LMFDB - Embedded newform 1050.2.s.f.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(101,1050)]

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, 0, 1]))

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

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

chi := DirichletCharacter("1050.101");

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.s (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:	$8.38429221223$
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:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.1
Root			$1.66557 + 0.475255i$ of defining polynomial
Character	$\chi$	$=$	1050.101
Dual form			1050.2.s.f.551.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.20480	+	1.24437i	−0.695592	+	0.718437i
$3$	−1.20480	+	1.24437i	−0.695592	+	0.718437i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.421203	−	1.68006i	0.171955	−	0.685880i
$7$	−0.0551777	−	2.64518i	−0.0208552	−	0.999783i
$7$	−0.0551777	−	2.64518i	−0.0208552	−	0.999783i
$8$			1.00000i			0.353553i
$9$	−0.0969112	−	2.99843i	−0.0323037	−	0.999478i
$10$		0			0
$11$	0.167855	+	0.0969112i	0.0506102	+	0.0292198i	0.525092	−	0.851046i	$-0.324031\pi$
$11$	0.167855	+	0.0969112i	0.0506102	+	0.0292198i	−0.474481	+	0.880266i	$0.657364\pi$
$12$	0.475255	+	1.66557i	0.137194	+	0.480809i
$13$		−	1.54892i		−	0.429594i	−0.976659	−	0.214797i	$-0.931091\pi$
$13$		−	1.54892i		−	0.429594i	0.976659	−	0.214797i	$-0.0689090\pi$
$14$	1.37037	+	2.26320i	0.366248	+	0.604866i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.264766	−	0.458589i	0.0642153	−	0.111224i	−0.832130	−	0.554580i	$-0.812879\pi$
$17$	0.264766	−	0.458589i	0.0642153	−	0.111224i	0.896346	+	0.443356i	$0.146212\pi$
$18$	1.58314	+	2.54826i	0.373151	+	0.600632i
$19$	−5.53332	+	3.19467i	−1.26943	+	0.732906i	−0.974880	−	0.222729i	$-0.928503\pi$
$19$	−5.53332	+	3.19467i	−1.26943	+	0.732906i	−0.294551	+	0.955636i	$0.595170\pi$
$20$		0			0
$21$	3.35805	+	3.11825i	0.732788	+	0.680457i
$22$	−0.193822			−0.0413231
$23$	−3.68040	+	2.12488i	−0.767416	+	0.443068i	−0.831952	−	0.554848i	$-0.812777\pi$
$23$	−3.68040	+	2.12488i	−0.767416	+	0.443068i	0.0645362	+	0.997915i	$0.479443\pi$
$24$	−1.24437	−	1.20480i	−0.254006	−	0.245929i
$25$		0			0
$26$	0.774462	+	1.34141i	0.151884	+	0.263072i
$27$	3.84792	+	3.49192i	0.740532	+	0.672021i
$28$	−2.31838	−	1.27480i	−0.438132	−	0.240915i
$29$			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	0.997946	−	0.0640639i	$-0.0204062\pi$
$31$	8.02559	+	4.63357i	1.44144	+	0.832214i	0.443492	+	0.896278i	$0.353739\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−0.322825	+	0.0921151i	−0.0561967	+	0.0160352i
$34$			0.529533i			0.0908141i
$35$		0			0
$36$	−2.64518	−	1.41529i	−0.440863	−	0.235882i
$37$	0.881634	+	1.52704i	0.144940	+	0.251043i	0.929350	−	0.369199i	$-0.120368\pi$
$37$	0.881634	+	1.52704i	0.144940	+	0.251043i	−0.784411	+	0.620242i	$0.787034\pi$
$38$	3.19467	−	5.53332i	0.518243	−	0.897623i
$39$	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	$0.781892\pi$
$42$	−4.46728	−	1.02145i	−0.689317	−	0.157614i
$43$	−11.4865			−1.75168			−0.875838	−	0.482606i	$-0.839690\pi$
$43$	−11.4865			−1.75168			−0.875838	+	0.482606i	$0.839690\pi$
$44$	0.167855	−	0.0969112i	0.0253051	−	0.0146099i
$45$		0			0
$46$	2.12488	−	3.68040i	0.313296	−	0.542645i
$47$	4.90186	+	8.49028i	0.715010	+	1.23843i	0.962956	+	0.269660i	$0.0869114\pi$
$47$	4.90186	+	8.49028i	0.715010	+	1.23843i	−0.247945	+	0.968774i	$0.579755\pi$
$48$	1.68006	+	0.421203i	0.242495	+	0.0607954i
$49$	−6.99391	+	0.291909i	−0.999130	+	0.0417014i
$50$		0			0
$51$	0.251663	+	0.881975i	0.0352399	+	0.123501i
$52$	−1.34141	−	0.774462i	−0.186020	−	0.107398i
$53$	0.0562751	+	0.0324905i	0.00772998	+	0.00446291i	0.503860	−	0.863785i	$-0.331913\pi$
$53$	0.0562751	+	0.0324905i	0.00772998	+	0.00446291i	−0.496130	+	0.868248i	$0.665246\pi$
$54$	−5.07836	−	1.10013i	−0.691077	−	0.149709i
$55$		0			0
$56$	2.64518	−	0.0551777i	0.353476	−	0.00737343i
$57$	2.69121	−	10.7344i	0.356459	−	1.42181i
$58$	−2.43674	−	4.22056i	−0.319960	−	0.554187i
$59$	−6.01371	+	10.4160i	−0.782918	+	1.35605i	0.147317	+	0.989089i	$0.452936\pi$
$59$	−6.01371	+	10.4160i	−0.782918	+	1.35605i	−0.930235	+	0.366964i	$0.880397\pi$
$60$		0			0
$61$	3.71180	−	2.14301i	0.475248	−	0.274384i	−0.243186	−	0.969980i	$-0.578193\pi$
$61$	3.71180	−	2.14301i	0.475248	−	0.274384i	0.718434	+	0.695595i	$0.244859\pi$
$62$	−9.26715			−1.17693
$63$	−7.92604	+	0.421794i	−0.998587	+	0.0531410i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	0.233517	−	0.241187i	0.0287440	−	0.0296880i
$67$	2.41529	−	4.18340i	0.295075	−	0.511084i	−0.679928	−	0.733279i	$-0.737989\pi$
$67$	2.41529	−	4.18340i	0.295075	−	0.511084i	0.975002	+	0.222195i	$0.0713222\pi$
$68$	−0.264766	−	0.458589i	−0.0321076	−	0.0556121i
$69$	1.79001	−	7.13983i	0.215492	−	0.859534i
$70$		0			0
$71$		−	6.29103i		−	0.746608i	−0.927709	−	0.373304i	$-0.878225\pi$
$71$		−	6.29103i		−	0.746608i	0.927709	−	0.373304i	$-0.121775\pi$
$72$	2.99843	−	0.0969112i	0.353369	−	0.0114211i
$73$	7.00763	+	4.04586i	0.820181	+	0.473532i	0.850479	−	0.526009i	$-0.176312\pi$
$73$	7.00763	+	4.04586i	0.820181	+	0.473532i	−0.0302980	+	0.999541i	$0.509646\pi$
$74$	−1.52704	−	0.881634i	−0.177514	−	0.102488i
$75$		0			0
$76$			6.38933i			0.732906i
$77$	0.247085	−	0.449354i	0.0281580	−	0.0512086i
$78$	−2.60228	−	0.652411i	−0.294650	−	0.0738710i
$79$	−3.38883	−	5.86962i	−0.381273	−	0.660384i	0.609971	−	0.792423i	$-0.291181\pi$
$79$	−3.38883	−	5.86962i	−0.381273	−	0.660384i	−0.991245	+	0.132039i	$0.957848\pi$
$80$		0			0
$81$	−8.98122	+	0.581164i	−0.997913	+	0.0645738i
$82$	8.58728	−	4.95787i	0.948306	−	0.547505i
$83$	−2.11036			−0.231642			−0.115821	−	0.993270i	$-0.536950\pi$
$83$	−2.11036			−0.231642			−0.115821	+	0.993270i	$0.536950\pi$
$84$	4.37951	−	1.34904i	0.477844	−	0.147192i
$85$		0			0
$86$	9.94760	−	5.74325i	1.07268	−	0.619311i
$87$	−6.06442	−	5.87158i	−0.650174	−	0.629500i
$88$	−0.0969112	+	0.167855i	−0.0103308	+	0.0178934i
$89$	−8.18773	−	14.1816i	−0.867898	−	1.50324i	−0.864141	−	0.503250i	$-0.832137\pi$
$89$	−8.18773	−	14.1816i	−0.867898	−	1.50324i	−0.00375740	−	0.999993i	$-0.501196\pi$
$90$		0			0
$91$	−4.09717	+	0.0854660i	−0.429501	+	0.00895927i
$92$			4.24976i			0.443068i
$93$	−15.4351	+	4.40426i	−1.60055	+	0.456701i
$94$	−8.49028	−	4.90186i	−0.875705	−	0.505589i
$95$		0			0
$96$	−1.66557	+	0.475255i	−0.169992	+	0.0485055i
$97$			8.24463i			0.837115i	0.908190	+	0.418557i	$0.137464\pi$
$97$			8.24463i			0.837115i	−0.908190	+	0.418557i	$0.862536\pi$
$98$	5.91095	−	3.74976i	0.597096	−	0.378783i
$99$	0.274315	−	0.512694i	0.0275697	−	0.0515277i
$100$		0			0
$101$	−2.22831	+	3.85955i	−0.221725	+	0.384040i	−0.955332	−	0.295535i	$-0.904502\pi$
$101$	−2.22831	+	3.85955i	−0.221725	+	0.384040i	0.733607	+	0.679574i	$0.237836\pi$
$102$	−0.658934	−	0.637981i	−0.0652442	−	0.0631696i
$103$	−7.29356	+	4.21094i	−0.718656	+	0.414916i	−0.814258	−	0.580504i	$-0.802856\pi$
$103$	−7.29356	+	4.21094i	−0.718656	+	0.414916i	0.0956021	+	0.995420i	$0.469522\pi$
$104$	1.54892			0.151884
$105$		0			0
$106$	−0.0649809			−0.00631151
$107$	−15.4270	+	8.90681i	−1.49139	+	0.861054i	−0.999951	−	0.00985883i	$-0.996862\pi$
$107$	−15.4270	+	8.90681i	−1.49139	+	0.861054i	−0.491438	+	0.870913i	$0.663528\pi$
$108$	4.94805	−	1.58643i	0.476127	−	0.152655i
$109$	−0.0739017	+	0.128001i	−0.00707850	+	0.0122603i	−0.869543	−	0.493857i	$-0.835587\pi$
$109$	−0.0739017	+	0.128001i	−0.00707850	+	0.0122603i	0.862464	+	0.506118i	$0.168920\pi$
$110$		0			0
$111$	−2.96239	−	0.742694i	−0.281178	−	0.0704934i
$112$	−2.26320	+	1.37037i	−0.213852	+	0.129488i
$113$			3.44771i			0.324334i	0.986763	+	0.162167i	$0.0518483\pi$
$113$			3.44771i			0.324334i	−0.986763	+	0.162167i	$0.948152\pi$
$114$	3.03656	+	10.6419i	0.284400	+	0.996705i
$115$		0			0
$116$	4.22056	+	2.43674i	0.391870	+	0.226246i
$117$	−4.64434	+	0.150108i	−0.429370	+	0.0138775i
$118$		−	12.0274i		−	1.10721i
$119$	−1.22766	−	0.675050i	−0.112539	−	0.0618817i
$120$		0			0
$121$	−5.48122	−	9.49375i	−0.498292	−	0.863068i
$122$	−2.14301	+	3.71180i	−0.194019	+	0.336051i
$123$	11.9465	−	12.3388i	1.07718	−	1.11256i
$124$	8.02559	−	4.63357i	0.720719	−	0.416107i
$125$		0			0
$126$	6.65325	−	4.32830i	0.592719	−	0.385596i
$127$	−5.49965			−0.488015			−0.244007	−	0.969773i	$-0.578462\pi$
$127$	−5.49965			−0.488015			−0.244007	+	0.969773i	$0.578462\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	13.8389	−	14.2935i	1.21845	−	1.25847i
$130$		0			0
$131$	2.99843	+	5.19344i	0.261974	+	0.453753i	0.966767	−	0.255661i	$-0.0822931\pi$
$131$	2.99843	+	5.19344i	0.261974	+	0.453753i	−0.704792	+	0.709414i	$0.748960\pi$
$132$	−0.0816386	+	0.325633i	−0.00710573	+	0.0283427i
$133$	8.75577	+	14.4603i	0.759221	+	1.25387i
$134$			4.83058i			0.417298i
$135$		0			0
$136$	0.458589	+	0.264766i	0.0393237	+	0.0227035i
$137$	0.746611	+	0.431056i	0.0637872	+	0.0368276i	0.531554	−	0.847024i	$-0.321608\pi$
$137$	0.746611	+	0.431056i	0.0637872	+	0.0368276i	−0.467767	+	0.883852i	$0.654941\pi$
$138$	2.01972	+	7.07828i	0.171930	+	0.602543i
$139$			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
$142$	3.14552	+	5.44820i	0.263966	+	0.457202i
$143$	0.150108	−	0.259995i	0.0125527	−	0.0217418i
$144$	−2.54826	+	1.58314i	−0.212355	+	0.131929i
$145$		0			0
$146$	−8.09171			−0.669675
$147$	8.06302	−	9.05470i	0.665027	−	0.746819i
$148$	1.76327			0.144940
$149$	−11.0505	+	6.38001i	−0.905292	+	0.522671i	−0.878913	−	0.476981i	$-0.841731\pi$
$149$	−11.0505	+	6.38001i	−0.905292	+	0.522671i	−0.0263788	+	0.999652i	$0.508398\pi$
$150$		0			0
$151$	8.75012	−	15.1557i	0.712075	−	1.23335i	−0.252002	−	0.967727i	$-0.581089\pi$
$151$	8.75012	−	15.1557i	0.712075	−	1.23335i	0.964077	−	0.265623i	$-0.0855778\pi$
$152$	−3.19467	−	5.53332i	−0.259122	−	0.448812i
$153$	−1.40071	−	0.749442i	−0.113240	−	0.0605888i
$154$	0.0106947	+	0.512694i	0.000861802	+	0.0413141i
$155$		0			0
$156$	2.57984	−	0.736134i	0.206553	−	0.0589379i
$157$	2.46479	+	1.42305i	0.196711	+	0.113571i	0.595121	−	0.803636i	$-0.297104\pi$
$157$	2.46479	+	1.42305i	0.196711	+	0.113571i	−0.398409	+	0.917208i	$0.630438\pi$
$158$	5.86962	+	3.38883i	0.466962	+	0.269601i
$159$	−0.108230	+	0.0308825i	−0.00858323	+	0.00244914i
$160$		0			0
$161$	5.82375	+	9.61805i	0.458976	+	0.758009i
$162$	7.48738	−	4.99391i	0.588264	−	0.392359i
$163$	6.17931	+	10.7029i	0.484001	+	0.838315i	0.999831	−	0.0183763i	$-0.00584968\pi$
$163$	6.17931	+	10.7029i	0.484001	+	0.838315i	−0.515830	+	0.856691i	$0.672516\pi$
$164$	−4.95787	+	8.58728i	−0.387144	+	0.670554i
$165$		0			0
$166$	1.82762	−	1.05518i	0.141851	−	0.0818977i
$167$	−4.99920			−0.386850			−0.193425	−	0.981115i	$-0.561960\pi$
$167$	−4.99920			−0.386850			−0.193425	+	0.981115i	$0.561960\pi$
$168$	−3.11825	+	3.35805i	−0.240578	+	0.259080i
$169$	10.6008			0.815449
$170$		0			0
$171$	10.1152	+	16.2817i	0.773531	+	1.24509i
$172$	−5.74325	+	9.94760i	−0.437919	+	0.758498i
$173$	−3.80403	−	6.58878i	−0.289215	−	0.500935i	0.684407	−	0.729100i	$-0.260061\pi$
$173$	−3.80403	−	6.58878i	−0.289215	−	0.500935i	−0.973623	+	0.228164i	$0.926728\pi$
$174$	8.18773	+	2.05273i	0.620710	+	0.155617i
$175$		0			0
$176$		−	0.193822i		−	0.0146099i
$177$	−5.71609	−	20.0325i	−0.429648	−	1.50574i
$178$	14.1816	+	8.18773i	1.06295	+	0.613697i
$179$	14.0520	+	8.11295i	1.05030	+	0.606390i	0.922733	−	0.385440i	$-0.125950\pi$
$179$	14.0520	+	8.11295i	1.05030	+	0.606390i	0.127566	+	0.991830i	$0.459284\pi$
$180$		0			0
$181$			4.03153i			0.299661i	0.988712	+	0.149831i	$0.0478729\pi$
$181$			4.03153i			0.299661i	−0.988712	+	0.149831i	$0.952127\pi$
$182$	3.50552	−	2.12260i	0.259847	−	0.157338i
$183$	−1.80529	+	7.20076i	−0.133451	+	0.532295i
$184$	−2.12488	−	3.68040i	−0.156648	−	0.271322i
$185$		0			0
$186$	11.1651	−	11.5318i	0.818662	−	0.845549i
$187$	0.0888848	−	0.0513177i	0.00649990	−	0.00375272i
$188$	9.80373			0.715010
$189$	9.02443	−	10.3711i	0.656431	−	0.754386i
$190$		0			0
$191$	−21.8544	+	12.6176i	−1.58133	+	0.912980i	−0.586661	+	0.809832i	$0.699558\pi$
$191$	−21.8544	+	12.6176i	−1.58133	+	0.912980i	−0.994666	+	0.103147i	$0.967109\pi$
$192$	1.20480	−	1.24437i	0.0869490	−	0.0898046i
$193$	12.6183	−	21.8556i	0.908286	−	1.57320i	0.0918418	−	0.995774i	$-0.470725\pi$
$193$	12.6183	−	21.8556i	0.908286	−	1.57320i	0.816444	−	0.577424i	$-0.195942\pi$
$194$	−4.12231	−	7.14006i	−0.295965	−	0.512626i
$195$		0			0
$196$	−3.24415	+	6.20286i	−0.231725	+	0.443061i
$197$		−	14.7364i		−	1.04993i	−0.851125	−	0.524964i	$-0.824079\pi$
$197$		−	14.7364i		−	1.04993i	0.851125	−	0.524964i	$-0.175921\pi$
$198$	0.0187836	+	0.581164i	0.00133489	+	0.0413015i
$199$	22.3991	+	12.9321i	1.58783	+	0.916734i	0.993664	+	0.112391i	$0.0358508\pi$
$199$	22.3991	+	12.9321i	1.58783	+	0.916734i	0.594165	+	0.804343i	$0.297483\pi$
$200$		0			0
$201$	2.29576	+	8.04568i	0.161930	+	0.567499i
$202$		−	4.45663i		−	0.313567i
$203$	12.8912	−	0.268908i	0.904787	−	0.0188736i
$204$	0.889645	+	0.223041i	0.0622876	+	0.0156160i
$205$		0			0
$206$	4.21094	−	7.29356i	0.293390	−	0.508166i
$207$	6.72798	+	10.8295i	0.467627	+	0.752703i
$208$	−1.34141	+	0.774462i	−0.0930098	+	0.0536992i
$209$	−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	$0.788516\pi$
$212$	0.0562751	−	0.0324905i	0.00386499	−	0.00223145i
$213$	7.82837	+	7.57944i	0.536391	+	0.519335i
$214$	8.90681	−	15.4270i	0.608857	−	1.05457i
$215$		0			0
$216$	−3.49192	+	3.84792i	−0.237595	+	0.261818i
$217$	11.8138	−	21.4848i	0.801972	−	1.45848i
$218$		−	0.147803i		−	0.0100105i
$219$	−13.4773	+	3.84563i	−0.910714	+	0.259864i
$220$		0			0
$221$	−0.710319	−	0.410103i	−0.0477812	−	0.0275865i
$222$	2.93685	−	0.838003i	0.197109	−	0.0562431i
$223$		−	0.00626282i		−	0.000419390i	−1.00000		0.000209695i	$-0.999933\pi$
$223$		−	0.00626282i		−	0.000419390i	1.00000		0.000209695i	$-6.67479e-5\pi$
$224$	1.27480	−	2.31838i	0.0851763	−	0.154903i
$225$		0			0
$226$	−1.72386	−	2.98581i	−0.114669	−	0.198613i
$227$	−9.41373	+	16.3051i	−0.624811	+	1.08220i	0.363766	+	0.931490i	$0.381491\pi$
$227$	−9.41373	+	16.3051i	−0.624811	+	1.08220i	−0.988577	+	0.150715i	$0.951843\pi$
$228$	−7.95069	−	7.69787i	−0.526547	−	0.509804i
$229$	6.75203	−	3.89829i	0.446187	−	0.257606i	−0.260032	−	0.965600i	$-0.583733\pi$
$229$	6.75203	−	3.89829i	0.446187	−	0.257606i	0.706218	+	0.707994i	$0.250400\pi$
$230$		0			0
$231$	0.261474	+	0.848847i	0.0172037	+	0.0558500i
$232$	−4.87349			−0.319960
$233$	11.2535	−	6.49718i	0.737238	−	0.425645i	−0.0838262	−	0.996480i	$-0.526714\pi$
$233$	11.2535	−	6.49718i	0.737238	−	0.425645i	0.821064	+	0.570836i	$0.193381\pi$
$234$	3.94707	−	2.45217i	0.258028	−	0.160303i
$235$		0			0
$236$	6.01371	+	10.4160i	0.391459	+	0.678027i
$237$	11.3868	+	2.85477i	0.739655	+	0.185437i
$238$	1.40071	−	0.0292184i	0.0907944	−	0.00189395i
$239$			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	0.711118	−	0.703072i	$-0.248189\pi$
$241$	7.10695	+	4.10320i	0.457799	+	0.264310i	−0.253319	+	0.967383i	$0.581522\pi$
$242$	9.49375	+	5.48122i	0.610281	+	0.352346i
$243$	10.0974	−	11.8761i	0.647748	−	0.761855i
$244$		−	4.28602i		−	0.274384i
$245$		0			0
$246$	−4.17654	+	16.6590i	−0.266286	+	1.06214i
$247$	4.94829	+	8.57069i	0.314852	+	0.545340i
$248$	−4.63357	+	8.02559i	−0.294232	+	0.509625i
$249$	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	$0.242745\pi$
$252$	−3.59774	+	7.07505i	−0.226636	+	0.445686i
$253$	−0.823698			−0.0517855
$254$	4.76283	−	2.74982i	0.298847	−	0.172539i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.54324	−	6.13707i	−0.221021	−	0.382820i	0.734097	−	0.679044i	$-0.237606\pi$
$257$	−3.54324	−	6.13707i	−0.221021	−	0.382820i	−0.955118	+	0.296225i	$0.904272\pi$
$258$	−4.83815	+	19.2980i	−0.301210	+	1.20144i
$259$	3.99063	−	2.41634i	0.247966	−	0.150144i
$260$		0			0
$261$	14.6128	−	0.472296i	0.904512	−	0.0292344i
$262$	−5.19344	−	2.99843i	−0.320852	−	0.185244i
$263$	−15.4744	−	8.93416i	−0.954194	−	0.550904i	−0.0598127	−	0.998210i	$-0.519050\pi$
$263$	−15.4744	−	8.93416i	−0.954194	−	0.550904i	−0.894381	+	0.447306i	$0.852384\pi$
$264$	−0.0921151	−	0.322825i	−0.00566930	−	0.0198685i
$265$		0			0
$266$	−14.8129	−	8.14514i	−0.908236	−	0.499410i
$267$	27.5117	+	6.89740i	1.68369	+	0.422114i
$268$	−2.41529	−	4.18340i	−0.147537	−	0.255542i
$269$	3.46273	−	5.99762i	0.211126	−	0.365682i	−0.740941	−	0.671570i	$-0.765620\pi$
$269$	3.46273	−	5.99762i	0.211126	−	0.365682i	0.952067	+	0.305889i	$0.0989535\pi$
$270$		0			0
$271$	−14.6520	+	8.45932i	−0.890044	+	0.513867i	−0.873957	−	0.486003i	$-0.838454\pi$
$271$	−14.6520	+	8.45932i	−0.890044	+	0.513867i	−0.0160872	+	0.999871i	$0.505121\pi$
$272$	−0.529533			−0.0321076
$273$	4.82993	−	5.20137i	0.292320	−	0.314801i
$274$	−0.862112			−0.0520821
$275$		0			0
$276$	−5.28827	−	5.12011i	−0.318316	−	0.308194i
$277$	−10.6505	+	18.4471i	−0.639924	+	1.10838i	0.345525	+	0.938410i	$0.387701\pi$
$277$	−10.6505	+	18.4471i	−0.639924	+	1.10838i	−0.985449	+	0.169972i	$0.945632\pi$
$278$	−8.09216	−	14.0160i	−0.485336	−	0.840626i
$279$	13.1157	−	24.5132i	0.785216	−	1.46757i
$280$		0			0
$281$		−	19.5927i		−	1.16880i	−0.811464	−	0.584402i	$-0.801329\pi$
$281$		−	19.5927i		−	1.16880i	0.811464	−	0.584402i	$-0.198671\pi$
$282$	16.3288	−	4.65927i	0.972367	−	0.277456i
$283$	13.0751	+	7.54892i	0.777235	+	0.448737i	0.835450	−	0.549567i	$-0.185207\pi$
$283$	13.0751	+	7.54892i	0.777235	+	0.448737i	−0.0582144	+	0.998304i	$0.518541\pi$
$284$	−5.44820	−	3.14552i	−0.323291	−	0.186652i
$285$		0			0
$286$			0.300216i			0.0177521i
$287$	0.547127	+	26.2289i	0.0322959	+	1.54824i
$288$	1.41529	−	2.64518i	0.0833967	−	0.155868i
$289$	8.35980	+	14.4796i	0.491753	+	0.851741i
$290$		0			0
$291$	−10.2594	−	9.93313i	−0.601414	−	0.582290i
$292$	7.00763	−	4.04586i	0.410090	−	0.236766i
$293$	−8.00534			−0.467677			−0.233839	−	0.972275i	$-0.575129\pi$
$293$	−8.00534			−0.467677			−0.233839	+	0.972275i	$0.575129\pi$
$294$	−2.45543	+	11.8731i	−0.143204	+	0.692454i
$295$		0			0
$296$	−1.52704	+	0.881634i	−0.0887571	+	0.0512439i
$297$	0.307487	+	0.959044i	0.0178422	+	0.0556494i
$298$	6.38001	−	11.0505i	0.369584	−	0.640138i
$299$	3.29127	+	5.70065i	0.190339	+	0.329677i
$300$		0			0
$301$	0.633799	+	30.3838i	0.0365316	+	1.75129i
$302$			17.5002i			1.00703i
$303$	−2.11804	−	7.42283i	−0.121678	−	0.426431i
$304$	5.53332	+	3.19467i	0.317358	+	0.183227i
$305$		0			0
$306$	1.58777	−	0.0513177i	0.0907667	−	0.00293364i
$307$		−	4.33663i		−	0.247505i	−0.992313	−	0.123752i	$-0.960507\pi$
$307$		−	4.33663i		−	0.247505i	0.992313	−	0.123752i	$-0.0394928\pi$
$308$	−0.265609	−	0.438659i	−0.0151345	−	0.0249949i
$309$	3.54732	−	14.1492i	0.201800	−	0.804921i
$310$		0			0
$311$	11.4192	−	19.7786i	0.647523	−	1.12154i	−0.336190	−	0.941794i	$-0.609138\pi$
$311$	11.4192	−	19.7786i	0.647523	−	1.12154i	0.983713	−	0.179748i	$-0.0575284\pi$
$312$	−1.86614	+	1.92743i	−0.105650	+	0.109119i
$313$	−21.9141	+	12.6521i	−1.23866	+	0.715140i	−0.968820	−	0.247766i	$-0.920304\pi$
$313$	−21.9141	+	12.6521i	−1.23866	+	0.715140i	−0.269838	+	0.962906i	$0.586970\pi$
$314$	−2.84609			−0.160614
$315$		0			0
$316$	−6.77766			−0.381273
$317$	13.0681	−	7.54489i	0.733979	−	0.423763i	−0.0858969	−	0.996304i	$-0.527376\pi$
$317$	13.0681	−	7.54489i	0.733979	−	0.423763i	0.819876	+	0.572541i	$0.194042\pi$
$318$	0.0782891	−	0.0808603i	0.00439023	−	0.00453442i
$319$	−0.472296	+	0.818040i	−0.0264435	+	0.0458015i
$320$		0			0
$321$	7.50315	−	29.9279i	0.418785	−	1.67041i
$322$	−9.85254	−	5.41760i	−0.549061	−	0.301911i
$323$			3.38336i			0.188255i
$324$	−3.98731	+	8.06854i	−0.221517	+	0.448252i
$325$		0			0
$326$	−10.7029	−	6.17931i	−0.592778	−	0.342241i
$327$	−0.0702443	−	0.246177i	−0.00388452	−	0.0136136i
$328$		−	9.91573i		−	0.547505i
$329$	22.1878	−	13.4348i	1.22325	−	0.740683i
$330$		0			0
$331$	−7.53086	−	13.0438i	−0.413933	−	0.716954i	0.581382	−	0.813630i	$-0.302512\pi$
$331$	−7.53086	−	13.0438i	−0.413933	−	0.716954i	−0.995316	+	0.0966768i	$0.969179\pi$
$332$	−1.05518	+	1.82762i	−0.0579104	+	0.100304i
$333$	4.49327	−	2.79151i	0.246230	−	0.152974i
$334$	4.32943	−	2.49960i	0.236896	−	0.136772i
$335$		0			0
$336$	1.02145	−	4.46728i	0.0557249	−	0.243710i
$337$	−14.9611			−0.814983			−0.407491	−	0.913209i	$-0.633596\pi$
$337$	−14.9611			−0.814983			−0.407491	+	0.913209i	$0.633596\pi$
$338$	−9.18059	+	5.30042i	−0.499359	+	0.288305i
$339$	−4.29023	−	4.15381i	−0.233013	−	0.225604i
$340$		0			0
$341$	0.898091	+	1.55554i	0.0486343	+	0.0842371i
$342$	−16.9009	−	9.04275i	−0.913896	−	0.488976i
$343$	1.15806	+	18.4840i	0.0625294	+	0.998043i
$344$		−	11.4865i		−	0.619311i
$345$		0			0
$346$	6.58878	+	3.80403i	0.354215	+	0.204506i
$347$	−3.50448	−	2.02331i	−0.188130	−	0.108617i	0.402977	−	0.915210i	$-0.367976\pi$
$347$	−3.50448	−	2.02331i	−0.188130	−	0.108617i	−0.591107	+	0.806593i	$0.701309\pi$
$348$	−8.11715	+	2.31615i	−0.435125	+	0.124159i
$349$			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
$352$	0.0969112	+	0.167855i	0.00516539	+	0.00894671i
$353$	−1.83358	+	3.17585i	−0.0975914	+	0.169033i	−0.910687	−	0.413097i	$-0.864447\pi$
$353$	−1.83358	+	3.17585i	−0.0975914	+	0.169033i	0.813096	+	0.582130i	$0.197780\pi$
$354$	14.9665	+	14.4906i	0.795463	+	0.770169i
$355$		0			0
$356$	−16.3755			−0.867898
$357$	2.31909	−	0.714359i	0.122739	−	0.0378079i
$358$	−16.2259			−0.857565
$359$	6.34163	−	3.66134i	0.334699	−	0.193238i	−0.323227	−	0.946322i	$-0.604768\pi$
$359$	6.34163	−	3.66134i	0.334699	−	0.193238i	0.657925	+	0.753083i	$0.271434\pi$
$360$		0			0
$361$	10.9118	−	18.8997i	0.574304	−	0.994723i
$362$	−2.01577	−	3.49141i	−0.105946	−	0.183504i
$363$	18.4175	+	4.61741i	0.966668	+	0.242351i
$364$	−1.97457	+	3.59099i	−0.103496	+	0.188219i
$365$		0			0
$366$	−2.03696	−	7.13868i	−0.106473	−	0.373145i
$367$	4.12769	+	2.38312i	0.215464	+	0.124398i	0.603848	−	0.797100i	$-0.293633\pi$
$367$	4.12769	+	2.38312i	0.215464	+	0.124398i	−0.388384	+	0.921497i	$0.626967\pi$
$368$	3.68040	+	2.12488i	0.191854	+	0.110767i
$369$	0.960946	+	29.7317i	0.0500248	+	1.54777i
$370$		0			0
$371$	0.0828379	−	0.150650i	0.00430073	−	0.00782138i
$372$	−3.90335	+	15.5693i	−0.202379	+	0.807232i
$373$	−8.64813	−	14.9790i	−0.447783	−	0.775584i	0.550458	−	0.834863i	$-0.314453\pi$
$373$	−8.64813	−	14.9790i	−0.447783	−	0.775584i	−0.998241	+	0.0592792i	$0.981120\pi$
$374$	−0.0513177	+	0.0888848i	−0.00265357	+	0.00459612i
$375$		0			0
$376$	−8.49028	+	4.90186i	−0.437853	+	0.252794i
$377$	7.54866			0.388776
$378$	−2.62983	+	13.4938i	−0.135264	+	0.694049i
$379$	−8.76645			−0.450302			−0.225151	−	0.974324i	$-0.572288\pi$
$379$	−8.76645			−0.450302			−0.225151	+	0.974324i	$0.572288\pi$
$380$		0			0
$381$	6.62598	−	6.84359i	0.339459	−	0.350608i
$382$	12.6176	−	21.8544i	0.645574	−	1.11817i
$383$	−14.2377	−	24.6604i	−0.727511	−	1.26009i	−0.957932	−	0.286995i	$-0.907344\pi$
$383$	−14.2377	−	24.6604i	−0.727511	−	1.26009i	0.230422	−	0.973091i	$-0.425989\pi$
$384$	−0.421203	+	1.68006i	−0.0214944	+	0.0857350i
$385$		0			0
$386$			25.2366i			1.28451i
$387$	1.11317	+	34.4415i	0.0565857	+	1.75076i
$388$	7.14006	+	4.12231i	0.362481	+	0.209279i
$389$	−18.2468	−	10.5348i	−0.925151	−	0.534136i	−0.0398761	−	0.999205i	$-0.512696\pi$
$389$	−18.2468	−	10.5348i	−0.925151	−	0.534136i	−0.885275	+	0.465069i	$0.846030\pi$
$390$		0			0
$391$			2.25039i			0.113807i
$392$	−0.291909	−	6.99391i	−0.0147437	−	0.353246i
$393$	−10.0751	−	2.52590i	−0.508220	−	0.127415i
$394$	7.36822	+	12.7621i	0.371205	+	0.642947i
$395$		0			0
$396$	−0.306849	−	0.493911i	−0.0154197	−	0.0248200i
$397$	−5.71412	+	3.29905i	−0.286783	+	0.165574i	−0.636490	−	0.771285i	$-0.719614\pi$
$397$	−5.71412	+	3.29905i	−0.286783	+	0.165574i	0.349707	+	0.936859i	$0.386281\pi$
$398$	−25.8642			−1.29646
$399$	−28.5430	−	6.52641i	−1.42894	−	0.326729i
$400$		0			0
$401$	−13.9699	+	8.06552i	−0.697623	+	0.402773i	−0.806461	−	0.591287i	$-0.798620\pi$
$401$	−13.9699	+	8.06552i	−0.697623	+	0.402773i	0.108839	+	0.994059i	$0.465287\pi$
$402$	−6.01103	−	5.81988i	−0.299803	−	0.290269i
$403$	7.17705	−	12.4310i	0.357514	−	0.619233i
$404$	2.22831	+	3.85955i	0.110863	+	0.192020i
$405$		0			0
$406$	−11.0297	+	6.67850i	−0.547394	+	0.331448i
$407$			0.341761i			0.0169405i
$408$	−0.881975	+	0.251663i	−0.0436643	+	0.0124592i
$409$	−22.8659	−	13.2016i	−1.13065	−	0.652779i	−0.186549	−	0.982446i	$-0.559730\pi$
$409$	−22.8659	−	13.2016i	−1.13065	−	0.652779i	−0.944097	+	0.329666i	$0.893064\pi$
$410$		0			0
$411$	−1.43591	+	0.409723i	−0.0708282	+	0.0202102i
$412$			8.42187i			0.414916i
$413$	27.8841	+	15.3326i	1.37209	+	0.754467i
$414$	−11.2414	−	6.01464i	−0.552482	−	0.295603i
$415$		0			0
$416$	0.774462	−	1.34141i	0.0379711	−	0.0657679i
$417$	−20.1393	−	19.4989i	−0.986225	−	0.954864i
$418$	1.07248	−	0.619198i	0.0524568	−	0.0302860i
$419$	−19.8312			−0.968819			−0.484409	−	0.874841i	$-0.660965\pi$
$419$	−19.8312			−0.968819			−0.484409	+	0.874841i	$0.660965\pi$
$420$		0			0
$421$	6.28009			0.306073			0.153036	−	0.988221i	$-0.451095\pi$
$421$	6.28009			0.306073			0.153036	+	0.988221i	$0.451095\pi$
$422$	19.8078	−	11.4360i	0.964228	−	0.556697i
$423$	24.9825	−	15.5207i	1.21469	−	0.754643i
$424$	−0.0324905	+	0.0562751i	−0.00157788	+	0.00273296i
$425$		0			0
$426$	−10.5693	−	2.64980i	−0.512084	−	0.128383i
$427$	−5.87345	−	9.70013i	−0.284236	−	0.469422i
$428$			17.8136i			0.861054i
$429$	0.142679	+	0.500032i	0.00688862	+	0.0241418i
$430$		0			0
$431$	3.94326	+	2.27664i	0.189940	+	0.109662i	0.591955	−	0.805971i	$-0.298356\pi$
$431$	3.94326	+	2.27664i	0.189940	+	0.109662i	−0.402014	+	0.915633i	$0.631690\pi$
$432$	1.10013	−	5.07836i	0.0529302	−	0.244333i
$433$			2.62801i			0.126294i	0.998004	+	0.0631471i	$0.0201137\pi$
$433$			2.62801i			0.126294i	−0.998004	+	0.0631471i	$0.979886\pi$
$434$	0.511340	+	24.5132i	0.0245451	+	1.17667i
$435$		0			0
$436$	0.0739017	+	0.128001i	0.00353925	+	0.00613016i
$437$	13.5765	−	23.5153i	0.649454	−	1.12489i
$438$	9.74890	−	10.0691i	0.465820	−	0.481119i
$439$	−5.05475	+	2.91836i	−0.241250	+	0.139286i	−0.615751	−	0.787941i	$-0.711147\pi$
$439$	−5.05475	+	2.91836i	−0.241250	+	0.139286i	0.374501	+	0.927226i	$0.377814\pi$
$440$		0			0
$441$	1.55306	+	20.9425i	0.0739552	+	0.997262i
$442$	0.820205			0.0390132
$443$	22.8164	−	13.1730i	1.08404	−	0.625870i	0.152056	−	0.988372i	$-0.451411\pi$
$443$	22.8164	−	13.1730i	1.08404	−	0.625870i	0.931983	+	0.362502i	$0.118077\pi$
$444$	−2.12439	+	2.19416i	−0.100819	+	0.104130i
$445$		0			0
$446$	0.00313141	+	0.00542376i	0.000148277	+	0.000256823i
$447$	5.37456	−	21.4375i	0.254208	−	1.01396i
$448$	0.0551777	+	2.64518i	0.00260690	+	0.124973i
$449$			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
$452$	2.98581	+	1.72386i	0.140441	+	0.0810834i
$453$	8.31709	+	29.1479i	0.390771	+	1.36949i
$454$		−	18.8275i		−	0.883617i
$455$		0			0
$456$	10.7344	+	2.69121i	0.502686	+	0.126027i
$457$	−0.360756	−	0.624848i	−0.0168755	−	0.0292292i	0.857464	−	0.514543i	$-0.172039\pi$
$457$	−0.360756	−	0.624848i	−0.0168755	−	0.0292292i	−0.874340	+	0.485314i	$0.838705\pi$
$458$	−3.89829	+	6.75203i	−0.182155	+	0.315502i
$459$	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	$0.204639\pi$
$462$	−0.650866	−	0.604386i	−0.0302810	−	0.0281186i
$463$	−41.3815			−1.92316			−0.961581	−	0.274522i	$-0.911480\pi$
$463$	−41.3815			−1.92316			−0.961581	+	0.274522i	$0.911480\pi$
$464$	4.22056	−	2.43674i	0.195935	−	0.113123i
$465$		0			0
$466$	−6.49718	+	11.2535i	−0.300976	+	0.521306i
$467$	−8.98343	−	15.5598i	−0.415704	−	0.720020i	0.579798	−	0.814760i	$-0.303131\pi$
$467$	−8.98343	−	15.5598i	−0.415704	−	0.720020i	−0.995502	+	0.0947401i	$0.969798\pi$
$468$	−2.19217	+	4.09717i	−0.101333	+	0.189392i
$469$	−11.1991	−	6.15804i	−0.517127	−	0.284352i
$470$		0			0
$471$	−4.74037	+	1.35262i	−0.218425	+	0.0623254i
$472$	−10.4160	−	6.01371i	−0.479437	−	0.276803i
$473$	−1.92807	−	1.11317i	−0.0886527	−	0.0511837i
$474$	−11.2887	+	3.22112i	−0.518506	+	0.147951i
$475$		0			0
$476$	−1.19844	+	0.725657i	−0.0549304	+	0.0332605i
$477$	0.0919668	−	0.171886i	0.00421087	−	0.00787012i
$478$	−8.58548	−	14.8705i	−0.392691	−	0.680160i
$479$	−4.50559	+	7.80391i	−0.205866	+	0.356570i	−0.950408	−	0.311005i	$-0.899334\pi$
$479$	−4.50559	+	7.80391i	−0.205866	+	0.356570i	0.744542	+	0.667575i	$0.232668\pi$
$480$		0			0
$481$	2.36526	−	1.36558i	0.107847	−	0.0622652i
$482$	−8.20640			−0.373791
$483$	−18.9849	−	4.34093i	−0.863842	−	0.197519i
$484$	−10.9624			−0.498292
$485$		0			0
$486$	−2.80653	+	15.3337i	−0.127307	+	0.695552i
$487$	−11.3648	+	19.6844i	−0.514987	+	0.891984i	0.484862	+	0.874591i	$0.338870\pi$
$487$	−11.3648	+	19.6844i	−0.514987	+	0.891984i	−0.999849	+	0.0173928i	$0.994463\pi$
$488$	2.14301	+	3.71180i	0.0970096	+	0.168025i
$489$	−20.7632	−	5.20549i	−0.938944	−	0.235401i
$490$		0			0
$491$			32.1654i			1.45160i	0.687904	+	0.725801i	$0.258531\pi$
$491$			32.1654i			1.45160i	−0.687904	+	0.725801i	$0.741469\pi$
$492$	−4.71250	−	16.5154i	−0.212456	−	0.744570i
$493$	2.23493	+	1.29034i	0.100656	+	0.0581138i
$494$	−8.57069	−	4.94829i	−0.385614	−	0.222634i
$495$		0			0
$496$		−	9.26715i		−	0.416107i
$497$	−16.6409	+	0.347125i	−0.746446	+	0.0155707i
$498$	−0.888888	+	3.54552i	−0.0398320	+	0.158878i
$499$	−10.6254	−	18.4037i	−0.475658	−	0.823864i	0.523953	−	0.851747i	$-0.324457\pi$
$499$	−10.6254	−	18.4037i	−0.475658	−	0.823864i	−0.999611	+	0.0278832i	$0.991123\pi$
$500$		0			0
$501$	6.02304	−	6.22085i	0.269089	−	0.277927i
$502$	−19.8408	+	11.4551i	−0.885537	+	0.511265i
$503$	20.9913			0.935957			0.467978	−	0.883740i	$-0.344982\pi$
$503$	20.9913			0.935957			0.467978	+	0.883740i	$0.344982\pi$
$504$	−0.421794	−	7.92604i	−0.0187882	−	0.353054i
$505$		0			0
$506$	0.713343	−	0.411849i	0.0317120	−	0.0183089i
$507$	−12.7719	+	13.1914i	−0.567220	+	0.585849i
$508$	−2.74982	+	4.76283i	−0.122004	+	0.211317i
$509$	−6.98403	−	12.0967i	−0.309562	−	0.536177i	0.668705	−	0.743528i	$-0.266849\pi$
$509$	−6.98403	−	12.0967i	−0.309562	−	0.536177i	−0.978267	+	0.207351i	$0.933516\pi$
$510$		0			0
$511$	10.3153	−	18.7597i	0.456324	−	0.829878i
$512$		−	1.00000i		−	0.0441942i
$513$	−32.4473	−	7.02912i	−1.43258	−	0.310343i
$514$	6.13707	+	3.54324i	0.270695	+	0.156286i
$515$		0			0
$516$	−5.45902	−	19.1316i	−0.240320	−	0.842222i
$517$			1.90018i			0.0835699i
$518$	−2.24782	+	4.08792i	−0.0987635	+	0.179613i
$519$	12.7820	+	3.20454i	0.561066	+	0.140664i
$520$		0			0
$521$	7.21208	−	12.4917i	0.315967	−	0.547271i	−0.663676	−	0.748020i	$-0.731004\pi$
$521$	7.21208	−	12.4917i	0.315967	−	0.547271i	0.979643	+	0.200750i	$0.0643378\pi$
$522$	−12.4189	+	7.71544i	−0.543562	+	0.337696i
$523$	25.2604	−	14.5841i	1.10456	−	0.637717i	0.167144	−	0.985932i	$-0.446545\pi$
$523$	25.2604	−	14.5841i	1.10456	−	0.637717i	0.937415	+	0.348215i	$0.113212\pi$
$524$	5.99687			0.261974
$525$		0			0
$526$	17.8683			0.779096
$527$	4.24981	−	2.45363i	0.185125	−	0.106882i
$528$	0.241187	+	0.233517i	0.0104963	+	0.0101625i
$529$	−2.46979	+	4.27779i	−0.107382	+	0.185991i
$530$		0			0
$531$	31.8146	+	17.0223i	1.38064	+	0.738704i
$532$	16.9009	−	0.352549i	0.732747	−	0.0152849i
$533$			15.3587i			0.665259i
$534$	−27.2745	+	7.78253i	−1.18028	+	0.336783i
$535$		0			0
$536$	4.18340	+	2.41529i	0.180696	+	0.104325i
$537$	−27.0254	+	7.71144i	−1.16623	+	0.332773i
$538$			6.92546i			0.298578i
$539$	−1.20225	−	0.628790i	−0.0517847	−	0.0270839i
$540$		0			0
$541$	12.4518	+	21.5672i	0.535345	+	0.927246i	0.999147	+	0.0413062i	$0.0131519\pi$
$541$	12.4518	+	21.5672i	0.535345	+	0.927246i	−0.463801	+	0.885939i	$0.653515\pi$
$542$	8.45932	−	14.6520i	0.363359	−	0.629356i
$543$	−5.01672	−	4.85719i	−0.215288	−	0.208442i
$544$	0.458589	−	0.264766i	0.0196618	−	0.0113518i
$545$		0			0
$546$	−1.58215	+	6.91948i	−0.0677100	+	0.296126i
$547$	0.655376			0.0280219			0.0140109	−	0.999902i	$-0.495540\pi$
$547$	0.655376			0.0280219			0.0140109	+	0.999902i	$0.495540\pi$
$548$	0.746611	−	0.431056i	0.0318936	−	0.0184138i
$549$	−6.78539	−	10.9219i	−0.289594	−	0.466136i
$550$		0			0
$551$	−15.5692	−	26.9666i	−0.663269	−	1.14882i
$552$	7.13983	+	1.79001i	0.303891	+	0.0761879i
$553$	−15.3392	+	9.28792i	−0.652289	+	0.394963i
$554$		−	21.3009i		−	0.904990i
$555$		0			0
$556$	14.0160	+	8.09216i	0.594412	+	0.343184i
$557$	−15.4016	−	8.89212i	−0.652587	−	0.376771i	0.136860	−	0.990590i	$-0.456299\pi$
$557$	−15.4016	−	8.89212i	−0.652587	−	0.376771i	−0.789446	+	0.613819i	$0.789632\pi$
$558$	0.898091	+	27.7869i	0.0380192	+	1.17631i
$559$			17.7917i			0.752509i
$560$		0			0
$561$	−0.0432303	+	0.172433i	−0.00182519	+	0.00728013i
$562$	9.79636	+	16.9678i	0.413235	+	0.715743i
$563$	−10.1362	+	17.5563i	−0.427188	+	0.739912i	−0.996622	−	0.0821256i	$-0.973829\pi$
$563$	−10.1362	+	17.5563i	−0.427188	+	0.739912i	0.569434	+	0.822037i	$0.307162\pi$
$564$	−11.8115	+	12.1995i	−0.497355	+	0.513690i
$565$		0			0
$566$	−15.0978			−0.634610
$567$	2.03284	+	23.7248i	0.0853714	+	0.996349i
$568$	6.29103			0.263966
$569$	38.9233	−	22.4724i	1.63175	−	0.942092i	0.648197	−	0.761473i	$-0.275523\pi$
$569$	38.9233	−	22.4724i	1.63175	−	0.942092i	0.983553	−	0.180619i	$-0.0578101\pi$
$570$		0			0
$571$	5.59451	−	9.68998i	0.234123	−	0.405513i	−0.724894	−	0.688860i	$-0.758111\pi$
$571$	5.59451	−	9.68998i	0.234123	−	0.405513i	0.959017	+	0.283347i	$0.0914448\pi$
$572$	−0.150108	−	0.259995i	−0.00627633	−	0.0108709i
$573$	10.6292	−	42.3967i	0.444040	−	1.77115i
$574$	−13.5883	−	22.4413i	−0.567163	−	0.936681i
$575$		0			0
$576$	0.0969112	+	2.99843i	0.00403797	+	0.124935i
$577$	8.42967	+	4.86687i	0.350932	+	0.202611i	0.665096	−	0.746758i	$-0.268391\pi$
$577$	8.42967	+	4.86687i	0.350932	+	0.202611i	−0.314164	+	0.949369i	$0.601724\pi$
$578$	−14.4796	−	8.35980i	−0.602272	−	0.347722i
$579$	11.9938	+	42.0334i	0.498447	+	1.74685i
$580$		0			0
$581$	0.116445	+	5.58226i	0.00483094	+	0.231591i
$582$	13.8514	+	3.47266i	0.574160	+	0.143946i
$583$	0.00629738	+	0.0109074i	0.000260811	+	0.000451738i
$584$	−4.04586	+	7.00763i	−0.167419	+	0.289978i
$585$		0			0
$586$	6.93283	−	4.00267i	0.286393	−	0.165349i
$587$	32.0185			1.32155			0.660773	−	0.750585i	$-0.270228\pi$
$587$	32.0185			1.32155			0.660773	+	0.750585i	$0.270228\pi$
$588$	−3.81009	−	11.5101i	−0.157125	−	0.474670i
$589$	−59.2109			−2.43974
$590$		0			0
$591$	18.3376	+	17.7545i	0.754307	+	0.730321i
$592$	0.881634	−	1.52704i	0.0362349	−	0.0627608i
$593$	16.2006	+	28.0603i	0.665280	+	1.15230i	0.979209	+	0.202852i	$0.0650211\pi$
$593$	16.2006	+	28.0603i	0.665280	+	1.15230i	−0.313930	+	0.949446i	$0.601646\pi$
$594$	−0.745813	−	0.676813i	−0.0306011	−	0.0277700i
$595$		0			0
$596$			12.7600i			0.522671i
$597$	−43.0788	+	12.2921i	−1.76310	+	0.503083i
$598$	−5.70065	−	3.29127i	−0.233117	−	0.134590i
$599$	9.13107	+	5.27183i	0.373086	+	0.215401i	0.674806	−	0.737996i	$-0.264227\pi$
$599$	9.13107	+	5.27183i	0.373086	+	0.215401i	−0.301720	+	0.953397i	$0.597561\pi$
$600$		0			0
$601$		−	24.6793i		−	1.00669i	−0.864086	−	0.503344i	$-0.832103\pi$
$601$		−	24.6793i		−	1.00669i	0.864086	−	0.503344i	$-0.167897\pi$
$602$	−15.7408	−	25.9963i	−0.641547	−	1.05953i
$603$	−12.7777	−	6.83667i	−0.520349	−	0.278411i
$604$	−8.75012	−	15.1557i	−0.356038	−	0.616675i
$605$		0			0
$606$	5.54569	+	5.36934i	0.225278	+	0.218115i
$607$	11.2456	−	6.49268i	0.456447	−	0.263530i	−0.254102	−	0.967177i	$-0.581780\pi$
$607$	11.2456	−	6.49268i	0.456447	−	0.263530i	0.710549	+	0.703648i	$0.248447\pi$
$608$	−6.38933			−0.259122
$609$	−15.1967	+	16.3654i	−0.615803	+	0.663161i
$610$		0			0
$611$	13.1508	−	7.59261i	0.532024	−	0.307164i
$612$	−1.34939	+	0.838327i	−0.0545458	+	0.0338874i
$613$	−13.3643	+	23.1477i	−0.539780	+	0.934926i	0.459136	+	0.888366i	$0.348159\pi$
$613$	−13.3643	+	23.1477i	−0.539780	+	0.934926i	−0.998915	+	0.0465601i	$0.985174\pi$
$614$	2.16832	+	3.75563i	0.0875061	+	0.151565i
$615$		0			0
$616$	0.449354	+	0.247085i	0.0181050	+	0.00995535i
$617$		−	13.2804i		−	0.534650i	−0.963606	−	0.267325i	$-0.913860\pi$
$617$		−	13.2804i		−	0.534650i	0.963606	−	0.267325i	$-0.0861397\pi$
$618$	4.00254	+	14.0272i	0.161006	+	0.564259i
$619$	8.56249	+	4.94355i	0.344155	+	0.198698i	0.662108	−	0.749408i	$-0.269662\pi$
$619$	8.56249	+	4.94355i	0.344155	+	0.198698i	−0.317953	+	0.948107i	$0.602995\pi$
$620$		0			0
$621$	−21.5818	−	4.67530i	−0.866047	−	0.187613i
$622$			22.8384i			0.915736i
$623$	−37.0610	+	22.4405i	−1.48482	+	0.899060i
$624$	0.652411	−	2.60228i	0.0261174	−	0.104174i
$625$		0			0
$626$	12.6521	−	21.9141i	0.505680	−	0.875864i
$627$	1.49202	−	1.54102i	0.0595855	−	0.0615425i
$628$	2.46479	−	1.42305i	0.0983557	−	0.0567857i
$629$	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	$0.676633\pi$
$632$	5.86962	−	3.38883i	0.233481	−	0.134800i
$633$	27.5563	−	28.4613i	1.09526	−	1.13123i
$634$	−7.54489	+	13.0681i	−0.299646	+	0.519002i
$635$		0			0
$636$	−0.0273702	+	0.109172i	−0.00108530	+	0.00432894i
$637$	0.452145	+	10.8330i	0.0179147	+	0.429220i
$638$		−	0.944591i		−	0.0373967i
$639$	−18.8633	+	0.609672i	−0.746219	+	0.0241182i
$640$		0			0
$641$	−20.3632	−	11.7567i	−0.804298	−	0.464362i	0.0406739	−	0.999172i	$-0.487050\pi$
$641$	−20.3632	−	11.7567i	−0.804298	−	0.464362i	−0.844972	+	0.534811i	$0.820383\pi$
$642$	8.46602	+	29.6699i	0.334127	+	1.17098i
$643$		−	20.1307i		−	0.793876i	−0.917846	−	0.396938i	$-0.870073\pi$
$643$		−	20.1307i		−	0.793876i	0.917846	−	0.396938i	$-0.129927\pi$
$644$	11.2414	−	0.234492i	0.442971	−	0.00924027i
$645$		0			0
$646$	−1.69168	−	2.93008i	−0.0665582	−	0.115282i
$647$	−5.16088	+	8.93890i	−0.202895	+	0.351424i	−0.949460	−	0.313888i	$-0.898368\pi$
$647$	−5.16088	+	8.93890i	−0.202895	+	0.351424i	0.746565	+	0.665312i	$0.231702\pi$
$648$	−0.581164	−	8.98122i	−0.0228303	−	0.352816i
$649$	−2.01886	+	1.16559i	−0.0792473	+	0.0457535i
$650$		0			0
$651$	12.5017	+	40.5856i	0.489981	+	1.59067i
$652$	12.3586			0.484001
$653$	2.88758	−	1.66715i	0.113000	−	0.0652404i	−0.442435	−	0.896801i	$-0.645885\pi$
$653$	2.88758	−	1.66715i	0.113000	−	0.0652404i	0.555435	+	0.831560i	$0.312552\pi$
$654$	0.183922	+	0.178074i	0.00719192	+	0.00696323i
$655$		0			0
$656$	4.95787	+	8.58728i	0.193572	+	0.335277i
$657$	11.4521	−	21.4040i	0.446790	−	0.835050i
$658$	−12.4978	+	22.7288i	−0.487216	+	0.886059i
$659$		−	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	0.495244	−	0.868754i	$-0.335079\pi$
$661$	−0.244148	−	0.140959i	−0.00949625	−	0.00548266i	−0.504741	+	0.863271i	$0.668412\pi$
$662$	13.0438	+	7.53086i	0.506963	+	0.292695i
$663$	1.36611	−	0.389807i	0.0530554	−	0.0151389i
$664$		−	2.11036i		−	0.0818977i
$665$		0			0
$666$	−2.49554	+	4.66415i	−0.0967000	+	0.180732i
$667$	−10.3556	−	17.9364i	−0.400969	−	0.694499i
$668$	−2.49960	+	4.32943i	−0.0967124	+	0.167511i
$669$	0.00779327	+	0.00754545i	0.000301305	+	0.000291724i
$670$		0			0
$671$	0.830727			0.0320699
$672$	1.34904	+	4.37951i	0.0520402	+	0.168943i
$673$	36.0090			1.38805			0.694023	−	0.719953i	$-0.255837\pi$
$673$	36.0090			1.38805			0.694023	+	0.719953i	$0.255837\pi$
$674$	12.9567	−	7.48055i	0.499073	−	0.288140i
$675$		0			0
$676$	5.30042	−	9.18059i	0.203862	−	0.353100i
$677$	2.00745	+	3.47701i	0.0771526	+	0.133632i	0.902020	−	0.431694i	$-0.142084\pi$
$677$	2.00745	+	3.47701i	0.0771526	+	0.133632i	−0.824868	+	0.565326i	$0.808750\pi$
$678$	5.79235	+	1.45219i	0.222454	+	0.0557709i
$679$	21.8085	−	0.454920i	0.836933	−	0.0174582i
$680$		0			0
$681$	−8.94785	−	31.3585i	−0.342882	−	1.20166i
$682$	−1.55554	−	0.898091i	−0.0595646	−	0.0343897i
$683$	31.6027	+	18.2458i	1.20924	+	0.698156i	0.962594	−	0.270949i	$-0.0873373\pi$
$683$	31.6027	+	18.2458i	1.20924	+	0.698156i	0.246649	+	0.969105i	$0.420671\pi$
$684$	19.1580	−	0.619198i	0.732524	−	0.0236756i
$685$		0			0
$686$	−10.2449	−	15.4286i	−0.391153	−	0.589067i
$687$	−3.28394	+	13.0987i	−0.125290	+	0.499746i
$688$	5.74325	+	9.94760i	0.218959	+	0.379249i
$689$	0.0503252	−	0.0871659i	0.00191724	−	0.00332075i
$690$		0			0
$691$	−7.57320	+	4.37239i	−0.288098	+	0.166334i	−0.637084	−	0.770795i	$-0.719860\pi$
$691$	−7.57320	+	4.37239i	−0.288098	+	0.166334i	0.348986	+	0.937128i	$0.386526\pi$
$692$	−7.60806			−0.289215
$693$	−1.37130	−	0.697322i	−0.0520915	−	0.0264891i
$694$	4.04662			0.153608
$695$		0			0
$696$	5.87158	−	6.06442i	0.222562	−	0.229871i
$697$	−2.62535	+	4.54724i	−0.0994423	+	0.172239i
$698$	−6.18475	−	10.7123i	−0.234096	−	0.405467i
$699$	−5.47327	+	21.8313i	−0.207018	+	0.825734i
$700$		0			0
$701$		−	21.5875i		−	0.815349i	−0.913127	−	0.407674i	$-0.866340\pi$
$701$		−	21.5875i		−	0.815349i	0.913127	−	0.407674i	$-0.133660\pi$
$702$	−1.70402	+	7.86598i	−0.0643142	+	0.296882i
$703$	−9.75673	−	5.63305i	−0.367982	−	0.212455i
$704$	−0.167855	−	0.0969112i	−0.00632628	−	0.00365248i
$705$		0			0
$706$		−	3.66715i		−	0.138015i
$707$	10.3321	+	5.68132i	0.388580	+	0.213668i
$708$	−20.2067	−	5.06598i	−0.759415	−	0.190391i
$709$	2.50743	+	4.34300i	0.0941685	+	0.163105i	0.909261	−	0.416226i	$-0.136647\pi$
$709$	2.50743	+	4.34300i	0.0941685	+	0.163105i	−0.815093	+	0.579330i	$0.803314\pi$
$710$		0			0
$711$	−17.2713	+	10.7300i	−0.647723	+	0.402407i
$712$	14.1816	−	8.18773i	0.531477	−	0.306848i
$713$	−39.3831			−1.47491
$714$	−1.65121	+	1.77820i	−0.0617951	+	0.0665475i
$715$		0			0
$716$	14.0520	−	8.11295i	0.525149	−	0.303195i
$717$	−21.3670	−	20.6876i	−0.797966	−	0.772592i
$718$	−3.66134	+	6.34163i	−0.136640	+	0.236668i
$719$	−17.1509	−	29.7062i	−0.639619	−	1.10785i	−0.985516	−	0.169580i	$-0.945759\pi$
$719$	−17.1509	−	29.7062i	−0.639619	−	1.10785i	0.345897	−	0.938272i	$-0.387575\pi$
$720$		0			0
$721$	11.5411	+	19.0604i	0.429813	+	0.709846i
$722$			21.8235i			0.812188i
$723$	−13.6684	+	3.90013i	−0.508331	+	0.145048i
$724$	3.49141	+	2.01577i	0.129757	+	0.0749154i
$725$		0			0
$726$	−18.2587	+	5.20996i	−0.677645	+	0.193360i
$727$		−	17.4763i		−	0.648159i	−0.946030	−	0.324080i	$-0.894945\pi$
$727$		−	17.4763i		−	0.648159i	0.946030	−	0.324080i	$-0.105055\pi$
$728$	−0.0854660	−	4.09717i	−0.00316758	−	0.151851i
$729$	2.61296	+	26.8733i	0.0967764	+	0.995306i
$730$		0			0
$731$	−3.04124	+	5.26758i	−0.112484	+	0.194829i
$732$	5.33340	+	5.16380i	0.197128	+	0.190860i
$733$	−45.0320	+	25.9992i	−1.66330	+	0.960304i	−0.692170	+	0.721734i	$0.743345\pi$
$733$	−45.0320	+	25.9992i	−1.66330	+	0.960304i	−0.971125	+	0.238570i	$0.923321\pi$
$734$	−4.76624			−0.175925
$735$		0			0
$736$	−4.24976			−0.156648
$737$	0.810838	−	0.468137i	0.0298676	−	0.0172441i
$738$	−15.6980	−	25.2679i	−0.577853	−	0.930125i
$739$	12.1033	−	20.9635i	0.445226	−	0.771155i	−0.552842	−	0.833286i	$-0.686457\pi$
$739$	12.1033	−	20.9635i	0.445226	−	0.771155i	0.998068	+	0.0621318i	$0.0197899\pi$
$740$		0			0
$741$	−16.6268	−	4.16847i	−0.610801	−	0.153133i
$742$	0.00358550	+	0.171886i	0.000131628	+	0.00631013i
$743$		−	48.1794i		−	1.76753i	−0.467932	−	0.883765i	$-0.655001\pi$
$743$		−	48.1794i		−	1.76753i	0.467932	−	0.883765i	$-0.344999\pi$
$744$	−4.40426	−	15.4351i	−0.161468	−	0.565879i
$745$		0			0
$746$	14.9790	+	8.64813i	0.548420	+	0.316631i
$747$	0.204517	+	6.32776i	0.00748289	+	0.231521i
$748$		−	0.102635i		−	0.00375272i
$749$	24.4113	+	40.3158i	0.891970	+	1.47311i
$750$		0			0
$751$	−2.58147	−	4.47123i	−0.0941991	−	0.163158i	0.815075	−	0.579355i	$-0.196696\pi$
$751$	−2.58147	−	4.47123i	−0.0941991	−	0.163158i	−0.909274	+	0.416198i	$0.863362\pi$
$752$	4.90186	−	8.49028i	0.178753	−	0.309609i
$753$	−27.6022	+	28.5087i	−1.00588	+	1.03891i
$754$	−6.53733	+	3.77433i	−0.238076	+	0.137453i
$755$		0			0
$756$	−4.46942	−	13.0009i	−0.162551	−	0.472839i
$757$	16.0842			0.584591			0.292295	−	0.956328i	$-0.405581\pi$
$757$	16.0842			0.584591			0.292295	+	0.956328i	$0.405581\pi$
$758$	7.59197	−	4.38323i	0.275753	−	0.159206i
$759$	0.992392	−	1.02498i	0.0360215	−	0.0372046i
$760$		0			0
$761$	−5.07895	−	8.79701i	−0.184112	−	0.318891i	0.759165	−	0.650898i	$-0.225608\pi$
$761$	−5.07895	−	8.79701i	−0.184112	−	0.318891i	−0.943277	+	0.332007i	$0.892274\pi$
$762$	−2.31647	+	9.23972i	−0.0839168	+	0.334720i
$763$	0.342664	+	0.188420i	0.0124053	+	0.00682127i
$764$			25.2353i			0.912980i
$765$		0			0
$766$	24.6604	+	14.2377i	0.891015	+	0.514428i
$767$	16.1337	+	9.31477i	0.582552	+	0.336337i
$768$	−0.475255	−	1.66557i	−0.0171493	−	0.0601012i
$769$		−	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
$772$	−12.6183	−	21.8556i	−0.454143	−	0.786599i
$773$	13.2852	−	23.0107i	0.477836	−	0.827636i	−0.521841	−	0.853043i	$-0.674755\pi$
$773$	13.2852	−	23.0107i	0.477836	−	0.827636i	0.999677	+	0.0254064i	$0.00808799\pi$
$774$	−18.1848	−	29.2707i	−0.653639	−	1.05211i
$775$		0			0
$776$	−8.24463			−0.295965
$777$	−1.80110	+	7.87702i	−0.0646141	+	0.282587i
$778$	21.0696			0.755382
$779$	54.8669	−	31.6774i	1.96581	−	1.13496i
$780$		0			0
$781$	0.609672	−	1.05598i	0.0218158	−	0.0377860i
$782$	−1.12519	−	1.94889i	−0.0402368	−	0.0696922i
$783$	−17.0178	+	18.7528i	−0.608168	+	0.670170i
$784$	3.74976	+	5.91095i	0.133920	+	0.211105i
$785$		0			0
$786$	9.98822	−	2.85004i	0.356268	−	0.101658i
$787$	−25.6272	−	14.7959i	−0.913510	−	0.527416i	−0.0319515	−	0.999489i	$-0.510172\pi$
$787$	−25.6272	−	14.7959i	−0.913510	−	0.527416i	−0.881559	+	0.472074i	$0.843506\pi$
$788$	−12.7621	−	7.36822i	−0.454632	−	0.262482i
$789$	29.7610	−	8.49202i	1.05952	−	0.302324i
$790$		0			0
$791$	9.11981	−	0.190237i	0.324263	−	0.00676405i
$792$	0.512694	+	0.274315i	0.0182178	+	0.00974735i
$793$	−3.31936	−	5.74930i	−0.117874	−	0.204164i
$794$	3.29905	−	5.71412i	0.117079	−	0.202786i
$795$		0			0
$796$	22.3991	−	12.9321i	0.793915	−	0.458367i
$797$	34.6019			1.22566			0.612830	−	0.790215i	$-0.290031\pi$
$797$	34.6019			1.22566			0.612830	+	0.790215i	$0.290031\pi$
$798$	27.9821	−	8.61944i	0.990557	−	0.305125i
$799$	5.19139			0.183658
$800$		0			0
$801$	−41.7290	+	25.9247i	−1.47442	+	0.916005i
$802$	8.06552	−	13.9699i	0.284803	−	0.493294i
$803$	0.784178	+	1.35824i	0.0276730	+	0.0479311i
$804$	8.11564	+	2.03465i	0.286217	+	0.0717567i
$805$		0			0
$806$			14.3541i			0.505602i
$807$	3.29136	+	11.5349i	0.115861	+	0.406046i
$808$	−3.85955	−	2.22831i	−0.135779	−	0.0783918i
$809$	−14.6105	−	8.43536i	−0.513677	−	0.296571i	0.220667	−	0.975349i	$-0.429177\pi$
$809$	−14.6105	−	8.43536i	−0.513677	−	0.296571i	−0.734344	+	0.678778i	$0.762510\pi$
$810$		0			0
$811$		−	11.1600i		−	0.391880i	−0.980616	−	0.195940i	$-0.937224\pi$
$811$		−	11.1600i		−	0.391880i	0.980616	−	0.195940i	$-0.0627758\pi$
$812$	6.21274	−	11.2986i	0.218024	−	0.396503i
$813$	7.12619	−	28.4243i	0.249926	−	0.996883i
$814$	−0.170880	−	0.295974i	−0.00598936	−	0.0103739i
$815$		0			0
$816$	0.637981	−	0.658934i	0.0223338	−	0.0230673i
$817$	63.5585	−	36.6955i	2.22363	−	1.28381i
$818$	26.4033			0.923169
$819$	0.653326	+	12.2768i	0.0228291	+	0.428987i
$820$		0			0
$821$	−34.0899	+	19.6818i	−1.18975	+	0.686901i	−0.958249	−	0.285934i	$-0.907696\pi$
$821$	−34.0899	+	19.6818i	−1.18975	+	0.686901i	−0.231498	+	0.972835i	$0.574363\pi$
$822$	1.03867	−	1.07279i	0.0362279	−	0.0374177i
$823$	20.3585	−	35.2620i	0.709654	−	1.22916i	−0.255332	−	0.966854i	$-0.582185\pi$
$823$	20.3585	−	35.2620i	0.709654	−	1.22916i	0.964986	−	0.262303i	$-0.0844820\pi$
$824$	−4.21094	−	7.29356i	−0.146695	−	0.254083i
$825$		0			0
$826$	−31.8146	+	0.663645i	−1.10697	+	0.0230912i
$827$		−	24.7892i		−	0.862006i	−0.902350	−	0.431003i	$-0.858160\pi$
$827$		−	24.7892i		−	0.862006i	0.902350	−	0.431003i	$-0.141840\pi$
$828$	12.7426	−	0.411849i	0.442837	−	0.0143127i
$829$	−0.897813	−	0.518352i	−0.0311823	−	0.0180031i	0.484328	−	0.874887i	$-0.339064\pi$
$829$	−0.897813	−	0.518352i	−0.0311823	−	0.0180031i	−0.515510	+	0.856883i	$0.672398\pi$
$830$		0			0
$831$	−10.1234	−	35.4782i	−0.351176	−	1.23073i
$832$			1.54892i			0.0536992i
$833$	−1.71789	+	3.28462i	−0.0595212	+	0.113805i
$834$	27.1906	+	6.81689i	0.941533	+	0.236050i
$835$		0			0
$836$	−0.619198	+	1.07248i	−0.0214154	+	0.0370926i
$837$	14.7017	+	45.8543i	0.508166	+	1.58496i
$838$	17.1743	−	9.91561i	0.593278	−	0.342529i
$839$	−19.4880			−0.672801			−0.336401	−	0.941719i	$-0.609210\pi$
$839$	−19.4880			−0.672801			−0.336401	+	0.941719i	$0.609210\pi$
$840$		0			0
$841$	5.24911			0.181004
$842$	−5.43872	+	3.14004i	−0.187431	+	0.108213i
$843$	24.3806	+	23.6053i	0.839712	+	0.813011i
$844$	−11.4360	+	19.8078i	−0.393644	+	0.681812i
$845$		0			0
$846$	−13.8751	+	25.9326i	−0.477036	+	0.891581i
$847$	−24.8102	+	15.0226i	−0.852488	+	0.516183i
$848$		−	0.0649809i		−	0.00223145i
$849$	−25.1466	+	7.17533i	−0.863028	+	0.246257i
$850$		0			0
$851$	−6.48953	−	3.74673i	−0.222458	−	0.128436i
$852$	10.4782	−	2.98985i	0.358976	−	0.102430i
$853$			3.93413i			0.134702i	0.997729	+	0.0673510i	$0.0214547\pi$
$853$			3.93413i			0.134702i	−0.997729	+	0.0673510i	$0.978545\pi$
$854$	9.93662	+	5.46383i	0.340024	+	0.186969i
$855$		0			0
$856$	−8.90681	−	15.4270i	−0.304429	−	0.527286i
$857$	4.49804	−	7.79083i	0.153650	−	0.266130i	−0.778917	−	0.627128i	$-0.784230\pi$
$857$	4.49804	−	7.79083i	0.153650	−	0.266130i	0.932567	+	0.360998i	$0.117564\pi$
$858$	−0.373580	−	0.361700i	−0.0127538	−	0.0123482i
$859$	35.2001	−	20.3228i	1.20101	−	0.693404i	0.240231	−	0.970716i	$-0.422777\pi$
$859$	35.2001	−	20.3228i	1.20101	−	0.693404i	0.960780	+	0.277312i	$0.0894435\pi$
$860$		0			0
$861$	−33.2976	−	30.9197i	−1.13478	−	1.05374i
$862$	−4.55329			−0.155086
$863$	28.7932	−	16.6238i	0.980133	−	0.565880i	0.0778229	−	0.996967i	$-0.475203\pi$
$863$	28.7932	−	16.6238i	0.980133	−	0.565880i	0.902310	+	0.431087i	$0.141870\pi$
$864$	1.58643	+	4.94805i	0.0539716	+	0.168336i
$865$		0			0
$866$	−1.31401	−	2.27592i	−0.0446517	−	0.0773391i
$867$	−28.0899	−	7.04235i	−0.953981	−	0.239171i
$868$	−12.6995	−	20.9734i	−0.431047	−	0.711884i
$869$		−	1.31366i		−	0.0445629i
$870$		0			0
$871$	−6.47977	−	3.74110i	−0.219559	−	0.126762i
$872$	−0.128001	−	0.0739017i	−0.00433468	−	0.00250263i
$873$	24.7210	−	0.798997i	0.836678	−	0.0270419i
$874$			27.1531i			0.918467i
$875$		0			0
$876$	−3.40825	+	13.5945i	−0.115154	+	0.459317i
$877$	14.1314	+	24.4763i	0.477184	+	0.826506i	0.999658	−	0.0261486i	$-0.00832430\pi$
$877$	14.1314	+	24.4763i	0.477184	+	0.826506i	−0.522474	+	0.852655i	$0.674991\pi$
$878$	2.91836	−	5.05475i	0.0984899	−	0.170590i
$879$	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	$0.304477\pi$
$882$	−11.8162	−	17.3602i	−0.397873	−	0.584548i
$883$	−4.09672			−0.137866			−0.0689328	−	0.997621i	$-0.521959\pi$
$883$	−4.09672			−0.137866			−0.0689328	+	0.997621i	$0.521959\pi$
$884$	−0.710319	+	0.410103i	−0.0238906	+	0.0137932i
$885$		0			0
$886$	−13.1730	+	22.8164i	−0.442557	+	0.766531i
$887$	0.926997	+	1.60561i	0.0311255	+	0.0539110i	0.881169	−	0.472802i	$-0.156758\pi$
$887$	0.926997	+	1.60561i	0.0311255	+	0.0539110i	−0.850043	+	0.526713i	$0.823424\pi$
$888$	0.742694	−	2.96239i	0.0249232	−	0.0994113i
$889$	0.303458	+	14.5475i	0.0101777	+	0.487909i
$890$		0			0
$891$	−1.56386	−	0.772829i	−0.0523914	−	0.0258908i
$892$	−0.00542376	−	0.00313141i	−0.000181601	−	0.000104847i
$893$	−54.2472	−	31.3196i	−1.81531	−	1.04807i
$894$	6.06427	+	21.2527i	0.202819	+	0.710798i
$895$		0			0
$896$	−1.37037	−	2.26320i	−0.0457810	−	0.0756082i
$897$	−11.0590	−	2.77259i	−0.369251	−	0.0925740i
$898$	−2.88319	−	4.99383i	−0.0962134	−	0.166646i
$899$	−22.5817	+	39.1126i	−0.753141	+	1.30448i
$900$		0			0
$901$	0.0297995	−	0.0172048i	0.000992766	−	0.000573174i
$902$	1.92189			0.0639920
$903$	−38.5723	−	35.8178i	−1.28361	−	1.19194i
$904$	−3.44771			−0.114669
$905$		0			0
$906$	−21.7768	−	21.0843i	−0.723485	−	0.700479i
$907$	16.8711	−	29.2217i	0.560197	−	0.970289i	−0.437282	−	0.899324i	$-0.644059\pi$
$907$	16.8711	−	29.2217i	0.560197	−	0.970289i	0.997479	−	0.0709647i	$-0.0226078\pi$
$908$	9.41373	+	16.3051i	0.312406	+	0.541102i
$909$	11.7886	+	6.30742i	0.391002	+	0.209204i
$910$		0			0
$911$		−	6.90180i		−	0.228667i	−0.993442	−	0.114333i	$-0.963527\pi$
$911$		−	6.90180i		−	0.228667i	0.993442	−	0.114333i	$-0.0364732\pi$
$912$	−10.6419	+	3.03656i	−0.352388	+	0.100551i
$913$	−0.354234	−	0.204517i	−0.0117234	−	0.00676853i
$914$	0.624848	+	0.360756i	0.0206682	+	0.0119328i
$915$		0			0
$916$		−	7.79658i		−	0.257606i
$917$	13.5721	−	8.21795i	0.448191	−	0.271381i
$918$	−1.84909	+	2.03760i	−0.0610290	+	0.0672508i
$919$	17.5128	+	30.3330i	0.577693	+	1.00059i	0.995743	+	0.0921698i	$0.0293803\pi$
$919$	17.5128	+	30.3330i	0.577693	+	1.00059i	−0.418050	+	0.908424i	$0.637286\pi$
$920$		0			0
$921$	5.39637	+	5.22477i	0.177816	+	0.172162i
$922$	−29.7646	+	17.1846i	−0.980243	+	0.565944i
$923$	−9.74433			−0.320738
$924$	0.865860	+	0.197981i	0.0284847	+	0.00651309i
$925$		0			0
$926$	35.8374	−	20.6908i	1.17769	−	0.679940i
$927$	13.3330	+	21.4612i	0.437915	+	0.704877i
$928$	−2.43674	+	4.22056i	−0.0799900	+	0.138547i
$929$	−10.5447	−	18.2639i	−0.345960	−	0.599220i	0.639568	−	0.768734i	$-0.279113\pi$
$929$	−10.5447	−	18.2639i	−0.345960	−	0.599220i	−0.985528	+	0.169515i	$0.945780\pi$
$930$		0			0
$931$	37.7670	−	23.9584i	1.23776	−	0.785206i
$932$		−	12.9944i		−	0.425645i
$933$	10.8541	+	38.0390i	0.355346	+	1.24534i
$934$	15.5598	+	8.98343i	0.509131	+	0.293947i
$935$		0			0
$936$	−0.150108	−	4.64434i	−0.00490643	−	0.151805i
$937$			44.5007i			1.45378i	0.686756	+	0.726888i	$0.259034\pi$
$937$			44.5007i			1.45378i	−0.686756	+	0.726888i	$0.740966\pi$
$938$	12.7777	−	0.266540i	0.417208	−	0.00870285i
$939$	10.6582	−	42.5125i	0.347818	−	1.38734i
$940$		0			0
$941$	−21.8197	+	37.7929i	−0.711303	+	1.23201i	0.253065	+	0.967449i	$0.418561\pi$
$941$	−21.8197	+	37.7929i	−0.711303	+	1.23201i	−0.964368	+	0.264564i	$0.914772\pi$
$942$	3.42897	−	3.54159i	0.111722	−	0.115391i
$943$	36.4938	−	21.0697i	1.18840	−	0.686125i
$944$	12.0274			0.391459
$945$		0			0
$946$	2.22634			0.0723846
$947$	11.1646	−	6.44589i	0.362801	−	0.209463i	−0.307508	−	0.951546i	$-0.599495\pi$
$947$	11.1646	−	6.44589i	0.362801	−	0.209463i	0.670309	+	0.742082i	$0.266162\pi$
$948$	8.16573	−	8.43391i	0.265210	−	0.273921i
$949$	6.26672	−	10.8543i	0.203426	−	0.352345i
$950$		0			0
$951$	−6.35586	+	25.3517i	−0.206103	+	0.822084i
$952$	0.675050	−	1.22766i	0.0218785	−	0.0397886i
$953$			47.2228i			1.52970i	0.644211	+	0.764848i	$0.277186\pi$
$953$			47.2228i			1.52970i	−0.644211	+	0.764848i	$0.722814\pi$
$954$	0.00629738	+	0.194841i	0.000203885	+	0.00630821i
$955$		0			0
$956$	14.8705	+	8.58548i	0.480946	+	0.277674i
$957$	−0.448922	−	1.57329i	−0.0145116	−	0.0508571i
$958$		−	9.01118i		−	0.291138i
$959$	1.09902	−	1.99870i	0.0354893	−	0.0645414i
$960$		0			0
$961$	27.4400	+	47.5275i	0.885162	+	1.53315i
$962$	−1.36558	+	2.36526i	−0.0440282	+	0.0762590i
$963$	28.2015	+	45.3938i	0.908782	+	1.46280i
$964$	7.10695	−	4.10320i	0.228899	−	0.132155i
$965$		0			0
$966$	18.6118	−	5.73308i	0.598826	−	0.184459i
$967$	7.93428			0.255149			0.127575	−	0.991829i	$-0.459281\pi$
$967$	7.93428			0.255149			0.127575	+	0.991829i	$0.459281\pi$
$968$	9.49375	−	5.48122i	0.305141	−	0.176173i
$969$	−4.21015	−	4.07627i	−0.135249	−	0.130949i
$970$		0			0
$971$	16.7632	+	29.0348i	0.537958	+	0.931770i	0.999014	+	0.0443991i	$0.0141373\pi$
$971$	16.7632	+	29.0348i	0.537958	+	0.931770i	−0.461056	+	0.887371i	$0.652529\pi$
$972$	−5.23634	−	14.6827i	−0.167956	−	0.470947i
$973$	42.8104	−	0.893014i	1.37244	−	0.0286287i
$974$		−	22.7295i		−	0.728302i
$975$		0			0
$976$	−3.71180	−	2.14301i	−0.118812	−	0.0685961i
$977$	−11.4767	−	6.62608i	−0.367172	−	0.211987i	0.305050	−	0.952336i	$-0.401327\pi$
$977$	−11.4767	−	6.62608i	−0.367172	−	0.211987i	−0.672222	+	0.740349i	$0.734660\pi$
$978$	20.5842	−	5.87350i	0.658210	−	0.187814i
$979$		−	3.17393i		−	0.101439i
$980$		0			0
$981$	0.390966	+	0.209185i	0.0124826	+	0.00667875i
$982$	−16.0827	−	27.8560i	−0.513219	−	0.888921i
$983$	−21.9739	+	38.0599i	−0.700858	+	1.21392i	0.267307	+	0.963611i	$0.413866\pi$
$983$	−21.9739	+	38.0599i	−0.700858	+	1.21392i	−0.968165	+	0.250311i	$0.919467\pi$
$984$	12.3388	+	11.9465i	0.393348	+	0.380840i
$985$		0			0
$986$	−2.58067			−0.0821853
$987$	−10.0141	+	43.7960i	−0.318751	+	1.39404i
$988$	9.89658			0.314852
$989$	42.2749	−	24.4074i	1.34426	−	0.776111i
$990$		0			0
$991$	−5.43257	+	9.40948i	−0.172571	+	0.298902i	−0.939318	−	0.343047i	$-0.888541\pi$
$991$	−5.43257	+	9.40948i	−0.172571	+	0.298902i	0.766747	+	0.641950i	$0.221874\pi$
$992$	4.63357	+	8.02559i	0.147116	+	0.254813i
$993$	25.3045	+	6.34404i	0.803015	+	0.201322i
$994$	14.2379	−	8.62106i	0.451598	−	0.273444i
$995$		0			0
$996$	−1.00296	−	3.51495i	−0.0317799	−	0.111375i
$997$	34.8191	+	20.1028i	1.10273	+	0.636662i	0.936937	−	0.349499i	$-0.113648\pi$
$997$	34.8191	+	20.1028i	1.10273	+	0.636662i	0.165794	+	0.986160i	$0.446981\pi$
$998$	18.4037	+	10.6254i	0.582560	+	0.336341i
$999$	−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.s.f.101.1		12
3.2	odd	2		1050.2.s.g.101.5		12
5.2	odd	4		1050.2.u.e.899.5		12
5.3	odd	4		1050.2.u.h.899.2		12
5.4	even	2		210.2.r.b.101.6	yes	12
7.5	odd	6		1050.2.s.g.551.5		12
15.2	even	4		1050.2.u.g.899.2		12
15.8	even	4		1050.2.u.f.899.5		12
15.14	odd	2		210.2.r.a.101.2	✓	12
21.5	even	6	inner	1050.2.s.f.551.1		12
35.4	even	6		1470.2.b.a.881.7		12
35.12	even	12		1050.2.u.f.299.5		12
35.19	odd	6		210.2.r.a.131.2	yes	12
35.24	odd	6		1470.2.b.b.881.12		12
35.33	even	12		1050.2.u.g.299.2		12
105.47	odd	12		1050.2.u.h.299.2		12
105.59	even	6		1470.2.b.a.881.1		12
105.68	odd	12		1050.2.u.e.299.5		12
105.74	odd	6		1470.2.b.b.881.6		12
105.89	even	6		210.2.r.b.131.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.2	✓	12	15.14	odd	2
210.2.r.a.131.2	yes	12	35.19	odd	6
210.2.r.b.101.6	yes	12	5.4	even	2
210.2.r.b.131.6	yes	12	105.89	even	6
1050.2.s.f.101.1		12	1.1	even	1	trivial
1050.2.s.f.551.1		12	21.5	even	6	inner
1050.2.s.g.101.5		12	3.2	odd	2
1050.2.s.g.551.5		12	7.5	odd	6
1050.2.u.e.299.5		12	105.68	odd	12
1050.2.u.e.899.5		12	5.2	odd	4
1050.2.u.f.299.5		12	35.12	even	12
1050.2.u.f.899.5		12	15.8	even	4
1050.2.u.g.299.2		12	35.33	even	12
1050.2.u.g.899.2		12	15.2	even	4
1050.2.u.h.299.2		12	105.47	odd	12
1050.2.u.h.899.2		12	5.3	odd	4
1470.2.b.a.881.1		12	105.59	even	6
1470.2.b.a.881.7		12	35.4	even	6
1470.2.b.b.881.6		12	105.74	odd	6
1470.2.b.b.881.12		12	35.24	odd	6

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.s (of order \(6\), degree \(2\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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