LMFDB - Embedded newform 1110.2.x.c.751.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(751,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1110.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.x (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{13} + 398 x^{12} - 136 x^{11} + 32 x^{10} - 824 x^{9} + 17825 x^{8} - 11480 x^{7} + \cdots + 20736 $ x^16 - 8x^13 + 398x^12 - 136x^11 + 32x^10 - 824x^9 + 17825x^8 - 11480x^7 + 3104x^6 + 11296x^5 + 68320x^4 - 21120x^3 + 4608x^2 + 13824*x + 20736
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.8
Root			$-0.459512 + 0.459512i$ of defining polynomial
Character	$\chi$	$=$	1110.751
Dual form			1110.2.x.c.841.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +1.00000i q^{6} +(2.35156 - 4.07303i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +1.00000i q^{6} +(2.35156 - 4.07303i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} -5.70313 q^{11} +(0.500000 + 0.866025i) q^{12} +(-2.29590 - 1.32554i) q^{13} -4.70313i q^{14} +(0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-6.60048 + 3.81079i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-1.08722 - 0.627705i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(2.35156 + 4.07303i) q^{21} +(-4.93905 + 2.85156i) q^{22} +6.24074i q^{23} +(0.866025 + 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} -2.65107 q^{26} +1.00000 q^{27} +(-2.35156 - 4.07303i) q^{28} -5.36674i q^{29} +(0.500000 - 0.866025i) q^{30} +2.85230i q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.85156 - 4.93905i) q^{33} +(-3.81079 + 6.60048i) q^{34} +(-4.07303 + 2.35156i) q^{35} -1.00000 q^{36} +(6.06704 + 0.436999i) q^{37} -1.25541 q^{38} +(2.29590 - 1.32554i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-2.54700 + 4.41154i) q^{41} +(4.07303 + 2.35156i) q^{42} -6.77214i q^{43} +(-2.85156 + 4.93905i) q^{44} +1.00000i q^{45} +(3.12037 + 5.40464i) q^{46} -1.88867 q^{47} +1.00000 q^{48} +(-7.55971 - 13.0938i) q^{49} +(0.866025 + 0.500000i) q^{50} -7.62158i q^{51} +(-2.29590 + 1.32554i) q^{52} +(-2.88339 - 4.99417i) q^{53} +(0.866025 - 0.500000i) q^{54} +(4.93905 + 2.85156i) q^{55} +(-4.07303 - 2.35156i) q^{56} +(1.08722 - 0.627705i) q^{57} +(-2.68337 - 4.64774i) q^{58} +(11.7153 - 6.76381i) q^{59} -1.00000i q^{60} +(-4.41154 - 2.54700i) q^{61} +(1.42615 + 2.47016i) q^{62} -4.70313 q^{63} -1.00000 q^{64} +(1.32554 + 2.29590i) q^{65} -5.70313i q^{66} +(-4.66291 + 8.07640i) q^{67} +7.62158i q^{68} +(-5.40464 - 3.12037i) q^{69} +(-2.35156 + 4.07303i) q^{70} +(4.58016 - 7.93306i) q^{71} +(-0.866025 + 0.500000i) q^{72} -4.29523 q^{73} +(5.47271 - 2.65507i) q^{74} -1.00000 q^{75} +(-1.08722 + 0.627705i) q^{76} +(-13.4113 + 23.2290i) q^{77} +(1.32554 - 2.29590i) q^{78} +(-2.91395 - 1.68237i) q^{79} +1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} +5.09400i q^{82} +(-7.45910 - 12.9195i) q^{83} +4.70313 q^{84} +7.62158 q^{85} +(-3.38607 - 5.86484i) q^{86} +(4.64774 + 2.68337i) q^{87} +5.70313i q^{88} +(-0.212481 + 0.122676i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-10.7979 + 6.23417i) q^{91} +(5.40464 + 3.12037i) q^{92} +(-2.47016 - 1.42615i) q^{93} +(-1.63563 + 0.944334i) q^{94} +(0.627705 + 1.08722i) q^{95} +(0.866025 - 0.500000i) q^{96} -18.5808i q^{97} +(-13.0938 - 7.55971i) q^{98} +(2.85156 + 4.93905i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} + 8 q^{12} - 12 q^{13} - 8 q^{16} - 6 q^{17} + 6 q^{19} - 2 q^{21} - 6 q^{22} + 8 q^{25} + 16 q^{27} + 2 q^{28} + 8 q^{30} + 6 q^{33} - 4 q^{34} - 6 q^{35} - 16 q^{36} + 18 q^{37} + 12 q^{38} + 12 q^{39} - 8 q^{40} + 6 q^{42} - 6 q^{44} - 4 q^{46} - 60 q^{47} + 16 q^{48} - 4 q^{49} - 12 q^{52} + 12 q^{53} + 6 q^{55} - 6 q^{56} - 6 q^{57} - 12 q^{58} + 12 q^{59} - 4 q^{62} + 4 q^{63} - 16 q^{64} + 22 q^{67} - 6 q^{69} + 2 q^{70} + 2 q^{71} + 24 q^{73} - 8 q^{74} - 16 q^{75} + 6 q^{76} - 58 q^{77} - 36 q^{79} - 8 q^{81} - 8 q^{83} - 4 q^{84} + 8 q^{85} - 2 q^{86} - 42 q^{89} + 8 q^{90} + 6 q^{92} - 6 q^{93} + 6 q^{94} - 6 q^{95} - 12 q^{98} + 6 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 + 8 * q^12 - 12 * q^13 - 8 * q^16 - 6 * q^17 + 6 * q^19 - 2 * q^21 - 6 * q^22 + 8 * q^25 + 16 * q^27 + 2 * q^28 + 8 * q^30 + 6 * q^33 - 4 * q^34 - 6 * q^35 - 16 * q^36 + 18 * q^37 + 12 * q^38 + 12 * q^39 - 8 * q^40 + 6 * q^42 - 6 * q^44 - 4 * q^46 - 60 * q^47 + 16 * q^48 - 4 * q^49 - 12 * q^52 + 12 * q^53 + 6 * q^55 - 6 * q^56 - 6 * q^57 - 12 * q^58 + 12 * q^59 - 4 * q^62 + 4 * q^63 - 16 * q^64 + 22 * q^67 - 6 * q^69 + 2 * q^70 + 2 * q^71 + 24 * q^73 - 8 * q^74 - 16 * q^75 + 6 * q^76 - 58 * q^77 - 36 * q^79 - 8 * q^81 - 8 * q^83 - 4 * q^84 + 8 * q^85 - 2 * q^86 - 42 * q^89 + 8 * q^90 + 6 * q^92 - 6 * q^93 + 6 * q^94 - 6 * q^95 - 12 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$			1.00000i			0.408248i
$7$	2.35156	−	4.07303i	0.888808	−	1.53946i	0.0475216	−	0.998870i	$-0.484868\pi$
$7$	2.35156	−	4.07303i	0.888808	−	1.53946i	0.841286	−	0.540590i	$-0.181799\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.00000			−0.316228
$11$	−5.70313			−1.71956			−0.859779	−	0.510666i	$-0.829399\pi$
$11$	−5.70313			−1.71956			−0.859779	+	0.510666i	$0.829399\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−2.29590	−	1.32554i	−0.636768	−	0.367638i	0.146601	−	0.989196i	$-0.453167\pi$
$13$	−2.29590	−	1.32554i	−0.636768	−	0.367638i	−0.783368	+	0.621558i	$0.786500\pi$
$14$		−	4.70313i		−	1.25696i
$15$	0.866025	−	0.500000i	0.223607	−	0.129099i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−6.60048	+	3.81079i	−1.60085	+	0.924253i	−0.609535	+	0.792759i	$0.708644\pi$
$17$	−6.60048	+	3.81079i	−1.60085	+	0.924253i	−0.991317	+	0.131494i	$0.958023\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	−1.08722	−	0.627705i	−0.249425	−	0.144005i	0.370076	−	0.929001i	$-0.379332\pi$
$19$	−1.08722	−	0.627705i	−0.249425	−	0.144005i	−0.619501	+	0.784996i	$0.712665\pi$
$20$	−0.866025	+	0.500000i	−0.193649	+	0.111803i
$21$	2.35156	+	4.07303i	0.513153	+	0.888808i
$22$	−4.93905	+	2.85156i	−1.05301	+	0.607956i
$23$			6.24074i			1.30128i	0.759384	+	0.650642i	$0.225500\pi$
$23$			6.24074i			1.30128i	−0.759384	+	0.650642i	$0.774500\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−2.65107			−0.519919
$27$	1.00000			0.192450
$28$	−2.35156	−	4.07303i	−0.444404	−	0.769730i
$29$		−	5.36674i		−	0.996579i	−0.867011	−	0.498290i	$-0.833962\pi$
$29$		−	5.36674i		−	0.996579i	0.867011	−	0.498290i	$-0.166038\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$			2.85230i			0.512288i	0.966639	+	0.256144i	$0.0824522\pi$
$31$			2.85230i			0.512288i	−0.966639	+	0.256144i	$0.917548\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	2.85156	−	4.93905i	0.496394	−	0.859779i
$34$	−3.81079	+	6.60048i	−0.653545	+	1.13197i
$35$	−4.07303	+	2.35156i	−0.688468	+	0.397487i
$36$	−1.00000			−0.166667
$37$	6.06704	+	0.436999i	0.997416	+	0.0718422i
$37$	6.06704	+	0.436999i	0.997416	+	0.0718422i
$38$	−1.25541			−0.203654
$39$	2.29590	−	1.32554i	0.367638	−	0.212256i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−2.54700	+	4.41154i	−0.397775	+	0.688966i	−0.993451	−	0.114258i	$-0.963551\pi$
$41$	−2.54700	+	4.41154i	−0.397775	+	0.688966i	0.595676	+	0.803225i	$0.296884\pi$
$42$	4.07303	+	2.35156i	0.628482	+	0.362854i
$43$		−	6.77214i		−	1.03274i	−0.856365	−	0.516371i	$-0.827283\pi$
$43$		−	6.77214i		−	1.03274i	0.856365	−	0.516371i	$-0.172717\pi$
$44$	−2.85156	+	4.93905i	−0.429890	+	0.744590i
$45$			1.00000i			0.149071i
$46$	3.12037	+	5.40464i	0.460074	+	0.796871i
$47$	−1.88867			−0.275490			−0.137745	−	0.990468i	$-0.543986\pi$
$47$	−1.88867			−0.275490			−0.137745	+	0.990468i	$0.543986\pi$
$48$	1.00000			0.144338
$49$	−7.55971	−	13.0938i	−1.07996	−	1.87054i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		−	7.62158i		−	1.06723i
$52$	−2.29590	+	1.32554i	−0.318384	+	0.183819i
$53$	−2.88339	−	4.99417i	−0.396064	−	0.686003i	0.597173	−	0.802113i	$-0.296291\pi$
$53$	−2.88339	−	4.99417i	−0.396064	−	0.686003i	−0.993236	+	0.116110i	$0.962957\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	4.93905	+	2.85156i	0.665982	+	0.384505i
$56$	−4.07303	−	2.35156i	−0.544281	−	0.314241i
$57$	1.08722	−	0.627705i	0.144005	−	0.0831416i
$58$	−2.68337	−	4.64774i	−0.352344	−	0.610278i
$59$	11.7153	−	6.76381i	1.52520	−	0.880573i	0.525644	−	0.850705i	$-0.323824\pi$
$59$	11.7153	−	6.76381i	1.52520	−	0.880573i	0.999554	−	0.0298686i	$-0.00950890\pi$
$60$		−	1.00000i		−	0.129099i
$61$	−4.41154	−	2.54700i	−0.564839	−	0.326110i	0.190246	−	0.981736i	$-0.439071\pi$
$61$	−4.41154	−	2.54700i	−0.564839	−	0.326110i	−0.755086	+	0.655626i	$0.772405\pi$
$62$	1.42615	+	2.47016i	0.181121	+	0.313711i
$63$	−4.70313			−0.592539
$64$	−1.00000			−0.125000
$65$	1.32554	+	2.29590i	0.164413	+	0.284771i
$66$		−	5.70313i		−	0.702007i
$67$	−4.66291	+	8.07640i	−0.569666	+	0.986690i	0.426933	+	0.904283i	$0.359594\pi$
$67$	−4.66291	+	8.07640i	−0.569666	+	0.986690i	−0.996599	+	0.0824066i	$0.973739\pi$
$68$			7.62158i			0.924253i
$69$	−5.40464	−	3.12037i	−0.650642	−	0.375648i
$70$	−2.35156	+	4.07303i	−0.281066	+	0.486820i
$71$	4.58016	−	7.93306i	0.543564	−	0.941481i	−0.455131	−	0.890424i	$-0.650408\pi$
$71$	4.58016	−	7.93306i	0.543564	−	0.941481i	0.998696	−	0.0510569i	$-0.0162590\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	−4.29523			−0.502719			−0.251359	−	0.967894i	$-0.580878\pi$
$73$	−4.29523			−0.502719			−0.251359	+	0.967894i	$0.580878\pi$
$74$	5.47271	−	2.65507i	0.636190	−	0.308646i
$75$	−1.00000			−0.115470
$76$	−1.08722	+	0.627705i	−0.124712	+	0.0720027i
$77$	−13.4113	+	23.2290i	−1.52836	+	2.64719i
$78$	1.32554	−	2.29590i	0.150088	−	0.259959i
$79$	−2.91395	−	1.68237i	−0.327845	−	0.189281i	0.327039	−	0.945011i	$-0.393949\pi$
$79$	−2.91395	−	1.68237i	−0.327845	−	0.189281i	−0.654884	+	0.755730i	$0.727282\pi$
$80$			1.00000i			0.111803i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$			5.09400i			0.562539i
$83$	−7.45910	−	12.9195i	−0.818742	−	1.41810i	−0.906609	−	0.421971i	$-0.861338\pi$
$83$	−7.45910	−	12.9195i	−0.818742	−	1.41810i	0.0878670	−	0.996132i	$-0.471995\pi$
$84$	4.70313			0.513153
$85$	7.62158			0.826677
$86$	−3.38607	−	5.86484i	−0.365129	−	0.632422i
$87$	4.64774	+	2.68337i	0.498290	+	0.287688i
$88$			5.70313i			0.607956i
$89$	−0.212481	+	0.122676i	−0.0225229	+	0.0130036i	−0.511219	−	0.859450i	$-0.670806\pi$
$89$	−0.212481	+	0.122676i	−0.0225229	+	0.0130036i	0.488696	+	0.872454i	$0.337473\pi$
$90$	0.500000	+	0.866025i	0.0527046	+	0.0912871i
$91$	−10.7979	+	6.23417i	−1.13193	+	0.653519i
$92$	5.40464	+	3.12037i	0.563473	+	0.325321i
$93$	−2.47016	−	1.42615i	−0.256144	−	0.147885i
$94$	−1.63563	+	0.944334i	−0.168703	+	0.0974006i
$95$	0.627705	+	1.08722i	0.0644012	+	0.111546i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$		−	18.5808i		−	1.88660i	−0.331943	−	0.943300i	$-0.607704\pi$
$97$		−	18.5808i		−	1.88660i	0.331943	−	0.943300i	$-0.392296\pi$
$98$	−13.0938	−	7.55971i	−1.32267	−	0.763646i
$99$	2.85156	+	4.93905i	0.286593	+	0.496394i
$100$	1.00000			0.100000
$101$	8.68791			0.864480			0.432240	−	0.901759i	$-0.357723\pi$
$101$	8.68791			0.864480			0.432240	+	0.901759i	$0.357723\pi$
$102$	−3.81079	−	6.60048i	−0.377325	−	0.653545i
$103$			1.40272i			0.138214i	0.997609	+	0.0691069i	$0.0220150\pi$
$103$			1.40272i			0.138214i	−0.997609	+	0.0691069i	$0.977985\pi$
$104$	−1.32554	+	2.29590i	−0.129980	+	0.225131i
$105$		−	4.70313i		−	0.458978i
$106$	−4.99417	−	2.88339i	−0.485077	−	0.280059i
$107$	6.78912	−	11.7591i	0.656329	−	1.13680i	−0.325230	−	0.945635i	$-0.605442\pi$
$107$	6.78912	−	11.7591i	0.656329	−	1.13680i	0.981559	−	0.191160i	$-0.0612251\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	8.56411	−	4.94449i	0.820293	−	0.473596i	−0.0302244	−	0.999543i	$-0.509622\pi$
$109$	8.56411	−	4.94449i	0.820293	−	0.473596i	0.850518	+	0.525947i	$0.176289\pi$
$110$	5.70313			0.543772
$111$	−3.41197	+	5.03572i	−0.323850	+	0.477969i
$112$	−4.70313			−0.444404
$113$	15.2737	−	8.81827i	1.43683	−	0.829553i	0.439200	−	0.898389i	$-0.355262\pi$
$113$	15.2737	−	8.81827i	1.43683	−	0.829553i	0.997628	+	0.0688363i	$0.0219286\pi$
$114$	0.627705	−	1.08722i	0.0587900	−	0.101827i
$115$	3.12037	−	5.40464i	0.290976	−	0.503985i
$116$	−4.64774	−	2.68337i	−0.431531	−	0.249145i
$117$			2.65107i			0.245092i
$118$	6.76381	−	11.7153i	0.622659	−	1.07848i
$119$			35.8453i			3.28593i
$120$	−0.500000	−	0.866025i	−0.0456435	−	0.0790569i
$121$	21.5257			1.95688
$122$	−5.09400			−0.461189
$123$	−2.54700	−	4.41154i	−0.229655	−	0.397775i
$124$	2.47016	+	1.42615i	0.221827	+	0.128072i
$125$		−	1.00000i		−	0.0894427i
$126$	−4.07303	+	2.35156i	−0.362854	+	0.209494i
$127$	−1.01299	−	1.75456i	−0.0898886	−	0.155692i	0.817575	−	0.575822i	$-0.195318\pi$
$127$	−1.01299	−	1.75456i	−0.0898886	−	0.155692i	−0.907464	+	0.420130i	$0.861984\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	5.86484	+	3.38607i	0.516371	+	0.298127i
$130$	2.29590	+	1.32554i	0.201364	+	0.116257i
$131$	−15.3928	+	8.88706i	−1.34488	+	0.776466i	−0.987519	−	0.157501i	$-0.949656\pi$
$131$	−15.3928	+	8.88706i	−1.34488	+	0.776466i	−0.357360	+	0.933967i	$0.616323\pi$
$132$	−2.85156	−	4.93905i	−0.248197	−	0.429890i
$133$	−5.11332	+	2.95218i	−0.443381	+	0.255986i
$134$			9.32583i			0.805629i
$135$	−0.866025	−	0.500000i	−0.0745356	−	0.0430331i
$136$	3.81079	+	6.60048i	0.326773	+	0.565987i
$137$	−4.97318			−0.424888			−0.212444	−	0.977173i	$-0.568142\pi$
$137$	−4.97318			−0.424888			−0.212444	+	0.977173i	$0.568142\pi$
$138$	−6.24074			−0.531247
$139$	0.384803	+	0.666498i	0.0326386	+	0.0565317i	0.881883	−	0.471468i	$-0.156276\pi$
$139$	0.384803	+	0.666498i	0.0326386	+	0.0565317i	−0.849245	+	0.527999i	$0.822942\pi$
$140$			4.70313i			0.397487i
$141$	0.944334	−	1.63563i	0.0795272	−	0.137745i
$142$		−	9.16031i		−	0.768716i
$143$	13.0938	+	7.55971i	1.09496	+	0.632175i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−2.68337	+	4.64774i	−0.222842	+	0.385973i
$146$	−3.71978	+	2.14761i	−0.307851	+	0.177738i
$147$	15.1194			1.24703
$148$	3.41197	−	5.03572i	0.280463	−	0.413933i
$149$	23.8659			1.95517			0.977584	−	0.210547i	$-0.0675244\pi$
$149$	23.8659			1.95517			0.977584	+	0.210547i	$0.0675244\pi$
$150$	−0.866025	+	0.500000i	−0.0707107	+	0.0408248i
$151$	−6.18851	+	10.7188i	−0.503614	+	0.872285i	0.496378	+	0.868107i	$0.334663\pi$
$151$	−6.18851	+	10.7188i	−0.503614	+	0.872285i	−0.999991	+	0.00417780i	$0.998670\pi$
$152$	−0.627705	+	1.08722i	−0.0509136	+	0.0881849i
$153$	6.60048	+	3.81079i	0.533617	+	0.308084i
$154$			26.8225i			2.16142i
$155$	1.42615	−	2.47016i	0.114551	−	0.198408i
$156$		−	2.65107i		−	0.212256i
$157$	0.744188	+	1.28897i	0.0593926	+	0.102871i	0.894193	−	0.447682i	$-0.147750\pi$
$157$	0.744188	+	1.28897i	0.0593926	+	0.102871i	−0.834800	+	0.550553i	$0.814417\pi$
$158$	−3.36474			−0.267684
$159$	5.76678			0.457335
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	25.4187	+	14.6755i	2.00328	+	1.15659i
$162$			1.00000i			0.0785674i
$163$	−8.62033	+	4.97695i	−0.675197	+	0.389825i	−0.798043	−	0.602601i	$-0.794131\pi$
$163$	−8.62033	+	4.97695i	−0.675197	+	0.389825i	0.122846	+	0.992426i	$0.460798\pi$
$164$	2.54700	+	4.41154i	0.198887	+	0.344483i
$165$	−4.93905	+	2.85156i	−0.384505	+	0.221994i
$166$	−12.9195	−	7.45910i	−1.00275	−	0.578938i
$167$	8.23764	+	4.75600i	0.637448	+	0.368031i	0.783631	−	0.621227i	$-0.213365\pi$
$167$	8.23764	+	4.75600i	0.637448	+	0.368031i	−0.146183	+	0.989258i	$0.546699\pi$
$168$	4.07303	−	2.35156i	0.314241	−	0.181427i
$169$	−2.98590	−	5.17173i	−0.229685	−	0.397826i
$170$	6.60048	−	3.81079i	0.506234	−	0.292274i
$171$			1.25541i			0.0960036i
$172$	−5.86484	−	3.38607i	−0.447190	−	0.258185i
$173$	−5.83028	−	10.0983i	−0.443268	−	0.767762i	0.554662	−	0.832076i	$-0.312848\pi$
$173$	−5.83028	−	10.0983i	−0.443268	−	0.767762i	−0.997930	+	0.0643136i	$0.979514\pi$
$174$	5.36674			0.406852
$175$	4.70313			0.355523
$176$	2.85156	+	4.93905i	0.214945	+	0.372295i
$177$			13.5276i			1.01680i
$178$	−0.122676	+	0.212481i	−0.00919494	+	0.0159261i
$179$			13.4301i			1.00381i	0.864922	+	0.501906i	$0.167368\pi$
$179$			13.4301i			1.00381i	−0.864922	+	0.501906i	$0.832632\pi$
$180$	0.866025	+	0.500000i	0.0645497	+	0.0372678i
$181$	11.4732	−	19.8721i	0.852793	−	1.47708i	−0.0258842	−	0.999665i	$-0.508240\pi$
$181$	11.4732	−	19.8721i	0.852793	−	1.47708i	0.878677	−	0.477416i	$-0.158427\pi$
$182$	−6.23417	+	10.7979i	−0.462108	+	0.800394i
$183$	4.41154	−	2.54700i	0.326110	−	0.188280i
$184$	6.24074			0.460074
$185$	−5.03572	−	3.41197i	−0.370233	−	0.250853i
$186$	−2.85230			−0.209141
$187$	37.6434	−	21.7334i	2.75276	−	1.58931i
$188$	−0.944334	+	1.63563i	−0.0688726	+	0.119291i
$189$	2.35156	−	4.07303i	0.171051	−	0.296269i
$190$	1.08722	+	0.627705i	0.0788750	+	0.0455385i
$191$			9.82801i			0.711130i	0.934652	+	0.355565i	$0.115712\pi$
$191$			9.82801i			0.711130i	−0.934652	+	0.355565i	$0.884288\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$			11.7654i			0.846890i	0.905922	+	0.423445i	$0.139179\pi$
$193$			11.7654i			0.846890i	−0.905922	+	0.423445i	$0.860821\pi$
$194$	−9.29042	−	16.0915i	−0.667013	−	1.15530i
$195$	−2.65107			−0.189847
$196$	−15.1194			−1.07996
$197$	−11.5668	−	20.0343i	−0.824103	−	1.42739i	−0.902603	−	0.430473i	$-0.858347\pi$
$197$	−11.5668	−	20.0343i	−0.824103	−	1.42739i	0.0785007	−	0.996914i	$-0.474987\pi$
$198$	4.93905	+	2.85156i	0.351003	+	0.202652i
$199$			19.6731i			1.39459i	0.716783	+	0.697296i	$0.245614\pi$
$199$			19.6731i			1.39459i	−0.716783	+	0.697296i	$0.754386\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	−4.66291	−	8.07640i	−0.328897	−	0.569666i
$202$	7.52395	−	4.34396i	0.529384	−	0.305640i
$203$	−21.8589	−	12.6202i	−1.53419	−	0.885767i
$204$	−6.60048	−	3.81079i	−0.462126	−	0.266809i
$205$	4.41154	−	2.54700i	0.308115	−	0.177890i
$206$	0.701359	+	1.21479i	0.0488660	+	0.0846384i
$207$	5.40464	−	3.12037i	0.375648	−	0.216881i
$208$			2.65107i			0.183819i
$209$	6.20054	+	3.57988i	0.428900	+	0.247626i
$210$	−2.35156	−	4.07303i	−0.162273	−	0.281066i
$211$	−4.10081			−0.282311			−0.141156	−	0.989987i	$-0.545082\pi$
$211$	−4.10081			−0.282311			−0.141156	+	0.989987i	$0.545082\pi$
$212$	−5.76678			−0.396064
$213$	4.58016	+	7.93306i	0.313827	+	0.543564i
$214$		−	13.5782i		−	0.928190i
$215$	−3.38607	+	5.86484i	−0.230928	+	0.399979i
$216$		−	1.00000i		−	0.0680414i
$217$	11.6175	+	6.70737i	0.788647	+	0.455326i
$218$	4.94449	−	8.56411i	0.334883	−	0.580035i
$219$	2.14761	−	3.71978i	0.145122	−	0.251359i
$220$	4.93905	−	2.85156i	0.332991	−	0.192252i
$221$	20.2054			1.35916
$222$	−0.436999	+	6.06704i	−0.0293295	+	0.407193i
$223$	−10.6213			−0.711253			−0.355627	−	0.934628i	$-0.615733\pi$
$223$	−10.6213			−0.711253			−0.355627	+	0.934628i	$0.615733\pi$
$224$	−4.07303	+	2.35156i	−0.272141	+	0.157121i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$	8.81827	−	15.2737i	0.586583	−	1.01599i
$227$	−8.68136	−	5.01219i	−0.576202	−	0.332671i	0.183420	−	0.983035i	$-0.441283\pi$
$227$	−8.68136	−	5.01219i	−0.576202	−	0.332671i	−0.759623	+	0.650364i	$0.774616\pi$
$228$		−	1.25541i		−	0.0831416i
$229$	−9.98570	+	17.2957i	−0.659874	+	1.14293i	0.320775	+	0.947156i	$0.396057\pi$
$229$	−9.98570	+	17.2957i	−0.659874	+	1.14293i	−0.980648	+	0.195779i	$0.937277\pi$
$230$		−	6.24074i		−	0.411502i
$231$	−13.4113	−	23.2290i	−0.882397	−	1.52836i
$232$	−5.36674			−0.352344
$233$	−25.0674			−1.64222			−0.821108	−	0.570772i	$-0.806644\pi$
$233$	−25.0674			−1.64222			−0.821108	+	0.570772i	$0.806644\pi$
$234$	1.32554	+	2.29590i	0.0866531	+	0.150088i
$235$	1.63563	+	0.944334i	0.106697	+	0.0616015i
$236$		−	13.5276i		−	0.880573i
$237$	2.91395	−	1.68237i	0.189281	−	0.109282i
$238$	17.9226	+	31.0429i	1.16175	+	2.01221i
$239$	−24.3817	+	14.0768i	−1.57712	+	0.910551i	−0.581862	+	0.813287i	$0.697676\pi$
$239$	−24.3817	+	14.0768i	−1.57712	+	0.910551i	−0.995259	+	0.0972638i	$0.968991\pi$
$240$	−0.866025	−	0.500000i	−0.0559017	−	0.0322749i
$241$	11.0003	+	6.35100i	0.708589	+	0.409104i	0.810538	−	0.585685i	$-0.199175\pi$
$241$	11.0003	+	6.35100i	0.708589	+	0.409104i	−0.101949	+	0.994790i	$0.532508\pi$
$242$	18.6418	−	10.7628i	1.19834	−	0.691861i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−4.41154	+	2.54700i	−0.282420	+	0.163055i
$245$			15.1194i			0.965944i
$246$	−4.41154	−	2.54700i	−0.281269	−	0.162391i
$247$	1.66409	+	2.88229i	0.105884	+	0.183396i
$248$	2.85230			0.181121
$249$	14.9182			0.945402
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$			1.23353i			0.0778599i	0.999242	+	0.0389300i	$0.0123949\pi$
$251$			1.23353i			0.0778599i	−0.999242	+	0.0389300i	$0.987605\pi$
$252$	−2.35156	+	4.07303i	−0.148135	+	0.256577i
$253$		−	35.5917i		−	2.23763i
$254$	−1.75456	−	1.01299i	−0.110091	−	0.0635609i
$255$	−3.81079	+	6.60048i	−0.238641	+	0.413338i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.4847	+	7.20803i	−0.778772	+	0.449624i	−0.835995	−	0.548737i	$-0.815109\pi$
$257$	−12.4847	+	7.20803i	−0.778772	+	0.449624i	0.0572227	+	0.998361i	$0.481775\pi$
$258$	6.77214			0.421615
$259$	16.0470	−	23.6836i	0.997109	−	1.47163i
$260$	2.65107			0.164413
$261$	−4.64774	+	2.68337i	−0.287688	+	0.166097i
$262$	−8.88706	+	15.3928i	−0.549044	+	0.950973i
$263$	−1.07034	+	1.85388i	−0.0659999	+	0.114315i	−0.897137	−	0.441752i	$-0.854357\pi$
$263$	−1.07034	+	1.85388i	−0.0659999	+	0.114315i	0.831137	+	0.556067i	$0.187690\pi$
$264$	−4.93905	−	2.85156i	−0.303978	−	0.175502i
$265$			5.76678i			0.354250i
$266$	−2.95218	+	5.11332i	−0.181010	+	0.313518i
$267$		−	0.245351i		−	0.0150153i
$268$	4.66291	+	8.07640i	0.284833	+	0.493345i
$269$	−20.7307			−1.26397			−0.631986	−	0.774980i	$-0.717760\pi$
$269$	−20.7307			−1.26397			−0.631986	+	0.774980i	$0.717760\pi$
$270$	−1.00000			−0.0608581
$271$	9.12544	+	15.8057i	0.554331	+	0.960129i	0.997955	+	0.0639162i	$0.0203590\pi$
$271$	9.12544	+	15.8057i	0.554331	+	0.960129i	−0.443625	+	0.896213i	$0.646308\pi$
$272$	6.60048	+	3.81079i	0.400213	+	0.231063i
$273$		−	12.4683i		−	0.754619i
$274$	−4.30690	+	2.48659i	−0.260190	+	0.150220i
$275$	−2.85156	−	4.93905i	−0.171956	−	0.297836i
$276$	−5.40464	+	3.12037i	−0.325321	+	0.187824i
$277$	2.06980	+	1.19500i	0.124362	+	0.0718006i	0.560891	−	0.827890i	$-0.310459\pi$
$277$	2.06980	+	1.19500i	0.124362	+	0.0718006i	−0.436528	+	0.899690i	$0.643792\pi$
$278$	0.666498	+	0.384803i	0.0399739	+	0.0230790i
$279$	2.47016	−	1.42615i	0.147885	−	0.0853814i
$280$	2.35156	+	4.07303i	0.140533	+	0.243410i
$281$	13.5271	−	7.80985i	0.806957	−	0.465897i	−0.0389410	−	0.999242i	$-0.512398\pi$
$281$	13.5271	−	7.80985i	0.806957	−	0.465897i	0.845898	+	0.533345i	$0.179065\pi$
$282$		−	1.88867i		−	0.112468i
$283$	−14.0941	−	8.13724i	−0.837808	−	0.483709i	0.0187104	−	0.999825i	$-0.494044\pi$
$283$	−14.0941	−	8.13724i	−0.837808	−	0.483709i	−0.856519	+	0.516116i	$0.827377\pi$
$284$	−4.58016	−	7.93306i	−0.271782	−	0.470741i
$285$	−1.25541			−0.0743641
$286$	15.1194			0.894030
$287$	11.9789	+	20.7480i	0.707091	+	1.22472i
$288$			1.00000i			0.0589256i
$289$	20.5443	−	35.5837i	1.20849	−	2.09316i
$290$			5.36674i			0.315146i
$291$	16.0915	+	9.29042i	0.943300	+	0.544614i
$292$	−2.14761	+	3.71978i	−0.125680	+	0.217684i
$293$	−5.74103	+	9.94375i	−0.335394	+	0.580920i	−0.983561	−	0.180579i	$-0.942203\pi$
$293$	−5.74103	+	9.94375i	−0.335394	+	0.580920i	0.648166	+	0.761499i	$0.275536\pi$
$294$	13.0938	−	7.55971i	0.763646	−	0.440891i
$295$	−13.5276			−0.787609
$296$	0.436999	−	6.06704i	0.0254001	−	0.352640i
$297$	−5.70313			−0.330929
$298$	20.6684	−	11.9329i	1.19729	−	0.691256i
$299$	8.27233	−	14.3281i	0.478401	−	0.828616i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	−27.5831	−	15.9251i	−1.58986	−	0.917908i
$302$			12.3770i			0.712217i
$303$	−4.34396	+	7.52395i	−0.249554	+	0.432240i
$304$			1.25541i			0.0720027i
$305$	2.54700	+	4.41154i	0.145841	+	0.252604i
$306$	7.62158			0.435697
$307$	11.1371			0.635627			0.317813	−	0.948153i	$-0.397051\pi$
$307$	11.1371			0.635627			0.317813	+	0.948153i	$0.397051\pi$
$308$	13.4113	+	23.2290i	0.764178	+	1.32360i
$309$	−1.21479	−	0.701359i	−0.0691069	−	0.0398989i
$310$		−	2.85230i		−	0.162000i
$311$	5.34316	−	3.08488i	0.302983	−	0.174927i	−0.340799	−	0.940136i	$-0.610698\pi$
$311$	5.34316	−	3.08488i	0.302983	−	0.174927i	0.643782	+	0.765209i	$0.277364\pi$
$312$	−1.32554	−	2.29590i	−0.0750438	−	0.129980i
$313$	2.56033	−	1.47820i	0.144718	−	0.0835531i	−0.425893	−	0.904774i	$-0.640040\pi$
$313$	2.56033	−	1.47820i	0.144718	−	0.0835531i	0.570611	+	0.821221i	$0.306707\pi$
$314$	1.28897	+	0.744188i	0.0727408	+	0.0419969i
$315$	4.07303	+	2.35156i	0.229489	+	0.132496i
$316$	−2.91395	+	1.68237i	−0.163922	+	0.0946406i
$317$	−1.88503	−	3.26496i	−0.105874	−	0.183379i	0.808221	−	0.588879i	$-0.200431\pi$
$317$	−1.88503	−	3.26496i	−0.105874	−	0.183379i	−0.914095	+	0.405501i	$0.867097\pi$
$318$	4.99417	−	2.88339i	0.280059	−	0.161692i
$319$			30.6072i			1.71368i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	6.78912	+	11.7591i	0.378932	+	0.656329i
$322$	29.3510			1.63567
$323$	9.56821			0.532389
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$		−	2.65107i		−	0.147055i
$326$	−4.97695	+	8.62033i	−0.275648	+	0.477436i
$327$			9.88898i			0.546862i
$328$	4.41154	+	2.54700i	0.243586	+	0.140635i
$329$	−4.44132	+	7.69260i	−0.244858	+	0.424107i
$330$	−2.85156	+	4.93905i	−0.156973	+	0.271886i
$331$	4.53064	−	2.61576i	0.249026	−	0.143775i	−0.370292	−	0.928915i	$-0.620742\pi$
$331$	4.53064	−	2.61576i	0.249026	−	0.143775i	0.619318	+	0.785140i	$0.287409\pi$
$332$	−14.9182			−0.818742
$333$	−2.65507	−	5.47271i	−0.145497	−	0.299903i
$334$	9.51201			0.520474
$335$	8.07640	−	4.66291i	0.441261	−	0.254762i
$336$	2.35156	−	4.07303i	0.128288	−	0.222202i
$337$	0.653680	−	1.13221i	0.0356082	−	0.0616753i	−0.847672	−	0.530521i	$-0.821996\pi$
$337$	0.653680	−	1.13221i	0.0356082	−	0.0616753i	0.883280	+	0.468845i	$0.155330\pi$
$338$	−5.17173	−	2.98590i	−0.281305	−	0.162412i
$339$			17.6365i			0.957885i
$340$	3.81079	−	6.60048i	0.206669	−	0.357961i
$341$		−	16.2670i		−	0.880909i
$342$	0.627705	+	1.08722i	0.0339424	+	0.0587900i
$343$	−38.1867			−2.06189
$344$	−6.77214			−0.365129
$345$	3.12037	+	5.40464i	0.167995	+	0.290976i
$346$	−10.0983	−	5.83028i	−0.542890	−	0.313438i
$347$		−	0.838435i		−	0.0450095i	−0.999747	−	0.0225048i	$-0.992836\pi$
$347$		−	0.838435i		−	0.0450095i	0.999747	−	0.0225048i	$-0.00716409\pi$
$348$	4.64774	−	2.68337i	0.249145	−	0.143844i
$349$	10.2020	+	17.6704i	0.546103	+	0.945877i	0.998537	+	0.0540795i	$0.0172225\pi$
$349$	10.2020	+	17.6704i	0.546103	+	0.945877i	−0.452434	+	0.891798i	$0.649444\pi$
$350$	4.07303	−	2.35156i	0.217713	−	0.125696i
$351$	−2.29590	−	1.32554i	−0.122546	−	0.0707519i
$352$	4.93905	+	2.85156i	0.263252	+	0.151989i
$353$	−19.7152	+	11.3826i	−1.04933	+	0.605833i	−0.922463	−	0.386086i	$-0.873827\pi$
$353$	−19.7152	+	11.3826i	−1.04933	+	0.605833i	−0.126871	+	0.991919i	$0.540493\pi$
$354$	6.76381	+	11.7153i	0.359493	+	0.622659i
$355$	−7.93306	+	4.58016i	−0.421043	+	0.243089i
$356$			0.245351i			0.0130036i
$357$	−31.0429	−	17.9226i	−1.64297	−	0.948567i
$358$	6.71504	+	11.6308i	0.354901	+	0.614707i
$359$	16.8447			0.889029			0.444514	−	0.895772i	$-0.353376\pi$
$359$	16.8447			0.889029			0.444514	+	0.895772i	$0.353376\pi$
$360$	1.00000			0.0527046
$361$	−8.71197	−	15.0896i	−0.458525	−	0.794188i
$362$		−	22.9463i		−	1.20603i
$363$	−10.7628	+	18.6418i	−0.564903	+	0.978440i
$364$			12.4683i			0.653519i
$365$	3.71978	+	2.14761i	0.194702	+	0.112411i
$366$	2.54700	−	4.41154i	0.133134	−	0.230595i
$367$	0.444157	−	0.769302i	0.0231848	−	0.0401572i	−0.854200	−	0.519944i	$-0.825953\pi$
$367$	0.444157	−	0.769302i	0.0231848	−	0.0401572i	0.877385	+	0.479787i	$0.159286\pi$
$368$	5.40464	−	3.12037i	0.281736	−	0.162661i
$369$	5.09400			0.265183
$370$	−6.06704	−	0.436999i	−0.315411	−	0.0227185i
$371$	−27.1219			−1.40810
$372$	−2.47016	+	1.42615i	−0.128072	+	0.0739424i
$373$	9.98090	−	17.2874i	0.516791	−	0.895109i	−0.483019	−	0.875610i	$-0.660460\pi$
$373$	9.98090	−	17.2874i	0.516791	−	0.895109i	0.999810	−	0.0194987i	$-0.00620702\pi$
$374$	21.7334	−	37.6434i	1.12381	−	1.94649i
$375$	0.866025	+	0.500000i	0.0447214	+	0.0258199i
$376$			1.88867i			0.0974006i
$377$	−7.11382	+	12.3215i	−0.366380	+	0.634589i
$378$		−	4.70313i		−	0.241903i
$379$	5.96581	+	10.3331i	0.306443	+	0.530775i	0.977582	−	0.210557i	$-0.0675277\pi$
$379$	5.96581	+	10.3331i	0.306443	+	0.530775i	−0.671138	+	0.741332i	$0.734194\pi$
$380$	1.25541			0.0644012
$381$	2.02599			0.103794
$382$	4.91401	+	8.51131i	0.251422	+	0.435476i
$383$	9.40579	+	5.43044i	0.480613	+	0.277482i	0.720672	−	0.693276i	$-0.243833\pi$
$383$	9.40579	+	5.43044i	0.480613	+	0.277482i	−0.240059	+	0.970758i	$0.577167\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	23.2290	−	13.4113i	1.18386	−	0.683502i
$386$	5.88269	+	10.1891i	0.299421	+	0.518612i
$387$	−5.86484	+	3.38607i	−0.298127	+	0.172124i
$388$	−16.0915	−	9.29042i	−0.816921	−	0.471650i
$389$	−10.4969	−	6.06040i	−0.532215	−	0.307274i	0.209703	−	0.977765i	$-0.432750\pi$
$389$	−10.4969	−	6.06040i	−0.532215	−	0.307274i	−0.741918	+	0.670491i	$0.766084\pi$
$390$	−2.29590	+	1.32554i	−0.116257	+	0.0671212i
$391$	−23.7822	−	41.1919i	−1.20272	−	2.08316i
$392$	−13.0938	+	7.55971i	−0.661337	+	0.381823i
$393$		−	17.7741i		−	0.896586i
$394$	−20.0343	−	11.5668i	−1.00932	−	0.582729i
$395$	1.68237	+	2.91395i	0.0846492	+	0.146617i
$396$	5.70313			0.286593
$397$	3.18042			0.159621			0.0798104	−	0.996810i	$-0.474569\pi$
$397$	3.18042			0.159621			0.0798104	+	0.996810i	$0.474569\pi$
$398$	9.83657	+	17.0374i	0.493063	+	0.854009i
$399$		−	5.90435i		−	0.295587i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$		−	10.9638i		−	0.547504i	−0.961800	−	0.273752i	$-0.911735\pi$
$401$		−	10.9638i		−	0.547504i	0.961800	−	0.273752i	$-0.0882647\pi$
$402$	−8.07640	−	4.66291i	−0.402814	−	0.232565i
$403$	3.78083	−	6.54859i	0.188337	−	0.326209i
$404$	4.34396	−	7.52395i	0.216120	−	0.374331i
$405$	0.866025	−	0.500000i	0.0430331	−	0.0248452i
$406$	−25.2405			−1.25266
$407$	−34.6011	−	2.49226i	−1.71511	−	0.123537i
$408$	−7.62158			−0.377325
$409$	26.7397	−	15.4382i	1.32219	−	0.763368i	0.338114	−	0.941105i	$-0.390211\pi$
$409$	26.7397	−	15.4382i	1.32219	−	0.763368i	0.984078	+	0.177737i	$0.0568778\pi$
$410$	2.54700	−	4.41154i	0.125787	−	0.217870i
$411$	2.48659	−	4.30690i	0.122655	−	0.212444i
$412$	1.21479	+	0.701359i	0.0598484	+	0.0345535i
$413$		−	63.6222i		−	3.13064i
$414$	3.12037	−	5.40464i	0.153358	−	0.265624i
$415$			14.9182i			0.732305i
$416$	1.32554	+	2.29590i	0.0649898	+	0.112566i
$417$	−0.769606			−0.0376878
$418$	7.15976			0.350196
$419$	−0.345691	−	0.598754i	−0.0168881	−	0.0292511i	0.857458	−	0.514554i	$-0.172043\pi$
$419$	−0.345691	−	0.598754i	−0.0168881	−	0.0292511i	−0.874346	+	0.485303i	$0.838709\pi$
$420$	−4.07303	−	2.35156i	−0.198743	−	0.114745i
$421$		−	13.6217i		−	0.663882i	−0.943300	−	0.331941i	$-0.892296\pi$
$421$		−	13.6217i		−	0.663882i	0.943300	−	0.331941i	$-0.107704\pi$
$422$	−3.55141	+	2.05041i	−0.172880	+	0.0998122i
$423$	0.944334	+	1.63563i	0.0459151	+	0.0795272i
$424$	−4.99417	+	2.88339i	−0.242539	+	0.140030i
$425$	−6.60048	−	3.81079i	−0.320170	−	0.184851i
$426$	7.93306	+	4.58016i	0.384358	+	0.221909i
$427$	−20.7480	+	11.9789i	−1.00407	+	0.579699i
$428$	−6.78912	−	11.7591i	−0.328165	−	0.568398i
$429$	−13.0938	+	7.55971i	−0.632175	+	0.364986i
$430$			6.77214i			0.326581i
$431$	14.1364	+	8.16168i	0.680929	+	0.393134i	0.800205	−	0.599727i	$-0.204724\pi$
$431$	14.1364	+	8.16168i	0.680929	+	0.393134i	−0.119276	+	0.992861i	$0.538057\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−6.88077			−0.330668			−0.165334	−	0.986238i	$-0.552870\pi$
$433$	−6.88077			−0.330668			−0.165334	+	0.986238i	$0.552870\pi$
$434$	13.4147			0.643928
$435$	−2.68337	−	4.64774i	−0.128658	−	0.222842i
$436$		−	9.88898i		−	0.473596i
$437$	3.91734	−	6.78504i	0.187392	−	0.324572i
$438$		−	4.29523i		−	0.205234i
$439$	−8.54478	−	4.93333i	−0.407820	−	0.235455i	0.282033	−	0.959405i	$-0.408991\pi$
$439$	−8.54478	−	4.93333i	−0.407820	−	0.235455i	−0.689853	+	0.723950i	$0.742325\pi$
$440$	2.85156	−	4.93905i	0.135943	−	0.235460i
$441$	−7.55971	+	13.0938i	−0.359986	+	0.623514i
$442$	17.4984	−	10.1027i	0.832313	−	0.480536i
$443$	−29.0156			−1.37857			−0.689286	−	0.724489i	$-0.742076\pi$
$443$	−29.0156			−1.37857			−0.689286	+	0.724489i	$0.742076\pi$
$444$	2.65507	+	5.47271i	0.126004	+	0.259724i
$445$	0.245351			0.0116308
$446$	−9.19830	+	5.31064i	−0.435552	+	0.251466i
$447$	−11.9329	+	20.6684i	−0.564408	+	0.977584i
$448$	−2.35156	+	4.07303i	−0.111101	+	0.192433i
$449$	30.6701	+	17.7074i	1.44741	+	0.835663i	0.998327	−	0.0578272i	$-0.0184173\pi$
$449$	30.6701	+	17.7074i	1.44741	+	0.835663i	0.449083	+	0.893490i	$0.351751\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	14.5259	−	25.1596i	0.683997	−	1.18472i
$452$		−	17.6365i		−	0.829553i
$453$	−6.18851	−	10.7188i	−0.290762	−	0.503614i
$454$	−10.0244			−0.470467
$455$	12.4683			0.584525
$456$	−0.627705	−	1.08722i	−0.0293950	−	0.0509136i
$457$	27.4309	+	15.8372i	1.28316	+	0.740834i	0.977425	−	0.211282i	$-0.0677639\pi$
$457$	27.4309	+	15.8372i	1.28316	+	0.740834i	0.305737	+	0.952116i	$0.401097\pi$
$458$			19.9714i			0.933202i
$459$	−6.60048	+	3.81079i	−0.308084	+	0.177872i
$460$	−3.12037	−	5.40464i	−0.145488	−	0.251993i
$461$	29.7480	−	17.1750i	1.38550	−	0.799919i	0.392697	−	0.919668i	$-0.371542\pi$
$461$	29.7480	−	17.1750i	1.38550	−	0.799919i	0.992804	+	0.119749i	$0.0382089\pi$
$462$	−23.2290	−	13.4113i	−1.08071	−	0.623949i
$463$	−6.71390	−	3.87627i	−0.312022	−	0.180146i	0.335809	−	0.941930i	$-0.390990\pi$
$463$	−6.71390	−	3.87627i	−0.312022	−	0.180146i	−0.647831	+	0.761784i	$0.724324\pi$
$464$	−4.64774	+	2.68337i	−0.215766	+	0.124572i
$465$	1.42615	+	2.47016i	0.0661361	+	0.114551i
$466$	−21.7090	+	12.5337i	−1.00565	+	0.580611i
$467$			24.0133i			1.11120i	0.831449	+	0.555601i	$0.187512\pi$
$467$			24.0133i			1.11120i	−0.831449	+	0.555601i	$0.812488\pi$
$468$	2.29590	+	1.32554i	0.106128	+	0.0612730i
$469$	21.9303	+	37.9844i	1.01265	+	1.75396i
$470$	1.88867			0.0871177
$471$	−1.48838			−0.0685807
$472$	−6.76381	−	11.7153i	−0.311330	−	0.539239i
$473$			38.6224i			1.77586i
$474$	1.68237	−	2.91395i	0.0772738	−	0.133842i
$475$		−	1.25541i		−	0.0576022i
$476$	31.0429	+	17.9226i	1.42285	+	0.821483i
$477$	−2.88339	+	4.99417i	−0.132021	+	0.228668i
$478$	−14.0768	+	24.3817i	−0.643857	+	1.11519i
$479$	−23.0877	+	13.3297i	−1.05490	+	0.609048i	−0.924018	−	0.382349i	$-0.875115\pi$
$479$	−23.0877	+	13.3297i	−1.05490	+	0.609048i	−0.130885	+	0.991398i	$0.541782\pi$
$480$	−1.00000			−0.0456435
$481$	−13.3501	−	9.04540i	−0.608710	−	0.412435i
$482$	12.7020			0.578561
$483$	−25.4187	+	14.6755i	−1.15659	+	0.667759i
$484$	10.7628	−	18.6418i	0.489220	−	0.847354i
$485$	−9.29042	+	16.0915i	−0.421856	+	0.730677i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$		−	15.6199i		−	0.707805i	−0.935282	−	0.353902i	$-0.884854\pi$
$487$		−	15.6199i		−	0.707805i	0.935282	−	0.353902i	$-0.115146\pi$
$488$	−2.54700	+	4.41154i	−0.115297	+	0.199701i
$489$		−	9.95390i		−	0.450131i
$490$	7.55971	+	13.0938i	0.341513	+	0.591518i
$491$	24.1149			1.08829			0.544146	−	0.838990i	$-0.316854\pi$
$491$	24.1149			1.08829			0.544146	+	0.838990i	$0.316854\pi$
$492$	−5.09400			−0.229655
$493$	20.4515	+	35.4231i	0.921091	+	1.59538i
$494$	2.88229	+	1.66409i	0.129681	+	0.0748711i
$495$		−	5.70313i		−	0.256337i
$496$	2.47016	−	1.42615i	0.110914	−	0.0640360i
$497$	−21.5411	−	37.3102i	−0.966249	−	1.67359i
$498$	12.9195	−	7.45910i	0.578938	−	0.334250i
$499$	6.28368	+	3.62788i	0.281296	+	0.162406i	0.634010	−	0.773325i	$-0.281408\pi$
$499$	6.28368	+	3.62788i	0.281296	+	0.162406i	−0.352714	+	0.935731i	$0.614741\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$	−8.23764	+	4.75600i	−0.368031	+	0.212483i
$502$	0.616767	+	1.06827i	0.0275276	+	0.0476793i
$503$	14.3588	−	8.29008i	0.640229	−	0.369636i	−0.144474	−	0.989509i	$-0.546149\pi$
$503$	14.3588	−	8.29008i	0.640229	−	0.369636i	0.784703	+	0.619872i	$0.212816\pi$
$504$			4.70313i			0.209494i
$505$	−7.52395	−	4.34396i	−0.334812	−	0.193304i
$506$	−17.7959	−	30.8234i	−0.791123	−	1.37027i
$507$	5.97180			0.265217
$508$	−2.02599			−0.0898886
$509$	−19.3010	−	33.4303i	−0.855503	−	1.48177i	−0.876178	−	0.481988i	$-0.839915\pi$
$509$	−19.3010	−	33.4303i	−0.855503	−	1.48177i	0.0206752	−	0.999786i	$-0.493418\pi$
$510$			7.62158i			0.337489i
$511$	−10.1005	+	17.4946i	−0.446820	+	0.773915i
$512$			1.00000i			0.0441942i
$513$	−1.08722	−	0.627705i	−0.0480018	−	0.0277139i
$514$	−7.20803	+	12.4847i	−0.317932	+	0.550675i
$515$	0.701359	−	1.21479i	0.0309056	−	0.0535300i
$516$	5.86484	−	3.38607i	0.258185	−	0.149063i
$517$	10.7713			0.473722
$518$	2.05526	−	28.5341i	0.0903031	−	1.25372i
$519$	11.6606			0.511841
$520$	2.29590	−	1.32554i	0.100682	−	0.0581287i
$521$	−9.88317	+	17.1182i	−0.432990	+	0.749960i	−0.997129	−	0.0757196i	$-0.975875\pi$
$521$	−9.88317	+	17.1182i	−0.432990	+	0.749960i	0.564140	+	0.825679i	$0.309208\pi$
$522$	−2.68337	+	4.64774i	−0.117448	+	0.203426i
$523$	−9.60540	−	5.54568i	−0.420015	−	0.242496i	0.275069	−	0.961425i	$-0.411299\pi$
$523$	−9.60540	−	5.54568i	−0.420015	−	0.242496i	−0.695084	+	0.718929i	$0.744633\pi$
$524$			17.7741i			0.776466i
$525$	−2.35156	+	4.07303i	−0.102631	+	0.177762i
$526$			2.14068i			0.0933379i
$527$	−10.8695	−	18.8266i	−0.473484	−	0.820098i
$528$	−5.70313			−0.248197
$529$	−15.9468			−0.693341
$530$	2.88339	+	4.99417i	0.125246	+	0.216933i
$531$	−11.7153	−	6.76381i	−0.508399	−	0.293524i
$532$			5.90435i			0.255986i
$533$	11.6953	−	6.75229i	0.506580	−	0.292474i
$534$	−0.122676	−	0.212481i	−0.00530870	−	0.00919494i
$535$	−11.7591	+	6.78912i	−0.508390	+	0.293519i
$536$	8.07640	+	4.66291i	0.348848	+	0.201407i
$537$	−11.6308	−	6.71504i	−0.501906	−	0.289775i
$538$	−17.9533	+	10.3653i	−0.774022	+	0.446882i
$539$	43.1140	+	74.6756i	1.85705	+	3.21651i
$540$	−0.866025	+	0.500000i	−0.0372678	+	0.0215166i
$541$			4.42153i			0.190097i	0.995473	+	0.0950483i	$0.0303005\pi$
$541$			4.42153i			0.190097i	−0.995473	+	0.0950483i	$0.969699\pi$
$542$	15.8057	+	9.12544i	0.678914	+	0.391971i
$543$	11.4732	+	19.8721i	0.492360	+	0.852793i
$544$	7.62158			0.326773
$545$	−9.88898			−0.423598
$546$	−6.23417	−	10.7979i	−0.266798	−	0.462108i
$547$		−	11.4402i		−	0.489146i	−0.969631	−	0.244573i	$-0.921352\pi$
$547$		−	11.4402i		−	0.489146i	0.969631	−	0.244573i	$-0.0786479\pi$
$548$	−2.48659	+	4.30690i	−0.106222	+	0.183982i
$549$			5.09400i			0.217407i
$550$	−4.93905	−	2.85156i	−0.210602	−	0.121591i
$551$	−3.36873	+	5.83481i	−0.143513	+	0.248571i
$552$	−3.12037	+	5.40464i	−0.132812	+	0.230037i
$553$	−13.7047	+	7.91240i	−0.582782	+	0.336469i
$554$	2.39000			0.101541
$555$	5.47271	−	2.65507i	0.232304	−	0.112701i
$556$	0.769606			0.0326386
$557$	16.6729	−	9.62611i	0.706454	−	0.407872i	−0.103293	−	0.994651i	$-0.532938\pi$
$557$	16.6729	−	9.62611i	0.706454	−	0.407872i	0.809747	+	0.586780i	$0.199604\pi$
$558$	1.42615	−	2.47016i	0.0603738	−	0.104570i
$559$	−8.97672	+	15.5481i	−0.379675	+	0.657616i
$560$	4.07303	+	2.35156i	0.172117	+	0.0993717i
$561$			43.4669i			1.83517i
$562$	7.80985	−	13.5271i	0.329439	−	0.570605i
$563$			36.7173i			1.54745i	0.633522	+	0.773724i	$0.281608\pi$
$563$			36.7173i			1.54745i	−0.633522	+	0.773724i	$0.718392\pi$
$564$	−0.944334	−	1.63563i	−0.0397636	−	0.0688726i
$565$	−17.6365			−0.741975
$566$	−16.2745			−0.684068
$567$	2.35156	+	4.07303i	0.0987564	+	0.171051i
$568$	−7.93306	−	4.58016i	−0.332864	−	0.192179i
$569$		−	23.0017i		−	0.964281i	−0.876094	−	0.482141i	$-0.839859\pi$
$569$		−	23.0017i		−	0.964281i	0.876094	−	0.482141i	$-0.160141\pi$
$570$	−1.08722	+	0.627705i	−0.0455385	+	0.0262917i
$571$	−0.151062	−	0.261647i	−0.00632174	−	0.0109496i	0.862847	−	0.505465i	$-0.168679\pi$
$571$	−0.151062	−	0.261647i	−0.00632174	−	0.0109496i	−0.869169	+	0.494515i	$0.835346\pi$
$572$	13.0938	−	7.55971i	0.547479	−	0.316087i
$573$	−8.51131	−	4.91401i	−0.355565	−	0.205286i
$574$	20.7480	+	11.9789i	0.866006	+	0.499989i
$575$	−5.40464	+	3.12037i	−0.225389	+	0.130128i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	5.67584	−	3.27695i	0.236288	−	0.136421i	−0.377181	−	0.926139i	$-0.623107\pi$
$577$	5.67584	−	3.27695i	0.236288	−	0.136421i	0.613470	+	0.789718i	$0.289773\pi$
$578$		−	41.0885i		−	1.70906i
$579$	−10.1891	−	5.88269i	−0.423445	−	0.244476i
$580$	2.68337	+	4.64774i	0.111421	+	0.192987i
$581$	−70.1622			−2.91082
$582$	18.5808			0.770201
$583$	16.4443	+	28.4824i	0.681055	+	1.17962i
$584$			4.29523i			0.177738i
$585$	1.32554	−	2.29590i	0.0548042	−	0.0949237i
$586$			11.4821i			0.474319i
$587$	−14.2149	−	8.20698i	−0.586712	−	0.338738i	0.177084	−	0.984196i	$-0.443333\pi$
$587$	−14.2149	−	8.20698i	−0.586712	−	0.338738i	−0.763796	+	0.645457i	$0.776667\pi$
$588$	7.55971	−	13.0938i	0.311757	−	0.539979i
$589$	1.79040	−	3.10107i	0.0737723	−	0.127777i
$590$	−11.7153	+	6.76381i	−0.482310	+	0.278462i
$591$	23.1337			0.951592
$592$	−2.65507	−	5.47271i	−0.109123	−	0.224927i
$593$	−11.1197			−0.456629			−0.228315	−	0.973587i	$-0.573322\pi$
$593$	−11.1197			−0.456629			−0.228315	+	0.973587i	$0.573322\pi$
$594$	−4.93905	+	2.85156i	−0.202652	+	0.117001i
$595$	17.9226	−	31.0429i	0.734757	−	1.27264i
$596$	11.9329	−	20.6684i	0.488792	−	0.846612i
$597$	−17.0374	−	9.83657i	−0.697296	−	0.402584i
$598$		−	16.5447i		−	0.676562i
$599$	20.6489	−	35.7649i	0.843691	−	1.46131i	−0.0430629	−	0.999072i	$-0.513712\pi$
$599$	20.6489	−	35.7649i	0.843691	−	1.46131i	0.886754	−	0.462243i	$-0.152955\pi$
$600$			1.00000i			0.0408248i
$601$	9.90730	+	17.1600i	0.404127	+	0.699969i	0.994219	−	0.107367i	$-0.0342419\pi$
$601$	9.90730	+	17.1600i	0.404127	+	0.699969i	−0.590092	+	0.807336i	$0.700909\pi$
$602$	−31.8502			−1.29812
$603$	9.32583			0.379777
$604$	6.18851	+	10.7188i	0.251807	+	0.436142i
$605$	−18.6418	−	10.7628i	−0.757896	−	0.437572i
$606$			8.68791i			0.352922i
$607$	10.7032	−	6.17949i	0.434429	−	0.250818i	−0.266802	−	0.963751i	$-0.585967\pi$
$607$	10.7032	−	6.17949i	0.434429	−	0.250818i	0.701232	+	0.712933i	$0.252634\pi$
$608$	0.627705	+	1.08722i	0.0254568	+	0.0440925i
$609$	21.8589	−	12.6202i	0.885767	−	0.511398i
$610$	4.41154	+	2.54700i	0.178618	+	0.103125i
$611$	4.33619	+	2.50350i	0.175423	+	0.101281i
$612$	6.60048	−	3.81079i	0.266809	−	0.154042i
$613$	−18.0847	−	31.3236i	−0.730433	−	1.26515i	−0.956698	−	0.291082i	$-0.905985\pi$
$613$	−18.0847	−	31.3236i	−0.730433	−	1.26515i	0.226265	−	0.974066i	$-0.427349\pi$
$614$	9.64500	−	5.56854i	0.389240	−	0.224728i
$615$			5.09400i			0.205410i
$616$	23.2290	+	13.4113i	0.935923	+	0.540356i
$617$	0.135136	+	0.234062i	0.00544037	+	0.00942300i	0.868733	−	0.495281i	$-0.164935\pi$
$617$	0.135136	+	0.234062i	0.00544037	+	0.00942300i	−0.863292	+	0.504704i	$0.831602\pi$
$618$	−1.40272			−0.0564256
$619$	−41.0436			−1.64968			−0.824840	−	0.565366i	$-0.808735\pi$
$619$	−41.0436			−1.64968			−0.824840	+	0.565366i	$0.808735\pi$
$620$	−1.42615	−	2.47016i	−0.0572756	−	0.0992042i
$621$			6.24074i			0.250432i
$622$	3.08488	−	5.34316i	0.123692	−	0.214241i
$623$			1.15392i			0.0462308i
$624$	−2.29590	−	1.32554i	−0.0919095	−	0.0530640i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	1.47820	−	2.56033i	0.0590809	−	0.102331i
$627$	−6.20054	+	3.57988i	−0.247626	+	0.142967i
$628$	1.48838			0.0593926
$629$	−41.7107	+	20.2358i	−1.66312	+	0.806856i
$630$	4.70313			0.187377
$631$	−22.6635	+	13.0848i	−0.902218	+	0.520896i	−0.877919	−	0.478809i	$-0.841069\pi$
$631$	−22.6635	+	13.0848i	−0.902218	+	0.520896i	−0.0242989	+	0.999705i	$0.507735\pi$
$632$	−1.68237	+	2.91395i	−0.0669210	+	0.115911i
$633$	2.05041	−	3.55141i	0.0814963	−	0.141156i
$634$	−3.26496	−	1.88503i	−0.129668	−	0.0748640i
$635$			2.02599i			0.0803988i
$636$	2.88339	−	4.99417i	0.114334	−	0.198032i
$637$			40.0827i			1.58813i
$638$	15.3036	+	26.5066i	0.605876	+	1.04941i
$639$	−9.16031			−0.362376
$640$	1.00000			0.0395285
$641$	8.95983	+	15.5189i	0.353892	+	0.612959i	0.986928	−	0.161164i	$-0.0515247\pi$
$641$	8.95983	+	15.5189i	0.353892	+	0.612959i	−0.633036	+	0.774123i	$0.718191\pi$
$642$	11.7591	+	6.78912i	0.464095	+	0.267945i
$643$			9.02712i			0.355995i	0.984031	+	0.177997i	$0.0569619\pi$
$643$			9.02712i			0.355995i	−0.984031	+	0.177997i	$0.943038\pi$
$644$	25.4187	−	14.6755i	1.00164	−	0.578296i
$645$	−3.38607	−	5.86484i	−0.133326	−	0.230928i
$646$	8.28631	−	4.78410i	0.326021	−	0.188228i
$647$	18.5940	+	10.7353i	0.731006	+	0.422047i	0.818790	−	0.574093i	$-0.194645\pi$
$647$	18.5940	+	10.7353i	0.731006	+	0.422047i	−0.0877839	+	0.996140i	$0.527979\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−66.8137	+	38.5749i	−2.62267	+	1.51420i
$650$	−1.32554	−	2.29590i	−0.0519919	−	0.0900525i
$651$	−11.6175	+	6.70737i	−0.455326	+	0.262882i
$652$			9.95390i			0.389825i
$653$	−9.80916	−	5.66332i	−0.383862	−	0.221623i	0.295635	−	0.955301i	$-0.404469\pi$
$653$	−9.80916	−	5.66332i	−0.383862	−	0.221623i	−0.679497	+	0.733678i	$0.737802\pi$
$654$	4.94449	+	8.56411i	0.193345	+	0.334883i
$655$	17.7741			0.694492
$656$	5.09400			0.198887
$657$	2.14761	+	3.71978i	0.0837864	+	0.145122i
$658$			8.88265i			0.346282i
$659$	19.4125	−	33.6235i	0.756205	−	1.30979i	−0.188568	−	0.982060i	$-0.560385\pi$
$659$	19.4125	−	33.6235i	0.756205	−	1.30979i	0.944773	−	0.327725i	$-0.106282\pi$
$660$			5.70313i			0.221994i
$661$	−4.59195	−	2.65116i	−0.178606	−	0.103118i	0.408032	−	0.912968i	$-0.366215\pi$
$661$	−4.59195	−	2.65116i	−0.178606	−	0.103118i	−0.586638	+	0.809850i	$0.699549\pi$
$662$	2.61576	−	4.53064i	0.101665	−	0.176088i
$663$	−10.1027	+	17.4984i	−0.392356	+	0.679581i
$664$	−12.9195	+	7.45910i	−0.501375	+	0.289469i
$665$	5.90435			0.228961
$666$	−5.03572	−	3.41197i	−0.195130	−	0.132211i
$667$	33.4924			1.29683
$668$	8.23764	−	4.75600i	0.318724	−	0.184015i
$669$	5.31064	−	9.19830i	0.205321	−	0.355627i
$670$	4.66291	−	8.07640i	0.180144	−	0.312019i
$671$	25.1596	+	14.5259i	0.971274	+	0.560765i
$672$		−	4.70313i		−	0.181427i
$673$	−13.4385	+	23.2762i	−0.518016	+	0.897230i	0.481765	+	0.876300i	$0.339996\pi$
$673$	−13.4385	+	23.2762i	−0.518016	+	0.897230i	−0.999781	+	0.0209293i	$0.993337\pi$
$674$		−	1.30736i		−	0.0503576i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	−5.97180			−0.229685
$677$	−27.0479			−1.03954			−0.519768	−	0.854308i	$-0.673982\pi$
$677$	−27.0479			−1.03954			−0.519768	+	0.854308i	$0.673982\pi$
$678$	8.81827	+	15.2737i	0.338664	+	0.586583i
$679$	−75.6803	−	43.6941i	−2.90434	−	1.67682i
$680$		−	7.62158i		−	0.292274i
$681$	8.68136	−	5.01219i	0.332671	−	0.192067i
$682$	−8.13352	−	14.0877i	−0.311449	−	0.539445i
$683$	26.1162	−	15.0782i	0.999308	−	0.576951i	0.0912643	−	0.995827i	$-0.470909\pi$
$683$	26.1162	−	15.0782i	0.999308	−	0.576951i	0.908043	+	0.418876i	$0.137576\pi$
$684$	1.08722	+	0.627705i	0.0415708	+	0.0240009i
$685$	4.30690	+	2.48659i	0.164558	+	0.0950078i
$686$	−33.0706	+	19.0933i	−1.26264	+	0.728987i
$687$	−9.98570	−	17.2957i	−0.380978	−	0.659874i
$688$	−5.86484	+	3.38607i	−0.223595	+	0.129093i
$689$			15.2882i			0.582432i
$690$	5.40464	+	3.12037i	0.205751	+	0.118790i
$691$	17.5142	+	30.3355i	0.666271	+	1.15402i	0.978939	+	0.204153i	$0.0654441\pi$
$691$	17.5142	+	30.3355i	0.666271	+	1.15402i	−0.312668	+	0.949863i	$0.601223\pi$
$692$	−11.6606			−0.443268
$693$	26.8225			1.01890
$694$	−0.419217	−	0.726106i	−0.0159133	−	0.0275626i
$695$		−	0.769606i		−	0.0291928i
$696$	2.68337	−	4.64774i	0.101713	−	0.176172i
$697$		−	38.8244i		−	1.47058i
$698$	17.6704	+	10.2020i	0.668836	+	0.386153i
$699$	12.5337	−	21.7090i	0.474067	−	0.821108i
$700$	2.35156	−	4.07303i	0.0888808	−	0.153946i
$701$	36.4719	−	21.0571i	1.37752	−	0.795314i	0.385664	−	0.922639i	$-0.373972\pi$
$701$	36.4719	−	21.0571i	1.37752	−	0.795314i	0.991861	+	0.127325i	$0.0406392\pi$
$702$	−2.65107			−0.100058
$703$	−6.32189	−	4.28343i	−0.238434	−	0.161553i
$704$	5.70313			0.214945
$705$	−1.63563	+	0.944334i	−0.0616015	+	0.0355657i
$706$	−11.3826	+	19.7152i	−0.428389	+	0.741991i
$707$	20.4302	−	35.3861i	0.768356	−	1.33083i
$708$	11.7153	+	6.76381i	0.440287	+	0.254200i
$709$			33.4669i			1.25687i	0.777860	+	0.628437i	$0.216305\pi$
$709$			33.4669i			1.25687i	−0.777860	+	0.628437i	$0.783695\pi$
$710$	−4.58016	+	7.93306i	−0.171890	+	0.297723i
$711$			3.36474i			0.126188i
$712$	0.122676	+	0.212481i	0.00459747	+	0.00796305i
$713$	−17.8005			−0.666633
$714$	−35.8453			−1.34148
$715$	−7.55971	−	13.0938i	−0.282717	−	0.489680i
$716$	11.6308	+	6.71504i	0.434663	+	0.250953i
$717$		−	28.1536i		−	1.05141i
$718$	14.5879	−	8.42234i	0.544417	−	0.314319i
$719$	−3.77631	−	6.54076i	−0.140833	−	0.243929i	0.786978	−	0.616981i	$-0.211645\pi$
$719$	−3.77631	−	6.54076i	−0.140833	−	0.243929i	−0.927810	+	0.373052i	$0.878311\pi$
$720$	0.866025	−	0.500000i	0.0322749	−	0.0186339i
$721$	5.71331	+	3.29858i	0.212775	+	0.122846i
$722$	−15.0896	−	8.71197i	−0.561576	−	0.324226i
$723$	−11.0003	+	6.35100i	−0.409104	+	0.236196i
$724$	−11.4732	−	19.8721i	−0.426397	−	0.738541i
$725$	4.64774	−	2.68337i	0.172613	−	0.0996579i
$726$			21.5257i			0.798893i
$727$	40.7310	+	23.5161i	1.51063	+	0.872163i	0.999923	+	0.0124086i	$0.00394989\pi$
$727$	40.7310	+	23.5161i	1.51063	+	0.872163i	0.510708	+	0.859754i	$0.329383\pi$
$728$	6.23417	+	10.7979i	0.231054	+	0.400197i
$729$	1.00000			0.0370370
$730$	4.29523			0.158974
$731$	25.8072	+	44.6994i	0.954514	+	1.65327i
$732$		−	5.09400i		−	0.188280i
$733$	−10.1919	+	17.6528i	−0.376445	+	0.652021i	−0.990542	−	0.137209i	$-0.956187\pi$
$733$	−10.1919	+	17.6528i	−0.376445	+	0.652021i	0.614097	+	0.789230i	$0.289520\pi$
$734$		−	0.888313i		−	0.0327882i
$735$	−13.0938	−	7.55971i	−0.482972	−	0.278844i
$736$	3.12037	−	5.40464i	0.115018	−	0.199218i
$737$	26.5932	−	46.0608i	0.979573	−	1.69667i
$738$	4.41154	−	2.54700i	0.162391	−	0.0937564i
$739$	1.05041			0.0386401			0.0193200	−	0.999813i	$-0.493850\pi$
$739$	1.05041			0.0386401			0.0193200	+	0.999813i	$0.493850\pi$
$740$	−5.47271	+	2.65507i	−0.201181	+	0.0976023i
$741$	−3.32819			−0.122264
$742$	−23.4882	+	13.5609i	−0.862281	+	0.497838i
$743$	0.193291	−	0.334790i	0.00709116	−	0.0122822i	−0.862458	−	0.506129i	$-0.831076\pi$
$743$	0.193291	−	0.334790i	0.00709116	−	0.0122822i	0.869549	+	0.493846i	$0.164409\pi$
$744$	−1.42615	+	2.47016i	−0.0522852	+	0.0905606i
$745$	−20.6684	−	11.9329i	−0.757233	−	0.437189i
$746$		−	19.9618i		−	0.730853i
$747$	−7.45910	+	12.9195i	−0.272914	+	0.472701i
$748$		−	43.4669i		−	1.58931i
$749$	−31.9301	−	55.3046i	−1.16670	−	2.02079i
$750$	1.00000			0.0365148
$751$	−22.1353			−0.807729			−0.403864	−	0.914819i	$-0.632333\pi$
$751$	−22.1353			−0.807729			−0.403864	+	0.914819i	$0.632333\pi$
$752$	0.944334	+	1.63563i	0.0344363	+	0.0596454i
$753$	−1.06827	−	0.616767i	−0.0389300	−	0.0224762i
$754$			14.2276i			0.518140i
$755$	10.7188	−	6.18851i	0.390098	−	0.225223i
$756$	−2.35156	−	4.07303i	−0.0855256	−	0.148135i
$757$	−10.5475	+	6.08961i	−0.383356	+	0.221331i	−0.679277	−	0.733882i	$-0.737707\pi$
$757$	−10.5475	+	6.08961i	−0.383356	+	0.221331i	0.295921	+	0.955212i	$0.404373\pi$
$758$	10.3331	+	5.96581i	0.375315	+	0.216688i
$759$	30.8234	+	17.7959i	1.11882	+	0.645949i
$760$	1.08722	−	0.627705i	0.0394375	−	0.0227693i
$761$	−11.7443	−	20.3417i	−0.425729	−	0.737385i	0.570759	−	0.821118i	$-0.306649\pi$
$761$	−11.7443	−	20.3417i	−0.425729	−	0.737385i	−0.996488	+	0.0837328i	$0.973316\pi$
$762$	1.75456	−	1.01299i	0.0635609	−	0.0366969i
$763$		−	46.5092i		−	1.68374i
$764$	8.51131	+	4.91401i	0.307928	+	0.177783i
$765$	−3.81079	−	6.60048i	−0.137779	−	0.238641i
$766$	10.8609			0.392419
$767$	−35.8627			−1.29493
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$		−	1.08420i		−	0.0390972i	−0.999809	−	0.0195486i	$-0.993777\pi$
$769$		−	1.08420i		−	0.0390972i	0.999809	−	0.0195486i	$-0.00622291\pi$
$770$	13.4113	−	23.2290i	0.483309	−	0.837115i
$771$		−	14.4161i		−	0.519182i
$772$	10.1891	+	5.88269i	0.366714	+	0.211723i
$773$	9.46918	−	16.4011i	0.340583	−	0.589906i	−0.643958	−	0.765060i	$-0.722709\pi$
$773$	9.46918	−	16.4011i	0.340583	−	0.589906i	0.984541	+	0.175154i	$0.0560424\pi$
$774$	−3.38607	+	5.86484i	−0.121710	+	0.210807i
$775$	−2.47016	+	1.42615i	−0.0887309	+	0.0512288i
$776$	−18.5808			−0.667013
$777$	12.4871	+	25.7389i	0.447974	+	0.923377i
$778$	−12.1208			−0.434551
$779$	5.53829	−	3.19753i	0.198430	−	0.114563i
$780$	−1.32554	+	2.29590i	−0.0474619	+	0.0822063i
$781$	−26.1212	+	45.2433i	−0.934691	+	1.61893i
$782$	−41.1919	−	23.7822i	−1.47302	−	0.850448i
$783$		−	5.36674i		−	0.191792i
$784$	−7.55971	+	13.0938i	−0.269990	+	0.467636i
$785$		−	1.48838i		−	0.0531224i
$786$	−8.88706	−	15.3928i	−0.316991	−	0.549044i
$787$	−37.4924			−1.33646			−0.668230	−	0.743955i	$-0.732948\pi$
$787$	−37.4924			−1.33646			−0.668230	+	0.743955i	$0.732948\pi$
$788$	−23.1337			−0.824103
$789$	−1.07034	−	1.85388i	−0.0381051	−	0.0659999i
$790$	2.91395	+	1.68237i	0.103674	+	0.0598560i
$791$		−	82.9469i		−	2.94925i
$792$	4.93905	−	2.85156i	0.175502	−	0.101326i
$793$	6.75229	+	11.6953i	0.239781	+	0.415313i
$794$	2.75432	−	1.59021i	0.0977473	−	0.0564344i
$795$	−4.99417	−	2.88339i	−0.177125	−	0.102263i
$796$	17.0374	+	9.83657i	0.603876	+	0.348648i
$797$	12.3319	−	7.11980i	0.436817	−	0.252196i	−0.265430	−	0.964130i	$-0.585514\pi$
$797$	12.3319	−	7.11980i	0.436817	−	0.252196i	0.702246	+	0.711934i	$0.252180\pi$
$798$	−2.95218	−	5.11332i	−0.104506	−	0.181010i
$799$	12.4661	−	7.19732i	0.441020	−	0.254623i
$800$		−	1.00000i		−	0.0353553i
$801$	0.212481	+	0.122676i	0.00750763	+	0.00433453i
$802$	−5.48188	−	9.49489i	−0.193572	−	0.335276i
$803$	24.4962			0.864454
$804$	−9.32583			−0.328897
$805$	−14.6755	−	25.4187i	−0.517244	−	0.895892i
$806$		−	7.56166i		−	0.266348i
$807$	10.3653	−	17.9533i	0.364877	−	0.631986i
$808$		−	8.68791i		−	0.305640i
$809$	−26.1508	−	15.0982i	−0.919413	−	0.530824i	−0.0359656	−	0.999353i	$-0.511451\pi$
$809$	−26.1508	−	15.0982i	−0.919413	−	0.530824i	−0.883448	+	0.468529i	$0.844784\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	−1.58351	+	2.74272i	−0.0556046	+	0.0963099i	−0.892488	−	0.451071i	$-0.851042\pi$
$811$	−1.58351	+	2.74272i	−0.0556046	+	0.0963099i	0.836883	+	0.547381i	$0.184375\pi$
$812$	−21.8589	+	12.6202i	−0.767097	+	0.442884i
$813$	−18.2509			−0.640086
$814$	−31.2116	+	15.1422i	−1.09397	+	0.530734i
$815$	9.95390			0.348670
$816$	−6.60048	+	3.81079i	−0.231063	+	0.133404i
$817$	−4.25090	+	7.36278i	−0.148720	+	0.257591i
$818$	15.4382	−	26.7397i	0.539783	−	0.934931i
$819$	10.7979	+	6.23417i	0.377309	+	0.217840i
$820$		−	5.09400i		−	0.177890i
$821$	11.2651	−	19.5118i	0.393156	−	0.680967i	−0.599708	−	0.800219i	$-0.704716\pi$
$821$	11.2651	−	19.5118i	0.393156	−	0.680967i	0.992864	+	0.119253i	$0.0380498\pi$
$822$		−	4.97318i		−	0.173460i
$823$	−16.3395	−	28.3008i	−0.569558	−	0.986503i	−0.996610	−	0.0822760i	$-0.973781\pi$
$823$	−16.3395	−	28.3008i	−0.569558	−	0.986503i	0.427052	−	0.904227i	$-0.359552\pi$
$824$	1.40272			0.0488660
$825$	5.70313			0.198557
$826$	−31.8111	−	55.0984i	−1.10685	−	1.91712i
$827$	−8.04386	−	4.64412i	−0.279712	−	0.161492i	0.353581	−	0.935404i	$-0.384964\pi$
$827$	−8.04386	−	4.64412i	−0.279712	−	0.161492i	−0.633293	+	0.773912i	$0.718297\pi$
$828$		−	6.24074i		−	0.216881i
$829$	−9.57327	+	5.52713i	−0.332493	+	0.191965i	−0.656948	−	0.753936i	$-0.728153\pi$
$829$	−9.57327	+	5.52713i	−0.332493	+	0.191965i	0.324454	+	0.945901i	$0.394819\pi$
$830$	7.45910	+	12.9195i	0.258909	+	0.448444i
$831$	−2.06980	+	1.19500i	−0.0718006	+	0.0414541i
$832$	2.29590	+	1.32554i	0.0795959	+	0.0459547i
$833$	99.7955	+	57.6170i	3.45771	+	1.99631i
$834$	−0.666498	+	0.384803i	−0.0230790	+	0.0133246i
$835$	−4.75600	−	8.23764i	−0.164588	−	0.285075i
$836$	6.20054	−	3.57988i	0.214450	−	0.123813i
$837$			2.85230i			0.0985899i
$838$	−0.598754	−	0.345691i	−0.0206836	−	0.0119417i
$839$	5.32703	+	9.22668i	0.183909	+	0.318540i	0.943208	−	0.332201i	$-0.107791\pi$
$839$	5.32703	+	9.22668i	0.183909	+	0.318540i	−0.759299	+	0.650742i	$0.774458\pi$
$840$	−4.70313			−0.162273
$841$	0.198073			0.00683010
$842$	−6.81086	−	11.7968i	−0.234718	−	0.406543i
$843$			15.6197i			0.537971i
$844$	−2.05041	+	3.55141i	−0.0705779	+	0.122244i
$845$			5.97180i			0.205436i
$846$	1.63563	+	0.944334i	0.0562342	+	0.0324669i
$847$	50.6190	−	87.6747i	1.73929	−	3.01254i
$848$	−2.88339	+	4.99417i	−0.0990160	+	0.171501i
$849$	14.0941	−	8.13724i	0.483709	−	0.279269i
$850$	−7.62158			−0.261418
$851$	−2.72720	+	37.8629i	−0.0934871	+	1.29792i
$852$	9.16031			0.313827
$853$	−22.1782	+	12.8046i	−0.759369	+	0.438422i	−0.829069	−	0.559146i	$-0.811129\pi$
$853$	−22.1782	+	12.8046i	−0.759369	+	0.438422i	0.0697003	+	0.997568i	$0.477796\pi$
$854$	−11.9789	+	20.7480i	−0.409909	+	0.709983i
$855$	0.627705	−	1.08722i	0.0214671	−	0.0371820i
$856$	−11.7591	−	6.78912i	−0.401918	−	0.232047i
$857$		−	8.00871i		−	0.273572i	−0.990601	−	0.136786i	$-0.956323\pi$
$857$		−	8.00871i		−	0.273572i	0.990601	−	0.136786i	$-0.0436773\pi$
$858$	−7.55971	+	13.0938i	−0.258084	+	0.447015i
$859$			0.819822i			0.0279720i	0.999902	+	0.0139860i	$0.00445202\pi$
$859$			0.819822i			0.0279720i	−0.999902	+	0.0139860i	$0.995548\pi$
$860$	3.38607	+	5.86484i	0.115464	+	0.199989i
$861$	−23.9578			−0.816478
$862$	16.3234			0.555976
$863$	−1.12119	−	1.94196i	−0.0381657	−	0.0661050i	0.846312	−	0.532688i	$-0.178818\pi$
$863$	−1.12119	−	1.94196i	−0.0381657	−	0.0661050i	−0.884477	+	0.466583i	$0.845485\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$			11.6606i			0.396471i
$866$	−5.95892	+	3.44038i	−0.202492	+	0.116909i
$867$	20.5443	+	35.5837i	0.697719	+	1.20849i
$868$	11.6175	−	6.70737i	0.394324	−	0.227663i
$869$	16.6186	+	9.59477i	0.563748	+	0.325480i
$870$	−4.64774	−	2.68337i	−0.157573	−	0.0909748i
$871$	21.4111	−	12.3617i	0.725489	−	0.418861i
$872$	−4.94449	−	8.56411i	−0.167442	−	0.290017i
$873$	−16.0915	+	9.29042i	−0.544614	+	0.314433i
$874$		−	7.83469i		−	0.265012i
$875$	−4.07303	−	2.35156i	−0.137694	−	0.0794974i
$876$	−2.14761	−	3.71978i	−0.0725612	−	0.125680i
$877$	−21.4359			−0.723838			−0.361919	−	0.932209i	$-0.617878\pi$
$877$	−21.4359			−0.723838			−0.361919	+	0.932209i	$0.617878\pi$
$878$	−9.86666			−0.332984
$879$	−5.74103	−	9.94375i	−0.193640	−	0.335394i
$880$		−	5.70313i		−	0.192252i
$881$	9.88803	−	17.1266i	0.333136	−	0.577009i	−0.649989	−	0.759944i	$-0.725226\pi$
$881$	9.88803	−	17.1266i	0.333136	−	0.577009i	0.983125	+	0.182935i	$0.0585598\pi$
$882$			15.1194i			0.509097i
$883$	−2.06508	−	1.19228i	−0.0694956	−	0.0401233i	0.464850	−	0.885390i	$-0.346108\pi$
$883$	−2.06508	−	1.19228i	−0.0694956	−	0.0401233i	−0.534345	+	0.845266i	$0.679442\pi$
$884$	10.1027	−	17.4984i	0.339790	−	0.588534i
$885$	6.76381	−	11.7153i	0.227363	−	0.393804i
$886$	−25.1282	+	14.5078i	−0.844200	+	0.487399i
$887$	3.41380			0.114624			0.0573121	−	0.998356i	$-0.481747\pi$
$887$	3.41380			0.114624			0.0573121	+	0.998356i	$0.481747\pi$
$888$	5.03572	+	3.41197i	0.168988	+	0.114498i
$889$	−9.52848			−0.319575
$890$	0.212481	−	0.122676i	0.00712237	−	0.00411210i
$891$	2.85156	−	4.93905i	0.0955310	−	0.165465i
$892$	−5.31064	+	9.19830i	−0.177813	+	0.307982i
$893$	2.05339	+	1.18553i	0.0687141	+	0.0396721i
$894$			23.8659i			0.798194i
$895$	6.71504	−	11.6308i	0.224459	−	0.388775i
$896$			4.70313i			0.157121i
$897$	8.27233	+	14.3281i	0.276205	+	0.478401i
$898$	35.4147			1.18181
$899$	15.3076			0.510536
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	38.0635	+	21.9760i	1.26808	+	0.732126i
$902$		−	29.0518i		−	0.967318i
$903$	27.5831	−	15.9251i	0.917908	−	0.529955i
$904$	−8.81827	−	15.2737i	−0.293291	−	0.507995i
$905$	−19.8721	+	11.4732i	−0.660571	+	0.381381i
$906$	−10.7188	−	6.18851i	−0.356109	−	0.205599i
$907$	15.6917	+	9.05961i	0.521035	+	0.300819i	0.737358	−	0.675502i	$-0.236073\pi$
$907$	15.6917	+	9.05961i	0.521035	+	0.300819i	−0.216323	+	0.976322i	$0.569406\pi$
$908$	−8.68136	+	5.01219i	−0.288101	+	0.166335i
$909$	−4.34396	−	7.52395i	−0.144080	−	0.249554i
$910$	10.7979	−	6.23417i	0.357947	−	0.206661i
$911$		−	15.0027i		−	0.497060i	−0.968624	−	0.248530i	$-0.920053\pi$
$911$		−	15.0027i		−	0.497060i	0.968624	−	0.248530i	$-0.0799475\pi$
$912$	−1.08722	−	0.627705i	−0.0360013	−	0.0207854i
$913$	42.5402	+	73.6818i	1.40787	+	2.43851i
$914$	31.6744			1.04770
$915$	−5.09400			−0.168403
$916$	9.98570	+	17.2957i	0.329937	+	0.571467i
$917$			83.5940i			2.76052i
$918$	−3.81079	+	6.60048i	−0.125775	+	0.217848i
$919$		−	12.0743i		−	0.398296i	−0.979969	−	0.199148i	$-0.936183\pi$
$919$		−	12.0743i		−	0.398296i	0.979969	−	0.199148i	$-0.0638174\pi$
$920$	−5.40464	−	3.12037i	−0.178186	−	0.102876i
$921$	−5.56854	+	9.64500i	−0.183490	+	0.317813i
$922$	17.1750	−	29.7480i	0.565628	−	0.979697i
$923$	−21.0311	+	12.1423i	−0.692248	+	0.399670i
$924$	−26.8225			−0.882397
$925$	2.65507	+	5.47271i	0.0872982	+	0.179942i
$926$	−7.75255			−0.254765
$927$	1.21479	−	0.701359i	0.0398989	−	0.0230356i
$928$	−2.68337	+	4.64774i	−0.0880860	+	0.152569i
$929$	5.55017	−	9.61318i	0.182095	−	0.315398i	−0.760499	−	0.649340i	$-0.775045\pi$
$929$	5.55017	−	9.61318i	0.182095	−	0.315398i	0.942594	+	0.333941i	$0.108379\pi$
$930$	2.47016	+	1.42615i	0.0809999	+	0.0467653i
$931$			18.9811i			0.622079i
$932$	−12.5337	+	21.7090i	−0.410554	+	0.711101i
$933$			6.16975i			0.201989i
$934$	12.0066	+	20.7961i	0.392869	+	0.680470i
$935$	−43.4669			−1.42152
$936$	2.65107			0.0866531
$937$	10.2758	+	17.7983i	0.335697	+	0.581444i	0.983618	−	0.180263i	$-0.0576949\pi$
$937$	10.2758	+	17.7983i	0.335697	+	0.581444i	−0.647922	+	0.761707i	$0.724362\pi$
$938$	37.9844	+	21.9303i	1.24023	+	0.716049i
$939$			2.95641i			0.0964788i
$940$	1.63563	−	0.944334i	0.0533485	−	0.0308008i
$941$	−5.46848	−	9.47169i	−0.178267	−	0.308768i	0.763020	−	0.646375i	$-0.223716\pi$
$941$	−5.46848	−	9.47169i	−0.178267	−	0.308768i	−0.941287	+	0.337607i	$0.890383\pi$
$942$	−1.28897	+	0.744188i	−0.0419969	+	0.0242469i
$943$	−27.5313	−	15.8952i	−0.896541	−	0.517618i
$944$	−11.7153	−	6.76381i	−0.381299	−	0.220143i
$945$	−4.07303	+	2.35156i	−0.132496	+	0.0764964i
$946$	19.3112	+	33.4480i	0.627861	+	1.08749i
$947$	−32.7455	+	18.9056i	−1.06409	+	0.614350i	−0.926560	−	0.376148i	$-0.877248\pi$
$947$	−32.7455	+	18.9056i	−1.06409	+	0.614350i	−0.137526	+	0.990498i	$0.543915\pi$
$948$		−	3.36474i		−	0.109282i
$949$	9.86141	+	5.69349i	0.320115	+	0.184818i
$950$	−0.627705	−	1.08722i	−0.0203654	−	0.0352740i
$951$	3.77005			0.122252
$952$	35.8453			1.16175
$953$	−17.0499	−	29.5313i	−0.552301	−	0.956614i	−0.998108	−	0.0614846i	$-0.980416\pi$
$953$	−17.0499	−	29.5313i	−0.552301	−	0.956614i	0.445807	−	0.895129i	$-0.352917\pi$
$954$			5.76678i			0.186706i
$955$	4.91401	−	8.51131i	0.159014	−	0.275420i
$956$			28.1536i			0.910551i
$957$	−26.5066	−	15.3036i	−0.856838	−	0.494696i
$958$	−13.3297	+	23.0877i	−0.430662	+	0.745929i
$959$	−11.6948	+	20.2559i	−0.377644	+	0.654098i
$960$	−0.866025	+	0.500000i	−0.0279508	+	0.0161374i
$961$	22.8644			0.737561
$962$	−16.0842	−	1.15852i	−0.518575	−	0.0373521i
$963$	−13.5782			−0.437553
$964$	11.0003	−	6.35100i	0.354295	−	0.204552i
$965$	5.88269	−	10.1891i	0.189370	−	0.327999i
$966$	−14.6755	+	25.4187i	−0.472177	+	0.817834i
$967$	−18.4986	−	10.6802i	−0.594876	−	0.343452i	0.172147	−	0.985071i	$-0.444930\pi$
$967$	−18.4986	−	10.6802i	−0.594876	−	0.343452i	−0.767023	+	0.641619i	$0.778263\pi$
$968$		−	21.5257i		−	0.691861i
$969$	−4.78410	+	8.28631i	−0.153688	+	0.266195i
$970$			18.5808i			0.596595i
$971$	28.1545	+	48.7650i	0.903520	+	1.56494i	0.822892	+	0.568199i	$0.192359\pi$
$971$	28.1545	+	48.7650i	0.903520	+	1.56494i	0.0806286	+	0.996744i	$0.474307\pi$
$972$	−1.00000			−0.0320750
$973$	3.61956			0.116038
$974$	−7.80995	−	13.5272i	−0.250247	−	0.433440i
$975$	2.29590	+	1.32554i	0.0735276	+	0.0424512i
$976$			5.09400i			0.163055i
$977$	20.6711	−	11.9345i	0.661326	−	0.381817i	−0.131456	−	0.991322i	$-0.541965\pi$
$977$	20.6711	−	11.9345i	0.661326	−	0.381817i	0.792782	+	0.609505i	$0.208632\pi$
$978$	−4.97695	−	8.62033i	−0.159145	−	0.275648i
$979$	1.21180	−	0.699636i	0.0387294	−	0.0223604i
$980$	13.0938	+	7.55971i	0.418266	+	0.241486i
$981$	−8.56411	−	4.94449i	−0.273431	−	0.157865i
$982$	20.8842	−	12.0575i	0.666440	−	0.384769i
$983$	−6.96731	−	12.0677i	−0.222223	−	0.384901i	0.733260	−	0.679948i	$-0.237998\pi$
$983$	−6.96731	−	12.0677i	−0.222223	−	0.384901i	−0.955483	+	0.295048i	$0.904665\pi$
$984$	−4.41154	+	2.54700i	−0.140635	+	0.0811955i
$985$			23.1337i			0.737100i
$986$	35.4231	+	20.4515i	1.12810	+	0.651310i
$987$	−4.44132	−	7.69260i	−0.141369	−	0.244858i
$988$	3.32819			0.105884
$989$	42.2631			1.34389
$990$	−2.85156	−	4.93905i	−0.0906287	−	0.156973i
$991$		−	19.6697i		−	0.624827i	−0.949946	−	0.312414i	$-0.898863\pi$
$991$		−	19.6697i		−	0.624827i	0.949946	−	0.312414i	$-0.101137\pi$
$992$	1.42615	−	2.47016i	0.0452803	−	0.0784278i
$993$			5.23153i			0.166018i
$994$	−37.3102	−	21.5411i	−1.18341	−	0.683241i
$995$	9.83657	−	17.0374i	0.311840	−	0.540123i
$996$	7.45910	−	12.9195i	0.236351	−	0.409371i
$997$	49.7168	−	28.7040i	1.57455	−	0.909066i	0.578948	−	0.815364i	$-0.303463\pi$
$997$	49.7168	−	28.7040i	1.57455	−	0.909066i	0.995600	−	0.0937016i	$-0.0298700\pi$
$998$	7.25576			0.229677
$999$	6.06704	+	0.436999i	0.191953	+	0.0138260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.c.751.8	✓	16
37.27	even	6	inner	1110.2.x.c.841.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.c.751.8	✓	16	1.1	even	1	trivial
1110.2.x.c.841.8	yes	16	37.27	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +1.00000i q^{6} +(2.35156 - 4.07303i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +1.00000i q^{6} +(2.35156 - 4.07303i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} -5.70313 q^{11} +(0.500000 + 0.866025i) q^{12} +(-2.29590 - 1.32554i) q^{13} -4.70313i q^{14} +(0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-6.60048 + 3.81079i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-1.08722 - 0.627705i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(2.35156 + 4.07303i) q^{21} +(-4.93905 + 2.85156i) q^{22} +6.24074i q^{23} +(0.866025 + 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} -2.65107 q^{26} +1.00000 q^{27} +(-2.35156 - 4.07303i) q^{28} -5.36674i q^{29} +(0.500000 - 0.866025i) q^{30} +2.85230i q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.85156 - 4.93905i) q^{33} +(-3.81079 + 6.60048i) q^{34} +(-4.07303 + 2.35156i) q^{35} -1.00000 q^{36} +(6.06704 + 0.436999i) q^{37} -1.25541 q^{38} +(2.29590 - 1.32554i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-2.54700 + 4.41154i) q^{41} +(4.07303 + 2.35156i) q^{42} -6.77214i q^{43} +(-2.85156 + 4.93905i) q^{44} +1.00000i q^{45} +(3.12037 + 5.40464i) q^{46} -1.88867 q^{47} +1.00000 q^{48} +(-7.55971 - 13.0938i) q^{49} +(0.866025 + 0.500000i) q^{50} -7.62158i q^{51} +(-2.29590 + 1.32554i) q^{52} +(-2.88339 - 4.99417i) q^{53} +(0.866025 - 0.500000i) q^{54} +(4.93905 + 2.85156i) q^{55} +(-4.07303 - 2.35156i) q^{56} +(1.08722 - 0.627705i) q^{57} +(-2.68337 - 4.64774i) q^{58} +(11.7153 - 6.76381i) q^{59} -1.00000i q^{60} +(-4.41154 - 2.54700i) q^{61} +(1.42615 + 2.47016i) q^{62} -4.70313 q^{63} -1.00000 q^{64} +(1.32554 + 2.29590i) q^{65} -5.70313i q^{66} +(-4.66291 + 8.07640i) q^{67} +7.62158i q^{68} +(-5.40464 - 3.12037i) q^{69} +(-2.35156 + 4.07303i) q^{70} +(4.58016 - 7.93306i) q^{71} +(-0.866025 + 0.500000i) q^{72} -4.29523 q^{73} +(5.47271 - 2.65507i) q^{74} -1.00000 q^{75} +(-1.08722 + 0.627705i) q^{76} +(-13.4113 + 23.2290i) q^{77} +(1.32554 - 2.29590i) q^{78} +(-2.91395 - 1.68237i) q^{79} +1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} +5.09400i q^{82} +(-7.45910 - 12.9195i) q^{83} +4.70313 q^{84} +7.62158 q^{85} +(-3.38607 - 5.86484i) q^{86} +(4.64774 + 2.68337i) q^{87} +5.70313i q^{88} +(-0.212481 + 0.122676i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-10.7979 + 6.23417i) q^{91} +(5.40464 + 3.12037i) q^{92} +(-2.47016 - 1.42615i) q^{93} +(-1.63563 + 0.944334i) q^{94} +(0.627705 + 1.08722i) q^{95} +(0.866025 - 0.500000i) q^{96} -18.5808i q^{97} +(-13.0938 - 7.55971i) q^{98} +(2.85156 + 4.93905i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} + 8 q^{12} - 12 q^{13} - 8 q^{16} - 6 q^{17} + 6 q^{19} - 2 q^{21} - 6 q^{22} + 8 q^{25} + 16 q^{27} + 2 q^{28} + 8 q^{30} + 6 q^{33} - 4 q^{34} - 6 q^{35} - 16 q^{36} + 18 q^{37} + 12 q^{38} + 12 q^{39} - 8 q^{40} + 6 q^{42} - 6 q^{44} - 4 q^{46} - 60 q^{47} + 16 q^{48} - 4 q^{49} - 12 q^{52} + 12 q^{53} + 6 q^{55} - 6 q^{56} - 6 q^{57} - 12 q^{58} + 12 q^{59} - 4 q^{62} + 4 q^{63} - 16 q^{64} + 22 q^{67} - 6 q^{69} + 2 q^{70} + 2 q^{71} + 24 q^{73} - 8 q^{74} - 16 q^{75} + 6 q^{76} - 58 q^{77} - 36 q^{79} - 8 q^{81} - 8 q^{83} - 4 q^{84} + 8 q^{85} - 2 q^{86} - 42 q^{89} + 8 q^{90} + 6 q^{92} - 6 q^{93} + 6 q^{94} - 6 q^{95} - 12 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 + 8 * q^12 - 12 * q^13 - 8 * q^16 - 6 * q^17 + 6 * q^19 - 2 * q^21 - 6 * q^22 + 8 * q^25 + 16 * q^27 + 2 * q^28 + 8 * q^30 + 6 * q^33 - 4 * q^34 - 6 * q^35 - 16 * q^36 + 18 * q^37 + 12 * q^38 + 12 * q^39 - 8 * q^40 + 6 * q^42 - 6 * q^44 - 4 * q^46 - 60 * q^47 + 16 * q^48 - 4 * q^49 - 12 * q^52 + 12 * q^53 + 6 * q^55 - 6 * q^56 - 6 * q^57 - 12 * q^58 + 12 * q^59 - 4 * q^62 + 4 * q^63 - 16 * q^64 + 22 * q^67 - 6 * q^69 + 2 * q^70 + 2 * q^71 + 24 * q^73 - 8 * q^74 - 16 * q^75 + 6 * q^76 - 58 * q^77 - 36 * q^79 - 8 * q^81 - 8 * q^83 - 4 * q^84 + 8 * q^85 - 2 * q^86 - 42 * q^89 + 8 * q^90 + 6 * q^92 - 6 * q^93 + 6 * q^94 - 6 * q^95 - 12 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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