LMFDB - Embedded newform 360.2.bm.a.11.18

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			11.18
Character	$\chi$	$=$	360.11
Dual form			360.2.bm.a.131.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.893891 + 1.09588i) q^{2} +(1.59734 + 0.669699i) q^{3} +(-0.401917 + 1.95920i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.693939 + 2.34914i) q^{6} +(2.53202 + 1.46186i) q^{7} +(-2.50632 + 1.31086i) q^{8} +(2.10301 + 2.13948i) q^{9} +O(q^{10})$	\(q+(0.893891 + 1.09588i) q^{2} +(1.59734 + 0.669699i) q^{3} +(-0.401917 + 1.95920i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.693939 + 2.34914i) q^{6} +(2.53202 + 1.46186i) q^{7} +(-2.50632 + 1.31086i) q^{8} +(2.10301 + 2.13948i) q^{9} +(0.502116 - 1.32207i) q^{10} +(-3.49775 - 2.01943i) q^{11} +(-1.95407 + 2.86035i) q^{12} +(0.913210 - 0.527242i) q^{13} +(0.661320 + 4.08154i) q^{14} +(-0.218694 - 1.71819i) q^{15} +(-3.67693 - 1.57487i) q^{16} -4.29962i q^{17} +(-0.464759 + 4.21711i) q^{18} -0.364276 q^{19} +(1.89767 - 0.631530i) q^{20} +(3.06549 + 4.03078i) q^{21} +(-0.913555 - 5.63828i) q^{22} +(2.16644 + 3.75238i) q^{23} +(-4.88134 + 0.415407i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.39411 + 0.529474i) q^{26} +(1.92641 + 4.82586i) q^{27} +(-3.88174 + 4.37318i) q^{28} +(3.13786 - 5.43493i) q^{29} +(1.68744 - 1.77554i) q^{30} +(-5.12224 + 2.95733i) q^{31} +(-1.56090 - 5.43724i) q^{32} +(-4.23470 - 5.56816i) q^{33} +(4.71187 - 3.84339i) q^{34} -2.92372i q^{35} +(-5.03690 + 3.26032i) q^{36} -0.135357i q^{37} +(-0.325623 - 0.399203i) q^{38} +(1.81180 - 0.230610i) q^{39} +(2.38840 + 1.51511i) q^{40} +(-4.36652 + 2.52101i) q^{41} +(-1.67705 + 6.96250i) q^{42} +(4.44596 - 7.70062i) q^{43} +(5.36227 - 6.04116i) q^{44} +(0.801340 - 2.89100i) q^{45} +(-2.17561 + 5.72838i) q^{46} +(5.06899 - 8.77974i) q^{47} +(-4.81862 - 4.97804i) q^{48} +(0.774071 + 1.34073i) q^{49} +(-1.39601 + 0.226191i) q^{50} +(2.87945 - 6.86796i) q^{51} +(0.665938 + 2.00107i) q^{52} -10.4796 q^{53} +(-3.56657 + 6.42492i) q^{54} +4.03886i q^{55} +(-8.26234 - 0.344778i) q^{56} +(-0.581873 - 0.243955i) q^{57} +(8.76095 - 1.41951i) q^{58} +(2.61734 - 1.51112i) q^{59} +(3.45417 + 0.262102i) q^{60} +(-3.96710 - 2.29040i) q^{61} +(-7.81960 - 2.96984i) q^{62} +(2.19723 + 8.49149i) q^{63} +(4.56330 - 6.57087i) q^{64} +(-0.913210 - 0.527242i) q^{65} +(2.31669 - 9.61807i) q^{66} +(6.31867 + 10.9443i) q^{67} +(8.42381 + 1.72809i) q^{68} +(0.947576 + 7.44469i) q^{69} +(3.20405 - 2.61349i) q^{70} +13.0054 q^{71} +(-8.07536 - 2.60548i) q^{72} -0.247708 q^{73} +(0.148336 - 0.120995i) q^{74} +(-1.37865 + 1.04849i) q^{75} +(0.146408 - 0.713689i) q^{76} +(-5.90425 - 10.2265i) q^{77} +(1.87228 + 1.77938i) q^{78} +(10.7826 + 6.22536i) q^{79} +(0.474586 + 3.97175i) q^{80} +(-0.154737 + 8.99867i) q^{81} +(-6.66593 - 2.53169i) q^{82} +(-15.2955 - 8.83085i) q^{83} +(-9.12918 + 4.38587i) q^{84} +(-3.72358 + 2.14981i) q^{85} +(12.4132 - 2.01127i) q^{86} +(8.65201 - 6.58002i) q^{87} +(11.4137 + 0.476280i) q^{88} +10.1741i q^{89} +(3.88450 - 1.70606i) q^{90} +3.08302 q^{91} +(-8.22239 + 2.73634i) q^{92} +(-10.1625 + 1.29350i) q^{93} +(14.1527 - 2.29312i) q^{94} +(0.182138 + 0.315472i) q^{95} +(1.14802 - 9.73047i) q^{96} +(4.44230 - 7.69430i) q^{97} +(-0.777347 + 2.04676i) q^{98} +(-3.03527 - 11.7302i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8}+O(q^{10}) $ 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8	$ 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8} - 15 q^{12} + 15 q^{14} + 12 q^{16} - 11 q^{18} - 4 q^{21} + 21 q^{22} - 24 q^{24} - 24 q^{25} + 12 q^{27} - 14 q^{30} - 8 q^{33} + 33 q^{34} - 23 q^{36} - 33 q^{38} + 16 q^{39} - 6 q^{40} + 12 q^{41} - 53 q^{42} - 24 q^{44} - 6 q^{46} + 12 q^{47} + 45 q^{48} + 24 q^{49} - 20 q^{51} - 36 q^{52} - 36 q^{54} + 21 q^{56} + 4 q^{57} - 51 q^{58} - 36 q^{59} + 15 q^{60} + 12 q^{61} + 42 q^{62} + 56 q^{63} - 12 q^{64} + 24 q^{66} + 57 q^{68} - 40 q^{69} - 15 q^{70} + 46 q^{72} + 30 q^{74} + 57 q^{76} + 78 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} - 31 q^{84} + 27 q^{86} + 36 q^{87} + 57 q^{88} + 4 q^{90} - 51 q^{92} + 57 q^{94} - 119 q^{96} + 42 q^{98} - 16 q^{99}+O(q^{100}) $ 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8 - 15 * q^12 + 15 * q^14 + 12 * q^16 - 11 * q^18 - 4 * q^21 + 21 * q^22 - 24 * q^24 - 24 * q^25 + 12 * q^27 - 14 * q^30 - 8 * q^33 + 33 * q^34 - 23 * q^36 - 33 * q^38 + 16 * q^39 - 6 * q^40 + 12 * q^41 - 53 * q^42 - 24 * q^44 - 6 * q^46 + 12 * q^47 + 45 * q^48 + 24 * q^49 - 20 * q^51 - 36 * q^52 - 36 * q^54 + 21 * q^56 + 4 * q^57 - 51 * q^58 - 36 * q^59 + 15 * q^60 + 12 * q^61 + 42 * q^62 + 56 * q^63 - 12 * q^64 + 24 * q^66 + 57 * q^68 - 40 * q^69 - 15 * q^70 + 46 * q^72 + 30 * q^74 + 57 * q^76 + 78 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 - 31 * q^84 + 27 * q^86 + 36 * q^87 + 57 * q^88 + 4 * q^90 - 51 * q^92 + 57 * q^94 - 119 * 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 $

$2$	0.893891	+	1.09588i	0.632077	+	0.774906i
$2$	0.893891	+	1.09588i	0.632077	+	0.774906i
$3$	1.59734	+	0.669699i	0.922226	+	0.386651i
$3$	1.59734	+	0.669699i	0.922226	+	0.386651i
$4$	−0.401917	+	1.95920i	−0.200958	+	0.979600i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.693939	+	2.34914i	0.283299	+	0.959032i
$7$	2.53202	+	1.46186i	0.957012	+	0.552531i	0.895252	−	0.445560i	$-0.146995\pi$
$7$	2.53202	+	1.46186i	0.957012	+	0.552531i	0.0617600	+	0.998091i	$0.480329\pi$
$8$	−2.50632	+	1.31086i	−0.886119	+	0.463458i
$9$	2.10301	+	2.13948i	0.701002	+	0.713160i
$10$	0.502116	−	1.32207i	0.158783	−	0.418076i
$11$	−3.49775	−	2.01943i	−1.05461	−	0.608881i	−0.130675	−	0.991425i	$-0.541715\pi$
$11$	−3.49775	−	2.01943i	−1.05461	−	0.608881i	−0.923937	+	0.382544i	$0.875048\pi$
$12$	−1.95407	+	2.86035i	−0.564092	+	0.825712i
$13$	0.913210	−	0.527242i	0.253279	−	0.146231i	−0.367986	−	0.929831i	$-0.619952\pi$
$13$	0.913210	−	0.527242i	0.253279	−	0.146231i	0.621265	+	0.783601i	$0.286619\pi$
$14$	0.661320	+	4.08154i	0.176745	+	1.09084i
$15$	−0.218694	−	1.71819i	−0.0564667	−	0.443634i
$16$	−3.67693	−	1.57487i	−0.919232	−	0.393717i
$17$		−	4.29962i		−	1.04281i	−0.853309	−	0.521405i	$-0.825408\pi$
$17$		−	4.29962i		−	1.04281i	0.853309	−	0.521405i	$-0.174592\pi$
$18$	−0.464759	+	4.21711i	−0.109545	+	0.993982i
$19$	−0.364276			−0.0835706			−0.0417853	−	0.999127i	$-0.513305\pi$
$19$	−0.364276			−0.0835706			−0.0417853	+	0.999127i	$0.513305\pi$
$20$	1.89767	−	0.631530i	0.424333	−	0.141214i
$21$	3.06549	+	4.03078i	0.668945	+	0.879589i
$22$	−0.913555	−	5.63828i	−0.194771	−	1.20208i
$23$	2.16644	+	3.75238i	0.451733	+	0.782425i	0.998494	−	0.0548640i	$-0.0174725\pi$
$23$	2.16644	+	3.75238i	0.451733	+	0.782425i	−0.546761	+	0.837289i	$0.684139\pi$
$24$	−4.88134	+	0.415407i	−0.996398	+	0.0847946i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.39411	+	0.529474i	0.273407	+	0.103838i
$27$	1.92641	+	4.82586i	0.370738	+	0.928737i
$28$	−3.88174	+	4.37318i	−0.733579	+	0.826453i
$29$	3.13786	−	5.43493i	0.582686	−	1.00924i	−0.412474	−	0.910969i	$-0.635335\pi$
$29$	3.13786	−	5.43493i	0.582686	−	1.00924i	0.995160	−	0.0982720i	$-0.0313315\pi$
$30$	1.68744	−	1.77554i	0.308084	−	0.324167i
$31$	−5.12224	+	2.95733i	−0.919981	+	0.531151i	−0.883629	−	0.468188i	$-0.844907\pi$
$31$	−5.12224	+	2.95733i	−0.919981	+	0.531151i	−0.0363520	+	0.999339i	$0.511574\pi$
$32$	−1.56090	−	5.43724i	−0.275931	−	0.961177i
$33$	−4.23470	−	5.56816i	−0.737167	−	0.969293i
$34$	4.71187	−	3.84339i	0.808080	−	0.659136i
$35$		−	2.92372i		−	0.494199i
$36$	−5.03690	+	3.26032i	−0.839483	+	0.543386i
$37$		−	0.135357i		−	0.0222526i	−0.999938	−	0.0111263i	$-0.996458\pi$
$37$		−	0.135357i		−	0.0222526i	0.999938	−	0.0111263i	$-0.00354169\pi$
$38$	−0.325623	−	0.399203i	−0.0528230	−	0.0647593i
$39$	1.81180	−	0.230610i	0.290121	−	0.0369271i
$40$	2.38840	+	1.51511i	0.377639	+	0.239560i
$41$	−4.36652	+	2.52101i	−0.681937	+	0.393716i	−0.800584	−	0.599220i	$-0.795477\pi$
$41$	−4.36652	+	2.52101i	−0.681937	+	0.393716i	0.118648	+	0.992936i	$0.462144\pi$
$42$	−1.67705	+	6.96250i	−0.258774	+	1.07434i
$43$	4.44596	−	7.70062i	0.678002	−	1.17433i	−0.297580	−	0.954697i	$-0.596179\pi$
$43$	4.44596	−	7.70062i	0.678002	−	1.17433i	0.975582	−	0.219637i	$-0.0704873\pi$
$44$	5.36227	−	6.04116i	0.808393	−	0.910738i
$45$	0.801340	−	2.89100i	0.119457	−	0.430964i
$46$	−2.17561	+	5.72838i	−0.320776	+	0.844603i
$47$	5.06899	−	8.77974i	0.739388	−	1.28066i	−0.213384	−	0.976968i	$-0.568449\pi$
$47$	5.06899	−	8.77974i	0.739388	−	1.28066i	0.952771	−	0.303688i	$-0.0982182\pi$
$48$	−4.81862	−	4.97804i	−0.695508	−	0.718518i
$49$	0.774071	+	1.34073i	0.110582	+	0.191533i
$50$	−1.39601	+	0.226191i	−0.197425	+	0.0319883i
$51$	2.87945	−	6.86796i	0.403204	−	0.961707i
$52$	0.665938	+	2.00107i	0.0923490	+	0.277498i
$53$	−10.4796			−1.43948			−0.719739	−	0.694244i	$-0.755739\pi$
$53$	−10.4796			−1.43948			−0.719739	+	0.694244i	$0.755739\pi$
$54$	−3.56657	+	6.42492i	−0.485349	+	0.874320i
$55$			4.03886i			0.544600i
$56$	−8.26234	−	0.344778i	−1.10410	−	0.0460730i
$57$	−0.581873	−	0.243955i	−0.0770710	−	0.0323127i
$58$	8.76095	−	1.41951i	1.15037	−	0.186391i
$59$	2.61734	−	1.51112i	0.340749	−	0.196731i	−0.319854	−	0.947467i	$-0.603634\pi$
$59$	2.61734	−	1.51112i	0.340749	−	0.196731i	0.660603	+	0.750735i	$0.270301\pi$
$60$	3.45417	+	0.262102i	0.445932	+	0.0338373i
$61$	−3.96710	−	2.29040i	−0.507935	−	0.293256i	0.224050	−	0.974578i	$-0.428072\pi$
$61$	−3.96710	−	2.29040i	−0.507935	−	0.293256i	−0.731984	+	0.681322i	$0.761406\pi$
$62$	−7.81960	−	2.96984i	−0.993091	−	0.377170i
$63$	2.19723	+	8.49149i	0.276824	+	1.06983i
$64$	4.56330	−	6.57087i	0.570413	−	0.821358i
$65$	−0.913210	−	0.527242i	−0.113270	−	0.0653963i
$66$	2.31669	−	9.61807i	0.285165	−	1.18390i
$67$	6.31867	+	10.9443i	0.771949	+	1.33705i	0.936494	+	0.350685i	$0.114051\pi$
$67$	6.31867	+	10.9443i	0.771949	+	1.33705i	−0.164545	+	0.986370i	$0.552616\pi$
$68$	8.42381	+	1.72809i	1.02154	+	0.209561i
$69$	0.947576	+	7.44469i	0.114075	+	0.896236i
$70$	3.20405	−	2.61349i	0.382958	−	0.312372i
$71$	13.0054			1.54345			0.771726	−	0.635955i	$-0.219394\pi$
$71$	13.0054			1.54345			0.771726	+	0.635955i	$0.219394\pi$
$72$	−8.07536	−	2.60548i	−0.951691	−	0.307059i
$73$	−0.247708			−0.0289920			−0.0144960	−	0.999895i	$-0.504614\pi$
$73$	−0.247708			−0.0289920			−0.0144960	+	0.999895i	$0.504614\pi$
$74$	0.148336	−	0.120995i	0.0172437	−	0.0140654i
$75$	−1.37865	+	1.04849i	−0.159193	+	0.121069i
$76$	0.146408	−	0.713689i	0.0167942	−	0.0818657i
$77$	−5.90425	−	10.2265i	−0.672851	−	1.16541i
$78$	1.87228	+	1.77938i	0.211994	+	0.201475i
$79$	10.7826	+	6.22536i	1.21314	+	0.700408i	0.963443	−	0.267915i	$-0.0863347\pi$
$79$	10.7826	+	6.22536i	1.21314	+	0.700408i	0.249700	+	0.968323i	$0.419668\pi$
$80$	0.474586	+	3.97175i	0.0530603	+	0.444055i
$81$	−0.154737	+	8.99867i	−0.0171930	+	0.999852i
$82$	−6.66593	−	2.53169i	−0.736129	−	0.279578i
$83$	−15.2955	−	8.83085i	−1.67890	−	0.969312i	−0.962366	−	0.271756i	$-0.912396\pi$
$83$	−15.2955	−	8.83085i	−1.67890	−	0.969312i	−0.716531	−	0.697555i	$-0.754271\pi$
$84$	−9.12918	+	4.38587i	−0.996075	+	0.478538i
$85$	−3.72358	+	2.14981i	−0.403879	+	0.233179i
$86$	12.4132	−	2.01127i	1.33855	−	0.216881i
$87$	8.65201	−	6.58002i	0.927592	−	0.705453i
$88$	11.4137	+	0.476280i	1.21670	+	0.0507717i
$89$			10.1741i			1.07846i	0.842159	+	0.539229i	$0.181284\pi$
$89$			10.1741i			1.07846i	−0.842159	+	0.539229i	$0.818716\pi$
$90$	3.88450	−	1.70606i	0.409462	−	0.179835i
$91$	3.08302			0.323188
$92$	−8.22239	+	2.73634i	−0.857243	+	0.285283i
$93$	−10.1625	+	1.29350i	−1.05380	+	0.134130i
$94$	14.1527	−	2.29312i	1.45974	−	0.236517i
$95$	0.182138	+	0.315472i	0.0186869	+	0.0323667i
$96$	1.14802	−	9.73047i	0.117170	−	0.993112i
$97$	4.44230	−	7.69430i	0.451048	−	0.781237i	−0.547404	−	0.836869i	$-0.684384\pi$
$97$	4.44230	−	7.69430i	0.451048	−	0.781237i	0.998451	+	0.0556313i	$0.0177171\pi$
$98$	−0.777347	+	2.04676i	−0.0785239	+	0.206754i
$99$	−3.03527	−	11.7302i	−0.305056	−	1.17893i
$100$	−1.49576	−	1.32767i	−0.149576	−	0.132767i
$101$	−2.62949	+	4.55441i	−0.261644	+	0.453180i	−0.966679	−	0.255992i	$-0.917598\pi$
$101$	−2.62949	+	4.55441i	−0.261644	+	0.453180i	0.705035	+	0.709172i	$0.250931\pi$
$102$	10.1004	−	2.98367i	1.00009	−	0.295427i
$103$	−13.9866	+	8.07516i	−1.37814	+	0.795669i	−0.991935	−	0.126744i	$-0.959547\pi$
$103$	−13.9866	+	8.07516i	−1.37814	+	0.795669i	−0.386204	+	0.922413i	$0.626214\pi$
$104$	−1.59766	+	2.51853i	−0.156663	+	0.246962i
$105$	1.95801	−	4.67018i	0.191083	−	0.455763i
$106$	−9.36759	−	11.4844i	−0.909861	−	1.11546i
$107$			5.41255i			0.523251i	0.965169	+	0.261625i	$0.0842585\pi$
$107$			5.41255i			0.523251i	−0.965169	+	0.261625i	$0.915741\pi$
$108$	−10.2291	+	1.83463i	−0.984294	+	0.176538i
$109$		−	16.9593i		−	1.62441i	−0.583372	−	0.812205i	$-0.698267\pi$
$109$		−	16.9593i		−	1.62441i	0.583372	−	0.812205i	$-0.301733\pi$
$110$	−4.42611	+	3.61030i	−0.422013	+	0.344229i
$111$	0.0906487	−	0.216212i	0.00860400	−	0.0205219i
$112$	−7.00780	−	9.36275i	−0.662175	−	0.884696i
$113$	−11.1276	+	6.42452i	−1.04680	+	0.604368i	−0.921751	−	0.387783i	$-0.873241\pi$
$113$	−11.1276	+	6.42452i	−1.04680	+	0.604368i	−0.125046	+	0.992151i	$0.539908\pi$
$114$	−0.252785	−	0.855734i	−0.0236755	−	0.0801468i
$115$	2.16644	−	3.75238i	0.202021	−	0.349911i
$116$	9.38696	+	8.33208i	0.871557	+	0.773614i
$117$	3.04851	+	0.845001i	0.281835	+	0.0781203i
$118$	3.99563	+	1.51752i	0.367828	+	0.139699i
$119$	6.28544	−	10.8867i	0.576185	−	0.997982i
$120$	2.80042	+	4.01966i	0.255642	+	0.366943i
$121$	2.65619	+	4.60065i	0.241472	+	0.418241i
$122$	−1.03614	−	6.39484i	−0.0938077	−	0.578962i
$123$	−8.66316	+	1.10266i	−0.781131	+	0.0994239i
$124$	−3.73528	−	11.2241i	−0.335438	−	1.00795i
$125$	1.00000			0.0894427
$126$	−7.34160	+	9.99837i	−0.654042	+	0.890726i
$127$			15.1195i			1.34164i	0.741622	+	0.670818i	$0.234057\pi$
$127$			15.1195i			1.34164i	−0.741622	+	0.670818i	$0.765943\pi$
$128$	11.2800	−	0.872798i	0.997020	−	0.0771452i
$129$	12.2588	−	9.32308i	1.07933	−	0.820851i
$130$	−0.238515	−	1.47207i	−0.0209192	−	0.129109i
$131$	1.40697	−	0.812314i	0.122927	−	0.0709722i	−0.437275	−	0.899328i	$-0.644056\pi$
$131$	1.40697	−	0.812314i	0.122927	−	0.0709722i	0.560203	+	0.828355i	$0.310723\pi$
$132$	12.6111	−	6.05869i	1.09766	−	0.527341i
$133$	−0.922352	−	0.532520i	−0.0799781	−	0.0461754i
$134$	−6.34542	+	16.7075i	−0.548161	+	1.44331i
$135$	3.21611	−	4.08125i	0.276799	−	0.351258i
$136$	5.63619	+	10.7762i	0.483299	+	0.924054i
$137$	−5.80182	−	3.34968i	−0.495683	−	0.286183i	0.231246	−	0.972895i	$-0.425720\pi$
$137$	−5.80182	−	3.34968i	−0.495683	−	0.286183i	−0.726929	+	0.686713i	$0.759053\pi$
$138$	−7.31148	+	7.69318i	−0.622395	+	0.654887i
$139$	5.43042	+	9.40577i	0.460602	+	0.797787i	0.998991	−	0.0449100i	$-0.0143001\pi$
$139$	5.43042	+	9.40577i	0.460602	+	0.797787i	−0.538389	+	0.842697i	$0.680967\pi$
$140$	5.72815	+	1.17509i	0.484117	+	0.0993134i
$141$	13.9767	−	10.6296i	1.17705	−	0.895170i
$142$	11.6254	+	14.2523i	0.975580	+	1.19603i
$143$	−4.25891			−0.356148
$144$	−4.36320	−	11.1787i	−0.363600	−	0.931555i
$145$	−6.27572			−0.521170
$146$	−0.221424	−	0.271459i	−0.0183252	−	0.0224661i
$147$	0.338570	+	2.66000i	0.0279248	+	0.219393i
$148$	0.265192	+	0.0544024i	0.0217987	+	0.00447185i
$149$	−4.98608	−	8.63615i	−0.408476	−	0.707501i	0.586243	−	0.810135i	$-0.300606\pi$
$149$	−4.98608	−	8.63615i	−0.408476	−	0.707501i	−0.994719	+	0.102634i	$0.967273\pi$
$150$	−2.38138	−	0.573600i	−0.194439	−	0.0468343i
$151$	−7.84025	−	4.52657i	−0.638030	−	0.368367i	0.145825	−	0.989310i	$-0.453416\pi$
$151$	−7.84025	−	4.52657i	−0.638030	−	0.368367i	−0.783855	+	0.620943i	$0.786750\pi$
$152$	0.912992	−	0.477514i	0.0740534	−	0.0387315i
$153$	9.19894	−	9.04212i	0.743690	−	0.731012i
$154$	5.92924	−	15.6117i	0.477792	−	1.25803i
$155$	5.12224	+	2.95733i	0.411428	+	0.237538i
$156$	−0.276383	+	3.64237i	−0.0221283	+	0.291623i
$157$	−6.01548	+	3.47304i	−0.480087	+	0.277179i	−0.720453	−	0.693504i	$-0.756066\pi$
$157$	−6.01548	+	3.47304i	−0.480087	+	0.277179i	0.240365	+	0.970682i	$0.422733\pi$
$158$	2.81625	+	17.3813i	0.224049	+	1.38278i
$159$	−16.7394	−	7.01816i	−1.32752	−	0.556576i
$160$	−3.92834	+	4.07040i	−0.310562	+	0.321793i
$161$			12.6681i			0.998387i
$162$	−9.99980	+	7.87426i	−0.785659	+	0.618660i
$163$	−0.804551			−0.0630173			−0.0315087	−	0.999503i	$-0.510031\pi$
$163$	−0.804551			−0.0630173			−0.0315087	+	0.999503i	$0.510031\pi$
$164$	−3.18419	−	9.56813i	−0.248644	−	0.747146i
$165$	−2.70482	+	6.45144i	−0.210570	+	0.502244i
$166$	−3.99492	−	24.6559i	−0.310066	−	1.91367i
$167$	1.87470	+	3.24708i	0.145069	+	0.251266i	0.929399	−	0.369078i	$-0.120326\pi$
$167$	1.87470	+	3.24708i	0.145069	+	0.251266i	−0.784330	+	0.620344i	$0.786993\pi$
$168$	−12.9669	−	6.08401i	−1.00042	−	0.469392i
$169$	−5.94403	+	10.2954i	−0.457233	+	0.791951i
$170$	−5.68441	−	2.15891i	−0.435974	−	0.165581i
$171$	−0.766074	−	0.779360i	−0.0585831	−	0.0595991i
$172$	13.3002	+	11.8055i	1.01413	+	0.900163i
$173$	−9.25528	+	16.0306i	−0.703666	+	1.21878i	0.263505	+	0.964658i	$0.415121\pi$
$173$	−9.25528	+	16.0306i	−0.703666	+	1.21878i	−0.967171	+	0.254127i	$0.918212\pi$
$174$	14.9449	+	3.59975i	1.13297	+	0.272897i
$175$	−2.53202	+	1.46186i	−0.191402	+	0.110506i
$176$	9.68064	+	12.9338i	0.729706	+	0.974922i
$177$	5.19279	−	0.660948i	0.390314	−	0.0496799i
$178$	−11.1497	+	9.09458i	−0.835703	+	0.681668i
$179$			18.4657i			1.38019i	0.723719	+	0.690095i	$0.242431\pi$
$179$			18.4657i			1.38019i	−0.723719	+	0.690095i	$0.757569\pi$
$180$	5.34197	+	2.73192i	0.398167	+	0.203626i
$181$		−	2.88050i		−	0.214106i	−0.994253	−	0.107053i	$-0.965859\pi$
$181$		−	2.88050i		−	0.214106i	0.994253	−	0.107053i	$-0.0341415\pi$
$182$	2.75588	+	3.37862i	0.204280	+	0.250440i
$183$	−4.80293	−	6.31532i	−0.355043	−	0.466842i
$184$	−10.3486	−	6.56478i	−0.762911	−	0.483962i
$185$	−0.117223	+	0.0676787i	−0.00861840	+	0.00497583i
$186$	−10.5017	−	9.98064i	−0.770021	−	0.731816i
$187$	−8.68277	+	15.0390i	−0.634947	+	1.09976i
$188$	15.1640	+	13.4599i	1.10595	+	0.981662i
$189$	−2.17703	+	15.0353i	−0.158355	+	1.09366i
$190$	−0.182909	+	0.481599i	−0.0132696	+	0.0349389i
$191$	−4.10309	+	7.10676i	−0.296889	+	0.514227i	−0.975423	−	0.220342i	$-0.929283\pi$
$191$	−4.10309	+	7.10676i	−0.296889	+	0.514227i	0.678533	+	0.734570i	$0.262616\pi$
$192$	11.6897	−	7.43988i	0.843629	−	0.536927i
$193$	3.30583	+	5.72587i	0.237959	+	0.412157i	0.960129	−	0.279559i	$-0.0901882\pi$
$193$	3.30583	+	5.72587i	0.237959	+	0.412157i	−0.722169	+	0.691716i	$0.756855\pi$
$194$	12.4030	−	2.00962i	0.890482	−	0.144282i
$195$	−1.10562	−	1.45376i	−0.0791748	−	0.104106i
$196$	−2.93787	+	0.977698i	−0.209848	+	0.0698355i
$197$	−25.1780			−1.79385			−0.896927	−	0.442178i	$-0.854206\pi$
$197$	−25.1780			−1.79385			−0.896927	+	0.442178i	$0.854206\pi$
$198$	10.1418	−	13.8119i	0.720744	−	0.981566i
$199$		−	5.92874i		−	0.420277i	−0.977672	−	0.210138i	$-0.932609\pi$
$199$		−	5.92874i		−	0.420277i	0.977672	−	0.210138i	$-0.0673915\pi$
$200$	0.117925	−	2.82597i	0.00833852	−	0.199826i
$201$	2.76372	+	21.7133i	0.194938	+	1.53154i
$202$	−7.34157	+	1.18954i	−0.516551	+	0.0836954i
$203$	15.8902	−	9.17422i	1.11527	−	0.643904i
$204$	12.2984	+	8.40177i	0.861061	+	0.588241i
$205$	4.36652	+	2.52101i	0.304971	+	0.176075i
$206$	−21.3519	−	8.10934i	−1.48766	−	0.565005i
$207$	−3.47210	+	12.5263i	−0.241328	+	0.870639i
$208$	−4.18814	+	0.500444i	−0.290396	+	0.0346995i
$209$	1.27415	+	0.735629i	0.0881346	+	0.0508845i
$210$	6.86822	−	2.02888i	0.473952	−	0.140006i
$211$	6.80629	+	11.7888i	0.468564	+	0.811577i	0.999354	−	0.0359264i	$-0.0114382\pi$
$211$	6.80629	+	11.7888i	0.468564	+	0.811577i	−0.530790	+	0.847503i	$0.678105\pi$
$212$	4.21191	−	20.5316i	0.289275	−	1.41011i
$213$	20.7740	+	8.70968i	1.42341	+	0.596778i
$214$	−5.93152	+	4.83823i	−0.405470	+	0.330735i
$215$	−8.89191			−0.606423
$216$	−11.1542	−	9.56991i	−0.758949	−	0.651150i
$217$	−17.2928			−1.17391
$218$	18.5854	−	15.1598i	1.25876	−	1.02675i
$219$	−0.395675	−	0.165890i	−0.0267372	−	0.0112098i
$220$	−7.91293	−	1.62328i	−0.533490	−	0.109442i
$221$	−2.26694	−	3.92645i	−0.152491	−	0.264122i
$222$	0.317973	−	0.0939297i	0.0213410	−	0.00630415i
$223$	−17.2032	−	9.93225i	−1.15201	−	0.665113i	−0.202633	−	0.979255i	$-0.564950\pi$
$223$	−17.2032	−	9.93225i	−1.15201	−	0.665113i	−0.949376	+	0.314142i	$0.898283\pi$
$224$	3.99626	−	16.0490i	0.267011	−	1.07232i
$225$	−2.90435	+	0.751517i	−0.193623	+	0.0501011i
$226$	−16.9874	−	6.45172i	−1.12998	−	0.429162i
$227$	1.46390	+	0.845180i	0.0971622	+	0.0560966i	0.547794	−	0.836613i	$-0.315468\pi$
$227$	1.46390	+	0.845180i	0.0971622	+	0.0560966i	−0.450632	+	0.892710i	$0.648801\pi$
$228$	0.711821	−	1.04196i	0.0471415	−	0.0690052i
$229$	−1.45187	+	0.838237i	−0.0959422	+	0.0553923i	−0.547203	−	0.837000i	$-0.684308\pi$
$229$	−1.45187	+	0.838237i	−0.0959422	+	0.0553923i	0.451261	+	0.892392i	$0.350974\pi$
$230$	6.04872	−	0.980059i	0.398841	−	0.0646232i
$231$	−2.58245	−	20.2892i	−0.169913	−	1.33493i
$232$	−0.740061	+	17.7350i	−0.0485874	+	1.16436i
$233$		−	11.2082i		−	0.734276i	−0.930167	−	0.367138i	$-0.880338\pi$
$233$		−	11.2082i		−	0.734276i	0.930167	−	0.367138i	$-0.119662\pi$
$234$	1.79901	+	4.09615i	0.117605	+	0.267773i
$235$	−10.1380			−0.661328
$236$	1.90864	+	5.73524i	0.124242	+	0.373332i
$237$	13.0545	+	17.1652i	0.847978	+	1.11500i
$238$	17.5490	−	2.84342i	1.13754	−	0.184312i
$239$	7.70075	+	13.3381i	0.498120	+	0.862769i	0.999998	−	0.00216939i	$-0.000690538\pi$
$239$	7.70075	+	13.3381i	0.498120	+	0.862769i	−0.501878	+	0.864939i	$0.667357\pi$
$240$	−1.90180	+	6.66207i	−0.122761	+	0.430035i
$241$	−1.32188	+	2.28957i	−0.0851501	+	0.147484i	−0.905455	−	0.424442i	$-0.860470\pi$
$241$	−1.32188	+	2.28957i	−0.0851501	+	0.147484i	0.820305	+	0.571926i	$0.193804\pi$
$242$	−2.66743	+	7.02335i	−0.171469	+	0.451478i
$243$	−6.27357	+	14.2703i	−0.402450	+	0.915442i
$244$	6.08180	−	6.85178i	0.389347	−	0.438640i
$245$	0.774071	−	1.34073i	0.0494536	−	0.0856561i
$246$	−8.95231	−	8.50814i	−0.570779	−	0.542459i
$247$	−0.332660	+	0.192062i	−0.0211667	+	0.0122206i
$248$	8.96134	−	14.1265i	0.569046	−	0.897036i
$249$	−18.5181	−	24.3493i	−1.17354	−	1.54307i
$250$	0.893891	+	1.09588i	0.0565347	+	0.0693097i
$251$		−	10.0921i		−	0.637010i	−0.947921	−	0.318505i	$-0.896819\pi$
$251$		−	10.0921i		−	0.637010i	0.947921	−	0.318505i	$-0.103181\pi$
$252$	−17.5196	+	0.891930i	−1.10363	+	0.0561863i
$253$		−	17.4999i		−	1.10021i
$254$	−16.5692	+	13.5152i	−1.03964	+	0.848017i
$255$	−7.38755	+	0.940303i	−0.462627	+	0.0588840i
$256$	11.0396	+	11.5814i	0.689973	+	0.723835i
$257$	18.6844	−	10.7875i	1.16550	−	0.672903i	0.212886	−	0.977077i	$-0.431714\pi$
$257$	18.6844	−	10.7875i	1.16550	−	0.672903i	0.952616	+	0.304174i	$0.0983805\pi$
$258$	21.1750	+	5.10041i	1.31830	+	0.317537i
$259$	0.197874	−	0.342727i	0.0122953	−	0.0212960i
$260$	1.40001	−	1.57725i	0.0868247	−	0.0978171i
$261$	18.2269	−	4.71631i	1.12821	−	0.291932i
$262$	2.14788	+	0.815752i	0.132696	+	0.0503974i
$263$	10.6378	−	18.4252i	0.655956	−	1.13615i	−0.325697	−	0.945474i	$-0.605599\pi$
$263$	10.6378	−	18.4252i	0.655956	−	1.13615i	0.981653	−	0.190675i	$-0.0610677\pi$
$264$	17.9126	+	8.40452i	1.10244	+	0.517262i
$265$	5.23978	+	9.07557i	0.321877	+	0.557508i
$266$	−0.240903	−	1.48680i	−0.0147707	−	0.0911618i
$267$	−6.81362	+	16.2516i	−0.416987	+	0.994581i
$268$	−23.9816	+	7.98086i	−1.46491	+	0.487509i
$269$	24.8154			1.51302			0.756510	−	0.653982i	$-0.226903\pi$
$269$	24.8154			1.51302			0.756510	+	0.653982i	$0.226903\pi$
$270$	7.34743	−	0.123715i	0.447150	−	0.00752907i
$271$			0.896966i			0.0544868i	0.999629	+	0.0272434i	$0.00867292\pi$
$271$			0.896966i			0.0544868i	−0.999629	+	0.0272434i	$0.991327\pi$
$272$	−6.77134	+	15.8094i	−0.410573	+	0.958584i
$273$	4.92463	+	2.06470i	0.298052	+	0.124961i
$274$	−1.51534	−	9.35237i	−0.0915450	−	0.564997i
$275$	3.49775	−	2.01943i	0.210922	−	0.121776i
$276$	−14.9665	−	1.13566i	−0.900877	−	0.0683585i
$277$	21.4704	+	12.3960i	1.29003	+	0.744801i	0.978660	−	0.205487i	$-0.0658779\pi$
$277$	21.4704	+	12.3960i	1.29003	+	0.744801i	0.311373	+	0.950288i	$0.399211\pi$
$278$	−5.45341	+	14.3588i	−0.327074	+	0.861186i
$279$	−17.0992	−	4.73965i	−1.02370	−	0.283755i
$280$	3.83258	+	7.32779i	0.229041	+	0.437919i
$281$	26.9384	+	15.5529i	1.60701	+	0.927807i	0.990035	+	0.140824i	$0.0449750\pi$
$281$	26.9384	+	15.5529i	1.60701	+	0.927807i	0.616974	+	0.786983i	$0.288358\pi$
$282$	24.1424	+	5.81514i	1.43766	+	0.346287i
$283$	−9.06954	−	15.7089i	−0.539128	−	0.933798i	−0.998951	−	0.0457870i	$-0.985420\pi$
$283$	−9.06954	−	15.7089i	−0.539128	−	0.933798i	0.459823	−	0.888011i	$-0.347913\pi$
$284$	−5.22707	+	25.4801i	−0.310170	+	1.51197i
$285$	0.0796651	+	0.625894i	0.00471895	+	0.0370748i
$286$	−3.80701	−	4.66727i	−0.225113	−	0.275981i
$287$	−14.7415			−0.870162
$288$	8.35028	−	14.7741i	0.492045	−	0.870570i
$289$	−1.48671			−0.0874533
$290$	−5.60981	−	6.87745i	−0.329419	−	0.403858i
$291$	12.2487	−	9.31542i	0.718034	−	0.546079i
$292$	0.0995580	−	0.485309i	0.00582619	−	0.0284006i
$293$	6.55697	+	11.3570i	0.383062	+	0.663483i	0.991498	−	0.130120i	$-0.0415362\pi$
$293$	6.55697	+	11.3570i	0.383062	+	0.663483i	−0.608436	+	0.793603i	$0.708203\pi$
$294$	−2.61240	+	2.74878i	−0.152358	+	0.160312i
$295$	−2.61734	−	1.51112i	−0.152387	−	0.0879809i
$296$	0.177434	+	0.339249i	0.0103132	+	0.0197185i
$297$	3.00737	−	20.7699i	0.174505	−	1.20519i
$298$	5.00719	−	13.1839i	0.290059	−	0.763725i
$299$	3.95682	+	2.28447i	0.228829	+	0.132115i
$300$	−1.50010	−	3.12245i	−0.0866082	−	0.180275i
$301$	22.5145	−	12.9987i	1.29771	−	0.749235i
$302$	−2.04774	−	12.6382i	−0.117834	−	0.727250i
$303$	−7.25028	+	5.51398i	−0.416517	+	0.316770i
$304$	1.33941	+	0.573687i	0.0768207	+	0.0329032i
$305$			4.58081i			0.262296i
$306$	18.1319	+	1.99828i	1.03653	+	0.114234i
$307$	1.16804			0.0666636			0.0333318	−	0.999444i	$-0.489388\pi$
$307$	1.16804			0.0666636			0.0333318	+	0.999444i	$0.489388\pi$
$308$	22.4087	−	7.45742i	1.27685	−	0.424926i
$309$	−27.7493	+	3.53199i	−1.57860	+	0.200928i
$310$	1.33784	+	8.25690i	0.0759844	+	0.468960i
$311$	1.84944	+	3.20333i	0.104872	+	0.181644i	0.913686	−	0.406421i	$-0.133223\pi$
$311$	1.84944	+	3.20333i	0.104872	+	0.181644i	−0.808814	+	0.588065i	$0.799890\pi$
$312$	−4.23867	+	2.95300i	−0.239967	+	0.167181i
$313$	12.1650	−	21.0703i	0.687605	−	1.19097i	−0.285006	−	0.958526i	$-0.591996\pi$
$313$	12.1650	−	21.0703i	0.687605	−	1.19097i	0.972611	−	0.232440i	$-0.0746711\pi$
$314$	−9.18322	−	3.48774i	−0.518239	−	0.196824i
$315$	6.25524	−	6.14860i	0.352443	−	0.346434i
$316$	−16.5305	+	18.6233i	−0.929911	+	1.04764i
$317$	−5.70500	+	9.88135i	−0.320425	+	0.554992i	−0.980576	−	0.196141i	$-0.937159\pi$
$317$	−5.70500	+	9.88135i	−0.320425	+	0.554992i	0.660151	+	0.751133i	$0.270492\pi$
$318$	−7.27217	−	24.6179i	−0.407803	−	1.38051i
$319$	−21.9509	+	12.6734i	−1.22902	+	0.709572i
$320$	−7.97219	−	0.666502i	−0.445659	−	0.0372586i
$321$	−3.62478	+	8.64569i	−0.202316	+	0.482556i
$322$	−13.8828	+	11.3239i	−0.773656	+	0.631057i
$323$			1.56625i			0.0871483i
$324$	−17.5680	−	3.91987i	−0.976000	−	0.217771i
$325$			1.05448i			0.0584923i
$326$	−0.719181	−	0.881694i	−0.0398318	−	0.0488325i
$327$	11.3577	−	27.0899i	0.628080	−	1.49807i
$328$	7.63923	−	12.0424i	0.421806	−	0.664929i
$329$	25.6695	−	14.8203i	1.41521	−	0.817069i
$330$	−9.48783	+	2.80272i	−0.522288	+	0.154285i
$331$	12.1584	−	21.0590i	0.668288	−	1.15751i	−0.310094	−	0.950706i	$-0.600361\pi$
$331$	12.1584	−	21.0590i	0.668288	−	1.15751i	0.978383	−	0.206803i	$-0.0663060\pi$
$332$	23.4489	−	26.4176i	1.28693	−	1.44986i
$333$	0.289594	−	0.284657i	0.0158697	−	0.0155991i
$334$	−1.88264	+	4.95699i	−0.103013	+	0.271234i
$335$	6.31867	−	10.9443i	0.345226	−	0.597949i
$336$	−4.92363	−	19.6486i	−0.268606	−	1.07192i
$337$	−14.0908	−	24.4060i	−0.767575	−	1.32948i	−0.938874	−	0.344260i	$-0.888130\pi$
$337$	−14.0908	−	24.4060i	−0.767575	−	1.32948i	0.171300	−	0.985219i	$-0.445203\pi$
$338$	−16.5958	+	2.68898i	−0.902694	+	0.146261i
$339$	−22.0771	+	2.81002i	−1.19906	+	0.152619i
$340$	−2.71534	−	8.15928i	−0.147260	−	0.442499i
$341$	23.8884			1.29363
$342$	0.169300	−	1.53619i	0.00915471	−	0.0830676i
$343$		−	15.9397i		−	0.860663i
$344$	−1.04857	+	25.1283i	−0.0565354	+	1.35483i
$345$	5.97351	−	4.54297i	0.321603	−	0.244585i
$346$	−25.8409	+	4.18693i	−1.38921	+	0.225091i
$347$	−11.8002	+	6.81285i	−0.633468	+	0.365733i	−0.782094	−	0.623160i	$-0.785848\pi$
$347$	−11.8002	+	6.81285i	−0.633468	+	0.365733i	0.148626	+	0.988894i	$0.452515\pi$
$348$	9.41420	+	19.5956i	0.504654	+	1.05044i
$349$	13.9771	+	8.06967i	0.748176	+	0.431960i	0.825034	−	0.565082i	$-0.191156\pi$
$349$	13.9771	+	8.06967i	0.748176	+	0.431960i	−0.0768584	+	0.997042i	$0.524489\pi$
$350$	−3.86537	−	1.46805i	−0.206613	−	0.0784705i
$351$	4.30362	+	3.39134i	0.229710	+	0.181016i
$352$	−5.52048	+	22.1703i	−0.294242	+	1.18168i
$353$	−27.9307	−	16.1258i	−1.48660	−	0.858289i	−0.486717	−	0.873560i	$-0.661806\pi$
$353$	−27.9307	−	16.1258i	−1.48660	−	0.858289i	−0.999883	+	0.0152706i	$0.995139\pi$
$354$	5.36611	+	5.09987i	0.285205	+	0.271055i
$355$	−6.50268	−	11.2630i	−0.345126	−	0.597776i
$356$	−19.9332	−	4.08916i	−1.05646	−	0.216725i
$357$	17.3308	−	13.1804i	0.917244	−	0.697582i
$358$	−20.2362	+	16.5063i	−1.06952	+	0.872386i
$359$	21.5828			1.13910			0.569549	−	0.821957i	$-0.307118\pi$
$359$	21.5828			1.13910			0.569549	+	0.821957i	$0.307118\pi$
$360$	1.78127	+	8.29621i	0.0938811	+	0.437249i
$361$	−18.8673			−0.993016
$362$	3.15669	−	2.57486i	0.165912	−	0.135332i
$363$	1.16179	+	9.12766i	0.0609780	+	0.479078i
$364$	−1.23912	+	6.04025i	−0.0649473	+	0.316595i
$365$	0.123854	+	0.214521i	0.00648282	+	0.0112286i
$366$	2.62755	−	10.9087i	0.137344	−	0.570205i
$367$	12.6247	+	7.28890i	0.659006	+	0.380477i	0.791898	−	0.610653i	$-0.209093\pi$
$367$	12.6247	+	7.28890i	0.659006	+	0.380477i	−0.132892	+	0.991131i	$0.542426\pi$
$368$	−2.05632	−	17.2091i	−0.107193	−	0.897085i
$369$	−14.5765	−	4.04038i	−0.758821	−	0.210334i
$370$	−0.178952	−	0.0679651i	−0.00930329	−	0.00353334i
$371$	−26.5344	−	15.3197i	−1.37760	−	0.795357i
$372$	1.55024	−	20.4302i	0.0803764	−	1.05926i
$373$	15.3438	−	8.85872i	0.794470	−	0.458687i	−0.0470640	−	0.998892i	$-0.514986\pi$
$373$	15.3438	−	8.85872i	0.794470	−	0.458687i	0.841534	+	0.540205i	$0.181653\pi$
$374$	−24.2424	+	3.92794i	−1.25355	+	0.203109i
$375$	1.59734	+	0.669699i	0.0824864	+	0.0345831i
$376$	−1.19552	+	28.6496i	−0.0616540	+	1.47749i
$377$		−	6.61765i		−	0.340826i
$378$	−18.4230	+	11.0542i	−0.947574	+	0.568565i
$379$	−23.9357			−1.22950			−0.614748	−	0.788723i	$-0.710742\pi$
$379$	−23.9357			−1.22950			−0.614748	+	0.788723i	$0.710742\pi$
$380$	−0.691277	+	0.230051i	−0.0354618	+	0.0118014i
$381$	−10.1255	+	24.1510i	−0.518745	+	1.23729i
$382$	−11.4559	+	1.85617i	−0.586134	+	0.0949698i
$383$	11.4768	+	19.8784i	0.586437	+	1.01574i	0.994695	+	0.102872i	$0.0328031\pi$
$383$	11.4768	+	19.8784i	0.586437	+	1.01574i	−0.408258	+	0.912867i	$0.633864\pi$
$384$	18.6025	+	6.16005i	0.949306	+	0.314354i
$385$	−5.90425	+	10.2265i	−0.300908	+	0.521188i
$386$	−3.31983	+	8.74111i	−0.168975	+	0.444911i
$387$	25.8252	−	6.68242i	1.31277	−	0.339687i
$388$	13.2892	+	11.7958i	0.674658	+	0.598842i
$389$	−10.4892	+	18.1678i	−0.531823	+	0.921145i	0.467487	+	0.884000i	$0.345160\pi$
$389$	−10.4892	+	18.1678i	−0.531823	+	0.921145i	−0.999310	+	0.0371448i	$0.988174\pi$
$390$	0.604853	−	2.51113i	0.0306279	−	0.127156i
$391$	16.1338	−	9.31485i	0.815921	−	0.471072i
$392$	−3.69758	−	2.34560i	−0.186756	−	0.118471i
$393$	2.79142	−	0.355297i	0.140808	−	0.0179224i
$394$	−22.5064	−	27.5921i	−1.13385	−	1.39007i
$395$		−	12.4507i		−	0.626464i
$396$	24.2018	−	1.23212i	1.21619	−	0.0619165i
$397$		−	29.3513i		−	1.47310i	−0.676385	−	0.736549i	$-0.736454\pi$
$397$		−	29.3513i		−	1.47310i	0.676385	−	0.736549i	$-0.263546\pi$
$398$	6.49720	−	5.29965i	0.325675	−	0.265647i
$399$	−1.11668	−	1.46832i	−0.0559041	−	0.0735077i
$400$	3.20234	−	2.39688i	0.160117	−	0.119844i
$401$	1.18977	−	0.686914i	0.0594143	−	0.0343028i	−0.469999	−	0.882667i	$-0.655746\pi$
$401$	1.18977	−	0.686914i	0.0594143	−	0.0343028i	0.529413	+	0.848364i	$0.322412\pi$
$402$	−21.3248	+	22.4381i	−1.06358	+	1.11911i
$403$	−3.11845	+	5.40132i	−0.155341	+	0.269059i
$404$	−7.86616	−	6.98218i	−0.391356	−	0.347377i
$405$	7.87044	−	4.36533i	0.391086	−	0.216915i
$406$	24.2580	+	9.21305i	1.20390	+	0.457236i
$407$	−0.273345	+	0.473447i	−0.0135492	+	0.0234679i
$408$	1.78609	+	20.9879i	0.0884247	+	1.03905i
$409$	−13.9275	−	24.1231i	−0.688671	−	1.19281i	−0.972268	−	0.233869i	$-0.924861\pi$
$409$	−13.9275	−	24.1231i	−0.688671	−	1.19281i	0.283597	−	0.958943i	$-0.408472\pi$
$410$	1.14046	+	7.03871i	0.0563235	+	0.347617i
$411$	−7.02421	−	9.23607i	−0.346479	−	0.455582i
$412$	−10.1994	−	30.6481i	−0.502489	−	1.50992i
$413$	8.83620			0.434801
$414$	−16.8311	+	7.39215i	−0.827201	+	0.363304i
$415$			17.6617i			0.866979i
$416$	−4.29217	−	4.14237i	−0.210441	−	0.203096i
$417$	2.37521	+	18.6610i	0.116314	+	0.913832i
$418$	0.332786	+	2.05389i	0.0162771	+	0.100459i
$419$	2.10264	−	1.21396i	0.102720	−	0.0593057i	−0.447760	−	0.894154i	$-0.647778\pi$
$419$	2.10264	−	1.21396i	0.102720	−	0.0593057i	0.550480	+	0.834848i	$0.314445\pi$
$420$	8.36286	+	5.71316i	0.408066	+	0.278774i
$421$	2.92860	+	1.69083i	0.142731	+	0.0824058i	0.569665	−	0.821877i	$-0.307073\pi$
$421$	2.92860	+	1.69083i	0.142731	+	0.0824058i	−0.426934	+	0.904283i	$0.640406\pi$
$422$	−6.83509	+	17.9968i	−0.332727	+	0.876072i
$423$	29.4442	−	7.61886i	1.43162	−	0.370441i
$424$	26.2652	−	13.7372i	1.27555	−	0.667138i
$425$	3.72358	+	2.14981i	0.180620	+	0.104281i
$426$	9.02492	+	30.5514i	0.437259	+	1.48022i
$427$	−6.69650	−	11.5987i	−0.324066	−	0.561299i
$428$	−10.6043	−	2.17539i	−0.512576	−	0.105152i
$429$	−6.80294	−	2.85219i	−0.328449	−	0.137705i
$430$	−7.94840	−	9.74449i	−0.383306	−	0.469921i
$431$	−23.0205			−1.10886			−0.554428	−	0.832232i	$-0.687063\pi$
$431$	−23.0205			−1.10886			−0.554428	+	0.832232i	$0.687063\pi$
$432$	0.516827	−	20.7782i	0.0248658	−	0.999691i
$433$	30.0706			1.44510			0.722549	−	0.691319i	$-0.242970\pi$
$433$	30.0706			1.44510			0.722549	+	0.691319i	$0.242970\pi$
$434$	−15.4579	−	18.9509i	−0.742002	−	0.909670i
$435$	−10.0245	−	4.20284i	−0.480637	−	0.201511i
$436$	33.2267	+	6.81624i	1.59127	+	0.326439i
$437$	−0.789180	−	1.36690i	−0.0377516	−	0.0653877i
$438$	−0.171894	−	0.581900i	−0.00821342	−	0.0278043i
$439$	26.7373	+	15.4368i	1.27610	+	0.736758i	0.976129	−	0.217190i	$-0.0696892\pi$
$439$	26.7373	+	15.4368i	1.27610	+	0.736758i	0.299972	+	0.953948i	$0.403023\pi$
$440$	−5.29437	−	10.1227i	−0.252399	−	0.482580i
$441$	−1.24059	+	4.47567i	−0.0590756	+	0.213127i
$442$	2.27653	−	5.99412i	0.108284	−	0.285111i
$443$	29.2538	+	16.8897i	1.38989	+	0.802452i	0.993302	−	0.115545i	$-0.0368616\pi$
$443$	29.2538	+	16.8897i	1.38989	+	0.802452i	0.396586	+	0.917998i	$0.370195\pi$
$444$	0.387169	+	0.264498i	0.0183742	+	0.0125525i
$445$	8.81107	−	5.08707i	0.417685	−	0.241150i
$446$	−4.49318	−	27.7310i	−0.212758	−	1.31310i
$447$	−2.18086	−	17.1341i	−0.103151	−	0.810413i
$448$	21.1600	−	9.96663i	0.999718	−	0.470879i
$449$			1.82692i			0.0862178i	0.999070	+	0.0431089i	$0.0137262\pi$
$449$			1.82692i			0.0862178i	−0.999070	+	0.0431089i	$0.986274\pi$
$450$	−3.41974	−	2.51105i	−0.161208	−	0.118372i
$451$	20.3640			0.958905
$452$	−8.11455	−	24.3833i	−0.381677	−	1.14689i
$453$	−9.49212	−	12.4811i	−0.445979	−	0.586413i
$454$	0.382345	+	2.35976i	0.0179443	+	0.110749i
$455$	−1.54151	−	2.66997i	−0.0722670	−	0.125170i
$456$	1.77815	−	0.151323i	0.0832696	−	0.00708633i
$457$	4.43478	−	7.68126i	0.207450	−	0.359314i	−0.743460	−	0.668780i	$-0.766817\pi$
$457$	4.43478	−	7.68126i	0.207450	−	0.359314i	0.950911	+	0.309466i	$0.100150\pi$
$458$	−2.21642	−	0.841785i	−0.103567	−	0.0393340i
$459$	20.7494	−	8.28283i	0.968497	−	0.386610i
$460$	6.48093	+	5.75263i	0.302175	+	0.268218i
$461$	−11.9185	+	20.6435i	−0.555101	+	0.961464i	0.442794	+	0.896623i	$0.353987\pi$
$461$	−11.9185	+	20.6435i	−0.555101	+	0.961464i	−0.997896	+	0.0648406i	$0.979346\pi$
$462$	19.9262	−	20.9664i	0.927049	−	0.975446i
$463$	3.38639	−	1.95513i	0.157379	−	0.0908627i	−0.419242	−	0.907874i	$-0.637704\pi$
$463$	3.38639	−	1.95513i	0.157379	−	0.0908627i	0.576621	+	0.817012i	$0.304371\pi$
$464$	−20.0970	+	15.0421i	−0.932979	+	0.698313i
$465$	6.20145	+	8.15422i	0.287585	+	0.378143i
$466$	12.2829	−	10.0189i	0.568994	−	0.464118i
$467$		−	7.94795i		−	0.367787i	−0.982946	−	0.183894i	$-0.941130\pi$
$467$		−	7.94795i		−	0.367787i	0.982946	−	0.183894i	$-0.0588702\pi$
$468$	−2.88077	+	5.63302i	−0.133164	+	0.260386i
$469$			36.9481i			1.70610i
$470$	−9.06224	−	11.1100i	−0.418010	−	0.512467i
$471$	−11.9347	+	1.51907i	−0.549921	+	0.0699950i
$472$	−4.57903	+	7.21832i	−0.210767	+	0.332250i
$473$	−31.1017	+	17.9566i	−1.43006	+	0.825645i
$474$	−7.14174	+	29.6499i	−0.328031	+	1.36187i
$475$	0.182138	−	0.315472i	0.00835706	−	0.0144748i
$476$	18.8030	+	16.6900i	0.861834	+	0.764984i
$477$	−22.0386	−	22.4208i	−1.00908	−	1.02658i
$478$	−7.73334	+	20.3619i	−0.353715	+	0.931332i
$479$	0.402957	−	0.697941i	0.0184116	−	0.0318897i	−0.856673	−	0.515860i	$-0.827472\pi$
$479$	0.402957	−	0.697941i	0.0184116	−	0.0318897i	0.875084	+	0.483970i	$0.160806\pi$
$480$	−9.00085	+	3.87102i	−0.410831	+	0.176687i
$481$	−0.0713661	−	0.123610i	−0.00325401	−	0.00563612i
$482$	−3.69072	+	0.597998i	−0.168108	+	0.0272381i
$483$	−8.48383	+	20.2353i	−0.386027	+	0.920739i
$484$	−10.0812	+	3.35492i	−0.458235	+	0.152497i
$485$	−8.88461			−0.403429
$486$	−21.2465	+	5.88103i	−0.963761	+	0.266769i
$487$		−	32.6393i		−	1.47903i	−0.673141	−	0.739514i	$-0.735055\pi$
$487$		−	32.6393i		−	1.47903i	0.673141	−	0.739514i	$-0.264945\pi$
$488$	12.9452	+	0.540190i	0.586002	+	0.0244532i
$489$	−1.28514	−	0.538807i	−0.0581162	−	0.0243657i
$490$	2.16122	−	0.350176i	0.0976339	−	0.0158194i
$491$	−13.6946	+	7.90656i	−0.618027	+	0.356818i	−0.776101	−	0.630609i	$-0.782805\pi$
$491$	−13.6946	+	7.90656i	−0.618027	+	0.356818i	0.158073	+	0.987427i	$0.449472\pi$
$492$	1.32153	−	17.4160i	0.0595791	−	0.785175i
$493$	−23.3681	−	13.4916i	−1.05245	−	0.607631i
$494$	−0.507839	−	0.192874i	−0.0228488	−	0.00867783i
$495$	−8.64105	+	8.49374i	−0.388386	+	0.381765i
$496$	23.4915	−	2.80701i	1.05480	−	0.126038i
$497$	32.9298	+	19.0120i	1.47710	+	0.852806i
$498$	10.1308	−	42.0593i	0.453970	−	1.88472i
$499$	11.2864	+	19.5486i	0.505248	+	0.875115i	0.999982	+	0.00607044i	$0.00193229\pi$
$499$	11.2864	+	19.5486i	0.505248	+	0.875115i	−0.494734	+	0.869045i	$0.664734\pi$
$500$	−0.401917	+	1.95920i	−0.0179743	+	0.0876181i
$501$	0.819973	+	6.44218i	0.0366337	+	0.287815i
$502$	11.0598	−	9.02128i	0.493623	−	0.402639i
$503$	−6.34768			−0.283029			−0.141515	−	0.989936i	$-0.545197\pi$
$503$	−6.34768			−0.283029			−0.141515	+	0.989936i	$0.545197\pi$
$504$	−16.6381	−	18.4022i	−0.741120	−	0.819698i
$505$	5.25898			0.234021
$506$	19.1778	−	15.6430i	0.852557	−	0.695415i
$507$	−16.3895	+	12.4645i	−0.727881	+	0.553568i
$508$	−29.6221	−	6.07677i	−1.31427	−	0.269613i
$509$	−5.97444	−	10.3480i	−0.264812	−	0.458668i	0.702702	−	0.711484i	$-0.251977\pi$
$509$	−5.97444	−	10.3480i	−0.264812	−	0.458668i	−0.967514	+	0.252816i	$0.918643\pi$
$510$	−7.63413	−	7.25536i	−0.338045	−	0.321273i
$511$	−0.627201	−	0.362115i	−0.0277457	−	0.0160190i
$512$	−2.82363	+	22.4505i	−0.124788	+	0.992183i
$513$	−0.701745	−	1.75794i	−0.0309828	−	0.0776151i
$514$	28.5236	+	10.8331i	1.25812	+	0.477828i
$515$	13.9866	+	8.07516i	0.616323	+	0.355834i
$516$	13.3387	+	27.7646i	0.587206	+	1.22227i
$517$	−35.4601	+	20.4729i	−1.55953	+	0.900398i
$518$	0.552466	−	0.0895146i	0.0242740	−	0.00393304i
$519$	−25.5195	+	19.4081i	−1.12018	+	0.851922i
$520$	2.97994	+	0.124350i	0.130679	+	0.00545309i
$521$		−	9.35220i		−	0.409727i	−0.978791	−	0.204864i	$-0.934325\pi$
$521$		−	9.35220i		−	0.409727i	0.978791	−	0.204864i	$-0.0656751\pi$
$522$	21.4613	+	15.7586i	0.939338	+	0.689736i
$523$	23.6543			1.03433			0.517164	−	0.855886i	$-0.326988\pi$
$523$	23.6543			1.03433			0.517164	+	0.855886i	$0.326988\pi$
$524$	1.02600	+	3.08302i	0.0448211	+	0.134682i
$525$	−5.02350	+	0.639402i	−0.219244	+	0.0279058i
$526$	29.7010	−	4.81237i	1.29502	−	0.209829i
$527$	12.7154	+	22.0237i	0.553890	+	0.959366i
$528$	6.80155	+	27.1428i	0.295999	+	1.18124i
$529$	2.11310	−	3.66000i	0.0918741	−	0.159131i
$530$	−5.26196	+	13.8548i	−0.228565	+	0.601812i
$531$	8.73730	+	2.42185i	0.379166	+	0.105099i
$532$	1.41402	−	1.59304i	0.0613056	−	0.0690672i
$533$	−2.65837	+	4.60443i	−0.115147	+	0.199440i
$534$	−23.9005	+	7.06023i	−1.03427	+	0.305526i
$535$	4.68741	−	2.70627i	0.202654	−	0.117002i
$536$	−30.1830	−	19.1470i	−1.30371	−	0.827023i
$537$	−12.3665	+	29.4960i	−0.533652	+	1.27285i
$538$	22.1822	+	27.1947i	0.956345	+	1.17245i
$539$		−	6.25272i		−	0.269324i
$540$	6.70338	+	7.94133i	0.288468	+	0.341740i
$541$			11.4118i			0.490630i	0.969443	+	0.245315i	$0.0788915\pi$
$541$			11.4118i			0.490630i	−0.969443	+	0.245315i	$0.921109\pi$
$542$	−0.982969	+	0.801790i	−0.0422221	+	0.0344398i
$543$	1.92907	−	4.60115i	0.0827844	−	0.197454i
$544$	−23.3781	+	6.71127i	−1.00233	+	0.287744i
$545$	−14.6872	+	8.47967i	−0.629131	+	0.363229i
$546$	2.13943	+	7.24243i	0.0915589	+	0.309948i
$547$	0.605841	−	1.04935i	0.0259039	−	0.0448669i	−0.852783	−	0.522266i	$-0.825087\pi$
$547$	0.605841	−	1.04935i	0.0259039	−	0.0448669i	0.878687	+	0.477399i	$0.158420\pi$
$548$	8.89455	−	10.0206i	0.379956	−	0.428060i
$549$	−3.44255	−	13.3042i	−0.146925	−	0.567812i
$550$	5.33967	+	2.02798i	0.227684	+	0.0864732i
$551$	−1.14305	+	1.97981i	−0.0486954	+	0.0843429i
$552$	−12.1339	−	17.4167i	−0.516452	−	0.741303i
$553$	18.2012	+	31.5254i	0.773995	+	1.34060i
$554$	5.60772	+	34.6097i	0.238249	+	1.47043i
$555$	−0.232569	+	0.0296019i	−0.00987202	+	0.00125653i
$556$	−20.6104	+	6.85895i	−0.874074	+	0.290884i
$557$	31.9445			1.35353			0.676766	−	0.736198i	$-0.263381\pi$
$557$	31.9445			1.35353			0.676766	+	0.736198i	$0.263381\pi$
$558$	−10.0908	−	22.9755i	−0.427176	−	0.972629i
$559$		−	9.37638i		−	0.396579i
$560$	−4.60448	+	10.7503i	−0.194575	+	0.454283i
$561$	−23.9410	+	18.2076i	−1.01079	+	0.768725i
$562$	7.03585	+	43.4239i	0.296790	+	1.83173i
$563$	10.3050	−	5.94959i	0.434304	−	0.250745i	−0.266875	−	0.963731i	$-0.585991\pi$
$563$	10.3050	−	5.94959i	0.434304	−	0.250745i	0.701178	+	0.712986i	$0.252658\pi$
$564$	15.2080	+	31.6553i	0.640370	+	1.33293i
$565$	11.1276	+	6.42452i	0.468142	+	0.270282i
$566$	9.10793	−	23.9812i	0.382835	−	1.00801i
$567$	−13.5466	+	22.5586i	−0.568903	+	0.947371i
$568$	−32.5956	+	17.0482i	−1.36768	+	0.715326i
$569$	8.34728	+	4.81931i	0.349936	+	0.202036i	0.664657	−	0.747148i	$-0.268578\pi$
$569$	8.34728	+	4.81931i	0.349936	+	0.202036i	−0.314721	+	0.949184i	$0.601911\pi$
$570$	−0.614695	+	0.646785i	−0.0257467	+	0.0270908i
$571$	2.64943	+	4.58894i	0.110875	+	0.192041i	0.916123	−	0.400897i	$-0.131301\pi$
$571$	2.64943	+	4.58894i	0.110875	+	0.192041i	−0.805248	+	0.592938i	$0.797968\pi$
$572$	1.71173	−	8.34406i	0.0715709	−	0.348883i
$573$	−11.3134	+	8.60409i	−0.472625	+	0.359441i
$574$	−13.1773	−	16.1549i	−0.550009	−	0.674294i
$575$	−4.33287			−0.180693
$576$	23.6549	−	4.05548i	0.985620	−	0.168978i
$577$	20.7215			0.862647			0.431324	−	0.902197i	$-0.358047\pi$
$577$	20.7215			0.862647			0.431324	+	0.902197i	$0.358047\pi$
$578$	−1.32895	−	1.62925i	−0.0552772	−	0.0677681i
$579$	1.44594	+	11.3601i	0.0600910	+	0.472109i
$580$	2.52232	−	12.2954i	0.104733	−	0.510538i
$581$	−25.8189	−	44.7197i	−1.07115	−	1.85529i
$582$	21.1576	+	5.09621i	0.877013	+	0.211245i
$583$	36.6549	+	21.1627i	1.51809	+	0.876471i
$584$	0.620836	−	0.324710i	0.0256904	−	0.0134366i
$585$	−0.792463	−	3.06259i	−0.0327643	−	0.126622i
$586$	−6.58472	+	17.3376i	−0.272012	+	0.716209i
$587$	−10.4960	−	6.05987i	−0.433216	−	0.250117i	0.267500	−	0.963558i	$-0.413803\pi$
$587$	−10.4960	−	6.05987i	−0.433216	−	0.250117i	−0.700716	+	0.713440i	$0.747136\pi$
$588$	−5.34755	−	0.405772i	−0.220529	−	0.0167337i
$589$	1.86591	−	1.07728i	0.0768833	−	0.0443886i
$590$	−0.683606	−	4.21908i	−0.0281436	−	0.173697i
$591$	−40.2178	−	16.8617i	−1.65434	−	0.693596i
$592$	−0.213170	+	0.497699i	−0.00876124	+	0.0204553i
$593$		−	5.54175i		−	0.227572i	−0.993505	−	0.113786i	$-0.963702\pi$
$593$		−	5.54175i		−	0.227572i	0.993505	−	0.113786i	$-0.0362979\pi$
$594$	25.4497	−	15.2703i	1.04421	−	0.626549i
$595$	−12.5709			−0.515356
$596$	18.9239	−	6.29772i	0.775154	−	0.257965i
$597$	3.97047	−	9.47022i	0.162501	−	0.387590i
$598$	1.03346	+	6.37829i	0.0422612	+	0.260827i
$599$	−9.19965	−	15.9343i	−0.375887	−	0.651056i	0.614572	−	0.788861i	$-0.289329\pi$
$599$	−9.19965	−	15.9343i	−0.375887	−	0.651056i	−0.990459	+	0.137805i	$0.955995\pi$
$600$	2.08091	−	4.43506i	0.0849530	−	0.181061i
$601$	22.9342	−	39.7232i	0.935506	−	1.62034i	0.161776	−	0.986828i	$-0.448278\pi$
$601$	22.9342	−	39.7232i	0.935506	−	1.62034i	0.773730	−	0.633516i	$-0.218389\pi$
$602$	34.3706	+	13.0538i	1.40084	+	0.532031i
$603$	−10.1268	+	36.5345i	−0.412396	+	1.48780i
$604$	12.0196	−	13.5413i	0.489070	−	0.550988i
$605$	2.65619	−	4.60065i	0.107989	−	0.187043i
$606$	−12.5236	−	3.01655i	−0.508738	−	0.122539i
$607$	−10.6441	+	6.14536i	−0.432030	+	0.249432i	−0.700211	−	0.713936i	$-0.746911\pi$
$607$	−10.6441	+	6.14536i	−0.432030	+	0.249432i	0.268181	+	0.963368i	$0.413577\pi$
$608$	0.568598	+	1.98065i	0.0230597	+	0.0803262i
$609$	31.5261	−	4.01270i	1.27750	−	0.162603i
$610$	−5.02003	+	4.09474i	−0.203255	+	0.165791i
$611$		−	10.6903i		−	0.432485i
$612$	14.0181	+	21.6567i	0.566648	+	0.875422i
$613$		−	18.1135i		−	0.731596i	−0.930694	−	0.365798i	$-0.880796\pi$
$613$		−	18.1135i		−	0.731596i	0.930694	−	0.365798i	$-0.119204\pi$
$614$	1.04410	+	1.28004i	0.0421365	+	0.0516580i
$615$	5.28651	+	6.95118i	0.213173	+	0.280299i
$616$	28.2034	+	17.8912i	1.13635	+	0.720855i
$617$	−26.2714	+	15.1678i	−1.05765	+	0.610633i	−0.924781	−	0.380501i	$-0.875752\pi$
$617$	−26.2714	+	15.1678i	−1.05765	+	0.610633i	−0.132867	+	0.991134i	$0.542418\pi$
$618$	−28.6755	−	27.2528i	−1.15350	−	1.09627i
$619$	−11.7414	+	20.3367i	−0.471927	+	0.817401i	−0.999484	−	0.0321183i	$-0.989775\pi$
$619$	−11.7414	+	20.3367i	−0.471927	+	0.817401i	0.527557	+	0.849519i	$0.323108\pi$
$620$	−7.85270	+	8.84689i	−0.315372	+	0.355300i
$621$	−13.9350	+	17.6836i	−0.559193	+	0.709616i
$622$	−1.85727	+	4.89020i	−0.0744697	+	0.196079i
$623$	−14.8732	+	25.7611i	−0.595881	+	1.03210i
$624$	−7.02505	−	2.00542i	−0.281227	−	0.0802810i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	33.9648	−	5.50322i	1.35751	−	0.219953i
$627$	1.54260	+	2.02835i	0.0616054	+	0.0810044i
$628$	−4.38665	−	13.1814i	−0.175047	−	0.525995i
$629$	−0.581985			−0.0232052
$630$	12.3296	+	1.35882i	0.491225	+	0.0541369i
$631$		−	17.8252i		−	0.709608i	−0.934941	−	0.354804i	$-0.884548\pi$
$631$		−	17.8252i		−	0.709608i	0.934941	−	0.354804i	$-0.115452\pi$
$632$	−35.1854	−	1.46825i	−1.39960	−	0.0584037i
$633$	2.97699	+	23.3890i	0.118325	+	0.929628i
$634$	−15.9285	+	2.58084i	−0.632600	+	0.102498i
$635$	13.0939	−	7.55974i	0.519614	−	0.299999i
$636$	20.4778	−	29.9752i	0.811999	−	1.18859i
$637$	1.41378	+	0.816246i	0.0560160	+	0.0323408i
$638$	−33.5103	−	12.7270i	−1.32668	−	0.503867i
$639$	27.3503	+	27.8247i	1.08196	+	1.10073i
$640$	−6.39586	−	9.33236i	−0.252819	−	0.368894i
$641$	−3.35938	−	1.93954i	−0.132687	−	0.0766071i	0.432187	−	0.901784i	$-0.357742\pi$
$641$	−3.35938	−	1.93954i	−0.132687	−	0.0766071i	−0.564874	+	0.825177i	$0.691075\pi$
$642$	−12.7148	+	3.75598i	−0.501814	+	0.148237i
$643$	−18.9015	−	32.7384i	−0.745402	−	1.29107i	−0.950007	−	0.312230i	$-0.898924\pi$
$643$	−18.9015	−	32.7384i	−0.745402	−	1.29107i	0.204604	−	0.978845i	$-0.434409\pi$
$644$	−24.8194	−	5.09152i	−0.978020	−	0.200634i
$645$	−14.2034	−	5.95491i	−0.559260	−	0.234474i
$646$	−1.71642	+	1.40005i	−0.0675317	+	0.0550844i
$647$	−11.5383			−0.453617			−0.226808	−	0.973939i	$-0.572829\pi$
$647$	−11.5383			−0.453617			−0.226808	+	0.973939i	$0.572829\pi$
$648$	−11.4082	−	22.7564i	−0.448155	−	0.893956i
$649$	−12.2064			−0.479144
$650$	−1.15559	+	0.942594i	−0.0453260	+	0.0369716i
$651$	−27.6225	−	11.5810i	−1.08261	−	0.453894i
$652$	0.323362	−	1.57628i	0.0126639	−	0.0617317i
$653$	10.9218	+	18.9171i	0.427402	+	0.740283i	0.996641	−	0.0818895i	$-0.0260955\pi$
$653$	10.9218	+	18.9171i	0.427402	+	0.740283i	−0.569239	+	0.822172i	$0.692762\pi$
$654$	39.8398	−	11.7687i	1.55786	−	0.460194i
$655$	−1.40697	−	0.812314i	−0.0549748	−	0.0317397i
$656$	20.0257	−	2.39288i	0.781871	−	0.0934261i
$657$	−0.520931	−	0.529966i	−0.0203235	−	0.0206759i
$658$	39.1871	+	14.8830i	1.52767	+	0.580201i
$659$	29.9390	+	17.2853i	1.16626	+	0.673340i	0.952796	−	0.303612i	$-0.0981925\pi$
$659$	29.9390	+	17.2853i	1.16626	+	0.673340i	0.213463	+	0.976951i	$0.431526\pi$
$660$	−11.5525	−	7.89222i	−0.449682	−	0.307204i
$661$	−19.4050	+	11.2035i	−0.754766	+	0.435764i	−0.827413	−	0.561593i	$-0.810189\pi$
$661$	−19.4050	+	11.2035i	−0.754766	+	0.435764i	0.0726475	+	0.997358i	$0.476855\pi$
$662$	33.9465	−	5.50027i	1.31937	−	0.213774i
$663$	−0.991534	−	7.79006i	−0.0385080	−	0.302541i
$664$	49.9114	+	2.08275i	1.93694	+	0.0808263i
$665$			1.06504i			0.0413005i
$666$	0.570816	+	0.0629085i	0.0221187	+	0.00243765i
$667$	27.1919			1.05287
$668$	−7.11514	+	2.36786i	−0.275293	+	0.0916152i
$669$	−20.8277	−	27.3861i	−0.805246	−	1.05881i
$670$	17.6418	−	2.85846i	0.681563	−	0.110432i
$671$	9.25062	+	16.0225i	0.357116	+	0.618543i
$672$	17.1314	−	22.9595i	0.660858	−	0.885680i
$673$	−8.60595	+	14.9059i	−0.331735	+	0.574582i	−0.982852	−	0.184396i	$-0.940967\pi$
$673$	−8.60595	+	14.9059i	−0.331735	+	0.574582i	0.651117	+	0.758977i	$0.274301\pi$
$674$	14.1504	−	37.2582i	0.545055	−	1.43513i
$675$	−5.14252	−	0.744609i	−0.197936	−	0.0286600i
$676$	−17.7817	−	15.7834i	−0.683910	−	0.607055i
$677$	10.0668	−	17.4362i	0.386897	−	0.670126i	−0.605133	−	0.796124i	$-0.706880\pi$
$677$	10.0668	−	17.4362i	0.386897	−	0.670126i	0.992030	+	0.125998i	$0.0402134\pi$
$678$	−22.8140	−	21.6820i	−0.876165	−	0.832694i
$679$	22.4960	−	12.9881i	0.863316	−	0.498436i
$680$	6.51439	−	10.2692i	0.249815	−	0.393806i
$681$	1.77233	+	2.33041i	0.0679157	+	0.0893016i
$682$	21.3537	+	26.1789i	0.817674	+	1.00244i
$683$			23.7521i			0.908847i	0.890786	+	0.454424i	$0.150155\pi$
$683$			23.7521i			0.908847i	−0.890786	+	0.454424i	$0.849845\pi$
$684$	1.83482	−	1.18765i	0.0701561	−	0.0454111i
$685$			6.69937i			0.255970i
$686$	17.4680	−	14.2484i	0.666933	−	0.544005i
$687$	−2.88050	+	0.366636i	−0.109898	+	0.0139880i
$688$	−28.4749	+	21.3128i	−1.08560	+	0.812544i
$689$	−9.57004	+	5.52527i	−0.364590	+	0.210496i
$690$	10.3182	+	2.48534i	0.392808	+	0.0946152i
$691$	2.45571	−	4.25341i	0.0934195	−	0.161807i	−0.815528	−	0.578717i	$-0.803554\pi$
$691$	2.45571	−	4.25341i	0.0934195	−	0.161807i	0.908948	+	0.416910i	$0.136887\pi$
$692$	−27.6873	−	24.5759i	−1.05251	−	0.934236i
$693$	9.46262	−	34.1383i	0.359455	−	1.29681i
$694$	−18.0142	−	6.84169i	−0.683809	−	0.259707i
$695$	5.43042	−	9.40577i	0.205988	−	0.356781i
$696$	−13.0592	+	27.8332i	−0.495009	+	1.05502i
$697$	10.8394	+	18.7744i	0.410571	+	0.711131i
$698$	3.65058	+	22.5306i	0.138177	+	0.852798i
$699$	7.50615	−	17.9034i	0.283908	−	0.677168i
$700$	−1.84642	−	5.54827i	−0.0697880	−	0.209705i
$701$	16.9444			0.639982			0.319991	−	0.947421i	$-0.396320\pi$
$701$	16.9444			0.639982			0.319991	+	0.947421i	$0.396320\pi$
$702$	0.130456	+	7.74775i	0.00492374	+	0.292420i
$703$			0.0493074i			0.00185966i
$704$	−29.2307	+	13.7680i	−1.10167	+	0.518901i
$705$	−16.1938	−	6.78939i	−0.609894	−	0.255703i
$706$	−7.29503	−	45.0235i	−0.274552	−	1.69448i
$707$	−13.3158	+	7.68789i	−0.500793	+	0.289133i
$708$	−0.792138	+	10.4394i	−0.0297704	+	0.392335i
$709$	−5.51221	−	3.18248i	−0.207015	−	0.119520i	0.392908	−	0.919578i	$-0.371469\pi$
$709$	−5.51221	−	3.18248i	−0.207015	−	0.119520i	−0.599924	+	0.800057i	$0.704802\pi$
$710$	6.53020	−	17.1940i	0.245074	−	0.645281i
$711$	9.35693	+	36.1612i	0.350912	+	1.35615i
$712$	−13.3369	−	25.4997i	−0.499820	−	0.955641i
$713$	−22.1940	−	12.8137i	−0.831172	−	0.479877i
$714$	29.9361	+	7.21066i	1.12033	+	0.269852i
$715$	2.12946	+	3.68833i	0.0796372	+	0.137936i
$716$	−36.1780	−	7.42167i	−1.35203	−	0.277361i
$717$	3.36822	+	26.4627i	0.125789	+	0.988267i
$718$	19.2927	+	23.6522i	0.719997	+	0.882694i
$719$	−0.0181272			−0.000676031			−0.000338016	−	1.00000i	$-0.500108\pi$
$719$	−0.0181272			−0.000676031			−0.000338016		1.00000i	$0.500108\pi$
$720$	−7.49941	+	9.36797i	−0.279486	+	0.349124i
$721$	−47.2190			−1.75853
$722$	−16.8653	−	20.6763i	−0.627662	−	0.769494i
$723$	−3.64483	+	2.77196i	−0.135553	+	0.103090i
$724$	5.64348	+	1.15772i	0.209738	+	0.0430264i
$725$	3.13786	+	5.43493i	0.116537	+	0.201848i
$726$	−8.96433	+	9.43232i	−0.332698	+	0.350066i
$727$	−12.7706	−	7.37313i	−0.473637	−	0.273454i	0.244124	−	0.969744i	$-0.421500\pi$
$727$	−12.7706	−	7.37313i	−0.473637	−	0.273454i	−0.717761	+	0.696290i	$0.754833\pi$
$728$	−7.72704	+	4.04140i	−0.286383	+	0.149784i
$729$	−19.5779	+	18.5932i	−0.725106	+	0.688637i
$730$	−0.124378	+	0.327488i	−0.00460345	+	0.0121209i
$731$	−33.1097	−	19.1159i	−1.22461	−	0.707027i
$732$	14.3034	−	6.87166i	0.528667	−	0.253984i
$733$	6.30705	−	3.64138i	0.232956	−	0.134497i	−0.378979	−	0.925405i	$-0.623725\pi$
$733$	6.30705	−	3.64138i	0.232956	−	0.134497i	0.611935	+	0.790908i	$0.290391\pi$
$734$	3.29737	+	20.3507i	0.121708	+	0.751159i
$735$	2.13434	−	1.62321i	0.0787264	−	0.0598730i
$736$	17.0210	−	17.6365i	0.627402	−	0.650091i
$737$		−	51.0404i		−	1.88010i
$738$	−8.60201	−	19.5858i	−0.316644	−	0.720962i
$739$	−23.7284			−0.872863			−0.436431	−	0.899737i	$-0.643758\pi$
$739$	−23.7284			−0.872863			−0.436431	+	0.899737i	$0.643758\pi$
$740$	−0.0854822	−	0.256864i	−0.00314239	−	0.00944252i
$741$	−0.659996	+	0.0840056i	−0.0242456	+	0.00308602i
$742$	−6.93035	−	42.7727i	−0.254421	−	1.57024i
$743$	−12.6970	−	21.9919i	−0.465809	−	0.806805i	0.533429	−	0.845845i	$-0.320903\pi$
$743$	−12.6970	−	21.9919i	−0.465809	−	0.806805i	−0.999238	+	0.0390402i	$0.987570\pi$
$744$	23.7749	−	16.5635i	0.871629	−	0.607248i
$745$	−4.98608	+	8.63615i	−0.182676	+	0.316404i
$746$	23.4238	+	8.89622i	0.857605	+	0.325714i
$747$	−13.2731	−	51.2957i	−0.485636	−	1.87681i
$748$	−25.9747	−	23.0557i	−0.949727	−	0.843000i
$749$	−7.91239	+	13.7047i	−0.289112	+	0.500758i
$750$	0.693939	+	2.34914i	0.0253391	+	0.0857784i
$751$	11.7844	−	6.80374i	0.430020	−	0.248272i	−0.269335	−	0.963046i	$-0.586804\pi$
$751$	11.7844	−	6.80374i	0.430020	−	0.248272i	0.699355	+	0.714774i	$0.253471\pi$
$752$	−32.4652	+	24.2995i	−1.18389	+	0.886110i
$753$	6.75870	−	16.1206i	0.246301	−	0.587467i
$754$	7.25216	−	5.91546i	0.264108	−	0.215428i
$755$			9.05314i			0.329477i
$756$	−28.5822	−	10.3082i	−1.03952	−	0.374905i
$757$			6.31857i			0.229652i	0.993386	+	0.114826i	$0.0366311\pi$
$757$			6.31857i			0.229652i	−0.993386	+	0.114826i	$0.963369\pi$
$758$	−21.3960	−	26.2308i	−0.777136	−	0.952744i
$759$	11.7196	−	27.9533i	0.425396	−	1.01464i
$760$	−0.870035	−	0.551918i	−0.0315595	−	0.0200202i
$761$	29.3655	−	16.9542i	1.06450	−	0.614588i	0.137825	−	0.990457i	$-0.455989\pi$
$761$	29.3655	−	16.9542i	1.06450	−	0.614588i	0.926673	+	0.375869i	$0.122656\pi$
$762$	−35.5177	+	10.4920i	−1.28667	+	0.380085i
$763$	24.7922	−	42.9413i	0.897537	−	1.55458i
$764$	−12.2745	−	10.8951i	−0.444074	−	0.394171i
$765$	−12.4302	−	3.44546i	−0.449414	−	0.124571i
$766$	−11.5254	+	30.3463i	−0.416429	+	1.09646i
$767$	1.59345	−	2.75994i	0.0575363	−	0.0996558i
$768$	9.87795	+	25.8926i	0.356440	+	0.934318i
$769$	−11.8841	−	20.5839i	−0.428551	−	0.742273i	0.568193	−	0.822895i	$-0.307643\pi$
$769$	−11.8841	−	20.5839i	−0.428551	−	0.742273i	−0.996745	+	0.0806224i	$0.974309\pi$
$770$	−16.4847	+	2.67098i	−0.594069	+	0.0962554i
$771$	37.0698	−	4.71831i	1.33504	−	0.169926i
$772$	−12.5468	+	4.17547i	−0.451569	+	0.150278i
$773$	5.04180			0.181341			0.0906705	−	0.995881i	$-0.471099\pi$
$773$	5.04180			0.181341			0.0906705	+	0.995881i	$0.471099\pi$
$774$	30.4081	+	22.3280i	1.09300	+	0.802564i
$775$		−	5.91465i		−	0.212461i
$776$	−1.04771	+	25.1076i	−0.0376107	+	0.901311i
$777$	0.545596	−	0.414937i	0.0195731	−	0.0148858i
$778$	−29.2860	+	4.74513i	−1.04995	+	0.170121i
$779$	1.59062	−	0.918344i	0.0569898	−	0.0329031i
$780$	3.29258	−	1.58183i	0.117893	−	0.0566386i
$781$	−45.4895	−	26.2634i	−1.62774	−	0.939778i
$782$	24.6298	+	9.35427i	0.880761	+	0.334508i
$783$	32.2730	+	4.67295i	1.15334	+	0.166998i
$784$	−0.734726	−	6.14883i	−0.0262402	−	0.219601i
$785$	6.01548	+	3.47304i	0.214702	+	0.123958i
$786$	2.88459	+	2.74147i	0.102890	+	0.0977850i
$787$	1.59165	+	2.75681i	0.0567361	+	0.0982698i	0.892998	−	0.450060i	$-0.148597\pi$
$787$	1.59165	+	2.75681i	0.0567361	+	0.0982698i	−0.836262	+	0.548330i	$0.815264\pi$
$788$	10.1194	−	49.3286i	0.360490	−	1.75726i
$789$	29.3316	−	22.3073i	1.04423	−	0.794160i
$790$	13.6445	−	11.1296i	0.485451	−	0.395973i
$791$	−37.5670			−1.33573
$792$	22.9840	+	25.4209i	0.816702	+	0.903294i
$793$	−4.83039			−0.171532
$794$	32.1655	−	26.2368i	1.14151	−	0.931110i
$795$	2.29182	+	18.0059i	0.0812826	+	0.638602i
$796$	11.6156	+	2.38286i	0.411703	+	0.0844581i
$797$	8.78019	+	15.2077i	0.311010	+	0.538686i	0.978581	−	0.205861i	$-0.0659993\pi$
$797$	8.78019	+	15.2077i	0.311010	+	0.538686i	−0.667571	+	0.744546i	$0.732666\pi$
$798$	0.610908	−	2.53627i	0.0216259	−	0.0897829i
$799$	−37.7495	−	21.7947i	−1.33548	−	0.771041i
$800$	5.48924	+	1.36684i	0.194074	+	0.0483251i
$801$	−21.7674	+	21.3963i	−0.769112	+	0.756001i
$802$	1.81630	+	0.689822i	0.0641359	+	0.0243584i
$803$	0.866422	+	0.500229i	0.0305754	+	0.0176527i
$804$	−43.6516	−	3.31228i	−1.53947	−	0.116815i
$805$	10.9709	−	6.33406i	0.386674	−	0.223246i
$806$	−8.70677	+	1.41073i	−0.306683	+	0.0496910i
$807$	39.6387	+	16.6188i	1.39535	+	0.585011i
$808$	0.620162	−	14.8617i	0.0218172	−	0.522833i
$809$			6.88515i			0.242069i	0.992648	+	0.121034i	$0.0386212\pi$
$809$			6.88515i			0.242069i	−0.992648	+	0.121034i	$0.961379\pi$
$810$	11.8192	+	4.72295i	0.415285	+	0.165948i
$811$	−26.3752			−0.926160			−0.463080	−	0.886317i	$-0.653256\pi$
$811$	−26.3752			−0.926160			−0.463080	+	0.886317i	$0.653256\pi$
$812$	11.5876	+	34.8194i	0.406645	+	1.22192i
$813$	−0.600698	+	1.43276i	−0.0210674	+	0.0502491i
$814$	−0.763182	+	0.123656i	−0.0267495	+	0.00433415i
$815$	0.402276	+	0.696762i	0.0140911	+	0.0244065i
$816$	−21.4037	+	20.7182i	−0.749278	+	0.725283i
$817$	−1.61955	+	2.80515i	−0.0566610	+	0.0981398i
$818$	13.9865	−	36.8264i	0.489025	−	1.28760i
$819$	6.48360	+	6.59605i	0.226555	+	0.230485i
$820$	−6.69415	+	7.54166i	−0.233770	+	0.263366i
$821$	3.14194	−	5.44201i	0.109655	−	0.189927i	−0.805976	−	0.591949i	$-0.798359\pi$
$821$	3.14194	−	5.44201i	0.109655	−	0.189927i	0.915630	+	0.402021i	$0.131692\pi$
$822$	3.84276	−	15.9538i	0.134032	−	0.556451i
$823$	−3.73129	+	2.15426i	−0.130065	+	0.0750928i	−0.563621	−	0.826034i	$-0.690592\pi$
$823$	−3.73129	+	2.15426i	−0.130065	+	0.0750928i	0.433556	+	0.901127i	$0.357259\pi$
$824$	24.4695	−	38.5734i	0.852436	−	1.34377i
$825$	6.93952	−	0.883276i	0.241603	−	0.0307517i
$826$	7.89860	+	9.68343i	0.274827	+	0.336930i
$827$		−	11.0709i		−	0.384973i	−0.981300	−	0.192486i	$-0.938345\pi$
$827$		−	11.0709i		−	0.384973i	0.981300	−	0.192486i	$-0.0616551\pi$
$828$	−23.1461	−	11.8371i	−0.804381	−	0.411367i
$829$		−	0.854258i		−	0.0296696i	−0.999890	−	0.0148348i	$-0.995278\pi$
$829$		−	0.854258i		−	0.0296696i	0.999890	−	0.0148348i	$-0.00472224\pi$
$830$	−19.3551	+	15.7876i	−0.671827	+	0.547997i
$831$	25.9941	+	34.1793i	0.901724	+	1.18567i
$832$	0.702816	−	8.40655i	0.0243658	−	0.291445i
$833$	5.76463	−	3.32821i	0.199732	−	0.115316i
$834$	−18.3271	+	19.2838i	−0.634614	+	0.667745i
$835$	1.87470	−	3.24708i	0.0648767	−	0.112370i
$836$	−1.95334	+	2.20065i	−0.0675578	+	0.0761109i
$837$	−24.1392	−	19.0222i	−0.834372	−	0.657503i
$838$	3.20988	+	1.21910i	0.110884	+	0.0421130i
$839$	18.5397	−	32.1117i	0.640061	−	1.10862i	−0.345357	−	0.938471i	$-0.612242\pi$
$839$	18.5397	−	32.1117i	0.640061	−	1.10862i	0.985419	−	0.170147i	$-0.0544244\pi$
$840$	1.21453	+	14.2717i	0.0419054	+	0.492419i
$841$	−5.19232	−	8.99336i	−0.179046	−	0.310116i
$842$	0.764900	+	4.72081i	0.0263602	+	0.162690i
$843$	32.6141	+	42.8839i	1.12329	+	1.47700i
$844$	−25.8322	+	8.59674i	−0.889182	+	0.295912i
$845$	11.8881			0.408962
$846$	34.6693	+	25.4569i	1.19195	+	0.875227i
$847$			15.5319i			0.533682i
$848$	38.5326	+	16.5039i	1.32321	+	0.566748i
$849$	−3.96692	−	31.1664i	−0.136144	−	1.06963i
$850$	0.972536	+	6.00230i	0.0333577	+	0.205877i
$851$	0.507912	−	0.293243i	0.0174110	−	0.0100522i
$852$	−25.4134	+	37.1999i	−0.870650	+	1.27445i
$853$	22.2849	+	12.8662i	0.763021	+	0.440531i	0.830379	−	0.557198i	$-0.188124\pi$
$853$	22.2849	+	12.8662i	0.763021	+	0.440531i	−0.0673581	+	0.997729i	$0.521457\pi$
$854$	6.72485	−	17.7065i	0.230119	−	0.605905i
$855$	−0.291909	+	1.05312i	−0.00998307	+	0.0360159i
$856$	−7.09509	−	13.5656i	−0.242505	−	0.463662i
$857$	14.1759	+	8.18448i	0.484241	+	0.279576i	0.722182	−	0.691703i	$-0.243139\pi$
$857$	14.1759	+	8.18448i	0.484241	+	0.279576i	−0.237941	+	0.971279i	$0.576473\pi$
$858$	−2.95542	−	10.0048i	−0.100897	−	0.341557i
$859$	10.1591	+	17.5961i	0.346625	+	0.600372i	0.985648	−	0.168816i	$-0.0539944\pi$
$859$	10.1591	+	17.5961i	0.346625	+	0.600372i	−0.639023	+	0.769188i	$0.720661\pi$
$860$	3.57381	−	17.4210i	0.121866	−	0.594052i
$861$	−23.5472	−	9.87236i	−0.802486	−	0.336449i
$862$	−20.5778	−	25.2277i	−0.700882	−	0.859259i
$863$	−27.0979			−0.922425			−0.461212	−	0.887290i	$-0.652585\pi$
$863$	−27.0979			−0.922425			−0.461212	+	0.887290i	$0.652585\pi$
$864$	23.2324	−	18.0071i	0.790383	−	0.612612i
$865$	18.5106			0.629378
$866$	26.8798	+	32.9538i	0.913413	+	1.11982i
$867$	−2.37478	−	0.995646i	−0.0806517	−	0.0338139i
$868$	6.95026	−	33.8800i	0.235907	−	1.14996i
$869$	−25.1434	−	43.5496i	−0.852930	−	1.47732i
$870$	−4.35496	−	14.7425i	−0.147647	−	0.499819i
$871$	11.5406	+	6.66294i	0.391037	+	0.225765i
$872$	22.2313	+	42.5056i	0.752846	+	1.43942i
$873$	25.8040	−	6.67693i	0.873332	−	0.225980i
$874$	0.792521	−	2.08671i	0.0268074	−	0.0705840i
$875$	2.53202	+	1.46186i	0.0855978	+	0.0494199i
$876$	0.484040	−	0.708531i	0.0163542	−	0.0239391i
$877$	−24.1219	+	13.9268i	−0.814539	+	0.470274i	−0.848529	−	0.529148i	$-0.822512\pi$
$877$	−24.1219	+	13.9268i	−0.814539	+	0.470274i	0.0339909	+	0.999422i	$0.489178\pi$
$878$	6.98334	+	43.0997i	0.235676	+	1.45455i
$879$	2.86795	+	22.5322i	0.0967334	+	0.759993i
$880$	6.36067	−	14.8506i	0.214418	−	0.500613i
$881$		−	28.6741i		−	0.966053i	−0.875606	−	0.483027i	$-0.839537\pi$
$881$		−	28.6741i		−	0.966053i	0.875606	−	0.483027i	$-0.160463\pi$
$882$	−6.01376	+	2.64122i	−0.202494	+	0.0889346i
$883$	−49.8383			−1.67719			−0.838597	−	0.544753i	$-0.816624\pi$
$883$	−49.8383			−1.67719			−0.838597	+	0.544753i	$0.816624\pi$
$884$	8.60383	−	2.86328i	0.289378	−	0.0963025i
$885$	−3.16879	−	4.16661i	−0.106518	−	0.140059i
$886$	7.64059	+	47.1562i	0.256691	+	1.58424i
$887$	20.3255	+	35.2048i	0.682463	+	1.18206i	0.974227	+	0.225570i	$0.0724245\pi$
$887$	20.3255	+	35.2048i	0.682463	+	1.18206i	−0.291764	+	0.956490i	$0.594242\pi$
$888$	0.0562284	+	0.660725i	0.00188690	+	0.0221725i
$889$	−22.1026	+	38.2828i	−0.741296	+	1.28396i
$890$	13.4510	+	5.10861i	0.450878	+	0.171241i
$891$	18.7134	−	31.1627i	0.626923	−	1.04399i
$892$	26.3735	−	29.7125i	0.883050	−	0.994848i
$893$	−1.84651	+	3.19825i	−0.0617910	+	0.107025i
$894$	16.8275	−	17.7060i	0.562795	−	0.592176i
$895$	15.9918	−	9.23284i	0.534545	−	0.308620i
$896$	29.8370	+	14.2798i	0.996785	+	0.477056i
$897$	4.79049	+	6.29897i	0.159950	+	0.210316i
$898$	−2.00209	+	1.63307i	−0.0668107	+	0.0544963i
$899$			37.1187i			1.23798i
$900$	−0.305067	−	5.99224i	−0.0101689	−	0.199741i
$901$			45.0581i			1.50110i
$902$	18.2032	+	22.3166i	0.606102	+	0.743061i
$903$	44.6686	−	5.68550i	1.48648	−	0.189202i
$904$	19.4677	−	30.6886i	0.647486	−	1.02069i
$905$	−2.49459	+	1.44025i	−0.0829230	+	0.0478756i
$906$	5.19288	−	21.5590i	0.172522	−	0.716249i
$907$	−10.9768	+	19.0124i	−0.364480	+	0.631298i	−0.988693	−	0.149957i	$-0.952087\pi$
$907$	−10.9768	+	19.0124i	−0.364480	+	0.631298i	0.624213	+	0.781254i	$0.285420\pi$
$908$	−2.24424	+	2.52837i	−0.0744778	+	0.0839069i
$909$	−15.2739	+	3.95221i	−0.506603	+	0.131086i
$910$	1.54803	−	4.07598i	0.0513168	−	0.135117i
$911$	−15.5386	+	26.9137i	−0.514818	+	0.891691i	0.485034	+	0.874495i	$0.338807\pi$
$911$	−15.5386	+	26.9137i	−0.514818	+	0.891691i	−0.999852	+	0.0171959i	$0.994526\pi$
$912$	1.75531	+	1.81338i	0.0581240	+	0.0600470i
$913$	35.6665	+	61.7763i	1.18039	+	2.04450i
$914$	12.3820	−	2.00622i	0.409559	−	0.0663597i
$915$	−3.06776	+	7.31712i	−0.101417	+	0.241896i
$916$	−1.05874	−	3.18140i	−0.0349819	−	0.105117i
$917$	4.74996			0.156857
$918$	27.6247	+	15.3349i	0.911750	+	0.506127i
$919$			30.7057i			1.01289i	0.862273	+	0.506443i	$0.169040\pi$
$919$			30.7057i			1.01289i	−0.862273	+	0.506443i	$0.830960\pi$
$920$	−0.510952	+	12.2446i	−0.0168456	+	0.403691i
$921$	1.86576	+	0.782237i	0.0614789	+	0.0257756i
$922$	−33.2767	+	5.39174i	−1.09591	+	0.177567i
$923$	11.8766	−	6.85697i	0.390924	−	0.225700i
$924$	40.7886	+	3.09503i	1.34185	+	0.101819i
$925$	0.117223	+	0.0676787i	0.00385426	+	0.00222526i
$926$	5.16966	+	1.96341i	0.169886	+	0.0645216i
$927$	−46.6905	−	12.9419i	−1.53352	−	0.425068i
$928$	−34.4489	−	8.57791i	−1.13084	−	0.281584i
$929$	14.4494	+	8.34235i	0.474069	+	0.273704i	0.717941	−	0.696104i	$-0.245085\pi$
$929$	14.4494	+	8.34235i	0.474069	+	0.273704i	−0.243873	+	0.969807i	$0.578418\pi$
$930$	−3.39265	+	14.0850i	−0.111249	+	0.461867i
$931$	−0.281975	−	0.488395i	−0.00924136	−	0.0160065i
$932$	21.9592	+	4.50477i	0.719296	+	0.147559i
$933$	0.808925	+	6.35538i	0.0264830	+	0.208066i
$934$	8.71002	−	7.10461i	0.285001	−	0.232470i
$935$	17.3655			0.567914
$936$	−8.74822	+	1.87832i	−0.285945	+	0.0613948i
$937$	−23.6377			−0.772210			−0.386105	−	0.922455i	$-0.626180\pi$
$937$	−23.6377			−0.772210			−0.386105	+	0.922455i	$0.626180\pi$
$938$	−40.4907	+	33.0276i	−1.32207	+	1.07839i
$939$	33.5424	−	25.5097i	1.09462	−	0.832477i
$940$	4.07462	−	19.8623i	0.132899	−	0.647837i
$941$	12.7980	+	22.1668i	0.417203	+	0.722616i	0.995657	−	0.0930986i	$-0.0296772\pi$
$941$	12.7980	+	22.1668i	0.417203	+	0.722616i	−0.578454	+	0.815715i	$0.696344\pi$
$942$	−12.3330	−	11.7211i	−0.401831	−	0.381894i
$943$	−18.9196	−	10.9232i	−0.616107	−	0.355710i
$944$	−12.0036	+	1.43432i	−0.390684	+	0.0466830i
$945$	14.1095	−	5.63229i	0.458981	−	0.183218i
$946$	−47.4799	−	18.0326i	−1.54370	−	0.586290i
$947$	8.16873	+	4.71622i	0.265448	+	0.153256i	0.626817	−	0.779166i	$-0.284357\pi$
$947$	8.16873	+	4.71622i	0.265448	+	0.153256i	−0.361369	+	0.932423i	$0.617691\pi$
$948$	−38.8768	+	18.6773i	−1.26266	+	0.606611i
$949$	−0.226209	+	0.130602i	−0.00734307	+	0.00423952i
$950$	0.508532	−	0.0823960i	0.0164989	−	0.00267328i
$951$	−15.7304	+	11.9633i	−0.510092	+	0.387935i
$952$	−1.48242	+	35.5249i	−0.0480453	+	1.15137i
$953$			21.3775i			0.692486i	0.938145	+	0.346243i	$0.112543\pi$
$953$			21.3775i			0.692486i	−0.938145	+	0.346243i	$0.887457\pi$
$954$	4.87047	−	44.1934i	0.157687	−	1.43082i
$955$	8.20618			0.265546
$956$	−29.2270	+	9.72651i	−0.945270	+	0.314578i
$957$	−43.5505	+	5.54319i	−1.40779	+	0.179186i
$958$	1.12506	−	0.182291i	0.0363491	−	0.00588954i
$959$	−9.79354	−	16.9629i	−0.316250	−	0.547761i
$960$	−12.2880	−	6.40360i	−0.396592	−	0.206675i
$961$	1.99155	−	3.44946i	0.0642435	−	0.111273i
$962$	0.0716682	−	0.188702i	0.00231067	−	0.00608401i
$963$	−11.5800	+	11.3826i	−0.373161	+	0.366800i
$964$	−3.95444	−	3.51005i	−0.127364	−	0.113051i
$965$	3.30583	−	5.72587i	0.106419	−	0.184322i
$966$	−29.7591	+	8.79089i	−0.957485	+	0.282842i
$967$	8.71542	−	5.03185i	0.280269	−	0.161813i	−0.353276	−	0.935519i	$-0.614932\pi$
$967$	8.71542	−	5.03185i	0.280269	−	0.161813i	0.633545	+	0.773706i	$0.281599\pi$
$968$	−12.6881	−	8.04883i	−0.407810	−	0.258699i
$969$	−1.04891	+	2.50183i	−0.0336960	+	0.0803704i
$970$	−7.94187	−	9.73648i	−0.254998	−	0.312620i
$971$			34.9485i			1.12155i	0.827968	+	0.560776i	$0.189497\pi$
$971$			34.9485i			1.12155i	−0.827968	+	0.560776i	$0.810503\pi$
$972$	−25.4370	−	18.0267i	−0.815891	−	0.578205i
$973$			31.7541i			1.01799i
$974$	35.7688	−	29.1760i	1.14611	−	0.934859i
$975$	−0.706188	+	1.68437i	−0.0226161	+	0.0539431i
$976$	10.9796	+	14.6693i	0.351449	+	0.469553i
$977$	−27.2905	+	15.7561i	−0.873099	+	0.504084i	−0.868377	−	0.495905i	$-0.834836\pi$
$977$	−27.2905	+	15.7561i	−0.873099	+	0.504084i	−0.00472211	+	0.999989i	$0.501503\pi$
$978$	−0.558309	−	1.89000i	−0.0178528	−	0.0604356i
$979$	20.5460	−	35.5867i	0.656652	−	1.13735i
$980$	2.31565	+	2.05542i	0.0739706	+	0.0656580i
$981$	36.2841	−	35.6656i	1.15846	−	1.13871i
$982$	−20.9061	−	7.94003i	−0.667141	−	0.253377i
$983$	1.39961	−	2.42420i	0.0446407	−	0.0773199i	−0.842842	−	0.538161i	$-0.819119\pi$
$983$	1.39961	−	2.42420i	0.0446407	−	0.0773199i	0.887482	+	0.460842i	$0.152452\pi$
$984$	20.2672	−	14.1198i	0.646096	−	0.450123i
$985$	12.5890	+	21.8047i	0.401118	+	0.694757i
$986$	−6.10336	−	37.6687i	−0.194371	−	1.19962i
$987$	50.9281	−	6.48223i	1.62106	−	0.206332i
$988$	−0.242585	−	0.728941i	−0.00771766	−	0.0231907i
$989$	38.5275			1.22510
$990$	−17.0323	−	1.87709i	−0.541322	−	0.0596580i
$991$			18.2611i			0.580084i	0.957014	+	0.290042i	$0.0936692\pi$
$991$			18.2611i			0.580084i	−0.957014	+	0.290042i	$0.906331\pi$
$992$	24.0750	+	23.2348i	0.764382	+	0.737704i
$993$	33.5244	−	25.4960i	1.06386	−	0.809091i
$994$	8.60071	+	53.0818i	0.272798	+	1.68365i
$995$	−5.13444	+	2.96437i	−0.162773	+	0.0939768i
$996$	55.1478	−	26.4943i	1.74742	−	0.839504i
$997$	−29.0686	−	16.7827i	−0.920611	−	0.531515i	−0.0367809	−	0.999323i	$-0.511710\pi$
$997$	−29.0686	−	16.7827i	−0.920611	−	0.531515i	−0.883830	+	0.467808i	$0.845044\pi$
$998$	−11.3342	+	29.8429i	−0.358776	+	0.944659i
$999$	0.653216	−	0.260754i	0.0206668	−	0.00824989i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bm.a.11.18	✓	48
3.2	odd	2		1080.2.bm.b.251.7		48
4.3	odd	2		1440.2.cc.a.911.4		48
8.3	odd	2		360.2.bm.b.11.23	yes	48
8.5	even	2		1440.2.cc.b.911.4		48
9.4	even	3		1080.2.bm.a.611.2		48
9.5	odd	6		360.2.bm.b.131.23	yes	48
12.11	even	2		4320.2.cc.b.1871.5		48
24.5	odd	2		4320.2.cc.a.1871.20		48
24.11	even	2		1080.2.bm.a.251.2		48
36.23	even	6		1440.2.cc.b.1391.4		48
36.31	odd	6		4320.2.cc.a.3311.20		48
72.5	odd	6		1440.2.cc.a.1391.4		48
72.13	even	6		4320.2.cc.b.3311.5		48
72.59	even	6	inner	360.2.bm.a.131.18	yes	48
72.67	odd	6		1080.2.bm.b.611.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.18	✓	48	1.1	even	1	trivial
360.2.bm.a.131.18	yes	48	72.59	even	6	inner
360.2.bm.b.11.23	yes	48	8.3	odd	2
360.2.bm.b.131.23	yes	48	9.5	odd	6
1080.2.bm.a.251.2		48	24.11	even	2
1080.2.bm.a.611.2		48	9.4	even	3
1080.2.bm.b.251.7		48	3.2	odd	2
1080.2.bm.b.611.7		48	72.67	odd	6
1440.2.cc.a.911.4		48	4.3	odd	2
1440.2.cc.a.1391.4		48	72.5	odd	6
1440.2.cc.b.911.4		48	8.5	even	2
1440.2.cc.b.1391.4		48	36.23	even	6
4320.2.cc.a.1871.20		48	24.5	odd	2
4320.2.cc.a.3311.20		48	36.31	odd	6
4320.2.cc.b.1871.5		48	12.11	even	2
4320.2.cc.b.3311.5		48	72.13	even	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)

\(f(q)\)	\(=\)	\(q+(0.893891 + 1.09588i) q^{2} +(1.59734 + 0.669699i) q^{3} +(-0.401917 + 1.95920i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.693939 + 2.34914i) q^{6} +(2.53202 + 1.46186i) q^{7} +(-2.50632 + 1.31086i) q^{8} +(2.10301 + 2.13948i) q^{9} +O(q^{10})\)	\(q+(0.893891 + 1.09588i) q^{2} +(1.59734 + 0.669699i) q^{3} +(-0.401917 + 1.95920i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.693939 + 2.34914i) q^{6} +(2.53202 + 1.46186i) q^{7} +(-2.50632 + 1.31086i) q^{8} +(2.10301 + 2.13948i) q^{9} +(0.502116 - 1.32207i) q^{10} +(-3.49775 - 2.01943i) q^{11} +(-1.95407 + 2.86035i) q^{12} +(0.913210 - 0.527242i) q^{13} +(0.661320 + 4.08154i) q^{14} +(-0.218694 - 1.71819i) q^{15} +(-3.67693 - 1.57487i) q^{16} -4.29962i q^{17} +(-0.464759 + 4.21711i) q^{18} -0.364276 q^{19} +(1.89767 - 0.631530i) q^{20} +(3.06549 + 4.03078i) q^{21} +(-0.913555 - 5.63828i) q^{22} +(2.16644 + 3.75238i) q^{23} +(-4.88134 + 0.415407i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.39411 + 0.529474i) q^{26} +(1.92641 + 4.82586i) q^{27} +(-3.88174 + 4.37318i) q^{28} +(3.13786 - 5.43493i) q^{29} +(1.68744 - 1.77554i) q^{30} +(-5.12224 + 2.95733i) q^{31} +(-1.56090 - 5.43724i) q^{32} +(-4.23470 - 5.56816i) q^{33} +(4.71187 - 3.84339i) q^{34} -2.92372i q^{35} +(-5.03690 + 3.26032i) q^{36} -0.135357i q^{37} +(-0.325623 - 0.399203i) q^{38} +(1.81180 - 0.230610i) q^{39} +(2.38840 + 1.51511i) q^{40} +(-4.36652 + 2.52101i) q^{41} +(-1.67705 + 6.96250i) q^{42} +(4.44596 - 7.70062i) q^{43} +(5.36227 - 6.04116i) q^{44} +(0.801340 - 2.89100i) q^{45} +(-2.17561 + 5.72838i) q^{46} +(5.06899 - 8.77974i) q^{47} +(-4.81862 - 4.97804i) q^{48} +(0.774071 + 1.34073i) q^{49} +(-1.39601 + 0.226191i) q^{50} +(2.87945 - 6.86796i) q^{51} +(0.665938 + 2.00107i) q^{52} -10.4796 q^{53} +(-3.56657 + 6.42492i) q^{54} +4.03886i q^{55} +(-8.26234 - 0.344778i) q^{56} +(-0.581873 - 0.243955i) q^{57} +(8.76095 - 1.41951i) q^{58} +(2.61734 - 1.51112i) q^{59} +(3.45417 + 0.262102i) q^{60} +(-3.96710 - 2.29040i) q^{61} +(-7.81960 - 2.96984i) q^{62} +(2.19723 + 8.49149i) q^{63} +(4.56330 - 6.57087i) q^{64} +(-0.913210 - 0.527242i) q^{65} +(2.31669 - 9.61807i) q^{66} +(6.31867 + 10.9443i) q^{67} +(8.42381 + 1.72809i) q^{68} +(0.947576 + 7.44469i) q^{69} +(3.20405 - 2.61349i) q^{70} +13.0054 q^{71} +(-8.07536 - 2.60548i) q^{72} -0.247708 q^{73} +(0.148336 - 0.120995i) q^{74} +(-1.37865 + 1.04849i) q^{75} +(0.146408 - 0.713689i) q^{76} +(-5.90425 - 10.2265i) q^{77} +(1.87228 + 1.77938i) q^{78} +(10.7826 + 6.22536i) q^{79} +(0.474586 + 3.97175i) q^{80} +(-0.154737 + 8.99867i) q^{81} +(-6.66593 - 2.53169i) q^{82} +(-15.2955 - 8.83085i) q^{83} +(-9.12918 + 4.38587i) q^{84} +(-3.72358 + 2.14981i) q^{85} +(12.4132 - 2.01127i) q^{86} +(8.65201 - 6.58002i) q^{87} +(11.4137 + 0.476280i) q^{88} +10.1741i q^{89} +(3.88450 - 1.70606i) q^{90} +3.08302 q^{91} +(-8.22239 + 2.73634i) q^{92} +(-10.1625 + 1.29350i) q^{93} +(14.1527 - 2.29312i) q^{94} +(0.182138 + 0.315472i) q^{95} +(1.14802 - 9.73047i) q^{96} +(4.44230 - 7.69430i) q^{97} +(-0.777347 + 2.04676i) q^{98} +(-3.03527 - 11.7302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8}+O(q^{10}) \) 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8	\( 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8} - 15 q^{12} + 15 q^{14} + 12 q^{16} - 11 q^{18} - 4 q^{21} + 21 q^{22} - 24 q^{24} - 24 q^{25} + 12 q^{27} - 14 q^{30} - 8 q^{33} + 33 q^{34} - 23 q^{36} - 33 q^{38} + 16 q^{39} - 6 q^{40} + 12 q^{41} - 53 q^{42} - 24 q^{44} - 6 q^{46} + 12 q^{47} + 45 q^{48} + 24 q^{49} - 20 q^{51} - 36 q^{52} - 36 q^{54} + 21 q^{56} + 4 q^{57} - 51 q^{58} - 36 q^{59} + 15 q^{60} + 12 q^{61} + 42 q^{62} + 56 q^{63} - 12 q^{64} + 24 q^{66} + 57 q^{68} - 40 q^{69} - 15 q^{70} + 46 q^{72} + 30 q^{74} + 57 q^{76} + 78 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} - 31 q^{84} + 27 q^{86} + 36 q^{87} + 57 q^{88} + 4 q^{90} - 51 q^{92} + 57 q^{94} - 119 q^{96} + 42 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8 - 15 * q^12 + 15 * q^14 + 12 * q^16 - 11 * q^18 - 4 * q^21 + 21 * q^22 - 24 * q^24 - 24 * q^25 + 12 * q^27 - 14 * q^30 - 8 * q^33 + 33 * q^34 - 23 * q^36 - 33 * q^38 + 16 * q^39 - 6 * q^40 + 12 * q^41 - 53 * q^42 - 24 * q^44 - 6 * q^46 + 12 * q^47 + 45 * q^48 + 24 * q^49 - 20 * q^51 - 36 * q^52 - 36 * q^54 + 21 * q^56 + 4 * q^57 - 51 * q^58 - 36 * q^59 + 15 * q^60 + 12 * q^61 + 42 * q^62 + 56 * q^63 - 12 * q^64 + 24 * q^66 + 57 * q^68 - 40 * q^69 - 15 * q^70 + 46 * q^72 + 30 * q^74 + 57 * q^76 + 78 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 - 31 * q^84 + 27 * q^86 + 36 * q^87 + 57 * q^88 + 4 * q^90 - 51 * q^92 + 57 * q^94 - 119 * q^96 + 42 * q^98 - 16 * q^99

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