LMFDB - Embedded newform 1470.2.b.c.881.10

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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 16x^{13} + 2x^{12} + 96x^{10} - 80x^{9} + 2x^{8} - 240x^{7} + 864x^{6} + 162x^{4} - 3888x^{3} + 6561 $ x^16 - 16x^13 + 2x^12 + 96x^10 - 80x^9 + 2x^8 - 240x^7 + 864x^6 + 162x^4 - 3888*x^3 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			881.10
Root			$1.71739 - 0.224843i$ of defining polynomial
Character	$\chi$	$=$	1470.881
Dual form			1470.2.b.c.881.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.67271 - 0.449490i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(0.449490 - 1.67271i) q^{6} -1.00000i q^{8} +(2.59592 + 1.50373i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-1.67271 - 0.449490i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(0.449490 - 1.67271i) q^{6} -1.00000i q^{8} +(2.59592 + 1.50373i) q^{9} -1.00000i q^{10} +2.37874i q^{11} +(1.67271 + 0.449490i) q^{12} -3.07531i q^{13} +(1.67271 + 0.449490i) q^{15} +1.00000 q^{16} -4.70529 q^{17} +(-1.50373 + 2.59592i) q^{18} +0.527004i q^{19} +1.00000 q^{20} -2.37874 q^{22} -4.62269i q^{23} +(-0.449490 + 1.67271i) q^{24} +1.00000 q^{25} +3.07531 q^{26} +(-3.66630 - 3.68215i) q^{27} +0.405050i q^{29} +(-0.449490 + 1.67271i) q^{30} -1.02895i q^{31} +1.00000i q^{32} +(1.06922 - 3.97894i) q^{33} -4.70529i q^{34} +(-2.59592 - 1.50373i) q^{36} -5.54367 q^{37} -0.527004 q^{38} +(-1.38232 + 5.14411i) q^{39} +1.00000i q^{40} +8.61981 q^{41} +11.5117 q^{43} -2.37874i q^{44} +(-2.59592 - 1.50373i) q^{45} +4.62269 q^{46} +8.82018 q^{47} +(-1.67271 - 0.449490i) q^{48} +1.00000i q^{50} +(7.87058 + 2.11498i) q^{51} +3.07531i q^{52} +12.2241i q^{53} +(3.68215 - 3.66630i) q^{54} -2.37874i q^{55} +(0.236883 - 0.881524i) q^{57} -0.405050 q^{58} -8.52051 q^{59} +(-1.67271 - 0.449490i) q^{60} +7.51223i q^{61} +1.02895 q^{62} -1.00000 q^{64} +3.07531i q^{65} +(3.97894 + 1.06922i) q^{66} +13.4124 q^{67} +4.70529 q^{68} +(-2.07786 + 7.73243i) q^{69} +11.7698i q^{71} +(1.50373 - 2.59592i) q^{72} -8.65046i q^{73} -5.54367i q^{74} +(-1.67271 - 0.449490i) q^{75} -0.527004i q^{76} +(-5.14411 - 1.38232i) q^{78} +1.91407 q^{79} -1.00000 q^{80} +(4.47757 + 7.80714i) q^{81} +8.61981i q^{82} +12.9078 q^{83} +4.70529 q^{85} +11.5117i q^{86} +(0.182066 - 0.677531i) q^{87} +2.37874 q^{88} +6.18780 q^{89} +(1.50373 - 2.59592i) q^{90} +4.62269i q^{92} +(-0.462503 + 1.72113i) q^{93} +8.82018i q^{94} -0.527004i q^{95} +(0.449490 - 1.67271i) q^{96} +19.6433i q^{97} +(-3.57699 + 6.17501i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} - 16 q^{4} - 16 q^{5} + 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 - 16 * q^4 - 16 * q^5 + 8 * q^9	$ 16 q - 8 q^{3} - 16 q^{4} - 16 q^{5} + 8 q^{9} + 8 q^{12} + 8 q^{15} + 16 q^{16} + 48 q^{17} + 16 q^{20} + 16 q^{25} - 16 q^{26} - 8 q^{27} - 8 q^{36} + 16 q^{41} + 16 q^{43} - 8 q^{45} - 16 q^{46} + 32 q^{47} - 8 q^{48} + 16 q^{51} + 32 q^{57} + 16 q^{58} + 32 q^{59} - 8 q^{60} + 16 q^{62} - 16 q^{64} + 16 q^{67} - 48 q^{68} - 8 q^{75} - 32 q^{78} - 48 q^{79} - 16 q^{80} + 8 q^{81} + 48 q^{83} - 48 q^{85} + 16 q^{89} - 64 q^{93} - 8 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 - 16 * q^4 - 16 * q^5 + 8 * q^9 + 8 * q^12 + 8 * q^15 + 16 * q^16 + 48 * q^17 + 16 * q^20 + 16 * q^25 - 16 * q^26 - 8 * q^27 - 8 * q^36 + 16 * q^41 + 16 * q^43 - 8 * q^45 - 16 * q^46 + 32 * q^47 - 8 * q^48 + 16 * q^51 + 32 * q^57 + 16 * q^58 + 32 * q^59 - 8 * q^60 + 16 * q^62 - 16 * q^64 + 16 * q^67 - 48 * q^68 - 8 * q^75 - 32 * q^78 - 48 * q^79 - 16 * q^80 + 8 * q^81 + 48 * q^83 - 48 * q^85 + 16 * q^89 - 64 * q^93 - 8 * 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
$3$	−1.67271	−	0.449490i	−0.965740	−	0.259513i
$3$	−1.67271	−	0.449490i	−0.965740	−	0.259513i
$4$	−1.00000			−0.500000
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.449490	−	1.67271i	0.183504	−	0.682881i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	2.59592	+	1.50373i	0.865306	+	0.501245i
$10$		−	1.00000i		−	0.316228i
$11$			2.37874i			0.717217i	0.933488	+	0.358609i	$0.116749\pi$
$11$			2.37874i			0.717217i	−0.933488	+	0.358609i	$0.883251\pi$
$12$	1.67271	+	0.449490i	0.482870	+	0.129757i
$13$		−	3.07531i		−	0.852938i	−0.904502	−	0.426469i	$-0.859757\pi$
$13$		−	3.07531i		−	0.852938i	0.904502	−	0.426469i	$-0.140243\pi$
$14$		0			0
$15$	1.67271	+	0.449490i	0.431892	+	0.116058i
$16$	1.00000			0.250000
$17$	−4.70529			−1.14120			−0.570600	−	0.821228i	$-0.693289\pi$
$17$	−4.70529			−1.14120			−0.570600	+	0.821228i	$0.693289\pi$
$18$	−1.50373	+	2.59592i	−0.354434	+	0.611863i
$19$			0.527004i			0.120903i	0.998171	+	0.0604515i	$0.0192540\pi$
$19$			0.527004i			0.120903i	−0.998171	+	0.0604515i	$0.980746\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	−2.37874			−0.507149
$23$		−	4.62269i		−	0.963898i	−0.876199	−	0.481949i	$-0.839929\pi$
$23$		−	4.62269i		−	0.963898i	0.876199	−	0.481949i	$-0.160071\pi$
$24$	−0.449490	+	1.67271i	−0.0917518	+	0.341440i
$25$	1.00000			0.200000
$26$	3.07531			0.603119
$27$	−3.66630	−	3.68215i	−0.705580	−	0.708630i
$28$		0			0
$29$			0.405050i			0.0752159i	0.999293	+	0.0376080i	$0.0119738\pi$
$29$			0.405050i			0.0752159i	−0.999293	+	0.0376080i	$0.988026\pi$
$30$	−0.449490	+	1.67271i	−0.0820653	+	0.305394i
$31$		−	1.02895i		−	0.184805i	−0.995722	−	0.0924024i	$-0.970545\pi$
$31$		−	1.02895i		−	0.184805i	0.995722	−	0.0924024i	$-0.0294546\pi$
$32$			1.00000i			0.176777i
$33$	1.06922	−	3.97894i	0.186127	−	0.692645i
$34$		−	4.70529i		−	0.806950i
$35$		0			0
$36$	−2.59592	−	1.50373i	−0.432653	−	0.250622i
$37$	−5.54367			−0.911374			−0.455687	−	0.890140i	$-0.650606\pi$
$37$	−5.54367			−0.911374			−0.455687	+	0.890140i	$0.650606\pi$
$38$	−0.527004			−0.0854913
$39$	−1.38232	+	5.14411i	−0.221349	+	0.823716i
$40$			1.00000i			0.158114i
$41$	8.61981			1.34619			0.673094	−	0.739557i	$-0.264965\pi$
$41$	8.61981			1.34619			0.673094	+	0.739557i	$0.264965\pi$
$42$		0			0
$43$	11.5117			1.75552			0.877762	−	0.479097i	$-0.159036\pi$
$43$	11.5117			1.75552			0.877762	+	0.479097i	$0.159036\pi$
$44$		−	2.37874i		−	0.358609i
$45$	−2.59592	−	1.50373i	−0.386976	−	0.224163i
$46$	4.62269			0.681579
$47$	8.82018			1.28655			0.643277	−	0.765633i	$-0.277574\pi$
$47$	8.82018			1.28655			0.643277	+	0.765633i	$0.277574\pi$
$48$	−1.67271	−	0.449490i	−0.241435	−	0.0648783i
$49$		0			0
$50$			1.00000i			0.141421i
$51$	7.87058	+	2.11498i	1.10210	+	0.296157i
$52$			3.07531i			0.426469i
$53$			12.2241i			1.67910i	0.543279	+	0.839552i	$0.317182\pi$
$53$			12.2241i			1.67910i	−0.543279	+	0.839552i	$0.682818\pi$
$54$	3.68215	−	3.66630i	0.501077	−	0.498920i
$55$		−	2.37874i		−	0.320749i
$56$		0			0
$57$	0.236883	−	0.881524i	0.0313759	−	0.116761i
$58$	−0.405050			−0.0531857
$59$	−8.52051			−1.10928			−0.554638	−	0.832092i	$-0.687143\pi$
$59$	−8.52051			−1.10928			−0.554638	+	0.832092i	$0.687143\pi$
$60$	−1.67271	−	0.449490i	−0.215946	−	0.0580290i
$61$			7.51223i			0.961843i	0.876764	+	0.480921i	$0.159698\pi$
$61$			7.51223i			0.961843i	−0.876764	+	0.480921i	$0.840302\pi$
$62$	1.02895			0.130677
$63$		0			0
$64$	−1.00000			−0.125000
$65$			3.07531i			0.381446i
$66$	3.97894	+	1.06922i	0.489774	+	0.131612i
$67$	13.4124			1.63858			0.819291	−	0.573377i	$-0.194367\pi$
$67$	13.4124			1.63858			0.819291	+	0.573377i	$0.194367\pi$
$68$	4.70529			0.570600
$69$	−2.07786	+	7.73243i	−0.250145	+	0.930875i
$70$		0			0
$71$			11.7698i			1.39682i	0.715700	+	0.698408i	$0.246108\pi$
$71$			11.7698i			1.39682i	−0.715700	+	0.698408i	$0.753892\pi$
$72$	1.50373	−	2.59592i	0.177217	−	0.305932i
$73$		−	8.65046i		−	1.01246i	−0.862398	−	0.506230i	$-0.831039\pi$
$73$		−	8.65046i		−	1.01246i	0.862398	−	0.506230i	$-0.168961\pi$
$74$		−	5.54367i		−	0.644439i
$75$	−1.67271	−	0.449490i	−0.193148	−	0.0519027i
$76$		−	0.527004i		−	0.0604515i
$77$		0			0
$78$	−5.14411	−	1.38232i	−0.582455	−	0.156517i
$79$	1.91407			0.215350			0.107675	−	0.994186i	$-0.465659\pi$
$79$	1.91407			0.215350			0.107675	+	0.994186i	$0.465659\pi$
$80$	−1.00000			−0.111803
$81$	4.47757	+	7.80714i	0.497508	+	0.867460i
$82$			8.61981i			0.951899i
$83$	12.9078			1.41682			0.708410	−	0.705801i	$-0.249413\pi$
$83$	12.9078			1.41682			0.708410	+	0.705801i	$0.249413\pi$
$84$		0			0
$85$	4.70529			0.510360
$86$			11.5117i			1.24134i
$87$	0.182066	−	0.677531i	0.0195195	−	0.0726390i
$88$	2.37874			0.253575
$89$	6.18780			0.655906			0.327953	−	0.944694i	$-0.393641\pi$
$89$	6.18780			0.655906			0.327953	+	0.944694i	$0.393641\pi$
$90$	1.50373	−	2.59592i	0.158507	−	0.273634i
$91$		0			0
$92$			4.62269i			0.481949i
$93$	−0.462503	+	1.72113i	−0.0479593	+	0.178473i
$94$			8.82018i			0.909732i
$95$		−	0.527004i		−	0.0540694i
$96$	0.449490	−	1.67271i	0.0458759	−	0.170720i
$97$			19.6433i			1.99447i	0.0742863	+	0.997237i	$0.476332\pi$
$97$			19.6433i			1.99447i	−0.0742863	+	0.997237i	$0.523668\pi$
$98$		0			0
$99$	−3.57699	+	6.17501i	−0.359501	+	0.620612i
$100$	−1.00000			−0.100000
$101$	7.09724			0.706202			0.353101	−	0.935585i	$-0.385127\pi$
$101$	7.09724			0.706202			0.353101	+	0.935585i	$0.385127\pi$
$102$	−2.11498	+	7.87058i	−0.209414	+	0.779303i
$103$		−	6.82964i		−	0.672944i	−0.941693	−	0.336472i	$-0.890766\pi$
$103$		−	6.82964i		−	0.672944i	0.941693	−	0.336472i	$-0.109234\pi$
$104$	−3.07531			−0.301559
$105$		0			0
$106$	−12.2241			−1.18731
$107$		−	13.1216i		−	1.26851i	−0.773124	−	0.634255i	$-0.781307\pi$
$107$		−	13.1216i		−	1.26851i	0.773124	−	0.634255i	$-0.218693\pi$
$108$	3.66630	+	3.68215i	0.352790	+	0.354315i
$109$	0.228271			0.0218644			0.0109322	−	0.999940i	$-0.496520\pi$
$109$	0.228271			0.0218644			0.0109322	+	0.999940i	$0.496520\pi$
$110$	2.37874			0.226804
$111$	9.27295	+	2.49183i	0.880150	+	0.236514i
$112$		0			0
$113$		−	5.86352i		−	0.551594i	−0.961216	−	0.275797i	$-0.911058\pi$
$113$		−	5.86352i		−	0.551594i	0.961216	−	0.275797i	$-0.0889417\pi$
$114$	0.881524	+	0.236883i	0.0825623	+	0.0221861i
$115$			4.62269i			0.431068i
$116$		−	0.405050i		−	0.0376080i
$117$	4.62445	−	7.98326i	0.427531	−	0.738052i
$118$		−	8.52051i		−	0.784377i
$119$		0			0
$120$	0.449490	−	1.67271i	0.0410327	−	0.152697i
$121$	5.34159			0.485599
$122$	−7.51223			−0.680125
$123$	−14.4184	−	3.87452i	−1.30007	−	0.349354i
$124$			1.02895i			0.0924024i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	7.49742			0.665288			0.332644	−	0.943052i	$-0.392059\pi$
$127$	7.49742			0.665288			0.332644	+	0.943052i	$0.392059\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−19.2558	−	5.17442i	−1.69538	−	0.455582i
$130$	−3.07531			−0.269723
$131$	−6.52049			−0.569698			−0.284849	−	0.958572i	$-0.591943\pi$
$131$	−6.52049			−0.569698			−0.284849	+	0.958572i	$0.591943\pi$
$132$	−1.06922	+	3.97894i	−0.0930637	+	0.346322i
$133$		0			0
$134$			13.4124i			1.15865i
$135$	3.66630	+	3.68215i	0.315545	+	0.316909i
$136$			4.70529i			0.403475i
$137$		−	7.24223i		−	0.618746i	−0.950941	−	0.309373i	$-0.899881\pi$
$137$		−	7.24223i		−	0.618746i	0.950941	−	0.309373i	$-0.100119\pi$
$138$	−7.73243	−	2.07786i	−0.658228	−	0.176879i
$139$			8.99820i			0.763218i	0.924324	+	0.381609i	$0.124630\pi$
$139$			8.99820i			0.763218i	−0.924324	+	0.381609i	$0.875370\pi$
$140$		0			0
$141$	−14.7536	−	3.96458i	−1.24248	−	0.333878i
$142$	−11.7698			−0.987698
$143$	7.31537			0.611742
$144$	2.59592	+	1.50373i	0.216326	+	0.125311i
$145$		−	0.405050i		−	0.0336376i
$146$	8.65046			0.715917
$147$		0			0
$148$	5.54367			0.455687
$149$			7.43451i			0.609059i	0.952503	+	0.304529i	$0.0984992\pi$
$149$			7.43451i			0.609059i	−0.952503	+	0.304529i	$0.901501\pi$
$150$	0.449490	−	1.67271i	0.0367007	−	0.136576i
$151$	19.4341			1.58152			0.790761	−	0.612125i	$-0.209685\pi$
$151$	19.4341			1.58152			0.790761	+	0.612125i	$0.209685\pi$
$152$	0.527004			0.0427456
$153$	−12.2145	−	7.07550i	−0.987486	−	0.572020i
$154$		0			0
$155$			1.02895i			0.0826473i
$156$	1.38232	−	5.14411i	0.110674	−	0.411858i
$157$			15.2417i			1.21642i	0.793777	+	0.608209i	$0.208112\pi$
$157$			15.2417i			1.21642i	−0.793777	+	0.608209i	$0.791888\pi$
$158$			1.91407i			0.152275i
$159$	5.49460	−	20.4473i	0.435750	−	1.62158i
$160$		−	1.00000i		−	0.0790569i
$161$		0			0
$162$	−7.80714	+	4.47757i	−0.613387	+	0.351791i
$163$	−23.0876			−1.80836			−0.904179	−	0.427155i	$-0.859516\pi$
$163$	−23.0876			−1.80836			−0.904179	+	0.427155i	$0.859516\pi$
$164$	−8.61981			−0.673094
$165$	−1.06922	+	3.97894i	−0.0832387	+	0.309760i
$166$			12.9078i			1.00184i
$167$	6.03310			0.466856			0.233428	−	0.972374i	$-0.425006\pi$
$167$	6.03310			0.466856			0.233428	+	0.972374i	$0.425006\pi$
$168$		0			0
$169$	3.54245			0.272496
$170$			4.70529i			0.360879i
$171$	−0.792473	+	1.36806i	−0.0606019	+	0.104618i
$172$	−11.5117			−0.877762
$173$	11.3332			0.861650			0.430825	−	0.902435i	$-0.358223\pi$
$173$	11.3332			0.861650			0.430825	+	0.902435i	$0.358223\pi$
$174$	0.677531	+	0.182066i	0.0513635	+	0.0138024i
$175$		0			0
$176$			2.37874i			0.179304i
$177$	14.2523	+	3.82989i	1.07127	+	0.287872i
$178$			6.18780i			0.463795i
$179$		−	19.1994i		−	1.43503i	−0.696544	−	0.717514i	$-0.745280\pi$
$179$		−	19.1994i		−	1.43503i	0.696544	−	0.717514i	$-0.254720\pi$
$180$	2.59592	+	1.50373i	0.193488	+	0.112082i
$181$			23.8389i			1.77193i	0.463753	+	0.885964i	$0.346502\pi$
$181$			23.8389i			1.77193i	−0.463753	+	0.885964i	$0.653498\pi$
$182$		0			0
$183$	3.37668	−	12.5658i	0.249611	−	0.928889i
$184$	−4.62269			−0.340789
$185$	5.54367			0.407579
$186$	−1.72113	−	0.462503i	−0.126200	−	0.0339124i
$187$		−	11.1927i		−	0.818488i
$188$	−8.82018			−0.643277
$189$		0			0
$190$	0.527004			0.0382329
$191$		−	10.4546i		−	0.756466i	−0.925710	−	0.378233i	$-0.876532\pi$
$191$		−	10.4546i		−	0.756466i	0.925710	−	0.378233i	$-0.123468\pi$
$192$	1.67271	+	0.449490i	0.120717	+	0.0324392i
$193$	−20.1184			−1.44816			−0.724079	−	0.689717i	$-0.757735\pi$
$193$	−20.1184			−1.44816			−0.724079	+	0.689717i	$0.757735\pi$
$194$	−19.6433			−1.41031
$195$	1.38232	−	5.14411i	0.0989903	−	0.368377i
$196$		0			0
$197$		−	20.5601i		−	1.46485i	−0.680849	−	0.732424i	$-0.738389\pi$
$197$		−	20.5601i		−	1.46485i	0.680849	−	0.732424i	$-0.261611\pi$
$198$	−6.17501	−	3.57699i	−0.438839	−	0.254206i
$199$		−	5.70991i		−	0.404765i	−0.979307	−	0.202382i	$-0.935132\pi$
$199$		−	5.70991i		−	0.404765i	0.979307	−	0.202382i	$-0.0648684\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	−22.4350	−	6.02874i	−1.58244	−	0.425234i
$202$			7.09724i			0.499360i
$203$		0			0
$204$	−7.87058	−	2.11498i	−0.551051	−	0.148078i
$205$	−8.61981			−0.602034
$206$	6.82964			0.475843
$207$	6.95130	−	12.0001i	0.483149	−	0.834067i
$208$		−	3.07531i		−	0.213235i
$209$	−1.25360			−0.0867136
$210$		0			0
$211$	13.3767			0.920891			0.460446	−	0.887688i	$-0.347690\pi$
$211$	13.3767			0.920891			0.460446	+	0.887688i	$0.347690\pi$
$212$		−	12.2241i		−	0.839552i
$213$	5.29040	−	19.6874i	0.362492	−	1.34896i
$214$	13.1216			0.896972
$215$	−11.5117			−0.785094
$216$	−3.68215	+	3.66630i	−0.250539	+	0.249460i
$217$		0			0
$218$			0.228271i			0.0154604i
$219$	−3.88830	+	14.4697i	−0.262747	+	0.977773i
$220$			2.37874i			0.160375i
$221$			14.4702i			0.973373i
$222$	−2.49183	+	9.27295i	−0.167240	+	0.622360i
$223$		−	24.5364i		−	1.64308i	−0.570153	−	0.821539i	$-0.693116\pi$
$223$		−	24.5364i		−	1.64308i	0.570153	−	0.821539i	$-0.306884\pi$
$224$		0			0
$225$	2.59592	+	1.50373i	0.173061	+	0.100249i
$226$	5.86352			0.390036
$227$	20.2310			1.34278			0.671390	−	0.741104i	$-0.265698\pi$
$227$	20.2310			1.34278			0.671390	+	0.741104i	$0.265698\pi$
$228$	−0.236883	+	0.881524i	−0.0156880	+	0.0583804i
$229$			25.1923i			1.66475i	0.554209	+	0.832377i	$0.313021\pi$
$229$			25.1923i			1.66475i	−0.554209	+	0.832377i	$0.686979\pi$
$230$	−4.62269			−0.304811
$231$		0			0
$232$	0.405050			0.0265928
$233$		−	2.40100i		−	0.157295i	−0.996902	−	0.0786474i	$-0.974940\pi$
$233$		−	2.40100i		−	0.157295i	0.996902	−	0.0786474i	$-0.0250601\pi$
$234$	7.98326	+	4.62445i	0.521882	+	0.302310i
$235$	−8.82018			−0.575365
$236$	8.52051			0.554638
$237$	−3.20169	−	0.860357i	−0.207972	−	0.0558862i
$238$		0			0
$239$		−	11.6579i		−	0.754086i	−0.926196	−	0.377043i	$-0.876941\pi$
$239$		−	11.6579i		−	0.754086i	0.926196	−	0.377043i	$-0.123059\pi$
$240$	1.67271	+	0.449490i	0.107973	+	0.0290145i
$241$		−	14.9969i		−	0.966038i	−0.875610	−	0.483019i	$-0.839540\pi$
$241$		−	14.9969i		−	0.966038i	0.875610	−	0.483019i	$-0.160460\pi$
$242$			5.34159i			0.343371i
$243$	−3.98044	−	15.0717i	−0.255345	−	0.966850i
$244$		−	7.51223i		−	0.480921i
$245$		0			0
$246$	3.87452	−	14.4184i	0.247031	−	0.919287i
$247$	1.62070			0.103123
$248$	−1.02895			−0.0653384
$249$	−21.5911	−	5.80195i	−1.36828	−	0.367684i
$250$		−	1.00000i		−	0.0632456i
$251$	−5.21694			−0.329290			−0.164645	−	0.986353i	$-0.552648\pi$
$251$	−5.21694			−0.329290			−0.164645	+	0.986353i	$0.552648\pi$
$252$		0			0
$253$	10.9962			0.691324
$254$			7.49742i			0.470430i
$255$	−7.87058	−	2.11498i	−0.492875	−	0.132445i
$256$	1.00000			0.0625000
$257$	−4.41292			−0.275270			−0.137635	−	0.990483i	$-0.543950\pi$
$257$	−4.41292			−0.275270			−0.137635	+	0.990483i	$0.543950\pi$
$258$	5.17442	−	19.2558i	0.322145	−	1.19881i
$259$		0			0
$260$		−	3.07531i		−	0.190723i
$261$	−0.609088	+	1.05148i	−0.0377016	+	0.0650848i
$262$		−	6.52049i		−	0.402837i
$263$			14.8146i			0.913509i	0.889593	+	0.456754i	$0.150988\pi$
$263$			14.8146i			0.913509i	−0.889593	+	0.456754i	$0.849012\pi$
$264$	−3.97894	−	1.06922i	−0.244887	−	0.0658060i
$265$		−	12.2241i		−	0.750918i
$266$		0			0
$267$	−10.3504	−	2.78136i	−0.633434	−	0.170216i
$268$	−13.4124			−0.819291
$269$	12.8575			0.783934			0.391967	−	0.919979i	$-0.371795\pi$
$269$	12.8575			0.783934			0.391967	+	0.919979i	$0.371795\pi$
$270$	−3.68215	+	3.66630i	−0.224089	+	0.223124i
$271$			10.7220i			0.651317i	0.945487	+	0.325659i	$0.105586\pi$
$271$			10.7220i			0.651317i	−0.945487	+	0.325659i	$0.894414\pi$
$272$	−4.70529			−0.285300
$273$		0			0
$274$	7.24223			0.437519
$275$			2.37874i			0.143443i
$276$	2.07786	−	7.73243i	0.125072	−	0.465437i
$277$	−4.06144			−0.244028			−0.122014	−	0.992528i	$-0.538935\pi$
$277$	−4.06144			−0.244028			−0.122014	+	0.992528i	$0.538935\pi$
$278$	−8.99820			−0.539676
$279$	1.54727	−	2.67107i	0.0926325	−	0.159913i
$280$		0			0
$281$		−	1.80282i		−	0.107547i	−0.998553	−	0.0537736i	$-0.982875\pi$
$281$		−	1.80282i		−	0.107547i	0.998553	−	0.0537736i	$-0.0171249\pi$
$282$	3.96458	−	14.7536i	0.236088	−	0.878564i
$283$			10.4139i			0.619044i	0.950892	+	0.309522i	$0.100169\pi$
$283$			10.4139i			0.619044i	−0.950892	+	0.309522i	$0.899831\pi$
$284$		−	11.7698i		−	0.698408i
$285$	−0.236883	+	0.881524i	−0.0140317	+	0.0522170i
$286$			7.31537i			0.432567i
$287$		0			0
$288$	−1.50373	+	2.59592i	−0.0886084	+	0.152966i
$289$	5.13971			0.302336
$290$	0.405050			0.0237854
$291$	8.82947	−	32.8575i	0.517593	−	1.92614i
$292$			8.65046i			0.506230i
$293$	−21.0309			−1.22864			−0.614319	−	0.789058i	$-0.710569\pi$
$293$	−21.0309			−1.22864			−0.614319	+	0.789058i	$0.710569\pi$
$294$		0			0
$295$	8.52051			0.496083
$296$			5.54367i			0.322219i
$297$	8.75888	−	8.72118i	0.508242	−	0.506054i
$298$	−7.43451			−0.430670
$299$	−14.2162			−0.822146
$300$	1.67271	+	0.449490i	0.0965740	+	0.0259513i
$301$		0			0
$302$			19.4341i			1.11831i
$303$	−11.8716	−	3.19014i	−0.682007	−	0.183269i
$304$			0.527004i			0.0302257i
$305$		−	7.51223i		−	0.430149i
$306$	7.07550	−	12.2145i	0.404479	−	0.698258i
$307$		−	3.52243i		−	0.201036i	−0.994935	−	0.100518i	$-0.967950\pi$
$307$		−	3.52243i		−	0.201036i	0.994935	−	0.100518i	$-0.0320500\pi$
$308$		0			0
$309$	−3.06986	+	11.4240i	−0.174638	+	0.649889i
$310$	−1.02895			−0.0584404
$311$	3.17187			0.179860			0.0899302	−	0.995948i	$-0.471336\pi$
$311$	3.17187			0.179860			0.0899302	+	0.995948i	$0.471336\pi$
$312$	5.14411	+	1.38232i	0.291228	+	0.0782587i
$313$			29.9466i			1.69268i	0.532640	+	0.846342i	$0.321200\pi$
$313$			29.9466i			1.69268i	−0.532640	+	0.846342i	$0.678800\pi$
$314$	−15.2417			−0.860138
$315$		0			0
$316$	−1.91407			−0.107675
$317$			16.3905i			0.920585i	0.887767	+	0.460292i	$0.152255\pi$
$317$			16.3905i			0.920585i	−0.887767	+	0.460292i	$0.847745\pi$
$318$	20.4473	+	5.49460i	1.14663	+	0.308122i
$319$	−0.963509			−0.0539462
$320$	1.00000			0.0559017
$321$	−5.89802	+	21.9486i	−0.329195	+	1.22505i
$322$		0			0
$323$		−	2.47970i		−	0.137974i
$324$	−4.47757	−	7.80714i	−0.248754	−	0.433730i
$325$		−	3.07531i		−	0.170588i
$326$		−	23.0876i		−	1.27870i
$327$	−0.381830	−	0.102605i	−0.0211153	−	0.00567409i
$328$		−	8.61981i		−	0.475950i
$329$		0			0
$330$	−3.97894	−	1.06922i	−0.219034	−	0.0588587i
$331$	15.5958			0.857224			0.428612	−	0.903489i	$-0.359003\pi$
$331$	15.5958			0.857224			0.428612	+	0.903489i	$0.359003\pi$
$332$	−12.9078			−0.708410
$333$	−14.3909	−	8.33621i	−0.788617	−	0.456821i
$334$			6.03310i			0.330117i
$335$	−13.4124			−0.732797
$336$		0			0
$337$	−9.26228			−0.504548			−0.252274	−	0.967656i	$-0.581178\pi$
$337$	−9.26228			−0.504548			−0.252274	+	0.967656i	$0.581178\pi$
$338$			3.54245i			0.192684i
$339$	−2.63560	+	9.80797i	−0.143146	+	0.532696i
$340$	−4.70529			−0.255180
$341$	2.44760			0.132545
$342$	−1.36806	−	0.792473i	−0.0739761	−	0.0428520i
$343$		0			0
$344$		−	11.5117i		−	0.620671i
$345$	2.07786	−	7.73243i	0.111868	−	0.416300i
$346$			11.3332i			0.609279i
$347$		−	17.1376i		−	0.919994i	−0.887920	−	0.459997i	$-0.847850\pi$
$347$		−	17.1376i		−	0.919994i	0.887920	−	0.459997i	$-0.152150\pi$
$348$	−0.182066	+	0.677531i	−0.00975977	+	0.0363195i
$349$			4.28660i			0.229457i	0.993397	+	0.114728i	$0.0365998\pi$
$349$			4.28660i			0.229457i	−0.993397	+	0.114728i	$0.963400\pi$
$350$		0			0
$351$	−11.3238	+	11.2750i	−0.604418	+	0.601816i
$352$	−2.37874			−0.126787
$353$	−4.02994			−0.214492			−0.107246	−	0.994233i	$-0.534203\pi$
$353$	−4.02994			−0.214492			−0.107246	+	0.994233i	$0.534203\pi$
$354$	−3.82989	+	14.2523i	−0.203556	+	0.757503i
$355$		−	11.7698i		−	0.624675i
$356$	−6.18780			−0.327953
$357$		0			0
$358$	19.1994			1.01472
$359$		−	15.3930i		−	0.812412i	−0.913782	−	0.406206i	$-0.866852\pi$
$359$		−	15.3930i		−	0.812412i	0.913782	−	0.406206i	$-0.133148\pi$
$360$	−1.50373	+	2.59592i	−0.0792537	+	0.136817i
$361$	18.7223			0.985382
$362$	−23.8389			−1.25294
$363$	−8.93494	−	2.40100i	−0.468963	−	0.126020i
$364$		0			0
$365$			8.65046i			0.452786i
$366$	12.5658	+	3.37668i	0.656824	+	0.176502i
$367$		−	2.00965i		−	0.104903i	−0.998623	−	0.0524514i	$-0.983297\pi$
$367$		−	2.00965i		−	0.104903i	0.998623	−	0.0524514i	$-0.0167035\pi$
$368$		−	4.62269i		−	0.240975i
$369$	22.3763	+	12.9619i	1.16486	+	0.674770i
$370$			5.54367i			0.288202i
$371$		0			0
$372$	0.462503	−	1.72113i	0.0239797	−	0.0892367i
$373$	8.85050			0.458262			0.229131	−	0.973396i	$-0.426412\pi$
$373$	8.85050			0.458262			0.229131	+	0.973396i	$0.426412\pi$
$374$	11.1927			0.578758
$375$	1.67271	+	0.449490i	0.0863784	+	0.0232116i
$376$		−	8.82018i		−	0.454866i
$377$	1.24566			0.0641546
$378$		0			0
$379$	11.4030			0.585731			0.292865	−	0.956154i	$-0.405391\pi$
$379$	11.4030			0.585731			0.292865	+	0.956154i	$0.405391\pi$
$380$			0.527004i			0.0270347i
$381$	−12.5410	−	3.37002i	−0.642495	−	0.172651i
$382$	10.4546			0.534902
$383$	−8.73221			−0.446195			−0.223098	−	0.974796i	$-0.571617\pi$
$383$	−8.73221			−0.446195			−0.223098	+	0.974796i	$0.571617\pi$
$384$	−0.449490	+	1.67271i	−0.0229380	+	0.0853601i
$385$		0			0
$386$		−	20.1184i		−	1.02400i
$387$	29.8835	+	17.3106i	1.51906	+	0.879947i
$388$		−	19.6433i		−	0.997237i
$389$		−	27.3884i		−	1.38865i	−0.719663	−	0.694324i	$-0.755704\pi$
$389$		−	27.3884i		−	1.38865i	0.719663	−	0.694324i	$-0.244296\pi$
$390$	5.14411	+	1.38232i	0.260482	+	0.0699967i
$391$			21.7511i			1.10000i
$392$		0			0
$393$	10.9069	+	2.93090i	0.550179	+	0.147844i
$394$	20.5601			1.03580
$395$	−1.91407			−0.0963074
$396$	3.57699	−	6.17501i	0.179751	−	0.310306i
$397$		−	1.55639i		−	0.0781127i	−0.999237	−	0.0390564i	$-0.987565\pi$
$397$		−	1.55639i		−	0.0781127i	0.999237	−	0.0390564i	$-0.0124352\pi$
$398$	5.70991			0.286212
$399$		0			0
$400$	1.00000			0.0500000
$401$		−	34.6328i		−	1.72948i	−0.502218	−	0.864741i	$-0.667483\pi$
$401$		−	34.6328i		−	1.72948i	0.502218	−	0.864741i	$-0.332517\pi$
$402$	6.02874	−	22.4350i	0.300686	−	1.11896i
$403$	−3.16434			−0.157627
$404$	−7.09724			−0.353101
$405$	−4.47757	−	7.80714i	−0.222492	−	0.387940i
$406$		0			0
$407$		−	13.1870i		−	0.653653i
$408$	2.11498	−	7.87058i	0.104707	−	0.389652i
$409$		−	13.5926i		−	0.672111i	−0.941842	−	0.336056i	$-0.890907\pi$
$409$		−	13.5926i		−	0.672111i	0.941842	−	0.336056i	$-0.109093\pi$
$410$		−	8.61981i		−	0.425702i
$411$	−3.25531	+	12.1142i	−0.160573	+	0.597547i
$412$			6.82964i			0.336472i
$413$		0			0
$414$	12.0001	+	6.95130i	0.589774	+	0.341638i
$415$	−12.9078			−0.633621
$416$	3.07531			0.150780
$417$	4.04461	−	15.0514i	0.198065	−	0.737069i
$418$		−	1.25360i		−	0.0613158i
$419$	−17.5962			−0.859631			−0.429815	−	0.902917i	$-0.641421\pi$
$419$	−17.5962			−0.859631			−0.429815	+	0.902917i	$0.641421\pi$
$420$		0			0
$421$	−31.7006			−1.54499			−0.772497	−	0.635019i	$-0.780992\pi$
$421$	−31.7006			−1.54499			−0.772497	+	0.635019i	$0.780992\pi$
$422$			13.3767i			0.651169i
$423$	22.8964	+	13.2632i	1.11326	+	0.644879i
$424$	12.2241			0.593653
$425$	−4.70529			−0.228240
$426$	19.6874	+	5.29040i	0.953859	+	0.256321i
$427$		0			0
$428$			13.1216i			0.634255i
$429$	−12.2365	−	3.28819i	−0.590784	−	0.158755i
$430$		−	11.5117i		−	0.555145i
$431$			10.3717i			0.499587i	0.968299	+	0.249793i	$0.0803627\pi$
$431$			10.3717i			0.499587i	−0.968299	+	0.249793i	$0.919637\pi$
$432$	−3.66630	−	3.68215i	−0.176395	−	0.177158i
$433$		−	41.0608i		−	1.97326i	−0.162987	−	0.986628i	$-0.552113\pi$
$433$		−	41.0608i		−	1.97326i	0.162987	−	0.986628i	$-0.447887\pi$
$434$		0			0
$435$	−0.182066	+	0.677531i	−0.00872940	+	0.0324851i
$436$	−0.228271			−0.0109322
$437$	2.43618			0.116538
$438$	−14.4697	−	3.88830i	−0.691390	−	0.185790i
$439$			10.6387i			0.507756i	0.967236	+	0.253878i	$0.0817062\pi$
$439$			10.6387i			0.507756i	−0.967236	+	0.253878i	$0.918294\pi$
$440$	−2.37874			−0.113402
$441$		0			0
$442$	−14.4702			−0.688279
$443$			20.3371i			0.966247i	0.875552	+	0.483123i	$0.160498\pi$
$443$			20.3371i			0.966247i	−0.875552	+	0.483123i	$0.839502\pi$
$444$	−9.27295	−	2.49183i	−0.440075	−	0.118257i
$445$	−6.18780			−0.293330
$446$	24.5364			1.16183
$447$	3.34174	−	12.4358i	0.158059	−	0.588192i
$448$		0			0
$449$		−	10.6792i		−	0.503983i	−0.967730	−	0.251991i	$-0.918915\pi$
$449$		−	10.6792i		−	0.503983i	0.967730	−	0.251991i	$-0.0810854\pi$
$450$	−1.50373	+	2.59592i	−0.0708867	+	0.122373i
$451$			20.5043i			0.965510i
$452$			5.86352i			0.275797i
$453$	−32.5076	−	8.73543i	−1.52734	−	0.410426i
$454$			20.2310i			0.949489i
$455$		0			0
$456$	−0.881524	−	0.236883i	−0.0412811	−	0.0110931i
$457$	1.04759			0.0490044			0.0245022	−	0.999700i	$-0.492200\pi$
$457$	1.04759			0.0490044			0.0245022	+	0.999700i	$0.492200\pi$
$458$	−25.1923			−1.17716
$459$	17.2510	+	17.3256i	0.805208	+	0.808688i
$460$		−	4.62269i		−	0.215534i
$461$	−0.442723			−0.0206197			−0.0103098	−	0.999947i	$-0.503282\pi$
$461$	−0.442723			−0.0206197			−0.0103098	+	0.999947i	$0.503282\pi$
$462$		0			0
$463$	1.83270			0.0851730			0.0425865	−	0.999093i	$-0.486440\pi$
$463$	1.83270			0.0851730			0.0425865	+	0.999093i	$0.486440\pi$
$464$			0.405050i			0.0188040i
$465$	0.462503	−	1.72113i	0.0214481	−	0.0798157i
$466$	2.40100			0.111224
$467$	−3.33622			−0.154382			−0.0771909	−	0.997016i	$-0.524595\pi$
$467$	−3.33622			−0.154382			−0.0771909	+	0.997016i	$0.524595\pi$
$468$	−4.62445	+	7.98326i	−0.213765	+	0.369026i
$469$		0			0
$470$		−	8.82018i		−	0.406844i
$471$	6.85099	−	25.4949i	0.315677	−	1.17474i
$472$			8.52051i			0.392188i
$473$			27.3834i			1.25909i
$474$	0.860357	−	3.20169i	0.0395175	−	0.147058i
$475$			0.527004i			0.0241806i
$476$		0			0
$477$	−18.3817	+	31.7326i	−0.841642	+	1.45294i
$478$	11.6579			0.533219
$479$	39.9415			1.82497			0.912487	−	0.409105i	$-0.134159\pi$
$479$	39.9415			1.82497			0.912487	+	0.409105i	$0.134159\pi$
$480$	−0.449490	+	1.67271i	−0.0205163	+	0.0763484i
$481$			17.0485i			0.777346i
$482$	14.9969			0.683092
$483$		0			0
$484$	−5.34159			−0.242800
$485$		−	19.6433i		−	0.891956i
$486$	15.0717	−	3.98044i	0.683666	−	0.180556i
$487$	25.7832			1.16835			0.584175	−	0.811628i	$-0.301418\pi$
$487$	25.7832			1.16835			0.584175	+	0.811628i	$0.301418\pi$
$488$	7.51223			0.340063
$489$	38.6188	+	10.3776i	1.74640	+	0.469293i
$490$		0			0
$491$			24.6154i			1.11088i	0.831557	+	0.555439i	$0.187450\pi$
$491$			24.6154i			1.11088i	−0.831557	+	0.555439i	$0.812550\pi$
$492$	14.4184	+	3.87452i	0.650034	+	0.174677i
$493$		−	1.90588i		−	0.0858364i
$494$			1.62070i			0.0729188i
$495$	3.57699	−	6.17501i	0.160774	−	0.277546i
$496$		−	1.02895i		−	0.0462012i
$497$		0			0
$498$	5.80195	−	21.5911i	0.259992	−	0.967520i
$499$	32.2260			1.44263			0.721316	−	0.692606i	$-0.243538\pi$
$499$	32.2260			1.44263			0.721316	+	0.692606i	$0.243538\pi$
$500$	1.00000			0.0447214
$501$	−10.0916	−	2.71182i	−0.450861	−	0.121155i
$502$		−	5.21694i		−	0.232843i
$503$	19.8072			0.883160			0.441580	−	0.897222i	$-0.354418\pi$
$503$	19.8072			0.883160			0.441580	+	0.897222i	$0.354418\pi$
$504$		0			0
$505$	−7.09724			−0.315823
$506$			10.9962i			0.488840i
$507$	−5.92549	−	1.59230i	−0.263160	−	0.0707163i
$508$	−7.49742			−0.332644
$509$	−23.3685			−1.03579			−0.517895	−	0.855444i	$-0.673284\pi$
$509$	−23.3685			−1.03579			−0.517895	+	0.855444i	$0.673284\pi$
$510$	2.11498	−	7.87058i	0.0936529	−	0.348515i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	1.94051	−	1.93215i	0.0856755	−	0.0853067i
$514$		−	4.41292i		−	0.194646i
$515$			6.82964i			0.300950i
$516$	19.2558	+	5.17442i	0.847689	+	0.227791i
$517$			20.9809i			0.922739i
$518$		0			0
$519$	−18.9572	−	5.09418i	−0.832130	−	0.223610i
$520$	3.07531			0.134861
$521$	−7.16731			−0.314006			−0.157003	−	0.987598i	$-0.550183\pi$
$521$	−7.16731			−0.314006			−0.157003	+	0.987598i	$0.550183\pi$
$522$	−1.05148	−	0.609088i	−0.0460219	−	0.0266590i
$523$		−	3.00258i		−	0.131294i	−0.997843	−	0.0656469i	$-0.979089\pi$
$523$		−	3.00258i		−	0.131294i	0.997843	−	0.0656469i	$-0.0209111\pi$
$524$	6.52049			0.284849
$525$		0			0
$526$	−14.8146			−0.645948
$527$			4.84150i			0.210899i
$528$	1.06922	−	3.97894i	0.0465319	−	0.173161i
$529$	1.63070			0.0709002
$530$	12.2241			0.530979
$531$	−22.1185	−	12.8126i	−0.959863	−	0.556019i
$532$		0			0
$533$		−	26.5086i		−	1.14822i
$534$	2.78136	−	10.3504i	0.120361	−	0.447906i
$535$			13.1216i			0.567295i
$536$		−	13.4124i		−	0.579327i
$537$	−8.62993	+	32.1150i	−0.372409	+	1.38586i
$538$			12.8575i			0.554325i
$539$		0			0
$540$	−3.66630	−	3.68215i	−0.157773	−	0.158455i
$541$	−40.5334			−1.74267			−0.871334	−	0.490691i	$-0.836744\pi$
$541$	−40.5334			−1.74267			−0.871334	+	0.490691i	$0.836744\pi$
$542$	−10.7220			−0.460551
$543$	10.7153	−	39.8755i	0.459839	−	1.71122i
$544$		−	4.70529i		−	0.201737i
$545$	−0.228271			−0.00977804
$546$		0			0
$547$	−22.2050			−0.949415			−0.474708	−	0.880144i	$-0.657446\pi$
$547$	−22.2050			−0.949415			−0.474708	+	0.880144i	$0.657446\pi$
$548$			7.24223i			0.309373i
$549$	−11.2964	+	19.5011i	−0.482119	+	0.832288i
$550$	−2.37874			−0.101430
$551$	−0.213463			−0.00909383
$552$	7.73243	+	2.07786i	0.329114	+	0.0884394i
$553$		0			0
$554$		−	4.06144i		−	0.172554i
$555$	−9.27295	−	2.49183i	−0.393615	−	0.105772i
$556$		−	8.99820i		−	0.381609i
$557$			22.3893i			0.948663i	0.880346	+	0.474332i	$0.157310\pi$
$557$			22.3893i			0.948663i	−0.880346	+	0.474332i	$0.842690\pi$
$558$	2.67107	+	1.54727i	0.113075	+	0.0655010i
$559$		−	35.4022i		−	1.49735i
$560$		0			0
$561$	−5.03099	+	18.7221i	−0.212409	+	0.790446i
$562$	1.80282			0.0760473
$563$	−19.5160			−0.822499			−0.411250	−	0.911523i	$-0.634908\pi$
$563$	−19.5160			−0.822499			−0.411250	+	0.911523i	$0.634908\pi$
$564$	14.7536	+	3.96458i	0.621238	+	0.166939i
$565$			5.86352i			0.246680i
$566$	−10.4139			−0.437730
$567$		0			0
$568$	11.7698			0.493849
$569$			5.99419i			0.251290i	0.992075	+	0.125645i	$0.0401000\pi$
$569$			5.99419i			0.251290i	−0.992075	+	0.125645i	$0.959900\pi$
$570$	−0.881524	−	0.236883i	−0.0369230	−	0.00992194i
$571$	11.2819			0.472131			0.236065	−	0.971737i	$-0.424142\pi$
$571$	11.2819			0.472131			0.236065	+	0.971737i	$0.424142\pi$
$572$	−7.31537			−0.305871
$573$	−4.69923	+	17.4875i	−0.196313	+	0.730549i
$574$		0			0
$575$		−	4.62269i		−	0.192780i
$576$	−2.59592	−	1.50373i	−0.108163	−	0.0626556i
$577$		−	17.8477i		−	0.743008i	−0.928431	−	0.371504i	$-0.878842\pi$
$577$		−	17.8477i		−	0.743008i	0.928431	−	0.371504i	$-0.121158\pi$
$578$			5.13971i			0.213784i
$579$	33.6523	+	9.04305i	1.39854	+	0.375816i
$580$			0.405050i			0.0168188i
$581$		0			0
$582$	32.8575	+	8.82947i	1.36199	+	0.365993i
$583$	−29.0779			−1.20428
$584$	−8.65046			−0.357959
$585$	−4.62445	+	7.98326i	−0.191198	+	0.330067i
$586$		−	21.0309i		−	0.868779i
$587$	7.42282			0.306373			0.153186	−	0.988197i	$-0.451047\pi$
$587$	7.42282			0.306373			0.153186	+	0.988197i	$0.451047\pi$
$588$		0			0
$589$	0.542260			0.0223434
$590$			8.52051i			0.350784i
$591$	−9.24158	+	34.3911i	−0.380148	+	1.41466i
$592$	−5.54367			−0.227843
$593$	36.9646			1.51796			0.758978	−	0.651116i	$-0.225699\pi$
$593$	36.9646			1.51796			0.758978	+	0.651116i	$0.225699\pi$
$594$	8.72118	+	8.75888i	0.357834	+	0.359381i
$595$		0			0
$596$		−	7.43451i		−	0.304529i
$597$	−2.56655	+	9.55102i	−0.105042	+	0.390897i
$598$		−	14.2162i		−	0.581345i
$599$			34.1065i			1.39355i	0.717288	+	0.696777i	$0.245383\pi$
$599$			34.1065i			1.39355i	−0.717288	+	0.696777i	$0.754617\pi$
$600$	−0.449490	+	1.67271i	−0.0183504	+	0.0682881i
$601$			19.2247i			0.784192i	0.919924	+	0.392096i	$0.128250\pi$
$601$			19.2247i			0.784192i	−0.919924	+	0.392096i	$0.871750\pi$
$602$		0			0
$603$	34.8174	+	20.1687i	1.41787	+	0.821331i
$604$	−19.4341			−0.790761
$605$	−5.34159			−0.217167
$606$	3.19014	−	11.8716i	0.129591	−	0.482252i
$607$		−	23.6482i		−	0.959849i	−0.877310	−	0.479925i	$-0.840664\pi$
$607$		−	23.6482i		−	0.959849i	0.877310	−	0.479925i	$-0.159336\pi$
$608$	−0.527004			−0.0213728
$609$		0			0
$610$	7.51223			0.304161
$611$		−	27.1248i		−	1.09735i
$612$	12.2145	+	7.07550i	0.493743	+	0.286010i
$613$	−29.9776			−1.21078			−0.605392	−	0.795928i	$-0.706984\pi$
$613$	−29.9776			−1.21078			−0.605392	+	0.795928i	$0.706984\pi$
$614$	3.52243			0.142154
$615$	14.4184	+	3.87452i	0.581408	+	0.156236i
$616$		0			0
$617$		−	9.68803i		−	0.390026i	−0.980801	−	0.195013i	$-0.937525\pi$
$617$		−	9.68803i		−	0.390026i	0.980801	−	0.195013i	$-0.0624748\pi$
$618$	−11.4240	−	3.06986i	−0.459541	−	0.123488i
$619$			6.19797i			0.249118i	0.992212	+	0.124559i	$0.0397515\pi$
$619$			6.19797i			0.249118i	−0.992212	+	0.124559i	$0.960248\pi$
$620$		−	1.02895i		−	0.0413236i
$621$	−17.0215	+	16.9482i	−0.683047	+	0.680107i
$622$			3.17187i			0.127180i
$623$		0			0
$624$	−1.38232	+	5.14411i	−0.0553372	+	0.205929i
$625$	1.00000			0.0400000
$626$	−29.9466			−1.19691
$627$	2.09692	+	0.563483i	0.0837428	+	0.0225034i
$628$		−	15.2417i		−	0.608209i
$629$	26.0846			1.04006
$630$		0			0
$631$	−7.86885			−0.313254			−0.156627	−	0.987658i	$-0.550062\pi$
$631$	−7.86885			−0.313254			−0.156627	+	0.987658i	$0.550062\pi$
$632$		−	1.91407i		−	0.0761377i
$633$	−22.3754	−	6.01271i	−0.889341	−	0.238984i
$634$	−16.3905			−0.650952
$635$	−7.49742			−0.297526
$636$	−5.49460	+	20.4473i	−0.217875	+	0.810789i
$637$		0			0
$638$		−	0.963509i		−	0.0381457i
$639$	−17.6986	+	30.5534i	−0.700146	+	1.20867i
$640$			1.00000i			0.0395285i
$641$			23.4908i			0.927832i	0.885879	+	0.463916i	$0.153556\pi$
$641$			23.4908i			0.927832i	−0.885879	+	0.463916i	$0.846444\pi$
$642$	−21.9486	−	5.89802i	−0.866241	−	0.232776i
$643$		−	13.9315i		−	0.549405i	−0.961529	−	0.274702i	$-0.911421\pi$
$643$		−	13.9315i		−	0.549405i	0.961529	−	0.274702i	$-0.0885793\pi$
$644$		0			0
$645$	19.2558	+	5.17442i	0.758196	+	0.203742i
$646$	2.47970			0.0975626
$647$	10.7038			0.420810			0.210405	−	0.977614i	$-0.432522\pi$
$647$	10.7038			0.420810			0.210405	+	0.977614i	$0.432522\pi$
$648$	7.80714	−	4.47757i	0.306693	−	0.175895i
$649$		−	20.2681i		−	0.795592i
$650$	3.07531			0.120624
$651$		0			0
$652$	23.0876			0.904179
$653$			19.0444i			0.745264i	0.927979	+	0.372632i	$0.121545\pi$
$653$			19.0444i			0.745264i	−0.927979	+	0.372632i	$0.878455\pi$
$654$	0.102605	−	0.381830i	0.00401219	−	0.0149308i
$655$	6.52049			0.254776
$656$	8.61981			0.336547
$657$	13.0080	−	22.4559i	0.507490	−	0.876087i
$658$		0			0
$659$		−	24.3453i		−	0.948359i	−0.880428	−	0.474179i	$-0.842745\pi$
$659$		−	24.3453i		−	0.948359i	0.880428	−	0.474179i	$-0.157255\pi$
$660$	1.06922	−	3.97894i	0.0416194	−	0.154880i
$661$			38.7658i			1.50782i	0.656980	+	0.753908i	$0.271834\pi$
$661$			38.7658i			1.50782i	−0.656980	+	0.753908i	$0.728166\pi$
$662$			15.5958i			0.606149i
$663$	6.50423	−	24.2045i	0.252603	−	0.940025i
$664$		−	12.9078i		−	0.500922i
$665$		0			0
$666$	8.33621	−	14.3909i	0.323021	−	0.557636i
$667$	1.87242			0.0725005
$668$	−6.03310			−0.233428
$669$	−11.0289	+	41.0423i	−0.426401	+	1.58679i
$670$		−	13.4124i		−	0.518165i
$671$	−17.8696			−0.689850
$672$		0			0
$673$	−16.2944			−0.628102			−0.314051	−	0.949406i	$-0.601686\pi$
$673$	−16.2944			−0.628102			−0.314051	+	0.949406i	$0.601686\pi$
$674$		−	9.26228i		−	0.356770i
$675$	−3.66630	−	3.68215i	−0.141116	−	0.141726i
$676$	−3.54245			−0.136248
$677$	49.6659			1.90881			0.954407	−	0.298507i	$-0.0964888\pi$
$677$	49.6659			1.90881			0.954407	+	0.298507i	$0.0964888\pi$
$678$	−9.80797	−	2.63560i	−0.376673	−	0.101219i
$679$		0			0
$680$		−	4.70529i		−	0.180439i
$681$	−33.8406	−	9.09365i	−1.29678	−	0.348469i
$682$			2.44760i			0.0937236i
$683$			8.27581i			0.316665i	0.987386	+	0.158332i	$0.0506118\pi$
$683$			8.27581i			0.316665i	−0.987386	+	0.158332i	$0.949388\pi$
$684$	0.792473	−	1.36806i	0.0303010	−	0.0523090i
$685$			7.24223i			0.276712i
$686$		0			0
$687$	11.3237	−	42.1394i	0.432026	−	1.60772i
$688$	11.5117			0.438881
$689$	37.5928			1.43217
$690$	7.73243	+	2.07786i	0.294368	+	0.0791026i
$691$		−	15.8177i		−	0.601733i	−0.953666	−	0.300867i	$-0.902724\pi$
$691$		−	15.8177i		−	0.601733i	0.953666	−	0.300867i	$-0.0972759\pi$
$692$	−11.3332			−0.430825
$693$		0			0
$694$	17.1376			0.650534
$695$		−	8.99820i		−	0.341321i
$696$	−0.677531	−	0.182066i	−0.0256818	−	0.00690120i
$697$	−40.5587			−1.53627
$698$	−4.28660			−0.162250
$699$	−1.07923	+	4.01618i	−0.0408201	+	0.151906i
$700$		0			0
$701$			44.6281i			1.68558i	0.538243	+	0.842790i	$0.319088\pi$
$701$			44.6281i			1.68558i	−0.538243	+	0.842790i	$0.680912\pi$
$702$	−11.2750	−	11.3238i	−0.425548	−	0.427388i
$703$		−	2.92153i		−	0.110188i
$704$		−	2.37874i		−	0.0896521i
$705$	14.7536	+	3.96458i	0.555653	+	0.149315i
$706$		−	4.02994i		−	0.151669i
$707$		0			0
$708$	−14.2523	−	3.82989i	−0.535636	−	0.143936i
$709$	−33.8584			−1.27158			−0.635790	−	0.771862i	$-0.719325\pi$
$709$	−33.8584			−1.27158			−0.635790	+	0.771862i	$0.719325\pi$
$710$	11.7698			0.441712
$711$	4.96877	+	2.87825i	0.186343	+	0.107943i
$712$		−	6.18780i		−	0.231898i
$713$	−4.75652			−0.178133
$714$		0			0
$715$	−7.31537			−0.273579
$716$			19.1994i			0.717514i
$717$	−5.24011	+	19.5003i	−0.195695	+	0.728251i
$718$	15.3930			0.574462
$719$	−18.9821			−0.707913			−0.353956	−	0.935262i	$-0.615164\pi$
$719$	−18.9821			−0.707913			−0.353956	+	0.935262i	$0.615164\pi$
$720$	−2.59592	−	1.50373i	−0.0967441	−	0.0560409i
$721$		0			0
$722$			18.7223i			0.696771i
$723$	−6.74098	+	25.0855i	−0.250700	+	0.932942i
$724$		−	23.8389i		−	0.885964i
$725$			0.405050i			0.0150432i
$726$	2.40100	−	8.93494i	0.0891093	−	0.331607i
$727$			3.67665i			0.136360i	0.997673	+	0.0681798i	$0.0217191\pi$
$727$			3.67665i			0.136360i	−0.997673	+	0.0681798i	$0.978281\pi$
$728$		0			0
$729$	−0.116463	+	26.9997i	−0.00431345	+	0.999991i
$730$	−8.65046			−0.320168
$731$	−54.1660			−2.00340
$732$	−3.37668	+	12.5658i	−0.124806	+	0.464445i
$733$		−	8.19545i		−	0.302706i	−0.988480	−	0.151353i	$-0.951637\pi$
$733$		−	8.19545i		−	0.302706i	0.988480	−	0.151353i	$-0.0483630\pi$
$734$	2.00965			0.0741776
$735$		0			0
$736$	4.62269			0.170395
$737$			31.9046i			1.17522i
$738$	−12.9619	+	22.3763i	−0.477134	+	0.823684i
$739$	32.3413			1.18969			0.594847	−	0.803839i	$-0.297212\pi$
$739$	32.3413			1.18969			0.594847	+	0.803839i	$0.297212\pi$
$740$	−5.54367			−0.203789
$741$	−2.71096	−	0.728490i	−0.0995897	−	0.0267617i
$742$		0			0
$743$			34.1355i			1.25231i	0.779698	+	0.626155i	$0.215372\pi$
$743$			34.1355i			1.25231i	−0.779698	+	0.626155i	$0.784628\pi$
$744$	1.72113	+	0.462503i	0.0630999	+	0.0169562i
$745$		−	7.43451i		−	0.272379i
$746$			8.85050i			0.324040i
$747$	33.5077	+	19.4100i	1.22598	+	0.710174i
$748$			11.1927i			0.409244i
$749$		0			0
$750$	−0.449490	+	1.67271i	−0.0164131	+	0.0610787i
$751$	43.8356			1.59958			0.799791	−	0.600278i	$-0.204944\pi$
$751$	43.8356			1.59958			0.799791	+	0.600278i	$0.204944\pi$
$752$	8.82018			0.321639
$753$	8.72642	+	2.34496i	0.318008	+	0.0854552i
$754$			1.24566i			0.0453641i
$755$	−19.4341			−0.707278
$756$		0			0
$757$	−24.2063			−0.879792			−0.439896	−	0.898049i	$-0.644985\pi$
$757$	−24.2063			−0.879792			−0.439896	+	0.898049i	$0.644985\pi$
$758$			11.4030i			0.414174i
$759$	−18.3934	−	4.94268i	−0.667639	−	0.179408i
$760$	−0.527004			−0.0191164
$761$	9.24874			0.335267			0.167633	−	0.985849i	$-0.446388\pi$
$761$	9.24874			0.335267			0.167633	+	0.985849i	$0.446388\pi$
$762$	3.37002	−	12.5410i	0.122083	−	0.454313i
$763$		0			0
$764$			10.4546i			0.378233i
$765$	12.2145	+	7.07550i	0.441617	+	0.255815i
$766$		−	8.73221i		−	0.315508i
$767$			26.2032i			0.946144i
$768$	−1.67271	−	0.449490i	−0.0603587	−	0.0162196i
$769$		−	28.3177i		−	1.02116i	−0.859830	−	0.510580i	$-0.829431\pi$
$769$		−	28.3177i		−	1.02116i	0.859830	−	0.510580i	$-0.170569\pi$
$770$		0			0
$771$	7.38153	+	1.98356i	0.265839	+	0.0714363i
$772$	20.1184			0.724079
$773$	−36.4274			−1.31020			−0.655101	−	0.755541i	$-0.727374\pi$
$773$	−36.4274			−1.31020			−0.655101	+	0.755541i	$0.727374\pi$
$774$	−17.3106	+	29.8835i	−0.622217	+	1.07414i
$775$		−	1.02895i		−	0.0369610i
$776$	19.6433			0.705153
$777$		0			0
$778$	27.3884			0.981922
$779$			4.54267i			0.162758i
$780$	−1.38232	+	5.14411i	−0.0494951	+	0.184189i
$781$	−27.9972			−1.00182
$782$	−21.7511			−0.777818
$783$	1.49146	−	1.48504i	0.0533003	−	0.0530709i
$784$		0			0
$785$		−	15.2417i		−	0.543999i
$786$	−2.93090	+	10.9069i	−0.104542	+	0.389036i
$787$			53.8639i			1.92004i	0.279930	+	0.960021i	$0.409689\pi$
$787$			53.8639i			1.92004i	−0.279930	+	0.960021i	$0.590311\pi$
$788$			20.5601i			0.732424i
$789$	6.65903	−	24.7806i	0.237068	−	0.882211i
$790$		−	1.91407i		−	0.0680996i
$791$		0			0
$792$	6.17501	+	3.57699i	0.219419	+	0.127103i
$793$	23.1025			0.820393
$794$	1.55639			0.0552340
$795$	−5.49460	+	20.4473i	−0.194873	+	0.725191i
$796$			5.70991i			0.202382i
$797$	36.1305			1.27981			0.639905	−	0.768454i	$-0.278974\pi$
$797$	36.1305			1.27981			0.639905	+	0.768454i	$0.278974\pi$
$798$		0			0
$799$	−41.5014			−1.46822
$800$			1.00000i			0.0353553i
$801$	16.0630	+	9.30481i	0.567559	+	0.328769i
$802$	34.6328			1.22293
$803$	20.5772			0.726154
$804$	22.4350	+	6.02874i	0.791222	+	0.212617i
$805$		0			0
$806$		−	3.16434i		−	0.111459i
$807$	−21.5068	−	5.77931i	−0.757076	−	0.203441i
$808$		−	7.09724i		−	0.249680i
$809$		−	32.5143i		−	1.14314i	−0.820552	−	0.571572i	$-0.806334\pi$
$809$		−	32.5143i		−	1.14314i	0.820552	−	0.571572i	$-0.193666\pi$
$810$	7.80714	−	4.47757i	0.274315	−	0.157326i
$811$		−	34.2613i		−	1.20308i	−0.798844	−	0.601538i	$-0.794555\pi$
$811$		−	34.2613i		−	1.20308i	0.798844	−	0.601538i	$-0.205445\pi$
$812$		0			0
$813$	4.81945	−	17.9349i	0.169026	−	0.629003i
$814$	13.1870			0.462202
$815$	23.0876			0.808722
$816$	7.87058	+	2.11498i	0.275525	+	0.0740391i
$817$			6.06673i			0.212248i
$818$	13.5926			0.475254
$819$		0			0
$820$	8.61981			0.301017
$821$			47.6242i			1.66209i	0.556202	+	0.831047i	$0.312258\pi$
$821$			47.6242i			1.66209i	−0.556202	+	0.831047i	$0.687742\pi$
$822$	−12.1142	−	3.25531i	−0.422530	−	0.113542i
$823$	−22.6266			−0.788712			−0.394356	−	0.918958i	$-0.629032\pi$
$823$	−22.6266			−0.788712			−0.394356	+	0.918958i	$0.629032\pi$
$824$	−6.82964			−0.237922
$825$	1.06922	−	3.97894i	0.0372255	−	0.138529i
$826$		0			0
$827$			40.2958i			1.40122i	0.713543	+	0.700612i	$0.247089\pi$
$827$			40.2958i			1.40122i	−0.713543	+	0.700612i	$0.752911\pi$
$828$	−6.95130	+	12.0001i	−0.241574	+	0.417033i
$829$		−	23.5997i		−	0.819652i	−0.912164	−	0.409826i	$-0.865589\pi$
$829$		−	23.5997i		−	0.819652i	0.912164	−	0.409826i	$-0.134411\pi$
$830$		−	12.9078i		−	0.448038i
$831$	6.79361	+	1.82558i	0.235668	+	0.0633286i
$832$			3.07531i			0.106617i
$833$		0			0
$834$	15.0514	+	4.04461i	0.521187	+	0.140053i
$835$	−6.03310			−0.208784
$836$	1.25360			0.0433568
$837$	−3.78875	+	3.77244i	−0.130958	+	0.130395i
$838$		−	17.5962i		−	0.607851i
$839$	−53.9263			−1.86174			−0.930871	−	0.365349i	$-0.880950\pi$
$839$	−53.9263			−1.86174			−0.930871	+	0.365349i	$0.880950\pi$
$840$		0			0
$841$	28.8359			0.994343
$842$		−	31.7006i		−	1.09248i
$843$	−0.810350	+	3.01559i	−0.0279099	+	0.103863i
$844$	−13.3767			−0.460446
$845$	−3.54245			−0.121864
$846$	−13.2632	+	22.8964i	−0.455998	+	0.787196i
$847$		0			0
$848$			12.2241i			0.419776i
$849$	4.68096	−	17.4195i	0.160650	−	0.597836i
$850$		−	4.70529i		−	0.161390i
$851$			25.6267i			0.878472i
$852$	−5.29040	+	19.6874i	−0.181246	+	0.674480i
$853$		−	7.89413i		−	0.270290i	−0.990826	−	0.135145i	$-0.956850\pi$
$853$		−	7.89413i		−	0.270290i	0.990826	−	0.135145i	$-0.0431500\pi$
$854$		0			0
$855$	0.792473	−	1.36806i	0.0271020	−	0.0467866i
$856$	−13.1216			−0.448486
$857$	4.65257			0.158929			0.0794643	−	0.996838i	$-0.474679\pi$
$857$	4.65257			0.158929			0.0794643	+	0.996838i	$0.474679\pi$
$858$	3.28819	−	12.2365i	0.112257	−	0.417747i
$859$		−	21.4003i		−	0.730167i	−0.930975	−	0.365084i	$-0.881040\pi$
$859$		−	21.4003i		−	0.730167i	0.930975	−	0.365084i	$-0.118960\pi$
$860$	11.5117			0.392547
$861$		0			0
$862$	−10.3717			−0.353261
$863$		−	6.53711i		−	0.222526i	−0.993791	−	0.111263i	$-0.964510\pi$
$863$		−	6.53711i		−	0.222526i	0.993791	−	0.111263i	$-0.0354896\pi$
$864$	3.68215	−	3.66630i	0.125269	−	0.124730i
$865$	−11.3332			−0.385342
$866$	41.0608			1.39530
$867$	−8.59725	−	2.31025i	−0.291978	−	0.0784602i
$868$		0			0
$869$			4.55308i			0.154453i
$870$	−0.677531	−	0.182066i	−0.0229705	−	0.00617262i
$871$		−	41.2473i		−	1.39761i
$872$		−	0.228271i		−	0.00773022i
$873$	−29.5383	+	50.9923i	−0.999719	+	1.72583i
$874$			2.43618i			0.0824049i
$875$		0			0
$876$	3.88830	−	14.4697i	0.131373	−	0.488886i
$877$	−12.1401			−0.409943			−0.204971	−	0.978768i	$-0.565710\pi$
$877$	−12.1401			−0.409943			−0.204971	+	0.978768i	$0.565710\pi$
$878$	−10.6387			−0.359038
$879$	35.1786	+	9.45319i	1.18654	+	0.318848i
$880$		−	2.37874i		−	0.0801873i
$881$	22.1583			0.746533			0.373266	−	0.927724i	$-0.378238\pi$
$881$	22.1583			0.746533			0.373266	+	0.927724i	$0.378238\pi$
$882$		0			0
$883$	−41.8759			−1.40924			−0.704618	−	0.709587i	$-0.748881\pi$
$883$	−41.8759			−1.40924			−0.704618	+	0.709587i	$0.748881\pi$
$884$		−	14.4702i		−	0.486686i
$885$	−14.2523	−	3.82989i	−0.479087	−	0.128740i
$886$	−20.3371			−0.683240
$887$	15.7929			0.530274			0.265137	−	0.964211i	$-0.414583\pi$
$887$	15.7929			0.530274			0.265137	+	0.964211i	$0.414583\pi$
$888$	2.49183	−	9.27295i	0.0836202	−	0.311180i
$889$		0			0
$890$		−	6.18780i		−	0.207416i
$891$	−18.5712	+	10.6510i	−0.622157	+	0.356821i
$892$			24.5364i			0.821539i
$893$			4.64826i			0.155548i
$894$	12.4358	+	3.34174i	0.415915	+	0.111765i
$895$			19.1994i			0.641764i
$896$		0			0
$897$	23.7796	+	6.39006i	0.793979	+	0.213358i
$898$	10.6792			0.356369
$899$	0.416776			0.0139003
$900$	−2.59592	−	1.50373i	−0.0865306	−	0.0501245i
$901$		−	57.5177i		−	1.91619i
$902$	−20.5043			−0.682719
$903$		0			0
$904$	−5.86352			−0.195018
$905$		−	23.8389i		−	0.792431i
$906$	8.73543	−	32.5076i	0.290215	−	1.07999i
$907$	−12.7671			−0.423926			−0.211963	−	0.977278i	$-0.567986\pi$
$907$	−12.7671			−0.423926			−0.211963	+	0.977278i	$0.567986\pi$
$908$	−20.2310			−0.671390
$909$	18.4238	+	10.6724i	0.611080	+	0.353980i
$910$		0			0
$911$		−	25.7485i		−	0.853086i	−0.904467	−	0.426543i	$-0.859731\pi$
$911$		−	25.7485i		−	0.853086i	0.904467	−	0.426543i	$-0.140269\pi$
$912$	0.236883	−	0.881524i	0.00784398	−	0.0291902i
$913$			30.7044i			1.01617i
$914$			1.04759i			0.0346513i
$915$	−3.37668	+	12.5658i	−0.111629	+	0.415412i
$916$		−	25.1923i		−	0.832377i
$917$		0			0
$918$	−17.3256	+	17.2510i	−0.571829	+	0.569368i
$919$	28.0971			0.926837			0.463418	−	0.886140i	$-0.346623\pi$
$919$	28.0971			0.926837			0.463418	+	0.886140i	$0.346623\pi$
$920$	4.62269			0.152406
$921$	−1.58330	+	5.89201i	−0.0521715	+	0.194148i
$922$		−	0.442723i		−	0.0145803i
$923$	36.1958			1.19140
$924$		0			0
$925$	−5.54367			−0.182275
$926$			1.83270i			0.0602264i
$927$	10.2700	−	17.7292i	0.337310	−	0.582302i
$928$	−0.405050			−0.0132964
$929$	52.5107			1.72282			0.861409	−	0.507911i	$-0.169582\pi$
$929$	52.5107			1.72282			0.861409	+	0.507911i	$0.169582\pi$
$930$	1.72113	+	0.462503i	0.0564382	+	0.0151661i
$931$		0			0
$932$			2.40100i			0.0786474i
$933$	−5.30562	−	1.42573i	−0.173698	−	0.0466762i
$934$		−	3.33622i		−	0.109164i
$935$			11.1927i			0.366039i
$936$	−7.98326	−	4.62445i	−0.260941	−	0.151155i
$937$		−	18.1141i		−	0.591762i	−0.955225	−	0.295881i	$-0.904387\pi$
$937$		−	18.1141i		−	0.591762i	0.955225	−	0.295881i	$-0.0956131\pi$
$938$		0			0
$939$	13.4607	−	50.0920i	0.439274	−	1.63469i
$940$	8.82018			0.287682
$941$	−2.94549			−0.0960201			−0.0480101	−	0.998847i	$-0.515288\pi$
$941$	−2.94549			−0.0960201			−0.0480101	+	0.998847i	$0.515288\pi$
$942$	25.4949	+	6.85099i	0.830669	+	0.223217i
$943$		−	39.8468i		−	1.29759i
$944$	−8.52051			−0.277319
$945$		0			0
$946$	−27.3834			−0.890312
$947$			27.5386i			0.894885i	0.894313	+	0.447442i	$0.147665\pi$
$947$			27.5386i			0.894885i	−0.894313	+	0.447442i	$0.852335\pi$
$948$	3.20169	+	0.860357i	0.103986	+	0.0279431i
$949$	−26.6029			−0.863566
$950$	−0.527004			−0.0170983
$951$	7.36739	−	27.4166i	0.238904	−	0.889045i
$952$		0			0
$953$			36.2980i			1.17581i	0.808931	+	0.587904i	$0.200047\pi$
$953$			36.2980i			1.17581i	−0.808931	+	0.587904i	$0.799953\pi$
$954$	−31.7326	−	18.3817i	−1.02738	−	0.595131i
$955$			10.4546i			0.338302i
$956$			11.6579i			0.377043i
$957$	1.61167	+	0.433088i	0.0520979	+	0.0139998i
$958$			39.9415i			1.29045i
$959$		0			0
$960$	−1.67271	−	0.449490i	−0.0539865	−	0.0145072i
$961$	29.9413			0.965847
$962$	−17.0485			−0.549666
$963$	19.7313	−	34.0625i	0.635834	−	1.09765i
$964$			14.9969i			0.483019i
$965$	20.1184			0.647636
$966$		0			0
$967$	26.5718			0.854493			0.427247	−	0.904135i	$-0.359484\pi$
$967$	26.5718			0.854493			0.427247	+	0.904135i	$0.359484\pi$
$968$		−	5.34159i		−	0.171685i
$969$	−1.11460	+	4.14782i	−0.0358062	+	0.133247i
$970$	19.6433			0.630708
$971$	−28.6200			−0.918461			−0.459230	−	0.888317i	$-0.651875\pi$
$971$	−28.6200			−0.918461			−0.459230	+	0.888317i	$0.651875\pi$
$972$	3.98044	+	15.0717i	0.127673	+	0.483425i
$973$		0			0
$974$			25.7832i			0.826149i
$975$	−1.38232	+	5.14411i	−0.0442698	+	0.164743i
$976$			7.51223i			0.240461i
$977$		−	30.2325i		−	0.967223i	−0.875283	−	0.483611i	$-0.839325\pi$
$977$		−	30.2325i		−	0.967223i	0.875283	−	0.483611i	$-0.160675\pi$
$978$	−10.3776	+	38.6188i	−0.331840	+	1.23489i
$979$			14.7192i			0.470427i
$980$		0			0
$981$	0.592571	+	0.343258i	0.0189193	+	0.0109594i
$982$	−24.6154			−0.785510
$983$	−7.02239			−0.223980			−0.111990	−	0.993709i	$-0.535722\pi$
$983$	−7.02239			−0.223980			−0.111990	+	0.993709i	$0.535722\pi$
$984$	−3.87452	+	14.4184i	−0.123515	+	0.459643i
$985$			20.5601i			0.655100i
$986$	1.90588			0.0606955
$987$		0			0
$988$	−1.62070			−0.0515614
$989$		−	53.2152i		−	1.69215i
$990$	6.17501	+	3.57699i	0.196255	+	0.113684i
$991$	33.0169			1.04882			0.524408	−	0.851467i	$-0.324287\pi$
$991$	33.0169			1.04882			0.524408	+	0.851467i	$0.324287\pi$
$992$	1.02895			0.0326692
$993$	−26.0873	−	7.01017i	−0.827855	−	0.222461i
$994$		0			0
$995$			5.70991i			0.181016i
$996$	21.5911	+	5.80195i	0.684140	+	0.183842i
$997$		−	49.4552i		−	1.56626i	−0.621857	−	0.783131i	$-0.713622\pi$
$997$		−	49.4552i		−	1.56626i	0.621857	−	0.783131i	$-0.286378\pi$
$998$			32.2260i			1.02009i
$999$	20.3248	+	20.4126i	0.643047	+	0.645827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.b.c.881.10	yes	16
3.2	odd	2		1470.2.b.d.881.7	yes	16
7.6	odd	2		1470.2.b.d.881.15	yes	16
21.20	even	2	inner	1470.2.b.c.881.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.b.c.881.2	✓	16	21.20	even	2	inner
1470.2.b.c.881.10	yes	16	1.1	even	1	trivial
1470.2.b.d.881.7	yes	16	3.2	odd	2
1470.2.b.d.881.15	yes	16	7.6	odd	2

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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.67271 - 0.449490i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(0.449490 - 1.67271i) q^{6} -1.00000i q^{8} +(2.59592 + 1.50373i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-1.67271 - 0.449490i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(0.449490 - 1.67271i) q^{6} -1.00000i q^{8} +(2.59592 + 1.50373i) q^{9} -1.00000i q^{10} +2.37874i q^{11} +(1.67271 + 0.449490i) q^{12} -3.07531i q^{13} +(1.67271 + 0.449490i) q^{15} +1.00000 q^{16} -4.70529 q^{17} +(-1.50373 + 2.59592i) q^{18} +0.527004i q^{19} +1.00000 q^{20} -2.37874 q^{22} -4.62269i q^{23} +(-0.449490 + 1.67271i) q^{24} +1.00000 q^{25} +3.07531 q^{26} +(-3.66630 - 3.68215i) q^{27} +0.405050i q^{29} +(-0.449490 + 1.67271i) q^{30} -1.02895i q^{31} +1.00000i q^{32} +(1.06922 - 3.97894i) q^{33} -4.70529i q^{34} +(-2.59592 - 1.50373i) q^{36} -5.54367 q^{37} -0.527004 q^{38} +(-1.38232 + 5.14411i) q^{39} +1.00000i q^{40} +8.61981 q^{41} +11.5117 q^{43} -2.37874i q^{44} +(-2.59592 - 1.50373i) q^{45} +4.62269 q^{46} +8.82018 q^{47} +(-1.67271 - 0.449490i) q^{48} +1.00000i q^{50} +(7.87058 + 2.11498i) q^{51} +3.07531i q^{52} +12.2241i q^{53} +(3.68215 - 3.66630i) q^{54} -2.37874i q^{55} +(0.236883 - 0.881524i) q^{57} -0.405050 q^{58} -8.52051 q^{59} +(-1.67271 - 0.449490i) q^{60} +7.51223i q^{61} +1.02895 q^{62} -1.00000 q^{64} +3.07531i q^{65} +(3.97894 + 1.06922i) q^{66} +13.4124 q^{67} +4.70529 q^{68} +(-2.07786 + 7.73243i) q^{69} +11.7698i q^{71} +(1.50373 - 2.59592i) q^{72} -8.65046i q^{73} -5.54367i q^{74} +(-1.67271 - 0.449490i) q^{75} -0.527004i q^{76} +(-5.14411 - 1.38232i) q^{78} +1.91407 q^{79} -1.00000 q^{80} +(4.47757 + 7.80714i) q^{81} +8.61981i q^{82} +12.9078 q^{83} +4.70529 q^{85} +11.5117i q^{86} +(0.182066 - 0.677531i) q^{87} +2.37874 q^{88} +6.18780 q^{89} +(1.50373 - 2.59592i) q^{90} +4.62269i q^{92} +(-0.462503 + 1.72113i) q^{93} +8.82018i q^{94} -0.527004i q^{95} +(0.449490 - 1.67271i) q^{96} +19.6433i q^{97} +(-3.57699 + 6.17501i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} - 16 q^{4} - 16 q^{5} + 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 - 16 * q^4 - 16 * q^5 + 8 * q^9	\( 16 q - 8 q^{3} - 16 q^{4} - 16 q^{5} + 8 q^{9} + 8 q^{12} + 8 q^{15} + 16 q^{16} + 48 q^{17} + 16 q^{20} + 16 q^{25} - 16 q^{26} - 8 q^{27} - 8 q^{36} + 16 q^{41} + 16 q^{43} - 8 q^{45} - 16 q^{46} + 32 q^{47} - 8 q^{48} + 16 q^{51} + 32 q^{57} + 16 q^{58} + 32 q^{59} - 8 q^{60} + 16 q^{62} - 16 q^{64} + 16 q^{67} - 48 q^{68} - 8 q^{75} - 32 q^{78} - 48 q^{79} - 16 q^{80} + 8 q^{81} + 48 q^{83} - 48 q^{85} + 16 q^{89} - 64 q^{93} - 8 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 - 16 * q^4 - 16 * q^5 + 8 * q^9 + 8 * q^12 + 8 * q^15 + 16 * q^16 + 48 * q^17 + 16 * q^20 + 16 * q^25 - 16 * q^26 - 8 * q^27 - 8 * q^36 + 16 * q^41 + 16 * q^43 - 8 * q^45 - 16 * q^46 + 32 * q^47 - 8 * q^48 + 16 * q^51 + 32 * q^57 + 16 * q^58 + 32 * q^59 - 8 * q^60 + 16 * q^62 - 16 * q^64 + 16 * q^67 - 48 * q^68 - 8 * q^75 - 32 * q^78 - 48 * q^79 - 16 * q^80 + 8 * q^81 + 48 * q^83 - 48 * q^85 + 16 * q^89 - 64 * q^93 - 8 * q^99

Introduction

L-functions

Modular forms

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Database

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