LMFDB - Embedded newform 360.2.bm.b.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(11,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("360.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.6
Character	$\chi$	$=$	360.11
Dual form			360.2.bm.b.131.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14743 - 0.826684i) q^{2} +(-0.952268 - 1.44678i) q^{3} +(0.633188 + 1.89712i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.103374 + 2.44731i) q^{6} +(-2.56287 - 1.47968i) q^{7} +(0.841782 - 2.70026i) q^{8} +(-1.18637 + 2.75545i) q^{9} +O(q^{10})$	\(q+(-1.14743 - 0.826684i) q^{2} +(-0.952268 - 1.44678i) q^{3} +(0.633188 + 1.89712i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.103374 + 2.44731i) q^{6} +(-2.56287 - 1.47968i) q^{7} +(0.841782 - 2.70026i) q^{8} +(-1.18637 + 2.75545i) q^{9} +(0.142215 - 1.40704i) q^{10} +(2.28478 + 1.31912i) q^{11} +(2.14176 - 2.72265i) q^{12} +(-5.81331 + 3.35631i) q^{13} +(1.71749 + 3.81651i) q^{14} +(0.776819 - 1.54808i) q^{15} +(-3.19815 + 2.40247i) q^{16} +1.13277i q^{17} +(3.63917 - 2.18093i) q^{18} -1.90413 q^{19} +(-1.32636 + 1.49692i) q^{20} +(0.299769 + 5.11697i) q^{21} +(-1.53113 - 3.40239i) q^{22} +(1.73629 + 3.00734i) q^{23} +(-4.70830 + 1.35349i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(9.44497 + 0.954634i) q^{26} +(5.11629 - 0.907502i) q^{27} +(1.18435 - 5.79899i) q^{28} +(-2.38991 + 4.13945i) q^{29} +(-2.17112 + 1.13413i) q^{30} +(1.93826 - 1.11906i) q^{31} +(5.65573 - 0.112808i) q^{32} +(-0.267242 - 4.56174i) q^{33} +(0.936442 - 1.29977i) q^{34} -2.95935i q^{35} +(-5.97863 - 0.505976i) q^{36} +11.4572i q^{37} +(2.18485 + 1.57411i) q^{38} +(10.3917 + 5.21450i) q^{39} +(2.75938 - 0.621125i) q^{40} +(8.25369 - 4.76527i) q^{41} +(3.88615 - 6.11918i) q^{42} +(-2.52551 + 4.37431i) q^{43} +(-1.05583 + 5.16976i) q^{44} +(-2.97948 + 0.350297i) q^{45} +(0.493851 - 4.88607i) q^{46} +(1.06917 - 1.85185i) q^{47} +(6.52135 + 2.33924i) q^{48} +(0.878877 + 1.52226i) q^{49} +(1.28964 - 0.580361i) q^{50} +(1.63887 - 1.07870i) q^{51} +(-10.0483 - 8.90338i) q^{52} -2.02679 q^{53} +(-6.62080 - 3.18826i) q^{54} +2.63824i q^{55} +(-6.15289 + 5.67486i) q^{56} +(1.81324 + 2.75487i) q^{57} +(6.16427 - 2.77402i) q^{58} +(-11.8879 + 6.86345i) q^{59} +(3.42877 + 0.493494i) q^{60} +(-6.75703 - 3.90117i) q^{61} +(-3.14912 - 0.318292i) q^{62} +(7.11770 - 5.30643i) q^{63} +(-6.58281 - 4.54606i) q^{64} +(-5.81331 - 3.35631i) q^{65} +(-3.46448 + 5.45520i) q^{66} +(-2.22742 - 3.85801i) q^{67} +(-2.14900 + 0.717255i) q^{68} +(2.69756 - 5.37583i) q^{69} +(-2.44645 + 3.39565i) q^{70} -13.5205 q^{71} +(6.44177 + 5.52301i) q^{72} +4.30531 q^{73} +(9.47147 - 13.1463i) q^{74} +(1.72909 - 0.101296i) q^{75} +(-1.20567 - 3.61237i) q^{76} +(-3.90374 - 6.76147i) q^{77} +(-7.61299 - 14.5739i) q^{78} +(-10.4990 - 6.06162i) q^{79} +(-3.67967 - 1.56844i) q^{80} +(-6.18504 - 6.53799i) q^{81} +(-13.4099 - 1.35538i) q^{82} +(1.80201 + 1.04039i) q^{83} +(-9.51771 + 3.80870i) q^{84} +(-0.981007 + 0.566384i) q^{85} +(6.51402 - 2.93142i) q^{86} +(8.26472 - 0.484174i) q^{87} +(5.48525 - 5.05909i) q^{88} +10.3071i q^{89} +(3.70833 + 2.06115i) q^{90} +19.8650 q^{91} +(-4.60590 + 5.19816i) q^{92} +(-3.46478 - 1.73861i) q^{93} +(-2.75769 + 1.24101i) q^{94} +(-0.952065 - 1.64903i) q^{95} +(-5.54898 - 8.07520i) q^{96} +(-4.06907 + 7.04783i) q^{97} +(0.249978 - 2.47324i) q^{98} +(-6.34537 + 4.73064i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.14743	−	0.826684i	−0.811355	−	0.584554i
$2$	−1.14743	−	0.826684i	−0.811355	−	0.584554i
$3$	−0.952268	−	1.44678i	−0.549792	−	0.835302i
$3$	−0.952268	−	1.44678i	−0.549792	−	0.835302i
$4$	0.633188	+	1.89712i	0.316594	+	0.948561i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.103374	+	2.44731i	−0.0422022	+	0.999109i
$7$	−2.56287	−	1.47968i	−0.968675	−	0.559265i	−0.0698428	−	0.997558i	$-0.522250\pi$
$7$	−2.56287	−	1.47968i	−0.968675	−	0.559265i	−0.898832	+	0.438293i	$0.855583\pi$
$8$	0.841782	−	2.70026i	0.297615	−	0.954686i
$9$	−1.18637	+	2.75545i	−0.395458	+	0.918484i
$10$	0.142215	−	1.40704i	0.0449722	−	0.444947i
$11$	2.28478	+	1.31912i	0.688887	+	0.397729i	0.803195	−	0.595716i	$-0.203132\pi$
$11$	2.28478	+	1.31912i	0.688887	+	0.397729i	−0.114308	+	0.993445i	$0.536465\pi$
$12$	2.14176	−	2.72265i	0.618274	−	0.785963i
$13$	−5.81331	+	3.35631i	−1.61232	+	0.930874i	−0.623491	+	0.781831i	$0.714286\pi$
$13$	−5.81331	+	3.35631i	−1.61232	+	0.930874i	−0.988831	+	0.149043i	$0.952381\pi$
$14$	1.71749	+	3.81651i	0.459019	+	1.02000i
$15$	0.776819	−	1.54808i	0.200574	−	0.399713i
$16$	−3.19815	+	2.40247i	−0.799537	+	0.600617i
$17$			1.13277i			0.274737i	0.990520	+	0.137368i	$0.0438644\pi$
$17$			1.13277i			0.274737i	−0.990520	+	0.137368i	$0.956136\pi$
$18$	3.63917	−	2.18093i	0.857760	−	0.514051i
$19$	−1.90413			−0.436837			−0.218419	−	0.975855i	$-0.570090\pi$
$19$	−1.90413			−0.436837			−0.218419	+	0.975855i	$0.570090\pi$
$20$	−1.32636	+	1.49692i	−0.296584	+	0.334721i
$21$	0.299769	+	5.11697i	0.0654149	+	1.11661i
$22$	−1.53113	−	3.40239i	−0.326438	−	0.725391i
$23$	1.73629	+	3.00734i	0.362041	+	0.627074i	0.988297	−	0.152544i	$-0.0487466\pi$
$23$	1.73629	+	3.00734i	0.362041	+	0.627074i	−0.626255	+	0.779618i	$0.715413\pi$
$24$	−4.70830	+	1.35349i	−0.961077	+	0.276280i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	9.44497	+	0.954634i	1.85231	+	0.187219i
$27$	5.11629	−	0.907502i	0.984631	−	0.174649i
$28$	1.18435	−	5.79899i	0.223820	−	1.09591i
$29$	−2.38991	+	4.13945i	−0.443795	+	0.768676i	−0.997967	−	0.0637261i	$-0.979702\pi$
$29$	−2.38991	+	4.13945i	−0.443795	+	0.768676i	0.554172	+	0.832402i	$0.313035\pi$
$30$	−2.17112	+	1.13413i	−0.396390	+	0.207063i
$31$	1.93826	−	1.11906i	0.348122	−	0.200988i	−0.315736	−	0.948847i	$-0.602251\pi$
$31$	1.93826	−	1.11906i	0.348122	−	0.200988i	0.663858	+	0.747859i	$0.268918\pi$
$32$	5.65573	−	0.112808i	0.999801	−	0.0199417i
$33$	−0.267242	−	4.56174i	−0.0465208	−	0.794097i
$34$	0.936442	−	1.29977i	0.160598	−	0.222909i
$35$		−	2.95935i		−	0.500221i
$36$	−5.97863	−	0.505976i	−0.996438	−	0.0843293i
$37$			11.4572i			1.88355i	0.336245	+	0.941775i	$0.390843\pi$
$37$			11.4572i			1.88355i	−0.336245	+	0.941775i	$0.609157\pi$
$38$	2.18485	+	1.57411i	0.354430	+	0.255355i
$39$	10.3917	+	5.21450i	1.66400	+	0.834988i
$40$	2.75938	−	0.621125i	0.436297	−	0.0982085i
$41$	8.25369	−	4.76527i	1.28901	−	0.744210i	0.310532	−	0.950563i	$-0.399493\pi$
$41$	8.25369	−	4.76527i	1.28901	−	0.744210i	0.978478	+	0.206353i	$0.0661596\pi$
$42$	3.88615	−	6.11918i	0.599647	−	0.944210i
$43$	−2.52551	+	4.37431i	−0.385137	+	0.667076i	−0.991788	−	0.127892i	$-0.959179\pi$
$43$	−2.52551	+	4.37431i	−0.385137	+	0.667076i	0.606651	+	0.794968i	$0.292512\pi$
$44$	−1.05583	+	5.16976i	−0.159173	+	0.779371i
$45$	−2.97948	+	0.350297i	−0.444154	+	0.0522192i
$46$	0.493851	−	4.88607i	0.0728144	−	0.720412i
$47$	1.06917	−	1.85185i	0.155954	−	0.270121i	−0.777452	−	0.628942i	$-0.783488\pi$
$47$	1.06917	−	1.85185i	0.155954	−	0.270121i	0.933406	+	0.358822i	$0.116821\pi$
$48$	6.52135	+	2.33924i	0.941275	+	0.337640i
$49$	0.878877	+	1.52226i	0.125554	+	0.217466i
$50$	1.28964	−	0.580361i	0.182383	−	0.0820754i
$51$	1.63887	−	1.07870i	0.229488	−	0.151048i
$52$	−10.0483	−	8.90338i	−1.39344	−	1.23468i
$53$	−2.02679			−0.278401			−0.139200	−	0.990264i	$-0.544453\pi$
$53$	−2.02679			−0.278401			−0.139200	+	0.990264i	$0.544453\pi$
$54$	−6.62080	−	3.18826i	−0.900977	−	0.433867i
$55$			2.63824i			0.355740i
$56$	−6.15289	+	5.67486i	−0.822214	+	0.758335i
$57$	1.81324	+	2.75487i	0.240170	+	0.364891i
$58$	6.16427	−	2.77402i	0.809408	−	0.364247i
$59$	−11.8879	+	6.86345i	−1.54767	+	0.893546i	−0.549347	+	0.835594i	$0.685123\pi$
$59$	−11.8879	+	6.86345i	−1.54767	+	0.893546i	−0.998319	+	0.0579512i	$0.981543\pi$
$60$	3.42877	+	0.493494i	0.442652	+	0.0637099i
$61$	−6.75703	−	3.90117i	−0.865149	−	0.499494i	0.000584137	−	1.00000i	$-0.499814\pi$
$61$	−6.75703	−	3.90117i	−0.865149	−	0.499494i	−0.865733	+	0.500506i	$0.833147\pi$
$62$	−3.14912	−	0.318292i	−0.399939	−	0.0404231i
$63$	7.11770	−	5.30643i	0.896746	−	0.668547i
$64$	−6.58281	−	4.54606i	−0.822851	−	0.568258i
$65$	−5.81331	−	3.35631i	−0.721052	−	0.416300i
$66$	−3.46448	+	5.45520i	−0.426448	+	0.671489i
$67$	−2.22742	−	3.85801i	−0.272123	−	0.471331i	0.697282	−	0.716797i	$-0.254392\pi$
$67$	−2.22742	−	3.85801i	−0.272123	−	0.471331i	−0.969405	+	0.245466i	$0.921059\pi$
$68$	−2.14900	+	0.717255i	−0.260605	+	0.0869800i
$69$	2.69756	−	5.37583i	0.324748	−	0.647174i
$70$	−2.44645	+	3.39565i	−0.292406	+	0.405857i
$71$	−13.5205			−1.60459			−0.802294	−	0.596929i	$-0.796387\pi$
$71$	−13.5205			−1.60459			−0.802294	+	0.596929i	$0.796387\pi$
$72$	6.44177	+	5.52301i	0.759170	+	0.650892i
$73$	4.30531			0.503898			0.251949	−	0.967741i	$-0.418928\pi$
$73$	4.30531			0.503898			0.251949	+	0.967741i	$0.418928\pi$
$74$	9.47147	−	13.1463i	1.10104	−	1.52823i
$75$	1.72909	−	0.101296i	0.199658	−	0.0116966i
$76$	−1.20567	−	3.61237i	−0.138300	−	0.414367i
$77$	−3.90374	−	6.76147i	−0.444872	−	0.770541i
$78$	−7.61299	−	14.5739i	−0.862001	−	1.65017i
$79$	−10.4990	−	6.06162i	−1.18123	−	0.681985i	−0.224933	−	0.974374i	$-0.572216\pi$
$79$	−10.4990	−	6.06162i	−1.18123	−	0.681985i	−0.956299	+	0.292389i	$0.905550\pi$
$80$	−3.67967	−	1.56844i	−0.411400	−	0.175357i
$81$	−6.18504	−	6.53799i	−0.687227	−	0.726443i
$82$	−13.4099	−	1.35538i	−1.48087	−	0.149677i
$83$	1.80201	+	1.04039i	0.197797	+	0.114198i	0.595627	−	0.803261i	$-0.296904\pi$
$83$	1.80201	+	1.04039i	0.197797	+	0.114198i	−0.397831	+	0.917459i	$0.630237\pi$
$84$	−9.51771	+	3.80870i	−1.03847	+	0.415563i
$85$	−0.981007	+	0.566384i	−0.106405	+	0.0614330i
$86$	6.51402	−	2.93142i	0.702425	−	0.316103i
$87$	8.26472	−	0.484174i	0.886071	−	0.0519090i
$88$	5.48525	−	5.05909i	0.584730	−	0.539301i
$89$			10.3071i			1.09255i	0.837607	+	0.546273i	$0.183954\pi$
$89$			10.3071i			1.09255i	−0.837607	+	0.546273i	$0.816046\pi$
$90$	3.70833	+	2.06115i	0.390892	+	0.217264i
$91$	19.8650			2.08242
$92$	−4.60590	+	5.19816i	−0.480198	+	0.541946i
$93$	−3.46478	−	1.73861i	−0.359280	−	0.180285i
$94$	−2.75769	+	1.24101i	−0.284434	+	0.128000i
$95$	−0.952065	−	1.64903i	−0.0976798	−	0.169186i
$96$	−5.54898	−	8.07520i	−0.566340	−	0.824172i
$97$	−4.06907	+	7.04783i	−0.413151	+	0.715599i	−0.995232	−	0.0975317i	$-0.968905\pi$
$97$	−4.06907	+	7.04783i	−0.413151	+	0.715599i	0.582081	+	0.813131i	$0.302239\pi$
$98$	0.249978	−	2.47324i	0.0252516	−	0.249835i
$99$	−6.34537	+	4.73064i	−0.637734	+	0.475447i
$100$	−1.95955	−	0.400205i	−0.195955	−	0.0400205i
$101$	6.42693	−	11.1318i	0.639503	−	1.10765i	−0.346039	−	0.938220i	$-0.612473\pi$
$101$	6.42693	−	11.1318i	0.639503	−	1.10765i	0.985542	−	0.169432i	$-0.0541933\pi$
$102$	−2.77223	−	0.117099i	−0.274492	−	0.0115945i
$103$	8.36590	−	4.83006i	0.824317	−	0.475920i	−0.0275858	−	0.999619i	$-0.508782\pi$
$103$	8.36590	−	4.83006i	0.824317	−	0.475920i	0.851903	+	0.523700i	$0.175449\pi$
$104$	4.16938	+	18.5227i	0.408842	+	1.81630i
$105$	−4.28154	+	2.81809i	−0.417836	+	0.275018i
$106$	2.32559	+	1.67551i	0.225882	+	0.162740i
$107$		−	7.08169i		−	0.684613i	−0.939588	−	0.342307i	$-0.888792\pi$
$107$		−	7.08169i		−	0.684613i	0.939588	−	0.342307i	$-0.111208\pi$
$108$	4.96122	+	9.13161i	0.477393	+	0.878690i
$109$			12.6799i			1.21452i	0.794504	+	0.607259i	$0.207731\pi$
$109$			12.6799i			1.21452i	−0.794504	+	0.607259i	$0.792269\pi$
$110$	2.18099	−	3.02719i	0.207949	−	0.288631i
$111$	16.5761	−	10.9103i	1.57333	−	1.03556i
$112$	11.7513	−	1.42500i	1.11039	−	0.134650i
$113$	−9.15072	+	5.28317i	−0.860827	+	0.496999i	−0.864289	−	0.502995i	$-0.832231\pi$
$113$	−9.15072	+	5.28317i	−0.860827	+	0.496999i	0.00346193	+	0.999994i	$0.498898\pi$
$114$	0.196837	−	4.65999i	0.0184355	−	0.436448i
$115$	−1.73629	+	3.00734i	−0.161910	+	0.280436i
$116$	−9.36630	−	1.91291i	−0.869639	−	0.177609i
$117$	−2.35142	−	20.0001i	−0.217388	−	1.84901i
$118$	19.3144	+	1.95217i	1.77803	+	0.179711i
$119$	1.67613	−	2.90314i	0.153651	−	0.266131i
$120$	−3.52631	−	3.40076i	−0.321906	−	0.310445i
$121$	−2.01985	−	3.49848i	−0.183623	−	0.318044i
$122$	4.52818	+	10.0622i	0.409962	+	0.910993i
$123$	−14.7540	−	7.40350i	−1.33033	−	0.667551i
$124$	3.35027	+	2.96855i	0.300863	+	0.266583i
$125$	−1.00000			−0.0894427
$126$	−12.5538	+	0.204665i	−1.11838	+	0.0182330i
$127$			2.64903i			0.235063i	0.993069	+	0.117532i	$0.0374982\pi$
$127$			2.64903i			0.235063i	−0.993069	+	0.117532i	$0.962502\pi$
$128$	3.79515	+	10.6582i	0.335447	+	0.942059i
$129$	8.73365	−	0.511646i	0.768955	−	0.0450479i
$130$	3.89575	+	8.65690i	0.341680	+	0.759260i
$131$	12.7812	−	7.37922i	1.11670	−	0.644726i	0.176142	−	0.984365i	$-0.443638\pi$
$131$	12.7812	−	7.37922i	1.11670	−	0.644726i	0.940556	+	0.339639i	$0.110305\pi$
$132$	8.48497	−	3.39543i	0.738522	−	0.295534i
$133$	4.88004	+	2.81749i	0.423153	+	0.244308i
$134$	−0.633544	+	6.26817i	−0.0547299	+	0.541487i
$135$	3.34407	+	3.97709i	0.287811	+	0.342293i
$136$	3.05877	+	0.953545i	0.262287	+	0.0817658i
$137$	3.27534	+	1.89102i	0.279831	+	0.161561i	0.633347	−	0.773868i	$-0.281681\pi$
$137$	3.27534	+	1.89102i	0.279831	+	0.161561i	−0.353516	+	0.935429i	$0.615014\pi$
$138$	−7.53938	+	3.93835i	−0.641794	+	0.335255i
$139$	−2.88176	−	4.99136i	−0.244428	−	0.423362i	0.717543	−	0.696515i	$-0.245267\pi$
$139$	−2.88176	−	4.99136i	−0.244428	−	0.423362i	−0.961971	+	0.273153i	$0.911934\pi$
$140$	5.61425	−	1.87382i	0.474491	−	0.158367i
$141$	−3.69737	+	0.216604i	−0.311375	+	0.0182413i
$142$	15.5138	+	11.1772i	1.30189	+	0.937968i
$143$	−17.7095			−1.48094
$144$	−2.82570	−	11.6626i	−0.235475	−	0.971880i
$145$	−4.77982			−0.396943
$146$	−4.94003	−	3.55913i	−0.408840	−	0.294555i
$147$	1.36546	−	2.72114i	0.112621	−	0.224436i
$148$	−21.7357	+	7.25455i	−1.78666	+	0.596320i
$149$	−2.82265	−	4.88897i	−0.231240	−	0.400520i	0.726933	−	0.686708i	$-0.240945\pi$
$149$	−2.82265	−	4.88897i	−0.231240	−	0.400520i	−0.958173	+	0.286188i	$0.907612\pi$
$150$	−2.06774	−	1.31318i	−0.168831	−	0.107221i
$151$	4.34401	+	2.50802i	0.353511	+	0.204100i	0.666230	−	0.745746i	$-0.267907\pi$
$151$	4.34401	+	2.50802i	0.353511	+	0.204100i	−0.312720	+	0.949845i	$0.601240\pi$
$152$	−1.60286	+	5.14165i	−0.130009	+	0.417043i
$153$	−3.12129	−	1.34389i	−0.252341	−	0.108647i
$154$	−1.11034	+	10.9855i	−0.0894734	+	0.885234i
$155$	1.93826	+	1.11906i	0.155685	+	0.0898847i
$156$	−3.31265	+	23.0161i	−0.265224	+	1.84276i
$157$	−1.88084	+	1.08590i	−0.150107	+	0.0866643i	−0.573172	−	0.819435i	$-0.694287\pi$
$157$	−1.88084	+	1.08590i	−0.150107	+	0.0866643i	0.423065	+	0.906099i	$0.360954\pi$
$158$	7.03585	+	15.6347i	0.559742	+	1.24383i
$159$	1.93004	+	2.93232i	0.153062	+	0.232548i
$160$	2.92556	+	4.84160i	0.231286	+	0.382762i
$161$		−	10.2766i		−	0.809908i
$162$	1.69205	+	12.6150i	0.132940	+	0.991124i
$163$	−18.7294			−1.46700			−0.733500	−	0.679690i	$-0.762114\pi$
$163$	−18.7294			−1.46700			−0.733500	+	0.679690i	$0.762114\pi$
$164$	14.2664	+	12.6409i	1.11402	+	0.987092i
$165$	3.81696	−	2.51231i	0.297150	−	0.195583i
$166$	−1.20761	−	2.68347i	−0.0937285	−	0.208278i
$167$	2.21409	+	3.83492i	0.171331	+	0.296755i	0.938886	−	0.344229i	$-0.111860\pi$
$167$	2.21409	+	3.83492i	0.171331	+	0.296755i	−0.767554	+	0.640984i	$0.778526\pi$
$168$	14.0695	+	3.49792i	1.08548	+	0.269871i
$169$	16.0297	−	27.7642i	1.23305	−	2.13571i
$170$	1.59386	+	0.161096i	0.122243	+	0.0123555i
$171$	2.25901	−	5.24674i	0.172751	−	0.401228i
$172$	−9.89773	−	2.02144i	−0.754695	−	0.154133i
$173$	11.1220	−	19.2638i	0.845588	−	1.46460i	−0.0395216	−	0.999219i	$-0.512583\pi$
$173$	11.1220	−	19.2638i	0.845588	−	1.46460i	0.885110	−	0.465383i	$-0.154083\pi$
$174$	−9.88345	−	6.27676i	−0.749262	−	0.475840i
$175$	2.56287	−	1.47968i	0.193735	−	0.111853i
$176$	−10.4762	+	1.27038i	−0.789674	+	0.0957586i
$177$	21.2504	+	10.6633i	1.59727	+	0.801504i
$178$	8.52068	−	11.8266i	0.638652	−	0.886443i
$179$			12.2714i			0.917209i	0.888640	+	0.458604i	$0.151651\pi$
$179$			12.2714i			0.917209i	−0.888640	+	0.458604i	$0.848349\pi$
$180$	−2.55113	−	5.43063i	−0.190150	−	0.404775i
$181$			23.6721i			1.75953i	0.475405	+	0.879767i	$0.342301\pi$
$181$			23.6721i			1.75953i	−0.475405	+	0.879767i	$0.657699\pi$
$182$	−22.7937	−	16.4221i	−1.68958	−	1.21729i
$183$	0.790343	+	13.4909i	0.0584238	+	0.997278i
$184$	9.58218	−	2.15691i	0.706408	−	0.159009i
$185$	−9.92221	+	5.72859i	−0.729496	+	0.421174i
$186$	2.53831	+	4.85920i	0.186118	+	0.356294i
$187$	−1.49426	+	2.58813i	−0.109271	+	0.189263i
$188$	4.19018	+	0.855772i	0.305600	+	0.0624136i
$189$	−14.4552	−	5.24464i	−1.05146	−	0.381491i
$190$	−0.270795	+	2.67920i	−0.0196455	+	0.194369i
$191$	2.86477	−	4.96193i	0.207287	−	0.359032i	−0.743572	−	0.668656i	$-0.766870\pi$
$191$	2.86477	−	4.96193i	0.207287	−	0.359032i	0.950859	+	0.309624i	$0.100203\pi$
$192$	−0.308580	+	13.8530i	−0.0222699	+	0.999752i
$193$	3.48670	+	6.03914i	0.250978	+	0.434707i	0.963795	−	0.266643i	$-0.0859145\pi$
$193$	3.48670	+	6.03914i	0.250978	+	0.434707i	−0.712817	+	0.701350i	$0.752581\pi$
$194$	10.4953	−	4.72306i	0.753518	−	0.339096i
$195$	0.679959	+	11.6067i	0.0486929	+	0.831174i
$196$	−2.33142	+	2.63121i	−0.166530	+	0.187944i
$197$	12.4687			0.888357			0.444179	−	0.895938i	$-0.353496\pi$
$197$	12.4687			0.888357			0.444179	+	0.895938i	$0.353496\pi$
$198$	11.1916	−	0.182457i	0.795353	−	0.0129667i
$199$		−	3.64372i		−	0.258297i	−0.991625	−	0.129148i	$-0.958776\pi$
$199$		−	3.64372i		−	0.258297i	0.991625	−	0.129148i	$-0.0412243\pi$
$200$	1.91760	+	2.07913i	0.135595	+	0.147017i
$201$	−3.46061	+	6.89646i	−0.244092	+	0.486439i
$202$	−16.5769	+	7.45988i	−1.16635	+	0.524875i
$203$	12.2501	−	7.07258i	0.859787	−	0.496398i
$204$	3.08414	+	2.42612i	0.215933	+	0.169863i
$205$	8.25369	+	4.76527i	0.576462	+	0.332821i
$206$	−13.5922	−	1.37381i	−0.947014	−	0.0957178i
$207$	−10.3465	+	1.21643i	−0.719130	+	0.0845481i
$208$	10.5284	−	24.7003i	0.730011	−	1.71266i
$209$	−4.35052	−	2.51177i	−0.300932	−	0.173743i
$210$	7.24244	+	0.305920i	0.499776	+	0.0211105i
$211$	10.9311	+	18.9332i	0.752526	+	1.30341i	0.946595	+	0.322426i	$0.104498\pi$
$211$	10.9311	+	18.9332i	0.752526	+	1.30341i	−0.194068	+	0.980988i	$0.562168\pi$
$212$	−1.28334	−	3.84506i	−0.0881399	−	0.264080i
$213$	12.8751	+	19.5613i	0.882190	+	1.34032i
$214$	−5.85432	+	8.12574i	−0.400193	+	0.555464i
$215$	−5.05102			−0.344477
$216$	1.85631	−	14.5792i	0.126306	−	0.991991i
$217$	−6.62335			−0.449623
$218$	10.4823	−	14.5493i	0.709951	−	0.985406i
$219$	−4.09980	−	6.22885i	−0.277039	−	0.420907i
$220$	−5.00506	+	1.67050i	−0.337441	+	0.112625i
$221$	−3.80193	−	6.58513i	−0.255745	−	0.442964i
$222$	−28.0393	−	1.18437i	−1.88187	−	0.0794900i
$223$	−8.10433	−	4.67904i	−0.542706	−	0.313332i	0.203469	−	0.979081i	$-0.434778\pi$
$223$	−8.10433	−	4.67904i	−0.542706	−	0.313332i	−0.746175	+	0.665750i	$0.768112\pi$
$224$	−14.6618	−	8.07953i	−0.979635	−	0.539836i
$225$	−1.79311	−	2.40516i	−0.119540	−	0.160344i
$226$	14.8673	+	1.50269i	0.988959	+	0.0999573i
$227$	−10.9005	−	6.29340i	−0.723491	−	0.417708i	0.0925450	−	0.995709i	$-0.470500\pi$
$227$	−10.9005	−	6.29340i	−0.723491	−	0.417708i	−0.816036	+	0.578001i	$0.803833\pi$
$228$	−4.07820	+	5.18429i	−0.270085	+	0.343338i
$229$	16.6656	−	9.62189i	1.10129	−	0.635833i	0.164734	−	0.986338i	$-0.447323\pi$
$229$	16.6656	−	9.62189i	1.10129	−	0.635833i	0.936561	+	0.350505i	$0.113990\pi$
$230$	4.47839	−	2.01535i	0.295296	−	0.132888i
$231$	−6.06499	+	12.0866i	−0.399047	+	0.795239i
$232$	9.16580	+	9.93789i	0.601764	+	0.652455i
$233$			2.85812i			0.187242i	0.995608	+	0.0936209i	$0.0298442\pi$
$233$			2.85812i			0.187242i	−0.995608	+	0.0936209i	$0.970156\pi$
$234$	−13.8357	+	24.8926i	−0.904468	+	1.62728i
$235$	2.13834			0.139490
$236$	−20.5481	−	18.2069i	−1.33756	−	1.18517i
$237$	1.22803	+	20.9621i	0.0797691	+	1.36164i
$238$	−4.32322	+	1.94552i	−0.280233	+	0.126109i
$239$	0.885290	+	1.53337i	0.0572647	+	0.0991853i	0.893237	−	0.449587i	$-0.148429\pi$
$239$	0.885290	+	1.53337i	0.0572647	+	0.0991853i	−0.835972	+	0.548772i	$0.815095\pi$
$240$	1.23484	+	6.81727i	0.0797083	+	0.440053i
$241$	−8.65729	+	14.9949i	−0.557665	+	0.965904i	0.440026	+	0.897985i	$0.354969\pi$
$241$	−8.65729	+	14.9949i	−0.557665	+	0.965904i	−0.997691	+	0.0679188i	$0.978364\pi$
$242$	−0.574504	+	5.68404i	−0.0369305	+	0.365384i
$243$	−3.56925	+	15.1743i	−0.228968	+	0.973434i
$244$	3.12253	−	15.2891i	0.199900	−	0.978784i
$245$	−0.878877	+	1.52226i	−0.0561494	+	0.0972536i
$246$	10.8089	+	20.6919i	0.689148	+	1.31927i
$247$	11.0693	−	6.39086i	0.704322	−	0.406641i
$248$	−1.39015	−	6.17581i	−0.0882744	−	0.392164i
$249$	−0.210774	−	3.59786i	−0.0133573	−	0.228005i
$250$	1.14743	+	0.826684i	0.0725698	+	0.0522841i
$251$			27.8879i			1.76027i	0.474723	+	0.880135i	$0.342548\pi$
$251$			27.8879i			1.76027i	−0.474723	+	0.880135i	$0.657452\pi$
$252$	14.5738	+	10.1432i	0.918062	+	0.638960i
$253$			9.16149i			0.575978i
$254$	2.18991	−	3.03957i	0.137407	−	0.190720i
$255$	1.75362	+	0.879956i	0.109816	+	0.0551050i
$256$	4.45628	−	15.3669i	0.278518	−	0.960431i
$257$	13.9238	−	8.03890i	0.868542	−	0.501453i	0.00167833	−	0.999999i	$-0.499466\pi$
$257$	13.9238	−	8.03890i	0.868542	−	0.501453i	0.866863	+	0.498546i	$0.166132\pi$
$258$	−10.4442	−	6.63289i	−0.650229	−	0.412946i
$259$	16.9529	−	29.3633i	1.05340	−	1.82455i
$260$	2.68642	−	13.1537i	0.166605	−	0.815760i
$261$	−8.57073	−	11.4962i	−0.530515	−	0.711598i
$262$	−20.7658	−	2.09887i	−1.28292	−	0.129668i
$263$	−0.277750	+	0.481076i	−0.0171268	+	0.0296644i	−0.874462	−	0.485094i	$-0.838785\pi$
$263$	−0.277750	+	0.481076i	−0.0171268	+	0.0296644i	0.857335	+	0.514759i	$0.172119\pi$
$264$	−12.5428	−	3.11837i	−0.771959	−	0.191922i
$265$	−1.01339	−	1.75525i	−0.0622523	−	0.107824i
$266$	−3.27033	−	7.26713i	−0.200517	−	0.445576i
$267$	14.9121	−	9.81508i	0.912606	−	0.600673i
$268$	5.90874	−	6.66854i	0.360934	−	0.407346i
$269$	27.0464			1.64905			0.824524	−	0.565827i	$-0.191443\pi$
$269$	27.0464			1.64905			0.824524	+	0.565827i	$0.191443\pi$
$270$	−0.549285	−	7.32791i	−0.0334284	−	0.445962i
$271$		−	25.9394i		−	1.57571i	−0.615863	−	0.787853i	$-0.711192\pi$
$271$		−	25.9394i		−	1.57571i	0.615863	−	0.787853i	$-0.288808\pi$
$272$	−2.72144	−	3.62276i	−0.165012	−	0.219662i
$273$	−18.9168	−	28.7404i	−1.14490	−	1.73945i
$274$	−2.19495	−	4.87748i	−0.132602	−	0.294660i
$275$	−2.28478	+	1.31912i	−0.137777	+	0.0795459i
$276$	11.9067	+	1.71370i	0.716697	+	0.103153i
$277$	7.43685	+	4.29366i	0.446837	+	0.257981i	0.706493	−	0.707720i	$-0.250276\pi$
$277$	7.43685	+	4.29366i	0.446837	+	0.257981i	−0.259657	+	0.965701i	$0.583609\pi$
$278$	−0.819658	+	8.10954i	−0.0491598	+	0.486378i
$279$	0.784004	+	6.66840i	0.0469371	+	0.399227i
$280$	−7.99101	−	2.49113i	−0.477554	−	0.148873i
$281$	−6.91069	−	3.98989i	−0.412257	−	0.238017i	0.279502	−	0.960145i	$-0.409831\pi$
$281$	−6.91069	−	3.98989i	−0.412257	−	0.238017i	−0.691759	+	0.722128i	$0.743164\pi$
$282$	4.42153	+	2.80802i	0.263298	+	0.167215i
$283$	−8.97715	−	15.5489i	−0.533636	−	0.924285i	−0.999228	−	0.0392851i	$-0.987492\pi$
$283$	−8.97715	−	15.5489i	−0.533636	−	0.924285i	0.465592	−	0.884999i	$-0.345841\pi$
$284$	−8.56102	−	25.6500i	−0.508003	−	1.52205i
$285$	−1.47916	+	2.94775i	−0.0876181	+	0.174609i
$286$	20.3204	+	14.6402i	1.20157	+	0.865691i
$287$	−28.2042			−1.66484
$288$	−6.39897	+	15.7179i	−0.377063	+	0.926188i
$289$	15.7168			0.924520
$290$	5.48451	+	3.95140i	0.322061	+	0.232034i
$291$	14.0715	−	0.824357i	0.824888	−	0.0483246i
$292$	2.72607	+	8.16769i	0.159531	+	0.477978i
$293$	−1.08776	−	1.88406i	−0.0635477	−	0.110068i	0.832501	−	0.554023i	$-0.186908\pi$
$293$	−1.08776	−	1.88406i	−0.0635477	−	0.110068i	−0.896049	+	0.443955i	$0.853575\pi$
$294$	−3.81629	+	1.99352i	−0.222571	+	0.116264i
$295$	−11.8879	−	6.86345i	−0.692137	−	0.399606i
$296$	30.9374	+	9.64445i	1.79820	+	0.560572i
$297$	12.8867	+	4.67555i	0.747763	+	0.271303i
$298$	−0.802843	+	7.94318i	−0.0465075	+	0.460136i
$299$	−20.1872	−	11.6551i	−1.16745	−	0.674030i
$300$	1.28701	+	3.21615i	0.0743053	+	0.185684i
$301$	12.9451	−	7.47387i	0.746145	−	0.430787i
$302$	−2.91111	−	6.46890i	−0.167516	−	0.372243i
$303$	−22.2254	+	1.30204i	−1.27682	+	0.0748001i
$304$	6.08969	−	4.57461i	0.349268	−	0.262372i
$305$		−	7.80235i		−	0.446761i
$306$	2.47049	+	4.12233i	0.141229	+	0.235658i
$307$	−24.3044			−1.38713			−0.693563	−	0.720396i	$-0.743960\pi$
$307$	−24.3044			−1.38713			−0.693563	+	0.720396i	$0.743960\pi$
$308$	10.3555	−	11.6871i	0.590061	−	0.665937i
$309$	−14.9546	−	7.50416i	−0.850739	−	0.426897i
$310$	−1.29891	−	2.88637i	−0.0737733	−	0.163935i
$311$	11.0615	+	19.1590i	0.627239	+	1.08641i	0.988103	+	0.153791i	$0.0491483\pi$
$311$	11.0615	+	19.1590i	0.627239	+	1.08641i	−0.360865	+	0.932618i	$0.617518\pi$
$312$	22.8280	−	23.6708i	1.29238	−	1.34009i
$313$	−10.8553	+	18.8019i	−0.613576	+	1.06275i	0.377056	+	0.926190i	$0.376936\pi$
$313$	−10.8553	+	18.8019i	−0.613576	+	1.06275i	−0.990632	+	0.136555i	$0.956397\pi$
$314$	3.05582	+	0.308862i	0.172450	+	0.0174301i
$315$	8.15435	+	3.51089i	0.459446	+	0.197816i
$316$	4.85177	−	23.7561i	0.272934	−	1.33638i
$317$	−0.354350	+	0.613753i	−0.0199023	+	0.0344718i	−0.875805	−	0.482665i	$-0.839669\pi$
$317$	−0.354350	+	0.613753i	−0.0199023	+	0.0344718i	0.855903	+	0.517137i	$0.173002\pi$
$318$	0.209517	−	4.96017i	0.0117491	−	0.278153i
$319$	−10.9208	+	6.30515i	−0.611450	+	0.353021i
$320$	0.645602	−	7.97391i	0.0360902	−	0.445755i
$321$	−10.2457	+	6.74367i	−0.571858	+	0.376395i
$322$	−8.49548	+	11.7916i	−0.473435	+	0.657123i
$323$		−	2.15694i		−	0.120015i
$324$	8.48707	−	15.8736i	0.471504	−	0.881864i
$325$		−	6.71263i		−	0.372350i
$326$	21.4907	+	15.4833i	1.19026	+	0.857540i
$327$	18.3452	−	12.0747i	1.01449	−	0.667732i
$328$	−5.91965	−	26.2984i	−0.326858	−	1.45209i
$329$	−5.48028	+	3.16404i	−0.302138	+	0.174439i
$330$	−6.45658	−	0.272725i	−0.355423	−	0.0150130i
$331$	−10.4265	+	18.0592i	−0.573092	+	0.992624i	0.423154	+	0.906058i	$0.360923\pi$
$331$	−10.4265	+	18.0592i	−0.573092	+	0.992624i	−0.996246	+	0.0865664i	$0.972411\pi$
$332$	−0.832740	+	4.07740i	−0.0457025	+	0.223777i
$333$	−31.5697	−	13.5925i	−1.73001	−	0.744864i
$334$	0.629752	−	6.23065i	0.0344585	−	0.340926i
$335$	2.22742	−	3.85801i	0.121697	−	0.210786i
$336$	−13.2521	−	15.6446i	−0.722960	−	0.853485i
$337$	7.88617	+	13.6592i	0.429587	+	0.744066i	0.996836	−	0.0794797i	$-0.0253259\pi$
$337$	7.88617	+	13.6592i	0.429587	+	0.744066i	−0.567250	+	0.823546i	$0.691993\pi$
$338$	−41.3452	+	18.6060i	−2.24888	+	1.01203i
$339$	16.3575	+	8.20813i	0.888420	+	0.445804i
$340$	−1.69566	−	1.50246i	−0.0919602	−	0.0814824i
$341$	5.90467			0.319756
$342$	−6.92945	+	4.15278i	−0.374702	+	0.224557i
$343$			15.5136i			0.837658i
$344$	9.68585	+	10.5018i	0.522226	+	0.566217i
$345$	6.00439	−	0.351757i	0.323265	−	0.0189379i
$346$	−28.6868	+	12.9095i	−1.54221	+	0.694020i
$347$	−10.5794	+	6.10805i	−0.567935	+	0.327897i	−0.756324	−	0.654197i	$-0.773007\pi$
$347$	−10.5794	+	6.10805i	−0.567935	+	0.327897i	0.188389	+	0.982094i	$0.439673\pi$
$348$	6.15166	+	15.3726i	0.329764	+	0.824059i
$349$	−24.1227	−	13.9273i	−1.29126	−	0.745509i	−0.312382	−	0.949957i	$-0.601127\pi$
$349$	−24.1227	−	13.9273i	−1.29126	−	0.745509i	−0.978878	+	0.204447i	$0.934460\pi$
$350$	−4.16394	−	0.420863i	−0.222572	−	0.0224961i
$351$	−26.6967	+	22.4475i	−1.42497	+	1.19816i
$352$	13.0709	+	7.20284i	0.696682	+	0.383913i
$353$	17.4231	+	10.0593i	0.927341	+	0.535400i	0.885970	−	0.463743i	$-0.153494\pi$
$353$	17.4231	+	10.0593i	0.927341	+	0.535400i	0.0413712	+	0.999144i	$0.486827\pi$
$354$	−15.5681	−	29.8027i	−0.827435	−	1.58400i
$355$	−6.76025	−	11.7091i	−0.358797	−	0.621454i
$356$	−19.5538	+	6.52631i	−1.03635	+	0.345893i
$357$	−5.79635	+	0.339569i	−0.306775	+	0.0179719i
$358$	10.1446	−	14.0806i	0.536158	−	0.744182i
$359$	−11.2511			−0.593811			−0.296906	−	0.954907i	$-0.595955\pi$
$359$	−11.2511			−0.593811			−0.296906	+	0.954907i	$0.595955\pi$
$360$	−1.56218	+	8.34024i	−0.0823340	+	0.439569i
$361$	−15.3743			−0.809173
$362$	19.5693	−	27.1621i	1.02854	−	1.42761i
$363$	−3.13811	+	6.25378i	−0.164708	+	0.328238i
$364$	12.5783	+	37.6864i	0.659281	+	1.97530i
$365$	2.15265	+	3.72850i	0.112675	+	0.195159i
$366$	10.2459	−	16.1333i	0.535560	−	0.843299i
$367$	−10.7193	−	6.18878i	−0.559542	−	0.323051i	0.193420	−	0.981116i	$-0.438042\pi$
$367$	−10.7193	−	6.18878i	−0.559542	−	0.323051i	−0.752961	+	0.658065i	$0.771375\pi$
$368$	−12.7780	−	5.44654i	−0.666097	−	0.283920i
$369$	3.33852	+	28.3960i	0.173796	+	1.47824i
$370$	16.1208	+	1.62938i	0.838079	+	0.0847073i
$371$	5.19440	+	2.99899i	0.269680	+	0.155700i
$372$	1.10450	−	7.67397i	0.0572654	−	0.397877i
$373$	7.94947	−	4.58963i	0.411608	−	0.237642i	−0.279872	−	0.960037i	$-0.590292\pi$
$373$	7.94947	−	4.58963i	0.411608	−	0.237642i	0.691480	+	0.722395i	$0.256959\pi$
$374$	3.85412	−	1.73442i	0.199292	−	0.0896846i
$375$	0.952268	+	1.44678i	0.0491749	+	0.0747116i
$376$	−4.10048	−	4.44589i	−0.211466	−	0.229279i
$377$		−	32.0852i		−	1.65247i
$378$	12.2507	+	17.9677i	0.630107	+	0.924161i
$379$	23.8996			1.22764			0.613819	−	0.789447i	$-0.289632\pi$
$379$	23.8996			1.22764			0.613819	+	0.789447i	$0.289632\pi$
$380$	2.52557	−	2.85033i	0.129559	−	0.146219i
$381$	3.83257	−	2.52258i	0.196349	−	0.129236i
$382$	−7.38906	+	3.32520i	−0.378057	+	0.170132i
$383$	6.07265	+	10.5181i	0.310298	+	0.537452i	0.978427	−	0.206594i	$-0.0662378\pi$
$383$	6.07265	+	10.5181i	0.310298	+	0.537452i	−0.668129	+	0.744046i	$0.732904\pi$
$384$	11.8061	−	15.6402i	0.602478	−	0.798136i
$385$	3.90374	−	6.76147i	0.198953	−	0.344596i
$386$	0.991718	−	9.81188i	0.0504771	−	0.499412i
$387$	−9.05702	−	12.1485i	−0.460394	−	0.617543i
$388$	−15.9471	−	3.25692i	−0.809591	−	0.165345i
$389$	1.84905	−	3.20264i	0.0937504	−	0.162380i	−0.815336	−	0.578988i	$-0.803448\pi$
$389$	1.84905	−	3.20264i	0.0937504	−	0.162380i	0.909086	+	0.416608i	$0.136781\pi$
$390$	8.81488	−	13.8800i	0.446359	−	0.702841i
$391$	−3.40662	+	1.96681i	−0.172280	+	0.0994661i
$392$	4.85032	−	1.09179i	0.244978	−	0.0551435i
$393$	−22.8473	−	11.4646i	−1.15249	−	0.578315i
$394$	−14.3069	−	10.3077i	−0.720773	−	0.519292i
$395$		−	12.1232i		−	0.609986i
$396$	−12.9924	−	9.04257i	−0.652893	−	0.454406i
$397$		−	27.6425i		−	1.38734i	−0.720295	−	0.693668i	$-0.755993\pi$
$397$		−	27.6425i		−	1.38734i	0.720295	−	0.693668i	$-0.244007\pi$
$398$	−3.01221	+	4.18091i	−0.150988	+	0.209570i
$399$	−0.570799	−	9.74338i	−0.0285757	−	0.487779i
$400$	−0.481526	−	3.97091i	−0.0240763	−	0.198546i
$401$	7.79380	−	4.49975i	0.389204	−	0.224707i	−0.292611	−	0.956231i	$-0.594524\pi$
$401$	7.79380	−	4.49975i	0.389204	−	0.224707i	0.681815	+	0.731525i	$0.261191\pi$
$402$	9.67199	−	5.05237i	0.482395	−	0.251989i
$403$	−7.51180	+	13.0108i	−0.374190	+	0.648115i
$404$	25.1878	+	5.14417i	1.25314	+	0.255932i
$405$	2.56954	−	8.62540i	0.127682	−	0.428599i
$406$	−19.9029	−	2.01165i	−0.987764	−	0.0998365i
$407$	−15.1134	+	26.1772i	−0.749143	+	1.29755i
$408$	−1.53319	−	5.33341i	−0.0759044	−	0.264043i
$409$	−0.570769	−	0.988600i	−0.0282227	−	0.0488831i	0.851569	−	0.524242i	$-0.175651\pi$
$409$	−0.570769	−	0.988600i	−0.0282227	−	0.0488831i	−0.879792	+	0.475359i	$0.842318\pi$
$410$	−5.53115	−	12.2910i	−0.273164	−	0.607009i
$411$	−0.383104	−	6.53947i	−0.0188971	−	0.322568i
$412$	14.4604	+	12.8128i	0.712413	+	0.631242i
$413$	40.6227			1.99891
$414$	12.8775	+	7.15749i	0.632892	+	0.351771i
$415$			2.08079i			0.102142i
$416$	−32.4999	+	19.6382i	−1.59344	+	0.962842i
$417$	−4.47722	+	8.92241i	−0.219250	+	0.436932i
$418$	2.91547	+	6.47859i	0.142600	+	0.316878i
$419$	6.22684	−	3.59507i	0.304201	−	0.175630i	−0.340128	−	0.940379i	$-0.610470\pi$
$419$	6.22684	−	3.59507i	0.304201	−	0.175630i	0.644329	+	0.764749i	$0.277137\pi$
$420$	−8.05729	−	6.33823i	−0.393155	−	0.309274i
$421$	18.2838	+	10.5561i	0.891097	+	0.514475i	0.874301	−	0.485384i	$-0.161320\pi$
$421$	18.2838	+	10.5561i	0.891097	+	0.514475i	0.0167956	+	0.999859i	$0.494654\pi$
$422$	3.10912	−	30.7610i	0.151349	−	1.49742i
$423$	3.83426	+	5.14303i	0.186428	+	0.250063i
$424$	−1.70611	+	5.47285i	−0.0828562	+	0.265785i
$425$	−0.981007	−	0.566384i	−0.0475858	−	0.0274737i
$426$	1.39767	−	33.0888i	0.0677172	−	1.60316i
$427$	11.5449	+	19.9964i	0.558699	+	0.967695i
$428$	13.4348	−	4.48404i	0.649397	−	0.216744i
$429$	16.8642	+	25.6219i	0.814211	+	1.23703i
$430$	5.79569	+	4.17560i	0.279493	+	0.201365i
$431$	8.14476			0.392319			0.196160	−	0.980572i	$-0.437153\pi$
$431$	8.14476			0.392319			0.196160	+	0.980572i	$0.437153\pi$
$432$	−14.1824	+	15.1941i	−0.682351	+	0.731024i
$433$	21.0438			1.01130			0.505651	−	0.862738i	$-0.331252\pi$
$433$	21.0438			1.01130			0.505651	+	0.862738i	$0.331252\pi$
$434$	7.59983	+	5.47542i	0.364804	+	0.262829i
$435$	4.55167	+	6.91537i	0.218236	+	0.331567i
$436$	−24.0554	+	8.02879i	−1.15204	+	0.384509i
$437$	−3.30612	−	5.72637i	−0.158153	−	0.273929i
$438$	−0.445056	+	10.5364i	−0.0212656	+	0.503449i
$439$	16.2515	+	9.38279i	0.775640	+	0.447816i	0.834883	−	0.550428i	$-0.185535\pi$
$439$	16.2515	+	9.38279i	0.775640	+	0.447816i	−0.0592429	+	0.998244i	$0.518869\pi$
$440$	7.12393	+	2.22082i	0.339620	+	0.105874i
$441$	−5.23719	+	0.615737i	−0.249390	+	0.0293208i
$442$	−1.08138	+	10.6990i	−0.0514360	+	0.508898i
$443$	24.4816	+	14.1345i	1.16316	+	0.671549i	0.952059	−	0.305915i	$-0.0989624\pi$
$443$	24.4816	+	14.1345i	1.16316	+	0.671549i	0.211099	+	0.977465i	$0.432296\pi$
$444$	31.1940	+	24.5386i	1.48040	+	1.16455i
$445$	−8.92618	+	5.15353i	−0.423141	+	0.244301i
$446$	5.43106	+	12.0686i	0.257168	+	0.571464i
$447$	−4.38537	+	8.73937i	−0.207421	+	0.413358i
$448$	10.1442	+	21.3914i	0.479268	+	1.01065i
$449$			18.1284i			0.855534i	0.903889	+	0.427767i	$0.140700\pi$
$449$			18.1284i			0.855534i	−0.903889	+	0.427767i	$0.859300\pi$
$450$	0.0691588	+	4.24208i	0.00326018	+	0.199973i
$451$	25.1438			1.18398
$452$	−15.8169	−	14.0148i	−0.743967	−	0.659201i
$453$	−0.508102	−	8.67315i	−0.0238727	−	0.407500i
$454$	7.30489	+	16.2325i	0.342836	+	0.761829i
$455$	9.93251	+	17.2036i	0.465643	+	0.806518i
$456$	8.96521	−	2.57723i	0.419834	−	0.120690i
$457$	6.58297	−	11.4020i	0.307938	−	0.533365i	−0.669973	−	0.742385i	$-0.733694\pi$
$457$	6.58297	−	11.4020i	0.307938	−	0.533365i	0.977911	+	0.209021i	$0.0670277\pi$
$458$	−27.0769	−	2.73675i	−1.26522	−	0.127880i
$459$	1.02799	+	5.79558i	0.0479825	+	0.270514i
$460$	−6.80469	−	1.38974i	−0.317270	−	0.0647970i
$461$	−18.9975	+	32.9047i	−0.884803	+	1.53252i	−0.0388637	+	0.999245i	$0.512374\pi$
$461$	−18.9975	+	32.9047i	−0.884803	+	1.53252i	−0.845939	+	0.533279i	$0.820960\pi$
$462$	16.9509	−	8.85468i	0.788629	−	0.411957i
$463$	2.23055	−	1.28781i	0.103662	−	0.0598495i	−0.447272	−	0.894398i	$-0.647605\pi$
$463$	2.23055	−	1.28781i	0.103662	−	0.0598495i	0.550935	+	0.834548i	$0.314271\pi$
$464$	−2.30161	−	18.9802i	−0.106850	−	0.881136i
$465$	−0.226711	−	3.86989i	−0.0105135	−	0.179462i
$466$	2.36276	−	3.27949i	0.109453	−	0.151920i
$467$		−	18.5778i		−	0.859678i	−0.902906	−	0.429839i	$-0.858570\pi$
$467$		−	18.5778i		−	0.859678i	0.902906	−	0.429839i	$-0.141430\pi$
$468$	36.4538	−	17.1248i	1.68508	−	0.791592i
$469$			13.1835i			0.608755i
$470$	−2.45359	−	1.76773i	−0.113176	−	0.0815392i
$471$	3.36212	+	1.68710i	0.154918	+	0.0777373i
$472$	8.52613	+	37.8778i	0.392447	+	1.74347i
$473$	−11.5405	+	6.66290i	−0.530632	+	0.306360i
$474$	15.9200	−	25.0677i	0.731228	−	1.15140i
$475$	0.952065	−	1.64903i	0.0436837	−	0.0756625i
$476$	6.56892	+	1.34159i	0.301086	+	0.0614917i
$477$	2.40452	−	5.58471i	0.110096	−	0.255707i
$478$	0.251802	−	2.49129i	0.0115172	−	0.113949i
$479$	−8.43853	+	14.6160i	−0.385566	+	0.667820i	−0.991848	−	0.127430i	$-0.959327\pi$
$479$	−8.43853	+	14.6160i	−0.385566	+	0.667820i	0.606281	+	0.795250i	$0.292660\pi$
$480$	4.21884	−	8.84315i	0.192563	−	0.403633i
$481$	−38.4539	−	66.6041i	−1.75335	−	3.03689i
$482$	22.3296	−	10.0487i	1.01709	−	0.457706i
$483$	−14.8680	+	9.78605i	−0.676517	+	0.445281i
$484$	5.35810	−	6.04710i	0.243550	−	0.274868i
$485$	−8.13814			−0.369534
$486$	16.6398	−	14.4608i	0.754798	−	0.655957i
$487$			20.9884i			0.951074i	0.879696	+	0.475537i	$0.157746\pi$
$487$			20.9884i			0.951074i	−0.879696	+	0.475537i	$0.842254\pi$
$488$	−16.2221	+	14.9618i	−0.734341	+	0.677289i
$489$	17.8354	+	27.0974i	0.806544	+	1.22539i
$490$	2.26688	−	1.02013i	0.102407	−	0.0460849i
$491$	−7.25692	+	4.18978i	−0.327500	+	0.189082i	−0.654731	−	0.755862i	$-0.727218\pi$
$491$	−7.25692	+	4.18978i	−0.327500	+	0.189082i	0.327231	+	0.944945i	$0.393885\pi$
$492$	4.70327	−	32.6780i	0.212040	−	1.47324i
$493$	−4.68904	−	2.70722i	−0.211184	−	0.121927i
$494$	−17.9845	−	1.81775i	−0.809159	−	0.0817843i
$495$	−7.26954	−	3.12993i	−0.326742	−	0.140680i
$496$	−3.51035	+	8.23552i	−0.157619	+	0.369786i
$497$	34.6513	+	20.0060i	1.55432	+	0.897390i
$498$	−2.73244	+	4.30253i	−0.122444	+	0.192801i
$499$	−10.0647	−	17.4325i	−0.450556	−	0.780386i	0.547865	−	0.836567i	$-0.315441\pi$
$499$	−10.0647	−	17.4325i	−0.450556	−	0.780386i	−0.998421	+	0.0561812i	$0.982108\pi$
$500$	−0.633188	−	1.89712i	−0.0283170	−	0.0848419i
$501$	3.43989	−	6.85518i	0.153683	−	0.306267i
$502$	23.0545	−	31.9994i	1.02897	−	1.42820i
$503$	18.4099			0.820858			0.410429	−	0.911893i	$-0.365379\pi$
$503$	18.4099			0.820858			0.410429	+	0.911893i	$0.365379\pi$
$504$	−8.33718	−	23.6865i	−0.371368	−	1.05508i
$505$	12.8539			0.571989
$506$	7.57365	−	10.5122i	0.336690	−	0.467323i
$507$	−55.4335	+	3.24747i	−2.46189	+	0.144225i
$508$	−5.02553	+	1.67733i	−0.222972	+	0.0744196i
$509$	2.98524	+	5.17060i	0.132319	+	0.229183i	0.924570	−	0.381012i	$-0.124424\pi$
$509$	2.98524	+	5.17060i	0.132319	+	0.229183i	−0.792251	+	0.610195i	$0.791091\pi$
$510$	−1.28471	−	2.45937i	−0.0568878	−	0.108903i
$511$	−11.0340	−	6.37045i	−0.488113	−	0.281812i
$512$	−17.8168	+	13.9485i	−0.787400	+	0.616442i
$513$	−9.74208	+	1.72800i	−0.430124	+	0.0762932i
$514$	−22.6222	−	2.28650i	−0.997822	−	0.100853i
$515$	8.36590	+	4.83006i	0.368646	+	0.212838i
$516$	6.50070	+	16.2448i	0.286177	+	0.715139i
$517$	4.88563	−	2.82072i	0.214870	−	0.124055i
$518$	−43.7264	+	19.6776i	−1.92123	+	0.864585i
$519$	−38.4617	+	2.25321i	−1.68828	+	0.0989050i
$520$	−13.9565	+	12.8722i	−0.612031	+	0.564481i
$521$			5.32249i			0.233183i	0.993180	+	0.116591i	$0.0371968\pi$
$521$			5.32249i			0.233183i	−0.993180	+	0.116591i	$0.962803\pi$
$522$	0.330567	+	20.2764i	0.0144685	+	0.887473i
$523$	−24.3102			−1.06301			−0.531504	−	0.847056i	$-0.678373\pi$
$523$	−24.3102			−1.06301			−0.531504	+	0.847056i	$0.678373\pi$
$524$	22.0922	+	19.5751i	0.965102	+	0.855140i
$525$	−4.58131	−	2.29888i	−0.199945	−	0.100331i
$526$	0.716396	−	0.322390i	0.0312364	−	0.0140569i
$527$	1.26763	+	2.19560i	0.0552189	+	0.0956419i
$528$	11.8141	+	13.9471i	0.514144	+	0.606969i
$529$	5.47060	−	9.47536i	0.237852	−	0.411972i
$530$	−0.288239	+	2.85178i	−0.0125203	+	0.123873i
$531$	−4.80850	−	40.8990i	−0.208671	−	1.77487i
$532$	−2.25515	+	11.0420i	−0.0977730	+	0.478733i
$533$	−31.9875	+	55.4039i	−1.38553	+	2.39981i
$534$	−25.2245	−	1.06548i	−1.09157	−	0.0461079i
$535$	6.13293	−	3.54085i	0.265150	−	0.153084i
$536$	−12.2926	+	2.76702i	−0.530961	+	0.119517i
$537$	17.7541	−	11.6857i	0.766146	−	0.504274i
$538$	−31.0338	−	22.3588i	−1.33796	−	0.963957i
$539$			4.63737i			0.199746i
$540$	−5.42760	+	8.86234i	−0.233567	+	0.381375i
$541$		−	25.9170i		−	1.11426i	−0.830426	−	0.557129i	$-0.811903\pi$
$541$		−	25.9170i		−	1.11426i	0.830426	−	0.557129i	$-0.188097\pi$
$542$	−21.4437	+	29.7636i	−0.921085	+	1.27846i
$543$	34.2484	−	22.5422i	1.46974	−	0.967377i
$544$	0.127785	+	6.40663i	0.00547873	+	0.274682i
$545$	−10.9812	+	6.33997i	−0.470381	+	0.271575i
$546$	−2.05353	+	48.6158i	−0.0878828	+	2.08056i
$547$	−3.87427	+	6.71043i	−0.165652	+	0.286917i	−0.936887	−	0.349633i	$-0.886306\pi$
$547$	−3.87427	+	6.71043i	−0.165652	+	0.286917i	0.771235	+	0.636551i	$0.219639\pi$
$548$	−1.51359	+	7.41109i	−0.0646573	+	0.316586i
$549$	18.7659	−	13.9904i	0.800907	−	0.597097i
$550$	3.71212	+	0.375196i	0.158285	+	0.0159984i
$551$	4.55070	−	7.88205i	0.193866	−	0.335786i
$552$	−12.2454	−	11.8094i	−0.521198	−	0.502641i
$553$	17.9384	+	31.0703i	0.762820	+	1.32124i
$554$	−4.98375	−	11.0746i	−0.211739	−	0.470515i
$555$	17.7366	+	8.90015i	0.752878	+	0.377790i
$556$	7.64453	−	8.62753i	0.324200	−	0.365889i
$557$	5.48676			0.232482			0.116241	−	0.993221i	$-0.462916\pi$
$557$	5.48676			0.232482			0.116241	+	0.993221i	$0.462916\pi$
$558$	4.61307	−	8.29964i	0.195287	−	0.351352i
$559$		−	33.9056i		−	1.43406i
$560$	7.10975	+	9.46444i	0.300442	+	0.399945i
$561$	5.16740	−	0.302723i	0.218168	−	0.0127810i
$562$	4.63115	+	10.2911i	0.195353	+	0.434103i
$563$	34.4191	−	19.8719i	1.45059	−	0.837500i	0.452078	−	0.891978i	$-0.350683\pi$
$563$	34.4191	−	19.8719i	1.45059	−	0.837500i	0.998515	+	0.0544783i	$0.0173496\pi$
$564$	−2.75205	−	6.87721i	−0.115882	−	0.289583i
$565$	−9.15072	−	5.28317i	−0.384974	−	0.222265i
$566$	−2.55336	+	25.2625i	−0.107326	+	1.06186i
$567$	6.17737	+	25.9079i	0.259425	+	1.08803i
$568$	−11.3813	+	36.5089i	−0.477549	+	1.53188i
$569$	−28.7684	−	16.6094i	−1.20603	−	0.696303i	−0.244142	−	0.969739i	$-0.578506\pi$
$569$	−28.7684	−	16.6094i	−1.20603	−	0.696303i	−0.961890	+	0.273436i	$0.911840\pi$
$570$	4.13409	−	2.15953i	0.173158	−	0.0904527i
$571$	2.92733	+	5.07028i	0.122505	+	0.212185i	0.920755	−	0.390142i	$-0.127574\pi$
$571$	2.92733	+	5.07028i	0.122505	+	0.212185i	−0.798250	+	0.602326i	$0.794241\pi$
$572$	−11.2134	−	33.5971i	−0.468858	−	1.40477i
$573$	−9.90687	+	0.580377i	−0.413865	+	0.0242456i
$574$	32.3623	+	23.3159i	1.35078	+	0.973189i
$575$	−3.47258			−0.144817
$576$	20.3361	−	12.7453i	0.847338	−	0.531054i
$577$	−6.20243			−0.258211			−0.129105	−	0.991631i	$-0.541211\pi$
$577$	−6.20243			−0.258211			−0.129105	+	0.991631i	$0.541211\pi$
$578$	−18.0340	−	12.9929i	−0.750114	−	0.540431i
$579$	5.41706	−	10.7954i	0.225125	−	0.448641i
$580$	−3.02652	−	9.06791i	−0.125670	−	0.376524i
$581$	−3.07889	−	5.33279i	−0.127734	−	0.221241i
$582$	−16.8276	−	10.6868i	−0.697526	−	0.442983i
$583$	−4.63076	−	2.67357i	−0.191787	−	0.110728i
$584$	3.62413	−	11.6254i	0.149968	−	0.481064i
$585$	16.1449	−	12.0365i	0.667510	−	0.497646i
$586$	−0.309391	+	3.06106i	−0.0127808	+	0.126451i
$587$	−1.19543	−	0.690183i	−0.0493407	−	0.0284869i	0.475127	−	0.879917i	$-0.342402\pi$
$587$	−1.19543	−	0.690183i	−0.0493407	−	0.0284869i	−0.524467	+	0.851430i	$0.675736\pi$
$588$	6.02693	+	0.867442i	0.248547	+	0.0357727i
$589$	−3.69070	+	2.13083i	−0.152073	+	0.0877992i
$590$	7.96656	+	17.7028i	0.327978	+	0.728814i
$591$	−11.8735	−	18.0395i	−0.488412	−	0.742046i
$592$	−27.5255	−	36.6418i	−1.13129	−	1.50597i
$593$			16.1922i			0.664933i	0.943115	+	0.332467i	$0.107881\pi$
$593$			16.1922i			0.664933i	−0.943115	+	0.332467i	$0.892119\pi$
$594$	−10.9214	−	16.0181i	−0.448110	−	0.657231i
$595$	3.35226			0.137429
$596$	7.48771	−	8.45055i	0.306708	−	0.346148i
$597$	−5.27168	+	3.46980i	−0.215756	+	0.142009i
$598$	13.5283	+	30.0618i	0.553213	+	1.22932i
$599$	19.0605	+	33.0137i	0.778790	+	1.34890i	0.932639	+	0.360810i	$0.117500\pi$
$599$	19.0605	+	33.0137i	0.778790	+	1.34890i	−0.153849	+	0.988094i	$0.549167\pi$
$600$	1.18199	−	4.75425i	0.0482545	−	0.194091i
$601$	−11.7812	+	20.4056i	−0.480565	+	0.832363i	−0.999751	−	0.0222980i	$-0.992902\pi$
$601$	−11.7812	+	20.4056i	−0.480565	+	0.832363i	0.519186	+	0.854661i	$0.326235\pi$
$602$	−21.0321	−	2.12579i	−0.857206	−	0.0866406i
$603$	13.2731	−	1.56052i	0.540523	−	0.0635493i
$604$	−2.00744	+	9.82917i	−0.0816815	+	0.399943i
$605$	2.01985	−	3.49848i	0.0821186	−	0.142234i
$606$	26.5785	+	16.8794i	1.07968	+	0.685679i
$607$	30.5010	−	17.6098i	1.23800	−	0.714759i	0.269314	−	0.963052i	$-0.413203\pi$
$607$	30.5010	−	17.6098i	1.23800	−	0.714759i	0.968685	+	0.248293i	$0.0798697\pi$
$608$	−10.7692	+	0.214800i	−0.436751	+	0.00871130i
$609$	−21.8979	−	10.9882i	−0.887346	−	0.445266i
$610$	−6.45007	+	8.95264i	−0.261156	+	0.362482i
$611$			14.3539i			0.580695i
$612$	0.573153	−	6.77240i	0.0231683	−	0.273758i
$613$		−	20.1341i		−	0.813209i	−0.913604	−	0.406605i	$-0.866713\pi$
$613$		−	20.1341i		−	0.813209i	0.913604	−	0.406605i	$-0.133287\pi$
$614$	27.8876	+	20.0921i	1.12545	+	0.810849i
$615$	−0.965400	−	16.4791i	−0.0389287	−	0.664502i
$616$	−21.5438	+	4.84942i	−0.868025	+	0.195389i
$617$	0.911560	−	0.526289i	0.0366980	−	0.0211876i	−0.481539	−	0.876425i	$-0.659922\pi$
$617$	0.911560	−	0.526289i	0.0366980	−	0.0211876i	0.518237	+	0.855237i	$0.326589\pi$
$618$	10.9558	+	20.9732i	0.440708	+	0.843668i
$619$	−6.49370	+	11.2474i	−0.261004	+	0.452072i	−0.966509	−	0.256633i	$-0.917387\pi$
$619$	−6.49370	+	11.2474i	−0.261004	+	0.452072i	0.705505	+	0.708705i	$0.250720\pi$
$620$	−0.895702	+	4.38569i	−0.0359723	+	0.176134i
$621$	11.6125	+	13.8107i	0.465995	+	0.554206i
$622$	3.14621	−	31.1280i	0.126151	−	1.24812i
$623$	15.2511	−	26.4157i	0.611023	−	1.05832i
$624$	−45.7618	+	8.28899i	−1.83194	+	0.331825i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	27.9989	−	12.6000i	1.11906	−	0.503596i
$627$	0.508863	+	8.68615i	0.0203220	+	0.346891i
$628$	−3.25101	−	2.88060i	−0.129729	−	0.114948i
$629$	−12.9783			−0.517480
$630$	−6.45414	−	10.7696i	−0.257139	−	0.429070i
$631$			18.3815i			0.731755i	0.930663	+	0.365878i	$0.119231\pi$
$631$			18.3815i			0.731755i	−0.930663	+	0.365878i	$0.880769\pi$
$632$	−25.2058	+	23.2475i	−1.00263	+	0.924738i
$633$	16.9829	−	33.8444i	0.675011	−	1.34519i
$634$	0.913971	−	0.411302i	0.0362984	−	0.0163349i
$635$	−2.29413	+	1.32451i	−0.0910396	+	0.0525618i
$636$	−4.34090	+	5.51824i	−0.172128	+	0.218812i
$637$	−10.2184	−	5.89958i	−0.404866	−	0.233750i
$638$	17.7433	+	1.79337i	0.702463	+	0.0710002i
$639$	16.0404	−	37.2551i	0.634547	−	1.47379i
$640$	−7.33268	+	8.61579i	−0.289850	+	0.340569i
$641$	−3.19297	−	1.84346i	−0.126115	−	0.0728125i	0.435615	−	0.900133i	$-0.356531\pi$
$641$	−3.19297	−	1.84346i	−0.126115	−	0.0728125i	−0.561730	+	0.827320i	$0.689864\pi$
$642$	17.3311	+	0.732062i	0.684003	+	0.0288922i
$643$	17.0536	+	29.5377i	0.672528	+	1.16485i	0.977185	+	0.212391i	$0.0681250\pi$
$643$	17.0536	+	29.5377i	0.672528	+	1.16485i	−0.304657	+	0.952462i	$0.598542\pi$
$644$	19.4959	−	6.50700i	0.768247	−	0.256412i
$645$	4.80992	+	7.30774i	0.189391	+	0.287742i
$646$	−1.78311	+	2.47494i	−0.0701554	+	0.0973750i
$647$	34.1504			1.34259			0.671296	−	0.741189i	$-0.265738\pi$
$647$	34.1504			1.34259			0.671296	+	0.741189i	$0.265738\pi$
$648$	−22.8607	+	11.1976i	−0.898054	+	0.439885i
$649$	−36.2149			−1.42156
$650$	−5.54922	+	7.70227i	−0.217658	+	0.302108i
$651$	6.30721	+	9.58257i	0.247199	+	0.375570i
$652$	−11.8592	−	35.5319i	−0.464443	−	1.39154i
$653$	−10.0442	−	17.3970i	−0.393058	−	0.680797i	0.599793	−	0.800155i	$-0.295250\pi$
$653$	−10.0442	−	17.3970i	−0.393058	−	0.680797i	−0.992851	+	0.119358i	$0.961916\pi$
$654$	−31.0317	−	1.31078i	−1.21344	−	0.0512554i
$655$	12.7812	+	7.37922i	0.499402	+	0.288330i
$656$	−14.9481	+	35.0693i	−0.583625	+	1.36922i
$657$	−5.10770	+	11.8631i	−0.199270	+	0.462822i
$658$	8.90390	+	0.899946i	0.347110	+	0.0350836i
$659$	−19.4299	−	11.2178i	−0.756880	−	0.436985i	0.0712943	−	0.997455i	$-0.477287\pi$
$659$	−19.4299	−	11.2178i	−0.756880	−	0.436985i	−0.828175	+	0.560470i	$0.810620\pi$
$660$	7.18301	+	5.65048i	0.279598	+	0.219945i
$661$	−25.1305	+	14.5091i	−0.977464	+	0.564339i	−0.901504	−	0.432771i	$-0.857536\pi$
$661$	−25.1305	+	14.5091i	−0.977464	+	0.564339i	−0.0759607	+	0.997111i	$0.524202\pi$
$662$	26.8929	−	12.1023i	1.04522	−	0.470368i
$663$	−5.90682	+	11.7714i	−0.229402	+	0.457163i
$664$	4.32623	−	3.99012i	0.167890	−	0.154847i
$665$			5.63499i			0.218515i
$666$	24.9873	+	41.6946i	0.968240	+	1.61563i
$667$	−16.5983			−0.642689
$668$	−5.87337	+	6.62862i	−0.227248	+	0.256469i
$669$	0.947931	+	16.1809i	0.0366491	+	0.625591i
$670$	−5.74517	+	2.58542i	−0.221955	+	0.0998835i
$671$	−10.2922	−	17.8267i	−0.397327	−	0.688190i
$672$	2.27264	+	28.9064i	0.0876692	+	1.11509i
$673$	−13.1952	+	22.8548i	−0.508639	+	0.880988i	0.491311	+	0.870984i	$0.336518\pi$
$673$	−13.1952	+	22.8548i	−0.508639	+	0.880988i	−0.999950	+	0.0100043i	$0.996815\pi$
$674$	2.24306	−	22.1924i	0.0863993	−	0.854818i
$675$	−1.77223	+	4.88459i	−0.0682130	+	0.188008i
$676$	62.8220	+	12.8303i	2.41623	+	0.493474i
$677$	−11.9863	+	20.7609i	−0.460671	+	0.797905i	−0.998994	−	0.0448332i	$-0.985724\pi$
$677$	−11.9863	+	20.7609i	−0.460671	+	0.797905i	0.538324	+	0.842738i	$0.319058\pi$
$678$	−11.9836	−	22.9408i	−0.460227	−	0.881035i
$679$	20.8570	−	12.0418i	0.800418	−	0.462122i
$680$	0.703591	+	3.12574i	0.0269815	+	0.119867i
$681$	1.27499	+	21.7637i	0.0488576	+	0.833986i
$682$	−6.77519	−	4.88129i	−0.259435	−	0.186914i
$683$		−	47.5367i		−	1.81894i	−0.415768	−	0.909471i	$-0.636487\pi$
$683$		−	47.5367i		−	1.81894i	0.415768	−	0.909471i	$-0.363513\pi$
$684$	11.3841	+	0.963443i	0.435281	+	0.0368382i
$685$			3.78204i			0.144504i
$686$	12.8249	−	17.8008i	0.489656	−	0.679638i
$687$	−29.7909	−	14.9489i	−1.13659	−	0.570337i
$688$	−2.43220	−	20.0572i	−0.0927267	−	0.764672i
$689$	11.7823	−	6.80253i	0.448871	−	0.259156i
$690$	−7.18040	−	4.56011i	−0.273353	−	0.173601i
$691$	8.82451	−	15.2845i	0.335700	−	0.581450i	−0.647919	−	0.761709i	$-0.724360\pi$
$691$	8.82451	−	15.2845i	0.335700	−	0.581450i	0.983619	+	0.180259i	$0.0576937\pi$
$692$	43.5881	+	8.90213i	1.65697	+	0.338408i
$693$	23.2622	−	2.73494i	0.883658	−	0.103892i
$694$	17.1886	+	1.73731i	0.652470	+	0.0659473i
$695$	2.88176	−	4.99136i	0.109312	−	0.189333i
$696$	5.64970	−	22.7245i	0.214151	−	0.861369i
$697$	5.39795	+	9.34952i	0.204462	+	0.354138i
$698$	16.1657	+	35.9224i	0.611880	+	1.35968i
$699$	4.13509	−	2.72170i	0.156403	−	0.102944i
$700$	4.42990	+	3.92517i	0.167435	+	0.148358i
$701$	37.1278			1.40230			0.701149	−	0.713015i	$-0.252671\pi$
$701$	37.1278			1.40230			0.701149	+	0.713015i	$0.252671\pi$
$702$	49.1896	−	3.68715i	1.85654	−	0.139162i
$703$		−	21.8160i		−	0.822805i
$704$	−9.04347	−	19.0703i	−0.340839	−	0.718737i
$705$	−2.03627	−	3.09371i	−0.0766903	−	0.116516i
$706$	−11.6760	−	25.9457i	−0.439432	−	0.976480i
$707$	−32.9428	+	19.0195i	−1.23894	+	0.715303i
$708$	−6.77415	+	47.0664i	−0.254588	+	1.76886i
$709$	−14.8747	−	8.58793i	−0.558632	−	0.322527i	0.193964	−	0.981009i	$-0.437866\pi$
$709$	−14.8747	−	8.58793i	−0.558632	−	0.322527i	−0.752596	+	0.658482i	$0.771199\pi$
$710$	−1.92281	+	19.0240i	−0.0721619	+	0.713956i
$711$	29.1583	−	21.7382i	1.09352	−	0.815248i
$712$	27.8317	+	8.67630i	1.04304	+	0.325158i
$713$	6.73076	+	3.88601i	0.252069	+	0.145532i
$714$	6.93161	+	4.40211i	0.259409	+	0.164745i
$715$	−8.85476	−	15.3369i	−0.331149	−	0.573567i
$716$	−23.2804	+	7.77011i	−0.870029	+	0.290383i
$717$	1.37542	−	2.74100i	0.0513660	−	0.102365i
$718$	12.9099	+	9.30112i	0.481792	+	0.347115i
$719$	3.91070			0.145845			0.0729223	−	0.997338i	$-0.476767\pi$
$719$	3.91070			0.145845			0.0729223	+	0.997338i	$0.476767\pi$
$720$	8.68723	−	8.27841i	0.323754	−	0.308518i
$721$	−28.5877			−1.06466
$722$	17.6409	+	12.7097i	0.656527	+	0.473005i
$723$	29.9384	−	1.75389i	1.11342	−	0.0652278i
$724$	−44.9089	+	14.9889i	−1.66903	+	0.557058i
$725$	−2.38991	−	4.13945i	−0.0887591	−	0.153735i
$726$	8.77066	−	4.58154i	0.325510	−	0.170037i
$727$	−19.7200	−	11.3853i	−0.731374	−	0.422259i	0.0875506	−	0.996160i	$-0.472096\pi$
$727$	−19.7200	−	11.3853i	−0.731374	−	0.422259i	−0.818925	+	0.573901i	$0.805429\pi$
$728$	16.7220	−	53.6407i	0.619759	−	1.98806i
$729$	25.3529	−	9.28609i	0.938996	−	0.343929i
$730$	0.612277	−	6.05776i	0.0226614	−	0.224208i
$731$	−4.95509	−	2.86082i	−0.183270	−	0.105811i
$732$	−25.0935	+	10.0417i	−0.927483	+	0.371151i
$733$	35.9198	−	20.7383i	1.32673	−	0.765988i	0.341937	−	0.939723i	$-0.388917\pi$
$733$	35.9198	−	20.7383i	1.32673	−	0.765988i	0.984792	+	0.173735i	$0.0555836\pi$
$734$	7.18345	+	15.9626i	0.265146	+	0.589192i
$735$	3.03931	−	0.178053i	0.112107	−	0.00656757i
$736$	10.1592	+	16.8128i	0.374474	+	0.619730i
$737$		−	11.7529i		−	0.432925i
$738$	19.6438	−	35.3423i	0.723099	−	1.30097i
$739$	14.8346			0.545699			0.272849	−	0.962057i	$-0.412034\pi$
$739$	14.8346			0.545699			0.272849	+	0.962057i	$0.412034\pi$
$740$	−17.1505	−	15.1964i	−0.630464	−	0.558630i
$741$	−19.7871	−	9.92908i	−0.726898	−	0.364754i
$742$	−3.48099	−	7.73525i	−0.127791	−	0.283970i
$743$	−14.2224	−	24.6339i	−0.521768	−	0.903729i	−0.999679	−	0.0253210i	$-0.991939\pi$
$743$	−14.2224	−	24.6339i	−0.521768	−	0.903729i	0.477911	−	0.878408i	$-0.341394\pi$
$744$	−7.61128	+	7.89227i	−0.279043	+	0.289345i
$745$	2.82265	−	4.88897i	0.103414	−	0.179118i
$746$	−12.9156	−	1.30542i	−0.472875	−	0.0477950i
$747$	−5.00461	+	3.73107i	−0.183109	+	0.136513i
$748$	−5.85614	−	1.19602i	−0.214122	−	0.0437307i
$749$	−10.4786	+	18.1495i	−0.382880	+	0.663167i
$750$	0.103374	−	2.44731i	0.00377468	−	0.0893630i
$751$	−8.71563	+	5.03197i	−0.318038	+	0.183619i	−0.650518	−	0.759491i	$-0.725448\pi$
$751$	−8.71563	+	5.03197i	−0.318038	+	0.183619i	0.332480	+	0.943110i	$0.392115\pi$
$752$	1.02966	+	8.49114i	0.0375480	+	0.309640i
$753$	40.3478	−	26.5568i	1.47036	−	0.967783i
$754$	−26.5243	+	36.8155i	−0.965958	+	1.34074i
$755$			5.01603i			0.182552i
$756$	0.796856	−	30.7441i	0.0289814	−	1.11815i
$757$			24.2934i			0.882960i	0.897271	+	0.441480i	$0.145546\pi$
$757$			24.2934i			0.882960i	−0.897271	+	0.441480i	$0.854454\pi$
$758$	−27.4231	−	19.7574i	−0.996050	−	0.717620i
$759$	13.2547	−	8.72419i	0.481115	−	0.316668i
$760$	−5.25423	+	1.18270i	−0.190591	+	0.0429011i
$761$	22.3930	−	12.9286i	0.811746	−	0.468662i	−0.0358158	−	0.999358i	$-0.511403\pi$
$761$	22.3930	−	12.9286i	0.811746	−	0.468662i	0.847562	+	0.530697i	$0.178070\pi$
$762$	−6.48299	−	0.273840i	−0.234854	−	0.00992019i
$763$	18.7622	−	32.4971i	0.679237	−	1.17647i
$764$	11.2273	+	2.29299i	0.406190	+	0.0829574i
$765$	−0.396806	−	3.37506i	−0.0143465	−	0.122026i
$766$	1.72724	−	17.0890i	0.0624077	−	0.617450i
$767$	46.0718	−	79.7987i	1.66356	−	2.88137i
$768$	−26.4762	+	8.18612i	−0.955376	+	0.295391i
$769$	4.19610	+	7.26785i	0.151315	+	0.262086i	0.931711	−	0.363200i	$-0.118316\pi$
$769$	4.19610	+	7.26785i	0.151315	+	0.262086i	−0.780396	+	0.625286i	$0.784983\pi$
$770$	−10.0689	+	4.53115i	−0.362856	+	0.163291i
$771$	−24.8897	−	12.4895i	−0.896382	−	0.449800i
$772$	−9.24925	+	10.4386i	−0.332888	+	0.375693i
$773$	−48.3100			−1.73759			−0.868794	−	0.495173i	$-0.835105\pi$
$773$	−48.3100			−1.73759			−0.868794	+	0.495173i	$0.835105\pi$
$774$	0.349323	+	21.4268i	0.0125561	+	0.770171i
$775$			2.23811i			0.0803953i
$776$	15.6057	+	16.9203i	0.560212	+	0.607403i
$777$	−58.6261	+	3.43451i	−2.10320	+	0.123212i
$778$	−4.76922	+	2.14623i	−0.170985	+	0.0769460i
$779$	−15.7161	+	9.07369i	−0.563087	+	0.325099i
$780$	−21.5888	+	8.63920i	−0.773004	+	0.309333i
$781$	−30.8914	−	17.8352i	−1.10538	−	0.638192i
$782$	5.53479	+	0.559419i	0.197924	+	0.0200048i
$783$	−8.47092	+	23.3475i	−0.302726	+	0.834370i
$784$	−6.46796	−	2.75693i	−0.230999	−	0.0984619i
$785$	−1.88084	−	1.08590i	−0.0671299	−	0.0387575i
$786$	16.7380	+	32.0423i	0.597024	+	1.14291i
$787$	6.46509	+	11.1979i	0.230456	+	0.399161i	0.957942	−	0.286961i	$-0.0926450\pi$
$787$	6.46509	+	11.1979i	0.230456	+	0.399161i	−0.727487	+	0.686122i	$0.759312\pi$
$788$	7.89502	+	23.6546i	0.281248	+	0.842661i
$789$	0.960506	−	0.0562696i	0.0341949	−	0.00200325i
$790$	−10.0221	+	13.9106i	−0.356570	+	0.494915i
$791$	31.2695			1.11182
$792$	7.43253	+	21.1163i	0.264104	+	0.750336i
$793$	52.3743			1.85986
$794$	−22.8516	+	31.7178i	−0.810973	+	1.12562i
$795$	−1.57445	+	3.13763i	−0.0558398	+	0.111280i
$796$	6.91259	−	2.30716i	0.245010	−	0.0817751i
$797$	9.02338	+	15.6290i	0.319625	+	0.553606i	0.980410	−	0.196969i	$-0.0631099\pi$
$797$	9.02338	+	15.6290i	0.319625	+	0.553606i	−0.660785	+	0.750575i	$0.729777\pi$
$798$	−7.39974	+	11.6517i	−0.261948	+	0.412466i
$799$	2.09772	+	1.21112i	0.0742121	+	0.0428464i
$800$	−2.73017	+	4.95441i	−0.0965261	+	0.175165i
$801$	−28.4006	−	12.2280i	−1.00349	−	0.432056i
$802$	−12.6627	−	1.27986i	−0.447136	−	0.0451934i
$803$	9.83668	+	5.67921i	0.347129	+	0.200415i
$804$	−15.2746	−	2.19844i	−0.538695	−	0.0775331i
$805$	8.89978	−	5.13829i	0.313676	−	0.181101i
$806$	19.3751	−	8.71912i	0.682459	−	0.307118i
$807$	−25.7554	−	39.1303i	−0.906634	−	1.37745i
$808$	−24.6486	−	26.7249i	−0.867134	−	0.940179i
$809$		−	1.09115i		−	0.0383628i	−0.999816	−	0.0191814i	$-0.993894\pi$
$809$		−	1.09115i		−	0.0383628i	0.999816	−	0.0191814i	$-0.00610600\pi$
$810$	−10.0788	+	7.77283i	−0.354135	+	0.273109i
$811$	−9.40229			−0.330159			−0.165080	−	0.986280i	$-0.552788\pi$
$811$	−9.40229			−0.330159			−0.165080	+	0.986280i	$0.552788\pi$
$812$	21.1742	+	18.7616i	0.743067	+	0.658404i
$813$	−37.5287	+	24.7013i	−1.31619	+	0.866311i
$814$	38.9818	−	17.5424i	1.36631	−	0.614862i
$815$	−9.36470	−	16.2201i	−0.328031	−	0.568166i
$816$	−2.64981	+	7.38718i	−0.0927620	+	0.258603i
$817$	4.80890	−	8.32926i	0.168242	−	0.291404i
$818$	−0.162343	+	1.60619i	−0.00567620	+	0.0561593i
$819$	−23.5673	+	54.7371i	−0.823509	+	1.91267i
$820$	−3.81416	+	18.6756i	−0.133196	+	0.652179i
$821$	−7.74302	+	13.4113i	−0.270233	+	0.468058i	−0.968921	−	0.247368i	$-0.920434\pi$
$821$	−7.74302	+	13.4113i	−0.270233	+	0.468058i	0.698688	+	0.715426i	$0.253768\pi$
$822$	−4.96649	+	7.82029i	−0.173226	+	0.272764i
$823$	−4.77544	+	2.75710i	−0.166461	+	0.0961064i	−0.580916	−	0.813963i	$-0.697306\pi$
$823$	−4.77544	+	2.75710i	−0.166461	+	0.0961064i	0.414455	+	0.910070i	$0.363972\pi$
$824$	−6.00014	−	26.6560i	−0.209025	−	0.928605i
$825$	4.08420	+	2.04943i	0.142194	+	0.0713521i
$826$	−46.6117	−	33.5822i	−1.62183	−	1.16847i
$827$			13.7388i			0.477744i	0.971051	+	0.238872i	$0.0767776\pi$
$827$			13.7388i			0.477744i	−0.971051	+	0.238872i	$0.923222\pi$
$828$	−8.85899	−	18.8583i	−0.307871	−	0.655371i
$829$		−	45.2216i		−	1.57061i	−0.619109	−	0.785305i	$-0.712506\pi$
$829$		−	45.2216i		−	1.57061i	0.619109	−	0.785305i	$-0.287494\pi$
$830$	1.72015	−	2.38756i	0.0597074	−	0.0828732i
$831$	−0.869858	−	14.8482i	−0.0301750	−	0.515080i
$832$	53.5259	+	4.33369i	1.85568	+	0.150243i
$833$	−1.72437	+	0.995565i	−0.0597458	+	0.0344943i
$834$	12.5133	−	6.53659i	0.433300	−	0.226343i
$835$	−2.21409	+	3.83492i	−0.0766218	+	0.132713i
$836$	2.01045	−	9.84390i	0.0695328	−	0.340458i
$837$	8.90116	−	7.48439i	0.307669	−	0.258698i
$838$	−10.1168	−	1.02254i	−0.349480	−	0.0353231i
$839$	20.6328	−	35.7370i	0.712322	−	1.23378i	−0.251661	−	0.967816i	$-0.580977\pi$
$839$	20.6328	−	35.7370i	0.712322	−	1.23378i	0.963983	−	0.265963i	$-0.0856899\pi$
$840$	4.00546	+	13.9335i	0.138201	+	0.480751i
$841$	3.07665	+	5.32892i	0.106091	+	0.183756i
$842$	−12.2527	−	27.2273i	−0.422257	−	0.938316i
$843$	0.808316	+	13.7977i	0.0278399	+	0.475219i
$844$	−28.9971	+	32.7258i	−0.998122	+	1.12647i
$845$	32.0594			1.10288
$846$	−0.147885	−	9.07099i	−0.00508439	−	0.311867i
$847$			11.9549i			0.410775i
$848$	6.48196	−	4.86929i	0.222591	−	0.167212i
$849$	−13.9472	+	27.7947i	−0.478668	+	0.953911i
$850$	0.657415	+	1.46087i	0.0225491	+	0.0501074i
$851$	−34.4557	+	19.8930i	−1.18112	+	0.681923i
$852$	−28.9577	+	36.8117i	−0.992075	+	1.26115i
$853$	−4.13182	−	2.38551i	−0.141471	−	0.0816783i	0.427594	−	0.903971i	$-0.359361\pi$
$853$	−4.13182	−	2.38551i	−0.141471	−	0.0816783i	−0.569065	+	0.822293i	$0.692695\pi$
$854$	3.28372	−	32.4885i	0.112366	−	1.11173i
$855$	5.67331	−	0.667012i	0.194023	−	0.0228113i
$856$	−19.1224	−	5.96124i	−0.653591	−	0.203751i
$857$	5.48136	+	3.16467i	0.187240	+	0.108103i	0.590690	−	0.806899i	$-0.298856\pi$
$857$	5.48136	+	3.16467i	0.187240	+	0.108103i	−0.403450	+	0.915002i	$0.632189\pi$
$858$	1.83070	−	43.3406i	0.0624991	−	1.47962i
$859$	−11.6015	−	20.0944i	−0.395839	−	0.685613i	0.597369	−	0.801966i	$-0.296213\pi$
$859$	−11.6015	−	20.0944i	−0.395839	−	0.685613i	−0.993208	+	0.116354i	$0.962879\pi$
$860$	−3.19824	−	9.58241i	−0.109059	−	0.326757i
$861$	26.8579	+	40.8054i	0.915316	+	1.39064i
$862$	−9.34553	−	6.73314i	−0.318310	−	0.229332i
$863$	−16.2590			−0.553463			−0.276732	−	0.960947i	$-0.589251\pi$
$863$	−16.2590			−0.553463			−0.276732	+	0.960947i	$0.589251\pi$
$864$	28.8340	−	5.70974i	0.980952	−	0.194249i
$865$	22.2439			0.756317
$866$	−24.1463	−	17.3966i	−0.820526	−	0.591161i
$867$	−14.9666	−	22.7389i	−0.508293	−	0.772253i
$868$	−4.19383	−	12.5653i	−0.142348	−	0.426495i
$869$	−15.9920	−	27.6989i	−0.542491	−	0.939622i
$870$	0.494109	−	11.6977i	0.0167519	−	0.396589i
$871$	25.8974	+	14.9519i	0.877500	+	0.506625i
$872$	34.2391	+	10.6738i	1.15948	+	0.361459i
$873$	−14.5925	−	19.5735i	−0.493883	−	0.662462i
$874$	−0.940357	+	9.30372i	−0.0318080	+	0.314703i
$875$	2.56287	+	1.47968i	0.0866409	+	0.0500221i
$876$	9.22095	−	11.7219i	0.311547	−	0.396045i
$877$	−3.54550	+	2.04700i	−0.119723	+	0.0691221i	−0.558666	−	0.829393i	$-0.688686\pi$
$877$	−3.54550	+	2.04700i	−0.119723	+	0.0691221i	0.438943	+	0.898515i	$0.355353\pi$
$878$	−10.8908	−	24.2009i	−0.367547	−	0.816741i
$879$	−1.68999	+	3.36789i	−0.0570019	+	0.113596i
$880$	−6.33829	−	8.43747i	−0.213664	−	0.284427i
$881$		−	31.6668i		−	1.06688i	−0.845837	−	0.533442i	$-0.820898\pi$
$881$		−	31.6668i		−	1.06688i	0.845837	−	0.533442i	$-0.179102\pi$
$882$	6.51833	+	3.62299i	0.219483	+	0.121992i
$883$	−52.5015			−1.76682			−0.883409	−	0.468603i	$-0.844757\pi$
$883$	−52.5015			−1.76682			−0.883409	+	0.468603i	$0.844757\pi$
$884$	10.0855	−	11.3823i	0.339211	−	0.382830i
$885$	1.39047	+	23.7350i	0.0467403	+	0.797844i
$886$	−16.4062	−	36.4569i	−0.551177	−	1.22479i
$887$	15.7292	+	27.2438i	0.528136	+	0.914759i	0.999462	+	0.0327995i	$0.0104423\pi$
$887$	15.7292	+	27.2438i	0.528136	+	0.914759i	−0.471326	+	0.881959i	$0.656224\pi$
$888$	−15.5072	−	53.9438i	−0.520388	−	1.81024i
$889$	3.91970	−	6.78912i	0.131463	−	0.227700i
$890$	14.5025	+	1.46581i	0.486125	+	0.0491342i
$891$	−5.50708	−	23.0967i	−0.184494	−	0.773768i
$892$	3.74515	−	18.3376i	0.125397	−	0.613989i
$893$	−2.03584	+	3.52617i	−0.0681266	+	0.117999i
$894$	12.2566	−	6.40250i	0.409922	−	0.214132i
$895$	−10.6274	+	6.13571i	−0.355234	+	0.205094i
$896$	6.04417	−	32.9311i	0.201921	−	1.10015i
$897$	2.36121	+	40.3052i	0.0788386	+	1.34575i
$898$	14.9865	−	20.8011i	0.500105	−	0.694142i
$899$			10.6978i			0.356791i
$900$	3.42750	−	4.92466i	0.114250	−	0.164155i
$901$		−	2.29588i		−	0.0764869i
$902$	−28.8508	−	20.7860i	−0.960625	−	0.692098i
$903$	−23.1403	−	11.6117i	−0.770061	−	0.386413i
$904$	6.56302	+	29.1566i	0.218283	+	0.969734i
$905$	−20.5006	+	11.8361i	−0.681464	+	0.393444i
$906$	−6.58695	+	10.3719i	−0.218837	+	0.344582i
$907$	17.7101	−	30.6748i	0.588055	−	1.01854i	−0.406432	−	0.913681i	$-0.633227\pi$
$907$	17.7101	−	30.6748i	0.588055	−	1.01854i	0.994487	−	0.104860i	$-0.0334394\pi$
$908$	5.03730	−	24.6645i	0.167169	−	0.818520i
$909$	23.0483	+	30.9155i	0.764465	+	1.02540i
$910$	2.82510	−	27.9510i	0.0936510	−	0.926566i
$911$	−6.19738	+	10.7342i	−0.205328	+	0.355639i	−0.950237	−	0.311527i	$-0.899160\pi$
$911$	−6.19738	+	10.7342i	−0.205328	+	0.355639i	0.744909	+	0.667166i	$0.232493\pi$
$912$	−12.4175	−	4.45421i	−0.411184	−	0.147494i
$913$	2.74481	+	4.75414i	0.0908398	+	0.157339i
$914$	−16.9794	+	7.64099i	−0.561627	+	0.252742i
$915$	−11.2883	+	7.42992i	−0.373180	+	0.245626i
$916$	28.8064	+	25.5242i	0.951789	+	0.843344i
$917$	−43.6754			−1.44229
$918$	3.61156	−	7.49984i	0.119199	−	0.247531i
$919$			56.7167i			1.87091i	0.353446	+	0.935455i	$0.385010\pi$
$919$			56.7167i			1.87091i	−0.353446	+	0.935455i	$0.614990\pi$
$920$	6.65902	+	7.21996i	0.219542	+	0.238035i
$921$	23.1443	+	35.1632i	0.762631	+	1.15867i
$922$	49.0001	−	22.0508i	1.61373	−	0.726206i
$923$	78.5988	−	45.3791i	2.58711	−	1.49367i
$924$	−26.7700	−	3.85294i	−0.880669	−	0.126753i
$925$	−9.92221	−	5.72859i	−0.326240	−	0.188355i
$926$	−3.62401	−	0.366290i	−0.119092	−	0.0120370i
$927$	3.38391	+	28.7821i	0.111142	+	0.945328i
$928$	−13.0497	+	23.6812i	−0.428378	+	0.777373i
$929$	−23.4529	−	13.5405i	−0.769464	−	0.444250i	0.0632192	−	0.998000i	$-0.479863\pi$
$929$	−23.4529	−	13.5405i	−0.769464	−	0.444250i	−0.832683	+	0.553749i	$0.813197\pi$
$930$	−2.93904	+	4.62784i	−0.0963749	+	0.151753i
$931$	−1.67350	−	2.89858i	−0.0548466	−	0.0949971i
$932$	−5.42220	+	1.80973i	−0.177610	+	0.0592796i
$933$	17.1855	−	34.2481i	0.562629	−	1.12123i
$934$	−15.3580	+	21.3167i	−0.502528	+	0.697504i
$935$	−2.98851			−0.0977349
$936$	−55.9849	−	10.4863i	−1.82992	−	0.342756i
$937$	−32.4177			−1.05904			−0.529520	−	0.848298i	$-0.677628\pi$
$937$	−32.4177			−1.05904			−0.529520	+	0.848298i	$0.677628\pi$
$938$	10.8985	−	15.1271i	0.355850	−	0.493917i
$939$	37.5394	−	2.19918i	1.22505	−	0.0717676i
$940$	1.35397	+	4.05669i	0.0441616	+	0.132315i
$941$	−13.4580	−	23.3099i	−0.438718	−	0.759882i	0.558873	−	0.829253i	$-0.311234\pi$
$941$	−13.4580	−	23.3099i	−0.438718	−	0.759882i	−0.997591	+	0.0693713i	$0.977901\pi$
$942$	−2.46310	−	4.71524i	−0.0802523	−	0.153631i
$943$	28.6616	+	16.5478i	0.933349	+	0.538869i
$944$	21.5299	−	50.5105i	0.700737	−	1.64398i
$945$	−2.68562	−	15.1409i	−0.0873631	−	0.492533i
$946$	18.7500	+	1.89512i	0.609615	+	0.0616157i
$947$	28.9926	+	16.7389i	0.942133	+	0.543941i	0.890628	−	0.454732i	$-0.150265\pi$
$947$	28.9926	+	16.7389i	0.942133	+	0.543941i	0.0515045	+	0.998673i	$0.483598\pi$
$948$	−38.9901	+	15.6027i	−1.26634	+	0.506751i
$949$	−25.0281	+	14.4500i	−0.812446	+	0.469066i
$950$	−2.45565	+	1.10508i	−0.0796718	+	0.0358536i
$951$	1.22540	−	0.0717882i	0.0397365	−	0.00232789i
$952$	−6.42830	−	6.96980i	−0.208342	−	0.225892i
$953$		−	0.127055i		−	0.00411571i	−0.999998	−	0.00205786i	$-0.999345\pi$
$953$		−	0.127055i		−	0.00411571i	0.999998	−	0.00205786i	$-0.000655036\pi$
$954$	−7.37582	+	4.42028i	−0.238801	+	0.143112i
$955$	5.72954			0.185404
$956$	−2.34843	+	2.65041i	−0.0759537	+	0.0857205i
$957$	19.5218	+	9.79592i	0.631049	+	0.316657i
$958$	21.7654	−	9.79478i	0.703208	−	0.316455i
$959$	−5.59619	−	9.69288i	−0.180710	−	0.313000i
$960$	−12.1513	+	6.65925i	−0.392182	+	0.214926i
$961$	−12.9954	+	22.5087i	−0.419207	+	0.726089i
$962$	−10.9374	+	108.213i	−0.352636	+	3.48892i
$963$	19.5133	+	8.40153i	0.628806	+	0.270735i
$964$	−33.9288	−	6.92937i	−1.09277	−	0.223180i
$965$	−3.48670	+	6.03914i	−0.112241	+	0.194407i
$966$	25.1499	+	1.06233i	0.809186	+	0.0341799i
$967$	−43.3295	+	25.0163i	−1.39338	+	0.804469i	−0.993688	−	0.112180i	$-0.964217\pi$
$967$	−43.3295	+	25.0163i	−1.39338	+	0.804469i	−0.399693	+	0.916649i	$0.630883\pi$
$968$	−11.1471	+	2.50916i	−0.358281	+	0.0806474i
$969$	−3.12063	+	2.05398i	−0.100249	+	0.0659835i
$970$	9.33793	+	6.72766i	0.299823	+	0.216012i
$971$			8.88789i			0.285226i	0.989779	+	0.142613i	$0.0455504\pi$
$971$			8.88789i			0.285226i	−0.989779	+	0.142613i	$0.954450\pi$
$972$	−31.0476	+	2.83690i	−0.995851	+	0.0909936i
$973$			17.0563i			0.546800i
$974$	17.3507	−	24.0827i	0.555954	−	0.771659i
$975$	−9.71173	+	6.39222i	−0.311024	+	0.204715i
$976$	30.9824	−	3.75703i	0.991723	−	0.120260i
$977$	−30.0268	+	17.3360i	−0.960641	+	0.554626i	−0.896370	−	0.443306i	$-0.853805\pi$
$977$	−30.0268	+	17.3360i	−0.960641	+	0.554626i	−0.0642708	+	0.997932i	$0.520472\pi$
$978$	1.93613	−	45.8366i	0.0619106	−	1.46569i
$979$	−13.5962	+	23.5494i	−0.434538	+	0.752642i
$980$	−3.44441	−	0.703461i	−0.110028	−	0.0224712i
$981$	−34.9390	−	15.0431i	−1.11552	−	0.480291i
$982$	11.7904	+	1.19170i	0.376248	+	0.0380286i
$983$	10.7174	−	18.5630i	0.341831	−	0.592069i	−0.642942	−	0.765915i	$-0.722286\pi$
$983$	10.7174	−	18.5630i	0.341831	−	0.592069i	0.984773	+	0.173846i	$0.0556196\pi$
$984$	−32.4110	+	33.6076i	−1.03323	+	1.07137i
$985$	6.23434	+	10.7982i	0.198643	+	0.344059i
$986$	3.14233	+	6.98269i	0.100072	+	0.222374i
$987$	9.79639	+	4.91578i	0.311822	+	0.156471i
$988$	19.1332	+	16.9532i	0.608708	+	0.539353i
$989$	−17.5401			−0.557742
$990$	5.75382	+	9.60099i	0.182868	+	0.305139i
$991$			54.9257i			1.74477i	0.488819	+	0.872385i	$0.337428\pi$
$991$			54.9257i			1.74477i	−0.488819	+	0.872385i	$0.662572\pi$
$992$	10.8360	−	6.54773i	0.344045	−	0.207890i
$993$	36.0566	−	2.11231i	1.14422	−	0.0670322i
$994$	−23.2213	−	51.6011i	−0.736536	−	1.63669i
$995$	3.15556	−	1.82186i	0.100038	−	0.0577569i
$996$	6.69212	−	2.67798i	0.212048	−	0.0848552i
$997$	23.3183	+	13.4628i	0.738499	+	0.426373i	0.821523	−	0.570175i	$-0.193125\pi$
$997$	23.3183	+	13.4628i	0.738499	+	0.426373i	−0.0830243	+	0.996548i	$0.526458\pi$
$998$	−2.86268	+	28.3228i	−0.0906166	+	0.896544i
$999$	10.3974	+	58.6183i	0.328960	+	1.85460i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bm.b.11.6	yes	48
3.2	odd	2		1080.2.bm.a.251.19		48
4.3	odd	2		1440.2.cc.b.911.17		48
8.3	odd	2		360.2.bm.a.11.4	✓	48
8.5	even	2		1440.2.cc.a.911.17		48
9.4	even	3		1080.2.bm.b.611.21		48
9.5	odd	6		360.2.bm.a.131.4	yes	48
12.11	even	2		4320.2.cc.a.1871.21		48
24.5	odd	2		4320.2.cc.b.1871.4		48
24.11	even	2		1080.2.bm.b.251.21		48
36.23	even	6		1440.2.cc.a.1391.17		48
36.31	odd	6		4320.2.cc.b.3311.4		48
72.5	odd	6		1440.2.cc.b.1391.17		48
72.13	even	6		4320.2.cc.a.3311.21		48
72.59	even	6	inner	360.2.bm.b.131.6	yes	48
72.67	odd	6		1080.2.bm.a.611.19		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.4	✓	48	8.3	odd	2
360.2.bm.a.131.4	yes	48	9.5	odd	6
360.2.bm.b.11.6	yes	48	1.1	even	1	trivial
360.2.bm.b.131.6	yes	48	72.59	even	6	inner
1080.2.bm.a.251.19		48	3.2	odd	2
1080.2.bm.a.611.19		48	72.67	odd	6
1080.2.bm.b.251.21		48	24.11	even	2
1080.2.bm.b.611.21		48	9.4	even	3
1440.2.cc.a.911.17		48	8.5	even	2
1440.2.cc.a.1391.17		48	36.23	even	6
1440.2.cc.b.911.17		48	4.3	odd	2
1440.2.cc.b.1391.17		48	72.5	odd	6
4320.2.cc.a.1871.21		48	12.11	even	2
4320.2.cc.a.3311.21		48	72.13	even	6
4320.2.cc.b.1871.4		48	24.5	odd	2
4320.2.cc.b.3311.4		48	36.31	odd	6

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14743 - 0.826684i) q^{2} +(-0.952268 - 1.44678i) q^{3} +(0.633188 + 1.89712i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.103374 + 2.44731i) q^{6} +(-2.56287 - 1.47968i) q^{7} +(0.841782 - 2.70026i) q^{8} +(-1.18637 + 2.75545i) q^{9} +O(q^{10})\)	\(q+(-1.14743 - 0.826684i) q^{2} +(-0.952268 - 1.44678i) q^{3} +(0.633188 + 1.89712i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.103374 + 2.44731i) q^{6} +(-2.56287 - 1.47968i) q^{7} +(0.841782 - 2.70026i) q^{8} +(-1.18637 + 2.75545i) q^{9} +(0.142215 - 1.40704i) q^{10} +(2.28478 + 1.31912i) q^{11} +(2.14176 - 2.72265i) q^{12} +(-5.81331 + 3.35631i) q^{13} +(1.71749 + 3.81651i) q^{14} +(0.776819 - 1.54808i) q^{15} +(-3.19815 + 2.40247i) q^{16} +1.13277i q^{17} +(3.63917 - 2.18093i) q^{18} -1.90413 q^{19} +(-1.32636 + 1.49692i) q^{20} +(0.299769 + 5.11697i) q^{21} +(-1.53113 - 3.40239i) q^{22} +(1.73629 + 3.00734i) q^{23} +(-4.70830 + 1.35349i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(9.44497 + 0.954634i) q^{26} +(5.11629 - 0.907502i) q^{27} +(1.18435 - 5.79899i) q^{28} +(-2.38991 + 4.13945i) q^{29} +(-2.17112 + 1.13413i) q^{30} +(1.93826 - 1.11906i) q^{31} +(5.65573 - 0.112808i) q^{32} +(-0.267242 - 4.56174i) q^{33} +(0.936442 - 1.29977i) q^{34} -2.95935i q^{35} +(-5.97863 - 0.505976i) q^{36} +11.4572i q^{37} +(2.18485 + 1.57411i) q^{38} +(10.3917 + 5.21450i) q^{39} +(2.75938 - 0.621125i) q^{40} +(8.25369 - 4.76527i) q^{41} +(3.88615 - 6.11918i) q^{42} +(-2.52551 + 4.37431i) q^{43} +(-1.05583 + 5.16976i) q^{44} +(-2.97948 + 0.350297i) q^{45} +(0.493851 - 4.88607i) q^{46} +(1.06917 - 1.85185i) q^{47} +(6.52135 + 2.33924i) q^{48} +(0.878877 + 1.52226i) q^{49} +(1.28964 - 0.580361i) q^{50} +(1.63887 - 1.07870i) q^{51} +(-10.0483 - 8.90338i) q^{52} -2.02679 q^{53} +(-6.62080 - 3.18826i) q^{54} +2.63824i q^{55} +(-6.15289 + 5.67486i) q^{56} +(1.81324 + 2.75487i) q^{57} +(6.16427 - 2.77402i) q^{58} +(-11.8879 + 6.86345i) q^{59} +(3.42877 + 0.493494i) q^{60} +(-6.75703 - 3.90117i) q^{61} +(-3.14912 - 0.318292i) q^{62} +(7.11770 - 5.30643i) q^{63} +(-6.58281 - 4.54606i) q^{64} +(-5.81331 - 3.35631i) q^{65} +(-3.46448 + 5.45520i) q^{66} +(-2.22742 - 3.85801i) q^{67} +(-2.14900 + 0.717255i) q^{68} +(2.69756 - 5.37583i) q^{69} +(-2.44645 + 3.39565i) q^{70} -13.5205 q^{71} +(6.44177 + 5.52301i) q^{72} +4.30531 q^{73} +(9.47147 - 13.1463i) q^{74} +(1.72909 - 0.101296i) q^{75} +(-1.20567 - 3.61237i) q^{76} +(-3.90374 - 6.76147i) q^{77} +(-7.61299 - 14.5739i) q^{78} +(-10.4990 - 6.06162i) q^{79} +(-3.67967 - 1.56844i) q^{80} +(-6.18504 - 6.53799i) q^{81} +(-13.4099 - 1.35538i) q^{82} +(1.80201 + 1.04039i) q^{83} +(-9.51771 + 3.80870i) q^{84} +(-0.981007 + 0.566384i) q^{85} +(6.51402 - 2.93142i) q^{86} +(8.26472 - 0.484174i) q^{87} +(5.48525 - 5.05909i) q^{88} +10.3071i q^{89} +(3.70833 + 2.06115i) q^{90} +19.8650 q^{91} +(-4.60590 + 5.19816i) q^{92} +(-3.46478 - 1.73861i) q^{93} +(-2.75769 + 1.24101i) q^{94} +(-0.952065 - 1.64903i) q^{95} +(-5.54898 - 8.07520i) q^{96} +(-4.06907 + 7.04783i) q^{97} +(0.249978 - 2.47324i) q^{98} +(-6.34537 + 4.73064i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

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