$571$	−9.65431	−	5.57392i	−0.404020	−	0.233261i	0.284197	−	0.958766i	$-0.408273\pi$
$571$	−9.65431	−	5.57392i	−0.404020	−	0.233261i	−0.688217	+	0.725505i	$0.741606\pi$
$572$	2.03942	−	1.84341i	0.0852726	−	0.0770769i
$573$		0			0
$574$	−0.982605	+	0.378270i	−0.0410131	+	0.0157887i
$575$	18.5346			0.772948
$576$		0			0
$577$	26.0394			1.08404			0.542018	−	0.840367i	$-0.317660\pi$
$577$	26.0394			1.08404			0.542018	+	0.840367i	$0.317660\pi$
$578$	19.8900	−	7.65700i	0.827316	−	0.318489i
$579$		0			0
$580$	1.16569	−	1.05365i	0.0484025	−	0.0437505i
$581$	−7.10266	−	4.10072i	−0.294668	−	0.170127i
$582$		0			0
$583$	1.98234	−	1.14450i	0.0821000	−	0.0474005i
$584$	−0.912610	+	1.80393i	−0.0377641	+	0.0746472i
$585$		0			0
$586$	17.4748	+	2.75053i	0.721878	+	0.113623i
$587$	−1.53840	−	2.66458i	−0.0634965	−	0.109979i	0.832530	−	0.553981i	$-0.186892\pi$
$587$	−1.53840	−	2.66458i	−0.0634965	−	0.109979i	−0.896026	+	0.444001i	$0.853559\pi$
$588$		0			0
$589$	34.5393	−	59.8238i	1.42317	−	2.46500i
$590$	1.07101	−	1.32519i	0.0440927	−	0.0545570i
$591$		0			0
$592$	1.70077	−	16.8026i	0.0699013	−	0.690582i
$593$		−	4.35742i		−	0.178938i	−0.995990	−	0.0894688i	$-0.971483\pi$
$593$		−	4.35742i		−	0.178938i	0.995990	−	0.0894688i	$-0.0285169\pi$
$594$		0			0
$595$			15.8338i			0.649121i
$596$	22.4948	−	4.82660i	0.921422	−	0.197705i
$597$		0			0
$598$	−35.2788	−	28.5122i	−1.44266	−	1.16595i
$599$	−16.0003	+	27.7133i	−0.653753	+	1.13233i	0.328452	+	0.944521i	$0.393473\pi$
$599$	−16.0003	+	27.7133i	−0.653753	+	1.13233i	−0.982205	+	0.187812i	$0.939860\pi$
$600$		0			0
$601$	−17.6951	−	30.6489i	−0.721799	−	1.25019i	−0.960278	−	0.279045i	$-0.909982\pi$
$601$	−17.6951	−	30.6489i	−0.721799	−	1.25019i	0.238478	−	0.971148i	$-0.423351\pi$
$602$	−1.60404	+	10.1909i	−0.0653758	+	0.415349i
$603$		0			0
$604$	2.98322	−	9.24178i	0.121385	−	0.376043i
$605$	26.4426	−	15.2667i	1.07505	−	0.620678i
$606$		0			0
$607$	2.32842	+	1.34431i	0.0945076	+	0.0545640i	0.546509	−	0.837453i	$-0.315956\pi$
$607$	2.32842	+	1.34431i	0.0945076	+	0.0545640i	−0.452001	+	0.892017i	$0.649290\pi$
$608$	−40.3465	+	11.0188i	−1.63627	+	0.446871i
$609$		0			0
$610$	−8.40660	−	21.8372i	−0.340373	−	0.884163i
$611$	−25.2574			−1.02181
$612$		0			0
$613$	41.2533			1.66621			0.833103	−	0.553117i	$-0.186562\pi$
$613$	41.2533			1.66621			0.833103	+	0.553117i	$0.186562\pi$
$614$	−1.38350	−	3.59383i	−0.0558336	−	0.145035i
$615$		0			0
$616$	0.667509	−	0.436226i	0.0268947	−	0.0175760i
$617$	−23.5137	−	13.5756i	−0.946626	−	0.546534i	−0.0545945	−	0.998509i	$-0.517387\pi$
$617$	−23.5137	−	13.5756i	−0.946626	−	0.546534i	−0.892031	+	0.451974i	$0.850720\pi$
$618$		0			0
$619$	8.12323	−	4.68995i	0.326500	−	0.188505i	−0.327786	−	0.944752i	$-0.606302\pi$
$619$	8.12323	−	4.68995i	0.326500	−	0.188505i	0.654286	+	0.756247i	$0.272969\pi$
$620$	−49.7198	−	16.0494i	−1.99679	−	0.644559i
$621$		0			0
$622$	1.85940	−	11.8132i	0.0745553	−	0.473668i
$623$	0.177112	+	0.306766i	0.00709583	+	0.0122903i
$624$		0			0
$625$	15.5746	−	26.9761i	0.622985	−	1.07904i
$626$	30.5062	+	24.6549i	1.21927	+	0.985409i
$627$		0			0
$628$	−8.47821	−	39.5134i	−0.338318	−	1.57676i
$629$			23.9102i			0.953362i
$630$		0			0
$631$		−	17.3945i		−	0.692463i	−0.938149	−	0.346232i	$-0.887461\pi$
$631$		−	17.3945i		−	0.692463i	0.938149	−	0.346232i	$-0.112539\pi$
$632$	−0.388330	−	7.02248i	−0.0154469	−	0.279339i
$633$		0			0
$634$	−21.2680	+	26.3154i	−0.844660	+	1.04512i
$635$	17.6023	−	30.4881i	0.698526	−	1.20988i
$636$		0			0
$637$	2.43776	+	4.22232i	0.0965874	+	0.167294i
$638$	0.110672	+	0.0174198i	0.00438155	+	0.000689655i
$639$		0			0
$640$	14.5501	+	28.0877i	0.575144	+	1.11026i
$641$	−25.0358	+	14.4544i	−0.988854	+	0.570915i	−0.904932	−	0.425557i	$-0.860078\pi$
$641$	−25.0358	+	14.4544i	−0.988854	+	0.570915i	−0.0839224	+	0.996472i	$0.526745\pi$
$642$		0			0
$643$	−12.0530	−	6.95879i	−0.475323	−	0.274428i	0.243142	−	0.969991i	$-0.421822\pi$
$643$	−12.0530	−	6.95879i	−0.475323	−	0.274428i	−0.718465	+	0.695563i	$0.755155\pi$
$644$	−8.82276	−	9.76089i	−0.347665	−	0.384633i
$645$		0			0
$646$	55.2600	−	21.2733i	2.17418	−	0.836986i
$647$	−20.5491			−0.807868			−0.403934	−	0.914788i	$-0.632357\pi$
$647$	−20.5491			−0.807868			−0.403934	+	0.914788i	$0.632357\pi$
$648$		0			0
$649$	0.121486			0.00476875
$650$	18.1289	−	6.97903i	0.711075	−	0.273740i
$651$		0			0
$652$	22.2355	+	24.5998i	0.870808	+	0.963402i
$653$	4.02988	+	2.32665i	0.157701	+	0.0910489i	0.576774	−	0.816904i	$-0.304311\pi$
$653$	4.02988	+	2.32665i	0.157701	+	0.0910489i	−0.419073	+	0.907953i	$0.637645\pi$
$654$		0			0
$655$	−20.0036	+	11.5491i	−0.781605	+	0.451260i
$656$	1.74118	−	2.41600i	0.0679818	−	0.0943291i
$657$		0			0
$658$	−7.23719	−	1.13913i	−0.282135	−	0.0444080i
$659$	13.4746	+	23.3387i	0.524895	+	0.909145i	0.999580	+	0.0289894i	$0.00922889\pi$
$659$	13.4746	+	23.3387i	0.524895	+	0.909145i	−0.474684	+	0.880156i	$0.657438\pi$
$660$		0			0
$661$	−15.9921	+	27.6992i	−0.622022	+	1.07737i	0.367087	+	0.930187i	$0.380355\pi$
$661$	−15.9921	+	27.6992i	−0.622022	+	1.07737i	−0.989109	+	0.147186i	$0.952978\pi$
$662$	25.3404	−	31.3544i	0.984884	−	1.21862i
$663$		0			0
$664$	23.1618	−	1.28080i	0.898852	−	0.0497048i
$665$			20.6720i			0.801625i
$666$		0			0
$667$		−	1.84858i		−	0.0715775i
$668$	2.84099	+	13.2407i	0.109921	+	0.512296i
$669$		0			0
$670$	−7.49711	−	6.05912i	−0.289638	−	0.234084i
$671$	0.834193	−	1.44487i	0.0322037	−	0.0557784i
$672$		0			0
$673$	3.85968	+	6.68517i	0.148780	+	0.257694i	0.930777	−	0.365588i	$-0.119132\pi$
$673$	3.85968	+	6.68517i	0.148780	+	0.257694i	−0.781997	+	0.623282i	$0.785799\pi$
$674$	−0.995143	+	6.32239i	−0.0383315	+	0.243529i
$675$		0			0
$676$	−20.4997	−	6.61724i	−0.788449	−	0.254509i
$677$	7.42656	−	4.28773i	0.285426	−	0.164791i	−0.350451	−	0.936581i	$-0.613972\pi$
$677$	7.42656	−	4.28773i	0.285426	−	0.164791i	0.635877	+	0.771790i	$0.280638\pi$
$678$		0			0
$679$	−0.240741	−	0.138992i	−0.00923879	−	0.00533402i
$680$	−24.4996	−	37.4891i	−0.939516	−	1.43764i
$681$		0			0
$682$	−1.33831	−	3.47644i	−0.0512467	−	0.133120i
$683$	5.18082			0.198238			0.0991192	−	0.995076i	$-0.468397\pi$
$683$	5.18082			0.198238			0.0991192	+	0.995076i	$0.468397\pi$
$684$		0			0
$685$	46.8241			1.78906
$686$	0.508077	+	1.31979i	0.0193985	+	0.0503900i
$687$		0			0
$688$	−11.9705	−	26.6105i	−0.456371	−	1.01452i
$689$	−34.2816	−	19.7925i	−1.30603	−	0.754034i
$690$		0			0
$691$	−13.4870	+	7.78675i	−0.513071	+	0.296222i	−0.734095	−	0.679047i	$-0.762393\pi$
$691$	−13.4870	+	7.78675i	−0.513071	+	0.296222i	0.221024	+	0.975268i	$0.429060\pi$
$692$	5.94576	−	18.4195i	0.226024	−	0.700204i
$693$		0			0
$694$	−6.56928	+	41.7362i	−0.249366	+	1.58429i
$695$	−32.5495	−	56.3774i	−1.23467	−	2.13852i
$696$		0			0
$697$	−2.10812	+	3.65137i	−0.0798508	+	0.138306i
$698$	20.7497	+	16.7698i	0.785388	+	0.634746i
$699$		0			0
$700$	5.50937	−	1.18212i	0.208235	−	0.0446799i
$701$			10.5008i			0.396609i	0.980140	+	0.198304i	$0.0635435\pi$
$701$			10.5008i			0.396609i	−0.980140	+	0.198304i	$0.936457\pi$
$702$		0			0
$703$			31.2163i			1.17735i
$704$	−0.905469	+	2.06568i	−0.0341261	+	0.0778531i
$705$		0			0
$706$	27.2559	−	33.7245i	1.02579	−	1.26924i
$707$	−7.04936	+	12.2098i	−0.265118	+	0.459199i
$708$		0			0
$709$	3.56049	+	6.16695i	0.133717	+	0.231605i	0.925107	−	0.379708i	$-0.123975\pi$
$709$	3.56049	+	6.16695i	0.133717	+	0.231605i	−0.791390	+	0.611312i	$0.790642\pi$
$710$	−9.65226	−	1.51926i	−0.362243	−	0.0570170i
$711$		0			0
$712$	−0.894002	−	0.452276i	−0.0335041	−	0.0169498i
$713$	−53.2306	+	30.7327i	−1.99350	+	1.15095i
$714$		0			0
$715$	3.32827	+	1.92157i	0.124470	+	0.0718628i
$716$	−9.96024	+	9.00295i	−0.372232	+	0.336456i
$717$		0			0
$718$	24.9393	−	9.60078i	0.930725	−	0.358298i
$719$	11.4166			0.425766			0.212883	−	0.977078i	$-0.431715\pi$
$719$	11.4166			0.425766			0.212883	+	0.977078i	$0.431715\pi$
$720$		0			0
$721$	10.7916			0.401901
$722$	47.0695	−	18.1202i	1.75174	−	0.674363i
$723$		0			0
$724$	15.6922	−	14.1840i	0.583196	−	0.527144i
$725$	0.685609	+	0.395837i	0.0254629	+	0.0147010i
$726$		0			0
$727$	11.2371	−	6.48771i	0.416759	−	0.240616i	−0.276931	−	0.960890i	$-0.589317\pi$
$727$	11.2371	−	6.48771i	0.416759	−	0.240616i	0.693690	+	0.720274i	$0.255984\pi$
$728$	−12.3050	−	6.22511i	−0.456054	−	0.230718i
$729$		0			0
$730$	−2.79184	−	0.439435i	−0.103331	−	0.0162642i
$731$	20.6554	+	35.7762i	0.763967	+	1.32323i
$732$		0			0
$733$	−12.2933	+	21.2926i	−0.454063	+	0.786460i	−0.998634	−	0.0522545i	$-0.983359\pi$
$733$	−12.2933	+	21.2926i	−0.454063	+	0.786460i	0.544571	+	0.838715i	$0.316693\pi$
$734$	−4.75514	+	5.88365i	−0.175515	+	0.217170i
$735$		0			0
$736$	35.9924	+	9.45909i	1.32670	+	0.348667i
$737$		−	0.687297i		−	0.0253169i
$738$		0			0
$739$		−	42.1439i		−	1.55029i	−0.631785	−	0.775144i	$-0.717678\pi$
$739$		−	42.1439i		−	1.55029i	0.631785	−	0.775144i	$-0.282322\pi$
$740$	23.0843	−	4.95309i	0.848596	−	0.182079i
$741$		0			0
$742$	−8.93029	−	7.21741i	−0.327841	−	0.264960i
$743$	0.0854917	−	0.148076i	0.00313639	−	0.00543238i	−0.864453	−	0.502714i	$-0.832335\pi$
$743$	0.0854917	−	0.148076i	0.00313639	−	0.00543238i	0.867589	+	0.497281i	$0.165668\pi$
$744$		0			0
$745$	16.0815	+	27.8540i	0.589180	+	1.02049i
$746$	3.30379	−	20.9898i	0.120960	−	0.768491i
$747$		0			0
$748$	0.980902	−	3.03876i	0.0358653	−	0.111108i
$749$	3.25911	−	1.88165i	0.119085	−	0.0687539i
$750$		0			0
$751$	10.7780	+	6.22269i	0.393295	+	0.227069i	0.683587	−	0.729869i	$-0.260419\pi$
$751$	10.7780	+	6.22269i	0.393295	+	0.227069i	−0.290292	+	0.956938i	$0.593752\pi$
$752$	18.8979	−	8.50103i	0.689134	−	0.310001i
$753$		0			0
$754$	−0.696066	−	1.80812i	−0.0253492	−	0.0658478i
$755$	13.5762			0.494090
$756$		0			0
$757$	34.3261			1.24760			0.623801	−	0.781583i	$-0.285587\pi$
$757$	34.3261			1.24760			0.623801	+	0.781583i	$0.285587\pi$
$758$	2.01783	+	5.24158i	0.0732910	+	0.190383i
$759$		0			0
$760$	−31.9858	−	48.9444i	−1.16025	−	1.77540i
$761$	9.19028	+	5.30601i	0.333148	+	0.192343i	0.657238	−	0.753683i	$-0.271725\pi$
$761$	9.19028	+	5.30601i	0.333148	+	0.192343i	−0.324090	+	0.946026i	$0.605058\pi$
$762$		0			0
$763$	5.29632	−	3.05783i	0.191740	−	0.110701i
$764$	−17.8295	−	5.75532i	−0.645050	−	0.208220i
$765$		0			0
$766$	4.42422	−	28.1082i	0.159854	−	1.01559i
$767$	−1.05046	−	1.81946i	−0.0379301	−	0.0656968i
$768$		0			0
$769$	−4.39685	+	7.61557i	−0.158554	+	0.274624i	−0.934348	−	0.356363i	$-0.884017\pi$
$769$	−4.39685	+	7.61557i	−0.158554	+	0.274624i	0.775793	+	0.630987i	$0.217350\pi$
$770$	0.867006	+	0.700710i	0.0312447	+	0.0252518i
$771$		0			0
$772$	0.368964	+	1.71959i	0.0132793	+	0.0618893i
$773$		−	1.24418i		−	0.0447501i	−0.999750	−	0.0223751i	$-0.992877\pi$
$773$		−	1.24418i		−	0.0447501i	0.999750	−	0.0223751i	$-0.00712279\pi$
$774$		0			0
$775$		−	26.3231i		−	0.945555i
$776$	0.785058	−	0.0434121i	0.0281819	−	0.00155840i
$777$		0			0
$778$	−31.7180	+	39.2455i	−1.13715	+	1.40702i
$779$	−2.75229	+	4.76710i	−0.0986110	+	0.170799i
$780$		0			0
$781$	−0.348340	−	0.603343i	−0.0124646	−	0.0215893i
$782$	−52.0466	−	8.19213i	−1.86118	−	0.292950i
$783$		0			0
$784$	−3.24508	−	2.33869i	−0.115896	−	0.0835246i
$785$	48.9271	−	28.2481i	1.74628	−	1.00822i
$786$		0			0
$787$	8.14573	+	4.70294i	0.290364	+	0.167642i	0.638106	−	0.769949i	$-0.279718\pi$
$787$	8.14573	+	4.70294i	0.290364	+	0.167642i	−0.347742	+	0.937590i	$0.613052\pi$
$788$	−19.4071	−	21.4707i	−0.691349	−	0.764861i
$789$		0			0
$790$	9.17584	−	3.53239i	0.326462	−	0.125677i
$791$	−2.05272			−0.0729864
$792$		0			0
$793$	−28.8523			−1.02458
$794$	−35.2660	+	13.5763i	−1.25155	+	0.481803i
$795$		0			0
$796$	−0.680970	−	0.753378i	−0.0241363	−	0.0267028i
$797$	−17.5415	−	10.1276i	−0.621351	−	0.358737i	0.156044	−	0.987750i	$-0.450126\pi$
$797$	−17.5415	−	10.1276i	−0.621351	−	0.358737i	−0.777395	+	0.629013i	$0.783459\pi$
$798$		0			0
$799$	−25.4070	+	14.6687i	−0.898834	+	0.518942i
$800$	−11.2153	+	11.3235i	−0.396520	+	0.400347i
$801$		0			0
$802$	31.4729	+	4.95382i	1.11135	+	0.174926i
$803$	−0.100755	−	0.174512i	−0.00355555	−	0.00615840i
$804$		0			0
$805$	9.19686	−	15.9294i	0.324147	−	0.561438i
$806$	−40.4933	+	50.1034i	−1.42632	+	1.76482i
$807$		0			0
$808$	−2.20177	−	39.8164i	−0.0774579	−	1.40073i
$809$			33.9641i			1.19411i	0.802199	+	0.597057i	$0.203663\pi$
$809$			33.9641i			1.19411i	−0.802199	+	0.597057i	$0.796337\pi$
$810$		0			0
$811$		−	53.9712i		−	1.89518i	−0.319482	−	0.947592i	$-0.603509\pi$
$811$		−	53.9712i		−	1.89518i	0.319482	−	0.947592i	$-0.396491\pi$
$812$	−0.117901	−	0.549486i	−0.00413750	−	0.0192832i
$813$		0			0
$814$	1.30925	+	1.05813i	0.0458891	+	0.0370873i
$815$	−23.1783	+	40.1460i	−0.811900	+	1.40625i
$816$		0			0
$817$	26.9669	+	46.7081i	0.943454	+	1.63411i
$818$	3.24565	−	20.6204i	0.113481	−	0.720975i
$819$		0			0
$820$	3.96196	+	1.27891i	0.138357	+	0.0446614i
$821$	−21.2044	+	12.2424i	−0.740039	+	0.427262i	−0.822084	−	0.569367i	$-0.807188\pi$
$821$	−21.2044	+	12.2424i	−0.740039	+	0.427262i	0.0820442	+	0.996629i	$0.473855\pi$
$822$		0			0
$823$	38.5728	+	22.2700i	1.34456	+	0.776284i	0.987473	−	0.157786i	$-0.0504357\pi$
$823$	38.5728	+	22.2700i	1.34456	+	0.776284i	0.357090	+	0.934070i	$0.383769\pi$
$824$	−25.5510	+	16.6979i	−0.890110	+	0.581698i
$825$		0			0
$826$	−0.218938	−	0.568718i	−0.00761781	−	0.0197882i
$827$	44.8362			1.55911			0.779554	−	0.626335i	$-0.215446\pi$
$827$	44.8362			1.55911			0.779554	+	0.626335i	$0.215446\pi$
$828$		0			0
$829$	−1.25945			−0.0437424			−0.0218712	−	0.999761i	$-0.506962\pi$
$829$	−1.25945			−0.0437424			−0.0218712	+	0.999761i	$0.506962\pi$
$830$	11.6507	+	30.2641i	0.404400	+	1.05048i
$831$		0			0
$832$	38.7663	−	4.30055i	1.34398	−	0.149095i
$833$	4.90438	+	2.83154i	0.169927	+	0.0981072i
$834$		0			0
$835$	−16.3951	+	9.46573i	−0.567377	+	0.327575i
$836$	1.28063	−	3.96730i	0.0442915	−	0.137212i
$837$		0			0
$838$	−6.64005	+	42.1859i	−0.229377	+	1.45729i
$839$	−21.0036	−	36.3793i	−0.725125	−	1.25595i	−0.958923	−	0.283668i	$-0.908449\pi$
$839$	−21.0036	−	36.3793i	−0.725125	−	1.25595i	0.233798	−	0.972285i	$-0.424885\pi$
$840$		0			0
$841$	−14.4605	+	25.0464i	−0.498639	+	0.863667i
$842$	−26.5118	−	21.4267i	−0.913658	−	0.738413i
$843$		0			0
$844$	−22.6553	+	4.86104i	−0.779826	+	0.167324i
$845$		−	30.1142i		−	1.03596i
$846$		0			0
$847$		−	10.9205i		−	0.375233i
$848$	32.3115	+	3.27060i	1.10958	+	0.112313i
$849$		0			0
$850$	14.1831	−	17.5491i	0.486475	−	0.601928i
$851$	13.8880	−	24.0547i	0.476073	−	0.824583i
$852$		0			0
$853$	15.4133	+	26.6966i	0.527741	+	0.914075i	0.999477	+	0.0323350i	$0.0102943\pi$
$853$	15.4133	+	26.6966i	0.527741	+	0.914075i	−0.471736	+	0.881740i	$0.656372\pi$
$854$	−8.26725	−	1.30126i	−0.282900	−	0.0445283i
$855$		0			0
$856$	−4.80502	+	9.49794i	−0.164232	+	0.324633i
$857$	−11.9804	+	6.91687i	−0.409242	+	0.236276i	−0.690464	−	0.723367i	$-0.742594\pi$
$857$	−11.9804	+	6.91687i	−0.409242	+	0.236276i	0.281222	+	0.959643i	$0.409260\pi$
$858$		0			0
$859$	32.0674	+	18.5141i	1.09413	+	0.631694i	0.934672	−	0.355511i	$-0.115693\pi$
$859$	32.0674	+	18.5141i	1.09413	+	0.631694i	0.159455	+	0.987205i	$0.449026\pi$
$860$	30.2616	−	27.3531i	1.03191	−	0.932733i
$861$		0			0
$862$	−35.4298	+	13.6393i	−1.20674	+	0.464556i
$863$	40.7856			1.38836			0.694178	−	0.719803i	$-0.255768\pi$
$863$	40.7856			1.38836			0.694178	+	0.719803i	$0.255768\pi$
$864$		0			0
$865$	27.0584			0.920013
$866$	−21.6976	+	8.35286i	−0.737315	+	0.283842i
$867$		0			0
$868$	−13.8625	+	12.5302i	−0.470525	+	0.425302i
$869$	0.607122	+	0.350522i	0.0205952	+	0.0118906i
$870$		0			0
$871$	−10.2934	+	5.94290i	−0.348778	+	0.201367i
$872$	−7.80854	+	15.4349i	−0.264431	+	0.522693i
$873$		0			0
$874$	−67.9503	−	10.6954i	−2.29845	−	0.361776i
$875$	−3.05125	−	5.28493i	−0.103151	−	0.178663i
$876$		0			0
$877$	11.2287	−	19.4487i	0.379167	−	0.656736i	−0.611775	−	0.791032i	$-0.709544\pi$
$877$	11.2287	−	19.4487i	0.379167	−	0.656736i	0.990941	+	0.134296i	$0.0428774\pi$
$878$	−10.4882	+	12.9774i	−0.353961	+	0.437965i
$879$		0			0
$880$	−3.13699	−	0.317529i	−0.105748	−	0.0107039i
$881$		−	2.14963i		−	0.0724228i	−0.999344	−	0.0362114i	$-0.988471\pi$
$881$		−	2.14963i		−	0.0724228i	0.999344	−	0.0362114i	$-0.0115290\pi$
$882$		0			0
$883$			55.0001i			1.85090i	0.378868	+	0.925451i	$0.376313\pi$
$883$			55.0001i			1.85090i	−0.378868	+	0.925451i	$0.623687\pi$
$884$	−53.9920	+	11.5848i	−1.81595	+	0.389640i
$885$		0			0
$886$	18.3847	+	14.8584i	0.617645	+	0.499177i
$887$	−10.4272	+	18.0604i	−0.350111	+	0.606410i	−0.986269	−	0.165149i	$-0.947189\pi$
$887$	−10.4272	+	18.0604i	−0.350111	+	0.606410i	0.636158	+	0.771559i	$0.280523\pi$
$888$		0			0
$889$	−6.29563	−	10.9043i	−0.211149	−	0.365720i
$890$	0.217778	−	1.38359i	0.00729992	−	0.0463782i
$891$		0			0
$892$	−8.16517	+	25.2951i	−0.273390	+	0.846942i
$893$	−33.1705	+	19.1510i	−1.11001	+	0.640863i
$894$		0			0
$895$	−16.2548	−	9.38468i	−0.543336	−	0.313695i
$896$	11.3019	+	0.516127i	0.377571	+	0.0172426i
$897$		0			0
$898$	−18.5143	−	48.0932i	−0.617829	−	1.60489i
$899$	−2.62538			−0.0875614
$900$		0			0
$901$	−45.9794			−1.53180
$902$	0.106644	+	0.277023i	0.00355087	+	0.00922384i
$903$		0			0
$904$	4.86017	−	3.17618i	0.161647	−	0.105638i
$905$	25.6091	+	14.7854i	0.851275	+	0.491484i
$906$		0			0
$907$	−40.3581	+	23.3007i	−1.34007	+	0.773689i	−0.986817	−	0.161840i	$-0.948257\pi$
$907$	−40.3581	+	23.3007i	−1.34007	+	0.773689i	−0.353251	+	0.935529i	$0.614924\pi$
$908$	16.1975	+	5.22849i	0.537531	+	0.173513i
$909$		0			0
$910$	2.99748	−	19.0437i	0.0993654	−	0.631293i
$911$	−29.2009	−	50.5774i	−0.967468	−	1.67570i	−0.702833	−	0.711355i	$-0.748082\pi$
$911$	−29.2009	−	50.5774i	−0.967468	−	1.67570i	−0.264635	−	0.964349i	$-0.585251\pi$
$912$		0			0
$913$	−1.15610	+	2.00243i	−0.0382614	+	0.0662708i
$914$	−35.9787	−	29.0778i	−1.19007	−	0.961809i
$915$		0			0
$916$	−4.42629	−	20.6291i	−0.146249	−	0.681605i
$917$			8.26127i			0.272811i
$918$		0			0
$919$		−	6.34959i		−	0.209454i	−0.994501	−	0.104727i	$-0.966603\pi$
$919$		−	6.34959i		−	0.209454i	0.994501	−	0.104727i	$-0.0333968\pi$
$920$	2.87251	+	51.9459i	0.0947037	+	1.71261i
$921$		0			0
$922$	−24.1441	+	29.8741i	−0.795143	+	0.983851i
$923$	−6.02404	+	10.4339i	−0.198284	+	0.343437i
$924$		0			0
$925$	5.94765	+	10.3016i	0.195558	+	0.338716i
$926$	25.0516	+	3.94312i	0.823246	+	0.129579i
$927$		0			0
$928$	1.12937	+	1.11857i	0.0370734	+	0.0367190i
$929$	17.4073	−	10.0501i	0.571116	−	0.329734i	−0.186479	−	0.982459i	$-0.559708\pi$
$929$	17.4073	−	10.0501i	0.571116	−	0.329734i	0.757595	+	0.652725i	$0.226374\pi$
$930$		0			0
$931$	6.40298	+	3.69676i	0.209849	+	0.121157i
$932$	−3.40651	−	3.76873i	−0.111584	−	0.123449i
$933$		0			0
$934$	32.1417	−	12.3735i	1.05171	−	0.404873i
$935$	4.46396			0.145987
$936$		0			0
$937$	−10.9126			−0.356501			−0.178250	−	0.983985i	$-0.557044\pi$
$937$	−10.9126			−0.356501			−0.178250	+	0.983985i	$0.557044\pi$
$938$	−3.21747	+	1.23862i	−0.105054	+	0.0404423i
$939$		0			0
$940$	19.4252	+	21.4907i	0.633580	+	0.700949i
$941$	44.5175	+	25.7022i	1.45123	+	0.837868i	0.998551	−	0.0538064i	$-0.0171354\pi$
$941$	44.5175	+	25.7022i	1.45123	+	0.837868i	0.452678	+	0.891674i	$0.350469\pi$
$942$		0			0
$943$	4.24172	−	2.44896i	0.138129	−	0.0797490i
$944$	1.39835	+	1.00777i	0.0455124	+	0.0328003i
$945$		0			0
$946$	2.87308	+	0.452222i	0.0934118	+	0.0147030i
$947$	22.3078	+	38.6382i	0.724906	+	1.25557i	0.959013	+	0.283363i	$0.0914502\pi$
$947$	22.3078	+	38.6382i	0.724906	+	1.25557i	−0.234107	+	0.972211i	$0.575217\pi$
$948$		0			0
$949$	−1.74240	+	3.01793i	−0.0565608	+	0.0979663i
$950$	18.5169	−	22.9114i	0.600768	−	0.743345i
$951$		0			0
$952$	−15.9932	+	0.884392i	−0.518342	+	0.0286633i
$953$			51.7549i			1.67651i	0.545281	+	0.838253i	$0.316423\pi$
$953$			51.7549i			1.67651i	−0.545281	+	0.838253i	$0.683577\pi$
$954$		0			0
$955$		−	26.1917i		−	0.847545i
$956$	−10.3507	−	48.2402i	−0.334765	−	1.56020i
$957$		0			0
$958$	−19.2333	−	15.5442i	−0.621399	−	0.502211i
$959$	8.37353	−	14.5034i	0.270395	−	0.468338i
$960$		0			0
$961$	28.1469	+	48.7519i	0.907966	+	1.57264i
$962$	4.52642	−	28.7575i	0.145938	−	0.927179i
$963$		0			0
$964$	−27.9189	−	9.01214i	−0.899208	−	0.290261i
$965$	−2.12926	+	1.22933i	−0.0685434	+	0.0395735i
$966$		0			0
$967$	19.3524	+	11.1731i	0.622331	+	0.359303i	0.777776	−	0.628542i	$-0.216348\pi$
$967$	19.3524	+	11.1731i	0.622331	+	0.359303i	−0.155445	+	0.987845i	$0.549681\pi$
$968$	16.8973	+	25.8562i	0.543101	+	0.831049i
$969$		0			0
$970$	0.394893	+	1.02579i	0.0126793	+	0.0329360i
$971$	11.2412			0.360747			0.180373	−	0.983598i	$-0.442269\pi$
$971$	11.2412			0.360747			0.180373	+	0.983598i	$0.442269\pi$
$972$		0			0
$973$	−23.2832			−0.746427
$974$	−2.92967	−	7.61020i	−0.0938727	−	0.243846i
$975$		0			0
$976$	21.5876	−	9.71097i	0.691001	−	0.310841i
$977$	−9.73245	−	5.61903i	−0.311369	−	0.179769i	0.336170	−	0.941801i	$-0.390868\pi$
$977$	−9.73245	−	5.61903i	−0.311369	−	0.179769i	−0.647539	+	0.762033i	$0.724202\pi$
$978$		0			0
$979$	0.0864857	−	0.0499325i	0.00276409	−	0.00159585i
$980$	1.71778	−	5.32154i	0.0548723	−	0.169990i
$981$		0			0
$982$	7.34043	−	46.6355i	0.234242	−	1.48820i
$983$	20.0804	+	34.7802i	0.640464	+	1.10932i	0.985329	+	0.170664i	$0.0545913\pi$
$983$	20.0804	+	34.7802i	0.640464	+	1.10932i	−0.344865	+	0.938652i	$0.612075\pi$
$984$		0			0
$985$	20.2300	−	35.0394i	0.644581	−	1.11645i
$986$	−1.75028	−	1.41457i	−0.0557404	−	0.0450491i
$987$		0			0
$988$	−70.4901	+	15.1247i	−2.24259	+	0.481182i
$989$		−	47.9898i		−	1.52599i
$990$		0			0
$991$		−	18.8697i		−	0.599417i	−0.954031	−	0.299709i	$-0.903111\pi$
$991$		−	18.8697i		−	0.599417i	0.954031	−	0.299709i	$-0.0968894\pi$
$992$	13.4339	−	51.1169i	0.426527	−	1.62296i
$993$		0			0
$994$	−2.19669	+	2.71802i	−0.0696747	+	0.0862103i
$995$	0.709844	−	1.22949i	0.0225036	−	0.0389773i
$996$		0			0
$997$	1.19746	+	2.07405i	0.0379238	+	0.0656860i	0.884364	−	0.466797i	$-0.154592\pi$
$997$	1.19746	+	2.07405i	0.0379238	+	0.0656860i	−0.846441	+	0.532483i	$0.821259\pi$
$998$	56.7196	+	8.92766i	1.79543	+	0.282600i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ba.a.71.5		72
3.2	odd	2		252.2.ba.a.239.32	yes	72
4.3	odd	2	inner	756.2.ba.a.71.8		72
9.2	odd	6	inner	756.2.ba.a.575.8		72
9.7	even	3		252.2.ba.a.155.29	✓	72
12.11	even	2		252.2.ba.a.239.29	yes	72
36.7	odd	6		252.2.ba.a.155.32	yes	72
36.11	even	6	inner	756.2.ba.a.575.5		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.29	✓	72	9.7	even	3
252.2.ba.a.155.32	yes	72	36.7	odd	6
252.2.ba.a.239.29	yes	72	12.11	even	2
252.2.ba.a.239.32	yes	72	3.2	odd	2
756.2.ba.a.71.5		72	1.1	even	1	trivial
756.2.ba.a.71.8		72	4.3	odd	2	inner
756.2.ba.a.575.5		72	36.11	even	6	inner
756.2.ba.a.575.8		72	9.2	odd	6	inner

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.ba (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.31979 + 0.508077i) q^{2} +(1.48372 - 1.34111i) q^{4} +(2.42137 + 1.39798i) q^{5} +(0.866025 - 0.500000i) q^{7} +(-1.27681 + 2.52384i) q^{8} +O(q^{10})\)	\(q+(-1.31979 + 0.508077i) q^{2} +(1.48372 - 1.34111i) q^{4} +(2.42137 + 1.39798i) q^{5} +(0.866025 - 0.500000i) q^{7} +(-1.27681 + 2.52384i) q^{8} +(-3.90599 - 0.614803i) q^{10} +(-0.140963 - 0.244156i) q^{11} +(-2.43776 + 4.22232i) q^{13} +(-0.888937 + 1.09990i) q^{14} +(0.402825 - 3.97966i) q^{16} +5.66309i q^{17} +7.39353i q^{19} +(5.46748 - 1.17313i) q^{20} +(0.310093 + 0.250615i) q^{22} +(3.28934 - 5.69730i) q^{23} +(1.40869 + 2.43992i) q^{25} +(1.07208 - 6.81116i) q^{26} +(0.614378 - 1.90330i) q^{28} +(0.243350 - 0.140498i) q^{29} +(-8.09138 - 4.67156i) q^{31} +(1.49033 + 5.45701i) q^{32} +(-2.87728 - 7.47411i) q^{34} +2.79596 q^{35} +4.22211 q^{37} +(-3.75648 - 9.75794i) q^{38} +(-6.61990 + 4.32619i) q^{40} +(0.644767 + 0.372257i) q^{41} +(6.31743 - 3.64737i) q^{43} +(-0.536590 - 0.173210i) q^{44} +(-1.44658 + 9.19051i) q^{46} +(2.59024 + 4.48642i) q^{47} +(0.500000 - 0.866025i) q^{49} +(-3.09885 - 2.50448i) q^{50} +(2.04567 + 9.53403i) q^{52} +8.11915i q^{53} -0.788256i q^{55} +(0.156168 + 2.82411i) q^{56} +(-0.249788 + 0.309069i) q^{58} +(-0.215457 + 0.373183i) q^{59} +(2.95890 + 5.12497i) q^{61} +(13.0525 + 2.05446i) q^{62} +(-4.73951 - 6.44493i) q^{64} +(-11.8054 + 6.81586i) q^{65} +(2.11124 + 1.21893i) q^{67} +(7.59485 + 8.40241i) q^{68} +(-3.69009 + 1.42056i) q^{70} +2.47114 q^{71} +0.714758 q^{73} +(-5.57232 + 2.14516i) q^{74} +(9.91556 + 10.9699i) q^{76} +(-0.244156 - 0.140963i) q^{77} +(-2.15347 + 1.24331i) q^{79} +(6.53888 - 9.07310i) q^{80} +(-1.04010 - 0.163711i) q^{82} +(-4.10072 - 7.10266i) q^{83} +(-7.91688 + 13.7124i) q^{85} +(-6.48457 + 8.02353i) q^{86} +(0.796193 - 0.0440279i) q^{88} +0.354223i q^{89} +4.87551i q^{91} +(-2.76029 - 12.8646i) q^{92} +(-5.69802 - 4.60511i) q^{94} +(-10.3360 + 17.9025i) q^{95} +(-0.138992 - 0.240741i) q^{97} +(-0.219890 + 1.39701i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100}) \) 72 * q + 42 * q^20 + 36 * q^25 - 30 * q^32 - 12 * q^34 - 12 * q^40 + 60 * q^41 - 24 * q^46 + 36 * q^49 + 78 * q^50 - 18 * q^52 - 18 * q^58 - 60 * q^64 - 24 * q^65 - 78 * q^68 - 24 * q^73 + 12 * q^76 - 36 * q^82 - 30 * q^86 + 24 * q^88 + 114 * q^92 + 42 * q^94 - 12 * q^97

Introduction

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