LMFDB - Embedded newform 1050.2.s.f.551.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1050,2,Mod(101,1050)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [12,0,-2,6,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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			551.1
Root			$1.66557 - 0.475255i$ of defining polynomial
Character	$\chi$	$=$	1050.551
Dual form			1050.2.s.f.101.1

$q$-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} +(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} + 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}+ \cdots + 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

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 $

$2$	−0.866025	−	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	−0.474481	−	0.880266i	$-0.657364\pi$
$11$	0.167855	−	0.0969112i	0.0506102	−	0.0292198i	0.525092	+	0.851046i	$0.324031\pi$
$12$	0.475255	−	1.66557i	0.137194	−	0.480809i
$13$			1.54892i			0.429594i	0.976659	+	0.214797i	$0.0689090\pi$
$13$			1.54892i			0.429594i	−0.976659	+	0.214797i	$0.931091\pi$
$14$	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	0.896346	−	0.443356i	$-0.146212\pi$
$17$	0.264766	+	0.458589i	0.0642153	+	0.111224i	−0.832130	+	0.554580i	$0.812879\pi$
$18$	1.58314	−	2.54826i	0.373151	−	0.600632i
$19$	−5.53332	−	3.19467i	−1.26943	−	0.732906i	−0.294551	−	0.955636i	$-0.595170\pi$
$19$	−5.53332	−	3.19467i	−1.26943	−	0.732906i	−0.974880	+	0.222729i	$0.928503\pi$
$20$		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	0.0645362	−	0.997915i	$-0.479443\pi$
$23$	−3.68040	−	2.12488i	−0.767416	−	0.443068i	−0.831952	+	0.554848i	$0.812777\pi$
$24$	−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	$-0.850535\pi$
$29$		−	4.87349i		−	0.904984i	0.891768	−	0.452492i	$-0.149465\pi$
$30$		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	$0.0204062\pi$
$32$	0.866025	−	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	−0.784411	−	0.620242i	$-0.787034\pi$
$37$	0.881634	−	1.52704i	0.144940	−	0.251043i	0.929350	+	0.369199i	$0.120368\pi$
$38$	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	−0.247945	−	0.968774i	$-0.579755\pi$
$47$	4.90186	−	8.49028i	0.715010	−	1.23843i	0.962956	−	0.269660i	$-0.0869114\pi$
$48$	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	−0.496130	−	0.868248i	$-0.665246\pi$
$53$	0.0562751	−	0.0324905i	0.00772998	−	0.00446291i	0.503860	+	0.863785i	$0.331913\pi$
$54$	−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	−0.930235	−	0.366964i	$-0.880397\pi$
$59$	−6.01371	−	10.4160i	−0.782918	−	1.35605i	0.147317	−	0.989089i	$-0.452936\pi$
$60$		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	$0.578193\pi$
$62$	−9.26715			−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	0.975002	−	0.222195i	$-0.0713222\pi$
$67$	2.41529	+	4.18340i	0.295075	+	0.511084i	−0.679928	+	0.733279i	$0.737989\pi$
$68$	−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	$0.121775\pi$
$71$			6.29103i			0.746608i	−0.927709	+	0.373304i	$0.878225\pi$
$72$	2.99843	+	0.0969112i	0.353369	+	0.0114211i
$73$	7.00763	−	4.04586i	0.820181	−	0.473532i	−0.0302980	−	0.999541i	$-0.509646\pi$
$73$	7.00763	−	4.04586i	0.820181	−	0.473532i	0.850479	+	0.526009i	$0.176312\pi$
$74$	−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	−0.991245	−	0.132039i	$-0.957848\pi$
$79$	−3.38883	+	5.86962i	−0.381273	+	0.660384i	0.609971	+	0.792423i	$0.291181\pi$
$80$		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	−0.00375740	+	0.999993i	$0.501196\pi$
$89$	−8.18773	+	14.1816i	−0.867898	+	1.50324i	−0.864141	+	0.503250i	$0.832137\pi$
$90$		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	$-0.862536\pi$
$97$		−	8.24463i		−	0.837115i	0.908190	−	0.418557i	$-0.137464\pi$
$98$	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	0.733607	−	0.679574i	$-0.237836\pi$
$101$	−2.22831	−	3.85955i	−0.221725	−	0.384040i	−0.955332	+	0.295535i	$0.904502\pi$
$102$	−0.658934	+	0.637981i	−0.0652442	+	0.0631696i
$103$	−7.29356	−	4.21094i	−0.718656	−	0.414916i	0.0956021	−	0.995420i	$-0.469522\pi$
$103$	−7.29356	−	4.21094i	−0.718656	−	0.414916i	−0.814258	+	0.580504i	$0.802856\pi$
$104$	1.54892			0.151884
$105$		0			0
$106$	−0.0649809			−0.00631151
$107$	−15.4270	−	8.90681i	−1.49139	−	0.861054i	−0.491438	−	0.870913i	$-0.663528\pi$
$107$	−15.4270	−	8.90681i	−1.49139	−	0.861054i	−0.999951	+	0.00985883i	$0.996862\pi$
$108$	4.94805	+	1.58643i	0.476127	+	0.152655i
$109$	−0.0739017	−	0.128001i	−0.00707850	−	0.0122603i	0.862464	−	0.506118i	$-0.168920\pi$
$109$	−0.0739017	−	0.128001i	−0.00707850	−	0.0122603i	−0.869543	+	0.493857i	$0.835587\pi$
$110$		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	$-0.948152\pi$
$113$		−	3.44771i		−	0.324334i	0.986763	−	0.162167i	$-0.0518483\pi$
$114$	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	−0.704792	−	0.709414i	$-0.748960\pi$
$131$	2.99843	−	5.19344i	0.261974	−	0.453753i	0.966767	+	0.255661i	$0.0822931\pi$
$132$	−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	−0.467767	−	0.883852i	$-0.654941\pi$
$137$	0.746611	−	0.431056i	0.0637872	−	0.0368276i	0.531554	+	0.847024i	$0.321608\pi$
$138$	2.01972	−	7.07828i	0.171930	−	0.602543i
$139$		−	16.1843i		−	1.37274i	−0.727254	−	0.686368i	$-0.759204\pi$
$139$		−	16.1843i		−	1.37274i	0.727254	−	0.686368i	$-0.240796\pi$
$140$		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	−0.0263788	−	0.999652i	$-0.508398\pi$
$149$	−11.0505	−	6.38001i	−0.905292	−	0.522671i	−0.878913	+	0.476981i	$0.841731\pi$
$150$		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	$0.581089\pi$
$152$	−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	−0.398409	−	0.917208i	$-0.630438\pi$
$157$	2.46479	−	1.42305i	0.196711	−	0.113571i	0.595121	+	0.803636i	$0.297104\pi$
$158$	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	−0.515830	−	0.856691i	$-0.672516\pi$
$163$	6.17931	−	10.7029i	0.484001	−	0.838315i	0.999831	+	0.0183763i	$0.00584968\pi$
$164$	−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	−0.973623	−	0.228164i	$-0.926728\pi$
$173$	−3.80403	+	6.58878i	−0.289215	+	0.500935i	0.684407	+	0.729100i	$0.260061\pi$
$174$	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	0.127566	−	0.991830i	$-0.459284\pi$
$179$	14.0520	−	8.11295i	1.05030	−	0.606390i	0.922733	+	0.385440i	$0.125950\pi$
$180$		0			0
$181$		−	4.03153i		−	0.299661i	−0.988712	−	0.149831i	$-0.952127\pi$
$181$		−	4.03153i		−	0.299661i	0.988712	−	0.149831i	$-0.0478729\pi$
$182$	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	−0.994666	−	0.103147i	$-0.967109\pi$
$191$	−21.8544	−	12.6176i	−1.58133	−	0.912980i	−0.586661	−	0.809832i	$-0.699558\pi$
$192$	1.20480	+	1.24437i	0.0869490	+	0.0898046i
$193$	12.6183	+	21.8556i	0.908286	+	1.57320i	0.816444	+	0.577424i	$0.195942\pi$
$193$	12.6183	+	21.8556i	0.908286	+	1.57320i	0.0918418	+	0.995774i	$0.470725\pi$
$194$	−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	$0.175921\pi$
$197$			14.7364i			1.04993i	−0.851125	+	0.524964i	$0.824079\pi$
$198$	0.0187836	−	0.581164i	0.00133489	−	0.0413015i
$199$	22.3991	−	12.9321i	1.58783	−	0.916734i	0.594165	−	0.804343i	$-0.297483\pi$
$199$	22.3991	−	12.9321i	1.58783	−	0.916734i	0.993664	−	0.112391i	$-0.0358508\pi$
$200$		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	$6.67479e-5\pi$
$223$			0.00626282i			0.000419390i	−1.00000		0.000209695i	$0.999933\pi$
$224$	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	−0.988577	−	0.150715i	$-0.951843\pi$
$227$	−9.41373	−	16.3051i	−0.624811	−	1.08220i	0.363766	−	0.931490i	$-0.381491\pi$
$228$	−7.95069	+	7.69787i	−0.526547	+	0.509804i
$229$	6.75203	+	3.89829i	0.446187	+	0.257606i	0.706218	−	0.707994i	$-0.250400\pi$
$229$	6.75203	+	3.89829i	0.446187	+	0.257606i	−0.260032	+	0.965600i	$0.583733\pi$
$230$		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	0.821064	−	0.570836i	$-0.193381\pi$
$233$	11.2535	+	6.49718i	0.737238	+	0.425645i	−0.0838262	+	0.996480i	$0.526714\pi$
$234$	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	$-0.812585\pi$
$239$		−	17.1710i		−	1.11070i	0.831618	−	0.555349i	$-0.187415\pi$
$240$		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	$0.248189\pi$
$242$	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	−0.955118	−	0.296225i	$-0.904272\pi$
$257$	−3.54324	+	6.13707i	−0.221021	+	0.382820i	0.734097	+	0.679044i	$0.237606\pi$
$258$	−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	−0.894381	−	0.447306i	$-0.852384\pi$
$263$	−15.4744	+	8.93416i	−0.954194	+	0.550904i	−0.0598127	+	0.998210i	$0.519050\pi$
$264$	−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	0.952067	−	0.305889i	$-0.0989535\pi$
$269$	3.46273	+	5.99762i	0.211126	+	0.365682i	−0.740941	+	0.671570i	$0.765620\pi$
$270$		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	$0.838454\pi$
$272$	−0.529533			−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	−0.985449	−	0.169972i	$-0.945632\pi$
$277$	−10.6505	−	18.4471i	−0.639924	−	1.10838i	0.345525	−	0.938410i	$-0.387701\pi$
$278$	−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	$0.198671\pi$
$281$			19.5927i			1.16880i	−0.811464	+	0.584402i	$0.801329\pi$
$282$	16.3288	+	4.65927i	0.972367	+	0.277456i
$283$	13.0751	−	7.54892i	0.777235	−	0.448737i	−0.0582144	−	0.998304i	$-0.518541\pi$
$283$	13.0751	−	7.54892i	0.777235	−	0.448737i	0.835450	+	0.549567i	$0.185207\pi$
$284$	−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	$0.0394928\pi$
$307$			4.33663i			0.247505i	−0.992313	+	0.123752i	$0.960507\pi$
$308$	−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	0.983713	+	0.179748i	$0.0575284\pi$
$311$	11.4192	+	19.7786i	0.647523	+	1.12154i	−0.336190	+	0.941794i	$0.609138\pi$
$312$	−1.86614	−	1.92743i	−0.105650	−	0.109119i
$313$	−21.9141	−	12.6521i	−1.23866	−	0.715140i	−0.269838	−	0.962906i	$-0.586970\pi$
$313$	−21.9141	−	12.6521i	−1.23866	−	0.715140i	−0.968820	+	0.247766i	$0.920304\pi$
$314$	−2.84609			−0.160614
$315$		0			0
$316$	−6.77766			−0.381273
$317$	13.0681	+	7.54489i	0.733979	+	0.423763i	0.819876	−	0.572541i	$-0.194042\pi$
$317$	13.0681	+	7.54489i	0.733979	+	0.423763i	−0.0858969	+	0.996304i	$0.527376\pi$
$318$	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	−0.995316	−	0.0966768i	$-0.969179\pi$
$331$	−7.53086	+	13.0438i	−0.413933	+	0.716954i	0.581382	+	0.813630i	$0.302512\pi$
$332$	−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	−0.591107	−	0.806593i	$-0.701309\pi$
$347$	−3.50448	+	2.02331i	−0.188130	+	0.108617i	0.402977	+	0.915210i	$0.367976\pi$
$348$	−8.11715	−	2.31615i	−0.435125	−	0.124159i
$349$		−	12.3695i		−	0.662124i	−0.943609	−	0.331062i	$-0.892593\pi$
$349$		−	12.3695i		−	0.662124i	0.943609	−	0.331062i	$-0.107407\pi$
$350$		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	0.813096	−	0.582130i	$-0.197780\pi$
$353$	−1.83358	−	3.17585i	−0.0975914	−	0.169033i	−0.910687	+	0.413097i	$0.864447\pi$
$354$	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	0.657925	−	0.753083i	$-0.271434\pi$
$359$	6.34163	+	3.66134i	0.334699	+	0.193238i	−0.323227	+	0.946322i	$0.604768\pi$
$360$		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	−0.388384	−	0.921497i	$-0.626967\pi$
$367$	4.12769	−	2.38312i	0.215464	−	0.124398i	0.603848	+	0.797100i	$0.293633\pi$
$368$	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	−0.998241	−	0.0592792i	$-0.981120\pi$
$373$	−8.64813	+	14.9790i	−0.447783	+	0.775584i	0.550458	+	0.834863i	$0.314453\pi$
$374$	−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	0.230422	+	0.973091i	$0.425989\pi$
$383$	−14.2377	+	24.6604i	−0.727511	+	1.26009i	−0.957932	+	0.286995i	$0.907344\pi$
$384$	−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	−0.885275	−	0.465069i	$-0.846030\pi$
$389$	−18.2468	+	10.5348i	−0.925151	+	0.534136i	−0.0398761	+	0.999205i	$0.512696\pi$
$390$		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	0.349707	−	0.936859i	$-0.386281\pi$
$397$	−5.71412	−	3.29905i	−0.286783	−	0.165574i	−0.636490	+	0.771285i	$0.719614\pi$
$398$	−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	0.108839	−	0.994059i	$-0.465287\pi$
$401$	−13.9699	−	8.06552i	−0.697623	−	0.402773i	−0.806461	+	0.591287i	$0.798620\pi$
$402$	−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	−0.944097	−	0.329666i	$-0.893064\pi$
$409$	−22.8659	+	13.2016i	−1.13065	+	0.652779i	−0.186549	+	0.982446i	$0.559730\pi$
$410$		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	−0.402014	−	0.915633i	$-0.631690\pi$
$431$	3.94326	−	2.27664i	0.189940	−	0.109662i	0.591955	+	0.805971i	$0.298356\pi$
$432$	1.10013	+	5.07836i	0.0529302	+	0.244333i
$433$		−	2.62801i		−	0.126294i	−0.998004	−	0.0631471i	$-0.979886\pi$
$433$		−	2.62801i		−	0.126294i	0.998004	−	0.0631471i	$-0.0201137\pi$
$434$	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	0.374501	−	0.927226i	$-0.377814\pi$
$439$	−5.05475	−	2.91836i	−0.241250	−	0.139286i	−0.615751	+	0.787941i	$0.711147\pi$
$440$		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	0.931983	−	0.362502i	$-0.118077\pi$
$443$	22.8164	+	13.1730i	1.08404	+	0.625870i	0.152056	+	0.988372i	$0.451411\pi$
$444$	−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	$-0.956554\pi$
$449$		−	5.76638i		−	0.272132i	0.990700	−	0.136066i	$-0.0434460\pi$
$450$		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	−0.874340	−	0.485314i	$-0.838705\pi$
$457$	−0.360756	+	0.624848i	−0.0168755	+	0.0292292i	0.857464	+	0.514543i	$0.172039\pi$
$458$	−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	−0.995502	−	0.0947401i	$-0.969798\pi$
$467$	−8.98343	+	15.5598i	−0.415704	+	0.720020i	0.579798	+	0.814760i	$0.303131\pi$
$468$	−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	0.744542	−	0.667575i	$-0.232668\pi$
$479$	−4.50559	−	7.80391i	−0.205866	−	0.356570i	−0.950408	+	0.311005i	$0.899334\pi$
$480$		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	−0.999849	−	0.0173928i	$-0.994463\pi$
$487$	−11.3648	−	19.6844i	−0.514987	−	0.891984i	0.484862	−	0.874591i	$-0.338870\pi$
$488$	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	$-0.741469\pi$
$491$		−	32.1654i		−	1.45160i	0.687904	−	0.725801i	$-0.258531\pi$
$492$	−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	−0.999611	−	0.0278832i	$-0.991123\pi$
$499$	−10.6254	+	18.4037i	−0.475658	+	0.823864i	0.523953	+	0.851747i	$0.324457\pi$
$500$		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	−0.978267	−	0.207351i	$-0.933516\pi$
$509$	−6.98403	+	12.0967i	−0.309562	+	0.536177i	0.668705	+	0.743528i	$0.266849\pi$
$510$		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	0.979643	−	0.200750i	$-0.0643378\pi$
$521$	7.21208	+	12.4917i	0.315967	+	0.547271i	−0.663676	+	0.748020i	$0.731004\pi$
$522$	−12.4189	−	7.71544i	−0.543562	−	0.337696i
$523$	25.2604	+	14.5841i	1.10456	+	0.637717i	0.937415	−	0.348215i	$-0.113212\pi$
$523$	25.2604	+	14.5841i	1.10456	+	0.637717i	0.167144	+	0.985932i	$0.446545\pi$
$524$	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	−0.463801	−	0.885939i	$-0.653515\pi$
$541$	12.4518	−	21.5672i	0.535345	−	0.927246i	0.999147	−	0.0413062i	$-0.0131519\pi$
$542$	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	−0.789446	−	0.613819i	$-0.789632\pi$
$557$	−15.4016	+	8.89212i	−0.652587	+	0.376771i	0.136860	+	0.990590i	$0.456299\pi$
$558$	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	0.569434	−	0.822037i	$-0.307162\pi$
$563$	−10.1362	−	17.5563i	−0.427188	−	0.739912i	−0.996622	+	0.0821256i	$0.973829\pi$
$564$	−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	0.983553	+	0.180619i	$0.0578101\pi$
$569$	38.9233	+	22.4724i	1.63175	+	0.942092i	0.648197	+	0.761473i	$0.275523\pi$
$570$		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	$0.758111\pi$
$572$	−0.150108	+	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	−0.314164	−	0.949369i	$-0.601724\pi$
$577$	8.42967	−	4.86687i	0.350932	−	0.202611i	0.665096	+	0.746758i	$0.268391\pi$
$578$	−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	−0.313930	−	0.949446i	$-0.601646\pi$
$593$	16.2006	−	28.0603i	0.665280	−	1.15230i	0.979209	−	0.202852i	$-0.0650211\pi$
$594$	−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	−0.301720	−	0.953397i	$-0.597561\pi$
$599$	9.13107	−	5.27183i	0.373086	−	0.215401i	0.674806	+	0.737996i	$0.264227\pi$
$600$		0			0
$601$			24.6793i			1.00669i	0.864086	+	0.503344i	$0.167897\pi$
$601$			24.6793i			1.00669i	−0.864086	+	0.503344i	$0.832103\pi$
$602$	−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	0.710549	−	0.703648i	$-0.248447\pi$
$607$	11.2456	+	6.49268i	0.456447	+	0.263530i	−0.254102	+	0.967177i	$0.581780\pi$
$608$	−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	−0.998915	−	0.0465601i	$-0.985174\pi$
$613$	−13.3643	−	23.1477i	−0.539780	−	0.934926i	0.459136	−	0.888366i	$-0.348159\pi$
$614$	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	$0.0861397\pi$
$617$			13.2804i			0.534650i	−0.963606	+	0.267325i	$0.913860\pi$
$618$	4.00254	−	14.0272i	0.161006	−	0.564259i
$619$	8.56249	−	4.94355i	0.344155	−	0.198698i	−0.317953	−	0.948107i	$-0.602995\pi$
$619$	8.56249	−	4.94355i	0.344155	−	0.198698i	0.662108	+	0.749408i	$0.269662\pi$
$620$		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	−0.844972	−	0.534811i	$-0.820383\pi$
$641$	−20.3632	+	11.7567i	−0.804298	+	0.464362i	0.0406739	+	0.999172i	$0.487050\pi$
$642$	8.46602	−	29.6699i	0.334127	−	1.17098i
$643$			20.1307i			0.793876i	0.917846	+	0.396938i	$0.129927\pi$
$643$			20.1307i			0.793876i	−0.917846	+	0.396938i	$0.870073\pi$
$644$	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	0.746565	−	0.665312i	$-0.231702\pi$
$647$	−5.16088	−	8.93890i	−0.202895	−	0.351424i	−0.949460	+	0.313888i	$0.898368\pi$
$648$	−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	0.555435	−	0.831560i	$-0.312552\pi$
$653$	2.88758	+	1.66715i	0.113000	+	0.0652404i	−0.442435	+	0.896801i	$0.645885\pi$
$654$	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	$0.0823733\pi$
$659$			13.1387i			0.511809i	−0.966702	+	0.255905i	$0.917627\pi$
$660$		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	$0.335079\pi$
$662$	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	−0.824868	−	0.565326i	$-0.808750\pi$
$677$	2.00745	−	3.47701i	0.0771526	−	0.133632i	0.902020	+	0.431694i	$0.142084\pi$
$678$	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	0.246649	−	0.969105i	$-0.420671\pi$
$683$	31.6027	−	18.2458i	1.20924	−	0.698156i	0.962594	+	0.270949i	$0.0873373\pi$
$684$	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	0.348986	−	0.937128i	$-0.386526\pi$
$691$	−7.57320	−	4.37239i	−0.288098	−	0.166334i	−0.637084	+	0.770795i	$0.719860\pi$
$692$	−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	$0.133660\pi$
$701$			21.5875i			0.815349i	−0.913127	+	0.407674i	$0.866340\pi$
$702$	−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	−0.815093	−	0.579330i	$-0.803314\pi$
$709$	2.50743	−	4.34300i	0.0941685	−	0.163105i	0.909261	+	0.416226i	$0.136647\pi$
$710$		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	0.345897	+	0.938272i	$0.387575\pi$
$719$	−17.1509	+	29.7062i	−0.639619	+	1.10785i	−0.985516	+	0.169580i	$0.945759\pi$
$720$		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	$0.105055\pi$
$727$			17.4763i			0.648159i	−0.946030	+	0.324080i	$0.894945\pi$
$728$	−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	−0.971125	−	0.238570i	$-0.923321\pi$
$733$	−45.0320	−	25.9992i	−1.66330	−	0.960304i	−0.692170	−	0.721734i	$-0.743345\pi$
$734$	−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	0.998068	−	0.0621318i	$-0.0197899\pi$
$739$	12.1033	+	20.9635i	0.445226	+	0.771155i	−0.552842	+	0.833286i	$0.686457\pi$
$740$		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	$0.344999\pi$
$743$			48.1794i			1.76753i	−0.467932	+	0.883765i	$0.655001\pi$
$744$	−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	−0.909274	−	0.416198i	$-0.863362\pi$
$751$	−2.58147	+	4.47123i	−0.0941991	+	0.163158i	0.815075	+	0.579355i	$0.196696\pi$
$752$	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	−0.943277	−	0.332007i	$-0.892274\pi$
$761$	−5.07895	+	8.79701i	−0.184112	+	0.318891i	0.759165	+	0.650898i	$0.225608\pi$
$762$	−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	$0.0384813\pi$
$769$			6.68859i			0.241197i	−0.992701	+	0.120598i	$0.961519\pi$
$770$		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	0.999677	−	0.0254064i	$-0.00808799\pi$
$773$	13.2852	+	23.0107i	0.477836	+	0.827636i	−0.521841	+	0.853043i	$0.674755\pi$
$774$	−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	−0.881559	−	0.472074i	$-0.843506\pi$
$787$	−25.6272	+	14.7959i	−0.913510	+	0.527416i	−0.0319515	+	0.999489i	$0.510172\pi$
$788$	−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	−0.734344	−	0.678778i	$-0.762510\pi$
$809$	−14.6105	+	8.43536i	−0.513677	+	0.296571i	0.220667	+	0.975349i	$0.429177\pi$
$810$		0			0
$811$			11.1600i			0.391880i	0.980616	+	0.195940i	$0.0627758\pi$
$811$			11.1600i			0.391880i	−0.980616	+	0.195940i	$0.937224\pi$
$812$	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	−0.231498	−	0.972835i	$-0.574363\pi$
$821$	−34.0899	−	19.6818i	−1.18975	−	0.686901i	−0.958249	+	0.285934i	$0.907696\pi$
$822$	1.03867	+	1.07279i	0.0362279	+	0.0374177i
$823$	20.3585	+	35.2620i	0.709654	+	1.22916i	0.964986	+	0.262303i	$0.0844820\pi$
$823$	20.3585	+	35.2620i	0.709654	+	1.22916i	−0.255332	+	0.966854i	$0.582185\pi$
$824$	−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	$0.141840\pi$
$827$			24.7892i			0.862006i	−0.902350	+	0.431003i	$0.858160\pi$
$828$	12.7426	+	0.411849i	0.442837	+	0.0143127i
$829$	−0.897813	+	0.518352i	−0.0311823	+	0.0180031i	−0.515510	−	0.856883i	$-0.672398\pi$
$829$	−0.897813	+	0.518352i	−0.0311823	+	0.0180031i	0.484328	+	0.874887i	$0.339064\pi$
$830$		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	$-0.978545\pi$
$853$		−	3.93413i		−	0.134702i	0.997729	−	0.0673510i	$-0.0214547\pi$
$854$	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	0.932567	−	0.360998i	$-0.117564\pi$
$857$	4.49804	+	7.79083i	0.153650	+	0.266130i	−0.778917	+	0.627128i	$0.784230\pi$
$858$	−0.373580	+	0.361700i	−0.0127538	+	0.0123482i
$859$	35.2001	+	20.3228i	1.20101	+	0.693404i	0.960780	−	0.277312i	$-0.0894435\pi$
$859$	35.2001	+	20.3228i	1.20101	+	0.693404i	0.240231	+	0.970716i	$0.422777\pi$
$860$		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	0.902310	−	0.431087i	$-0.141870\pi$
$863$	28.7932	+	16.6238i	0.980133	+	0.565880i	0.0778229	+	0.996967i	$0.475203\pi$
$864$	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	−0.522474	−	0.852655i	$-0.674991\pi$
$877$	14.1314	−	24.4763i	0.477184	−	0.826506i	0.999658	+	0.0261486i	$0.00832430\pi$
$878$	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	−0.850043	−	0.526713i	$-0.823424\pi$
$887$	0.926997	−	1.60561i	0.0311255	−	0.0539110i	0.881169	+	0.472802i	$0.156758\pi$
$888$	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	0.997479	+	0.0709647i	$0.0226078\pi$
$907$	16.8711	+	29.2217i	0.560197	+	0.970289i	−0.437282	+	0.899324i	$0.644059\pi$
$908$	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	$0.0364732\pi$
$911$			6.90180i			0.228667i	−0.993442	+	0.114333i	$0.963527\pi$
$912$	−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	−0.418050	−	0.908424i	$-0.637286\pi$
$919$	17.5128	−	30.3330i	0.577693	−	1.00059i	0.995743	−	0.0921698i	$-0.0293803\pi$
$920$		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	−0.985528	−	0.169515i	$-0.945780\pi$
$929$	−10.5447	+	18.2639i	−0.345960	+	0.599220i	0.639568	+	0.768734i	$0.279113\pi$
$930$		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	$-0.740966\pi$
$937$		−	44.5007i		−	1.45378i	0.686756	−	0.726888i	$-0.259034\pi$
$938$	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	−0.964368	−	0.264564i	$-0.914772\pi$
$941$	−21.8197	−	37.7929i	−0.711303	−	1.23201i	0.253065	−	0.967449i	$-0.418561\pi$
$942$	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	0.670309	−	0.742082i	$-0.266162\pi$
$947$	11.1646	+	6.44589i	0.362801	+	0.209463i	−0.307508	+	0.951546i	$0.599495\pi$
$948$	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	$-0.722814\pi$
$953$		−	47.2228i		−	1.52970i	0.644211	−	0.764848i	$-0.277186\pi$
$954$	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	−0.461056	−	0.887371i	$-0.652529\pi$
$971$	16.7632	−	29.0348i	0.537958	−	0.931770i	0.999014	−	0.0443991i	$-0.0141373\pi$
$972$	−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	−0.672222	−	0.740349i	$-0.734660\pi$
$977$	−11.4767	+	6.62608i	−0.367172	+	0.211987i	0.305050	+	0.952336i	$0.401327\pi$
$978$	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	−0.968165	−	0.250311i	$-0.919467\pi$
$983$	−21.9739	−	38.0599i	−0.700858	−	1.21392i	0.267307	−	0.963611i	$-0.413866\pi$
$984$	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	0.766747	−	0.641950i	$-0.221874\pi$
$991$	−5.43257	−	9.40948i	−0.172571	−	0.298902i	−0.939318	+	0.343047i	$0.888541\pi$
$992$	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	0.165794	−	0.986160i	$-0.446981\pi$
$997$	34.8191	−	20.1028i	1.10273	−	0.636662i	0.936937	+	0.349499i	$0.113648\pi$
$998$	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.551.1		12
3.2	odd	2		1050.2.s.g.551.5		12
5.2	odd	4		1050.2.u.h.299.2		12
5.3	odd	4		1050.2.u.e.299.5		12
5.4	even	2		210.2.r.b.131.6	yes	12
7.3	odd	6		1050.2.s.g.101.5		12
15.2	even	4		1050.2.u.f.299.5		12
15.8	even	4		1050.2.u.g.299.2		12
15.14	odd	2		210.2.r.a.131.2	yes	12
21.17	even	6	inner	1050.2.s.f.101.1		12
35.3	even	12		1050.2.u.f.899.5		12
35.9	even	6		1470.2.b.a.881.1		12
35.17	even	12		1050.2.u.g.899.2		12
35.19	odd	6		1470.2.b.b.881.6		12
35.24	odd	6		210.2.r.a.101.2	✓	12
105.17	odd	12		1050.2.u.e.899.5		12
105.38	odd	12		1050.2.u.h.899.2		12
105.44	odd	6		1470.2.b.b.881.12		12
105.59	even	6		210.2.r.b.101.6	yes	12
105.89	even	6		1470.2.b.a.881.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.2	✓	12	35.24	odd	6
210.2.r.a.131.2	yes	12	15.14	odd	2
210.2.r.b.101.6	yes	12	105.59	even	6
210.2.r.b.131.6	yes	12	5.4	even	2
1050.2.s.f.101.1		12	21.17	even	6	inner
1050.2.s.f.551.1		12	1.1	even	1	trivial
1050.2.s.g.101.5		12	7.3	odd	6
1050.2.s.g.551.5		12	3.2	odd	2
1050.2.u.e.299.5		12	5.3	odd	4
1050.2.u.e.899.5		12	105.17	odd	12
1050.2.u.f.299.5		12	15.2	even	4
1050.2.u.f.899.5		12	35.3	even	12
1050.2.u.g.299.2		12	15.8	even	4
1050.2.u.g.899.2		12	35.17	even	12
1050.2.u.h.299.2		12	5.2	odd	4
1050.2.u.h.899.2		12	105.38	odd	12
1470.2.b.a.881.1		12	35.9	even	6
1470.2.b.a.881.7		12	105.89	even	6
1470.2.b.b.881.6		12	35.19	odd	6
1470.2.b.b.881.12		12	105.44	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 $\F_{q}$
Belyi maps

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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} + 6 q^{4} + 2 q^{6} - 8 q^{7} + 12 q^{11} + 2 q^{12} - 12 q^{14} - 6 q^{16} + 12 q^{17} + 4 q^{18} + 4 q^{21} - 24 q^{23} - 2 q^{24} + 4 q^{26} - 8 q^{27} - 4 q^{28} + 12 q^{31} + 2 q^{33}+ \cdots + 48 q^{99}+O(q^{100}) \) 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

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Representations

Groups

Database

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