LMFDB - Embedded newform 1050.2.u.e.299.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(299,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("1050.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.u (of order $6$, degree $2$, not 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 11 x^{10} - 32 x^{9} + 64 x^{8} - 120 x^{7} + 237 x^{6} - 360 x^{5} + 576 x^{4} + \cdots + 729 $ x^12 - 4x^11 + 11x^10 - 32x^9 + 64x^8 - 120x^7 + 237x^6 - 360x^5 + 576x^4 - 864x^3 + 891x^2 - 972*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			299.5
Root			$1.66557 - 0.475255i$ of defining polynomial
Character	$\chi$	$=$	1050.299
Dual form			1050.2.u.e.899.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.24437 - 1.20480i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.421203 + 1.68006i) q^{6} +(2.64518 + 0.0551777i) q^{7} +1.00000 q^{8} +(0.0969112 - 2.99843i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.24437 - 1.20480i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.421203 + 1.68006i) q^{6} +(2.64518 + 0.0551777i) q^{7} +1.00000 q^{8} +(0.0969112 - 2.99843i) q^{9} +(0.167855 - 0.0969112i) q^{11} +(-1.66557 - 0.475255i) q^{12} -1.54892 q^{13} +(-1.37037 + 2.26320i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.458589 - 0.264766i) q^{17} +(2.54826 + 1.58314i) q^{18} +(5.53332 + 3.19467i) q^{19} +(3.35805 - 3.11825i) q^{21} +0.193822i q^{22} +(2.12488 - 3.68040i) q^{23} +(1.24437 - 1.20480i) q^{24} +(0.774462 - 1.34141i) q^{26} +(-3.49192 - 3.84792i) q^{27} +(-1.27480 - 2.31838i) q^{28} +4.87349i q^{29} +(8.02559 - 4.63357i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.0921151 - 0.322825i) q^{33} +0.529533i q^{34} +(-2.64518 + 1.41529i) q^{36} +(-1.52704 - 0.881634i) q^{37} +(-5.53332 + 3.19467i) q^{38} +(-1.92743 + 1.86614i) q^{39} -9.91573 q^{41} +(1.02145 + 4.46728i) q^{42} -11.4865i q^{43} +(-0.167855 - 0.0969112i) q^{44} +(2.12488 + 3.68040i) q^{46} +(-8.49028 - 4.90186i) q^{47} +(0.421203 + 1.68006i) q^{48} +(6.99391 + 0.291909i) q^{49} +(0.251663 - 0.881975i) q^{51} +(0.774462 + 1.34141i) q^{52} +(0.0324905 + 0.0562751i) q^{53} +(5.07836 - 1.10013i) q^{54} +(2.64518 + 0.0551777i) q^{56} +(10.7344 - 2.69121i) q^{57} +(-4.22056 - 2.43674i) q^{58} +(6.01371 + 10.4160i) q^{59} +(3.71180 + 2.14301i) q^{61} +9.26715i q^{62} +(0.421794 - 7.92604i) q^{63} +1.00000 q^{64} +(0.233517 + 0.241187i) q^{66} +(4.18340 - 2.41529i) q^{67} +(-0.458589 - 0.264766i) q^{68} +(-1.79001 - 7.13983i) q^{69} +6.29103i q^{71} +(0.0969112 - 2.99843i) q^{72} +(4.04586 + 7.00763i) q^{73} +(1.52704 - 0.881634i) q^{74} -6.38933i q^{76} +(0.449354 - 0.247085i) q^{77} +(-0.652411 - 2.60228i) q^{78} +(3.38883 - 5.86962i) q^{79} +(-8.98122 - 0.581164i) q^{81} +(4.95787 - 8.58728i) q^{82} -2.11036i q^{83} +(-4.37951 - 1.34904i) q^{84} +(9.94760 + 5.74325i) q^{86} +(5.87158 + 6.06442i) q^{87} +(0.167855 - 0.0969112i) q^{88} +(8.18773 - 14.1816i) q^{89} +(-4.09717 - 0.0854660i) q^{91} -4.24976 q^{92} +(4.40426 - 15.4351i) q^{93} +(8.49028 - 4.90186i) q^{94} +(-1.66557 - 0.475255i) q^{96} -8.24463 q^{97} +(-3.74976 + 5.91095i) q^{98} +(-0.274315 - 0.512694i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} + 2 q^{3} - 6 q^{4} + 2 q^{6} - 6 q^{7} + 12 q^{8}+O(q^{10}) $ 12 * q - 6 * q^2 + 2 * q^3 - 6 * q^4 + 2 * q^6 - 6 * q^7 + 12 * q^8	$ 12 q - 6 q^{2} + 2 q^{3} - 6 q^{4} + 2 q^{6} - 6 q^{7} + 12 q^{8} + 12 q^{11} - 4 q^{12} - 8 q^{13} + 12 q^{14} - 6 q^{16} + 12 q^{17} - 6 q^{18} + 4 q^{21} + 2 q^{23} + 2 q^{24} + 4 q^{26} - 28 q^{27} - 6 q^{28} + 12 q^{31} - 6 q^{32} + 34 q^{33} + 6 q^{36} + 42 q^{39} + 4 q^{41} + 16 q^{42} - 12 q^{44} + 2 q^{46} + 24 q^{47} + 2 q^{48} + 14 q^{49} - 8 q^{51} + 4 q^{52} + 8 q^{53} + 32 q^{54} - 6 q^{56} - 20 q^{57} + 18 q^{58} + 12 q^{59} - 30 q^{61} + 2 q^{63} + 12 q^{64} - 14 q^{66} - 6 q^{67} - 12 q^{68} + 50 q^{69} - 20 q^{77} - 12 q^{78} + 4 q^{79} - 40 q^{81} - 2 q^{82} - 20 q^{84} + 54 q^{86} - 8 q^{87} + 12 q^{88} + 26 q^{89} + 28 q^{91} - 4 q^{92} - 24 q^{93} - 24 q^{94} - 4 q^{96} + 72 q^{97} + 2 q^{98} - 48 q^{99}+O(q^{100}) $ 12 * q - 6 * q^2 + 2 * q^3 - 6 * q^4 + 2 * q^6 - 6 * q^7 + 12 * q^8 + 12 * q^11 - 4 * q^12 - 8 * q^13 + 12 * q^14 - 6 * q^16 + 12 * q^17 - 6 * q^18 + 4 * q^21 + 2 * q^23 + 2 * q^24 + 4 * q^26 - 28 * q^27 - 6 * q^28 + 12 * q^31 - 6 * q^32 + 34 * q^33 + 6 * q^36 + 42 * q^39 + 4 * q^41 + 16 * q^42 - 12 * q^44 + 2 * q^46 + 24 * q^47 + 2 * q^48 + 14 * q^49 - 8 * q^51 + 4 * q^52 + 8 * q^53 + 32 * q^54 - 6 * q^56 - 20 * q^57 + 18 * q^58 + 12 * q^59 - 30 * q^61 + 2 * q^63 + 12 * q^64 - 14 * q^66 - 6 * q^67 - 12 * q^68 + 50 * q^69 - 20 * q^77 - 12 * q^78 + 4 * q^79 - 40 * q^81 - 2 * q^82 - 20 * q^84 + 54 * q^86 - 8 * q^87 + 12 * q^88 + 26 * q^89 + 28 * q^91 - 4 * q^92 - 24 * q^93 - 24 * q^94 - 4 * q^96 + 72 * q^97 + 2 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.24437	−	1.20480i	0.718437	−	0.695592i
$3$	1.24437	−	1.20480i	0.718437	−	0.695592i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.421203	+	1.68006i	0.171955	+	0.685880i
$7$	2.64518	+	0.0551777i	0.999783	+	0.0208552i
$7$	2.64518	+	0.0551777i	0.999783	+	0.0208552i
$8$	1.00000			0.353553
$9$	0.0969112	−	2.99843i	0.0323037	−	0.999478i
$10$		0			0
$11$	0.167855	−	0.0969112i	0.0506102	−	0.0292198i	−0.474481	−	0.880266i	$-0.657364\pi$
$11$	0.167855	−	0.0969112i	0.0506102	−	0.0292198i	0.525092	+	0.851046i	$0.324031\pi$
$12$	−1.66557	−	0.475255i	−0.480809	−	0.137194i
$13$	−1.54892			−0.429594			−0.214797	−	0.976659i	$-0.568909\pi$
$13$	−1.54892			−0.429594			−0.214797	+	0.976659i	$0.568909\pi$
$14$	−1.37037	+	2.26320i	−0.366248	+	0.604866i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.458589	−	0.264766i	0.111224	−	0.0642153i	−0.443356	−	0.896346i	$-0.646212\pi$
$17$	0.458589	−	0.264766i	0.111224	−	0.0642153i	0.554580	+	0.832130i	$0.312879\pi$
$18$	2.54826	+	1.58314i	0.600632	+	0.373151i
$19$	5.53332	+	3.19467i	1.26943	+	0.732906i	0.974880	−	0.222729i	$-0.0714966\pi$
$19$	5.53332	+	3.19467i	1.26943	+	0.732906i	0.294551	+	0.955636i	$0.404830\pi$
$20$		0			0
$21$	3.35805	−	3.11825i	0.732788	−	0.680457i
$22$			0.193822i			0.0413231i
$23$	2.12488	−	3.68040i	0.443068	−	0.767416i	−0.554848	−	0.831952i	$-0.687223\pi$
$23$	2.12488	−	3.68040i	0.443068	−	0.767416i	0.997915	+	0.0645362i	$0.0205568\pi$
$24$	1.24437	−	1.20480i	0.254006	−	0.245929i
$25$		0			0
$26$	0.774462	−	1.34141i	0.151884	−	0.263072i
$27$	−3.49192	−	3.84792i	−0.672021	−	0.740532i
$28$	−1.27480	−	2.31838i	−0.240915	−	0.438132i
$29$			4.87349i			0.904984i	0.891768	+	0.452492i	$0.149465\pi$
$29$			4.87349i			0.904984i	−0.891768	+	0.452492i	$0.850535\pi$
$30$		0			0
$31$	8.02559	−	4.63357i	1.44144	−	0.832214i	0.443492	−	0.896278i	$-0.353739\pi$
$31$	8.02559	−	4.63357i	1.44144	−	0.832214i	0.997946	+	0.0640639i	$0.0204062\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.0921151	−	0.322825i	0.0160352	−	0.0561967i
$34$			0.529533i			0.0908141i
$35$		0			0
$36$	−2.64518	+	1.41529i	−0.440863	+	0.235882i
$37$	−1.52704	−	0.881634i	−0.251043	−	0.144940i	0.369199	−	0.929350i	$-0.379632\pi$
$37$	−1.52704	−	0.881634i	−0.251043	−	0.144940i	−0.620242	+	0.784411i	$0.712966\pi$
$38$	−5.53332	+	3.19467i	−0.897623	+	0.518243i
$39$	−1.92743	+	1.86614i	−0.308636	+	0.298822i
$40$		0			0
$41$	−9.91573			−1.54858			−0.774289	−	0.632833i	$-0.781892\pi$
$41$	−9.91573			−1.54858			−0.774289	+	0.632833i	$0.781892\pi$
$42$	1.02145	+	4.46728i	0.157614	+	0.689317i
$43$		−	11.4865i		−	1.75168i	−0.482606	−	0.875838i	$-0.660310\pi$
$43$		−	11.4865i		−	1.75168i	0.482606	−	0.875838i	$-0.339690\pi$
$44$	−0.167855	−	0.0969112i	−0.0253051	−	0.0146099i
$45$		0			0
$46$	2.12488	+	3.68040i	0.313296	+	0.542645i
$47$	−8.49028	−	4.90186i	−1.23843	−	0.715010i	−0.269660	−	0.962956i	$-0.586911\pi$
$47$	−8.49028	−	4.90186i	−1.23843	−	0.715010i	−0.968774	+	0.247945i	$0.920245\pi$
$48$	0.421203	+	1.68006i	0.0607954	+	0.242495i
$49$	6.99391	+	0.291909i	0.999130	+	0.0417014i
$50$		0			0
$51$	0.251663	−	0.881975i	0.0352399	−	0.123501i
$52$	0.774462	+	1.34141i	0.107398	+	0.186020i
$53$	0.0324905	+	0.0562751i	0.00446291	+	0.00772998i	0.868248	−	0.496130i	$-0.165246\pi$
$53$	0.0324905	+	0.0562751i	0.00446291	+	0.00772998i	−0.863785	+	0.503860i	$0.831913\pi$
$54$	5.07836	−	1.10013i	0.691077	−	0.149709i
$55$		0			0
$56$	2.64518	+	0.0551777i	0.353476	+	0.00737343i
$57$	10.7344	−	2.69121i	1.42181	−	0.356459i
$58$	−4.22056	−	2.43674i	−0.554187	−	0.319960i
$59$	6.01371	+	10.4160i	0.782918	+	1.35605i	0.930235	+	0.366964i	$0.119603\pi$
$59$	6.01371	+	10.4160i	0.782918	+	1.35605i	−0.147317	+	0.989089i	$0.547064\pi$
$60$		0			0
$61$	3.71180	+	2.14301i	0.475248	+	0.274384i	0.718434	−	0.695595i	$-0.244859\pi$
$61$	3.71180	+	2.14301i	0.475248	+	0.274384i	−0.243186	+	0.969980i	$0.578193\pi$
$62$			9.26715i			1.17693i
$63$	0.421794	−	7.92604i	0.0531410	−	0.998587i
$64$	1.00000			0.125000
$65$		0			0
$66$	0.233517	+	0.241187i	0.0287440	+	0.0296880i
$67$	4.18340	−	2.41529i	0.511084	−	0.295075i	−0.222195	−	0.975002i	$-0.571322\pi$
$67$	4.18340	−	2.41529i	0.511084	−	0.295075i	0.733279	+	0.679928i	$0.237989\pi$
$68$	−0.458589	−	0.264766i	−0.0556121	−	0.0321076i
$69$	−1.79001	−	7.13983i	−0.215492	−	0.859534i
$70$		0			0
$71$			6.29103i			0.746608i	0.927709	+	0.373304i	$0.121775\pi$
$71$			6.29103i			0.746608i	−0.927709	+	0.373304i	$0.878225\pi$
$72$	0.0969112	−	2.99843i	0.0114211	−	0.353369i
$73$	4.04586	+	7.00763i	0.473532	+	0.820181i	0.999541	−	0.0302980i	$-0.00964561\pi$
$73$	4.04586	+	7.00763i	0.473532	+	0.820181i	−0.526009	+	0.850479i	$0.676312\pi$
$74$	1.52704	−	0.881634i	0.177514	−	0.102488i
$75$		0			0
$76$		−	6.38933i		−	0.732906i
$77$	0.449354	−	0.247085i	0.0512086	−	0.0281580i
$78$	−0.652411	−	2.60228i	−0.0738710	−	0.294650i
$79$	3.38883	−	5.86962i	0.381273	−	0.660384i	−0.609971	−	0.792423i	$-0.708819\pi$
$79$	3.38883	−	5.86962i	0.381273	−	0.660384i	0.991245	+	0.132039i	$0.0421525\pi$
$80$		0			0
$81$	−8.98122	−	0.581164i	−0.997913	−	0.0645738i
$82$	4.95787	−	8.58728i	0.547505	−	0.948306i
$83$		−	2.11036i		−	0.231642i	−0.993270	−	0.115821i	$-0.963050\pi$
$83$		−	2.11036i		−	0.231642i	0.993270	−	0.115821i	$-0.0369498\pi$
$84$	−4.37951	−	1.34904i	−0.477844	−	0.147192i
$85$		0			0
$86$	9.94760	+	5.74325i	1.07268	+	0.619311i
$87$	5.87158	+	6.06442i	0.629500	+	0.650174i
$88$	0.167855	−	0.0969112i	0.0178934	−	0.0103308i
$89$	8.18773	−	14.1816i	0.867898	−	1.50324i	0.00375740	−	0.999993i	$-0.498804\pi$
$89$	8.18773	−	14.1816i	0.867898	−	1.50324i	0.864141	−	0.503250i	$-0.167863\pi$
$90$		0			0
$91$	−4.09717	−	0.0854660i	−0.429501	−	0.00895927i
$92$	−4.24976			−0.443068
$93$	4.40426	−	15.4351i	0.456701	−	1.60055i
$94$	8.49028	−	4.90186i	0.875705	−	0.505589i
$95$		0			0
$96$	−1.66557	−	0.475255i	−0.169992	−	0.0485055i
$97$	−8.24463			−0.837115			−0.418557	−	0.908190i	$-0.637464\pi$
$97$	−8.24463			−0.837115			−0.418557	+	0.908190i	$0.637464\pi$
$98$	−3.74976	+	5.91095i	−0.378783	+	0.597096i
$99$	−0.274315	−	0.512694i	−0.0275697	−	0.0515277i
$100$		0			0
$101$	−2.22831	−	3.85955i	−0.221725	−	0.384040i	0.733607	−	0.679574i	$-0.237836\pi$
$101$	−2.22831	−	3.85955i	−0.221725	−	0.384040i	−0.955332	+	0.295535i	$0.904502\pi$
$102$	0.637981	+	0.658934i	0.0631696	+	0.0652442i
$103$	4.21094	−	7.29356i	0.414916	−	0.718656i	−0.580504	−	0.814258i	$-0.697144\pi$
$103$	4.21094	−	7.29356i	0.414916	−	0.718656i	0.995420	+	0.0956021i	$0.0304776\pi$
$104$	−1.54892			−0.151884
$105$		0			0
$106$	−0.0649809			−0.00631151
$107$	−8.90681	+	15.4270i	−0.861054	+	1.49139i	0.00985883	+	0.999951i	$0.496862\pi$
$107$	−8.90681	+	15.4270i	−0.861054	+	1.49139i	−0.870913	+	0.491438i	$0.836472\pi$
$108$	−1.58643	+	4.94805i	−0.152655	+	0.476127i
$109$	0.0739017	+	0.128001i	0.00707850	+	0.0122603i	0.869543	−	0.493857i	$-0.164413\pi$
$109$	0.0739017	+	0.128001i	0.00707850	+	0.0122603i	−0.862464	+	0.506118i	$0.831080\pi$
$110$		0			0
$111$	−2.96239	+	0.742694i	−0.281178	+	0.0704934i
$112$	−1.37037	+	2.26320i	−0.129488	+	0.213852i
$113$	3.44771			0.324334			0.162167	−	0.986763i	$-0.448152\pi$
$113$	3.44771			0.324334			0.162167	+	0.986763i	$0.448152\pi$
$114$	−3.03656	+	10.6419i	−0.284400	+	0.996705i
$115$		0			0
$116$	4.22056	−	2.43674i	0.391870	−	0.226246i
$117$	−0.150108	+	4.64434i	−0.0138775	+	0.429370i
$118$	−12.0274			−1.10721
$119$	1.22766	−	0.675050i	0.112539	−	0.0618817i
$120$		0			0
$121$	−5.48122	+	9.49375i	−0.498292	+	0.863068i
$122$	−3.71180	+	2.14301i	−0.336051	+	0.194019i
$123$	−12.3388	+	11.9465i	−1.11256	+	1.07718i
$124$	−8.02559	−	4.63357i	−0.720719	−	0.416107i
$125$		0			0
$126$	6.65325	+	4.32830i	0.592719	+	0.385596i
$127$			5.49965i			0.488015i	0.969773	+	0.244007i	$0.0784621\pi$
$127$			5.49965i			0.488015i	−0.969773	+	0.244007i	$0.921538\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−13.8389	−	14.2935i	−1.21845	−	1.25847i
$130$		0			0
$131$	2.99843	−	5.19344i	0.261974	−	0.453753i	−0.704792	−	0.709414i	$-0.748960\pi$
$131$	2.99843	−	5.19344i	0.261974	−	0.453753i	0.966767	+	0.255661i	$0.0822931\pi$
$132$	−0.325633	+	0.0816386i	−0.0283427	+	0.00710573i
$133$	14.4603	+	8.75577i	1.25387	+	0.759221i
$134$			4.83058i			0.417298i
$135$		0			0
$136$	0.458589	−	0.264766i	0.0393237	−	0.0227035i
$137$	−0.431056	−	0.746611i	−0.0368276	−	0.0637872i	0.847024	−	0.531554i	$-0.178392\pi$
$137$	−0.431056	−	0.746611i	−0.0368276	−	0.0637872i	−0.883852	+	0.467767i	$0.845059\pi$
$138$	7.07828	+	2.01972i	0.602543	+	0.171930i
$139$			16.1843i			1.37274i	0.727254	+	0.686368i	$0.240796\pi$
$139$			16.1843i			1.37274i	−0.727254	+	0.686368i	$0.759204\pi$
$140$		0			0
$141$	−16.4708	+	4.12936i	−1.38709	+	0.347755i
$142$	−5.44820	−	3.14552i	−0.457202	−	0.263966i
$143$	−0.259995	+	0.150108i	−0.0217418	+	0.0125527i
$144$	2.54826	+	1.58314i	0.212355	+	0.131929i
$145$		0			0
$146$	−8.09171			−0.669675
$147$	9.05470	−	8.06302i	0.746819	−	0.665027i
$148$			1.76327i			0.144940i
$149$	11.0505	+	6.38001i	0.905292	+	0.522671i	0.878913	−	0.476981i	$-0.158269\pi$
$149$	11.0505	+	6.38001i	0.905292	+	0.522671i	0.0263788	+	0.999652i	$0.491602\pi$
$150$		0			0
$151$	8.75012	+	15.1557i	0.712075	+	1.23335i	0.964077	+	0.265623i	$0.0855778\pi$
$151$	8.75012	+	15.1557i	0.712075	+	1.23335i	−0.252002	+	0.967727i	$0.581089\pi$
$152$	5.53332	+	3.19467i	0.448812	+	0.259122i
$153$	−0.749442	−	1.40071i	−0.0605888	−	0.113240i
$154$	−0.0106947	+	0.512694i	−0.000861802	+	0.0413141i
$155$		0			0
$156$	2.57984	+	0.736134i	0.206553	+	0.0589379i
$157$	−1.42305	−	2.46479i	−0.113571	−	0.196711i	0.803636	−	0.595121i	$-0.202896\pi$
$157$	−1.42305	−	2.46479i	−0.113571	−	0.196711i	−0.917208	+	0.398409i	$0.869562\pi$
$158$	3.38883	+	5.86962i	0.269601	+	0.466962i
$159$	0.108230	+	0.0308825i	0.00858323	+	0.00244914i
$160$		0			0
$161$	5.82375	−	9.61805i	0.458976	−	0.758009i
$162$	4.99391	−	7.48738i	0.392359	−	0.588264i
$163$	10.7029	+	6.17931i	0.838315	+	0.484001i	0.856691	−	0.515830i	$-0.172516\pi$
$163$	10.7029	+	6.17931i	0.838315	+	0.484001i	−0.0183763	+	0.999831i	$0.505850\pi$
$164$	4.95787	+	8.58728i	0.387144	+	0.670554i
$165$		0			0
$166$	1.82762	+	1.05518i	0.141851	+	0.0818977i
$167$			4.99920i			0.386850i	0.981115	+	0.193425i	$0.0619596\pi$
$167$			4.99920i			0.386850i	−0.981115	+	0.193425i	$0.938040\pi$
$168$	3.35805	−	3.11825i	0.259080	−	0.240578i
$169$	−10.6008			−0.815449
$170$		0			0
$171$	10.1152	−	16.2817i	0.773531	−	1.24509i
$172$	−9.94760	+	5.74325i	−0.758498	+	0.437919i
$173$	−6.58878	−	3.80403i	−0.500935	−	0.289215i	0.228164	−	0.973623i	$-0.426728\pi$
$173$	−6.58878	−	3.80403i	−0.500935	−	0.289215i	−0.729100	+	0.684407i	$0.760061\pi$
$174$	−8.18773	+	2.05273i	−0.620710	+	0.155617i
$175$		0			0
$176$			0.193822i			0.0146099i
$177$	20.0325	+	5.71609i	1.50574	+	0.429648i
$178$	8.18773	+	14.1816i	0.613697	+	1.06295i
$179$	−14.0520	+	8.11295i	−1.05030	+	0.606390i	−0.922733	−	0.385440i	$-0.874050\pi$
$179$	−14.0520	+	8.11295i	−1.05030	+	0.606390i	−0.127566	+	0.991830i	$0.540716\pi$
$180$		0			0
$181$		−	4.03153i		−	0.299661i	−0.988712	−	0.149831i	$-0.952127\pi$
$181$		−	4.03153i		−	0.299661i	0.988712	−	0.149831i	$-0.0478729\pi$
$182$	2.12260	−	3.50552i	0.157338	−	0.259847i
$183$	7.20076	−	1.80529i	0.532295	−	0.133451i
$184$	2.12488	−	3.68040i	0.156648	−	0.271322i
$185$		0			0
$186$	11.1651	+	11.5318i	0.818662	+	0.845549i
$187$	0.0513177	−	0.0888848i	0.00375272	−	0.00649990i
$188$			9.80373i			0.715010i
$189$	−9.02443	−	10.3711i	−0.656431	−	0.754386i
$190$		0			0
$191$	−21.8544	−	12.6176i	−1.58133	−	0.912980i	−0.994666	−	0.103147i	$-0.967109\pi$
$191$	−21.8544	−	12.6176i	−1.58133	−	0.912980i	−0.586661	−	0.809832i	$-0.699558\pi$
$192$	1.24437	−	1.20480i	0.0898046	−	0.0869490i
$193$	−21.8556	+	12.6183i	−1.57320	+	0.908286i	−0.577424	+	0.816444i	$0.695942\pi$
$193$	−21.8556	+	12.6183i	−1.57320	+	0.908286i	−0.995774	+	0.0918418i	$0.970725\pi$
$194$	4.12231	−	7.14006i	0.295965	−	0.512626i
$195$		0			0
$196$	−3.24415	−	6.20286i	−0.231725	−	0.443061i
$197$	14.7364			1.04993			0.524964	−	0.851125i	$-0.324079\pi$
$197$	14.7364			1.04993			0.524964	+	0.851125i	$0.324079\pi$
$198$	0.581164	+	0.0187836i	0.0413015	+	0.00133489i
$199$	−22.3991	+	12.9321i	−1.58783	+	0.916734i	−0.594165	+	0.804343i	$0.702517\pi$
$199$	−22.3991	+	12.9321i	−1.58783	+	0.916734i	−0.993664	+	0.112391i	$0.964149\pi$
$200$		0			0
$201$	2.29576	−	8.04568i	0.161930	−	0.567499i
$202$	4.45663			0.313567
$203$	−0.268908	+	12.8912i	−0.0188736	+	0.904787i
$204$	−0.889645	+	0.223041i	−0.0622876	+	0.0156160i
$205$		0			0
$206$	4.21094	+	7.29356i	0.293390	+	0.508166i
$207$	−10.8295	−	6.72798i	−0.752703	−	0.467627i
$208$	0.774462	−	1.34141i	0.0536992	−	0.0930098i
$209$	1.23840			0.0856616
$210$		0			0
$211$	−22.8721			−1.57458			−0.787289	−	0.616585i	$-0.788516\pi$
$211$	−22.8721			−1.57458			−0.787289	+	0.616585i	$0.788516\pi$
$212$	0.0324905	−	0.0562751i	0.00223145	−	0.00386499i
$213$	7.57944	+	7.82837i	0.519335	+	0.536391i
$214$	−8.90681	−	15.4270i	−0.608857	−	1.05457i
$215$		0			0
$216$	−3.49192	−	3.84792i	−0.237595	−	0.261818i
$217$	21.4848	−	11.8138i	1.45848	−	0.801972i
$218$	−0.147803			−0.0100105
$219$	13.4773	+	3.84563i	0.910714	+	0.259864i
$220$		0			0
$221$	−0.710319	+	0.410103i	−0.0477812	+	0.0275865i
$222$	0.838003	−	2.93685i	0.0562431	−	0.197109i
$223$	−0.00626282			−0.000419390			−0.000209695	−	1.00000i	$-0.500067\pi$
$223$	−0.00626282			−0.000419390			−0.000209695		1.00000i	$0.500067\pi$
$224$	−1.27480	−	2.31838i	−0.0851763	−	0.154903i
$225$		0			0
$226$	−1.72386	+	2.98581i	−0.114669	+	0.198613i
$227$	−16.3051	+	9.41373i	−1.08220	+	0.624811i	−0.931490	−	0.363766i	$-0.881491\pi$
$227$	−16.3051	+	9.41373i	−1.08220	+	0.624811i	−0.150715	+	0.988577i	$0.548157\pi$
$228$	−7.69787	−	7.95069i	−0.509804	−	0.526547i
$229$	−6.75203	−	3.89829i	−0.446187	−	0.257606i	0.260032	−	0.965600i	$-0.416267\pi$
$229$	−6.75203	−	3.89829i	−0.446187	−	0.257606i	−0.706218	+	0.707994i	$0.749600\pi$
$230$		0			0
$231$	0.261474	−	0.848847i	0.0172037	−	0.0558500i
$232$			4.87349i			0.319960i
$233$	−6.49718	+	11.2535i	−0.425645	+	0.737238i	−0.996480	−	0.0838262i	$-0.973286\pi$
$233$	−6.49718	+	11.2535i	−0.425645	+	0.737238i	0.570836	+	0.821064i	$0.306619\pi$
$234$	−3.94707	−	2.45217i	−0.258028	−	0.160303i
$235$		0			0
$236$	6.01371	−	10.4160i	0.391459	−	0.678027i
$237$	−2.85477	−	11.3868i	−0.185437	−	0.739655i
$238$	−0.0292184	+	1.40071i	−0.00189395	+	0.0907944i
$239$			17.1710i			1.11070i	0.831618	+	0.555349i	$0.187415\pi$
$239$			17.1710i			1.11070i	−0.831618	+	0.555349i	$0.812585\pi$
$240$		0			0
$241$	7.10695	−	4.10320i	0.457799	−	0.264310i	−0.253319	−	0.967383i	$-0.581522\pi$
$241$	7.10695	−	4.10320i	0.457799	−	0.264310i	0.711118	+	0.703072i	$0.248189\pi$
$242$	−5.48122	−	9.49375i	−0.352346	−	0.610281i
$243$	−11.8761	+	10.0974i	−0.761855	+	0.647748i
$244$		−	4.28602i		−	0.274384i
$245$		0			0
$246$	−4.17654	−	16.6590i	−0.266286	−	1.06214i
$247$	−8.57069	−	4.94829i	−0.545340	−	0.314852i
$248$	8.02559	−	4.63357i	0.509625	−	0.294232i
$249$	−2.54256	−	2.62606i	−0.161128	−	0.166420i
$250$		0			0
$251$	22.9102			1.44608			0.723038	−	0.690808i	$-0.242745\pi$
$251$	22.9102			1.44608			0.723038	+	0.690808i	$0.242745\pi$
$252$	−7.07505	+	3.59774i	−0.445686	+	0.226636i
$253$		−	0.823698i		−	0.0517855i
$254$	−4.76283	−	2.74982i	−0.298847	−	0.172539i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.13707	+	3.54324i	0.382820	+	0.221021i	0.679044	−	0.734097i	$-0.262394\pi$
$257$	6.13707	+	3.54324i	0.382820	+	0.221021i	−0.296225	+	0.955118i	$0.595728\pi$
$258$	19.2980	−	4.83815i	1.20144	−	0.301210i
$259$	−3.99063	−	2.41634i	−0.247966	−	0.150144i
$260$		0			0
$261$	14.6128	+	0.472296i	0.904512	+	0.0292344i
$262$	2.99843	+	5.19344i	0.185244	+	0.320852i
$263$	−8.93416	−	15.4744i	−0.550904	−	0.954194i	−0.998210	−	0.0598127i	$-0.980950\pi$
$263$	−8.93416	−	15.4744i	−0.550904	−	0.954194i	0.447306	−	0.894381i	$-0.352384\pi$
$264$	0.0921151	−	0.322825i	0.00566930	−	0.0198685i
$265$		0			0
$266$	−14.8129	+	8.14514i	−0.908236	+	0.499410i
$267$	−6.89740	−	27.5117i	−0.422114	−	1.68369i
$268$	−4.18340	−	2.41529i	−0.255542	−	0.147537i
$269$	−3.46273	−	5.99762i	−0.211126	−	0.365682i	0.740941	−	0.671570i	$-0.234380\pi$
$269$	−3.46273	−	5.99762i	−0.211126	−	0.365682i	−0.952067	+	0.305889i	$0.901047\pi$
$270$		0			0
$271$	−14.6520	−	8.45932i	−0.890044	−	0.513867i	−0.0160872	−	0.999871i	$-0.505121\pi$
$271$	−14.6520	−	8.45932i	−0.890044	−	0.513867i	−0.873957	+	0.486003i	$0.838454\pi$
$272$			0.529533i			0.0321076i
$273$	−5.20137	+	4.82993i	−0.314801	+	0.292320i
$274$	0.862112			0.0520821
$275$		0			0
$276$	−5.28827	+	5.12011i	−0.318316	+	0.308194i
$277$	−18.4471	+	10.6505i	−1.10838	+	0.639924i	−0.938410	−	0.345525i	$-0.887701\pi$
$277$	−18.4471	+	10.6505i	−1.10838	+	0.639924i	−0.169972	+	0.985449i	$0.554368\pi$
$278$	−14.0160	−	8.09216i	−0.840626	−	0.485336i
$279$	−13.1157	−	24.5132i	−0.785216	−	1.46757i
$280$		0			0
$281$			19.5927i			1.16880i	0.811464	+	0.584402i	$0.198671\pi$
$281$			19.5927i			1.16880i	−0.811464	+	0.584402i	$0.801329\pi$
$282$	4.65927	−	16.3288i	0.277456	−	0.972367i
$283$	7.54892	+	13.0751i	0.448737	+	0.777235i	0.998304	−	0.0582144i	$-0.0185407\pi$
$283$	7.54892	+	13.0751i	0.448737	+	0.777235i	−0.549567	+	0.835450i	$0.685207\pi$
$284$	5.44820	−	3.14552i	0.323291	−	0.186652i
$285$		0			0
$286$		−	0.300216i		−	0.0177521i
$287$	−26.2289	−	0.547127i	−1.54824	−	0.0322959i
$288$	−2.64518	+	1.41529i	−0.155868	+	0.0833967i
$289$	−8.35980	+	14.4796i	−0.491753	+	0.851741i
$290$		0			0
$291$	−10.2594	+	9.93313i	−0.601414	+	0.582290i
$292$	4.04586	−	7.00763i	0.236766	−	0.410090i
$293$		−	8.00534i		−	0.467677i	−0.972275	−	0.233839i	$-0.924871\pi$
$293$		−	8.00534i		−	0.467677i	0.972275	−	0.233839i	$-0.0751287\pi$
$294$	2.45543	+	11.8731i	0.143204	+	0.692454i
$295$		0			0
$296$	−1.52704	−	0.881634i	−0.0887571	−	0.0512439i
$297$	−0.959044	−	0.307487i	−0.0556494	−	0.0178422i
$298$	−11.0505	+	6.38001i	−0.640138	+	0.369584i
$299$	−3.29127	+	5.70065i	−0.190339	+	0.329677i
$300$		0			0
$301$	0.633799	−	30.3838i	0.0365316	−	1.75129i
$302$	−17.5002			−1.00703
$303$	−7.42283	−	2.11804i	−0.426431	−	0.121678i
$304$	−5.53332	+	3.19467i	−0.317358	+	0.183227i
$305$		0			0
$306$	1.58777	+	0.0513177i	0.0907667	+	0.00293364i
$307$	4.33663			0.247505			0.123752	−	0.992313i	$-0.460507\pi$
$307$	4.33663			0.247505			0.123752	+	0.992313i	$0.460507\pi$
$308$	−0.438659	−	0.265609i	−0.0249949	−	0.0151345i
$309$	−3.54732	−	14.1492i	−0.201800	−	0.804921i
$310$		0			0
$311$	11.4192	+	19.7786i	0.647523	+	1.12154i	0.983713	+	0.179748i	$0.0575284\pi$
$311$	11.4192	+	19.7786i	0.647523	+	1.12154i	−0.336190	+	0.941794i	$0.609138\pi$
$312$	−1.92743	+	1.86614i	−0.109119	+	0.105650i
$313$	12.6521	−	21.9141i	0.715140	−	1.23866i	−0.247766	−	0.968820i	$-0.579696\pi$
$313$	12.6521	−	21.9141i	0.715140	−	1.23866i	0.962906	−	0.269838i	$-0.0869702\pi$
$314$	2.84609			0.160614
$315$		0			0
$316$	−6.77766			−0.381273
$317$	7.54489	−	13.0681i	0.423763	−	0.733979i	−0.572541	−	0.819876i	$-0.694042\pi$
$317$	7.54489	−	13.0681i	0.423763	−	0.733979i	0.996304	+	0.0858969i	$0.0273756\pi$
$318$	−0.0808603	+	0.0782891i	−0.00453442	+	0.00439023i
$319$	0.472296	+	0.818040i	0.0264435	+	0.0458015i
$320$		0			0
$321$	7.50315	+	29.9279i	0.418785	+	1.67041i
$322$	5.41760	+	9.85254i	0.301911	+	0.549061i
$323$	3.38336			0.188255
$324$	3.98731	+	8.06854i	0.221517	+	0.448252i
$325$		0			0
$326$	−10.7029	+	6.17931i	−0.592778	+	0.342241i
$327$	0.246177	+	0.0702443i	0.0136136	+	0.00388452i
$328$	−9.91573			−0.547505
$329$	−22.1878	−	13.4348i	−1.22325	−	0.740683i
$330$		0			0
$331$	−7.53086	+	13.0438i	−0.413933	+	0.716954i	−0.995316	−	0.0966768i	$-0.969179\pi$
$331$	−7.53086	+	13.0438i	−0.413933	+	0.716954i	0.581382	+	0.813630i	$0.302512\pi$
$332$	−1.82762	+	1.05518i	−0.100304	+	0.0579104i
$333$	−2.79151	+	4.49327i	−0.152974	+	0.246230i
$334$	−4.32943	−	2.49960i	−0.236896	−	0.136772i
$335$		0			0
$336$	1.02145	+	4.46728i	0.0557249	+	0.243710i
$337$			14.9611i			0.814983i	0.913209	+	0.407491i	$0.133596\pi$
$337$			14.9611i			0.814983i	−0.913209	+	0.407491i	$0.866404\pi$
$338$	5.30042	−	9.18059i	0.288305	−	0.499359i
$339$	4.29023	−	4.15381i	0.233013	−	0.225604i
$340$		0			0
$341$	0.898091	−	1.55554i	0.0486343	−	0.0842371i
$342$	9.04275	+	16.9009i	0.488976	+	0.913896i
$343$	18.4840	+	1.15806i	0.998043	+	0.0625294i
$344$		−	11.4865i		−	0.619311i
$345$		0			0
$346$	6.58878	−	3.80403i	0.354215	−	0.204506i
$347$	2.02331	+	3.50448i	0.108617	+	0.188130i	0.915210	−	0.402977i	$-0.132024\pi$
$347$	2.02331	+	3.50448i	0.108617	+	0.188130i	−0.806593	+	0.591107i	$0.798691\pi$
$348$	2.31615	−	8.11715i	0.124159	−	0.435125i
$349$			12.3695i			0.662124i	0.943609	+	0.331062i	$0.107407\pi$
$349$			12.3695i			0.662124i	−0.943609	+	0.331062i	$0.892593\pi$
$350$		0			0
$351$	5.40872	+	5.96013i	0.288696	+	0.318128i
$352$	−0.167855	−	0.0969112i	−0.00894671	−	0.00516539i
$353$	3.17585	−	1.83358i	0.169033	−	0.0975914i	−0.413097	−	0.910687i	$-0.635553\pi$
$353$	3.17585	−	1.83358i	0.169033	−	0.0975914i	0.582130	+	0.813096i	$0.302220\pi$
$354$	−14.9665	+	14.4906i	−0.795463	+	0.770169i
$355$		0			0
$356$	−16.3755			−0.867898
$357$	0.714359	−	2.31909i	0.0378079	−	0.122739i
$358$		−	16.2259i		−	0.857565i
$359$	−6.34163	−	3.66134i	−0.334699	−	0.193238i	0.323227	−	0.946322i	$-0.395232\pi$
$359$	−6.34163	−	3.66134i	−0.334699	−	0.193238i	−0.657925	+	0.753083i	$0.728566\pi$
$360$		0			0
$361$	10.9118	+	18.8997i	0.574304	+	0.994723i
$362$	3.49141	+	2.01577i	0.183504	+	0.105946i
$363$	4.61741	+	18.4175i	0.242351	+	0.966668i
$364$	1.97457	+	3.59099i	0.103496	+	0.188219i
$365$		0			0
$366$	−2.03696	+	7.13868i	−0.106473	+	0.373145i
$367$	−2.38312	−	4.12769i	−0.124398	−	0.215464i	0.797100	−	0.603848i	$-0.206367\pi$
$367$	−2.38312	−	4.12769i	−0.124398	−	0.215464i	−0.921497	+	0.388384i	$0.873033\pi$
$368$	2.12488	+	3.68040i	0.110767	+	0.191854i
$369$	−0.960946	+	29.7317i	−0.0500248	+	1.54777i
$370$		0			0
$371$	0.0828379	+	0.150650i	0.00430073	+	0.00782138i
$372$	−15.5693	+	3.90335i	−0.807232	+	0.202379i
$373$	−14.9790	−	8.64813i	−0.775584	−	0.447783i	0.0592792	−	0.998241i	$-0.481120\pi$
$373$	−14.9790	−	8.64813i	−0.775584	−	0.447783i	−0.834863	+	0.550458i	$0.814453\pi$
$374$	0.0513177	+	0.0888848i	0.00265357	+	0.00459612i
$375$		0			0
$376$	−8.49028	−	4.90186i	−0.437853	−	0.252794i
$377$		−	7.54866i		−	0.388776i
$378$	13.4938	−	2.62983i	0.694049	−	0.135264i
$379$	8.76645			0.450302			0.225151	−	0.974324i	$-0.427712\pi$
$379$	8.76645			0.450302			0.225151	+	0.974324i	$0.427712\pi$
$380$		0			0
$381$	6.62598	+	6.84359i	0.339459	+	0.350608i
$382$	21.8544	−	12.6176i	1.11817	−	0.645574i
$383$	−24.6604	−	14.2377i	−1.26009	−	0.727511i	−0.286995	−	0.957932i	$-0.592656\pi$
$383$	−24.6604	−	14.2377i	−1.26009	−	0.727511i	−0.973091	+	0.230422i	$0.925989\pi$
$384$	0.421203	+	1.68006i	0.0214944	+	0.0857350i
$385$		0			0
$386$		−	25.2366i		−	1.28451i
$387$	−34.4415	−	1.11317i	−1.75076	−	0.0565857i
$388$	4.12231	+	7.14006i	0.209279	+	0.362481i
$389$	18.2468	−	10.5348i	0.925151	−	0.534136i	0.0398761	−	0.999205i	$-0.487304\pi$
$389$	18.2468	−	10.5348i	0.925151	−	0.534136i	0.885275	+	0.465069i	$0.153970\pi$
$390$		0			0
$391$		−	2.25039i		−	0.113807i
$392$	6.99391	+	0.291909i	0.353246	+	0.0147437i
$393$	−2.52590	−	10.0751i	−0.127415	−	0.508220i
$394$	−7.36822	+	12.7621i	−0.371205	+	0.642947i
$395$		0			0
$396$	−0.306849	+	0.493911i	−0.0154197	+	0.0248200i
$397$	−3.29905	+	5.71412i	−0.165574	+	0.286783i	−0.936859	−	0.349707i	$-0.886281\pi$
$397$	−3.29905	+	5.71412i	−0.165574	+	0.286783i	0.771285	+	0.636490i	$0.219614\pi$
$398$		−	25.8642i		−	1.29646i
$399$	28.5430	−	6.52641i	1.42894	−	0.326729i
$400$		0			0
$401$	−13.9699	−	8.06552i	−0.697623	−	0.402773i	0.108839	−	0.994059i	$-0.465287\pi$
$401$	−13.9699	−	8.06552i	−0.697623	−	0.402773i	−0.806461	+	0.591287i	$0.798620\pi$
$402$	5.81988	+	6.01103i	0.290269	+	0.299803i
$403$	−12.4310	+	7.17705i	−0.619233	+	0.357514i
$404$	−2.22831	+	3.85955i	−0.110863	+	0.192020i
$405$		0			0
$406$	−11.0297	−	6.67850i	−0.547394	−	0.331448i
$407$	−0.341761			−0.0169405
$408$	0.251663	−	0.881975i	0.0124592	−	0.0436643i
$409$	22.8659	−	13.2016i	1.13065	−	0.652779i	0.186549	−	0.982446i	$-0.440270\pi$
$409$	22.8659	−	13.2016i	1.13065	−	0.652779i	0.944097	+	0.329666i	$0.106936\pi$
$410$		0			0
$411$	−1.43591	−	0.409723i	−0.0708282	−	0.0202102i
$412$	−8.42187			−0.414916
$413$	15.3326	+	27.8841i	0.754467	+	1.37209i
$414$	11.2414	−	6.01464i	0.552482	−	0.295603i
$415$		0			0
$416$	0.774462	+	1.34141i	0.0379711	+	0.0657679i
$417$	19.4989	+	20.1393i	0.954864	+	0.986225i
$418$	−0.619198	+	1.07248i	−0.0302860	+	0.0524568i
$419$	19.8312			0.968819			0.484409	−	0.874841i	$-0.339035\pi$
$419$	19.8312			0.968819			0.484409	+	0.874841i	$0.339035\pi$
$420$		0			0
$421$	6.28009			0.306073			0.153036	−	0.988221i	$-0.451095\pi$
$421$	6.28009			0.306073			0.153036	+	0.988221i	$0.451095\pi$
$422$	11.4360	−	19.8078i	0.556697	−	0.964228i
$423$	−15.5207	+	24.9825i	−0.754643	+	1.21469i
$424$	0.0324905	+	0.0562751i	0.00157788	+	0.00273296i
$425$		0			0
$426$	−10.5693	+	2.64980i	−0.512084	+	0.128383i
$427$	9.70013	+	5.87345i	0.469422	+	0.284236i
$428$	17.8136			0.861054
$429$	−0.142679	+	0.500032i	−0.00688862	+	0.0241418i
$430$		0			0
$431$	3.94326	−	2.27664i	0.189940	−	0.109662i	−0.402014	−	0.915633i	$-0.631690\pi$
$431$	3.94326	−	2.27664i	0.189940	−	0.109662i	0.591955	+	0.805971i	$0.298356\pi$
$432$	5.07836	−	1.10013i	0.244333	−	0.0529302i
$433$	2.62801			0.126294			0.0631471	−	0.998004i	$-0.479886\pi$
$433$	2.62801			0.126294			0.0631471	+	0.998004i	$0.479886\pi$
$434$	−0.511340	+	24.5132i	−0.0245451	+	1.17667i
$435$		0			0
$436$	0.0739017	−	0.128001i	0.00353925	−	0.00613016i
$437$	23.5153	−	13.5765i	1.12489	−	0.649454i
$438$	−10.0691	+	9.74890i	−0.481119	+	0.465820i
$439$	5.05475	+	2.91836i	0.241250	+	0.139286i	0.615751	−	0.787941i	$-0.288853\pi$
$439$	5.05475	+	2.91836i	0.241250	+	0.139286i	−0.374501	+	0.927226i	$0.622186\pi$
$440$		0			0
$441$	1.55306	−	20.9425i	0.0739552	−	0.997262i
$442$		−	0.820205i		−	0.0390132i
$443$	−13.1730	+	22.8164i	−0.625870	+	1.08404i	0.362502	+	0.931983i	$0.381923\pi$
$443$	−13.1730	+	22.8164i	−0.625870	+	1.08404i	−0.988372	+	0.152056i	$0.951411\pi$
$444$	2.12439	+	2.19416i	0.100819	+	0.104130i
$445$		0			0
$446$	0.00313141	−	0.00542376i	0.000148277	−	0.000256823i
$447$	21.4375	−	5.37456i	1.01396	−	0.254208i
$448$	2.64518	+	0.0551777i	0.124973	+	0.00260690i
$449$			5.76638i			0.272132i	0.990700	+	0.136066i	$0.0434460\pi$
$449$			5.76638i			0.272132i	−0.990700	+	0.136066i	$0.956554\pi$
$450$		0			0
$451$	−1.66441	+	0.960946i	−0.0783738	+	0.0452492i
$452$	−1.72386	−	2.98581i	−0.0810834	−	0.140441i
$453$	29.1479	+	8.31709i	1.36949	+	0.390771i
$454$		−	18.8275i		−	0.883617i
$455$		0			0
$456$	10.7344	−	2.69121i	0.502686	−	0.126027i
$457$	0.624848	+	0.360756i	0.0292292	+	0.0168755i	0.514543	−	0.857464i	$-0.327961\pi$
$457$	0.624848	+	0.360756i	0.0292292	+	0.0168755i	−0.485314	+	0.874340i	$0.661295\pi$
$458$	6.75203	−	3.89829i	0.315502	−	0.182155i
$459$	−2.62016	−	0.840069i	−0.122298	−	0.0392111i
$460$		0			0
$461$	34.3692			1.60073			0.800365	−	0.599512i	$-0.204639\pi$
$461$	34.3692			1.60073			0.800365	+	0.599512i	$0.204639\pi$
$462$	0.604386	+	0.650866i	0.0281186	+	0.0302810i
$463$		−	41.3815i		−	1.92316i	−0.274522	−	0.961581i	$-0.588520\pi$
$463$		−	41.3815i		−	1.92316i	0.274522	−	0.961581i	$-0.411480\pi$
$464$	−4.22056	−	2.43674i	−0.195935	−	0.113123i
$465$		0			0
$466$	−6.49718	−	11.2535i	−0.300976	−	0.521306i
$467$	15.5598	+	8.98343i	0.720020	+	0.415704i	0.814760	−	0.579798i	$-0.196869\pi$
$467$	15.5598	+	8.98343i	0.720020	+	0.415704i	−0.0947401	+	0.995502i	$0.530202\pi$
$468$	4.09717	−	2.19217i	0.189392	−	0.101333i
$469$	11.1991	−	6.15804i	0.517127	−	0.284352i
$470$		0			0
$471$	−4.74037	−	1.35262i	−0.218425	−	0.0623254i
$472$	6.01371	+	10.4160i	0.276803	+	0.479437i
$473$	−1.11317	−	1.92807i	−0.0511837	−	0.0886527i
$474$	11.2887	+	3.22112i	0.518506	+	0.147951i
$475$		0			0
$476$	−1.19844	−	0.725657i	−0.0549304	−	0.0332605i
$477$	0.171886	−	0.0919668i	0.00787012	−	0.00421087i
$478$	−14.8705	−	8.58548i	−0.680160	−	0.392691i
$479$	4.50559	+	7.80391i	0.205866	+	0.356570i	0.950408	−	0.311005i	$-0.100666\pi$
$479$	4.50559	+	7.80391i	0.205866	+	0.356570i	−0.744542	+	0.667575i	$0.767332\pi$
$480$		0			0
$481$	2.36526	+	1.36558i	0.107847	+	0.0622652i
$482$			8.20640i			0.373791i
$483$	−4.34093	−	18.9849i	−0.197519	−	0.863842i
$484$	10.9624			0.498292
$485$		0			0
$486$	−2.80653	−	15.3337i	−0.127307	−	0.695552i
$487$	−19.6844	+	11.3648i	−0.891984	+	0.514987i	−0.874591	−	0.484862i	$-0.838870\pi$
$487$	−19.6844	+	11.3648i	−0.891984	+	0.514987i	−0.0173928	+	0.999849i	$0.505537\pi$
$488$	3.71180	+	2.14301i	0.168025	+	0.0970096i
$489$	20.7632	−	5.20549i	0.938944	−	0.235401i
$490$		0			0
$491$		−	32.1654i		−	1.45160i	−0.687904	−	0.725801i	$-0.741469\pi$
$491$		−	32.1654i		−	1.45160i	0.687904	−	0.725801i	$-0.258531\pi$
$492$	16.5154	+	4.71250i	0.744570	+	0.212456i
$493$	1.29034	+	2.23493i	0.0581138	+	0.100656i
$494$	8.57069	−	4.94829i	0.385614	−	0.222634i
$495$		0			0
$496$			9.26715i			0.416107i
$497$	−0.347125	+	16.6409i	−0.0155707	+	0.746446i
$498$	3.54552	−	0.888888i	0.158878	−	0.0398320i
$499$	10.6254	−	18.4037i	0.475658	−	0.823864i	−0.523953	−	0.851747i	$-0.675543\pi$
$499$	10.6254	−	18.4037i	0.475658	−	0.823864i	0.999611	+	0.0278832i	$0.00887665\pi$
$500$		0			0
$501$	6.02304	+	6.22085i	0.269089	+	0.277927i
$502$	−11.4551	+	19.8408i	−0.511265	+	0.885537i
$503$			20.9913i			0.935957i	0.883740	+	0.467978i	$0.155018\pi$
$503$			20.9913i			0.935957i	−0.883740	+	0.467978i	$0.844982\pi$
$504$	0.421794	−	7.92604i	0.0187882	−	0.353054i
$505$		0			0
$506$	0.713343	+	0.411849i	0.0317120	+	0.0183089i
$507$	−13.1914	+	12.7719i	−0.585849	+	0.567220i
$508$	4.76283	−	2.74982i	0.211317	−	0.122004i
$509$	6.98403	−	12.0967i	0.309562	−	0.536177i	−0.668705	−	0.743528i	$-0.733151\pi$
$509$	6.98403	−	12.0967i	0.309562	−	0.536177i	0.978267	+	0.207351i	$0.0664843\pi$
$510$		0			0
$511$	10.3153	+	18.7597i	0.456324	+	0.829878i
$512$	1.00000			0.0441942
$513$	−7.02912	−	32.4473i	−0.310343	−	1.43258i
$514$	−6.13707	+	3.54324i	−0.270695	+	0.156286i
$515$		0			0
$516$	−5.45902	+	19.1316i	−0.240320	+	0.842222i
$517$	−1.90018			−0.0835699
$518$	4.08792	−	2.24782i	0.179613	−	0.0987635i
$519$	−12.7820	+	3.20454i	−0.561066	+	0.140664i
$520$		0			0
$521$	7.21208	+	12.4917i	0.315967	+	0.547271i	0.979643	−	0.200750i	$-0.0643378\pi$
$521$	7.21208	+	12.4917i	0.315967	+	0.547271i	−0.663676	+	0.748020i	$0.731004\pi$
$522$	−7.71544	+	12.4189i	−0.337696	+	0.543562i
$523$	−14.5841	+	25.2604i	−0.637717	+	1.10456i	0.348215	+	0.937415i	$0.386788\pi$
$523$	−14.5841	+	25.2604i	−0.637717	+	1.10456i	−0.985932	+	0.167144i	$0.946545\pi$
$524$	−5.99687			−0.261974
$525$		0			0
$526$	17.8683			0.779096
$527$	2.45363	−	4.24981i	0.106882	−	0.185125i
$528$	0.233517	+	0.241187i	0.0101625	+	0.0104963i
$529$	2.46979	+	4.27779i	0.107382	+	0.185991i
$530$		0			0
$531$	31.8146	−	17.0223i	1.38064	−	0.738704i
$532$	0.352549	−	16.9009i	0.0152849	−	0.732747i
$533$	15.3587			0.665259
$534$	27.2745	+	7.78253i	1.18028	+	0.336783i
$535$		0			0
$536$	4.18340	−	2.41529i	0.180696	−	0.104325i
$537$	−7.71144	+	27.0254i	−0.332773	+	1.16623i
$538$	6.92546			0.298578
$539$	1.20225	−	0.628790i	0.0517847	−	0.0270839i
$540$		0			0
$541$	12.4518	−	21.5672i	0.535345	−	0.927246i	−0.463801	−	0.885939i	$-0.653515\pi$
$541$	12.4518	−	21.5672i	0.535345	−	0.927246i	0.999147	−	0.0413062i	$-0.0131519\pi$
$542$	14.6520	−	8.45932i	0.629356	−	0.363359i
$543$	−4.85719	−	5.01672i	−0.208442	−	0.215288i
$544$	−0.458589	−	0.264766i	−0.0196618	−	0.0113518i
$545$		0			0
$546$	−1.58215	−	6.91948i	−0.0677100	−	0.296126i
$547$		−	0.655376i		−	0.0280219i	−0.999902	−	0.0140109i	$-0.995540\pi$
$547$		−	0.655376i		−	0.0280219i	0.999902	−	0.0140109i	$-0.00445996\pi$
$548$	−0.431056	+	0.746611i	−0.0184138	+	0.0318936i
$549$	6.78539	−	10.9219i	0.289594	−	0.466136i
$550$		0			0
$551$	−15.5692	+	26.9666i	−0.663269	+	1.14882i
$552$	−1.79001	−	7.13983i	−0.0761879	−	0.303891i
$553$	9.28792	−	15.3392i	0.394963	−	0.652289i
$554$		−	21.3009i		−	0.904990i
$555$		0			0
$556$	14.0160	−	8.09216i	0.594412	−	0.343184i
$557$	8.89212	+	15.4016i	0.376771	+	0.652587i	0.990590	−	0.136860i	$-0.0437010\pi$
$557$	8.89212	+	15.4016i	0.376771	+	0.652587i	−0.613819	+	0.789446i	$0.710368\pi$
$558$	27.7869	+	0.898091i	1.17631	+	0.0380192i
$559$			17.7917i			0.752509i
$560$		0			0
$561$	−0.0432303	−	0.172433i	−0.00182519	−	0.00728013i
$562$	−16.9678	−	9.79636i	−0.715743	−	0.413235i
$563$	17.5563	−	10.1362i	0.739912	−	0.427188i	−0.0821256	−	0.996622i	$-0.526171\pi$
$563$	17.5563	−	10.1362i	0.739912	−	0.427188i	0.822037	+	0.569434i	$0.192838\pi$
$564$	11.8115	+	12.1995i	0.497355	+	0.513690i
$565$		0			0
$566$	−15.0978			−0.634610
$567$	−23.7248	−	2.03284i	−0.996349	−	0.0853714i
$568$			6.29103i			0.263966i
$569$	−38.9233	−	22.4724i	−1.63175	−	0.942092i	−0.983553	−	0.180619i	$-0.942190\pi$
$569$	−38.9233	−	22.4724i	−1.63175	−	0.942092i	−0.648197	−	0.761473i	$-0.724477\pi$
$570$		0			0
$571$	5.59451	+	9.68998i	0.234123	+	0.405513i	0.959017	−	0.283347i	$-0.0914448\pi$
$571$	5.59451	+	9.68998i	0.234123	+	0.405513i	−0.724894	+	0.688860i	$0.758111\pi$
$572$	0.259995	+	0.150108i	0.0108709	+	0.00627633i
$573$	−42.3967	+	10.6292i	−1.77115	+	0.444040i
$574$	13.5883	−	22.4413i	0.567163	−	0.936681i
$575$		0			0
$576$	0.0969112	−	2.99843i	0.00403797	−	0.124935i
$577$	−4.86687	−	8.42967i	−0.202611	−	0.350932i	0.746758	−	0.665096i	$-0.231609\pi$
$577$	−4.86687	−	8.42967i	−0.202611	−	0.350932i	−0.949369	+	0.314164i	$0.898276\pi$
$578$	−8.35980	−	14.4796i	−0.347722	−	0.602272i
$579$	−11.9938	+	42.0334i	−0.498447	+	1.74685i
$580$		0			0
$581$	0.116445	−	5.58226i	0.00483094	−	0.231591i
$582$	−3.47266	−	13.8514i	−0.143946	−	0.574160i
$583$	0.0109074	+	0.00629738i	0.000451738	+	0.000260811i
$584$	4.04586	+	7.00763i	0.167419	+	0.289978i
$585$		0			0
$586$	6.93283	+	4.00267i	0.286393	+	0.165349i
$587$		−	32.0185i		−	1.32155i	−0.750585	−	0.660773i	$-0.770228\pi$
$587$		−	32.0185i		−	1.32155i	0.750585	−	0.660773i	$-0.229772\pi$
$588$	−11.5101	−	3.81009i	−0.474670	−	0.157125i
$589$	59.2109			2.43974
$590$		0			0
$591$	18.3376	−	17.7545i	0.754307	−	0.730321i
$592$	1.52704	−	0.881634i	0.0627608	−	0.0362349i
$593$	28.0603	+	16.2006i	1.15230	+	0.665280i	0.949446	−	0.313930i	$-0.101646\pi$
$593$	28.0603	+	16.2006i	1.15230	+	0.665280i	0.202852	+	0.979209i	$0.434979\pi$
$594$	0.745813	−	0.676813i	0.0306011	−	0.0277700i
$595$		0			0
$596$		−	12.7600i		−	0.522671i
$597$	−12.2921	+	43.0788i	−0.503083	+	1.76310i
$598$	−3.29127	−	5.70065i	−0.134590	−	0.233117i
$599$	−9.13107	+	5.27183i	−0.373086	+	0.215401i	−0.674806	−	0.737996i	$-0.735773\pi$
$599$	−9.13107	+	5.27183i	−0.373086	+	0.215401i	0.301720	+	0.953397i	$0.402439\pi$
$600$		0			0
$601$			24.6793i			1.00669i	0.864086	+	0.503344i	$0.167897\pi$
$601$			24.6793i			1.00669i	−0.864086	+	0.503344i	$0.832103\pi$
$602$	25.9963	+	15.7408i	1.05953	+	0.641547i
$603$	−6.83667	−	12.7777i	−0.278411	−	0.520349i
$604$	8.75012	−	15.1557i	0.356038	−	0.616675i
$605$		0			0
$606$	5.54569	−	5.36934i	0.225278	−	0.218115i
$607$	6.49268	−	11.2456i	0.263530	−	0.456447i	−0.703648	−	0.710549i	$-0.748447\pi$
$607$	6.49268	−	11.2456i	0.263530	−	0.456447i	0.967177	+	0.254102i	$0.0817800\pi$
$608$		−	6.38933i		−	0.259122i
$609$	15.1967	+	16.3654i	0.615803	+	0.663161i
$610$		0			0
$611$	13.1508	+	7.59261i	0.532024	+	0.307164i
$612$	−0.838327	+	1.34939i	−0.0338874	+	0.0545458i
$613$	23.1477	−	13.3643i	0.934926	−	0.539780i	0.0465601	−	0.998915i	$-0.485174\pi$
$613$	23.1477	−	13.3643i	0.934926	−	0.539780i	0.888366	+	0.459136i	$0.151841\pi$
$614$	−2.16832	+	3.75563i	−0.0875061	+	0.151565i
$615$		0			0
$616$	0.449354	−	0.247085i	0.0181050	−	0.00995535i
$617$	13.2804			0.534650			0.267325	−	0.963606i	$-0.413860\pi$
$617$	13.2804			0.534650			0.267325	+	0.963606i	$0.413860\pi$
$618$	14.0272	+	4.00254i	0.564259	+	0.161006i
$619$	−8.56249	+	4.94355i	−0.344155	+	0.198698i	−0.662108	−	0.749408i	$-0.730338\pi$
$619$	−8.56249	+	4.94355i	−0.344155	+	0.198698i	0.317953	+	0.948107i	$0.397005\pi$
$620$		0			0
$621$	−21.5818	+	4.67530i	−0.866047	+	0.187613i
$622$	−22.8384			−0.915736
$623$	22.4405	−	37.0610i	0.899060	−	1.48482i
$624$	−0.652411	−	2.60228i	−0.0261174	−	0.104174i
$625$		0			0
$626$	12.6521	+	21.9141i	0.505680	+	0.875864i
$627$	1.54102	−	1.49202i	0.0615425	−	0.0595855i
$628$	−1.42305	+	2.46479i	−0.0567857	+	0.0983557i
$629$	−0.933708			−0.0372294
$630$		0			0
$631$	−26.4695			−1.05373			−0.526867	−	0.849948i	$-0.676633\pi$
$631$	−26.4695			−1.05373			−0.526867	+	0.849948i	$0.676633\pi$
$632$	3.38883	−	5.86962i	0.134800	−	0.233481i
$633$	−28.4613	+	27.5563i	−1.13123	+	1.09526i
$634$	7.54489	+	13.0681i	0.299646	+	0.519002i
$635$		0			0
$636$	−0.0273702	−	0.109172i	−0.00108530	−	0.00432894i
$637$	−10.8330	−	0.452145i	−0.429220	−	0.0179147i
$638$	−0.944591			−0.0373967
$639$	18.8633	+	0.609672i	0.746219	+	0.0241182i
$640$		0			0
$641$	−20.3632	+	11.7567i	−0.804298	+	0.464362i	−0.844972	−	0.534811i	$-0.820383\pi$
$641$	−20.3632	+	11.7567i	−0.804298	+	0.464362i	0.0406739	+	0.999172i	$0.487050\pi$
$642$	−29.6699	−	8.46602i	−1.17098	−	0.334127i
$643$	−20.1307			−0.793876			−0.396938	−	0.917846i	$-0.629927\pi$
$643$	−20.1307			−0.793876			−0.396938	+	0.917846i	$0.629927\pi$
$644$	−11.2414	−	0.234492i	−0.442971	−	0.00924027i
$645$		0			0
$646$	−1.69168	+	2.93008i	−0.0665582	+	0.115282i
$647$	−8.93890	+	5.16088i	−0.351424	+	0.202895i	−0.665312	−	0.746565i	$-0.731702\pi$
$647$	−8.93890	+	5.16088i	−0.351424	+	0.202895i	0.313888	+	0.949460i	$0.398368\pi$
$648$	−8.98122	−	0.581164i	−0.352816	−	0.0228303i
$649$	2.01886	+	1.16559i	0.0792473	+	0.0457535i
$650$		0			0
$651$	12.5017	−	40.5856i	0.489981	−	1.59067i
$652$		−	12.3586i		−	0.484001i
$653$	−1.66715	+	2.88758i	−0.0652404	+	0.113000i	−0.896801	−	0.442435i	$-0.854115\pi$
$653$	−1.66715	+	2.88758i	−0.0652404	+	0.113000i	0.831560	+	0.555435i	$0.187448\pi$
$654$	−0.183922	+	0.178074i	−0.00719192	+	0.00696323i
$655$		0			0
$656$	4.95787	−	8.58728i	0.193572	−	0.335277i
$657$	21.4040	−	11.4521i	0.835050	−	0.446790i
$658$	22.7288	−	12.4978i	0.886059	−	0.487216i
$659$		−	13.1387i		−	0.511809i	−0.966702	−	0.255905i	$-0.917627\pi$
$659$		−	13.1387i		−	0.511809i	0.966702	−	0.255905i	$-0.0823733\pi$
$660$		0			0
$661$	−0.244148	+	0.140959i	−0.00949625	+	0.00548266i	−0.504741	−	0.863271i	$-0.668412\pi$
$661$	−0.244148	+	0.140959i	−0.00949625	+	0.00548266i	0.495244	+	0.868754i	$0.335079\pi$
$662$	−7.53086	−	13.0438i	−0.292695	−	0.506963i
$663$	−0.389807	+	1.36611i	−0.0151389	+	0.0530554i
$664$		−	2.11036i		−	0.0818977i
$665$		0			0
$666$	−2.49554	−	4.66415i	−0.0967000	−	0.180732i
$667$	17.9364	+	10.3556i	0.694499	+	0.400969i
$668$	4.32943	−	2.49960i	0.167511	−	0.0967124i
$669$	−0.00779327	+	0.00754545i	−0.000301305	+	0.000291724i
$670$		0			0
$671$	0.830727			0.0320699
$672$	−4.37951	−	1.34904i	−0.168943	−	0.0520402i
$673$			36.0090i			1.38805i	0.719953	+	0.694023i	$0.244163\pi$
$673$			36.0090i			1.38805i	−0.719953	+	0.694023i	$0.755837\pi$
$674$	−12.9567	−	7.48055i	−0.499073	−	0.288140i
$675$		0			0
$676$	5.30042	+	9.18059i	0.203862	+	0.353100i
$677$	−3.47701	−	2.00745i	−0.133632	−	0.0771526i	0.431694	−	0.902020i	$-0.357916\pi$
$677$	−3.47701	−	2.00745i	−0.133632	−	0.0771526i	−0.565326	+	0.824868i	$0.691250\pi$
$678$	1.45219	+	5.79235i	0.0557709	+	0.222454i
$679$	−21.8085	−	0.454920i	−0.836933	−	0.0174582i
$680$		0			0
$681$	−8.94785	+	31.3585i	−0.342882	+	1.20166i
$682$	0.898091	+	1.55554i	0.0343897	+	0.0595646i
$683$	18.2458	+	31.6027i	0.698156	+	1.20924i	0.969105	+	0.246649i	$0.0793293\pi$
$683$	18.2458	+	31.6027i	0.698156	+	1.20924i	−0.270949	+	0.962594i	$0.587337\pi$
$684$	−19.1580	−	0.619198i	−0.732524	−	0.0236756i
$685$		0			0
$686$	−10.2449	+	15.4286i	−0.391153	+	0.589067i
$687$	−13.0987	+	3.28394i	−0.499746	+	0.125290i
$688$	9.94760	+	5.74325i	0.379249	+	0.218959i
$689$	−0.0503252	−	0.0871659i	−0.00191724	−	0.00332075i
$690$		0			0
$691$	−7.57320	−	4.37239i	−0.288098	−	0.166334i	0.348986	−	0.937128i	$-0.386526\pi$
$691$	−7.57320	−	4.37239i	−0.288098	−	0.166334i	−0.637084	+	0.770795i	$0.719860\pi$
$692$			7.60806i			0.289215i
$693$	−0.697322	−	1.37130i	−0.0264891	−	0.0520915i
$694$	−4.04662			−0.153608
$695$		0			0
$696$	5.87158	+	6.06442i	0.222562	+	0.229871i
$697$	−4.54724	+	2.62535i	−0.172239	+	0.0994423i
$698$	−10.7123	−	6.18475i	−0.405467	−	0.234096i
$699$	5.47327	+	21.8313i	0.207018	+	0.825734i
$700$		0			0
$701$			21.5875i			0.815349i	0.913127	+	0.407674i	$0.133660\pi$
$701$			21.5875i			0.815349i	−0.913127	+	0.407674i	$0.866340\pi$
$702$	−7.86598	+	1.70402i	−0.296882	+	0.0643142i
$703$	−5.63305	−	9.75673i	−0.212455	−	0.367982i
$704$	0.167855	−	0.0969112i	0.00632628	−	0.00365248i
$705$		0			0
$706$			3.66715i			0.138015i
$707$	−5.68132	−	10.3321i	−0.213668	−	0.388580i
$708$	−5.06598	−	20.2067i	−0.190391	−	0.759415i
$709$	−2.50743	+	4.34300i	−0.0941685	+	0.163105i	−0.909261	−	0.416226i	$-0.863353\pi$
$709$	−2.50743	+	4.34300i	−0.0941685	+	0.163105i	0.815093	+	0.579330i	$0.196686\pi$
$710$		0			0
$711$	−17.2713	−	10.7300i	−0.647723	−	0.402407i
$712$	8.18773	−	14.1816i	0.306848	−	0.531477i
$713$		−	39.3831i		−	1.47491i
$714$	1.65121	+	1.77820i	0.0617951	+	0.0665475i
$715$		0			0
$716$	14.0520	+	8.11295i	0.525149	+	0.303195i
$717$	20.6876	+	21.3670i	0.772592	+	0.797966i
$718$	6.34163	−	3.66134i	0.236668	−	0.136640i
$719$	17.1509	−	29.7062i	0.639619	−	1.10785i	−0.345897	−	0.938272i	$-0.612425\pi$
$719$	17.1509	−	29.7062i	0.639619	−	1.10785i	0.985516	−	0.169580i	$-0.0542412\pi$
$720$		0			0
$721$	11.5411	−	19.0604i	0.429813	−	0.709846i
$722$	−21.8235			−0.812188
$723$	3.90013	−	13.6684i	0.145048	−	0.508331i
$724$	−3.49141	+	2.01577i	−0.129757	+	0.0749154i
$725$		0			0
$726$	−18.2587	−	5.20996i	−0.677645	−	0.193360i
$727$	17.4763			0.648159			0.324080	−	0.946030i	$-0.394945\pi$
$727$	17.4763			0.648159			0.324080	+	0.946030i	$0.394945\pi$
$728$	−4.09717	−	0.0854660i	−0.151851	−	0.00316758i
$729$	−2.61296	+	26.8733i	−0.0967764	+	0.995306i
$730$		0			0
$731$	−3.04124	−	5.26758i	−0.112484	−	0.194829i
$732$	−5.16380	−	5.33340i	−0.190860	−	0.197128i
$733$	25.9992	−	45.0320i	0.960304	−	1.66330i	0.238570	−	0.971125i	$-0.423321\pi$
$733$	25.9992	−	45.0320i	0.960304	−	1.66330i	0.721734	−	0.692170i	$-0.243345\pi$
$734$	4.76624			0.175925
$735$		0			0
$736$	−4.24976			−0.156648
$737$	0.468137	−	0.810838i	0.0172441	−	0.0298676i
$738$	−25.2679	−	15.6980i	−0.930125	−	0.577853i
$739$	−12.1033	−	20.9635i	−0.445226	−	0.771155i	0.552842	−	0.833286i	$-0.313543\pi$
$739$	−12.1033	−	20.9635i	−0.445226	−	0.771155i	−0.998068	+	0.0621318i	$0.980210\pi$
$740$		0			0
$741$	−16.6268	+	4.16847i	−0.610801	+	0.153133i
$742$	−0.171886	−	0.00358550i	−0.00631013	−	0.000131628i
$743$	−48.1794			−1.76753			−0.883765	−	0.467932i	$-0.844999\pi$
$743$	−48.1794			−1.76753			−0.883765	+	0.467932i	$0.844999\pi$
$744$	4.40426	−	15.4351i	0.161468	−	0.565879i
$745$		0			0
$746$	14.9790	−	8.64813i	0.548420	−	0.316631i
$747$	−6.32776	−	0.204517i	−0.231521	−	0.00748289i
$748$	−0.102635			−0.00375272
$749$	−24.4113	+	40.3158i	−0.891970	+	1.47311i
$750$		0			0
$751$	−2.58147	+	4.47123i	−0.0941991	+	0.163158i	−0.909274	−	0.416198i	$-0.863362\pi$
$751$	−2.58147	+	4.47123i	−0.0941991	+	0.163158i	0.815075	+	0.579355i	$0.196696\pi$
$752$	8.49028	−	4.90186i	0.309609	−	0.178753i
$753$	28.5087	−	27.6022i	1.03891	−	1.00588i
$754$	6.53733	+	3.77433i	0.238076	+	0.137453i
$755$		0			0
$756$	−4.46942	+	13.0009i	−0.162551	+	0.472839i
$757$		−	16.0842i		−	0.584591i	−0.956328	−	0.292295i	$-0.905581\pi$
$757$		−	16.0842i		−	0.584591i	0.956328	−	0.292295i	$-0.0944190\pi$
$758$	−4.38323	+	7.59197i	−0.159206	+	0.275753i
$759$	−0.992392	−	1.02498i	−0.0360215	−	0.0372046i
$760$		0			0
$761$	−5.07895	+	8.79701i	−0.184112	+	0.318891i	−0.943277	−	0.332007i	$-0.892274\pi$
$761$	−5.07895	+	8.79701i	−0.184112	+	0.318891i	0.759165	+	0.650898i	$0.225608\pi$
$762$	−9.23972	+	2.31647i	−0.334720	+	0.0839168i
$763$	0.188420	+	0.342664i	0.00682127	+	0.0124053i
$764$			25.2353i			0.912980i
$765$		0			0
$766$	24.6604	−	14.2377i	0.891015	−	0.514428i
$767$	−9.31477	−	16.1337i	−0.336337	−	0.582552i
$768$	−1.66557	−	0.475255i	−0.0601012	−	0.0171493i
$769$		−	6.68859i		−	0.241197i	−0.992701	−	0.120598i	$-0.961519\pi$
$769$		−	6.68859i		−	0.241197i	0.992701	−	0.120598i	$-0.0384813\pi$
$770$		0			0
$771$	11.9057	−	2.98485i	0.428773	−	0.107497i
$772$	21.8556	+	12.6183i	0.786599	+	0.454143i
$773$	−23.0107	+	13.2852i	−0.827636	+	0.477836i	−0.853043	−	0.521841i	$-0.825245\pi$
$773$	−23.0107	+	13.2852i	−0.827636	+	0.477836i	0.0254064	+	0.999677i	$0.491912\pi$
$774$	18.1848	−	29.2707i	0.653639	−	1.05211i
$775$		0			0
$776$	−8.24463			−0.295965
$777$	−7.87702	+	1.80110i	−0.282587	+	0.0646141i
$778$			21.0696i			0.755382i
$779$	−54.8669	−	31.6774i	−1.96581	−	1.13496i
$780$		0			0
$781$	0.609672	+	1.05598i	0.0218158	+	0.0377860i
$782$	1.94889	+	1.12519i	0.0696922	+	0.0402368i
$783$	18.7528	−	17.0178i	0.670170	−	0.608168i
$784$	−3.74976	+	5.91095i	−0.133920	+	0.211105i
$785$		0			0
$786$	9.98822	+	2.85004i	0.356268	+	0.101658i
$787$	14.7959	+	25.6272i	0.527416	+	0.913510i	0.999489	+	0.0319515i	$0.0101722\pi$
$787$	14.7959	+	25.6272i	0.527416	+	0.913510i	−0.472074	+	0.881559i	$0.656494\pi$
$788$	−7.36822	−	12.7621i	−0.262482	−	0.454632i
$789$	−29.7610	−	8.49202i	−1.05952	−	0.302324i
$790$		0			0
$791$	9.11981	+	0.190237i	0.324263	+	0.00676405i
$792$	−0.274315	−	0.512694i	−0.00974735	−	0.0182178i
$793$	−5.74930	−	3.31936i	−0.204164	−	0.117874i
$794$	−3.29905	−	5.71412i	−0.117079	−	0.202786i
$795$		0			0
$796$	22.3991	+	12.9321i	0.793915	+	0.458367i
$797$		−	34.6019i		−	1.22566i	−0.790215	−	0.612830i	$-0.790031\pi$
$797$		−	34.6019i		−	1.22566i	0.790215	−	0.612830i	$-0.209969\pi$
$798$	−8.61944	+	27.9821i	−0.305125	+	0.990557i
$799$	−5.19139			−0.183658
$800$		0			0
$801$	−41.7290	−	25.9247i	−1.47442	−	0.916005i
$802$	13.9699	−	8.06552i	0.493294	−	0.284803i
$803$	1.35824	+	0.784178i	0.0479311	+	0.0276730i
$804$	−8.11564	+	2.03465i	−0.286217	+	0.0717567i
$805$		0			0
$806$		−	14.3541i		−	0.505602i
$807$	−11.5349	−	3.29136i	−0.406046	−	0.115861i
$808$	−2.22831	−	3.85955i	−0.0783918	−	0.135779i
$809$	14.6105	−	8.43536i	0.513677	−	0.296571i	−0.220667	−	0.975349i	$-0.570823\pi$
$809$	14.6105	−	8.43536i	0.513677	−	0.296571i	0.734344	+	0.678778i	$0.237490\pi$
$810$		0			0
$811$			11.1600i			0.391880i	0.980616	+	0.195940i	$0.0627758\pi$
$811$			11.1600i			0.391880i	−0.980616	+	0.195940i	$0.937224\pi$
$812$	11.2986	−	6.21274i	0.396503	−	0.218024i
$813$	−28.4243	+	7.12619i	−0.996883	+	0.249926i
$814$	0.170880	−	0.295974i	0.00598936	−	0.0103739i
$815$		0			0
$816$	0.637981	+	0.658934i	0.0223338	+	0.0230673i
$817$	36.6955	−	63.5585i	1.28381	−	2.22363i
$818$			26.4033i			0.923169i
$819$	−0.653326	+	12.2768i	−0.0228291	+	0.428987i
$820$		0			0
$821$	−34.0899	−	19.6818i	−1.18975	−	0.686901i	−0.231498	−	0.972835i	$-0.574363\pi$
$821$	−34.0899	−	19.6818i	−1.18975	−	0.686901i	−0.958249	+	0.285934i	$0.907696\pi$
$822$	1.07279	−	1.03867i	0.0374177	−	0.0362279i
$823$	−35.2620	+	20.3585i	−1.22916	+	0.709654i	−0.966854	−	0.255332i	$-0.917815\pi$
$823$	−35.2620	+	20.3585i	−1.22916	+	0.709654i	−0.262303	+	0.964986i	$0.584482\pi$
$824$	4.21094	−	7.29356i	0.146695	−	0.254083i
$825$		0			0
$826$	−31.8146	−	0.663645i	−1.10697	−	0.0230912i
$827$	24.7892			0.862006			0.431003	−	0.902350i	$-0.358160\pi$
$827$	24.7892			0.862006			0.431003	+	0.902350i	$0.358160\pi$
$828$	−0.411849	+	12.7426i	−0.0143127	+	0.442837i
$829$	0.897813	−	0.518352i	0.0311823	−	0.0180031i	−0.484328	−	0.874887i	$-0.660936\pi$
$829$	0.897813	−	0.518352i	0.0311823	−	0.0180031i	0.515510	+	0.856883i	$0.327602\pi$
$830$		0			0
$831$	−10.1234	+	35.4782i	−0.351176	+	1.23073i
$832$	−1.54892			−0.0536992
$833$	3.28462	−	1.71789i	0.113805	−	0.0595212i
$834$	−27.1906	+	6.81689i	−0.941533	+	0.236050i
$835$		0			0
$836$	−0.619198	−	1.07248i	−0.0214154	−	0.0370926i
$837$	−45.8543	−	14.7017i	−1.58496	−	0.508166i
$838$	−9.91561	+	17.1743i	−0.342529	+	0.593278i
$839$	19.4880			0.672801			0.336401	−	0.941719i	$-0.390790\pi$
$839$	19.4880			0.672801			0.336401	+	0.941719i	$0.390790\pi$
$840$		0			0
$841$	5.24911			0.181004
$842$	−3.14004	+	5.43872i	−0.108213	+	0.187431i
$843$	23.6053	+	24.3806i	0.813011	+	0.839712i
$844$	11.4360	+	19.8078i	0.393644	+	0.681812i
$845$		0			0
$846$	−13.8751	−	25.9326i	−0.477036	−	0.891581i
$847$	−15.0226	+	24.8102i	−0.516183	+	0.852488i
$848$	−0.0649809			−0.00223145
$849$	25.1466	+	7.17533i	0.863028	+	0.246257i
$850$		0			0
$851$	−6.48953	+	3.74673i	−0.222458	+	0.128436i
$852$	2.98985	−	10.4782i	0.102430	−	0.358976i
$853$	3.93413			0.134702			0.0673510	−	0.997729i	$-0.478545\pi$
$853$	3.93413			0.134702			0.0673510	+	0.997729i	$0.478545\pi$
$854$	−9.93662	+	5.46383i	−0.340024	+	0.186969i
$855$		0			0
$856$	−8.90681	+	15.4270i	−0.304429	+	0.527286i
$857$	7.79083	−	4.49804i	0.266130	−	0.153650i	−0.360998	−	0.932567i	$-0.617564\pi$
$857$	7.79083	−	4.49804i	0.266130	−	0.153650i	0.627128	+	0.778917i	$0.284230\pi$
$858$	−0.361700	−	0.373580i	−0.0123482	−	0.0127538i
$859$	−35.2001	−	20.3228i	−1.20101	−	0.693404i	−0.240231	−	0.970716i	$-0.577223\pi$
$859$	−35.2001	−	20.3228i	−1.20101	−	0.693404i	−0.960780	+	0.277312i	$0.910556\pi$
$860$		0			0
$861$	−33.2976	+	30.9197i	−1.13478	+	1.05374i
$862$			4.55329i			0.155086i
$863$	−16.6238	+	28.7932i	−0.565880	+	0.980133i	0.431087	+	0.902310i	$0.358130\pi$
$863$	−16.6238	+	28.7932i	−0.565880	+	0.980133i	−0.996967	+	0.0778229i	$0.975203\pi$
$864$	−1.58643	+	4.94805i	−0.0539716	+	0.168336i
$865$		0			0
$866$	−1.31401	+	2.27592i	−0.0446517	+	0.0773391i
$867$	7.04235	+	28.0899i	0.239171	+	0.953981i
$868$	−20.9734	−	12.6995i	−0.711884	−	0.431047i
$869$		−	1.31366i		−	0.0445629i
$870$		0			0
$871$	−6.47977	+	3.74110i	−0.219559	+	0.126762i
$872$	0.0739017	+	0.128001i	0.00250263	+	0.00433468i
$873$	−0.798997	+	24.7210i	−0.0270419	+	0.836678i
$874$			27.1531i			0.918467i
$875$		0			0
$876$	−3.40825	−	13.5945i	−0.115154	−	0.459317i
$877$	−24.4763	−	14.1314i	−0.826506	−	0.477184i	0.0261486	−	0.999658i	$-0.491676\pi$
$877$	−24.4763	−	14.1314i	−0.826506	−	0.477184i	−0.852655	+	0.522474i	$0.825009\pi$
$878$	−5.05475	+	2.91836i	−0.170590	+	0.0984899i
$879$	−9.64484	−	9.96160i	−0.325312	−	0.335997i
$880$		0			0
$881$	34.2140			1.15270			0.576350	−	0.817203i	$-0.304477\pi$
$881$	34.2140			1.15270			0.576350	+	0.817203i	$0.304477\pi$
$882$	17.3602	+	11.8162i	0.584548	+	0.397873i
$883$		−	4.09672i		−	0.137866i	−0.997621	−	0.0689328i	$-0.978041\pi$
$883$		−	4.09672i		−	0.137866i	0.997621	−	0.0689328i	$-0.0219594\pi$
$884$	0.710319	+	0.410103i	0.0238906	+	0.0137932i
$885$		0			0
$886$	−13.1730	−	22.8164i	−0.442557	−	0.766531i
$887$	−1.60561	−	0.926997i	−0.0539110	−	0.0311255i	0.472802	−	0.881169i	$-0.343242\pi$
$887$	−1.60561	−	0.926997i	−0.0539110	−	0.0311255i	−0.526713	+	0.850043i	$0.676576\pi$
$888$	−2.96239	+	0.742694i	−0.0994113	+	0.0249232i
$889$	−0.303458	+	14.5475i	−0.0101777	+	0.487909i
$890$		0			0
$891$	−1.56386	+	0.772829i	−0.0523914	+	0.0258908i
$892$	0.00313141	+	0.00542376i	0.000104847	+	0.000181601i
$893$	−31.3196	−	54.2472i	−1.04807	−	1.81531i
$894$	−6.06427	+	21.2527i	−0.202819	+	0.710798i
$895$		0			0
$896$	−1.37037	+	2.26320i	−0.0457810	+	0.0756082i
$897$	2.77259	+	11.0590i	0.0925740	+	0.369251i
$898$	−4.99383	−	2.88319i	−0.166646	−	0.0962134i
$899$	22.5817	+	39.1126i	0.753141	+	1.30448i
$900$		0			0
$901$	0.0297995	+	0.0172048i	0.000992766	+	0.000573174i
$902$		−	1.92189i		−	0.0639920i
$903$	−35.8178	−	38.5723i	−1.19194	−	1.28361i
$904$	3.44771			0.114669
$905$		0			0
$906$	−21.7768	+	21.0843i	−0.723485	+	0.700479i
$907$	29.2217	−	16.8711i	0.970289	−	0.560197i	0.0709647	−	0.997479i	$-0.477392\pi$
$907$	29.2217	−	16.8711i	0.970289	−	0.560197i	0.899324	+	0.437282i	$0.144059\pi$
$908$	16.3051	+	9.41373i	0.541102	+	0.312406i
$909$	−11.7886	+	6.30742i	−0.391002	+	0.209204i
$910$		0			0
$911$			6.90180i			0.228667i	0.993442	+	0.114333i	$0.0364732\pi$
$911$			6.90180i			0.228667i	−0.993442	+	0.114333i	$0.963527\pi$
$912$	−3.03656	+	10.6419i	−0.100551	+	0.352388i
$913$	−0.204517	−	0.354234i	−0.00676853	−	0.0117234i
$914$	−0.624848	+	0.360756i	−0.0206682	+	0.0119328i
$915$		0			0
$916$			7.79658i			0.257606i
$917$	8.21795	−	13.5721i	0.271381	−	0.448191i
$918$	2.03760	−	1.84909i	0.0672508	−	0.0610290i
$919$	−17.5128	+	30.3330i	−0.577693	+	1.00059i	0.418050	+	0.908424i	$0.362714\pi$
$919$	−17.5128	+	30.3330i	−0.577693	+	1.00059i	−0.995743	+	0.0921698i	$0.970620\pi$
$920$		0			0
$921$	5.39637	−	5.22477i	0.177816	−	0.172162i
$922$	−17.1846	+	29.7646i	−0.565944	+	0.980243i
$923$		−	9.74433i		−	0.320738i
$924$	−0.865860	+	0.197981i	−0.0284847	+	0.00651309i
$925$		0			0
$926$	35.8374	+	20.6908i	1.17769	+	0.679940i
$927$	−21.4612	−	13.3330i	−0.704877	−	0.437915i
$928$	4.22056	−	2.43674i	0.138547	−	0.0799900i
$929$	10.5447	−	18.2639i	0.345960	−	0.599220i	−0.639568	−	0.768734i	$-0.720887\pi$
$929$	10.5447	−	18.2639i	0.345960	−	0.599220i	0.985528	+	0.169515i	$0.0542201\pi$
$930$		0			0
$931$	37.7670	+	23.9584i	1.23776	+	0.785206i
$932$	12.9944			0.425645
$933$	38.0390	+	10.8541i	1.24534	+	0.355346i
$934$	−15.5598	+	8.98343i	−0.509131	+	0.293947i
$935$		0			0
$936$	−0.150108	+	4.64434i	−0.00490643	+	0.151805i
$937$	−44.5007			−1.45378			−0.726888	−	0.686756i	$-0.759034\pi$
$937$	−44.5007			−1.45378			−0.726888	+	0.686756i	$0.759034\pi$
$938$	−0.266540	+	12.7777i	−0.00870285	+	0.417208i
$939$	−10.6582	−	42.5125i	−0.347818	−	1.38734i
$940$		0			0
$941$	−21.8197	−	37.7929i	−0.711303	−	1.23201i	−0.964368	−	0.264564i	$-0.914772\pi$
$941$	−21.8197	−	37.7929i	−0.711303	−	1.23201i	0.253065	−	0.967449i	$-0.418561\pi$
$942$	3.54159	−	3.42897i	0.115391	−	0.111722i
$943$	−21.0697	+	36.4938i	−0.686125	+	1.18840i
$944$	−12.0274			−0.391459
$945$		0			0
$946$	2.22634			0.0723846
$947$	6.44589	−	11.1646i	0.209463	−	0.362801i	−0.742082	−	0.670309i	$-0.766162\pi$
$947$	6.44589	−	11.1646i	0.209463	−	0.362801i	0.951546	+	0.307508i	$0.0994950\pi$
$948$	−8.43391	+	8.16573i	−0.273921	+	0.265210i
$949$	−6.26672	−	10.8543i	−0.203426	−	0.352345i
$950$		0			0
$951$	−6.35586	−	25.3517i	−0.206103	−	0.822084i
$952$	1.22766	−	0.675050i	0.0397886	−	0.0218785i
$953$	47.2228			1.52970			0.764848	−	0.644211i	$-0.222814\pi$
$953$	47.2228			1.52970			0.764848	+	0.644211i	$0.222814\pi$
$954$	−0.00629738	+	0.194841i	−0.000203885	+	0.00630821i
$955$		0			0
$956$	14.8705	−	8.58548i	0.480946	−	0.277674i
$957$	1.57329	+	0.448922i	0.0508571	+	0.0145116i
$958$	−9.01118			−0.291138
$959$	−1.09902	−	1.99870i	−0.0354893	−	0.0645414i
$960$		0			0
$961$	27.4400	−	47.5275i	0.885162	−	1.53315i
$962$	−2.36526	+	1.36558i	−0.0762590	+	0.0440282i
$963$	45.3938	+	28.2015i	1.46280	+	0.908782i
$964$	−7.10695	−	4.10320i	−0.228899	−	0.132155i
$965$		0			0
$966$	18.6118	+	5.73308i	0.598826	+	0.184459i
$967$		−	7.93428i		−	0.255149i	−0.991829	−	0.127575i	$-0.959281\pi$
$967$		−	7.93428i		−	0.255149i	0.991829	−	0.127575i	$-0.0407192\pi$
$968$	−5.48122	+	9.49375i	−0.176173	+	0.305141i
$969$	4.21015	−	4.07627i	0.135249	−	0.130949i
$970$		0			0
$971$	16.7632	−	29.0348i	0.537958	−	0.931770i	−0.461056	−	0.887371i	$-0.652529\pi$
$971$	16.7632	−	29.0348i	0.537958	−	0.931770i	0.999014	−	0.0443991i	$-0.0141373\pi$
$972$	14.6827	+	5.23634i	0.470947	+	0.167956i
$973$	−0.893014	+	42.8104i	−0.0286287	+	1.37244i
$974$		−	22.7295i		−	0.728302i
$975$		0			0
$976$	−3.71180	+	2.14301i	−0.118812	+	0.0685961i
$977$	6.62608	+	11.4767i	0.211987	+	0.367172i	0.952336	−	0.305050i	$-0.0986732\pi$
$977$	6.62608	+	11.4767i	0.211987	+	0.367172i	−0.740349	+	0.672222i	$0.765340\pi$
$978$	−5.87350	+	20.5842i	−0.187814	+	0.658210i
$979$		−	3.17393i		−	0.101439i
$980$		0			0
$981$	0.390966	−	0.209185i	0.0124826	−	0.00667875i
$982$	27.8560	+	16.0827i	0.888921	+	0.513219i
$983$	38.0599	−	21.9739i	1.21392	−	0.700858i	0.250311	−	0.968165i	$-0.419467\pi$
$983$	38.0599	−	21.9739i	1.21392	−	0.700858i	0.963611	+	0.267307i	$0.0861338\pi$
$984$	−12.3388	+	11.9465i	−0.393348	+	0.380840i
$985$		0			0
$986$	−2.58067			−0.0821853
$987$	−43.7960	+	10.0141i	−1.39404	+	0.318751i
$988$			9.89658i			0.314852i
$989$	−42.2749	−	24.4074i	−1.34426	−	0.776111i
$990$		0			0
$991$	−5.43257	−	9.40948i	−0.172571	−	0.298902i	0.766747	−	0.641950i	$-0.221874\pi$
$991$	−5.43257	−	9.40948i	−0.172571	−	0.298902i	−0.939318	+	0.343047i	$0.888541\pi$
$992$	−8.02559	−	4.63357i	−0.254813	−	0.147116i
$993$	6.34404	+	25.3045i	0.201322	+	0.803015i
$994$	−14.2379	−	8.62106i	−0.451598	−	0.273444i
$995$		0			0
$996$	−1.00296	+	3.51495i	−0.0317799	+	0.111375i
$997$	−20.1028	−	34.8191i	−0.636662	−	1.10273i	−0.986160	−	0.165794i	$-0.946981\pi$
$997$	−20.1028	−	34.8191i	−0.636662	−	1.10273i	0.349499	−	0.936937i	$-0.386352\pi$
$998$	10.6254	+	18.4037i	0.336341	+	0.582560i
$999$	1.93983	+	8.95450i	0.0613735	+	0.283308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.u.e.299.5		12
3.2	odd	2		1050.2.u.g.299.2		12
5.2	odd	4		1050.2.s.f.551.1		12
5.3	odd	4		210.2.r.b.131.6	yes	12
5.4	even	2		1050.2.u.h.299.2		12
7.3	odd	6		1050.2.u.f.899.5		12
15.2	even	4		1050.2.s.g.551.5		12
15.8	even	4		210.2.r.a.131.2	yes	12
15.14	odd	2		1050.2.u.f.299.5		12
21.17	even	6		1050.2.u.h.899.2		12
35.3	even	12		210.2.r.a.101.2	✓	12
35.17	even	12		1050.2.s.g.101.5		12
35.23	odd	12		1470.2.b.a.881.1		12
35.24	odd	6		1050.2.u.g.899.2		12
35.33	even	12		1470.2.b.b.881.6		12
105.17	odd	12		1050.2.s.f.101.1		12
105.23	even	12		1470.2.b.b.881.12		12
105.38	odd	12		210.2.r.b.101.6	yes	12
105.59	even	6	inner	1050.2.u.e.899.5		12
105.68	odd	12		1470.2.b.a.881.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.2	✓	12	35.3	even	12
210.2.r.a.131.2	yes	12	15.8	even	4
210.2.r.b.101.6	yes	12	105.38	odd	12
210.2.r.b.131.6	yes	12	5.3	odd	4
1050.2.s.f.101.1		12	105.17	odd	12
1050.2.s.f.551.1		12	5.2	odd	4
1050.2.s.g.101.5		12	35.17	even	12
1050.2.s.g.551.5		12	15.2	even	4
1050.2.u.e.299.5		12	1.1	even	1	trivial
1050.2.u.e.899.5		12	105.59	even	6	inner
1050.2.u.f.299.5		12	15.14	odd	2
1050.2.u.f.899.5		12	7.3	odd	6
1050.2.u.g.299.2		12	3.2	odd	2
1050.2.u.g.899.2		12	35.24	odd	6
1050.2.u.h.299.2		12	5.4	even	2
1050.2.u.h.899.2		12	21.17	even	6
1470.2.b.a.881.1		12	35.23	odd	12
1470.2.b.a.881.7		12	105.68	odd	12
1470.2.b.b.881.6		12	35.33	even	12
1470.2.b.b.881.12		12	105.23	even	12

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.24437 - 1.20480i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.421203 + 1.68006i) q^{6} +(2.64518 + 0.0551777i) q^{7} +1.00000 q^{8} +(0.0969112 - 2.99843i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.24437 - 1.20480i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.421203 + 1.68006i) q^{6} +(2.64518 + 0.0551777i) q^{7} +1.00000 q^{8} +(0.0969112 - 2.99843i) q^{9} +(0.167855 - 0.0969112i) q^{11} +(-1.66557 - 0.475255i) q^{12} -1.54892 q^{13} +(-1.37037 + 2.26320i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.458589 - 0.264766i) q^{17} +(2.54826 + 1.58314i) q^{18} +(5.53332 + 3.19467i) q^{19} +(3.35805 - 3.11825i) q^{21} +0.193822i q^{22} +(2.12488 - 3.68040i) q^{23} +(1.24437 - 1.20480i) q^{24} +(0.774462 - 1.34141i) q^{26} +(-3.49192 - 3.84792i) q^{27} +(-1.27480 - 2.31838i) q^{28} +4.87349i q^{29} +(8.02559 - 4.63357i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.0921151 - 0.322825i) q^{33} +0.529533i q^{34} +(-2.64518 + 1.41529i) q^{36} +(-1.52704 - 0.881634i) q^{37} +(-5.53332 + 3.19467i) q^{38} +(-1.92743 + 1.86614i) q^{39} -9.91573 q^{41} +(1.02145 + 4.46728i) q^{42} -11.4865i q^{43} +(-0.167855 - 0.0969112i) q^{44} +(2.12488 + 3.68040i) q^{46} +(-8.49028 - 4.90186i) q^{47} +(0.421203 + 1.68006i) q^{48} +(6.99391 + 0.291909i) q^{49} +(0.251663 - 0.881975i) q^{51} +(0.774462 + 1.34141i) q^{52} +(0.0324905 + 0.0562751i) q^{53} +(5.07836 - 1.10013i) q^{54} +(2.64518 + 0.0551777i) q^{56} +(10.7344 - 2.69121i) q^{57} +(-4.22056 - 2.43674i) q^{58} +(6.01371 + 10.4160i) q^{59} +(3.71180 + 2.14301i) q^{61} +9.26715i q^{62} +(0.421794 - 7.92604i) q^{63} +1.00000 q^{64} +(0.233517 + 0.241187i) q^{66} +(4.18340 - 2.41529i) q^{67} +(-0.458589 - 0.264766i) q^{68} +(-1.79001 - 7.13983i) q^{69} +6.29103i q^{71} +(0.0969112 - 2.99843i) q^{72} +(4.04586 + 7.00763i) q^{73} +(1.52704 - 0.881634i) q^{74} -6.38933i q^{76} +(0.449354 - 0.247085i) q^{77} +(-0.652411 - 2.60228i) q^{78} +(3.38883 - 5.86962i) q^{79} +(-8.98122 - 0.581164i) q^{81} +(4.95787 - 8.58728i) q^{82} -2.11036i q^{83} +(-4.37951 - 1.34904i) q^{84} +(9.94760 + 5.74325i) q^{86} +(5.87158 + 6.06442i) q^{87} +(0.167855 - 0.0969112i) q^{88} +(8.18773 - 14.1816i) q^{89} +(-4.09717 - 0.0854660i) q^{91} -4.24976 q^{92} +(4.40426 - 15.4351i) q^{93} +(8.49028 - 4.90186i) q^{94} +(-1.66557 - 0.475255i) q^{96} -8.24463 q^{97} +(-3.74976 + 5.91095i) q^{98} +(-0.274315 - 0.512694i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} + 2 q^{3} - 6 q^{4} + 2 q^{6} - 6 q^{7} + 12 q^{8}+O(q^{10}) \) 12 * q - 6 * q^2 + 2 * q^3 - 6 * q^4 + 2 * q^6 - 6 * q^7 + 12 * q^8	\( 12 q - 6 q^{2} + 2 q^{3} - 6 q^{4} + 2 q^{6} - 6 q^{7} + 12 q^{8} + 12 q^{11} - 4 q^{12} - 8 q^{13} + 12 q^{14} - 6 q^{16} + 12 q^{17} - 6 q^{18} + 4 q^{21} + 2 q^{23} + 2 q^{24} + 4 q^{26} - 28 q^{27} - 6 q^{28} + 12 q^{31} - 6 q^{32} + 34 q^{33} + 6 q^{36} + 42 q^{39} + 4 q^{41} + 16 q^{42} - 12 q^{44} + 2 q^{46} + 24 q^{47} + 2 q^{48} + 14 q^{49} - 8 q^{51} + 4 q^{52} + 8 q^{53} + 32 q^{54} - 6 q^{56} - 20 q^{57} + 18 q^{58} + 12 q^{59} - 30 q^{61} + 2 q^{63} + 12 q^{64} - 14 q^{66} - 6 q^{67} - 12 q^{68} + 50 q^{69} - 20 q^{77} - 12 q^{78} + 4 q^{79} - 40 q^{81} - 2 q^{82} - 20 q^{84} + 54 q^{86} - 8 q^{87} + 12 q^{88} + 26 q^{89} + 28 q^{91} - 4 q^{92} - 24 q^{93} - 24 q^{94} - 4 q^{96} + 72 q^{97} + 2 q^{98} - 48 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 + 2 * q^3 - 6 * q^4 + 2 * q^6 - 6 * q^7 + 12 * q^8 + 12 * q^11 - 4 * q^12 - 8 * q^13 + 12 * q^14 - 6 * q^16 + 12 * q^17 - 6 * q^18 + 4 * q^21 + 2 * q^23 + 2 * q^24 + 4 * q^26 - 28 * q^27 - 6 * q^28 + 12 * q^31 - 6 * q^32 + 34 * q^33 + 6 * q^36 + 42 * q^39 + 4 * q^41 + 16 * q^42 - 12 * q^44 + 2 * q^46 + 24 * q^47 + 2 * q^48 + 14 * q^49 - 8 * q^51 + 4 * q^52 + 8 * q^53 + 32 * q^54 - 6 * q^56 - 20 * q^57 + 18 * q^58 + 12 * q^59 - 30 * q^61 + 2 * q^63 + 12 * q^64 - 14 * q^66 - 6 * q^67 - 12 * q^68 + 50 * q^69 - 20 * q^77 - 12 * q^78 + 4 * q^79 - 40 * q^81 - 2 * q^82 - 20 * q^84 + 54 * q^86 - 8 * q^87 + 12 * q^88 + 26 * q^89 + 28 * q^91 - 4 * q^92 - 24 * q^93 - 24 * q^94 - 4 * q^96 + 72 * q^97 + 2 * q^98 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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