LMFDB - Embedded newform 220.2.d.c.131.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(131,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.131"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,12,-8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.31116960000.7
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{5} + 53x^{4} - 134x^{3} - 218x^{2} + 288x + 904 $ x^8 - 4x^7 + 14x^5 + 53x^4 - 134x^3 - 218x^2 + 288x + 904
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.3
Root			$-1.43649 - 1.82288i$ of defining polynomial
Character	$\chi$	$=$	220.131
Dual form			220.2.d.c.131.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32288 + 0.500000i) q^{2} -0.613616i q^{3} +(1.50000 - 1.32288i) q^{4} -1.00000 q^{5} +(0.306808 + 0.811738i) q^{6} +0.613616 q^{7} +(-1.32288 + 2.50000i) q^{8} +2.62348 q^{9} +(1.32288 - 0.500000i) q^{10} +(-0.613616 - 3.25937i) q^{11} +(-0.811738 - 0.920424i) q^{12} -2.00000i q^{13} +(-0.811738 + 0.306808i) q^{14} +0.613616i q^{15} +(0.500000 - 3.96863i) q^{16} -5.62348i q^{17} +(-3.47053 + 1.31174i) q^{18} +7.13235 q^{19} +(-1.50000 + 1.32288i) q^{20} -0.376525i q^{21} +(2.44142 + 4.00493i) q^{22} +6.51873i q^{23} +(1.53404 + 0.811738i) q^{24} +1.00000 q^{25} +(1.00000 + 2.64575i) q^{26} -3.45065i q^{27} +(0.920424 - 0.811738i) q^{28} -7.62348i q^{29} +(-0.306808 - 0.811738i) q^{30} -0.613616i q^{31} +(1.32288 + 5.50000i) q^{32} +(-2.00000 + 0.376525i) q^{33} +(2.81174 + 7.43916i) q^{34} -0.613616 q^{35} +(3.93521 - 3.47053i) q^{36} +5.62348 q^{37} +(-9.43521 + 3.56618i) q^{38} -1.22723 q^{39} +(1.32288 - 2.50000i) q^{40} +8.00000i q^{41} +(0.188262 + 0.498095i) q^{42} -6.51873 q^{43} +(-5.23216 - 4.07731i) q^{44} -2.62348 q^{45} +(-3.25937 - 8.62348i) q^{46} +6.51873i q^{47} +(-2.43521 - 0.306808i) q^{48} -6.62348 q^{49} +(-1.32288 + 0.500000i) q^{50} -3.45065 q^{51} +(-2.64575 - 3.00000i) q^{52} -9.62348 q^{53} +(1.72533 + 4.56479i) q^{54} +(0.613616 + 3.25937i) q^{55} +(-0.811738 + 1.53404i) q^{56} -4.37652i q^{57} +(3.81174 + 10.0849i) q^{58} +4.06427i q^{59} +(0.811738 + 0.920424i) q^{60} +11.6235i q^{61} +(0.306808 + 0.811738i) q^{62} +1.60981 q^{63} +(-4.50000 - 6.61438i) q^{64} +2.00000i q^{65} +(2.45749 - 1.49810i) q^{66} -7.74597i q^{67} +(-7.43916 - 8.43521i) q^{68} +4.00000 q^{69} +(0.811738 - 0.306808i) q^{70} -1.84085i q^{71} +(-3.47053 + 6.55869i) q^{72} +2.00000i q^{73} +(-7.43916 + 2.81174i) q^{74} -0.613616i q^{75} +(10.6985 - 9.43521i) q^{76} +(-0.376525 - 2.00000i) q^{77} +(1.62348 - 0.613616i) q^{78} -2.45446 q^{79} +(-0.500000 + 3.96863i) q^{80} +5.75305 q^{81} +(-4.00000 - 10.5830i) q^{82} +7.74597 q^{83} +(-0.498095 - 0.564787i) q^{84} +5.62348i q^{85} +(8.62348 - 3.25937i) q^{86} -4.67789 q^{87} +(8.96016 + 2.77770i) q^{88} +1.62348 q^{89} +(3.47053 - 1.31174i) q^{90} -1.22723i q^{91} +(8.62348 + 9.77810i) q^{92} -0.376525 q^{93} +(-3.25937 - 8.62348i) q^{94} -7.13235 q^{95} +(3.37489 - 0.811738i) q^{96} +2.00000 q^{97} +(8.76203 - 3.31174i) q^{98} +(-1.60981 - 8.55087i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{4} - 8 q^{5} - 20 q^{9} + 14 q^{12} + 14 q^{14} + 4 q^{16} - 12 q^{20} - 14 q^{22} + 8 q^{25} + 8 q^{26} - 16 q^{33} + 2 q^{34} - 30 q^{36} + 4 q^{37} - 14 q^{38} + 22 q^{42} - 14 q^{44} + 20 q^{45}+ \cdots + 16 q^{97}+O(q^{100}) $ 8 * q + 12 * q^4 - 8 * q^5 - 20 * q^9 + 14 * q^12 + 14 * q^14 + 4 * q^16 - 12 * q^20 - 14 * q^22 + 8 * q^25 + 8 * q^26 - 16 * q^33 + 2 * q^34 - 30 * q^36 + 4 * q^37 - 14 * q^38 + 22 * q^42 - 14 * q^44 + 20 * q^45 + 42 * q^48 - 12 * q^49 - 36 * q^53 + 14 * q^56 + 10 * q^58 - 14 * q^60 - 36 * q^64 - 22 * q^66 + 32 * q^69 - 14 * q^70 - 44 * q^77 - 28 * q^78 - 4 * q^80 + 128 * q^81 - 32 * q^82 + 28 * q^86 - 14 * q^88 - 28 * q^89 + 28 * q^92 - 44 * q^93 + 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−1.32288	+	0.500000i	−0.935414	+	0.353553i
$2$	−1.32288	+	0.500000i	−0.935414	+	0.353553i
$3$		−	0.613616i		−	0.354271i	−0.984186	−	0.177136i	$-0.943317\pi$
$3$		−	0.613616i		−	0.354271i	0.984186	−	0.177136i	$-0.0566831\pi$
$4$	1.50000	−	1.32288i	0.750000	−	0.661438i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.306808	+	0.811738i	0.125254	+	0.331391i
$7$	0.613616			0.231925			0.115963	−	0.993254i	$-0.463005\pi$
$7$	0.613616			0.231925			0.115963	+	0.993254i	$0.463005\pi$
$8$	−1.32288	+	2.50000i	−0.467707	+	0.883883i
$9$	2.62348			0.874492
$10$	1.32288	−	0.500000i	0.418330	−	0.158114i
$11$	−0.613616	−	3.25937i	−0.185012	−	0.982736i
$11$	−0.613616	−	3.25937i	−0.185012	−	0.982736i
$12$	−0.811738	−	0.920424i	−0.234328	−	0.265704i
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$	−0.811738	+	0.306808i	−0.216946	+	0.0819979i
$15$			0.613616i			0.158435i
$16$	0.500000	−	3.96863i	0.125000	−	0.992157i
$17$		−	5.62348i		−	1.36389i	−0.731402	−	0.681947i	$-0.761134\pi$
$17$		−	5.62348i		−	1.36389i	0.731402	−	0.681947i	$-0.238866\pi$
$18$	−3.47053	+	1.31174i	−0.818012	+	0.309180i
$19$	7.13235			1.63627			0.818137	−	0.575024i	$-0.195007\pi$
$19$	7.13235			1.63627			0.818137	+	0.575024i	$0.195007\pi$
$20$	−1.50000	+	1.32288i	−0.335410	+	0.295804i
$21$		−	0.376525i		−	0.0821644i
$22$	2.44142	+	4.00493i	0.520513	+	0.853854i
$23$			6.51873i			1.35925i	0.733560	+	0.679625i	$0.237858\pi$
$23$			6.51873i			1.35925i	−0.733560	+	0.679625i	$0.762142\pi$
$24$	1.53404	+	0.811738i	0.313135	+	0.165695i
$25$	1.00000			0.200000
$26$	1.00000	+	2.64575i	0.196116	+	0.518875i
$27$		−	3.45065i		−	0.664079i
$28$	0.920424	−	0.811738i	0.173944	−	0.153404i
$29$		−	7.62348i		−	1.41564i	−0.706391	−	0.707822i	$-0.749678\pi$
$29$		−	7.62348i		−	1.41564i	0.706391	−	0.707822i	$-0.250322\pi$
$30$	−0.306808	−	0.811738i	−0.0560152	−	0.148202i
$31$		−	0.613616i		−	0.110209i	−0.998481	−	0.0551043i	$-0.982451\pi$
$31$		−	0.613616i		−	0.110209i	0.998481	−	0.0551043i	$-0.0175491\pi$
$32$	1.32288	+	5.50000i	0.233854	+	0.972272i
$33$	−2.00000	+	0.376525i	−0.348155	+	0.0655445i
$34$	2.81174	+	7.43916i	0.482209	+	1.27581i
$35$	−0.613616			−0.103720
$36$	3.93521	−	3.47053i	0.655869	−	0.578422i
$37$	5.62348			0.924494			0.462247	−	0.886751i	$-0.347043\pi$
$37$	5.62348			0.924494			0.462247	+	0.886751i	$0.347043\pi$
$38$	−9.43521	+	3.56618i	−1.53059	+	0.578510i
$39$	−1.22723			−0.196514
$40$	1.32288	−	2.50000i	0.209165	−	0.395285i
$41$			8.00000i			1.24939i	0.780869	+	0.624695i	$0.214777\pi$
$41$			8.00000i			1.24939i	−0.780869	+	0.624695i	$0.785223\pi$
$42$	0.188262	+	0.498095i	0.0290495	+	0.0768578i
$43$	−6.51873			−0.994098			−0.497049	−	0.867723i	$-0.665583\pi$
$43$	−6.51873			−0.994098			−0.497049	+	0.867723i	$0.665583\pi$
$44$	−5.23216	−	4.07731i	−0.788778	−	0.614678i
$45$	−2.62348			−0.391085
$46$	−3.25937	−	8.62348i	−0.480567	−	1.27146i
$47$			6.51873i			0.950855i	0.879755	+	0.475428i	$0.157707\pi$
$47$			6.51873i			0.950855i	−0.879755	+	0.475428i	$0.842293\pi$
$48$	−2.43521	−	0.306808i	−0.351493	−	0.0442839i
$49$	−6.62348			−0.946211
$50$	−1.32288	+	0.500000i	−0.187083	+	0.0707107i
$51$	−3.45065			−0.483188
$52$	−2.64575	−	3.00000i	−0.366900	−	0.416025i
$53$	−9.62348			−1.32189			−0.660943	−	0.750436i	$-0.729844\pi$
$53$	−9.62348			−1.32189			−0.660943	+	0.750436i	$0.729844\pi$
$54$	1.72533	+	4.56479i	0.234787	+	0.621189i
$55$	0.613616	+	3.25937i	0.0827400	+	0.439493i
$56$	−0.811738	+	1.53404i	−0.108473	+	0.204995i
$57$		−	4.37652i		−	0.579685i
$58$	3.81174	+	10.0849i	0.500506	+	1.32421i
$59$			4.06427i			0.529123i	0.964369	+	0.264561i	$0.0852272\pi$
$59$			4.06427i			0.529123i	−0.964369	+	0.264561i	$0.914773\pi$
$60$	0.811738	+	0.920424i	0.104795	+	0.118826i
$61$			11.6235i			1.48823i	0.668050	+	0.744117i	$0.267129\pi$
$61$			11.6235i			1.48823i	−0.668050	+	0.744117i	$0.732871\pi$
$62$	0.306808	+	0.811738i	0.0389647	+	0.103091i
$63$	1.60981			0.202817
$64$	−4.50000	−	6.61438i	−0.562500	−	0.826797i
$65$			2.00000i			0.248069i
$66$	2.45749	−	1.49810i	0.302496	−	0.184403i
$67$		−	7.74597i		−	0.946320i	−0.880976	−	0.473160i	$-0.843113\pi$
$67$		−	7.74597i		−	0.946320i	0.880976	−	0.473160i	$-0.156887\pi$
$68$	−7.43916	−	8.43521i	−0.902131	−	1.02292i
$69$	4.00000			0.481543
$70$	0.811738	−	0.306808i	0.0970212	−	0.0366706i
$71$		−	1.84085i		−	0.218468i	−0.994016	−	0.109234i	$-0.965160\pi$
$71$		−	1.84085i		−	0.218468i	0.994016	−	0.109234i	$-0.0348399\pi$
$72$	−3.47053	+	6.55869i	−0.409006	+	0.772949i
$73$			2.00000i			0.234082i	0.993127	+	0.117041i	$0.0373409\pi$
$73$			2.00000i			0.234082i	−0.993127	+	0.117041i	$0.962659\pi$
$74$	−7.43916	+	2.81174i	−0.864785	+	0.326858i
$75$		−	0.613616i		−	0.0708543i
$76$	10.6985	−	9.43521i	1.22721	−	1.08229i
$77$	−0.376525	−	2.00000i	−0.0429090	−	0.227921i
$78$	1.62348	−	0.613616i	0.183822	−	0.0694783i
$79$	−2.45446			−0.276149			−0.138074	−	0.990422i	$-0.544091\pi$
$79$	−2.45446			−0.276149			−0.138074	+	0.990422i	$0.544091\pi$
$80$	−0.500000	+	3.96863i	−0.0559017	+	0.443706i
$81$	5.75305			0.639228
$82$	−4.00000	−	10.5830i	−0.441726	−	1.16870i
$83$	7.74597			0.850230			0.425115	−	0.905139i	$-0.360234\pi$
$83$	7.74597			0.850230			0.425115	+	0.905139i	$0.360234\pi$
$84$	−0.498095	−	0.564787i	−0.0543466	−	0.0616233i
$85$			5.62348i			0.609952i
$86$	8.62348	−	3.25937i	0.929893	−	0.351467i
$87$	−4.67789			−0.501522
$88$	8.96016	+	2.77770i	0.955156	+	0.296104i
$89$	1.62348			0.172088			0.0860440	−	0.996291i	$-0.472577\pi$
$89$	1.62348			0.172088			0.0860440	+	0.996291i	$0.472577\pi$
$90$	3.47053	−	1.31174i	0.365826	−	0.138269i
$91$		−	1.22723i		−	0.128649i
$92$	8.62348	+	9.77810i	0.899059	+	1.01944i
$93$	−0.376525			−0.0390438
$94$	−3.25937	−	8.62348i	−0.336178	−	0.889444i
$95$	−7.13235			−0.731764
$96$	3.37489	−	0.811738i	0.344448	−	0.0828476i
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$	8.76203	−	3.31174i	0.885099	−	0.334536i
$99$	−1.60981	−	8.55087i	−0.161792	−	0.859395i
$100$	1.50000	−	1.32288i	0.150000	−	0.132288i
$101$			7.24695i			0.721099i	0.932740	+	0.360549i	$0.117411\pi$
$101$			7.24695i			0.721099i	−0.932740	+	0.360549i	$0.882589\pi$
$102$	4.56479	−	1.72533i	0.451981	−	0.170833i
$103$			6.51873i			0.642310i	0.947027	+	0.321155i	$0.104071\pi$
$103$			6.51873i			0.642310i	−0.947027	+	0.321155i	$0.895929\pi$
$104$	5.00000	+	2.64575i	0.490290	+	0.259437i
$105$			0.376525i			0.0367450i
$106$	12.7307	−	4.81174i	1.23651	−	0.467357i
$107$	15.8745			1.53465			0.767323	−	0.641260i	$-0.221588\pi$
$107$	15.8745			1.53465			0.767323	+	0.641260i	$0.221588\pi$
$108$	−4.56479	−	5.17598i	−0.439247	−	0.498059i
$109$			11.2470i			1.07726i	0.842542	+	0.538631i	$0.181058\pi$
$109$			11.2470i			1.07726i	−0.842542	+	0.538631i	$0.818942\pi$
$110$	−2.44142	−	4.00493i	−0.232780	−	0.381855i
$111$		−	3.45065i		−	0.327522i
$112$	0.306808	−	2.43521i	0.0289906	−	0.230106i
$113$	10.0000			0.940721			0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000			0.940721			0.470360	+	0.882474i	$0.344124\pi$
$114$	2.18826	+	5.78960i	0.204950	+	0.542246i
$115$		−	6.51873i		−	0.607875i
$116$	−10.0849	−	11.4352i	−0.936360	−	1.06173i
$117$		−	5.24695i		−	0.485081i
$118$	−2.03214	−	5.37652i	−0.187073	−	0.494949i
$119$		−	3.45065i		−	0.316321i
$120$	−1.53404	−	0.811738i	−0.140038	−	0.0741012i
$121$	−10.2470	+	4.00000i	−0.931541	+	0.363636i
$122$	−5.81174	−	15.3764i	−0.526170	−	1.39211i
$123$	4.90893			0.442623
$124$	−0.811738	−	0.920424i	−0.0728962	−	0.0826565i
$125$	−1.00000			−0.0894427
$126$	−2.12957	+	0.804903i	−0.189718	+	0.0717065i
$127$	7.74597			0.687343			0.343672	−	0.939090i	$-0.388329\pi$
$127$	7.74597			0.687343			0.343672	+	0.939090i	$0.388329\pi$
$128$	9.26013	+	6.50000i	0.818488	+	0.574524i
$129$			4.00000i			0.352180i
$130$	−1.00000	−	2.64575i	−0.0877058	−	0.232048i
$131$	−17.7154			−1.54780			−0.773899	−	0.633309i	$-0.781696\pi$
$131$	−17.7154			−1.54780			−0.773899	+	0.633309i	$0.781696\pi$
$132$	−2.50190	+	3.21054i	−0.217763	+	0.279441i
$133$	4.37652			0.379493
$134$	3.87298	+	10.2470i	0.334575	+	0.885202i
$135$			3.45065i			0.296985i
$136$	14.0587	+	7.43916i	1.20552	+	0.637903i
$137$	−6.00000			−0.512615			−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000			−0.512615			−0.256307	+	0.966595i	$0.582506\pi$
$138$	−5.29150	+	2.00000i	−0.450443	+	0.170251i
$139$	−14.2647			−1.20992			−0.604958	−	0.796257i	$-0.706810\pi$
$139$	−14.2647			−1.20992			−0.604958	+	0.796257i	$0.706810\pi$
$140$	−0.920424	+	0.811738i	−0.0777900	+	0.0686044i
$141$	4.00000			0.336861
$142$	0.920424	+	2.43521i	0.0772403	+	0.204359i
$143$	−6.51873	+	1.22723i	−0.545124	+	0.102626i
$144$	1.31174	−	10.4116i	0.109311	−	0.867633i
$145$			7.62348i			0.633095i
$146$	−1.00000	−	2.64575i	−0.0827606	−	0.218964i
$147$			4.06427i			0.335215i
$148$	8.43521	−	7.43916i	0.693370	−	0.611495i
$149$		−	8.37652i		−	0.686232i	−0.939293	−	0.343116i	$-0.888518\pi$
$149$		−	8.37652i		−	0.686232i	0.939293	−	0.343116i	$-0.111482\pi$
$150$	0.306808	+	0.811738i	0.0250508	+	0.0662781i
$151$	−1.22723			−0.0998707			−0.0499354	−	0.998752i	$-0.515902\pi$
$151$	−1.22723			−0.0998707			−0.0499354	+	0.998752i	$0.515902\pi$
$152$	−9.43521	+	17.8309i	−0.765297	+	1.44628i
$153$		−	14.7530i		−	1.19271i
$154$	1.49810	+	2.45749i	0.120720	+	0.198030i
$155$			0.613616i			0.0492868i
$156$	−1.84085	+	1.62348i	−0.147386	+	0.129982i
$157$	−1.62348			−0.129567			−0.0647837	−	0.997899i	$-0.520636\pi$
$157$	−1.62348			−0.129567			−0.0647837	+	0.997899i	$0.520636\pi$
$158$	3.24695	−	1.22723i	0.258314	−	0.0976333i
$159$			5.90512i			0.468306i
$160$	−1.32288	−	5.50000i	−0.104583	−	0.434813i
$161$			4.00000i			0.315244i
$162$	−7.61057	+	2.87652i	−0.597943	+	0.226001i
$163$		−	21.7796i		−	1.70591i	−0.521983	−	0.852956i	$-0.674807\pi$
$163$		−	21.7796i		−	1.70591i	0.521983	−	0.852956i	$-0.325193\pi$
$164$	10.5830	+	12.0000i	0.826394	+	0.937043i
$165$	2.00000	−	0.376525i	0.155700	−	0.0293124i
$166$	−10.2470	+	3.87298i	−0.795318	+	0.300602i
$167$	−1.84085			−0.142449			−0.0712245	−	0.997460i	$-0.522691\pi$
$167$	−1.84085			−0.142449			−0.0712245	+	0.997460i	$0.522691\pi$
$168$	0.941312	+	0.498095i	0.0726238	+	0.0384289i
$169$	9.00000			0.692308
$170$	−2.81174	−	7.43916i	−0.215650	−	0.570557i
$171$	18.7115			1.43091
$172$	−9.77810	+	8.62348i	−0.745573	+	0.657534i
$173$		−	1.24695i		−	0.0948039i	−0.998876	−	0.0474020i	$-0.984906\pi$
$173$		−	1.24695i		−	0.0948039i	0.998876	−	0.0474020i	$-0.0150942\pi$
$174$	6.18826	−	2.33894i	0.469131	−	0.177315i
$175$	0.613616			0.0463850
$176$	−13.2420	+	0.805529i	−0.998155	+	0.0607191i
$177$	2.49390			0.187453
$178$	−2.14766	+	0.811738i	−0.160974	+	0.0608423i
$179$		−	1.60981i		−	0.120323i	−0.998189	−	0.0601613i	$-0.980838\pi$
$179$		−	1.60981i		−	0.120323i	0.998189	−	0.0601613i	$-0.0191615\pi$
$180$	−3.93521	+	3.47053i	−0.293313	+	0.258678i
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$	0.613616	+	1.62348i	0.0454842	+	0.120340i
$183$	7.13235			0.527239
$184$	−16.2968	−	8.62348i	−1.20142	−	0.635731i
$185$	−5.62348			−0.413446
$186$	0.498095	−	0.188262i	0.0365221	−	0.0138041i
$187$	−18.3290	+	3.45065i	−1.34035	+	0.252337i
$188$	8.62348	+	9.77810i	0.628932	+	0.713141i
$189$		−	2.11738i		−	0.154017i
$190$	9.43521	−	3.56618i	0.684502	−	0.258718i
$191$			15.8745i			1.14864i	0.818631	+	0.574320i	$0.194733\pi$
$191$			15.8745i			1.14864i	−0.818631	+	0.574320i	$0.805267\pi$
$192$	−4.05869	+	2.76127i	−0.292911	+	0.199278i
$193$			13.6235i			0.980639i	0.871543	+	0.490320i	$0.163120\pi$
$193$			13.6235i			0.980639i	−0.871543	+	0.490320i	$0.836880\pi$
$194$	−2.64575	+	1.00000i	−0.189954	+	0.0717958i
$195$	1.22723			0.0878839
$196$	−9.93521	+	8.76203i	−0.709658	+	0.625860i
$197$		−	20.4939i		−	1.46013i	−0.683378	−	0.730065i	$-0.739490\pi$
$197$		−	20.4939i		−	1.46013i	0.683378	−	0.730065i	$-0.260510\pi$
$198$	6.40501	+	10.5068i	0.455184	+	0.746688i
$199$			9.96939i			0.706711i	0.935489	+	0.353356i	$0.114959\pi$
$199$			9.96939i			0.706711i	−0.935489	+	0.353356i	$0.885041\pi$
$200$	−1.32288	+	2.50000i	−0.0935414	+	0.176777i
$201$	−4.75305			−0.335254
$202$	−3.62348	−	9.58681i	−0.254947	−	0.674526i
$203$		−	4.67789i		−	0.328323i
$204$	−5.17598	+	4.56479i	−0.362391	+	0.319599i
$205$		−	8.00000i		−	0.558744i
$206$	−3.25937	−	8.62348i	−0.227091	−	0.600826i
$207$			17.1017i			1.18865i
$208$	−7.93725	−	1.00000i	−0.550350	−	0.0693375i
$209$	−4.37652	−	23.2470i	−0.302731	−	1.60803i
$210$	−0.188262	−	0.498095i	−0.0129913	−	0.0343718i
$211$	5.90512			0.406525			0.203263	−	0.979124i	$-0.434845\pi$
$211$	5.90512			0.406525			0.203263	+	0.979124i	$0.434845\pi$
$212$	−14.4352	+	12.7307i	−0.991415	+	0.874345i
$213$	−1.12957			−0.0773971
$214$	−21.0000	+	7.93725i	−1.43553	+	0.542580i
$215$	6.51873			0.444574
$216$	8.62664	+	4.56479i	0.586968	+	0.310594i
$217$		−	0.376525i		−	0.0255602i
$218$	−5.62348	−	14.8783i	−0.380870	−	1.00769i
$219$	1.22723			0.0829287
$220$	5.23216	+	4.07731i	0.352752	+	0.274892i
$221$	−11.2470			−0.756552
$222$	1.72533	+	4.56479i	0.115796	+	0.306368i
$223$			18.3290i			1.22740i	0.789540	+	0.613699i	$0.210319\pi$
$223$			18.3290i			1.22740i	−0.789540	+	0.613699i	$0.789681\pi$
$224$	0.811738	+	3.37489i	0.0542365	+	0.225494i
$225$	2.62348			0.174898
$226$	−13.2288	+	5.00000i	−0.879964	+	0.332595i
$227$	18.3290			1.21654			0.608268	−	0.793731i	$-0.291864\pi$
$227$	18.3290			1.21654			0.608268	+	0.793731i	$0.291864\pi$
$228$	−5.78960	−	6.56479i	−0.383425	−	0.434764i
$229$	−16.4939			−1.08995			−0.544974	−	0.838453i	$-0.683460\pi$
$229$	−16.4939			−1.08995			−0.544974	+	0.838453i	$0.683460\pi$
$230$	3.25937	+	8.62348i	0.214916	+	0.568615i
$231$	−1.22723	+	0.231042i	−0.0807459	+	0.0152014i
$232$	19.0587	+	10.0849i	1.25126	+	0.662107i
$233$		−	9.62348i		−	0.630455i	−0.949016	−	0.315227i	$-0.897919\pi$
$233$		−	9.62348i		−	0.630455i	0.949016	−	0.315227i	$-0.102081\pi$
$234$	2.62348	+	6.94106i	0.171502	+	0.453752i
$235$		−	6.51873i		−	0.425235i
$236$	5.37652	+	6.09641i	0.349982	+	0.396842i
$237$			1.50610i			0.0978316i
$238$	1.72533	+	4.56479i	0.111836	+	0.295891i
$239$	26.0749			1.68665			0.843324	−	0.537406i	$-0.180596\pi$
$239$	26.0749			1.68665			0.843324	+	0.537406i	$0.180596\pi$
$240$	2.43521	+	0.306808i	0.157192	+	0.0198044i
$241$		−	7.24695i		−	0.466817i	−0.972379	−	0.233409i	$-0.925012\pi$
$241$		−	7.24695i		−	0.466817i	0.972379	−	0.233409i	$-0.0749880\pi$
$242$	11.5554	−	10.4150i	0.742812	−	0.669500i
$243$		−	13.8821i		−	0.890539i
$244$	15.3764	+	17.4352i	0.984374	+	1.11618i
$245$	6.62348			0.423158
$246$	−6.49390	+	2.45446i	−0.414036	+	0.156491i
$247$		−	14.2647i		−	0.907641i
$248$	1.53404	+	0.811738i	0.0974116	+	0.0515454i
$249$		−	4.75305i		−	0.301212i
$250$	1.32288	−	0.500000i	0.0836660	−	0.0316228i
$251$			18.3290i			1.15691i	0.815713	+	0.578457i	$0.196345\pi$
$251$			18.3290i			1.15691i	−0.815713	+	0.578457i	$0.803655\pi$
$252$	2.41471	−	2.12957i	0.152112	−	0.134151i
$253$	21.2470	−	4.00000i	1.33578	−	0.251478i
$254$	−10.2470	+	3.87298i	−0.642951	+	0.243013i
$255$	3.45065			0.216088
$256$	−15.5000	−	3.96863i	−0.968750	−	0.248039i
$257$	2.75305			0.171730			0.0858652	−	0.996307i	$-0.472635\pi$
$257$	2.75305			0.171730			0.0858652	+	0.996307i	$0.472635\pi$
$258$	−2.00000	−	5.29150i	−0.124515	−	0.329435i
$259$	3.45065			0.214413
$260$	2.64575	+	3.00000i	0.164083	+	0.186052i
$261$		−	20.0000i		−	1.23797i
$262$	23.4352	−	8.85768i	1.44783	−	0.547229i
$263$	−21.7796			−1.34299			−0.671495	−	0.741009i	$-0.734347\pi$
$263$	−21.7796			−1.34299			−0.671495	+	0.741009i	$0.734347\pi$
$264$	1.70444	−	5.49810i	0.104901	−	0.338384i
$265$	9.62348			0.591165
$266$	−5.78960	+	2.18826i	−0.354983	+	0.134171i
$267$		−	0.996190i		−	0.0609659i
$268$	−10.2470	−	11.6190i	−0.625932	−	0.709740i
$269$	20.4939			1.24954			0.624768	−	0.780811i	$-0.285194\pi$
$269$	20.4939			1.24954			0.624768	+	0.780811i	$0.285194\pi$
$270$	−1.72533	−	4.56479i	−0.105000	−	0.277804i
$271$	−22.3932			−1.36029			−0.680146	−	0.733076i	$-0.738084\pi$
$271$	−22.3932			−1.36029			−0.680146	+	0.733076i	$0.738084\pi$
$272$	−22.3175	−	2.81174i	−1.35320	−	0.170487i
$273$	−0.753049			−0.0455766
$274$	7.93725	−	3.00000i	0.479507	−	0.181237i
$275$	−0.613616	−	3.25937i	−0.0370024	−	0.196547i
$276$	6.00000	−	5.29150i	0.361158	−	0.318511i
$277$			16.4939i			0.991022i	0.868602	+	0.495511i	$0.165019\pi$
$277$			16.4939i			0.991022i	−0.868602	+	0.495511i	$0.834981\pi$
$278$	18.8704	−	7.13235i	1.13177	−	0.427770i
$279$		−	1.60981i		−	0.0963766i
$280$	0.811738	−	1.53404i	0.0485106	−	0.0916764i
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	−5.29150	+	2.00000i	−0.315104	+	0.119098i
$283$	10.2004			0.606353			0.303176	−	0.952934i	$-0.401953\pi$
$283$	10.2004			0.606353			0.303176	+	0.952934i	$0.401953\pi$
$284$	−2.43521	−	2.76127i	−0.144503	−	0.163851i
$285$			4.37652i			0.259243i
$286$	8.00986	−	4.88284i	0.473633	−	0.288729i
$287$			4.90893i			0.289765i
$288$	3.47053	+	14.4291i	0.204503	+	0.850244i
$289$	−14.6235			−0.860204
$290$	−3.81174	−	10.0849i	−0.223833	−	0.592206i
$291$		−	1.22723i		−	0.0719416i
$292$	2.64575	+	3.00000i	0.154831	+	0.175562i
$293$			28.4939i			1.66463i	0.554302	+	0.832316i	$0.312985\pi$
$293$			28.4939i			1.66463i	−0.554302	+	0.832316i	$0.687015\pi$
$294$	−2.03214	−	5.37652i	−0.118517	−	0.313565i
$295$		−	4.06427i		−	0.236631i
$296$	−7.43916	+	14.0587i	−0.432392	+	0.817145i
$297$	−11.2470	+	2.11738i	−0.652614	+	0.122863i
$298$	4.18826	+	11.0811i	0.242620	+	0.641911i
$299$	13.0375			0.753976
$300$	−0.811738	−	0.920424i	−0.0468657	−	0.0531407i
$301$	−4.00000			−0.230556
$302$	1.62348	−	0.613616i	0.0934205	−	0.0353096i
$303$	4.44685			0.255465
$304$	3.56618	−	28.3056i	0.204534	−	1.62344i
$305$		−	11.6235i		−	0.665558i
$306$	7.37652	+	19.5164i	0.421688	+	1.11568i
$307$	−2.83704			−0.161918			−0.0809592	−	0.996717i	$-0.525798\pi$
$307$	−2.83704			−0.161918			−0.0809592	+	0.996717i	$0.525798\pi$
$308$	−3.21054	−	2.50190i	−0.182937	−	0.142559i
$309$	4.00000			0.227552
$310$	−0.306808	−	0.811738i	−0.0174255	−	0.0461036i
$311$		−	30.3703i		−	1.72214i	−0.508487	−	0.861069i	$-0.669795\pi$
$311$		−	30.3703i		−	1.72214i	0.508487	−	0.861069i	$-0.330205\pi$
$312$	1.62348	−	3.06808i	0.0919112	−	0.173696i
$313$	−13.2470			−0.748762			−0.374381	−	0.927275i	$-0.622145\pi$
$313$	−13.2470			−0.748762			−0.374381	+	0.927275i	$0.622145\pi$
$314$	2.14766	−	0.811738i	0.121199	−	0.0458090i
$315$	−1.60981			−0.0907023
$316$	−3.68170	+	3.24695i	−0.207112	+	0.182655i
$317$	12.8704			0.722875			0.361438	−	0.932396i	$-0.382286\pi$
$317$	12.8704			0.722875			0.361438	+	0.932396i	$0.382286\pi$
$318$	−2.95256	−	7.81174i	−0.165571	−	0.438060i
$319$	−24.8477	+	4.67789i	−1.39120	+	0.261911i
$320$	4.50000	+	6.61438i	0.251558	+	0.369755i
$321$		−	9.74085i		−	0.543681i
$322$	−2.00000	−	5.29150i	−0.111456	−	0.294884i
$323$		−	40.1086i		−	2.23170i
$324$	8.62957	−	7.61057i	0.479421	−	0.422809i
$325$		−	2.00000i		−	0.110940i
$326$	10.8898	+	28.8117i	0.603131	+	1.59573i
$327$	6.90131			0.381643
$328$	−20.0000	−	10.5830i	−1.10432	−	0.584349i
$329$			4.00000i			0.220527i
$330$	−2.45749	+	1.49810i	−0.135280	+	0.0824674i
$331$			22.0107i			1.20982i	0.796295	+	0.604908i	$0.206790\pi$
$331$			22.0107i			1.20982i	−0.796295	+	0.604908i	$0.793210\pi$
$332$	11.6190	−	10.2470i	0.637673	−	0.562374i
$333$	14.7530			0.808462
$334$	2.43521	−	0.920424i	0.133249	−	0.0503634i
$335$			7.74597i			0.423207i
$336$	−1.49429	−	0.188262i	−0.0815200	−	0.0102706i
$337$			16.8704i			0.918991i	0.888180	+	0.459495i	$0.151970\pi$
$337$			16.8704i			0.918991i	−0.888180	+	0.459495i	$0.848030\pi$
$338$	−11.9059	+	4.50000i	−0.647595	+	0.244768i
$339$		−	6.13616i		−	0.333270i
$340$	7.43916	+	8.43521i	0.403445	+	0.457464i
$341$	−2.00000	+	0.376525i	−0.108306	+	0.0203900i
$342$	−24.7530	+	9.35577i	−1.33849	+	0.505902i
$343$	−8.35958			−0.451375
$344$	8.62348	−	16.2968i	0.464947	−	0.878667i
$345$	−4.00000			−0.215353
$346$	0.623475	+	1.64956i	0.0335182	+	0.0886809i
$347$	−28.9120			−1.55208			−0.776038	−	0.630686i	$-0.782774\pi$
$347$	−28.9120			−1.55208			−0.776038	+	0.630686i	$0.782774\pi$
$348$	−7.01683	+	6.18826i	−0.376142	+	0.331726i
$349$			12.7530i			0.682655i	0.939944	+	0.341328i	$0.110877\pi$
$349$			12.7530i			0.682655i	−0.939944	+	0.341328i	$0.889123\pi$
$350$	−0.811738	+	0.306808i	−0.0433892	+	0.0163996i
$351$	−6.90131			−0.368365
$352$	17.1148	−	7.68663i	0.912221	−	0.409699i
$353$	2.75305			0.146530			0.0732650	−	0.997313i	$-0.476658\pi$
$353$	2.75305			0.146530			0.0732650	+	0.997313i	$0.476658\pi$
$354$	−3.29912	+	1.24695i	−0.175346	+	0.0662747i
$355$			1.84085i			0.0977021i
$356$	2.43521	−	2.14766i	0.129066	−	0.113826i
$357$	−2.11738			−0.112063
$358$	0.804903	+	2.12957i	0.0425405	+	0.112551i
$359$	14.2647			0.752862			0.376431	−	0.926445i	$-0.377151\pi$
$359$	14.2647			0.752862			0.376431	+	0.926445i	$0.377151\pi$
$360$	3.47053	−	6.55869i	0.182913	−	0.345673i
$361$	31.8704			1.67739
$362$	7.93725	−	3.00000i	0.417173	−	0.157676i
$363$	2.45446	+	6.28769i	0.128826	+	0.330018i
$364$	−1.62348	−	1.84085i	−0.0850932	−	0.0964867i
$365$		−	2.00000i		−	0.104685i
$366$	−9.43521	+	3.56618i	−0.493186	+	0.186407i
$367$		−	5.29150i		−	0.276214i	−0.990417	−	0.138107i	$-0.955898\pi$
$367$		−	5.29150i		−	0.276214i	0.990417	−	0.138107i	$-0.0441018\pi$
$368$	25.8704	+	3.25937i	1.34859	+	0.169906i
$369$			20.9878i			1.09258i
$370$	7.43916	−	2.81174i	0.386743	−	0.146175i
$371$	−5.90512			−0.306578
$372$	−0.564787	+	0.498095i	−0.0292828	+	0.0258250i
$373$		−	16.4939i		−	0.854022i	−0.904246	−	0.427011i	$-0.859567\pi$
$373$		−	16.4939i		−	0.854022i	0.904246	−	0.427011i	$-0.140433\pi$
$374$	22.5216	−	13.7293i	1.16457	−	0.709924i
$375$			0.613616i			0.0316870i
$376$	−16.2968	−	8.62348i	−0.840445	−	0.444722i
$377$	−15.2470			−0.785258
$378$	1.05869	+	2.80103i	0.0544531	+	0.144069i
$379$			8.97320i			0.460922i	0.973082	+	0.230461i	$0.0740235\pi$
$379$			8.97320i			0.460922i	−0.973082	+	0.230461i	$0.925977\pi$
$380$	−10.6985	+	9.43521i	−0.548823	+	0.484016i
$381$		−	4.75305i		−	0.243506i
$382$	−7.93725	−	21.0000i	−0.406105	−	1.07445i
$383$			4.06427i			0.207675i	0.994594	+	0.103837i	$0.0331121\pi$
$383$			4.06427i			0.207675i	−0.994594	+	0.103837i	$0.966888\pi$
$384$	3.98850	−	5.68216i	0.203537	−	0.289967i
$385$	0.376525	+	2.00000i	0.0191895	+	0.101929i
$386$	−6.81174	−	18.0222i	−0.346708	−	0.917304i
$387$	−17.1017			−0.869330
$388$	3.00000	−	2.64575i	0.152302	−	0.134318i
$389$	−10.7530			−0.545201			−0.272601	−	0.962127i	$-0.587884\pi$
$389$	−10.7530			−0.545201			−0.272601	+	0.962127i	$0.587884\pi$
$390$	−1.62348	+	0.613616i	−0.0822079	+	0.0310717i
$391$	36.6579			1.85387
$392$	8.76203	−	16.5587i	0.442550	−	0.836340i
$393$			10.8704i			0.548340i
$394$	10.2470	+	27.1109i	0.516234	+	1.36583i
$395$	2.45446			0.123497
$396$	−13.7264	−	10.6967i	−0.689780	−	0.537531i
$397$	−4.49390			−0.225542			−0.112771	−	0.993621i	$-0.535973\pi$
$397$	−4.49390			−0.225542			−0.112771	+	0.993621i	$0.535973\pi$
$398$	−4.98469	−	13.1883i	−0.249860	−	0.661068i
$399$		−	2.68551i		−	0.134443i
$400$	0.500000	−	3.96863i	0.0250000	−	0.198431i
$401$	17.6235			0.880074			0.440037	−	0.897980i	$-0.354965\pi$
$401$	17.6235			0.880074			0.440037	+	0.897980i	$0.354965\pi$
$402$	6.28769	−	2.37652i	0.313602	−	0.118530i
$403$	−1.22723			−0.0611328
$404$	9.58681	+	10.8704i	0.476962	+	0.540824i
$405$	−5.75305			−0.285871
$406$	2.33894	+	6.18826i	0.116080	+	0.307118i
$407$	−3.45065	−	18.3290i	−0.171043	−	0.908533i
$408$	4.56479	−	8.62664i	0.225991	−	0.427082i
$409$			28.0000i			1.38451i	0.721653	+	0.692255i	$0.243383\pi$
$409$			28.0000i			1.38451i	−0.721653	+	0.692255i	$0.756617\pi$
$410$	4.00000	+	10.5830i	0.197546	+	0.522657i
$411$			3.68170i			0.181605i
$412$	8.62348	+	9.77810i	0.424848	+	0.481733i
$413$			2.49390i			0.122717i
$414$	−8.55087	−	22.6235i	−0.420252	−	1.11188i
$415$	−7.74597			−0.380235
$416$	11.0000	−	2.64575i	0.539319	−	0.129719i
$417$			8.75305i			0.428639i
$418$	17.4131	+	28.5646i	0.851701	+	1.39714i
$419$		−	20.7834i		−	1.01534i	−0.861552	−	0.507669i	$-0.830507\pi$
$419$		−	20.7834i		−	1.01534i	0.861552	−	0.507669i	$-0.169493\pi$
$420$	0.498095	+	0.564787i	0.0243046	+	0.0275588i
$421$	−14.7530			−0.719020			−0.359510	−	0.933141i	$-0.617056\pi$
$421$	−14.7530			−0.719020			−0.359510	+	0.933141i	$0.617056\pi$
$422$	−7.81174	+	2.95256i	−0.380269	+	0.143728i
$423$			17.1017i			0.831515i
$424$	12.7307	−	24.0587i	0.618256	−	1.16839i
$425$		−	5.62348i		−	0.272779i
$426$	1.49429	−	0.564787i	0.0723984	−	0.0273640i
$427$			7.13235i			0.345159i
$428$	23.8118	−	21.0000i	1.15098	−	1.01507i
$429$	0.753049	+	4.00000i	0.0363576	+	0.193122i
$430$	−8.62348	+	3.25937i	−0.415861	+	0.157181i
$431$	24.8477			1.19687			0.598436	−	0.801171i	$-0.295789\pi$
$431$	24.8477			1.19687			0.598436	+	0.801171i	$0.295789\pi$
$432$	−13.6944	−	1.72533i	−0.658870	−	0.0830098i
$433$	−21.2470			−1.02106			−0.510532	−	0.859859i	$-0.670551\pi$
$433$	−21.2470			−1.02106			−0.510532	+	0.859859i	$0.670551\pi$
$434$	0.188262	+	0.498095i	0.00903688	+	0.0239093i
$435$	4.67789			0.224287
$436$	14.8783	+	16.8704i	0.712542	+	0.807947i
$437$			46.4939i			2.22410i
$438$	−1.62348	+	0.613616i	−0.0775727	+	0.0293197i
$439$	−4.90893			−0.234290			−0.117145	−	0.993115i	$-0.537374\pi$
$439$	−4.90893			−0.234290			−0.117145	+	0.993115i	$0.537374\pi$
$440$	−8.96016	−	2.77770i	−0.427159	−	0.132422i
$441$	−17.3765			−0.827454
$442$	14.8783	−	5.62348i	0.707689	−	0.267481i
$443$			15.8745i			0.754221i	0.926168	+	0.377110i	$0.123082\pi$
$443$			15.8745i			0.754221i	−0.926168	+	0.377110i	$0.876918\pi$
$444$	−4.56479	−	5.17598i	−0.216635	−	0.245641i
$445$	−1.62348			−0.0769601
$446$	−9.16449	−	24.2470i	−0.433951	−	1.14813i
$447$	−5.13997			−0.243112
$448$	−2.76127	−	4.05869i	−0.130458	−	0.191755i
$449$	28.4939			1.34471			0.672355	−	0.740229i	$-0.265283\pi$
$449$	28.4939			1.34471			0.672355	+	0.740229i	$0.265283\pi$
$450$	−3.47053	+	1.31174i	−0.163602	+	0.0618359i
$451$	26.0749	−	4.90893i	1.22782	−	0.231152i
$452$	15.0000	−	13.2288i	0.705541	−	0.622228i
$453$			0.753049i			0.0353813i
$454$	−24.2470	+	9.16449i	−1.13797	+	0.430111i
$455$			1.22723i			0.0575335i
$456$	10.9413	+	5.78960i	0.512374	+	0.271123i
$457$		−	4.87043i		−	0.227829i	−0.993491	−	0.113914i	$-0.963661\pi$
$457$		−	4.87043i		−	0.227829i	0.993491	−	0.113914i	$-0.0363390\pi$
$458$	21.8194	−	8.24695i	1.01955	−	0.385355i
$459$	−19.4047			−0.905732
$460$	−8.62348	−	9.77810i	−0.402072	−	0.455906i
$461$		−	20.3765i		−	0.949029i	−0.880248	−	0.474515i	$-0.842624\pi$
$461$		−	20.3765i		−	0.949029i	0.880248	−	0.474515i	$-0.157376\pi$
$462$	1.50795	−	0.919255i	0.0701564	−	0.0427676i
$463$			25.6924i			1.19403i	0.802232	+	0.597013i	$0.203646\pi$
$463$			25.6924i			1.19403i	−0.802232	+	0.597013i	$0.796354\pi$
$464$	−30.2547	−	3.81174i	−1.40454	−	0.176955i
$465$	0.376525			0.0174609
$466$	4.81174	+	12.7307i	0.222899	+	0.589736i
$467$			39.7260i			1.83830i	0.393906	+	0.919151i	$0.371123\pi$
$467$			39.7260i			1.83830i	−0.393906	+	0.919151i	$0.628877\pi$
$468$	−6.94106	−	7.87043i	−0.320851	−	0.363811i
$469$		−	4.75305i		−	0.219475i
$470$	3.25937	+	8.62348i	0.150343	+	0.397771i
$471$			0.996190i			0.0459020i
$472$	−10.1607	−	5.37652i	−0.467683	−	0.247475i
$473$	4.00000	+	21.2470i	0.183920	+	0.976936i
$474$	−0.753049	−	1.99238i	−0.0345887	−	0.0915131i
$475$	7.13235			0.327255
$476$	−4.56479	−	5.17598i	−0.209227	−	0.237241i
$477$	−25.2470			−1.15598
$478$	−34.4939	+	13.0375i	−1.57771	+	0.596320i
$479$	−30.5218			−1.39458			−0.697288	−	0.716791i	$-0.745610\pi$
$479$	−30.5218			−1.39458			−0.697288	+	0.716791i	$0.745610\pi$
$480$	−3.37489	+	0.811738i	−0.154042	+	0.0370506i
$481$		−	11.2470i		−	0.512817i
$482$	3.62348	+	9.58681i	0.165045	+	0.436667i
$483$	2.45446			0.111682
$484$	−10.0789	+	19.5554i	−0.458133	+	0.888884i
$485$	−2.00000			−0.0908153
$486$	6.94106	+	18.3643i	0.314853	+	0.833023i
$487$		−	43.1767i		−	1.95652i	−0.207377	−	0.978261i	$-0.566493\pi$
$487$		−	43.1767i		−	1.95652i	0.207377	−	0.978261i	$-0.433507\pi$
$488$	−29.0587	−	15.3764i	−1.31543	−	0.696057i
$489$	−13.3643			−0.604356
$490$	−8.76203	+	3.31174i	−0.395828	+	0.149609i
$491$	−36.8890			−1.66478			−0.832388	−	0.554193i	$-0.813027\pi$
$491$	−36.8890			−1.66478			−0.832388	+	0.554193i	$0.813027\pi$
$492$	7.36339	−	6.49390i	0.331967	−	0.292768i
$493$	−42.8704			−1.93079
$494$	7.13235	+	18.8704i	0.320900	+	0.849021i
$495$	1.60981	+	8.55087i	0.0723554	+	0.384333i
$496$	−2.43521	−	0.306808i	−0.109344	−	0.0137761i
$497$		−	1.12957i		−	0.0506683i
$498$	2.37652	+	6.28769i	0.106495	+	0.281758i
$499$			1.60981i			0.0720648i	0.999351	+	0.0360324i	$0.0114720\pi$
$499$			1.60981i			0.0720648i	−0.999351	+	0.0360324i	$0.988528\pi$
$500$	−1.50000	+	1.32288i	−0.0670820	+	0.0591608i
$501$			1.12957i			0.0504656i
$502$	−9.16449	−	24.2470i	−0.409031	−	1.08219i
$503$	20.7834			0.926688			0.463344	−	0.886179i	$-0.346650\pi$
$503$	20.7834			0.926688			0.463344	+	0.886179i	$0.346650\pi$
$504$	−2.12957	+	4.02452i	−0.0948588	+	0.179266i
$505$		−	7.24695i		−	0.322485i
$506$	−26.1071	+	15.9150i	−1.16060	+	0.707507i
$507$		−	5.52254i		−	0.245265i
$508$	11.6190	−	10.2470i	0.515508	−	0.454635i
$509$	−1.24695			−0.0552701			−0.0276351	−	0.999618i	$-0.508798\pi$
$509$	−1.24695			−0.0552701			−0.0276351	+	0.999618i	$0.508798\pi$
$510$	−4.56479	+	1.72533i	−0.202132	+	0.0763988i
$511$			1.22723i			0.0542895i
$512$	22.4889	−	2.50000i	0.993878	−	0.110485i
$513$		−	24.6113i		−	1.08661i
$514$	−3.64194	+	1.37652i	−0.160639	+	0.0607159i
$515$		−	6.51873i		−	0.287250i
$516$	5.29150	+	6.00000i	0.232945	+	0.264135i
$517$	21.2470	−	4.00000i	0.934440	−	0.175920i
$518$	−4.56479	+	1.72533i	−0.200565	+	0.0758065i
$519$	−0.765149			−0.0335863
$520$	−5.00000	−	2.64575i	−0.219265	−	0.116024i
$521$	28.4939			1.24834			0.624170	−	0.781288i	$-0.285437\pi$
$521$	28.4939			1.24834			0.624170	+	0.781288i	$0.285437\pi$
$522$	10.0000	+	26.4575i	0.437688	+	1.15801i
$523$	−8.97320			−0.392371			−0.196185	−	0.980567i	$-0.562855\pi$
$523$	−8.97320			−0.392371			−0.196185	+	0.980567i	$0.562855\pi$
$524$	−26.5730	+	23.4352i	−1.16085	+	1.02377i
$525$		−	0.376525i		−	0.0164329i
$526$	28.8117	−	10.8898i	1.25625	−	0.474818i
$527$	−3.45065			−0.150313
$528$	0.494286	+	8.12552i	0.0215110	+	0.353618i
$529$	−19.4939			−0.847561
$530$	−12.7307	+	4.81174i	−0.552985	+	0.209009i
$531$			10.6625i			0.462714i
$532$	6.56479	−	5.78960i	0.284620	−	0.251011i
$533$	16.0000			0.693037
$534$	0.498095	+	1.31784i	0.0215547	+	0.0570283i
$535$	−15.8745			−0.686315
$536$	19.3649	+	10.2470i	0.836437	+	0.442601i
$537$	−0.987803			−0.0426268
$538$	−27.1109	+	10.2470i	−1.16883	+	0.441777i
$539$	4.06427	+	21.5883i	0.175061	+	0.929876i
$540$	4.56479	+	5.17598i	0.196437	+	0.222739i
$541$		−	28.3765i		−	1.22000i	−0.792401	−	0.610001i	$-0.791169\pi$
$541$		−	28.3765i		−	1.22000i	0.792401	−	0.610001i	$-0.208831\pi$
$542$	29.6235	−	11.1966i	1.27244	−	0.480936i
$543$			3.68170i			0.157997i
$544$	30.9291	−	7.43916i	1.32607	−	0.318951i
$545$		−	11.2470i		−	0.481766i
$546$	0.996190	−	0.376525i	0.0426330	−	0.0161138i
$547$	18.3290			0.783690			0.391845	−	0.920031i	$-0.371837\pi$
$547$	18.3290			0.783690			0.391845	+	0.920031i	$0.371837\pi$
$548$	−9.00000	+	7.93725i	−0.384461	+	0.339063i
$549$			30.4939i			1.30145i
$550$	2.44142	+	4.00493i	0.104103	+	0.170771i
$551$		−	54.3733i		−	2.31638i
$552$	−5.29150	+	10.0000i	−0.225221	+	0.425628i
$553$	−1.50610			−0.0640458
$554$	−8.24695	−	21.8194i	−0.350379	−	0.927017i
$555$			3.45065i			0.146472i
$556$	−21.3971	+	18.8704i	−0.907437	+	0.800284i
$557$			25.2470i			1.06975i	0.844932	+	0.534874i	$0.179641\pi$
$557$			25.2470i			1.06975i	−0.844932	+	0.534874i	$0.820359\pi$
$558$	0.804903	+	2.12957i	0.0340743	+	0.0901520i
$559$			13.0375i			0.551426i
$560$	−0.306808	+	2.43521i	−0.0129650	+	0.102907i
$561$	2.11738	+	11.2470i	0.0893957	+	0.474847i
$562$		0			0
$563$	−11.4277			−0.481619			−0.240809	−	0.970572i	$-0.577413\pi$
$563$	−11.4277			−0.481619			−0.240809	+	0.970572i	$0.577413\pi$
$564$	6.00000	−	5.29150i	0.252646	−	0.222812i
$565$	−10.0000			−0.420703
$566$	−13.4939	+	5.10022i	−0.567191	+	0.214378i
$567$	3.53016			0.148253
$568$	4.60212	+	2.43521i	0.193101	+	0.102179i
$569$		−	17.7409i		−	0.743735i	−0.928286	−	0.371868i	$-0.878718\pi$
$569$		−	17.7409i		−	0.743735i	0.928286	−	0.371868i	$-0.121282\pi$
$570$	−2.18826	−	5.78960i	−0.0916562	−	0.242500i
$571$	12.8064			0.535932			0.267966	−	0.963428i	$-0.413648\pi$
$571$	12.8064			0.535932			0.267966	+	0.963428i	$0.413648\pi$
$572$	−8.15463	+	10.4643i	−0.340962	+	0.437535i
$573$	9.74085			0.406930
$574$	−2.45446	−	6.49390i	−0.102447	−	0.271050i
$575$			6.51873i			0.271850i
$576$	−11.8056	−	17.3527i	−0.491902	−	0.723027i
$577$	38.9878			1.62308			0.811542	−	0.584294i	$-0.198629\pi$
$577$	38.9878			1.62308			0.811542	+	0.584294i	$0.198629\pi$
$578$	19.3450	−	7.31174i	0.804648	−	0.304128i
$579$	8.35958			0.347412
$580$	10.0849	+	11.4352i	0.418753	+	0.474821i
$581$	4.75305			0.197190
$582$	0.613616	+	1.62348i	0.0254352	+	0.0672952i
$583$	5.90512	+	31.3664i	0.244565	+	1.29907i
$584$	−5.00000	−	2.64575i	−0.206901	−	0.109482i
$585$			5.24695i			0.216935i
$586$	−14.2470	−	37.6939i	−0.588536	−	1.55712i
$587$			18.0979i			0.746982i	0.927634	+	0.373491i	$0.121839\pi$
$587$			18.0979i			0.746982i	−0.927634	+	0.373491i	$0.878161\pi$
$588$	5.37652	+	6.09641i	0.221724	+	0.251412i
$589$		−	4.37652i		−	0.180332i
$590$	2.03214	+	5.37652i	0.0836617	+	0.221348i
$591$	−12.5754			−0.517282
$592$	2.81174	−	22.3175i	0.115562	−	0.917243i
$593$			24.4939i			1.00584i	0.864332	+	0.502922i	$0.167742\pi$
$593$			24.4939i			1.00584i	−0.864332	+	0.502922i	$0.832258\pi$
$594$	13.8196	−	8.42450i	0.567026	−	0.345661i
$595$			3.45065i			0.141463i
$596$	−11.0811	−	12.5648i	−0.453900	−	0.514674i
$597$	6.11738			0.250368
$598$	−17.2470	+	6.51873i	−0.705280	+	0.266571i
$599$		−	31.5975i		−	1.29104i	−0.763744	−	0.645519i	$-0.776641\pi$
$599$		−	31.5975i		−	1.29104i	0.763744	−	0.645519i	$-0.223359\pi$
$600$	1.53404	+	0.811738i	0.0626269	+	0.0331391i
$601$		−	47.2470i		−	1.92724i	−0.267270	−	0.963622i	$-0.586122\pi$
$601$		−	47.2470i		−	1.92724i	0.267270	−	0.963622i	$-0.413878\pi$
$602$	5.29150	−	2.00000i	0.215666	−	0.0815139i
$603$		−	20.3214i		−	0.827549i
$604$	−1.84085	+	1.62348i	−0.0749030	+	0.0660583i
$605$	10.2470	−	4.00000i	0.416598	−	0.162623i
$606$	−5.88262	+	2.22342i	−0.238965	+	0.0903204i
$607$	−11.1966			−0.454457			−0.227228	−	0.973841i	$-0.572966\pi$
$607$	−11.1966			−0.454457			−0.227228	+	0.973841i	$0.572966\pi$
$608$	9.43521	+	39.2279i	0.382648	+	1.59090i
$609$	−2.87043			−0.116316
$610$	5.81174	+	15.3764i	0.235310	+	0.622573i
$611$	13.0375			0.527440
$612$	−19.5164	−	22.1296i	−0.788906	−	0.894535i
$613$		−	24.4939i		−	0.989299i	−0.869092	−	0.494650i	$-0.835296\pi$
$613$		−	24.4939i		−	0.989299i	0.869092	−	0.494650i	$-0.164704\pi$
$614$	3.75305	−	1.41852i	0.151461	−	0.0572468i
$615$	−4.90893			−0.197947
$616$	5.49810	+	1.70444i	0.221525	+	0.0686738i
$617$	−13.2470			−0.533302			−0.266651	−	0.963793i	$-0.585917\pi$
$617$	−13.2470			−0.533302			−0.266651	+	0.963793i	$0.585917\pi$
$618$	−5.29150	+	2.00000i	−0.212855	+	0.0804518i
$619$			0.844658i			0.0339497i	0.999856	+	0.0169748i	$0.00540351\pi$
$619$			0.844658i			0.0339497i	−0.999856	+	0.0169748i	$0.994596\pi$
$620$	0.811738	+	0.920424i	0.0326002	+	0.0369651i
$621$	22.4939			0.902649
$622$	15.1851	+	40.1761i	0.608868	+	1.61091i
$623$	0.996190			0.0399115
$624$	−0.613616	+	4.87043i	−0.0245643	+	0.194973i
$625$	1.00000			0.0400000
$626$	17.5241	−	6.62348i	0.700403	−	0.264727i
$627$	−14.2647	+	2.68551i	−0.569677	+	0.107249i
$628$	−2.43521	+	2.14766i	−0.0971756	+	0.0857008i
$629$		−	31.6235i		−	1.26091i
$630$	2.12957	−	0.804903i	0.0848443	−	0.0320681i
$631$		−	25.4613i		−	1.01360i	−0.862064	−	0.506800i	$-0.830828\pi$
$631$		−	25.4613i		−	1.01360i	0.862064	−	0.506800i	$-0.169172\pi$
$632$	3.24695	−	6.13616i	0.129157	−	0.244083i
$633$		−	3.62348i		−	0.144020i
$634$	−17.0260	+	6.43521i	−0.676188	+	0.255575i
$635$	−7.74597			−0.307389
$636$	7.81174	+	8.85768i	0.309756	+	0.351230i
$637$			13.2470i			0.524863i
$638$	30.5315	−	18.6121i	1.20875	−	0.736861i
$639$		−	4.82942i		−	0.191049i
$640$	−9.26013	−	6.50000i	−0.366039	−	0.256935i
$641$	−28.8704			−1.14031			−0.570157	−	0.821536i	$-0.693117\pi$
$641$	−28.8704			−1.14031			−0.570157	+	0.821536i	$0.693117\pi$
$642$	4.87043	+	12.8859i	0.192220	+	0.508567i
$643$		−	21.7796i		−	0.858905i	−0.903090	−	0.429452i	$-0.858707\pi$
$643$		−	21.7796i		−	0.858905i	0.903090	−	0.429452i	$-0.141293\pi$
$644$	5.29150	+	6.00000i	0.208514	+	0.236433i
$645$		−	4.00000i		−	0.157500i
$646$	20.0543	+	53.0587i	0.789026	+	2.08757i
$647$		−	36.2754i		−	1.42613i	−0.701097	−	0.713066i	$-0.747306\pi$
$647$		−	36.2754i		−	1.42613i	0.701097	−	0.713066i	$-0.252694\pi$
$648$	−7.61057	+	14.3826i	−0.298971	+	0.565003i
$649$	13.2470	−	2.49390i	0.519988	−	0.0978942i
$650$	1.00000	+	2.64575i	0.0392232	+	0.103775i
$651$	−0.231042			−0.00905523
$652$	−28.8117	−	32.6694i	−1.12835	−	1.27943i
$653$	−47.3643			−1.85351			−0.926755	−	0.375667i	$-0.877414\pi$
$653$	−47.3643			−1.85351			−0.926755	+	0.375667i	$0.877414\pi$
$654$	−9.12957	+	3.45065i	−0.356995	+	0.134931i
$655$	17.7154			0.692196
$656$	31.7490	+	4.00000i	1.23959	+	0.156174i
$657$			5.24695i			0.204703i
$658$	−2.00000	−	5.29150i	−0.0779681	−	0.206284i
$659$	2.22342			0.0866122			0.0433061	−	0.999062i	$-0.486211\pi$
$659$	2.22342			0.0866122			0.0433061	+	0.999062i	$0.486211\pi$
$660$	2.50190	−	3.21054i	0.0973865	−	0.124970i
$661$	43.7409			1.70132			0.850661	−	0.525715i	$-0.176202\pi$
$661$	43.7409			1.70132			0.850661	+	0.525715i	$0.176202\pi$
$662$	−11.0053	−	29.1174i	−0.427734	−	1.13168i
$663$			6.90131i			0.268025i
$664$	−10.2470	+	19.3649i	−0.397659	+	0.751505i
$665$	−4.37652			−0.169714
$666$	−19.5164	+	7.37652i	−0.756247	+	0.285835i
$667$	49.6954			1.92421
$668$	−2.76127	+	2.43521i	−0.106837	+	0.0942212i
$669$	11.2470			0.434832
$670$	−3.87298	−	10.2470i	−0.149626	−	0.395874i
$671$	37.8852	−	7.13235i	1.46254	−	0.275341i
$672$	2.07089	−	0.498095i	0.0798861	−	0.0192144i
$673$		−	32.8704i		−	1.26706i	−0.773717	−	0.633531i	$-0.781605\pi$
$673$		−	32.8704i		−	1.26706i	0.773717	−	0.633531i	$-0.218395\pi$
$674$	−8.43521	−	22.3175i	−0.324912	−	0.859637i
$675$		−	3.45065i		−	0.132816i
$676$	13.5000	−	11.9059i	0.519231	−	0.457918i
$677$		−	30.0000i		−	1.15299i	−0.817099	−	0.576497i	$-0.804419\pi$
$677$		−	30.0000i		−	1.15299i	0.817099	−	0.576497i	$-0.195581\pi$
$678$	3.06808	+	8.11738i	0.117829	+	0.311746i
$679$	1.22723			0.0470968
$680$	−14.0587	−	7.43916i	−0.539126	−	0.285279i
$681$		−	11.2470i		−	0.430984i
$682$	2.45749	−	1.49810i	0.0941021	−	0.0573650i
$683$			13.6511i			0.522344i	0.965292	+	0.261172i	$0.0841090\pi$
$683$			13.6511i			0.522344i	−0.965292	+	0.261172i	$0.915891\pi$
$684$	28.0673	−	24.7530i	1.07318	−	0.946456i
$685$	6.00000			0.229248
$686$	11.0587	−	4.17979i	0.422223	−	0.159585i
$687$			10.1209i			0.386137i
$688$	−3.25937	+	25.8704i	−0.124262	+	0.986301i
$689$			19.2470i			0.733250i
$690$	5.29150	−	2.00000i	0.201444	−	0.0761387i
$691$			39.4950i			1.50246i	0.660041	+	0.751230i	$0.270539\pi$
$691$			39.4950i			1.50246i	−0.660041	+	0.751230i	$0.729461\pi$
$692$	−1.64956	−	1.87043i	−0.0627069	−	0.0711029i
$693$	−0.987803	−	5.24695i	−0.0375235	−	0.199315i
$694$	38.2470	−	14.4560i	1.45183	−	0.548742i
$695$	14.2647			0.541091
$696$	6.18826	−	11.6947i	0.234565	−	0.443287i
$697$	44.9878			1.70403
$698$	−6.37652	−	16.8707i	−0.241355	−	0.638565i
$699$	−5.90512			−0.223352
$700$	0.920424	−	0.811738i	0.0347888	−	0.0306808i
$701$			3.62348i			0.136857i	0.997656	+	0.0684284i	$0.0217985\pi$
$701$			3.62348i			0.136857i	−0.997656	+	0.0684284i	$0.978202\pi$
$702$	9.12957	−	3.45065i	0.344574	−	0.130237i
$703$	40.1086			1.51272
$704$	−18.7974	+	18.7258i	−0.708454	+	0.705757i
$705$	−4.00000			−0.150649
$706$	−3.64194	+	1.37652i	−0.137066	+	0.0518062i
$707$			4.44685i			0.167241i
$708$	3.74085	−	3.29912i	0.140590	−	0.123989i
$709$	−14.7530			−0.554062			−0.277031	−	0.960861i	$-0.589351\pi$
$709$	−14.7530			−0.554062			−0.277031	+	0.960861i	$0.589351\pi$
$710$	−0.920424	−	2.43521i	−0.0345429	−	0.0913919i
$711$	−6.43923			−0.241490
$712$	−2.14766	+	4.05869i	−0.0804868	+	0.152106i
$713$	4.00000			0.149801
$714$	2.80103	−	1.05869i	0.104826	−	0.0396204i
$715$	6.51873	−	1.22723i	0.243787	−	0.0458959i
$716$	−2.12957	−	2.41471i	−0.0795859	−	0.0902419i
$717$		−	16.0000i		−	0.597531i
$718$	−18.8704	+	7.13235i	−0.704238	+	0.266177i
$719$		−	33.5899i		−	1.25269i	−0.779546	−	0.626345i	$-0.784550\pi$
$719$		−	33.5899i		−	1.25269i	0.779546	−	0.626345i	$-0.215450\pi$
$720$	−1.31174	+	10.4116i	−0.0488856	+	0.388017i
$721$			4.00000i			0.148968i
$722$	−42.1606	+	15.9352i	−1.56906	+	0.593047i
$723$	−4.44685			−0.165380
$724$	−9.00000	+	7.93725i	−0.334482	+	0.294986i
$725$		−	7.62348i		−	0.283129i
$726$	−6.39080	−	7.09060i	−0.237185	−	0.263157i
$727$			1.60981i			0.0597044i	0.999554	+	0.0298522i	$0.00950367\pi$
$727$			1.60981i			0.0597044i	−0.999554	+	0.0298522i	$0.990496\pi$
$728$	3.06808	+	1.62348i	0.113711	+	0.0601700i
$729$	8.74085			0.323735
$730$	1.00000	+	2.64575i	0.0370117	+	0.0979236i
$731$			36.6579i			1.35584i
$732$	10.6985	−	9.43521i	0.395429	−	0.348736i
$733$		−	10.7530i		−	0.397173i	−0.980083	−	0.198586i	$-0.936365\pi$
$733$		−	10.7530i		−	0.397173i	0.980083	−	0.198586i	$-0.0636351\pi$
$734$	2.64575	+	7.00000i	0.0976565	+	0.258375i
$735$		−	4.06427i		−	0.149913i
$736$	−35.8530	+	8.62348i	−1.32156	+	0.317866i
$737$	−25.2470	+	4.75305i	−0.929983	+	0.175081i
$738$	−10.4939	−	27.7643i	−0.386286	−	1.02202i
$739$	−4.44685			−0.163580			−0.0817899	−	0.996650i	$-0.526064\pi$
$739$	−4.44685			−0.163580			−0.0817899	+	0.996650i	$0.526064\pi$
$740$	−8.43521	+	7.43916i	−0.310085	+	0.273469i
$741$	−8.75305			−0.321551
$742$	7.81174	−	2.95256i	0.286778	−	0.108392i
$743$	−47.8546			−1.75561			−0.877807	−	0.479015i	$-0.840994\pi$
$743$	−47.8546			−1.75561			−0.877807	+	0.479015i	$0.840994\pi$
$744$	0.498095	−	0.941312i	0.0182611	−	0.0345102i
$745$			8.37652i			0.306892i
$746$	8.24695	+	21.8194i	0.301942	+	0.798864i
$747$	20.3214			0.743519
$748$	−22.9287	+	29.4229i	−0.838355	+	1.07581i
$749$	9.74085			0.355923
$750$	−0.306808	−	0.811738i	−0.0112030	−	0.0296405i
$751$		−	32.3626i		−	1.18093i	−0.807064	−	0.590465i	$-0.798945\pi$
$751$		−	32.3626i		−	1.18093i	0.807064	−	0.590465i	$-0.201055\pi$
$752$	25.8704	+	3.25937i	0.943397	+	0.118857i
$753$	11.2470			0.409862
$754$	20.1698	−	7.62348i	0.734542	−	0.277631i
$755$	1.22723			0.0446635
$756$	−2.80103	−	3.17607i	−0.101872	−	0.115512i
$757$	0.493902			0.0179512			0.00897558	−	0.999960i	$-0.497143\pi$
$757$	0.493902			0.0179512			0.00897558	+	0.999960i	$0.497143\pi$
$758$	−4.48660	−	11.8704i	−0.162961	−	0.431153i
$759$	−2.45446	−	13.0375i	−0.0890914	−	0.473230i
$760$	9.43521	−	17.8309i	0.342251	−	0.646794i
$761$			38.4939i			1.39540i	0.716389	+	0.697701i	$0.245794\pi$
$761$			38.4939i			1.39540i	−0.716389	+	0.697701i	$0.754206\pi$
$762$	2.37652	+	6.28769i	0.0860924	+	0.227779i
$763$			6.90131i			0.249844i
$764$	21.0000	+	23.8118i	0.759753	+	0.861479i
$765$			14.7530i			0.533398i
$766$	−2.03214	−	5.37652i	−0.0734240	−	0.194262i
$767$	8.12854			0.293505
$768$	−2.43521	+	9.51105i	−0.0878732	+	0.343200i
$769$		−	12.0000i		−	0.432731i	−0.976312	−	0.216366i	$-0.930580\pi$
$769$		−	12.0000i		−	0.432731i	0.976312	−	0.216366i	$-0.0694203\pi$
$770$	−1.49810	−	2.45749i	−0.0539876	−	0.0885618i
$771$		−	1.68932i		−	0.0608392i
$772$	18.0222	+	20.4352i	0.648632	+	0.735479i
$773$	22.3765			0.804828			0.402414	−	0.915458i	$-0.368171\pi$
$773$	22.3765			0.804828			0.402414	+	0.915458i	$0.368171\pi$
$774$	22.6235	−	8.55087i	0.813184	−	0.307355i
$775$		−	0.613616i		−	0.0220417i
$776$	−2.64575	+	5.00000i	−0.0949769	+	0.179490i
$777$		−	2.11738i		−	0.0759605i
$778$	14.2249	−	5.37652i	0.509989	−	0.192758i
$779$			57.0588i			2.04434i
$780$	1.84085	−	1.62348i	0.0659129	−	0.0581297i
$781$	−6.00000	+	1.12957i	−0.214697	+	0.0404193i
$782$	−48.4939	+	18.3290i	−1.73414	+	0.655443i
$783$	−26.3060			−0.940099
$784$	−3.31174	+	26.2861i	−0.118276	+	0.938789i
$785$	1.62348			0.0579443
$786$	−5.43521	−	14.3802i	−0.193868	−	0.512926i
$787$	−48.0856			−1.71407			−0.857033	−	0.515261i	$-0.827695\pi$
$787$	−48.0856			−1.71407			−0.857033	+	0.515261i	$0.827695\pi$
$788$	−27.1109	−	30.7409i	−0.965785	−	1.09510i
$789$			13.3643i			0.475783i
$790$	−3.24695	+	1.22723i	−0.115521	+	0.0436630i
$791$	6.13616			0.218177
$792$	23.5067	+	7.28722i	0.835276	+	0.258940i
$793$	23.2470			0.825523
$794$	5.94487	−	2.24695i	0.210976	−	0.0797413i
$795$		−	5.90512i		−	0.209433i
$796$	13.1883	+	14.9541i	0.467446	+	0.530033i
$797$	−28.4939			−1.00931			−0.504653	−	0.863322i	$-0.668380\pi$
$797$	−28.4939			−1.00931			−0.504653	+	0.863322i	$0.668380\pi$
$798$	1.34275	+	3.55259i	0.0475329	+	0.125760i
$799$	36.6579			1.29686
$800$	1.32288	+	5.50000i	0.0467707	+	0.194454i
$801$	4.25915			0.150490
$802$	−23.3137	+	8.81174i	−0.823234	+	0.311153i
$803$	6.51873	−	1.22723i	0.230041	−	0.0433081i
$804$	−7.12957	+	6.28769i	−0.251441	+	0.221750i
$805$		−	4.00000i		−	0.140981i
$806$	1.62348	−	0.613616i	0.0571845	−	0.0216137i
$807$		−	12.5754i		−	0.442675i
$808$	−18.1174	−	9.58681i	−0.637367	−	0.337263i
$809$		−	33.7409i		−	1.18627i	−0.805105	−	0.593133i	$-0.797891\pi$
$809$		−	33.7409i		−	1.18627i	0.805105	−	0.593133i	$-0.202109\pi$
$810$	7.61057	−	2.87652i	0.267408	−	0.101071i
$811$	−50.6916			−1.78002			−0.890011	−	0.455938i	$-0.849304\pi$
$811$	−50.6916			−1.78002			−0.890011	+	0.455938i	$0.849304\pi$
$812$	−6.18826	−	7.01683i	−0.217165	−	0.246242i
$813$			13.7409i			0.481913i
$814$	13.7293	+	22.5216i	0.481211	+	0.789382i
$815$			21.7796i			0.762907i
$816$	−1.72533	+	13.6944i	−0.0603985	+	0.479399i
$817$	−46.4939			−1.62662
$818$	−14.0000	−	37.0405i	−0.489499	−	1.29509i
$819$		−	3.21961i		−	0.112502i
$820$	−10.5830	−	12.0000i	−0.369575	−	0.419058i
$821$		−	5.74085i		−	0.200357i	−0.994969	−	0.100179i	$-0.968059\pi$
$821$		−	5.74085i		−	0.200357i	0.994969	−	0.100179i	$-0.0319414\pi$
$822$	−1.84085	−	4.87043i	−0.0642069	−	0.169876i
$823$		−	7.74597i		−	0.270007i	−0.990845	−	0.135004i	$-0.956895\pi$
$823$		−	7.74597i		−	0.270007i	0.990845	−	0.135004i	$-0.0431046\pi$
$824$	−16.2968	−	8.62348i	−0.567727	−	0.300413i
$825$	−2.00000	+	0.376525i	−0.0696311	+	0.0131089i
$826$	−1.24695	−	3.29912i	−0.0433870	−	0.114791i
$827$	−26.9196			−0.936086			−0.468043	−	0.883706i	$-0.655041\pi$
$827$	−26.9196			−0.936086			−0.468043	+	0.883706i	$0.655041\pi$
$828$	22.6235	+	25.6526i	0.786220	+	0.891490i
$829$	−12.4939			−0.433931			−0.216966	−	0.976179i	$-0.569616\pi$
$829$	−12.4939			−0.433931			−0.216966	+	0.976179i	$0.569616\pi$
$830$	10.2470	−	3.87298i	0.355677	−	0.134433i
$831$	10.1209			0.351091
$832$	−13.2288	+	9.00000i	−0.458625	+	0.312019i
$833$			37.2470i			1.29053i
$834$	−4.37652	−	11.5792i	−0.151547	−	0.400955i
$835$	1.84085			0.0637052
$836$	−37.3176	−	29.0808i	−1.29066	−	1.00578i
$837$	−2.11738			−0.0731873
$838$	10.3917	+	27.4939i	0.358976	+	0.949761i
$839$			7.74597i			0.267420i	0.991020	+	0.133710i	$0.0426891\pi$
$839$			7.74597i			0.267420i	−0.991020	+	0.133710i	$0.957311\pi$
$840$	−0.941312	−	0.498095i	−0.0324783	−	0.0171859i
$841$	−29.1174			−1.00405
$842$	19.5164	−	7.37652i	0.672581	−	0.254212i
$843$		0			0
$844$	8.85768	−	7.81174i	0.304894	−	0.268891i
$845$	−9.00000			−0.309609
$846$	−8.55087	−	22.6235i	−0.293985	−	0.777811i
$847$	−6.28769	+	2.45446i	−0.216048	+	0.0843364i
$848$	−4.81174	+	38.1920i	−0.165236	+	1.31152i
$849$		−	6.25915i		−	0.214813i
$850$	2.81174	+	7.43916i	0.0964418	+	0.255161i
$851$			36.6579i			1.25662i
$852$	−1.69436	+	1.49429i	−0.0580478	+	0.0511934i
$853$		−	1.24695i		−	0.0426948i	−0.999772	−	0.0213474i	$-0.993204\pi$
$853$		−	1.24695i		−	0.0426948i	0.999772	−	0.0213474i	$-0.00679560\pi$
$854$	−3.56618	−	9.43521i	−0.122032	−	0.322866i
$855$	−18.7115			−0.639921
$856$	−21.0000	+	39.6863i	−0.717765	+	1.35645i
$857$			25.6235i			0.875281i	0.899150	+	0.437641i	$0.144186\pi$
$857$			25.6235i			0.875281i	−0.899150	+	0.437641i	$0.855814\pi$
$858$	−2.99619	−	4.91498i	−0.102288	−	0.167795i
$859$			14.6473i			0.499759i	0.968277	+	0.249879i	$0.0803909\pi$
$859$			14.6473i			0.499759i	−0.968277	+	0.249879i	$0.919609\pi$
$860$	9.77810	−	8.62348i	0.333431	−	0.294058i
$861$	3.01220			0.102655
$862$	−32.8704	+	12.4239i	−1.11957	+	0.423158i
$863$		−	12.6549i		−	0.430778i	−0.976528	−	0.215389i	$-0.930898\pi$
$863$		−	12.6549i		−	0.430778i	0.976528	−	0.215389i	$-0.0691019\pi$
$864$	18.9786	−	4.56479i	0.645665	−	0.155297i
$865$			1.24695i			0.0423976i
$866$	28.1071	−	10.6235i	0.955117	−	0.361000i
$867$			8.97320i			0.304746i
$868$	−0.498095	−	0.564787i	−0.0169065	−	0.0191701i
$869$	1.50610	+	8.00000i	0.0510909	+	0.271381i
$870$	−6.18826	+	2.33894i	−0.209802	+	0.0792976i
$871$	−15.4919			−0.524924
$872$	−28.1174	−	14.8783i	−0.952175	−	0.503843i
$873$	5.24695			0.177582
$874$	−23.2470	−	61.5057i	−0.786340	−	2.08046i
$875$	−0.613616			−0.0207440
$876$	1.84085	−	1.62348i	0.0621965	−	0.0548521i
$877$		−	53.2470i		−	1.79802i	−0.437926	−	0.899011i	$-0.644287\pi$
$877$		−	53.2470i		−	1.79802i	0.437926	−	0.899011i	$-0.355713\pi$
$878$	6.49390	−	2.45446i	0.219159	−	0.0828342i
$879$	17.4843			0.589731
$880$	13.2420	−	0.805529i	0.446388	−	0.0271544i
$881$	−44.4939			−1.49904			−0.749519	−	0.661983i	$-0.769715\pi$
$881$	−44.4939			−1.49904			−0.749519	+	0.661983i	$0.769715\pi$
$882$	22.9870	−	8.68826i	0.774012	−	0.292549i
$883$		−	24.2341i		−	0.815542i	−0.913084	−	0.407771i	$-0.866306\pi$
$883$		−	24.2341i		−	0.815542i	0.913084	−	0.407771i	$-0.133694\pi$
$884$	−16.8704	+	14.8783i	−0.567414	+	0.500412i
$885$	−2.49390			−0.0838316
$886$	−7.93725	−	21.0000i	−0.266657	−	0.705509i
$887$	36.2754			1.21801			0.609004	−	0.793167i	$-0.291569\pi$
$887$	36.2754			1.21801			0.609004	+	0.793167i	$0.291569\pi$
$888$	8.62664	+	4.56479i	0.289491	+	0.153184i
$889$	4.75305			0.159412
$890$	2.14766	−	0.811738i	0.0719896	−	0.0272095i
$891$	−3.53016	−	18.7513i	−0.118265	−	0.628192i
$892$	24.2470	+	27.4935i	0.811848	+	0.920549i
$893$			46.4939i			1.55586i
$894$	6.79954	−	2.56998i	0.227411	−	0.0859532i
$895$			1.60981i			0.0538099i
$896$	5.68216	+	3.98850i	0.189828	+	0.133247i
$897$		−	8.00000i		−	0.267112i
$898$	−37.6939	+	14.2470i	−1.25786	+	0.475427i
$899$	−4.67789			−0.156016
$900$	3.93521	−	3.47053i	0.131174	−	0.115684i
$901$			54.1174i			1.80291i
$902$	−32.0394	+	19.5314i	−1.06680	+	0.650324i
$903$			2.45446i			0.0816794i
$904$	−13.2288	+	25.0000i	−0.439982	+	0.831488i
$905$	6.00000			0.199447
$906$	−0.376525	−	0.996190i	−0.0125092	−	0.0330962i
$907$			4.29531i			0.142623i	0.997454	+	0.0713117i	$0.0227185\pi$
$907$			4.29531i			0.142623i	−0.997454	+	0.0713117i	$0.977281\pi$
$908$	27.4935	−	24.2470i	0.912402	−	0.804663i
$909$			19.0122i			0.630595i
$910$	−0.613616	−	1.62348i	−0.0203412	−	0.0538177i
$911$		−	19.3252i		−	0.640271i	−0.947372	−	0.320136i	$-0.896272\pi$
$911$		−	19.3252i		−	0.640271i	0.947372	−	0.320136i	$-0.103728\pi$
$912$	−17.3688	−	2.18826i	−0.575138	−	0.0724606i
$913$	−4.75305	−	25.2470i	−0.157303	−	0.835552i
$914$	2.43521	+	6.44297i	0.0805497	+	0.213114i
$915$	−7.13235			−0.235788
$916$	−24.7409	+	21.8194i	−0.817461	+	0.720933i
$917$	−10.8704			−0.358973
$918$	25.6700	−	9.70234i	0.847235	−	0.320225i
$919$	−2.45446			−0.0809653			−0.0404826	−	0.999180i	$-0.512890\pi$
$919$	−2.45446			−0.0809653			−0.0404826	+	0.999180i	$0.512890\pi$
$920$	16.2968	+	8.62348i	0.537291	+	0.284308i
$921$			1.74085i			0.0573630i
$922$	10.1883	+	26.9556i	0.335533	+	0.887736i
$923$	−3.68170			−0.121185
$924$	−1.53521	+	1.97004i	−0.0505047	+	0.0648095i
$925$	5.62348			0.184899
$926$	−12.8462	−	33.9878i	−0.422152	−	1.11691i
$927$			17.1017i			0.561695i
$928$	41.9291	−	10.0849i	1.37639	−	0.331053i
$929$	20.8704			0.684736			0.342368	−	0.939566i	$-0.388771\pi$
$929$	20.8704			0.684736			0.342368	+	0.939566i	$0.388771\pi$
$930$	−0.498095	+	0.188262i	−0.0163332	+	0.00617336i
$931$	−47.2409			−1.54826
$932$	−12.7307	−	14.4352i	−0.417007	−	0.472841i
$933$	−18.6357			−0.610105
$934$	−19.8630	−	52.5526i	−0.649938	−	1.71957i
$935$	18.3290	−	3.45065i	0.599421	−	0.112848i
$936$	13.1174	+	6.94106i	0.428755	+	0.226876i
$937$		−	2.00000i		−	0.0653372i	−0.999466	−	0.0326686i	$-0.989599\pi$
$937$		−	2.00000i		−	0.0653372i	0.999466	−	0.0326686i	$-0.0104006\pi$
$938$	2.37652	+	6.28769i	0.0775963	+	0.205300i
$939$			8.12854i			0.265265i
$940$	−8.62348	−	9.77810i	−0.281267	−	0.318927i
$941$			34.1174i			1.11219i	0.831117	+	0.556097i	$0.187702\pi$
$941$			34.1174i			1.11219i	−0.831117	+	0.556097i	$0.812298\pi$
$942$	−0.498095	−	1.31784i	−0.0162288	−	0.0429374i
$943$	−52.1499			−1.69823
$944$	16.1296	+	2.03214i	0.524973	+	0.0661404i
$945$			2.11738i			0.0688783i
$946$	−15.9150	−	26.1071i	−0.517441	−	0.848814i
$947$			18.5600i			0.603119i	0.953447	+	0.301560i	$0.0975073\pi$
$947$			18.5600i			0.603119i	−0.953447	+	0.301560i	$0.902493\pi$
$948$	1.99238	+	2.25915i	0.0647095	+	0.0733737i
$949$	4.00000			0.129845
$950$	−9.43521	+	3.56618i	−0.306119	+	0.115702i
$951$		−	7.89750i		−	0.256094i
$952$	8.62664	+	4.56479i	0.279591	+	0.147946i
$953$			27.3643i			0.886418i	0.896418	+	0.443209i	$0.146160\pi$
$953$			27.3643i			0.886418i	−0.896418	+	0.443209i	$0.853840\pi$
$954$	33.3986	−	12.6235i	1.08132	−	0.408700i
$955$		−	15.8745i		−	0.513687i
$956$	39.1124	−	34.4939i	1.26499	−	1.11561i
$957$	2.87043	+	15.2470i	0.0927877	+	0.492864i
$958$	40.3765	−	15.2609i	1.30451	−	0.493057i
$959$	−3.68170			−0.118888
$960$	4.05869	−	2.76127i	0.130994	−	0.0891197i
$961$	30.6235			0.987854
$962$	5.62348	+	14.8783i	0.181308	+	0.479696i
$963$	41.6464			1.34204
$964$	−9.58681	−	10.8704i	−0.308771	−	0.350113i
$965$		−	13.6235i		−	0.438555i
$966$	−3.24695	+	1.22723i	−0.104469	+	0.0394855i
$967$	50.3090			1.61783			0.808915	−	0.587926i	$-0.200055\pi$
$967$	50.3090			1.61783			0.808915	+	0.587926i	$0.200055\pi$
$968$	3.55544	−	30.9089i	0.114276	−	0.993449i
$969$	−24.6113			−0.790628
$970$	2.64575	−	1.00000i	0.0849500	−	0.0321081i
$971$			50.5401i			1.62191i	0.585110	+	0.810954i	$0.301051\pi$
$971$			50.5401i			1.62191i	−0.585110	+	0.810954i	$0.698949\pi$
$972$	−18.3643	−	20.8232i	−0.589036	−	0.667904i
$973$	−8.75305			−0.280610
$974$	21.5883	+	57.1174i	0.691735	+	1.83016i
$975$	−1.22723			−0.0393029
$976$	46.1292	+	5.81174i	1.47656	+	0.186029i
$977$	3.50610			0.112170			0.0560850	−	0.998426i	$-0.482138\pi$
$977$	3.50610			0.112170			0.0560850	+	0.998426i	$0.482138\pi$
$978$	17.6793	−	6.68216i	0.565323	−	0.213672i
$979$	−0.996190	−	5.29150i	−0.0318384	−	0.169117i
$980$	9.93521	−	8.76203i	0.317369	−	0.279893i
$981$			29.5061i			0.942057i
$982$	48.7995	−	18.4445i	1.55726	−	0.588587i
$983$		−	24.0030i		−	0.765578i	−0.923836	−	0.382789i	$-0.874964\pi$
$983$		−	24.0030i		−	0.765578i	0.923836	−	0.382789i	$-0.125036\pi$
$984$	−6.49390	+	12.2723i	−0.207018	+	0.391227i
$985$			20.4939i			0.652990i
$986$	56.7122	−	21.4352i	1.80609	−	0.682636i
$987$	2.45446			0.0781265
$988$	−18.8704	−	21.3971i	−0.600348	−	0.680731i
$989$		−	42.4939i		−	1.35123i
$990$	−6.40501	−	10.5068i	−0.203565	−	0.333929i
$991$			10.9656i			0.348333i	0.984716	+	0.174167i	$0.0557231\pi$
$991$			10.9656i			0.348333i	−0.984716	+	0.174167i	$0.944277\pi$
$992$	3.37489	−	0.811738i	0.107153	−	0.0257727i
$993$	13.5061			0.428603
$994$	0.564787	+	1.49429i	0.0179140	+	0.0473959i
$995$		−	9.96939i		−	0.316051i
$996$	−6.28769	−	7.12957i	−0.199233	−	0.225909i
$997$		−	3.74085i		−	0.118474i	−0.998244	−	0.0592370i	$-0.981133\pi$
$997$		−	3.74085i		−	0.118474i	0.998244	−	0.0592370i	$-0.0188668\pi$
$998$	−0.804903	−	2.12957i	−0.0254788	−	0.0674105i
$999$		−	19.4047i		−	0.613937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.d.c.131.3	yes	8
4.3	odd	2	inner	220.2.d.c.131.8	yes	8
8.3	odd	2		3520.2.f.i.2111.3		8
8.5	even	2		3520.2.f.i.2111.6		8
11.10	odd	2	inner	220.2.d.c.131.5	yes	8
44.43	even	2	inner	220.2.d.c.131.2	✓	8
88.21	odd	2		3520.2.f.i.2111.5		8
88.43	even	2		3520.2.f.i.2111.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.d.c.131.2	✓	8	44.43	even	2	inner
220.2.d.c.131.3	yes	8	1.1	even	1	trivial
220.2.d.c.131.5	yes	8	11.10	odd	2	inner
220.2.d.c.131.8	yes	8	4.3	odd	2	inner
3520.2.f.i.2111.3		8	8.3	odd	2
3520.2.f.i.2111.4		8	88.43	even	2
3520.2.f.i.2111.5		8	88.21	odd	2
3520.2.f.i.2111.6		8	8.5	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32288 + 0.500000i) q^{2} -0.613616i q^{3} +(1.50000 - 1.32288i) q^{4} -1.00000 q^{5} +(0.306808 + 0.811738i) q^{6} +0.613616 q^{7} +(-1.32288 + 2.50000i) q^{8} +2.62348 q^{9} +(1.32288 - 0.500000i) q^{10} +(-0.613616 - 3.25937i) q^{11} +(-0.811738 - 0.920424i) q^{12} -2.00000i q^{13} +(-0.811738 + 0.306808i) q^{14} +0.613616i q^{15} +(0.500000 - 3.96863i) q^{16} -5.62348i q^{17} +(-3.47053 + 1.31174i) q^{18} +7.13235 q^{19} +(-1.50000 + 1.32288i) q^{20} -0.376525i q^{21} +(2.44142 + 4.00493i) q^{22} +6.51873i q^{23} +(1.53404 + 0.811738i) q^{24} +1.00000 q^{25} +(1.00000 + 2.64575i) q^{26} -3.45065i q^{27} +(0.920424 - 0.811738i) q^{28} -7.62348i q^{29} +(-0.306808 - 0.811738i) q^{30} -0.613616i q^{31} +(1.32288 + 5.50000i) q^{32} +(-2.00000 + 0.376525i) q^{33} +(2.81174 + 7.43916i) q^{34} -0.613616 q^{35} +(3.93521 - 3.47053i) q^{36} +5.62348 q^{37} +(-9.43521 + 3.56618i) q^{38} -1.22723 q^{39} +(1.32288 - 2.50000i) q^{40} +8.00000i q^{41} +(0.188262 + 0.498095i) q^{42} -6.51873 q^{43} +(-5.23216 - 4.07731i) q^{44} -2.62348 q^{45} +(-3.25937 - 8.62348i) q^{46} +6.51873i q^{47} +(-2.43521 - 0.306808i) q^{48} -6.62348 q^{49} +(-1.32288 + 0.500000i) q^{50} -3.45065 q^{51} +(-2.64575 - 3.00000i) q^{52} -9.62348 q^{53} +(1.72533 + 4.56479i) q^{54} +(0.613616 + 3.25937i) q^{55} +(-0.811738 + 1.53404i) q^{56} -4.37652i q^{57} +(3.81174 + 10.0849i) q^{58} +4.06427i q^{59} +(0.811738 + 0.920424i) q^{60} +11.6235i q^{61} +(0.306808 + 0.811738i) q^{62} +1.60981 q^{63} +(-4.50000 - 6.61438i) q^{64} +2.00000i q^{65} +(2.45749 - 1.49810i) q^{66} -7.74597i q^{67} +(-7.43916 - 8.43521i) q^{68} +4.00000 q^{69} +(0.811738 - 0.306808i) q^{70} -1.84085i q^{71} +(-3.47053 + 6.55869i) q^{72} +2.00000i q^{73} +(-7.43916 + 2.81174i) q^{74} -0.613616i q^{75} +(10.6985 - 9.43521i) q^{76} +(-0.376525 - 2.00000i) q^{77} +(1.62348 - 0.613616i) q^{78} -2.45446 q^{79} +(-0.500000 + 3.96863i) q^{80} +5.75305 q^{81} +(-4.00000 - 10.5830i) q^{82} +7.74597 q^{83} +(-0.498095 - 0.564787i) q^{84} +5.62348i q^{85} +(8.62348 - 3.25937i) q^{86} -4.67789 q^{87} +(8.96016 + 2.77770i) q^{88} +1.62348 q^{89} +(3.47053 - 1.31174i) q^{90} -1.22723i q^{91} +(8.62348 + 9.77810i) q^{92} -0.376525 q^{93} +(-3.25937 - 8.62348i) q^{94} -7.13235 q^{95} +(3.37489 - 0.811738i) q^{96} +2.00000 q^{97} +(8.76203 - 3.31174i) q^{98} +(-1.60981 - 8.55087i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{4} - 8 q^{5} - 20 q^{9} + 14 q^{12} + 14 q^{14} + 4 q^{16} - 12 q^{20} - 14 q^{22} + 8 q^{25} + 8 q^{26} - 16 q^{33} + 2 q^{34} - 30 q^{36} + 4 q^{37} - 14 q^{38} + 22 q^{42} - 14 q^{44} + 20 q^{45}+ \cdots + 16 q^{97}+O(q^{100}) \) 8 * q + 12 * q^4 - 8 * q^5 - 20 * q^9 + 14 * q^12 + 14 * q^14 + 4 * q^16 - 12 * q^20 - 14 * q^22 + 8 * q^25 + 8 * q^26 - 16 * q^33 + 2 * q^34 - 30 * q^36 + 4 * q^37 - 14 * q^38 + 22 * q^42 - 14 * q^44 + 20 * q^45 + 42 * q^48 - 12 * q^49 - 36 * q^53 + 14 * q^56 + 10 * q^58 - 14 * q^60 - 36 * q^64 - 22 * q^66 + 32 * q^69 - 14 * q^70 - 44 * q^77 - 28 * q^78 - 4 * q^80 + 128 * q^81 - 32 * q^82 + 28 * q^86 - 14 * q^88 - 28 * q^89 + 28 * q^92 - 44 * q^93 + 16 * q^97

Introduction

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