LMFDB - Embedded newform 547.2.h.a.13.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(13,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([22]))

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

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

chi := DirichletCharacter("547.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.h (of order $21$, degree $12$, 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:	$4.36781699056$
Analytic rank:	$0$
Dimension:	$540$
Relative dimension:	$45$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			13.17
Character	$\chi$	$=$	547.13
Dual form			547.2.h.a.505.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0447565 + 0.597235i) q^{2} +(-1.37304 + 1.72174i) q^{3} +(1.62298 + 0.244624i) q^{4} +(-2.26785 + 2.10426i) q^{5} +(-0.966831 - 0.897088i) q^{6} +(2.04652 - 0.308464i) q^{7} +(-0.485277 + 2.12614i) q^{8} +(-0.411584 - 1.80327i) q^{9} +O(q^{10})$	\(q+(-0.0447565 + 0.597235i) q^{2} +(-1.37304 + 1.72174i) q^{3} +(1.62298 + 0.244624i) q^{4} +(-2.26785 + 2.10426i) q^{5} +(-0.966831 - 0.897088i) q^{6} +(2.04652 - 0.308464i) q^{7} +(-0.485277 + 2.12614i) q^{8} +(-0.411584 - 1.80327i) q^{9} +(-1.15524 - 1.44862i) q^{10} +(-1.60961 + 2.78793i) q^{11} +(-2.64960 + 2.45847i) q^{12} +(-0.287872 + 0.196268i) q^{13} +(0.0926300 + 1.23606i) q^{14} +(-0.509133 - 6.79390i) q^{15} +(1.88870 + 0.582585i) q^{16} +(0.434912 + 0.134153i) q^{17} +(1.09540 - 0.165104i) q^{18} +(-0.0322891 - 0.430868i) q^{19} +(-4.19543 + 2.86039i) q^{20} +(-2.27887 + 3.94712i) q^{21} +(-1.59301 - 1.08609i) q^{22} +(-0.146881 - 1.95999i) q^{23} +(-2.99435 - 3.75480i) q^{24} +(0.341597 - 4.55830i) q^{25} +(-0.104334 - 0.180711i) q^{26} +(-2.28243 - 1.09916i) q^{27} +3.39692 q^{28} +(-0.177603 + 0.778131i) q^{29} +4.08034 q^{30} +(1.36727 - 1.71450i) q^{31} +(-2.02595 + 5.16204i) q^{32} +(-2.59003 - 6.59928i) q^{33} +(-0.0995857 + 0.253740i) q^{34} +(-3.99213 + 5.00597i) q^{35} +(-0.226868 - 3.02734i) q^{36} +(-2.76197 - 0.851956i) q^{37} +0.258774 q^{38} +(0.0573381 - 0.765124i) q^{39} +(-3.37341 - 5.84291i) q^{40} +(4.74919 - 8.22584i) q^{41} +(-2.25536 - 1.53768i) q^{42} +(2.98329 - 0.449659i) q^{43} +(-3.29435 + 4.13099i) q^{44} +(4.72796 + 3.22347i) q^{45} +1.17715 q^{46} +(-2.86418 - 4.96091i) q^{47} +(-3.59632 + 2.45193i) q^{48} +(-2.59590 + 0.800728i) q^{49} +(2.70708 + 0.408027i) q^{50} +(-0.828129 + 0.564609i) q^{51} +(-0.515220 + 0.248117i) q^{52} +(-5.26668 + 3.59076i) q^{53} +(0.758610 - 1.31395i) q^{54} +(-2.21617 - 9.70966i) q^{55} +(-0.337294 + 4.50088i) q^{56} +(0.786177 + 0.536007i) q^{57} +(-0.456778 - 0.140897i) q^{58} +(-4.66637 + 8.08239i) q^{59} +(0.835643 - 11.1509i) q^{60} +(3.66376 + 1.13012i) q^{61} +(0.962765 + 0.893315i) q^{62} +(-1.39856 - 3.56347i) q^{63} +(0.569266 + 0.274144i) q^{64} +(0.239853 - 1.05086i) q^{65} +(4.05724 - 1.25149i) q^{66} +(4.85841 + 1.49862i) q^{67} +(0.673034 + 0.324116i) q^{68} +(3.57628 + 2.43826i) q^{69} +(-2.81107 - 2.60829i) q^{70} +(14.2213 + 4.38670i) q^{71} +4.03372 q^{72} +(-0.767305 + 10.2390i) q^{73} +(0.632434 - 1.61142i) q^{74} +(7.37918 + 6.84688i) q^{75} +(0.0529963 - 0.707187i) q^{76} +(-2.43413 + 6.20207i) q^{77} +(0.454392 + 0.0684886i) q^{78} +(3.05262 + 3.82787i) q^{79} +(-5.50920 + 2.65309i) q^{80} +(10.0258 - 4.82815i) q^{81} +(4.70020 + 3.20454i) q^{82} +(-4.85034 + 8.40103i) q^{83} +(-4.66411 + 5.84861i) q^{84} +(-1.26861 + 0.610930i) q^{85} +(0.135030 + 1.80185i) q^{86} +(-1.09588 - 1.37419i) q^{87} +(-5.14641 - 4.77517i) q^{88} +(0.193487 - 0.847721i) q^{89} +(-2.13677 + 2.67943i) q^{90} +(-0.528595 + 0.490464i) q^{91} +(0.241077 - 3.21695i) q^{92} +(1.07461 + 4.70817i) q^{93} +(3.09102 - 1.48856i) q^{94} +(0.979885 + 0.909201i) q^{95} +(-6.10598 - 10.5759i) q^{96} +(-0.701790 - 9.36474i) q^{97} +(-0.362039 - 1.58620i) q^{98} +(5.68987 + 1.75509i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 540 q - 13 q^{2} - 10 q^{3} + 33 q^{4} - 15 q^{5} + 10 q^{6} - 2 q^{7} - 26 q^{8} - 96 q^{9}+O(q^{10}) $ 540 * q - 13 * q^2 - 10 * q^3 + 33 * q^4 - 15 * q^5 + 10 * q^6 - 2 * q^7 - 26 * q^8 - 96 * q^9	\( 540 q - 13 q^{2} - 10 q^{3} + 33 q^{4} - 15 q^{5} + 10 q^{6} - 2 q^{7} - 26 q^{8} - 96 q^{9} - 4 q^{10} - 8 q^{11} - 18 q^{12} - 11 q^{13} + 5 q^{14} - 7 q^{15} + 53 q^{16} - 10 q^{17} - 59 q^{18} - 12 q^{19} - 18 q^{20} + 20 q^{21} + 70 q^{22} - 15 q^{23} - 46 q^{24} + 26 q^{25} - 39 q^{26} - q^{27} - 56 q^{28} - 40 q^{29} - 100 q^{30} + 59 q^{31} - 5 q^{32} - 15 q^{33} - 8 q^{34} + 36 q^{35} + 43 q^{36} - 32 q^{37} - 108 q^{38} + 34 q^{39} - 27 q^{40} + 39 q^{41} + 46 q^{42} - 16 q^{43} - 110 q^{44} - 103 q^{45} + 12 q^{46} - 60 q^{47} + 42 q^{48} + 57 q^{49} - 168 q^{50} + 57 q^{51} - 46 q^{52} - 30 q^{53} + 113 q^{54} + 38 q^{55} + 64 q^{56} + 22 q^{57} - 88 q^{58} + 55 q^{59} + 9 q^{60} + 26 q^{61} - 32 q^{62} + 6 q^{63} - 50 q^{64} + 73 q^{65} + 72 q^{66} - 104 q^{67} - 181 q^{68} - 125 q^{69} - 50 q^{70} + 39 q^{71} - 434 q^{72} + 46 q^{73} - 178 q^{74} + 248 q^{75} - 126 q^{76} - 52 q^{77} - 82 q^{78} + 86 q^{79} + 208 q^{80} - 4 q^{81} + 177 q^{82} + 39 q^{83} + 124 q^{84} - 12 q^{85} + 2 q^{86} + 162 q^{87} - 34 q^{88} + 63 q^{89} + 121 q^{90} + 21 q^{91} + q^{92} - 57 q^{93} + 67 q^{94} - 143 q^{95} + 489 q^{96} + 119 q^{97} - 10 q^{98} - 120 q^{99}+O(q^{100}) \) 540 * q - 13 * q^2 - 10 * q^3 + 33 * q^4 - 15 * q^5 + 10 * q^6 - 2 * q^7 - 26 * q^8 - 96 * q^9 - 4 * q^10 - 8 * q^11 - 18 * q^12 - 11 * q^13 + 5 * q^14 - 7 * q^15 + 53 * q^16 - 10 * q^17 - 59 * q^18 - 12 * q^19 - 18 * q^20 + 20 * q^21 + 70 * q^22 - 15 * q^23 - 46 * q^24 + 26 * q^25 - 39 * q^26 - q^27 - 56 * q^28 - 40 * q^29 - 100 * q^30 + 59 * q^31 - 5 * q^32 - 15 * q^33 - 8 * q^34 + 36 * q^35 + 43 * q^36 - 32 * q^37 - 108 * q^38 + 34 * q^39 - 27 * q^40 + 39 * q^41 + 46 * q^42 - 16 * q^43 - 110 * q^44 - 103 * q^45 + 12 * q^46 - 60 * q^47 + 42 * q^48 + 57 * q^49 - 168 * q^50 + 57 * q^51 - 46 * q^52 - 30 * q^53 + 113 * q^54 + 38 * q^55 + 64 * q^56 + 22 * q^57 - 88 * q^58 + 55 * q^59 + 9 * q^60 + 26 * q^61 - 32 * q^62 + 6 * q^63 - 50 * q^64 + 73 * q^65 + 72 * q^66 - 104 * q^67 - 181 * q^68 - 125 * q^69 - 50 * q^70 + 39 * q^71 - 434 * q^72 + 46 * q^73 - 178 * q^74 + 248 * q^75 - 126 * q^76 - 52 * q^77 - 82 * q^78 + 86 * q^79 + 208 * q^80 - 4 * q^81 + 177 * q^82 + 39 * q^83 + 124 * q^84 - 12 * q^85 + 2 * q^86 + 162 * q^87 - 34 * q^88 + 63 * q^89 + 121 * q^90 + 21 * q^91 + q^92 - 57 * q^93 + 67 * q^94 - 143 * q^95 + 489 * q^96 + 119 * q^97 - 10 * q^98 - 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{21}\right)$

Coefficient data

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

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

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

$2$	−0.0447565	+	0.597235i	−0.0316477	+	0.422309i	0.958768	+	0.284190i	$0.0917246\pi$
$2$	−0.0447565	+	0.597235i	−0.0316477	+	0.422309i	−0.990416	+	0.138119i	$0.955894\pi$
$3$	−1.37304	+	1.72174i	−0.792727	+	0.994048i	0.207149	+	0.978309i	$0.433581\pi$
$3$	−1.37304	+	1.72174i	−0.792727	+	0.994048i	−0.999876	+	0.0157387i	$0.994990\pi$
$4$	1.62298	+	0.244624i	0.811488	+	0.122312i
$5$	−2.26785	+	2.10426i	−1.01422	+	0.941054i	−0.998269	−	0.0588185i	$-0.981267\pi$
$5$	−2.26785	+	2.10426i	−1.01422	+	0.941054i	−0.0159467	+	0.999873i	$0.505076\pi$
$6$	−0.966831	−	0.897088i	−0.394707	−	0.366235i
$7$	2.04652	−	0.308464i	0.773513	−	0.116588i	0.249588	−	0.968352i	$-0.419705\pi$
$7$	2.04652	−	0.308464i	0.773513	−	0.116588i	0.523926	+	0.851764i	$0.324467\pi$
$8$	−0.485277	+	2.12614i	−0.171571	+	0.751702i
$9$	−0.411584	−	1.80327i	−0.137195	−	0.601089i
$10$	−1.15524	−	1.44862i	−0.365318	−	0.458094i
$11$	−1.60961	+	2.78793i	−0.485316	+	0.840592i	−0.999858	−	0.0168733i	$-0.994629\pi$
$11$	−1.60961	+	2.78793i	−0.485316	+	0.840592i	0.514542	+	0.857465i	$0.327962\pi$
$12$	−2.64960	+	2.45847i	−0.764872	+	0.709698i
$13$	−0.287872	+	0.196268i	−0.0798412	+	0.0544348i	−0.602583	−	0.798056i	$-0.705862\pi$
$13$	−0.287872	+	0.196268i	−0.0798412	+	0.0544348i	0.522742	+	0.852491i	$0.324909\pi$
$14$	0.0926300	+	1.23606i	0.0247564	+	0.330351i
$15$	−0.509133	−	6.79390i	−0.131457	−	1.75418i
$16$	1.88870	+	0.582585i	0.472174	+	0.145646i
$17$	0.434912	+	0.134153i	0.105482	+	0.0325368i	0.347047	−	0.937848i	$-0.387185\pi$
$17$	0.434912	+	0.134153i	0.105482	+	0.0325368i	−0.241565	+	0.970385i	$0.577661\pi$
$18$	1.09540	−	0.165104i	0.258187	−	0.0389154i
$19$	−0.0322891	−	0.430868i	−0.00740762	−	0.0988479i	0.992274	−	0.124062i	$-0.0395922\pi$
$19$	−0.0322891	−	0.430868i	−0.00740762	−	0.0988479i	−0.999682	+	0.0252143i	$0.991973\pi$
$20$	−4.19543	+	2.86039i	−0.938126	+	0.639603i
$21$	−2.27887	+	3.94712i	−0.497290	+	0.861332i
$22$	−1.59301	−	1.08609i	−0.339630	−	0.231556i
$23$	−0.146881	−	1.95999i	−0.0306269	−	0.408687i	−0.991356	−	0.131199i	$-0.958117\pi$
$23$	−0.146881	−	1.95999i	−0.0306269	−	0.408687i	0.960729	−	0.277488i	$-0.0895018\pi$
$24$	−2.99435	−	3.75480i	−0.611219	−	0.766445i
$25$	0.341597	−	4.55830i	0.0683194	−	0.911660i
$26$	−0.104334	−	0.180711i	−0.0204615	−	0.0354404i
$27$	−2.28243	−	1.09916i	−0.439254	−	0.211534i
$28$	3.39692			0.641957
$29$	−0.177603	+	0.778131i	−0.0329801	+	0.144495i	−0.988737	−	0.149661i	$-0.952182\pi$
$29$	−0.177603	+	0.778131i	−0.0329801	+	0.144495i	0.955757	+	0.294157i	$0.0950388\pi$
$30$	4.08034			0.744965
$31$	1.36727	−	1.71450i	0.245569	−	0.307933i	−0.643737	−	0.765247i	$-0.722617\pi$
$31$	1.36727	−	1.71450i	0.245569	−	0.307933i	0.889306	+	0.457314i	$0.151188\pi$
$32$	−2.02595	+	5.16204i	−0.358141	+	0.912529i
$33$	−2.59003	−	6.59928i	−0.450866	−	1.14879i
$34$	−0.0995857	+	0.253740i	−0.0170788	+	0.0435161i
$35$	−3.99213	+	5.00597i	−0.674793	+	0.846164i
$36$	−0.226868	−	3.02734i	−0.0378113	−	0.504557i
$37$	−2.76197	−	0.851956i	−0.454066	−	0.140061i	0.0592823	−	0.998241i	$-0.481119\pi$
$37$	−2.76197	−	0.851956i	−0.454066	−	0.140061i	−0.513348	+	0.858181i	$0.671595\pi$
$38$	0.258774			0.0419787
$39$	0.0573381	−	0.765124i	0.00918145	−	0.122518i
$40$	−3.37341	−	5.84291i	−0.533383	−	0.923846i
$41$	4.74919	−	8.22584i	0.741699	−	1.28466i	−0.210022	−	0.977697i	$-0.567354\pi$
$41$	4.74919	−	8.22584i	0.741699	−	1.28466i	0.951721	−	0.306964i	$-0.0993131\pi$
$42$	−2.25536	−	1.53768i	−0.348010	−	0.237269i
$43$	2.98329	−	0.449659i	0.454947	−	0.0685723i	0.0824287	−	0.996597i	$-0.473732\pi$
$43$	2.98329	−	0.449659i	0.454947	−	0.0685723i	0.372519	+	0.928025i	$0.378494\pi$
$44$	−3.29435	+	4.13099i	−0.496643	+	0.622770i
$45$	4.72796	+	3.22347i	0.704803	+	0.480526i
$46$	1.17715			0.173561
$47$	−2.86418	−	4.96091i	−0.417784	−	0.723623i	0.577932	−	0.816085i	$-0.303860\pi$
$47$	−2.86418	−	4.96091i	−0.417784	−	0.723623i	−0.995716	+	0.0924616i	$0.970526\pi$
$48$	−3.59632	+	2.45193i	−0.519084	+	0.353906i
$49$	−2.59590	+	0.800728i	−0.370843	+	0.114390i
$50$	2.70708	+	0.408027i	0.382840	+	0.0577038i
$51$	−0.828129	+	0.564609i	−0.115961	+	0.0790610i
$52$	−0.515220	+	0.248117i	−0.0714482	+	0.0344076i
$53$	−5.26668	+	3.59076i	−0.723434	+	0.493229i	−0.868186	−	0.496239i	$-0.834714\pi$
$53$	−5.26668	+	3.59076i	−0.723434	+	0.493229i	0.144752	+	0.989468i	$0.453762\pi$
$54$	0.758610	−	1.31395i	0.103234	−	0.178806i
$55$	−2.21617	−	9.70966i	−0.298828	−	1.30925i
$56$	−0.337294	+	4.50088i	−0.0450728	+	0.601455i
$57$	0.786177	+	0.536007i	0.104132	+	0.0709958i
$58$	−0.456778	−	0.140897i	−0.0599779	−	0.0185007i
$59$	−4.66637	+	8.08239i	−0.607509	+	1.05224i	0.384140	+	0.923275i	$0.374498\pi$
$59$	−4.66637	+	8.08239i	−0.607509	+	1.05224i	−0.991649	+	0.128962i	$0.958835\pi$
$60$	0.835643	−	11.1509i	0.107881	−	1.43957i
$61$	3.66376	+	1.13012i	0.469096	+	0.144697i	0.520286	−	0.853992i	$-0.325825\pi$
$61$	3.66376	+	1.13012i	0.469096	+	0.144697i	−0.0511899	+	0.998689i	$0.516301\pi$
$62$	0.962765	+	0.893315i	0.122271	+	0.113451i
$63$	−1.39856	−	3.56347i	−0.176202	−	0.448955i
$64$	0.569266	+	0.274144i	0.0711582	+	0.0342680i
$65$	0.239853	−	1.05086i	0.0297501	−	0.130344i
$66$	4.05724	−	1.25149i	0.499412	−	0.154048i
$67$	4.85841	+	1.49862i	0.593550	+	0.183086i	0.576954	−	0.816776i	$-0.304241\pi$
$67$	4.85841	+	1.49862i	0.593550	+	0.183086i	0.0165955	+	0.999862i	$0.494717\pi$
$68$	0.673034	+	0.324116i	0.0816174	+	0.0393049i
$69$	3.57628	+	2.43826i	0.430533	+	0.293533i
$70$	−2.81107	−	2.60829i	−0.335987	−	0.311750i
$71$	14.2213	+	4.38670i	1.68776	+	0.520606i	0.982167	−	0.188009i	$-0.0602033\pi$
$71$	14.2213	+	4.38670i	1.68776	+	0.520606i	0.705596	+	0.708615i	$0.250679\pi$
$72$	4.03372			0.475379
$73$	−0.767305	+	10.2390i	−0.0898063	+	1.19838i	0.752208	+	0.658926i	$0.228989\pi$
$73$	−0.767305	+	10.2390i	−0.0898063	+	1.19838i	−0.842014	+	0.539456i	$0.818630\pi$
$74$	0.632434	−	1.61142i	0.0735190	−	0.187323i
$75$	7.37918	+	6.84688i	0.852075	+	0.790610i
$76$	0.0529963	−	0.707187i	0.00607909	−	0.0811199i
$77$	−2.43413	+	6.20207i	−0.277395	+	0.706792i
$78$	0.454392	+	0.0684886i	0.0514498	+	0.00775481i
$79$	3.05262	+	3.82787i	0.343447	+	0.430669i	0.923316	−	0.384041i	$-0.125468\pi$
$79$	3.05262	+	3.82787i	0.343447	+	0.430669i	−0.579869	+	0.814710i	$0.696896\pi$
$80$	−5.50920	+	2.65309i	−0.615947	+	0.296625i
$81$	10.0258	−	4.82815i	1.11397	−	0.536461i
$82$	4.70020	+	3.20454i	0.519050	+	0.353882i
$83$	−4.85034	+	8.40103i	−0.532394	+	0.922133i	0.466891	+	0.884315i	$0.345374\pi$
$83$	−4.85034	+	8.40103i	−0.532394	+	0.922133i	−0.999285	+	0.0378180i	$0.987959\pi$
$84$	−4.66411	+	5.84861i	−0.508897	+	0.638136i
$85$	−1.26861	+	0.610930i	−0.137600	+	0.0662646i
$86$	0.135030	+	1.80185i	0.0145607	+	0.194298i
$87$	−1.09588	−	1.37419i	−0.117491	−	0.147329i
$88$	−5.14641	−	4.77517i	−0.548609	−	0.509035i
$89$	0.193487	−	0.847721i	0.0205096	−	0.0898582i	−0.963637	−	0.267214i	$-0.913897\pi$
$89$	0.193487	−	0.847721i	0.0205096	−	0.0898582i	0.984147	+	0.177355i	$0.0567542\pi$
$90$	−2.13677	+	2.67943i	−0.225236	+	0.282437i
$91$	−0.528595	+	0.490464i	−0.0554118	+	0.0514146i
$92$	0.241077	−	3.21695i	0.0251340	−	0.335391i
$93$	1.07461	+	4.70817i	0.111432	+	0.488214i
$94$	3.09102	−	1.48856i	0.318814	−	0.153533i
$95$	0.979885	+	0.909201i	0.100534	+	0.0932820i
$96$	−6.10598	−	10.5759i	−0.623189	−	1.07940i
$97$	−0.701790	−	9.36474i	−0.0712560	−	0.950845i	−0.912206	−	0.409732i	$-0.865622\pi$
$97$	−0.701790	−	9.36474i	−0.0712560	−	0.950845i	0.840950	−	0.541113i	$-0.181997\pi$
$98$	−0.362039	−	1.58620i	−0.0365715	−	0.160230i
$99$	5.68987	+	1.75509i	0.571854	+	0.176394i
$100$	1.66947	−	7.31444i	0.166947	−	0.731444i
$101$	1.18683	+	5.19986i	0.118094	+	0.517405i	0.999025	+	0.0441589i	$0.0140608\pi$
$101$	1.18683	+	5.19986i	0.118094	+	0.517405i	−0.880930	+	0.473246i	$0.843082\pi$
$102$	−0.300140	−	0.519857i	−0.0297182	−	0.0514735i
$103$	−14.1544	+	6.81641i	−1.39468	+	0.671641i	−0.972074	−	0.234674i	$-0.924598\pi$
$103$	−14.1544	+	6.81641i	−1.39468	+	0.671641i	−0.422603	+	0.906315i	$0.638883\pi$
$104$	−0.277594	−	0.707298i	−0.0272203	−	0.0693563i
$105$	−3.13763	−	13.7468i	−0.306201	−	1.34155i
$106$	−1.90881	−	3.30615i	−0.185400	−	0.321122i
$107$	7.00589			0.677285			0.338642	−	0.940915i	$-0.390032\pi$
$107$	7.00589			0.677285			0.338642	+	0.940915i	$0.390032\pi$
$108$	−3.43545	−	2.34225i	−0.330576	−	0.225383i
$109$	5.14894	−	4.77752i	0.493179	−	0.457603i	−0.393945	−	0.919134i	$-0.628890\pi$
$109$	5.14894	−	4.77752i	0.493179	−	0.457603i	0.887124	+	0.461531i	$0.152700\pi$
$110$	5.89813	−	0.889000i	0.562365	−	0.0847629i
$111$	5.25916	−	3.58563i	0.499177	−	0.340333i
$112$	4.04497	+	0.609681i	0.382214	+	0.0576094i
$113$	7.54668	+	5.14524i	0.709932	+	0.484023i	0.863650	−	0.504091i	$-0.168173\pi$
$113$	7.54668	+	5.14524i	0.709932	+	0.484023i	−0.153718	+	0.988115i	$0.549125\pi$
$114$	−0.355308	+	0.445543i	−0.0332777	+	0.0417289i
$115$	4.45744	+	4.13590i	0.415659	+	0.385675i
$116$	−0.478596	+	1.21944i	−0.0444365	+	0.113222i
$117$	0.472406	+	0.438329i	0.0436740	+	0.0405235i
$118$	−4.61823	−	3.14866i	−0.425143	−	0.289857i
$119$	0.931439	+	0.140392i	0.0853848	+	0.0128697i
$120$	14.6918	+	2.21444i	1.34117	+	0.202149i
$121$	0.318303	+	0.551316i	0.0289366	+	0.0501197i
$122$	−0.838924	+	2.13754i	−0.0759526	+	0.193524i
$123$	7.64193	+	19.4713i	0.689050	+	1.75567i
$124$	2.63845	−	2.44813i	0.236940	−	0.219848i
$125$	−0.827344	−	1.03746i	−0.0739999	−	0.0927929i
$126$	2.19082	−	0.675780i	0.195174	−	0.0602032i
$127$	0.892268	+	11.9065i	0.0791760	+	1.05653i	0.885373	+	0.464882i	$0.153903\pi$
$127$	0.892268	+	11.9065i	0.0791760	+	1.05653i	−0.806197	+	0.591648i	$0.798478\pi$
$128$	−5.73458	+	9.93258i	−0.506870	+	0.877925i
$129$	−3.32199	+	5.75386i	−0.292485	+	0.506599i
$130$	0.616877	+	0.190281i	0.0541037	+	0.0166888i
$131$	−0.326478	−	1.43039i	−0.0285245	−	0.124974i	0.958661	−	0.284550i	$-0.0918443\pi$
$131$	−0.326478	−	1.43039i	−0.0285245	−	0.124974i	−0.987186	+	0.159576i	$0.948987\pi$
$132$	−2.58921	−	11.3441i	−0.225362	−	0.987373i
$133$	−0.198988	−	0.871821i	−0.0172544	−	0.0755965i
$134$	−1.11247	+	2.83454i	−0.0961032	+	0.244867i
$135$	7.48914	−	2.31009i	0.644563	−	0.198821i
$136$	−0.496279	+	0.859580i	−0.0425556	+	0.0737084i
$137$	9.95760	−	1.50087i	0.850735	−	0.128228i	0.290820	−	0.956778i	$-0.406072\pi$
$137$	9.95760	−	1.50087i	0.850735	−	0.128228i	0.559915	+	0.828550i	$0.310834\pi$
$138$	−1.61628	+	2.02675i	−0.137587	+	0.172528i
$139$	6.13000	+	15.6190i	0.519940	+	1.32478i	0.914005	+	0.405702i	$0.132973\pi$
$139$	6.13000	+	15.6190i	0.519940	+	1.32478i	−0.394066	+	0.919082i	$0.628932\pi$
$140$	−7.70371	+	7.14800i	−0.651083	+	0.604116i
$141$	12.4741	+	1.88016i	1.05050	+	0.158338i
$142$	−3.25639	+	8.29715i	−0.273270	+	0.696281i
$143$	−0.0838185	−	1.11848i	−0.00700925	−	0.0935320i
$144$	0.273201	−	3.64561i	0.0227667	−	0.303801i
$145$	−1.23461	−	2.13841i	−0.102529	−	0.177585i
$146$	−6.08073	−	0.916523i	−0.503245	−	0.0758520i
$147$	2.18563	−	5.56890i	0.180268	−	0.459315i
$148$	−4.27421	−	2.05835i	−0.351338	−	0.169195i
$149$	17.0872	−	8.22874i	1.39983	−	0.674125i	0.426707	−	0.904390i	$-0.359674\pi$
$149$	17.0872	−	8.22874i	1.39983	−	0.674125i	0.973128	+	0.230265i	$0.0739594\pi$
$150$	−4.41946	+	4.10066i	−0.360848	+	0.334818i
$151$	14.8331	+	7.14324i	1.20710	+	0.581308i	0.925691	−	0.378280i	$-0.123484\pi$
$151$	14.8331	+	7.14324i	1.20710	+	0.581308i	0.281408	+	0.959588i	$0.409199\pi$
$152$	0.931752	+	0.140439i	0.0755751	+	0.0113911i
$153$	0.0629101	−	0.839477i	0.00508598	−	0.0678677i
$154$	−3.59515	−	1.73133i	−0.289705	−	0.139515i
$155$	0.506991	+	6.76533i	0.0407225	+	0.543404i
$156$	0.280226	−	1.22775i	0.0224361	−	0.0982988i
$157$	−3.07406	+	2.09586i	−0.245337	+	0.167268i	−0.679745	−	0.733448i	$-0.737910\pi$
$157$	−3.07406	+	2.09586i	−0.245337	+	0.167268i	0.434409	+	0.900716i	$0.356957\pi$
$158$	−2.42276	+	1.65181i	−0.192744	+	0.131411i
$159$	1.04902	−	13.9981i	0.0831923	−	1.11012i
$160$	−6.26772	−	15.9699i	−0.495507	−	1.26253i
$161$	−0.905183	−	3.96587i	−0.0713384	−	0.312554i
$162$	2.43482	+	6.20382i	0.191298	+	0.487418i
$163$	−1.75723	−	4.47734i	−0.137637	−	0.350693i	0.845391	−	0.534147i	$-0.179367\pi$
$163$	−1.75723	−	4.47734i	−0.137637	−	0.350693i	−0.983028	+	0.183455i	$0.941272\pi$
$164$	9.72006	−	12.1886i	0.759009	−	0.951768i
$165$	19.7604	+	9.51612i	1.53835	+	0.740829i
$166$	−4.80030	−	3.27279i	−0.372576	−	0.254018i
$167$	7.29121	+	9.14288i	0.564210	+	0.707497i	0.979330	−	0.202269i	$-0.0648317\pi$
$167$	7.29121	+	9.14288i	0.564210	+	0.707497i	−0.415120	+	0.909767i	$0.636260\pi$
$168$	−7.28623	−	6.76063i	−0.562145	−	0.521594i
$169$	−4.70508	+	11.9884i	−0.361930	+	0.922181i
$170$	−0.308090	−	0.785000i	−0.0236294	−	0.0602068i
$171$	−0.763680	+	0.235564i	−0.0584001	+	0.0180140i
$172$	4.95180			0.377572
$173$	−8.10590	−	10.1645i	−0.616280	−	0.772791i	0.371535	−	0.928419i	$-0.378831\pi$
$173$	−8.10590	−	10.1645i	−0.616280	−	0.772791i	−0.987816	+	0.155628i	$0.950260\pi$
$174$	0.869765	−	0.592996i	0.0659367	−	0.0449549i
$175$	−0.706983	−	9.43404i	−0.0534429	−	0.713146i
$176$	−4.66427	+	4.32781i	−0.351583	+	0.326221i
$177$	−7.50866	−	19.1317i	−0.564385	−	1.43803i
$178$	0.497628	+	0.153498i	0.0372988	+	0.0115052i
$179$	−0.816048	+	3.57534i	−0.0609943	+	0.267233i	−0.996225	−	0.0868044i	$-0.972334\pi$
$179$	−0.816048	+	3.57534i	−0.0609943	+	0.267233i	0.935231	+	0.354038i	$0.115192\pi$
$180$	6.88483	+	6.38818i	0.513165	+	0.476147i
$181$	−9.57925	−	16.5918i	−0.712020	−	1.23326i	−0.964098	−	0.265548i	$-0.914447\pi$
$181$	−9.57925	−	16.5918i	−0.712020	−	1.23326i	0.252077	−	0.967707i	$-0.418886\pi$
$182$	−0.269264	−	0.337647i	−0.0199592	−	0.0250280i
$183$	−6.97628	+	4.75634i	−0.515701	+	0.351599i
$184$	4.23849	+	0.638850i	0.312466	+	0.0470966i
$185$	8.05649	−	3.87980i	0.592325	−	0.285249i
$186$	−2.85998	+	0.431072i	−0.209704	+	0.0316077i
$187$	−1.07405	+	0.996570i	−0.0785421	+	0.0728764i
$188$	−3.43494	−	8.75209i	−0.250519	−	0.638311i
$189$	−5.01010	−	1.54541i	−0.364431	−	0.112412i
$190$	−0.586862	+	0.544529i	−0.0425755	+	0.0395043i
$191$	4.02048	−	10.2440i	0.290912	−	0.741231i	−0.708459	−	0.705752i	$-0.750609\pi$
$191$	4.02048	−	10.2440i	0.290912	−	0.741231i	0.999370	−	0.0354785i	$-0.0112955\pi$
$192$	−1.25363	+	0.603717i	−0.0904731	+	0.0435695i
$193$	−16.2619	+	5.01613i	−1.17056	+	0.361069i	−0.818276	−	0.574825i	$-0.805070\pi$
$193$	−16.2619	+	5.01613i	−1.17056	+	0.361069i	−0.352281	+	0.935894i	$0.614594\pi$
$194$	5.62436			0.403805
$195$	1.47999	+	1.85585i	0.105984	+	0.132900i
$196$	−4.40896	+	0.664543i	−0.314925	+	0.0474674i
$197$	−16.1971			−1.15400			−0.576999	−	0.816745i	$-0.695776\pi$
$197$	−16.1971			−1.15400			−0.576999	+	0.816745i	$0.695776\pi$
$198$	−1.30286	+	3.31964i	−0.0925903	+	0.235916i
$199$	0.701326	+	1.21473i	0.0497157	+	0.0861100i	0.889812	−	0.456327i	$-0.150835\pi$
$199$	0.701326	+	1.21473i	0.0497157	+	0.0861100i	−0.840097	+	0.542437i	$0.817502\pi$
$200$	9.52579	+	2.93832i	0.673575	+	0.207770i
$201$	−9.25105	+	6.30726i	−0.652519	+	0.444880i
$202$	−3.15865	+	0.476090i	−0.222242	+	0.0334976i
$203$	−0.123444	+	1.64725i	−0.00866409	+	0.115614i
$204$	−1.48215	+	0.713766i	−0.103771	+	0.0499736i
$205$	6.53885	+	28.6486i	0.456693	+	2.00090i
$206$	−3.43749	−	8.75859i	−0.239501	−	0.610240i
$207$	−3.47394	+	1.07157i	−0.241456	+	0.0744792i
$208$	−0.658045	+	0.202980i	−0.0456272	+	0.0140741i
$209$	1.25320	+	0.603510i	0.0866858	+	0.0417457i
$210$	8.35051	−	1.25864i	0.576240	−	0.0868542i
$211$	6.66976	−	6.18863i	0.459165	−	0.426043i	−0.416371	−	0.909195i	$-0.636698\pi$
$211$	6.66976	−	6.18863i	0.459165	−	0.426043i	0.875537	+	0.483151i	$0.160508\pi$
$212$	−9.42608	+	4.53936i	−0.647386	+	0.311765i
$213$	−27.0793	+	18.4623i	−1.85544	+	1.26502i
$214$	−0.313559	+	4.18416i	−0.0214345	+	0.286023i
$215$	−5.81947	+	7.29738i	−0.396884	+	0.497677i
$216$	3.44457	−	4.31936i	0.234374	−	0.293895i
$217$	2.26929	−	3.93052i	0.154049	−	0.266821i
$218$	2.62285	+	3.28895i	0.177642	+	0.222756i
$219$	−16.5753	−	15.3797i	−1.12006	−	1.03926i
$220$	−1.22157	−	16.3007i	−0.0823580	−	1.09899i
$221$	−0.151529	+	0.0467404i	−0.0101929	+	0.00314410i
$222$	1.90608	+	3.30143i	0.127928	+	0.221578i
$223$	−0.324016	+	0.0999456i	−0.0216977	+	0.00669285i	−0.305585	−	0.952165i	$-0.598852\pi$
$223$	−0.324016	+	0.0999456i	−0.0216977	+	0.00669285i	0.283887	+	0.958858i	$0.408376\pi$
$224$	−2.55386	+	11.1892i	−0.170637	+	0.747608i
$225$	−8.36043	+	1.26013i	−0.557362	+	0.0840088i
$226$	−3.41068	+	4.27685i	−0.226875	+	0.284492i
$227$	0.0766089	−	0.0236307i	0.00508471	−	0.00156843i	−0.292212	−	0.956354i	$-0.594391\pi$
$227$	0.0766089	−	0.0236307i	0.00508471	−	0.00156843i	0.297296	+	0.954785i	$0.403915\pi$
$228$	1.14483	+	1.06224i	0.0758180	+	0.0703488i
$229$	7.26935	+	1.09568i	0.480372	+	0.0724044i	0.384765	−	0.923015i	$-0.374283\pi$
$229$	7.26935	+	1.09568i	0.480372	+	0.0724044i	0.0956073	+	0.995419i	$0.469521\pi$
$230$	−2.66960	+	2.47703i	−0.176029	+	0.163331i
$231$	−7.33619	−	12.7067i	−0.482686	−	0.836037i
$232$	−1.56823	−	0.755218i	−0.102959	−	0.0495825i
$233$	−14.0441	−	24.3251i	−0.920061	−	1.59359i	−0.799318	−	0.600908i	$-0.794806\pi$
$233$	−14.0441	−	24.3251i	−0.920061	−	1.59359i	−0.120742	−	0.992684i	$-0.538527\pi$
$234$	−0.282929	+	0.262519i	−0.0184956	+	0.0171614i
$235$	16.9346	+	5.22363i	1.10469	+	0.340752i
$236$	−9.55055	+	11.9760i	−0.621688	+	0.779572i
$237$	−10.7820			−0.700365
$238$	−0.125535	+	0.550004i	−0.00813721	+	0.0356515i
$239$	13.1282	−	22.7387i	0.849192	−	1.47084i	−0.0327375	−	0.999464i	$-0.510423\pi$
$239$	13.1282	−	22.7387i	0.849192	−	1.47084i	0.881930	−	0.471380i	$-0.156244\pi$
$240$	2.99643	−	13.1282i	0.193419	−	0.847423i
$241$	−2.52961	−	0.381277i	−0.162946	−	0.0245602i	0.0670624	−	0.997749i	$-0.478637\pi$
$241$	−2.52961	−	0.381277i	−0.162946	−	0.0245602i	−0.230009	+	0.973189i	$0.573875\pi$
$242$	−0.343511	+	0.165426i	−0.0220817	+	0.0106340i
$243$	−3.76183	+	16.4816i	−0.241321	+	1.05730i
$244$	5.66974	+	2.73040i	0.362968	+	0.174796i
$245$	4.20218	−	7.27838i	0.268467	−	0.464999i
$246$	−11.9710	+	3.69256i	−0.763241	+	0.235429i
$247$	0.0938605	+	0.117697i	0.00597220	+	0.00748890i
$248$	2.98176	+	3.73900i	0.189342	+	0.237427i
$249$	−7.80468	−	19.8860i	−0.494602	−	1.26022i
$250$	0.656634	−	0.447685i	0.0415292	−	0.0283141i
$251$	0.299741	−	0.519166i	0.0189195	−	0.0327695i	−0.856411	−	0.516295i	$-0.827311\pi$
$251$	0.299741	−	0.519166i	0.0189195	−	0.0327695i	0.875330	+	0.483526i	$0.160644\pi$
$252$	−1.39812	−	6.12555i	−0.0880731	−	0.385873i
$253$	5.70074	+	2.74533i	0.358403	+	0.172598i
$254$	−7.15090			−0.448687
$255$	0.689991	−	3.02305i	0.0432089	−	0.189311i
$256$	−4.63133	−	3.15758i	−0.289458	−	0.197349i
$257$	−25.6149	+	12.3355i	−1.59781	+	0.769465i	−0.999494	−	0.0317950i	$-0.989878\pi$
$257$	−25.6149	+	12.3355i	−1.59781	+	0.769465i	−0.598316	+	0.801260i	$0.704163\pi$
$258$	−3.28772	−	2.24153i	−0.204685	−	0.139552i
$259$	−5.91524	−	0.891580i	−0.367555	−	0.0554001i
$260$	0.646342	−	1.64685i	0.0400844	−	0.102133i
$261$	1.47628			0.0913793
$262$	0.868892	−	0.130964i	0.0536803	−	0.00809101i
$263$	17.6366	+	8.49336i	1.08752	+	0.523723i	0.889714	−	0.456518i	$-0.150903\pi$
$263$	17.6366	+	8.49336i	1.08752	+	0.523723i	0.197808	+	0.980241i	$0.436618\pi$
$264$	15.2878	−	2.30427i	0.940902	−	0.141818i
$265$	4.38816	−	19.2258i	0.269563	−	1.18103i
$266$	0.529588	−	0.0798225i	0.0324711	−	0.00489423i
$267$	1.19389	+	1.49709i	0.0730649	+	0.0916205i
$268$	7.51849	+	3.62071i	0.459265	+	0.221170i
$269$	−13.7824	+	4.25129i	−0.840325	+	0.259206i	−0.684896	−	0.728641i	$-0.740152\pi$
$269$	−13.7824	+	4.25129i	−0.840325	+	0.259206i	−0.155429	+	0.987847i	$0.549676\pi$
$270$	1.04448	+	4.57617i	0.0635650	+	0.278497i
$271$	1.47970	+	1.37296i	0.0898855	+	0.0834016i	0.723836	−	0.689972i	$-0.242377\pi$
$271$	1.47970	+	1.37296i	0.0898855	+	0.0834016i	−0.633950	+	0.773374i	$0.718568\pi$
$272$	0.743261	+	0.506747i	0.0450668	+	0.0307260i
$273$	−0.118669	−	1.58353i	−0.00718220	−	0.0958397i
$274$	0.450702	+	6.01420i	0.0272279	+	0.363331i
$275$	12.1584	+	8.28944i	0.733177	+	0.499872i
$276$	5.20775	+	4.83209i	0.313470	+	0.290858i
$277$	−2.46830	−	10.8143i	−0.148306	−	0.649771i	−0.993356	−	0.115083i	$-0.963287\pi$
$277$	−2.46830	−	10.8143i	−0.148306	−	0.649771i	0.845050	−	0.534687i	$-0.179571\pi$
$278$	−9.60255	+	2.96199i	−0.575923	+	0.177649i
$279$	−3.65445	−	1.75989i	−0.218786	−	0.105362i
$280$	−8.70609	−	10.9171i	−0.520288	−	0.652421i
$281$	−1.16665	+	0.175845i	−0.0695967	+	0.0104900i	−0.183748	−	0.982973i	$-0.558823\pi$
$281$	−1.16665	+	0.175845i	−0.0695967	+	0.0104900i	0.114152	+	0.993463i	$0.463585\pi$
$282$	−1.68119	+	7.36579i	−0.100114	+	0.438626i
$283$	25.1692	−	3.79364i	1.49615	−	0.225509i	0.650608	−	0.759414i	$-0.274514\pi$
$283$	25.1692	−	3.79364i	1.49615	−	0.225509i	0.845544	+	0.533905i	$0.179276\pi$
$284$	22.0078	+	10.5984i	1.30592	+	0.628899i
$285$	−2.91083	+	0.438738i	−0.172423	+	0.0259886i
$286$	0.671746			0.0397212
$287$	7.18196	−	18.2993i	0.423938	−	1.08018i
$288$	10.1424	+	1.52872i	0.597646	+	0.0900807i
$289$	−13.8749	−	9.45975i	−0.816171	−	0.556456i
$290$	1.33239	−	0.641646i	0.0782407	−	0.0376787i
$291$	17.0872	+	11.6499i	1.00167	+	0.682929i
$292$	−3.75002	+	16.4299i	−0.219453	+	0.961488i
$293$	−13.6095			−0.795075			−0.397537	−	0.917586i	$-0.630135\pi$
$293$	−13.6095			−0.795075			−0.397537	+	0.917586i	$0.630135\pi$
$294$	3.22812	+	1.55458i	0.188268	+	0.0906649i
$295$	−6.42481	−	28.1489i	−0.374067	−	1.63889i
$296$	3.15170	−	5.45890i	0.183189	−	0.317292i
$297$	6.73821	−	4.59403i	0.390990	−	0.266573i
$298$	4.14973	+	10.5733i	0.240387	+	0.612497i
$299$	0.426966	+	0.535399i	0.0246921	+	0.0309629i
$300$	10.3013	+	12.9175i	0.594747	+	0.745789i
$301$	5.96667	−	1.84047i	0.343913	−	0.106083i
$302$	−4.93006	+	8.53912i	−0.283693	+	0.491371i
$303$	−10.5824	−	5.09621i	−0.607942	−	0.292769i
$304$	0.190033	−	0.832589i	0.0108991	−	0.0477523i
$305$	−10.6869	+	5.14656i	−0.611933	+	0.294691i
$306$	0.498549	+	0.0751442i	0.0285002	+	0.00429571i
$307$	1.56096	−	6.83901i	0.0890886	−	0.390323i	−0.910650	−	0.413178i	$-0.864419\pi$
$307$	1.56096	−	6.83901i	0.0890886	−	0.390323i	0.999739	+	0.0228556i	$0.00727578\pi$
$308$	−5.46772	+	9.47036i	−0.311552	+	0.539624i
$309$	7.69853	−	33.7295i	0.437954	−	1.91880i
$310$	−4.06318			−0.230773
$311$	−0.948711	+	1.18965i	−0.0537965	+	0.0674586i	−0.808002	−	0.589180i	$-0.799451\pi$
$311$	−0.948711	+	1.18965i	−0.0537965	+	0.0674586i	0.754205	+	0.656639i	$0.228022\pi$
$312$	1.59893	+	0.493206i	0.0905218	+	0.0279223i
$313$	−17.7605	+	16.4793i	−1.00388	+	0.931466i	−0.997650	−	0.0685147i	$-0.978174\pi$
$313$	−17.7605	+	16.4793i	−1.00388	+	0.931466i	−0.00623133	+	0.999981i	$0.501984\pi$
$314$	−1.11414	−	1.92974i	−0.0628743	−	0.108901i
$315$	10.6702	+	5.13850i	0.601198	+	0.289522i
$316$	4.01794	+	6.95928i	0.226027	+	0.391490i
$317$	14.5192	−	13.4718i	0.815477	−	0.756652i	−0.157509	−	0.987518i	$-0.550346\pi$
$317$	14.5192	−	13.4718i	0.815477	−	0.756652i	0.972986	+	0.230866i	$0.0741558\pi$
$318$	8.31322	+	1.25302i	0.466182	+	0.0702657i
$319$	−1.88350	−	1.74763i	−0.105456	−	0.0978487i
$320$	−1.86788	+	0.576165i	−0.104418	+	0.0322086i
$321$	−9.61939	+	12.0623i	−0.536902	+	0.673254i
$322$	2.40907	−	0.363108i	0.134252	−	0.0202352i
$323$	0.0437591	−	0.191721i	0.00243482	−	0.0106677i
$324$	17.4526	−	5.38343i	0.969591	−	0.299079i
$325$	0.796310	+	1.37925i	0.0441713	+	0.0765070i
$326$	2.75267	−	0.849087i	0.152456	−	0.0470266i
$327$	1.15593	+	15.4249i	0.0639233	+	0.852998i
$328$	15.1846	+	14.0892i	0.838428	+	0.777948i
$329$	−7.39188	−	9.26913i	−0.407528	−	0.511024i
$330$	−6.56776	+	11.3757i	−0.361543	+	0.626211i
$331$	−6.85773	+	8.59932i	−0.376935	+	0.472661i	−0.933725	−	0.357992i	$-0.883461\pi$
$331$	−6.85773	+	8.59932i	−0.376935	+	0.472661i	0.556790	+	0.830653i	$0.312033\pi$
$332$	−9.92707	+	12.4482i	−0.544819	+	0.683181i
$333$	−0.399521	+	5.33123i	−0.0218936	+	0.292150i
$334$	−5.78677	+	3.94536i	−0.316638	+	0.215880i
$335$	−14.1717	+	6.82472i	−0.774281	+	0.372874i
$336$	−6.60363	+	6.12727i	−0.360258	+	0.334270i
$337$	−9.80004	+	1.47712i	−0.533842	+	0.0804637i	−0.410431	−	0.911892i	$-0.634622\pi$
$337$	−9.80004	+	1.47712i	−0.533842	+	0.0804637i	−0.123411	+	0.992356i	$0.539384\pi$
$338$	−6.94928	−	3.34660i	−0.377991	−	0.182031i
$339$	−19.2207	+	5.92880i	−1.04392	+	0.322008i
$340$	−2.20837	+	0.681192i	−0.119766	+	0.0369428i
$341$	2.57913	+	6.57153i	0.139668	+	0.355868i
$342$	−0.106507	−	0.466639i	−0.00575926	−	0.0252330i
$343$	−18.1183	+	8.72533i	−0.978299	+	0.471124i
$344$	−0.491685	+	6.56109i	−0.0265099	+	0.353750i
$345$	−13.2412	+	1.99579i	−0.712884	+	0.107450i
$346$	6.43337	−	4.38620i	0.345860	−	0.235803i
$347$	19.8759	+	6.13089i	1.06699	+	0.329124i	0.778037	−	0.628219i	$-0.216216\pi$
$347$	19.8759	+	6.13089i	1.06699	+	0.329124i	0.288956	+	0.957342i	$0.406692\pi$
$348$	−1.44243	−	2.49836i	−0.0773224	−	0.133926i
$349$	4.52235	−	11.5228i	0.242076	−	0.616800i	−0.757265	−	0.653108i	$-0.773465\pi$
$349$	4.52235	−	11.5228i	0.242076	−	0.616800i	0.999341	+	0.0363085i	$0.0115599\pi$
$350$	5.66598			0.302859
$351$	0.872776	−	0.131550i	0.0465854	−	0.00702161i
$352$	−11.1304	−	13.9571i	−0.593253	−	0.743916i
$353$	36.8305			1.96029			0.980144	−	0.198285i	$-0.0635373\pi$
$353$	36.8305			1.96029			0.980144	+	0.198285i	$0.0635373\pi$
$354$	11.7622	−	3.62816i	0.625154	−	0.192834i
$355$	−41.4827	+	19.9770i	−2.20167	+	1.06027i
$356$	0.521397	−	1.32850i	0.0276340	−	0.0704103i
$357$	−1.52062	+	1.41093i	−0.0804800	+	0.0746745i
$358$	−2.09879	−	0.647392i	−0.110925	−	0.0342157i
$359$	7.86404	+	20.0372i	0.415048	+	1.05752i	0.973642	+	0.228083i	$0.0732459\pi$
$359$	7.86404	+	20.0372i	0.415048	+	1.05752i	−0.558594	+	0.829441i	$0.688659\pi$
$360$	−9.14790	+	8.48801i	−0.482137	+	0.447357i
$361$	18.6032	−	2.80398i	0.979115	−	0.147578i
$362$	10.3379	−	4.97847i	0.543348	−	0.261663i
$363$	−1.38627	−	0.208946i	−0.0727602	−	0.0109668i
$364$	−0.977876	+	0.666705i	−0.0512546	+	0.0349448i
$365$	−19.8054	−	24.8351i	−1.03666	−	1.29993i
$366$	−2.52842	−	4.37935i	−0.132163	−	0.228912i
$367$	15.2792	+	14.1770i	0.797567	+	0.740034i	0.969504	−	0.245074i	$-0.0788123\pi$
$367$	15.2792	+	14.1770i	0.797567	+	0.740034i	−0.171938	+	0.985108i	$0.555003\pi$
$368$	0.864450	−	3.78740i	0.0450626	−	0.197432i
$369$	−16.7881	−	5.17844i	−0.873953	−	0.269579i
$370$	1.95657	+	4.98526i	0.101717	+	0.259171i
$371$	−9.67077	+	8.97316i	−0.502081	+	0.465863i
$372$	0.592332	+	7.90411i	0.0307110	+	0.409809i
$373$	−6.05080	+	4.12537i	−0.313299	+	0.213603i	−0.709752	−	0.704451i	$-0.751193\pi$
$373$	−6.05080	+	4.12537i	−0.313299	+	0.213603i	0.396454	+	0.918055i	$0.370241\pi$
$374$	−0.547115	−	0.686061i	−0.0282907	−	0.0354754i
$375$	2.92221			0.150902
$376$	11.9375	−	3.68223i	0.615629	−	0.189896i
$377$	−0.101595	−	0.258860i	−0.00523241	−	0.0133320i
$378$	1.14721	−	2.92304i	0.0590060	−	0.150345i
$379$	−4.09063	−	3.79555i	−0.210122	−	0.194964i	0.568090	−	0.822966i	$-0.307683\pi$
$379$	−4.09063	−	3.79555i	−0.210122	−	0.194964i	−0.778212	+	0.628002i	$0.783873\pi$
$380$	1.36792	+	1.71531i	0.0701727	+	0.0879938i
$381$	−21.7250	−	14.8119i	−1.11301	−	0.758835i
$382$	5.93814	+	2.85966i	0.303821	+	0.146313i
$383$	9.57854	−	12.0111i	0.489440	−	0.613739i	−0.474371	−	0.880325i	$-0.657324\pi$
$383$	9.57854	−	12.0111i	0.489440	−	0.613739i	0.963811	+	0.266586i	$0.0858957\pi$
$384$	−9.22752	−	23.5113i	−0.470890	−	1.19981i
$385$	−7.53052	−	19.1874i	−0.383791	−	0.977883i
$386$	−2.26798	−	9.93668i	−0.115437	−	0.505763i
$387$	−2.03873	−	5.19460i	−0.103634	−	0.264056i
$388$	1.15185	−	15.3704i	0.0584765	−	0.780315i
$389$	−13.2888	+	9.06013i	−0.673768	+	0.459367i	−0.851252	−	0.524757i	$-0.824156\pi$
$389$	−13.2888	+	9.06013i	−0.673768	+	0.459367i	0.177485	+	0.984124i	$0.443204\pi$
$390$	−1.17461	+	0.800838i	−0.0594789	+	0.0405520i
$391$	0.199058	−	0.872129i	0.0100668	−	0.0441055i
$392$	−0.442729	−	5.90780i	−0.0223612	−	0.298389i
$393$	2.91104	+	1.40188i	0.146842	+	0.0707155i
$394$	0.724927	−	9.67348i	0.0365213	−	0.487343i
$395$	−14.9777	−	2.25753i	−0.753612	−	0.113589i
$396$	8.80519	+	4.24035i	0.442477	+	0.213086i
$397$	23.7588	−	22.0450i	1.19242	−	1.10641i	0.200482	−	0.979697i	$-0.435749\pi$
$397$	23.7588	−	22.0450i	1.19242	−	1.10641i	0.991940	−	0.126709i	$-0.0404413\pi$
$398$	−0.756869	+	0.364489i	−0.0379384	+	0.0182702i
$399$	1.77427	+	0.854443i	0.0888246	+	0.0427757i
$400$	3.30077	−	8.41023i	0.165039	−	0.420511i
$401$	−15.5344	−	2.34144i	−0.775752	−	0.116926i	−0.250779	−	0.968044i	$-0.580687\pi$
$401$	−15.5344	−	2.34144i	−0.775752	−	0.116926i	−0.524973	+	0.851119i	$0.675925\pi$
$402$	−3.35287	−	5.80734i	−0.167226	−	0.289644i
$403$	−0.0570970	+	0.761906i	−0.00284420	+	0.0379533i
$404$	0.654191	+	8.72957i	0.0325472	+	0.434312i
$405$	−12.5773	+	32.0464i	−0.624969	+	1.59240i
$406$	−0.978269	−	0.147450i	−0.0485507	−	0.00731784i
$407$	6.82090	−	6.32887i	0.338099	−	0.313710i
$408$	−0.798563	−	2.03470i	−0.0395347	−	0.100733i
$409$	16.2703	−	20.4023i	0.804515	−	1.00883i	−0.195092	−	0.980785i	$-0.562500\pi$
$409$	16.2703	−	20.4023i	0.804515	−	1.00883i	0.999607	−	0.0280448i	$-0.00892812\pi$
$410$	−17.4026	+	2.62301i	−0.859451	+	0.129541i
$411$	−11.0881	+	19.2052i	−0.546936	+	0.947321i
$412$	−24.6397	+	7.60035i	−1.21391	+	0.374443i
$413$	−7.05671	+	17.9802i	−0.347238	+	0.884748i
$414$	−0.484496	−	2.12272i	−0.0238117	−	0.104326i
$415$	−6.67811	−	29.2587i	−0.327815	−	1.43625i
$416$	−0.429927	−	1.88363i	−0.0210789	−	0.0923528i
$417$	−35.3086	−	10.8913i	−1.72907	−	0.533347i
$418$	−0.416526	+	0.721444i	−0.0203730	+	0.0352870i
$419$	4.04154	−	7.00016i	0.197442	−	0.341980i	−0.750256	−	0.661147i	$-0.770070\pi$
$419$	4.04154	−	7.00016i	0.197442	−	0.341980i	0.947698	+	0.319167i	$0.103403\pi$
$420$	−1.72948	−	23.0783i	−0.0843900	−	1.12611i
$421$	18.1913	−	5.61127i	0.886589	−	0.273476i	0.182175	−	0.983266i	$-0.441686\pi$
$421$	18.1913	−	5.61127i	0.886589	−	0.273476i	0.704414	+	0.709790i	$0.251210\pi$
$422$	3.39755	+	4.26039i	0.165390	+	0.207393i
$423$	−7.76700	+	7.20672i	−0.377644	+	0.350403i
$424$	−5.07865	−	12.9402i	−0.246641	−	0.628431i
$425$	0.760072	−	1.93663i	0.0368689	−	0.0939404i
$426$	−9.81438	−	16.9990i	−0.475508	−	0.823604i
$427$	7.84658	+	1.18268i	0.379722	+	0.0572339i
$428$	11.3704	+	1.71381i	0.549608	+	0.0828401i
$429$	2.04082	+	1.39141i	0.0985317	+	0.0671778i
$430$	−4.09779	−	3.80219i	−0.197613	−	0.183358i
$431$	5.56965	−	14.1912i	0.268280	−	0.683567i	−0.731718	−	0.681608i	$-0.761281\pi$
$431$	5.56965	−	14.1912i	0.268280	−	0.683567i	0.999998	−	0.00195957i	$-0.000623752\pi$
$432$	−3.67046	−	3.40569i	−0.176595	−	0.163856i
$433$	16.2872	−	20.4235i	0.782713	−	0.981490i	−0.217273	−	0.976111i	$-0.569716\pi$
$433$	16.2872	−	20.4235i	0.782713	−	0.981490i	0.999986	−	0.00537961i	$-0.00171239\pi$
$434$	2.24588	+	1.53121i	0.107806	+	0.0735006i
$435$	5.37697	+	0.810448i	0.257806	+	0.0388580i
$436$	9.52530	−	6.49424i	0.456179	−	0.311018i
$437$	−0.839756	+	0.126573i	−0.0401710	+	0.00605480i
$438$	9.92712	−	9.21102i	0.474336	−	0.440120i
$439$	−9.34565	−	6.37176i	−0.446044	−	0.304107i	0.319389	−	0.947624i	$-0.396522\pi$
$439$	−9.34565	−	6.37176i	−0.446044	−	0.304107i	−0.765432	+	0.643516i	$0.777475\pi$
$440$	21.7195			1.03544
$441$	2.51236	+	4.35153i	0.119636	+	0.207216i
$442$	−0.0211331	−	0.0925900i	−0.00100520	−	0.00440406i
$443$	8.32394	+	21.2090i	0.395482	+	1.00767i	0.980477	+	0.196635i	$0.0630014\pi$
$443$	8.32394	+	21.2090i	0.395482	+	1.00767i	−0.584995	+	0.811037i	$0.698903\pi$
$444$	9.41262	−	4.53288i	0.446703	−	0.215121i
$445$	1.34503	+	2.32965i	0.0637604	+	0.110436i
$446$	−0.0451891	−	0.197987i	−0.00213977	−	0.00937494i
$447$	−9.29364	+	40.7181i	−0.439574	+	1.92590i
$448$	1.24958	+	0.385444i	0.0590371	+	0.0182105i
$449$	−5.63845	−	24.7037i	−0.266095	−	1.16584i	−0.914514	−	0.404554i	$-0.867427\pi$
$449$	−5.63845	−	24.7037i	−0.266095	−	1.16584i	0.648419	−	0.761283i	$-0.275430\pi$
$450$	−0.378410	−	5.04954i	−0.0178384	−	0.238037i
$451$	15.2887	+	26.4808i	0.719917	+	1.24693i
$452$	10.9894	+	10.1967i	0.516899	+	0.479612i
$453$	−32.6653	+	15.7308i	−1.53475	+	0.739096i
$454$	0.0106843	+	0.0468111i	0.000501441	+	0.00219695i
$455$	0.166711	−	2.22460i	0.00781553	−	0.104291i
$456$	−1.52114	+	1.41141i	−0.0712337	+	0.0660952i
$457$	1.14792	−	1.43945i	0.0536974	−	0.0673344i	−0.754258	−	0.656579i	$-0.772003\pi$
$457$	1.14792	−	1.43945i	0.0536974	−	0.0673344i	0.807955	+	0.589244i	$0.200574\pi$
$458$	−0.979728	+	4.29247i	−0.0457797	+	0.200574i
$459$	−0.845201	−	0.784232i	−0.0394506	−	0.0366048i
$460$	6.22258	+	7.80287i	0.290129	+	0.363811i
$461$	0.753404	+	10.0535i	0.0350895	+	0.468237i	0.986876	+	0.161477i	$0.0516258\pi$
$461$	0.753404	+	10.0535i	0.0350895	+	0.468237i	−0.951787	+	0.306760i	$0.900755\pi$
$462$	7.91720	−	3.81272i	0.368341	−	0.177384i
$463$	0.770514	−	0.966194i	0.0358088	−	0.0449028i	−0.763605	−	0.645684i	$-0.776572\pi$
$463$	0.770514	−	0.966194i	0.0358088	−	0.0449028i	0.799413	+	0.600781i	$0.205144\pi$
$464$	−0.788767	+	1.36618i	−0.0366176	+	0.0634235i
$465$	−12.3443	−	8.41618i	−0.572452	−	0.390291i
$466$	15.1564	−	7.29892i	0.702105	−	0.338116i
$467$	32.9310	−	15.8588i	1.52387	−	0.733856i	0.530376	−	0.847763i	$-0.322051\pi$
$467$	32.9310	−	15.8588i	1.52387	−	0.733856i	0.993491	+	0.113907i	$0.0363366\pi$
$468$	0.659478	+	0.826959i	0.0304844	+	0.0382262i
$469$	10.4051	+	1.56832i	0.480464	+	0.0724184i
$470$	−3.87767	+	9.88014i	−0.178864	+	0.455737i
$471$	0.612290	−	8.17045i	0.0282128	−	0.376474i
$472$	−14.9198	−	13.8435i	−0.686738	−	0.637200i
$473$	−3.54832	+	9.04097i	−0.163152	+	0.415704i
$474$	0.482564	−	6.43937i	0.0221649	−	0.295770i
$475$	−1.97505			−0.0906217
$476$	1.47736	+	0.455705i	0.0677146	+	0.0208872i
$477$	8.64279	+	8.01933i	0.395726	+	0.367180i
$478$	12.9928	+	8.85832i	0.594275	+	0.405170i
$479$	10.7264	+	5.16558i	0.490104	+	0.236022i	0.662579	−	0.748992i	$-0.269462\pi$
$479$	10.7264	+	5.16558i	0.490104	+	0.236022i	−0.172475	+	0.985014i	$0.555176\pi$
$480$	36.1019	+	11.1360i	1.64782	+	0.508285i
$481$	0.962305	−	0.296832i	0.0438773	−	0.0135344i
$482$	0.340928	−	1.49370i	0.0155288	−	0.0680363i
$483$	8.07106	+	3.88682i	0.367246	+	0.176856i
$484$	0.381732	+	0.972638i	0.0173515	+	0.0442108i
$485$	21.2974	+	19.7611i	0.967066	+	0.897306i
$486$	−9.67504	−	2.98436i	−0.438869	−	0.135373i
$487$	−2.21462	+	29.5520i	−0.100354	+	1.33913i	0.688808	+	0.724944i	$0.258134\pi$
$487$	−2.21462	+	29.5520i	−0.100354	+	1.33913i	−0.789162	+	0.614185i	$0.789485\pi$
$488$	−4.18073	+	7.24123i	−0.189253	+	0.327795i
$489$	10.1216	+	3.12209i	0.457714	+	0.141186i
$490$	4.15883	+	2.83544i	0.187877	+	0.128092i
$491$	−2.37316	+	31.6676i	−0.107099	+	1.42914i	0.642013	+	0.766694i	$0.278099\pi$
$491$	−2.37316	+	31.6676i	−0.107099	+	1.42914i	−0.749112	+	0.662443i	$0.769520\pi$
$492$	7.63951	+	33.4709i	0.344416	+	1.50898i
$493$	−0.181630	+	0.314592i	−0.00818021	+	0.0141685i
$494$	−0.0744938	+	0.0507890i	−0.00335163	+	0.00228511i
$495$	−16.5970	+	7.99268i	−0.745979	+	0.359244i
$496$	3.58120	−	2.44162i	0.160801	−	0.109632i
$497$	30.4575	+	4.59072i	1.36620	+	0.205922i
$498$	12.2259	−	3.77120i	0.547857	−	0.168991i
$499$	30.6666	−	20.9081i	1.37283	−	0.935977i	0.372858	−	0.927888i	$-0.378378\pi$
$499$	30.6666	−	20.9081i	1.37283	−	0.935977i	0.999967	−	0.00808845i	$-0.00257466\pi$
$500$	−1.08897	−	1.88615i	−0.0487003	−	0.0843514i
$501$	−25.7528			−1.15055
$502$	0.296648	+	0.202251i	0.0132401	+	0.00902693i
$503$	−11.5919	+	14.5358i	−0.516859	+	0.648121i	−0.969939	−	0.243349i	$-0.921754\pi$
$503$	−11.5919	+	14.5358i	−0.516859	+	0.648121i	0.453080	+	0.891470i	$0.350325\pi$
$504$	8.25511	−	1.24426i	0.367712	−	0.0554237i
$505$	−13.6334	−	9.29511i	−0.606679	−	0.413627i
$506$	−1.89475	+	3.28181i	−0.0842321	+	0.145894i
$507$	−14.1806	−	24.5615i	−0.629781	−	1.09081i
$508$	−1.46449	+	19.5422i	−0.0649761	+	0.867045i
$509$	44.1746			1.95800			0.979002	−	0.203851i	$-0.0653457\pi$
$509$	44.1746			1.95800			0.979002	+	0.203851i	$0.0653457\pi$
$510$	1.77459	+	0.547388i	0.0785801	+	0.0242387i
$511$	1.58805	+	21.1910i	0.0702510	+	0.937435i
$512$	−12.2087	+	15.3092i	−0.539554	+	0.676579i
$513$	−0.399895	+	1.01892i	−0.0176558	+	0.0449863i
$514$	−6.22073	−	15.8502i	−0.274385	−	0.699121i
$515$	17.7567	−	45.2432i	0.782452	−	1.99365i
$516$	−6.79904	+	8.52573i	−0.299311	+	0.375324i
$517$	18.4409			0.811029
$518$	0.797228	−	3.49288i	0.0350282	−	0.153469i
$519$	28.6304			1.25673
$520$	2.11788	+	1.01992i	0.0928753	+	0.0447264i
$521$	−1.18460	−	2.05179i	−0.0518984	−	0.0898906i	0.838909	−	0.544271i	$-0.183194\pi$
$521$	−1.18460	−	2.05179i	−0.0518984	−	0.0898906i	−0.890808	+	0.454381i	$0.849861\pi$
$522$	−0.0660731	+	0.881684i	−0.00289194	+	0.0385903i
$523$	−2.02568	−	2.54013i	−0.0885770	−	0.111072i	0.735568	−	0.677451i	$-0.236915\pi$
$523$	−2.02568	−	2.54013i	−0.0885770	−	0.111072i	−0.824145	+	0.566379i	$0.808344\pi$
$524$	−0.179957	−	2.40136i	−0.00786145	−	0.104904i
$525$	17.2137	+	11.7361i	0.751267	+	0.512205i
$526$	−5.86188	+	10.1531i	−0.255590	+	0.442695i
$527$	0.824646	−	0.562234i	0.0359221	−	0.0244913i
$528$	−1.04713	−	13.9729i	−0.0455704	−	0.608094i
$529$	18.9231	−	2.85220i	0.822744	−	0.124009i
$530$	11.2859	+	3.48124i	0.490229	+	0.151216i
$531$	16.4953	+	5.08813i	0.715836	+	0.220806i
$532$	−0.109683	−	1.46362i	−0.00475538	−	0.0634561i
$533$	0.247308	+	3.30010i	0.0107121	+	0.142943i
$534$	−0.947549	+	0.646028i	−0.0410045	+	0.0279564i
$535$	−15.8883	+	14.7422i	−0.686913	+	0.637362i
$536$	−5.54395	+	9.60240i	−0.239462	+	0.414760i
$537$	−5.03534	−	6.31412i	−0.217291	−	0.272474i
$538$	−1.92217	−	8.42157i	−0.0828706	−	0.363080i
$539$	1.94601	−	8.52604i	0.0838207	−	0.367243i
$540$	12.7198	−	1.91720i	0.547373	−	0.0825032i
$541$	−8.08907	−	7.50556i	−0.347776	−	0.322689i	0.486871	−	0.873474i	$-0.338138\pi$
$541$	−8.08907	−	7.50556i	−0.347776	−	0.322689i	−0.834648	+	0.550784i	$0.814329\pi$
$542$	−0.886208	+	0.822280i	−0.0380659	+	0.0353200i
$543$	41.7194	+	6.28819i	1.79035	+	0.269852i
$544$	−1.57361	+	1.97325i	−0.0674680	+	0.0846022i
$545$	−1.62390	+	21.6694i	−0.0695602	+	0.928216i
$546$	0.951052			0.0407012
$547$	−21.7074	+	8.70573i	−0.928140	+	0.372230i
$547$	−21.7074	+	8.70573i	−0.928140	+	0.372230i
$548$	16.5281			0.706045
$549$	0.529964	−	7.07188i	0.0226183	−	0.301821i
$550$	−5.49491	+	6.89039i	−0.234304	+	0.293807i
$551$	0.341006	+	0.0513984i	0.0145274	+	0.00218965i
$552$	−6.91956	+	6.42042i	−0.294516	+	0.273271i
$553$	7.42802	+	6.89220i	0.315872	+	0.293086i
$554$	6.56917	−	0.990143i	0.279097	−	0.0420671i
$555$	−4.38190	+	19.1983i	−0.186001	+	0.814924i
$556$	6.12806	+	26.8488i	0.259887	+	1.13864i
$557$	19.1959	+	24.0709i	0.813356	+	1.01992i	0.999302	+	0.0373561i	$0.0118936\pi$
$557$	19.1959	+	24.0709i	0.813356	+	1.01992i	−0.185946	+	0.982560i	$0.559535\pi$
$558$	1.21463	−	2.10380i	0.0514193	−	0.0890608i
$559$	−0.770551	+	0.714967i	−0.0325908	+	0.0302399i
$560$	−10.4563	+	7.12900i	−0.441860	+	0.301255i
$561$	−0.241123	−	3.21756i	−0.0101802	−	0.135846i
$562$	−0.0528052	−	0.704636i	−0.00222745	−	0.0297233i
$563$	−26.2541	−	8.09830i	−1.10648	−	0.341303i	−0.312908	−	0.949784i	$-0.601303\pi$
$563$	−26.2541	−	8.09830i	−1.10648	−	0.341303i	−0.793569	+	0.608481i	$0.791779\pi$
$564$	19.7852	+	6.10291i	0.833105	+	0.256979i
$565$	−27.9417	+	4.21153i	−1.17552	+	0.177181i
$566$	1.13921	+	15.2017i	0.0478845	+	0.638975i
$567$	19.0286	−	12.9735i	0.799128	−	0.544836i
$568$	−16.2280	+	28.1077i	−0.680912	+	1.17937i
$569$	−9.76598	−	6.65833i	−0.409411	−	0.279132i	0.341052	−	0.940045i	$-0.389217\pi$
$569$	−9.76598	−	6.65833i	−0.409411	−	0.279132i	−0.750463	+	0.660913i	$0.770169\pi$
$570$	−0.131750	−	1.75809i	−0.00551842	−	0.0736382i
$571$	7.12683	+	8.93676i	0.298249	+	0.373992i	0.908264	−	0.418398i	$-0.137408\pi$
$571$	7.12683	+	8.93676i	0.298249	+	0.373992i	−0.610015	+	0.792390i	$0.708837\pi$
$572$	0.137572	−	1.83577i	0.00575217	−	0.0767574i
$573$	12.1173	+	20.9877i	0.506205	+	0.876774i
$574$	10.6076	+	5.10833i	0.442751	+	0.213218i
$575$	−8.98441			−0.374676
$576$	0.260054	−	1.13937i	0.0108356	−	0.0474738i
$577$	−32.6845			−1.36067			−0.680336	−	0.732900i	$-0.738166\pi$
$577$	−32.6845			−1.36067			−0.680336	+	0.732900i	$0.738166\pi$
$578$	6.27068	−	7.86319i	0.260826	−	0.327066i
$579$	13.6918	−	34.8862i	0.569012	−	1.44982i
$580$	−1.48064	−	3.77261i	−0.0614802	−	0.156649i
$581$	−7.33492	+	18.6891i	−0.304304	+	0.775353i
$582$	−7.72248	+	9.68369i	−0.320107	+	0.401402i
$583$	−1.53348	−	20.4629i	−0.0635102	−	0.847485i
$584$	−21.3971	−	6.60013i	−0.885418	−	0.273115i
$585$	−1.99371			−0.0824297
$586$	0.609114	−	8.12806i	0.0251623	−	0.335767i
$587$	−2.86568	−	4.96351i	−0.118279	−	0.204866i	0.800806	−	0.598923i	$-0.204405\pi$
$587$	−2.86568	−	4.96351i	−0.118279	−	0.204866i	−0.919086	+	0.394057i	$0.871071\pi$
$588$	4.90952	−	8.50353i	0.202465	−	0.350680i
$589$	−0.782871	−	0.533752i	−0.0322576	−	0.0219929i
$590$	17.0991	−	2.57727i	0.703958	−	0.106105i
$591$	22.2394	−	27.8873i	0.914805	−	1.14713i
$592$	−4.72019	−	3.21817i	−0.193999	−	0.132266i
$593$	23.4053			0.961142			0.480571	−	0.876956i	$-0.340429\pi$
$593$	23.4053			0.961142			0.480571	+	0.876956i	$0.340429\pi$
$594$	2.44214	+	4.22990i	0.100202	+	0.173555i
$595$	−2.40779	+	1.64160i	−0.0987097	+	0.0672991i
$596$	29.7450	−	9.17511i	1.21840	−	0.375827i
$597$	−3.05440	−	0.460377i	−0.125008	−	0.0188420i
$598$	−0.338868	+	0.231036i	−0.0138573	+	0.00944778i
$599$	−21.5801	+	10.3924i	−0.881738	+	0.424622i	−0.819259	−	0.573424i	$-0.805615\pi$
$599$	−21.5801	+	10.3924i	−0.881738	+	0.424622i	−0.0624788	+	0.998046i	$0.519901\pi$
$600$	−18.1383	+	12.3665i	−0.740495	+	0.504861i
$601$	11.4189	−	19.7782i	0.465788	−	0.806769i	−0.533448	−	0.845833i	$-0.679104\pi$
$601$	11.4189	−	19.7782i	0.465788	−	0.806769i	0.999237	+	0.0390636i	$0.0124375\pi$
$602$	0.832147	+	3.64588i	0.0339158	+	0.148595i
$603$	0.702771	−	9.37783i	0.0286191	−	0.381895i
$604$	22.3263	+	15.2218i	0.908445	+	0.619367i
$605$	−1.88198	−	0.580513i	−0.0765133	−	0.0236012i
$606$	3.51726	−	6.09208i	0.142879	−	0.247474i
$607$	1.82928	−	24.4101i	0.0742483	−	0.990774i	−0.828328	−	0.560244i	$-0.810707\pi$
$607$	1.82928	−	24.4101i	0.0742483	−	0.990774i	0.902576	−	0.430530i	$-0.141673\pi$
$608$	2.28957	+	0.706240i	0.0928545	+	0.0286418i
$609$	−2.66664	−	2.47428i	−0.108058	−	0.100263i
$610$	−2.59539	−	6.61295i	−0.105084	−	0.267751i
$611$	1.79818	+	0.865959i	0.0727467	+	0.0350330i
$612$	0.307458	−	1.34706i	0.0124283	−	0.0544518i
$613$	24.2734	−	7.48734i	0.980392	−	0.302411i	0.237179	−	0.971466i	$-0.423777\pi$
$613$	24.2734	−	7.48734i	0.980392	−	0.302411i	0.743213	+	0.669055i	$0.233301\pi$
$614$	4.01463	+	1.23835i	0.162017	+	0.0499757i
$615$	−58.3035	−	28.0775i	−2.35103	−	1.13219i
$616$	−12.0052	−	8.18502i	−0.483704	−	0.329784i
$617$	−30.9291	−	28.6980i	−1.24516	−	1.15534i	−0.981653	−	0.190678i	$-0.938931\pi$
$617$	−30.9291	−	28.6980i	−1.24516	−	1.15534i	−0.263504	−	0.964658i	$-0.584878\pi$
$618$	19.7999	+	6.10745i	0.796467	+	0.245678i
$619$	26.4910			1.06476			0.532381	−	0.846505i	$-0.321298\pi$
$619$	26.4910			1.06476			0.532381	+	0.846505i	$0.321298\pi$
$620$	−0.832129	+	11.1040i	−0.0334191	+	0.445947i
$621$	−1.81910	+	4.63500i	−0.0729980	+	0.185996i
$622$	−0.668037	−	0.619847i	−0.0267858	−	0.0248536i
$623$	0.134484	−	1.79457i	0.00538799	−	0.0718977i
$624$	0.554045	−	1.41168i	0.0221795	−	0.0565125i
$625$	26.6595	+	4.01827i	1.06638	+	0.160731i
$626$	−9.04712	−	11.3447i	−0.361596	−	0.453426i
$627$	−2.75979	+	1.32904i	−0.110215	+	0.0530769i
$628$	−5.50182	+	2.64954i	−0.219547	+	0.105728i
$629$	−1.08692	−	0.741052i	−0.0433385	−	0.0295477i
$630$	−3.54645	+	6.14264i	−0.141294	+	0.244728i
$631$	−29.1862	+	36.5984i	−1.16189	+	1.45696i	−0.297080	+	0.954853i	$0.596013\pi$
$631$	−29.1862	+	36.5984i	−1.16189	+	1.45696i	−0.864806	+	0.502106i	$0.832559\pi$
$632$	−9.61993	+	4.63271i	−0.382660	+	0.184279i
$633$	1.49736	+	19.9809i	0.0595147	+	0.794168i
$634$	7.39600	+	9.27429i	0.293733	+	0.368329i
$635$	−27.0779	−	25.1246i	−1.07455	−	0.997040i
$636$	5.12681	−	22.4620i	0.203291	−	0.890677i
$637$	0.590128	−	0.739997i	0.0233817	−	0.0293198i
$638$	1.12805	−	1.04667i	0.0446598	−	0.0414382i
$639$	2.05712	−	27.4504i	0.0813785	−	1.08592i
$640$	−7.89556	−	34.5927i	−0.312099	−	1.36740i
$641$	−0.309776	+	0.149180i	−0.0122354	+	0.00589227i	−0.439991	−	0.898002i	$-0.645019\pi$
$641$	−0.309776	+	0.149180i	−0.0122354	+	0.00589227i	0.427756	+	0.903894i	$0.359304\pi$
$642$	−6.77351	−	6.28490i	−0.267329	−	0.248045i
$643$	6.78259	+	11.7478i	0.267479	+	0.463287i	0.968210	−	0.250138i	$-0.0804760\pi$
$643$	6.78259	+	11.7478i	0.267479	+	0.463287i	−0.700731	+	0.713426i	$0.747143\pi$
$644$	−0.498943	−	6.65794i	−0.0196611	−	0.262359i
$645$	−4.57383	−	20.0392i	−0.180094	−	0.789044i
$646$	0.112544	+	0.0347152i	0.00442798	+	0.00136585i
$647$	5.10723	−	22.3762i	0.200786	−	0.879701i	−0.769674	−	0.638437i	$-0.779581\pi$
$647$	5.10723	−	22.3762i	0.200786	−	0.879701i	0.970460	−	0.241263i	$-0.0775618\pi$
$648$	5.40004	+	23.6591i	0.212133	+	0.929417i
$649$	−15.0221	−	26.0190i	−0.589668	−	1.02134i
$650$	−0.859375	+	0.413853i	−0.0337075	+	0.0162327i
$651$	3.65151	+	9.30390i	0.143114	+	0.364649i
$652$	−1.75667	−	7.69648i	−0.0687966	−	0.301417i
$653$	−5.90805	−	10.2330i	−0.231200	−	0.400450i	0.726962	−	0.686678i	$-0.240932\pi$
$653$	−5.90805	−	10.2330i	−0.231200	−	0.400450i	−0.958161	+	0.286228i	$0.907598\pi$
$654$	−9.26400			−0.362251
$655$	3.75032	+	2.55693i	0.146537	+	0.0999075i
$656$	13.7620	−	12.7693i	0.537317	−	0.498558i
$657$	18.7794	−	2.83054i	0.732655	−	0.110430i
$658$	5.86668	−	3.99983i	0.228707	−	0.155930i
$659$	−21.0682	−	3.17553i	−0.820702	−	0.123701i	−0.274748	−	0.961516i	$-0.588595\pi$
$659$	−21.0682	−	3.17553i	−0.820702	−	0.123701i	−0.545954	+	0.837815i	$0.683833\pi$
$660$	29.7428	+	20.2783i	1.15774	+	0.789332i
$661$	0.160005	−	0.200640i	0.00622349	−	0.00780401i	−0.778710	−	0.627384i	$-0.784126\pi$
$661$	0.160005	−	0.200640i	0.00622349	−	0.00780401i	0.784933	+	0.619580i	$0.212697\pi$
$662$	−4.82888	−	4.48055i	−0.187680	−	0.174141i
$663$	0.127580	−	0.325070i	0.00495481	−	0.0126247i
$664$	−15.5080	−	14.3893i	−0.601826	−	0.558413i
$665$	2.28582	+	1.55844i	0.0886401	+	0.0604338i
$666$	−3.16611	−	0.477215i	−0.122684	−	0.0184917i
$667$	1.55122	+	0.233809i	0.0600634	+	0.00905311i
$668$	9.59688	+	16.6223i	0.371314	+	0.643135i
$669$	0.272807	−	0.695101i	0.0105473	−	0.0268742i
$670$	−3.44168	−	8.76926i	−0.132964	−	0.338786i
$671$	−9.04793	+	8.39525i	−0.349291	+	0.324095i
$672$	−15.7583	−	19.7603i	−0.607890	−	0.762270i
$673$	−13.5250	+	4.17191i	−0.521350	+	0.160815i	−0.544251	−	0.838922i	$-0.683186\pi$
$673$	−13.5250	+	4.17191i	−0.521350	+	0.160815i	0.0229007	+	0.999738i	$0.492710\pi$
$674$	−0.443570	−	5.91903i	−0.0170857	−	0.227993i
$675$	−5.78997	+	10.0285i	−0.222856	+	0.385998i
$676$	−10.5689	+	18.3058i	−0.406495	+	0.704071i
$677$	0.631647	+	0.194837i	0.0242762	+	0.00748821i	0.306869	−	0.951752i	$-0.400718\pi$
$677$	0.631647	+	0.194837i	0.0242762	+	0.00748821i	−0.282593	+	0.959240i	$0.591195\pi$
$678$	−2.68063	−	11.7446i	−0.102949	−	0.451049i
$679$	−4.32491	−	18.9487i	−0.165975	−	0.727184i
$680$	−0.683293	−	2.99370i	−0.0262031	−	0.114803i
$681$	−0.0645014	+	0.164347i	−0.00247170	+	0.00629778i
$682$	−4.04018	+	1.24623i	−0.154706	+	0.0477206i
$683$	4.95735	−	8.58637i	0.189688	−	0.328548i	−0.755459	−	0.655196i	$-0.772586\pi$
$683$	4.95735	−	8.58637i	0.189688	−	0.328548i	0.945146	+	0.326648i	$0.105919\pi$
$684$	−1.29706	+	0.195500i	−0.0495943	+	0.00747514i
$685$	−19.4242	+	24.3571i	−0.742160	+	0.930639i
$686$	−4.40016	−	11.2114i	−0.167999	−	0.428054i
$687$	−11.8676	+	11.0115i	−0.452777	+	0.420116i
$688$	5.89649	+	0.888753i	0.224802	+	0.0338834i
$689$	0.811378	−	2.06736i	0.0309110	−	0.0787600i
$690$	−0.599325	−	7.99744i	−0.0228159	−	0.304457i
$691$	−0.645634	+	8.61539i	−0.0245611	+	0.327745i	0.971366	+	0.237587i	$0.0763563\pi$
$691$	−0.645634	+	8.61539i	−0.0245611	+	0.327745i	−0.995927	+	0.0901583i	$0.971263\pi$
$692$	−10.6692	−	18.4796i	−0.405582	−	0.702489i
$693$	12.1858	+	1.83672i	0.462902	+	0.0697713i
$694$	−4.55116	+	11.5962i	−0.172760	+	0.440184i
$695$	−46.7684	−	22.5225i	−1.77402	−	0.854325i
$696$	3.45353	−	1.66313i	0.130906	−	0.0630409i
$697$	3.16900	−	2.94040i	0.120034	−	0.111376i
$698$	6.67939	+	3.21663i	0.252819	+	0.121751i
$699$	61.1648	+	9.21910i	2.31346	+	0.348699i
$700$	1.16038	−	15.4842i	0.0438581	−	0.585246i
$701$	−23.5076	−	11.3207i	−0.887870	−	0.427576i	−0.0663775	−	0.997795i	$-0.521144\pi$
$701$	−23.5076	−	11.3207i	−0.887870	−	0.427576i	−0.821493	+	0.570219i	$0.806858\pi$
$702$	0.0395037	+	0.527140i	0.00149097	+	0.0198956i
$703$	−0.277899	+	1.21755i	−0.0104812	+	0.0459209i
$704$	−1.68059	+	1.14581i	−0.0633396	+	0.0431842i
$705$	−32.2457	+	21.9847i	−1.21444	+	0.827993i
$706$	−1.64841	+	21.9964i	−0.0620385	+	0.827847i
$707$	4.03285	+	10.2755i	0.151671	+	0.386451i
$708$	−7.50628	−	32.8872i	−0.282103	−	1.23598i
$709$	−0.539075	−	1.37354i	−0.0202454	−	0.0515844i	0.920394	−	0.390993i	$-0.127868\pi$
$709$	−0.539075	−	1.37354i	−0.0202454	−	0.0515844i	−0.940639	+	0.339409i	$0.889773\pi$
$710$	−10.0743	−	25.6690i	−0.378083	−	0.963341i
$711$	5.64626	−	7.08019i	0.211751	−	0.265528i
$712$	1.70847	+	0.822758i	0.0640278	+	0.0308342i
$713$	−3.56124	−	2.42801i	−0.133369	−	0.0909297i
$714$	−0.774600	−	0.971318i	−0.0289887	−	0.0363507i
$715$	2.54366	+	2.36017i	0.0951276	+	0.0882655i
$716$	−2.19904	+	5.60307i	−0.0821820	+	0.209396i
$717$	21.1246	+	53.8246i	0.788912	+	2.01012i
$718$	−12.3189	+	3.79988i	−0.459737	+	0.141810i
$719$	−40.8890			−1.52490			−0.762450	−	0.647047i	$-0.776004\pi$
$719$	−40.8890			−1.52490			−0.762450	+	0.647047i	$0.776004\pi$
$720$	7.05173	+	8.84259i	0.262803	+	0.329544i
$721$	−26.8648	+	18.3161i	−1.00050	+	0.682126i
$722$	0.842019	+	11.2360i	0.0313367	+	0.418159i
$723$	4.12972	−	3.83182i	0.153586	−	0.142507i
$724$	−11.4881	−	29.2713i	−0.426954	−	1.08786i
$725$	3.48629	+	1.07538i	0.129477	+	0.0399385i
$726$	0.186834	−	0.818575i	0.00693408	−	0.0303802i
$727$	−7.89319	−	7.32381i	−0.292742	−	0.271625i	0.520105	−	0.854102i	$-0.325893\pi$
$727$	−7.89319	−	7.32381i	−0.292742	−	0.271625i	−0.812847	+	0.582478i	$0.802083\pi$
$728$	−0.786279	−	1.36187i	−0.0291414	−	0.0504744i
$729$	−2.39787	−	3.00684i	−0.0888101	−	0.111364i
$730$	15.7188	−	10.7169i	0.581779	−	0.396651i
$731$	1.35779	+	0.204654i	0.0502197	+	0.00756940i
$732$	−12.4858	+	6.01287i	−0.461490	+	0.222242i
$733$	2.80939	−	0.423447i	0.103767	−	0.0156404i	−0.0969535	−	0.995289i	$-0.530910\pi$
$733$	2.80939	−	0.423447i	0.103767	−	0.0156404i	0.200720	+	0.979649i	$0.435672\pi$
$734$	−9.15084	+	8.49074i	−0.337764	+	0.313399i
$735$	6.76173	+	17.2286i	0.249410	+	0.635486i
$736$	10.4151	+	3.21265i	0.383907	+	0.118420i
$737$	−11.9982	+	11.1327i	−0.441960	+	0.410079i
$738$	3.84412	−	9.79466i	0.141504	−	0.360546i
$739$	−29.9556	+	14.4258i	−1.10193	+	0.530663i	−0.894266	−	0.447536i	$-0.852302\pi$
$739$	−29.9556	+	14.4258i	−1.10193	+	0.530663i	−0.207668	+	0.978199i	$0.566587\pi$
$740$	14.0246	−	4.32601i	0.515554	−	0.159027i
$741$	−0.331519			−0.0121787
$742$	−4.92625	−	6.17732i	−0.180848	−	0.226777i
$743$	−7.60489	+	1.14625i	−0.278996	+	0.0420520i	−0.287050	−	0.957916i	$-0.592675\pi$
$743$	−7.60489	+	1.14625i	−0.278996	+	0.0420520i	0.00805346	+	0.999968i	$0.497436\pi$
$744$	−10.5317			−0.386110
$745$	−21.4358	+	54.6174i	−0.785346	+	2.00103i
$746$	−2.19300	−	3.79838i	−0.0802914	−	0.139069i
$747$	17.1456	+	5.28873i	0.627326	+	0.193504i
$748$	−1.98694	+	1.35467i	−0.0726496	+	0.0495317i
$749$	14.3377	−	2.16106i	0.523889	−	0.0789635i
$750$	−0.130788	+	1.74525i	−0.00477570	+	0.0637274i
$751$	29.1159	−	14.0215i	1.06246	−	0.511652i	0.180788	−	0.983522i	$-0.442135\pi$
$751$	29.1159	−	14.0215i	1.06246	−	0.511652i	0.881668	+	0.471870i	$0.156421\pi$
$752$	−2.51942	−	11.0383i	−0.0918736	−	0.402525i
$753$	0.482313	+	1.22891i	0.0175765	+	0.0447841i
$754$	0.159147	−	0.0490903i	0.00579579	−	0.00178776i
$755$	−48.6705	+	15.0129i	−1.77130	+	0.546374i
$756$	−7.75323	−	3.73376i	−0.281982	−	0.135795i
$757$	11.1768	−	1.68463i	0.406227	−	0.0612289i	0.0572495	−	0.998360i	$-0.481767\pi$
$757$	11.1768	−	1.68463i	0.406227	−	0.0612289i	0.348978	+	0.937131i	$0.386529\pi$
$758$	2.44992	−	2.27319i	0.0889850	−	0.0825660i
$759$	−12.5541	+	6.04575i	−0.455686	+	0.219447i
$760$	−2.40860	+	1.64216i	−0.0873691	+	0.0595672i
$761$	−1.74336	+	23.2635i	−0.0631967	+	0.843301i	0.872075	+	0.489371i	$0.162774\pi$
$761$	−1.74336	+	23.2635i	−0.0631967	+	0.843301i	−0.935272	+	0.353929i	$0.884845\pi$
$762$	9.81850	−	12.3120i	0.355687	−	0.446017i
$763$	9.06373	−	11.3656i	0.328129	−	0.411461i
$764$	9.03107	−	15.6423i	0.326733	−	0.565918i
$765$	1.62381	+	2.03619i	0.0587089	+	0.0736187i
$766$	6.74475	+	6.25821i	0.243698	+	0.226118i
$767$	−0.242995	−	3.24255i	−0.00877405	−	0.117082i
$768$	11.7956	−	3.63845i	0.425635	−	0.131291i
$769$	−5.89250	−	10.2061i	−0.212489	−	0.368042i	0.740004	−	0.672603i	$-0.234824\pi$
$769$	−5.89250	−	10.2061i	−0.212489	−	0.368042i	−0.952493	+	0.304561i	$0.901490\pi$
$770$	11.7964	−	3.63872i	0.425114	−	0.131130i
$771$	13.9318	−	61.0393i	0.501742	−	2.19828i
$772$	−27.6197	+	4.16301i	−0.994056	+	0.149830i
$773$	5.19784	−	6.51788i	0.186953	−	0.234432i	−0.679518	−	0.733659i	$-0.737811\pi$
$773$	5.19784	−	6.51788i	0.186953	−	0.234432i	0.866471	+	0.499227i	$0.166383\pi$
$774$	3.19364	−	0.985108i	0.114793	−	0.0354090i
$775$	−7.34815	−	6.81809i	−0.263953	−	0.244913i
$776$	20.2513	+	3.05239i	0.726978	+	0.109574i
$777$	9.65696	−	8.96035i	0.346441	−	0.321451i
$778$	−4.81627	−	8.34202i	−0.172671	−	0.299076i
$779$	−3.69760	−	1.78067i	−0.132480	−	0.0637991i
$780$	1.94800	+	3.37403i	0.0697495	+	0.120810i
$781$	−35.1207	+	32.5872i	−1.25672	+	1.16606i
$782$	0.511956	+	0.157918i	0.0183075	+	0.00564712i
$783$	1.26066	−	1.58082i	0.0450523	−	0.0564937i
$784$	−5.36935			−0.191763
$785$	2.56129	−	11.2217i	0.0914163	−	0.400521i
$786$	−0.967540	+	1.67583i	−0.0345110	+	0.0597748i
$787$	10.0667	−	44.1051i	0.358839	−	1.57218i	−0.397252	−	0.917709i	$-0.630036\pi$
$787$	10.0667	−	44.1051i	0.358839	−	1.57218i	0.756091	−	0.654466i	$-0.227107\pi$
$788$	−26.2875	−	3.96221i	−0.936455	−	0.141148i
$789$	−38.8393	+	18.7040i	−1.38271	+	0.665880i
$790$	2.01863	−	8.84418i	0.0718195	−	0.314662i
$791$	17.0316	+	8.20198i	0.605573	+	0.291629i
$792$	−6.49273	+	11.2457i	−0.230709	+	0.399600i
$793$	−1.27650	+	0.393748i	−0.0453298	+	0.0139824i
$794$	12.1027	+	15.1763i	0.429507	+	0.538585i
$795$	27.0767	+	33.9531i	0.960312	+	1.20419i
$796$	0.841082	+	2.14304i	0.0298114	+	0.0759581i
$797$	35.0794	−	23.9167i	1.24258	−	0.847174i	0.249935	−	0.968263i	$-0.419591\pi$
$797$	35.0794	−	23.9167i	1.24258	−	0.847174i	0.992642	+	0.121088i	$0.0386385\pi$
$798$	−0.589713	+	1.02141i	−0.0208756	+	0.0361576i
$799$	−0.580148	−	2.54180i	−0.0205242	−	0.0899223i
$800$	22.8381	+	10.9982i	0.807448	+	0.388846i
$801$	−1.60830			−0.0568266
$802$	2.09365	−	9.17290i	0.0739295	−	0.323906i
$803$	−27.3105	−	18.6200i	−0.963766	−	0.657084i
$804$	−16.5571	+	7.97350i	−0.583925	+	0.281204i
$805$	10.3980	+	7.08927i	0.366483	+	0.249864i
$806$	−0.452481	−	0.0682006i	−0.0159380	−	0.00240226i
$807$	11.6041	−	29.5669i	0.408485	−	1.04080i
$808$	−11.6315			−0.409196
$809$	1.37825	−	0.207738i	0.0484567	−	0.00730367i	−0.124769	−	0.992186i	$-0.539819\pi$
$809$	1.37825	−	0.207738i	0.0484567	−	0.00730367i	0.173226	+	0.984882i	$0.444581\pi$
$810$	−18.5763	−	8.94586i	−0.652704	−	0.314326i
$811$	−47.5454	+	7.16632i	−1.66955	+	0.251644i	−0.914663	−	0.404217i	$-0.867544\pi$
$811$	−47.5454	+	7.16632i	−1.66955	+	0.251644i	−0.754882	+	0.655860i	$0.772306\pi$
$812$	−0.603304	+	2.64325i	−0.0211718	+	0.0927598i
$813$	−4.39558	+	0.662528i	−0.154160	+	0.0232359i
$814$	3.47454	+	4.35693i	0.121783	+	0.152710i
$815$	13.4066	+	6.45630i	0.469614	+	0.226154i
$816$	−1.89302	+	0.583918i	−0.0662688	+	0.0204412i
$817$	−0.290071	−	1.27088i	−0.0101483	−	0.0444626i
$818$	11.4568	+	10.6303i	0.400577	+	0.371681i
$819$	1.10200	+	0.751331i	0.0385070	+	0.0262536i
$820$	3.60426	+	48.0955i	0.125866	+	1.67957i
$821$	3.27807	+	43.7428i	0.114405	+	1.52663i	0.698891	+	0.715229i	$0.253677\pi$
$821$	3.27807	+	43.7428i	0.114405	+	1.52663i	−0.584485	+	0.811404i	$0.698704\pi$
$822$	−10.9737	−	7.48176i	−0.382753	−	0.260956i
$823$	11.8689	+	11.0127i	0.413724	+	0.383880i	0.859391	−	0.511319i	$-0.170843\pi$
$823$	11.8689	+	11.0127i	0.413724	+	0.383880i	−0.445667	+	0.895199i	$0.647033\pi$
$824$	−7.62380	−	33.4021i	−0.265588	−	1.16362i
$825$	−30.9662	+	9.55182i	−1.07811	+	0.332552i
$826$	−10.4226	−	5.01924i	−0.362647	−	0.174642i
$827$	−11.7688	−	14.7576i	−0.409242	−	0.513173i	0.533907	−	0.845543i	$-0.320723\pi$
$827$	−11.7688	−	14.7576i	−0.409242	−	0.513173i	−0.943149	+	0.332370i	$0.892152\pi$
$828$	−5.90025	+	0.889320i	−0.205048	+	0.0309060i
$829$	5.85459	−	25.6506i	0.203338	−	0.890883i	−0.765548	−	0.643378i	$-0.777532\pi$
$829$	5.85459	−	25.6506i	0.203338	−	0.890883i	0.968887	−	0.247505i	$-0.0796107\pi$
$830$	17.7732	−	2.67888i	0.616916	−	0.0929852i
$831$	22.0086	+	10.5988i	0.763469	+	0.367667i
$832$	−0.217681	+	0.0328101i	−0.00754673	+	0.00113749i
$833$	−1.23641			−0.0428389
$834$	8.08493	−	20.6001i	0.279958	−	0.713322i
$835$	−35.7744	−	5.39212i	−1.23802	−	0.186602i
$836$	1.88628	+	1.28605i	0.0652384	+	0.0444788i
$837$	−5.00521	+	2.41038i	−0.173005	+	0.0833149i
$838$	3.99985	+	2.72705i	0.138173	+	0.0942045i
$839$	−1.24950	+	5.47442i	−0.0431376	+	0.188998i	−0.991906	−	0.126974i	$-0.959473\pi$
$839$	−1.24950	+	5.47442i	−0.0431376	+	0.188998i	0.948768	+	0.315972i	$0.102331\pi$
$840$	30.7502			1.06098
$841$	25.5542	+	12.3062i	0.881178	+	0.424353i
$842$	2.53706	+	11.1156i	0.0874330	+	0.383069i
$843$	1.29911	−	2.25012i	0.0447436	−	0.0774982i
$844$	12.3388	−	8.41242i	0.424717	−	0.289567i
$845$	−14.5562	−	37.0886i	−0.500748	−	1.27589i
$846$	−3.95648	−	4.96127i	−0.136027	−	0.170572i
$847$	0.821475	+	1.03010i	0.0282262	+	0.0353946i
$848$	−12.0391	+	3.71356i	−0.413424	+	0.127524i
$849$	−28.0267	+	48.5437i	−0.961874	+	1.66601i
$850$	1.12261	+	0.540618i	0.0385050	+	0.0185430i
$851$	−1.26415	+	5.53859i	−0.0433344	+	0.189860i
$852$	−48.4654	+	23.3397i	−1.66040	+	0.799605i
$853$	43.6256	+	6.57551i	1.49371	+	0.225141i	0.844537	−	0.535497i	$-0.179876\pi$
$853$	43.6256	+	6.57551i	1.49371	+	0.225141i	0.649176	+	0.760638i	$0.275114\pi$
$854$	−1.05752	+	4.63331i	−0.0361877	+	0.158549i
$855$	1.23623	−	2.14121i	0.0422781	−	0.0732278i
$856$	−3.39979	+	14.8955i	−0.116203	+	0.509117i
$857$	−15.3791			−0.525339			−0.262670	−	0.964886i	$-0.584603\pi$
$857$	−15.3791			−0.525339			−0.262670	+	0.964886i	$0.584603\pi$
$858$	−0.922337	+	1.15657i	−0.0314881	+	0.0394848i
$859$	18.6938	+	5.76628i	0.637824	+	0.196743i	0.596768	−	0.802414i	$-0.296451\pi$
$859$	18.6938	+	5.76628i	0.637824	+	0.196743i	0.0410567	+	0.999157i	$0.486928\pi$
$860$	−11.2300	+	10.4199i	−0.382939	+	0.355315i
$861$	21.6456	+	37.4913i	0.737680	+	1.27770i
$862$	8.22621	+	3.96154i	0.280186	+	0.134930i
$863$	−13.0357	−	22.5784i	−0.443739	−	0.768579i	0.554224	−	0.832367i	$-0.313015\pi$
$863$	−13.0357	−	22.5784i	−0.443739	−	0.768579i	−0.997963	+	0.0637885i	$0.979682\pi$
$864$	10.2980	−	9.55516i	0.350345	−	0.325073i
$865$	39.7717	+	5.99462i	1.35228	+	0.203823i
$866$	11.4687	+	10.6414i	0.389721	+	0.361608i
$867$	35.3381	−	10.9004i	1.20014	−	0.370196i
$868$	4.64450	−	5.82402i	0.157645	−	0.197680i
$869$	−15.5854	+	2.34911i	−0.528697	+	0.0796883i
$870$	−0.724682	+	3.17504i	−0.0245690	+	0.107644i
$871$	−1.69273	+	0.522138i	−0.0573560	+	0.0176920i
$872$	7.65899	+	13.2658i	0.259366	+	0.449235i
$873$	−16.5983	+	5.11989i	−0.561767	+	0.173282i
$874$	−0.0380091	−	0.507196i	−0.00128568	−	0.0171562i
$875$	−2.01320	−	1.86797i	−0.0680585	−	0.0631490i
$876$	−23.1391	−	29.0155i	−0.781799	−	0.980344i
$877$	−5.13969	+	8.90220i	−0.173555	+	0.300606i	−0.939660	−	0.342109i	$-0.888859\pi$
$877$	−5.13969	+	8.90220i	−0.173555	+	0.300606i	0.766105	+	0.642715i	$0.222192\pi$
$878$	4.22371	−	5.29637i	0.142543	−	0.178744i
$879$	18.6864	−	23.4320i	0.630277	−	0.790342i
$880$	1.47104	−	19.6297i	0.0495888	−	0.661717i
$881$	−18.0672	+	12.3180i	−0.608700	+	0.415005i	−0.828060	−	0.560639i	$-0.810556\pi$
$881$	−18.0672	+	12.3180i	−0.608700	+	0.415005i	0.219360	+	0.975644i	$0.429603\pi$
$882$	−2.71133	+	1.30571i	−0.0912952	+	0.0439655i
$883$	−38.0019	+	35.2606i	−1.27887	+	1.18662i	−0.306836	+	0.951762i	$0.599270\pi$
$883$	−38.0019	+	35.2606i	−1.27887	+	1.18662i	−0.972031	+	0.234853i	$0.924539\pi$
$884$	−0.257361	+	0.0387909i	−0.00865599	+	0.00130468i
$885$	57.2867	+	27.5878i	1.92567	+	0.927355i
$886$	−13.0393	+	4.02210i	−0.438065	+	0.135125i
$887$	39.0448	−	12.0437i	1.31100	−	0.404388i	0.441026	−	0.897494i	$-0.354615\pi$
$887$	39.0448	−	12.0437i	1.31100	−	0.404388i	0.869969	+	0.493106i	$0.164138\pi$
$888$	5.07140	+	12.9217i	0.170185	+	0.433624i
$889$	5.49877	+	24.0917i	0.184423	+	0.808009i
$890$	−1.45155	+	0.699029i	−0.0486560	+	0.0234315i
$891$	−2.67703	+	35.7225i	−0.0896840	+	1.19675i
$892$	−0.550319	+	0.0829472i	−0.0184260	+	0.00277728i
$893$	−2.04501	+	1.39427i	−0.0684338	+	0.0466574i
$894$	−23.9023	−	7.37288i	−0.799412	−	0.246586i
$895$	−5.67277	−	9.82553i	−0.189620	−	0.328431i
$896$	−8.67211	+	22.0962i	−0.289715	+	0.738182i
$897$	−1.50806			−0.0503527
$898$	15.0062	−	2.26183i	0.500764	−	0.0754781i
$899$	1.09127	+	1.36842i	0.0363961	+	0.0456392i
$900$	−13.8770			−0.462568
$901$	−2.77225	+	0.855126i	−0.0923571	+	0.0284884i
$902$	−16.4995	+	7.94575i	−0.549374	+	0.264565i
$903$	−5.02368	+	12.8001i	−0.167177	+	0.425961i
$904$	−14.6017	+	13.5484i	−0.485645	+	0.450613i
$905$	56.6377	+	17.4704i	1.88270	+	0.580737i
$906$	−7.93297	−	20.2129i	−0.263555	−	0.671528i
$907$	−27.3905	+	25.4147i	−0.909488	+	0.843881i	−0.988224	−	0.153014i	$-0.951102\pi$
$907$	−27.3905	+	25.4147i	−0.909488	+	0.843881i	0.0787363	+	0.996895i	$0.474912\pi$
$908$	0.130115	−	0.0196117i	0.00431802	−	0.000650837i
$909$	8.88825	−	4.28036i	0.294805	−	0.141970i
$910$	1.32115	+	0.199131i	0.0437956	+	0.00660113i
$911$	32.4314	−	22.1113i	1.07450	−	0.732582i	0.109277	−	0.994011i	$-0.465146\pi$
$911$	32.4314	−	22.1113i	1.07450	−	0.732582i	0.965223	+	0.261430i	$0.0841940\pi$
$912$	1.17258	+	1.47037i	0.0388280	+	0.0486888i
$913$	−15.6143	−	27.0448i	−0.516758	−	0.895052i
$914$	0.808310	+	0.750002i	0.0267365	+	0.0248079i
$915$	5.81259	−	25.4666i	0.192158	−	0.841900i
$916$	11.5299	+	3.55652i	0.380960	+	0.117511i
$917$	−1.10937	−	2.82663i	−0.0366346	−	0.0933435i
$918$	0.506199	−	0.469684i	0.0167070	−	0.0155019i
$919$	1.67699	+	22.3779i	0.0553188	+	0.738178i	0.954044	+	0.299666i	$0.0968752\pi$
$919$	1.67699	+	22.3779i	0.0553188	+	0.738178i	−0.898725	+	0.438512i	$0.855506\pi$
$920$	−10.9566	+	7.47007i	−0.361228	+	0.246281i
$921$	9.63174	+	12.0778i	0.317377	+	0.397978i
$922$	−6.03801			−0.198851
$923$	−4.95489	+	1.52838i	−0.163092	+	0.0503073i
$924$	−8.79811	−	22.4172i	−0.289436	−	0.737472i
$925$	−4.82695	+	12.2989i	−0.158709	+	0.404385i
$926$	0.542559	+	0.503421i	0.0178296	+	0.0165434i
$927$	18.1175	+	22.7187i	0.595058	+	0.746180i
$928$	−3.65693	−	2.49325i	−0.120045	−	0.0818450i
$929$	−40.9306	−	19.7111i	−1.34289	−	0.646701i	−0.382135	−	0.924106i	$-0.624811\pi$
$929$	−40.9306	−	19.7111i	−1.34289	−	0.646701i	−0.960753	+	0.277405i	$0.910526\pi$
$930$	5.57892	−	6.99574i	0.182940	−	0.229400i
$931$	0.428827	+	1.09263i	0.0140542	+	0.0358096i
$932$	−16.8427	−	42.9146i	−0.551702	−	1.40571i
$933$	−0.745642	−	3.26687i	−0.0244112	−	0.106953i
$934$	7.99752	+	20.3773i	0.261687	+	0.666767i
$935$	0.338738	−	4.52015i	0.0110779	−	0.147825i
$936$	−1.16119	+	0.791689i	−0.0379548	+	0.0258772i
$937$	−39.7503	+	27.1013i	−1.29858	+	0.885360i	−0.997666	−	0.0682897i	$-0.978246\pi$
$937$	−39.7503	+	27.1013i	−1.29858	+	0.885360i	−0.300919	+	0.953650i	$0.597293\pi$
$938$	−1.40235	+	6.14411i	−0.0457885	+	0.200612i
$939$	−3.98722	−	53.2058i	−0.130118	−	1.73630i
$940$	26.2066	+	12.6204i	0.854766	+	0.411634i
$941$	−3.73090	+	49.7854i	−0.121624	+	1.62296i	0.518771	+	0.854913i	$0.326390\pi$
$941$	−3.73090	+	49.7854i	−0.121624	+	1.62296i	−0.640395	+	0.768046i	$0.721229\pi$
$942$	4.85227	+	0.731362i	0.158095	+	0.0238291i
$943$	−16.8202	−	8.10017i	−0.547740	−	0.263778i
$944$	−13.5220	+	12.5466i	−0.440105	+	0.408357i
$945$	14.6141	−	7.03779i	0.475398	−	0.228939i
$946$	−5.24077	−	2.52382i	−0.170392	−	0.0820566i
$947$	21.6165	−	55.0780i	0.702443	−	1.78980i	0.0949336	−	0.995484i	$-0.469736\pi$
$947$	21.6165	−	55.0780i	0.702443	−	1.78980i	0.607510	−	0.794312i	$-0.292169\pi$
$948$	−17.4989	−	2.63753i	−0.568338	−	0.0856631i
$949$	−1.78869	−	3.09811i	−0.0580635	−	0.100569i
$950$	0.0883966	−	1.17957i	0.00286796	−	0.0382703i
$951$	3.25955	+	43.4956i	0.105698	+	1.41044i
$952$	−0.750497	+	1.91224i	−0.0243238	+	0.0619759i
$953$	−41.1182	−	6.19757i	−1.33195	−	0.200759i	−0.555803	−	0.831314i	$-0.687589\pi$
$953$	−41.1182	−	6.19757i	−1.33195	−	0.200759i	−0.776145	+	0.630555i	$0.782827\pi$
$954$	−5.17624	+	4.80285i	−0.167587	+	0.155498i
$955$	12.4382	+	31.6921i	0.402491	+	1.02553i
$956$	26.8692	−	33.6929i	0.869011	−	1.08971i
$957$	5.59510	−	0.843326i	0.180864	−	0.0272609i
$958$	−3.56514	+	6.17501i	−0.115185	+	0.199506i
$959$	19.9155	−	6.14312i	0.643105	−	0.198372i
$960$	1.57268	−	4.00711i	0.0507579	−	0.129329i
$961$	5.82806	+	25.5344i	0.188002	+	0.823690i
$962$	0.134209	+	0.588007i	0.00432707	+	0.0189581i
$963$	−2.88351	−	12.6335i	−0.0929199	−	0.407109i
$964$	−4.01222	−	1.23761i	−0.129225	−	0.0398606i
$965$	26.3244	−	45.5952i	0.847412	−	1.46776i
$966$	−2.68257	+	4.64635i	−0.0863104	+	0.149494i
$967$	−3.72786	−	49.7449i	−0.119880	−	1.59969i	−0.655478	−	0.755214i	$-0.727533\pi$
$967$	−3.72786	−	49.7449i	−0.119880	−	1.59969i	0.535598	−	0.844473i	$-0.320086\pi$
$968$	−1.32664	+	0.409214i	−0.0426398	+	0.0131526i
$969$	0.270011	+	0.338583i	0.00867401	+	0.0108769i
$970$	−12.7552	+	11.8351i	−0.409545	+	0.380003i
$971$	−15.6515	−	39.8793i	−0.502280	−	1.27979i	−0.927203	−	0.374559i	$-0.877794\pi$
$971$	−15.6515	−	39.8793i	−0.502280	−	1.27979i	0.424923	−	0.905229i	$-0.360301\pi$
$972$	−10.1372	+	25.8291i	−0.325150	+	0.828468i
$973$	17.3631	+	30.0737i	0.556635	+	0.964120i
$974$	−17.5504	−	2.64529i	−0.562350	−	0.0847606i
$975$	−3.46808	−	0.522729i	−0.111067	−	0.0167407i
$976$	6.26134	+	4.26891i	0.200421	+	0.136644i
$977$	10.3187	+	9.57440i	0.330126	+	0.306312i	0.827768	−	0.561070i	$-0.189610\pi$
$977$	10.3187	+	9.57440i	0.330126	+	0.306312i	−0.497642	+	0.867382i	$0.665801\pi$
$978$	−2.31763	+	5.90522i	−0.0741096	+	0.188828i
$979$	2.05195	+	1.90393i	0.0655805	+	0.0608498i
$980$	8.60050	−	10.7847i	0.274733	−	0.344504i
$981$	−10.7344	−	7.31856i	−0.342722	−	0.233664i
$982$	−18.8067	−	2.83466i	−0.600147	−	0.0904577i
$983$	37.7105	−	25.7106i	1.20278	−	0.820040i	0.215108	−	0.976590i	$-0.430990\pi$
$983$	37.7105	−	25.7106i	1.20278	−	0.820040i	0.987670	+	0.156550i	$0.0500373\pi$
$984$	−45.1071	+	6.79880i	−1.43796	+	0.216738i
$985$	36.7327	−	34.0830i	1.17040	−	1.08597i
$986$	−0.179756	−	0.122556i	−0.00572461	−	0.00390297i
$987$	26.1084			0.831040
$988$	0.123542	+	0.213980i	0.00393038	+	0.00680762i
$989$	−1.31952	−	5.78118i	−0.0419582	−	0.183831i
$990$	−4.03068	−	10.2700i	−0.128104	−	0.326402i
$991$	−6.23558	+	3.00290i	−0.198080	+	0.0953902i	−0.530294	−	0.847814i	$-0.677919\pi$
$991$	−6.23558	+	3.00290i	−0.198080	+	0.0953902i	0.332214	+	0.943204i	$0.392204\pi$
$992$	6.08030	+	10.5314i	0.193050	+	0.334372i
$993$	−5.38985	−	23.6145i	−0.171042	−	0.749383i
$994$	−4.10491	+	17.9848i	−0.130200	+	0.570443i
$995$	−4.14662	−	1.27906i	−0.131457	−	0.0405490i
$996$	−7.80221	−	34.1837i	−0.247223	−	1.08315i
$997$	0.312144	+	4.16528i	0.00988571	+	0.131916i	0.999963	−	0.00860863i	$-0.00274024\pi$
$997$	0.312144	+	4.16528i	0.00988571	+	0.131916i	−0.990077	+	0.140524i	$0.955121\pi$
$998$	11.1145	+	19.2509i	0.351824	+	0.609378i
$999$	5.36758	+	4.98038i	0.169823	+	0.157572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.h.a.13.17	✓	540
547.505	even	21	inner	547.2.h.a.505.17	yes	540

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.h.a.13.17	✓	540	1.1	even	1	trivial
547.2.h.a.505.17	yes	540	547.505	even	21	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.h (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0447565 + 0.597235i) q^{2} +(-1.37304 + 1.72174i) q^{3} +(1.62298 + 0.244624i) q^{4} +(-2.26785 + 2.10426i) q^{5} +(-0.966831 - 0.897088i) q^{6} +(2.04652 - 0.308464i) q^{7} +(-0.485277 + 2.12614i) q^{8} +(-0.411584 - 1.80327i) q^{9} +O(q^{10})\)	\(q+(-0.0447565 + 0.597235i) q^{2} +(-1.37304 + 1.72174i) q^{3} +(1.62298 + 0.244624i) q^{4} +(-2.26785 + 2.10426i) q^{5} +(-0.966831 - 0.897088i) q^{6} +(2.04652 - 0.308464i) q^{7} +(-0.485277 + 2.12614i) q^{8} +(-0.411584 - 1.80327i) q^{9} +(-1.15524 - 1.44862i) q^{10} +(-1.60961 + 2.78793i) q^{11} +(-2.64960 + 2.45847i) q^{12} +(-0.287872 + 0.196268i) q^{13} +(0.0926300 + 1.23606i) q^{14} +(-0.509133 - 6.79390i) q^{15} +(1.88870 + 0.582585i) q^{16} +(0.434912 + 0.134153i) q^{17} +(1.09540 - 0.165104i) q^{18} +(-0.0322891 - 0.430868i) q^{19} +(-4.19543 + 2.86039i) q^{20} +(-2.27887 + 3.94712i) q^{21} +(-1.59301 - 1.08609i) q^{22} +(-0.146881 - 1.95999i) q^{23} +(-2.99435 - 3.75480i) q^{24} +(0.341597 - 4.55830i) q^{25} +(-0.104334 - 0.180711i) q^{26} +(-2.28243 - 1.09916i) q^{27} +3.39692 q^{28} +(-0.177603 + 0.778131i) q^{29} +4.08034 q^{30} +(1.36727 - 1.71450i) q^{31} +(-2.02595 + 5.16204i) q^{32} +(-2.59003 - 6.59928i) q^{33} +(-0.0995857 + 0.253740i) q^{34} +(-3.99213 + 5.00597i) q^{35} +(-0.226868 - 3.02734i) q^{36} +(-2.76197 - 0.851956i) q^{37} +0.258774 q^{38} +(0.0573381 - 0.765124i) q^{39} +(-3.37341 - 5.84291i) q^{40} +(4.74919 - 8.22584i) q^{41} +(-2.25536 - 1.53768i) q^{42} +(2.98329 - 0.449659i) q^{43} +(-3.29435 + 4.13099i) q^{44} +(4.72796 + 3.22347i) q^{45} +1.17715 q^{46} +(-2.86418 - 4.96091i) q^{47} +(-3.59632 + 2.45193i) q^{48} +(-2.59590 + 0.800728i) q^{49} +(2.70708 + 0.408027i) q^{50} +(-0.828129 + 0.564609i) q^{51} +(-0.515220 + 0.248117i) q^{52} +(-5.26668 + 3.59076i) q^{53} +(0.758610 - 1.31395i) q^{54} +(-2.21617 - 9.70966i) q^{55} +(-0.337294 + 4.50088i) q^{56} +(0.786177 + 0.536007i) q^{57} +(-0.456778 - 0.140897i) q^{58} +(-4.66637 + 8.08239i) q^{59} +(0.835643 - 11.1509i) q^{60} +(3.66376 + 1.13012i) q^{61} +(0.962765 + 0.893315i) q^{62} +(-1.39856 - 3.56347i) q^{63} +(0.569266 + 0.274144i) q^{64} +(0.239853 - 1.05086i) q^{65} +(4.05724 - 1.25149i) q^{66} +(4.85841 + 1.49862i) q^{67} +(0.673034 + 0.324116i) q^{68} +(3.57628 + 2.43826i) q^{69} +(-2.81107 - 2.60829i) q^{70} +(14.2213 + 4.38670i) q^{71} +4.03372 q^{72} +(-0.767305 + 10.2390i) q^{73} +(0.632434 - 1.61142i) q^{74} +(7.37918 + 6.84688i) q^{75} +(0.0529963 - 0.707187i) q^{76} +(-2.43413 + 6.20207i) q^{77} +(0.454392 + 0.0684886i) q^{78} +(3.05262 + 3.82787i) q^{79} +(-5.50920 + 2.65309i) q^{80} +(10.0258 - 4.82815i) q^{81} +(4.70020 + 3.20454i) q^{82} +(-4.85034 + 8.40103i) q^{83} +(-4.66411 + 5.84861i) q^{84} +(-1.26861 + 0.610930i) q^{85} +(0.135030 + 1.80185i) q^{86} +(-1.09588 - 1.37419i) q^{87} +(-5.14641 - 4.77517i) q^{88} +(0.193487 - 0.847721i) q^{89} +(-2.13677 + 2.67943i) q^{90} +(-0.528595 + 0.490464i) q^{91} +(0.241077 - 3.21695i) q^{92} +(1.07461 + 4.70817i) q^{93} +(3.09102 - 1.48856i) q^{94} +(0.979885 + 0.909201i) q^{95} +(-6.10598 - 10.5759i) q^{96} +(-0.701790 - 9.36474i) q^{97} +(-0.362039 - 1.58620i) q^{98} +(5.68987 + 1.75509i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 540 q - 13 q^{2} - 10 q^{3} + 33 q^{4} - 15 q^{5} + 10 q^{6} - 2 q^{7} - 26 q^{8} - 96 q^{9}+O(q^{10}) \) 540 * q - 13 * q^2 - 10 * q^3 + 33 * q^4 - 15 * q^5 + 10 * q^6 - 2 * q^7 - 26 * q^8 - 96 * q^9	\( 540 q - 13 q^{2} - 10 q^{3} + 33 q^{4} - 15 q^{5} + 10 q^{6} - 2 q^{7} - 26 q^{8} - 96 q^{9} - 4 q^{10} - 8 q^{11} - 18 q^{12} - 11 q^{13} + 5 q^{14} - 7 q^{15} + 53 q^{16} - 10 q^{17} - 59 q^{18} - 12 q^{19} - 18 q^{20} + 20 q^{21} + 70 q^{22} - 15 q^{23} - 46 q^{24} + 26 q^{25} - 39 q^{26} - q^{27} - 56 q^{28} - 40 q^{29} - 100 q^{30} + 59 q^{31} - 5 q^{32} - 15 q^{33} - 8 q^{34} + 36 q^{35} + 43 q^{36} - 32 q^{37} - 108 q^{38} + 34 q^{39} - 27 q^{40} + 39 q^{41} + 46 q^{42} - 16 q^{43} - 110 q^{44} - 103 q^{45} + 12 q^{46} - 60 q^{47} + 42 q^{48} + 57 q^{49} - 168 q^{50} + 57 q^{51} - 46 q^{52} - 30 q^{53} + 113 q^{54} + 38 q^{55} + 64 q^{56} + 22 q^{57} - 88 q^{58} + 55 q^{59} + 9 q^{60} + 26 q^{61} - 32 q^{62} + 6 q^{63} - 50 q^{64} + 73 q^{65} + 72 q^{66} - 104 q^{67} - 181 q^{68} - 125 q^{69} - 50 q^{70} + 39 q^{71} - 434 q^{72} + 46 q^{73} - 178 q^{74} + 248 q^{75} - 126 q^{76} - 52 q^{77} - 82 q^{78} + 86 q^{79} + 208 q^{80} - 4 q^{81} + 177 q^{82} + 39 q^{83} + 124 q^{84} - 12 q^{85} + 2 q^{86} + 162 q^{87} - 34 q^{88} + 63 q^{89} + 121 q^{90} + 21 q^{91} + q^{92} - 57 q^{93} + 67 q^{94} - 143 q^{95} + 489 q^{96} + 119 q^{97} - 10 q^{98} - 120 q^{99}+O(q^{100}) \) 540 * q - 13 * q^2 - 10 * q^3 + 33 * q^4 - 15 * q^5 + 10 * q^6 - 2 * q^7 - 26 * q^8 - 96 * q^9 - 4 * q^10 - 8 * q^11 - 18 * q^12 - 11 * q^13 + 5 * q^14 - 7 * q^15 + 53 * q^16 - 10 * q^17 - 59 * q^18 - 12 * q^19 - 18 * q^20 + 20 * q^21 + 70 * q^22 - 15 * q^23 - 46 * q^24 + 26 * q^25 - 39 * q^26 - q^27 - 56 * q^28 - 40 * q^29 - 100 * q^30 + 59 * q^31 - 5 * q^32 - 15 * q^33 - 8 * q^34 + 36 * q^35 + 43 * q^36 - 32 * q^37 - 108 * q^38 + 34 * q^39 - 27 * q^40 + 39 * q^41 + 46 * q^42 - 16 * q^43 - 110 * q^44 - 103 * q^45 + 12 * q^46 - 60 * q^47 + 42 * q^48 + 57 * q^49 - 168 * q^50 + 57 * q^51 - 46 * q^52 - 30 * q^53 + 113 * q^54 + 38 * q^55 + 64 * q^56 + 22 * q^57 - 88 * q^58 + 55 * q^59 + 9 * q^60 + 26 * q^61 - 32 * q^62 + 6 * q^63 - 50 * q^64 + 73 * q^65 + 72 * q^66 - 104 * q^67 - 181 * q^68 - 125 * q^69 - 50 * q^70 + 39 * q^71 - 434 * q^72 + 46 * q^73 - 178 * q^74 + 248 * q^75 - 126 * q^76 - 52 * q^77 - 82 * q^78 + 86 * q^79 + 208 * q^80 - 4 * q^81 + 177 * q^82 + 39 * q^83 + 124 * q^84 - 12 * q^85 + 2 * q^86 + 162 * q^87 - 34 * q^88 + 63 * q^89 + 121 * q^90 + 21 * q^91 + q^92 - 57 * q^93 + 67 * q^94 - 143 * q^95 + 489 * q^96 + 119 * q^97 - 10 * q^98 - 120 * q^99

Introduction

L-functions

Modular forms

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