LMFDB - Embedded newform 1110.2.bb.d.1099.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(1009,1110)]

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, 3, 4]))

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

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

chi := DirichletCharacter("1110.1009");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.bb (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:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1099.2
Character	$\chi$	$=$	1110.1099
Dual form			1110.2.bb.d.1009.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.589266 + 2.15703i) q^{5} +1.00000 q^{6} +(-3.59896 - 2.07786i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.589266 + 2.15703i) q^{5} +1.00000 q^{6} +(-3.59896 - 2.07786i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.568195 - 2.16267i) q^{10} +3.62754 q^{11} +(-0.866025 + 0.500000i) q^{12} +(1.85017 + 1.06819i) q^{13} +4.15572 q^{14} +(1.58883 - 1.57341i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00089 - 0.577862i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-3.73087 + 6.46205i) q^{19} +(1.57341 + 1.58883i) q^{20} +(2.07786 + 3.59896i) q^{21} +(-3.14154 + 1.81377i) q^{22} -0.363708i q^{23} +(0.500000 - 0.866025i) q^{24} +(-4.30553 - 2.54212i) q^{25} -2.13639 q^{26} -1.00000i q^{27} +(-3.59896 + 2.07786i) q^{28} -5.15572 q^{29} +(-0.589266 + 2.15703i) q^{30} +3.49115 q^{31} +(0.866025 + 0.500000i) q^{32} +(-3.14154 - 1.81377i) q^{33} +(-0.577862 + 1.00089i) q^{34} +(6.60275 - 6.53865i) q^{35} +1.00000 q^{36} +(-6.08252 - 0.0539383i) q^{37} -7.46174i q^{38} +(-1.06819 - 1.85017i) q^{39} +(-2.15703 - 0.589266i) q^{40} +(6.04397 - 10.4685i) q^{41} +(-3.59896 - 2.07786i) q^{42} -12.3681i q^{43} +(1.81377 - 3.14154i) q^{44} +(-2.16267 + 0.568195i) q^{45} +(0.181854 + 0.314980i) q^{46} -2.21747i q^{47} +1.00000i q^{48} +(5.13502 + 8.89411i) q^{49} +(4.99976 + 0.0487778i) q^{50} -1.15572 q^{51} +(1.85017 - 1.06819i) q^{52} +(-9.47411 + 5.46988i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.13758 + 7.82470i) q^{55} +(2.07786 - 3.59896i) q^{56} +(6.46205 - 3.73087i) q^{57} +(4.46499 - 2.57786i) q^{58} +(-4.88507 - 8.46118i) q^{59} +(-0.568195 - 2.16267i) q^{60} +(-3.12535 + 5.41327i) q^{61} +(-3.02342 + 1.74558i) q^{62} -4.15572i q^{63} -1.00000 q^{64} +(-3.39436 + 3.36141i) q^{65} +3.62754 q^{66} +(-13.3985 - 7.73561i) q^{67} -1.15572i q^{68} +(-0.181854 + 0.314980i) q^{69} +(-2.44882 + 8.96401i) q^{70} +(-0.0732348 + 0.126846i) q^{71} +(-0.866025 + 0.500000i) q^{72} +9.63375i q^{73} +(5.29459 - 2.99455i) q^{74} +(2.45764 + 4.35431i) q^{75} +(3.73087 + 6.46205i) q^{76} +(-13.0554 - 7.53753i) q^{77} +(1.85017 + 1.06819i) q^{78} +(7.85583 - 13.6067i) q^{79} +(2.16267 - 0.568195i) q^{80} +(-0.500000 + 0.866025i) q^{81} +12.0879i q^{82} +(11.9781 - 6.91556i) q^{83} +4.15572 q^{84} +(0.656676 + 2.49945i) q^{85} +(6.18403 + 10.7111i) q^{86} +(4.46499 + 2.57786i) q^{87} +3.62754i q^{88} +(-5.67966 - 9.83745i) q^{89} +(1.58883 - 1.57341i) q^{90} +(-4.43912 - 7.68878i) q^{91} +(-0.314980 - 0.181854i) q^{92} +(-3.02342 - 1.74558i) q^{93} +(1.10873 + 1.92038i) q^{94} +(-11.7404 - 11.8554i) q^{95} +(-0.500000 - 0.866025i) q^{96} +11.6594i q^{97} +(-8.89411 - 5.13502i) q^{98} +(1.81377 + 3.14154i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9}+O(q^{10}) $ 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9	$ 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9} + 4 q^{10} - 12 q^{11} + 8 q^{14} + 2 q^{15} - 14 q^{16} - 20 q^{19} - 2 q^{20} + 4 q^{21} + 14 q^{24} - 8 q^{25} - 20 q^{26} - 36 q^{29} + 2 q^{30} + 24 q^{31} + 38 q^{34} - 2 q^{35} + 28 q^{36} - 10 q^{39} + 2 q^{40} - 6 q^{44} + 4 q^{45} + 8 q^{46} + 50 q^{49} - 4 q^{50} + 76 q^{51} + 14 q^{54} - 28 q^{55} + 4 q^{56} - 26 q^{59} + 4 q^{60} - 28 q^{61} - 28 q^{64} + 60 q^{65} - 12 q^{66} - 8 q^{69} - 10 q^{70} - 64 q^{71} + 24 q^{74} - 8 q^{75} + 20 q^{76} + 32 q^{79} - 4 q^{80} - 14 q^{81} + 8 q^{84} + 16 q^{85} - 8 q^{86} + 76 q^{89} + 2 q^{90} - 8 q^{91} - 38 q^{94} - 70 q^{95} - 14 q^{96} - 6 q^{99}+O(q^{100}) $ 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9 + 4 * q^10 - 12 * q^11 + 8 * q^14 + 2 * q^15 - 14 * q^16 - 20 * q^19 - 2 * q^20 + 4 * q^21 + 14 * q^24 - 8 * q^25 - 20 * q^26 - 36 * q^29 + 2 * q^30 + 24 * q^31 + 38 * q^34 - 2 * q^35 + 28 * q^36 - 10 * q^39 + 2 * q^40 - 6 * q^44 + 4 * q^45 + 8 * q^46 + 50 * q^49 - 4 * q^50 + 76 * q^51 + 14 * q^54 - 28 * q^55 + 4 * q^56 - 26 * q^59 + 4 * q^60 - 28 * q^61 - 28 * q^64 + 60 * q^65 - 12 * q^66 - 8 * q^69 - 10 * q^70 - 64 * q^71 + 24 * q^74 - 8 * q^75 + 20 * q^76 + 32 * q^79 - 4 * q^80 - 14 * q^81 + 8 * q^84 + 16 * q^85 - 8 * q^86 + 76 * q^89 + 2 * q^90 - 8 * q^91 - 38 * q^94 - 70 * q^95 - 14 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

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
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.589266	+	2.15703i	−0.263528	+	0.964652i
$5$	−0.589266	+	2.15703i	−0.263528	+	0.964652i
$6$	1.00000			0.408248
$7$	−3.59896	−	2.07786i	−1.36028	−	0.785358i	−0.370619	−	0.928785i	$-0.620854\pi$
$7$	−3.59896	−	2.07786i	−1.36028	−	0.785358i	−0.989661	+	0.143427i	$0.954188\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.568195	−	2.16267i	−0.179679	−	0.683897i
$11$	3.62754			1.09374			0.546872	−	0.837216i	$-0.315818\pi$
$11$	3.62754			1.09374			0.546872	+	0.837216i	$0.315818\pi$
$12$	−0.866025	+	0.500000i	−0.250000	+	0.144338i
$13$	1.85017	+	1.06819i	0.513144	+	0.296264i	0.734125	−	0.679014i	$-0.237593\pi$
$13$	1.85017	+	1.06819i	0.513144	+	0.296264i	−0.220981	+	0.975278i	$0.570926\pi$
$14$	4.15572			1.11066
$15$	1.58883	−	1.57341i	0.410235	−	0.406252i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.00089	−	0.577862i	0.242750	−	0.140152i	−0.373690	−	0.927554i	$-0.621908\pi$
$17$	1.00089	−	0.577862i	0.242750	−	0.140152i	0.616440	+	0.787402i	$0.288574\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	−3.73087	+	6.46205i	−0.855920	+	1.48250i	0.0198694	+	0.999803i	$0.493675\pi$
$19$	−3.73087	+	6.46205i	−0.855920	+	1.48250i	−0.875789	+	0.482694i	$0.839658\pi$
$20$	1.57341	+	1.58883i	0.351825	+	0.355274i
$21$	2.07786	+	3.59896i	0.453427	+	0.785358i
$22$	−3.14154	+	1.81377i	−0.669779	+	0.386697i
$23$		−	0.363708i		−	0.0758383i	−0.999281	−	0.0379191i	$-0.987927\pi$
$23$		−	0.363708i		−	0.0758383i	0.999281	−	0.0379191i	$-0.0120729\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−4.30553	−	2.54212i	−0.861106	−	0.508425i
$26$	−2.13639			−0.418980
$27$		−	1.00000i		−	0.192450i
$28$	−3.59896	+	2.07786i	−0.680140	+	0.392679i
$29$	−5.15572			−0.957394			−0.478697	−	0.877980i	$-0.658891\pi$
$29$	−5.15572			−0.957394			−0.478697	+	0.877980i	$0.658891\pi$
$30$	−0.589266	+	2.15703i	−0.107585	+	0.393817i
$31$	3.49115			0.627029			0.313515	−	0.949583i	$-0.398494\pi$
$31$	3.49115			0.627029			0.313515	+	0.949583i	$0.398494\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−3.14154	−	1.81377i	−0.546872	−	0.315737i
$34$	−0.577862	+	1.00089i	−0.0991025	+	0.171651i
$35$	6.60275	−	6.53865i	1.11607	−	1.10523i
$36$	1.00000			0.166667
$37$	−6.08252	−	0.0539383i	−0.999961	−	0.00886741i
$37$	−6.08252	−	0.0539383i	−0.999961	−	0.00886741i
$38$		−	7.46174i		−	1.21045i
$39$	−1.06819	−	1.85017i	−0.171048	−	0.296264i
$40$	−2.15703	−	0.589266i	−0.341056	−	0.0931711i
$41$	6.04397	−	10.4685i	0.943910	−	1.63490i	0.185991	−	0.982551i	$-0.440450\pi$
$41$	6.04397	−	10.4685i	0.943910	−	1.63490i	0.757919	−	0.652349i	$-0.226216\pi$
$42$	−3.59896	−	2.07786i	−0.555332	−	0.320621i
$43$		−	12.3681i		−	1.88611i	−0.332634	−	0.943056i	$-0.607937\pi$
$43$		−	12.3681i		−	1.88611i	0.332634	−	0.943056i	$-0.392063\pi$
$44$	1.81377	−	3.14154i	0.273436	−	0.473605i
$45$	−2.16267	+	0.568195i	−0.322392	+	0.0847014i
$46$	0.181854	+	0.314980i	0.0268129	+	0.0464413i
$47$		−	2.21747i		−	0.323451i	−0.986836	−	0.161726i	$-0.948294\pi$
$47$		−	2.21747i		−	0.323451i	0.986836	−	0.161726i	$-0.0517059\pi$
$48$			1.00000i			0.144338i
$49$	5.13502	+	8.89411i	0.733574	+	1.27059i
$50$	4.99976	+	0.0487778i	0.707073	+	0.00689822i
$51$	−1.15572			−0.161834
$52$	1.85017	−	1.06819i	0.256572	−	0.148132i
$53$	−9.47411	+	5.46988i	−1.30137	+	0.751346i	−0.980639	−	0.195825i	$-0.937262\pi$
$53$	−9.47411	+	5.46988i	−1.30137	+	0.751346i	−0.320730	+	0.947171i	$0.603928\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−2.13758	+	7.82470i	−0.288232	+	1.05508i
$56$	2.07786	−	3.59896i	0.277666	−	0.480932i
$57$	6.46205	−	3.73087i	0.855920	−	0.494165i
$58$	4.46499	−	2.57786i	0.586282	−	0.338490i
$59$	−4.88507	−	8.46118i	−0.635982	−	1.10155i	−0.986306	−	0.164924i	$-0.947262\pi$
$59$	−4.88507	−	8.46118i	−0.635982	−	1.10155i	0.350325	−	0.936628i	$-0.386071\pi$
$60$	−0.568195	−	2.16267i	−0.0733536	−	0.279200i
$61$	−3.12535	+	5.41327i	−0.400160	+	0.693098i	−0.993745	−	0.111674i	$-0.964379\pi$
$61$	−3.12535	+	5.41327i	−0.400160	+	0.693098i	0.593585	+	0.804772i	$0.297712\pi$
$62$	−3.02342	+	1.74558i	−0.383975	+	0.221688i
$63$		−	4.15572i		−	0.523572i
$64$	−1.00000			−0.125000
$65$	−3.39436	+	3.36141i	−0.421019	+	0.416932i
$66$	3.62754			0.446519
$67$	−13.3985	−	7.73561i	−1.63688	−	0.945055i	−0.981897	−	0.189415i	$-0.939341\pi$
$67$	−13.3985	−	7.73561i	−1.63688	−	0.945055i	−0.654986	−	0.755641i	$-0.727326\pi$
$68$		−	1.15572i		−	0.140152i
$69$	−0.181854	+	0.314980i	−0.0218926	+	0.0379191i
$70$	−2.44882	+	8.96401i	−0.292691	+	1.07140i
$71$	−0.0732348	+	0.126846i	−0.00869137	+	0.0150539i	−0.870338	−	0.492454i	$-0.836100\pi$
$71$	−0.0732348	+	0.126846i	−0.00869137	+	0.0150539i	0.861647	+	0.507508i	$0.169433\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$			9.63375i			1.12754i	0.825930	+	0.563772i	$0.190650\pi$
$73$			9.63375i			1.12754i	−0.825930	+	0.563772i	$0.809350\pi$
$74$	5.29459	−	2.99455i	0.615483	−	0.348109i
$75$	2.45764	+	4.35431i	0.283784	+	0.502792i
$76$	3.73087	+	6.46205i	0.427960	+	0.741248i
$77$	−13.0554	−	7.53753i	−1.48780	−	0.858981i
$78$	1.85017	+	1.06819i	0.209490	+	0.120949i
$79$	7.85583	−	13.6067i	0.883850	−	1.53087i	0.0368247	−	0.999322i	$-0.488276\pi$
$79$	7.85583	−	13.6067i	0.883850	−	1.53087i	0.847026	−	0.531552i	$-0.178391\pi$
$80$	2.16267	−	0.568195i	0.241794	−	0.0635261i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$			12.0879i			1.33489i
$83$	11.9781	−	6.91556i	1.31477	−	0.759082i	0.331886	−	0.943319i	$-0.392315\pi$
$83$	11.9781	−	6.91556i	1.31477	−	0.759082i	0.982882	+	0.184238i	$0.0589816\pi$
$84$	4.15572			0.453427
$85$	0.656676	+	2.49945i	0.0712265	+	0.271104i
$86$	6.18403	+	10.7111i	0.666841	+	1.15500i
$87$	4.46499	+	2.57786i	0.478697	+	0.276376i
$88$			3.62754i			0.386697i
$89$	−5.67966	−	9.83745i	−0.602042	−	1.04277i	−0.992511	−	0.122152i	$-0.961021\pi$
$89$	−5.67966	−	9.83745i	−0.602042	−	1.04277i	0.390469	−	0.920616i	$-0.372313\pi$
$90$	1.58883	−	1.57341i	0.167478	−	0.165852i
$91$	−4.43912	−	7.68878i	−0.465346	−	0.806004i
$92$	−0.314980	−	0.181854i	−0.0328389	−	0.0189596i
$93$	−3.02342	−	1.74558i	−0.313515	−	0.181008i
$94$	1.10873	+	1.92038i	0.114357	+	0.198073i
$95$	−11.7404	−	11.8554i	−1.20453	−	1.21634i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$			11.6594i			1.18384i	0.805998	+	0.591919i	$0.201629\pi$
$97$			11.6594i			1.18384i	−0.805998	+	0.591919i	$0.798371\pi$
$98$	−8.89411	−	5.13502i	−0.898441	−	0.518715i
$99$	1.81377	+	3.14154i	0.182291	+	0.315737i
$100$	−4.35431	+	2.45764i	−0.435431	+	0.245764i
$101$	−10.4486			−1.03968			−0.519838	−	0.854265i	$-0.674008\pi$
$101$	−10.4486			−1.03968			−0.519838	+	0.854265i	$0.674008\pi$
$102$	1.00089	−	0.577862i	0.0991025	−	0.0572168i
$103$		−	9.76260i		−	0.961938i	−0.876738	−	0.480969i	$-0.840285\pi$
$103$		−	9.76260i		−	0.961938i	0.876738	−	0.480969i	$-0.159715\pi$
$104$	−1.06819	+	1.85017i	−0.104745	+	0.181424i
$105$	−8.98747	+	2.36126i	−0.877087	+	0.230435i
$106$	5.46988	−	9.47411i	0.531282	−	0.920207i
$107$	1.06082	+	0.612466i	0.102554	+	0.0592093i	0.550400	−	0.834901i	$-0.314475\pi$
$107$	1.06082	+	0.612466i	0.102554	+	0.0592093i	−0.447846	+	0.894111i	$0.647809\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	−4.94812	−	8.57040i	−0.473944	−	0.820896i	0.525611	−	0.850725i	$-0.323837\pi$
$109$	−4.94812	−	8.57040i	−0.473944	−	0.820896i	−0.999555	+	0.0298295i	$0.990504\pi$
$110$	−2.06115	−	7.84518i	−0.196523	−	0.748009i
$111$	5.24065	+	3.08797i	0.497421	+	0.293097i
$112$			4.15572i			0.392679i
$113$	7.25569	−	4.18907i	0.682558	−	0.394075i	−0.118260	−	0.992983i	$-0.537732\pi$
$113$	7.25569	−	4.18907i	0.682558	−	0.394075i	0.800818	+	0.598908i	$0.204398\pi$
$114$	−3.73087	+	6.46205i	−0.349428	+	0.605227i
$115$	0.784527	+	0.214320i	0.0731575	+	0.0199855i
$116$	−2.57786	+	4.46499i	−0.239348	+	0.414564i
$117$			2.13639i			0.197509i
$118$	8.46118	+	4.88507i	0.778915	+	0.449707i
$119$	−4.80287			−0.440278
$120$	1.57341	+	1.58883i	0.143632	+	0.145040i
$121$	2.15904			0.196276
$122$		−	6.25070i		−	0.565912i
$123$	−10.4685	+	6.04397i	−0.943910	+	0.544967i
$124$	1.74558	−	3.02342i	0.156757	−	0.271512i
$125$	8.02053	−	7.78916i	0.717378	−	0.696684i
$126$	2.07786	+	3.59896i	0.185111	+	0.320621i
$127$	4.57107	−	2.63911i	0.405617	−	0.234183i	−0.283288	−	0.959035i	$-0.591425\pi$
$127$	4.57107	−	2.63911i	0.405617	−	0.234183i	0.688905	+	0.724852i	$0.258092\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−6.18403	+	10.7111i	−0.544474	+	0.943056i
$130$	1.25890	−	4.60825i	0.110413	−	0.404170i
$131$	−7.60944	−	13.1799i	−0.664840	−	1.15154i	−0.979329	−	0.202275i	$-0.935167\pi$
$131$	−7.60944	−	13.1799i	−0.664840	−	1.15154i	0.314489	−	0.949261i	$-0.398167\pi$
$132$	−3.14154	+	1.81377i	−0.273436	+	0.157868i
$133$	26.8545	−	15.5045i	2.32858	−	1.34441i
$134$	15.4712			1.33651
$135$	2.15703	+	0.589266i	0.185647	+	0.0507159i
$136$	0.577862	+	1.00089i	0.0495512	+	0.0858253i
$137$			6.94371i			0.593241i	0.954995	+	0.296620i	$0.0958596\pi$
$137$			6.94371i			0.593241i	−0.954995	+	0.296620i	$0.904140\pi$
$138$		−	0.363708i		−	0.0309609i
$139$	−6.89557	−	11.9435i	−0.584874	−	1.01303i	−0.994891	−	0.100954i	$-0.967811\pi$
$139$	−6.89557	−	11.9435i	−0.584874	−	1.01303i	0.410017	−	0.912078i	$-0.365523\pi$
$140$	−2.36126	−	8.98747i	−0.199563	−	0.759580i
$141$	−1.10873	+	1.92038i	−0.0933723	+	0.161726i
$142$		−	0.146470i		−	0.0122915i
$143$	6.71155	+	3.87492i	0.561248	+	0.324037i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	3.03809	−	11.1210i	0.252300	−	0.923552i
$146$	−4.81687	−	8.34307i	−0.398647	−	0.690477i
$147$		−	10.2700i		−	0.847058i
$148$	−3.08797	+	5.24065i	−0.253830	+	0.430779i
$149$	−5.53123			−0.453136			−0.226568	−	0.973995i	$-0.572751\pi$
$149$	−5.53123			−0.453136			−0.226568	+	0.973995i	$0.572751\pi$
$150$	−4.30553	−	2.54212i	−0.351545	−	0.207564i
$151$	−11.1149	+	19.2515i	−0.904517	+	1.56667i	−0.0829517	+	0.996554i	$0.526435\pi$
$151$	−11.1149	+	19.2515i	−0.904517	+	1.56667i	−0.821565	+	0.570115i	$0.806899\pi$
$152$	−6.46205	−	3.73087i	−0.524142	−	0.302613i
$153$	1.00089	+	0.577862i	0.0809168	+	0.0467174i
$154$	15.0751			1.21478
$155$	−2.05721	+	7.53051i	−0.165239	+	0.604865i
$156$	−2.13639			−0.171048
$157$	−7.34502	+	4.24065i	−0.586197	+	0.338441i	−0.763592	−	0.645699i	$-0.776566\pi$
$157$	−7.34502	+	4.24065i	−0.586197	+	0.338441i	0.177396	+	0.984140i	$0.443233\pi$
$158$			15.7117i			1.24995i
$159$	10.9398			0.867579
$160$	−1.58883	+	1.57341i	−0.125608	+	0.124389i
$161$	−0.755734	+	1.30897i	−0.0595602	+	0.103161i
$162$		−	1.00000i		−	0.0785674i
$163$	−21.4841	+	12.4039i	−1.68277	+	0.971546i	−0.722957	+	0.690893i	$0.757217\pi$
$163$	−21.4841	+	12.4039i	−1.68277	+	0.971546i	−0.959810	+	0.280652i	$0.909449\pi$
$164$	−6.04397	−	10.4685i	−0.471955	−	0.817450i
$165$	5.76355	−	5.70760i	0.448692	−	0.444336i
$166$	−6.91556	+	11.9781i	−0.536752	+	0.929681i
$167$	9.99502	+	5.77063i	0.773438	+	0.446545i	0.834100	−	0.551614i	$-0.185988\pi$
$167$	9.99502	+	5.77063i	0.773438	+	0.446545i	−0.0606617	+	0.998158i	$0.519321\pi$
$168$	−3.59896	+	2.07786i	−0.277666	+	0.160311i
$169$	−4.21792	−	7.30565i	−0.324455	−	0.561973i
$170$	−1.81842	−	1.83625i	−0.139467	−	0.140834i
$171$	−7.46174			−0.570613
$172$	−10.7111	−	6.18403i	−0.816711	−	0.471528i
$173$	−3.13632	+	1.81075i	−0.238450	+	0.137669i	−0.614464	−	0.788945i	$-0.710628\pi$
$173$	−3.13632	+	1.81075i	−0.238450	+	0.137669i	0.376014	+	0.926614i	$0.377294\pi$
$174$	−5.15572			−0.390854
$175$	10.2133	+	18.0953i	0.772050	+	1.36788i
$176$	−1.81377	−	3.14154i	−0.136718	−	0.236803i
$177$			9.77013i			0.734368i
$178$	9.83745	+	5.67966i	0.737348	+	0.425708i
$179$	12.5453			0.937680			0.468840	−	0.883283i	$-0.344672\pi$
$179$	12.5453			0.937680			0.468840	+	0.883283i	$0.344672\pi$
$180$	−0.589266	+	2.15703i	−0.0439213	+	0.160775i
$181$	−1.46011	+	2.52899i	−0.108529	+	0.187979i	−0.915175	−	0.403057i	$-0.867948\pi$
$181$	−1.46011	+	2.52899i	−0.108529	+	0.187979i	0.806645	+	0.591036i	$0.201281\pi$
$182$	7.68878	+	4.43912i	0.569931	+	0.329050i
$183$	5.41327	−	3.12535i	0.400160	−	0.231033i
$184$	0.363708			0.0268129
$185$	3.70057	−	13.0884i	0.272071	−	0.962277i
$186$	3.49115			0.255984
$187$	3.63075	−	2.09622i	0.265507	−	0.153291i
$188$	−1.92038	−	1.10873i	−0.140058	−	0.0808628i
$189$	−2.07786	+	3.59896i	−0.151142	+	0.261786i
$190$	16.0952	+	4.39694i	1.16767	+	0.318988i
$191$	20.4211			1.47762			0.738808	−	0.673916i	$-0.235389\pi$
$191$	20.4211			1.47762			0.738808	+	0.673916i	$0.235389\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$			4.78676i			0.344558i	0.985048	+	0.172279i	$0.0551131\pi$
$193$			4.78676i			0.344558i	−0.985048	+	0.172279i	$0.944887\pi$
$194$	−5.82972	−	10.0974i	−0.418550	−	0.724949i
$195$	4.62031	−	1.21388i	0.330867	−	0.0869281i
$196$	10.2700			0.733574
$197$	−3.56459	+	2.05802i	−0.253967	+	0.146628i	−0.621579	−	0.783351i	$-0.713509\pi$
$197$	−3.56459	+	2.05802i	−0.253967	+	0.146628i	0.367613	+	0.929979i	$0.380175\pi$
$198$	−3.14154	−	1.81377i	−0.223260	−	0.128899i
$199$	−6.59431			−0.467458			−0.233729	−	0.972302i	$-0.575093\pi$
$199$	−6.59431			−0.467458			−0.233729	+	0.972302i	$0.575093\pi$
$200$	2.54212	−	4.30553i	0.179755	−	0.304447i
$201$	7.73561	+	13.3985i	0.545628	+	0.945055i
$202$	9.04876	−	5.22430i	0.636668	−	0.367581i
$203$	18.5553	+	10.7129i	1.30232	+	0.751897i
$204$	−0.577862	+	1.00089i	−0.0404584	+	0.0700760i
$205$	19.0193	+	19.2057i	1.32836	+	1.34139i
$206$	4.88130	+	8.45466i	0.340096	+	0.589064i
$207$	0.314980	−	0.181854i	0.0218926	−	0.0126397i
$208$		−	2.13639i		−	0.148132i
$209$	−13.5339	+	23.4413i	−0.936157	+	1.62147i
$210$	6.60275	−	6.53865i	0.455633	−	0.451209i
$211$	−3.49904			−0.240884			−0.120442	−	0.992720i	$-0.538431\pi$
$211$	−3.49904			−0.240884			−0.120442	+	0.992720i	$0.538431\pi$
$212$			10.9398i			0.751346i
$213$	0.126846	−	0.0732348i	0.00869137	−	0.00501797i
$214$	−1.22493			−0.0837346
$215$	26.6783	+	7.28808i	1.81944	+	0.497043i
$216$	1.00000			0.0680414
$217$	−12.5645	−	7.25413i	−0.852935	−	0.492442i
$218$	8.57040	+	4.94812i	0.580461	+	0.335129i
$219$	4.81687	−	8.34307i	0.325494	−	0.563772i
$220$	5.70760	+	5.76355i	0.384806	+	0.388579i
$221$	2.46908			0.166088
$222$	−6.08252	−	0.0539383i	−0.408232	−	0.00362010i
$223$		−	11.9286i		−	0.798799i	−0.916777	−	0.399400i	$-0.869219\pi$
$223$		−	11.9286i		−	0.798799i	0.916777	−	0.399400i	$-0.130781\pi$
$224$	−2.07786	−	3.59896i	−0.138833	−	0.240466i
$225$	0.0487778	−	4.99976i	0.00325185	−	0.333317i
$226$	−4.18907	+	7.25569i	−0.278653	+	0.482641i
$227$	−6.93104	−	4.00164i	−0.460030	−	0.265598i	0.252027	−	0.967720i	$-0.418903\pi$
$227$	−6.93104	−	4.00164i	−0.460030	−	0.265598i	−0.712057	+	0.702122i	$0.752236\pi$
$228$		−	7.46174i		−	0.494165i
$229$	−1.64726	+	2.85314i	−0.108854	+	0.188541i	−0.915306	−	0.402759i	$-0.868051\pi$
$229$	−1.64726	+	2.85314i	−0.108854	+	0.188541i	0.806452	+	0.591299i	$0.201385\pi$
$230$	−0.786581	+	0.206657i	−0.0518656	+	0.0136265i
$231$	7.53753	+	13.0554i	0.495933	+	0.858981i
$232$		−	5.15572i		−	0.338490i
$233$			9.21492i			0.603690i	0.953357	+	0.301845i	$0.0976024\pi$
$233$			9.21492i			0.603690i	−0.953357	+	0.301845i	$0.902398\pi$
$234$	−1.06819	−	1.85017i	−0.0698301	−	0.120949i
$235$	4.78314	+	1.30668i	0.312018	+	0.0852383i
$236$	−9.77013			−0.635982
$237$	−13.6067	+	7.85583i	−0.883850	+	0.510291i
$238$	4.15940	−	2.40143i	0.269614	−	0.155662i
$239$	9.36223	+	16.2159i	0.605592	+	1.04892i	0.991958	+	0.126570i	$0.0403970\pi$
$239$	9.36223	+	16.2159i	0.605592	+	1.04892i	−0.386366	+	0.922346i	$0.626270\pi$
$240$	−2.15703	−	0.589266i	−0.139236	−	0.0380369i
$241$	8.14642	−	14.1100i	0.524757	−	0.908906i	−0.474827	−	0.880079i	$-0.657489\pi$
$241$	8.14642	−	14.1100i	0.524757	−	0.908906i	0.999584	−	0.0288271i	$-0.00917722\pi$
$242$	−1.86978	+	1.07952i	−0.120194	+	0.0693942i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	3.12535	+	5.41327i	0.200080	+	0.346549i
$245$	−22.2107	+	5.83538i	−1.41899	+	0.372809i
$246$	6.04397	−	10.4685i	0.385350	−	0.667445i
$247$	−13.8055	+	7.97059i	−0.878420	+	0.507156i
$248$			3.49115i			0.221688i
$249$	−13.8311			−0.876512
$250$	−3.05140	+	10.7559i	−0.192988	+	0.680262i
$251$	16.7386			1.05653			0.528264	−	0.849080i	$-0.322843\pi$
$251$	16.7386			1.05653			0.528264	+	0.849080i	$0.322843\pi$
$252$	−3.59896	−	2.07786i	−0.226713	−	0.130893i
$253$		−	1.31936i		−	0.0829477i
$254$	−2.63911	+	4.57107i	−0.165592	+	0.286814i
$255$	0.681028	−	2.49293i	0.0426476	−	0.156113i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.15672	−	3.55458i	0.384046	−	0.221729i	−0.295531	−	0.955333i	$-0.595497\pi$
$257$	6.15672	−	3.55458i	0.384046	−	0.221729i	0.679577	+	0.733604i	$0.262163\pi$
$258$		−	12.3681i		−	0.770002i
$259$	21.7787	+	12.8328i	1.35326	+	0.797389i
$260$	1.21388	+	4.62031i	0.0752819	+	0.286540i
$261$	−2.57786	−	4.46499i	−0.159566	−	0.276376i
$262$	13.1799	+	7.60944i	0.814259	+	0.470113i
$263$	6.83430	+	3.94578i	0.421421	+	0.243307i	0.695685	−	0.718347i	$-0.255101\pi$
$263$	6.83430	+	3.94578i	0.421421	+	0.243307i	−0.274264	+	0.961654i	$0.588434\pi$
$264$	1.81377	−	3.14154i	0.111630	−	0.193348i
$265$	−6.21591	−	23.6591i	−0.381840	−	1.45337i
$266$	−15.5045	+	26.8545i	−0.950639	+	1.64656i
$267$			11.3593i			0.695179i
$268$	−13.3985	+	7.73561i	−0.818442	+	0.472528i
$269$	−0.806147			−0.0491516			−0.0245758	−	0.999698i	$-0.507824\pi$
$269$	−0.806147			−0.0491516			−0.0245758	+	0.999698i	$0.507824\pi$
$270$	−2.16267	+	0.568195i	−0.131616	+	0.0345792i
$271$	−4.63125	−	8.02156i	−0.281329	−	0.487275i	0.690384	−	0.723443i	$-0.257442\pi$
$271$	−4.63125	−	8.02156i	−0.281329	−	0.487275i	−0.971712	+	0.236168i	$0.924108\pi$
$272$	−1.00089	−	0.577862i	−0.0606876	−	0.0350380i
$273$			8.87824i			0.537336i
$274$	−3.47185	−	6.01343i	−0.209742	−	0.363284i
$275$	−15.6185	−	9.22165i	−0.941830	−	0.556087i
$276$	0.181854	+	0.314980i	0.0109463	+	0.0189596i
$277$	−5.54699	−	3.20256i	−0.333287	−	0.192423i	0.324013	−	0.946053i	$-0.394968\pi$
$277$	−5.54699	−	3.20256i	−0.333287	−	0.192423i	−0.657299	+	0.753630i	$0.728301\pi$
$278$	11.9435	+	6.89557i	0.716322	+	0.413569i
$279$	1.74558	+	3.02342i	0.104505	+	0.181008i
$280$	6.53865	+	6.60275i	0.390759	+	0.394590i
$281$	−4.39344	−	7.60967i	−0.262091	−	0.453955i	0.704706	−	0.709499i	$-0.251079\pi$
$281$	−4.39344	−	7.60967i	−0.262091	−	0.453955i	−0.966797	+	0.255544i	$0.917745\pi$
$282$		−	2.21747i		−	0.132048i
$283$	−8.33863	−	4.81431i	−0.495680	−	0.286181i	0.231248	−	0.972895i	$-0.425719\pi$
$283$	−8.33863	−	4.81431i	−0.495680	−	0.286181i	−0.726928	+	0.686714i	$0.759053\pi$
$284$	0.0732348	+	0.126846i	0.00434569	+	0.00752695i
$285$	4.23972	+	16.1373i	0.251139	+	0.955891i
$286$	−7.74984			−0.458257
$287$	−43.5041	+	25.1171i	−2.56796	+	1.48261i
$288$			1.00000i			0.0589256i
$289$	−7.83215	+	13.5657i	−0.460715	+	0.797981i
$290$	2.92945	+	11.1501i	0.172023	+	0.654759i
$291$	5.82972	−	10.0974i	0.341744	−	0.591919i
$292$	8.34307	+	4.81687i	0.488241	+	0.281886i
$293$	15.0103	+	8.66622i	0.876913	+	0.506286i	0.869639	−	0.493687i	$-0.164351\pi$
$293$	15.0103	+	8.66622i	0.876913	+	0.506286i	0.00727385	+	0.999974i	$0.497685\pi$
$294$	5.13502	+	8.89411i	0.299480	+	0.518715i
$295$	21.1296	−	5.55134i	1.23021	−	0.323211i
$296$	0.0539383	−	6.08252i	0.00313510	−	0.353539i
$297$		−	3.62754i		−	0.210491i
$298$	4.79019	−	2.76562i	0.277488	−	0.160208i
$299$	0.388511	−	0.672920i	0.0224681	−	0.0389160i
$300$	4.99976	+	0.0487778i	0.288661	+	0.00281619i
$301$	−25.6991	+	44.5122i	−1.48127	+	2.56564i
$302$		−	22.2298i		−	1.27918i
$303$	9.04876	+	5.22430i	0.519838	+	0.300128i
$304$	7.46174			0.427960
$305$	−9.83490	−	9.93132i	−0.563145	−	0.568666i
$306$	−1.15572			−0.0660683
$307$			28.2983i			1.61507i	0.589820	+	0.807535i	$0.299199\pi$
$307$			28.2983i			1.61507i	−0.589820	+	0.807535i	$0.700801\pi$
$308$	−13.0554	+	7.53753i	−0.743899	+	0.429490i
$309$	−4.88130	+	8.45466i	−0.277687	+	0.480969i
$310$	−1.98365	−	7.55022i	−0.112664	−	0.428823i
$311$	−1.26886	−	2.19774i	−0.0719506	−	0.124622i	0.827806	−	0.561015i	$-0.189589\pi$
$311$	−1.26886	−	2.19774i	−0.0719506	−	0.124622i	−0.899756	+	0.436393i	$0.856256\pi$
$312$	1.85017	−	1.06819i	0.104745	−	0.0604746i
$313$	9.42952	−	5.44413i	0.532988	−	0.307721i	−0.209245	−	0.977863i	$-0.567100\pi$
$313$	9.42952	−	5.44413i	0.532988	−	0.307721i	0.742232	+	0.670143i	$0.233767\pi$
$314$	4.24065	−	7.34502i	0.239314	−	0.414504i
$315$	8.96401	+	2.44882i	0.505065	+	0.137976i
$316$	−7.85583	−	13.6067i	−0.441925	−	0.765437i
$317$	0.878780	−	0.507364i	0.0493572	−	0.0284964i	−0.475118	−	0.879922i	$-0.657595\pi$
$317$	0.878780	−	0.507364i	0.0493572	−	0.0284964i	0.524476	+	0.851426i	$0.324261\pi$
$318$	−9.47411	+	5.46988i	−0.531282	+	0.306736i
$319$	−18.7026			−1.04714
$320$	0.589266	−	2.15703i	0.0329409	−	0.120581i
$321$	−0.612466	−	1.06082i	−0.0341845	−	0.0592093i
$322$		−	1.51147i		−	0.0842308i
$323$			8.62370i			0.479836i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−5.25047	−	9.30250i	−0.291244	−	0.516010i
$326$	12.4039	−	21.4841i	0.686986	−	1.18990i
$327$			9.89625i			0.547264i
$328$	10.4685	+	6.04397i	0.578025	+	0.333723i
$329$	−4.60760	+	7.98059i	−0.254025	+	0.439984i
$330$	−2.13758	+	7.82470i	−0.117670	+	0.430736i
$331$	−4.88646	−	8.46359i	−0.268584	−	0.465201i	0.699912	−	0.714229i	$-0.253222\pi$
$331$	−4.88646	−	8.46359i	−0.268584	−	0.465201i	−0.968496	+	0.249028i	$0.919889\pi$
$332$		−	13.8311i		−	0.759082i
$333$	−2.99455	−	5.29459i	−0.164100	−	0.290142i
$334$	−11.5413			−0.631509
$335$	24.5812	−	24.3425i	1.34301	−	1.32997i
$336$	2.07786	−	3.59896i	0.113357	−	0.196339i
$337$	8.78297	+	5.07085i	0.478439	+	0.276227i	0.719766	−	0.694217i	$-0.244249\pi$
$337$	8.78297	+	5.07085i	0.478439	+	0.276227i	−0.241327	+	0.970444i	$0.577583\pi$
$338$	7.30565	+	4.21792i	0.397375	+	0.229425i
$339$	−8.37815			−0.455038
$340$	2.49293	+	0.681028i	0.135198	+	0.0369339i
$341$	12.6643			0.685809
$342$	6.46205	−	3.73087i	0.349428	−	0.201742i
$343$		−	13.5894i		−	0.733757i
$344$	12.3681			0.666841
$345$	−0.572260	−	0.577871i	−0.0308095	−	0.0311115i
$346$	1.81075	−	3.13632i	0.0973468	−	0.168610i
$347$			16.3722i			0.878906i	0.898266	+	0.439453i	$0.144828\pi$
$347$			16.3722i			0.878906i	−0.898266	+	0.439453i	$0.855172\pi$
$348$	4.46499	−	2.57786i	0.239348	−	0.138188i
$349$	7.28289	+	12.6143i	0.389844	+	0.675230i	0.992428	−	0.122826i	$-0.0391956\pi$
$349$	7.28289	+	12.6143i	0.389844	+	0.675230i	−0.602584	+	0.798055i	$0.705862\pi$
$350$	−17.8926	−	10.5644i	−0.956400	−	0.564689i
$351$	1.06819	−	1.85017i	0.0570160	−	0.0987546i
$352$	3.14154	+	1.81377i	0.167445	+	0.0966742i
$353$	20.7462	−	11.9778i	1.10421	−	0.637516i	0.166887	−	0.985976i	$-0.446629\pi$
$353$	20.7462	−	11.9778i	1.10421	−	0.637516i	0.937324	+	0.348460i	$0.113295\pi$
$354$	−4.88507	−	8.46118i	−0.259638	−	0.449707i
$355$	−0.230456	−	0.232716i	−0.0122314	−	0.0123513i
$356$	−11.3593			−0.602042
$357$	4.15940	+	2.40143i	0.220139	+	0.127097i
$358$	−10.8646	+	6.27265i	−0.574210	+	0.331520i
$359$	−31.6699			−1.67147			−0.835736	−	0.549132i	$-0.814958\pi$
$359$	−31.6699			−1.67147			−0.835736	+	0.549132i	$0.814958\pi$
$360$	−0.568195	−	2.16267i	−0.0299465	−	0.113983i
$361$	−18.3387	−	31.7636i	−0.965197	−	1.67177i
$362$		−	2.92023i		−	0.153484i
$363$	−1.86978	−	1.07952i	−0.0981382	−	0.0566601i
$364$	−8.87824			−0.465346
$365$	−20.7802	−	5.67683i	−1.08769	−	0.297139i
$366$	−3.12535	+	5.41327i	−0.163365	+	0.282956i
$367$	−18.6346	−	10.7587i	−0.972720	−	0.561600i	−0.0726556	−	0.997357i	$-0.523147\pi$
$367$	−18.6346	−	10.7587i	−0.972720	−	0.561600i	−0.900064	+	0.435757i	$0.856481\pi$
$368$	−0.314980	+	0.181854i	−0.0164195	+	0.00947979i
$369$	12.0879			0.629273
$370$	3.33941	+	13.1852i	0.173607	+	0.685464i
$371$	45.4626			2.36030
$372$	−3.02342	+	1.74558i	−0.156757	+	0.0905039i
$373$	−8.45399	−	4.88092i	−0.437731	−	0.252724i	0.264904	−	0.964275i	$-0.414660\pi$
$373$	−8.45399	−	4.88092i	−0.437731	−	0.252724i	−0.702635	+	0.711551i	$0.747993\pi$
$374$	−2.09622	+	3.63075i	−0.108393	+	0.187742i
$375$	−10.8406	+	2.73535i	−0.559804	+	0.141253i
$376$	2.21747			0.114357
$377$	−9.53895	−	5.50732i	−0.491281	−	0.283641i
$378$		−	4.15572i		−	0.213747i
$379$	11.7727	+	20.3909i	0.604722	+	1.04741i	0.992095	+	0.125486i	$0.0400489\pi$
$379$	11.7727	+	20.3909i	0.604722	+	1.04741i	−0.387374	+	0.921923i	$0.626618\pi$
$380$	−16.1373	+	4.23972i	−0.827826	+	0.217493i
$381$	−5.27821			−0.270411
$382$	−17.6852	+	10.2105i	−0.904851	+	0.522416i
$383$	−5.85258	−	3.37899i	−0.299053	−	0.172658i	0.342965	−	0.939348i	$-0.388569\pi$
$383$	−5.85258	−	3.37899i	−0.299053	−	0.172658i	−0.642017	+	0.766690i	$0.721902\pi$
$384$	−1.00000			−0.0510310
$385$	23.9517	−	23.7192i	1.22069	−	1.20884i
$386$	−2.39338	−	4.14545i	−0.121820	−	0.210998i
$387$	10.7111	−	6.18403i	0.544474	−	0.314352i
$388$	10.0974	+	5.82972i	0.512617	+	0.295959i
$389$	2.80650	−	4.86100i	0.142295	−	0.246462i	−0.786065	−	0.618143i	$-0.787885\pi$
$389$	2.80650	−	4.86100i	0.142295	−	0.246462i	0.928361	+	0.371681i	$0.121218\pi$
$390$	−3.39436	+	3.36141i	−0.171880	+	0.170212i
$391$	−0.210173	−	0.364030i	−0.0106289	−	0.0184098i
$392$	−8.89411	+	5.13502i	−0.449221	+	0.259358i
$393$			15.2189i			0.767691i
$394$	2.05802	−	3.56459i	0.103681	−	0.179581i
$395$	24.7209	+	24.9632i	1.24384	+	1.25604i
$396$	3.62754			0.182291
$397$		−	24.5689i		−	1.23308i	−0.787324	−	0.616540i	$-0.788534\pi$
$397$		−	24.5689i		−	1.23308i	0.787324	−	0.616540i	$-0.211466\pi$
$398$	5.71084	−	3.29715i	0.286258	−	0.165271i
$399$	−31.0089			−1.55239
$400$	−0.0487778	+	4.99976i	−0.00243889	+	0.249988i
$401$	33.1745			1.65665			0.828327	−	0.560245i	$-0.189293\pi$
$401$	33.1745			1.65665			0.828327	+	0.560245i	$0.189293\pi$
$402$	−13.3985	−	7.73561i	−0.668255	−	0.385817i
$403$	6.45921	+	3.72923i	0.321756	+	0.185766i
$404$	−5.22430	+	9.04876i	−0.259919	+	0.450193i
$405$	−1.57341	−	1.58883i	−0.0781832	−	0.0789497i
$406$	−21.4258			−1.06334
$407$	−22.0646	−	0.195663i	−1.09370	−	0.00969867i
$408$		−	1.15572i		−	0.0572168i
$409$	−13.1498	−	22.7761i	−0.650215	−	1.12621i	−0.983070	−	0.183228i	$-0.941345\pi$
$409$	−13.1498	−	22.7761i	−0.650215	−	1.12621i	0.332855	−	0.942978i	$-0.391988\pi$
$410$	−26.0740	−	7.12301i	−1.28770	−	0.351780i
$411$	3.47185	−	6.01343i	0.171254	−	0.296620i
$412$	−8.45466	−	4.88130i	−0.416531	−	0.240484i
$413$			40.6020i			1.99789i
$414$	−0.181854	+	0.314980i	−0.00893763	+	0.0154804i
$415$	7.85877	+	29.9122i	0.385772	+	1.46833i
$416$	1.06819	+	1.85017i	0.0523725	+	0.0907119i
$417$			13.7911i			0.675355i
$418$		−	27.0677i		−	1.32393i
$419$	−16.1912	−	28.0440i	−0.790991	−	1.37004i	−0.925354	−	0.379105i	$-0.876232\pi$
$419$	−16.1912	−	28.0440i	−0.790991	−	1.37004i	0.134363	−	0.990932i	$-0.457101\pi$
$420$	−2.44882	+	8.96401i	−0.119490	+	0.437399i
$421$	7.22310			0.352032			0.176016	−	0.984387i	$-0.443679\pi$
$421$	7.22310			0.352032			0.176016	+	0.984387i	$0.443679\pi$
$422$	3.03026	−	1.74952i	0.147511	−	0.0851652i
$423$	1.92038	−	1.10873i	0.0933723	−	0.0539085i
$424$	−5.46988	−	9.47411i	−0.265641	−	0.460103i
$425$	−5.77834	−	0.0563736i	−0.280291	−	0.00273452i
$426$	−0.0732348	+	0.126846i	−0.00354824	+	0.00614573i
$427$	22.4960	−	12.9881i	1.08866	−	0.628538i
$428$	1.06082	−	0.612466i	0.0512768	−	0.0296046i
$429$	−3.87492	−	6.71155i	−0.187083	−	0.324037i
$430$	−26.7481	+	7.02747i	−1.28991	+	0.338895i
$431$	−2.04698	+	3.54547i	−0.0985995	+	0.170779i	−0.911105	−	0.412174i	$-0.864770\pi$
$431$	−2.04698	+	3.54547i	−0.0985995	+	0.170779i	0.812506	+	0.582953i	$0.198103\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$			1.11862i			0.0537574i	0.999639	+	0.0268787i	$0.00855678\pi$
$433$			1.11862i			0.0537574i	−0.999639	+	0.0268787i	$0.991443\pi$
$434$	14.5083			0.696419
$435$	−8.19158	+	8.11205i	−0.392756	+	0.388943i
$436$	−9.89625			−0.473944
$437$	2.35030	+	1.35695i	0.112430	+	0.0649115i
$438$			9.63375i			0.460318i
$439$	−2.98041	+	5.16221i	−0.142247	+	0.246379i	−0.928342	−	0.371726i	$-0.878766\pi$
$439$	−2.98041	+	5.16221i	−0.142247	+	0.246379i	0.786095	+	0.618105i	$0.212099\pi$
$440$	−7.82470	−	2.13758i	−0.373028	−	0.101905i
$441$	−5.13502	+	8.89411i	−0.244525	+	0.423529i
$442$	−2.13828	+	1.23454i	−0.101708	+	0.0587210i
$443$		−	10.0305i		−	0.476563i	−0.971196	−	0.238282i	$-0.923416\pi$
$443$		−	10.0305i		−	0.476563i	0.971196	−	0.238282i	$-0.0765841\pi$
$444$	5.29459	−	2.99455i	0.251270	−	0.142115i
$445$	24.5665	−	6.45430i	1.16456	−	0.305963i
$446$	5.96431	+	10.3305i	0.282418	+	0.489163i
$447$	4.79019	+	2.76562i	0.226568	+	0.130809i
$448$	3.59896	+	2.07786i	0.170035	+	0.0981697i
$449$	7.09889	−	12.2956i	0.335017	−	0.580267i	−0.648471	−	0.761239i	$-0.724591\pi$
$449$	7.09889	−	12.2956i	0.335017	−	0.580267i	0.983488	+	0.180972i	$0.0579245\pi$
$450$	2.45764	+	4.35431i	0.115854	+	0.205264i
$451$	21.9248	−	37.9748i	1.03240	−	1.78816i
$452$		−	8.37815i		−	0.394075i
$453$	19.2515	−	11.1149i	0.904517	−	0.522223i
$454$	8.00328			0.375613
$455$	19.2007	−	5.04457i	0.900144	−	0.236493i
$456$	3.73087	+	6.46205i	0.174714	+	0.302613i
$457$	9.49114	+	5.47971i	0.443977	+	0.256330i	0.705283	−	0.708926i	$-0.250820\pi$
$457$	9.49114	+	5.47971i	0.443977	+	0.256330i	−0.261306	+	0.965256i	$0.584153\pi$
$458$		−	3.29452i		−	0.153943i
$459$	−0.577862	−	1.00089i	−0.0269723	−	0.0467174i
$460$	0.577871	−	0.572260i	0.0269434	−	0.0266818i
$461$	13.1296	+	22.7411i	0.611506	+	1.05916i	0.990987	+	0.133959i	$0.0427692\pi$
$461$	13.1296	+	22.7411i	0.611506	+	1.05916i	−0.379481	+	0.925199i	$0.623897\pi$
$462$	−13.0554	−	7.53753i	−0.607391	−	0.350677i
$463$	21.8170	+	12.5961i	1.01392	+	0.585388i	0.912338	−	0.409439i	$-0.134275\pi$
$463$	21.8170	+	12.5961i	1.01392	+	0.585388i	0.101584	+	0.994827i	$0.467609\pi$
$464$	2.57786	+	4.46499i	0.119674	+	0.207282i
$465$	5.54685	−	5.49300i	0.257229	−	0.254732i
$466$	−4.60746	−	7.98036i	−0.213437	−	0.369683i
$467$		−	22.8651i		−	1.05807i	−0.848600	−	0.529035i	$-0.822554\pi$
$467$		−	22.8651i		−	1.05807i	0.848600	−	0.529035i	$-0.177446\pi$
$468$	1.85017	+	1.06819i	0.0855240	+	0.0493773i
$469$	32.1471	+	55.6803i	1.48441	+	2.57108i
$470$	−4.79566	+	1.25995i	−0.221207	+	0.0581174i
$471$	8.48130			0.390798
$472$	8.46118	−	4.88507i	0.389458	−	0.224853i
$473$		−	44.8656i		−	2.06292i
$474$	7.85583	−	13.6067i	0.360830	−	0.624977i
$475$	32.4907	−	18.3382i	1.49078	−	0.841416i
$476$	−2.40143	+	4.15940i	−0.110070	+	0.190646i
$477$	−9.47411	−	5.46988i	−0.433790	−	0.250449i
$478$	−16.2159	−	9.36223i	−0.741696	−	0.428218i
$479$	12.4085	+	21.4922i	0.566960	+	0.982004i	0.996864	+	0.0791292i	$0.0252140\pi$
$479$	12.4085	+	21.4922i	0.566960	+	0.982004i	−0.429904	+	0.902874i	$0.641453\pi$
$480$	2.16267	−	0.568195i	0.0987121	−	0.0259344i
$481$	−11.1961	−	6.59711i	−0.510497	−	0.300802i
$482$			16.2928i			0.742119i
$483$	1.30897	−	0.755734i	0.0595602	−	0.0343871i
$484$	1.07952	−	1.86978i	0.0490691	−	0.0849902i
$485$	−25.1497	−	6.87051i	−1.14199	−	0.311974i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$		−	12.1033i		−	0.548454i	−0.961665	−	0.274227i	$-0.911578\pi$
$487$		−	12.1033i		−	0.548454i	0.961665	−	0.274227i	$-0.0884220\pi$
$488$	−5.41327	−	3.12535i	−0.245047	−	0.141478i
$489$	24.8077			1.12184
$490$	16.3174	−	16.1590i	0.737144	−	0.729987i
$491$	−33.2720			−1.50154			−0.750772	−	0.660562i	$-0.770318\pi$
$491$	−33.2720			−1.50154			−0.750772	+	0.660562i	$0.770318\pi$
$492$			12.0879i			0.544967i
$493$	−5.16029	+	2.97930i	−0.232408	+	0.134181i
$494$	7.97059	−	13.8055i	0.358614	−	0.621137i
$495$	−7.84518	+	2.06115i	−0.352615	+	0.0926417i
$496$	−1.74558	−	3.02342i	−0.0783786	−	0.135756i
$497$	0.527139	−	0.304344i	0.0236454	−	0.0136517i
$498$	11.9781	−	6.91556i	0.536752	−	0.309894i
$499$	−9.98553	+	17.2955i	−0.447014	+	0.774251i	−0.998190	−	0.0601381i	$-0.980846\pi$
$499$	−9.98553	+	17.2955i	−0.447014	+	0.774251i	0.551176	+	0.834389i	$0.314179\pi$
$500$	−2.73535	−	10.8406i	−0.122328	−	0.484805i
$501$	−5.77063	−	9.99502i	−0.257813	−	0.446545i
$502$	−14.4960	+	8.36928i	−0.646989	+	0.373539i
$503$	2.50589	−	1.44678i	0.111732	−	0.0645086i	−0.443092	−	0.896476i	$-0.646119\pi$
$503$	2.50589	−	1.44678i	0.111732	−	0.0645086i	0.554825	+	0.831967i	$0.312785\pi$
$504$	4.15572			0.185111
$505$	6.15700	−	22.5379i	0.273983	−	1.00292i
$506$	0.659682	+	1.14260i	0.0293264	+	0.0507949i
$507$			8.43584i			0.374649i
$508$		−	5.27821i		−	0.234183i
$509$	−6.90016	−	11.9514i	−0.305844	−	0.529738i	0.671605	−	0.740910i	$-0.265605\pi$
$509$	−6.90016	−	11.9514i	−0.305844	−	0.529738i	−0.977449	+	0.211172i	$0.932272\pi$
$510$	0.656676	+	2.49945i	0.0290781	+	0.110678i
$511$	20.0176	−	34.6715i	0.885526	−	1.53378i
$512$		−	1.00000i		−	0.0441942i
$513$	6.46205	+	3.73087i	0.285307	+	0.164722i
$514$	−3.55458	+	6.15672i	−0.156786	+	0.271561i
$515$	21.0582	+	5.75277i	0.927935	+	0.253497i
$516$	6.18403	+	10.7111i	0.272237	+	0.471528i
$517$		−	8.04396i		−	0.353773i
$518$	−25.2773	−	0.224153i	−1.11062	−	0.00984871i
$519$	3.62151			0.158967
$520$	−3.36141	−	3.39436i	−0.147408	−	0.148853i
$521$	−4.95593	+	8.58393i	−0.217123	+	0.376069i	−0.953927	−	0.300038i	$-0.903001\pi$
$521$	−4.95593	+	8.58393i	−0.217123	+	0.376069i	0.736804	+	0.676106i	$0.236334\pi$
$522$	4.46499	+	2.57786i	0.195427	+	0.112830i
$523$	−34.6236	−	19.9900i	−1.51399	−	0.874100i	−0.999866	−	0.0163822i	$-0.994785\pi$
$523$	−34.6236	−	19.9900i	−1.51399	−	0.874100i	−0.514120	−	0.857718i	$-0.671882\pi$
$524$	−15.2189			−0.664840
$525$	0.202707	−	20.7776i	0.00884686	−	0.906810i
$526$	−7.89156			−0.344089
$527$	3.49424	−	2.01740i	0.152212	−	0.0878794i
$528$			3.62754i			0.157868i
$529$	22.8677			0.994249
$530$	17.2127	+	17.3814i	0.747672	+	0.755002i
$531$	4.88507	−	8.46118i	0.211994	−	0.367184i
$532$		−	31.0089i		−	1.34441i
$533$	22.3647	−	12.9123i	0.968724	−	0.559293i
$534$	−5.67966	−	9.83745i	−0.245783	−	0.425708i
$535$	−1.94621	+	1.92732i	−0.0841420	+	0.0833252i
$536$	7.73561	−	13.3985i	0.334127	−	0.578726i
$537$	−10.8646	−	6.27265i	−0.468840	−	0.270685i
$538$	0.698143	−	0.403073i	0.0300991	−	0.0173777i
$539$	18.6275	+	32.2637i	0.802342	+	1.38970i
$540$	1.58883	−	1.57341i	0.0683725	−	0.0677087i
$541$	−7.11266			−0.305797			−0.152899	−	0.988242i	$-0.548861\pi$
$541$	−7.11266			−0.305797			−0.152899	+	0.988242i	$0.548861\pi$
$542$	8.02156	+	4.63125i	0.344556	+	0.198929i
$543$	2.52899	−	1.46011i	0.108529	−	0.0626595i
$544$	1.15572			0.0495512
$545$	21.4024	−	5.62300i	0.916776	−	0.240863i
$546$	−4.43912	−	7.68878i	−0.189977	−	0.329050i
$547$		−	10.4605i		−	0.447260i	−0.974674	−	0.223630i	$-0.928209\pi$
$547$		−	10.4605i		−	0.447260i	0.974674	−	0.223630i	$-0.0717907\pi$
$548$	6.01343	+	3.47185i	0.256881	+	0.148310i
$549$	−6.25070			−0.266774
$550$	18.1368	+	0.176943i	0.773357	+	0.00754489i
$551$	19.2353	−	33.3166i	0.819452	−	1.41933i
$552$	−0.314980	−	0.181854i	−0.0134064	−	0.00774021i
$553$	−56.5457	+	32.6467i	−2.40457	+	1.38828i
$554$	6.40512			0.272127
$555$	−9.74898	+	9.48459i	−0.413821	+	0.402598i
$556$	−13.7911			−0.584874
$557$	−11.6439	+	6.72259i	−0.493367	+	0.284845i	−0.725970	−	0.687726i	$-0.758609\pi$
$557$	−11.6439	+	6.72259i	−0.493367	+	0.284845i	0.232603	+	0.972572i	$0.425276\pi$
$558$	−3.02342	−	1.74558i	−0.127992	−	0.0738961i
$559$	13.2115	−	22.8830i	0.558787	−	0.967847i
$560$	−8.96401	−	2.44882i	−0.378798	−	0.103482i
$561$	−4.19243			−0.177005
$562$	7.60967	+	4.39344i	0.320994	+	0.185326i
$563$			7.95921i			0.335441i	0.985835	+	0.167720i	$0.0536406\pi$
$563$			7.95921i			0.335441i	−0.985835	+	0.167720i	$0.946359\pi$
$564$	1.10873	+	1.92038i	0.0466862	+	0.0808628i
$565$	4.76042	+	18.1192i	0.200272	+	0.762280i
$566$	9.62862			0.404721
$567$	3.59896	−	2.07786i	0.151142	−	0.0872620i
$568$	−0.126846	−	0.0732348i	−0.00532236	−	0.00307287i
$569$	−6.60381			−0.276846			−0.138423	−	0.990373i	$-0.544203\pi$
$569$	−6.60381			−0.276846			−0.138423	+	0.990373i	$0.544203\pi$
$570$	−11.7404	−	11.8554i	−0.491749	−	0.496570i
$571$	8.02353	+	13.8972i	0.335774	+	0.581578i	0.983633	−	0.180182i	$-0.0576687\pi$
$571$	8.02353	+	13.8972i	0.335774	+	0.581578i	−0.647859	+	0.761760i	$0.724335\pi$
$572$	6.71155	−	3.87492i	0.280624	−	0.162018i
$573$	−17.6852	−	10.2105i	−0.738808	−	0.426551i
$574$	25.1171	−	43.5041i	1.04837	−	1.81582i
$575$	−0.924590	+	1.56595i	−0.0385581	+	0.0653048i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	21.9490	−	12.6723i	0.913749	−	0.527553i	0.0321136	−	0.999484i	$-0.489776\pi$
$577$	21.9490	−	12.6723i	0.913749	−	0.527553i	0.881636	+	0.471931i	$0.156443\pi$
$578$		−	15.6643i		−	0.651549i
$579$	2.39338	−	4.14545i	0.0994654	−	0.172279i
$580$	−8.11205	−	8.19158i	−0.336835	−	0.340137i
$581$	−57.4783			−2.38460
$582$			11.6594i			0.483300i
$583$	−34.3677	+	19.8422i	−1.42336	+	0.821780i
$584$	−9.63375			−0.398647
$585$	−4.60825	−	1.25890i	−0.190528	−	0.0520491i
$586$	−17.3324			−0.715997
$587$	−1.63238	−	0.942454i	−0.0673754	−	0.0388992i	0.465934	−	0.884820i	$-0.345718\pi$
$587$	−1.63238	−	0.942454i	−0.0673754	−	0.0388992i	−0.533309	+	0.845920i	$0.679052\pi$
$588$	−8.89411	−	5.13502i	−0.366787	−	0.211765i
$589$	−13.0250	+	22.5600i	−0.536687	+	0.929568i
$590$	−15.5231	+	15.3724i	−0.639076	+	0.632872i
$591$	4.11603			0.169311
$592$	2.99455	+	5.29459i	0.123075	+	0.217606i
$593$		−	5.11792i		−	0.210168i	−0.994463	−	0.105084i	$-0.966489\pi$
$593$		−	5.11792i		−	0.210168i	0.994463	−	0.105084i	$-0.0335111\pi$
$594$	1.81377	+	3.14154i	0.0744199	+	0.128899i
$595$	2.83016	−	10.3599i	0.116025	−	0.424715i
$596$	−2.76562	+	4.79019i	−0.113284	+	0.196214i
$597$	5.71084	+	3.29715i	0.233729	+	0.134943i
$598$			0.777021i			0.0317748i
$599$	−1.84896	+	3.20250i	−0.0755466	+	0.130851i	−0.901324	−	0.433146i	$-0.857404\pi$
$599$	−1.84896	+	3.20250i	−0.0755466	+	0.130851i	0.825777	+	0.563996i	$0.190737\pi$
$600$	−4.35431	+	2.45764i	−0.177764	+	0.100333i
$601$	−12.3196	−	21.3383i	−0.502529	−	0.870406i	−0.999996	−	0.00292268i	$-0.999070\pi$
$601$	−12.3196	−	21.3383i	−0.502529	−	0.870406i	0.497467	−	0.867483i	$-0.334264\pi$
$602$		−	51.3983i		−	2.09484i
$603$		−	15.4712i		−	0.630037i
$604$	11.1149	+	19.2515i	0.452258	+	0.783334i
$605$	−1.27225	+	4.65711i	−0.0517243	+	0.189338i
$606$	−10.4486			−0.424446
$607$	−25.1410	+	14.5152i	−1.02044	+	0.589153i	−0.914232	−	0.405190i	$-0.867205\pi$
$607$	−25.1410	+	14.5152i	−1.02044	+	0.589153i	−0.106211	+	0.994344i	$0.533872\pi$
$608$	−6.46205	+	3.73087i	−0.262071	+	0.151307i
$609$	−10.7129	−	18.5553i	−0.434108	−	0.751897i
$610$	13.4829	+	3.68332i	0.545908	+	0.149133i
$611$	2.36869	−	4.10269i	0.0958269	−	0.165977i
$612$	1.00089	−	0.577862i	0.0404584	−	0.0233587i
$613$	7.41060	−	4.27851i	0.299311	−	0.172807i	−0.342822	−	0.939400i	$-0.611383\pi$
$613$	7.41060	−	4.27851i	0.299311	−	0.172807i	0.642133	+	0.766593i	$0.278050\pi$
$614$	−14.1491	−	24.5070i	−0.571013	−	0.989024i
$615$	−6.86831	−	26.1423i	−0.276957	−	1.05416i
$616$	7.53753	−	13.0554i	0.303696	−	0.526016i
$617$	−18.6337	+	10.7581i	−0.750163	+	0.433107i	−0.825753	−	0.564032i	$-0.809249\pi$
$617$	−18.6337	+	10.7581i	−0.750163	+	0.433107i	0.0755901	+	0.997139i	$0.475916\pi$
$618$		−	9.76260i		−	0.392709i
$619$	0.00690520			0.000277543			0.000138772	−	1.00000i	$-0.499956\pi$
$619$	0.00690520			0.000277543			0.000138772		1.00000i	$0.499956\pi$
$620$	5.49300	+	5.54685i	0.220604	+	0.222767i
$621$	−0.363708			−0.0145951
$622$	2.19774	+	1.26886i	0.0881212	+	0.0508768i
$623$			47.2062i			1.89127i
$624$	−1.06819	+	1.85017i	−0.0427620	+	0.0740660i
$625$	12.0752	+	21.8904i	0.483009	+	0.875616i
$626$	−5.44413	+	9.42952i	−0.217591	+	0.376879i
$627$	23.4413	−	13.5339i	0.936157	−	0.540491i
$628$			8.48130i			0.338441i
$629$	−6.11908	+	3.46087i	−0.243984	+	0.137994i
$630$	−8.98747	+	2.36126i	−0.358069	+	0.0940748i
$631$	−8.60323	−	14.9012i	−0.342489	−	0.593209i	0.642405	−	0.766365i	$-0.277937\pi$
$631$	−8.60323	−	14.9012i	−0.342489	−	0.593209i	−0.984894	+	0.173157i	$0.944603\pi$
$632$	13.6067	+	7.85583i	0.541246	+	0.312488i
$633$	3.03026	+	1.74952i	0.120442	+	0.0695371i
$634$	−0.507364	+	0.878780i	−0.0201500	+	0.0349008i
$635$	2.99905	+	11.4150i	0.119014	+	0.452992i
$636$	5.46988	−	9.47411i	0.216895	−	0.375673i
$637$			21.9408i			0.869326i
$638$	16.1969	−	9.35129i	0.641242	−	0.370221i
$639$	−0.146470			−0.00579425
$640$	0.568195	+	2.16267i	0.0224599	+	0.0854872i
$641$	9.46037	+	16.3858i	0.373662	+	0.647202i	0.990126	−	0.140182i	$-0.0447686\pi$
$641$	9.46037	+	16.3858i	0.373662	+	0.647202i	−0.616464	+	0.787383i	$0.711435\pi$
$642$	1.06082	+	0.612466i	0.0418673	+	0.0241721i
$643$		−	42.2666i		−	1.66683i	−0.552647	−	0.833415i	$-0.686382\pi$
$643$		−	42.2666i		−	1.66683i	0.552647	−	0.833415i	$-0.313618\pi$
$644$	0.755734	+	1.30897i	0.0297801	+	0.0515806i
$645$	−19.4600	−	19.6508i	−0.766237	−	0.773749i
$646$	−4.31185	−	7.46835i	−0.169648	−	0.293838i
$647$	−36.1233	−	20.8558i	−1.42015	−	0.819926i	−0.423841	−	0.905736i	$-0.639319\pi$
$647$	−36.1233	−	20.8558i	−1.42015	−	0.819926i	−0.996311	+	0.0858109i	$0.972652\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−17.7208	−	30.6933i	−0.695601	−	1.20482i
$650$	9.19829	+	5.43097i	0.360787	+	0.213020i
$651$	7.25413	+	12.5645i	0.284312	+	0.492442i
$652$			24.8077i			0.971546i
$653$	−27.3064	−	15.7653i	−1.06858	−	0.616946i	−0.140788	−	0.990040i	$-0.544964\pi$
$653$	−27.3064	−	15.7653i	−1.06858	−	0.616946i	−0.927793	+	0.373094i	$0.878297\pi$
$654$	−4.94812	−	8.57040i	−0.193487	−	0.335129i
$655$	32.9134	−	8.64728i	1.28603	−	0.337877i
$656$	−12.0879			−0.471955
$657$	−8.34307	+	4.81687i	−0.325494	+	0.187924i
$658$		−	9.21519i		−	0.359246i
$659$	−23.8572	+	41.3218i	−0.929343	+	1.60967i	−0.144919	+	0.989443i	$0.546292\pi$
$659$	−23.8572	+	41.3218i	−0.929343	+	1.60967i	−0.784423	+	0.620226i	$0.787041\pi$
$660$	−2.06115	−	7.84518i	−0.0802301	−	0.305373i
$661$	−18.8385	+	32.6293i	−0.732733	+	1.26913i	0.222978	+	0.974824i	$0.428422\pi$
$661$	−18.8385	+	32.6293i	−0.732733	+	1.26913i	−0.955711	+	0.294307i	$0.904911\pi$
$662$	8.46359	+	4.88646i	0.328947	+	0.189918i
$663$	−2.13828	−	1.23454i	−0.0830440	−	0.0479455i
$664$	6.91556	+	11.9781i	0.268376	+	0.464841i
$665$	17.6191	+	67.0621i	0.683239	+	2.60056i
$666$	5.24065	+	3.08797i	0.203071	+	0.119657i
$667$			1.87518i			0.0726071i
$668$	9.99502	−	5.77063i	0.386719	−	0.223272i
$669$	−5.96431	+	10.3305i	−0.230593	+	0.399400i
$670$	−9.11666	+	33.3718i	−0.352207	+	1.28927i
$671$	−11.3373	+	19.6368i	−0.437673	+	0.758072i
$672$			4.15572i			0.160311i
$673$	−25.4131	−	14.6723i	−0.979603	−	0.565574i	−0.0774530	−	0.996996i	$-0.524679\pi$
$673$	−25.4131	−	14.6723i	−0.979603	−	0.565574i	−0.902150	+	0.431422i	$0.858012\pi$
$674$	−10.1417			−0.390644
$675$	−2.54212	+	4.30553i	−0.0978464	+	0.165720i
$676$	−8.43584			−0.324455
$677$			20.0254i			0.769639i	0.922992	+	0.384820i	$0.125736\pi$
$677$			20.0254i			0.769639i	−0.922992	+	0.384820i	$0.874264\pi$
$678$	7.25569	−	4.18907i	0.278653	−	0.160880i
$679$	24.2267	−	41.9619i	0.929736	−	1.61035i
$680$	−2.49945	+	0.656676i	−0.0958496	+	0.0251824i
$681$	4.00164	+	6.93104i	0.153343	+	0.265598i
$682$	−10.9676	+	6.33214i	−0.419971	+	0.242470i
$683$	−22.8200	+	13.1751i	−0.873183	+	0.504133i	−0.868405	−	0.495856i	$-0.834854\pi$
$683$	−22.8200	+	13.1751i	−0.873183	+	0.504133i	−0.00477842	+	0.999989i	$0.501521\pi$
$684$	−3.73087	+	6.46205i	−0.142653	+	0.247083i
$685$	−14.9778	−	4.09169i	−0.572271	−	0.156335i
$686$	6.79469	+	11.7687i	0.259422	+	0.449333i
$687$	2.85314	−	1.64726i	0.108854	−	0.0628469i
$688$	−10.7111	+	6.18403i	−0.408355	+	0.235764i
$689$	−23.3716			−0.890386
$690$	0.784527	+	0.214320i	0.0298664	+	0.00815904i
$691$	−16.1086	−	27.9009i	−0.612801	−	1.06140i	−0.990766	−	0.135582i	$-0.956709\pi$
$691$	−16.1086	−	27.9009i	−0.612801	−	1.06140i	0.377965	−	0.925820i	$-0.376624\pi$
$692$			3.62151i			0.137669i
$693$		−	15.0751i		−	0.572654i
$694$	−8.18610	−	14.1787i	−0.310740	−	0.538218i
$695$	29.8257	−	7.83605i	1.13135	−	0.297238i
$696$	−2.57786	+	4.46499i	−0.0977136	+	0.169245i
$697$		−	13.9703i		−	0.529164i
$698$	−12.6143	−	7.28289i	−0.477459	−	0.275661i
$699$	4.60746	−	7.98036i	0.174270	−	0.301845i
$700$	20.7776	+	0.202707i	0.785321	+	0.00766161i
$701$	19.8955	+	34.4600i	0.751442	+	1.30154i	0.947124	+	0.320868i	$0.103975\pi$
$701$	19.8955	+	34.4600i	0.751442	+	1.30154i	−0.195682	+	0.980667i	$0.562692\pi$
$702$			2.13639i			0.0806328i
$703$	23.0416	−	39.1043i	0.869032	−	1.47485i
$704$	−3.62754			−0.136718
$705$	−3.48898	−	3.52319i	−0.131403	−	0.132691i
$706$	−11.9778	+	20.7462i	−0.450792	+	0.780795i
$707$	37.6041	+	21.7108i	1.41425	+	0.816517i
$708$	8.46118	+	4.88507i	0.317991	+	0.183592i
$709$	−38.2518			−1.43658			−0.718288	−	0.695746i	$-0.755074\pi$
$709$	−38.2518			−1.43658			−0.718288	+	0.695746i	$0.755074\pi$
$710$	0.315939	+	0.0863095i	0.0118570	+	0.00323914i
$711$	15.7117			0.589234
$712$	9.83745	−	5.67966i	0.368674	−	0.212854i
$713$		−	1.26976i		−	0.0475528i
$714$	−4.80287			−0.179743
$715$	−12.3132	+	12.1936i	−0.460487	+	0.456017i
$716$	6.27265	−	10.8646i	0.234420	−	0.406027i
$717$		−	18.7245i		−	0.699277i
$718$	27.4269	−	15.8349i	1.02356	−	0.590954i
$719$	−14.0689	−	24.3681i	−0.524681	−	0.908775i	−0.999587	−	0.0287381i	$-0.990851\pi$
$719$	−14.0689	−	24.3681i	−0.524681	−	0.908775i	0.474906	−	0.880037i	$-0.342482\pi$
$720$	1.57341	+	1.58883i	0.0586374	+	0.0592123i
$721$	−20.2853	+	35.1352i	−0.755465	+	1.30850i
$722$	31.7636	+	18.3387i	1.18212	+	0.682497i
$723$	−14.1100	+	8.14642i	−0.524757	+	0.302969i
$724$	1.46011	+	2.52899i	0.0542647	+	0.0939893i
$725$	22.1981	+	13.1065i	0.824418	+	0.486763i
$726$	2.15904			0.0801295
$727$	−8.63854	−	4.98746i	−0.320386	−	0.184975i	0.331179	−	0.943568i	$-0.392554\pi$
$727$	−8.63854	−	4.98746i	−0.320386	−	0.184975i	−0.651564	+	0.758593i	$0.725887\pi$
$728$	7.68878	−	4.43912i	0.284965	−	0.164525i
$729$	−1.00000			−0.0370370
$730$	20.8346	−	5.47384i	0.771125	−	0.202596i
$731$	−7.14703	−	12.3790i	−0.264343	−	0.457855i
$732$		−	6.25070i		−	0.231033i
$733$	8.08570	+	4.66828i	0.298652	+	0.172427i	0.641837	−	0.766841i	$-0.278172\pi$
$733$	8.08570	+	4.66828i	0.298652	+	0.172427i	−0.343185	+	0.939268i	$0.611506\pi$
$734$	21.5174			0.794223
$735$	22.1527	+	6.05178i	0.817116	+	0.223223i
$736$	0.181854	−	0.314980i	0.00670322	−	0.0116103i
$737$	−48.6035	−	28.0612i	−1.79033	−	1.03365i
$738$	−10.4685	+	6.04397i	−0.385350	+	0.222482i
$739$	34.3088			1.26207			0.631035	−	0.775754i	$-0.282630\pi$
$739$	34.3088			1.26207			0.631035	+	0.775754i	$0.282630\pi$
$740$	−9.48459	−	9.74898i	−0.348660	−	0.358380i
$741$	15.9412			0.585614
$742$	−39.3718	+	22.7313i	−1.44538	+	0.834492i
$743$	6.05632	+	3.49662i	0.222185	+	0.128278i	0.606962	−	0.794731i	$-0.292388\pi$
$743$	6.05632	+	3.49662i	0.222185	+	0.128278i	−0.384777	+	0.923010i	$0.625722\pi$
$744$	1.74558	−	3.02342i	0.0639959	−	0.110844i
$745$	3.25936	−	11.9310i	0.119414	−	0.437119i
$746$	9.76183			0.357406
$747$	11.9781	+	6.91556i	0.438256	+	0.253027i
$748$		−	4.19243i		−	0.153291i
$749$	−2.54524	−	4.40848i	−0.0930010	−	0.161082i
$750$	8.02053	−	7.78916i	0.292868	−	0.284420i
$751$	−3.07125			−0.112071			−0.0560357	−	0.998429i	$-0.517846\pi$
$751$	−3.07125			−0.112071			−0.0560357	+	0.998429i	$0.517846\pi$
$752$	−1.92038	+	1.10873i	−0.0700292	+	0.0404314i
$753$	−14.4960	−	8.36928i	−0.528264	−	0.304994i
$754$	11.0146			0.401129
$755$	−34.9765	−	35.3194i	−1.27292	−	1.28540i
$756$	2.07786	+	3.59896i	0.0755711	+	0.130893i
$757$	26.9227	−	15.5438i	0.978523	−	0.564950i	0.0766990	−	0.997054i	$-0.475562\pi$
$757$	26.9227	−	15.5438i	0.978523	−	0.564950i	0.901824	+	0.432104i	$0.142229\pi$
$758$	−20.3909	−	11.7727i	−0.740630	−	0.427603i
$759$	−0.659682	+	1.14260i	−0.0239449	+	0.0414738i
$760$	11.8554	−	11.7404i	0.430042	−	0.425867i
$761$	16.6558	+	28.8487i	0.603772	+	1.04576i	0.992244	+	0.124304i	$0.0396698\pi$
$761$	16.6558	+	28.8487i	0.603772	+	1.04576i	−0.388472	+	0.921461i	$0.626997\pi$
$762$	4.57107	−	2.63911i	0.165592	−	0.0956047i
$763$			41.1261i			1.48886i
$764$	10.2105	−	17.6852i	0.369404	−	0.639826i
$765$	−1.83625	+	1.81842i	−0.0663898	+	0.0657453i
$766$	6.75798			0.244176
$767$		−	20.8728i		−	0.753673i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	33.0922			1.19333			0.596667	−	0.802489i	$-0.296491\pi$
$769$	33.0922			1.19333			0.596667	+	0.802489i	$0.296491\pi$
$770$	−8.88321	+	32.5173i	−0.320129	+	1.17184i
$771$	−7.10917			−0.256030
$772$	4.14545	+	2.39338i	0.149198	+	0.0861396i
$773$	−23.9790	−	13.8443i	−0.862464	−	0.497944i	0.00237240	−	0.999997i	$-0.499245\pi$
$773$	−23.9790	−	13.8443i	−0.862464	−	0.497944i	−0.864837	+	0.502053i	$0.832578\pi$
$774$	−6.18403	+	10.7111i	−0.222280	+	0.385001i
$775$	−15.0313	−	8.87494i	−0.539939	−	0.318797i
$776$	−11.6594			−0.418550
$777$	−12.4445	−	22.0028i	−0.446445	−	0.789348i
$778$			5.61300i			0.201236i
$779$	45.0985	+	78.1129i	1.61582	+	2.79869i
$780$	1.25890	−	4.60825i	0.0450759	−	0.165002i
$781$	−0.265662	+	0.460140i	−0.00950614	+	0.0164651i
$782$	0.364030	+	0.210173i	0.0130177	+	0.00751576i
$783$			5.15572i			0.184251i
$784$	5.13502	−	8.89411i	0.183394	−	0.317647i
$785$	−4.81903	−	18.3423i	−0.171999	−	0.654664i
$786$	−7.60944	−	13.1799i	−0.271420	−	0.470113i
$787$			22.5730i			0.804640i	0.915499	+	0.402320i	$0.131796\pi$
$787$			22.5730i			0.804640i	−0.915499	+	0.402320i	$0.868204\pi$
$788$			4.11603i			0.146628i
$789$	−3.94578	−	6.83430i	−0.140474	−	0.243307i
$790$	−33.8905	−	9.25835i	−1.20577	−	0.329397i
$791$	−34.8173			−1.23796
$792$	−3.14154	+	1.81377i	−0.111630	+	0.0644495i
$793$	−11.5648	+	6.67697i	−0.410680	+	0.237106i
$794$	12.2845	+	21.2773i	0.435959	+	0.755104i
$795$	−6.44642	+	23.5974i	−0.228631	+	0.836912i
$796$	−3.29715	+	5.71084i	−0.116864	+	0.202415i
$797$	18.4492	−	10.6517i	0.653505	−	0.377301i	−0.136293	−	0.990669i	$-0.543519\pi$
$797$	18.4492	−	10.6517i	0.653505	−	0.377301i	0.789798	+	0.613367i	$0.210186\pi$
$798$	26.8545	−	15.5045i	0.950639	−	0.548852i
$799$	−1.28139	−	2.21943i	−0.0453323	−	0.0785179i
$800$	−2.45764	−	4.35431i	−0.0868906	−	0.153948i
$801$	5.67966	−	9.83745i	0.200681	−	0.347589i
$802$	−28.7299	+	16.5872i	−1.01449	+	0.585716i
$803$			34.9468i			1.23325i
$804$	15.4712			0.545628
$805$	−2.37816	−	2.40147i	−0.0838190	−	0.0846407i
$806$	−7.45846			−0.262713
$807$	0.698143	+	0.403073i	0.0245758	+	0.0141889i
$808$		−	10.4486i		−	0.367581i
$809$	6.26611	−	10.8532i	0.220305	−	0.381579i	−0.734596	−	0.678505i	$-0.762628\pi$
$809$	6.26611	−	10.8532i	0.220305	−	0.381579i	0.954900	+	0.296926i	$0.0959615\pi$
$810$	2.15703	+	0.589266i	0.0757902	+	0.0207047i
$811$	5.68068	−	9.83922i	0.199476	−	0.345502i	−0.748883	−	0.662702i	$-0.769409\pi$
$811$	5.68068	−	9.83922i	0.199476	−	0.345502i	0.948358	+	0.317201i	$0.102743\pi$
$812$	18.5553	−	10.7129i	0.651162	−	0.375948i
$813$			9.26250i			0.324850i
$814$	19.2063	−	10.8628i	0.673181	−	0.380743i
$815$	−14.0956	−	53.6510i	−0.493748	−	1.87931i
$816$	0.577862	+	1.00089i	0.0202292	+	0.0350380i
$817$	79.9231	+	46.1436i	2.79615	+	1.61436i
$818$	22.7761	+	13.1498i	0.796348	+	0.459772i
$819$	4.43912	−	7.68878i	0.155115	−	0.268668i
$820$	26.1423	−	6.86831i	0.912928	−	0.239852i
$821$	−11.6332	+	20.1492i	−0.406000	+	0.703213i	−0.994437	−	0.105330i	$-0.966410\pi$
$821$	−11.6332	+	20.1492i	−0.406000	+	0.703213i	0.588437	+	0.808543i	$0.299743\pi$
$822$			6.94371i			0.242190i
$823$	−20.1796	+	11.6507i	−0.703416	+	0.406118i	−0.808619	−	0.588333i	$-0.799784\pi$
$823$	−20.1796	+	11.6507i	−0.703416	+	0.406118i	0.105202	+	0.994451i	$0.466451\pi$
$824$	9.76260			0.340096
$825$	8.91518	+	15.7954i	0.310387	+	0.549926i
$826$	−20.3010	−	35.1623i	−0.706362	−	1.22345i
$827$	−6.85682	−	3.95879i	−0.238435	−	0.137660i	0.376022	−	0.926611i	$-0.377292\pi$
$827$	−6.85682	−	3.95879i	−0.238435	−	0.137660i	−0.614457	+	0.788950i	$0.710625\pi$
$828$		−	0.363708i		−	0.0126397i
$829$	1.81551	+	3.14455i	0.0630552	+	0.109215i	0.895830	−	0.444398i	$-0.146582\pi$
$829$	1.81551	+	3.14455i	0.0630552	+	0.109215i	−0.832774	+	0.553612i	$0.813249\pi$
$830$	−21.7620	−	21.9753i	−0.755370	−	0.762775i
$831$	3.20256	+	5.54699i	0.111096	+	0.192423i
$832$	−1.85017	−	1.06819i	−0.0641430	−	0.0370330i
$833$	10.2791	+	5.93466i	0.356151	+	0.205624i
$834$	−6.89557	−	11.9435i	−0.238774	−	0.413569i
$835$	−18.3371	+	18.1591i	−0.634582	+	0.628422i
$836$	13.5339	+	23.4413i	0.468079	+	0.810736i
$837$		−	3.49115i		−	0.120672i
$838$	28.0440	+	16.1912i	0.968762	+	0.559315i
$839$	23.1752	+	40.1407i	0.800097	+	1.38581i	0.919552	+	0.392969i	$0.128552\pi$
$839$	23.1752	+	40.1407i	0.800097	+	1.38581i	−0.119454	+	0.992840i	$0.538114\pi$
$840$	−2.36126	−	8.98747i	−0.0814712	−	0.310097i
$841$	−2.41852			−0.0833971
$842$	−6.25539	+	3.61155i	−0.215575	+	0.124462i
$843$			8.78689i			0.302636i
$844$	−1.74952	+	3.03026i	−0.0602209	+	0.104306i
$845$	18.2440	−	4.79320i	0.627612	−	0.164891i
$846$	−1.10873	+	1.92038i	−0.0381191	+	0.0660242i
$847$	−7.77031	−	4.48619i	−0.266991	−	0.154147i
$848$	9.47411	+	5.46988i	0.325342	+	0.187836i
$849$	4.81431	+	8.33863i	0.165227	+	0.286181i
$850$	5.03238	−	2.84035i	0.172609	−	0.0974232i
$851$	−0.0196178	+	2.21226i	−0.000672489	+	0.0758353i
$852$		−	0.146470i		−	0.00501797i
$853$	14.3566	−	8.28879i	0.491561	−	0.283803i	−0.233661	−	0.972318i	$-0.575071\pi$
$853$	14.3566	−	8.28879i	0.491561	−	0.283803i	0.725222	+	0.688516i	$0.241737\pi$
$854$	−12.9881	+	22.4960i	−0.444444	+	0.769799i
$855$	4.39694	−	16.0952i	0.150372	−	0.550443i
$856$	−0.612466	+	1.06082i	−0.0209336	+	0.0362581i
$857$			11.8858i			0.406010i	0.979178	+	0.203005i	$0.0650707\pi$
$857$			11.8858i			0.406010i	−0.979178	+	0.203005i	$0.934929\pi$
$858$	6.71155	+	3.87492i	0.229129	+	0.132288i
$859$	−0.176667			−0.00602779			−0.00301390	−	0.999995i	$-0.500959\pi$
$859$	−0.176667			−0.00602779			−0.00301390	+	0.999995i	$0.500959\pi$
$860$	19.6508	−	19.4600i	0.670086	−	0.663581i
$861$	50.2342			1.71198
$862$		−	4.09396i		−	0.139441i
$863$	22.6023	−	13.0494i	0.769390	−	0.444207i	−0.0632671	−	0.997997i	$-0.520152\pi$
$863$	22.6023	−	13.0494i	0.769390	−	0.444207i	0.832657	+	0.553789i	$0.186819\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−2.05772	−	7.83214i	−0.0699646	−	0.266301i
$866$	−0.559309	−	0.968752i	−0.0190061	−	0.0329195i
$867$	13.5657	−	7.83215i	0.460715	−	0.265994i
$868$	−12.5645	+	7.25413i	−0.426467	+	0.246221i
$869$	28.4973	−	49.3589i	0.966706	−	1.67438i
$870$	3.03809	−	11.1210i	0.103001	−	0.377038i
$871$	−16.5263	−	28.6243i	−0.559971	−	0.969899i
$872$	8.57040	−	4.94812i	0.290230	−	0.167565i
$873$	−10.0974	+	5.82972i	−0.341744	+	0.197306i
$874$	−2.71389			−0.0917987
$875$	−45.0504	+	11.3673i	−1.52298	+	0.384286i
$876$	−4.81687	−	8.34307i	−0.162747	−	0.281886i
$877$		−	49.2324i		−	1.66246i	−0.555930	−	0.831229i	$-0.687638\pi$
$877$		−	49.2324i		−	1.66246i	0.555930	−	0.831229i	$-0.312362\pi$
$878$		−	5.96081i		−	0.201168i
$879$	−8.66622	−	15.0103i	−0.292304	−	0.506286i
$880$	7.84518	−	2.06115i	0.264461	−	0.0694813i
$881$	−25.4930	+	44.1551i	−0.858880	+	1.48762i	0.0141179	+	0.999900i	$0.495506\pi$
$881$	−25.4930	+	44.1551i	−0.858880	+	1.48762i	−0.872998	+	0.487724i	$0.837827\pi$
$882$		−	10.2700i		−	0.345810i
$883$	11.5905	+	6.69179i	0.390052	+	0.225197i	0.682183	−	0.731182i	$-0.261031\pi$
$883$	11.5905	+	6.69179i	0.390052	+	0.225197i	−0.292131	+	0.956378i	$0.594364\pi$
$884$	1.23454	−	2.13828i	0.0415220	−	0.0719182i
$885$	−21.0744	−	5.75720i	−0.708410	−	0.193526i
$886$	5.01525	+	8.68666i	0.168490	+	0.291834i
$887$		−	37.4208i		−	1.25647i	−0.778025	−	0.628233i	$-0.783778\pi$
$887$		−	37.4208i		−	1.25647i	0.778025	−	0.628233i	$-0.216222\pi$
$888$	−3.08797	+	5.24065i	−0.103626	+	0.175865i
$889$	−21.9348			−0.735669
$890$	−18.0480	+	17.8728i	−0.604972	+	0.599099i
$891$	−1.81377	+	3.14154i	−0.0607636	+	0.105246i
$892$	−10.3305	−	5.96431i	−0.345890	−	0.199700i
$893$	14.3294	+	8.27309i	0.479515	+	0.276848i
$894$	−5.53123			−0.184992
$895$	−7.39252	+	27.0606i	−0.247105	+	0.904535i
$896$	−4.15572			−0.138833
$897$	−0.672920	+	0.388511i	−0.0224681	+	0.0129720i
$898$			14.1978i			0.473786i
$899$	−17.9994			−0.600314
$900$	−4.30553	−	2.54212i	−0.143518	−	0.0847375i
$901$	−6.32167	+	10.9494i	−0.210605	+	0.364779i
$902$			43.8495i			1.46003i
$903$	44.5122	−	25.6991i	1.48127	−	0.855213i
$904$	4.18907	+	7.25569i	0.139326	+	0.241321i
$905$	−4.59471	−	4.63976i	−0.152733	−	0.154231i
$906$	−11.1149	+	19.2515i	−0.369267	+	0.639590i
$907$	16.7162	+	9.65113i	0.555054	+	0.320460i	0.751158	−	0.660123i	$-0.229496\pi$
$907$	16.7162	+	9.65113i	0.555054	+	0.320460i	−0.196104	+	0.980583i	$0.562829\pi$
$908$	−6.93104	+	4.00164i	−0.230015	+	0.132799i
$909$	−5.22430	−	9.04876i	−0.173279	−	0.300128i
$910$	−14.1060	+	13.9691i	−0.467611	+	0.463071i
$911$	2.02228			0.0670011			0.0335006	−	0.999439i	$-0.489334\pi$
$911$	2.02228			0.0670011			0.0335006	+	0.999439i	$0.489334\pi$
$912$	−6.46205	−	3.73087i	−0.213980	−	0.123541i
$913$	43.4511	−	25.0865i	1.43802	−	0.830241i
$914$	−10.9594			−0.362506
$915$	3.55162	+	13.5182i	0.117413	+	0.446899i
$916$	1.64726	+	2.85314i	0.0544270	+	0.0942703i
$917$			63.2454i			2.08855i
$918$	1.00089	+	0.577862i	0.0330342	+	0.0190723i
$919$	−26.5602			−0.876140			−0.438070	−	0.898941i	$-0.644338\pi$
$919$	−26.5602			−0.876140			−0.438070	+	0.898941i	$0.644338\pi$
$920$	−0.214320	+	0.784527i	−0.00706593	+	0.0258651i
$921$	14.1491	−	24.5070i	0.466230	−	0.807535i
$922$	−22.7411	−	13.1296i	−0.748938	−	0.432400i
$923$	−0.270993	+	0.156458i	−0.00891986	+	0.00514988i
$924$	15.0751			0.495933
$925$	26.0514	+	15.6948i	0.856564	+	0.516041i
$926$	−25.1921			−0.827864
$927$	8.45466	−	4.88130i	0.277687	−	0.160323i
$928$	−4.46499	−	2.57786i	−0.146570	−	0.0846225i
$929$	10.1946	−	17.6576i	0.334475	−	0.579327i	−0.648909	−	0.760866i	$-0.724774\pi$
$929$	10.1946	−	17.6576i	0.334475	−	0.579327i	0.983384	+	0.181539i	$0.0581078\pi$
$930$	−2.05721	+	7.53051i	−0.0674587	+	0.246935i
$931$	−76.6323			−2.51152
$932$	7.98036	+	4.60746i	0.261405	+	0.150922i
$933$			2.53773i			0.0830814i
$934$	11.4326	+	19.8018i	0.374085	+	0.647933i
$935$	2.38212	+	9.06686i	0.0779036	+	0.296518i
$936$	−2.13639			−0.0698301
$937$	3.69613	−	2.13396i	0.120747	−	0.0697134i	−0.438410	−	0.898775i	$-0.644458\pi$
$937$	3.69613	−	2.13396i	0.120747	−	0.0697134i	0.559157	+	0.829062i	$0.311125\pi$
$938$	−55.6803	−	32.1471i	−1.81803	−	1.04964i
$939$	−10.8883			−0.355325
$940$	3.52319	−	3.48898i	0.114914	−	0.113798i
$941$	19.5603	+	33.8794i	0.637647	+	1.10444i	0.985948	+	0.167054i	$0.0534254\pi$
$941$	19.5603	+	33.8794i	0.637647	+	1.10444i	−0.348301	+	0.937383i	$0.613241\pi$
$942$	−7.34502	+	4.24065i	−0.239314	+	0.138168i
$943$	−3.80746	−	2.19824i	−0.123988	−	0.0715845i
$944$	−4.88507	+	8.46118i	−0.158995	+	0.275388i
$945$	−6.53865	−	6.60275i	−0.212702	−	0.214787i
$946$	22.4328	+	38.8548i	0.729354	+	1.26328i
$947$	48.8996	−	28.2322i	1.58902	−	0.917422i	0.595554	−	0.803315i	$-0.296933\pi$
$947$	48.8996	−	28.2322i	1.58902	−	0.917422i	0.993468	−	0.114107i	$-0.0364007\pi$
$948$			15.7117i			0.510291i
$949$	−10.2907	+	17.8240i	−0.334051	+	0.578593i
$950$	−18.9687	+	32.1267i	−0.615424	+	1.04233i
$951$	−1.01473			−0.0329048
$952$		−	4.80287i		−	0.155662i
$953$	11.4334	−	6.60107i	0.370364	−	0.213830i	−0.303253	−	0.952910i	$-0.598073\pi$
$953$	11.4334	−	6.60107i	0.370364	−	0.213830i	0.673617	+	0.739080i	$0.264740\pi$
$954$	10.9398			0.354188
$955$	−12.0334	+	44.0488i	−0.389393	+	1.42538i
$956$	18.7245			0.605592
$957$	16.1969	+	9.35129i	0.523572	+	0.302284i
$958$	−21.4922	−	12.4085i	−0.694381	−	0.400901i
$959$	14.4281	−	24.9901i	0.465906	−	0.806974i
$960$	−1.58883	+	1.57341i	−0.0512794	+	0.0507815i
$961$	−18.8119			−0.606835
$962$	12.9946	+	0.115233i	0.418964	+	0.00371527i
$963$			1.22493i			0.0394729i
$964$	−8.14642	−	14.1100i	−0.262379	−	0.454453i
$965$	−10.3252	−	2.82067i	−0.332379	−	0.0908006i
$966$	−0.755734	+	1.30897i	−0.0243153	+	0.0421154i
$967$	46.3588	+	26.7652i	1.49080	+	0.860712i	0.999945	−	0.0105306i	$-0.00335205\pi$
$967$	46.3588	+	26.7652i	1.49080	+	0.860712i	0.490853	+	0.871243i	$0.336685\pi$
$968$			2.15904i			0.0693942i
$969$	4.31185	−	7.46835i	0.138517	−	0.239918i
$970$	25.2156	−	6.62483i	0.809623	−	0.212711i
$971$	−19.2660	−	33.3697i	−0.618275	−	1.07088i	−0.989800	−	0.142461i	$-0.954498\pi$
$971$	−19.2660	−	33.3697i	−0.618275	−	1.07088i	0.371525	−	0.928423i	$-0.378835\pi$
$972$		−	1.00000i		−	0.0320750i
$973$			57.3121i			1.83734i
$974$	6.05167	+	10.4818i	0.193908	+	0.335858i
$975$	−0.104208	+	10.6814i	−0.00333734	+	0.342080i
$976$	6.25070			0.200080
$977$	0.907703	−	0.524063i	0.0290400	−	0.0167663i	−0.485410	−	0.874287i	$-0.661330\pi$
$977$	0.907703	−	0.524063i	0.0290400	−	0.0167663i	0.514450	+	0.857521i	$0.327996\pi$
$978$	−21.4841	+	12.4039i	−0.686986	+	0.396632i
$979$	−20.6032	−	35.6857i	−0.658480	−	1.14052i
$980$	−6.05178	+	22.1527i	−0.193317	+	0.707644i
$981$	4.94812	−	8.57040i	0.157981	−	0.273632i
$982$	28.8144	−	16.6360i	0.919504	−	0.530876i
$983$	2.46606	−	1.42378i	0.0786553	−	0.0454116i	−0.460157	−	0.887838i	$-0.652207\pi$
$983$	2.46606	−	1.42378i	0.0786553	−	0.0454116i	0.538812	+	0.842426i	$0.318873\pi$
$984$	−6.04397	−	10.4685i	−0.192675	−	0.333723i
$985$	−2.33871	−	8.90164i	−0.0745174	−	0.283630i
$986$	2.97930	−	5.16029i	0.0948801	−	0.164337i
$987$	7.98059	−	4.60760i	0.254025	−	0.146661i
$988$			15.9412i			0.507156i
$989$	−4.49836			−0.143040
$990$	5.76355	−	5.70760i	0.183178	−	0.181399i
$991$	2.23806			0.0710942			0.0355471	−	0.999368i	$-0.488683\pi$
$991$	2.23806			0.0710942			0.0355471	+	0.999368i	$0.488683\pi$
$992$	3.02342	+	1.74558i	0.0959938	+	0.0554221i
$993$			9.77291i			0.310134i
$994$	−0.304344	+	0.527139i	−0.00965320	+	0.0167198i
$995$	3.88580	−	14.2241i	0.123188	−	0.450934i
$996$	−6.91556	+	11.9781i	−0.219128	+	0.379541i
$997$	−32.0051	+	18.4782i	−1.01361	+	0.585210i	−0.912247	−	0.409640i	$-0.865654\pi$
$997$	−32.0051	+	18.4782i	−1.01361	+	0.585210i	−0.101365	+	0.994849i	$0.532321\pi$
$998$		−	19.9711i		−	0.632173i
$999$	−0.0539383	+	6.08252i	−0.00170653	+	0.192443i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.bb.d.1099.2	yes	28
5.4	even	2	inner	1110.2.bb.d.1099.13	yes	28
37.10	even	3	inner	1110.2.bb.d.1009.13	yes	28
185.84	even	6	inner	1110.2.bb.d.1009.2	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.bb.d.1009.2	✓	28	185.84	even	6	inner
1110.2.bb.d.1009.13	yes	28	37.10	even	3	inner
1110.2.bb.d.1099.2	yes	28	1.1	even	1	trivial
1110.2.bb.d.1099.13	yes	28	5.4	even	2	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.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.589266 + 2.15703i) q^{5} +1.00000 q^{6} +(-3.59896 - 2.07786i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.589266 + 2.15703i) q^{5} +1.00000 q^{6} +(-3.59896 - 2.07786i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.568195 - 2.16267i) q^{10} +3.62754 q^{11} +(-0.866025 + 0.500000i) q^{12} +(1.85017 + 1.06819i) q^{13} +4.15572 q^{14} +(1.58883 - 1.57341i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00089 - 0.577862i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-3.73087 + 6.46205i) q^{19} +(1.57341 + 1.58883i) q^{20} +(2.07786 + 3.59896i) q^{21} +(-3.14154 + 1.81377i) q^{22} -0.363708i q^{23} +(0.500000 - 0.866025i) q^{24} +(-4.30553 - 2.54212i) q^{25} -2.13639 q^{26} -1.00000i q^{27} +(-3.59896 + 2.07786i) q^{28} -5.15572 q^{29} +(-0.589266 + 2.15703i) q^{30} +3.49115 q^{31} +(0.866025 + 0.500000i) q^{32} +(-3.14154 - 1.81377i) q^{33} +(-0.577862 + 1.00089i) q^{34} +(6.60275 - 6.53865i) q^{35} +1.00000 q^{36} +(-6.08252 - 0.0539383i) q^{37} -7.46174i q^{38} +(-1.06819 - 1.85017i) q^{39} +(-2.15703 - 0.589266i) q^{40} +(6.04397 - 10.4685i) q^{41} +(-3.59896 - 2.07786i) q^{42} -12.3681i q^{43} +(1.81377 - 3.14154i) q^{44} +(-2.16267 + 0.568195i) q^{45} +(0.181854 + 0.314980i) q^{46} -2.21747i q^{47} +1.00000i q^{48} +(5.13502 + 8.89411i) q^{49} +(4.99976 + 0.0487778i) q^{50} -1.15572 q^{51} +(1.85017 - 1.06819i) q^{52} +(-9.47411 + 5.46988i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.13758 + 7.82470i) q^{55} +(2.07786 - 3.59896i) q^{56} +(6.46205 - 3.73087i) q^{57} +(4.46499 - 2.57786i) q^{58} +(-4.88507 - 8.46118i) q^{59} +(-0.568195 - 2.16267i) q^{60} +(-3.12535 + 5.41327i) q^{61} +(-3.02342 + 1.74558i) q^{62} -4.15572i q^{63} -1.00000 q^{64} +(-3.39436 + 3.36141i) q^{65} +3.62754 q^{66} +(-13.3985 - 7.73561i) q^{67} -1.15572i q^{68} +(-0.181854 + 0.314980i) q^{69} +(-2.44882 + 8.96401i) q^{70} +(-0.0732348 + 0.126846i) q^{71} +(-0.866025 + 0.500000i) q^{72} +9.63375i q^{73} +(5.29459 - 2.99455i) q^{74} +(2.45764 + 4.35431i) q^{75} +(3.73087 + 6.46205i) q^{76} +(-13.0554 - 7.53753i) q^{77} +(1.85017 + 1.06819i) q^{78} +(7.85583 - 13.6067i) q^{79} +(2.16267 - 0.568195i) q^{80} +(-0.500000 + 0.866025i) q^{81} +12.0879i q^{82} +(11.9781 - 6.91556i) q^{83} +4.15572 q^{84} +(0.656676 + 2.49945i) q^{85} +(6.18403 + 10.7111i) q^{86} +(4.46499 + 2.57786i) q^{87} +3.62754i q^{88} +(-5.67966 - 9.83745i) q^{89} +(1.58883 - 1.57341i) q^{90} +(-4.43912 - 7.68878i) q^{91} +(-0.314980 - 0.181854i) q^{92} +(-3.02342 - 1.74558i) q^{93} +(1.10873 + 1.92038i) q^{94} +(-11.7404 - 11.8554i) q^{95} +(-0.500000 - 0.866025i) q^{96} +11.6594i q^{97} +(-8.89411 - 5.13502i) q^{98} +(1.81377 + 3.14154i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9}+O(q^{10}) \) 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9	\( 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9} + 4 q^{10} - 12 q^{11} + 8 q^{14} + 2 q^{15} - 14 q^{16} - 20 q^{19} - 2 q^{20} + 4 q^{21} + 14 q^{24} - 8 q^{25} - 20 q^{26} - 36 q^{29} + 2 q^{30} + 24 q^{31} + 38 q^{34} - 2 q^{35} + 28 q^{36} - 10 q^{39} + 2 q^{40} - 6 q^{44} + 4 q^{45} + 8 q^{46} + 50 q^{49} - 4 q^{50} + 76 q^{51} + 14 q^{54} - 28 q^{55} + 4 q^{56} - 26 q^{59} + 4 q^{60} - 28 q^{61} - 28 q^{64} + 60 q^{65} - 12 q^{66} - 8 q^{69} - 10 q^{70} - 64 q^{71} + 24 q^{74} - 8 q^{75} + 20 q^{76} + 32 q^{79} - 4 q^{80} - 14 q^{81} + 8 q^{84} + 16 q^{85} - 8 q^{86} + 76 q^{89} + 2 q^{90} - 8 q^{91} - 38 q^{94} - 70 q^{95} - 14 q^{96} - 6 q^{99}+O(q^{100}) \) 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9 + 4 * q^10 - 12 * q^11 + 8 * q^14 + 2 * q^15 - 14 * q^16 - 20 * q^19 - 2 * q^20 + 4 * q^21 + 14 * q^24 - 8 * q^25 - 20 * q^26 - 36 * q^29 + 2 * q^30 + 24 * q^31 + 38 * q^34 - 2 * q^35 + 28 * q^36 - 10 * q^39 + 2 * q^40 - 6 * q^44 + 4 * q^45 + 8 * q^46 + 50 * q^49 - 4 * q^50 + 76 * q^51 + 14 * q^54 - 28 * q^55 + 4 * q^56 - 26 * q^59 + 4 * q^60 - 28 * q^61 - 28 * q^64 + 60 * q^65 - 12 * q^66 - 8 * q^69 - 10 * q^70 - 64 * q^71 + 24 * q^74 - 8 * q^75 + 20 * q^76 + 32 * q^79 - 4 * q^80 - 14 * q^81 + 8 * q^84 + 16 * q^85 - 8 * q^86 + 76 * q^89 + 2 * q^90 - 8 * q^91 - 38 * q^94 - 70 * q^95 - 14 * q^96 - 6 * q^99

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