LMFDB - Embedded newform 144.2.k.b.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,2,Mod(37,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("144.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	144.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.14984578911$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.2
Root			$0.500000 - 0.691860i$ of defining polynomial
Character	$\chi$	$=$	144.109
Dual form			144.2.k.b.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.635665 + 1.26330i) q^{2} +(-1.19186 - 1.60607i) q^{4} +(2.68554 - 2.68554i) q^{5} -2.15894i q^{7} +(2.78658 - 0.484753i) q^{8} +O(q^{10})$	\(q+(-0.635665 + 1.26330i) q^{2} +(-1.19186 - 1.60607i) q^{4} +(2.68554 - 2.68554i) q^{5} -2.15894i q^{7} +(2.78658 - 0.484753i) q^{8} +(1.68554 + 5.09976i) q^{10} +(-1.79793 + 1.79793i) q^{11} +(1.38372 + 1.38372i) q^{13} +(2.72739 + 1.37236i) q^{14} +(-1.15894 + 3.82843i) q^{16} +0.224777 q^{17} +(0.158942 + 0.158942i) q^{19} +(-7.51397 - 1.11239i) q^{20} +(-1.12845 - 3.41421i) q^{22} +2.82843i q^{23} -9.42429i q^{25} +(-2.62764 + 0.868472i) q^{26} +(-3.46742 + 2.57316i) q^{28} +(1.85712 + 1.85712i) q^{29} +1.84106 q^{31} +(-4.09976 - 3.89769i) q^{32} +(-0.142883 + 0.283962i) q^{34} +(-5.79793 - 5.79793i) q^{35} +(-3.66949 + 3.66949i) q^{37} +(-0.301825 + 0.0997575i) q^{38} +(6.18165 - 8.78530i) q^{40} -5.88163i q^{41} +(-7.75481 + 7.75481i) q^{43} +(5.03049 + 0.744728i) q^{44} +(-3.57316 - 1.79793i) q^{46} +2.82843 q^{47} +2.33897 q^{49} +(11.9057 + 5.99069i) q^{50} +(0.573155 - 3.87155i) q^{52} +(-7.51397 + 7.51397i) q^{53} +9.65685i q^{55} +(-1.04655 - 6.01606i) q^{56} +(-3.52660 + 1.16559i) q^{58} +(-4.00000 + 4.00000i) q^{59} +(5.98737 + 5.98737i) q^{61} +(-1.17030 + 2.32581i) q^{62} +(7.53003 - 2.70160i) q^{64} +7.43208 q^{65} +(-10.4243 - 10.4243i) q^{67} +(-0.267903 - 0.361009i) q^{68} +(11.0101 - 3.63899i) q^{70} -4.31788i q^{71} +5.97474i q^{73} +(-2.30310 - 6.96823i) q^{74} +(0.0658358 - 0.444708i) q^{76} +(3.88163 + 3.88163i) q^{77} +15.0075 q^{79} +(7.16902 + 13.3938i) q^{80} +(7.43027 + 3.73875i) q^{82} +(10.1158 + 10.1158i) q^{83} +(0.603650 - 0.603650i) q^{85} +(-4.86720 - 14.7261i) q^{86} +(-4.13853 + 5.88163i) q^{88} -1.42847i q^{89} +(2.98737 - 2.98737i) q^{91} +(4.54266 - 3.37109i) q^{92} +(-1.79793 + 3.57316i) q^{94} +0.853690 q^{95} -16.3990 q^{97} +(-1.48680 + 2.95482i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} + 12 q^{8}+O(q^{10}) $ 8 * q - 4 * q^4 + 12 * q^8	$ 8 q - 4 q^{4} + 12 q^{8} - 8 q^{10} + 8 q^{11} - 12 q^{14} - 8 q^{19} - 16 q^{20} - 20 q^{26} + 8 q^{28} + 16 q^{29} + 24 q^{31} - 24 q^{35} - 16 q^{37} + 8 q^{38} + 16 q^{40} - 8 q^{43} + 40 q^{44} - 8 q^{46} - 8 q^{49} + 36 q^{50} - 16 q^{52} - 16 q^{53} - 16 q^{58} - 32 q^{59} + 16 q^{61} + 12 q^{62} + 8 q^{64} + 16 q^{65} - 16 q^{67} - 32 q^{68} + 32 q^{70} - 52 q^{74} + 8 q^{76} - 16 q^{77} - 24 q^{79} - 8 q^{80} + 40 q^{82} + 40 q^{83} - 16 q^{85} + 16 q^{86} + 32 q^{88} - 8 q^{91} + 16 q^{92} + 8 q^{94} + 48 q^{95} + 40 q^{98}+O(q^{100}) $ 8 * q - 4 * q^4 + 12 * q^8 - 8 * q^10 + 8 * q^11 - 12 * q^14 - 8 * q^19 - 16 * q^20 - 20 * q^26 + 8 * q^28 + 16 * q^29 + 24 * q^31 - 24 * q^35 - 16 * q^37 + 8 * q^38 + 16 * q^40 - 8 * q^43 + 40 * q^44 - 8 * q^46 - 8 * q^49 + 36 * q^50 - 16 * q^52 - 16 * q^53 - 16 * q^58 - 32 * q^59 + 16 * q^61 + 12 * q^62 + 8 * q^64 + 16 * q^65 - 16 * q^67 - 32 * q^68 + 32 * q^70 - 52 * q^74 + 8 * q^76 - 16 * q^77 - 24 * q^79 - 8 * q^80 + 40 * q^82 + 40 * q^83 - 16 * q^85 + 16 * q^86 + 32 * q^88 - 8 * q^91 + 16 * q^92 + 8 * q^94 + 48 * q^95 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.635665	+	1.26330i	−0.449483	+	0.893289i
$2$	−0.635665	+	1.26330i	−0.449483	+	0.893289i
$3$		0			0
$3$		0			0
$4$	−1.19186	−	1.60607i	−0.595930	−	0.803037i
$5$	2.68554	−	2.68554i	1.20101	−	1.20101i	0.227153	−	0.973859i	$-0.427058\pi$
$5$	2.68554	−	2.68554i	1.20101	−	1.20101i	0.973859	−	0.227153i	$-0.0729416\pi$
$6$		0			0
$7$		−	2.15894i		−	0.816003i	−0.912981	−	0.408002i	$-0.866226\pi$
$7$		−	2.15894i		−	0.816003i	0.912981	−	0.408002i	$-0.133774\pi$
$8$	2.78658	−	0.484753i	0.985204	−	0.171386i
$9$		0			0
$10$	1.68554	+	5.09976i	0.533016	+	1.61268i
$11$	−1.79793	+	1.79793i	−0.542097	+	0.542097i	−0.924143	−	0.382046i	$-0.875220\pi$
$11$	−1.79793	+	1.79793i	−0.542097	+	0.542097i	0.382046	+	0.924143i	$0.375220\pi$
$12$		0			0
$13$	1.38372	+	1.38372i	0.383775	+	0.383775i	0.872460	−	0.488685i	$-0.162523\pi$
$13$	1.38372	+	1.38372i	0.383775	+	0.383775i	−0.488685	+	0.872460i	$0.662523\pi$
$14$	2.72739	+	1.37236i	0.728927	+	0.366780i
$15$		0			0
$16$	−1.15894	+	3.82843i	−0.289735	+	0.957107i
$17$	0.224777			0.0545165			0.0272583	−	0.999628i	$-0.491322\pi$
$17$	0.224777			0.0545165			0.0272583	+	0.999628i	$0.491322\pi$
$18$		0			0
$19$	0.158942	+	0.158942i	0.0364637	+	0.0364637i	0.725104	−	0.688640i	$-0.241792\pi$
$19$	0.158942	+	0.158942i	0.0364637	+	0.0364637i	−0.688640	+	0.725104i	$0.741792\pi$
$20$	−7.51397	−	1.11239i	−1.68018	−	0.248738i
$21$		0			0
$22$	−1.12845	−	3.41421i	−0.240586	−	0.727913i
$23$			2.82843i			0.589768i	0.955533	+	0.294884i	$0.0952810\pi$
$23$			2.82843i			0.589768i	−0.955533	+	0.294884i	$0.904719\pi$
$24$		0			0
$25$		−	9.42429i		−	1.88486i
$26$	−2.62764	+	0.868472i	−0.515322	+	0.170321i
$27$		0			0
$28$	−3.46742	+	2.57316i	−0.655280	+	0.486281i
$29$	1.85712	+	1.85712i	0.344858	+	0.344858i	0.858190	−	0.513332i	$-0.171589\pi$
$29$	1.85712	+	1.85712i	0.344858	+	0.344858i	−0.513332	+	0.858190i	$0.671589\pi$
$30$		0			0
$31$	1.84106			0.330664			0.165332	−	0.986238i	$-0.447130\pi$
$31$	1.84106			0.330664			0.165332	+	0.986238i	$0.447130\pi$
$32$	−4.09976	−	3.89769i	−0.724742	−	0.689021i
$33$		0			0
$34$	−0.142883	+	0.283962i	−0.0245043	+	0.0486990i
$35$	−5.79793	−	5.79793i	−0.980029	−	0.980029i
$36$		0			0
$37$	−3.66949	+	3.66949i	−0.603260	+	0.603260i	−0.941176	−	0.337916i	$-0.890278\pi$
$37$	−3.66949	+	3.66949i	−0.603260	+	0.603260i	0.337916	+	0.941176i	$0.390278\pi$
$38$	−0.301825	+	0.0997575i	−0.0489625	+	0.0161828i
$39$		0			0
$40$	6.18165	−	8.78530i	0.977405	−	1.38908i
$41$		−	5.88163i		−	0.918557i	−0.888292	−	0.459278i	$-0.848108\pi$
$41$		−	5.88163i		−	0.918557i	0.888292	−	0.459278i	$-0.151892\pi$
$42$		0			0
$43$	−7.75481	+	7.75481i	−1.18260	+	1.18260i	−0.203528	+	0.979069i	$0.565241\pi$
$43$	−7.75481	+	7.75481i	−1.18260	+	1.18260i	−0.979069	+	0.203528i	$0.934759\pi$
$44$	5.03049	+	0.744728i	0.758376	+	0.112272i
$45$		0			0
$46$	−3.57316	−	1.79793i	−0.526833	−	0.265091i
$47$	2.82843			0.412568			0.206284	−	0.978492i	$-0.433863\pi$
$47$	2.82843			0.412568			0.206284	+	0.978492i	$0.433863\pi$
$48$		0			0
$49$	2.33897			0.334139
$50$	11.9057	+	5.99069i	1.68372	+	0.847212i
$51$		0			0
$52$	0.573155	−	3.87155i	0.0794823	−	0.536888i
$53$	−7.51397	+	7.51397i	−1.03212	+	1.03212i	−0.0326567	+	0.999467i	$0.510397\pi$
$53$	−7.51397	+	7.51397i	−1.03212	+	1.03212i	−0.999467	+	0.0326567i	$0.989603\pi$
$54$		0			0
$55$			9.65685i			1.30213i
$56$	−1.04655	−	6.01606i	−0.139852	−	0.803930i
$57$		0			0
$58$	−3.52660	+	1.16559i	−0.463066	+	0.153050i
$59$	−4.00000	+	4.00000i	−0.520756	+	0.520756i	−0.917800	−	0.397044i	$-0.870036\pi$
$59$	−4.00000	+	4.00000i	−0.520756	+	0.520756i	0.397044	+	0.917800i	$0.370036\pi$
$60$		0			0
$61$	5.98737	+	5.98737i	0.766604	+	0.766604i	0.977507	−	0.210903i	$-0.0676404\pi$
$61$	5.98737	+	5.98737i	0.766604	+	0.766604i	−0.210903	+	0.977507i	$0.567640\pi$
$62$	−1.17030	+	2.32581i	−0.148628	+	0.295378i
$63$		0			0
$64$	7.53003	−	2.70160i	0.941254	−	0.337700i
$65$	7.43208			0.921836
$66$		0			0
$67$	−10.4243	−	10.4243i	−1.27353	−	1.27353i	−0.944223	−	0.329307i	$-0.893185\pi$
$67$	−10.4243	−	10.4243i	−1.27353	−	1.27353i	−0.329307	−	0.944223i	$-0.606815\pi$
$68$	−0.267903	−	0.361009i	−0.0324880	−	0.0437788i
$69$		0			0
$70$	11.0101	−	3.63899i	1.31596	−	0.434943i
$71$		−	4.31788i		−	0.512438i	−0.966619	−	0.256219i	$-0.917523\pi$
$71$		−	4.31788i		−	0.512438i	0.966619	−	0.256219i	$-0.0824769\pi$
$72$		0			0
$73$			5.97474i			0.699290i	0.936882	+	0.349645i	$0.113698\pi$
$73$			5.97474i			0.699290i	−0.936882	+	0.349645i	$0.886302\pi$
$74$	−2.30310	−	6.96823i	−0.267730	−	0.810040i
$75$		0			0
$76$	0.0658358	−	0.444708i	0.00755188	−	0.0510115i
$77$	3.88163	+	3.88163i	0.442353	+	0.442353i
$78$		0			0
$79$	15.0075			1.68848			0.844239	−	0.535966i	$-0.180053\pi$
$79$	15.0075			1.68848			0.844239	+	0.535966i	$0.180053\pi$
$80$	7.16902	+	13.3938i	0.801521	+	1.49747i
$81$		0			0
$82$	7.43027	+	3.73875i	0.820536	+	0.412876i
$83$	10.1158	+	10.1158i	1.11036	+	1.11036i	0.993102	+	0.117253i	$0.0374088\pi$
$83$	10.1158	+	10.1158i	1.11036	+	1.11036i	0.117253	+	0.993102i	$0.462591\pi$
$84$		0			0
$85$	0.603650	−	0.603650i	0.0654750	−	0.0654750i
$86$	−4.86720	−	14.7261i	−0.524843	−	1.58796i
$87$		0			0
$88$	−4.13853	+	5.88163i	−0.441168	+	0.626984i
$89$		−	1.42847i		−	0.151417i	−0.997130	−	0.0757086i	$-0.975878\pi$
$89$		−	1.42847i		−	0.151417i	0.997130	−	0.0757086i	$-0.0241219\pi$
$90$		0			0
$91$	2.98737	−	2.98737i	0.313161	−	0.313161i
$92$	4.54266	−	3.37109i	0.473605	−	0.351460i
$93$		0			0
$94$	−1.79793	+	3.57316i	−0.185443	+	0.368543i
$95$	0.853690			0.0875867
$96$		0			0
$97$	−16.3990			−1.66507			−0.832535	−	0.553973i	$-0.813111\pi$
$97$	−16.3990			−1.66507			−0.832535	+	0.553973i	$0.813111\pi$
$98$	−1.48680	+	2.95482i	−0.150190	+	0.298482i
$99$		0			0
$100$	−15.1361	+	11.2324i	−1.51361	+	1.12324i
$101$	−0.0818942	+	0.0818942i	−0.00814878	+	0.00814878i	−0.711169	−	0.703021i	$-0.751834\pi$
$101$	−0.0818942	+	0.0818942i	−0.00814878	+	0.00814878i	0.703021	+	0.711169i	$0.251834\pi$
$102$		0			0
$103$		−	13.3507i		−	1.31548i	−0.753245	−	0.657740i	$-0.771512\pi$
$103$		−	13.3507i		−	1.31548i	0.753245	−	0.657740i	$-0.228488\pi$
$104$	4.52660	+	3.18508i	0.443870	+	0.312323i
$105$		0			0
$106$	−4.71604	−	14.2688i	−0.458062	−	1.38591i
$107$	7.27798	−	7.27798i	0.703589	−	0.703589i	−0.261590	−	0.965179i	$-0.584247\pi$
$107$	7.27798	−	7.27798i	0.703589	−	0.703589i	0.965179	+	0.261590i	$0.0842468\pi$
$108$		0			0
$109$	−7.04057	−	7.04057i	−0.674365	−	0.674365i	0.284355	−	0.958719i	$-0.408221\pi$
$109$	−7.04057	−	7.04057i	−0.674365	−	0.674365i	−0.958719	+	0.284355i	$0.908221\pi$
$110$	−12.1995	−	6.13853i	−1.16318	−	0.585285i
$111$		0			0
$112$	8.26535	+	2.50209i	0.781002	+	0.236425i
$113$	−18.8486			−1.77313			−0.886563	−	0.462608i	$-0.846914\pi$
$113$	−18.8486			−1.77313			−0.886563	+	0.462608i	$0.846914\pi$
$114$		0			0
$115$	7.59587	+	7.59587i	0.708318	+	0.708318i
$116$	0.769243	−	5.19609i	0.0714224	−	0.482445i
$117$		0			0
$118$	−2.51054	−	7.59587i	−0.231114	−	0.699256i
$119$		−	0.485281i		−	0.0444857i
$120$		0			0
$121$			4.53488i			0.412261i
$122$	−11.3698	+	3.75789i	−1.02937	+	0.340223i
$123$		0			0
$124$	−2.19428	−	2.95687i	−0.197052	−	0.265535i
$125$	−11.8816	−	11.8816i	−1.06273	−	1.06273i
$126$		0			0
$127$	−3.81580			−0.338597			−0.169299	−	0.985565i	$-0.554150\pi$
$127$	−3.81580			−0.338597			−0.169299	+	0.985565i	$0.554150\pi$
$128$	−1.37364	+	11.2300i	−0.121414	+	0.992602i
$129$		0			0
$130$	−4.72431	+	9.38895i	−0.414350	+	0.823465i
$131$	0.767438	+	0.767438i	0.0670514	+	0.0670514i	0.739837	−	0.672786i	$-0.234902\pi$
$131$	0.767438	+	0.767438i	0.0670514	+	0.0670514i	−0.672786	+	0.739837i	$0.734902\pi$
$132$		0			0
$133$	0.343146	−	0.343146i	0.0297545	−	0.0297545i
$134$	19.7954	−	6.54266i	1.71006	−	0.565200i
$135$		0			0
$136$	0.626360	−	0.108961i	0.0537099	−	0.00934337i
$137$			5.31010i			0.453672i	0.973933	+	0.226836i	$0.0728382\pi$
$137$			5.31010i			0.453672i	−0.973933	+	0.226836i	$0.927162\pi$
$138$		0			0
$139$	8.76744	−	8.76744i	0.743644	−	0.743644i	−0.229633	−	0.973277i	$-0.573753\pi$
$139$	8.76744	−	8.76744i	0.743644	−	0.743644i	0.973277	+	0.229633i	$0.0737526\pi$
$140$	−2.40158	+	16.2222i	−0.202971	+	1.37103i
$141$		0			0
$142$	5.45479	+	2.74473i	0.457756	+	0.230332i
$143$	−4.97567			−0.416086
$144$		0			0
$145$	9.97474			0.828357
$146$	−7.54789	−	3.79793i	−0.624668	−	0.314319i
$147$		0			0
$148$	10.2670	+	1.51995i	0.843940	+	0.124939i
$149$	1.02869	−	1.02869i	0.0842735	−	0.0842735i	−0.663713	−	0.747987i	$-0.731021\pi$
$149$	1.02869	−	1.02869i	0.0842735	−	0.0842735i	0.747987	+	0.663713i	$0.231021\pi$
$150$		0			0
$151$			2.03696i			0.165766i	0.996559	+	0.0828829i	$0.0264127\pi$
$151$			2.03696i			0.165766i	−0.996559	+	0.0828829i	$0.973587\pi$
$152$	0.519951	+	0.365856i	0.0421736	+	0.0296748i
$153$		0			0
$154$	−7.37109	+	2.43625i	−0.593979	+	0.196319i
$155$	4.94424	−	4.94424i	0.397131	−	0.397131i
$156$		0			0
$157$	6.09378	+	6.09378i	0.486336	+	0.486336i	0.907148	−	0.420812i	$-0.138255\pi$
$157$	6.09378	+	6.09378i	0.486336	+	0.486336i	−0.420812	+	0.907148i	$0.638255\pi$
$158$	−9.53976	+	18.9590i	−0.758943	+	1.50830i
$159$		0			0
$160$	−21.4775	+	0.542661i	−1.69795	+	0.0429011i
$161$	6.10641			0.481252
$162$		0			0
$163$	3.43692	+	3.43692i	0.269201	+	0.269201i	0.828778	−	0.559577i	$-0.189037\pi$
$163$	3.43692	+	3.43692i	0.269201	+	0.269201i	−0.559577	+	0.828778i	$0.689037\pi$
$164$	−9.44633	+	7.01008i	−0.737634	+	0.547395i
$165$		0			0
$166$	−19.2096	+	6.34905i	−1.49095	+	0.492782i
$167$		−	21.7023i		−	1.67937i	−0.543072	−	0.839686i	$-0.682739\pi$
$167$		−	21.7023i		−	1.67937i	0.543072	−	0.839686i	$-0.317261\pi$
$168$		0			0
$169$		−	9.17064i		−	0.705434i
$170$	0.378872	+	1.14631i	0.0290582	+	0.0879180i
$171$		0			0
$172$	21.6974	+	3.21215i	1.65441	+	0.244924i
$173$	8.74653	+	8.74653i	0.664987	+	0.664987i	0.956551	−	0.291565i	$-0.0941758\pi$
$173$	8.74653	+	8.74653i	0.664987	+	0.664987i	−0.291565	+	0.956551i	$0.594176\pi$
$174$		0			0
$175$	−20.3465			−1.53805
$176$	−4.79956	−	8.96695i	−0.361780	−	0.675910i
$177$		0			0
$178$	1.80458	+	0.908027i	0.135259	+	0.0680595i
$179$	−8.23163	−	8.23163i	−0.615261	−	0.615261i	0.329051	−	0.944312i	$-0.393271\pi$
$179$	−8.23163	−	8.23163i	−0.615261	−	0.615261i	−0.944312	+	0.329051i	$0.893271\pi$
$180$		0			0
$181$	6.72269	−	6.72269i	0.499694	−	0.499694i	−0.411649	−	0.911343i	$-0.635047\pi$
$181$	6.72269	−	6.72269i	0.499694	−	0.499694i	0.911343	+	0.411649i	$0.135047\pi$
$182$	1.87498	+	5.67291i	0.138983	+	0.420504i
$183$		0			0
$184$	1.37109	+	7.88163i	0.101078	+	0.581042i
$185$			19.7091i			1.44904i
$186$		0			0
$187$	−0.404135	+	0.404135i	−0.0295533	+	0.0295533i
$188$	−3.37109	−	4.54266i	−0.245862	−	0.331308i
$189$		0			0
$190$	−0.542661	+	1.07847i	−0.0393687	+	0.0782402i
$191$	20.8032			1.50526			0.752632	−	0.658441i	$-0.228784\pi$
$191$	20.8032			1.50526			0.752632	+	0.658441i	$0.228784\pi$
$192$		0			0
$193$	14.1454			1.01821			0.509103	−	0.860705i	$-0.329977\pi$
$193$	14.1454			1.01821			0.509103	+	0.860705i	$0.329977\pi$
$194$	10.4243	−	20.7169i	0.748421	−	1.48739i
$195$		0			0
$196$	−2.78772	−	3.75656i	−0.199123	−	0.268326i
$197$	2.42865	−	2.42865i	0.173034	−	0.173034i	−0.615277	−	0.788311i	$-0.710956\pi$
$197$	2.42865	−	2.42865i	0.173034	−	0.173034i	0.788311	+	0.615277i	$0.210956\pi$
$198$		0			0
$199$		−	0.306182i		−	0.0217047i	−0.999941	−	0.0108523i	$-0.996546\pi$
$199$		−	0.306182i		−	0.0217047i	0.999941	−	0.0108523i	$-0.00345447\pi$
$200$	−4.56845	−	26.2615i	−0.323038	−	1.85697i
$201$		0			0
$202$	−0.0513998	−	0.155514i	−0.00361648	−	0.0109420i
$203$	4.00941	−	4.00941i	0.281405	−	0.281405i
$204$		0			0
$205$	−15.7954	−	15.7954i	−1.10320	−	1.10320i
$206$	16.8659	+	8.48656i	1.17510	+	0.591286i
$207$		0			0
$208$	−6.90112	+	3.69382i	−0.478506	+	0.256120i
$209$	−0.571533			−0.0395337
$210$		0			0
$211$	7.23256	+	7.23256i	0.497910	+	0.497910i	0.910787	−	0.412877i	$-0.135476\pi$
$211$	7.23256	+	7.23256i	0.497910	+	0.497910i	−0.412877	+	0.910787i	$0.635476\pi$
$212$	21.0236	+	3.11239i	1.44391	+	0.213760i
$213$		0			0
$214$	4.56792	+	13.8206i	0.312257	+	0.944760i
$215$			41.6517i			2.84063i
$216$		0			0
$217$		−	3.97474i		−	0.269823i
$218$	13.3698	−	4.41892i	0.905518	−	0.299287i
$219$		0			0
$220$	15.5096	−	11.5096i	1.04566	−	0.775978i
$221$	0.311029	+	0.311029i	0.0209221	+	0.0209221i
$222$		0			0
$223$	−1.71908			−0.115118			−0.0575591	−	0.998342i	$-0.518332\pi$
$223$	−1.71908			−0.115118			−0.0575591	+	0.998342i	$0.518332\pi$
$224$	−8.41489	+	8.85114i	−0.562243	+	0.591391i
$225$		0			0
$226$	11.9814	−	23.8114i	0.796990	−	1.58391i
$227$	−10.1158	−	10.1158i	−0.671410	−	0.671410i	0.286631	−	0.958041i	$-0.407465\pi$
$227$	−10.1158	−	10.1158i	−0.671410	−	0.671410i	−0.958041	+	0.286631i	$0.907465\pi$
$228$		0			0
$229$	−12.0195	+	12.0195i	−0.794270	+	0.794270i	−0.982185	−	0.187915i	$-0.939827\pi$
$229$	−12.0195	+	12.0195i	−0.794270	+	0.794270i	0.187915	+	0.982185i	$0.439827\pi$
$230$	−14.4243	+	4.76744i	−0.951110	+	0.314356i
$231$		0			0
$232$	6.07524	+	4.27476i	0.398859	+	0.280652i
$233$		−	13.3779i		−	0.876418i	−0.898873	−	0.438209i	$-0.855613\pi$
$233$		−	13.3779i		−	0.876418i	0.898873	−	0.438209i	$-0.144387\pi$
$234$		0			0
$235$	7.59587	−	7.59587i	0.495500	−	0.495500i
$236$	11.1917	+	1.65685i	0.728520	+	0.107852i
$237$		0			0
$238$	0.613057	+	0.308476i	0.0397386	+	0.0199956i
$239$	−13.3675			−0.864670			−0.432335	−	0.901713i	$-0.642310\pi$
$239$	−13.3675			−0.864670			−0.432335	+	0.901713i	$0.642310\pi$
$240$		0			0
$241$	0.211474			0.0136222			0.00681112	−	0.999977i	$-0.497832\pi$
$241$	0.211474			0.0136222			0.00681112	+	0.999977i	$0.497832\pi$
$242$	−5.72891	−	2.88266i	−0.368269	−	0.185305i
$243$		0			0
$244$	2.48005	−	16.7523i	0.158769	−	1.07245i
$245$	6.28141	−	6.28141i	0.401305	−	0.401305i
$246$		0			0
$247$			0.439861i			0.0279877i
$248$	5.13025	−	0.892458i	0.325771	−	0.0566711i
$249$		0			0
$250$	22.5628	−	7.45734i	1.42700	−	0.471644i
$251$	−10.4337	+	10.4337i	−0.658569	+	0.658569i	−0.955041	−	0.296472i	$-0.904190\pi$
$251$	−10.4337	+	10.4337i	−0.658569	+	0.658569i	0.296472	+	0.955041i	$0.404190\pi$
$252$		0			0
$253$	−5.08532	−	5.08532i	−0.319711	−	0.319711i
$254$	2.42557	−	4.82050i	0.152194	−	0.302465i
$255$		0			0
$256$	−13.3137	−	8.87385i	−0.832107	−	0.554615i
$257$	0.742176			0.0462957			0.0231478	−	0.999732i	$-0.492631\pi$
$257$	0.742176			0.0462957			0.0231478	+	0.999732i	$0.492631\pi$
$258$		0			0
$259$	7.92221	+	7.92221i	0.492262	+	0.492262i
$260$	−8.85799	−	11.9365i	−0.549349	−	0.740268i
$261$		0			0
$262$	−1.45734	+	0.481672i	−0.0900347	+	0.0297578i
$263$			5.48435i			0.338180i	0.985601	+	0.169090i	$0.0540828\pi$
$263$			5.48435i			0.338180i	−0.985601	+	0.169090i	$0.945917\pi$
$264$		0			0
$265$			40.3582i			2.47918i
$266$	0.215371	+	0.651622i	0.0132052	+	0.0399535i
$267$		0			0
$268$	−4.31788	+	29.1665i	−0.263757	+	1.78163i
$269$	−14.4741	−	14.4741i	−0.882500	−	0.882500i	0.111289	−	0.993788i	$-0.464502\pi$
$269$	−14.4741	−	14.4741i	−0.882500	−	0.882500i	−0.993788	+	0.111289i	$0.964502\pi$
$270$		0			0
$271$	−14.0370			−0.852685			−0.426342	−	0.904562i	$-0.640198\pi$
$271$	−14.0370			−0.852685			−0.426342	+	0.904562i	$0.640198\pi$
$272$	−0.260504	+	0.860544i	−0.0157954	+	0.0521781i
$273$		0			0
$274$	−6.70825	−	3.37545i	−0.405260	−	0.203918i
$275$	16.9442	+	16.9442i	1.02178	+	1.02178i
$276$		0			0
$277$	9.49013	−	9.49013i	0.570207	−	0.570207i	−0.361980	−	0.932186i	$-0.617899\pi$
$277$	9.49013	−	9.49013i	0.570207	−	0.570207i	0.932186	+	0.361980i	$0.117899\pi$
$278$	5.50276	+	16.6491i	0.330034	+	0.998545i
$279$		0			0
$280$	−18.9670	−	13.3458i	−1.13349	−	0.797566i
$281$			3.89359i			0.232272i	0.993233	+	0.116136i	$0.0370509\pi$
$281$			3.89359i			0.232272i	−0.993233	+	0.116136i	$0.962949\pi$
$282$		0			0
$283$	−12.4853	+	12.4853i	−0.742173	+	0.742173i	−0.972996	−	0.230823i	$-0.925858\pi$
$283$	−12.4853	+	12.4853i	−0.742173	+	0.742173i	0.230823	+	0.972996i	$0.425858\pi$
$284$	−6.93484	+	5.14631i	−0.411507	+	0.305377i
$285$		0			0
$286$	3.16286	−	6.28577i	0.187024	−	0.371685i
$287$	−12.6981			−0.749545
$288$		0			0
$289$	−16.9495			−0.997028
$290$	−6.34059	+	12.6011i	−0.372332	+	0.739962i
$291$		0			0
$292$	9.59587	−	7.12105i	0.561556	−	0.416728i
$293$	11.1553	−	11.1553i	0.651697	−	0.651697i	−0.301704	−	0.953402i	$-0.597556\pi$
$293$	11.1553	−	11.1553i	0.651697	−	0.651697i	0.953402	+	0.301704i	$0.0975556\pi$
$294$		0			0
$295$			21.4844i			1.25087i
$296$	−8.44651	+	12.0041i	−0.490944	+	0.697724i
$297$		0			0
$298$	0.645643	+	1.95345i	0.0374011	+	0.113160i
$299$	−3.91375	+	3.91375i	−0.226338	+	0.226338i
$300$		0			0
$301$	16.7422	+	16.7422i	0.965003	+	0.965003i
$302$	−2.57330	−	1.29483i	−0.148077	−	0.0745089i
$303$		0			0
$304$	−0.792701	+	0.424292i	−0.0454645	+	0.0243348i
$305$	32.1587			1.84140
$306$		0			0
$307$	−5.40320	−	5.40320i	−0.308377	−	0.308377i	0.535903	−	0.844280i	$-0.319971\pi$
$307$	−5.40320	−	5.40320i	−0.308377	−	0.308377i	−0.844280	+	0.535903i	$0.819971\pi$
$308$	1.60782	−	10.8605i	0.0916143	−	0.618837i
$309$		0			0
$310$	3.10318	+	9.38895i	0.176249	+	0.533257i
$311$		−	24.1623i		−	1.37012i	−0.728488	−	0.685059i	$-0.759776\pi$
$311$		−	24.1623i		−	1.37012i	0.728488	−	0.685059i	$-0.240224\pi$
$312$		0			0
$313$			16.6105i			0.938881i	0.882964	+	0.469441i	$0.155544\pi$
$313$			16.6105i			0.938881i	−0.882964	+	0.469441i	$0.844456\pi$
$314$	−11.5719	+	3.82467i	−0.653039	+	0.215839i
$315$		0			0
$316$	−17.8869	−	24.1032i	−1.00621	−	1.35591i
$317$	−1.81170	−	1.81170i	−0.101755	−	0.101755i	0.654397	−	0.756152i	$-0.272923\pi$
$317$	−1.81170	−	1.81170i	−0.101755	−	0.101755i	−0.756152	+	0.654397i	$0.772923\pi$
$318$		0			0
$319$	−6.67794			−0.373893
$320$	12.9670	−	27.4775i	0.724875	−	1.53604i
$321$		0			0
$322$	−3.88163	+	7.71423i	−0.216315	+	0.429897i
$323$	0.0357265	+	0.0357265i	0.00198788	+	0.00198788i
$324$		0			0
$325$	13.0406	−	13.0406i	0.723361	−	0.723361i
$326$	−6.52660	+	2.15714i	−0.361475	+	0.119473i
$327$		0			0
$328$	−2.85114	−	16.3896i	−0.157428	−	0.904966i
$329$		−	6.10641i		−	0.336657i
$330$		0			0
$331$	13.5252	−	13.5252i	0.743411	−	0.743411i	−0.229822	−	0.973233i	$-0.573814\pi$
$331$	13.5252	−	13.5252i	0.743411	−	0.743411i	0.973233	+	0.229822i	$0.0738142\pi$
$332$	4.19011	−	28.3034i	0.229962	−	1.55335i
$333$		0			0
$334$	27.4165	+	13.7954i	1.50016	+	0.754850i
$335$	−55.9898			−3.05905
$336$		0			0
$337$	−1.12615			−0.0613454			−0.0306727	−	0.999529i	$-0.509765\pi$
$337$	−1.12615			−0.0613454			−0.0306727	+	0.999529i	$0.509765\pi$
$338$	11.5853	+	5.82946i	0.630156	+	0.317081i
$339$		0			0
$340$	−1.68897	−	0.250040i	−0.0915973	−	0.0135603i
$341$	−3.31010	+	3.31010i	−0.179252	+	0.179252i
$342$		0			0
$343$		−	20.1623i		−	1.08866i
$344$	−17.8502	+	25.3685i	−0.962419	+	1.36778i
$345$		0			0
$346$	−16.6094	+	5.48964i	−0.892925	+	0.295125i
$347$	−20.7938	+	20.7938i	−1.11627	+	1.11627i	−0.123983	+	0.992284i	$0.539567\pi$
$347$	−20.7938	+	20.7938i	−1.11627	+	1.11627i	−0.992284	+	0.123983i	$0.960433\pi$
$348$		0			0
$349$	−19.2855	−	19.2855i	−1.03233	−	1.03233i	−0.999460	−	0.0328700i	$-0.989535\pi$
$349$	−19.2855	−	19.2855i	−1.03233	−	1.03233i	−0.0328700	−	0.999460i	$-0.510465\pi$
$350$	12.9336	−	25.7038i	0.691328	−	1.37392i
$351$		0			0
$352$	14.3789	−	0.363303i	0.766396	−	0.0193641i
$353$	−25.5908			−1.36206			−0.681029	−	0.732256i	$-0.738467\pi$
$353$	−25.5908			−1.36206			−0.681029	+	0.732256i	$0.738467\pi$
$354$		0			0
$355$	−11.5959	−	11.5959i	−0.615445	−	0.615445i
$356$	−2.29422	+	1.70253i	−0.121594	+	0.0902340i
$357$		0			0
$358$	15.6316	−	5.16647i	0.826155	−	0.273056i
$359$			3.77296i			0.199129i	0.995031	+	0.0995645i	$0.0317450\pi$
$359$			3.77296i			0.199129i	−0.995031	+	0.0995645i	$0.968255\pi$
$360$		0			0
$361$		−	18.9495i		−	0.997341i
$362$	4.21940	+	12.7662i	0.221767	+	0.670975i
$363$		0			0
$364$	−8.35846	−	1.23741i	−0.438102	−	0.0648578i
$365$	16.0454	+	16.0454i	0.839856	+	0.839856i
$366$		0			0
$367$	−27.4474			−1.43274			−0.716371	−	0.697720i	$-0.754198\pi$
$367$	−27.4474			−1.43274			−0.716371	+	0.697720i	$0.754198\pi$
$368$	−10.8284	−	3.27798i	−0.564471	−	0.170877i
$369$		0			0
$370$	−24.8986	−	12.5284i	−1.29441	−	0.651321i
$371$	16.2222	+	16.2222i	0.842216	+	0.842216i
$372$		0			0
$373$	12.6231	−	12.6231i	0.653601	−	0.653601i	−0.300257	−	0.953858i	$-0.597072\pi$
$373$	12.6231	−	12.6231i	0.653601	−	0.653601i	0.953858	+	0.300257i	$0.0970725\pi$
$374$	−0.253649	−	0.767438i	−0.0131159	−	0.0396833i
$375$		0			0
$376$	7.88163	−	1.37109i	0.406464	−	0.0707085i
$377$			5.13946i			0.264695i
$378$		0			0
$379$	−11.6686	+	11.6686i	−0.599373	+	0.599373i	−0.940146	−	0.340772i	$-0.889311\pi$
$379$	−11.6686	+	11.6686i	−0.599373	+	0.599373i	0.340772	+	0.940146i	$0.389311\pi$
$380$	−1.01748	−	1.37109i	−0.0521955	−	0.0703353i
$381$		0			0
$382$	−13.2238	+	26.2807i	−0.676591	+	1.34464i
$383$	17.1885			0.878291			0.439145	−	0.898416i	$-0.355281\pi$
$383$	17.1885			0.878291			0.439145	+	0.898416i	$0.355281\pi$
$384$		0			0
$385$	20.8486			1.06254
$386$	−8.99173	+	17.8699i	−0.457667	+	0.909553i
$387$		0			0
$388$	19.5453	+	26.3380i	0.992264	+	1.33711i
$389$	1.88238	−	1.88238i	0.0954404	−	0.0954404i	−0.657774	−	0.753215i	$-0.728502\pi$
$389$	1.88238	−	1.88238i	0.0954404	−	0.0954404i	0.753215	+	0.657774i	$0.228502\pi$
$390$		0			0
$391$			0.635767i			0.0321521i
$392$	6.51772	−	1.13382i	0.329195	−	0.0572667i
$393$		0			0
$394$	1.52431	+	4.61192i	0.0767935	+	0.232345i
$395$	40.3034	−	40.3034i	2.02788	−	2.02788i
$396$		0			0
$397$	8.41166	+	8.41166i	0.422169	+	0.422169i	0.885950	−	0.463781i	$-0.153507\pi$
$397$	8.41166	+	8.41166i	0.422169	+	0.422169i	−0.463781	+	0.885950i	$0.653507\pi$
$398$	0.386800	+	0.194629i	0.0193885	+	0.00975588i
$399$		0			0
$400$	36.0802	+	10.9222i	1.80401	+	0.546110i
$401$	−1.12389			−0.0561242			−0.0280621	−	0.999606i	$-0.508934\pi$
$401$	−1.12389			−0.0561242			−0.0280621	+	0.999606i	$0.508934\pi$
$402$		0			0
$403$	2.54751	+	2.54751i	0.126900	+	0.126900i
$404$	0.229135	+	0.0339217i	0.0113999	+	0.00168767i
$405$		0			0
$406$	2.51645	+	7.61373i	0.124889	+	0.377863i
$407$		−	13.1950i		−	0.654051i
$408$		0			0
$409$		−	13.7211i		−	0.678464i	−0.940703	−	0.339232i	$-0.889833\pi$
$409$		−	13.7211i		−	0.678464i	0.940703	−	0.339232i	$-0.110167\pi$
$410$	29.9949	−	9.91375i	1.48134	−	0.489605i
$411$		0			0
$412$	−21.4422	+	15.9121i	−1.05638	+	0.783934i
$413$	8.63577	+	8.63577i	0.424938	+	0.424938i
$414$		0			0
$415$	54.3329			2.66710
$416$	−0.279604	−	11.0662i	−0.0137087	−	0.542566i
$417$		0			0
$418$	0.363303	−	0.722018i	0.0177698	−	0.0353151i
$419$	9.30755	+	9.30755i	0.454703	+	0.454703i	0.896912	−	0.442209i	$-0.145805\pi$
$419$	9.30755	+	9.30755i	0.454703	+	0.454703i	−0.442209	+	0.896912i	$0.645805\pi$
$420$		0			0
$421$	8.44378	−	8.44378i	0.411525	−	0.411525i	−0.470745	−	0.882269i	$-0.656015\pi$
$421$	8.44378	−	8.44378i	0.411525	−	0.411525i	0.882269	+	0.470745i	$0.156015\pi$
$422$	−13.7344	+	4.53942i	−0.668580	+	0.220975i
$423$		0			0
$424$	−17.2958	+	24.5807i	−0.839960	+	1.19374i
$425$		−	2.11837i		−	0.102756i
$426$		0			0
$427$	12.9264	−	12.9264i	0.625551	−	0.625551i
$428$	−20.3633	−	3.01464i	−0.984297	−	0.145718i
$429$		0			0
$430$	−52.6187	−	26.4766i	−2.53750	−	1.27681i
$431$	30.6054			1.47421			0.737105	−	0.675778i	$-0.236192\pi$
$431$	30.6054			1.47421			0.737105	+	0.675778i	$0.236192\pi$
$432$		0			0
$433$	−15.3137			−0.735930			−0.367965	−	0.929840i	$-0.619945\pi$
$433$	−15.3137			−0.735930			−0.367965	+	0.929840i	$0.619945\pi$
$434$	5.02129	+	2.52660i	0.241030	+	0.121281i
$435$		0			0
$436$	−2.91630	+	19.6991i	−0.139665	+	0.943413i
$437$	−0.449555	+	0.449555i	−0.0215051	+	0.0215051i
$438$		0			0
$439$			33.3676i			1.59255i	0.604936	+	0.796274i	$0.293199\pi$
$439$			33.3676i			1.59255i	−0.604936	+	0.796274i	$0.706801\pi$
$440$	4.68119	+	26.9096i	0.223167	+	1.28286i
$441$		0			0
$442$	−0.590633	+	0.195213i	−0.0280936	+	0.00928533i
$443$	−2.28832	+	2.28832i	−0.108721	+	0.108721i	−0.759375	−	0.650653i	$-0.774495\pi$
$443$	−2.28832	+	2.28832i	−0.108721	+	0.108721i	0.650653	+	0.759375i	$0.274495\pi$
$444$		0			0
$445$	−3.83621	−	3.83621i	−0.181854	−	0.181854i
$446$	1.09276	−	2.17172i	0.0517437	−	0.102834i
$447$		0			0
$448$	−5.83260	−	16.2569i	−0.275565	−	0.768066i
$449$	27.4165			1.29387			0.646933	−	0.762547i	$-0.276052\pi$
$449$	27.4165			1.29387			0.646933	+	0.762547i	$0.276052\pi$
$450$		0			0
$451$	10.5748	+	10.5748i	0.497947	+	0.497947i
$452$	22.4649	+	30.2722i	1.05666	+	1.42388i
$453$		0			0
$454$	19.2096	−	6.34905i	0.901551	−	0.297976i
$455$		−	16.0454i		−	0.752221i
$456$		0			0
$457$		−	10.9147i		−	0.510567i	−0.966866	−	0.255284i	$-0.917831\pi$
$457$		−	10.9147i		−	0.510567i	0.966866	−	0.255284i	$-0.0821688\pi$
$458$	−7.54386	−	22.8246i	−0.352501	−	1.06652i
$459$		0			0
$460$	3.14631	−	21.2527i	0.146697	−	0.990913i
$461$	−17.8319	−	17.8319i	−0.830512	−	0.830512i	0.157075	−	0.987587i	$-0.449794\pi$
$461$	−17.8319	−	17.8319i	−0.830512	−	0.830512i	−0.987587	+	0.157075i	$0.949794\pi$
$462$		0			0
$463$	22.4937			1.04537			0.522686	−	0.852525i	$-0.324930\pi$
$463$	22.4937			1.04537			0.522686	+	0.852525i	$0.324930\pi$
$464$	−9.26213	+	4.95755i	−0.429983	+	0.230148i
$465$		0			0
$466$	16.9004	+	8.50389i	0.782895	+	0.393935i
$467$	−24.2171	−	24.2171i	−1.12063	−	1.12063i	−0.991646	−	0.128989i	$-0.958827\pi$
$467$	−24.2171	−	24.2171i	−1.12063	−	1.12063i	−0.128989	−	0.991646i	$-0.541173\pi$
$468$		0			0
$469$	−22.5054	+	22.5054i	−1.03920	+	1.03920i
$470$	4.76744	+	14.4243i	0.219906	+	0.665343i
$471$		0			0
$472$	−9.20730	+	13.0853i	−0.423800	+	0.602301i
$473$		−	27.8852i		−	1.28216i
$474$		0			0
$475$	1.49791	−	1.49791i	0.0687289	−	0.0687289i
$476$	−0.779397	+	0.578387i	−0.0357236	+	0.0265103i
$477$		0			0
$478$	8.49724	−	16.8872i	0.388655	−	0.772400i
$479$	36.2362			1.65568			0.827838	−	0.560968i	$-0.189571\pi$
$479$	36.2362			1.65568			0.827838	+	0.560968i	$0.189571\pi$
$480$		0			0
$481$	−10.1551			−0.463032
$482$	−0.134427	+	0.267156i	−0.00612297	+	0.0121686i
$483$		0			0
$484$	7.28334	−	5.40494i	0.331061	−	0.245679i
$485$	−44.0403	+	44.0403i	−1.99977	+	1.99977i
$486$		0			0
$487$		−	16.8200i		−	0.762186i	−0.924537	−	0.381093i	$-0.875548\pi$
$487$		−	16.8200i		−	0.762186i	0.924537	−	0.381093i	$-0.124452\pi$
$488$	19.5867	+	13.7819i	0.886646	+	0.623876i
$489$		0			0
$490$	3.94244	+	11.9282i	0.178101	+	0.538860i
$491$	−6.10641	+	6.10641i	−0.275578	+	0.275578i	−0.831341	−	0.555763i	$-0.812426\pi$
$491$	−6.10641	+	6.10641i	−0.275578	+	0.275578i	0.555763	+	0.831341i	$0.312426\pi$
$492$		0			0
$493$	0.417438	+	0.417438i	0.0188005	+	0.0188005i
$494$	−0.555677	−	0.279604i	−0.0250011	−	0.0125800i
$495$		0			0
$496$	−2.13368	+	7.04836i	−0.0958050	+	0.316481i
$497$	−9.32206			−0.418151
$498$		0			0
$499$	−19.6770	−	19.6770i	−0.880864	−	0.880864i	0.112758	−	0.993622i	$-0.464031\pi$
$499$	−19.6770	−	19.6770i	−0.880864	−	0.880864i	−0.993622	+	0.112758i	$0.964031\pi$
$500$	−4.92153	+	33.2440i	−0.220098	+	1.48672i
$501$		0			0
$502$	−6.54856	−	19.8132i	−0.292277	−	0.884308i
$503$			25.7308i			1.14728i	0.819108	+	0.573639i	$0.194469\pi$
$503$			25.7308i			1.14728i	−0.819108	+	0.573639i	$0.805531\pi$
$504$		0			0
$505$			0.439861i			0.0195736i
$506$	9.65685	−	3.19173i	0.429300	−	0.141890i
$507$		0			0
$508$	4.54789	+	6.12845i	0.201780	+	0.271906i
$509$	−1.73514	−	1.73514i	−0.0769087	−	0.0769087i	0.667606	−	0.744515i	$-0.267319\pi$
$509$	−1.73514	−	1.73514i	−0.0769087	−	0.0769087i	−0.744515	+	0.667606i	$0.767319\pi$
$510$		0			0
$511$	12.8991			0.570623
$512$	19.6734	−	11.1784i	0.869450	−	0.494021i
$513$		0			0
$514$	−0.471775	+	0.937591i	−0.0208091	+	0.0413554i
$515$	−35.8538	−	35.8538i	−1.57991	−	1.57991i
$516$		0			0
$517$	−5.08532	+	5.08532i	−0.223652	+	0.223652i
$518$	−15.0440	+	4.97226i	−0.660995	+	0.218469i
$519$		0			0
$520$	20.7101	−	3.60272i	0.908196	−	0.157990i
$521$			33.5944i			1.47180i	0.677092	+	0.735898i	$0.263240\pi$
$521$			33.5944i			1.47180i	−0.677092	+	0.735898i	$0.736760\pi$
$522$		0			0
$523$	−21.8158	+	21.8158i	−0.953938	+	0.953938i	−0.998985	−	0.0450467i	$-0.985656\pi$
$523$	−21.8158	+	21.8158i	−0.953938	+	0.953938i	0.0450467	+	0.998985i	$0.485656\pi$
$524$	0.317883	−	2.14724i	0.0138868	−	0.0938026i
$525$		0			0
$526$	−6.92839	−	3.48621i	−0.302092	−	0.152006i
$527$	0.413828			0.0180266
$528$		0			0
$529$	15.0000			0.652174
$530$	−50.9846	−	25.6543i	−2.21463	−	1.11435i
$531$		0			0
$532$	−0.960099	−	0.142136i	−0.0416256	−	0.00616236i
$533$	8.13853	−	8.13853i	0.352519	−	0.352519i
$534$		0			0
$535$		−	39.0907i		−	1.69004i
$536$	−34.1013	−	23.9949i	−1.47295	−	1.03642i
$537$		0			0
$538$	27.4858	−	9.08445i	1.18500	−	0.391658i
$539$	−4.20531	+	4.20531i	−0.181136	+	0.181136i
$540$		0			0
$541$	27.2112	+	27.2112i	1.16990	+	1.16990i	0.982232	+	0.187669i	$0.0600933\pi$
$541$	27.2112	+	27.2112i	1.16990	+	1.16990i	0.187669	+	0.982232i	$0.439907\pi$
$542$	8.92281	−	17.7329i	0.383267	−	0.761694i
$543$		0			0
$544$	−0.921533	−	0.876113i	−0.0395104	−	0.0375630i
$545$	−37.8155			−1.61984
$546$		0			0
$547$	−6.80116	−	6.80116i	−0.290796	−	0.290796i	0.546598	−	0.837395i	$-0.315922\pi$
$547$	−6.80116	−	6.80116i	−0.290796	−	0.290796i	−0.837395	+	0.546598i	$0.815922\pi$
$548$	8.52841	−	6.32889i	0.364315	−	0.270357i
$549$		0			0
$550$	−32.1765	+	10.6348i	−1.37201	+	0.453470i
$551$			0.590346i			0.0251496i
$552$		0			0
$553$		−	32.4004i		−	1.37780i
$554$	5.95635	+	18.0214i	0.253061	+	0.765657i
$555$		0			0
$556$	−24.5307	−	3.63159i	−1.04033	−	0.154014i
$557$	4.29337	+	4.29337i	0.181916	+	0.181916i	0.792190	−	0.610274i	$-0.208941\pi$
$557$	4.29337	+	4.29337i	0.181916	+	0.181916i	−0.610274	+	0.792190i	$0.708941\pi$
$558$		0			0
$559$	−21.4609			−0.907701
$560$	28.9164	−	15.4775i	1.22194	−	0.654044i
$561$		0			0
$562$	−4.91878	−	2.47502i	−0.207486	−	0.104402i
$563$	10.0801	+	10.0801i	0.424825	+	0.424825i	0.886861	−	0.462036i	$-0.152881\pi$
$563$	10.0801	+	10.0801i	0.424825	+	0.424825i	−0.462036	+	0.886861i	$0.652881\pi$
$564$		0			0
$565$	−50.6187	+	50.6187i	−2.12954	+	2.12954i
$566$	−7.83621	−	23.7091i	−0.329381	−	0.996569i
$567$		0			0
$568$	−2.09311	−	12.0321i	−0.0878248	−	0.504856i
$569$		−	32.5018i		−	1.36255i	−0.732029	−	0.681274i	$-0.761426\pi$
$569$		−	32.5018i		−	1.36255i	0.732029	−	0.681274i	$-0.238574\pi$
$570$		0			0
$571$	−9.17157	+	9.17157i	−0.383818	+	0.383818i	−0.872476	−	0.488657i	$-0.837487\pi$
$571$	−9.17157	+	9.17157i	−0.383818	+	0.383818i	0.488657	+	0.872476i	$0.337487\pi$
$572$	5.93030	+	7.99129i	0.247958	+	0.334132i
$573$		0			0
$574$	8.07174	−	16.0415i	0.336908	−	0.669560i
$575$	26.6559			1.11163
$576$		0			0
$577$	11.7536			0.489308			0.244654	−	0.969611i	$-0.421326\pi$
$577$	11.7536			0.489308			0.244654	+	0.969611i	$0.421326\pi$
$578$	10.7742	−	21.4123i	0.448147	−	0.890634i
$579$		0			0
$580$	−11.8885	−	16.0202i	−0.493643	−	0.665201i
$581$	21.8395	−	21.8395i	0.906053	−	0.906053i
$582$		0			0
$583$		−	27.0192i		−	1.11902i
$584$	2.89627	+	16.6491i	0.119849	+	0.688943i
$585$		0			0
$586$	7.00144	+	21.1835i	0.289227	+	0.875081i
$587$	−6.46002	+	6.46002i	−0.266634	+	0.266634i	−0.827742	−	0.561109i	$-0.810375\pi$
$587$	−6.46002	+	6.46002i	−0.266634	+	0.266634i	0.561109	+	0.827742i	$0.310375\pi$
$588$		0			0
$589$	0.292621	+	0.292621i	0.0120572	+	0.0120572i
$590$	−27.1412	−	13.6569i	−1.11739	−	0.562244i
$591$		0			0
$592$	−9.79564	−	18.3011i	−0.402598	−	0.752170i
$593$	−5.49270			−0.225558			−0.112779	−	0.993620i	$-0.535975\pi$
$593$	−5.49270			−0.225558			−0.112779	+	0.993620i	$0.535975\pi$
$594$		0			0
$595$	−1.30324	−	1.30324i	−0.0534278	−	0.0534278i
$596$	−2.87820	−	0.426097i	−0.117896	−	0.0174536i
$597$		0			0
$598$	−2.45641	−	7.43208i	−0.100450	−	0.303920i
$599$			36.4348i			1.48868i	0.667799	+	0.744342i	$0.267237\pi$
$599$			36.4348i			1.48868i	−0.667799	+	0.744342i	$0.732763\pi$
$600$		0			0
$601$			9.97474i			0.406878i	0.979088	+	0.203439i	$0.0652119\pi$
$601$			9.97474i			0.406878i	−0.979088	+	0.203439i	$0.934788\pi$
$602$	−31.7928	+	10.5080i	−1.29578	+	0.428274i
$603$		0			0
$604$	3.27151	−	2.42777i	0.133116	−	0.0987848i
$605$	12.1786	+	12.1786i	0.495131	+	0.495131i
$606$		0			0
$607$	4.51900			0.183421			0.0917103	−	0.995786i	$-0.470767\pi$
$607$	4.51900			0.183421			0.0917103	+	0.995786i	$0.470767\pi$
$608$	−0.0321169	−	1.27113i	−0.00130251	−	0.0515510i
$609$		0			0
$610$	−20.4422	+	40.6261i	−0.827679	+	1.64490i
$611$	3.91375	+	3.91375i	0.158333	+	0.158333i
$612$		0			0
$613$	−8.43692	+	8.43692i	−0.340764	+	0.340764i	−0.856655	−	0.515890i	$-0.827461\pi$
$613$	−8.43692	+	8.43692i	−0.340764	+	0.340764i	0.515890	+	0.856655i	$0.327461\pi$
$614$	10.2605	−	3.39125i	0.414080	−	0.136860i
$615$		0			0
$616$	12.6981	+	8.93484i	0.511621	+	0.359995i
$617$			32.1201i			1.29311i	0.762869	+	0.646554i	$0.223790\pi$
$617$			32.1201i			1.29311i	−0.762869	+	0.646554i	$0.776210\pi$
$618$		0			0
$619$	15.0412	−	15.0412i	0.604559	−	0.604559i	−0.336960	−	0.941519i	$-0.609399\pi$
$619$	15.0412	−	15.0412i	0.604559	−	0.604559i	0.941519	+	0.336960i	$0.109399\pi$
$620$	−13.8337	−	2.04797i	−0.555573	−	0.0822486i
$621$		0			0
$622$	30.5243	+	15.3591i	1.22391	+	0.615845i
$623$	−3.08398			−0.123557
$624$		0			0
$625$	−16.6958			−0.667833
$626$	−20.9841	−	10.5587i	−0.838692	−	0.422011i
$627$		0			0
$628$	2.52413	−	17.0500i	0.100724	−	0.680368i
$629$	−0.824818	+	0.824818i	−0.0328876	+	0.0328876i
$630$		0			0
$631$			36.4685i			1.45179i	0.687807	+	0.725894i	$0.258574\pi$
$631$			36.4685i			1.45179i	−0.687807	+	0.725894i	$0.741426\pi$
$632$	41.8196	−	7.27494i	1.66350	−	0.289382i
$633$		0			0
$634$	3.44035	−	1.13709i	0.136634	−	0.0451595i
$635$	−10.2475	+	10.2475i	−0.406659	+	0.406659i
$636$		0			0
$637$	3.23648	+	3.23648i	0.128234	+	0.128234i
$638$	4.24494	−	8.43625i	0.168059	−	0.333994i
$639$		0			0
$640$	26.4697	+	33.8477i	1.04631	+	1.33795i
$641$	−14.0036			−0.553109			−0.276555	−	0.960998i	$-0.589193\pi$
$641$	−14.0036			−0.553109			−0.276555	+	0.960998i	$0.589193\pi$
$642$		0			0
$643$	16.6034	+	16.6034i	0.654774	+	0.654774i	0.954139	−	0.299365i	$-0.0967748\pi$
$643$	16.6034	+	16.6034i	0.654774	+	0.654774i	−0.299365	+	0.954139i	$0.596775\pi$
$644$	−7.27798	−	9.80734i	−0.286793	−	0.386463i
$645$		0			0
$646$	−0.0678434	+	0.0224232i	−0.00266926	+	0.000882230i
$647$		−	12.1908i		−	0.479270i	−0.970863	−	0.239635i	$-0.922972\pi$
$647$		−	12.1908i		−	0.479270i	0.970863	−	0.239635i	$-0.0770277\pi$
$648$		0			0
$649$		−	14.3835i		−	0.564600i
$650$	8.18473	+	24.7636i	0.321032	+	0.971309i
$651$		0			0
$652$	1.42362	−	9.61628i	0.0557533	−	0.376603i
$653$	−0.983270	−	0.983270i	−0.0384783	−	0.0384783i	0.687606	−	0.726084i	$-0.258662\pi$
$653$	−0.983270	−	0.983270i	−0.0384783	−	0.0384783i	−0.726084	+	0.687606i	$0.758662\pi$
$654$		0			0
$655$	4.12198			0.161059
$656$	22.5174	+	6.81647i	0.879157	+	0.266138i
$657$		0			0
$658$	7.71423	+	3.88163i	0.300732	+	0.151322i
$659$	18.0559	+	18.0559i	0.703357	+	0.703357i	0.965130	−	0.261772i	$-0.0843069\pi$
$659$	18.0559	+	18.0559i	0.703357	+	0.703357i	−0.261772	+	0.965130i	$0.584307\pi$
$660$		0			0
$661$	−4.55890	+	4.55890i	−0.177321	+	0.177321i	−0.790187	−	0.612866i	$-0.790017\pi$
$661$	−4.55890	+	4.55890i	−0.177321	+	0.177321i	0.612866	+	0.790187i	$0.290017\pi$
$662$	8.48889	+	25.6839i	0.329930	+	0.998232i
$663$		0			0
$664$	33.0922	+	23.2848i	1.28423	+	0.903627i
$665$		−	1.84307i		−	0.0714710i
$666$		0			0
$667$	−5.25272	+	5.25272i	−0.203386	+	0.203386i
$668$	−34.8554	+	25.8661i	−1.34860	+	1.00079i
$669$		0			0
$670$	35.5908	−	70.7320i	1.37499	−	2.73261i
$671$	−21.5298			−0.831148
$672$		0			0
$673$	−10.8569			−0.418504			−0.209252	−	0.977862i	$-0.567103\pi$
$673$	−10.8569			−0.418504			−0.209252	+	0.977862i	$0.567103\pi$
$674$	0.715856	−	1.42267i	0.0275737	−	0.0547992i
$675$		0			0
$676$	−14.7287	+	10.9301i	−0.566489	+	0.420389i
$677$	−23.7066	+	23.7066i	−0.911120	+	0.911120i	−0.996360	−	0.0852405i	$-0.972834\pi$
$677$	−23.7066	+	23.7066i	−0.911120	+	0.911120i	0.0852405	+	0.996360i	$0.472834\pi$
$678$		0			0
$679$			35.4045i			1.35870i
$680$	1.38950	−	1.97474i	0.0532847	−	0.0757277i
$681$		0			0
$682$	−2.07754	−	6.28577i	−0.0795530	−	0.240694i
$683$	17.8337	−	17.8337i	0.682386	−	0.682386i	−0.278151	−	0.960537i	$-0.589722\pi$
$683$	17.8337	−	17.8337i	0.682386	−	0.682386i	0.960537	+	0.278151i	$0.0897217\pi$
$684$		0			0
$685$	14.2605	+	14.2605i	0.544866	+	0.544866i
$686$	25.4710	+	12.8165i	0.972489	+	0.489335i
$687$		0			0
$688$	−20.7013	−	38.6761i	−0.789231	−	1.47451i
$689$	−20.7945			−0.792205
$690$		0			0
$691$	10.8557	+	10.8557i	0.412970	+	0.412970i	0.882772	−	0.469802i	$-0.155675\pi$
$691$	10.8557	+	10.8557i	0.412970	+	0.412970i	−0.469802	+	0.882772i	$0.655675\pi$
$692$	3.62293	−	24.4722i	0.137723	−	0.930294i
$693$		0			0
$694$	−13.0509	−	39.4866i	−0.495406	−	1.49889i
$695$		−	47.0907i		−	1.78625i
$696$		0			0
$697$		−	1.32206i		−	0.0500765i
$698$	36.6225	−	12.1043i	1.38618	−	0.458154i
$699$		0			0
$700$	24.2502	+	32.6780i	0.916570	+	1.23511i
$701$	6.08875	+	6.08875i	0.229969	+	0.229969i	0.812680	−	0.582711i	$-0.198008\pi$
$701$	6.08875	+	6.08875i	0.229969	+	0.229969i	−0.582711	+	0.812680i	$0.698008\pi$
$702$		0			0
$703$	−1.16647			−0.0439942
$704$	−8.68119	+	18.3958i	−0.327185	+	0.693317i
$705$		0			0
$706$	16.2672	−	32.3288i	0.612222	−	1.21671i
$707$	0.176805	+	0.176805i	0.00664943	+	0.00664943i
$708$		0			0
$709$	22.8836	−	22.8836i	0.859413	−	0.859413i	−0.131856	−	0.991269i	$-0.542094\pi$
$709$	22.8836	−	22.8836i	0.859413	−	0.859413i	0.991269	+	0.131856i	$0.0420936\pi$
$710$	22.0202	−	7.27798i	0.826402	−	0.273138i
$711$		0			0
$712$	−0.692453	−	3.98053i	−0.0259508	−	0.149177i
$713$			5.20730i			0.195015i
$714$		0			0
$715$	−13.3624	+	13.3624i	−0.499724	+	0.499724i
$716$	−3.40965	+	23.0316i	−0.127425	+	0.860729i
$717$		0			0
$718$	−4.76638	−	2.39834i	−0.177880	−	0.0895052i
$719$	1.46744			0.0547262			0.0273631	−	0.999626i	$-0.491289\pi$
$719$	1.46744			0.0547262			0.0273631	+	0.999626i	$0.491289\pi$
$720$		0			0
$721$	−28.8233			−1.07344
$722$	23.9389	+	12.0455i	0.890913	+	0.448288i
$723$		0			0
$724$	−18.8096	−	2.78463i	−0.699055	−	0.103490i
$725$	17.5020	−	17.5020i	0.650008	−	0.650008i
$726$		0			0
$727$		−	15.3928i		−	0.570889i	−0.958395	−	0.285445i	$-0.907859\pi$
$727$		−	15.3928i		−	0.570889i	0.958395	−	0.285445i	$-0.0921412\pi$
$728$	6.87640	−	9.77267i	0.254856	−	0.362199i
$729$		0			0
$730$	−30.4697	+	10.0707i	−1.12773	+	0.372733i
$731$	−1.74311	+	1.74311i	−0.0644711	+	0.0644711i
$732$		0			0
$733$	−12.4185	−	12.4185i	−0.458688	−	0.458688i	0.439536	−	0.898225i	$-0.355143\pi$
$733$	−12.4185	−	12.4185i	−0.458688	−	0.458688i	−0.898225	+	0.439536i	$0.855143\pi$
$734$	17.4473	−	34.6743i	0.643993	−	1.27985i
$735$		0			0
$736$	11.0243	−	11.5959i	0.406362	−	0.427429i
$737$	37.4844			1.38075
$738$		0			0
$739$	−14.6559	−	14.6559i	−0.539127	−	0.539127i	0.384146	−	0.923273i	$-0.374496\pi$
$739$	−14.6559	−	14.6559i	−0.539127	−	0.539127i	−0.923273	+	0.384146i	$0.874496\pi$
$740$	31.6543	−	23.4905i	1.16364	−	0.863528i
$741$		0			0
$742$	−30.8055	+	10.1817i	−1.13090	+	0.373780i
$743$		−	31.7821i		−	1.16597i	−0.812482	−	0.582986i	$-0.801884\pi$
$743$		−	31.7821i		−	1.16597i	0.812482	−	0.582986i	$-0.198116\pi$
$744$		0			0
$745$		−	5.52518i		−	0.202427i
$746$	7.92273	+	23.9709i	0.290072	+	0.877637i
$747$		0			0
$748$	1.13074	+	0.167398i	0.0413440	+	0.00612068i
$749$	−15.7127	−	15.7127i	−0.574131	−	0.574131i
$750$		0			0
$751$	29.7594			1.08594			0.542968	−	0.839753i	$-0.317301\pi$
$751$	29.7594			1.08594			0.542968	+	0.839753i	$0.317301\pi$
$752$	−3.27798	+	10.8284i	−0.119536	+	0.394872i
$753$		0			0
$754$	−6.49268	−	3.26697i	−0.236449	−	0.118976i
$755$	5.47036	+	5.47036i	0.199087	+	0.199087i
$756$		0			0
$757$	15.6355	−	15.6355i	0.568282	−	0.568282i	−0.363365	−	0.931647i	$-0.618372\pi$
$757$	15.6355	−	15.6355i	0.568282	−	0.568282i	0.931647	+	0.363365i	$0.118372\pi$
$758$	−7.32361	−	22.1582i	−0.266005	−	0.804822i
$759$		0			0
$760$	2.37887	−	0.413828i	0.0862908	−	0.0150111i
$761$		−	4.55957i		−	0.165284i	−0.996579	−	0.0826422i	$-0.973664\pi$
$761$		−	4.55957i		−	0.165284i	0.996579	−	0.0826422i	$-0.0263359\pi$
$762$		0			0
$763$	−15.2002	+	15.2002i	−0.550284	+	0.550284i
$764$	−24.7945	−	33.4114i	−0.897032	−	1.20878i
$765$		0			0
$766$	−10.9261	+	21.7142i	−0.394777	+	0.784567i
$767$	−11.0698			−0.399706
$768$		0			0
$769$	36.5794			1.31909			0.659543	−	0.751667i	$-0.270750\pi$
$769$	36.5794			1.31909			0.659543	+	0.751667i	$0.270750\pi$
$770$	−13.2527	+	26.3380i	−0.477595	+	0.949157i
$771$		0			0
$772$	−16.8593	−	22.7185i	−0.606780	−	0.817657i
$773$	18.7108	−	18.7108i	0.672981	−	0.672981i	−0.285421	−	0.958402i	$-0.592133\pi$
$773$	18.7108	−	18.7108i	0.672981	−	0.672981i	0.958402	+	0.285421i	$0.0921335\pi$
$774$		0			0
$775$		−	17.3507i		−	0.623255i
$776$	−45.6972	+	7.94948i	−1.64043	+	0.285370i
$777$		0			0
$778$	1.18145	+	3.57457i	0.0423570	+	0.128155i
$779$	0.934836	−	0.934836i	0.0334940	−	0.0334940i
$780$		0			0
$781$	7.76326	+	7.76326i	0.277791	+	0.277791i
$782$	−0.803165	−	0.404135i	−0.0287211	−	0.0144518i
$783$		0			0
$784$	−2.71073	+	8.95458i	−0.0968118	+	0.319806i
$785$	32.7302			1.16819
$786$		0			0
$787$	13.3759	+	13.3759i	0.476801	+	0.476801i	0.904107	−	0.427306i	$-0.140537\pi$
$787$	13.3759	+	13.3759i	0.476801	+	0.476801i	−0.427306	+	0.904107i	$0.640537\pi$
$788$	−6.79520	−	1.00598i	−0.242069	−	0.0358365i
$789$		0			0
$790$	25.2958	+	76.5347i	0.899986	+	2.72298i
$791$			40.6930i			1.44688i
$792$		0			0
$793$			16.5697i			0.588406i
$794$	−15.9735	+	5.27946i	−0.566877	+	0.187361i
$795$		0			0
$796$	−0.491751	+	0.364926i	−0.0174296	+	0.0129345i
$797$	33.8043	+	33.8043i	1.19741	+	1.19741i	0.974939	+	0.222471i	$0.0714124\pi$
$797$	33.8043	+	33.8043i	1.19741	+	1.19741i	0.222471	+	0.974939i	$0.428588\pi$
$798$		0			0
$799$	0.635767			0.0224918
$800$	−36.7330	+	38.6373i	−1.29871	+	1.36604i
$801$		0			0
$802$	0.714416	−	1.41981i	0.0252269	−	0.0501352i
$803$	−10.7422	−	10.7422i	−0.379083	−	0.379083i
$804$		0			0
$805$	16.3990	−	16.3990i	0.577990	−	0.577990i
$806$	−4.83763	+	1.59891i	−0.170398	+	0.0563191i
$807$		0			0
$808$	−0.188506	+	0.267903i	−0.00663163	+	0.00942480i
$809$		−	29.9862i		−	1.05426i	−0.849785	−	0.527129i	$-0.823268\pi$
$809$		−	29.9862i		−	1.05426i	0.849785	−	0.527129i	$-0.176732\pi$
$810$		0			0
$811$	−8.05388	+	8.05388i	−0.282810	+	0.282810i	−0.834229	−	0.551419i	$-0.814087\pi$
$811$	−8.05388	+	8.05388i	−0.282810	+	0.282810i	0.551419	+	0.834229i	$0.314087\pi$
$812$	−11.2181	−	1.66075i	−0.393676	−	0.0582809i
$813$		0			0
$814$	16.6692	+	8.38759i	0.584256	+	0.293985i
$815$	18.4600			0.646626
$816$		0			0
$817$	−2.46512			−0.0862438
$818$	17.3339	+	8.72202i	0.606064	+	0.304958i
$819$		0			0
$820$	−6.54266	+	44.1944i	−0.228480	+	1.54334i
$821$	−13.9250	+	13.9250i	−0.485984	+	0.485984i	−0.907036	−	0.421052i	$-0.861661\pi$
$821$	−13.9250	+	13.9250i	−0.485984	+	0.485984i	0.421052	+	0.907036i	$0.361661\pi$
$822$		0			0
$823$			22.4666i			0.783137i	0.920149	+	0.391568i	$0.128067\pi$
$823$			22.4666i			0.783137i	−0.920149	+	0.391568i	$0.871933\pi$
$824$	−6.47178	−	37.2027i	−0.225455	−	1.29602i
$825$		0			0
$826$	−16.3990	+	5.42012i	−0.570595	+	0.188590i
$827$	−7.63159	+	7.63159i	−0.265376	+	0.265376i	−0.827234	−	0.561858i	$-0.810087\pi$
$827$	−7.63159	+	7.63159i	−0.265376	+	0.265376i	0.561858	+	0.827234i	$0.310087\pi$
$828$		0			0
$829$	−32.4860	−	32.4860i	−1.12828	−	1.12828i	−0.990456	−	0.137828i	$-0.955988\pi$
$829$	−32.4860	−	32.4860i	−1.12828	−	1.12828i	−0.137828	−	0.990456i	$-0.544012\pi$
$830$	−34.5376	+	68.6389i	−1.19882	+	2.38249i
$831$		0			0
$832$	14.1577	+	6.68119i	0.490830	+	0.231628i
$833$	0.525748			0.0182161
$834$		0			0
$835$	−58.2824	−	58.2824i	−2.01695	−	2.01695i
$836$	0.681187	+	0.917923i	0.0235593	+	0.0317470i
$837$		0			0
$838$	−17.6747	+	5.84175i	−0.610563	+	0.201800i
$839$			22.9142i			0.791085i	0.918448	+	0.395542i	$0.129443\pi$
$839$			22.9142i			0.791085i	−0.918448	+	0.395542i	$0.870557\pi$
$840$		0			0
$841$		−	22.1022i		−	0.762146i
$842$	5.29962	+	16.0345i	0.182637	+	0.552584i
$843$		0			0
$844$	2.99583	−	20.2362i	0.103121	−	0.696559i
$845$	−24.6282	−	24.6282i	−0.847235	−	0.847235i
$846$		0			0
$847$	9.79053			0.336407
$848$	−20.0584	−	37.4749i	−0.688810	−	1.28689i
$849$		0			0
$850$	2.67614	+	1.34657i	0.0917907	+	0.0461871i
$851$	−10.3789	−	10.3789i	−0.355783	−	0.355783i
$852$		0			0
$853$	38.9424	−	38.9424i	1.33336	−	1.33336i	0.431018	−	0.902344i	$-0.358155\pi$
$853$	38.9424	−	38.9424i	1.33336	−	1.33336i	0.902344	−	0.431018i	$-0.141845\pi$
$854$	8.11306	+	24.5468i	0.277623	+	0.839973i
$855$		0			0
$856$	16.7526	−	23.8087i	0.572593	−	0.813764i
$857$		−	1.79079i		−	0.0611723i	−0.999532	−	0.0305861i	$-0.990263\pi$
$857$		−	1.79079i		−	0.0611723i	0.999532	−	0.0305861i	$-0.00973739\pi$
$858$		0			0
$859$	18.0643	−	18.0643i	0.616347	−	0.616347i	−0.328245	−	0.944593i	$-0.606457\pi$
$859$	18.0643	−	18.0643i	0.616347	−	0.616347i	0.944593	+	0.328245i	$0.106457\pi$
$860$	66.8958	−	49.6430i	2.28113	−	1.69281i
$861$		0			0
$862$	−19.4548	+	38.6638i	−0.662633	+	1.31690i
$863$	−42.1150			−1.43361			−0.716806	−	0.697273i	$-0.754397\pi$
$863$	−42.1150			−1.43361			−0.716806	+	0.697273i	$0.754397\pi$
$864$		0			0
$865$	46.9784			1.59731
$866$	9.73439	−	19.3458i	0.330788	−	0.657398i
$867$		0			0
$868$	−6.38372	+	4.73733i	−0.216678	+	0.160795i
$869$	−26.9825	+	26.9825i	−0.915319	+	0.915319i
$870$		0			0
$871$		−	28.8486i		−	0.977497i
$872$	−23.0320	−	16.2062i	−0.779963	−	0.548810i
$873$		0			0
$874$	−0.282157	−	0.853690i	−0.00954410	−	0.0288765i
$875$	−25.6517	+	25.6517i	−0.867187	+	0.867187i
$876$		0			0
$877$	0.714491	+	0.714491i	0.0241267	+	0.0241267i	0.719067	−	0.694941i	$-0.244569\pi$
$877$	0.714491	+	0.714491i	0.0241267	+	0.0241267i	−0.694941	+	0.719067i	$0.744569\pi$
$878$	−42.1533	−	21.2106i	−1.42261	−	0.715823i
$879$		0			0
$880$	−36.9706	−	11.1917i	−1.24628	−	0.377273i
$881$	44.3972			1.49578			0.747889	−	0.663823i	$-0.231067\pi$
$881$	44.3972			1.49578			0.747889	+	0.663823i	$0.231067\pi$
$882$		0			0
$883$	1.28968	+	1.28968i	0.0434013	+	0.0434013i	0.728474	−	0.685073i	$-0.240230\pi$
$883$	1.28968	+	1.28968i	0.0434013	+	0.0434013i	−0.685073	+	0.728474i	$0.740230\pi$
$884$	0.128832	−	0.870238i	0.00433310	−	0.0292693i
$885$		0			0
$886$	−1.43623	−	4.34544i	−0.0482511	−	0.145988i
$887$		−	4.38532i		−	0.147245i	−0.997286	−	0.0736223i	$-0.976544\pi$
$887$		−	4.38532i		−	0.147245i	0.997286	−	0.0736223i	$-0.0234559\pi$
$888$		0			0
$889$			8.23808i			0.276296i
$890$	7.28484	−	2.40774i	0.244188	−	0.0807078i
$891$		0			0
$892$	2.04890	+	2.76097i	0.0686023	+	0.0924441i
$893$	0.449555	+	0.449555i	0.0150438	+	0.0150438i
$894$		0			0
$895$	−44.2128			−1.47787
$896$	24.2449	+	2.96561i	0.809966	+	0.0990740i
$897$		0			0
$898$	−17.4277	+	34.6353i	−0.581571	+	1.15580i
$899$	3.41906	+	3.41906i	0.114032	+	0.114032i
$900$		0			0
$901$	−1.68897	+	1.68897i	−0.0562678	+	0.0562678i
$902$	−20.0811	+	6.63711i	−0.668629	+	0.220992i
$903$		0			0
$904$	−52.5230	+	9.13690i	−1.74689	+	0.303889i
$905$		−	36.1082i		−	1.20028i
$906$		0			0
$907$	−2.87261	+	2.87261i	−0.0953835	+	0.0953835i	−0.753188	−	0.657805i	$-0.771485\pi$
$907$	−2.87261	+	2.87261i	−0.0953835	+	0.0953835i	0.657805	+	0.753188i	$0.271485\pi$
$908$	−4.19011	+	28.3034i	−0.139054	+	0.939280i
$909$		0			0
$910$	20.2702	+	10.1995i	0.671951	+	0.338111i
$911$	−42.3784			−1.40406			−0.702029	−	0.712149i	$-0.747722\pi$
$911$	−42.3784			−1.40406			−0.702029	+	0.712149i	$0.747722\pi$
$912$		0			0
$913$	−36.3751			−1.20384
$914$	13.7885	+	6.93808i	0.456084	+	0.229491i
$915$		0			0
$916$	33.6297	+	4.97863i	1.11116	+	0.164499i
$917$	1.65685	−	1.65685i	0.0547141	−	0.0547141i
$918$		0			0
$919$			44.8603i			1.47980i	0.672715	+	0.739902i	$0.265128\pi$
$919$			44.8603i			1.47980i	−0.672715	+	0.739902i	$0.734872\pi$
$920$	24.8486	+	17.4844i	0.819234	+	0.576442i
$921$		0			0
$922$	33.8621	−	11.1919i	1.11519	−	0.368586i
$923$	5.97474	−	5.97474i	0.196661	−	0.196661i
$924$		0			0
$925$	34.5823	+	34.5823i	1.13706	+	1.13706i
$926$	−14.2985	+	28.4164i	−0.469877	+	0.933820i
$927$		0			0
$928$	−0.375263	−	14.8522i	−0.0123186	−	0.487547i
$929$	2.96695			0.0973426			0.0486713	−	0.998815i	$-0.484501\pi$
$929$	2.96695			0.0973426			0.0486713	+	0.998815i	$0.484501\pi$
$930$		0			0
$931$	0.371760	+	0.371760i	0.0121839	+	0.0121839i
$932$	−21.4860	+	15.9446i	−0.703796	+	0.522284i
$933$		0			0
$934$	45.9875	−	15.1995i	1.50476	−	0.497344i
$935$			2.17064i			0.0709876i
$936$		0			0
$937$			54.7669i			1.78916i	0.446910	+	0.894579i	$0.352524\pi$
$937$			54.7669i			1.78916i	−0.446910	+	0.894579i	$0.647476\pi$
$938$	−14.1252	−	42.7371i	−0.461205	−	1.39541i
$939$		0			0
$940$	−21.2527	−	3.14631i	−0.693187	−	0.102621i
$941$	6.29012	+	6.29012i	0.205052	+	0.205052i	0.802161	−	0.597108i	$-0.203684\pi$
$941$	6.29012	+	6.29012i	0.205052	+	0.205052i	−0.597108	+	0.802161i	$0.703684\pi$
$942$		0			0
$943$	16.6358			0.541735
$944$	−10.6779	−	19.9495i	−0.347537	−	0.649300i
$945$		0			0
$946$	35.2275	+	17.7257i	1.14534	+	0.576311i
$947$	11.2105	+	11.2105i	0.364294	+	0.364294i	0.865391	−	0.501097i	$-0.167070\pi$
$947$	11.2105	+	11.2105i	0.364294	+	0.364294i	−0.501097	+	0.865391i	$0.667070\pi$
$948$		0			0
$949$	−8.26736	+	8.26736i	−0.268370	+	0.268370i
$950$	0.940144	+	2.84449i	0.0305023	+	0.0922873i
$951$		0			0
$952$	−0.235241	−	1.35227i	−0.00762422	−	0.0438275i
$953$		−	30.2807i		−	0.980887i	−0.871473	−	0.490443i	$-0.836835\pi$
$953$		−	30.2807i		−	0.980887i	0.871473	−	0.490443i	$-0.163165\pi$
$954$		0			0
$955$	55.8678	−	55.8678i	1.80784	−	1.80784i
$956$	15.9322	+	21.4691i	0.515283	+	0.694362i
$957$		0			0
$958$	−23.0341	+	45.7773i	−0.744198	+	1.47900i
$959$	11.4642			0.370198
$960$		0			0
$961$	−27.6105			−0.890661
$962$	6.45523	−	12.8289i	0.208125	−	0.413621i
$963$		0			0
$964$	−0.252048	−	0.339643i	−0.00811790	−	0.0109392i
$965$	37.9880	−	37.9880i	1.22288	−	1.22288i
$966$		0			0
$967$			10.5273i			0.338537i	0.985570	+	0.169268i	$0.0541405\pi$
$967$			10.5273i			0.338537i	−0.985570	+	0.169268i	$0.945860\pi$
$968$	2.19829	+	12.6368i	0.0706558	+	0.406162i
$969$		0			0
$970$	−27.6413	−	83.6311i	−0.887508	−	2.68523i
$971$	−27.3685	+	27.3685i	−0.878298	+	0.878298i	−0.993358	−	0.115060i	$-0.963294\pi$
$971$	−27.3685	+	27.3685i	−0.878298	+	0.878298i	0.115060	+	0.993358i	$0.463294\pi$
$972$		0			0
$973$	−18.9284	−	18.9284i	−0.606816	−	0.606816i
$974$	21.2487	+	10.6919i	0.680852	+	0.342590i
$975$		0			0
$976$	−29.8612	+	15.9832i	−0.955834	+	0.511610i
$977$	16.9009			0.540706			0.270353	−	0.962761i	$-0.412860\pi$
$977$	16.9009			0.540706			0.270353	+	0.962761i	$0.412860\pi$
$978$		0			0
$979$	2.56829	+	2.56829i	0.0820828	+	0.0820828i
$980$	−17.5750	−	2.60184i	−0.561412	−	0.0831129i
$981$		0			0
$982$	−3.83260	−	11.5959i	−0.122303	−	0.370039i
$983$			10.0798i			0.321496i	0.986995	+	0.160748i	$0.0513906\pi$
$983$			10.0798i			0.321496i	−0.986995	+	0.160748i	$0.948609\pi$
$984$		0			0
$985$		−	13.0445i		−	0.415632i
$986$	−0.792701	+	0.261999i	−0.0252447	+	0.00834375i
$987$		0			0
$988$	0.706449	−	0.524253i	0.0224751	−	0.0166787i
$989$	−21.9339	−	21.9339i	−0.697458	−	0.697458i
$990$		0			0
$991$	−42.3446			−1.34512			−0.672561	−	0.740042i	$-0.734806\pi$
$991$	−42.3446			−1.34512			−0.672561	+	0.740042i	$0.734806\pi$
$992$	−7.54789	−	7.17587i	−0.239646	−	0.227834i
$993$		0			0
$994$	5.92571	−	11.7766i	0.187952	−	0.373530i
$995$	−0.822265	−	0.822265i	−0.0260676	−	0.0260676i
$996$		0			0
$997$	−33.6676	+	33.6676i	−1.06626	+	1.06626i	−0.0686216	+	0.997643i	$0.521860\pi$
$997$	−33.6676	+	33.6676i	−1.06626	+	1.06626i	−0.997643	+	0.0686216i	$0.978140\pi$
$998$	37.3660	−	12.3500i	1.18280	−	0.390932i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.2.k.b.109.2		8
3.2	odd	2		48.2.j.a.13.3	✓	8
4.3	odd	2		576.2.k.b.145.4		8
8.3	odd	2		1152.2.k.f.289.1		8
8.5	even	2		1152.2.k.c.289.1		8
12.11	even	2		192.2.j.a.145.1		8
16.3	odd	4		1152.2.k.f.865.1		8
16.5	even	4	inner	144.2.k.b.37.2		8
16.11	odd	4		576.2.k.b.433.4		8
16.13	even	4		1152.2.k.c.865.1		8
24.5	odd	2		384.2.j.b.289.2		8
24.11	even	2		384.2.j.a.289.4		8
32.5	even	8		9216.2.a.bo.1.4		4
32.11	odd	8		9216.2.a.x.1.1		4
32.21	even	8		9216.2.a.y.1.1		4
32.27	odd	8		9216.2.a.bn.1.4		4
48.5	odd	4		48.2.j.a.37.3	yes	8
48.11	even	4		192.2.j.a.49.1		8
48.29	odd	4		384.2.j.b.97.2		8
48.35	even	4		384.2.j.a.97.4		8
96.5	odd	8		3072.2.a.i.1.1		4
96.11	even	8		3072.2.a.n.1.4		4
96.29	odd	8		3072.2.d.f.1537.5		8
96.35	even	8		3072.2.d.i.1537.1		8
96.53	odd	8		3072.2.a.t.1.4		4
96.59	even	8		3072.2.a.o.1.1		4
96.77	odd	8		3072.2.d.f.1537.4		8
96.83	even	8		3072.2.d.i.1537.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.2.j.a.13.3	✓	8	3.2	odd	2
48.2.j.a.37.3	yes	8	48.5	odd	4
144.2.k.b.37.2		8	16.5	even	4	inner
144.2.k.b.109.2		8	1.1	even	1	trivial
192.2.j.a.49.1		8	48.11	even	4
192.2.j.a.145.1		8	12.11	even	2
384.2.j.a.97.4		8	48.35	even	4
384.2.j.a.289.4		8	24.11	even	2
384.2.j.b.97.2		8	48.29	odd	4
384.2.j.b.289.2		8	24.5	odd	2
576.2.k.b.145.4		8	4.3	odd	2
576.2.k.b.433.4		8	16.11	odd	4
1152.2.k.c.289.1		8	8.5	even	2
1152.2.k.c.865.1		8	16.13	even	4
1152.2.k.f.289.1		8	8.3	odd	2
1152.2.k.f.865.1		8	16.3	odd	4
3072.2.a.i.1.1		4	96.5	odd	8
3072.2.a.n.1.4		4	96.11	even	8
3072.2.a.o.1.1		4	96.59	even	8
3072.2.a.t.1.4		4	96.53	odd	8
3072.2.d.f.1537.4		8	96.77	odd	8
3072.2.d.f.1537.5		8	96.29	odd	8
3072.2.d.i.1537.1		8	96.35	even	8
3072.2.d.i.1537.8		8	96.83	even	8
9216.2.a.x.1.1		4	32.11	odd	8
9216.2.a.y.1.1		4	32.21	even	8
9216.2.a.bn.1.4		4	32.27	odd	8
9216.2.a.bo.1.4		4	32.5	even	8

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.635665 + 1.26330i) q^{2} +(-1.19186 - 1.60607i) q^{4} +(2.68554 - 2.68554i) q^{5} -2.15894i q^{7} +(2.78658 - 0.484753i) q^{8} +O(q^{10})\)	\(q+(-0.635665 + 1.26330i) q^{2} +(-1.19186 - 1.60607i) q^{4} +(2.68554 - 2.68554i) q^{5} -2.15894i q^{7} +(2.78658 - 0.484753i) q^{8} +(1.68554 + 5.09976i) q^{10} +(-1.79793 + 1.79793i) q^{11} +(1.38372 + 1.38372i) q^{13} +(2.72739 + 1.37236i) q^{14} +(-1.15894 + 3.82843i) q^{16} +0.224777 q^{17} +(0.158942 + 0.158942i) q^{19} +(-7.51397 - 1.11239i) q^{20} +(-1.12845 - 3.41421i) q^{22} +2.82843i q^{23} -9.42429i q^{25} +(-2.62764 + 0.868472i) q^{26} +(-3.46742 + 2.57316i) q^{28} +(1.85712 + 1.85712i) q^{29} +1.84106 q^{31} +(-4.09976 - 3.89769i) q^{32} +(-0.142883 + 0.283962i) q^{34} +(-5.79793 - 5.79793i) q^{35} +(-3.66949 + 3.66949i) q^{37} +(-0.301825 + 0.0997575i) q^{38} +(6.18165 - 8.78530i) q^{40} -5.88163i q^{41} +(-7.75481 + 7.75481i) q^{43} +(5.03049 + 0.744728i) q^{44} +(-3.57316 - 1.79793i) q^{46} +2.82843 q^{47} +2.33897 q^{49} +(11.9057 + 5.99069i) q^{50} +(0.573155 - 3.87155i) q^{52} +(-7.51397 + 7.51397i) q^{53} +9.65685i q^{55} +(-1.04655 - 6.01606i) q^{56} +(-3.52660 + 1.16559i) q^{58} +(-4.00000 + 4.00000i) q^{59} +(5.98737 + 5.98737i) q^{61} +(-1.17030 + 2.32581i) q^{62} +(7.53003 - 2.70160i) q^{64} +7.43208 q^{65} +(-10.4243 - 10.4243i) q^{67} +(-0.267903 - 0.361009i) q^{68} +(11.0101 - 3.63899i) q^{70} -4.31788i q^{71} +5.97474i q^{73} +(-2.30310 - 6.96823i) q^{74} +(0.0658358 - 0.444708i) q^{76} +(3.88163 + 3.88163i) q^{77} +15.0075 q^{79} +(7.16902 + 13.3938i) q^{80} +(7.43027 + 3.73875i) q^{82} +(10.1158 + 10.1158i) q^{83} +(0.603650 - 0.603650i) q^{85} +(-4.86720 - 14.7261i) q^{86} +(-4.13853 + 5.88163i) q^{88} -1.42847i q^{89} +(2.98737 - 2.98737i) q^{91} +(4.54266 - 3.37109i) q^{92} +(-1.79793 + 3.57316i) q^{94} +0.853690 q^{95} -16.3990 q^{97} +(-1.48680 + 2.95482i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} + 12 q^{8}+O(q^{10}) \) 8 * q - 4 * q^4 + 12 * q^8	\( 8 q - 4 q^{4} + 12 q^{8} - 8 q^{10} + 8 q^{11} - 12 q^{14} - 8 q^{19} - 16 q^{20} - 20 q^{26} + 8 q^{28} + 16 q^{29} + 24 q^{31} - 24 q^{35} - 16 q^{37} + 8 q^{38} + 16 q^{40} - 8 q^{43} + 40 q^{44} - 8 q^{46} - 8 q^{49} + 36 q^{50} - 16 q^{52} - 16 q^{53} - 16 q^{58} - 32 q^{59} + 16 q^{61} + 12 q^{62} + 8 q^{64} + 16 q^{65} - 16 q^{67} - 32 q^{68} + 32 q^{70} - 52 q^{74} + 8 q^{76} - 16 q^{77} - 24 q^{79} - 8 q^{80} + 40 q^{82} + 40 q^{83} - 16 q^{85} + 16 q^{86} + 32 q^{88} - 8 q^{91} + 16 q^{92} + 8 q^{94} + 48 q^{95} + 40 q^{98}+O(q^{100}) \) 8 * q - 4 * q^4 + 12 * q^8 - 8 * q^10 + 8 * q^11 - 12 * q^14 - 8 * q^19 - 16 * q^20 - 20 * q^26 + 8 * q^28 + 16 * q^29 + 24 * q^31 - 24 * q^35 - 16 * q^37 + 8 * q^38 + 16 * q^40 - 8 * q^43 + 40 * q^44 - 8 * q^46 - 8 * q^49 + 36 * q^50 - 16 * q^52 - 16 * q^53 - 16 * q^58 - 32 * q^59 + 16 * q^61 + 12 * q^62 + 8 * q^64 + 16 * q^65 - 16 * q^67 - 32 * q^68 + 32 * q^70 - 52 * q^74 + 8 * q^76 - 16 * q^77 - 24 * q^79 - 8 * q^80 + 40 * q^82 + 40 * q^83 - 16 * q^85 + 16 * q^86 + 32 * q^88 - 8 * q^91 + 16 * q^92 + 8 * q^94 + 48 * q^95 + 40 * q^98

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