LMFDB - Embedded newform 1110.2.x.e.751.6

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} + 44x^{14} + 724x^{12} + 5750x^{10} + 23344x^{8} + 47024x^{6} + 43297x^{4} + 13976x^{2} + 676 $ x^16 + 44x^14 + 724x^12 + 5750x^10 + 23344x^8 + 47024x^6 + 43297x^4 + 13976*x^2 + 676
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.6
Root			$-1.35400i$ of defining polynomial
Character	$\chi$	$=$	1110.751
Dual form			1110.2.x.e.841.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(-2.34998 + 4.07029i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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} +(-2.34998 + 4.07029i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} +6.11984 q^{11} +(-0.500000 - 0.866025i) q^{12} +(5.75756 + 3.32413i) q^{13} +4.69996i q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.13561 - 2.38770i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-4.76196 - 2.74932i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(2.34998 + 4.07029i) q^{21} +(5.29993 - 3.05992i) q^{22} -5.04363i q^{23} +(-0.866025 - 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} +6.64825 q^{26} -1.00000 q^{27} +(2.34998 + 4.07029i) q^{28} +4.78061i q^{29} +(-0.500000 + 0.866025i) q^{30} -0.756111i q^{31} +(-0.866025 - 0.500000i) q^{32} +(3.05992 - 5.29993i) q^{33} +(2.38770 - 4.13561i) q^{34} +(4.07029 - 2.34998i) q^{35} -1.00000 q^{36} +(3.40356 + 5.04141i) q^{37} -5.49864 q^{38} +(5.75756 - 3.32413i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(2.34737 - 4.06577i) q^{41} +(4.07029 + 2.34998i) q^{42} -5.21208i q^{43} +(3.05992 - 5.29993i) q^{44} +1.00000i q^{45} +(-2.52181 - 4.36791i) q^{46} +6.93891 q^{47} -1.00000 q^{48} +(-7.54482 - 13.0680i) q^{49} +(0.866025 + 0.500000i) q^{50} -4.77539i q^{51} +(5.75756 - 3.32413i) q^{52} +(1.42802 + 2.47341i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-5.29993 - 3.05992i) q^{55} +(4.07029 + 2.34998i) q^{56} +(-4.76196 + 2.74932i) q^{57} +(2.39031 + 4.14013i) q^{58} +(-6.36667 + 3.67580i) q^{59} +1.00000i q^{60} +(-3.28799 - 1.89832i) q^{61} +(-0.378056 - 0.654812i) q^{62} +4.69996 q^{63} -1.00000 q^{64} +(-3.32413 - 5.75756i) q^{65} -6.11984i q^{66} +(1.03370 - 1.79042i) q^{67} -4.77539i q^{68} +(-4.36791 - 2.52181i) q^{69} +(2.34998 - 4.07029i) q^{70} +(-2.71185 + 4.69706i) q^{71} +(-0.866025 + 0.500000i) q^{72} +3.93200 q^{73} +(5.46827 + 2.66421i) q^{74} +1.00000 q^{75} +(-4.76196 + 2.74932i) q^{76} +(-14.3815 + 24.9095i) q^{77} +(3.32413 - 5.75756i) q^{78} +(11.6166 + 6.70686i) q^{79} +1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} -4.69474i q^{82} +(2.99002 + 5.17887i) q^{83} +4.69996 q^{84} -4.77539 q^{85} +(-2.60604 - 4.51380i) q^{86} +(4.14013 + 2.39031i) q^{87} -6.11984i q^{88} +(-13.9536 + 8.05612i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-27.0603 + 15.6233i) q^{91} +(-4.36791 - 2.52181i) q^{92} +(-0.654812 - 0.378056i) q^{93} +(6.00928 - 3.46946i) q^{94} +(2.74932 + 4.76196i) q^{95} +(-0.866025 + 0.500000i) q^{96} +10.1967i q^{97} +(-13.0680 - 7.54482i) q^{98} +(-3.05992 - 5.29993i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 8 q^{4} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 8 * q^4 - 4 * q^7 - 8 * q^9	$ 16 q + 8 q^{3} + 8 q^{4} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 8 q^{16} - 6 q^{17} - 6 q^{19} + 4 q^{21} + 12 q^{22} + 8 q^{25} - 8 q^{26} - 16 q^{27} + 4 q^{28} - 8 q^{30} - 2 q^{33} + 2 q^{34} + 18 q^{35} - 16 q^{36} - 12 q^{37} + 12 q^{38} - 8 q^{40} + 4 q^{41} + 18 q^{42} - 2 q^{44} + 12 q^{47} - 16 q^{48} - 42 q^{49} - 16 q^{53} - 12 q^{55} + 18 q^{56} - 6 q^{57} + 2 q^{58} + 48 q^{59} - 12 q^{61} - 4 q^{62} + 8 q^{63} - 16 q^{64} + 4 q^{65} + 6 q^{67} - 18 q^{69} + 4 q^{70} - 6 q^{71} - 52 q^{73} - 16 q^{74} + 16 q^{75} - 6 q^{76} + 10 q^{77} - 4 q^{78} + 78 q^{79} - 8 q^{81} + 36 q^{83} + 8 q^{84} - 4 q^{85} - 6 q^{86} + 12 q^{87} + 18 q^{89} + 8 q^{90} - 66 q^{91} - 18 q^{92} - 36 q^{93} + 12 q^{94} - 6 q^{95} - 12 q^{98} + 2 q^{99}+O(q^{100}) $ 16 * q + 8 * q^3 + 8 * q^4 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 8 * q^16 - 6 * q^17 - 6 * q^19 + 4 * q^21 + 12 * q^22 + 8 * q^25 - 8 * q^26 - 16 * q^27 + 4 * q^28 - 8 * q^30 - 2 * q^33 + 2 * q^34 + 18 * q^35 - 16 * q^36 - 12 * q^37 + 12 * q^38 - 8 * q^40 + 4 * q^41 + 18 * q^42 - 2 * q^44 + 12 * q^47 - 16 * q^48 - 42 * q^49 - 16 * q^53 - 12 * q^55 + 18 * q^56 - 6 * q^57 + 2 * q^58 + 48 * q^59 - 12 * q^61 - 4 * q^62 + 8 * q^63 - 16 * q^64 + 4 * q^65 + 6 * q^67 - 18 * q^69 + 4 * q^70 - 6 * q^71 - 52 * q^73 - 16 * q^74 + 16 * q^75 - 6 * q^76 + 10 * q^77 - 4 * q^78 + 78 * q^79 - 8 * q^81 + 36 * q^83 + 8 * q^84 - 4 * q^85 - 6 * q^86 + 12 * q^87 + 18 * q^89 + 8 * q^90 - 66 * q^91 - 18 * q^92 - 36 * q^93 + 12 * q^94 - 6 * q^95 - 12 * q^98 + 2 * 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
$7$	−2.34998	+	4.07029i	−0.888209	+	1.53842i	−0.0462188	+	0.998931i	$0.514717\pi$
$7$	−2.34998	+	4.07029i	−0.888209	+	1.53842i	−0.841991	+	0.539492i	$0.818616\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.00000			−0.316228
$11$	6.11984			1.84520			0.922600	−	0.385758i	$-0.126060\pi$
$11$	6.11984			1.84520			0.922600	+	0.385758i	$0.126060\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	5.75756	+	3.32413i	1.59686	+	0.921947i	0.992088	+	0.125547i	$0.0400687\pi$
$13$	5.75756	+	3.32413i	1.59686	+	0.921947i	0.604771	+	0.796399i	$0.293265\pi$
$14$			4.69996i			1.25612i
$15$	−0.866025	+	0.500000i	−0.223607	+	0.129099i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	4.13561	−	2.38770i	1.00303	−	0.579102i	0.0938890	−	0.995583i	$-0.470070\pi$
$17$	4.13561	−	2.38770i	1.00303	−	0.579102i	0.909144	+	0.416481i	$0.136737\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	−4.76196	−	2.74932i	−1.09247	−	0.630737i	−0.158236	−	0.987401i	$-0.550581\pi$
$19$	−4.76196	−	2.74932i	−1.09247	−	0.630737i	−0.934233	+	0.356664i	$0.883914\pi$
$20$	−0.866025	+	0.500000i	−0.193649	+	0.111803i
$21$	2.34998	+	4.07029i	0.512808	+	0.888209i
$22$	5.29993	−	3.05992i	1.12995	−	0.652377i
$23$		−	5.04363i		−	1.05167i	−0.850587	−	0.525834i	$-0.823753\pi$
$23$		−	5.04363i		−	1.05167i	0.850587	−	0.525834i	$-0.176247\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	6.64825			1.30383
$27$	−1.00000			−0.192450
$28$	2.34998	+	4.07029i	0.444105	+	0.769212i
$29$			4.78061i			0.887738i	0.896092	+	0.443869i	$0.146394\pi$
$29$			4.78061i			0.887738i	−0.896092	+	0.443869i	$0.853606\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$		−	0.756111i		−	0.135802i	−0.997692	−	0.0679008i	$-0.978370\pi$
$31$		−	0.756111i		−	0.135802i	0.997692	−	0.0679008i	$-0.0216301\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	3.05992	−	5.29993i	0.532663	−	0.922600i
$34$	2.38770	−	4.13561i	0.409487	−	0.709252i
$35$	4.07029	−	2.34998i	0.688004	−	0.397219i
$36$	−1.00000			−0.166667
$37$	3.40356	+	5.04141i	0.559542	+	0.828802i
$37$	3.40356	+	5.04141i	0.559542	+	0.828802i
$38$	−5.49864			−0.891997
$39$	5.75756	−	3.32413i	0.921947	−	0.532286i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	2.34737	−	4.06577i	0.366598	−	0.634966i	−0.622433	−	0.782673i	$-0.713856\pi$
$41$	2.34737	−	4.06577i	0.366598	−	0.634966i	0.989031	+	0.147707i	$0.0471892\pi$
$42$	4.07029	+	2.34998i	0.628059	+	0.362610i
$43$		−	5.21208i		−	0.794835i	−0.917638	−	0.397418i	$-0.869906\pi$
$43$		−	5.21208i		−	0.794835i	0.917638	−	0.397418i	$-0.130094\pi$
$44$	3.05992	−	5.29993i	0.461300	−	0.798995i
$45$			1.00000i			0.149071i
$46$	−2.52181	−	4.36791i	−0.371821	−	0.644013i
$47$	6.93891			1.01214			0.506072	−	0.862491i	$-0.331097\pi$
$47$	6.93891			1.01214			0.506072	+	0.862491i	$0.331097\pi$
$48$	−1.00000			−0.144338
$49$	−7.54482	−	13.0680i	−1.07783	−	1.86686i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		−	4.77539i		−	0.668689i
$52$	5.75756	−	3.32413i	0.798429	−	0.460973i
$53$	1.42802	+	2.47341i	0.196154	+	0.339749i	0.947278	−	0.320412i	$-0.103821\pi$
$53$	1.42802	+	2.47341i	0.196154	+	0.339749i	−0.751124	+	0.660161i	$0.770488\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	−5.29993	−	3.05992i	−0.714643	−	0.412599i
$56$	4.07029	+	2.34998i	0.543915	+	0.314029i
$57$	−4.76196	+	2.74932i	−0.630737	+	0.364156i
$58$	2.39031	+	4.14013i	0.313863	+	0.543626i
$59$	−6.36667	+	3.67580i	−0.828869	+	0.478548i	−0.853465	−	0.521149i	$-0.825503\pi$
$59$	−6.36667	+	3.67580i	−0.828869	+	0.478548i	0.0245959	+	0.999697i	$0.492170\pi$
$60$			1.00000i			0.129099i
$61$	−3.28799	−	1.89832i	−0.420984	−	0.243055i	0.274514	−	0.961583i	$-0.411483\pi$
$61$	−3.28799	−	1.89832i	−0.420984	−	0.243055i	−0.695498	+	0.718528i	$0.744816\pi$
$62$	−0.378056	−	0.654812i	−0.0480131	−	0.0831612i
$63$	4.69996			0.592140
$64$	−1.00000			−0.125000
$65$	−3.32413	−	5.75756i	−0.412307	−	0.714137i
$66$		−	6.11984i		−	0.753300i
$67$	1.03370	−	1.79042i	0.126287	−	0.218735i	−0.795948	−	0.605364i	$-0.793027\pi$
$67$	1.03370	−	1.79042i	0.126287	−	0.218735i	0.922235	+	0.386629i	$0.126361\pi$
$68$		−	4.77539i		−	0.579102i
$69$	−4.36791	−	2.52181i	−0.525834	−	0.303591i
$70$	2.34998	−	4.07029i	0.280876	−	0.486492i
$71$	−2.71185	+	4.69706i	−0.321837	+	0.557439i	−0.980867	−	0.194678i	$-0.937634\pi$
$71$	−2.71185	+	4.69706i	−0.321837	+	0.557439i	0.659030	+	0.752117i	$0.270967\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	3.93200			0.460206			0.230103	−	0.973166i	$-0.426094\pi$
$73$	3.93200			0.460206			0.230103	+	0.973166i	$0.426094\pi$
$74$	5.46827	+	2.66421i	0.635674	+	0.309708i
$75$	1.00000			0.115470
$76$	−4.76196	+	2.74932i	−0.546234	+	0.315369i
$77$	−14.3815	+	24.9095i	−1.63892	+	2.83870i
$78$	3.32413	−	5.75756i	0.376383	−	0.651915i
$79$	11.6166	+	6.70686i	1.30697	+	0.754581i	0.981590	−	0.191002i	$-0.0611737\pi$
$79$	11.6166	+	6.70686i	1.30697	+	0.754581i	0.325382	+	0.945583i	$0.394507\pi$
$80$			1.00000i			0.111803i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		−	4.69474i		−	0.518448i
$83$	2.99002	+	5.17887i	0.328197	+	0.568455i	0.982154	−	0.188077i	$-0.0602255\pi$
$83$	2.99002	+	5.17887i	0.328197	+	0.568455i	−0.653957	+	0.756532i	$0.726892\pi$
$84$	4.69996			0.512808
$85$	−4.77539			−0.517964
$86$	−2.60604	−	4.51380i	−0.281017	−	0.486735i
$87$	4.14013	+	2.39031i	0.443869	+	0.256268i
$88$		−	6.11984i		−	0.652377i
$89$	−13.9536	+	8.05612i	−1.47908	+	0.853948i	−0.999720	−	0.0236704i	$-0.992465\pi$
$89$	−13.9536	+	8.05612i	−1.47908	+	0.853948i	−0.479361	+	0.877618i	$0.659131\pi$
$90$	0.500000	+	0.866025i	0.0527046	+	0.0912871i
$91$	−27.0603	+	15.6233i	−2.83669	+	1.63776i
$92$	−4.36791	−	2.52181i	−0.455386	−	0.262917i
$93$	−0.654812	−	0.378056i	−0.0679008	−	0.0392025i
$94$	6.00928	−	3.46946i	0.619810	−	0.357847i
$95$	2.74932	+	4.76196i	0.282074	+	0.488567i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$			10.1967i			1.03532i	0.855586	+	0.517660i	$0.173197\pi$
$97$			10.1967i			1.03532i	−0.855586	+	0.517660i	$0.826803\pi$
$98$	−13.0680	−	7.54482i	−1.32007	−	0.762142i
$99$	−3.05992	−	5.29993i	−0.307533	−	0.532663i
$100$	1.00000			0.100000
$101$	−3.64807			−0.362997			−0.181499	−	0.983391i	$-0.558095\pi$
$101$	−3.64807			−0.362997			−0.181499	+	0.983391i	$0.558095\pi$
$102$	−2.38770	−	4.13561i	−0.236417	−	0.409487i
$103$		−	8.51880i		−	0.839383i	−0.907667	−	0.419691i	$-0.862138\pi$
$103$		−	8.51880i		−	0.839383i	0.907667	−	0.419691i	$-0.137862\pi$
$104$	3.32413	−	5.75756i	0.325957	−	0.564575i
$105$		−	4.69996i		−	0.458669i
$106$	2.47341	+	1.42802i	0.240239	+	0.138702i
$107$	8.49969	−	14.7219i	0.821696	−	1.42322i	−0.0827224	−	0.996573i	$-0.526361\pi$
$107$	8.49969	−	14.7219i	0.821696	−	1.42322i	0.904418	−	0.426647i	$-0.140305\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−5.72959	+	3.30798i	−0.548795	+	0.316847i	−0.748636	−	0.662982i	$-0.769291\pi$
$109$	−5.72959	+	3.30798i	−0.548795	+	0.316847i	0.199841	+	0.979828i	$0.435957\pi$
$110$	−6.11984			−0.583504
$111$	6.06777	−	0.426867i	0.575927	−	0.0405164i
$112$	4.69996			0.444105
$113$	−7.59323	+	4.38396i	−0.714311	+	0.412408i	−0.812655	−	0.582745i	$-0.801979\pi$
$113$	−7.59323	+	4.38396i	−0.714311	+	0.412408i	0.0983439	+	0.995152i	$0.468645\pi$
$114$	−2.74932	+	4.76196i	−0.257497	+	0.445998i
$115$	−2.52181	+	4.36791i	−0.235160	+	0.407310i
$116$	4.14013	+	2.39031i	0.384402	+	0.221934i
$117$		−	6.64825i		−	0.614631i
$118$	−3.67580	+	6.36667i	−0.338385	+	0.586099i
$119$			22.4442i			2.05745i
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	26.4524			2.40476
$122$	−3.79665			−0.343732
$123$	−2.34737	−	4.06577i	−0.211655	−	0.366598i
$124$	−0.654812	−	0.378056i	−0.0588038	−	0.0339504i
$125$		−	1.00000i		−	0.0894427i
$126$	4.07029	−	2.34998i	0.362610	−	0.209353i
$127$	−10.5658	−	18.3004i	−0.937559	−	1.62390i	−0.770006	−	0.638037i	$-0.779747\pi$
$127$	−10.5658	−	18.3004i	−0.937559	−	1.62390i	−0.167554	−	0.985863i	$-0.553587\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−4.51380	−	2.60604i	−0.397418	−	0.229449i
$130$	−5.75756	−	3.32413i	−0.504971	−	0.291545i
$131$	2.93015	−	1.69173i	0.256009	−	0.147807i	−0.366504	−	0.930417i	$-0.619445\pi$
$131$	2.93015	−	1.69173i	0.256009	−	0.147807i	0.622513	+	0.782610i	$0.286112\pi$
$132$	−3.05992	−	5.29993i	−0.266332	−	0.461300i
$133$	22.3810	−	12.9217i	1.94068	−	1.12045i
$134$		−	2.06740i		−	0.178597i
$135$	0.866025	+	0.500000i	0.0745356	+	0.0430331i
$136$	−2.38770	−	4.13561i	−0.204743	−	0.354626i
$137$	−14.3435			−1.22544			−0.612722	−	0.790298i	$-0.709926\pi$
$137$	−14.3435			−1.22544			−0.612722	+	0.790298i	$0.709926\pi$
$138$	−5.04363			−0.429342
$139$	−1.48679	−	2.57519i	−0.126108	−	0.218425i	0.796058	−	0.605221i	$-0.206915\pi$
$139$	−1.48679	−	2.57519i	−0.126108	−	0.218425i	−0.922165	+	0.386796i	$0.873582\pi$
$140$		−	4.69996i		−	0.397219i
$141$	3.46946	−	6.00928i	0.292181	−	0.506072i
$142$			5.42370i			0.455147i
$143$	35.2353	+	20.3431i	2.94652	+	1.70118i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	2.39031	−	4.14013i	0.198504	−	0.343819i
$146$	3.40521	−	1.96600i	0.281817	−	0.162707i
$147$	−15.0896			−1.24457
$148$	6.06777	−	0.426867i	0.498767	−	0.0350883i
$149$	15.9232			1.30448			0.652240	−	0.758012i	$-0.273829\pi$
$149$	15.9232			1.30448			0.652240	+	0.758012i	$0.273829\pi$
$150$	0.866025	−	0.500000i	0.0707107	−	0.0408248i
$151$	−4.38779	+	7.59987i	−0.357073	+	0.618469i	−0.987470	−	0.157804i	$-0.949559\pi$
$151$	−4.38779	+	7.59987i	−0.357073	+	0.618469i	0.630397	+	0.776273i	$0.282892\pi$
$152$	−2.74932	+	4.76196i	−0.222999	+	0.386246i
$153$	−4.13561	−	2.38770i	−0.334344	−	0.193034i
$154$			28.7630i			2.31779i
$155$	−0.378056	+	0.654812i	−0.0303662	+	0.0525957i
$156$		−	6.64825i		−	0.532286i
$157$	−10.1880	−	17.6462i	−0.813094	−	1.40832i	−0.910688	−	0.413095i	$-0.864448\pi$
$157$	−10.1880	−	17.6462i	−0.813094	−	1.40832i	0.0975937	−	0.995226i	$-0.468885\pi$
$158$	13.4137			1.06714
$159$	2.85605			0.226499
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	20.5290	+	11.8524i	1.61791	+	0.934102i
$162$			1.00000i			0.0785674i
$163$	−11.6013	+	6.69803i	−0.908686	+	0.524630i	−0.880008	−	0.474959i	$-0.842463\pi$
$163$	−11.6013	+	6.69803i	−0.908686	+	0.524630i	−0.0286778	+	0.999589i	$0.509130\pi$
$164$	−2.34737	−	4.06577i	−0.183299	−	0.317483i
$165$	−5.29993	+	3.05992i	−0.412599	+	0.238214i
$166$	5.17887	+	2.99002i	0.401958	+	0.232071i
$167$	−12.3715	−	7.14269i	−0.957336	−	0.552718i	−0.0619840	−	0.998077i	$-0.519743\pi$
$167$	−12.3715	−	7.14269i	−0.957336	−	0.552718i	−0.895352	+	0.445359i	$0.853076\pi$
$168$	4.07029	−	2.34998i	0.314029	−	0.181305i
$169$	15.5996	+	27.0194i	1.19997	+	2.07841i
$170$	−4.13561	+	2.38770i	−0.317187	+	0.183128i
$171$			5.49864i			0.420491i
$172$	−4.51380	−	2.60604i	−0.344174	−	0.198709i
$173$	6.96232	+	12.0591i	0.529336	+	0.916836i	0.999415	+	0.0342119i	$0.0108921\pi$
$173$	6.96232	+	12.0591i	0.529336	+	0.916836i	−0.470079	+	0.882624i	$0.655775\pi$
$174$	4.78061			0.362417
$175$	−4.69996			−0.355284
$176$	−3.05992	−	5.29993i	−0.230650	−	0.399498i
$177$			7.35159i			0.552580i
$178$	−8.05612	+	13.9536i	−0.603832	+	1.04587i
$179$			1.64405i			0.122882i	0.998111	+	0.0614409i	$0.0195696\pi$
$179$			1.64405i			0.122882i	−0.998111	+	0.0614409i	$0.980430\pi$
$180$	0.866025	+	0.500000i	0.0645497	+	0.0372678i
$181$	−0.376249	+	0.651682i	−0.0279664	+	0.0484392i	−0.879670	−	0.475585i	$-0.842236\pi$
$181$	−0.376249	+	0.651682i	−0.0279664	+	0.0484392i	0.851703	+	0.524024i	$0.175570\pi$
$182$	−15.6233	+	27.0603i	−1.15807	+	2.00584i
$183$	−3.28799	+	1.89832i	−0.243055	+	0.140328i
$184$	−5.04363			−0.371821
$185$	−0.426867	−	6.06777i	−0.0313839	−	0.446111i
$186$	−0.756111			−0.0554408
$187$	25.3093	−	14.6123i	1.85080	−	1.06856i
$188$	3.46946	−	6.00928i	0.253036	−	0.438272i
$189$	2.34998	−	4.07029i	0.170936	−	0.296070i
$190$	4.76196	+	2.74932i	0.345469	+	0.199457i
$191$		−	0.0744212i		−	0.00538493i	−0.999996	−	0.00269247i	$-0.999143\pi$
$191$		−	0.0744212i		−	0.00538493i	0.999996	−	0.00269247i	$-0.000857039\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$			7.49268i			0.539335i	0.962953	+	0.269668i	$0.0869138\pi$
$193$			7.49268i			0.539335i	−0.962953	+	0.269668i	$0.913086\pi$
$194$	5.09836	+	8.83062i	0.366041	+	0.634002i
$195$	−6.64825			−0.476091
$196$	−15.0896			−1.07783
$197$	0.647715	+	1.12188i	0.0461478	+	0.0799303i	0.888177	−	0.459502i	$-0.151972\pi$
$197$	0.647715	+	1.12188i	0.0461478	+	0.0799303i	−0.842029	+	0.539432i	$0.818639\pi$
$198$	−5.29993	−	3.05992i	−0.376650	−	0.217459i
$199$		−	3.50288i		−	0.248312i	−0.992263	−	0.124156i	$-0.960378\pi$
$199$		−	3.50288i		−	0.248312i	0.992263	−	0.124156i	$-0.0396224\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	−1.03370	−	1.79042i	−0.0729117	−	0.126287i
$202$	−3.15933	+	1.82404i	−0.222289	+	0.128339i
$203$	−19.4585	−	11.2344i	−1.36572	−	0.788497i
$204$	−4.13561	−	2.38770i	−0.289551	−	0.167172i
$205$	−4.06577	+	2.34737i	−0.283965	+	0.163948i
$206$	−4.25940	−	7.37750i	−0.296767	−	0.514015i
$207$	−4.36791	+	2.52181i	−0.303591	+	0.175278i
$208$		−	6.64825i		−	0.460973i
$209$	−29.1424	−	16.8254i	−2.01582	−	1.16384i
$210$	−2.34998	−	4.07029i	−0.162164	−	0.280876i
$211$	−25.8912			−1.78243			−0.891213	−	0.453585i	$-0.850145\pi$
$211$	−25.8912			−1.78243			−0.891213	+	0.453585i	$0.850145\pi$
$212$	2.85605			0.196154
$213$	2.71185	+	4.69706i	0.185813	+	0.321837i
$214$		−	16.9994i		−	1.16205i
$215$	−2.60604	+	4.51380i	−0.177731	+	0.307838i
$216$			1.00000i			0.0680414i
$217$	3.07759	+	1.77685i	0.208920	+	0.120620i
$218$	−3.30798	+	5.72959i	−0.224045	+	0.388056i
$219$	1.96600	−	3.40521i	0.132850	−	0.230103i
$220$	−5.29993	+	3.05992i	−0.357321	+	0.206300i
$221$	31.7480			2.13560
$222$	5.04141	−	3.40356i	0.338357	−	0.228432i
$223$	3.87314			0.259365			0.129682	−	0.991556i	$-0.458604\pi$
$223$	3.87314			0.259365			0.129682	+	0.991556i	$0.458604\pi$
$224$	4.07029	−	2.34998i	0.271957	−	0.157015i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$	−4.38396	+	7.59323i	−0.291616	+	0.505094i
$227$	−15.1837	−	8.76632i	−1.00778	−	0.581841i	−0.0972382	−	0.995261i	$-0.531001\pi$
$227$	−15.1837	−	8.76632i	−1.00778	−	0.581841i	−0.910541	+	0.413420i	$0.864334\pi$
$228$			5.49864i			0.364156i
$229$	−13.0785	+	22.6526i	−0.864250	+	1.49692i	0.00354089	+	0.999994i	$0.498873\pi$
$229$	−13.0785	+	22.6526i	−0.864250	+	1.49692i	−0.867790	+	0.496930i	$0.834460\pi$
$230$			5.04363i			0.332567i
$231$	14.3815	+	24.9095i	0.946233	+	1.63892i
$232$	4.78061			0.313863
$233$	26.1451			1.71282			0.856411	−	0.516295i	$-0.172689\pi$
$233$	26.1451			1.71282			0.856411	+	0.516295i	$0.172689\pi$
$234$	−3.32413	−	5.75756i	−0.217305	−	0.376383i
$235$	−6.00928	−	3.46946i	−0.392002	−	0.226322i
$236$			7.35159i			0.478548i
$237$	11.6166	−	6.70686i	0.754581	−	0.435657i
$238$	11.2221	+	19.4372i	0.727420	+	1.25993i
$239$	−15.0597	+	8.69470i	−0.974128	+	0.562413i	−0.900492	−	0.434872i	$-0.856794\pi$
$239$	−15.0597	+	8.69470i	−0.974128	+	0.562413i	−0.0736359	+	0.997285i	$0.523460\pi$
$240$	0.866025	+	0.500000i	0.0559017	+	0.0322749i
$241$	−7.15404	−	4.13038i	−0.460832	−	0.266061i	0.251562	−	0.967841i	$-0.419056\pi$
$241$	−7.15404	−	4.13038i	−0.460832	−	0.266061i	−0.712394	+	0.701780i	$0.752389\pi$
$242$	22.9085	−	13.2262i	1.47261	−	0.850212i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−3.28799	+	1.89832i	−0.210492	+	0.121528i
$245$			15.0896i			0.964042i
$246$	−4.06577	−	2.34737i	−0.259224	−	0.149663i
$247$	−18.2782	−	31.6587i	−1.16301	−	2.01440i
$248$	−0.756111			−0.0480131
$249$	5.98004			0.378970
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$		−	2.13497i		−	0.134758i	−0.997727	−	0.0673791i	$-0.978536\pi$
$251$		−	2.13497i		−	0.134758i	0.997727	−	0.0673791i	$-0.0214637\pi$
$252$	2.34998	−	4.07029i	0.148035	−	0.256404i
$253$		−	30.8662i		−	1.94054i
$254$	−18.3004	−	10.5658i	−1.14827	−	0.662954i
$255$	−2.38770	+	4.13561i	−0.149523	+	0.258982i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.88413	−	3.39720i	0.367042	−	0.211912i	−0.305123	−	0.952313i	$-0.598698\pi$
$257$	5.88413	−	3.39720i	0.367042	−	0.211912i	0.672165	+	0.740401i	$0.265364\pi$
$258$	−5.21208			−0.324490
$259$	−28.5183	+	2.00626i	−1.77204	+	0.124663i
$260$	−6.64825			−0.412307
$261$	4.14013	−	2.39031i	0.256268	−	0.147956i
$262$	1.69173	−	2.93015i	0.104515	−	0.181026i
$263$	2.75525	−	4.77224i	0.169896	−	0.294269i	−0.768487	−	0.639865i	$-0.778990\pi$
$263$	2.75525	−	4.77224i	0.169896	−	0.294269i	0.938383	+	0.345597i	$0.112323\pi$
$264$	−5.29993	−	3.05992i	−0.326188	−	0.188325i
$265$		−	2.85605i		−	0.175445i
$266$	12.9217	−	22.3810i	0.792280	−	1.37227i
$267$			16.1122i			0.986054i
$268$	−1.03370	−	1.79042i	−0.0631434	−	0.109368i
$269$	−2.05080			−0.125040			−0.0625198	−	0.998044i	$-0.519914\pi$
$269$	−2.05080			−0.125040			−0.0625198	+	0.998044i	$0.519914\pi$
$270$	1.00000			0.0608581
$271$	−10.0615	−	17.4271i	−0.611195	−	1.05862i	−0.991039	−	0.133570i	$-0.957356\pi$
$271$	−10.0615	−	17.4271i	−0.611195	−	1.05862i	0.379845	−	0.925050i	$-0.375977\pi$
$272$	−4.13561	−	2.38770i	−0.250758	−	0.144775i
$273$			31.2465i			1.89113i
$274$	−12.4218	+	7.17173i	−0.750428	+	0.433260i
$275$	3.05992	+	5.29993i	0.184520	+	0.319598i
$276$	−4.36791	+	2.52181i	−0.262917	+	0.151795i
$277$	2.11528	+	1.22126i	0.127095	+	0.0733782i	0.562199	−	0.827002i	$-0.309955\pi$
$277$	2.11528	+	1.22126i	0.127095	+	0.0733782i	−0.435105	+	0.900380i	$0.643289\pi$
$278$	−2.57519	−	1.48679i	−0.154450	−	0.0891715i
$279$	−0.654812	+	0.378056i	−0.0392025	+	0.0226336i
$280$	−2.34998	−	4.07029i	−0.140438	−	0.243246i
$281$	−26.2683	+	15.1660i	−1.56704	+	0.904729i	−0.570525	+	0.821280i	$0.693260\pi$
$281$	−26.2683	+	15.1660i	−1.56704	+	0.904729i	−0.996512	+	0.0834487i	$0.973407\pi$
$282$		−	6.93891i		−	0.413206i
$283$	−22.8978	−	13.2200i	−1.36113	−	0.785849i	−0.371356	−	0.928490i	$-0.621107\pi$
$283$	−22.8978	−	13.2200i	−1.36113	−	0.785849i	−0.989774	+	0.142641i	$0.954440\pi$
$284$	2.71185	+	4.69706i	0.160919	+	0.278719i
$285$	5.49864			0.325711
$286$	40.6862			2.40583
$287$	11.0326	+	19.1089i	0.651231	+	1.12797i
$288$			1.00000i			0.0589256i
$289$	2.90220	−	5.02675i	0.170717	−	0.295691i
$290$		−	4.78061i		−	0.280727i
$291$	8.83062	+	5.09836i	0.517660	+	0.298871i
$292$	1.96600	−	3.40521i	0.115052	−	0.199275i
$293$	−2.99531	+	5.18802i	−0.174988	+	0.303088i	−0.940157	−	0.340742i	$-0.889322\pi$
$293$	−2.99531	+	5.18802i	−0.174988	+	0.303088i	0.765169	+	0.643829i	$0.222655\pi$
$294$	−13.0680	+	7.54482i	−0.762142	+	0.440023i
$295$	7.35159			0.428026
$296$	5.04141	−	3.40356i	0.293026	−	0.197828i
$297$	−6.11984			−0.355109
$298$	13.7899	−	7.96161i	0.798828	−	0.461204i
$299$	16.7657	−	29.0390i	0.969583	−	1.67937i
$300$	0.500000	−	0.866025i	0.0288675	−	0.0500000i
$301$	21.2147	+	12.2483i	1.22279	+	0.705980i
$302$			8.77557i			0.504977i
$303$	−1.82404	+	3.15933i	−0.104788	+	0.181499i
$304$			5.49864i			0.315369i
$305$	1.89832	+	3.28799i	0.108698	+	0.188270i
$306$	−4.77539			−0.272991
$307$	−4.94905			−0.282457			−0.141228	−	0.989977i	$-0.545105\pi$
$307$	−4.94905			−0.282457			−0.141228	+	0.989977i	$0.545105\pi$
$308$	14.3815	+	24.9095i	0.819462	+	1.41935i
$309$	−7.37750	−	4.25940i	−0.419691	−	0.242309i
$310$			0.756111i			0.0429442i
$311$	−2.59531	+	1.49840i	−0.147166	+	0.0849665i	−0.571775	−	0.820410i	$-0.693745\pi$
$311$	−2.59531	+	1.49840i	−0.147166	+	0.0849665i	0.424609	+	0.905377i	$0.360412\pi$
$312$	−3.32413	−	5.75756i	−0.188192	−	0.325957i
$313$	9.06005	−	5.23082i	0.512104	−	0.295663i	−0.221594	−	0.975139i	$-0.571126\pi$
$313$	9.06005	−	5.23082i	0.512104	−	0.295663i	0.733698	+	0.679476i	$0.237793\pi$
$314$	−17.6462	−	10.1880i	−0.995833	−	0.574945i
$315$	−4.07029	−	2.34998i	−0.229335	−	0.132406i
$316$	11.6166	−	6.70686i	0.653486	−	0.377290i
$317$	2.25066	+	3.89825i	0.126409	+	0.218948i	0.922283	−	0.386515i	$-0.126321\pi$
$317$	2.25066	+	3.89825i	0.126409	+	0.218948i	−0.795874	+	0.605463i	$0.792988\pi$
$318$	2.47341	−	1.42802i	0.138702	−	0.0800795i
$319$			29.2566i			1.63805i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	−8.49969	−	14.7219i	−0.474406	−	0.821696i
$322$	23.7049			1.32102
$323$	−26.2582			−1.46104
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$			6.64825i			0.368779i
$326$	−6.69803	+	11.6013i	−0.370969	+	0.642538i
$327$			6.61596i			0.365863i
$328$	−4.06577	−	2.34737i	−0.224494	−	0.129612i
$329$	−16.3063	+	28.2434i	−0.898996	+	1.55711i
$330$	−3.05992	+	5.29993i	−0.168443	+	0.291752i
$331$	4.86839	−	2.81077i	0.267591	−	0.154494i	−0.360201	−	0.932875i	$-0.617292\pi$
$331$	4.86839	−	2.81077i	0.267591	−	0.154494i	0.627792	+	0.778381i	$0.283959\pi$
$332$	5.98004			0.328197
$333$	2.66421	−	5.46827i	0.145998	−	0.299660i
$334$	−14.2854			−0.781662
$335$	−1.79042	+	1.03370i	−0.0978213	+	0.0564772i
$336$	2.34998	−	4.07029i	0.128202	−	0.222052i
$337$	2.08900	−	3.61826i	0.113795	−	0.197099i	−0.803502	−	0.595302i	$-0.797033\pi$
$337$	2.08900	−	3.61826i	0.113795	−	0.197099i	0.917297	+	0.398203i	$0.130366\pi$
$338$	27.0194	+	15.5996i	1.46966	+	0.848508i
$339$			8.76791i			0.476208i
$340$	−2.38770	+	4.13561i	−0.129491	+	0.224285i
$341$		−	4.62728i		−	0.250581i
$342$	2.74932	+	4.76196i	0.148666	+	0.257497i
$343$	38.0210			2.05294
$344$	−5.21208			−0.281017
$345$	2.52181	+	4.36791i	0.135770	+	0.235160i
$346$	12.0591	+	6.96232i	0.648301	+	0.374297i
$347$			22.2875i			1.19646i	0.801325	+	0.598229i	$0.204129\pi$
$347$			22.2875i			1.19646i	−0.801325	+	0.598229i	$0.795871\pi$
$348$	4.14013	−	2.39031i	0.221934	−	0.128134i
$349$	−17.7722	−	30.7824i	−0.951327	−	1.64775i	−0.742559	−	0.669781i	$-0.766388\pi$
$349$	−17.7722	−	30.7824i	−0.951327	−	1.64775i	−0.208768	−	0.977965i	$-0.566945\pi$
$350$	−4.07029	+	2.34998i	−0.217566	+	0.125612i
$351$	−5.75756	−	3.32413i	−0.307316	−	0.177429i
$352$	−5.29993	−	3.05992i	−0.282487	−	0.163094i
$353$	30.2860	−	17.4857i	1.61196	−	0.930668i	0.623049	−	0.782183i	$-0.285894\pi$
$353$	30.2860	−	17.4857i	1.61196	−	0.930668i	0.988915	−	0.148485i	$-0.0474395\pi$
$354$	3.67580	+	6.36667i	0.195366	+	0.338385i
$355$	4.69706	−	2.71185i	0.249294	−	0.143930i
$356$			16.1122i			0.853948i
$357$	19.4372	+	11.2221i	1.02873	+	0.593936i
$358$	0.822024	+	1.42379i	0.0434453	+	0.0752495i
$359$	6.32142			0.333632			0.166816	−	0.985988i	$-0.446651\pi$
$359$	6.32142			0.333632			0.166816	+	0.985988i	$0.446651\pi$
$360$	1.00000			0.0527046
$361$	5.61751	+	9.72982i	0.295659	+	0.512096i
$362$			0.752498i			0.0395504i
$363$	13.2262	−	22.9085i	0.694196	−	1.20238i
$364$			31.2465i			1.63776i
$365$	−3.40521	−	1.96600i	−0.178237	−	0.102905i
$366$	−1.89832	+	3.28799i	−0.0992270	+	0.171866i
$367$	−7.41265	+	12.8391i	−0.386937	+	0.670195i	−0.992036	−	0.125956i	$-0.959800\pi$
$367$	−7.41265	+	12.8391i	−0.386937	+	0.670195i	0.605099	+	0.796150i	$0.293134\pi$
$368$	−4.36791	+	2.52181i	−0.227693	+	0.131459i
$369$	−4.69474			−0.244399
$370$	−3.40356	−	5.04141i	−0.176943	−	0.262090i
$371$	−13.4233			−0.696903
$372$	−0.654812	+	0.378056i	−0.0339504	+	0.0196013i
$373$	−4.16303	+	7.21059i	−0.215554	+	0.373350i	−0.953444	−	0.301571i	$-0.902489\pi$
$373$	−4.16303	+	7.21059i	−0.215554	+	0.373350i	0.737890	+	0.674921i	$0.235822\pi$
$374$	14.6123	−	25.3093i	0.755585	−	1.30871i
$375$	−0.866025	−	0.500000i	−0.0447214	−	0.0258199i
$376$		−	6.93891i		−	0.357847i
$377$	−15.8914	+	27.5246i	−0.818447	+	1.41759i
$378$		−	4.69996i		−	0.241740i
$379$	−15.7329	−	27.2502i	−0.808146	−	1.39975i	−0.914147	−	0.405383i	$-0.867138\pi$
$379$	−15.7329	−	27.2502i	−0.808146	−	1.39975i	0.106001	−	0.994366i	$-0.466195\pi$
$380$	5.49864			0.282074
$381$	−21.1315			−1.08260
$382$	−0.0372106	−	0.0644507i	−0.00190386	−	0.00329758i
$383$	−19.6542	−	11.3474i	−1.00428	−	0.579823i	−0.0947707	−	0.995499i	$-0.530212\pi$
$383$	−19.6542	−	11.3474i	−1.00428	−	0.579823i	−0.909513	+	0.415676i	$0.863545\pi$
$384$			1.00000i			0.0510310i
$385$	24.9095	−	14.3815i	1.26951	−	0.732949i
$386$	3.74634	+	6.48885i	0.190684	+	0.330274i
$387$	−4.51380	+	2.60604i	−0.229449	+	0.132473i
$388$	8.83062	+	5.09836i	0.448307	+	0.258830i
$389$	11.0765	+	6.39501i	0.561600	+	0.324240i	0.753787	−	0.657118i	$-0.228225\pi$
$389$	11.0765	+	6.39501i	0.561600	+	0.324240i	−0.192187	+	0.981358i	$0.561558\pi$
$390$	−5.75756	+	3.32413i	−0.291545	+	0.168324i
$391$	−12.0427	−	20.8585i	−0.609023	−	1.05486i
$392$	−13.0680	+	7.54482i	−0.660034	+	0.381071i
$393$		−	3.38345i		−	0.170672i
$394$	1.12188	+	0.647715i	0.0565193	+	0.0326314i
$395$	−6.70686	−	11.6166i	−0.337459	−	0.584496i
$396$	−6.11984			−0.307533
$397$	−11.2565			−0.564949			−0.282475	−	0.959275i	$-0.591155\pi$
$397$	−11.2565			−0.564949			−0.282475	+	0.959275i	$0.591155\pi$
$398$	−1.75144	−	3.03358i	−0.0877917	−	0.152060i
$399$		−	25.8434i		−	1.29379i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$		−	26.3516i		−	1.31594i	−0.753046	−	0.657968i	$-0.771416\pi$
$401$		−	26.3516i		−	1.31594i	0.753046	−	0.657968i	$-0.228584\pi$
$402$	−1.79042	−	1.03370i	−0.0892983	−	0.0515564i
$403$	2.51341	−	4.35335i	0.125202	−	0.216856i
$404$	−1.82404	+	3.15933i	−0.0907493	+	0.157182i
$405$	0.866025	−	0.500000i	0.0430331	−	0.0248452i
$406$	−22.4687			−1.11510
$407$	20.8292	+	30.8526i	1.03247	+	1.52931i
$408$	−4.77539			−0.236417
$409$	−17.4841	+	10.0945i	−0.864535	+	0.499140i	−0.865528	−	0.500860i	$-0.833017\pi$
$409$	−17.4841	+	10.0945i	−0.864535	+	0.499140i	0.000993021		1.00000i	$0.499684\pi$
$410$	−2.34737	+	4.06577i	−0.115928	+	0.200794i
$411$	−7.17173	+	12.4218i	−0.353755	+	0.612722i
$412$	−7.37750	−	4.25940i	−0.363463	−	0.209846i
$413$		−	34.5522i		−	1.70020i
$414$	−2.52181	+	4.36791i	−0.123940	+	0.214671i
$415$		−	5.98004i		−	0.293549i
$416$	−3.32413	−	5.75756i	−0.162979	−	0.282287i
$417$	−2.97357			−0.145616
$418$	−33.6508			−1.64591
$419$	2.18873	+	3.79099i	0.106926	+	0.185202i	0.914524	−	0.404532i	$-0.132566\pi$
$419$	2.18873	+	3.79099i	0.106926	+	0.185202i	−0.807597	+	0.589734i	$0.799232\pi$
$420$	−4.07029	−	2.34998i	−0.198610	−	0.114667i
$421$		−	28.0953i		−	1.36928i	−0.728880	−	0.684641i	$-0.759959\pi$
$421$		−	28.0953i		−	1.36928i	0.728880	−	0.684641i	$-0.240041\pi$
$422$	−22.4225	+	12.9456i	−1.09151	+	0.630183i
$423$	−3.46946	−	6.00928i	−0.168691	−	0.292181i
$424$	2.47341	−	1.42802i	0.120119	−	0.0693509i
$425$	4.13561	+	2.38770i	0.200607	+	0.115820i
$426$	4.69706	+	2.71185i	0.227573	+	0.131390i
$427$	15.4534	−	8.92205i	0.747845	−	0.431768i
$428$	−8.49969	−	14.7219i	−0.410848	−	0.711610i
$429$	35.2353	−	20.3431i	1.70118	−	0.982175i
$430$			5.21208i			0.251349i
$431$	−4.33768	−	2.50436i	−0.208939	−	0.120631i	0.391879	−	0.920017i	$-0.371825\pi$
$431$	−4.33768	−	2.50436i	−0.208939	−	0.120631i	−0.600818	+	0.799386i	$0.705158\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	12.1807			0.585365			0.292683	−	0.956210i	$-0.405452\pi$
$433$	12.1807			0.585365			0.292683	+	0.956210i	$0.405452\pi$
$434$	3.55369			0.170583
$435$	−2.39031	−	4.14013i	−0.114606	−	0.198504i
$436$			6.61596i			0.316847i
$437$	−13.8665	+	24.0175i	−0.663326	+	1.14892i
$438$		−	3.93200i		−	0.187878i
$439$	−6.20456	−	3.58220i	−0.296127	−	0.170969i	0.344574	−	0.938759i	$-0.388023\pi$
$439$	−6.20456	−	3.58220i	−0.296127	−	0.170969i	−0.640702	+	0.767790i	$0.721357\pi$
$440$	−3.05992	+	5.29993i	−0.145876	+	0.252664i
$441$	−7.54482	+	13.0680i	−0.359277	+	0.622286i
$442$	27.4946	−	15.8740i	1.30778	−	0.755050i
$443$	−1.43697			−0.0682726			−0.0341363	−	0.999417i	$-0.510868\pi$
$443$	−1.43697			−0.0682726			−0.0341363	+	0.999417i	$0.510868\pi$
$444$	2.66421	−	5.46827i	0.126438	−	0.259513i
$445$	16.1122			0.763794
$446$	3.35424	−	1.93657i	0.158828	−	0.0916993i
$447$	7.96161	−	13.7899i	0.376571	−	0.652240i
$448$	2.34998	−	4.07029i	0.111026	−	0.192303i
$449$	−3.67693	−	2.12288i	−0.173525	−	0.100185i	0.410722	−	0.911761i	$-0.365277\pi$
$449$	−3.67693	−	2.12288i	−0.173525	−	0.100185i	−0.584247	+	0.811576i	$0.698610\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	14.3655	−	24.8818i	0.676446	−	1.17164i
$452$			8.76791i			0.412408i
$453$	4.38779	+	7.59987i	0.206156	+	0.357073i
$454$	−17.5326			−0.822848
$455$	31.2465			1.46486
$456$	2.74932	+	4.76196i	0.128749	+	0.222999i
$457$	−18.9202	−	10.9236i	−0.885047	−	0.510982i	−0.0127281	−	0.999919i	$-0.504052\pi$
$457$	−18.9202	−	10.9236i	−0.885047	−	0.510982i	−0.872319	+	0.488937i	$0.837385\pi$
$458$			26.1569i			1.22223i
$459$	−4.13561	+	2.38770i	−0.193034	+	0.111448i
$460$	2.52181	+	4.36791i	0.117580	+	0.203655i
$461$	−21.8499	+	12.6150i	−1.01765	+	0.587541i	−0.913422	−	0.407013i	$-0.866570\pi$
$461$	−21.8499	+	12.6150i	−1.01765	+	0.587541i	−0.104228	+	0.994553i	$0.533237\pi$
$462$	24.9095	+	14.3815i	1.15889	+	0.669088i
$463$	26.5953	+	15.3548i	1.23599	+	0.713598i	0.968272	−	0.249900i	$-0.0803979\pi$
$463$	26.5953	+	15.3548i	1.23599	+	0.713598i	0.267716	+	0.963498i	$0.413731\pi$
$464$	4.14013	−	2.39031i	0.192201	−	0.110967i
$465$	0.378056	+	0.654812i	0.0175319	+	0.0303662i
$466$	22.6423	−	13.0725i	1.04888	−	0.605574i
$467$		−	10.8065i		−	0.500067i	−0.968237	−	0.250034i	$-0.919558\pi$
$467$		−	10.8065i		−	0.500067i	0.968237	−	0.250034i	$-0.0804417\pi$
$468$	−5.75756	−	3.32413i	−0.266143	−	0.153658i
$469$	4.85836	+	8.41493i	0.224338	+	0.388565i
$470$	−6.93891			−0.320068
$471$	−20.3761			−0.938881
$472$	3.67580	+	6.36667i	0.169192	+	0.293050i
$473$		−	31.8971i		−	1.46663i
$474$	6.70686	−	11.6166i	0.308056	−	0.533569i
$475$		−	5.49864i		−	0.252295i
$476$	19.4372	+	11.2221i	0.890904	+	0.514363i
$477$	1.42802	−	2.47341i	0.0653847	−	0.113250i
$478$	−8.69470	+	15.0597i	−0.397686	+	0.688813i
$479$	8.14921	−	4.70495i	0.372347	−	0.214974i	−0.302136	−	0.953265i	$-0.597700\pi$
$479$	8.14921	−	4.70495i	0.372347	−	0.214974i	0.674483	+	0.738290i	$0.264367\pi$
$480$	1.00000			0.0456435
$481$	2.83792	+	40.3400i	0.129398	+	1.83935i
$482$	−8.26077			−0.376268
$483$	20.5290	−	11.8524i	0.934102	−	0.539304i
$484$	13.2262	−	22.9085i	0.601191	−	1.04129i
$485$	5.09836	−	8.83062i	0.231505	−	0.400978i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$		−	15.5824i		−	0.706108i	−0.935603	−	0.353054i	$-0.885143\pi$
$487$		−	15.5824i		−	0.706108i	0.935603	−	0.353054i	$-0.114857\pi$
$488$	−1.89832	+	3.28799i	−0.0859331	+	0.148840i
$489$			13.3961i			0.605791i
$490$	7.54482	+	13.0680i	0.340840	+	0.590353i
$491$	15.1120			0.681995			0.340997	−	0.940064i	$-0.389235\pi$
$491$	15.1120			0.681995			0.340997	+	0.940064i	$0.389235\pi$
$492$	−4.69474			−0.211655
$493$	11.4147	+	19.7708i	0.514090	+	0.890430i
$494$	−31.6587	−	18.2782i	−1.42439	−	0.822374i
$495$			6.11984i			0.275066i
$496$	−0.654812	+	0.378056i	−0.0294019	+	0.0169752i
$497$	−12.7456	−	22.0760i	−0.571718	−	0.990245i
$498$	5.17887	−	2.99002i	0.232071	−	0.133986i
$499$	24.4908	+	14.1398i	1.09636	+	0.632984i	0.935263	−	0.353955i	$-0.115163\pi$
$499$	24.4908	+	14.1398i	1.09636	+	0.632984i	0.161098	+	0.986938i	$0.448497\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$	−12.3715	+	7.14269i	−0.552718	+	0.319112i
$502$	−1.06749	−	1.84894i	−0.0476442	−	0.0825222i
$503$	−20.2470	+	11.6896i	−0.902769	+	0.521214i	−0.878097	−	0.478482i	$-0.841187\pi$
$503$	−20.2470	+	11.6896i	−0.902769	+	0.521214i	−0.0246713	+	0.999696i	$0.507854\pi$
$504$		−	4.69996i		−	0.209353i
$505$	3.15933	+	1.82404i	0.140588	+	0.0811686i
$506$	−15.4331	−	26.7309i	−0.686084	−	1.18833i
$507$	31.1993			1.38561
$508$	−21.1315			−0.937559
$509$	4.79507	+	8.30530i	0.212538	+	0.368126i	0.952508	−	0.304514i	$-0.0984939\pi$
$509$	4.79507	+	8.30530i	0.212538	+	0.368126i	−0.739970	+	0.672639i	$0.765161\pi$
$510$			4.77539i			0.211458i
$511$	−9.24013	+	16.0044i	−0.408759	+	0.707992i
$512$			1.00000i			0.0441942i
$513$	4.76196	+	2.74932i	0.210246	+	0.121385i
$514$	3.39720	−	5.88413i	0.149844	−	0.259538i
$515$	−4.25940	+	7.37750i	−0.187692	+	0.325092i
$516$	−4.51380	+	2.60604i	−0.198709	+	0.114725i
$517$	42.4650			1.86761
$518$	−23.6944	+	15.9966i	−1.04107	+	0.702851i
$519$	13.9246			0.611224
$520$	−5.75756	+	3.32413i	−0.252486	+	0.145773i
$521$	17.4879	−	30.2899i	0.766157	−	1.32702i	−0.173475	−	0.984838i	$-0.555500\pi$
$521$	17.4879	−	30.2899i	0.766157	−	1.32702i	0.939633	−	0.342185i	$-0.111167\pi$
$522$	2.39031	−	4.14013i	0.104621	−	0.181209i
$523$	−10.3957	−	6.00196i	−0.454572	−	0.262447i	0.255187	−	0.966892i	$-0.417863\pi$
$523$	−10.3957	−	6.00196i	−0.454572	−	0.262447i	−0.709759	+	0.704444i	$0.751196\pi$
$524$		−	3.38345i		−	0.147807i
$525$	−2.34998	+	4.07029i	−0.102562	+	0.177642i
$526$		−	5.51051i		−	0.240269i
$527$	−1.80536	−	3.12698i	−0.0786429	−	0.136214i
$528$	−6.11984			−0.266332
$529$	−2.43816			−0.106007
$530$	−1.42802	−	2.47341i	−0.0620293	−	0.107438i
$531$	6.36667	+	3.67580i	0.276290	+	0.159516i
$532$		−	25.8434i		−	1.12045i
$533$	27.0302	−	15.6059i	1.17081	−	0.675967i
$534$	8.05612	+	13.9536i	0.348623	+	0.603832i
$535$	−14.7219	+	8.49969i	−0.636483	+	0.367474i
$536$	−1.79042	−	1.03370i	−0.0773346	−	0.0446491i
$537$	1.42379	+	0.822024i	0.0614409	+	0.0354729i
$538$	−1.77605	+	1.02540i	−0.0765708	+	0.0442082i
$539$	−46.1731	−	79.9741i	−1.98882	−	3.44473i
$540$	0.866025	−	0.500000i	0.0372678	−	0.0215166i
$541$		−	19.1961i		−	0.825305i	−0.910889	−	0.412653i	$-0.864602\pi$
$541$		−	19.1961i		−	0.825305i	0.910889	−	0.412653i	$-0.135398\pi$
$542$	−17.4271	−	10.0615i	−0.748558	−	0.432180i
$543$	0.376249	+	0.651682i	0.0161464	+	0.0279664i
$544$	−4.77539			−0.204743
$545$	6.61596			0.283396
$546$	15.6233	+	27.0603i	0.668614	+	1.15807i
$547$			27.2388i			1.16465i	0.812957	+	0.582323i	$0.197856\pi$
$547$			27.2388i			1.16465i	−0.812957	+	0.582323i	$0.802144\pi$
$548$	−7.17173	+	12.4218i	−0.306361	+	0.530633i
$549$			3.79665i			0.162037i
$550$	5.29993	+	3.05992i	0.225990	+	0.130475i
$551$	13.1434	−	22.7651i	0.559929	−	0.969825i
$552$	−2.52181	+	4.36791i	−0.107335	+	0.185911i
$553$	−54.5977	+	31.5220i	−2.32173	+	1.34045i
$554$	2.44251			0.103772
$555$	−5.46827	−	2.66421i	−0.232115	−	0.113089i
$556$	−2.97357			−0.126108
$557$	24.0770	−	13.9008i	1.02017	−	0.588998i	0.106020	−	0.994364i	$-0.466189\pi$
$557$	24.0770	−	13.9008i	1.02017	−	0.588998i	0.914154	+	0.405366i	$0.132856\pi$
$558$	−0.378056	+	0.654812i	−0.0160044	+	0.0277204i
$559$	17.3256	−	30.0089i	0.732796	−	1.26924i
$560$	−4.07029	−	2.34998i	−0.172001	−	0.0993048i
$561$		−	29.2246i		−	1.23387i
$562$	−15.1660	+	26.2683i	−0.639740	+	1.10806i
$563$			7.25832i			0.305902i	0.988234	+	0.152951i	$0.0488776\pi$
$563$			7.25832i			0.305902i	−0.988234	+	0.152951i	$0.951122\pi$
$564$	−3.46946	−	6.00928i	−0.146091	−	0.253036i
$565$	8.76791			0.368869
$566$	−26.4401			−1.11136
$567$	−2.34998	−	4.07029i	−0.0986899	−	0.170936i
$568$	4.69706	+	2.71185i	0.197084	+	0.113787i
$569$		−	0.492917i		−	0.0206642i	−0.999947	−	0.0103321i	$-0.996711\pi$
$569$		−	0.492917i		−	0.0206642i	0.999947	−	0.0103321i	$-0.00328886\pi$
$570$	4.76196	−	2.74932i	0.199457	−	0.115156i
$571$	4.82235	+	8.35255i	0.201809	+	0.349543i	0.949111	−	0.314941i	$-0.101985\pi$
$571$	4.82235	+	8.35255i	0.201809	+	0.349543i	−0.747302	+	0.664484i	$0.768651\pi$
$572$	35.2353	−	20.3431i	1.47326	−	0.850588i
$573$	−0.0644507	−	0.0372106i	−0.00269247	−	0.00155450i
$574$	19.1089	+	11.0326i	0.797592	+	0.460490i
$575$	4.36791	−	2.52181i	0.182154	−	0.105167i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−10.7563	+	6.21016i	−0.447791	+	0.258532i	−0.706897	−	0.707317i	$-0.749906\pi$
$577$	−10.7563	+	6.21016i	−0.447791	+	0.258532i	0.259106	+	0.965849i	$0.416572\pi$
$578$		−	5.80439i		−	0.241431i
$579$	6.48885	+	3.74634i	0.269668	+	0.155693i
$580$	−2.39031	−	4.14013i	−0.0992521	−	0.171910i
$581$	−28.1060			−1.16603
$582$	10.1967			0.422668
$583$	8.73927	+	15.1369i	0.361943	+	0.626904i
$584$		−	3.93200i		−	0.162707i
$585$	−3.32413	+	5.75756i	−0.137436	+	0.238046i
$586$			5.99061i			0.247470i
$587$	11.5954	+	6.69463i	0.478595	+	0.276317i	0.719831	−	0.694150i	$-0.244219\pi$
$587$	11.5954	+	6.69463i	0.478595	+	0.276317i	−0.241236	+	0.970467i	$0.577553\pi$
$588$	−7.54482	+	13.0680i	−0.311143	+	0.538916i
$589$	−2.07879	+	3.60057i	−0.0856551	+	0.148359i
$590$	6.36667	−	3.67580i	0.262112	−	0.151330i
$591$	1.29543			0.0532869
$592$	2.66421	−	5.46827i	0.109498	−	0.224745i
$593$	4.58582			0.188317			0.0941585	−	0.995557i	$-0.469984\pi$
$593$	4.58582			0.188317			0.0941585	+	0.995557i	$0.469984\pi$
$594$	−5.29993	+	3.05992i	−0.217459	+	0.125550i
$595$	11.2221	−	19.4372i	0.460061	−	0.796848i
$596$	7.96161	−	13.7899i	0.326120	−	0.564857i
$597$	−3.03358	−	1.75144i	−0.124156	−	0.0716816i
$598$		−	33.5313i		−	1.37120i
$599$	−16.6977	+	28.9213i	−0.682250	+	1.18169i	0.292043	+	0.956405i	$0.405665\pi$
$599$	−16.6977	+	28.9213i	−0.682250	+	1.18169i	−0.974293	+	0.225286i	$0.927668\pi$
$600$		−	1.00000i		−	0.0408248i
$601$	5.02374	+	8.70137i	0.204923	+	0.354936i	0.950108	−	0.311921i	$-0.100972\pi$
$601$	5.02374	+	8.70137i	0.204923	+	0.354936i	−0.745186	+	0.666857i	$0.767639\pi$
$602$	24.4966			0.998406
$603$	−2.06740			−0.0841912
$604$	4.38779	+	7.59987i	0.178536	+	0.309234i
$605$	−22.9085	−	13.2262i	−0.931361	−	0.537722i
$606$			3.64807i			0.148193i
$607$	4.78079	−	2.76019i	0.194046	−	0.112033i	−0.399829	−	0.916590i	$-0.630931\pi$
$607$	4.78079	−	2.76019i	0.194046	−	0.112033i	0.593875	+	0.804557i	$0.297597\pi$
$608$	2.74932	+	4.76196i	0.111500	+	0.193123i
$609$	−19.4585	+	11.2344i	−0.788497	+	0.455239i
$610$	3.28799	+	1.89832i	0.133127	+	0.0768609i
$611$	39.9512	+	23.0658i	1.61625	+	0.933144i
$612$	−4.13561	+	2.38770i	−0.167172	+	0.0965169i
$613$	23.4855	+	40.6781i	0.948572	+	1.64297i	0.748437	+	0.663206i	$0.230805\pi$
$613$	23.4855	+	40.6781i	0.948572	+	1.64297i	0.200135	+	0.979768i	$0.435862\pi$
$614$	−4.28600	+	2.47452i	−0.172969	+	0.0998636i
$615$			4.69474i			0.189310i
$616$	24.9095	+	14.3815i	1.00363	+	0.579447i
$617$	8.69332	+	15.0573i	0.349980	+	0.606183i	0.986246	−	0.165287i	$-0.0528550\pi$
$617$	8.69332	+	15.0573i	0.349980	+	0.606183i	−0.636265	+	0.771470i	$0.719522\pi$
$618$	−8.51880			−0.342677
$619$	8.09040			0.325181			0.162590	−	0.986694i	$-0.448015\pi$
$619$	8.09040			0.325181			0.162590	+	0.986694i	$0.448015\pi$
$620$	0.378056	+	0.654812i	0.0151831	+	0.0262979i
$621$			5.04363i			0.202394i
$622$	−1.49840	+	2.59531i	−0.0600804	+	0.104062i
$623$		−	75.7270i		−	3.03394i
$624$	−5.75756	−	3.32413i	−0.230487	−	0.133072i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	5.23082	−	9.06005i	0.209066	−	0.362112i
$627$	−29.1424	+	16.8254i	−1.16384	+	0.671941i
$628$	−20.3761			−0.813094
$629$	26.1132	+	12.7226i	1.04120	+	0.507284i
$630$	−4.69996			−0.187251
$631$	−27.9515	+	16.1378i	−1.11273	+	0.642436i	−0.939535	−	0.342452i	$-0.888743\pi$
$631$	−27.9515	+	16.1378i	−1.11273	+	0.642436i	−0.173196	+	0.984887i	$0.555409\pi$
$632$	6.70686	−	11.6166i	0.266785	−	0.462084i
$633$	−12.9456	+	22.4225i	−0.514542	+	0.891213i
$634$	3.89825	+	2.25066i	0.154819	+	0.0893850i
$635$			21.1315i			0.838578i
$636$	1.42802	−	2.47341i	0.0566248	−	0.0980770i
$637$		−	100.320i		−	3.97481i
$638$	14.6283	+	25.3369i	0.579139	+	1.00310i
$639$	5.42370			0.214558
$640$	1.00000			0.0395285
$641$	9.83603	+	17.0365i	0.388500	+	0.672902i	0.992248	−	0.124274i	$-0.0396600\pi$
$641$	9.83603	+	17.0365i	0.388500	+	0.672902i	−0.603748	+	0.797175i	$0.706327\pi$
$642$	−14.7219	−	8.49969i	−0.581027	−	0.335456i
$643$			32.7355i			1.29096i	0.763776	+	0.645482i	$0.223343\pi$
$643$			32.7355i			1.29096i	−0.763776	+	0.645482i	$0.776657\pi$
$644$	20.5290	−	11.8524i	0.808956	−	0.467051i
$645$	2.60604	+	4.51380i	0.102613	+	0.177731i
$646$	−22.7402	+	13.1291i	−0.894703	+	0.516557i
$647$	−25.6358	−	14.8009i	−1.00785	−	0.581882i	−0.0972879	−	0.995256i	$-0.531017\pi$
$647$	−25.6358	−	14.8009i	−1.00785	−	0.581882i	−0.910561	+	0.413374i	$0.864350\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−38.9630	+	22.4953i	−1.52943	+	0.883017i
$650$	3.32413	+	5.75756i	0.130383	+	0.225830i
$651$	3.07759	−	1.77685i	0.120620	−	0.0696401i
$652$			13.3961i			0.524630i
$653$	21.1214	+	12.1944i	0.826543	+	0.477205i	0.852667	−	0.522454i	$-0.174983\pi$
$653$	21.1214	+	12.1944i	0.826543	+	0.477205i	−0.0261248	+	0.999659i	$0.508317\pi$
$654$	3.30798	+	5.72959i	0.129352	+	0.224045i
$655$	−3.38345			−0.132202
$656$	−4.69474			−0.183299
$657$	−1.96600	−	3.40521i	−0.0767010	−	0.132850i
$658$			32.6126i			1.27137i
$659$	19.5760	−	33.9066i	0.762573	−	1.32082i	−0.178947	−	0.983859i	$-0.557269\pi$
$659$	19.5760	−	33.9066i	0.762573	−	1.32082i	0.941520	−	0.336957i	$-0.109398\pi$
$660$			6.11984i			0.238214i
$661$	2.26617	+	1.30837i	0.0881436	+	0.0508897i	0.543424	−	0.839458i	$-0.317128\pi$
$661$	2.26617	+	1.30837i	0.0881436	+	0.0508897i	−0.455280	+	0.890348i	$0.650461\pi$
$662$	2.81077	−	4.86839i	0.109244	−	0.189215i
$663$	15.8740	−	27.4946i	0.616496	−	1.06780i
$664$	5.17887	−	2.99002i	0.200979	−	0.116035i
$665$	−25.8434			−1.00216
$666$	−0.426867	−	6.06777i	−0.0165408	−	0.235121i
$667$	24.1116			0.933606
$668$	−12.3715	+	7.14269i	−0.478668	+	0.276359i
$669$	1.93657	−	3.35424i	0.0748721	−	0.129682i
$670$	−1.03370	+	1.79042i	−0.0399354	+	0.0691701i
$671$	−20.1220	−	11.6174i	−0.776801	−	0.448486i
$672$		−	4.69996i		−	0.181305i
$673$	3.60763	−	6.24860i	0.139064	−	0.240866i	−0.788079	−	0.615575i	$-0.788924\pi$
$673$	3.60763	−	6.24860i	0.139064	−	0.240866i	0.927143	+	0.374709i	$0.122257\pi$
$674$		−	4.17800i		−	0.160931i
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	31.1993			1.19997
$677$	44.5594			1.71256			0.856278	−	0.516515i	$-0.172771\pi$
$677$	44.5594			1.71256			0.856278	+	0.516515i	$0.172771\pi$
$678$	4.38396	+	7.59323i	0.168365	+	0.291616i
$679$	−41.5036	−	23.9621i	−1.59276	−	0.919581i
$680$			4.77539i			0.183128i
$681$	−15.1837	+	8.76632i	−0.581841	+	0.335926i
$682$	−2.31364	−	4.00734i	−0.0885938	−	0.153449i
$683$	28.5354	−	16.4749i	1.09187	−	0.630394i	0.157800	−	0.987471i	$-0.449560\pi$
$683$	28.5354	−	16.4749i	1.09187	−	0.630394i	0.934075	+	0.357077i	$0.116227\pi$
$684$	4.76196	+	2.74932i	0.182078	+	0.105123i
$685$	12.4218	+	7.17173i	0.474613	+	0.274018i
$686$	32.9272	−	19.0105i	1.25716	−	0.725824i
$687$	13.0785	+	22.6526i	0.498975	+	0.864250i
$688$	−4.51380	+	2.60604i	−0.172087	+	0.0993544i
$689$			18.9877i			0.723374i
$690$	4.36791	+	2.52181i	0.166283	+	0.0960038i
$691$	4.30282	+	7.45270i	0.163687	+	0.283514i	0.936188	−	0.351499i	$-0.114328\pi$
$691$	4.30282	+	7.45270i	0.163687	+	0.283514i	−0.772501	+	0.635013i	$0.780995\pi$
$692$	13.9246			0.529336
$693$	28.7630			1.09262
$694$	11.1438	+	19.3016i	0.423012	+	0.732678i
$695$			2.97357i			0.112794i
$696$	2.39031	−	4.14013i	0.0906043	−	0.156931i
$697$		−	22.4192i		−	0.849190i
$698$	−30.7824	−	17.7722i	−1.16513	−	0.672689i
$699$	13.0725	−	22.6423i	0.494449	−	0.856411i
$700$	−2.34998	+	4.07029i	−0.0888209	+	0.153842i
$701$	6.63328	−	3.82973i	0.250536	−	0.144647i	−0.369474	−	0.929241i	$-0.620462\pi$
$701$	6.63328	−	3.82973i	0.250536	−	0.144647i	0.620009	+	0.784594i	$0.287129\pi$
$702$	−6.64825			−0.250922
$703$	−2.34719	−	33.3645i	−0.0885259	−	1.25836i
$704$	−6.11984			−0.230650
$705$	−6.00928	+	3.46946i	−0.226322	+	0.130667i
$706$	17.4857	−	30.2860i	0.658081	−	1.13983i
$707$	8.57291	−	14.8487i	0.322417	−	0.558443i
$708$	6.36667	+	3.67580i	0.239274	+	0.138145i
$709$		−	2.13452i		−	0.0801634i	−0.999196	−	0.0400817i	$-0.987238\pi$
$709$		−	2.13452i		−	0.0801634i	0.999196	−	0.0400817i	$-0.0127618\pi$
$710$	2.71185	−	4.69706i	0.101774	−	0.176278i
$711$		−	13.4137i		−	0.503054i
$712$	8.05612	+	13.9536i	0.301916	+	0.522934i
$713$	−3.81354			−0.142818
$714$	22.4442			0.839952
$715$	−20.3431	−	35.2353i	−0.760789	−	1.31773i
$716$	1.42379	+	0.822024i	0.0532094	+	0.0307205i
$717$			17.3894i			0.649419i
$718$	5.47451	−	3.16071i	0.204307	−	0.117957i
$719$	−7.96642	−	13.7982i	−0.297097	−	0.514587i	0.678373	−	0.734717i	$-0.262685\pi$
$719$	−7.96642	−	13.7982i	−0.297097	−	0.514587i	−0.975471	+	0.220130i	$0.929352\pi$
$720$	0.866025	−	0.500000i	0.0322749	−	0.0186339i
$721$	34.6740	+	20.0190i	1.29133	+	0.745548i
$722$	9.72982	+	5.61751i	0.362106	+	0.209062i
$723$	−7.15404	+	4.13038i	−0.266061	+	0.153611i
$724$	0.376249	+	0.651682i	0.0139832	+	0.0242196i
$725$	−4.14013	+	2.39031i	−0.153761	+	0.0887738i
$726$		−	26.4524i		−	0.981741i
$727$	27.4745	+	15.8624i	1.01897	+	0.588304i	0.913806	−	0.406150i	$-0.133129\pi$
$727$	27.4745	+	15.8624i	1.01897	+	0.588304i	0.105167	+	0.994455i	$0.466462\pi$
$728$	15.6233	+	27.0603i	0.579037	+	1.00292i
$729$	1.00000			0.0370370
$730$	−3.93200			−0.145530
$731$	−12.4449	−	21.5552i	−0.460290	−	0.797246i
$732$			3.79665i			0.140328i
$733$	−16.1888	+	28.0398i	−0.597946	+	1.03567i	0.395178	+	0.918604i	$0.370683\pi$
$733$	−16.1888	+	28.0398i	−0.597946	+	1.03567i	−0.993124	+	0.117068i	$0.962651\pi$
$734$			14.8253i			0.547212i
$735$	13.0680	+	7.54482i	0.482021	+	0.278295i
$736$	−2.52181	+	4.36791i	−0.0929553	+	0.161003i
$737$	6.32609	−	10.9571i	0.233024	−	0.403610i
$738$	−4.06577	+	2.34737i	−0.149663	+	0.0864079i
$739$	−28.7513			−1.05764			−0.528818	−	0.848735i	$-0.677364\pi$
$739$	−28.7513			−1.05764			−0.528818	+	0.848735i	$0.677364\pi$
$740$	−5.46827	−	2.66421i	−0.201018	−	0.0979381i
$741$	−36.5563			−1.34293
$742$	−11.6249	+	6.71165i	−0.426764	+	0.246393i
$743$	15.7264	−	27.2390i	0.576947	−	0.999301i	−0.418881	−	0.908041i	$-0.637577\pi$
$743$	15.7264	−	27.2390i	0.576947	−	0.999301i	0.995827	−	0.0912595i	$-0.0290893\pi$
$744$	−0.378056	+	0.654812i	−0.0138602	+	0.0240066i
$745$	−13.7899	−	7.96161i	−0.505223	−	0.291691i
$746$			8.32607i			0.304839i
$747$	2.99002	−	5.17887i	0.109399	−	0.189485i
$748$		−	29.2246i		−	1.06856i
$749$	39.9482	+	69.1923i	1.45968	+	2.52823i
$750$	−1.00000			−0.0365148
$751$	−42.2486			−1.54167			−0.770836	−	0.637034i	$-0.780161\pi$
$751$	−42.2486			−1.54167			−0.770836	+	0.637034i	$0.780161\pi$
$752$	−3.46946	−	6.00928i	−0.126518	−	0.219136i
$753$	−1.84894	−	1.06749i	−0.0673791	−	0.0389014i
$754$			31.7827i			1.15746i
$755$	7.59987	−	4.38779i	0.276588	−	0.159688i
$756$	−2.34998	−	4.07029i	−0.0854680	−	0.148035i
$757$	27.3379	−	15.7835i	0.993613	−	0.573663i	0.0872605	−	0.996186i	$-0.472189\pi$
$757$	27.3379	−	15.7835i	0.993613	−	0.573663i	0.906352	+	0.422523i	$0.138855\pi$
$758$	−27.2502	−	15.7329i	−0.989772	−	0.571445i
$759$	−26.7309	−	15.4331i	−0.970270	−	0.560185i
$760$	4.76196	−	2.74932i	0.172734	−	0.0997283i
$761$	7.13366	+	12.3559i	0.258595	+	0.447900i	0.965866	−	0.259043i	$-0.0834072\pi$
$761$	7.13366	+	12.3559i	0.258595	+	0.447900i	−0.707271	+	0.706943i	$0.750074\pi$
$762$	−18.3004	+	10.5658i	−0.662954	+	0.382757i
$763$		−	31.0947i		−	1.12571i
$764$	−0.0644507	−	0.0372106i	−0.00233174	−	0.00134623i
$765$	2.38770	+	4.13561i	0.0863274	+	0.149523i
$766$	−22.6947			−0.819994
$767$	−48.8753			−1.76478
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$			4.95944i			0.178842i	0.995994	+	0.0894210i	$0.0285016\pi$
$769$			4.95944i			0.178842i	−0.995994	+	0.0894210i	$0.971498\pi$
$770$	14.3815	−	24.9095i	0.518273	−	0.897676i
$771$		−	6.79441i		−	0.244695i
$772$	6.48885	+	3.74634i	0.233539	+	0.134834i
$773$	16.5902	−	28.7350i	0.596706	−	1.03353i	−0.396597	−	0.917993i	$-0.629809\pi$
$773$	16.5902	−	28.7350i	0.596706	−	1.03353i	0.993304	−	0.115533i	$-0.0368576\pi$
$774$	−2.60604	+	4.51380i	−0.0936722	+	0.162245i
$775$	0.654812	−	0.378056i	0.0235215	−	0.0135802i
$776$	10.1967			0.366041
$777$	−12.5217	+	25.7007i	−0.449212	+	0.922007i
$778$	12.7900			0.458545
$779$	−22.3562	+	12.9073i	−0.800993	+	0.462454i
$780$	−3.32413	+	5.75756i	−0.119023	+	0.206154i
$781$	−16.5961	+	28.7453i	−0.593855	+	1.02859i
$782$	−20.8585	−	12.0427i	−0.745898	−	0.430644i
$783$		−	4.78061i		−	0.170845i
$784$	−7.54482	+	13.0680i	−0.269458	+	0.466715i
$785$			20.3761i			0.727254i
$786$	−1.69173	−	2.93015i	−0.0603418	−	0.104515i
$787$	32.4343			1.15616			0.578078	−	0.815981i	$-0.303803\pi$
$787$	32.4343			1.15616			0.578078	+	0.815981i	$0.303803\pi$
$788$	1.29543			0.0461478
$789$	−2.75525	−	4.77224i	−0.0980896	−	0.169896i
$790$	−11.6166	−	6.70686i	−0.413301	−	0.238619i
$791$		−	41.2089i		−	1.46522i
$792$	−5.29993	+	3.05992i	−0.188325	+	0.108729i
$793$	−12.6205	−	21.8594i	−0.448168	−	0.776250i
$794$	−9.74845	+	5.62827i	−0.345959	+	0.199740i
$795$	−2.47341	−	1.42802i	−0.0877227	−	0.0506467i
$796$	−3.03358	−	1.75144i	−0.107522	−	0.0620781i
$797$	1.23061	−	0.710491i	0.0435903	−	0.0251669i	−0.478046	−	0.878335i	$-0.658655\pi$
$797$	1.23061	−	0.710491i	0.0435903	−	0.0251669i	0.521637	+	0.853168i	$0.325322\pi$
$798$	−12.9217	−	22.3810i	−0.457423	−	0.792280i
$799$	28.6967	−	16.5680i	1.01521	−	0.586135i
$800$		−	1.00000i		−	0.0353553i
$801$	13.9536	+	8.05612i	0.493027	+	0.284649i
$802$	−13.1758	−	22.8212i	−0.465254	−	0.805843i
$803$	24.0632			0.849172
$804$	−2.06740			−0.0729117
$805$	−11.8524	−	20.5290i	−0.417743	−	0.723552i
$806$		−	5.02682i		−	0.177062i
$807$	−1.02540	+	1.77605i	−0.0360958	+	0.0625198i
$808$			3.64807i			0.128339i
$809$	−3.71407	−	2.14432i	−0.130580	−	0.0753903i	0.433287	−	0.901256i	$-0.357354\pi$
$809$	−3.71407	−	2.14432i	−0.130580	−	0.0753903i	−0.563867	+	0.825866i	$0.690687\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	2.14891	−	3.72201i	0.0754583	−	0.130698i	−0.825827	−	0.563923i	$-0.809291\pi$
$811$	2.14891	−	3.72201i	0.0754583	−	0.130698i	0.901285	+	0.433226i	$0.142625\pi$
$812$	−19.4585	+	11.2344i	−0.682858	+	0.394248i
$813$	−20.1231			−0.705747
$814$	33.4649	+	16.3045i	1.17295	+	0.571472i
$815$	13.3961			0.469243
$816$	−4.13561	+	2.38770i	−0.144775	+	0.0835861i
$817$	−14.3297	+	24.8197i	−0.501332	+	0.868332i
$818$	−10.0945	+	17.4841i	−0.352945	+	0.611319i
$819$	27.0603	+	15.6233i	0.945563	+	0.545921i
$820$			4.69474i			0.163948i
$821$	3.75492	−	6.50372i	0.131048	−	0.226981i	−0.793033	−	0.609179i	$-0.791499\pi$
$821$	3.75492	−	6.50372i	0.131048	−	0.226981i	0.924081	+	0.382197i	$0.124833\pi$
$822$			14.3435i			0.500286i
$823$	3.38820	+	5.86854i	0.118105	+	0.204564i	0.919017	−	0.394218i	$-0.128985\pi$
$823$	3.38820	+	5.86854i	0.118105	+	0.204564i	−0.800911	+	0.598783i	$0.795651\pi$
$824$	−8.51880			−0.296767
$825$	6.11984			0.213065
$826$	−17.2761	−	29.9231i	−0.601113	−	1.04116i
$827$	−17.3357	−	10.0088i	−0.602822	−	0.348039i	0.167329	−	0.985901i	$-0.446486\pi$
$827$	−17.3357	−	10.0088i	−0.602822	−	0.348039i	−0.770151	+	0.637862i	$0.779819\pi$
$828$			5.04363i			0.175278i
$829$	−30.7546	+	17.7562i	−1.06815	+	0.616698i	−0.927676	−	0.373387i	$-0.878196\pi$
$829$	−30.7546	+	17.7562i	−1.06815	+	0.616698i	−0.140476	+	0.990084i	$0.544863\pi$
$830$	−2.99002	−	5.17887i	−0.103785	−	0.179761i
$831$	2.11528	−	1.22126i	0.0733782	−	0.0423649i
$832$	−5.75756	−	3.32413i	−0.199607	−	0.115243i
$833$	−62.4049	−	36.0295i	−2.16220	−	1.24835i
$834$	−2.57519	+	1.48679i	−0.0891715	+	0.0514832i
$835$	7.14269	+	12.3715i	0.247183	+	0.428134i
$836$	−29.1424	+	16.8254i	−1.00791	+	0.581918i
$837$			0.756111i			0.0261350i
$838$	3.79099	+	2.18873i	0.130958	+	0.0756084i
$839$	−3.07090	−	5.31895i	−0.106019	−	0.183631i	0.808135	−	0.588997i	$-0.200477\pi$
$839$	−3.07090	−	5.31895i	−0.106019	−	0.183631i	−0.914154	+	0.405367i	$0.867144\pi$
$840$	−4.69996			−0.162164
$841$	6.14574			0.211922
$842$	−14.0477	−	24.3313i	−0.484115	−	0.838511i
$843$			30.3320i			1.04469i
$844$	−12.9456	+	22.4225i	−0.445606	+	0.771813i
$845$		−	31.1993i		−	1.07329i
$846$	−6.00928	−	3.46946i	−0.206603	−	0.119282i
$847$	−62.1626	+	107.669i	−2.13593	+	3.69955i
$848$	1.42802	−	2.47341i	0.0490385	−	0.0849372i
$849$	−22.8978	+	13.2200i	−0.785849	+	0.453710i
$850$	4.77539			0.163795
$851$	25.4270	−	17.1663i	0.871625	−	0.588453i
$852$	5.42370			0.185813
$853$	−40.5297	+	23.3998i	−1.38771	+	0.801195i	−0.993057	−	0.117635i	$-0.962469\pi$
$853$	−40.5297	+	23.3998i	−1.38771	+	0.801195i	−0.394654	+	0.918830i	$0.629135\pi$
$854$	8.92205	−	15.4534i	0.305306	−	0.528806i
$855$	2.74932	−	4.76196i	0.0940247	−	0.162856i
$856$	−14.7219	−	8.49969i	−0.503184	−	0.290513i
$857$		−	26.0861i		−	0.891085i	−0.895261	−	0.445542i	$-0.853011\pi$
$857$		−	26.0861i		−	0.891085i	0.895261	−	0.445542i	$-0.146989\pi$
$858$	20.3431	−	35.2353i	0.694502	−	1.20291i
$859$		−	40.1933i		−	1.37138i	−0.727895	−	0.685689i	$-0.759501\pi$
$859$		−	40.1933i		−	1.37138i	0.727895	−	0.685689i	$-0.240499\pi$
$860$	2.60604	+	4.51380i	0.0888653	+	0.153919i
$861$	22.0651			0.751977
$862$	−5.00872			−0.170598
$863$	17.0011	+	29.4467i	0.578723	+	1.00238i	0.995626	+	0.0934271i	$0.0297822\pi$
$863$	17.0011	+	29.4467i	0.578723	+	1.00238i	−0.416903	+	0.908951i	$0.636884\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$		−	13.9246i		−	0.473452i
$866$	10.5488	−	6.09033i	0.358462	−	0.206958i
$867$	−2.90220	−	5.02675i	−0.0985637	−	0.170717i
$868$	3.07759	−	1.77685i	0.104460	−	0.0603101i
$869$	71.0918	+	41.0449i	2.41162	+	1.39235i
$870$	−4.14013	−	2.39031i	−0.140364	−	0.0810390i
$871$	11.9032	−	6.87231i	0.403324	−	0.232859i
$872$	3.30798	+	5.72959i	0.112022	+	0.194028i
$873$	8.83062	−	5.09836i	0.298871	−	0.172553i
$874$			27.7331i			0.938085i
$875$	4.07029	+	2.34998i	0.137601	+	0.0794439i
$876$	−1.96600	−	3.40521i	−0.0664250	−	0.115052i
$877$	2.73644			0.0924031			0.0462016	−	0.998932i	$-0.485288\pi$
$877$	2.73644			0.0924031			0.0462016	+	0.998932i	$0.485288\pi$
$878$	−7.16441			−0.241787
$879$	2.99531	+	5.18802i	0.101029	+	0.174988i
$880$			6.11984i			0.206300i
$881$	2.41622	−	4.18501i	0.0814044	−	0.140997i	−0.822449	−	0.568839i	$-0.807393\pi$
$881$	2.41622	−	4.18501i	0.0814044	−	0.140997i	0.903853	+	0.427842i	$0.140726\pi$
$882$			15.0896i			0.508095i
$883$	37.5958	+	21.7059i	1.26520	+	0.730462i	0.974075	−	0.226223i	$-0.0726379\pi$
$883$	37.5958	+	21.7059i	1.26520	+	0.730462i	0.291123	+	0.956686i	$0.405971\pi$
$884$	15.8740	−	27.4946i	0.533901	−	0.924743i
$885$	3.67580	−	6.36667i	0.123561	−	0.214013i
$886$	−1.24446	+	0.718487i	−0.0418083	+	0.0241380i
$887$	28.8953			0.970211			0.485105	−	0.874456i	$-0.338781\pi$
$887$	28.8953			0.970211			0.485105	+	0.874456i	$0.338781\pi$
$888$	−0.426867	−	6.06777i	−0.0143247	−	0.203621i
$889$	99.3173			3.33100
$890$	13.9536	−	8.05612i	0.467726	−	0.270042i
$891$	−3.05992	+	5.29993i	−0.102511	+	0.177554i
$892$	1.93657	−	3.35424i	0.0648412	−	0.112308i
$893$	−33.0428	−	19.0773i	−1.10574	−	0.638397i
$894$		−	15.9232i		−	0.532552i
$895$	0.822024	−	1.42379i	0.0274772	−	0.0475919i
$896$		−	4.69996i		−	0.157015i
$897$	−16.7657	−	29.0390i	−0.559789	−	0.969583i
$898$	−4.24576			−0.141683
$899$	3.61468			0.120556
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	11.8115	+	6.81937i	0.393498	+	0.227186i
$902$		−	28.7311i		−	0.956640i
$903$	21.2147	−	12.2483i	0.705980	−	0.407598i
$904$	4.38396	+	7.59323i	0.145808	+	0.252547i
$905$	0.651682	−	0.376249i	0.0216626	−	0.0125069i
$906$	7.59987	+	4.38779i	0.252489	+	0.145774i
$907$	−29.8375	−	17.2267i	−0.990738	−	0.572003i	−0.0852432	−	0.996360i	$-0.527167\pi$
$907$	−29.8375	−	17.2267i	−0.990738	−	0.572003i	−0.905495	+	0.424357i	$0.860500\pi$
$908$	−15.1837	+	8.76632i	−0.503889	+	0.290921i
$909$	1.82404	+	3.15933i	0.0604995	+	0.104788i
$910$	27.0603	−	15.6233i	0.897040	−	0.517906i
$911$			21.0424i			0.697166i	0.937278	+	0.348583i	$0.113337\pi$
$911$			21.0424i			0.697166i	−0.937278	+	0.348583i	$0.886663\pi$
$912$	4.76196	+	2.74932i	0.157684	+	0.0910391i
$913$	18.2984	+	31.6938i	0.605590	+	1.04891i
$914$	−21.8471			−0.722638
$915$	3.79665			0.125513
$916$	13.0785	+	22.6526i	0.432125	+	0.748462i
$917$			15.9021i			0.525133i
$918$	−2.38770	+	4.13561i	−0.0788057	+	0.136496i
$919$		−	4.07698i		−	0.134487i	−0.997737	−	0.0672435i	$-0.978580\pi$
$919$		−	4.07698i		−	0.134487i	0.997737	−	0.0672435i	$-0.0214204\pi$
$920$	4.36791	+	2.52181i	0.144006	+	0.0831417i
$921$	−2.47452	+	4.28600i	−0.0815383	+	0.141228i
$922$	−12.6150	+	21.8499i	−0.415454	+	0.719587i
$923$	−31.2273	+	18.0291i	−1.02786	+	0.593434i
$924$	28.7630			0.946233
$925$	−2.66421	+	5.46827i	−0.0875985	+	0.179796i
$926$	30.7096			1.00918
$927$	−7.37750	+	4.25940i	−0.242309	+	0.139897i
$928$	2.39031	−	4.14013i	0.0784657	−	0.135907i
$929$	−12.9889	+	22.4974i	−0.426151	+	0.738116i	−0.996527	−	0.0832680i	$-0.973464\pi$
$929$	−12.9889	+	22.4974i	−0.426151	+	0.738116i	0.570376	+	0.821384i	$0.306798\pi$
$930$	0.654812	+	0.378056i	0.0214721	+	0.0123969i
$931$			82.9725i			2.71931i
$932$	13.0725	−	22.6423i	0.428205	−	0.741674i
$933$			2.99680i			0.0981109i
$934$	−5.40327	−	9.35874i	−0.176800	−	0.306227i
$935$	−29.2246			−0.955748
$936$	−6.64825			−0.217305
$937$	−0.269372	−	0.466566i	−0.00880000	−	0.0152420i	0.861592	−	0.507602i	$-0.169468\pi$
$937$	−0.269372	−	0.466566i	−0.00880000	−	0.0152420i	−0.870392	+	0.492360i	$0.836134\pi$
$938$	8.41493	+	4.85836i	0.274757	+	0.158631i
$939$		−	10.4616i		−	0.341403i
$940$	−6.00928	+	3.46946i	−0.196001	+	0.113161i
$941$	−23.7682	−	41.1678i	−0.774823	−	1.34203i	−0.934894	−	0.354927i	$-0.884506\pi$
$941$	−23.7682	−	41.1678i	−0.774823	−	1.34203i	0.160072	−	0.987105i	$-0.448828\pi$
$942$	−17.6462	+	10.1880i	−0.574945	+	0.331944i
$943$	−20.5062	−	11.8393i	−0.667774	−	0.385539i
$944$	6.36667	+	3.67580i	0.207217	+	0.119637i
$945$	−4.07029	+	2.34998i	−0.132406	+	0.0764449i
$946$	−15.9485	−	27.6237i	−0.518532	−	0.898124i
$947$	28.6400	−	16.5353i	0.930674	−	0.537325i	0.0436494	−	0.999047i	$-0.486102\pi$
$947$	28.6400	−	16.5353i	0.930674	−	0.537325i	0.887025	+	0.461722i	$0.152768\pi$
$948$		−	13.4137i		−	0.435657i
$949$	22.6387	+	13.0705i	0.734884	+	0.424285i
$950$	−2.74932	−	4.76196i	−0.0891997	−	0.154498i
$951$	4.50131			0.145965
$952$	22.4442			0.727420
$953$	21.2891	+	36.8739i	0.689623	+	1.19446i	0.971960	+	0.235146i	$0.0755570\pi$
$953$	21.2891	+	36.8739i	0.689623	+	1.19446i	−0.282337	+	0.959315i	$0.591110\pi$
$954$		−	2.85605i		−	0.0924679i
$955$	−0.0372106	+	0.0644507i	−0.00120411	+	0.00208557i
$956$			17.3894i			0.562413i
$957$	25.3369	+	14.6283i	0.819027	+	0.472865i
$958$	4.70495	−	8.14921i	0.152010	−	0.263289i
$959$	33.7069	−	58.3820i	1.08845	−	1.88525i
$960$	0.866025	−	0.500000i	0.0279508	−	0.0161374i
$961$	30.4283			0.981558
$962$	22.6277	+	33.5165i	0.729547	+	1.08062i
$963$	−16.9994			−0.547797
$964$	−7.15404	+	4.13038i	−0.230416	+	0.133031i
$965$	3.74634	−	6.48885i	0.120599	−	0.208884i
$966$	11.8524	−	20.5290i	0.381346	−	0.660510i
$967$	24.3383	+	14.0517i	0.782666	+	0.451872i	0.837374	−	0.546630i	$-0.184090\pi$
$967$	24.3383	+	14.0517i	0.782666	+	0.451872i	−0.0547083	+	0.998502i	$0.517423\pi$
$968$		−	26.4524i		−	0.850212i
$969$	−13.1291	+	22.7402i	−0.421767	+	0.730522i
$970$		−	10.1967i		−	0.327397i
$971$	−11.8982	−	20.6082i	−0.381830	−	0.661350i	0.609494	−	0.792791i	$-0.291373\pi$
$971$	−11.8982	−	20.6082i	−0.381830	−	0.661350i	−0.991324	+	0.131441i	$0.958039\pi$
$972$	1.00000			0.0320750
$973$	13.9757			0.448039
$974$	−7.79122	−	13.4948i	−0.249647	−	0.432401i
$975$	5.75756	+	3.32413i	0.184389	+	0.106457i
$976$			3.79665i			0.121528i
$977$	−23.9089	+	13.8038i	−0.764915	+	0.441624i	−0.831057	−	0.556187i	$-0.812264\pi$
$977$	−23.9089	+	13.8038i	−0.764915	+	0.441624i	0.0661430	+	0.997810i	$0.478931\pi$
$978$	6.69803	+	11.6013i	0.214179	+	0.370969i
$979$	−85.3939	+	49.3022i	−2.72920	+	1.57570i
$980$	13.0680	+	7.54482i	0.417442	+	0.241010i
$981$	5.72959	+	3.30798i	0.182932	+	0.105616i
$982$	13.0874	−	7.55600i	0.417635	−	0.241122i
$983$	−18.1365	−	31.4133i	−0.578464	−	1.00193i	−0.995656	−	0.0931100i	$-0.970319\pi$
$983$	−18.1365	−	31.4133i	−0.578464	−	1.00193i	0.417192	−	0.908818i	$-0.363014\pi$
$984$	−4.06577	+	2.34737i	−0.129612	+	0.0748315i
$985$		−	1.29543i		−	0.0412758i
$986$	19.7708	+	11.4147i	0.629629	+	0.363517i
$987$	16.3063	+	28.2434i	0.519036	+	0.898996i
$988$	−36.5563			−1.16301
$989$	−26.2878			−0.835903
$990$	3.05992	+	5.29993i	0.0972506	+	0.168443i
$991$			25.3445i			0.805094i	0.915399	+	0.402547i	$0.131875\pi$
$991$			25.3445i			0.805094i	−0.915399	+	0.402547i	$0.868125\pi$
$992$	−0.378056	+	0.654812i	−0.0120033	+	0.0207903i
$993$		−	5.62154i		−	0.178394i
$994$	−22.0760	−	12.7456i	−0.700209	−	0.404266i
$995$	−1.75144	+	3.03358i	−0.0555244	+	0.0961710i
$996$	2.99002	−	5.17887i	0.0947424	−	0.164099i
$997$	3.45896	−	1.99703i	0.109546	−	0.0632466i	−0.444226	−	0.895915i	$-0.646521\pi$
$997$	3.45896	−	1.99703i	0.109546	−	0.0632466i	0.553772	+	0.832668i	$0.313188\pi$
$998$	28.2796			0.895174
$999$	−3.40356	−	5.04141i	−0.107684	−	0.159503i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.e.751.6	✓	16
37.27	even	6	inner	1110.2.x.e.841.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.e.751.6	✓	16	1.1	even	1	trivial
1110.2.x.e.841.6	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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(-2.34998 + 4.07029i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(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} +(-2.34998 + 4.07029i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} +6.11984 q^{11} +(-0.500000 - 0.866025i) q^{12} +(5.75756 + 3.32413i) q^{13} +4.69996i q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.13561 - 2.38770i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-4.76196 - 2.74932i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(2.34998 + 4.07029i) q^{21} +(5.29993 - 3.05992i) q^{22} -5.04363i q^{23} +(-0.866025 - 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} +6.64825 q^{26} -1.00000 q^{27} +(2.34998 + 4.07029i) q^{28} +4.78061i q^{29} +(-0.500000 + 0.866025i) q^{30} -0.756111i q^{31} +(-0.866025 - 0.500000i) q^{32} +(3.05992 - 5.29993i) q^{33} +(2.38770 - 4.13561i) q^{34} +(4.07029 - 2.34998i) q^{35} -1.00000 q^{36} +(3.40356 + 5.04141i) q^{37} -5.49864 q^{38} +(5.75756 - 3.32413i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(2.34737 - 4.06577i) q^{41} +(4.07029 + 2.34998i) q^{42} -5.21208i q^{43} +(3.05992 - 5.29993i) q^{44} +1.00000i q^{45} +(-2.52181 - 4.36791i) q^{46} +6.93891 q^{47} -1.00000 q^{48} +(-7.54482 - 13.0680i) q^{49} +(0.866025 + 0.500000i) q^{50} -4.77539i q^{51} +(5.75756 - 3.32413i) q^{52} +(1.42802 + 2.47341i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-5.29993 - 3.05992i) q^{55} +(4.07029 + 2.34998i) q^{56} +(-4.76196 + 2.74932i) q^{57} +(2.39031 + 4.14013i) q^{58} +(-6.36667 + 3.67580i) q^{59} +1.00000i q^{60} +(-3.28799 - 1.89832i) q^{61} +(-0.378056 - 0.654812i) q^{62} +4.69996 q^{63} -1.00000 q^{64} +(-3.32413 - 5.75756i) q^{65} -6.11984i q^{66} +(1.03370 - 1.79042i) q^{67} -4.77539i q^{68} +(-4.36791 - 2.52181i) q^{69} +(2.34998 - 4.07029i) q^{70} +(-2.71185 + 4.69706i) q^{71} +(-0.866025 + 0.500000i) q^{72} +3.93200 q^{73} +(5.46827 + 2.66421i) q^{74} +1.00000 q^{75} +(-4.76196 + 2.74932i) q^{76} +(-14.3815 + 24.9095i) q^{77} +(3.32413 - 5.75756i) q^{78} +(11.6166 + 6.70686i) q^{79} +1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} -4.69474i q^{82} +(2.99002 + 5.17887i) q^{83} +4.69996 q^{84} -4.77539 q^{85} +(-2.60604 - 4.51380i) q^{86} +(4.14013 + 2.39031i) q^{87} -6.11984i q^{88} +(-13.9536 + 8.05612i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-27.0603 + 15.6233i) q^{91} +(-4.36791 - 2.52181i) q^{92} +(-0.654812 - 0.378056i) q^{93} +(6.00928 - 3.46946i) q^{94} +(2.74932 + 4.76196i) q^{95} +(-0.866025 + 0.500000i) q^{96} +10.1967i q^{97} +(-13.0680 - 7.54482i) q^{98} +(-3.05992 - 5.29993i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 8 q^{4} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 8 * q^4 - 4 * q^7 - 8 * q^9	\( 16 q + 8 q^{3} + 8 q^{4} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 8 q^{16} - 6 q^{17} - 6 q^{19} + 4 q^{21} + 12 q^{22} + 8 q^{25} - 8 q^{26} - 16 q^{27} + 4 q^{28} - 8 q^{30} - 2 q^{33} + 2 q^{34} + 18 q^{35} - 16 q^{36} - 12 q^{37} + 12 q^{38} - 8 q^{40} + 4 q^{41} + 18 q^{42} - 2 q^{44} + 12 q^{47} - 16 q^{48} - 42 q^{49} - 16 q^{53} - 12 q^{55} + 18 q^{56} - 6 q^{57} + 2 q^{58} + 48 q^{59} - 12 q^{61} - 4 q^{62} + 8 q^{63} - 16 q^{64} + 4 q^{65} + 6 q^{67} - 18 q^{69} + 4 q^{70} - 6 q^{71} - 52 q^{73} - 16 q^{74} + 16 q^{75} - 6 q^{76} + 10 q^{77} - 4 q^{78} + 78 q^{79} - 8 q^{81} + 36 q^{83} + 8 q^{84} - 4 q^{85} - 6 q^{86} + 12 q^{87} + 18 q^{89} + 8 q^{90} - 66 q^{91} - 18 q^{92} - 36 q^{93} + 12 q^{94} - 6 q^{95} - 12 q^{98} + 2 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 + 8 * q^4 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 8 * q^16 - 6 * q^17 - 6 * q^19 + 4 * q^21 + 12 * q^22 + 8 * q^25 - 8 * q^26 - 16 * q^27 + 4 * q^28 - 8 * q^30 - 2 * q^33 + 2 * q^34 + 18 * q^35 - 16 * q^36 - 12 * q^37 + 12 * q^38 - 8 * q^40 + 4 * q^41 + 18 * q^42 - 2 * q^44 + 12 * q^47 - 16 * q^48 - 42 * q^49 - 16 * q^53 - 12 * q^55 + 18 * q^56 - 6 * q^57 + 2 * q^58 + 48 * q^59 - 12 * q^61 - 4 * q^62 + 8 * q^63 - 16 * q^64 + 4 * q^65 + 6 * q^67 - 18 * q^69 + 4 * q^70 - 6 * q^71 - 52 * q^73 - 16 * q^74 + 16 * q^75 - 6 * q^76 + 10 * q^77 - 4 * q^78 + 78 * q^79 - 8 * q^81 + 36 * q^83 + 8 * q^84 - 4 * q^85 - 6 * q^86 + 12 * q^87 + 18 * q^89 + 8 * q^90 - 66 * q^91 - 18 * q^92 - 36 * q^93 + 12 * q^94 - 6 * q^95 - 12 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more