LMFDB - Embedded newform 1470.2.b.b.881.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(881,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("1470.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.b (of order $2$, degree $1$, 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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$12$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			881.6
Root			$1.66557 + 0.475255i$ of defining polynomial
Character	$\chi$	$=$	1470.881
Dual form			1470.2.b.b.881.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.68006 - 0.421203i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-0.421203 - 1.68006i) q^{6} +1.00000i q^{8} +(2.64518 - 1.41529i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.68006 - 0.421203i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-0.421203 - 1.68006i) q^{6} +1.00000i q^{8} +(2.64518 - 1.41529i) q^{9} +1.00000i q^{10} +0.193822i q^{11} +(-1.68006 + 0.421203i) q^{12} +1.54892i q^{13} +(-1.68006 + 0.421203i) q^{15} +1.00000 q^{16} -0.529533 q^{17} +(-1.41529 - 2.64518i) q^{18} -6.38933i q^{19} +1.00000 q^{20} +0.193822 q^{22} -4.24976i q^{23} +(0.421203 + 1.68006i) q^{24} +1.00000 q^{25} +1.54892 q^{26} +(3.84792 - 3.49192i) q^{27} -4.87349i q^{29} +(0.421203 + 1.68006i) q^{30} -9.26715i q^{31} -1.00000i q^{32} +(0.0816386 + 0.325633i) q^{33} +0.529533i q^{34} +(-2.64518 + 1.41529i) q^{36} +1.76327 q^{37} -6.38933 q^{38} +(0.652411 + 2.60228i) q^{39} -1.00000i q^{40} +9.91573 q^{41} +11.4865 q^{43} -0.193822i q^{44} +(-2.64518 + 1.41529i) q^{45} -4.24976 q^{46} -9.80373 q^{47} +(1.68006 - 0.421203i) q^{48} -1.00000i q^{50} +(-0.889645 + 0.223041i) q^{51} -1.54892i q^{52} -0.0649809i q^{53} +(-3.49192 - 3.84792i) q^{54} -0.193822i q^{55} +(-2.69121 - 10.7344i) q^{57} -4.87349 q^{58} -12.0274 q^{59} +(1.68006 - 0.421203i) q^{60} +4.28602i q^{61} -9.26715 q^{62} -1.00000 q^{64} -1.54892i q^{65} +(0.325633 - 0.0816386i) q^{66} +4.83058 q^{67} +0.529533 q^{68} +(-1.79001 - 7.13983i) q^{69} +6.29103i q^{71} +(1.41529 + 2.64518i) q^{72} +8.09171i q^{73} -1.76327i q^{74} +(1.68006 - 0.421203i) q^{75} +6.38933i q^{76} +(2.60228 - 0.652411i) q^{78} +6.77766 q^{79} -1.00000 q^{80} +(4.99391 - 7.48738i) q^{81} -9.91573i q^{82} -2.11036 q^{83} +0.529533 q^{85} -11.4865i q^{86} +(-2.05273 - 8.18773i) q^{87} -0.193822 q^{88} -16.3755 q^{89} +(1.41529 + 2.64518i) q^{90} +4.24976i q^{92} +(-3.90335 - 15.5693i) q^{93} +9.80373i q^{94} +6.38933i q^{95} +(-0.421203 - 1.68006i) q^{96} -8.24463i q^{97} +(0.274315 + 0.512694i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} - 12 q^{4} - 12 q^{5} - 2 q^{6} - 6 q^{9}+O(q^{10}) $ 12 * q + 4 * q^3 - 12 * q^4 - 12 * q^5 - 2 * q^6 - 6 * q^9	$ 12 q + 4 q^{3} - 12 q^{4} - 12 q^{5} - 2 q^{6} - 6 q^{9} - 4 q^{12} - 4 q^{15} + 12 q^{16} - 24 q^{17} + 8 q^{18} + 12 q^{20} + 2 q^{24} + 12 q^{25} + 8 q^{26} - 8 q^{27} + 2 q^{30} + 20 q^{33} + 6 q^{36} + 16 q^{37} - 16 q^{38} + 12 q^{39} - 4 q^{41} + 6 q^{45} - 4 q^{46} - 32 q^{47} + 4 q^{48} + 4 q^{51} - 28 q^{54} - 36 q^{57} - 16 q^{58} - 24 q^{59} + 4 q^{60} + 8 q^{62} - 12 q^{64} + 20 q^{66} + 8 q^{67} + 24 q^{68} + 50 q^{69} - 8 q^{72} + 4 q^{75} + 32 q^{78} + 8 q^{79} - 12 q^{80} - 10 q^{81} - 40 q^{83} + 24 q^{85} + 56 q^{87} - 52 q^{89} - 8 q^{90} + 28 q^{93} - 2 q^{96} + 48 q^{99}+O(q^{100}) $ 12 * q + 4 * q^3 - 12 * q^4 - 12 * q^5 - 2 * q^6 - 6 * q^9 - 4 * q^12 - 4 * q^15 + 12 * q^16 - 24 * q^17 + 8 * q^18 + 12 * q^20 + 2 * q^24 + 12 * q^25 + 8 * q^26 - 8 * q^27 + 2 * q^30 + 20 * q^33 + 6 * q^36 + 16 * q^37 - 16 * q^38 + 12 * q^39 - 4 * q^41 + 6 * q^45 - 4 * q^46 - 32 * q^47 + 4 * q^48 + 4 * q^51 - 28 * q^54 - 36 * q^57 - 16 * q^58 - 24 * q^59 + 4 * q^60 + 8 * q^62 - 12 * q^64 + 20 * q^66 + 8 * q^67 + 24 * q^68 + 50 * q^69 - 8 * q^72 + 4 * q^75 + 32 * q^78 + 8 * q^79 - 12 * q^80 - 10 * q^81 - 40 * q^83 + 24 * q^85 + 56 * q^87 - 52 * q^89 - 8 * q^90 + 28 * q^93 - 2 * q^96 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.68006	−	0.421203i	0.969981	−	0.243182i
$3$	1.68006	−	0.421203i	0.969981	−	0.243182i
$4$	−1.00000			−0.500000
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.421203	−	1.68006i	−0.171955	−	0.685880i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	2.64518	−	1.41529i	0.881725	−	0.471763i
$10$			1.00000i			0.316228i
$11$			0.193822i			0.0584397i	0.999573	+	0.0292198i	$0.00930228\pi$
$11$			0.193822i			0.0584397i	−0.999573	+	0.0292198i	$0.990698\pi$
$12$	−1.68006	+	0.421203i	−0.484990	+	0.121591i
$13$			1.54892i			0.429594i	0.976659	+	0.214797i	$0.0689090\pi$
$13$			1.54892i			0.429594i	−0.976659	+	0.214797i	$0.931091\pi$
$14$		0			0
$15$	−1.68006	+	0.421203i	−0.433789	+	0.108754i
$16$	1.00000			0.250000
$17$	−0.529533			−0.128431			−0.0642153	−	0.997936i	$-0.520454\pi$
$17$	−0.529533			−0.128431			−0.0642153	+	0.997936i	$0.520454\pi$
$18$	−1.41529	−	2.64518i	−0.333587	−	0.623474i
$19$		−	6.38933i		−	1.46581i	−0.680329	−	0.732906i	$-0.738163\pi$
$19$		−	6.38933i		−	1.46581i	0.680329	−	0.732906i	$-0.261837\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	0.193822			0.0413231
$23$		−	4.24976i		−	0.886135i	−0.896488	−	0.443068i	$-0.853890\pi$
$23$		−	4.24976i		−	0.886135i	0.896488	−	0.443068i	$-0.146110\pi$
$24$	0.421203	+	1.68006i	0.0859777	+	0.342940i
$25$	1.00000			0.200000
$26$	1.54892			0.303769
$27$	3.84792	−	3.49192i	0.740532	−	0.672021i
$28$		0			0
$29$		−	4.87349i		−	0.904984i	−0.891768	−	0.452492i	$-0.850535\pi$
$29$		−	4.87349i		−	0.904984i	0.891768	−	0.452492i	$-0.149465\pi$
$30$	0.421203	+	1.68006i	0.0769008	+	0.306735i
$31$		−	9.26715i		−	1.66443i	−0.554454	−	0.832214i	$-0.687073\pi$
$31$		−	9.26715i		−	1.66443i	0.554454	−	0.832214i	$-0.312927\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.0816386	+	0.325633i	0.0142115	+	0.0566853i
$34$			0.529533i			0.0908141i
$35$		0			0
$36$	−2.64518	+	1.41529i	−0.440863	+	0.235882i
$37$	1.76327			0.289880			0.144940	−	0.989440i	$-0.453701\pi$
$37$	1.76327			0.289880			0.144940	+	0.989440i	$0.453701\pi$
$38$	−6.38933			−1.03649
$39$	0.652411	+	2.60228i	0.104469	+	0.416698i
$40$		−	1.00000i		−	0.158114i
$41$	9.91573			1.54858			0.774289	−	0.632833i	$-0.218108\pi$
$41$	9.91573			1.54858			0.774289	+	0.632833i	$0.218108\pi$
$42$		0			0
$43$	11.4865			1.75168			0.875838	−	0.482606i	$-0.160310\pi$
$43$	11.4865			1.75168			0.875838	+	0.482606i	$0.160310\pi$
$44$		−	0.193822i		−	0.0292198i
$45$	−2.64518	+	1.41529i	−0.394320	+	0.210979i
$46$	−4.24976			−0.626592
$47$	−9.80373			−1.43002			−0.715010	−	0.699114i	$-0.753578\pi$
$47$	−9.80373			−1.43002			−0.715010	+	0.699114i	$0.753578\pi$
$48$	1.68006	−	0.421203i	0.242495	−	0.0607954i
$49$		0			0
$50$		−	1.00000i		−	0.141421i
$51$	−0.889645	+	0.223041i	−0.124575	+	0.0312320i
$52$		−	1.54892i		−	0.214797i
$53$		−	0.0649809i		−	0.00892582i	−0.999990	−	0.00446291i	$-0.998579\pi$
$53$		−	0.0649809i		−	0.00892582i	0.999990	−	0.00446291i	$-0.00142059\pi$
$54$	−3.49192	−	3.84792i	−0.475190	−	0.523635i
$55$		−	0.193822i		−	0.0261350i
$56$		0			0
$57$	−2.69121	−	10.7344i	−0.356459	−	1.42181i
$58$	−4.87349			−0.639920
$59$	−12.0274			−1.56584			−0.782918	−	0.622125i	$-0.786270\pi$
$59$	−12.0274			−1.56584			−0.782918	+	0.622125i	$0.786270\pi$
$60$	1.68006	−	0.421203i	0.216894	−	0.0543771i
$61$			4.28602i			0.548769i	0.961620	+	0.274384i	$0.0884741\pi$
$61$			4.28602i			0.548769i	−0.961620	+	0.274384i	$0.911526\pi$
$62$	−9.26715			−1.17693
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	1.54892i		−	0.192120i
$66$	0.325633	−	0.0816386i	0.0400826	−	0.0100490i
$67$	4.83058			0.590149			0.295075	−	0.955474i	$-0.404656\pi$
$67$	4.83058			0.590149			0.295075	+	0.955474i	$0.404656\pi$
$68$	0.529533			0.0642153
$69$	−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	$0.878225\pi$
$72$	1.41529	+	2.64518i	0.166793	+	0.311737i
$73$			8.09171i			0.947063i	0.880777	+	0.473532i	$0.157021\pi$
$73$			8.09171i			0.947063i	−0.880777	+	0.473532i	$0.842979\pi$
$74$		−	1.76327i		−	0.204976i
$75$	1.68006	−	0.421203i	0.193996	−	0.0486363i
$76$			6.38933i			0.732906i
$77$		0			0
$78$	2.60228	−	0.652411i	0.294650	−	0.0738710i
$79$	6.77766			0.762546			0.381273	−	0.924462i	$-0.375486\pi$
$79$	6.77766			0.762546			0.381273	+	0.924462i	$0.375486\pi$
$80$	−1.00000			−0.111803
$81$	4.99391	−	7.48738i	0.554879	−	0.831931i
$82$		−	9.91573i		−	1.09501i
$83$	−2.11036			−0.231642			−0.115821	−	0.993270i	$-0.536950\pi$
$83$	−2.11036			−0.231642			−0.115821	+	0.993270i	$0.536950\pi$
$84$		0			0
$85$	0.529533			0.0574359
$86$		−	11.4865i		−	1.23862i
$87$	−2.05273	−	8.18773i	−0.220076	−	0.877817i
$88$	−0.193822			−0.0206615
$89$	−16.3755			−1.73580			−0.867898	−	0.496742i	$-0.834529\pi$
$89$	−16.3755			−1.73580			−0.867898	+	0.496742i	$0.834529\pi$
$90$	1.41529	+	2.64518i	0.149185	+	0.278826i
$91$		0			0
$92$			4.24976i			0.443068i
$93$	−3.90335	−	15.5693i	−0.404759	−	1.61446i
$94$			9.80373i			1.01118i
$95$			6.38933i			0.655531i
$96$	−0.421203	−	1.68006i	−0.0429889	−	0.171470i
$97$		−	8.24463i		−	0.837115i	−0.908190	−	0.418557i	$-0.862536\pi$
$97$		−	8.24463i		−	0.837115i	0.908190	−	0.418557i	$-0.137464\pi$
$98$		0			0
$99$	0.274315	+	0.512694i	0.0275697	+	0.0515277i
$100$	−1.00000			−0.100000
$101$	−4.45663			−0.443451			−0.221725	−	0.975109i	$-0.571169\pi$
$101$	−4.45663			−0.443451			−0.221725	+	0.975109i	$0.571169\pi$
$102$	0.223041	+	0.889645i	0.0220843	+	0.0880879i
$103$			8.42187i			0.829832i	0.909860	+	0.414916i	$0.136189\pi$
$103$			8.42187i			0.829832i	−0.909860	+	0.414916i	$0.863811\pi$
$104$	−1.54892			−0.151884
$105$		0			0
$106$	−0.0649809			−0.00631151
$107$		−	17.8136i		−	1.72211i	−0.508514	−	0.861054i	$-0.669805\pi$
$107$		−	17.8136i		−	1.72211i	0.508514	−	0.861054i	$-0.330195\pi$
$108$	−3.84792	+	3.49192i	−0.370266	+	0.336010i
$109$	0.147803			0.0141570			0.00707850	−	0.999975i	$-0.497747\pi$
$109$	0.147803			0.0141570			0.00707850	+	0.999975i	$0.497747\pi$
$110$	−0.193822			−0.0184802
$111$	2.96239	−	0.742694i	0.281178	−	0.0704934i
$112$		0			0
$113$			3.44771i			0.324334i	0.986763	+	0.162167i	$0.0518483\pi$
$113$			3.44771i			0.324334i	−0.986763	+	0.162167i	$0.948152\pi$
$114$	−10.7344	+	2.69121i	−1.00537	+	0.252055i
$115$			4.24976i			0.396292i
$116$			4.87349i			0.452492i
$117$	2.19217	+	4.09717i	0.202667	+	0.378784i
$118$			12.0274i			1.10721i
$119$		0			0
$120$	−0.421203	−	1.68006i	−0.0384504	−	0.153367i
$121$	10.9624			0.996585
$122$	4.28602			0.388038
$123$	16.6590	−	4.17654i	1.50209	−	0.376586i
$124$			9.26715i			0.832214i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	5.49965			0.488015			0.244007	−	0.969773i	$-0.421538\pi$
$127$	5.49965			0.488015			0.244007	+	0.969773i	$0.421538\pi$
$128$			1.00000i			0.0883883i
$129$	19.2980	−	4.83815i	1.69909	−	0.425975i
$130$	−1.54892			−0.135850
$131$	5.99687			0.523949			0.261974	−	0.965075i	$-0.415626\pi$
$131$	5.99687			0.523949			0.261974	+	0.965075i	$0.415626\pi$
$132$	−0.0816386	−	0.325633i	−0.00710573	−	0.0283427i
$133$		0			0
$134$		−	4.83058i		−	0.417298i
$135$	−3.84792	+	3.49192i	−0.331176	+	0.300537i
$136$		−	0.529533i		−	0.0454071i
$137$		−	0.862112i		−	0.0736552i	−0.999322	−	0.0368276i	$-0.988275\pi$
$137$		−	0.862112i		−	0.0736552i	0.999322	−	0.0368276i	$-0.0117252\pi$
$138$	−7.13983	+	1.79001i	−0.607783	+	0.152376i
$139$			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
$142$	6.29103			0.527932
$143$	−0.300216			−0.0251053
$144$	2.64518	−	1.41529i	0.220431	−	0.117941i
$145$			4.87349i			0.404721i
$146$	8.09171			0.669675
$147$		0			0
$148$	−1.76327			−0.144940
$149$			12.7600i			1.04534i	0.852535	+	0.522671i	$0.175064\pi$
$149$			12.7600i			1.04534i	−0.852535	+	0.522671i	$0.824936\pi$
$150$	−0.421203	−	1.68006i	−0.0343911	−	0.137176i
$151$	−17.5002			−1.42415			−0.712075	−	0.702103i	$-0.752244\pi$
$151$	−17.5002			−1.42415			−0.712075	+	0.702103i	$0.752244\pi$
$152$	6.38933			0.518243
$153$	−1.40071	+	0.749442i	−0.113240	+	0.0605888i
$154$		0			0
$155$			9.26715i			0.744355i
$156$	−0.652411	−	2.60228i	−0.0522347	−	0.208349i
$157$			2.84609i			0.227143i	0.993530	+	0.113571i	$0.0362291\pi$
$157$			2.84609i			0.227143i	−0.993530	+	0.113571i	$0.963771\pi$
$158$		−	6.77766i		−	0.539201i
$159$	−0.0273702	−	0.109172i	−0.00217060	−	0.00865787i
$160$			1.00000i			0.0790569i
$161$		0			0
$162$	−7.48738	−	4.99391i	−0.588264	−	0.392359i
$163$	12.3586			0.968002			0.484001	−	0.875067i	$-0.339183\pi$
$163$	12.3586			0.968002			0.484001	+	0.875067i	$0.339183\pi$
$164$	−9.91573			−0.774289
$165$	−0.0816386	−	0.325633i	−0.00635556	−	0.0253505i
$166$			2.11036i			0.163795i
$167$	−4.99920			−0.386850			−0.193425	−	0.981115i	$-0.561960\pi$
$167$	−4.99920			−0.386850			−0.193425	+	0.981115i	$0.561960\pi$
$168$		0			0
$169$	10.6008			0.815449
$170$		−	0.529533i		−	0.0406133i
$171$	−9.04275	−	16.9009i	−0.691517	−	1.29244i
$172$	−11.4865			−0.875838
$173$	7.60806			0.578430			0.289215	−	0.957264i	$-0.406606\pi$
$173$	7.60806			0.578430			0.289215	+	0.957264i	$0.406606\pi$
$174$	−8.18773	+	2.05273i	−0.620710	+	0.155617i
$175$		0			0
$176$			0.193822i			0.0146099i
$177$	−20.2067	+	5.06598i	−1.51883	+	0.380783i
$178$			16.3755i			1.22739i
$179$			16.2259i			1.21278i	0.795167	+	0.606390i	$0.207383\pi$
$179$			16.2259i			1.21278i	−0.795167	+	0.606390i	$0.792617\pi$
$180$	2.64518	−	1.41529i	0.197160	−	0.105489i
$181$			4.03153i			0.299661i	0.988712	+	0.149831i	$0.0478729\pi$
$181$			4.03153i			0.299661i	−0.988712	+	0.149831i	$0.952127\pi$
$182$		0			0
$183$	1.80529	+	7.20076i	0.133451	+	0.532295i
$184$	4.24976			0.313296
$185$	−1.76327			−0.129638
$186$	−15.5693	+	3.90335i	−1.14160	+	0.286208i
$187$		−	0.102635i		−	0.00750544i
$188$	9.80373			0.715010
$189$		0			0
$190$	6.38933			0.463531
$191$			25.2353i			1.82596i	0.408005	+	0.912980i	$0.366225\pi$
$191$			25.2353i			1.82596i	−0.408005	+	0.912980i	$0.633775\pi$
$192$	−1.68006	+	0.421203i	−0.121248	+	0.0303977i
$193$	25.2366			1.81657			0.908286	−	0.418349i	$-0.137391\pi$
$193$	25.2366			1.81657			0.908286	+	0.418349i	$0.137391\pi$
$194$	−8.24463			−0.591930
$195$	−0.652411	−	2.60228i	−0.0467201	−	0.186353i
$196$		0			0
$197$		−	14.7364i		−	1.04993i	−0.851125	−	0.524964i	$-0.824079\pi$
$197$		−	14.7364i		−	1.04993i	0.851125	−	0.524964i	$-0.175921\pi$
$198$	0.512694	−	0.274315i	0.0364356	−	0.0194947i
$199$		−	25.8642i		−	1.83347i	−0.399499	−	0.916734i	$-0.630816\pi$
$199$		−	25.8642i		−	1.83347i	0.399499	−	0.916734i	$-0.369184\pi$
$200$			1.00000i			0.0707107i
$201$	8.11564	−	2.03465i	0.572433	−	0.143513i
$202$			4.45663i			0.313567i
$203$		0			0
$204$	0.889645	−	0.223041i	0.0622876	−	0.0156160i
$205$	−9.91573			−0.692545
$206$	8.42187			0.586780
$207$	−6.01464	−	11.2414i	−0.418046	−	0.781328i
$208$			1.54892i			0.107398i
$209$	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	$0.788516\pi$
$212$			0.0649809i			0.00446291i
$213$	2.64980	+	10.5693i	0.181562	+	0.724196i
$214$	−17.8136			−1.21771
$215$	−11.4865			−0.783373
$216$	3.49192	+	3.84792i	0.237595	+	0.261818i
$217$		0			0
$218$		−	0.147803i		−	0.0100105i
$219$	3.40825	+	13.5945i	0.230308	+	0.918633i
$220$			0.193822i			0.0130675i
$221$		−	0.820205i		−	0.0551730i
$222$	−0.742694	−	2.96239i	−0.0498464	−	0.198823i
$223$			0.00626282i			0.000419390i	1.00000		0.000209695i	$6.67479e-5\pi$
$223$			0.00626282i			0.000419390i	−1.00000		0.000209695i	$0.999933\pi$
$224$		0			0
$225$	2.64518	−	1.41529i	0.176345	−	0.0943526i
$226$	3.44771			0.229338
$227$	18.8275			1.24962			0.624811	−	0.780776i	$-0.285176\pi$
$227$	18.8275			1.24962			0.624811	+	0.780776i	$0.285176\pi$
$228$	2.69121	+	10.7344i	0.178229	+	0.710905i
$229$			7.79658i			0.515212i	0.966250	+	0.257606i	$0.0829337\pi$
$229$			7.79658i			0.515212i	−0.966250	+	0.257606i	$0.917066\pi$
$230$	4.24976			0.280221
$231$		0			0
$232$	4.87349			0.319960
$233$			12.9944i			0.851289i	0.904890	+	0.425645i	$0.139953\pi$
$233$			12.9944i			0.851289i	−0.904890	+	0.425645i	$0.860047\pi$
$234$	4.09717	−	2.19217i	0.267841	−	0.143307i
$235$	9.80373			0.639525
$236$	12.0274			0.782918
$237$	11.3868	−	2.85477i	0.739655	−	0.185437i
$238$		0			0
$239$		−	17.1710i		−	1.11070i	−0.831618	−	0.555349i	$-0.812585\pi$
$239$		−	17.1710i		−	1.11070i	0.831618	−	0.555349i	$-0.187415\pi$
$240$	−1.68006	+	0.421203i	−0.108447	+	0.0271885i
$241$		−	8.20640i		−	0.528620i	−0.964438	−	0.264310i	$-0.914856\pi$
$241$		−	8.20640i		−	0.528620i	0.964438	−	0.264310i	$-0.0851443\pi$
$242$		−	10.9624i		−	0.704692i
$243$	5.23634	−	14.6827i	0.335911	−	0.941894i
$244$		−	4.28602i		−	0.274384i
$245$		0			0
$246$	−4.17654	−	16.6590i	−0.266286	−	1.06214i
$247$	9.89658			0.629704
$248$	9.26715			0.588464
$249$	−3.54552	+	0.888888i	−0.224688	+	0.0563310i
$250$			1.00000i			0.0632456i
$251$	−22.9102			−1.44608			−0.723038	−	0.690808i	$-0.757255\pi$
$251$	−22.9102			−1.44608			−0.723038	+	0.690808i	$0.757255\pi$
$252$		0			0
$253$	0.823698			0.0517855
$254$		−	5.49965i		−	0.345079i
$255$	0.889645	−	0.223041i	0.0557117	−	0.0139674i
$256$	1.00000			0.0625000
$257$	7.08648			0.442042			0.221021	−	0.975269i	$-0.429061\pi$
$257$	7.08648			0.442042			0.221021	+	0.975269i	$0.429061\pi$
$258$	−4.83815	−	19.2980i	−0.301210	−	1.20144i
$259$		0			0
$260$			1.54892i			0.0960601i
$261$	−6.89740	−	12.8912i	−0.426938	−	0.797947i
$262$		−	5.99687i		−	0.370488i
$263$			17.8683i			1.10181i	0.834569	+	0.550904i	$0.185717\pi$
$263$			17.8683i			1.10181i	−0.834569	+	0.550904i	$0.814283\pi$
$264$	−0.325633	+	0.0816386i	−0.0200413	+	0.00502451i
$265$			0.0649809i			0.00399175i
$266$		0			0
$267$	−27.5117	+	6.89740i	−1.68369	+	0.422114i
$268$	−4.83058			−0.295075
$269$	6.92546			0.422253			0.211126	−	0.977459i	$-0.432287\pi$
$269$	6.92546			0.422253			0.211126	+	0.977459i	$0.432287\pi$
$270$	3.49192	+	3.84792i	0.212512	+	0.234177i
$271$		−	16.9186i		−	1.02773i	−0.857870	−	0.513867i	$-0.828212\pi$
$271$		−	16.9186i		−	1.02773i	0.857870	−	0.513867i	$-0.171788\pi$
$272$	−0.529533			−0.0321076
$273$		0			0
$274$	−0.862112			−0.0520821
$275$			0.193822i			0.0116879i
$276$	1.79001	+	7.13983i	0.107746	+	0.429767i
$277$	−21.3009			−1.27985			−0.639924	−	0.768438i	$-0.721034\pi$
$277$	−21.3009			−1.27985			−0.639924	+	0.768438i	$0.721034\pi$
$278$	16.1843			0.970671
$279$	−13.1157	−	24.5132i	−0.785216	−	1.46757i
$280$		0			0
$281$			19.5927i			1.16880i	0.811464	+	0.584402i	$0.198671\pi$
$281$			19.5927i			1.16880i	−0.811464	+	0.584402i	$0.801329\pi$
$282$	4.12936	+	16.4708i	0.245900	+	0.980823i
$283$			15.0978i			0.897474i	0.893664	+	0.448737i	$0.148126\pi$
$283$			15.0978i			0.897474i	−0.893664	+	0.448737i	$0.851874\pi$
$284$		−	6.29103i		−	0.373304i
$285$	2.69121	+	10.7344i	0.159413	+	0.635853i
$286$			0.300216i			0.0177521i
$287$		0			0
$288$	−1.41529	−	2.64518i	−0.0833967	−	0.155868i
$289$	−16.7196			−0.983506
$290$	4.87349			0.286181
$291$	−3.47266	−	13.8514i	−0.203571	−	0.811985i
$292$		−	8.09171i		−	0.473532i
$293$	−8.00534			−0.467677			−0.233839	−	0.972275i	$-0.575129\pi$
$293$	−8.00534			−0.467677			−0.233839	+	0.972275i	$0.575129\pi$
$294$		0			0
$295$	12.0274			0.700263
$296$			1.76327i			0.102488i
$297$	0.676813	+	0.745813i	0.0392727	+	0.0432765i
$298$	12.7600			0.739168
$299$	6.58255			0.380678
$300$	−1.68006	+	0.421203i	−0.0969981	+	0.0243182i
$301$		0			0
$302$			17.5002i			1.00703i
$303$	−7.48738	+	1.87714i	−0.430139	+	0.107839i
$304$		−	6.38933i		−	0.366453i
$305$		−	4.28602i		−	0.245417i
$306$	0.749442	+	1.40071i	0.0428428	+	0.0800731i
$307$			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			0
$309$	3.54732	+	14.1492i	0.201800	+	0.804921i
$310$	9.26715			0.526339
$311$	22.8384			1.29505			0.647523	−	0.762046i	$-0.275805\pi$
$311$	22.8384			1.29505			0.647523	+	0.762046i	$0.275805\pi$
$312$	−2.60228	+	0.652411i	−0.147325	+	0.0369355i
$313$			25.3042i			1.43028i	0.698982	+	0.715140i	$0.253637\pi$
$313$			25.3042i			1.43028i	−0.698982	+	0.715140i	$0.746363\pi$
$314$	2.84609			0.160614
$315$		0			0
$316$	−6.77766			−0.381273
$317$			15.0898i			0.847526i	0.905773	+	0.423763i	$0.139291\pi$
$317$			15.0898i			0.847526i	−0.905773	+	0.423763i	$0.860709\pi$
$318$	−0.109172	+	0.0273702i	−0.00612204	+	0.00153484i
$319$	0.944591			0.0528870
$320$	1.00000			0.0559017
$321$	−7.50315	−	29.9279i	−0.418785	−	1.67041i
$322$		0			0
$323$			3.38336i			0.188255i
$324$	−4.99391	+	7.48738i	−0.277439	+	0.415966i
$325$			1.54892i			0.0859188i
$326$		−	12.3586i		−	0.684481i
$327$	0.248318	−	0.0622552i	0.0137320	−	0.00344272i
$328$			9.91573i			0.547505i
$329$		0			0
$330$	−0.325633	+	0.0816386i	−0.0179255	+	0.00449406i
$331$	15.0617			0.827867			0.413933	−	0.910307i	$-0.364155\pi$
$331$	15.0617			0.827867			0.413933	+	0.910307i	$0.364155\pi$
$332$	2.11036			0.115821
$333$	4.66415	−	2.49554i	0.255594	−	0.136754i
$334$			4.99920i			0.273544i
$335$	−4.83058			−0.263923
$336$		0			0
$337$	14.9611			0.814983			0.407491	−	0.913209i	$-0.366404\pi$
$337$	14.9611			0.814983			0.407491	+	0.913209i	$0.366404\pi$
$338$		−	10.6008i		−	0.576610i
$339$	1.45219	+	5.79235i	0.0788720	+	0.314597i
$340$	−0.529533			−0.0287179
$341$	1.79618			0.0972687
$342$	−16.9009	+	9.04275i	−0.913896	+	0.488976i
$343$		0			0
$344$			11.4865i			0.619311i
$345$	1.79001	+	7.13983i	0.0963709	+	0.384395i
$346$		−	7.60806i		−	0.409012i
$347$			4.04662i			0.217234i	0.994084	+	0.108617i	$0.0346422\pi$
$347$			4.04662i			0.217234i	−0.994084	+	0.108617i	$0.965358\pi$
$348$	2.05273	+	8.18773i	0.110038	+	0.438909i
$349$			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
$352$	0.193822			0.0103308
$353$	3.66715			0.195183			0.0975914	−	0.995227i	$-0.468886\pi$
$353$	3.66715			0.195183			0.0975914	+	0.995227i	$0.468886\pi$
$354$	5.06598	+	20.2067i	0.269254	+	1.07398i
$355$		−	6.29103i		−	0.333893i
$356$	16.3755			0.867898
$357$		0			0
$358$	16.2259			0.857565
$359$		−	7.32269i		−	0.386477i	−0.981152	−	0.193238i	$-0.938101\pi$
$359$		−	7.32269i		−	0.386477i	0.981152	−	0.193238i	$-0.0618990\pi$
$360$	−1.41529	−	2.64518i	−0.0745923	−	0.139413i
$361$	−21.8235			−1.14861
$362$	4.03153			0.211893
$363$	18.4175	−	4.61741i	0.966668	−	0.242351i
$364$		0			0
$365$		−	8.09171i		−	0.423540i
$366$	7.20076	−	1.80529i	0.376390	−	0.0943638i
$367$			4.76624i			0.248796i	0.992232	+	0.124398i	$0.0396999\pi$
$367$			4.76624i			0.248796i	−0.992232	+	0.124398i	$0.960300\pi$
$368$		−	4.24976i		−	0.221534i
$369$	26.2289	−	14.0336i	1.36542	−	0.730562i
$370$			1.76327i			0.0916679i
$371$		0			0
$372$	3.90335	+	15.5693i	0.202379	+	0.807232i
$373$	−17.2963			−0.895567			−0.447783	−	0.894142i	$-0.647786\pi$
$373$	−17.2963			−0.895567			−0.447783	+	0.894142i	$0.647786\pi$
$374$	−0.102635			−0.00530715
$375$	−1.68006	+	0.421203i	−0.0867577	+	0.0217508i
$376$		−	9.80373i		−	0.505589i
$377$	7.54866			0.388776
$378$		0			0
$379$	−8.76645			−0.450302			−0.225151	−	0.974324i	$-0.572288\pi$
$379$	−8.76645			−0.450302			−0.225151	+	0.974324i	$0.572288\pi$
$380$		−	6.38933i		−	0.327766i
$381$	9.23972	−	2.31647i	0.473365	−	0.118676i
$382$	25.2353			1.29115
$383$	28.4753			1.45502			0.727511	−	0.686096i	$-0.240677\pi$
$383$	28.4753			1.45502			0.727511	+	0.686096i	$0.240677\pi$
$384$	0.421203	+	1.68006i	0.0214944	+	0.0857350i
$385$		0			0
$386$		−	25.2366i		−	1.28451i
$387$	30.3838	−	16.2567i	1.54450	−	0.826376i
$388$			8.24463i			0.418557i
$389$		−	21.0696i		−	1.06827i	−0.845399	−	0.534136i	$-0.820637\pi$
$389$		−	21.0696i		−	1.06827i	0.845399	−	0.534136i	$-0.179363\pi$
$390$	−2.60228	+	0.652411i	−0.131771	+	0.0330361i
$391$			2.25039i			0.113807i
$392$		0			0
$393$	10.0751	−	2.52590i	0.508220	−	0.127415i
$394$	−14.7364			−0.742411
$395$	−6.77766			−0.341021
$396$	−0.274315	−	0.512694i	−0.0137848	−	0.0257639i
$397$			6.59809i			0.331149i	0.986197	+	0.165574i	$0.0529478\pi$
$397$			6.59809i			0.331149i	−0.986197	+	0.165574i	$0.947052\pi$
$398$	−25.8642			−1.29646
$399$		0			0
$400$	1.00000			0.0500000
$401$			16.1310i			0.805546i	0.915300	+	0.402773i	$0.131954\pi$
$401$			16.1310i			0.805546i	−0.915300	+	0.402773i	$0.868046\pi$
$402$	−2.03465	−	8.11564i	−0.101479	−	0.404771i
$403$	14.3541			0.715029
$404$	4.45663			0.221725
$405$	−4.99391	+	7.48738i	−0.248149	+	0.372051i
$406$		0			0
$407$			0.341761i			0.0169405i
$408$	−0.223041	−	0.889645i	−0.0110422	−	0.0440440i
$409$			26.4033i			1.30556i	0.757548	+	0.652779i	$0.226397\pi$
$409$			26.4033i			1.30556i	−0.757548	+	0.652779i	$0.773603\pi$
$410$			9.91573i			0.489703i
$411$	−0.363124	−	1.44840i	−0.0179116	−	0.0714441i
$412$		−	8.42187i		−	0.414916i
$413$		0			0
$414$	−11.2414	+	6.01464i	−0.552482	+	0.295603i
$415$	2.11036			0.103593
$416$	1.54892			0.0759422
$417$	6.81689	+	27.1906i	0.333824	+	1.33153i
$418$		−	1.23840i		−	0.0605719i
$419$	19.8312			0.968819			0.484409	−	0.874841i	$-0.339035\pi$
$419$	19.8312			0.968819			0.484409	+	0.874841i	$0.339035\pi$
$420$		0			0
$421$	6.28009			0.306073			0.153036	−	0.988221i	$-0.451095\pi$
$421$	6.28009			0.306073			0.153036	+	0.988221i	$0.451095\pi$
$422$			22.8721i			1.11339i
$423$	−25.9326	+	13.8751i	−1.26089	+	0.674631i
$424$	0.0649809			0.00315575
$425$	−0.529533			−0.0256861
$426$	10.5693	−	2.64980i	0.512084	−	0.128383i
$427$		0			0
$428$			17.8136i			0.861054i
$429$	−0.504380	+	0.126452i	−0.0243517	+	0.00610516i
$430$			11.4865i			0.553928i
$431$			4.55329i			0.219324i	0.993969	+	0.109662i	$0.0349769\pi$
$431$			4.55329i			0.219324i	−0.993969	+	0.109662i	$0.965023\pi$
$432$	3.84792	−	3.49192i	0.185133	−	0.168005i
$433$		−	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			0
$435$	2.05273	+	8.18773i	0.0984208	+	0.392572i
$436$	−0.147803			−0.00707850
$437$	−27.1531			−1.29891
$438$	13.5945	−	3.40825i	0.649572	−	0.162853i
$439$		−	5.83672i		−	0.278572i	−0.990252	−	0.139286i	$-0.955519\pi$
$439$		−	5.83672i		−	0.278572i	0.990252	−	0.139286i	$-0.0444807\pi$
$440$	0.193822			0.00924012
$441$		0			0
$442$	−0.820205			−0.0390132
$443$			26.3461i			1.25174i	0.779927	+	0.625870i	$0.215256\pi$
$443$			26.3461i			1.25174i	−0.779927	+	0.625870i	$0.784744\pi$
$444$	−2.96239	+	0.742694i	−0.140589	+	0.0352467i
$445$	16.3755			0.776272
$446$	0.00626282			0.000296553
$447$	5.37456	+	21.4375i	0.254208	+	1.01396i
$448$		0			0
$449$		−	5.76638i		−	0.272132i	−0.990700	−	0.136066i	$-0.956554\pi$
$449$		−	5.76638i		−	0.272132i	0.990700	−	0.136066i	$-0.0434460\pi$
$450$	−1.41529	−	2.64518i	−0.0667174	−	0.124695i
$451$			1.92189i			0.0904983i
$452$		−	3.44771i		−	0.162167i
$453$	−29.4014	+	7.37116i	−1.38140	+	0.346327i
$454$		−	18.8275i		−	0.883617i
$455$		0			0
$456$	10.7344	−	2.69121i	0.502686	−	0.126027i
$457$	−0.721513			−0.0337509			−0.0168755	−	0.999858i	$-0.505372\pi$
$457$	−0.721513			−0.0337509			−0.0168755	+	0.999858i	$0.505372\pi$
$458$	7.79658			0.364310
$459$	−2.03760	+	1.84909i	−0.0951070	+	0.0863080i
$460$		−	4.24976i		−	0.198146i
$461$	−34.3692			−1.60073			−0.800365	−	0.599512i	$-0.795361\pi$
$461$	−34.3692			−1.60073			−0.800365	+	0.599512i	$0.795361\pi$
$462$		0			0
$463$	41.3815			1.92316			0.961581	−	0.274522i	$-0.0885197\pi$
$463$	41.3815			1.92316			0.961581	+	0.274522i	$0.0885197\pi$
$464$		−	4.87349i		−	0.226246i
$465$	3.90335	+	15.5693i	0.181014	+	0.722010i
$466$	12.9944			0.601952
$467$	17.9669			0.831407			0.415704	−	0.909500i	$-0.363535\pi$
$467$	17.9669			0.831407			0.415704	+	0.909500i	$0.363535\pi$
$468$	−2.19217	−	4.09717i	−0.101333	−	0.189392i
$469$		0			0
$470$		−	9.80373i		−	0.452212i
$471$	1.19878	+	4.78159i	0.0552370	+	0.220324i
$472$		−	12.0274i		−	0.553607i
$473$			2.22634i			0.102367i
$474$	−2.85477	−	11.3868i	−0.131124	−	0.523015i
$475$		−	6.38933i		−	0.293163i
$476$		0			0
$477$	−0.0919668	−	0.171886i	−0.00421087	−	0.00787012i
$478$	−17.1710			−0.785382
$479$	−9.01118			−0.411731			−0.205866	−	0.978580i	$-0.566001\pi$
$479$	−9.01118			−0.411731			−0.205866	+	0.978580i	$0.566001\pi$
$480$	0.421203	+	1.68006i	0.0192252	+	0.0766837i
$481$			2.73117i			0.124530i
$482$	−8.20640			−0.373791
$483$		0			0
$484$	−10.9624			−0.498292
$485$			8.24463i			0.374369i
$486$	−14.6827	−	5.23634i	−0.666019	−	0.237525i
$487$	−22.7295			−1.02997			−0.514987	−	0.857198i	$-0.672203\pi$
$487$	−22.7295			−1.02997			−0.514987	+	0.857198i	$0.672203\pi$
$488$	−4.28602			−0.194019
$489$	20.7632	−	5.20549i	0.938944	−	0.235401i
$490$		0			0
$491$		−	32.1654i		−	1.45160i	−0.687904	−	0.725801i	$-0.741469\pi$
$491$		−	32.1654i		−	1.45160i	0.687904	−	0.725801i	$-0.258531\pi$
$492$	−16.6590	+	4.17654i	−0.751045	+	0.188293i
$493$			2.58067i			0.116228i
$494$		−	9.89658i		−	0.445268i
$495$	−0.274315	−	0.512694i	−0.0123295	−	0.0230439i
$496$		−	9.26715i		−	0.416107i
$497$		0			0
$498$	0.888888	+	3.54552i	0.0398320	+	0.158878i
$499$	21.2508			0.951316			0.475658	−	0.879630i	$-0.342210\pi$
$499$	21.2508			0.951316			0.475658	+	0.879630i	$0.342210\pi$
$500$	1.00000			0.0447214
$501$	−8.39893	+	2.10568i	−0.375237	+	0.0940748i
$502$			22.9102i			1.02253i
$503$	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			0
$505$	4.45663			0.198317
$506$		−	0.823698i		−	0.0366178i
$507$	17.8100	−	4.46511i	0.790970	−	0.198302i
$508$	−5.49965			−0.244007
$509$	−13.9681			−0.619124			−0.309562	−	0.950879i	$-0.600182\pi$
$509$	−13.9681			−0.619124			−0.309562	+	0.950879i	$0.600182\pi$
$510$	−0.223041	−	0.889645i	−0.00987641	−	0.0393941i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−22.3110	−	24.5856i	−0.985057	−	1.08548i
$514$		−	7.08648i		−	0.312571i
$515$		−	8.42187i		−	0.371112i
$516$	−19.2980	+	4.83815i	−0.849546	+	0.212988i
$517$		−	1.90018i		−	0.0835699i
$518$		0			0
$519$	12.7820	−	3.20454i	0.561066	−	0.140664i
$520$	1.54892			0.0679248
$521$	14.4242			0.631934			0.315967	−	0.948770i	$-0.397671\pi$
$521$	14.4242			0.631934			0.315967	+	0.948770i	$0.397671\pi$
$522$	−12.8912	+	6.89740i	−0.564234	+	0.301891i
$523$		−	29.1682i		−	1.27543i	−0.770270	−	0.637717i	$-0.779879\pi$
$523$		−	29.1682i		−	1.27543i	0.770270	−	0.637717i	$-0.220121\pi$
$524$	−5.99687			−0.261974
$525$		0			0
$526$	17.8683			0.779096
$527$			4.90726i			0.213764i
$528$	0.0816386	+	0.325633i	0.00355286	+	0.0141713i
$529$	4.93957			0.214764
$530$	0.0649809			0.00282259
$531$	−31.8146	+	17.0223i	−1.38064	+	0.738704i
$532$		0			0
$533$			15.3587i			0.665259i
$534$	6.89740	+	27.5117i	0.298480	+	1.19055i
$535$			17.8136i			0.770150i
$536$			4.83058i			0.208649i
$537$	6.83440	+	27.2604i	0.294926	+	1.17637i
$538$		−	6.92546i		−	0.298578i
$539$		0			0
$540$	3.84792	−	3.49192i	0.165588	−	0.150268i
$541$	−24.9036			−1.07069			−0.535345	−	0.844633i	$-0.679819\pi$
$541$	−24.9036			−1.07069			−0.535345	+	0.844633i	$0.679819\pi$
$542$	−16.9186			−0.726718
$543$	1.69809	+	6.77320i	0.0728722	+	0.290666i
$544$			0.529533i			0.0227035i
$545$	−0.147803			−0.00633120
$546$		0			0
$547$	−0.655376			−0.0280219			−0.0140109	−	0.999902i	$-0.504460\pi$
$547$	−0.655376			−0.0280219			−0.0140109	+	0.999902i	$0.504460\pi$
$548$			0.862112i			0.0368276i
$549$	6.06596	+	11.3373i	0.258889	+	0.483863i
$550$	0.193822			0.00826462
$551$	−31.1383			−1.32654
$552$	7.13983	−	1.79001i	0.303891	−	0.0761879i
$553$		0			0
$554$			21.3009i			0.904990i
$555$	−2.96239	+	0.742694i	−0.125746	+	0.0315256i
$556$		−	16.1843i		−	0.686368i
$557$			17.7842i			0.753542i	0.926306	+	0.376771i	$0.122966\pi$
$557$			17.7842i			0.753542i	−0.926306	+	0.376771i	$0.877034\pi$
$558$	−24.5132	+	13.1157i	−1.03773	+	0.555232i
$559$			17.7917i			0.752509i
$560$		0			0
$561$	−0.0432303	−	0.172433i	−0.00182519	−	0.00728013i
$562$	19.5927			0.826469
$563$	20.2723			0.854376			0.427188	−	0.904163i	$-0.359504\pi$
$563$	20.2723			0.854376			0.427188	+	0.904163i	$0.359504\pi$
$564$	16.4708	−	4.12936i	0.693546	−	0.173877i
$565$		−	3.44771i		−	0.145046i
$566$	15.0978			0.634610
$567$		0			0
$568$	−6.29103			−0.263966
$569$		−	44.9448i		−	1.88418i	−0.335356	−	0.942092i	$-0.608857\pi$
$569$		−	44.9448i		−	1.88418i	0.335356	−	0.942092i	$-0.391143\pi$
$570$	10.7344	−	2.69121i	0.449616	−	0.112722i
$571$	−11.1890			−0.468246			−0.234123	−	0.972207i	$-0.575222\pi$
$571$	−11.1890			−0.468246			−0.234123	+	0.972207i	$0.575222\pi$
$572$	0.300216			0.0125527
$573$	10.6292	+	42.3967i	0.444040	+	1.77115i
$574$		0			0
$575$		−	4.24976i		−	0.177227i
$576$	−2.64518	+	1.41529i	−0.110216	+	0.0589704i
$577$			9.73375i			0.405221i	0.979259	+	0.202611i	$0.0649426\pi$
$577$			9.73375i			0.405221i	−0.979259	+	0.202611i	$0.935057\pi$
$578$			16.7196i			0.695443i
$579$	42.3989	−	10.6297i	1.76204	−	0.441757i
$580$		−	4.87349i		−	0.202361i
$581$		0			0
$582$	−13.8514	+	3.47266i	−0.574160	+	0.143946i
$583$	0.0125948			0.000521622
$584$	−8.09171			−0.334837
$585$	−2.19217	−	4.09717i	−0.0906353	−	0.169397i
$586$			8.00534i			0.330698i
$587$	32.0185			1.32155			0.660773	−	0.750585i	$-0.270228\pi$
$587$	32.0185			1.32155			0.660773	+	0.750585i	$0.270228\pi$
$588$		0			0
$589$	−59.2109			−2.43974
$590$		−	12.0274i		−	0.495161i
$591$	−6.20703	−	24.7580i	−0.255323	−	1.01841i
$592$	1.76327			0.0724699
$593$	−32.4012			−1.33056			−0.665280	−	0.746594i	$-0.731688\pi$
$593$	−32.4012			−1.33056			−0.665280	+	0.746594i	$0.731688\pi$
$594$	0.745813	−	0.676813i	0.0306011	−	0.0277700i
$595$		0			0
$596$		−	12.7600i		−	0.522671i
$597$	−10.8941	−	43.4534i	−0.445866	−	1.77843i
$598$		−	6.58255i		−	0.269180i
$599$			10.5437i			0.430802i	0.976526	+	0.215401i	$0.0691059\pi$
$599$			10.5437i			0.430802i	−0.976526	+	0.215401i	$0.930894\pi$
$600$	0.421203	+	1.68006i	0.0171955	+	0.0685880i
$601$		−	24.6793i		−	1.00669i	−0.864086	−	0.503344i	$-0.832103\pi$
$601$		−	24.6793i		−	1.00669i	0.864086	−	0.503344i	$-0.167897\pi$
$602$		0			0
$603$	12.7777	−	6.83667i	0.520349	−	0.278411i
$604$	17.5002			0.712075
$605$	−10.9624			−0.445686
$606$	1.87714	+	7.48738i	0.0762538	+	0.304154i
$607$		−	12.9854i		−	0.527059i	−0.964651	−	0.263530i	$-0.915113\pi$
$607$		−	12.9854i		−	0.527059i	0.964651	−	0.263530i	$-0.0848867\pi$
$608$	−6.38933			−0.259122
$609$		0			0
$610$	−4.28602			−0.173536
$611$		−	15.1852i		−	0.614328i
$612$	1.40071	−	0.749442i	0.0566202	−	0.0302944i
$613$	−26.7286			−1.07956			−0.539780	−	0.841806i	$-0.681493\pi$
$613$	−26.7286			−1.07956			−0.539780	+	0.841806i	$0.681493\pi$
$614$	4.33663			0.175012
$615$	−16.6590	+	4.17654i	−0.671755	+	0.168414i
$616$		0			0
$617$		−	13.2804i		−	0.534650i	−0.963606	−	0.267325i	$-0.913860\pi$
$617$		−	13.2804i		−	0.534650i	0.963606	−	0.267325i	$-0.0861397\pi$
$618$	14.1492	−	3.54732i	0.569165	−	0.142694i
$619$		−	9.88711i		−	0.397396i	−0.980061	−	0.198698i	$-0.936329\pi$
$619$		−	9.88711i		−	0.397396i	0.980061	−	0.198698i	$-0.0636714\pi$
$620$		−	9.26715i		−	0.372178i
$621$	−14.8398	−	16.3527i	−0.595501	−	0.656212i
$622$		−	22.8384i		−	0.915736i
$623$		0			0
$624$	0.652411	+	2.60228i	0.0261174	+	0.104174i
$625$	1.00000			0.0400000
$626$	25.3042			1.01136
$627$	2.08057	−	0.521616i	0.0830901	−	0.0208313i
$628$		−	2.84609i		−	0.113571i
$629$	−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	$0.676633\pi$
$632$			6.77766i			0.269601i
$633$	−38.4263	+	9.63378i	−1.52731	+	0.382908i
$634$	15.0898			0.599292
$635$	−5.49965			−0.218247
$636$	0.0273702	+	0.109172i	0.00108530	+	0.00432894i
$637$		0			0
$638$		−	0.944591i		−	0.0373967i
$639$	8.90363	+	16.6409i	0.352222	+	0.658303i
$640$		−	1.00000i		−	0.0395285i
$641$		−	23.5134i		−	0.928723i	−0.885646	−	0.464362i	$-0.846284\pi$
$641$		−	23.5134i		−	0.928723i	0.885646	−	0.464362i	$-0.153716\pi$
$642$	−29.9279	+	7.50315i	−1.18116	+	0.296126i
$643$			20.1307i			0.793876i	0.917846	+	0.396938i	$0.129927\pi$
$643$			20.1307i			0.793876i	−0.917846	+	0.396938i	$0.870073\pi$
$644$		0			0
$645$	−19.2980	+	4.83815i	−0.759857	+	0.190502i
$646$	3.38336			0.133116
$647$	10.3218			0.405790			0.202895	−	0.979200i	$-0.434965\pi$
$647$	10.3218			0.405790			0.202895	+	0.979200i	$0.434965\pi$
$648$	7.48738	+	4.99391i	0.294132	+	0.196179i
$649$		−	2.33118i		−	0.0915069i
$650$	1.54892			0.0607538
$651$		0			0
$652$	−12.3586			−0.484001
$653$			3.33429i			0.130481i	0.997870	+	0.0652404i	$0.0207814\pi$
$653$			3.33429i			0.130481i	−0.997870	+	0.0652404i	$0.979219\pi$
$654$	−0.0622552	−	0.248318i	−0.00243437	−	0.00971000i
$655$	−5.99687			−0.234317
$656$	9.91573			0.387144
$657$	11.4521	+	21.4040i	0.446790	+	0.835050i
$658$		0			0
$659$			13.1387i			0.511809i	0.966702	+	0.255905i	$0.0823733\pi$
$659$			13.1387i			0.511809i	−0.966702	+	0.255905i	$0.917627\pi$
$660$	0.0816386	+	0.325633i	0.00317778	+	0.0126752i
$661$			0.281918i			0.0109653i	0.999985	+	0.00548266i	$0.00174519\pi$
$661$			0.281918i			0.0109653i	−0.999985	+	0.00548266i	$0.998255\pi$
$662$		−	15.0617i		−	0.585390i
$663$	−0.345473	−	1.37799i	−0.0134171	−	0.0535167i
$664$		−	2.11036i		−	0.0818977i
$665$		0			0
$666$	−2.49554	−	4.66415i	−0.0967000	−	0.180732i
$667$	−20.7111			−0.801939
$668$	4.99920			0.193425
$669$	0.00263792	+	0.0105219i	0.000101988	+	0.000406800i
$670$			4.83058i			0.186622i
$671$	−0.830727			−0.0320699
$672$		0			0
$673$	−36.0090			−1.38805			−0.694023	−	0.719953i	$-0.744163\pi$
$673$	−36.0090			−1.38805			−0.694023	+	0.719953i	$0.744163\pi$
$674$		−	14.9611i		−	0.576280i
$675$	3.84792	−	3.49192i	0.148106	−	0.134404i
$676$	−10.6008			−0.407725
$677$	−4.01490			−0.154305			−0.0771526	−	0.997019i	$-0.524583\pi$
$677$	−4.01490			−0.154305			−0.0771526	+	0.997019i	$0.524583\pi$
$678$	5.79235	−	1.45219i	0.222454	−	0.0557709i
$679$		0			0
$680$			0.529533i			0.0203067i
$681$	31.6312	−	7.93019i	1.21211	−	0.303885i
$682$		−	1.79618i		−	0.0687793i
$683$		−	36.4916i		−	1.39631i	−0.715945	−	0.698156i	$-0.754004\pi$
$683$		−	36.4916i		−	1.39631i	0.715945	−	0.698156i	$-0.245996\pi$
$684$	9.04275	+	16.9009i	0.345758	+	0.646222i
$685$			0.862112i			0.0329396i
$686$		0			0
$687$	3.28394	+	13.0987i	0.125290	+	0.499746i
$688$	11.4865			0.437919
$689$	0.100650			0.00383448
$690$	7.13983	−	1.79001i	0.271809	−	0.0681445i
$691$		−	8.74478i		−	0.332667i	−0.986070	−	0.166334i	$-0.946807\pi$
$691$		−	8.74478i		−	0.332667i	0.986070	−	0.166334i	$-0.0531928\pi$
$692$	−7.60806			−0.289215
$693$		0			0
$694$	4.04662			0.153608
$695$		−	16.1843i		−	0.613906i
$696$	8.18773	−	2.05273i	0.310355	−	0.0778085i
$697$	−5.25070			−0.198885
$698$	12.3695			0.468193
$699$	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	$0.866340\pi$
$702$	5.96013	−	5.40872i	0.224951	−	0.204139i
$703$		−	11.2661i		−	0.424909i
$704$		−	0.193822i		−	0.00730496i
$705$	16.4708	−	4.12936i	0.620327	−	0.155521i
$706$		−	3.66715i		−	0.138015i
$707$		0			0
$708$	20.2067	−	5.06598i	0.759415	−	0.190391i
$709$	−5.01486			−0.188337			−0.0941685	−	0.995556i	$-0.530019\pi$
$709$	−5.01486			−0.188337			−0.0941685	+	0.995556i	$0.530019\pi$
$710$	−6.29103			−0.236098
$711$	17.9281	−	9.59235i	0.672356	−	0.359741i
$712$		−	16.3755i		−	0.613697i
$713$	−39.3831			−1.47491
$714$		0			0
$715$	0.300216			0.0112274
$716$		−	16.2259i		−	0.606390i
$717$	−7.23246	−	28.8482i	−0.270101	−	1.07736i
$718$	−7.32269			−0.273280
$719$	−34.3017			−1.27924			−0.639619	−	0.768692i	$-0.720908\pi$
$719$	−34.3017			−1.27924			−0.639619	+	0.768692i	$0.720908\pi$
$720$	−2.64518	+	1.41529i	−0.0985799	+	0.0527447i
$721$		0			0
$722$			21.8235i			0.812188i
$723$	−3.45656	−	13.7872i	−0.128551	−	0.512752i
$724$		−	4.03153i		−	0.149831i
$725$		−	4.87349i		−	0.180997i
$726$	−4.61741	−	18.4175i	−0.171368	−	0.683538i
$727$			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			0
$729$	2.61296	−	26.8733i	0.0967764	−	0.995306i
$730$	−8.09171			−0.299488
$731$	−6.08248			−0.224969
$732$	−1.80529	−	7.20076i	−0.0667253	−	0.266148i
$733$			51.9985i			1.92061i	0.278955	+	0.960304i	$0.410012\pi$
$733$			51.9985i			1.92061i	−0.278955	+	0.960304i	$0.589988\pi$
$734$	4.76624			0.175925
$735$		0			0
$736$	−4.24976			−0.156648
$737$			0.936275i			0.0344881i
$738$	−14.0336	−	26.2289i	−0.516585	−	0.965497i
$739$	−24.2066			−0.890453			−0.445226	−	0.895418i	$-0.646877\pi$
$739$	−24.2066			−0.890453			−0.445226	+	0.895418i	$0.646877\pi$
$740$	1.76327			0.0648190
$741$	16.6268	−	4.16847i	0.610801	−	0.153133i
$742$		0			0
$743$		−	48.1794i		−	1.76753i	−0.467932	−	0.883765i	$-0.655001\pi$
$743$		−	48.1794i		−	1.76753i	0.467932	−	0.883765i	$-0.344999\pi$
$744$	15.5693	−	3.90335i	0.570799	−	0.143104i
$745$		−	12.7600i		−	0.467491i
$746$			17.2963i			0.633261i
$747$	−5.58226	+	2.98676i	−0.204244	+	0.109280i
$748$			0.102635i			0.00375272i
$749$		0			0
$750$	0.421203	+	1.68006i	0.0153802	+	0.0613470i
$751$	5.16293			0.188398			0.0941991	−	0.995553i	$-0.469971\pi$
$751$	5.16293			0.188398			0.0941991	+	0.995553i	$0.469971\pi$
$752$	−9.80373			−0.357505
$753$	−38.4903	+	9.64983i	−1.40267	+	0.351659i
$754$		−	7.54866i		−	0.274906i
$755$	17.5002			0.636899
$756$		0			0
$757$	−16.0842			−0.584591			−0.292295	−	0.956328i	$-0.594419\pi$
$757$	−16.0842			−0.584591			−0.292295	+	0.956328i	$0.594419\pi$
$758$			8.76645i			0.318412i
$759$	1.38386	−	0.346944i	0.0502309	−	0.0125933i
$760$	−6.38933			−0.231765
$761$	−10.1579			−0.368224			−0.184112	−	0.982905i	$-0.558941\pi$
$761$	−10.1579			−0.368224			−0.184112	+	0.982905i	$0.558941\pi$
$762$	−2.31647	−	9.23972i	−0.0839168	−	0.334720i
$763$		0			0
$764$		−	25.2353i		−	0.912980i
$765$	1.40071	−	0.749442i	0.0506427	−	0.0270961i
$766$		−	28.4753i		−	1.02886i
$767$		−	18.6295i		−	0.672674i
$768$	1.68006	−	0.421203i	0.0606238	−	0.0151989i
$769$		−	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
$772$	−25.2366			−0.908286
$773$	−26.5704			−0.955672			−0.477836	−	0.878449i	$-0.658579\pi$
$773$	−26.5704			−0.955672			−0.477836	+	0.878449i	$0.658579\pi$
$774$	−16.2567	−	30.3838i	−0.584336	−	1.09212i
$775$		−	9.26715i		−	0.332886i
$776$	8.24463			0.295965
$777$		0			0
$778$	−21.0696			−0.755382
$779$		−	63.3549i		−	2.26992i
$780$	0.652411	+	2.60228i	0.0233601	+	0.0931765i
$781$	−1.21934			−0.0436315
$782$	2.25039			0.0804736
$783$	−17.0178	−	18.7528i	−0.608168	−	0.670170i
$784$		0			0
$785$		−	2.84609i		−	0.101581i
$786$	−2.52590	−	10.0751i	−0.0900959	−	0.359366i
$787$		−	29.5917i		−	1.05483i	−0.849607	−	0.527416i	$-0.823161\pi$
$787$		−	29.5917i		−	1.05483i	0.849607	−	0.527416i	$-0.176839\pi$
$788$			14.7364i			0.524964i
$789$	7.52619	+	30.0198i	0.267940	+	1.06873i
$790$			6.77766i			0.241138i
$791$		0			0
$792$	−0.512694	+	0.274315i	−0.0182178	+	0.00974735i
$793$	−6.63872			−0.235748
$794$	6.59809			0.234158
$795$	0.0273702	+	0.109172i	0.000970720	+	0.00387192i
$796$			25.8642i			0.916734i
$797$	34.6019			1.22566			0.612830	−	0.790215i	$-0.290031\pi$
$797$	34.6019			1.22566			0.612830	+	0.790215i	$0.290031\pi$
$798$		0			0
$799$	5.19139			0.183658
$800$		−	1.00000i		−	0.0353553i
$801$	−43.3160	+	23.1760i	−1.53050	+	0.818885i
$802$	16.1310			0.569607
$803$	−1.56836			−0.0553461
$804$	−8.11564	+	2.03465i	−0.286217	+	0.0717567i
$805$		0			0
$806$		−	14.3541i		−	0.505602i
$807$	11.6352	−	2.91703i	0.409577	−	0.102684i
$808$		−	4.45663i		−	0.156784i
$809$		−	16.8707i		−	0.593143i	−0.955011	−	0.296571i	$-0.904157\pi$
$809$		−	16.8707i		−	0.593143i	0.955011	−	0.296571i	$-0.0958433\pi$
$810$	7.48738	+	4.99391i	0.263080	+	0.175468i
$811$		−	11.1600i		−	0.391880i	−0.980616	−	0.195940i	$-0.937224\pi$
$811$		−	11.1600i		−	0.391880i	0.980616	−	0.195940i	$-0.0627758\pi$
$812$		0			0
$813$	−7.12619	−	28.4243i	−0.249926	−	0.996883i
$814$	0.341761			0.0119787
$815$	−12.3586			−0.432904
$816$	−0.889645	+	0.223041i	−0.0311438	+	0.00780799i
$817$		−	73.3911i		−	2.56763i
$818$	26.4033			0.923169
$819$		0			0
$820$	9.91573			0.346272
$821$			39.3637i			1.37380i	0.726751	+	0.686901i	$0.241029\pi$
$821$			39.3637i			1.37380i	−0.726751	+	0.686901i	$0.758971\pi$
$822$	−1.44840	+	0.363124i	−0.0505186	+	0.0126654i
$823$	40.7171			1.41931			0.709654	−	0.704551i	$-0.248851\pi$
$823$	40.7171			1.41931			0.709654	+	0.704551i	$0.248851\pi$
$824$	−8.42187			−0.293390
$825$	0.0816386	+	0.325633i	0.00284229	+	0.0113371i
$826$		0			0
$827$		−	24.7892i		−	0.862006i	−0.902350	−	0.431003i	$-0.858160\pi$
$827$		−	24.7892i		−	0.862006i	0.902350	−	0.431003i	$-0.141840\pi$
$828$	6.01464	+	11.2414i	0.209023	+	0.390664i
$829$			1.03670i			0.0360062i	0.999838	+	0.0180031i	$0.00573088\pi$
$829$			1.03670i			0.0360062i	−0.999838	+	0.0180031i	$0.994269\pi$
$830$		−	2.11036i		−	0.0732515i
$831$	−35.7867	+	8.97202i	−1.24143	+	0.311236i
$832$		−	1.54892i		−	0.0536992i
$833$		0			0
$834$	27.1906	−	6.81689i	0.941533	−	0.236050i
$835$	4.99920			0.173004
$836$	−1.23840			−0.0428308
$837$	−32.3602	−	35.6592i	−1.11853	−	1.23256i
$838$		−	19.8312i		−	0.685058i
$839$	19.4880			0.672801			0.336401	−	0.941719i	$-0.390790\pi$
$839$	19.4880			0.672801			0.336401	+	0.941719i	$0.390790\pi$
$840$		0			0
$841$	5.24911			0.181004
$842$		−	6.28009i		−	0.216426i
$843$	8.25252	+	32.9169i	0.284232	+	1.13372i
$844$	22.8721			0.787289
$845$	−10.6008			−0.364680
$846$	13.8751	+	25.9326i	0.477036	+	0.891581i
$847$		0			0
$848$		−	0.0649809i		−	0.00223145i
$849$	6.35926	+	25.3652i	0.218249	+	0.870532i
$850$			0.529533i			0.0181628i
$851$		−	7.49346i		−	0.256873i
$852$	−2.64980	−	10.5693i	−0.0907808	−	0.362098i
$853$		−	3.93413i		−	0.134702i	−0.997729	−	0.0673510i	$-0.978545\pi$
$853$		−	3.93413i		−	0.134702i	0.997729	−	0.0673510i	$-0.0214547\pi$
$854$		0			0
$855$	9.04275	+	16.9009i	0.309256	+	0.577999i
$856$	17.8136			0.608857
$857$	−8.99608			−0.307300			−0.153650	−	0.988125i	$-0.549103\pi$
$857$	−8.99608			−0.307300			−0.153650	+	0.988125i	$0.549103\pi$
$858$	0.126452	+	0.504380i	0.00431700	+	0.0172192i
$859$			40.6455i			1.38681i	0.720549	+	0.693404i	$0.243890\pi$
$859$			40.6455i			1.38681i	−0.720549	+	0.693404i	$0.756110\pi$
$860$	11.4865			0.391687
$861$		0			0
$862$	4.55329			0.155086
$863$			33.2476i			1.13176i	0.824487	+	0.565880i	$0.191464\pi$
$863$			33.2476i			1.13176i	−0.824487	+	0.565880i	$0.808536\pi$
$864$	−3.49192	−	3.84792i	−0.118798	−	0.130909i
$865$	−7.60806			−0.258682
$866$	−2.62801			−0.0893035
$867$	−28.0899	+	7.04235i	−0.953981	+	0.239171i
$868$		0			0
$869$			1.31366i			0.0445629i
$870$	8.18773	−	2.05273i	0.277590	−	0.0695940i
$871$			7.48220i			0.253525i
$872$			0.147803i			0.00500525i
$873$	−11.6685	−	21.8085i	−0.394920	−	0.738105i
$874$			27.1531i			0.918467i
$875$		0			0
$876$	−3.40825	−	13.5945i	−0.115154	−	0.459317i
$877$	28.2628			0.954367			0.477184	−	0.878804i	$-0.341658\pi$
$877$	28.2628			0.954367			0.477184	+	0.878804i	$0.341658\pi$
$878$	−5.83672			−0.196980
$879$	−13.4494	+	3.37188i	−0.453638	+	0.113731i
$880$		−	0.193822i		−	0.00653375i
$881$	−34.2140			−1.15270			−0.576350	−	0.817203i	$-0.695523\pi$
$881$	−34.2140			−1.15270			−0.576350	+	0.817203i	$0.695523\pi$
$882$		0			0
$883$	4.09672			0.137866			0.0689328	−	0.997621i	$-0.478041\pi$
$883$	4.09672			0.137866			0.0689328	+	0.997621i	$0.478041\pi$
$884$			0.820205i			0.0275865i
$885$	20.2067	−	5.06598i	0.679242	−	0.170291i
$886$	26.3461			0.885114
$887$	−1.85399			−0.0622510			−0.0311255	−	0.999515i	$-0.509909\pi$
$887$	−1.85399			−0.0622510			−0.0311255	+	0.999515i	$0.509909\pi$
$888$	0.742694	+	2.96239i	0.0249232	+	0.0994113i
$889$		0			0
$890$		−	16.3755i		−	0.548907i
$891$	1.45122	+	0.967932i	0.0486178	+	0.0324269i
$892$		−	0.00626282i		−	0.000209695i
$893$			62.6393i			2.09614i
$894$	21.4375	−	5.37456i	0.716979	−	0.179752i
$895$		−	16.2259i		−	0.542372i
$896$		0			0
$897$	11.0590	−	2.77259i	0.369251	−	0.0925740i
$898$	−5.76638			−0.192427
$899$	−45.1633			−1.50628
$900$	−2.64518	+	1.41529i	−0.0881725	+	0.0471763i
$901$			0.0344095i			0.00114635i
$902$	1.92189			0.0639920
$903$		0			0
$904$	−3.44771			−0.114669
$905$		−	4.03153i		−	0.134013i
$906$	7.37116	+	29.4014i	0.244890	+	0.976796i
$907$	33.7423			1.12039			0.560197	−	0.828360i	$-0.310726\pi$
$907$	33.7423			1.12039			0.560197	+	0.828360i	$0.310726\pi$
$908$	−18.8275			−0.624811
$909$	−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	$0.963527\pi$
$912$	−2.69121	−	10.7344i	−0.0891147	−	0.355453i
$913$		−	0.409034i		−	0.0135371i
$914$			0.721513i			0.0238655i
$915$	−1.80529	−	7.20076i	−0.0596809	−	0.238050i
$916$		−	7.79658i		−	0.257606i
$917$		0			0
$918$	1.84909	+	2.03760i	0.0610290	+	0.0672508i
$919$	−35.0255			−1.15539			−0.577693	−	0.816254i	$-0.696047\pi$
$919$	−35.0255			−1.15539			−0.577693	+	0.816254i	$0.696047\pi$
$920$	−4.24976			−0.140110
$921$	1.82660	+	7.28578i	0.0601886	+	0.240075i
$922$			34.3692i			1.13189i
$923$	−9.74433			−0.320738
$924$		0			0
$925$	1.76327			0.0579759
$926$		−	41.3815i		−	1.35988i
$927$	11.9194	+	22.2773i	0.391484	+	0.731684i
$928$	−4.87349			−0.159980
$929$	−21.0894			−0.691919			−0.345960	−	0.938249i	$-0.612447\pi$
$929$	−21.0894			−0.691919			−0.345960	+	0.938249i	$0.612447\pi$
$930$	15.5693	−	3.90335i	0.510538	−	0.127996i
$931$		0			0
$932$		−	12.9944i		−	0.425645i
$933$	38.3698	−	9.61960i	1.25617	−	0.314932i
$934$		−	17.9669i		−	0.587894i
$935$			0.102635i			0.00335653i
$936$	−4.09717	+	2.19217i	−0.133920	+	0.0716535i
$937$		−	44.5007i		−	1.45378i	−0.686756	−	0.726888i	$-0.740966\pi$
$937$		−	44.5007i		−	1.45378i	0.686756	−	0.726888i	$-0.259034\pi$
$938$		0			0
$939$	10.6582	+	42.5125i	0.347818	+	1.38734i
$940$	−9.80373			−0.319762
$941$	−43.6395			−1.42261			−0.711303	−	0.702885i	$-0.751895\pi$
$941$	−43.6395			−1.42261			−0.711303	+	0.702885i	$0.751895\pi$
$942$	4.78159	−	1.19878i	0.155793	−	0.0390584i
$943$		−	42.1394i		−	1.37225i
$944$	−12.0274			−0.391459
$945$		0			0
$946$	2.22634			0.0723846
$947$			12.8918i			0.418927i	0.977816	+	0.209463i	$0.0671717\pi$
$947$			12.8918i			0.418927i	−0.977816	+	0.209463i	$0.932828\pi$
$948$	−11.3868	+	2.85477i	−0.369827	+	0.0927186i
$949$	−12.5334			−0.406853
$950$	−6.38933			−0.207297
$951$	6.35586	+	25.3517i	0.206103	+	0.822084i
$952$		0			0
$953$			47.2228i			1.52970i	0.644211	+	0.764848i	$0.277186\pi$
$953$			47.2228i			1.52970i	−0.644211	+	0.764848i	$0.722814\pi$
$954$	−0.171886	+	0.0919668i	−0.00556501	+	0.00297754i
$955$		−	25.2353i		−	0.816594i
$956$			17.1710i			0.555349i
$957$	1.58697	−	0.397865i	0.0512993	−	0.0128611i
$958$			9.01118i			0.291138i
$959$		0			0
$960$	1.68006	−	0.421203i	0.0542236	−	0.0135943i
$961$	−54.8800			−1.77032
$962$	2.73117			0.0880564
$963$	−25.2114	−	47.1202i	−0.812427	−	1.51843i
$964$			8.20640i			0.264310i
$965$	−25.2366			−0.812396
$966$		0			0
$967$	−7.93428			−0.255149			−0.127575	−	0.991829i	$-0.540719\pi$
$967$	−7.93428			−0.255149			−0.127575	+	0.991829i	$0.540719\pi$
$968$			10.9624i			0.352346i
$969$	1.42508	+	5.68423i	0.0457802	+	0.182604i
$970$	8.24463			0.264719
$971$	33.5265			1.07592			0.537958	−	0.842972i	$-0.319196\pi$
$971$	33.5265			1.07592			0.537958	+	0.842972i	$0.319196\pi$
$972$	−5.23634	+	14.6827i	−0.167956	+	0.470947i
$973$		0			0
$974$			22.7295i			0.728302i
$975$	0.652411	+	2.60228i	0.0208939	+	0.0833396i
$976$			4.28602i			0.137192i
$977$			13.2522i			0.423974i	0.977272	+	0.211987i	$0.0679935\pi$
$977$			13.2522i			0.423974i	−0.977272	+	0.211987i	$0.932007\pi$
$978$	−5.20549	−	20.7632i	−0.166453	−	0.663933i
$979$		−	3.17393i		−	0.101439i
$980$		0			0
$981$	0.390966	−	0.209185i	0.0124826	−	0.00667875i
$982$	−32.1654			−1.02644
$983$	43.9478			1.40172			0.700858	−	0.713300i	$-0.252800\pi$
$983$	43.9478			1.40172			0.700858	+	0.713300i	$0.252800\pi$
$984$	4.17654	+	16.6590i	0.133143	+	0.531069i
$985$			14.7364i			0.469542i
$986$	2.58067			0.0821853
$987$		0			0
$988$	−9.89658			−0.314852
$989$		−	48.8148i		−	1.55222i
$990$	−0.512694	+	0.274315i	−0.0162945	+	0.00871830i
$991$	10.8651			0.345142			0.172571	−	0.984997i	$-0.444793\pi$
$991$	10.8651			0.345142			0.172571	+	0.984997i	$0.444793\pi$
$992$	−9.26715			−0.294232
$993$	25.3045	−	6.34404i	0.803015	−	0.201322i
$994$		0			0
$995$			25.8642i			0.819952i
$996$	3.54552	−	0.888888i	0.112344	−	0.0281655i
$997$			40.2056i			1.27332i	0.771143	+	0.636662i	$0.219685\pi$
$997$			40.2056i			1.27332i	−0.771143	+	0.636662i	$0.780315\pi$
$998$		−	21.2508i		−	0.672682i
$999$	6.78491	−	6.15720i	0.214665	−	0.194805i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.b.b.881.6		12
3.2	odd	2		1470.2.b.a.881.7		12
7.2	even	3		210.2.r.a.101.2	✓	12
7.3	odd	6		210.2.r.b.131.6	yes	12
7.6	odd	2		1470.2.b.a.881.1		12
21.2	odd	6		210.2.r.b.101.6	yes	12
21.17	even	6		210.2.r.a.131.2	yes	12
21.20	even	2	inner	1470.2.b.b.881.12		12
35.2	odd	12		1050.2.u.f.899.5		12
35.3	even	12		1050.2.u.h.299.2		12
35.9	even	6		1050.2.s.g.101.5		12
35.17	even	12		1050.2.u.e.299.5		12
35.23	odd	12		1050.2.u.g.899.2		12
35.24	odd	6		1050.2.s.f.551.1		12
105.2	even	12		1050.2.u.h.899.2		12
105.17	odd	12		1050.2.u.g.299.2		12
105.23	even	12		1050.2.u.e.899.5		12
105.38	odd	12		1050.2.u.f.299.5		12
105.44	odd	6		1050.2.s.f.101.1		12
105.59	even	6		1050.2.s.g.551.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.2	✓	12	7.2	even	3
210.2.r.a.131.2	yes	12	21.17	even	6
210.2.r.b.101.6	yes	12	21.2	odd	6
210.2.r.b.131.6	yes	12	7.3	odd	6
1050.2.s.f.101.1		12	105.44	odd	6
1050.2.s.f.551.1		12	35.24	odd	6
1050.2.s.g.101.5		12	35.9	even	6
1050.2.s.g.551.5		12	105.59	even	6
1050.2.u.e.299.5		12	35.17	even	12
1050.2.u.e.899.5		12	105.23	even	12
1050.2.u.f.299.5		12	105.38	odd	12
1050.2.u.f.899.5		12	35.2	odd	12
1050.2.u.g.299.2		12	105.17	odd	12
1050.2.u.g.899.2		12	35.23	odd	12
1050.2.u.h.299.2		12	35.3	even	12
1050.2.u.h.899.2		12	105.2	even	12
1470.2.b.a.881.1		12	7.6	odd	2
1470.2.b.a.881.7		12	3.2	odd	2
1470.2.b.b.881.6		12	1.1	even	1	trivial
1470.2.b.b.881.12		12	21.20	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.68006 - 0.421203i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-0.421203 - 1.68006i) q^{6} +1.00000i q^{8} +(2.64518 - 1.41529i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.68006 - 0.421203i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-0.421203 - 1.68006i) q^{6} +1.00000i q^{8} +(2.64518 - 1.41529i) q^{9} +1.00000i q^{10} +0.193822i q^{11} +(-1.68006 + 0.421203i) q^{12} +1.54892i q^{13} +(-1.68006 + 0.421203i) q^{15} +1.00000 q^{16} -0.529533 q^{17} +(-1.41529 - 2.64518i) q^{18} -6.38933i q^{19} +1.00000 q^{20} +0.193822 q^{22} -4.24976i q^{23} +(0.421203 + 1.68006i) q^{24} +1.00000 q^{25} +1.54892 q^{26} +(3.84792 - 3.49192i) q^{27} -4.87349i q^{29} +(0.421203 + 1.68006i) q^{30} -9.26715i q^{31} -1.00000i q^{32} +(0.0816386 + 0.325633i) q^{33} +0.529533i q^{34} +(-2.64518 + 1.41529i) q^{36} +1.76327 q^{37} -6.38933 q^{38} +(0.652411 + 2.60228i) q^{39} -1.00000i q^{40} +9.91573 q^{41} +11.4865 q^{43} -0.193822i q^{44} +(-2.64518 + 1.41529i) q^{45} -4.24976 q^{46} -9.80373 q^{47} +(1.68006 - 0.421203i) q^{48} -1.00000i q^{50} +(-0.889645 + 0.223041i) q^{51} -1.54892i q^{52} -0.0649809i q^{53} +(-3.49192 - 3.84792i) q^{54} -0.193822i q^{55} +(-2.69121 - 10.7344i) q^{57} -4.87349 q^{58} -12.0274 q^{59} +(1.68006 - 0.421203i) q^{60} +4.28602i q^{61} -9.26715 q^{62} -1.00000 q^{64} -1.54892i q^{65} +(0.325633 - 0.0816386i) q^{66} +4.83058 q^{67} +0.529533 q^{68} +(-1.79001 - 7.13983i) q^{69} +6.29103i q^{71} +(1.41529 + 2.64518i) q^{72} +8.09171i q^{73} -1.76327i q^{74} +(1.68006 - 0.421203i) q^{75} +6.38933i q^{76} +(2.60228 - 0.652411i) q^{78} +6.77766 q^{79} -1.00000 q^{80} +(4.99391 - 7.48738i) q^{81} -9.91573i q^{82} -2.11036 q^{83} +0.529533 q^{85} -11.4865i q^{86} +(-2.05273 - 8.18773i) q^{87} -0.193822 q^{88} -16.3755 q^{89} +(1.41529 + 2.64518i) q^{90} +4.24976i q^{92} +(-3.90335 - 15.5693i) q^{93} +9.80373i q^{94} +6.38933i q^{95} +(-0.421203 - 1.68006i) q^{96} -8.24463i q^{97} +(0.274315 + 0.512694i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} - 12 q^{4} - 12 q^{5} - 2 q^{6} - 6 q^{9}+O(q^{10}) \) 12 * q + 4 * q^3 - 12 * q^4 - 12 * q^5 - 2 * q^6 - 6 * q^9	\( 12 q + 4 q^{3} - 12 q^{4} - 12 q^{5} - 2 q^{6} - 6 q^{9} - 4 q^{12} - 4 q^{15} + 12 q^{16} - 24 q^{17} + 8 q^{18} + 12 q^{20} + 2 q^{24} + 12 q^{25} + 8 q^{26} - 8 q^{27} + 2 q^{30} + 20 q^{33} + 6 q^{36} + 16 q^{37} - 16 q^{38} + 12 q^{39} - 4 q^{41} + 6 q^{45} - 4 q^{46} - 32 q^{47} + 4 q^{48} + 4 q^{51} - 28 q^{54} - 36 q^{57} - 16 q^{58} - 24 q^{59} + 4 q^{60} + 8 q^{62} - 12 q^{64} + 20 q^{66} + 8 q^{67} + 24 q^{68} + 50 q^{69} - 8 q^{72} + 4 q^{75} + 32 q^{78} + 8 q^{79} - 12 q^{80} - 10 q^{81} - 40 q^{83} + 24 q^{85} + 56 q^{87} - 52 q^{89} - 8 q^{90} + 28 q^{93} - 2 q^{96} + 48 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 - 12 * q^4 - 12 * q^5 - 2 * q^6 - 6 * q^9 - 4 * q^12 - 4 * q^15 + 12 * q^16 - 24 * q^17 + 8 * q^18 + 12 * q^20 + 2 * q^24 + 12 * q^25 + 8 * q^26 - 8 * q^27 + 2 * q^30 + 20 * q^33 + 6 * q^36 + 16 * q^37 - 16 * q^38 + 12 * q^39 - 4 * q^41 + 6 * q^45 - 4 * q^46 - 32 * q^47 + 4 * q^48 + 4 * q^51 - 28 * q^54 - 36 * q^57 - 16 * q^58 - 24 * q^59 + 4 * q^60 + 8 * q^62 - 12 * q^64 + 20 * q^66 + 8 * q^67 + 24 * q^68 + 50 * q^69 - 8 * q^72 + 4 * q^75 + 32 * q^78 + 8 * q^79 - 12 * q^80 - 10 * q^81 - 40 * q^83 + 24 * q^85 + 56 * q^87 - 52 * q^89 - 8 * q^90 + 28 * q^93 - 2 * q^96 + 48 * q^99

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