LMFDB - Embedded newform 572.2.b.c.571.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(571,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("572.571");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.b (of order $2$, degree $1$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			571.12
Character	$\chi$	$=$	572.571
Dual form			572.2.b.c.571.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28473 + 0.591168i) q^{2} +1.41709i q^{3} +(1.30104 - 1.51898i) q^{4} +1.72500i q^{5} +(-0.837739 - 1.82057i) q^{6} +3.58187i q^{7} +(-0.773512 + 2.72060i) q^{8} +0.991852 q^{9} +O(q^{10})$	\(q+(-1.28473 + 0.591168i) q^{2} +1.41709i q^{3} +(1.30104 - 1.51898i) q^{4} +1.72500i q^{5} +(-0.837739 - 1.82057i) q^{6} +3.58187i q^{7} +(-0.773512 + 2.72060i) q^{8} +0.991852 q^{9} +(-1.01976 - 2.21615i) q^{10} +(3.26484 + 0.583781i) q^{11} +(2.15253 + 1.84369i) q^{12} +(1.11210 + 3.42976i) q^{13} +(-2.11749 - 4.60173i) q^{14} -2.44448 q^{15} +(-0.614582 - 3.95250i) q^{16} -6.49142i q^{17} +(-1.27426 + 0.586351i) q^{18} -1.29651i q^{19} +(2.62023 + 2.24430i) q^{20} -5.07584 q^{21} +(-4.53954 + 1.18007i) q^{22} +5.30582i q^{23} +(-3.85534 - 1.09614i) q^{24} +2.02438 q^{25} +(-3.45630 - 3.74886i) q^{26} +5.65682i q^{27} +(5.44078 + 4.66017i) q^{28} -0.722301i q^{29} +(3.14049 - 1.44510i) q^{30} -2.71352 q^{31} +(3.12616 + 4.71456i) q^{32} +(-0.827271 + 4.62658i) q^{33} +(3.83752 + 8.33969i) q^{34} -6.17873 q^{35} +(1.29044 - 1.50660i) q^{36} -9.05093i q^{37} +(0.766454 + 1.66566i) q^{38} +(-4.86028 + 1.57594i) q^{39} +(-4.69304 - 1.33431i) q^{40} -8.00093 q^{41} +(6.52107 - 3.00067i) q^{42} +11.6226 q^{43} +(5.13445 - 4.19970i) q^{44} +1.71094i q^{45} +(-3.13663 - 6.81653i) q^{46} -7.04449 q^{47} +(5.60106 - 0.870918i) q^{48} -5.82982 q^{49} +(-2.60077 + 1.19675i) q^{50} +9.19893 q^{51} +(6.65661 + 2.77301i) q^{52} -12.2853 q^{53} +(-3.34413 - 7.26746i) q^{54} +(-1.00702 + 5.63185i) q^{55} +(-9.74485 - 2.77062i) q^{56} +1.83727 q^{57} +(0.427001 + 0.927959i) q^{58} -7.05441 q^{59} +(-3.18037 + 3.71311i) q^{60} +2.72151i q^{61} +(3.48613 - 1.60415i) q^{62} +3.55269i q^{63} +(-6.80336 - 4.20884i) q^{64} +(-5.91633 + 1.91837i) q^{65} +(-1.67227 - 6.43294i) q^{66} +6.90178 q^{67} +(-9.86031 - 8.44560i) q^{68} -7.51883 q^{69} +(7.93797 - 3.65267i) q^{70} +3.38095 q^{71} +(-0.767209 + 2.69844i) q^{72} +8.15467 q^{73} +(5.35062 + 11.6280i) q^{74} +2.86873i q^{75} +(-1.96937 - 1.68681i) q^{76} +(-2.09103 + 11.6943i) q^{77} +(5.31248 - 4.89790i) q^{78} -10.5217 q^{79} +(6.81807 - 1.06015i) q^{80} -5.04067 q^{81} +(10.2790 - 4.72989i) q^{82} -5.99135i q^{83} +(-6.60388 + 7.71009i) q^{84} +11.1977 q^{85} +(-14.9318 + 6.87088i) q^{86} +1.02357 q^{87} +(-4.11363 + 8.43078i) q^{88} -14.6453i q^{89} +(-1.01145 - 2.19809i) q^{90} +(-12.2850 + 3.98339i) q^{91} +(8.05942 + 6.90309i) q^{92} -3.84531i q^{93} +(9.05024 - 4.16447i) q^{94} +2.23648 q^{95} +(-6.68097 + 4.43006i) q^{96} +0.803270i q^{97} +(7.48972 - 3.44640i) q^{98} +(3.23824 + 0.579024i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{4} - 32 q^{9}+O(q^{10}) $ 56 * q + 4 * q^4 - 32 * q^9	$ 56 q + 4 q^{4} - 32 q^{9} - 12 q^{14} - 4 q^{16} - 4 q^{22} - 192 q^{25} + 4 q^{26} + 28 q^{36} + 24 q^{38} + 88 q^{42} + 56 q^{48} + 40 q^{49} - 8 q^{53} - 68 q^{56} + 28 q^{64} - 76 q^{66} - 16 q^{69} + 32 q^{77} + 108 q^{78} - 152 q^{81} - 60 q^{82} + 52 q^{88} + 132 q^{92}+O(q^{100}) $ 56 * q + 4 * q^4 - 32 * q^9 - 12 * q^14 - 4 * q^16 - 4 * q^22 - 192 * q^25 + 4 * q^26 + 28 * q^36 + 24 * q^38 + 88 * q^42 + 56 * q^48 + 40 * q^49 - 8 * q^53 - 68 * q^56 + 28 * q^64 - 76 * q^66 - 16 * q^69 + 32 * q^77 + 108 * q^78 - 152 * q^81 - 60 * q^82 + 52 * q^88 + 132 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.28473	+	0.591168i	−0.908438	+	0.418019i
$2$	−1.28473	+	0.591168i	−0.908438	+	0.418019i
$3$			1.41709i			0.818158i	0.912499	+	0.409079i	$0.134150\pi$
$3$			1.41709i			0.818158i	−0.912499	+	0.409079i	$0.865850\pi$
$4$	1.30104	−	1.51898i	0.650521	−	0.759488i
$5$			1.72500i			0.771443i	0.922615	+	0.385722i	$0.126047\pi$
$5$			1.72500i			0.771443i	−0.922615	+	0.385722i	$0.873953\pi$
$6$	−0.837739	−	1.82057i	−0.342005	−	0.743246i
$7$			3.58187i			1.35382i	0.736065	+	0.676910i	$0.236682\pi$
$7$			3.58187i			1.35382i	−0.736065	+	0.676910i	$0.763318\pi$
$8$	−0.773512	+	2.72060i	−0.273478	+	0.961878i
$9$	0.991852			0.330617
$10$	−1.01976	−	2.21615i	−0.322478	−	0.700809i
$11$	3.26484	+	0.583781i	0.984387	+	0.176017i
$11$	3.26484	+	0.583781i	0.984387	+	0.176017i
$12$	2.15253	+	1.84369i	0.621382	+	0.532229i
$13$	1.11210	+	3.42976i	0.308441	+	0.951244i
$13$	1.11210	+	3.42976i	0.308441	+	0.951244i
$14$	−2.11749	−	4.60173i	−0.565922	−	1.22986i
$15$	−2.44448			−0.631162
$16$	−0.614582	−	3.95250i	−0.153645	−	0.988126i
$17$		−	6.49142i		−	1.57440i	−0.616698	−	0.787200i	$-0.711530\pi$
$17$		−	6.49142i		−	1.57440i	0.616698	−	0.787200i	$-0.288470\pi$
$18$	−1.27426	+	0.586351i	−0.300346	+	0.138204i
$19$		−	1.29651i		−	0.297439i	−0.988879	−	0.148720i	$-0.952485\pi$
$19$		−	1.29651i		−	0.297439i	0.988879	−	0.148720i	$-0.0475152\pi$
$20$	2.62023	+	2.24430i	0.585902	+	0.501840i
$21$	−5.07584			−1.10764
$22$	−4.53954	+	1.18007i	−0.967833	+	0.251592i
$23$			5.30582i			1.10634i	0.833068	+	0.553170i	$0.186582\pi$
$23$			5.30582i			1.10634i	−0.833068	+	0.553170i	$0.813418\pi$
$24$	−3.85534	−	1.09614i	−0.786969	−	0.223748i
$25$	2.02438			0.404875
$26$	−3.45630	−	3.74886i	−0.677837	−	0.735212i
$27$			5.65682i			1.08866i
$28$	5.44078	+	4.66017i	1.02821	+	0.880689i
$29$		−	0.722301i		−	0.134128i	−0.997749	−	0.0670640i	$-0.978637\pi$
$29$		−	0.722301i		−	0.134128i	0.997749	−	0.0670640i	$-0.0213632\pi$
$30$	3.14049	−	1.44510i	0.573372	−	0.263838i
$31$	−2.71352			−0.487363			−0.243681	−	0.969855i	$-0.578355\pi$
$31$	−2.71352			−0.487363			−0.243681	+	0.969855i	$0.578355\pi$
$32$	3.12616	+	4.71456i	0.552633	+	0.833425i
$33$	−0.827271	+	4.62658i	−0.144009	+	0.805384i
$34$	3.83752	+	8.33969i	0.658129	+	1.43025i
$35$	−6.17873			−1.04440
$36$	1.29044	−	1.50660i	0.215073	−	0.251100i
$37$		−	9.05093i		−	1.48796i	−0.668200	−	0.743982i	$-0.732935\pi$
$37$		−	9.05093i		−	1.48796i	0.668200	−	0.743982i	$-0.267065\pi$
$38$	0.766454	+	1.66566i	0.124335	+	0.270205i
$39$	−4.86028	+	1.57594i	−0.778268	+	0.252353i
$40$	−4.69304	−	1.33431i	−0.742034	−	0.210973i
$41$	−8.00093			−1.24954			−0.624768	−	0.780811i	$-0.714806\pi$
$41$	−8.00093			−1.24954			−0.624768	+	0.780811i	$0.714806\pi$
$42$	6.52107	−	3.00067i	1.00622	−	0.463014i
$43$	11.6226			1.77242			0.886211	−	0.463281i	$-0.153328\pi$
$43$	11.6226			1.77242			0.886211	+	0.463281i	$0.153328\pi$
$44$	5.13445	−	4.19970i	0.774047	−	0.633128i
$45$			1.71094i			0.255053i
$46$	−3.13663	−	6.81653i	−0.462471	−	1.00504i
$47$	−7.04449			−1.02754			−0.513772	−	0.857927i	$-0.671752\pi$
$47$	−7.04449			−1.02754			−0.513772	+	0.857927i	$0.671752\pi$
$48$	5.60106	−	0.870918i	0.808443	−	0.125706i
$49$	−5.82982			−0.832831
$50$	−2.60077	+	1.19675i	−0.367804	+	0.169245i
$51$	9.19893			1.28811
$52$	6.65661	+	2.77301i	0.923106	+	0.384547i
$53$	−12.2853			−1.68751			−0.843755	−	0.536729i	$-0.819660\pi$
$53$	−12.2853			−1.68751			−0.843755	+	0.536729i	$0.819660\pi$
$54$	−3.34413	−	7.26746i	−0.455078	−	0.988976i
$55$	−1.00702	+	5.63185i	−0.135787	+	0.759399i
$56$	−9.74485	−	2.77062i	−1.30221	−	0.370240i
$57$	1.83727			0.243352
$58$	0.427001	+	0.927959i	0.0560680	+	0.121847i
$59$	−7.05441			−0.918406			−0.459203	−	0.888331i	$-0.651865\pi$
$59$	−7.05441			−0.918406			−0.459203	+	0.888331i	$0.651865\pi$
$60$	−3.18037	+	3.71311i	−0.410584	+	0.479361i
$61$			2.72151i			0.348453i	0.984706	+	0.174227i	$0.0557425\pi$
$61$			2.72151i			0.348453i	−0.984706	+	0.174227i	$0.944257\pi$
$62$	3.48613	−	1.60415i	0.442739	−	0.203727i
$63$			3.55269i			0.447597i
$64$	−6.80336	−	4.20884i	−0.850420	−	0.526105i
$65$	−5.91633	+	1.91837i	−0.733830	+	0.237944i
$66$	−1.67227	−	6.43294i	−0.205842	−	0.791841i
$67$	6.90178			0.843187			0.421593	−	0.906785i	$-0.361471\pi$
$67$	6.90178			0.843187			0.421593	+	0.906785i	$0.361471\pi$
$68$	−9.86031	−	8.44560i	−1.19574	−	1.02418i
$69$	−7.51883			−0.905161
$70$	7.93797	−	3.65267i	0.948769	−	0.436577i
$71$	3.38095			0.401245			0.200623	−	0.979669i	$-0.435704\pi$
$71$	3.38095			0.401245			0.200623	+	0.979669i	$0.435704\pi$
$72$	−0.767209	+	2.69844i	−0.0904165	+	0.318014i
$73$	8.15467			0.954432			0.477216	−	0.878786i	$-0.341646\pi$
$73$	8.15467			0.954432			0.477216	+	0.878786i	$0.341646\pi$
$74$	5.35062	+	11.6280i	0.621997	+	1.35172i
$75$			2.86873i			0.331252i
$76$	−1.96937	−	1.68681i	−0.225902	−	0.193490i
$77$	−2.09103	+	11.6943i	−0.238295	+	1.33268i
$78$	5.31248	−	4.89790i	0.601520	−	0.554578i
$79$	−10.5217			−1.18378			−0.591892	−	0.806018i	$-0.701619\pi$
$79$	−10.5217			−1.18378			−0.591892	+	0.806018i	$0.701619\pi$
$80$	6.81807	−	1.06015i	0.762283	−	0.118529i
$81$	−5.04067			−0.560075
$82$	10.2790	−	4.72989i	1.13513	−	0.522329i
$83$		−	5.99135i		−	0.657636i	−0.944393	−	0.328818i	$-0.893350\pi$
$83$		−	5.99135i		−	0.657636i	0.944393	−	0.328818i	$-0.106650\pi$
$84$	−6.60388	+	7.71009i	−0.720543	+	0.841239i
$85$	11.1977			1.21456
$86$	−14.9318	+	6.87088i	−1.61014	+	0.740906i
$87$	1.02357			0.109738
$88$	−4.11363	+	8.43078i	−0.438514	+	0.898724i
$89$		−	14.6453i		−	1.55240i	−0.630487	−	0.776200i	$-0.717145\pi$
$89$		−	14.6453i		−	1.55240i	0.630487	−	0.776200i	$-0.282855\pi$
$90$	−1.01145	−	2.19809i	−0.106617	−	0.231700i
$91$	−12.2850	+	3.98339i	−1.28781	+	0.417573i
$92$	8.05942	+	6.90309i	0.840252	+	0.719697i
$93$		−	3.84531i		−	0.398740i
$94$	9.05024	−	4.16447i	0.933461	−	0.429533i
$95$	2.23648			0.229458
$96$	−6.68097	+	4.43006i	−0.681873	+	0.452141i
$97$			0.803270i			0.0815597i	0.999168	+	0.0407798i	$0.0129842\pi$
$97$			0.803270i			0.0815597i	−0.999168	+	0.0407798i	$0.987016\pi$
$98$	7.48972	−	3.44640i	0.756576	−	0.348139i
$99$	3.23824	+	0.579024i	0.325456	+	0.0581941i
$100$	2.63380	−	3.07498i	0.263380	−	0.307498i
$101$		−	11.9780i		−	1.19186i	−0.803038	−	0.595928i	$-0.796784\pi$
$101$		−	11.9780i		−	1.19186i	0.803038	−	0.595928i	$-0.203216\pi$
$102$	−11.8181	+	5.43811i	−1.17017	+	0.538453i
$103$			0.871384i			0.0858600i	0.999078	+	0.0429300i	$0.0136692\pi$
$103$			0.871384i			0.0858600i	−0.999078	+	0.0429300i	$0.986331\pi$
$104$	−10.1912	+	0.372619i	−0.999332	+	0.0365383i
$105$		−	8.75582i		−	0.854481i
$106$	15.7832	−	7.26265i	1.53300	−	0.705410i
$107$	−6.28024			−0.607134			−0.303567	−	0.952810i	$-0.598178\pi$
$107$	−6.28024			−0.607134			−0.303567	+	0.952810i	$0.598178\pi$
$108$	8.59258	+	7.35976i	0.826821	+	0.708193i
$109$	14.3971			1.37899			0.689495	−	0.724291i	$-0.257833\pi$
$109$	14.3971			1.37899			0.689495	+	0.724291i	$0.257833\pi$
$110$	−2.03562	−	7.83071i	−0.194089	−	0.746628i
$111$	12.8260			1.21739
$112$	14.1574	−	2.20135i	1.33775	−	0.208008i
$113$	5.96916			0.561531			0.280766	−	0.959776i	$-0.409412\pi$
$113$	5.96916			0.561531			0.280766	+	0.959776i	$0.409412\pi$
$114$	−2.36039	+	1.08613i	−0.221071	+	0.101726i
$115$	−9.15254			−0.853478
$116$	−1.09716	−	0.939744i	−0.101869	−	0.0872530i
$117$	1.10304	+	3.40181i	0.101976	+	0.314498i
$118$	9.06298	−	4.17034i	0.834315	−	0.383911i
$119$	23.2514			2.13146
$120$	1.89084	−	6.65046i	0.172609	−	0.607101i
$121$	10.3184	+	3.81191i	0.938036	+	0.346537i
$122$	−1.60887	−	3.49639i	−0.145660	−	0.316548i
$123$		−	11.3381i		−	1.02232i
$124$	−3.53040	+	4.12177i	−0.317039	+	0.370146i
$125$			12.1170i			1.08378i
$126$	−2.10023	−	4.56423i	−0.187104	−	0.406614i
$127$	3.26004			0.289282			0.144641	−	0.989484i	$-0.453797\pi$
$127$	3.26004			0.289282			0.144641	+	0.989484i	$0.453797\pi$
$128$	11.2286	+	1.38528i	0.992476	+	0.122442i
$129$			16.4702i			1.45012i
$130$	6.46678	−	5.96212i	0.567175	−	0.522913i
$131$	15.6769			1.36969			0.684847	−	0.728687i	$-0.259869\pi$
$131$	15.6769			1.36969			0.684847	+	0.728687i	$0.259869\pi$
$132$	5.95136	+	7.27598i	0.517999	+	0.633293i
$133$	4.64393			0.402680
$134$	−8.86690	+	4.08011i	−0.765983	+	0.352468i
$135$	−9.75801			−0.839836
$136$	17.6606	+	5.02119i	1.51438	+	0.430563i
$137$			20.2603i			1.73095i	0.500948	+	0.865477i	$0.332985\pi$
$137$			20.2603i			1.73095i	−0.500948	+	0.865477i	$0.667015\pi$
$138$	9.65964	−	4.44489i	0.822283	−	0.378374i
$139$	−5.34231			−0.453129			−0.226564	−	0.973996i	$-0.572749\pi$
$139$	−5.34231			−0.453129			−0.226564	+	0.973996i	$0.572749\pi$
$140$	−8.03878	+	9.38535i	−0.679401	+	0.793207i
$141$		−	9.98269i		−	0.840694i
$142$	−4.34360	+	1.99871i	−0.364506	+	0.167728i
$143$	1.62860	+	11.8468i	0.136190	+	0.990683i
$144$	−0.609574	−	3.92030i	−0.0507978	−	0.326692i
$145$	1.24597			0.103472
$146$	−10.4765	+	4.82078i	−0.867043	+	0.398970i
$147$		−	8.26138i		−	0.681387i
$148$	−13.7482	−	11.7756i	−1.13009	−	0.967951i
$149$	13.3960			1.09744			0.548722	−	0.836005i	$-0.315115\pi$
$149$	13.3960			1.09744			0.548722	+	0.836005i	$0.315115\pi$
$150$	−1.69590	−	3.68553i	−0.138470	−	0.300922i
$151$		−	12.9008i		−	1.04985i	−0.851148	−	0.524926i	$-0.824093\pi$
$151$		−	12.9008i		−	1.04985i	0.851148	−	0.524926i	$-0.175907\pi$
$152$	3.52728	+	1.00286i	0.286100	+	0.0813430i
$153$		−	6.43853i		−	0.520524i
$154$	−4.22687	−	16.2601i	−0.340611	−	1.31027i
$155$		−	4.68082i		−	0.375972i
$156$	−3.92960	+	9.43302i	−0.314620	+	0.755246i
$157$	22.9083			1.82828			0.914139	−	0.405400i	$-0.132868\pi$
$157$	22.9083			1.82828			0.914139	+	0.405400i	$0.132868\pi$
$158$	13.5175	−	6.22009i	1.07539	−	0.494843i
$159$		−	17.4093i		−	1.38065i
$160$	−8.13262	+	5.39263i	−0.642940	+	0.426325i
$161$	−19.0048			−1.49779
$162$	6.47588	−	2.97988i	0.508793	−	0.234122i
$163$	−7.24270			−0.567292			−0.283646	−	0.958929i	$-0.591544\pi$
$163$	−7.24270			−0.567292			−0.283646	+	0.958929i	$0.591544\pi$
$164$	−10.4095	+	12.1532i	−0.812849	+	0.949008i
$165$	−7.98085	−	1.42704i	−0.621308	−	0.111095i
$166$	3.54189	+	7.69724i	0.274904	+	0.597422i
$167$		−	9.72511i		−	0.752551i	−0.926508	−	0.376276i	$-0.877205\pi$
$167$		−	9.72511i		−	0.752551i	0.926508	−	0.376276i	$-0.122795\pi$
$168$	3.92622	−	13.8093i	0.302915	−	1.06541i
$169$	−10.5265	+	7.62845i	−0.809729	+	0.586804i
$170$	−14.3860	+	6.61971i	−1.10335	+	0.507709i
$171$		−	1.28594i		−	0.0983386i
$172$	15.1214	−	17.6544i	1.15300	−	1.34613i
$173$		−	1.53622i		−	0.116797i	−0.998293	−	0.0583983i	$-0.981401\pi$
$173$		−	1.53622i		−	0.116797i	0.998293	−	0.0583983i	$-0.0185994\pi$
$174$	−1.31500	+	0.605099i	−0.0996901	+	0.0458725i
$175$			7.25106i			0.548129i
$176$	0.300884	−	13.2631i	0.0226800	−	0.999743i
$177$		−	9.99674i		−	0.751401i
$178$	8.65784	+	18.8152i	0.648932	+	1.41026i
$179$		−	18.3943i		−	1.37485i	−0.726254	−	0.687427i	$-0.758740\pi$
$179$		−	18.3943i		−	1.37485i	0.726254	−	0.687427i	$-0.241260\pi$
$180$	2.59888	+	2.22601i	0.193709	+	0.165917i
$181$	5.64422			0.419531			0.209766	−	0.977752i	$-0.432730\pi$
$181$	5.64422			0.419531			0.209766	+	0.977752i	$0.432730\pi$
$182$	13.4280	−	12.3800i	0.995346	−	0.917670i
$183$	−3.85662			−0.285090
$184$	−14.4350	−	4.10412i	−1.06416	−	0.302559i
$185$	15.6128			1.14788
$186$	2.27322	+	4.94016i	0.166681	+	0.362230i
$187$	3.78956	−	21.1935i	0.277120	−	1.54982i
$188$	−9.16517	+	10.7004i	−0.668439	+	0.780408i
$189$	−20.2620			−1.47384
$190$	−2.87326	+	1.32213i	−0.208448	+	0.0959175i
$191$			1.20222i			0.0869897i	0.999054	+	0.0434949i	$0.0138492\pi$
$191$			1.20222i			0.0869897i	−0.999054	+	0.0434949i	$0.986151\pi$
$192$	5.96431	−	9.64098i	0.430437	−	0.695778i
$193$	−4.51442			−0.324955			−0.162477	−	0.986712i	$-0.551948\pi$
$193$	−4.51442			−0.324955			−0.162477	+	0.986712i	$0.551948\pi$
$194$	−0.474867	−	1.03198i	−0.0340935	−	0.0740919i
$195$	−2.71850	−	8.38398i	−0.194676	−	0.600389i
$196$	−7.58483	+	8.85536i	−0.541774	+	0.632526i
$197$	10.2808			0.732475			0.366237	−	0.930521i	$-0.380646\pi$
$197$	10.2808			0.732475			0.366237	+	0.930521i	$0.380646\pi$
$198$	−4.50255	+	1.17046i	−0.319983	+	0.0831807i
$199$			16.4063i			1.16301i	0.813543	+	0.581504i	$0.197536\pi$
$199$			16.4063i			1.16301i	−0.813543	+	0.581504i	$0.802464\pi$
$200$	−1.56588	+	5.50753i	−0.110724	+	0.389441i
$201$			9.78045i			0.689860i
$202$	7.08101	+	15.3885i	0.498218	+	1.08273i
$203$	2.58719			0.181585
$204$	11.9682	−	13.9730i	0.837941	−	0.978303i
$205$		−	13.8016i		−	0.963946i
$206$	−0.515134	−	1.11949i	−0.0358911	−	0.0779985i
$207$			5.26259i			0.365775i
$208$	12.8727	−	6.50344i	0.892558	−	0.450932i
$209$	0.756877	−	4.23290i	0.0523542	−	0.292795i
$210$	5.17616	+	11.2488i	0.357189	+	0.776243i
$211$	−4.32561			−0.297787			−0.148894	−	0.988853i	$-0.547571\pi$
$211$	−4.32561			−0.297787			−0.148894	+	0.988853i	$0.547571\pi$
$212$	−15.9836	+	18.6610i	−1.09776	+	1.28164i
$213$			4.79112i			0.328282i
$214$	8.06839	−	3.71268i	0.551544	−	0.253793i
$215$			20.0489i			1.36732i
$216$	−15.3900	−	4.37562i	−1.04715	−	0.297723i
$217$		−	9.71948i		−	0.659802i
$218$	−18.4963	+	8.51108i	−1.25273	+	0.576443i
$219$			11.5559i			0.780876i
$220$	7.24448	+	8.85692i	0.488422	+	0.597133i
$221$	22.2640	−	7.21909i	1.49764	−	0.485609i
$222$	−16.4779	+	7.58231i	−1.10592	+	0.508892i
$223$	−10.8075			−0.723721			−0.361860	−	0.932232i	$-0.617858\pi$
$223$	−10.8075			−0.723721			−0.361860	+	0.932232i	$0.617858\pi$
$224$	−16.8870	+	11.1975i	−1.12831	+	0.748165i
$225$	2.00788			0.133859
$226$	−7.66874	+	3.52878i	−0.510117	+	0.234731i
$227$		−	6.55993i		−	0.435398i	−0.976016	−	0.217699i	$-0.930145\pi$
$227$		−	6.55993i		−	0.435398i	0.976016	−	0.217699i	$-0.0698551\pi$
$228$	2.39037	−	2.79077i	0.158306	−	0.184823i
$229$		−	3.13986i		−	0.207488i	−0.994604	−	0.103744i	$-0.966918\pi$
$229$		−	3.13986i		−	0.207488i	0.994604	−	0.103744i	$-0.0330823\pi$
$230$	11.7585	−	5.41068i	0.775333	−	0.356770i
$231$	−16.5718	−	2.96318i	−1.09035	−	0.194963i
$232$	1.96509	+	0.558708i	0.129015	+	0.0366810i
$233$			24.9138i			1.63216i	0.577939	+	0.816080i	$0.303857\pi$
$233$			24.9138i			1.63216i	−0.577939	+	0.816080i	$0.696143\pi$
$234$	−3.42814	−	3.71832i	−0.224105	−	0.243074i
$235$		−	12.1517i		−	0.792692i
$236$	−9.17808	+	10.7155i	−0.597442	+	0.697519i
$237$		−	14.9102i		−	0.968522i
$238$	−29.8717	+	13.7455i	−1.93630	+	0.890988i
$239$			25.3333i			1.63868i	0.573311	+	0.819338i	$0.305659\pi$
$239$			25.3333i			1.63868i	−0.573311	+	0.819338i	$0.694341\pi$
$240$	1.50233	+	9.66182i	0.0969752	+	0.623668i
$241$	−2.09418			−0.134898			−0.0674489	−	0.997723i	$-0.521486\pi$
$241$	−2.09418			−0.134898			−0.0674489	+	0.997723i	$0.521486\pi$
$242$	−15.5098	+	1.20265i	−0.997007	+	0.0773093i
$243$			9.82736i			0.630426i
$244$	4.13391	+	3.54079i	0.264646	+	0.226676i
$245$		−	10.0564i		−	0.642482i
$246$	6.70269	+	14.5663i	0.427348	+	0.928713i
$247$	4.44671	−	1.44184i	0.282937	−	0.0917424i
$248$	2.09894	−	7.38241i	0.133283	−	0.468783i
$249$	8.49029			0.538050
$250$	−7.16321	−	15.5671i	−0.453041	−	0.984549i
$251$		−	17.9705i		−	1.13429i	−0.823619	−	0.567143i	$-0.808049\pi$
$251$		−	17.9705i		−	1.13429i	0.823619	−	0.567143i	$-0.191951\pi$
$252$	5.39645	+	4.62220i	0.339945	+	0.291171i
$253$	−3.09744	+	17.3227i	−0.194734	+	1.08907i
$254$	−4.18826	+	1.92723i	−0.262795	+	0.120925i
$255$			15.8681i			0.993702i
$256$	−15.2446	+	4.85827i	−0.952786	+	0.303642i
$257$	1.78384			0.111273			0.0556365	−	0.998451i	$-0.482281\pi$
$257$	1.78384			0.111273			0.0556365	+	0.998451i	$0.482281\pi$
$258$	−9.73666	−	21.1597i	−0.606178	−	1.31735i
$259$	32.4193			2.01444
$260$	−4.78343	+	11.4826i	−0.296656	+	0.712123i
$261$		−	0.716416i		−	0.0443450i
$262$	−20.1405	+	9.26765i	−1.24428	+	0.572557i
$263$	−13.9515			−0.860285			−0.430142	−	0.902761i	$-0.641537\pi$
$263$	−13.9515			−0.860285			−0.430142	+	0.902761i	$0.641537\pi$
$264$	−11.9472	−	5.82939i	−0.735298	−	0.358774i
$265$		−	21.1921i		−	1.30182i
$266$	−5.96617	+	2.74534i	−0.365810	+	0.168328i
$267$	20.7537			1.27011
$268$	8.97950	−	10.4836i	0.548510	−	0.640391i
$269$	−4.49535			−0.274086			−0.137043	−	0.990565i	$-0.543760\pi$
$269$	−4.49535			−0.274086			−0.137043	+	0.990565i	$0.543760\pi$
$270$	12.5364	−	5.76862i	0.762939	−	0.351067i
$271$		−	7.60943i		−	0.462240i	−0.972925	−	0.231120i	$-0.925761\pi$
$271$		−	7.60943i		−	0.462240i	0.972925	−	0.231120i	$-0.0742390\pi$
$272$	−25.6574	+	3.98951i	−1.55571	+	0.241899i
$273$	−5.64483	−	17.4089i	−0.341641	−	1.05364i
$274$	−11.9772	−	26.0289i	−0.723571	−	1.57247i
$275$	6.60927	+	1.18179i	0.398554	+	0.0712648i
$276$	−9.78231	+	11.4209i	−0.588826	+	0.687459i
$277$			19.5879i			1.17692i	0.808526	+	0.588461i	$0.200266\pi$
$277$			19.5879i			1.17692i	−0.808526	+	0.588461i	$0.799734\pi$
$278$	6.86340	−	3.15820i	0.411639	−	0.189416i
$279$	−2.69141			−0.161131
$280$	4.77932	−	16.8099i	0.285619	−	1.00458i
$281$	4.69051			0.279812			0.139906	−	0.990165i	$-0.455320\pi$
$281$	4.69051			0.279812			0.139906	+	0.990165i	$0.455320\pi$
$282$	5.90144	+	12.8250i	0.351426	+	0.763719i
$283$	−15.3777			−0.914107			−0.457054	−	0.889439i	$-0.651095\pi$
$283$	−15.3777			−0.914107			−0.457054	+	0.889439i	$0.651095\pi$
$284$	4.39876	−	5.13559i	0.261018	−	0.304741i
$285$			3.16929i			0.187733i
$286$	−9.09577	−	14.2572i	−0.537844	−	0.843044i
$287$		−	28.6583i		−	1.69165i
$288$	3.10069	+	4.67615i	0.182710	+	0.275545i
$289$	−25.1385			−1.47873
$290$	−1.60073	+	0.736576i	−0.0939980	+	0.0432533i
$291$	−1.13831			−0.0667287
$292$	10.6096	−	12.3868i	0.620878	−	0.724880i
$293$	1.30696			0.0763532			0.0381766	−	0.999271i	$-0.487845\pi$
$293$	1.30696			0.0763532			0.0381766	+	0.999271i	$0.487845\pi$
$294$	4.88386	+	10.6136i	0.284833	+	0.618999i
$295$		−	12.1688i		−	0.708498i
$296$	24.6240	+	7.00100i	1.43124	+	0.406925i
$297$	−3.30234	+	18.4686i	−0.191621	+	1.07166i
$298$	−17.2102	+	7.91929i	−0.996960	+	0.458752i
$299$	−18.1977	+	5.90059i	−1.05240	+	0.341240i
$300$	4.35753	+	3.73233i	0.251582	+	0.215486i
$301$			41.6305i			2.39954i
$302$	7.62653	+	16.5740i	0.438858	+	0.953726i
$303$	16.9739			0.975127
$304$	−5.12445	+	0.796810i	−0.293908	+	0.0457002i
$305$	−4.69460			−0.268812
$306$	3.80625	+	8.27174i	0.217589	+	0.472864i
$307$		−	2.96736i		−	0.169356i	−0.996408	−	0.0846780i	$-0.973014\pi$
$307$		−	2.96736i		−	0.169356i	0.996408	−	0.0846780i	$-0.0269862\pi$
$308$	15.0428	+	18.3909i	0.857142	+	1.04792i
$309$	−1.23483			−0.0702471
$310$	2.76715	+	6.01357i	0.157164	+	0.341548i
$311$		−	21.6787i		−	1.22929i	−0.788804	−	0.614644i	$-0.789300\pi$
$311$		−	21.6787i		−	1.22929i	0.788804	−	0.614644i	$-0.210700\pi$
$312$	−0.528035	−	14.4419i	−0.0298941	−	0.817612i
$313$	−19.9275			−1.12637			−0.563183	−	0.826332i	$-0.690423\pi$
$313$	−19.9275			−1.12637			−0.563183	+	0.826332i	$0.690423\pi$
$314$	−29.4308	+	13.5426i	−1.66088	+	0.764255i
$315$	−6.12839			−0.345295
$316$	−13.6892	+	15.9822i	−0.770075	+	0.899070i
$317$		−	16.5725i		−	0.930807i	−0.885099	−	0.465403i	$-0.845909\pi$
$317$		−	16.5725i		−	0.930807i	0.885099	−	0.465403i	$-0.154091\pi$
$318$	10.2918	+	22.3662i	0.577137	+	1.25424i
$319$	0.421666	−	2.35820i	0.0236087	−	0.132034i
$320$	7.26024	−	11.7358i	0.405860	−	0.656051i
$321$		−	8.89968i		−	0.496732i
$322$	24.4159	−	11.2350i	1.36065	−	0.626103i
$323$	−8.41617			−0.468288
$324$	−6.55813	+	7.65667i	−0.364340	+	0.425370i
$325$	2.25131	+	6.94312i	0.124880	+	0.385135i
$326$	9.30488	−	4.28165i	0.515350	−	0.237139i
$327$			20.4020i			1.12823i
$328$	6.18882	−	21.7674i	0.341720	−	1.20190i
$329$		−	25.2325i		−	1.39111i
$330$	11.0968	−	2.88466i	0.610860	−	0.158795i
$331$	28.8347			1.58490			0.792450	−	0.609937i	$-0.208805\pi$
$331$	28.8347			1.58490			0.792450	+	0.609937i	$0.208805\pi$
$332$	−9.10072	−	7.79500i	−0.499467	−	0.427806i
$333$		−	8.97718i		−	0.491947i
$334$	5.74917	+	12.4941i	0.314581	+	0.683647i
$335$			11.9056i			0.650471i
$336$	3.11952	+	20.0623i	0.170184	+	1.09449i
$337$		−	3.09064i		−	0.168358i	−0.996451	−	0.0841790i	$-0.973173\pi$
$337$		−	3.09064i		−	0.168358i	0.996451	−	0.0841790i	$-0.0268267\pi$
$338$	9.01394	−	16.0234i	0.490294	−	0.871557i
$339$			8.45885i			0.459422i
$340$	14.5687	−	17.0090i	0.790097	−	0.922444i
$341$	−8.85922	−	1.58410i	−0.479753	−	0.0857839i
$342$	0.760209	+	1.65209i	0.0411074	+	0.0893346i
$343$			4.19145i			0.226317i
$344$	−8.99018	+	31.6203i	−0.484718	+	1.70485i
$345$		−	12.9700i		−	0.698280i
$346$	0.908164	+	1.97362i	0.0488232	+	0.106103i
$347$	−3.31992			−0.178223			−0.0891115	−	0.996022i	$-0.528403\pi$
$347$	−3.31992			−0.178223			−0.0891115	+	0.996022i	$0.528403\pi$
$348$	1.33170	−	1.55477i	0.0713868	−	0.0833446i
$349$	−29.7791			−1.59404			−0.797020	−	0.603953i	$-0.793592\pi$
$349$	−29.7791			−1.59404			−0.797020	+	0.603953i	$0.793592\pi$
$350$	−4.28659	−	9.31563i	−0.229128	−	0.497941i
$351$	−19.4015	+	6.29094i	−1.03558	+	0.335785i
$352$	7.45415	+	17.2173i	0.397308	+	0.917685i
$353$			0.586982i			0.0312419i	0.999878	+	0.0156210i	$0.00497251\pi$
$353$			0.586982i			0.0312419i	−0.999878	+	0.0156210i	$0.995027\pi$
$354$	5.90975	+	12.8431i	0.314100	+	0.682602i
$355$			5.83214i			0.309538i
$356$	−22.2459	−	19.0542i	−1.17903	−	1.00987i
$357$			32.9494i			1.74387i
$358$	10.8741	+	23.6316i	0.574714	+	1.24897i
$359$			8.16087i			0.430714i	0.976535	+	0.215357i	$0.0690916\pi$
$359$			8.16087i			0.430714i	−0.976535	+	0.215357i	$0.930908\pi$
$360$	−4.65480	−	1.32344i	−0.245329	−	0.0697512i
$361$	17.3191			0.911530
$362$	−7.25127	+	3.33668i	−0.381118	+	0.175372i
$363$	−5.40182	+	14.6221i	−0.283522	+	0.767462i
$364$	−9.93256	+	23.8431i	−0.520607	+	1.24972i
$365$			14.0668i			0.736290i
$366$	4.95470	−	2.27991i	0.258987	−	0.119173i
$367$			8.30934i			0.433744i	0.976200	+	0.216872i	$0.0695854\pi$
$367$			8.30934i			0.433744i	−0.976200	+	0.216872i	$0.930415\pi$
$368$	20.9713	−	3.26086i	1.09320	−	0.169984i
$369$	−7.93574			−0.413118
$370$	−20.0582	+	9.22981i	−1.04278	+	0.479835i
$371$		−	44.0042i		−	2.28459i
$372$	−5.84093	−	5.00290i	−0.302838	−	0.259388i
$373$		−	7.26318i		−	0.376073i	−0.982162	−	0.188037i	$-0.939788\pi$
$373$		−	7.26318i		−	0.376073i	0.982162	−	0.188037i	$-0.0602124\pi$
$374$	7.66033	+	29.4681i	0.396106	+	1.52376i
$375$	−17.1710			−0.886705
$376$	5.44900	−	19.1653i	0.281011	−	0.988373i
$377$	2.47732	−	0.803270i	0.127588	−	0.0413705i
$378$	26.0311	−	11.9782i	1.33890	−	0.616094i
$379$	5.86109			0.301064			0.150532	−	0.988605i	$-0.451901\pi$
$379$	5.86109			0.301064			0.150532	+	0.988605i	$0.451901\pi$
$380$	2.90975	−	3.39715i	0.149267	−	0.174270i
$381$			4.61978i			0.236678i
$382$	−0.710715	−	1.54453i	−0.0363633	−	0.0790248i
$383$	30.7334			1.57041			0.785203	−	0.619239i	$-0.212559\pi$
$383$	30.7334			1.57041			0.785203	+	0.619239i	$0.212559\pi$
$384$	−1.96306	+	15.9119i	−0.100177	+	0.812002i
$385$	−20.1726	−	3.60702i	−1.02809	−	0.183831i
$386$	5.79979	−	2.66878i	0.295202	−	0.135837i
$387$	11.5279			0.585994
$388$	1.22015	+	1.04509i	0.0619436	+	0.0530563i
$389$	29.1368			1.47730			0.738648	−	0.674091i	$-0.235464\pi$
$389$	29.1368			1.47730			0.738648	+	0.674091i	$0.235464\pi$
$390$	8.44887	+	9.16402i	0.427825	+	0.464038i
$391$	34.4423			1.74182
$392$	4.50943	−	15.8606i	0.227761	−	0.801082i
$393$			22.2155i			1.12063i
$394$	−13.2080	+	6.07766i	−0.665408	+	0.306188i
$395$		−	18.1499i		−	0.913221i
$396$	5.09261	−	4.16548i	0.255913	−	0.209323i
$397$		−	25.9731i		−	1.30355i	−0.758410	−	0.651777i	$-0.774024\pi$
$397$		−	25.9731i		−	1.30355i	0.758410	−	0.651777i	$-0.225976\pi$
$398$	−9.69884	−	21.0775i	−0.486159	−	1.05652i
$399$			6.58087i			0.329456i
$400$	−1.24415	−	8.00136i	−0.0622073	−	0.400068i
$401$			24.3219i			1.21458i	0.794481	+	0.607289i	$0.207743\pi$
$401$			24.3219i			1.21458i	−0.794481	+	0.607289i	$0.792257\pi$
$402$	−5.78189	−	12.5652i	−0.288374	−	0.626695i
$403$	−3.01770	−	9.30671i	−0.150322	−	0.463600i
$404$	−18.1943	−	15.5839i	−0.905201	−	0.775327i
$405$		−	8.69516i		−	0.432066i
$406$	−3.32383	+	1.52946i	−0.164959	+	0.0759060i
$407$	5.28376	−	29.5499i	0.261906	−	1.46473i
$408$	−7.11548	+	25.0266i	−0.352269	+	1.23900i
$409$	6.87768			0.340079			0.170040	−	0.985437i	$-0.445610\pi$
$409$	6.87768			0.340079			0.170040	+	0.985437i	$0.445610\pi$
$410$	8.15906	+	17.7313i	0.402947	+	0.875685i
$411$	−28.7107			−1.41619
$412$	1.32361	+	1.13371i	0.0652097	+	0.0558537i
$413$		−	25.2680i		−	1.24336i
$414$	−3.11107	−	6.76098i	−0.152901	−	0.332284i
$415$	10.3351			0.507329
$416$	−12.6932	+	15.9650i	−0.622336	+	0.782750i
$417$		−	7.57054i		−	0.370731i
$418$	1.52997	+	5.88555i	0.0748334	+	0.287872i
$419$			5.59578i			0.273372i	0.990614	+	0.136686i	$0.0436451\pi$
$419$			5.59578i			0.273372i	−0.990614	+	0.136686i	$0.956355\pi$
$420$	−13.2999	−	11.3917i	−0.648968	−	0.555858i
$421$		−	20.7586i		−	1.01171i	−0.862618	−	0.505856i	$-0.831177\pi$
$421$		−	20.7586i		−	1.01171i	0.862618	−	0.505856i	$-0.168823\pi$
$422$	5.55723	−	2.55716i	0.270522	−	0.124481i
$423$	−6.98709			−0.339724
$424$	9.50279	−	33.4233i	0.461496	−	1.62318i
$425$		−	13.1411i		−	0.637436i
$426$	−2.83235	−	6.15527i	−0.137228	−	0.298224i
$427$	−9.74809			−0.471743
$428$	−8.17086	+	9.53954i	−0.394953	+	0.461111i
$429$	−16.7881	+	2.30787i	−0.810535	+	0.111425i
$430$	−11.8523	−	25.7573i	−0.571567	−	1.24213i
$431$		−	2.95150i		−	0.142169i	−0.997470	−	0.0710845i	$-0.977354\pi$
$431$		−	2.95150i		−	0.142169i	0.997470	−	0.0710845i	$-0.0226460\pi$
$432$	22.3586	−	3.47658i	1.07573	−	0.167267i
$433$	−31.1409			−1.49654			−0.748269	−	0.663395i	$-0.769115\pi$
$433$	−31.1409			−1.49654			−0.748269	+	0.663395i	$0.769115\pi$
$434$	5.74584	+	12.4869i	0.275809	+	0.599389i
$435$			1.76565i			0.0846565i
$436$	18.7312	−	21.8688i	0.897061	−	1.04733i
$437$	6.87904			0.329069
$438$	−6.83148	−	14.8462i	−0.326421	−	0.709378i
$439$	−3.25317			−0.155265			−0.0776327	−	0.996982i	$-0.524736\pi$
$439$	−3.25317			−0.155265			−0.0776327	+	0.996982i	$0.524736\pi$
$440$	−14.5431	−	7.09601i	−0.693315	−	0.338289i
$441$	−5.78232			−0.275348
$442$	−24.3354	+	22.4363i	−1.15752	+	1.06719i
$443$			26.4182i			1.25517i	0.778549	+	0.627584i	$0.215956\pi$
$443$			26.4182i			1.25517i	−0.778549	+	0.627584i	$0.784044\pi$
$444$	16.6872	−	19.4824i	0.791937	−	0.924593i
$445$	25.2632			1.19759
$446$	13.8846	−	6.38902i	0.657456	−	0.302529i
$447$			18.9834i			0.897883i
$448$	15.0755	−	24.3688i	0.712251	−	1.15132i
$449$			11.4673i			0.541176i	0.962695	+	0.270588i	$0.0872181\pi$
$449$			11.4673i			0.541176i	−0.962695	+	0.270588i	$0.912782\pi$
$450$	−2.57958	+	1.18700i	−0.121603	+	0.0559555i
$451$	−26.1218	−	4.67079i	−1.23003	−	0.219939i
$452$	7.76613	−	9.06702i	0.365288	−	0.426477i
$453$	18.2816			0.858945
$454$	3.87802	+	8.42771i	0.182004	+	0.395532i
$455$	−6.87135	−	21.1915i	−0.322134	−	0.993475i
$456$	−1.42115	+	4.99848i	−0.0665515	+	0.234075i
$457$	−17.4515			−0.816347			−0.408173	−	0.912904i	$-0.633834\pi$
$457$	−17.4515			−0.816347			−0.408173	+	0.912904i	$0.633834\pi$
$458$	1.85619	+	4.03386i	0.0867338	+	0.188490i
$459$	36.7208			1.71398
$460$	−11.9078	+	13.9025i	−0.555205	+	0.648207i
$461$	−14.1465			−0.658870			−0.329435	−	0.944178i	$-0.606858\pi$
$461$	−14.1465			−0.658870			−0.329435	+	0.944178i	$0.606858\pi$
$462$	23.0420	−	5.98985i	1.07201	−	0.278673i
$463$	20.9199			0.972231			0.486116	−	0.873894i	$-0.338413\pi$
$463$	20.9199			0.972231			0.486116	+	0.873894i	$0.338413\pi$
$464$	−2.85490	+	0.443913i	−0.132535	+	0.0206081i
$465$	6.63315			0.307605
$466$	−14.7283	−	32.0074i	−0.682273	−	1.48272i
$467$		−	24.3113i		−	1.12499i	−0.826800	−	0.562497i	$-0.809841\pi$
$467$		−	24.3113i		−	1.12499i	0.826800	−	0.562497i	$-0.190159\pi$
$468$	6.60237	+	2.75041i	0.305195	+	0.127138i
$469$			24.7213i			1.14152i
$470$	7.18372	+	15.6117i	0.331360	+	0.720112i
$471$			32.4631i			1.49582i
$472$	5.45667	−	19.1922i	0.251164	−	0.883395i
$473$	37.9458	+	6.78502i	1.74475	+	0.311976i
$474$	8.81443	+	19.1555i	0.404860	+	0.879842i
$475$		−	2.62462i		−	0.120426i
$476$	30.2511	−	35.3184i	1.38656	−	1.61882i
$477$	−12.1852			−0.557920
$478$	−14.9762	−	32.5464i	−0.684997	−	1.48864i
$479$			23.5859i			1.07767i	0.842413	+	0.538833i	$0.181135\pi$
$479$			23.5859i			1.07767i	−0.842413	+	0.538833i	$0.818865\pi$
$480$	−7.64184	−	11.5247i	−0.348801	−	0.526027i
$481$	31.0425	−	10.0655i	1.41542	−	0.458948i
$482$	2.69044	−	1.23801i	0.122546	−	0.0563898i
$483$		−	26.9315i		−	1.22543i
$484$	19.2149	−	10.7140i	0.873403	−	0.486998i
$485$	−1.38564			−0.0629187
$486$	−5.80962	−	12.6255i	−0.263530	−	0.572703i
$487$	3.64370			0.165112			0.0825560	−	0.996586i	$-0.473692\pi$
$487$	3.64370			0.165112			0.0825560	+	0.996586i	$0.473692\pi$
$488$	−7.40414	−	2.10512i	−0.335170	−	0.0952942i
$489$		−	10.2636i		−	0.464134i
$490$	5.94504	+	12.9198i	0.268569	+	0.583655i
$491$	−26.9828			−1.21772			−0.608858	−	0.793279i	$-0.708372\pi$
$491$	−26.9828			−1.21772			−0.608858	+	0.793279i	$0.708372\pi$
$492$	−17.2222	−	14.7513i	−0.776438	−	0.665039i
$493$	−4.68876			−0.211171
$494$	−4.86043	+	4.48112i	−0.218681	+	0.201615i
$495$	−0.998816	+	5.58596i	−0.0448935	+	0.251070i
$496$	1.66768	+	10.7252i	0.0748810	+	0.481576i
$497$			12.1101i			0.543214i
$498$	−10.9077	+	5.01919i	−0.488786	+	0.224915i
$499$	−30.0725			−1.34623			−0.673114	−	0.739539i	$-0.735044\pi$
$499$	−30.0725			−1.34623			−0.673114	+	0.739539i	$0.735044\pi$
$500$	18.4055	+	15.7648i	0.823120	+	0.705022i
$501$	13.7814			0.615706
$502$	10.6236	+	23.0871i	0.474153	+	1.03043i
$503$	−34.5542			−1.54070			−0.770349	−	0.637623i	$-0.779918\pi$
$503$	−34.5542			−1.54070			−0.770349	+	0.637623i	$0.779918\pi$
$504$	−9.66545	−	2.74805i	−0.430534	−	0.122408i
$505$	20.6621			0.919449
$506$	−6.26125	−	24.0860i	−0.278346	−	1.07075i
$507$	−10.8102	−	14.9170i	−0.480099	−	0.662486i
$508$	4.24145	−	4.95193i	0.188184	−	0.219706i
$509$			32.9354i			1.45983i	0.683536	+	0.729917i	$0.260441\pi$
$509$			32.9354i			1.45983i	−0.683536	+	0.729917i	$0.739559\pi$
$510$	−9.38074	−	20.3862i	−0.415386	−	0.902717i
$511$			29.2090i			1.29213i
$512$	16.7131	−	15.2537i	0.738620	−	0.674123i
$513$	7.33411			0.323809
$514$	−2.29175	+	1.05455i	−0.101085	+	0.0465142i
$515$	−1.50314			−0.0662361
$516$	25.0179	+	21.4284i	1.10135	+	0.943334i
$517$	−22.9992	−	4.11244i	−1.01150	−	0.180865i
$518$	−41.6499	+	19.1652i	−1.82999	+	0.842072i
$519$	2.17696			0.0955582
$520$	−0.642768	−	17.5799i	−0.0281872	−	0.770928i
$521$	27.4572			1.20292			0.601460	−	0.798903i	$-0.294586\pi$
$521$	27.4572			1.20292			0.601460	+	0.798903i	$0.294586\pi$
$522$	0.423522	+	0.920398i	0.0185370	+	0.0402847i
$523$	12.1845			0.532792			0.266396	−	0.963864i	$-0.414167\pi$
$523$	12.1845			0.532792			0.266396	+	0.963864i	$0.414167\pi$
$524$	20.3962	−	23.8128i	0.891014	−	1.04027i
$525$	−10.2754			−0.448456
$526$	17.9238	−	8.24766i	0.781516	−	0.359615i
$527$			17.6146i			0.767303i
$528$	18.7950	+	0.426380i	0.817948	+	0.0185558i
$529$	−5.15173			−0.223988
$530$	12.5281	+	27.2260i	0.544184	+	1.18262i
$531$	−6.99693			−0.303641
$532$	6.04194	−	7.05402i	0.261951	−	0.305831i
$533$	−8.89782	−	27.4413i	−0.385407	−	1.18861i
$534$	−26.6629	+	12.2689i	−1.15382	+	0.530929i
$535$		−	10.8334i		−	0.468369i
$536$	−5.33861	+	18.7770i	−0.230593	+	0.811043i
$537$	26.0664			1.12485
$538$	5.77529	−	2.65751i	0.248991	−	0.114573i
$539$	−19.0334	−	3.40334i	−0.819828	−	0.146592i
$540$	−12.6956	+	14.8222i	−0.546331	+	0.637846i
$541$	29.7887			1.28072			0.640358	−	0.768077i	$-0.278786\pi$
$541$	29.7887			1.28072			0.640358	+	0.768077i	$0.278786\pi$
$542$	4.49845	+	9.77604i	0.193225	+	0.419917i
$543$			7.99837i			0.343243i
$544$	30.6042	−	20.2932i	1.31214	−	0.870065i
$545$			24.8349i			1.06381i
$546$	17.5436	+	19.0286i	0.750799	+	0.814350i
$547$	−4.22420			−0.180614			−0.0903068	−	0.995914i	$-0.528785\pi$
$547$	−4.22420			−0.180614			−0.0903068	+	0.995914i	$0.528785\pi$
$548$	30.7749	+	26.3595i	1.31464	+	1.12602i
$549$			2.69933i			0.115205i
$550$	−9.18974	+	2.38891i	−0.391852	+	0.101863i
$551$	−0.936469			−0.0398949
$552$	5.81591	−	20.4558i	0.247541	−	0.870655i
$553$		−	37.6874i		−	1.60263i
$554$	−11.5797	−	25.1651i	−0.491975	−	1.06916i
$555$			22.1248i			0.939147i
$556$	−6.95056	+	8.11484i	−0.294770	+	0.344146i
$557$	19.4806			0.825418			0.412709	−	0.910863i	$-0.364583\pi$
$557$	19.4806			0.825418			0.412709	+	0.910863i	$0.364583\pi$
$558$	3.45772	−	1.59107i	0.146377	−	0.0673556i
$559$	12.9254	+	39.8625i	0.546687	+	1.68601i
$560$	3.79733	+	24.4215i	0.160467	+	1.03199i
$561$	30.0331	+	5.37016i	1.26800	+	0.226728i
$562$	−6.02602	+	2.77288i	−0.254192	+	0.116967i
$563$	38.1118			1.60622			0.803110	−	0.595831i	$-0.203177\pi$
$563$	38.1118			1.60622			0.803110	+	0.595831i	$0.203177\pi$
$564$	−15.1635	−	12.9879i	−0.638497	−	0.546889i
$565$			10.2968i			0.433190i
$566$	19.7561	−	9.09078i	0.830410	−	0.382114i
$567$		−	18.0551i		−	0.758241i
$568$	−2.61521	+	9.19822i	−0.109732	+	0.385949i
$569$			6.05753i			0.253945i	0.991906	+	0.126972i	$0.0405260\pi$
$569$			6.05753i			0.253945i	−0.991906	+	0.126972i	$0.959474\pi$
$570$	−1.87358	−	4.07167i	−0.0784757	−	0.170543i
$571$	34.9135			1.46108			0.730542	−	0.682868i	$-0.239268\pi$
$571$	34.9135			1.46108			0.730542	+	0.682868i	$0.239268\pi$
$572$	20.1140	+	12.9394i	0.841007	+	0.541025i
$573$	−1.70366			−0.0711713
$574$	16.9419	+	36.8181i	0.707140	+	1.53676i
$575$			10.7410i			0.447930i
$576$	−6.74793	−	4.17454i	−0.281164	−	0.173939i
$577$		−	13.1020i		−	0.545442i	−0.962093	−	0.272721i	$-0.912076\pi$
$577$		−	13.1020i		−	0.545442i	0.962093	−	0.272721i	$-0.0879236\pi$
$578$	32.2961	−	14.8611i	1.34334	−	0.618139i
$579$		−	6.39734i		−	0.265864i
$580$	1.62106	−	1.89260i	0.0673107	−	0.0785858i
$581$	21.4603			0.890322
$582$	1.46241	−	0.672930i	0.0606189	−	0.0278938i
$583$	−40.1094	−	7.17190i	−1.66116	−	0.297030i
$584$	−6.30774	+	22.1856i	−0.261016	+	0.918048i
$585$	−5.86812	+	1.90274i	−0.242617	+	0.0786685i
$586$	−1.67908	+	0.772630i	−0.0693622	+	0.0319171i
$587$	−13.7661			−0.568188			−0.284094	−	0.958797i	$-0.591693\pi$
$587$	−13.7661			−0.568188			−0.284094	+	0.958797i	$0.591693\pi$
$588$	−12.5489	−	10.7484i	−0.517506	−	0.443257i
$589$			3.51810i			0.144961i
$590$	7.19383	+	15.6336i	0.296165	+	0.643627i
$591$			14.5688i			0.599280i
$592$	−35.7738	+	5.56253i	−1.47030	+	0.228619i
$593$	−12.4320			−0.510520			−0.255260	−	0.966872i	$-0.582161\pi$
$593$	−12.4320			−0.510520			−0.255260	+	0.966872i	$0.582161\pi$
$594$	−6.67545	−	25.6794i	−0.273897	−	1.05364i
$595$			40.1087i			1.64430i
$596$	17.4288	−	20.3482i	0.713910	−	0.833496i
$597$	−23.2492			−0.951525
$598$	19.8908	−	18.3385i	0.813395	−	0.749918i
$599$			20.2394i			0.826959i	0.910513	+	0.413479i	$0.135687\pi$
$599$			20.2394i			0.826959i	−0.910513	+	0.413479i	$0.864313\pi$
$600$	−7.80467	−	2.21899i	−0.318624	−	0.0905901i
$601$			20.0465i			0.817714i	0.912598	+	0.408857i	$0.134073\pi$
$601$			20.0465i			0.817714i	−0.912598	+	0.408857i	$0.865927\pi$
$602$	−24.6106	−	53.4838i	−1.00305	−	2.17984i
$603$	6.84555			0.278772
$604$	−19.5960	−	16.7845i	−0.797350	−	0.682950i
$605$	−6.57553	+	17.7992i	−0.267334	+	0.723642i
$606$	−21.8068	+	10.0344i	−0.885843	+	0.407621i
$607$	−39.8530			−1.61758			−0.808792	−	0.588095i	$-0.799878\pi$
$607$	−39.8530			−1.61758			−0.808792	+	0.588095i	$0.799878\pi$
$608$	6.11247	−	4.05309i	0.247893	−	0.164375i
$609$			3.66629i			0.148565i
$610$	6.03127	−	2.77529i	0.244199	−	0.112368i
$611$	−7.83416	−	24.1609i	−0.316936	−	0.977445i
$612$	−9.77997	−	8.37679i	−0.395332	−	0.338612i
$613$	11.9364			0.482108			0.241054	−	0.970512i	$-0.422507\pi$
$613$	11.9364			0.482108			0.241054	+	0.970512i	$0.422507\pi$
$614$	1.75421	+	3.81224i	0.0707940	+	0.153850i
$615$	19.5581			0.788660
$616$	−30.1980	−	14.7345i	−1.21671	−	0.593670i
$617$		−	18.8951i		−	0.760687i	−0.924845	−	0.380344i	$-0.875806\pi$
$617$		−	18.8951i		−	0.760687i	0.924845	−	0.380344i	$-0.124194\pi$
$618$	1.58642	−	0.729992i	0.0638151	−	0.0293646i
$619$	29.8033			1.19790			0.598949	−	0.800787i	$-0.295585\pi$
$619$	29.8033			1.19790			0.598949	+	0.800787i	$0.295585\pi$
$620$	−7.11006	−	6.08994i	−0.285547	−	0.244578i
$621$	−30.0141			−1.20442
$622$	12.8158	+	27.8512i	0.513866	+	1.11673i
$623$	52.4577			2.10167
$624$	9.21597	+	18.2417i	0.368934	+	0.730254i
$625$	−10.7800			−0.431200
$626$	25.6013	−	11.7805i	1.02323	−	0.470842i
$627$	5.99840	+	1.07256i	0.239553	+	0.0428341i
$628$	29.8046	−	34.7971i	1.18933	−	1.38856i
$629$	−58.7534			−2.34265
$630$	7.87330	−	3.62290i	0.313680	−	0.144340i
$631$	21.4089			0.852274			0.426137	−	0.904659i	$-0.359874\pi$
$631$	21.4089			0.852274			0.426137	+	0.904659i	$0.359874\pi$
$632$	8.13866	−	28.6253i	0.323738	−	1.13866i
$633$		−	6.12979i		−	0.243637i
$634$	9.79715	+	21.2912i	0.389095	+	0.845581i
$635$			5.62357i			0.223165i
$636$	−26.4444	−	22.6503i	−1.04859	−	0.898141i
$637$	−6.48333	−	19.9949i	−0.256879	−	0.792225i
$638$	0.852367	+	3.27892i	0.0337455	+	0.129813i
$639$	3.35340			0.132659
$640$	−2.38960	+	19.3693i	−0.0944573	+	0.765639i
$641$	26.8941			1.06225			0.531126	−	0.847293i	$-0.321769\pi$
$641$	26.8941			1.06225			0.531126	+	0.847293i	$0.321769\pi$
$642$	5.26120	+	11.4336i	0.207643	+	0.451250i
$643$	−1.62382			−0.0640371			−0.0320186	−	0.999487i	$-0.510194\pi$
$643$	−1.62382			−0.0640371			−0.0320186	+	0.999487i	$0.510194\pi$
$644$	−24.7260	+	28.8678i	−0.974341	+	1.13755i
$645$	−28.4111			−1.11869
$646$	10.8125	−	4.97537i	0.425411	−	0.195753i
$647$		−	7.07581i		−	0.278179i	−0.990280	−	0.139089i	$-0.955582\pi$
$647$		−	7.07581i		−	0.278179i	0.990280	−	0.139089i	$-0.0444175\pi$
$648$	3.89902	−	13.7137i	0.153168	−	0.538724i
$649$	−23.0315	−	4.11823i	−0.904067	−	0.161655i
$650$	−6.99686	−	7.58911i	−0.274439	−	0.297669i
$651$	13.7734			0.539822
$652$	−9.42305	+	11.0015i	−0.369035	+	0.430851i
$653$	−31.8521			−1.24647			−0.623234	−	0.782036i	$-0.714181\pi$
$653$	−31.8521			−1.24647			−0.623234	+	0.782036i	$0.714181\pi$
$654$	−12.0610	−	26.2109i	−0.471622	−	1.02493i
$655$			27.0426i			1.05664i
$656$	4.91723	+	31.6237i	0.191985	+	1.23470i
$657$	8.08823			0.315552
$658$	14.9166	+	32.4168i	0.581510	+	1.26374i
$659$	−17.5968			−0.685473			−0.342737	−	0.939432i	$-0.611354\pi$
$659$	−17.5968			−0.685473			−0.342737	+	0.939432i	$0.611354\pi$
$660$	−12.5511	+	10.2661i	−0.488549	+	0.399607i
$661$		−	12.5662i		−	0.488768i	−0.969679	−	0.244384i	$-0.921414\pi$
$661$		−	12.5662i		−	0.488768i	0.969679	−	0.244384i	$-0.0785858\pi$
$662$	−37.0447	+	17.0462i	−1.43978	+	0.662518i
$663$	10.2301	+	31.5501i	0.397305	+	1.22530i
$664$	16.3001	+	4.63438i	0.632566	+	0.179849i
$665$			8.01077i			0.310644i
$666$	5.30702	+	11.5332i	0.205643	+	0.446903i
$667$	3.83240			0.148391
$668$	−14.7722	−	12.6528i	−0.571554	−	0.489550i
$669$		−	15.3151i		−	0.592118i
$670$	−7.03819	−	15.2954i	−0.271909	−	0.590912i
$671$	−1.58876	+	8.88529i	−0.0613335	+	0.343013i
$672$	−15.8679	−	23.9304i	−0.612118	−	0.923134i
$673$			14.2894i			0.550817i	0.961327	+	0.275408i	$0.0888130\pi$
$673$			14.2894i			0.550817i	−0.961327	+	0.275408i	$0.911187\pi$
$674$	1.82709	+	3.97063i	0.0703768	+	0.152943i
$675$			11.4515i			0.440770i
$676$	−2.10794	+	25.9144i	−0.0810745	+	0.996708i
$677$			9.86152i			0.379009i	0.981880	+	0.189504i	$0.0606881\pi$
$677$			9.86152i			0.379009i	−0.981880	+	0.189504i	$0.939312\pi$
$678$	−5.00060	−	10.8673i	−0.192047	−	0.417356i
$679$	−2.87721			−0.110417
$680$	−8.66155	+	30.4645i	−0.332155	+	1.16826i
$681$	9.29602			0.356224
$682$	12.3181	−	3.20215i	0.471686	−	0.122617i
$683$	−15.0955			−0.577615			−0.288807	−	0.957387i	$-0.593259\pi$
$683$	−15.0955			−0.577615			−0.288807	+	0.957387i	$0.593259\pi$
$684$	−1.95332	−	1.67307i	−0.0746870	−	0.0639713i
$685$	−34.9490			−1.33533
$686$	−2.47785	−	5.38486i	−0.0946046	−	0.205595i
$687$	4.44947			0.169758
$688$	−7.14301	−	45.9382i	−0.272325	−	1.75138i
$689$	−13.6624	−	42.1354i	−0.520496	−	1.60523i
$690$	7.66743	+	16.6629i	0.291894	+	0.634345i
$691$	−41.5782			−1.58171			−0.790856	−	0.612003i	$-0.790364\pi$
$691$	−41.5782			−1.58171			−0.790856	+	0.612003i	$0.790364\pi$
$692$	−2.33348	−	1.99869i	−0.0887057	−	0.0759787i
$693$	−2.07399	+	11.5990i	−0.0787844	+	0.440608i
$694$	4.26519	−	1.96263i	0.161905	−	0.0745005i
$695$		−	9.21548i		−	0.349563i
$696$	−0.791741	+	2.78472i	−0.0300109	+	0.105554i
$697$			51.9374i			1.96727i
$698$	38.2580	−	17.6045i	1.44809	−	0.666339i
$699$	−35.3052			−1.33536
$700$	11.0142	+	9.43393i	0.416298	+	0.356569i
$701$		−	44.8101i		−	1.69245i	−0.532822	−	0.846227i	$-0.678869\pi$
$701$		−	44.8101i		−	1.69245i	0.532822	−	0.846227i	$-0.321131\pi$
$702$	21.2066	−	19.5517i	0.800393	−	0.737931i
$703$	−11.7346			−0.442579
$704$	−19.7549	−	17.7129i	−0.744539	−	0.667579i
$705$	17.2201			0.648547
$706$	−0.347005	−	0.754112i	−0.0130597	−	0.0283814i
$707$	42.9037			1.61356
$708$	−15.1848	−	13.0062i	−0.570680	−	0.488802i
$709$			14.9379i			0.561005i	0.959853	+	0.280502i	$0.0905010\pi$
$709$			14.9379i			0.561005i	−0.959853	+	0.280502i	$0.909499\pi$
$710$	−3.44777	−	7.49270i	−0.129393	−	0.281196i
$711$	−10.4360			−0.391379
$712$	39.8441	+	11.3283i	1.49322	+	0.424547i
$713$		−	14.3974i		−	0.539189i
$714$	−19.4786	−	42.3310i	−0.728969	−	1.58420i
$715$	−20.4358	+	2.80933i	−0.764255	+	0.105063i
$716$	−27.9405	−	23.9317i	−1.04419	−	0.894371i
$717$	−35.8996			−1.34070
$718$	−4.82444	−	10.4845i	−0.180047	−	0.391277i
$719$			5.01260i			0.186939i	0.995622	+	0.0934693i	$0.0297957\pi$
$719$			5.01260i			0.186939i	−0.995622	+	0.0934693i	$0.970204\pi$
$720$	6.76251	−	1.05151i	0.252024	−	0.0391876i
$721$	−3.12119			−0.116239
$722$	−22.2503	+	10.2385i	−0.828069	+	0.381036i
$723$		−	2.96764i		−	0.110368i
$724$	7.34336	−	8.57343i	0.272914	−	0.318629i
$725$		−	1.46221i		−	0.0543051i
$726$	−1.70427	−	21.9788i	−0.0632512	−	0.815709i
$727$			13.1847i			0.488992i	0.969650	+	0.244496i	$0.0786225\pi$
$727$			13.1847i			0.488992i	−0.969650	+	0.244496i	$0.921377\pi$
$728$	−1.33467	−	36.5037i	−0.0494663	−	1.35292i
$729$	−29.0483			−1.07586
$730$	−8.31584	−	18.0720i	−0.307783	−	0.668874i
$731$		−	75.4468i		−	2.79050i
$732$	−5.01763	+	5.85812i	−0.185457	+	0.216522i
$733$	−1.41996			−0.0524475			−0.0262237	−	0.999656i	$-0.508348\pi$
$733$	−1.41996			−0.0524475			−0.0262237	+	0.999656i	$0.508348\pi$
$734$	−4.91221	−	10.6752i	−0.181313	−	0.394030i
$735$	14.2509			0.525652
$736$	−25.0146	+	16.5869i	−0.922051	+	0.611399i
$737$	22.5332	+	4.02913i	0.830022	+	0.148415i
$738$	10.1953	−	4.69135i	0.375292	−	0.172691i
$739$		−	38.7649i		−	1.42599i	−0.701170	−	0.712994i	$-0.747339\pi$
$739$		−	38.7649i		−	1.42599i	0.701170	−	0.712994i	$-0.252661\pi$
$740$	20.3130	−	23.7156i	0.746719	−	0.871801i
$741$	2.04322	+	6.30139i	0.0750597	+	0.231487i
$742$	26.0139	+	56.5334i	0.954999	+	2.07541i
$743$		−	31.8216i		−	1.16742i	−0.811962	−	0.583710i	$-0.801600\pi$
$743$		−	31.8216i		−	1.16742i	0.811962	−	0.583710i	$-0.198400\pi$
$744$	10.4615	+	2.97439i	0.383539	+	0.109046i
$745$			23.1081i			0.846616i
$746$	4.29376	+	9.33119i	0.157206	+	0.341639i
$747$		−	5.94253i		−	0.217426i
$748$	−27.2620	−	33.3298i	−0.996797	−	1.21866i
$749$		−	22.4950i		−	0.821951i
$750$	22.0600	−	10.1509i	0.805517	−	0.370659i
$751$		−	45.0374i		−	1.64344i	−0.569893	−	0.821719i	$-0.693016\pi$
$751$		−	45.0374i		−	1.64344i	0.569893	−	0.821719i	$-0.306984\pi$
$752$	4.32941	+	27.8434i	0.157877	+	1.01534i
$753$	25.4658			0.928025
$754$	−2.70781	+	2.49649i	−0.0986125	+	0.0909169i
$755$	22.2539			0.809901
$756$	−26.3617	+	30.7775i	−0.958766	+	1.11937i
$757$	−6.91413			−0.251298			−0.125649	−	0.992075i	$-0.540101\pi$
$757$	−6.91413			−0.251298			−0.125649	+	0.992075i	$0.540101\pi$
$758$	−7.52990	+	3.46489i	−0.273498	+	0.125850i
$759$	−24.5478	−	4.38935i	−0.891029	−	0.159323i
$760$	−1.72994	+	6.08456i	−0.0627515	+	0.220710i
$761$	18.8371			0.682845			0.341422	−	0.939910i	$-0.389091\pi$
$761$	18.8371			0.682845			0.341422	+	0.939910i	$0.389091\pi$
$762$	−2.73106	−	5.93515i	−0.0989360	−	0.215008i
$763$			51.5685i			1.86690i
$764$	1.82615	+	1.56414i	0.0660677	+	0.0565886i
$765$	11.1065			0.401555
$766$	−39.4840	+	18.1686i	−1.42662	+	0.656459i
$767$	−7.84519	−	24.1949i	−0.283274	−	0.873628i
$768$	−6.88462	−	21.6030i	−0.248427	−	0.779530i
$769$	−12.2150			−0.440483			−0.220241	−	0.975445i	$-0.570684\pi$
$769$	−12.2150			−0.440483			−0.220241	+	0.975445i	$0.570684\pi$
$770$	28.0486	−	7.29134i	1.01080	−	0.262762i
$771$			2.52787i			0.0910389i
$772$	−5.87345	+	6.85730i	−0.211390	+	0.246799i
$773$		−	5.46590i		−	0.196595i	−0.995157	−	0.0982974i	$-0.968660\pi$
$773$		−	5.46590i		−	0.196595i	0.995157	−	0.0982974i	$-0.0313396\pi$
$774$	−14.8101	+	6.81489i	−0.532339	+	0.244956i
$775$	−5.49319			−0.197321
$776$	−2.18538	−	0.621339i	−0.0784505	−	0.0223048i
$777$			45.9411i			1.64813i
$778$	−37.4329	+	17.2248i	−1.34203	+	0.617538i
$779$			10.3733i			0.371661i
$780$	−16.2720	−	6.77856i	−0.582630	−	0.242711i
$781$	11.0383	+	1.97373i	0.394980	+	0.0706258i
$782$	−44.2489	+	20.3612i	−1.58234	+	0.728114i
$783$	4.08593			0.146019
$784$	3.58290	+	23.0424i	0.127961	+	0.822942i
$785$			39.5167i			1.41041i
$786$	−13.1331	−	28.5409i	−0.468442	−	1.01802i
$787$			10.1286i			0.361046i	0.983571	+	0.180523i	$0.0577790\pi$
$787$			10.1286i			0.361046i	−0.983571	+	0.180523i	$0.942221\pi$
$788$	13.3757	−	15.6163i	0.476490	−	0.556306i
$789$		−	19.7705i		−	0.703849i
$790$	10.7296	+	23.3177i	0.381744	+	0.829605i
$791$			21.3808i			0.760213i
$792$	−4.08011	+	8.36209i	−0.144981	+	0.297134i
$793$	−9.33411	+	3.02658i	−0.331464	+	0.107477i
$794$	15.3545	+	33.3684i	0.544910	+	1.18420i
$795$	30.0311			1.06509
$796$	24.9207	+	21.3452i	0.883291	+	0.756561i
$797$	−30.5047			−1.08053			−0.540266	−	0.841494i	$-0.681676\pi$
$797$	−30.5047			−1.08053			−0.540266	+	0.841494i	$0.681676\pi$
$798$	−3.89040	−	8.45461i	−0.137719	−	0.299290i
$799$			45.7287i			1.61777i
$800$	6.32853	+	9.54406i	0.223747	+	0.337433i
$801$		−	14.5260i		−	0.513251i
$802$	−14.3783	−	31.2470i	−0.507716	−	1.10337i
$803$	26.6237	+	4.76054i	0.939531	+	0.167996i
$804$	14.8563	+	12.7248i	0.523941	+	0.448768i
$805$		−	32.7832i		−	1.15546i
$806$	9.37875	+	10.1726i	0.330352	+	0.358315i
$807$		−	6.37032i		−	0.224246i
$808$	32.5874	+	9.26513i	1.14642	+	0.325946i
$809$		−	17.4888i		−	0.614875i	−0.951568	−	0.307437i	$-0.900529\pi$
$809$		−	17.4888i		−	0.614875i	0.951568	−	0.307437i	$-0.0994715\pi$
$810$	5.14030	+	11.1709i	0.180612	+	0.392505i
$811$			49.3573i			1.73317i	0.499031	+	0.866584i	$0.333689\pi$
$811$			49.3573i			1.73317i	−0.499031	+	0.866584i	$0.666311\pi$
$812$	3.36604	−	3.92988i	0.118125	−	0.137912i
$813$	10.7833			0.378186
$814$	10.6807	+	41.0871i	0.374360	+	1.44010i
$815$		−	12.4936i		−	0.437633i
$816$	−5.65349	−	36.3588i	−0.197912	−	1.27281i
$817$		−	15.0687i		−	0.527188i
$818$	−8.83593	+	4.06586i	−0.308941	+	0.142159i
$819$	−12.1849	+	3.95094i	−0.425774	+	0.138057i
$820$	−20.9643	−	17.9565i	−0.732106	−	0.627067i
$821$	9.90587			0.345717			0.172859	−	0.984947i	$-0.444700\pi$
$821$	9.90587			0.345717			0.172859	+	0.984947i	$0.444700\pi$
$822$	36.8854	−	16.9728i	1.28653	−	0.591996i
$823$		−	11.0689i		−	0.385839i	−0.981215	−	0.192919i	$-0.938204\pi$
$823$		−	11.0689i		−	0.385839i	0.981215	−	0.192919i	$-0.0617956\pi$
$824$	−2.37069	−	0.674026i	−0.0825869	−	0.0234808i
$825$	−1.67471	+	9.36594i	−0.0583059	+	0.326080i
$826$	14.9376	+	32.4625i	0.519746	+	1.12951i
$827$			15.2352i			0.529780i	0.964279	+	0.264890i	$0.0853356\pi$
$827$			15.2352i			0.529780i	−0.964279	+	0.264890i	$0.914664\pi$
$828$	7.99375	+	6.84685i	0.277802	+	0.237944i
$829$	5.31593			0.184630			0.0923149	−	0.995730i	$-0.470573\pi$
$829$	5.31593			0.184630			0.0923149	+	0.995730i	$0.470573\pi$
$830$	−13.2777	+	6.10976i	−0.460877	+	0.212073i
$831$	−27.7578			−0.962908
$832$	6.86929	−	28.0145i	0.238150	−	0.971228i
$833$			37.8438i			1.31121i
$834$	4.47546	+	9.72607i	0.154972	+	0.336786i
$835$	16.7758			0.580551
$836$	−5.44494	−	6.65685i	−0.188317	−	0.230232i
$837$		−	15.3499i		−	0.530570i
$838$	−3.30805	−	7.18905i	−0.114275	−	0.248342i
$839$	4.29341			0.148225			0.0741125	−	0.997250i	$-0.476388\pi$
$839$	4.29341			0.148225			0.0741125	+	0.997250i	$0.476388\pi$
$840$	23.8211	+	6.77273i	0.821907	+	0.233682i
$841$	28.4783			0.982010
$842$	12.2718	+	26.6691i	0.422915	+	0.919079i
$843$			6.64688i			0.228931i
$844$	−5.62780	+	6.57051i	−0.193717	+	0.226166i
$845$	−13.1591	−	18.1582i	−0.452686	−	0.624660i
$846$	8.97650	−	4.13054i	0.308618	−	0.142011i
$847$	−13.6538	+	36.9592i	−0.469149	+	1.26993i
$848$	7.55029	+	48.5575i	0.259278	+	1.66747i
$849$		−	21.7915i		−	0.747884i
$850$	7.76858	+	16.8827i	0.266460	+	0.579071i
$851$	48.0226			1.64619
$852$	7.27759	+	6.23344i	0.249326	+	0.213554i
$853$	13.2081			0.452236			0.226118	−	0.974100i	$-0.427396\pi$
$853$	13.2081			0.452236			0.226118	+	0.974100i	$0.427396\pi$
$854$	12.5236	−	5.76276i	0.428550	−	0.197197i
$855$	2.21825			0.0758627
$856$	4.85784	−	17.0860i	0.166038	−	0.583989i
$857$			17.5807i			0.600544i	0.953854	+	0.300272i	$0.0970775\pi$
$857$			17.5807i			0.600544i	−0.953854	+	0.300272i	$0.902923\pi$
$858$	20.2037	−	12.8895i	0.689743	−	0.440042i
$859$		−	26.9105i		−	0.918176i	−0.888391	−	0.459088i	$-0.848176\pi$
$859$		−	26.9105i		−	0.918176i	0.888391	−	0.459088i	$-0.151824\pi$
$860$	30.4538	+	26.0844i	1.03847	+	0.889472i
$861$	40.6115			1.38404
$862$	1.74483	+	3.79187i	0.0594293	+	0.129152i
$863$	−27.3717			−0.931744			−0.465872	−	0.884852i	$-0.654259\pi$
$863$	−27.3717			−0.931744			−0.465872	+	0.884852i	$0.654259\pi$
$864$	−26.6694	+	17.6841i	−0.907313	+	0.601626i
$865$	2.64998			0.0901020
$866$	40.0076	−	18.4095i	1.35951	−	0.625581i
$867$		−	35.6235i		−	1.20984i
$868$	−14.7637	−	12.6455i	−0.501112	−	0.429215i
$869$	−34.3517	−	6.14236i	−1.16530	−	0.208365i
$870$	−1.04380	−	2.26838i	−0.0353880	−	0.0769052i
$871$	7.67546	+	23.6714i	0.260073	+	0.802076i
$872$	−11.1363	+	39.1687i	−0.377123	+	1.32642i
$873$			0.796725i			0.0269650i
$874$	−8.83768	+	4.06667i	−0.298939	+	0.137557i
$875$	−43.4017			−1.46725
$876$	17.5532	+	15.0347i	0.593067	+	0.507976i
$877$	−12.3107			−0.415704			−0.207852	−	0.978160i	$-0.566647\pi$
$877$	−12.3107			−0.415704			−0.207852	+	0.978160i	$0.566647\pi$
$878$	4.17943	−	1.92317i	0.141049	−	0.0649038i
$879$			1.85208i			0.0624690i
$880$	22.8788	+	0.519024i	0.771245	+	0.0174963i
$881$	3.41391			0.115018			0.0575088	−	0.998345i	$-0.481684\pi$
$881$	3.41391			0.115018			0.0575088	+	0.998345i	$0.481684\pi$
$882$	7.42869	−	3.41832i	0.250137	−	0.115101i
$883$			0.976914i			0.0328758i	0.999865	+	0.0164379i	$0.00523258\pi$
$883$			0.976914i			0.0328758i	−0.999865	+	0.0164379i	$0.994767\pi$
$884$	18.0007	−	43.2108i	0.605430	−	1.45334i
$885$	17.2444			0.579663
$886$	−15.6176	−	33.9402i	−0.524684	−	1.14024i
$887$	12.8701			0.432136			0.216068	−	0.976378i	$-0.430677\pi$
$887$	12.8701			0.432136			0.216068	+	0.976378i	$0.430677\pi$
$888$	−9.92106	+	34.8944i	−0.332929	+	1.17098i
$889$			11.6771i			0.391636i
$890$	−32.4562	+	14.9348i	−1.08794	+	0.500614i
$891$	−16.4570	−	2.94265i	−0.551330	−	0.0985824i
$892$	−14.0609	+	16.4163i	−0.470795	+	0.549657i
$893$			9.13324i			0.305632i
$894$	−11.2224	−	24.3884i	−0.375332	−	0.815671i
$895$	31.7301			1.06062
$896$	−4.96189	+	40.2194i	−0.165765	+	1.34363i
$897$	−8.36168	−	25.7878i	−0.279188	−	0.861029i
$898$	−6.77911	−	14.7324i	−0.226222	−	0.491625i
$899$			1.95998i			0.0653689i
$900$	2.61234	−	3.04993i	0.0870780	−	0.101664i
$901$			79.7487i			2.65681i
$902$	36.3206	−	9.44167i	1.20934	−	0.314373i
$903$	−58.9942			−1.96321
$904$	−4.61722	+	16.2397i	−0.153566	+	0.540125i
$905$			9.73627i			0.323645i
$906$	−23.4868	+	10.8075i	−0.780298	+	0.359055i
$907$			36.4050i			1.20881i	0.796678	+	0.604404i	$0.206589\pi$
$907$			36.4050i			1.20881i	−0.796678	+	0.604404i	$0.793411\pi$
$908$	−9.96438	−	8.53474i	−0.330680	−	0.283235i
$909$		−	11.8804i		−	0.394048i
$910$	21.3556	+	23.1632i	0.707930	+	0.767853i
$911$		−	41.2058i		−	1.36521i	−0.730789	−	0.682604i	$-0.760847\pi$
$911$		−	41.2058i		−	1.36521i	0.730789	−	0.682604i	$-0.239153\pi$
$912$	−1.12915	−	7.26182i	−0.0373900	−	0.240463i
$913$	3.49764	−	19.5608i	0.115755	−	0.647369i
$914$	22.4204	−	10.3168i	0.741601	−	0.341248i
$915$		−	6.65267i		−	0.219931i
$916$	−4.76938	−	4.08509i	−0.157585	−	0.134975i
$917$			56.1525i			1.85432i
$918$	−47.1761	+	21.7081i	−1.55704	+	0.716475i
$919$	−33.6479			−1.10994			−0.554972	−	0.831869i	$-0.687271\pi$
$919$	−33.6479			−1.10994			−0.554972	+	0.831869i	$0.687271\pi$
$920$	7.07960	−	24.9004i	0.233407	−	0.820942i
$921$	4.20502			0.138560
$922$	18.1744	−	8.36298i	0.598543	−	0.275420i
$923$	3.75995	+	11.5958i	0.123760	+	0.381682i
$924$	−26.0616	+	21.3170i	−0.857365	+	0.701278i
$925$		−	18.3225i		−	0.602440i
$926$	−26.8764	+	12.3672i	−0.883212	+	0.406411i
$927$			0.864284i			0.0283868i
$928$	3.40533	−	2.25803i	0.111786	−	0.0741235i
$929$		−	39.8419i		−	1.30717i	−0.756853	−	0.653585i	$-0.773264\pi$
$929$		−	39.8419i		−	1.30717i	0.756853	−	0.653585i	$-0.226736\pi$
$930$	−8.52178	+	3.92130i	−0.279440	+	0.128585i
$931$			7.55841i			0.247717i
$932$	37.8435	+	32.4139i	1.23961	+	1.06175i
$933$	30.7208			1.00575
$934$	14.3721	+	31.2334i	0.470268	+	1.02199i
$935$	36.5587	+	6.53700i	1.19560	+	0.213783i
$936$	−10.1082	+	0.369583i	−0.330397	+	0.0120802i
$937$		−	41.2656i		−	1.34809i	−0.738691	−	0.674044i	$-0.764556\pi$
$937$		−	41.2656i		−	1.34809i	0.738691	−	0.674044i	$-0.235444\pi$
$938$	−14.6144	−	31.7601i	−0.477178	−	1.03700i
$939$		−	28.2390i		−	0.921546i
$940$	−18.4582	−	15.8099i	−0.602041	−	0.515663i
$941$	2.78132			0.0906683			0.0453342	−	0.998972i	$-0.485565\pi$
$941$	2.78132			0.0906683			0.0453342	+	0.998972i	$0.485565\pi$
$942$	−19.1911	−	41.7062i	−0.625281	−	1.35886i
$943$		−	42.4515i		−	1.38241i
$944$	4.33551	+	27.8826i	0.141109	+	0.907501i
$945$		−	34.9520i		−	1.13699i
$946$	−52.7610	+	13.7154i	−1.71541	+	0.445927i
$947$	47.6840			1.54952			0.774760	−	0.632255i	$-0.217871\pi$
$947$	47.6840			1.54952			0.774760	+	0.632255i	$0.217871\pi$
$948$	−22.6483	−	19.3988i	−0.735581	−	0.630043i
$949$	9.06880	+	27.9685i	0.294386	+	0.907898i
$950$	1.55159	+	3.37192i	0.0503403	+	0.109400i
$951$	23.4848			0.761547
$952$	−17.9853	+	63.2579i	−0.582906	+	2.05020i
$953$			0.860926i			0.0278881i	0.999903	+	0.0139441i	$0.00443868\pi$
$953$			0.860926i			0.0278881i	−0.999903	+	0.0139441i	$0.995561\pi$
$954$	15.6546	−	7.20347i	0.506836	−	0.233221i
$955$	−2.07383			−0.0671076
$956$	38.4807	+	32.9597i	1.24456	+	1.06599i
$957$	3.34178	+	0.597539i	0.108025	+	0.0193157i
$958$	−13.9432	−	30.3014i	−0.450485	−	0.978993i
$959$	−72.5698			−2.34340
$960$	16.6307	+	10.2884i	0.536753	+	0.332057i
$961$	−23.6368			−0.762478
$962$	−33.9307	+	31.2828i	−1.09397	+	1.00860i
$963$	−6.22907			−0.200729
$964$	−2.72461	+	3.18101i	−0.0877538	+	0.102453i
$965$		−	7.78737i		−	0.250684i
$966$	15.9210	+	34.5996i	0.512251	+	1.11322i
$967$		−	40.9601i		−	1.31719i	−0.752498	−	0.658594i	$-0.771151\pi$
$967$		−	40.9601i		−	1.31719i	0.752498	−	0.658594i	$-0.228849\pi$
$968$	−18.3521	+	25.1237i	−0.589858	+	0.807507i
$969$		−	11.9265i		−	0.383134i
$970$	1.78017	−	0.819145i	0.0571577	−	0.0263012i
$971$			2.50851i			0.0805018i	0.999190	+	0.0402509i	$0.0128157\pi$
$971$			2.50851i			0.0805018i	−0.999190	+	0.0402509i	$0.987184\pi$
$972$	14.9275	+	12.7858i	0.478801	+	0.410105i
$973$		−	19.1355i		−	0.613455i
$974$	−4.68116	+	2.15404i	−0.149994	+	0.0690199i
$975$	−9.83904	+	3.19031i	−0.315101	+	0.102172i
$976$	10.7568	−	1.67259i	0.344316	−	0.0535382i
$977$		−	44.8006i		−	1.43330i	−0.697434	−	0.716649i	$-0.745675\pi$
$977$		−	44.8006i		−	1.43330i	0.697434	−	0.716649i	$-0.254325\pi$
$978$	6.06749	+	13.1859i	0.194017	+	0.421637i
$979$	8.54965	−	47.8147i	0.273248	−	1.52816i
$980$	−15.2755	−	13.0838i	−0.487958	−	0.417948i
$981$	14.2798			0.455918
$982$	34.6655	−	15.9514i	1.10622	−	0.509028i
$983$	−3.98454			−0.127087			−0.0635435	−	0.997979i	$-0.520240\pi$
$983$	−3.98454			−0.127087			−0.0635435	+	0.997979i	$0.520240\pi$
$984$	30.8463	+	8.77012i	0.983345	+	0.279581i
$985$			17.7343i			0.565063i
$986$	6.02377	−	2.77184i	0.191836	−	0.0882734i
$987$	35.7567			1.13815
$988$	3.59522	−	8.63035i	0.114379	−	0.274568i
$989$			61.6672i			1.96090i
$990$	−2.01904	−	7.76690i	−0.0641692	−	0.246848i
$991$		−	14.9072i		−	0.473542i	−0.971565	−	0.236771i	$-0.923911\pi$
$991$		−	14.9072i		−	0.473542i	0.971565	−	0.236771i	$-0.0760892\pi$
$992$	−8.48290	−	12.7931i	−0.269332	−	0.406180i
$993$			40.8615i			1.29670i
$994$	−7.15912	−	15.5582i	−0.227074	−	0.493476i
$995$	−28.3008			−0.897195
$996$	11.0462	−	12.8966i	0.350013	−	0.408643i
$997$		−	42.7230i		−	1.35305i	−0.736419	−	0.676525i	$-0.763485\pi$
$997$		−	42.7230i		−	1.35305i	0.736419	−	0.676525i	$-0.236515\pi$
$998$	38.6349	−	17.7779i	1.22297	−	0.562749i
$999$	51.1995			1.61988

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.b.c.571.12	yes	56
4.3	odd	2	inner	572.2.b.c.571.10	yes	56
11.10	odd	2	inner	572.2.b.c.571.46	yes	56
13.12	even	2	inner	572.2.b.c.571.45	yes	56
44.43	even	2	inner	572.2.b.c.571.48	yes	56
52.51	odd	2	inner	572.2.b.c.571.47	yes	56
143.142	odd	2	inner	572.2.b.c.571.11	yes	56
572.571	even	2	inner	572.2.b.c.571.9	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.b.c.571.9	✓	56	572.571	even	2	inner
572.2.b.c.571.10	yes	56	4.3	odd	2	inner
572.2.b.c.571.11	yes	56	143.142	odd	2	inner
572.2.b.c.571.12	yes	56	1.1	even	1	trivial
572.2.b.c.571.45	yes	56	13.12	even	2	inner
572.2.b.c.571.46	yes	56	11.10	odd	2	inner
572.2.b.c.571.47	yes	56	52.51	odd	2	inner
572.2.b.c.571.48	yes	56	44.43	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28473 + 0.591168i) q^{2} +1.41709i q^{3} +(1.30104 - 1.51898i) q^{4} +1.72500i q^{5} +(-0.837739 - 1.82057i) q^{6} +3.58187i q^{7} +(-0.773512 + 2.72060i) q^{8} +0.991852 q^{9} +O(q^{10})\)	\(q+(-1.28473 + 0.591168i) q^{2} +1.41709i q^{3} +(1.30104 - 1.51898i) q^{4} +1.72500i q^{5} +(-0.837739 - 1.82057i) q^{6} +3.58187i q^{7} +(-0.773512 + 2.72060i) q^{8} +0.991852 q^{9} +(-1.01976 - 2.21615i) q^{10} +(3.26484 + 0.583781i) q^{11} +(2.15253 + 1.84369i) q^{12} +(1.11210 + 3.42976i) q^{13} +(-2.11749 - 4.60173i) q^{14} -2.44448 q^{15} +(-0.614582 - 3.95250i) q^{16} -6.49142i q^{17} +(-1.27426 + 0.586351i) q^{18} -1.29651i q^{19} +(2.62023 + 2.24430i) q^{20} -5.07584 q^{21} +(-4.53954 + 1.18007i) q^{22} +5.30582i q^{23} +(-3.85534 - 1.09614i) q^{24} +2.02438 q^{25} +(-3.45630 - 3.74886i) q^{26} +5.65682i q^{27} +(5.44078 + 4.66017i) q^{28} -0.722301i q^{29} +(3.14049 - 1.44510i) q^{30} -2.71352 q^{31} +(3.12616 + 4.71456i) q^{32} +(-0.827271 + 4.62658i) q^{33} +(3.83752 + 8.33969i) q^{34} -6.17873 q^{35} +(1.29044 - 1.50660i) q^{36} -9.05093i q^{37} +(0.766454 + 1.66566i) q^{38} +(-4.86028 + 1.57594i) q^{39} +(-4.69304 - 1.33431i) q^{40} -8.00093 q^{41} +(6.52107 - 3.00067i) q^{42} +11.6226 q^{43} +(5.13445 - 4.19970i) q^{44} +1.71094i q^{45} +(-3.13663 - 6.81653i) q^{46} -7.04449 q^{47} +(5.60106 - 0.870918i) q^{48} -5.82982 q^{49} +(-2.60077 + 1.19675i) q^{50} +9.19893 q^{51} +(6.65661 + 2.77301i) q^{52} -12.2853 q^{53} +(-3.34413 - 7.26746i) q^{54} +(-1.00702 + 5.63185i) q^{55} +(-9.74485 - 2.77062i) q^{56} +1.83727 q^{57} +(0.427001 + 0.927959i) q^{58} -7.05441 q^{59} +(-3.18037 + 3.71311i) q^{60} +2.72151i q^{61} +(3.48613 - 1.60415i) q^{62} +3.55269i q^{63} +(-6.80336 - 4.20884i) q^{64} +(-5.91633 + 1.91837i) q^{65} +(-1.67227 - 6.43294i) q^{66} +6.90178 q^{67} +(-9.86031 - 8.44560i) q^{68} -7.51883 q^{69} +(7.93797 - 3.65267i) q^{70} +3.38095 q^{71} +(-0.767209 + 2.69844i) q^{72} +8.15467 q^{73} +(5.35062 + 11.6280i) q^{74} +2.86873i q^{75} +(-1.96937 - 1.68681i) q^{76} +(-2.09103 + 11.6943i) q^{77} +(5.31248 - 4.89790i) q^{78} -10.5217 q^{79} +(6.81807 - 1.06015i) q^{80} -5.04067 q^{81} +(10.2790 - 4.72989i) q^{82} -5.99135i q^{83} +(-6.60388 + 7.71009i) q^{84} +11.1977 q^{85} +(-14.9318 + 6.87088i) q^{86} +1.02357 q^{87} +(-4.11363 + 8.43078i) q^{88} -14.6453i q^{89} +(-1.01145 - 2.19809i) q^{90} +(-12.2850 + 3.98339i) q^{91} +(8.05942 + 6.90309i) q^{92} -3.84531i q^{93} +(9.05024 - 4.16447i) q^{94} +2.23648 q^{95} +(-6.68097 + 4.43006i) q^{96} +0.803270i q^{97} +(7.48972 - 3.44640i) q^{98} +(3.23824 + 0.579024i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{4} - 32 q^{9}+O(q^{10}) \) 56 * q + 4 * q^4 - 32 * q^9	\( 56 q + 4 q^{4} - 32 q^{9} - 12 q^{14} - 4 q^{16} - 4 q^{22} - 192 q^{25} + 4 q^{26} + 28 q^{36} + 24 q^{38} + 88 q^{42} + 56 q^{48} + 40 q^{49} - 8 q^{53} - 68 q^{56} + 28 q^{64} - 76 q^{66} - 16 q^{69} + 32 q^{77} + 108 q^{78} - 152 q^{81} - 60 q^{82} + 52 q^{88} + 132 q^{92}+O(q^{100}) \) 56 * q + 4 * q^4 - 32 * q^9 - 12 * q^14 - 4 * q^16 - 4 * q^22 - 192 * q^25 + 4 * q^26 + 28 * q^36 + 24 * q^38 + 88 * q^42 + 56 * q^48 + 40 * q^49 - 8 * q^53 - 68 * q^56 + 28 * q^64 - 76 * q^66 - 16 * q^69 + 32 * q^77 + 108 * q^78 - 152 * q^81 - 60 * q^82 + 52 * q^88 + 132 * q^92

Introduction

L-functions

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