LMFDB - Embedded newform 1110.2.x.e.841.4

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			841.4
Root			$0.241301i$ of defining polynomial
Character	$\chi$	$=$	1110.841
Dual form			1110.2.x.e.751.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(2.38947 + 4.13868i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(2.38947 + 4.13868i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} -2.82833 q^{11} +(-0.500000 + 0.866025i) q^{12} +(-3.23678 + 1.86876i) q^{13} -4.77894i q^{14} +(0.866025 + 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.65646 + 2.11106i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-6.31758 + 3.64746i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-2.38947 + 4.13868i) q^{21} +(2.44941 + 1.41417i) q^{22} -1.57043i q^{23} +(0.866025 - 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} +3.73751 q^{26} -1.00000 q^{27} +(-2.38947 + 4.13868i) q^{28} +2.13619i q^{29} +(-0.500000 - 0.866025i) q^{30} +2.98150i q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.41417 - 2.44941i) q^{33} +(-2.11106 - 3.65646i) q^{34} +(4.13868 + 2.38947i) q^{35} -1.00000 q^{36} +(-3.99548 - 4.58652i) q^{37} +7.29492 q^{38} +(-3.23678 - 1.86876i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-5.56862 - 9.64513i) q^{41} +(4.13868 - 2.38947i) q^{42} -4.99510i q^{43} +(-1.41417 - 2.44941i) q^{44} +1.00000i q^{45} +(-0.785213 + 1.36003i) q^{46} -3.09525 q^{47} -1.00000 q^{48} +(-7.91911 + 13.7163i) q^{49} +(-0.866025 + 0.500000i) q^{50} +4.22211i q^{51} +(-3.23678 - 1.86876i) q^{52} +(0.346506 - 0.600165i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-2.44941 + 1.41417i) q^{55} +(4.13868 - 2.38947i) q^{56} +(-6.31758 - 3.64746i) q^{57} +(1.06810 - 1.84999i) q^{58} +(9.67139 + 5.58378i) q^{59} +1.00000i q^{60} +(13.3008 - 7.67919i) q^{61} +(1.49075 - 2.58205i) q^{62} -4.77894 q^{63} -1.00000 q^{64} +(-1.86876 + 3.23678i) q^{65} +2.82833i q^{66} +(-1.86976 - 3.23851i) q^{67} +4.22211i q^{68} +(1.36003 - 0.785213i) q^{69} +(-2.38947 - 4.13868i) q^{70} +(7.93390 + 13.7419i) q^{71} +(0.866025 + 0.500000i) q^{72} +9.27744 q^{73} +(1.16693 + 5.96978i) q^{74} +1.00000 q^{75} +(-6.31758 - 3.64746i) q^{76} +(-6.75821 - 11.7056i) q^{77} +(1.86876 + 3.23678i) q^{78} +(-10.8209 + 6.24742i) q^{79} +1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} +11.1372i q^{82} +(-4.53064 + 7.84729i) q^{83} -4.77894 q^{84} +4.22211 q^{85} +(-2.49755 + 4.32589i) q^{86} +(-1.84999 + 1.06810i) q^{87} +2.82833i q^{88} +(1.94204 + 1.12123i) q^{89} +(0.500000 - 0.866025i) q^{90} +(-15.4684 - 8.93067i) q^{91} +(1.36003 - 0.785213i) q^{92} +(-2.58205 + 1.49075i) q^{93} +(2.68057 + 1.54763i) q^{94} +(-3.64746 + 6.31758i) q^{95} +(0.866025 + 0.500000i) q^{96} +16.0748i q^{97} +(13.7163 - 7.91911i) q^{98} +(1.41417 - 2.44941i) 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

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

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
$7$	2.38947	+	4.13868i	0.903134	+	1.56427i	0.823403	+	0.567458i	$0.192073\pi$
$7$	2.38947	+	4.13868i	0.903134	+	1.56427i	0.0797313	+	0.996816i	$0.474594\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.00000			−0.316228
$11$	−2.82833			−0.852775			−0.426387	−	0.904541i	$-0.640214\pi$
$11$	−2.82833			−0.852775			−0.426387	+	0.904541i	$0.640214\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−3.23678	+	1.86876i	−0.897722	+	0.518300i	−0.876460	−	0.481474i	$-0.840102\pi$
$13$	−3.23678	+	1.86876i	−0.897722	+	0.518300i	−0.0212612	+	0.999774i	$0.506768\pi$
$14$		−	4.77894i		−	1.27722i
$15$	0.866025	+	0.500000i	0.223607	+	0.129099i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.65646	+	2.11106i	0.886821	+	0.512007i	0.872901	−	0.487896i	$-0.162236\pi$
$17$	3.65646	+	2.11106i	0.886821	+	0.512007i	0.0139200	+	0.999903i	$0.495569\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−6.31758	+	3.64746i	−1.44935	+	0.836784i	−0.998443	−	0.0557848i	$-0.982234\pi$
$19$	−6.31758	+	3.64746i	−1.44935	+	0.836784i	−0.450910	+	0.892569i	$0.648901\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$	−2.38947	+	4.13868i	−0.521425	+	0.903134i
$22$	2.44941	+	1.41417i	0.522216	+	0.301501i
$23$		−	1.57043i		−	0.327456i	−0.986505	−	0.163728i	$-0.947648\pi$
$23$		−	1.57043i		−	0.327456i	0.986505	−	0.163728i	$-0.0523520\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	3.73751			0.732987
$27$	−1.00000			−0.192450
$28$	−2.38947	+	4.13868i	−0.451567	+	0.782137i
$29$			2.13619i			0.396681i	0.980133	+	0.198340i	$0.0635551\pi$
$29$			2.13619i			0.396681i	−0.980133	+	0.198340i	$0.936445\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$			2.98150i			0.535493i	0.963489	+	0.267746i	$0.0862790\pi$
$31$			2.98150i			0.535493i	−0.963489	+	0.267746i	$0.913721\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−1.41417	−	2.44941i	−0.246175	−	0.426387i
$34$	−2.11106	−	3.65646i	−0.362043	−	0.627077i
$35$	4.13868	+	2.38947i	0.699565	+	0.403894i
$36$	−1.00000			−0.166667
$37$	−3.99548	−	4.58652i	−0.656853	−	0.754019i
$37$	−3.99548	−	4.58652i	−0.656853	−	0.754019i
$38$	7.29492			1.18339
$39$	−3.23678	−	1.86876i	−0.518300	−	0.299241i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−5.56862	−	9.64513i	−0.869672	−	1.50632i	−0.862332	−	0.506344i	$-0.830997\pi$
$41$	−5.56862	−	9.64513i	−0.869672	−	1.50632i	−0.00734063	−	0.999973i	$-0.502337\pi$
$42$	4.13868	−	2.38947i	0.638612	−	0.368703i
$43$		−	4.99510i		−	0.761746i	−0.924627	−	0.380873i	$-0.875623\pi$
$43$		−	4.99510i		−	0.761746i	0.924627	−	0.380873i	$-0.124377\pi$
$44$	−1.41417	−	2.44941i	−0.213194	−	0.369262i
$45$			1.00000i			0.149071i
$46$	−0.785213	+	1.36003i	−0.115773	+	0.200525i
$47$	−3.09525			−0.451489			−0.225745	−	0.974187i	$-0.572481\pi$
$47$	−3.09525			−0.451489			−0.225745	+	0.974187i	$0.572481\pi$
$48$	−1.00000			−0.144338
$49$	−7.91911	+	13.7163i	−1.13130	+	1.95947i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$			4.22211i			0.591214i
$52$	−3.23678	−	1.86876i	−0.448861	−	0.259150i
$53$	0.346506	−	0.600165i	0.0475962	−	0.0824390i	−0.841246	−	0.540653i	$-0.818177\pi$
$53$	0.346506	−	0.600165i	0.0475962	−	0.0824390i	0.888842	+	0.458214i	$0.151511\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	−2.44941	+	1.41417i	−0.330278	+	0.190686i
$56$	4.13868	−	2.38947i	0.553054	−	0.319306i
$57$	−6.31758	−	3.64746i	−0.836784	−	0.483118i
$58$	1.06810	−	1.84999i	0.140248	−	0.242916i
$59$	9.67139	+	5.58378i	1.25911	+	0.726946i	0.972901	−	0.231222i	$-0.0742724\pi$
$59$	9.67139	+	5.58378i	1.25911	+	0.726946i	0.286206	+	0.958168i	$0.407606\pi$
$60$			1.00000i			0.129099i
$61$	13.3008	−	7.67919i	1.70299	−	0.983220i	0.760282	−	0.649594i	$-0.225061\pi$
$61$	13.3008	−	7.67919i	1.70299	−	0.983220i	0.942705	−	0.333626i	$-0.108272\pi$
$62$	1.49075	−	2.58205i	0.189325	−	0.327921i
$63$	−4.77894			−0.602089
$64$	−1.00000			−0.125000
$65$	−1.86876	+	3.23678i	−0.231791	+	0.401473i
$66$			2.82833i			0.348144i
$67$	−1.86976	−	3.23851i	−0.228427	−	0.395647i	0.728915	−	0.684604i	$-0.240025\pi$
$67$	−1.86976	−	3.23851i	−0.228427	−	0.395647i	−0.957342	+	0.288957i	$0.906692\pi$
$68$			4.22211i			0.512007i
$69$	1.36003	−	0.785213i	0.163728	−	0.0945285i
$70$	−2.38947	−	4.13868i	−0.285596	−	0.494667i
$71$	7.93390	+	13.7419i	0.941581	+	1.63087i	0.762456	+	0.647040i	$0.223993\pi$
$71$	7.93390	+	13.7419i	0.941581	+	1.63087i	0.179125	+	0.983826i	$0.442673\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	9.27744			1.08584			0.542921	−	0.839784i	$-0.317318\pi$
$73$	9.27744			1.08584			0.542921	+	0.839784i	$0.317318\pi$
$74$	1.16693	+	5.96978i	0.135653	+	0.693973i
$75$	1.00000			0.115470
$76$	−6.31758	−	3.64746i	−0.724677	−	0.418392i
$77$	−6.75821	−	11.7056i	−0.770170	−	1.33397i
$78$	1.86876	+	3.23678i	0.211595	+	0.366493i
$79$	−10.8209	+	6.24742i	−1.21744	+	0.702890i	−0.964370	−	0.264558i	$-0.914774\pi$
$79$	−10.8209	+	6.24742i	−1.21744	+	0.702890i	−0.253071	+	0.967448i	$0.581441\pi$
$80$			1.00000i			0.111803i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$			11.1372i			1.22990i
$83$	−4.53064	+	7.84729i	−0.497302	+	0.861352i	−0.999995	−	0.00311251i	$-0.999009\pi$
$83$	−4.53064	+	7.84729i	−0.497302	+	0.861352i	0.502693	+	0.864465i	$0.332343\pi$
$84$	−4.77894			−0.521425
$85$	4.22211			0.457953
$86$	−2.49755	+	4.32589i	−0.269318	+	0.466472i
$87$	−1.84999	+	1.06810i	−0.198340	+	0.114512i
$88$			2.82833i			0.301501i
$89$	1.94204	+	1.12123i	0.205855	+	0.118851i	0.599384	−	0.800462i	$-0.295412\pi$
$89$	1.94204	+	1.12123i	0.205855	+	0.118851i	−0.393528	+	0.919312i	$0.628746\pi$
$90$	0.500000	−	0.866025i	0.0527046	−	0.0912871i
$91$	−15.4684	−	8.93067i	−1.62153	−	0.936188i
$92$	1.36003	−	0.785213i	0.141793	−	0.0818641i
$93$	−2.58205	+	1.49075i	−0.267746	+	0.154584i
$94$	2.68057	+	1.54763i	0.276479	+	0.159625i
$95$	−3.64746	+	6.31758i	−0.374221	+	0.648170i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$			16.0748i			1.63215i	0.577947	+	0.816074i	$0.303854\pi$
$97$			16.0748i			1.63215i	−0.577947	+	0.816074i	$0.696146\pi$
$98$	13.7163	−	7.91911i	1.38556	−	0.799951i
$99$	1.41417	−	2.44941i	0.142129	−	0.246175i
$100$	1.00000			0.100000
$101$	−2.70797			−0.269453			−0.134726	−	0.990883i	$-0.543016\pi$
$101$	−2.70797			−0.269453			−0.134726	+	0.990883i	$0.543016\pi$
$102$	2.11106	−	3.65646i	0.209026	−	0.362043i
$103$			11.4602i			1.12920i	0.825363	+	0.564602i	$0.190970\pi$
$103$			11.4602i			1.12920i	−0.825363	+	0.564602i	$0.809030\pi$
$104$	1.86876	+	3.23678i	0.183247	+	0.317392i
$105$			4.77894i			0.466376i
$106$	−0.600165	+	0.346506i	−0.0582932	+	0.0336556i
$107$	−7.55146	−	13.0795i	−0.730027	−	1.26444i	−0.956871	−	0.290513i	$-0.906174\pi$
$107$	−7.55146	−	13.0795i	−0.730027	−	1.26444i	0.226844	−	0.973931i	$-0.427159\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	17.2488	+	9.95858i	1.65213	+	0.953859i	0.976194	+	0.216901i	$0.0695948\pi$
$109$	17.2488	+	9.95858i	1.65213	+	0.953859i	0.675938	+	0.736958i	$0.263739\pi$
$110$	2.82833			0.269671
$111$	1.97430	−	5.75345i	0.187392	−	0.546093i
$112$	−4.77894			−0.451567
$113$	−0.970268	−	0.560185i	−0.0912752	−	0.0526977i	0.453668	−	0.891171i	$-0.350115\pi$
$113$	−0.970268	−	0.560185i	−0.0912752	−	0.0526977i	−0.544943	+	0.838473i	$0.683449\pi$
$114$	3.64746	+	6.31758i	0.341616	+	0.591696i
$115$	−0.785213	−	1.36003i	−0.0732215	−	0.126823i
$116$	−1.84999	+	1.06810i	−0.171768	+	0.0991701i
$117$		−	3.73751i		−	0.345533i
$118$	−5.58378	−	9.67139i	−0.514028	−	0.890323i
$119$			20.1772i			1.84964i
$120$	0.500000	−	0.866025i	0.0456435	−	0.0790569i
$121$	−3.00052			−0.272775
$122$	−15.3584			−1.39048
$123$	5.56862	−	9.64513i	0.502106	−	0.869672i
$124$	−2.58205	+	1.49075i	−0.231875	+	0.133873i
$125$		−	1.00000i		−	0.0894427i
$126$	4.13868	+	2.38947i	0.368703	+	0.212871i
$127$	−1.81569	+	3.14487i	−0.161117	+	0.279062i	−0.935269	−	0.353937i	$-0.884843\pi$
$127$	−1.81569	+	3.14487i	−0.161117	+	0.279062i	0.774153	+	0.632999i	$0.218176\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	4.32589	−	2.49755i	0.380873	−	0.219897i
$130$	3.23678	−	1.86876i	0.283884	−	0.163901i
$131$	8.98867	+	5.18961i	0.785344	+	0.453419i	0.838321	−	0.545177i	$-0.183538\pi$
$131$	8.98867	+	5.18961i	0.785344	+	0.453419i	−0.0529768	+	0.998596i	$0.516871\pi$
$132$	1.41417	−	2.44941i	0.123087	−	0.213194i
$133$	−30.1913	−	17.4310i	−2.61792	−	1.51146i
$134$			3.73951i			0.323045i
$135$	−0.866025	+	0.500000i	−0.0745356	+	0.0430331i
$136$	2.11106	−	3.65646i	0.181022	−	0.313539i
$137$	−7.84028			−0.669840			−0.334920	−	0.942247i	$-0.608709\pi$
$137$	−7.84028			−0.669840			−0.334920	+	0.942247i	$0.608709\pi$
$138$	−1.57043			−0.133683
$139$	−2.33928	+	4.05175i	−0.198415	+	0.343665i	−0.948015	−	0.318227i	$-0.896913\pi$
$139$	−2.33928	+	4.05175i	−0.198415	+	0.343665i	0.749600	+	0.661891i	$0.230246\pi$
$140$			4.77894i			0.403894i
$141$	−1.54763	−	2.68057i	−0.130334	−	0.225745i
$142$		−	15.8678i		−	1.33160i
$143$	9.15470	−	5.28547i	0.765554	−	0.441993i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	1.06810	+	1.84999i	0.0887005	+	0.153634i
$146$	−8.03450	−	4.63872i	−0.664940	−	0.383903i
$147$	−15.8382			−1.30631
$148$	1.97430	−	5.75345i	0.162287	−	0.472930i
$149$	19.3072			1.58170			0.790852	−	0.612007i	$-0.209638\pi$
$149$	19.3072			1.58170			0.790852	+	0.612007i	$0.209638\pi$
$150$	−0.866025	−	0.500000i	−0.0707107	−	0.0408248i
$151$	1.09628	+	1.89882i	0.0892143	+	0.154524i	0.907179	−	0.420744i	$-0.138231\pi$
$151$	1.09628	+	1.89882i	0.0892143	+	0.154524i	−0.817965	+	0.575268i	$0.804898\pi$
$152$	3.64746	+	6.31758i	0.295848	+	0.512424i
$153$	−3.65646	+	2.11106i	−0.295607	+	0.170669i
$154$			13.5164i			1.08918i
$155$	1.49075	+	2.58205i	0.119740	+	0.207396i
$156$		−	3.73751i		−	0.299241i
$157$	3.81635	−	6.61012i	0.304578	−	0.527545i	−0.672589	−	0.740016i	$-0.734818\pi$
$157$	3.81635	−	6.61012i	0.304578	−	0.527545i	0.977167	+	0.212471i	$0.0681512\pi$
$158$	12.4948			0.994036
$159$	0.693011			0.0549594
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	6.49949	−	3.75248i	0.512231	−	0.295737i
$162$			1.00000i			0.0785674i
$163$	16.5993	+	9.58358i	1.30015	+	0.750644i	0.980430	−	0.196866i	$-0.0630766\pi$
$163$	16.5993	+	9.58358i	1.30015	+	0.750644i	0.319724	+	0.947511i	$0.396410\pi$
$164$	5.56862	−	9.64513i	0.434836	−	0.753158i
$165$	−2.44941	−	1.41417i	−0.190686	−	0.110093i
$166$	7.84729	−	4.53064i	0.609068	−	0.351646i
$167$	18.1416	−	10.4741i	1.40384	−	0.810508i	0.409057	−	0.912509i	$-0.365858\pi$
$167$	18.1416	−	10.4741i	1.40384	−	0.810508i	0.994784	+	0.102000i	$0.0325243\pi$
$168$	4.13868	+	2.38947i	0.319306	+	0.184351i
$169$	0.484500	−	0.839179i	0.0372693	−	0.0645523i
$170$	−3.65646	−	2.11106i	−0.280438	−	0.161911i
$171$		−	7.29492i		−	0.557856i
$172$	4.32589	−	2.49755i	0.329846	−	0.190437i
$173$	1.49729	−	2.59339i	0.113837	−	0.197172i	−0.803477	−	0.595336i	$-0.797019\pi$
$173$	1.49729	−	2.59339i	0.113837	−	0.197172i	0.917314	+	0.398164i	$0.130352\pi$
$174$	2.13619			0.161944
$175$	4.77894			0.361254
$176$	1.41417	−	2.44941i	0.106597	−	0.184631i
$177$			11.1676i			0.839405i
$178$	−1.12123	−	1.94204i	−0.0840401	−	0.145562i
$179$		−	4.16205i		−	0.311087i	−0.987829	−	0.155543i	$-0.950287\pi$
$179$		−	4.16205i		−	0.311087i	0.987829	−	0.155543i	$-0.0497128\pi$
$180$	−0.866025	+	0.500000i	−0.0645497	+	0.0372678i
$181$	−4.38018	−	7.58669i	−0.325576	−	0.563914i	0.656053	−	0.754715i	$-0.272225\pi$
$181$	−4.38018	−	7.58669i	−0.325576	−	0.563914i	−0.981629	+	0.190801i	$0.938892\pi$
$182$	8.93067	+	15.4684i	0.661985	+	1.14659i
$183$	13.3008	+	7.67919i	0.983220	+	0.567662i
$184$	−1.57043			−0.115773
$185$	−5.75345	−	1.97430i	−0.423002	−	0.145153i
$186$	2.98150			0.218614
$187$	−10.3417	−	5.97078i	−0.756259	−	0.436626i
$188$	−1.54763	−	2.68057i	−0.112872	−	0.195500i
$189$	−2.38947	−	4.13868i	−0.173808	−	0.301045i
$190$	6.31758	−	3.64746i	0.458326	−	0.264614i
$191$			17.0813i			1.23596i	0.786195	+	0.617978i	$0.212048\pi$
$191$			17.0813i			1.23596i	−0.786195	+	0.617978i	$0.787952\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$			2.15174i			0.154886i	0.996997	+	0.0774429i	$0.0246756\pi$
$193$			2.15174i			0.154886i	−0.996997	+	0.0774429i	$0.975324\pi$
$194$	8.03740	−	13.9212i	0.577052	−	0.999483i
$195$	−3.73751			−0.267649
$196$	−15.8382			−1.13130
$197$	0.929608	−	1.61013i	0.0662318	−	0.114717i	−0.831008	−	0.556261i	$-0.812236\pi$
$197$	0.929608	−	1.61013i	0.0662318	−	0.114717i	0.897240	+	0.441544i	$0.145569\pi$
$198$	−2.44941	+	1.41417i	−0.174072	+	0.100500i
$199$			23.6695i			1.67788i	0.544221	+	0.838942i	$0.316825\pi$
$199$			23.6695i			1.67788i	−0.544221	+	0.838942i	$0.683175\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$	1.86976	−	3.23851i	0.131882	−	0.228427i
$202$	2.34517	+	1.35398i	0.165005	+	0.0952659i
$203$	−8.84101	+	5.10436i	−0.620517	+	0.358256i
$204$	−3.65646	+	2.11106i	−0.256003	+	0.147804i
$205$	−9.64513	−	5.56862i	−0.673645	−	0.388929i
$206$	5.73009	−	9.92480i	0.399234	−	0.691494i
$207$	1.36003	+	0.785213i	0.0945285	+	0.0545760i
$208$		−	3.73751i		−	0.259150i
$209$	17.8682	−	10.3162i	1.23597	−	0.713589i
$210$	2.38947	−	4.13868i	0.164889	−	0.285596i
$211$	−11.5346			−0.794073			−0.397037	−	0.917803i	$-0.629961\pi$
$211$	−11.5346			−0.794073			−0.397037	+	0.917803i	$0.629961\pi$
$212$	0.693011			0.0475962
$213$	−7.93390	+	13.7419i	−0.543622	+	0.941581i
$214$			15.1029i			1.03241i
$215$	−2.49755	−	4.32589i	−0.170332	−	0.295023i
$216$			1.00000i			0.0680414i
$217$	−12.3395	+	7.12420i	−0.837658	+	0.483622i
$218$	−9.95858	−	17.2488i	−0.674480	−	1.16823i
$219$	4.63872	+	8.03450i	0.313456	+	0.542921i
$220$	−2.44941	−	1.41417i	−0.165139	−	0.0953431i
$221$	−15.7802			−1.06149
$222$	−4.58652	+	3.99548i	−0.307827	+	0.268159i
$223$	12.0201			0.804927			0.402463	−	0.915436i	$-0.368154\pi$
$223$	12.0201			0.804927			0.402463	+	0.915436i	$0.368154\pi$
$224$	4.13868	+	2.38947i	0.276527	+	0.159653i
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$	0.560185	+	0.970268i	0.0372629	+	0.0645413i
$227$	21.9971	−	12.7000i	1.46000	−	0.842930i	0.460986	−	0.887407i	$-0.347496\pi$
$227$	21.9971	−	12.7000i	1.46000	−	0.842930i	0.999010	+	0.0444777i	$0.0141623\pi$
$228$		−	7.29492i		−	0.483118i
$229$	−2.45890	−	4.25894i	−0.162489	−	0.281439i	0.773272	−	0.634075i	$-0.218619\pi$
$229$	−2.45890	−	4.25894i	−0.162489	−	0.281439i	−0.935761	+	0.352636i	$0.885285\pi$
$230$			1.57043i			0.103551i
$231$	6.75821	−	11.7056i	0.444658	−	0.770170i
$232$	2.13619			0.140248
$233$	15.9927			1.04772			0.523858	−	0.851806i	$-0.324492\pi$
$233$	15.9927			1.04772			0.523858	+	0.851806i	$0.324492\pi$
$234$	−1.86876	+	3.23678i	−0.122164	+	0.211595i
$235$	−2.68057	+	1.54763i	−0.174861	+	0.100956i
$236$			11.1676i			0.726946i
$237$	−10.8209	−	6.24742i	−0.702890	−	0.405814i
$238$	10.0886	−	17.4740i	0.653947	−	1.13267i
$239$	11.6105	+	6.70335i	0.751024	+	0.433604i	0.826064	−	0.563577i	$-0.190575\pi$
$239$	11.6105	+	6.70335i	0.751024	+	0.433604i	−0.0750399	+	0.997181i	$0.523908\pi$
$240$	−0.866025	+	0.500000i	−0.0559017	+	0.0322749i
$241$	−8.23003	+	4.75161i	−0.530143	+	0.306078i	−0.741075	−	0.671423i	$-0.765684\pi$
$241$	−8.23003	+	4.75161i	−0.530143	+	0.306078i	0.210932	+	0.977501i	$0.432350\pi$
$242$	2.59853	+	1.50026i	0.167040	+	0.0964405i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	13.3008	+	7.67919i	0.851493	+	0.491610i
$245$			15.8382i			1.01187i
$246$	−9.64513	+	5.56862i	−0.614951	+	0.355042i
$247$	13.6324	−	23.6121i	0.867410	−	1.50240i
$248$	2.98150			0.189325
$249$	−9.06127			−0.574235
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$		−	25.9869i		−	1.64028i	−0.572162	−	0.820141i	$-0.693895\pi$
$251$		−	25.9869i		−	1.64028i	0.572162	−	0.820141i	$-0.306105\pi$
$252$	−2.38947	−	4.13868i	−0.150522	−	0.260712i
$253$			4.44169i			0.279247i
$254$	3.14487	−	1.81569i	0.197327	−	0.113927i
$255$	2.11106	+	3.65646i	0.132200	+	0.228976i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−19.2162	−	11.0945i	−1.19867	−	0.692053i	−0.238412	−	0.971164i	$-0.576627\pi$
$257$	−19.2162	−	11.0945i	−1.19867	−	0.692053i	−0.960259	+	0.279111i	$0.909960\pi$
$258$	−4.99510			−0.310982
$259$	9.43506	−	27.4953i	0.586266	−	1.70848i
$260$	−3.73751			−0.231791
$261$	−1.84999	−	1.06810i	−0.114512	−	0.0661134i
$262$	−5.18961	−	8.98867i	−0.320615	−	0.555322i
$263$	−9.82345	−	17.0147i	−0.605740	−	1.04917i	−0.991934	−	0.126755i	$-0.959544\pi$
$263$	−9.82345	−	17.0147i	−0.605740	−	1.04917i	0.386194	−	0.922417i	$-0.373789\pi$
$264$	−2.44941	+	1.41417i	−0.150751	+	0.0870360i
$265$		−	0.693011i		−	0.0425713i
$266$	17.4310	+	30.1913i	1.06876	+	1.85115i
$267$			2.24247i			0.137237i
$268$	1.86976	−	3.23851i	0.114214	−	0.197824i
$269$	−13.2171			−0.805859			−0.402929	−	0.915231i	$-0.632008\pi$
$269$	−13.2171			−0.805859			−0.402929	+	0.915231i	$0.632008\pi$
$270$	1.00000			0.0608581
$271$	5.55441	−	9.62052i	0.337406	−	0.584405i	−0.646538	−	0.762882i	$-0.723784\pi$
$271$	5.55441	−	9.62052i	0.337406	−	0.584405i	0.983944	+	0.178477i	$0.0571171\pi$
$272$	−3.65646	+	2.11106i	−0.221705	+	0.128002i
$273$		−	17.8613i		−	1.08102i
$274$	6.78988	+	3.92014i	0.410192	+	0.236824i
$275$	−1.41417	+	2.44941i	−0.0852775	+	0.147705i
$276$	1.36003	+	0.785213i	0.0818641	+	0.0472642i
$277$	4.52021	−	2.60974i	0.271593	−	0.156804i	−0.358018	−	0.933715i	$-0.616548\pi$
$277$	4.52021	−	2.60974i	0.271593	−	0.156804i	0.629611	+	0.776910i	$0.283214\pi$
$278$	4.05175	−	2.33928i	0.243008	−	0.140301i
$279$	−2.58205	−	1.49075i	−0.154584	−	0.0892488i
$280$	2.38947	−	4.13868i	0.142798	−	0.247333i
$281$	2.91361	+	1.68217i	0.173811	+	0.100350i	0.584382	−	0.811479i	$-0.301337\pi$
$281$	2.91361	+	1.68217i	0.173811	+	0.100350i	−0.410570	+	0.911829i	$0.634670\pi$
$282$			3.09525i			0.184320i
$283$	20.0633	−	11.5836i	1.19264	−	0.688572i	0.233737	−	0.972300i	$-0.424904\pi$
$283$	20.0633	−	11.5836i	1.19264	−	0.688572i	0.958905	+	0.283727i	$0.0915711\pi$
$284$	−7.93390	+	13.7419i	−0.470791	+	0.815433i
$285$	−7.29492			−0.432114
$286$	−10.5709			−0.625073
$287$	26.6121	−	46.0935i	1.57086	−	2.72081i
$288$			1.00000i			0.0589256i
$289$	0.413127	+	0.715556i	0.0243016	+	0.0420915i
$290$		−	2.13619i		−	0.125441i
$291$	−13.9212	+	8.03740i	−0.816074	+	0.471161i
$292$	4.63872	+	8.03450i	0.271461	+	0.470184i
$293$	−14.9033	−	25.8134i	−0.870663	−	1.50803i	−0.861312	−	0.508076i	$-0.830357\pi$
$293$	−14.9033	−	25.8134i	−0.870663	−	1.50803i	−0.00935030	−	0.999956i	$-0.502976\pi$
$294$	13.7163	+	7.91911i	0.799951	+	0.461852i
$295$	11.1676			0.650200
$296$	−4.58652	+	3.99548i	−0.266586	+	0.232233i
$297$	2.82833			0.164117
$298$	−16.7205	−	9.65358i	−0.968592	−	0.559217i
$299$	2.93474	+	5.08312i	0.169721	+	0.293965i
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$	20.6731	−	11.9356i	1.19158	−	0.687959i
$302$		−	2.19257i		−	0.126168i
$303$	−1.35398	−	2.34517i	−0.0777843	−	0.134726i
$304$		−	7.29492i		−	0.418392i
$305$	7.67919	−	13.3008i	0.439709	−	0.761599i
$306$	4.22211			0.241362
$307$	24.3336			1.38879			0.694396	−	0.719593i	$-0.255672\pi$
$307$	24.3336			1.38879			0.694396	+	0.719593i	$0.255672\pi$
$308$	6.75821	−	11.7056i	0.385085	−	0.666987i
$309$	−9.92480	+	5.73009i	−0.564602	+	0.325973i
$310$		−	2.98150i		−	0.169338i
$311$	4.83982	+	2.79427i	0.274441	+	0.158449i	0.630904	−	0.775861i	$-0.282684\pi$
$311$	4.83982	+	2.79427i	0.274441	+	0.158449i	−0.356463	+	0.934309i	$0.616017\pi$
$312$	−1.86876	+	3.23678i	−0.105797	+	0.183247i
$313$	9.77499	+	5.64359i	0.552515	+	0.318995i	0.750136	−	0.661284i	$-0.229988\pi$
$313$	9.77499	+	5.64359i	0.552515	+	0.318995i	−0.197621	+	0.980279i	$0.563321\pi$
$314$	−6.61012	+	3.81635i	−0.373030	+	0.215369i
$315$	−4.13868	+	2.38947i	−0.233188	+	0.134631i
$316$	−10.8209	−	6.24742i	−0.608721	−	0.351445i
$317$	−4.64653	+	8.04803i	−0.260975	+	0.452023i	−0.966501	−	0.256661i	$-0.917377\pi$
$317$	−4.64653	+	8.04803i	−0.260975	+	0.452023i	0.705526	+	0.708684i	$0.250711\pi$
$318$	−0.600165	−	0.346506i	−0.0336556	−	0.0194311i
$319$		−	6.04186i		−	0.338279i
$320$	−0.866025	+	0.500000i	−0.0484123	+	0.0279508i
$321$	7.55146	−	13.0795i	0.421481	−	0.730027i
$322$	−7.50496			−0.418235
$323$	−30.8000			−1.71376
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$			3.73751i			0.207320i
$326$	−9.58358	−	16.5993i	−0.530786	−	0.919348i
$327$			19.9172i			1.10142i
$328$	−9.64513	+	5.56862i	−0.532563	+	0.307476i
$329$	−7.39601	−	12.8103i	−0.407755	−	0.706253i
$330$	1.41417	+	2.44941i	0.0778473	+	0.134836i
$331$	24.9554	+	14.4080i	1.37167	+	0.791935i	0.991138	−	0.132833i	$-0.0424072\pi$
$331$	24.9554	+	14.4080i	1.37167	+	0.791935i	0.380533	+	0.924767i	$0.375741\pi$
$332$	−9.06127			−0.497302
$333$	5.96978	−	1.16693i	0.327142	−	0.0639473i
$334$	−20.9482			−1.14623
$335$	−3.23851	−	1.86976i	−0.176939	−	0.102156i
$336$	−2.38947	−	4.13868i	−0.130356	−	0.225783i
$337$	−2.73770	−	4.74183i	−0.149132	−	0.258304i	0.781775	−	0.623561i	$-0.214315\pi$
$337$	−2.73770	−	4.74183i	−0.149132	−	0.258304i	−0.930907	+	0.365257i	$0.880981\pi$
$338$	−0.839179	+	0.484500i	−0.0456453	+	0.0263534i
$339$		−	1.12037i		−	0.0608501i
$340$	2.11106	+	3.65646i	0.114488	+	0.198299i
$341$		−	8.43268i		−	0.456655i
$342$	−3.64746	+	6.31758i	−0.197232	+	0.341616i
$343$	−42.2373			−2.28060
$344$	−4.99510			−0.269318
$345$	0.785213	−	1.36003i	0.0422744	−	0.0732215i
$346$	−2.59339	+	1.49729i	−0.139421	+	0.0804950i
$347$			7.30719i			0.392271i	0.980577	+	0.196135i	$0.0628392\pi$
$347$			7.30719i			0.392271i	−0.980577	+	0.196135i	$0.937161\pi$
$348$	−1.84999	−	1.06810i	−0.0991701	−	0.0572559i
$349$	−16.1626	+	27.9944i	−0.865163	+	1.49851i	0.00172267	+	0.999999i	$0.499452\pi$
$349$	−16.1626	+	27.9944i	−0.865163	+	1.49851i	−0.866885	+	0.498507i	$0.833882\pi$
$350$	−4.13868	−	2.38947i	−0.221222	−	0.127722i
$351$	3.23678	−	1.86876i	0.172767	−	0.0997468i
$352$	−2.44941	+	1.41417i	−0.130554	+	0.0753754i
$353$	−3.24724	−	1.87480i	−0.172833	−	0.0997854i	0.411088	−	0.911596i	$-0.365149\pi$
$353$	−3.24724	−	1.87480i	−0.172833	−	0.0997854i	−0.583921	+	0.811810i	$0.698482\pi$
$354$	5.58378	−	9.67139i	0.296774	−	0.514028i
$355$	13.7419	+	7.93390i	0.729346	+	0.421088i
$356$			2.24247i			0.118851i
$357$	−17.4740	+	10.0886i	−0.924821	+	0.533946i
$358$	−2.08103	+	3.60444i	−0.109986	+	0.190501i
$359$	−28.8927			−1.52490			−0.762450	−	0.647048i	$-0.776003\pi$
$359$	−28.8927			−1.52490			−0.762450	+	0.647048i	$0.776003\pi$
$360$	1.00000			0.0527046
$361$	17.1079	−	29.6318i	0.900416	−	1.55957i
$362$			8.76035i			0.460434i
$363$	−1.50026	−	2.59853i	−0.0787433	−	0.136387i
$364$		−	17.8613i		−	0.936188i
$365$	8.03450	−	4.63872i	0.420545	−	0.242802i
$366$	−7.67919	−	13.3008i	−0.401398	−	0.695242i
$367$	0.529694	+	0.917456i	0.0276498	+	0.0478908i	0.879519	−	0.475863i	$-0.157864\pi$
$367$	0.529694	+	0.917456i	0.0276498	+	0.0478908i	−0.851869	+	0.523754i	$0.824531\pi$
$368$	1.36003	+	0.785213i	0.0708964	+	0.0409320i
$369$	11.1372			0.579782
$370$	3.99548	+	4.58652i	0.207715	+	0.238442i
$371$	3.31186			0.171943
$372$	−2.58205	−	1.49075i	−0.133873	−	0.0772918i
$373$	0.477801	+	0.827575i	0.0247396	+	0.0428502i	0.878130	−	0.478422i	$-0.158791\pi$
$373$	0.477801	+	0.827575i	0.0247396	+	0.0428502i	−0.853391	+	0.521272i	$0.825458\pi$
$374$	5.97078	+	10.3417i	0.308742	+	0.534756i
$375$	0.866025	−	0.500000i	0.0447214	−	0.0258199i
$376$			3.09525i			0.159625i
$377$	−3.99202	−	6.91438i	−0.205599	−	0.356109i
$378$			4.77894i			0.245802i
$379$	0.641986	−	1.11195i	0.0329766	−	0.0571172i	−0.849066	−	0.528287i	$-0.822835\pi$
$379$	0.641986	−	1.11195i	0.0329766	−	0.0571172i	0.882043	+	0.471169i	$0.156168\pi$
$380$	−7.29492			−0.374221
$381$	−3.63138			−0.186041
$382$	8.54063	−	14.7928i	0.436977	−	0.756866i
$383$	7.70082	−	4.44607i	0.393493	−	0.227183i	−0.290179	−	0.956972i	$-0.593715\pi$
$383$	7.70082	−	4.44607i	0.393493	−	0.227183i	0.683673	+	0.729789i	$0.260382\pi$
$384$			1.00000i			0.0510310i
$385$	−11.7056	−	6.75821i	−0.596571	−	0.344431i
$386$	1.07587	−	1.86346i	0.0547604	−	0.0948479i
$387$	4.32589	+	2.49755i	0.219897	+	0.126958i
$388$	−13.9212	+	8.03740i	−0.706741	+	0.408037i
$389$	3.20434	−	1.85003i	0.162467	−	0.0938002i	−0.416562	−	0.909107i	$-0.636765\pi$
$389$	3.20434	−	1.85003i	0.162467	−	0.0938002i	0.579029	+	0.815307i	$0.303432\pi$
$390$	3.23678	+	1.86876i	0.163901	+	0.0946282i
$391$	3.31526	−	5.74219i	0.167660	−	0.290395i
$392$	13.7163	+	7.91911i	0.692778	+	0.399976i
$393$			10.3792i			0.523563i
$394$	−1.61013	+	0.929608i	−0.0811171	+	0.0468330i
$395$	−6.24742	+	10.8209i	−0.314342	+	0.544456i
$396$	2.82833			0.142129
$397$	10.7552			0.539789			0.269895	−	0.962890i	$-0.413011\pi$
$397$	10.7552			0.539789			0.269895	+	0.962890i	$0.413011\pi$
$398$	11.8347	−	20.4984i	0.593221	−	1.02749i
$399$		−	34.8619i		−	1.74528i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$			11.6448i			0.581513i	0.956797	+	0.290757i	$0.0939070\pi$
$401$			11.6448i			0.581513i	−0.956797	+	0.290757i	$0.906093\pi$
$402$	−3.23851	+	1.86976i	−0.161522	+	0.0932549i
$403$	−5.57169	−	9.65046i	−0.277546	−	0.480724i
$404$	−1.35398	−	2.34517i	−0.0673632	−	0.116676i
$405$	−0.866025	−	0.500000i	−0.0430331	−	0.0248452i
$406$	10.2087			0.506650
$407$	11.3006	+	12.9722i	0.560148	+	0.643008i
$408$	4.22211			0.209026
$409$	1.25197	+	0.722823i	0.0619058	+	0.0357413i	0.530633	−	0.847601i	$-0.321954\pi$
$409$	1.25197	+	0.722823i	0.0619058	+	0.0357413i	−0.468728	+	0.883343i	$0.655287\pi$
$410$	5.56862	+	9.64513i	0.275015	+	0.476339i
$411$	−3.92014	−	6.78988i	−0.193366	−	0.334920i
$412$	−9.92480	+	5.73009i	−0.488960	+	0.282301i
$413$			53.3690i			2.62612i
$414$	−0.785213	−	1.36003i	−0.0385911	−	0.0668417i
$415$			9.06127i			0.444800i
$416$	−1.86876	+	3.23678i	−0.0916233	+	0.158696i
$417$	−4.67856			−0.229110
$418$	−20.6325			−1.00917
$419$	−7.11457	+	12.3228i	−0.347570	+	0.602008i	−0.985817	−	0.167823i	$-0.946326\pi$
$419$	−7.11457	+	12.3228i	−0.347570	+	0.602008i	0.638247	+	0.769831i	$0.279660\pi$
$420$	−4.13868	+	2.38947i	−0.201947	+	0.116594i
$421$		−	10.5629i		−	0.514805i	−0.966304	−	0.257403i	$-0.917133\pi$
$421$		−	10.5629i		−	0.514805i	0.966304	−	0.257403i	$-0.0828666\pi$
$422$	9.98924	+	5.76729i	0.486269	+	0.280747i
$423$	1.54763	−	2.68057i	0.0752482	−	0.130334i
$424$	−0.600165	−	0.346506i	−0.0291466	−	0.0168278i
$425$	3.65646	−	2.11106i	0.177364	−	0.102401i
$426$	13.7419	−	7.93390i	0.665798	−	0.384399i
$427$	63.5634	+	36.6984i	3.07605	+	1.77596i
$428$	7.55146	−	13.0795i	0.365014	−	0.632222i
$429$	9.15470	+	5.28547i	0.441993	+	0.255185i
$430$			4.99510i			0.240885i
$431$	25.9536	−	14.9843i	1.25014	−	0.721771i	0.279005	−	0.960290i	$-0.409995\pi$
$431$	25.9536	−	14.9843i	1.25014	−	0.721771i	0.971138	+	0.238519i	$0.0766619\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	5.48213			0.263454			0.131727	−	0.991286i	$-0.457948\pi$
$433$	5.48213			0.263454			0.131727	+	0.991286i	$0.457948\pi$
$434$	14.2484			0.683945
$435$	−1.06810	+	1.84999i	−0.0512112	+	0.0887005i
$436$			19.9172i			0.953859i
$437$	5.72806	+	9.92129i	0.274010	+	0.474600i
$438$		−	9.27744i		−	0.443293i
$439$	−12.6506	+	7.30383i	−0.603780	+	0.348593i	−0.770527	−	0.637407i	$-0.780007\pi$
$439$	−12.6506	+	7.30383i	−0.603780	+	0.348593i	0.166747	+	0.986000i	$0.446674\pi$
$440$	1.41417	+	2.44941i	0.0674178	+	0.116771i
$441$	−7.91911	−	13.7163i	−0.377101	−	0.653157i
$442$	13.6661	+	7.89010i	0.650028	+	0.375294i
$443$	−33.0457			−1.57005			−0.785024	−	0.619465i	$-0.787349\pi$
$443$	−33.0457			−1.57005			−0.785024	+	0.619465i	$0.787349\pi$
$444$	5.96978	−	1.16693i	0.283313	−	0.0553799i
$445$	2.24247			0.106303
$446$	−10.4097	−	6.01006i	−0.492915	−	0.284585i
$447$	9.65358	+	16.7205i	0.456599	+	0.790852i
$448$	−2.38947	−	4.13868i	−0.112892	−	0.195534i
$449$	−31.5995	+	18.2440i	−1.49127	+	0.860986i	−0.999950	−	0.00999239i	$-0.996819\pi$
$449$	−31.5995	+	18.2440i	−1.49127	+	0.860986i	−0.491321	+	0.870978i	$0.663486\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	15.7499	+	27.2797i	0.741635	+	1.28455i
$452$		−	1.12037i		−	0.0526977i
$453$	−1.09628	+	1.89882i	−0.0515079	+	0.0892143i
$454$	−25.4000			−1.19208
$455$	−17.8613			−0.837352
$456$	−3.64746	+	6.31758i	−0.170808	+	0.295848i
$457$	12.0974	−	6.98444i	0.565893	−	0.326718i	−0.189614	−	0.981859i	$-0.560724\pi$
$457$	12.0974	−	6.98444i	0.565893	−	0.326718i	0.755507	+	0.655140i	$0.227390\pi$
$458$			4.91780i			0.229794i
$459$	−3.65646	−	2.11106i	−0.170669	−	0.0985357i
$460$	0.785213	−	1.36003i	0.0366107	−	0.0634116i
$461$	−16.1797	−	9.34134i	−0.753563	−	0.435070i	0.0734169	−	0.997301i	$-0.476610\pi$
$461$	−16.1797	−	9.34134i	−0.753563	−	0.435070i	−0.826980	+	0.562232i	$0.809943\pi$
$462$	−11.7056	+	6.75821i	−0.544592	+	0.314421i
$463$	15.9768	−	9.22419i	0.742503	−	0.428684i	−0.0804756	−	0.996757i	$-0.525644\pi$
$463$	15.9768	−	9.22419i	0.742503	−	0.428684i	0.822979	+	0.568072i	$0.192311\pi$
$464$	−1.84999	−	1.06810i	−0.0858839	−	0.0495851i
$465$	−1.49075	+	2.58205i	−0.0691318	+	0.119740i
$466$	−13.8501	−	7.99634i	−0.641592	−	0.370423i
$467$			15.8147i			0.731818i	0.930651	+	0.365909i	$0.119242\pi$
$467$			15.8147i			0.731818i	−0.930651	+	0.365909i	$0.880758\pi$
$468$	3.23678	−	1.86876i	0.149620	−	0.0863833i
$469$	8.93544	−	15.4766i	0.412600	−	0.714645i
$470$	3.09525			0.142773
$471$	7.63271			0.351697
$472$	5.58378	−	9.67139i	0.257014	−	0.445162i
$473$			14.1278i			0.649598i
$474$	6.24742	+	10.8209i	0.286954	+	0.497018i
$475$			7.29492i			0.334714i
$476$	−17.4740	+	10.0886i	−0.800919	+	0.462411i
$477$	0.346506	+	0.600165i	0.0158654	+	0.0274797i
$478$	−6.70335	−	11.6105i	−0.306604	−	0.531054i
$479$	13.5705	+	7.83495i	0.620053	+	0.357988i	0.776890	−	0.629637i	$-0.216796\pi$
$479$	13.5705	+	7.83495i	0.620053	+	0.357988i	−0.156836	+	0.987625i	$0.550130\pi$
$480$	1.00000			0.0456435
$481$	21.5036	+	7.37898i	0.980479	+	0.336452i
$482$	9.50322			0.432860
$483$	6.49949	+	3.75248i	0.295737	+	0.170744i
$484$	−1.50026	−	2.59853i	−0.0681937	−	0.118115i
$485$	8.03740	+	13.9212i	0.364959	+	0.632128i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$		−	37.1828i		−	1.68492i	−0.538762	−	0.842458i	$-0.681108\pi$
$487$		−	37.1828i		−	1.68492i	0.538762	−	0.842458i	$-0.318892\pi$
$488$	−7.67919	−	13.3008i	−0.347621	−	0.602097i
$489$			19.1672i			0.866769i
$490$	7.91911	−	13.7163i	0.357749	−	0.619640i
$491$	−6.54232			−0.295251			−0.147625	−	0.989043i	$-0.547163\pi$
$491$	−6.54232			−0.295251			−0.147625	+	0.989043i	$0.547163\pi$
$492$	11.1372			0.502106
$493$	−4.50962	+	7.81089i	−0.203103	+	0.351785i
$494$	−23.6121	+	13.6324i	−1.06236	+	0.613352i
$495$		−	2.82833i		−	0.127124i
$496$	−2.58205	−	1.49075i	−0.115938	−	0.0669366i
$497$	−37.9156	+	65.6718i	−1.70075	+	2.94578i
$498$	7.84729	+	4.53064i	0.351646	+	0.203023i
$499$	−24.3594	+	14.0639i	−1.09048	+	0.629586i	−0.933703	−	0.358049i	$-0.883442\pi$
$499$	−24.3594	+	14.0639i	−1.09048	+	0.629586i	−0.156772	+	0.987635i	$0.550109\pi$
$500$	0.866025	−	0.500000i	0.0387298	−	0.0223607i
$501$	18.1416	+	10.4741i	0.810508	+	0.467947i
$502$	−12.9935	+	22.5054i	−0.579927	+	1.00446i
$503$	21.2691	+	12.2797i	0.948343	+	0.547526i	0.892566	−	0.450917i	$-0.148903\pi$
$503$	21.2691	+	12.2797i	0.948343	+	0.547526i	0.0557773	+	0.998443i	$0.482236\pi$
$504$			4.77894i			0.212871i
$505$	−2.34517	+	1.35398i	−0.104359	+	0.0602514i
$506$	2.22084	−	3.84661i	0.0987286	−	0.171003i
$507$	0.969001			0.0430348
$508$	−3.63138			−0.161117
$509$	6.41827	−	11.1168i	0.284485	−	0.492742i	−0.687999	−	0.725711i	$-0.741511\pi$
$509$	6.41827	−	11.1168i	0.284485	−	0.492742i	0.972484	+	0.232969i	$0.0748442\pi$
$510$		−	4.22211i		−	0.186958i
$511$	22.1681	+	38.3964i	0.980661	+	1.69856i
$512$			1.00000i			0.0441942i
$513$	6.31758	−	3.64746i	0.278928	−	0.161039i
$514$	11.0945	+	19.2162i	0.489355	+	0.847588i
$515$	5.73009	+	9.92480i	0.252498	+	0.437339i
$516$	4.32589	+	2.49755i	0.190437	+	0.109949i
$517$	8.75441			0.385019
$518$	−21.9187	+	19.0941i	−0.963051	+	0.838948i
$519$	2.99459			0.131448
$520$	3.23678	+	1.86876i	0.141942	+	0.0819504i
$521$	−0.222716	−	0.385756i	−0.00975738	−	0.0169003i	0.861105	−	0.508426i	$-0.169773\pi$
$521$	−0.222716	−	0.385756i	−0.00975738	−	0.0169003i	−0.870863	+	0.491526i	$0.836439\pi$
$522$	1.06810	+	1.84999i	0.0467492	+	0.0809721i
$523$	−17.3888	+	10.0394i	−0.760360	+	0.438994i	−0.829425	−	0.558618i	$-0.811332\pi$
$523$	−17.3888	+	10.0394i	−0.760360	+	0.438994i	0.0690652	+	0.997612i	$0.477998\pi$
$524$			10.3792i			0.453419i
$525$	2.38947	+	4.13868i	0.104285	+	0.180627i
$526$			19.6469i			0.856645i
$527$	−6.29411	+	10.9017i	−0.274176	+	0.474887i
$528$	2.82833			0.123087
$529$	20.5338			0.892772
$530$	−0.346506	+	0.600165i	−0.0150512	+	0.0260695i
$531$	−9.67139	+	5.58378i	−0.419702	+	0.242315i
$532$		−	34.8619i		−	1.51146i
$533$	36.0488	+	20.8128i	1.56145	+	0.901502i
$534$	1.12123	−	1.94204i	0.0485206	−	0.0840401i
$535$	−13.0795	−	7.55146i	−0.565477	−	0.326478i
$536$	−3.23851	+	1.86976i	−0.139882	+	0.0807612i
$537$	3.60444	−	2.08103i	0.155543	−	0.0898029i
$538$	11.4463	+	6.60853i	0.493486	+	0.284914i
$539$	22.3979	−	38.7943i	0.964746	−	1.67099i
$540$	−0.866025	−	0.500000i	−0.0372678	−	0.0215166i
$541$		−	34.5078i		−	1.48361i	−0.670617	−	0.741804i	$-0.733971\pi$
$541$		−	34.5078i		−	1.48361i	0.670617	−	0.741804i	$-0.266029\pi$
$542$	−9.62052	+	5.55441i	−0.413237	+	0.238582i
$543$	4.38018	−	7.58669i	0.187971	−	0.325576i
$544$	4.22211			0.181022
$545$	19.9172			0.853157
$546$	−8.93067	+	15.4684i	−0.382197	+	0.661985i
$547$			15.2506i			0.652071i	0.945358	+	0.326035i	$0.105713\pi$
$547$			15.2506i			0.652071i	−0.945358	+	0.326035i	$0.894287\pi$
$548$	−3.92014	−	6.78988i	−0.167460	−	0.290049i
$549$			15.3584i			0.655480i
$550$	2.44941	−	1.41417i	0.104443	−	0.0603003i
$551$	−7.79167	−	13.4956i	−0.331936	−	0.574930i
$552$	−0.785213	−	1.36003i	−0.0334209	−	0.0578866i
$553$	−51.7122	−	29.8560i	−2.19902	−	1.26961i
$554$	−5.21948			−0.221755
$555$	−1.16693	−	5.96978i	−0.0495333	−	0.253403i
$556$	−4.67856			−0.198415
$557$	−14.6696	−	8.46950i	−0.621571	−	0.358864i	0.155909	−	0.987771i	$-0.450169\pi$
$557$	−14.6696	−	8.46950i	−0.621571	−	0.358864i	−0.777481	+	0.628907i	$0.783503\pi$
$558$	1.49075	+	2.58205i	0.0631085	+	0.109307i
$559$	9.33463	+	16.1681i	0.394813	+	0.683836i
$560$	−4.13868	+	2.38947i	−0.174891	+	0.100973i
$561$		−	11.9416i		−	0.504173i
$562$	−1.68217	−	2.91361i	−0.0709582	−	0.122903i
$563$		−	34.7848i		−	1.46601i	−0.680225	−	0.733003i	$-0.738118\pi$
$563$		−	34.7848i		−	1.46601i	0.680225	−	0.733003i	$-0.261882\pi$
$564$	1.54763	−	2.68057i	0.0651668	−	0.112872i
$565$	−1.12037			−0.0471343
$566$	−23.1672			−0.973788
$567$	2.38947	−	4.13868i	0.100348	−	0.173808i
$568$	13.7419	−	7.93390i	0.576598	−	0.332899i
$569$		−	4.56606i		−	0.191419i	−0.995409	−	0.0957096i	$-0.969488\pi$
$569$		−	4.56606i		−	0.191419i	0.995409	−	0.0957096i	$-0.0305120\pi$
$570$	6.31758	+	3.64746i	0.264614	+	0.152775i
$571$	−5.24149	+	9.07853i	−0.219349	+	0.379924i	−0.954609	−	0.297861i	$-0.903727\pi$
$571$	−5.24149	+	9.07853i	−0.219349	+	0.379924i	0.735260	+	0.677785i	$0.237060\pi$
$572$	9.15470	+	5.28547i	0.382777	+	0.220997i
$573$	−14.7928	+	8.54063i	−0.617978	+	0.356790i
$574$	−46.0935	+	26.6121i	−1.92390	+	1.11077i
$575$	−1.36003	−	0.785213i	−0.0567171	−	0.0327456i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	26.5337	+	15.3193i	1.10461	+	0.637749i	0.937429	−	0.348176i	$-0.113199\pi$
$577$	26.5337	+	15.3193i	1.10461	+	0.637749i	0.167185	+	0.985926i	$0.446532\pi$
$578$		−	0.826253i		−	0.0343676i
$579$	−1.86346	+	1.07587i	−0.0774429	+	0.0447117i
$580$	−1.06810	+	1.84999i	−0.0443502	+	0.0768169i
$581$	−43.3033			−1.79652
$582$	16.0748			0.666322
$583$	−0.980034	+	1.69747i	−0.0405888	+	0.0703019i
$584$		−	9.27744i		−	0.383903i
$585$	−1.86876	−	3.23678i	−0.0772636	−	0.133824i
$586$			29.8067i			1.23130i
$587$	−5.57820	+	3.22057i	−0.230237	+	0.132927i	−0.610681	−	0.791876i	$-0.709104\pi$
$587$	−5.57820	+	3.22057i	−0.230237	+	0.132927i	0.380444	+	0.924804i	$0.375771\pi$
$588$	−7.91911	−	13.7163i	−0.326579	−	0.565651i
$589$	−10.8749	−	18.8359i	−0.448092	−	0.776118i
$590$	−9.67139	−	5.58378i	−0.398165	−	0.229880i
$591$	1.85922			0.0764779
$592$	5.96978	−	1.16693i	0.245356	−	0.0479604i
$593$	10.4265			0.428163			0.214082	−	0.976816i	$-0.431324\pi$
$593$	10.4265			0.428163			0.214082	+	0.976816i	$0.431324\pi$
$594$	−2.44941	−	1.41417i	−0.100500	−	0.0580240i
$595$	10.0886	+	17.4740i	0.413593	+	0.716363i
$596$	9.65358	+	16.7205i	0.395426	+	0.684898i
$597$	−20.4984	+	11.8347i	−0.838942	+	0.484363i
$598$		−	5.86948i		−	0.240021i
$599$	4.59263	+	7.95466i	0.187650	+	0.325019i	0.944466	−	0.328609i	$-0.106580\pi$
$599$	4.59263	+	7.95466i	0.187650	+	0.325019i	−0.756817	+	0.653627i	$0.773246\pi$
$600$		−	1.00000i		−	0.0408248i
$601$	−13.0228	+	22.5561i	−0.531209	+	0.920082i	0.468127	+	0.883661i	$0.344929\pi$
$601$	−13.0228	+	22.5561i	−0.531209	+	0.920082i	−0.999337	+	0.0364206i	$0.988404\pi$
$602$	−23.8713			−0.972921
$603$	3.73951			0.152285
$604$	−1.09628	+	1.89882i	−0.0446072	+	0.0772619i
$605$	−2.59853	+	1.50026i	−0.105645	+	0.0609943i
$606$			2.70797i			0.110004i
$607$	−6.32103	−	3.64945i	−0.256563	−	0.148126i	0.366203	−	0.930535i	$-0.380658\pi$
$607$	−6.32103	−	3.64945i	−0.256563	−	0.148126i	−0.622765	+	0.782409i	$0.713991\pi$
$608$	−3.64746	+	6.31758i	−0.147924	+	0.256212i
$609$	−8.84101	−	5.10436i	−0.358256	−	0.206839i
$610$	−13.3008	+	7.67919i	−0.538532	+	0.310921i
$611$	10.0187	−	5.78427i	0.405311	−	0.234007i
$612$	−3.65646	−	2.11106i	−0.147804	−	0.0853344i
$613$	11.0972	−	19.2208i	0.448210	−	0.776322i	−0.550060	−	0.835125i	$-0.685395\pi$
$613$	11.0972	−	19.2208i	0.448210	−	0.776322i	0.998270	+	0.0588029i	$0.0187284\pi$
$614$	−21.0735	−	12.1668i	−0.850458	−	0.491012i
$615$		−	11.1372i		−	0.449097i
$616$	−11.7056	+	6.75821i	−0.471631	+	0.272296i
$617$	3.30386	−	5.72245i	0.133008	−	0.230377i	−0.791827	−	0.610746i	$-0.790870\pi$
$617$	3.30386	−	5.72245i	0.133008	−	0.230377i	0.924835	+	0.380369i	$0.124203\pi$
$618$	11.4602			0.460996
$619$	41.8773			1.68319			0.841596	−	0.540108i	$-0.181617\pi$
$619$	41.8773			1.68319			0.841596	+	0.540108i	$0.181617\pi$
$620$	−1.49075	+	2.58205i	−0.0598699	+	0.103698i
$621$			1.57043i			0.0630190i
$622$	−2.79427	−	4.83982i	−0.112040	−	0.194059i
$623$			10.7166i			0.429352i
$624$	3.23678	−	1.86876i	0.129575	−	0.0748101i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−5.64359	−	9.77499i	−0.225563	−	0.390687i
$627$	17.8682	+	10.3162i	0.713589	+	0.411991i
$628$	7.63271			0.304578
$629$	−4.92690	−	25.2051i	−0.196449	−	1.00499i
$630$	4.77894			0.190397
$631$	−20.3284	−	11.7366i	−0.809263	−	0.467228i	0.0374370	−	0.999299i	$-0.488081\pi$
$631$	−20.3284	−	11.7366i	−0.809263	−	0.467228i	−0.846700	+	0.532071i	$0.821414\pi$
$632$	6.24742	+	10.8209i	0.248509	+	0.430430i
$633$	−5.76729	−	9.98924i	−0.229229	−	0.397037i
$634$	8.04803	−	4.64653i	0.319628	−	0.184537i
$635$			3.63138i			0.144107i
$636$	0.346506	+	0.600165i	0.0137398	+	0.0237981i
$637$		−	59.1956i		−	2.34541i
$638$	−3.02093	+	5.23240i	−0.119600	+	0.207153i
$639$	−15.8678			−0.627721
$640$	1.00000			0.0395285
$641$	−15.8576	+	27.4661i	−0.626336	+	1.08485i	0.361945	+	0.932199i	$0.382113\pi$
$641$	−15.8576	+	27.4661i	−0.626336	+	1.08485i	−0.988281	+	0.152646i	$0.951221\pi$
$642$	−13.0795	+	7.55146i	−0.516207	+	0.298032i
$643$		−	13.2986i		−	0.524447i	−0.965007	−	0.262224i	$-0.915544\pi$
$643$		−	13.2986i		−	0.524447i	0.965007	−	0.262224i	$-0.0844558\pi$
$644$	6.49949	+	3.75248i	0.256116	+	0.147868i
$645$	2.49755	−	4.32589i	0.0983410	−	0.170332i
$646$	26.6736	+	15.4000i	1.04946	+	0.605904i
$647$	3.57658	−	2.06494i	0.140610	−	0.0811812i	−0.428045	−	0.903758i	$-0.640797\pi$
$647$	3.57658	−	2.06494i	0.140610	−	0.0811812i	0.568655	+	0.822576i	$0.307464\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−27.3539	−	15.7928i	−1.07374	−	0.619921i
$650$	1.86876	−	3.23678i	0.0732987	−	0.126957i
$651$	−12.3395	−	7.12420i	−0.483622	−	0.279219i
$652$			19.1672i			0.750644i
$653$	−11.4854	+	6.63112i	−0.449460	+	0.259496i	−0.707602	−	0.706611i	$-0.750223\pi$
$653$	−11.4854	+	6.63112i	−0.449460	+	0.259496i	0.258142	+	0.966107i	$0.416890\pi$
$654$	9.95858	−	17.2488i	0.389411	−	0.674480i
$655$	10.3792			0.405550
$656$	11.1372			0.434836
$657$	−4.63872	+	8.03450i	−0.180974	+	0.313456i
$658$			14.7920i			0.576653i
$659$	−5.59767	−	9.69545i	−0.218054	−	0.377681i	0.736159	−	0.676809i	$-0.236638\pi$
$659$	−5.59767	−	9.69545i	−0.218054	−	0.377681i	−0.954213	+	0.299128i	$0.903304\pi$
$660$		−	2.82833i		−	0.110093i
$661$	16.8191	−	9.71049i	0.654186	−	0.377694i	−0.135872	−	0.990726i	$-0.543384\pi$
$661$	16.8191	−	9.71049i	0.654186	−	0.377694i	0.790058	+	0.613032i	$0.210050\pi$
$662$	−14.4080	−	24.9554i	−0.559983	−	0.969918i
$663$	−7.89010	−	13.6661i	−0.306426	−	0.530746i
$664$	7.84729	+	4.53064i	0.304534	+	0.175823i
$665$	−34.8619			−1.35189
$666$	−5.75345	−	1.97430i	−0.222941	−	0.0765026i
$667$	3.35473			0.129896
$668$	18.1416	+	10.4741i	0.701921	+	0.405254i
$669$	6.01006	+	10.4097i	0.232362	+	0.402463i
$670$	1.86976	+	3.23851i	0.0722350	+	0.125115i
$671$	−37.6190	+	21.7193i	−1.45226	+	0.838465i
$672$			4.77894i			0.184351i
$673$	20.4917	+	35.4927i	0.789897	+	1.36814i	0.926029	+	0.377451i	$0.123199\pi$
$673$	20.4917	+	35.4927i	0.789897	+	1.36814i	−0.136132	+	0.990691i	$0.543467\pi$
$674$			5.47539i			0.210904i
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	0.969001			0.0372693
$677$	−0.580197			−0.0222988			−0.0111494	−	0.999938i	$-0.503549\pi$
$677$	−0.580197			−0.0222988			−0.0111494	+	0.999938i	$0.503549\pi$
$678$	−0.560185	+	0.970268i	−0.0215138	+	0.0372629i
$679$	−66.5284	+	38.4102i	−2.55313	+	1.47405i
$680$		−	4.22211i		−	0.161911i
$681$	21.9971	+	12.7000i	0.842930	+	0.486666i
$682$	−4.21634	+	7.30291i	−0.161452	+	0.279643i
$683$	−5.05803	−	2.92026i	−0.193540	−	0.111741i	0.400099	−	0.916472i	$-0.368976\pi$
$683$	−5.05803	−	2.92026i	−0.193540	−	0.111741i	−0.593639	+	0.804732i	$0.702309\pi$
$684$	6.31758	−	3.64746i	0.241559	−	0.139464i
$685$	−6.78988	+	3.92014i	−0.259428	+	0.149781i
$686$	36.5786	+	21.1187i	1.39658	+	0.806314i
$687$	2.45890	−	4.25894i	0.0938129	−	0.162489i
$688$	4.32589	+	2.49755i	0.164923	+	0.0952183i
$689$			2.59014i			0.0986764i
$690$	−1.36003	+	0.785213i	−0.0517754	+	0.0298925i
$691$	−22.0567	+	38.2033i	−0.839075	+	1.45332i	0.0515933	+	0.998668i	$0.483570\pi$
$691$	−22.0567	+	38.2033i	−0.839075	+	1.45332i	−0.890669	+	0.454653i	$0.849763\pi$
$692$	2.99459			0.113837
$693$	13.5164			0.513447
$694$	3.65360	−	6.32821i	0.138689	−	0.240216i
$695$			4.67856i			0.177468i
$696$	1.06810	+	1.84999i	0.0404860	+	0.0701239i
$697$		−	47.0227i		−	1.78111i
$698$	27.9944	−	16.1626i	1.05960	−	0.611762i
$699$	7.99634	+	13.8501i	0.302449	+	0.523858i
$700$	2.38947	+	4.13868i	0.0903134	+	0.156427i
$701$	5.22580	+	3.01712i	0.197376	+	0.113955i	0.595431	−	0.803407i	$-0.296981\pi$
$701$	5.22580	+	3.01712i	0.197376	+	0.113955i	−0.398055	+	0.917362i	$0.630315\pi$
$702$	−3.73751			−0.141063
$703$	41.9709	+	14.4024i	1.58296	+	0.543195i
$704$	2.82833			0.106597
$705$	−2.68057	−	1.54763i	−0.100956	−	0.0582870i
$706$	1.87480	+	3.24724i	0.0705589	+	0.122212i
$707$	−6.47060	−	11.2074i	−0.243352	−	0.421498i
$708$	−9.67139	+	5.58378i	−0.363473	+	0.209851i
$709$			10.0743i			0.378348i	0.981944	+	0.189174i	$0.0605810\pi$
$709$			10.0743i			0.378348i	−0.981944	+	0.189174i	$0.939419\pi$
$710$	−7.93390	−	13.7419i	−0.297754	−	0.515725i
$711$		−	12.4948i		−	0.468593i
$712$	1.12123	−	1.94204i	0.0420200	−	0.0727809i
$713$	4.68222			0.175351
$714$	20.1772			0.755113
$715$	5.28547	−	9.15470i	0.197665	−	0.342366i
$716$	3.60444	−	2.08103i	0.134704	−	0.0777716i
$717$			13.4067i			0.500683i
$718$	25.0218	+	14.4464i	0.933806	+	0.539133i
$719$	12.7927	−	22.1576i	0.477086	−	0.826337i	−0.522569	−	0.852597i	$-0.675026\pi$
$719$	12.7927	−	22.1576i	0.477086	−	0.826337i	0.999655	+	0.0262596i	$0.00835965\pi$
$720$	−0.866025	−	0.500000i	−0.0322749	−	0.0186339i
$721$	−47.4300	+	27.3837i	−1.76638	+	1.01982i
$722$	−29.6318	+	17.1079i	−1.10278	+	0.636691i
$723$	−8.23003	−	4.75161i	−0.306078	−	0.176714i
$724$	4.38018	−	7.58669i	0.162788	−	0.281957i
$725$	1.84999	+	1.06810i	0.0687071	+	0.0396681i
$726$			3.00052i			0.111360i
$727$	−9.09626	+	5.25173i	−0.337361	+	0.194776i	−0.659105	−	0.752051i	$-0.729065\pi$
$727$	−9.09626	+	5.25173i	−0.337361	+	0.194776i	0.321743	+	0.946827i	$0.395731\pi$
$728$	−8.93067	+	15.4684i	−0.330993	+	0.573296i
$729$	1.00000			0.0370370
$730$	−9.27744			−0.343374
$731$	10.5449	−	18.2644i	0.390019	−	0.675533i
$732$			15.3584i			0.567662i
$733$	0.618498	+	1.07127i	0.0228447	+	0.0395682i	0.877222	−	0.480085i	$-0.159394\pi$
$733$	0.618498	+	1.07127i	0.0228447	+	0.0395682i	−0.854377	+	0.519654i	$0.826061\pi$
$734$		−	1.05939i		−	0.0391027i
$735$	−13.7163	+	7.91911i	−0.505934	+	0.292101i
$736$	−0.785213	−	1.36003i	−0.0289433	−	0.0501313i
$737$	5.28830	+	9.15960i	0.194797	+	0.337398i
$738$	−9.64513	−	5.56862i	−0.355042	−	0.204984i
$739$	3.76413			0.138466			0.0692329	−	0.997601i	$-0.477945\pi$
$739$	3.76413			0.138466			0.0692329	+	0.997601i	$0.477945\pi$
$740$	−1.16693	−	5.96978i	−0.0428971	−	0.219453i
$741$	27.2648			1.00160
$742$	−2.86815	−	1.65593i	−0.105293	−	0.0607910i
$743$	−11.0967	−	19.2201i	−0.407099	−	0.705117i	0.587464	−	0.809250i	$-0.300126\pi$
$743$	−11.0967	−	19.2201i	−0.407099	−	0.705117i	−0.994563	+	0.104134i	$0.966793\pi$
$744$	1.49075	+	2.58205i	0.0546535	+	0.0946627i
$745$	16.7205	−	9.65358i	0.612591	−	0.353680i
$746$		−	0.955602i		−	0.0349871i
$747$	−4.53064	−	7.84729i	−0.165767	−	0.287117i
$748$		−	11.9416i		−	0.436626i
$749$	36.0879	−	62.5061i	1.31862	−	2.28392i
$750$	−1.00000			−0.0365148
$751$	18.7537			0.684334			0.342167	−	0.939639i	$-0.388839\pi$
$751$	18.7537			0.684334			0.342167	+	0.939639i	$0.388839\pi$
$752$	1.54763	−	2.68057i	0.0564361	−	0.0977502i
$753$	22.5054	−	12.9935i	0.820141	−	0.473509i
$754$			7.98404i			0.290761i
$755$	1.89882	+	1.09628i	0.0691051	+	0.0398978i
$756$	2.38947	−	4.13868i	0.0869041	−	0.150522i
$757$	−46.1489	−	26.6441i	−1.67731	−	0.968397i	−0.963364	−	0.268198i	$-0.913572\pi$
$757$	−46.1489	−	26.6441i	−1.67731	−	0.968397i	−0.713948	−	0.700198i	$-0.753095\pi$
$758$	−1.11195	+	0.641986i	−0.0403879	+	0.0233180i
$759$	−3.84661	+	2.22084i	−0.139623	+	0.0806115i
$760$	6.31758	+	3.64746i	0.229163	+	0.132307i
$761$	20.4723	−	35.4591i	0.742120	−	1.28539i	−0.209408	−	0.977828i	$-0.567154\pi$
$761$	20.4723	−	35.4591i	0.742120	−	1.28539i	0.951528	−	0.307561i	$-0.0995130\pi$
$762$	3.14487	+	1.81569i	0.113927	+	0.0657756i
$763$			95.1828i			3.44585i
$764$	−14.7928	+	8.54063i	−0.535185	+	0.308989i
$765$	−2.11106	+	3.65646i	−0.0763254	+	0.132200i
$766$	−8.89214			−0.321286
$767$	−41.7389			−1.50710
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$		−	14.4550i		−	0.521262i	−0.965439	−	0.260631i	$-0.916069\pi$
$769$		−	14.4550i		−	0.521262i	0.965439	−	0.260631i	$-0.0839305\pi$
$770$	6.75821	+	11.7056i	0.243549	+	0.421839i
$771$		−	22.1889i		−	0.799114i
$772$	−1.86346	+	1.07587i	−0.0670676	+	0.0387215i
$773$	−4.88713	−	8.46475i	−0.175778	−	0.304456i	0.764652	−	0.644443i	$-0.222911\pi$
$773$	−4.88713	−	8.46475i	−0.175778	−	0.304456i	−0.940430	+	0.339987i	$0.889577\pi$
$774$	−2.49755	−	4.32589i	−0.0897726	−	0.155491i
$775$	2.58205	+	1.49075i	0.0927501	+	0.0535493i
$776$	16.0748			0.577052
$777$	28.5292	−	5.57667i	1.02348	−	0.200062i
$778$	−3.70006			−0.132653
$779$	70.3605	+	40.6226i	2.52092	+	1.45546i
$780$	−1.86876	−	3.23678i	−0.0669122	−	0.115895i
$781$	−22.4397	−	38.8668i	−0.802957	−	1.39076i
$782$	−5.74219	+	3.31526i	−0.205340	+	0.118553i
$783$		−	2.13619i		−	0.0763412i
$784$	−7.91911	−	13.7163i	−0.282825	−	0.489868i
$785$		−	7.63271i		−	0.272423i
$786$	5.18961	−	8.98867i	0.185107	−	0.320615i
$787$	49.0476			1.74836			0.874178	−	0.485605i	$-0.161401\pi$
$787$	49.0476			1.74836			0.874178	+	0.485605i	$0.161401\pi$
$788$	1.85922			0.0662318
$789$	9.82345	−	17.0147i	0.349724	−	0.605740i
$790$	10.8209	−	6.24742i	0.384989	−	0.222273i
$791$		−	5.35417i		−	0.190372i
$792$	−2.44941	−	1.41417i	−0.0870360	−	0.0502502i
$793$	−28.7011	+	49.7117i	−1.01921	+	1.76532i
$794$	−9.31430	−	5.37761i	−0.330552	−	0.190844i
$795$	0.600165	−	0.346506i	0.0212857	−	0.0122893i
$796$	−20.4984	+	11.8347i	−0.726545	+	0.419471i
$797$	−34.1626	−	19.7238i	−1.21010	−	0.698652i	−0.247319	−	0.968934i	$-0.579550\pi$
$797$	−34.1626	−	19.7238i	−1.21010	−	0.698652i	−0.962781	+	0.270282i	$0.912883\pi$
$798$	−17.4310	+	30.1913i	−0.617050	+	1.06876i
$799$	−11.3177	−	6.53426i	−0.400390	−	0.231165i
$800$		−	1.00000i		−	0.0353553i
$801$	−1.94204	+	1.12123i	−0.0686184	+	0.0396169i
$802$	5.82240	−	10.0847i	0.205596	−	0.356103i
$803$	−26.2397			−0.925979
$804$	3.73951			0.131882
$805$	3.75248	−	6.49949i	0.132258	−	0.229077i
$806$			11.1434i			0.392509i
$807$	−6.60853	−	11.4463i	−0.232631	−	0.402929i
$808$			2.70797i			0.0952659i
$809$	17.0991	−	9.87219i	0.601173	−	0.347088i	−0.168330	−	0.985731i	$-0.553837\pi$
$809$	17.0991	−	9.87219i	0.601173	−	0.347088i	0.769503	+	0.638643i	$0.220504\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	−4.11350	−	7.12479i	−0.144444	−	0.250185i	0.784721	−	0.619849i	$-0.212806\pi$
$811$	−4.11350	−	7.12479i	−0.144444	−	0.250185i	−0.929166	+	0.369664i	$0.879473\pi$
$812$	−8.84101	−	5.10436i	−0.310259	−	0.179128i
$813$	11.1088			0.389603
$814$	−3.30046	−	16.8845i	−0.115681	−	0.591803i
$815$	19.1672			0.671397
$816$	−3.65646	−	2.11106i	−0.128002	−	0.0739018i
$817$	18.2194	+	31.5570i	0.637417	+	1.10404i
$818$	−0.722823	−	1.25197i	−0.0252729	−	0.0437740i
$819$	15.4684	−	8.93067i	0.540509	−	0.312063i
$820$		−	11.1372i		−	0.388929i
$821$	−3.24804	−	5.62576i	−0.113357	−	0.196340i	0.803765	−	0.594947i	$-0.202827\pi$
$821$	−3.24804	−	5.62576i	−0.113357	−	0.196340i	−0.917122	+	0.398607i	$0.869494\pi$
$822$			7.84028i			0.273461i
$823$	−4.75970	+	8.24404i	−0.165913	+	0.287369i	−0.936979	−	0.349386i	$-0.886390\pi$
$823$	−4.75970	+	8.24404i	−0.165913	+	0.287369i	0.771066	+	0.636755i	$0.219724\pi$
$824$	11.4602			0.399234
$825$	−2.82833			−0.0984700
$826$	26.6845	−	46.2189i	0.928473	−	1.60816i
$827$	−8.07985	+	4.66491i	−0.280964	+	0.162215i	−0.633860	−	0.773448i	$-0.718530\pi$
$827$	−8.07985	+	4.66491i	−0.280964	+	0.162215i	0.352896	+	0.935663i	$0.385197\pi$
$828$			1.57043i			0.0545760i
$829$	−13.7551	−	7.94151i	−0.477734	−	0.275820i	0.241737	−	0.970342i	$-0.422283\pi$
$829$	−13.7551	−	7.94151i	−0.477734	−	0.275820i	−0.719472	+	0.694522i	$0.755616\pi$
$830$	4.53064	−	7.84729i	0.157261	−	0.272384i
$831$	4.52021	+	2.60974i	0.156804	+	0.0905309i
$832$	3.23678	−	1.86876i	0.112215	−	0.0647875i
$833$	−57.9118	+	33.4354i	−2.00653	+	1.15847i
$834$	4.05175	+	2.33928i	0.140301	+	0.0810026i
$835$	10.4741	−	18.1416i	0.362470	−	0.627817i
$836$	17.8682	+	10.3162i	0.617986	+	0.356794i
$837$		−	2.98150i		−	0.103056i
$838$	12.3228	−	7.11457i	0.425684	−	0.245769i
$839$	−16.8619	+	29.2056i	−0.582136	+	1.00829i	0.413090	+	0.910690i	$0.364450\pi$
$839$	−16.8619	+	29.2056i	−0.582136	+	1.00829i	−0.995226	+	0.0975988i	$0.968884\pi$
$840$	4.77894			0.164889
$841$	24.4367			0.842645
$842$	−5.28146	+	9.14776i	−0.182011	+	0.315252i
$843$			3.36435i			0.115874i
$844$	−5.76729	−	9.98924i	−0.198518	−	0.343844i
$845$		−	0.969001i		−	0.0333346i
$846$	−2.68057	+	1.54763i	−0.0921598	+	0.0532085i
$847$	−7.16966	−	12.4182i	−0.246352	−	0.426695i
$848$	0.346506	+	0.600165i	0.0118990	+	0.0206098i
$849$	20.0633	+	11.5836i	0.688572	+	0.397547i
$850$	−4.22211			−0.144817
$851$	−7.20278	+	6.27460i	−0.246908	+	0.215091i
$852$	−15.8678			−0.543622
$853$	−8.98327	−	5.18650i	−0.307581	−	0.177582i	0.338262	−	0.941052i	$-0.390161\pi$
$853$	−8.98327	−	5.18650i	−0.307581	−	0.177582i	−0.645844	+	0.763470i	$0.723494\pi$
$854$	−36.6984	−	63.5634i	−1.25579	−	2.17510i
$855$	−3.64746	−	6.31758i	−0.124740	−	0.216057i
$856$	−13.0795	+	7.55146i	−0.447048	+	0.258104i
$857$			23.4130i			0.799773i	0.916565	+	0.399887i	$0.130950\pi$
$857$			23.4130i			0.799773i	−0.916565	+	0.399887i	$0.869050\pi$
$858$	−5.28547	−	9.15470i	−0.180443	−	0.312536i
$859$		−	5.97865i		−	0.203989i	−0.994785	−	0.101994i	$-0.967478\pi$
$859$		−	5.97865i		−	0.203989i	0.994785	−	0.101994i	$-0.0325224\pi$
$860$	2.49755	−	4.32589i	0.0851658	−	0.147511i
$861$	53.2242			1.81387
$862$	−29.9687			−1.02074
$863$	8.26321	−	14.3123i	0.281283	−	0.487196i	−0.690418	−	0.723411i	$-0.742573\pi$
$863$	8.26321	−	14.3123i	0.281283	−	0.487196i	0.971701	+	0.236214i	$0.0759067\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$		−	2.99459i		−	0.101819i
$866$	−4.74766	−	2.74107i	−0.161332	−	0.0931452i
$867$	−0.413127	+	0.715556i	−0.0140305	+	0.0243016i
$868$	−12.3395	−	7.12420i	−0.418829	−	0.241811i
$869$	30.6050	−	17.6698i	1.03820	−	0.599407i
$870$	1.84999	−	1.06810i	0.0627207	−	0.0362118i
$871$	12.1040	+	6.98824i	0.410128	+	0.236787i
$872$	9.95858	−	17.2488i	0.337240	−	0.584117i
$873$	−13.9212	−	8.03740i	−0.471161	−	0.272025i
$874$		−	11.4561i		−	0.387509i
$875$	4.13868	−	2.38947i	0.139913	−	0.0807788i
$876$	−4.63872	+	8.03450i	−0.156728	+	0.271461i
$877$	−10.1639			−0.343211			−0.171605	−	0.985166i	$-0.554895\pi$
$877$	−10.1639			−0.343211			−0.171605	+	0.985166i	$0.554895\pi$
$878$	14.6077			0.492984
$879$	14.9033	−	25.8134i	0.502677	−	0.870663i
$880$		−	2.82833i		−	0.0953431i
$881$	−17.8782	−	30.9659i	−0.602331	−	1.04327i	−0.992467	−	0.122511i	$-0.960905\pi$
$881$	−17.8782	−	30.9659i	−0.602331	−	1.04327i	0.390136	−	0.920757i	$-0.372428\pi$
$882$			15.8382i			0.533301i
$883$	29.3441	−	16.9418i	0.987509	−	0.570138i	0.0829800	−	0.996551i	$-0.473556\pi$
$883$	29.3441	−	16.9418i	0.987509	−	0.570138i	0.904529	+	0.426413i	$0.140223\pi$
$884$	−7.89010	−	13.6661i	−0.265373	−	0.459639i
$885$	5.58378	+	9.67139i	0.187697	+	0.325100i
$886$	28.6184	+	16.5228i	0.961454	+	0.555096i
$887$	−11.8085			−0.396492			−0.198246	−	0.980152i	$-0.563525\pi$
$887$	−11.8085			−0.396492			−0.198246	+	0.980152i	$0.563525\pi$
$888$	−5.75345	−	1.97430i	−0.193073	−	0.0662532i
$889$	−17.3542			−0.582040
$890$	−1.94204	−	1.12123i	−0.0650972	−	0.0375839i
$891$	1.41417	+	2.44941i	0.0473764	+	0.0820583i
$892$	6.01006	+	10.4097i	0.201232	+	0.348543i
$893$	19.5545	−	11.2898i	0.654367	−	0.377799i
$894$		−	19.3072i		−	0.645728i
$895$	−2.08103	−	3.60444i	−0.0695611	−	0.120483i
$896$			4.77894i			0.159653i
$897$	−2.93474	+	5.08312i	−0.0979882	+	0.169721i
$898$	36.4879			1.21762
$899$	−6.36905			−0.212420
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	2.53397	−	1.46299i	0.0844187	−	0.0487391i
$902$		−	31.4998i		−	1.04883i
$903$	20.6731	+	11.9356i	0.687959	+	0.397193i
$904$	−0.560185	+	0.970268i	−0.0186315	+	0.0322706i
$905$	−7.58669	−	4.38018i	−0.252190	−	0.145602i
$906$	1.89882	−	1.09628i	0.0630840	−	0.0364216i
$907$	−17.2750	+	9.97372i	−0.573606	+	0.331172i	−0.758588	−	0.651570i	$-0.774111\pi$
$907$	−17.2750	+	9.97372i	−0.573606	+	0.331172i	0.184982	+	0.982742i	$0.440777\pi$
$908$	21.9971	+	12.7000i	0.729998	+	0.421465i
$909$	1.35398	−	2.34517i	0.0449088	−	0.0777843i
$910$	15.4684	+	8.93067i	0.512771	+	0.296049i
$911$		−	6.10017i		−	0.202108i	−0.994881	−	0.101054i	$-0.967779\pi$
$911$		−	6.10017i		−	0.202108i	0.994881	−	0.101054i	$-0.0322214\pi$
$912$	6.31758	−	3.64746i	0.209196	−	0.120779i
$913$	12.8142	−	22.1948i	0.424087	−	0.734540i
$914$	−13.9689			−0.462050
$915$	15.3584			0.507733
$916$	2.45890	−	4.25894i	0.0812444	−	0.140719i
$917$			49.6017i			1.63799i
$918$	2.11106	+	3.65646i	0.0696753	+	0.120681i
$919$			0.160046i			0.00527944i	0.999997	+	0.00263972i	$0.000840250\pi$
$919$			0.160046i			0.00527944i	−0.999997	+	0.00263972i	$0.999160\pi$
$920$	−1.36003	+	0.785213i	−0.0448388	+	0.0258877i
$921$	12.1668	+	21.0735i	0.400910	+	0.694396i
$922$	9.34134	+	16.1797i	0.307641	+	0.532849i
$923$	−51.3606	−	29.6531i	−1.69056	−	0.976043i
$924$	13.5164			0.444658
$925$	−5.96978	+	1.16693i	−0.196285	+	0.0383684i
$926$	−18.4484			−0.606251
$927$	−9.92480	−	5.73009i	−0.325973	−	0.188201i
$928$	1.06810	+	1.84999i	0.0350619	+	0.0607291i
$929$	28.1426	+	48.7444i	0.923328	+	1.59925i	0.794228	+	0.607620i	$0.207875\pi$
$929$	28.1426	+	48.7444i	0.923328	+	1.59925i	0.129100	+	0.991632i	$0.458791\pi$
$930$	2.58205	−	1.49075i	0.0846689	−	0.0488836i
$931$		−	115.539i		−	3.78662i
$932$	7.99634	+	13.8501i	0.261929	+	0.453674i
$933$			5.58855i			0.182961i
$934$	7.90736	−	13.6959i	0.258737	−	0.448145i
$935$	−11.9416			−0.390531
$936$	−3.73751			−0.122164
$937$	4.42166	−	7.65854i	0.144449	−	0.250193i	−0.784718	−	0.619853i	$-0.787192\pi$
$937$	4.42166	−	7.65854i	0.144449	−	0.250193i	0.929167	+	0.369659i	$0.120526\pi$
$938$	−15.4766	+	8.93544i	−0.505330	+	0.291753i
$939$			11.2872i			0.368343i
$940$	−2.68057	−	1.54763i	−0.0874305	−	0.0504780i
$941$	−18.3759	+	31.8279i	−0.599036	+	1.03756i	0.393928	+	0.919141i	$0.371116\pi$
$941$	−18.3759	+	31.8279i	−0.599036	+	1.03756i	−0.992964	+	0.118419i	$0.962217\pi$
$942$	−6.61012	−	3.81635i	−0.215369	−	0.124343i
$943$	−15.1470	+	8.74510i	−0.493253	+	0.284780i
$944$	−9.67139	+	5.58378i	−0.314777	+	0.181736i
$945$	−4.13868	−	2.38947i	−0.134631	−	0.0777294i
$946$	7.06391	−	12.2351i	0.229668	−	0.397796i
$947$	10.0167	+	5.78313i	0.325498	+	0.187926i	0.653841	−	0.756632i	$-0.273157\pi$
$947$	10.0167	+	5.78313i	0.325498	+	0.187926i	−0.328342	+	0.944559i	$0.606490\pi$
$948$		−	12.4948i		−	0.405814i
$949$	−30.0290	+	17.3373i	−0.974784	+	0.562792i
$950$	3.64746	−	6.31758i	0.118339	−	0.204969i
$951$	−9.29307			−0.301348
$952$	20.1772			0.653947
$953$	17.5954	−	30.4762i	0.569972	−	0.987220i	−0.426596	−	0.904442i	$-0.640287\pi$
$953$	17.5954	−	30.4762i	0.569972	−	0.987220i	0.996568	−	0.0827778i	$-0.0263792\pi$
$954$		−	0.693011i		−	0.0224371i
$955$	8.54063	+	14.7928i	0.276368	+	0.478684i
$956$			13.4067i			0.433604i
$957$	5.23240	−	3.02093i	0.169140	−	0.0976528i
$958$	−7.83495	−	13.5705i	−0.253136	−	0.438444i
$959$	−18.7341	−	32.4484i	−0.604956	−	1.04781i
$960$	−0.866025	−	0.500000i	−0.0279508	−	0.0161374i
$961$	22.1107			0.713247
$962$	−14.9332	−	17.1422i	−0.481464	−	0.552686i
$963$	15.1029			0.486685
$964$	−8.23003	−	4.75161i	−0.265072	−	0.153039i
$965$	1.07587	+	1.86346i	0.0346335	+	0.0599870i
$966$	−3.75248	−	6.49949i	−0.120734	−	0.209118i
$967$	15.5459	−	8.97542i	0.499922	−	0.288630i	−0.228759	−	0.973483i	$-0.573467\pi$
$967$	15.5459	−	8.97542i	0.499922	−	0.288630i	0.728681	+	0.684853i	$0.240134\pi$
$968$			3.00052i			0.0964405i
$969$	−15.4000	−	26.6736i	−0.494719	−	0.856878i
$970$		−	16.0748i		−	0.516131i
$971$	−11.0299	+	19.1043i	−0.353965	+	0.613086i	−0.986940	−	0.161086i	$-0.948500\pi$
$971$	−11.0299	+	19.1043i	−0.353965	+	0.613086i	0.632975	+	0.774172i	$0.281834\pi$
$972$	1.00000			0.0320750
$973$	−22.3585			−0.716781
$974$	−18.5914	+	32.2013i	−0.595708	+	1.03180i
$975$	−3.23678	+	1.86876i	−0.103660	+	0.0598481i
$976$			15.3584i			0.491610i
$977$	−19.7065	−	11.3776i	−0.630467	−	0.364000i	0.150466	−	0.988615i	$-0.451923\pi$
$977$	−19.7065	−	11.3776i	−0.630467	−	0.364000i	−0.780933	+	0.624615i	$0.785256\pi$
$978$	9.58358	−	16.5993i	0.306449	−	0.530786i
$979$	−5.49273	−	3.17123i	−0.175548	−	0.101353i
$980$	−13.7163	+	7.91911i	−0.438151	+	0.252967i
$981$	−17.2488	+	9.95858i	−0.550711	+	0.317953i
$982$	5.66581	+	3.27116i	0.180803	+	0.104387i
$983$	−8.34196	+	14.4487i	−0.266067	+	0.460842i	−0.967843	−	0.251556i	$-0.919058\pi$
$983$	−8.34196	+	14.4487i	−0.266067	+	0.460842i	0.701775	+	0.712398i	$0.252391\pi$
$984$	−9.64513	−	5.56862i	−0.307476	−	0.177521i
$985$		−	1.85922i		−	0.0592395i
$986$	7.81089	−	4.50962i	0.248749	−	0.143616i
$987$	7.39601	−	12.8103i	0.235418	−	0.407755i
$988$	27.2648			0.867410
$989$	−7.84444			−0.249439
$990$	−1.41417	+	2.44941i	−0.0449452	+	0.0778473i
$991$		−	20.7952i		−	0.660581i	−0.943879	−	0.330291i	$-0.892853\pi$
$991$		−	20.7952i		−	0.660581i	0.943879	−	0.330291i	$-0.107147\pi$
$992$	1.49075	+	2.58205i	0.0473313	+	0.0819803i
$993$			28.8160i			0.914448i
$994$	65.6718	−	37.9156i	2.08298	−	1.20261i
$995$	11.8347	+	20.4984i	0.375186	+	0.649842i
$996$	−4.53064	−	7.84729i	−0.143559	−	0.248651i
$997$	7.40987	+	4.27809i	0.234673	+	0.135489i	0.612726	−	0.790295i	$-0.290073\pi$
$997$	7.40987	+	4.27809i	0.234673	+	0.135489i	−0.378053	+	0.925784i	$0.623406\pi$
$998$	28.1278			0.890369
$999$	3.99548	+	4.58652i	0.126411	+	0.145111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.e.841.4	yes	16
37.11	even	6	inner	1110.2.x.e.751.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.e.751.4	✓	16	37.11	even	6	inner
1110.2.x.e.841.4	yes	16	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(2.38947 + 4.13868i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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} +(2.38947 + 4.13868i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} -2.82833 q^{11} +(-0.500000 + 0.866025i) q^{12} +(-3.23678 + 1.86876i) q^{13} -4.77894i q^{14} +(0.866025 + 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.65646 + 2.11106i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-6.31758 + 3.64746i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-2.38947 + 4.13868i) q^{21} +(2.44941 + 1.41417i) q^{22} -1.57043i q^{23} +(0.866025 - 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} +3.73751 q^{26} -1.00000 q^{27} +(-2.38947 + 4.13868i) q^{28} +2.13619i q^{29} +(-0.500000 - 0.866025i) q^{30} +2.98150i q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.41417 - 2.44941i) q^{33} +(-2.11106 - 3.65646i) q^{34} +(4.13868 + 2.38947i) q^{35} -1.00000 q^{36} +(-3.99548 - 4.58652i) q^{37} +7.29492 q^{38} +(-3.23678 - 1.86876i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-5.56862 - 9.64513i) q^{41} +(4.13868 - 2.38947i) q^{42} -4.99510i q^{43} +(-1.41417 - 2.44941i) q^{44} +1.00000i q^{45} +(-0.785213 + 1.36003i) q^{46} -3.09525 q^{47} -1.00000 q^{48} +(-7.91911 + 13.7163i) q^{49} +(-0.866025 + 0.500000i) q^{50} +4.22211i q^{51} +(-3.23678 - 1.86876i) q^{52} +(0.346506 - 0.600165i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-2.44941 + 1.41417i) q^{55} +(4.13868 - 2.38947i) q^{56} +(-6.31758 - 3.64746i) q^{57} +(1.06810 - 1.84999i) q^{58} +(9.67139 + 5.58378i) q^{59} +1.00000i q^{60} +(13.3008 - 7.67919i) q^{61} +(1.49075 - 2.58205i) q^{62} -4.77894 q^{63} -1.00000 q^{64} +(-1.86876 + 3.23678i) q^{65} +2.82833i q^{66} +(-1.86976 - 3.23851i) q^{67} +4.22211i q^{68} +(1.36003 - 0.785213i) q^{69} +(-2.38947 - 4.13868i) q^{70} +(7.93390 + 13.7419i) q^{71} +(0.866025 + 0.500000i) q^{72} +9.27744 q^{73} +(1.16693 + 5.96978i) q^{74} +1.00000 q^{75} +(-6.31758 - 3.64746i) q^{76} +(-6.75821 - 11.7056i) q^{77} +(1.86876 + 3.23678i) q^{78} +(-10.8209 + 6.24742i) q^{79} +1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} +11.1372i q^{82} +(-4.53064 + 7.84729i) q^{83} -4.77894 q^{84} +4.22211 q^{85} +(-2.49755 + 4.32589i) q^{86} +(-1.84999 + 1.06810i) q^{87} +2.82833i q^{88} +(1.94204 + 1.12123i) q^{89} +(0.500000 - 0.866025i) q^{90} +(-15.4684 - 8.93067i) q^{91} +(1.36003 - 0.785213i) q^{92} +(-2.58205 + 1.49075i) q^{93} +(2.68057 + 1.54763i) q^{94} +(-3.64746 + 6.31758i) q^{95} +(0.866025 + 0.500000i) q^{96} +16.0748i q^{97} +(13.7163 - 7.91911i) q^{98} +(1.41417 - 2.44941i) 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

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