LMFDB - Embedded newform 1470.2.b.d.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			$-1.50062 - 0.864947i$ of defining polynomial
Character	$\chi$	$=$	1470.881
Dual form			1470.2.b.d.881.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.05539 - 1.37337i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(1.37337 - 1.05539i) q^{6} -1.00000i q^{8} +(-0.772290 + 2.89889i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-1.05539 - 1.37337i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(1.37337 - 1.05539i) q^{6} -1.00000i q^{8} +(-0.772290 + 2.89889i) q^{9} +1.00000i q^{10} +1.09853i q^{11} +(1.05539 + 1.37337i) q^{12} -3.66110i q^{13} +(-1.05539 - 1.37337i) q^{15} +1.00000 q^{16} -4.39664 q^{17} +(-2.89889 - 0.772290i) q^{18} -4.59752i q^{19} -1.00000 q^{20} -1.09853 q^{22} +1.51296i q^{23} +(-1.37337 + 1.05539i) q^{24} +1.00000 q^{25} +3.66110 q^{26} +(4.79632 - 1.99883i) q^{27} -1.85498i q^{29} +(1.37337 - 1.05539i) q^{30} +4.34954i q^{31} +1.00000i q^{32} +(1.50869 - 1.15938i) q^{33} -4.39664i q^{34} +(0.772290 - 2.89889i) q^{36} -11.7498 q^{37} +4.59752 q^{38} +(-5.02804 + 3.86390i) q^{39} -1.00000i q^{40} +6.08749 q^{41} -1.89061 q^{43} -1.09853i q^{44} +(-0.772290 + 2.89889i) q^{45} -1.51296 q^{46} +5.13720 q^{47} +(-1.05539 - 1.37337i) q^{48} +1.00000i q^{50} +(4.64019 + 6.03822i) q^{51} +3.66110i q^{52} -11.5604i q^{53} +(1.99883 + 4.79632i) q^{54} +1.09853i q^{55} +(-6.31410 + 4.85220i) q^{57} +1.85498 q^{58} -8.82794 q^{59} +(1.05539 + 1.37337i) q^{60} -11.4583i q^{61} -4.34954 q^{62} -1.00000 q^{64} -3.66110i q^{65} +(1.15938 + 1.50869i) q^{66} -12.2073 q^{67} +4.39664 q^{68} +(2.07786 - 1.59677i) q^{69} +2.24305i q^{71} +(2.89889 + 0.772290i) q^{72} -6.69260i q^{73} -11.7498i q^{74} +(-1.05539 - 1.37337i) q^{75} +4.59752i q^{76} +(-3.86390 - 5.02804i) q^{78} -14.9041 q^{79} +1.00000 q^{80} +(-7.80714 - 4.47757i) q^{81} +6.08749i q^{82} -15.3788 q^{83} -4.39664 q^{85} -1.89061i q^{86} +(-2.54758 + 1.95774i) q^{87} +1.09853 q^{88} +1.22806 q^{89} +(-2.89889 - 0.772290i) q^{90} -1.51296i q^{92} +(5.97353 - 4.59048i) q^{93} +5.13720i q^{94} -4.59752i q^{95} +(1.37337 - 1.05539i) q^{96} -8.60646i q^{97} +(-3.18453 - 0.848386i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.05539	−	1.37337i	−0.609332	−	0.792915i
$3$	−1.05539	−	1.37337i	−0.609332	−	0.792915i
$4$	−1.00000			−0.500000
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.37337	−	1.05539i	0.560676	−	0.430863i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−0.772290	+	2.89889i	−0.257430	+	0.966297i
$10$			1.00000i			0.316228i
$11$			1.09853i			0.331220i	0.986191	+	0.165610i	$0.0529593\pi$
$11$			1.09853i			0.331220i	−0.986191	+	0.165610i	$0.947041\pi$
$12$	1.05539	+	1.37337i	0.304666	+	0.396458i
$13$		−	3.66110i		−	1.01541i	−0.861532	−	0.507703i	$-0.830495\pi$
$13$		−	3.66110i		−	1.01541i	0.861532	−	0.507703i	$-0.169505\pi$
$14$		0			0
$15$	−1.05539	−	1.37337i	−0.272501	−	0.354603i
$16$	1.00000			0.250000
$17$	−4.39664			−1.06634			−0.533171	−	0.846007i	$-0.679000\pi$
$17$	−4.39664			−1.06634			−0.533171	+	0.846007i	$0.679000\pi$
$18$	−2.89889	−	0.772290i	−0.683275	−	0.182030i
$19$		−	4.59752i		−	1.05474i	−0.849634	−	0.527372i	$-0.823177\pi$
$19$		−	4.59752i		−	1.05474i	0.849634	−	0.527372i	$-0.176823\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	−1.09853			−0.234208
$23$			1.51296i			0.315474i	0.987481	+	0.157737i	$0.0504199\pi$
$23$			1.51296i			0.315474i	−0.987481	+	0.157737i	$0.949580\pi$
$24$	−1.37337	+	1.05539i	−0.280338	+	0.215431i
$25$	1.00000			0.200000
$26$	3.66110			0.718001
$27$	4.79632	−	1.99883i	0.923052	−	0.384675i
$28$		0			0
$29$		−	1.85498i		−	0.344462i	−0.985057	−	0.172231i	$-0.944902\pi$
$29$		−	1.85498i		−	0.344462i	0.985057	−	0.172231i	$-0.0550975\pi$
$30$	1.37337	−	1.05539i	0.250742	−	0.192688i
$31$			4.34954i			0.781201i	0.920560	+	0.390600i	$0.127733\pi$
$31$			4.34954i			0.781201i	−0.920560	+	0.390600i	$0.872267\pi$
$32$			1.00000i			0.176777i
$33$	1.50869	−	1.15938i	0.262630	−	0.201823i
$34$		−	4.39664i		−	0.754018i
$35$		0			0
$36$	0.772290	−	2.89889i	0.128715	−	0.483148i
$37$	−11.7498			−1.93166			−0.965828	−	0.259184i	$-0.916546\pi$
$37$	−11.7498			−1.93166			−0.965828	+	0.259184i	$0.916546\pi$
$38$	4.59752			0.745817
$39$	−5.02804	+	3.86390i	−0.805131	+	0.618719i
$40$		−	1.00000i		−	0.158114i
$41$	6.08749			0.950706			0.475353	−	0.879795i	$-0.342320\pi$
$41$	6.08749			0.950706			0.475353	+	0.879795i	$0.342320\pi$
$42$		0			0
$43$	−1.89061			−0.288315			−0.144157	−	0.989555i	$-0.546047\pi$
$43$	−1.89061			−0.288315			−0.144157	+	0.989555i	$0.546047\pi$
$44$		−	1.09853i		−	0.165610i
$45$	−0.772290	+	2.89889i	−0.115126	+	0.432141i
$46$	−1.51296			−0.223074
$47$	5.13720			0.749338			0.374669	−	0.927159i	$-0.377756\pi$
$47$	5.13720			0.749338			0.374669	+	0.927159i	$0.377756\pi$
$48$	−1.05539	−	1.37337i	−0.152333	−	0.198229i
$49$		0			0
$50$			1.00000i			0.141421i
$51$	4.64019	+	6.03822i	0.649756	+	0.845519i
$52$			3.66110i			0.507703i
$53$		−	11.5604i		−	1.58795i	−0.607953	−	0.793973i	$-0.708009\pi$
$53$		−	11.5604i		−	1.58795i	0.607953	−	0.793973i	$-0.291991\pi$
$54$	1.99883	+	4.79632i	0.272006	+	0.652696i
$55$			1.09853i			0.148126i
$56$		0			0
$57$	−6.31410	+	4.85220i	−0.836323	+	0.642689i
$58$	1.85498			0.243571
$59$	−8.82794			−1.14930			−0.574650	−	0.818399i	$-0.694862\pi$
$59$	−8.82794			−1.14930			−0.574650	+	0.818399i	$0.694862\pi$
$60$	1.05539	+	1.37337i	0.136251	+	0.177301i
$61$		−	11.4583i		−	1.46709i	−0.679641	−	0.733544i	$-0.737865\pi$
$61$		−	11.4583i		−	1.46709i	0.679641	−	0.733544i	$-0.262135\pi$
$62$	−4.34954			−0.552392
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	3.66110i		−	0.454104i
$66$	1.15938	+	1.50869i	0.142710	+	0.185707i
$67$	−12.2073			−1.49136			−0.745682	−	0.666302i	$-0.767876\pi$
$67$	−12.2073			−1.49136			−0.745682	+	0.666302i	$0.767876\pi$
$68$	4.39664			0.533171
$69$	2.07786	−	1.59677i	0.250145	−	0.192228i
$70$		0			0
$71$			2.24305i			0.266201i	0.991103	+	0.133101i	$0.0424933\pi$
$71$			2.24305i			0.266201i	−0.991103	+	0.133101i	$0.957507\pi$
$72$	2.89889	+	0.772290i	0.341638	+	0.0910152i
$73$		−	6.69260i		−	0.783309i	−0.920112	−	0.391655i	$-0.871903\pi$
$73$		−	6.69260i		−	0.783309i	0.920112	−	0.391655i	$-0.128097\pi$
$74$		−	11.7498i		−	1.36589i
$75$	−1.05539	−	1.37337i	−0.121866	−	0.158583i
$76$			4.59752i			0.527372i
$77$		0			0
$78$	−3.86390	−	5.02804i	−0.437501	−	0.569314i
$79$	−14.9041			−1.67684			−0.838421	−	0.545023i	$-0.816521\pi$
$79$	−14.9041			−1.67684			−0.838421	+	0.545023i	$0.816521\pi$
$80$	1.00000			0.111803
$81$	−7.80714	−	4.47757i	−0.867460	−	0.497508i
$82$			6.08749i			0.672251i
$83$	−15.3788			−1.68805			−0.844023	−	0.536306i	$-0.819819\pi$
$83$	−15.3788			−1.68805			−0.844023	+	0.536306i	$0.819819\pi$
$84$		0			0
$85$	−4.39664			−0.476883
$86$		−	1.89061i		−	0.203869i
$87$	−2.54758	+	1.95774i	−0.273129	+	0.209892i
$88$	1.09853			0.117104
$89$	1.22806			0.130174			0.0650870	−	0.997880i	$-0.479268\pi$
$89$	1.22806			0.130174			0.0650870	+	0.997880i	$0.479268\pi$
$90$	−2.89889	−	0.772290i	−0.305570	−	0.0814065i
$91$		0			0
$92$		−	1.51296i		−	0.157737i
$93$	5.97353	−	4.59048i	0.619426	−	0.476010i
$94$			5.13720i			0.529862i
$95$		−	4.59752i		−	0.471696i
$96$	1.37337	−	1.05539i	0.140169	−	0.107716i
$97$		−	8.60646i		−	0.873853i	−0.899497	−	0.436927i	$-0.856067\pi$
$97$		−	8.60646i		−	0.873853i	0.899497	−	0.436927i	$-0.143933\pi$
$98$		0			0
$99$	−3.18453	−	0.848386i	−0.320057	−	0.0852660i
$100$	−1.00000			−0.100000
$101$	−9.56243			−0.951497			−0.475748	−	0.879581i	$-0.657823\pi$
$101$	−9.56243			−0.951497			−0.475748	+	0.879581i	$0.657823\pi$
$102$	−6.03822	+	4.64019i	−0.597872	+	0.459447i
$103$		−	15.8943i		−	1.56611i	−0.621952	−	0.783055i	$-0.713660\pi$
$103$		−	15.8943i		−	1.56611i	0.621952	−	0.783055i	$-0.286340\pi$
$104$	−3.66110			−0.359000
$105$		0			0
$106$	11.5604			1.12285
$107$		−	6.61505i		−	0.639501i	−0.947502	−	0.319751i	$-0.896401\pi$
$107$		−	6.61505i		−	0.639501i	0.947502	−	0.319751i	$-0.103599\pi$
$108$	−4.79632	+	1.99883i	−0.461526	+	0.192338i
$109$	10.9297			1.04688			0.523439	−	0.852063i	$-0.324649\pi$
$109$	10.9297			1.04688			0.523439	+	0.852063i	$0.324649\pi$
$110$	−1.09853			−0.104741
$111$	12.4007	+	16.1368i	1.17702	+	1.53164i
$112$		0			0
$113$			17.0903i			1.60772i	0.594818	+	0.803860i	$0.297224\pi$
$113$			17.0903i			1.60772i	−0.594818	+	0.803860i	$0.702776\pi$
$114$	−4.85220	−	6.31410i	−0.454450	−	0.591370i
$115$			1.51296i			0.141084i
$116$			1.85498i			0.172231i
$117$	10.6131	+	2.82743i	0.981184	+	0.261396i
$118$		−	8.82794i		−	0.812677i
$119$		0			0
$120$	−1.37337	+	1.05539i	−0.125371	+	0.0963438i
$121$	9.79322			0.890293
$122$	11.4583			1.03739
$123$	−6.42469	−	8.36037i	−0.579295	−	0.753829i
$124$		−	4.34954i		−	0.390600i
$125$	1.00000			0.0894427
$126$		0			0
$127$	10.2688			0.911208			0.455604	−	0.890183i	$-0.349423\pi$
$127$	10.2688			0.911208			0.455604	+	0.890183i	$0.349423\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	1.99533	+	2.59650i	0.175679	+	0.228609i
$130$	3.66110			0.321100
$131$	−15.5240			−1.35634			−0.678169	−	0.734906i	$-0.737226\pi$
$131$	−15.5240			−1.35634			−0.678169	+	0.734906i	$0.737226\pi$
$132$	−1.50869	+	1.15938i	−0.131315	+	0.100912i
$133$		0			0
$134$		−	12.2073i		−	1.05455i
$135$	4.79632	−	1.99883i	0.412801	−	0.172032i
$136$			4.39664i			0.377009i
$137$		−	4.68182i		−	0.399995i	−0.979796	−	0.199997i	$-0.935907\pi$
$137$		−	4.68182i		−	0.399995i	0.979796	−	0.199997i	$-0.0640934\pi$
$138$	1.59677	+	2.07786i	0.135926	+	0.176879i
$139$			8.58014i			0.727758i	0.931446	+	0.363879i	$0.118548\pi$
$139$			8.58014i			0.727758i	−0.931446	+	0.363879i	$0.881452\pi$
$140$		0			0
$141$	−5.42177	−	7.05528i	−0.456595	−	0.594161i
$142$	−2.24305			−0.188233
$143$	4.02184			0.336323
$144$	−0.772290	+	2.89889i	−0.0643575	+	0.241574i
$145$		−	1.85498i		−	0.154048i
$146$	6.69260			0.553883
$147$		0			0
$148$	11.7498			0.965828
$149$		−	10.0442i		−	0.822850i	−0.911444	−	0.411425i	$-0.865031\pi$
$149$		−	10.0442i		−	0.822850i	0.911444	−	0.411425i	$-0.134969\pi$
$150$	1.37337	−	1.05539i	0.112135	−	0.0861725i
$151$	−8.52641			−0.693869			−0.346935	−	0.937889i	$-0.612777\pi$
$151$	−8.52641			−0.693869			−0.346935	+	0.937889i	$0.612777\pi$
$152$	−4.59752			−0.372908
$153$	3.39548	−	12.7454i	0.274508	−	1.03040i
$154$		0			0
$155$			4.34954i			0.349364i
$156$	5.02804	−	3.86390i	0.402566	−	0.309360i
$157$		−	18.2619i		−	1.45746i	−0.684802	−	0.728729i	$-0.740111\pi$
$157$		−	18.2619i		−	1.45746i	0.684802	−	0.728729i	$-0.259889\pi$
$158$		−	14.9041i		−	1.18571i
$159$	−15.8767	+	12.2008i	−1.25911	+	0.967586i
$160$			1.00000i			0.0790569i
$161$		0			0
$162$	4.47757	−	7.80714i	0.351791	−	0.613387i
$163$	6.82233			0.534366			0.267183	−	0.963646i	$-0.413907\pi$
$163$	6.82233			0.534366			0.267183	+	0.963646i	$0.413907\pi$
$164$	−6.08749			−0.475353
$165$	1.50869	−	1.15938i	0.117452	−	0.0902580i
$166$		−	15.3788i		−	1.19363i
$167$	11.9700			0.926270			0.463135	−	0.886288i	$-0.346725\pi$
$167$	11.9700			0.926270			0.463135	+	0.886288i	$0.346725\pi$
$168$		0			0
$169$	−0.403652			−0.0310502
$170$		−	4.39664i		−	0.337207i
$171$	13.3277	+	3.55062i	1.01920	+	0.271523i
$172$	1.89061			0.144157
$173$	−23.6045			−1.79462			−0.897310	−	0.441400i	$-0.854482\pi$
$173$	−23.6045			−1.79462			−0.897310	+	0.441400i	$0.854482\pi$
$174$	−1.95774	−	2.54758i	−0.148416	−	0.193132i
$175$		0			0
$176$			1.09853i			0.0828051i
$177$	9.31694	+	12.1240i	0.700304	+	0.911297i
$178$			1.22806i			0.0920469i
$179$			15.5223i			1.16019i	0.814549	+	0.580095i	$0.196984\pi$
$179$			15.5223i			1.16019i	−0.814549	+	0.580095i	$0.803016\pi$
$180$	0.772290	−	2.89889i	0.0575631	−	0.216071i
$181$			20.4343i			1.51887i	0.650585	+	0.759433i	$0.274524\pi$
$181$			20.4343i			1.51887i	−0.650585	+	0.759433i	$0.725476\pi$
$182$		0			0
$183$	−15.7365	+	12.0930i	−1.16328	+	0.893944i
$184$	1.51296			0.111537
$185$	−11.7498			−0.863863
$186$	4.59048	+	5.97353i	0.336590	+	0.438001i
$187$		−	4.82986i		−	0.353194i
$188$	−5.13720			−0.374669
$189$		0			0
$190$	4.59752			0.333539
$191$			9.13497i			0.660983i	0.943809	+	0.330492i	$0.107215\pi$
$191$			9.13497i			0.660983i	−0.943809	+	0.330492i	$0.892785\pi$
$192$	1.05539	+	1.37337i	0.0761665	+	0.0991144i
$193$	18.8039			1.35354			0.676769	−	0.736196i	$-0.263380\pi$
$193$	18.8039			1.35354			0.676769	+	0.736196i	$0.263380\pi$
$194$	8.60646			0.617908
$195$	−5.02804	+	3.86390i	−0.360066	+	0.276700i
$196$		0			0
$197$		−	2.95703i		−	0.210680i	−0.994436	−	0.105340i	$-0.966407\pi$
$197$		−	2.95703i		−	0.210680i	0.994436	−	0.105340i	$-0.0335930\pi$
$198$	0.848386	−	3.18453i	0.0602922	−	0.226315i
$199$			13.3017i			0.942935i	0.881884	+	0.471467i	$0.156275\pi$
$199$			13.3017i			0.942935i	−0.881884	+	0.471467i	$0.843725\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	12.8835	+	16.7652i	0.908735	+	1.18253i
$202$		−	9.56243i		−	0.672810i
$203$		0			0
$204$	−4.64019	−	6.03822i	−0.324878	−	0.422760i
$205$	6.08749			0.425169
$206$	15.8943			1.10741
$207$	−4.38591	−	1.16845i	−0.304842	−	0.0812125i
$208$		−	3.66110i		−	0.253852i
$209$	5.05053			0.349353
$210$		0			0
$211$	9.64158			0.663754			0.331877	−	0.943323i	$-0.392318\pi$
$211$	9.64158			0.663754			0.331877	+	0.943323i	$0.392318\pi$
$212$			11.5604i			0.793973i
$213$	3.08054	−	2.36730i	0.211075	−	0.162205i
$214$	6.61505			0.452196
$215$	−1.89061			−0.128938
$216$	−1.99883	−	4.79632i	−0.136003	−	0.326348i
$217$		0			0
$218$			10.9297i			0.740254i
$219$	−9.19141	+	7.06332i	−0.621098	+	0.477295i
$220$		−	1.09853i		−	0.0740631i
$221$			16.0965i			1.08277i
$222$	−16.1368	+	12.4007i	−1.08303	+	0.832278i
$223$		−	9.34880i		−	0.626042i	−0.949746	−	0.313021i	$-0.898659\pi$
$223$		−	9.34880i		−	0.626042i	0.949746	−	0.313021i	$-0.101341\pi$
$224$		0			0
$225$	−0.772290	+	2.89889i	−0.0514860	+	0.193259i
$226$	−17.0903			−1.13683
$227$	−1.90274			−0.126289			−0.0631446	−	0.998004i	$-0.520113\pi$
$227$	−1.90274			−0.126289			−0.0631446	+	0.998004i	$0.520113\pi$
$228$	6.31410	−	4.85220i	0.418162	−	0.321345i
$229$		−	5.81373i		−	0.384182i	−0.981377	−	0.192091i	$-0.938473\pi$
$229$		−	5.81373i		−	0.384182i	0.981377	−	0.192091i	$-0.0615269\pi$
$230$	−1.51296			−0.0997618
$231$		0			0
$232$	−1.85498			−0.121786
$233$		−	12.6237i		−	0.827007i	−0.910503	−	0.413503i	$-0.864305\pi$
$233$		−	12.6237i		−	0.827007i	0.910503	−	0.413503i	$-0.135695\pi$
$234$	−2.82743	+	10.6131i	−0.184835	+	0.693802i
$235$	5.13720			0.335114
$236$	8.82794			0.574650
$237$	15.7297	+	20.4688i	1.02175	+	1.32959i
$238$		0			0
$239$			2.59987i			0.168171i	0.996459	+	0.0840857i	$0.0267970\pi$
$239$			2.59987i			0.168171i	−0.996459	+	0.0840857i	$0.973203\pi$
$240$	−1.05539	−	1.37337i	−0.0681253	−	0.0886506i
$241$		−	5.59136i		−	0.360171i	−0.983651	−	0.180086i	$-0.942363\pi$
$241$		−	5.59136i		−	0.360171i	0.983651	−	0.180086i	$-0.0576375\pi$
$242$			9.79322i			0.629532i
$243$	2.09024	+	15.4477i	0.134089	+	0.990969i
$244$			11.4583i			0.733544i
$245$		0			0
$246$	8.36037	−	6.42469i	0.533038	−	0.409624i
$247$	−16.8320			−1.07099
$248$	4.34954			0.276196
$249$	16.2307	+	21.1208i	1.02858	+	1.33848i
$250$			1.00000i			0.0632456i
$251$	17.0387			1.07547			0.537737	−	0.843113i	$-0.319280\pi$
$251$	17.0387			1.07547			0.537737	+	0.843113i	$0.319280\pi$
$252$		0			0
$253$	−1.66204			−0.104492
$254$			10.2688i			0.644321i
$255$	4.64019	+	6.03822i	0.290580	+	0.378128i
$256$	1.00000			0.0625000
$257$	22.0807			1.37736			0.688678	−	0.725068i	$-0.258192\pi$
$257$	22.0807			1.37736			0.688678	+	0.725068i	$0.258192\pi$
$258$	−2.59650	+	1.99533i	−0.161651	+	0.124224i
$259$		0			0
$260$			3.66110i			0.227052i
$261$	5.37740	+	1.43259i	0.332853	+	0.0886748i
$262$		−	15.5240i		−	0.959075i
$263$			24.6207i			1.51818i	0.650986	+	0.759090i	$0.274356\pi$
$263$			24.6207i			1.51818i	−0.650986	+	0.759090i	$0.725644\pi$
$264$	−1.15938	−	1.50869i	−0.0713552	−	0.0928536i
$265$		−	11.5604i		−	0.710151i
$266$		0			0
$267$	−1.29609	−	1.68658i	−0.0793192	−	0.103217i
$268$	12.2073			0.745682
$269$	−6.74076			−0.410992			−0.205496	−	0.978658i	$-0.565881\pi$
$269$	−6.74076			−0.410992			−0.205496	+	0.978658i	$0.565881\pi$
$270$	1.99883	+	4.79632i	0.121645	+	0.291895i
$271$			23.0387i			1.39950i	0.714387	+	0.699751i	$0.246706\pi$
$271$			23.0387i			1.39950i	−0.714387	+	0.699751i	$0.753294\pi$
$272$	−4.39664			−0.266586
$273$		0			0
$274$	4.68182			0.282839
$275$			1.09853i			0.0662441i
$276$	−2.07786	+	1.59677i	−0.125072	+	0.0961142i
$277$	14.5920			0.876746			0.438373	−	0.898793i	$-0.355555\pi$
$277$	14.5920			0.876746			0.438373	+	0.898793i	$0.355555\pi$
$278$	−8.58014			−0.514603
$279$	−12.6088	−	3.35911i	−0.754872	−	0.201105i
$280$		0			0
$281$		−	29.4382i		−	1.75613i	−0.478538	−	0.878067i	$-0.658833\pi$
$281$		−	29.4382i		−	1.75613i	0.478538	−	0.878067i	$-0.341167\pi$
$282$	7.05528	−	5.42177i	0.420136	−	0.322862i
$283$		−	26.2275i		−	1.55906i	−0.626362	−	0.779532i	$-0.715457\pi$
$283$		−	26.2275i		−	1.55906i	0.626362	−	0.779532i	$-0.284543\pi$
$284$		−	2.24305i		−	0.133101i
$285$	−6.31410	+	4.85220i	−0.374015	+	0.287419i
$286$			4.02184i			0.237816i
$287$		0			0
$288$	−2.89889	−	0.772290i	−0.170819	−	0.0455076i
$289$	2.33046			0.137086
$290$	1.85498			0.108928
$291$	−11.8198	+	9.08320i	−0.692892	+	0.532466i
$292$			6.69260i			0.391655i
$293$	−16.9845			−0.992248			−0.496124	−	0.868252i	$-0.665244\pi$
$293$	−16.9845			−0.992248			−0.496124	+	0.868252i	$0.665244\pi$
$294$		0			0
$295$	−8.82794			−0.513982
$296$			11.7498i			0.682944i
$297$	2.19578	+	5.26892i	0.127412	+	0.305734i
$298$	10.0442			0.581843
$299$	5.53910			0.320335
$300$	1.05539	+	1.37337i	0.0609332	+	0.0792915i
$301$		0			0
$302$		−	8.52641i		−	0.490640i
$303$	10.0921	+	13.1327i	0.579777	+	0.754457i
$304$		−	4.59752i		−	0.263686i
$305$		−	11.4583i		−	0.656102i
$306$	12.7454	+	3.39548i	0.728605	+	0.194107i
$307$			2.71276i			0.154825i	0.996999	+	0.0774126i	$0.0246659\pi$
$307$			2.71276i			0.154825i	−0.996999	+	0.0774126i	$0.975334\pi$
$308$		0			0
$309$	−21.8287	+	16.7747i	−1.24179	+	0.954281i
$310$	−4.34954			−0.247037
$311$	21.6732			1.22897			0.614486	−	0.788927i	$-0.289363\pi$
$311$	21.6732			1.22897			0.614486	+	0.788927i	$0.289363\pi$
$312$	3.86390	+	5.02804i	0.218750	+	0.284657i
$313$			4.66085i			0.263447i	0.991287	+	0.131723i	$0.0420510\pi$
$313$			4.66085i			0.263447i	−0.991287	+	0.131723i	$0.957949\pi$
$314$	18.2619			1.03058
$315$		0			0
$316$	14.9041			0.838421
$317$			7.13944i			0.400991i	0.979695	+	0.200496i	$0.0642552\pi$
$317$			7.13944i			0.400991i	−0.979695	+	0.200496i	$0.935745\pi$
$318$	−12.2008	−	15.8767i	−0.684186	−	0.890323i
$319$	2.03776			0.114093
$320$	−1.00000			−0.0559017
$321$	−9.08492	+	6.98148i	−0.507071	+	0.389668i
$322$		0			0
$323$			20.2137i			1.12472i
$324$	7.80714	+	4.47757i	0.433730	+	0.248754i
$325$		−	3.66110i		−	0.203081i
$326$			6.82233i			0.377854i
$327$	−11.5352	−	15.0106i	−0.637896	−	0.830086i
$328$		−	6.08749i		−	0.336125i
$329$		0			0
$330$	1.15938	+	1.50869i	0.0638220	+	0.0830508i
$331$	−6.57307			−0.361288			−0.180644	−	0.983549i	$-0.557818\pi$
$331$	−6.57307			−0.361288			−0.180644	+	0.983549i	$0.557818\pi$
$332$	15.3788			0.844023
$333$	9.07425	−	34.0614i	0.497266	−	1.86655i
$334$			11.9700i			0.654972i
$335$	−12.2073			−0.666958
$336$		0			0
$337$	15.0962			0.822341			0.411170	−	0.911558i	$-0.365120\pi$
$337$	15.0962			0.822341			0.411170	+	0.911558i	$0.365120\pi$
$338$		−	0.403652i		−	0.0219558i
$339$	23.4713	−	18.0370i	1.27479	−	0.979635i
$340$	4.39664			0.238441
$341$	−4.77812			−0.258750
$342$	−3.55062	+	13.3277i	−0.191996	+	0.720681i
$343$		0			0
$344$			1.89061i			0.101935i
$345$	2.07786	−	1.59677i	0.111868	−	0.0859672i
$346$		−	23.6045i		−	1.26899i
$347$			34.9057i			1.87384i	0.349548	+	0.936918i	$0.386335\pi$
$347$			34.9057i			1.87384i	−0.349548	+	0.936918i	$0.613665\pi$
$348$	2.54758	−	1.95774i	0.136565	−	0.104946i
$349$			11.4710i			0.614029i	0.951705	+	0.307014i	$0.0993300\pi$
$349$			11.4710i			0.614029i	−0.951705	+	0.307014i	$0.900670\pi$
$350$		0			0
$351$	−7.31792	−	17.5598i	−0.390602	−	0.937273i
$352$	−1.09853			−0.0585520
$353$	−5.63774			−0.300067			−0.150033	−	0.988681i	$-0.547938\pi$
$353$	−5.63774			−0.300067			−0.150033	+	0.988681i	$0.547938\pi$
$354$	−12.1240	+	9.31694i	−0.644384	+	0.495190i
$355$			2.24305i			0.119049i
$356$	−1.22806			−0.0650870
$357$		0			0
$358$	−15.5223			−0.820378
$359$		−	19.5879i		−	1.03381i	−0.856042	−	0.516906i	$-0.827084\pi$
$359$		−	19.5879i		−	1.03381i	0.856042	−	0.516906i	$-0.172916\pi$
$360$	2.89889	+	0.772290i	0.152785	+	0.0407032i
$361$	−2.13723			−0.112486
$362$	−20.4343			−1.07400
$363$	−10.3357	−	13.4497i	−0.542484	−	0.705927i
$364$		0			0
$365$		−	6.69260i		−	0.350307i
$366$	−12.0930	−	15.7365i	−0.632114	−	0.822561i
$367$			5.84158i			0.304928i	0.988309	+	0.152464i	$0.0487208\pi$
$367$			5.84158i			0.304928i	−0.988309	+	0.152464i	$0.951279\pi$
$368$			1.51296i			0.0788686i
$369$	−4.70131	+	17.6470i	−0.244740	+	0.918664i
$370$		−	11.7498i		−	0.610843i
$371$		0			0
$372$	−5.97353	+	4.59048i	−0.309713	+	0.238005i
$373$	10.8349			0.561010			0.280505	−	0.959853i	$-0.409498\pi$
$373$	10.8349			0.561010			0.280505	+	0.959853i	$0.409498\pi$
$374$	4.82986			0.249746
$375$	−1.05539	−	1.37337i	−0.0545003	−	0.0709205i
$376$		−	5.13720i		−	0.264931i
$377$	−6.79128			−0.349769
$378$		0			0
$379$	24.1798			1.24203			0.621016	−	0.783798i	$-0.286720\pi$
$379$	24.1798			1.24203			0.621016	+	0.783798i	$0.286720\pi$
$380$			4.59752i			0.235848i
$381$	−10.8376	−	14.1028i	−0.555228	−	0.722511i
$382$	−9.13497			−0.467386
$383$	−6.71052			−0.342892			−0.171446	−	0.985194i	$-0.554844\pi$
$383$	−6.71052			−0.342892			−0.171446	+	0.985194i	$0.554844\pi$
$384$	−1.37337	+	1.05539i	−0.0700845	+	0.0538578i
$385$		0			0
$386$			18.8039i			0.957096i
$387$	1.46010	−	5.48066i	0.0742209	−	0.278598i
$388$			8.60646i			0.436927i
$389$		−	15.7508i		−	0.798598i	−0.916821	−	0.399299i	$-0.869254\pi$
$389$		−	15.7508i		−	0.798598i	0.916821	−	0.399299i	$-0.130746\pi$
$390$	−3.86390	−	5.02804i	−0.195656	−	0.254605i
$391$		−	6.65195i		−	0.336404i
$392$		0			0
$393$	16.3839	+	21.3202i	0.826459	+	1.07546i
$394$	2.95703			0.148973
$395$	−14.9041			−0.749907
$396$	3.18453	+	0.848386i	0.160029	+	0.0426330i
$397$		−	8.50643i		−	0.426925i	−0.976951	−	0.213463i	$-0.931526\pi$
$397$		−	8.50643i		−	0.426925i	0.976951	−	0.213463i	$-0.0684742\pi$
$398$	−13.3017			−0.666756
$399$		0			0
$400$	1.00000			0.0500000
$401$			37.0725i			1.85131i	0.378365	+	0.925657i	$0.376487\pi$
$401$			37.0725i			1.85131i	−0.378365	+	0.925657i	$0.623513\pi$
$402$	−16.7652	+	12.8835i	−0.836172	+	0.642573i
$403$	15.9241			0.793236
$404$	9.56243			0.475748
$405$	−7.80714	−	4.47757i	−0.387940	−	0.222492i
$406$		0			0
$407$		−	12.9076i		−	0.639804i
$408$	6.03822	−	4.64019i	0.298936	−	0.229723i
$409$		−	20.0437i		−	0.991099i	−0.868580	−	0.495549i	$-0.834967\pi$
$409$		−	20.0437i		−	0.991099i	0.868580	−	0.495549i	$-0.165033\pi$
$410$			6.08749i			0.300640i
$411$	−6.42987	+	4.94116i	−0.317162	+	0.243730i
$412$			15.8943i			0.783055i
$413$		0			0
$414$	1.16845	−	4.38591i	0.0574259	−	0.215556i
$415$	−15.3788			−0.754918
$416$	3.66110			0.179500
$417$	11.7837	−	9.05543i	0.577051	−	0.443446i
$418$			5.05053i			0.247030i
$419$	−17.7909			−0.869141			−0.434570	−	0.900638i	$-0.643100\pi$
$419$	−17.7909			−0.869141			−0.434570	+	0.900638i	$0.643100\pi$
$420$		0			0
$421$	12.4583			0.607182			0.303591	−	0.952802i	$-0.401814\pi$
$421$	12.4583			0.607182			0.303591	+	0.952802i	$0.401814\pi$
$422$			9.64158i			0.469345i
$423$	−3.96741	+	14.8922i	−0.192902	+	0.724083i
$424$	−11.5604			−0.561424
$425$	−4.39664			−0.213268
$426$	2.36730	+	3.08054i	0.114696	+	0.149253i
$427$		0			0
$428$			6.61505i			0.319751i
$429$	−4.24462	−	5.52348i	−0.204932	−	0.266676i
$430$		−	1.89061i		−	0.0911732i
$431$			30.1606i			1.45278i	0.687281	+	0.726392i	$0.258804\pi$
$431$			30.1606i			1.45278i	−0.687281	+	0.726392i	$0.741196\pi$
$432$	4.79632	−	1.99883i	0.230763	−	0.0961688i
$433$			11.8201i			0.568039i	0.958819	+	0.284019i	$0.0916680\pi$
$433$			11.8201i			0.568039i	−0.958819	+	0.284019i	$0.908332\pi$
$434$		0			0
$435$	−2.54758	+	1.95774i	−0.122147	+	0.0938664i
$436$	−10.9297			−0.523439
$437$	6.95588			0.332745
$438$	−7.06332	−	9.19141i	−0.337499	−	0.439183i
$439$		−	15.2453i		−	0.727617i	−0.931474	−	0.363809i	$-0.881476\pi$
$439$		−	15.2453i		−	0.727617i	0.931474	−	0.363809i	$-0.118524\pi$
$440$	1.09853			0.0523705
$441$		0			0
$442$	−16.0965			−0.765634
$443$		−	6.21871i		−	0.295460i	−0.989028	−	0.147730i	$-0.952803\pi$
$443$		−	6.21871i		−	0.295460i	0.989028	−	0.147730i	$-0.0471967\pi$
$444$	−12.4007	−	16.1368i	−0.588510	−	0.765820i
$445$	1.22806			0.0582156
$446$	9.34880			0.442678
$447$	−13.7944	+	10.6005i	−0.652451	+	0.501389i
$448$		0			0
$449$		−	18.1053i		−	0.854443i	−0.904147	−	0.427221i	$-0.859493\pi$
$449$		−	18.1053i		−	0.854443i	0.904147	−	0.427221i	$-0.140507\pi$
$450$	−2.89889	−	0.772290i	−0.136655	−	0.0364061i
$451$			6.68731i			0.314893i
$452$		−	17.0903i		−	0.803860i
$453$	8.99871	+	11.7099i	0.422796	+	0.550180i
$454$		−	1.90274i		−	0.0893000i
$455$		0			0
$456$	4.85220	+	6.31410i	0.227225	+	0.295685i
$457$	−25.2516			−1.18122			−0.590609	−	0.806958i	$-0.701113\pi$
$457$	−25.2516			−1.18122			−0.590609	+	0.806958i	$0.701113\pi$
$458$	5.81373			0.271658
$459$	−21.0877	+	8.78814i	−0.984289	+	0.410195i
$460$		−	1.51296i		−	0.0705422i
$461$	−0.942963			−0.0439181			−0.0219591	−	0.999759i	$-0.506990\pi$
$461$	−0.942963			−0.0439181			−0.0219591	+	0.999759i	$0.506990\pi$
$462$		0			0
$463$	−8.47895			−0.394050			−0.197025	−	0.980398i	$-0.563128\pi$
$463$	−8.47895			−0.394050			−0.197025	+	0.980398i	$0.563128\pi$
$464$		−	1.85498i		−	0.0861155i
$465$	5.97353	−	4.59048i	0.277016	−	0.212878i
$466$	12.6237			0.584782
$467$	−9.23547			−0.427367			−0.213683	−	0.976903i	$-0.568546\pi$
$467$	−9.23547			−0.427367			−0.213683	+	0.976903i	$0.568546\pi$
$468$	−10.6131	−	2.82743i	−0.490592	−	0.130698i
$469$		0			0
$470$			5.13720i			0.236961i
$471$	−25.0803	+	19.2735i	−1.15564	+	0.888075i
$472$			8.82794i			0.406339i
$473$		−	2.07690i		−	0.0954957i
$474$	−20.4688	+	15.7297i	−0.940165	+	0.722488i
$475$		−	4.59752i		−	0.210949i
$476$		0			0
$477$	33.5124	+	8.92799i	1.53443	+	0.408785i
$478$	−2.59987			−0.118915
$479$	4.39627			0.200871			0.100435	−	0.994944i	$-0.467976\pi$
$479$	4.39627			0.200871			0.100435	+	0.994944i	$0.467976\pi$
$480$	1.37337	−	1.05539i	0.0626855	−	0.0481719i
$481$			43.0172i			1.96142i
$482$	5.59136			0.254679
$483$		0			0
$484$	−9.79322			−0.445147
$485$		−	8.60646i		−	0.390799i
$486$	−15.4477	+	2.09024i	−0.700721	+	0.0948153i
$487$	18.8932			0.856134			0.428067	−	0.903747i	$-0.359195\pi$
$487$	18.8932			0.856134			0.428067	+	0.903747i	$0.359195\pi$
$488$	−11.4583			−0.518694
$489$	−7.20024	−	9.36958i	−0.325606	−	0.423707i
$490$		0			0
$491$		−	0.828339i		−	0.0373824i	−0.999825	−	0.0186912i	$-0.994050\pi$
$491$		−	0.828339i		−	0.0373824i	0.999825	−	0.0186912i	$-0.00594994\pi$
$492$	6.42469	+	8.36037i	0.289648	+	0.376915i
$493$			8.15570i			0.367314i
$494$		−	16.8320i		−	0.757307i
$495$	−3.18453	−	0.848386i	−0.143134	−	0.0381321i
$496$			4.34954i			0.195300i
$497$		0			0
$498$	−21.1208	+	16.2307i	−0.946447	+	0.727316i
$499$	32.7999			1.46833			0.734163	−	0.678973i	$-0.237575\pi$
$499$	32.7999			1.46833			0.734163	+	0.678973i	$0.237575\pi$
$500$	−1.00000			−0.0447214
$501$	−12.6331	−	16.4393i	−0.564405	−	0.734454i
$502$			17.0387i			0.760474i
$503$	−41.0560			−1.83060			−0.915299	−	0.402775i	$-0.868046\pi$
$503$	−41.0560			−1.83060			−0.915299	+	0.402775i	$0.868046\pi$
$504$		0			0
$505$	−9.56243			−0.425522
$506$		−	1.66204i		−	0.0738867i
$507$	0.426012	+	0.554364i	0.0189198	+	0.0246202i
$508$	−10.2688			−0.455604
$509$	35.4367			1.57070			0.785351	−	0.619050i	$-0.212482\pi$
$509$	35.4367			1.57070			0.785351	+	0.619050i	$0.212482\pi$
$510$	−6.03822	+	4.64019i	−0.267377	+	0.205471i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	−9.18967	−	22.0512i	−0.405734	−	0.973584i
$514$			22.0807i			0.973937i
$515$		−	15.8943i		−	0.700386i
$516$	−1.99533	−	2.59650i	−0.0878397	−	0.114305i
$517$			5.64339i			0.248196i
$518$		0			0
$519$	24.9121	+	32.4178i	1.09352	+	1.42298i
$520$	−3.66110			−0.160550
$521$	−23.8571			−1.04520			−0.522599	−	0.852579i	$-0.675037\pi$
$521$	−23.8571			−1.04520			−0.522599	+	0.852579i	$0.675037\pi$
$522$	−1.43259	+	5.37740i	−0.0627026	+	0.235362i
$523$		−	36.9288i		−	1.61479i	−0.590015	−	0.807393i	$-0.700878\pi$
$523$		−	36.9288i		−	1.61479i	0.590015	−	0.807393i	$-0.299122\pi$
$524$	15.5240			0.678169
$525$		0			0
$526$	−24.6207			−1.07352
$527$		−	19.1234i		−	0.833028i
$528$	1.50869	−	1.15938i	0.0656574	−	0.0504558i
$529$	20.7109			0.900476
$530$	11.5604			0.502153
$531$	6.81773	−	25.5912i	0.295864	−	1.11056i
$532$		0			0
$533$		−	22.2869i		−	0.965353i
$534$	1.68658	−	1.29609i	0.0729855	−	0.0560871i
$535$		−	6.61505i		−	0.285994i
$536$			12.2073i			0.527277i
$537$	21.3178	−	16.3821i	0.919932	−	0.706940i
$538$		−	6.74076i		−	0.290615i
$539$		0			0
$540$	−4.79632	+	1.99883i	−0.206401	+	0.0860160i
$541$	−18.5092			−0.795774			−0.397887	−	0.917434i	$-0.630256\pi$
$541$	−18.5092			−0.795774			−0.397887	+	0.917434i	$0.630256\pi$
$542$	−23.0387			−0.989598
$543$	28.0638	−	21.5662i	1.20433	−	0.925493i
$544$		−	4.39664i		−	0.188504i
$545$	10.9297			0.468178
$546$		0			0
$547$	23.7237			1.01435			0.507176	−	0.861843i	$-0.330690\pi$
$547$	23.7237			1.01435			0.507176	+	0.861843i	$0.330690\pi$
$548$			4.68182i			0.199997i
$549$	33.2165	+	8.84915i	1.41764	+	0.377673i
$550$	−1.09853			−0.0468416
$551$	−8.52834			−0.363319
$552$	−1.59677	−	2.07786i	−0.0679630	−	0.0884394i
$553$		0			0
$554$			14.5920i			0.619953i
$555$	12.4007	+	16.1368i	0.526379	+	0.684970i
$556$		−	8.58014i		−	0.363879i
$557$		−	17.4985i		−	0.741434i	−0.928746	−	0.370717i	$-0.879112\pi$
$557$		−	17.4985i		−	0.741434i	0.928746	−	0.370717i	$-0.120888\pi$
$558$	3.35911	−	12.6088i	0.142202	−	0.533775i
$559$			6.92170i			0.292757i
$560$		0			0
$561$	−6.63318	+	5.09740i	−0.280053	+	0.215212i
$562$	29.4382			1.24177
$563$	20.2411			0.853062			0.426531	−	0.904473i	$-0.359736\pi$
$563$	20.2411			0.853062			0.426531	+	0.904473i	$0.359736\pi$
$564$	5.42177	+	7.05528i	0.228298	+	0.297081i
$565$			17.0903i			0.718994i
$566$	26.2275			1.10243
$567$		0			0
$568$	2.24305			0.0941163
$569$			30.4021i			1.27452i	0.770647	+	0.637262i	$0.219933\pi$
$569$			30.4021i			1.27452i	−0.770647	+	0.637262i	$0.780067\pi$
$570$	−4.85220	−	6.31410i	−0.203236	−	0.264469i
$571$	−39.1537			−1.63853			−0.819266	−	0.573414i	$-0.805619\pi$
$571$	−39.1537			−1.63853			−0.819266	+	0.573414i	$0.805619\pi$
$572$	−4.02184			−0.168162
$573$	12.5457	−	9.64099i	0.524104	−	0.402758i
$574$		0			0
$575$			1.51296i			0.0630949i
$576$	0.772290	−	2.89889i	0.0321787	−	0.120787i
$577$			30.8441i			1.28406i	0.766680	+	0.642029i	$0.221907\pi$
$577$			30.8441i			1.28406i	−0.766680	+	0.642029i	$0.778093\pi$
$578$			2.33046i			0.0969342i
$579$	−19.8456	−	25.8248i	−0.824753	−	1.07324i
$580$			1.85498i			0.0770240i
$581$		0			0
$582$	−9.08320	−	11.8198i	−0.376511	−	0.489948i
$583$	12.6995			0.525960
$584$	−6.69260			−0.276942
$585$	10.6131	+	2.82743i	0.438799	+	0.116900i
$586$		−	16.9845i		−	0.701625i
$587$	19.5179			0.805590			0.402795	−	0.915290i	$-0.368039\pi$
$587$	19.5179			0.805590			0.402795	+	0.915290i	$0.368039\pi$
$588$		0			0
$589$	19.9971			0.823967
$590$		−	8.82794i		−	0.363440i
$591$	−4.06110	+	3.12083i	−0.167051	+	0.128374i
$592$	−11.7498			−0.482914
$593$	−3.22864			−0.132584			−0.0662922	−	0.997800i	$-0.521117\pi$
$593$	−3.22864			−0.132584			−0.0662922	+	0.997800i	$0.521117\pi$
$594$	−5.26892	+	2.19578i	−0.216186	+	0.0900940i
$595$		0			0
$596$			10.0442i			0.411425i
$597$	18.2682	−	14.0386i	0.747668	−	0.574560i
$598$			5.53910i			0.226511i
$599$		−	23.2001i		−	0.947932i	−0.880543	−	0.473966i	$-0.842822\pi$
$599$		−	23.2001i		−	0.947932i	0.880543	−	0.473966i	$-0.157178\pi$
$600$	−1.37337	+	1.05539i	−0.0560676	+	0.0430863i
$601$		−	4.42798i		−	0.180621i	−0.995914	−	0.0903106i	$-0.971214\pi$
$601$		−	4.42798i		−	0.180621i	0.995914	−	0.0903106i	$-0.0287860\pi$
$602$		0			0
$603$	9.42760	−	35.3877i	0.383922	−	1.44110i
$604$	8.52641			0.346935
$605$	9.79322			0.398151
$606$	−13.1327	+	10.0921i	−0.533481	+	0.409964i
$607$		−	5.46811i		−	0.221944i	−0.993824	−	0.110972i	$-0.964604\pi$
$607$		−	5.46811i		−	0.221944i	0.993824	−	0.110972i	$-0.0353963\pi$
$608$	4.59752			0.186454
$609$		0			0
$610$	11.4583			0.463934
$611$		−	18.8078i		−	0.760882i
$612$	−3.39548	+	12.7454i	−0.137254	+	0.515202i
$613$	−12.4342			−0.502214			−0.251107	−	0.967959i	$-0.580795\pi$
$613$	−12.4342			−0.502214			−0.251107	+	0.967959i	$0.580795\pi$
$614$	−2.71276			−0.109478
$615$	−6.42469	−	8.36037i	−0.259069	−	0.337123i
$616$		0			0
$617$		−	24.7992i		−	0.998376i	−0.866494	−	0.499188i	$-0.833632\pi$
$617$		−	24.7992i		−	0.998376i	0.866494	−	0.499188i	$-0.166368\pi$
$618$	−16.7747	−	21.8287i	−0.674778	−	0.878081i
$619$			29.9740i			1.20476i	0.798210	+	0.602379i	$0.205780\pi$
$619$			29.9740i			1.20476i	−0.798210	+	0.602379i	$0.794220\pi$
$620$		−	4.34954i		−	0.174682i
$621$	3.02415	+	7.25665i	0.121355	+	0.291199i
$622$			21.6732i			0.869015i
$623$		0			0
$624$	−5.02804	+	3.86390i	−0.201283	+	0.154680i
$625$	1.00000			0.0400000
$626$	−4.66085			−0.186285
$627$	−5.33030	−	6.93625i	−0.212872	−	0.277007i
$628$			18.2619i			0.728729i
$629$	51.6597			2.05981
$630$		0			0
$631$	−28.5379			−1.13608			−0.568038	−	0.823003i	$-0.692297\pi$
$631$	−28.5379			−1.13608			−0.568038	+	0.823003i	$0.692297\pi$
$632$			14.9041i			0.592853i
$633$	−10.1757	−	13.2415i	−0.404446	−	0.526301i
$634$	−7.13944			−0.283544
$635$	10.2688			0.407505
$636$	15.8767	−	12.2008i	0.629553	−	0.483793i
$637$		0			0
$638$			2.03776i			0.0806758i
$639$	−6.50236	−	1.73229i	−0.257229	−	0.0685282i
$640$		−	1.00000i		−	0.0395285i
$641$			11.3542i			0.448463i	0.974536	+	0.224232i	$0.0719873\pi$
$641$			11.3542i			0.448463i	−0.974536	+	0.224232i	$0.928013\pi$
$642$	−6.98148	−	9.08492i	−0.275537	−	0.358553i
$643$		−	26.2818i		−	1.03645i	−0.855243	−	0.518227i	$-0.826592\pi$
$643$		−	26.2818i		−	1.03645i	0.855243	−	0.518227i	$-0.173408\pi$
$644$		0			0
$645$	1.99533	+	2.59650i	0.0785662	+	0.102237i
$646$	−20.2137			−0.795296
$647$	23.2061			0.912327			0.456164	−	0.889896i	$-0.349223\pi$
$647$	23.2061			0.912327			0.456164	+	0.889896i	$0.349223\pi$
$648$	−4.47757	+	7.80714i	−0.175895	+	0.306693i
$649$		−	9.69778i		−	0.380671i
$650$	3.66110			0.143600
$651$		0			0
$652$	−6.82233			−0.267183
$653$		−	45.6679i		−	1.78712i	−0.448942	−	0.893561i	$-0.648199\pi$
$653$		−	45.6679i		−	1.78712i	0.448942	−	0.893561i	$-0.351801\pi$
$654$	15.0106	−	11.5352i	0.586959	−	0.451060i
$655$	−15.5240			−0.606572
$656$	6.08749			0.237676
$657$	19.4011	+	5.16863i	0.756910	+	0.201647i
$658$		0			0
$659$		−	19.5851i		−	0.762927i	−0.924384	−	0.381463i	$-0.875420\pi$
$659$		−	19.5851i		−	0.762927i	0.924384	−	0.381463i	$-0.124580\pi$
$660$	−1.50869	+	1.15938i	−0.0587258	+	0.0451290i
$661$			28.4801i			1.10775i	0.832601	+	0.553873i	$0.186851\pi$
$661$			28.4801i			1.10775i	−0.832601	+	0.553873i	$0.813149\pi$
$662$		−	6.57307i		−	0.255470i
$663$	22.1065	−	16.9882i	0.858546	−	0.659766i
$664$			15.3788i			0.596815i
$665$		0			0
$666$	34.0614	+	9.07425i	1.31985	+	0.351620i
$667$	2.80652			0.108669
$668$	−11.9700			−0.463135
$669$	−12.8394	+	9.86666i	−0.496398	+	0.381467i
$670$		−	12.2073i		−	0.471611i
$671$	12.5874			0.485930
$672$		0			0
$673$	−44.0060			−1.69631			−0.848154	−	0.529750i	$-0.822286\pi$
$673$	−44.0060			−1.69631			−0.848154	+	0.529750i	$0.822286\pi$
$674$			15.0962i			0.581483i
$675$	4.79632	−	1.99883i	0.184610	−	0.0769350i
$676$	0.403652			0.0155251
$677$	−11.7583			−0.451909			−0.225954	−	0.974138i	$-0.572550\pi$
$677$	−11.7583			−0.451909			−0.225954	+	0.974138i	$0.572550\pi$
$678$	18.0370	+	23.4713i	0.692706	+	0.901410i
$679$		0			0
$680$			4.39664i			0.168604i
$681$	2.00814	+	2.61317i	0.0769520	+	0.100137i
$682$		−	4.77812i		−	0.182964i
$683$			33.9821i			1.30029i	0.759811	+	0.650144i	$0.225291\pi$
$683$			33.9821i			1.30029i	−0.759811	+	0.650144i	$0.774709\pi$
$684$	−13.3277	−	3.55062i	−0.509598	−	0.135761i
$685$		−	4.68182i		−	0.178883i
$686$		0			0
$687$	−7.98440	+	6.13577i	−0.304624	+	0.234094i
$688$	−1.89061			−0.0720787
$689$	−42.3238			−1.61241
$690$	1.59677	+	2.07786i	0.0607880	+	0.0791026i
$691$			7.99973i			0.304324i	0.988356	+	0.152162i	$0.0486236\pi$
$691$			7.99973i			0.304324i	−0.988356	+	0.152162i	$0.951376\pi$
$692$	23.6045			0.897310
$693$		0			0
$694$	−34.9057			−1.32500
$695$			8.58014i			0.325463i
$696$	1.95774	+	2.54758i	0.0742079	+	0.0965658i
$697$	−26.7645			−1.01378
$698$	−11.4710			−0.434184
$699$	−17.3370	+	13.3230i	−0.655747	+	0.503921i
$700$		0			0
$701$		−	20.2581i		−	0.765138i	−0.923927	−	0.382569i	$-0.875039\pi$
$701$		−	20.2581i		−	0.765138i	0.923927	−	0.382569i	$-0.124961\pi$
$702$	17.5598	−	7.31792i	0.662752	−	0.276197i
$703$			54.0200i			2.03740i
$704$		−	1.09853i		−	0.0414025i
$705$	−5.42177	−	7.05528i	−0.204196	−	0.265717i
$706$		−	5.63774i		−	0.212179i
$707$		0			0
$708$	−9.31694	−	12.1240i	−0.350152	−	0.455649i
$709$	46.8871			1.76088			0.880441	−	0.474156i	$-0.157247\pi$
$709$	46.8871			1.76088			0.880441	+	0.474156i	$0.157247\pi$
$710$	−2.24305			−0.0841802
$711$	11.5103	−	43.2054i	0.431669	−	1.62033i
$712$		−	1.22806i		−	0.0460235i
$713$	−6.58069			−0.246449
$714$		0			0
$715$	4.02184			0.150408
$716$		−	15.5223i		−	0.580095i
$717$	3.57058	−	2.74388i	0.133346	−	0.102472i
$718$	19.5879			0.731016
$719$	24.0650			0.897475			0.448737	−	0.893664i	$-0.351874\pi$
$719$	24.0650			0.897475			0.448737	+	0.893664i	$0.351874\pi$
$720$	−0.772290	+	2.89889i	−0.0287815	+	0.108035i
$721$		0			0
$722$		−	2.13723i		−	0.0795394i
$723$	−7.67901	+	5.90108i	−0.285585	+	0.219464i
$724$		−	20.4343i		−	0.759433i
$725$		−	1.85498i		−	0.0688924i
$726$	13.4497	−	10.3357i	0.499166	−	0.383594i
$727$		−	34.8935i		−	1.29413i	−0.762435	−	0.647065i	$-0.775996\pi$
$727$		−	34.8935i		−	1.29413i	0.762435	−	0.647065i	$-0.224004\pi$
$728$		0			0
$729$	19.0094	−	19.1741i	0.704050	−	0.710150i
$730$	6.69260			0.247704
$731$	8.31232			0.307442
$732$	15.7365	−	12.0930i	0.581639	−	0.446972i
$733$		−	2.99259i		−	0.110534i	−0.998472	−	0.0552670i	$-0.982399\pi$
$733$		−	2.99259i		−	0.110534i	0.998472	−	0.0552670i	$-0.0176010\pi$
$734$	−5.84158			−0.215617
$735$		0			0
$736$	−1.51296			−0.0557685
$737$		−	13.4102i		−	0.493970i
$738$	−17.6470	−	4.70131i	−0.649594	−	0.173057i
$739$	−26.4346			−0.972413			−0.486207	−	0.873844i	$-0.661620\pi$
$739$	−26.4346			−0.972413			−0.486207	+	0.873844i	$0.661620\pi$
$740$	11.7498			0.431931
$741$	17.7644	+	23.1166i	0.652591	+	0.849208i
$742$		0			0
$743$			8.25042i			0.302679i	0.988482	+	0.151339i	$0.0483586\pi$
$743$			8.25042i			0.302679i	−0.988482	+	0.151339i	$0.951641\pi$
$744$	−4.59048	−	5.97353i	−0.168295	−	0.219000i
$745$		−	10.0442i		−	0.367990i
$746$			10.8349i			0.396694i
$747$	11.8769	−	44.5816i	0.434554	−	1.63115i
$748$			4.82986i			0.176597i
$749$		0			0
$750$	1.37337	−	1.05539i	0.0501484	−	0.0385375i
$751$	28.9960			1.05808			0.529039	−	0.848597i	$-0.322552\pi$
$751$	28.9960			1.05808			0.529039	+	0.848597i	$0.322552\pi$
$752$	5.13720			0.187334
$753$	−17.9825	−	23.4004i	−0.655320	−	0.852759i
$754$		−	6.79128i		−	0.247324i
$755$	−8.52641			−0.310308
$756$		0			0
$757$	0.754967			0.0274397			0.0137199	−	0.999906i	$-0.495633\pi$
$757$	0.754967			0.0274397			0.0137199	+	0.999906i	$0.495633\pi$
$758$			24.1798i			0.878250i
$759$	1.75411	+	2.28259i	0.0636700	+	0.0828529i
$760$	−4.59752			−0.166770
$761$	10.9663			0.397528			0.198764	−	0.980047i	$-0.436307\pi$
$761$	10.9663			0.397528			0.198764	+	0.980047i	$0.436307\pi$
$762$	14.1028	−	10.8376i	0.510892	−	0.392605i
$763$		0			0
$764$		−	9.13497i		−	0.330492i
$765$	3.39548	−	12.7454i	0.122764	−	0.460810i
$766$		−	6.71052i		−	0.242461i
$767$			32.3200i			1.16701i
$768$	−1.05539	−	1.37337i	−0.0380832	−	0.0495572i
$769$		−	28.7134i		−	1.03543i	−0.855553	−	0.517715i	$-0.826783\pi$
$769$		−	28.7134i		−	1.03543i	0.855553	−	0.517715i	$-0.173217\pi$
$770$		0			0
$771$	−23.3038	−	30.3250i	−0.839266	−	1.09213i
$772$	−18.8039			−0.676769
$773$	18.6134			0.669476			0.334738	−	0.942311i	$-0.391352\pi$
$773$	18.6134			0.669476			0.334738	+	0.942311i	$0.391352\pi$
$774$	5.48066	+	1.46010i	0.196998	+	0.0524821i
$775$			4.34954i			0.156240i
$776$	−8.60646			−0.308954
$777$		0			0
$778$	15.7508			0.564694
$779$		−	27.9874i		−	1.00275i
$780$	5.02804	−	3.86390i	0.180033	−	0.138350i
$781$	−2.46407			−0.0881712
$782$	6.65195			0.237873
$783$	−3.70780	−	8.89710i	−0.132506	−	0.317956i
$784$		0			0
$785$		−	18.2619i		−	0.651795i
$786$	−21.3202	+	16.3839i	−0.760466	+	0.584395i
$787$		−	32.9752i		−	1.17544i	−0.809065	−	0.587720i	$-0.800026\pi$
$787$		−	32.9752i		−	1.17544i	0.809065	−	0.587720i	$-0.199974\pi$
$788$			2.95703i			0.105340i
$789$	33.8134	−	25.9846i	1.20379	−	0.925075i
$790$		−	14.9041i		−	0.530264i
$791$		0			0
$792$	−0.848386	+	3.18453i	−0.0301461	+	0.113157i
$793$	−41.9501			−1.48969
$794$	8.50643			0.301882
$795$	−15.8767	+	12.2008i	−0.563090	+	0.432717i
$796$		−	13.3017i		−	0.471467i
$797$	3.82813			0.135599			0.0677997	−	0.997699i	$-0.478402\pi$
$797$	3.82813			0.135599			0.0677997	+	0.997699i	$0.478402\pi$
$798$		0			0
$799$	−22.5864			−0.799050
$800$			1.00000i			0.0353553i
$801$	−0.948418	+	3.56001i	−0.0335107	+	0.125787i
$802$	−37.0725			−1.30908
$803$	7.35204			0.259448
$804$	−12.8835	−	16.7652i	−0.454368	−	0.591263i
$805$		0			0
$806$			15.9241i			0.560903i
$807$	7.11416	+	9.25756i	0.250430	+	0.325882i
$808$			9.56243i			0.336405i
$809$		−	45.4589i		−	1.59825i	−0.601164	−	0.799125i	$-0.705296\pi$
$809$		−	45.4589i		−	1.59825i	0.601164	−	0.799125i	$-0.294704\pi$
$810$	4.47757	−	7.80714i	0.157326	−	0.274315i
$811$		−	19.6898i		−	0.691402i	−0.938345	−	0.345701i	$-0.887641\pi$
$811$		−	19.6898i		−	0.691402i	0.938345	−	0.345701i	$-0.112359\pi$
$812$		0			0
$813$	31.6407	−	24.3149i	1.10969	−	0.852761i
$814$	12.9076			0.452410
$815$	6.82233			0.238976
$816$	4.64019	+	6.03822i	0.162439	+	0.211380i
$817$			8.69211i			0.304098i
$818$	20.0437			0.700813
$819$		0			0
$820$	−6.08749			−0.212584
$821$			12.1176i			0.422907i	0.977388	+	0.211453i	$0.0678196\pi$
$821$			12.1176i			0.422907i	−0.977388	+	0.211453i	$0.932180\pi$
$822$	−4.94116	−	6.42987i	−0.172343	−	0.224267i
$823$	−1.26153			−0.0439742			−0.0219871	−	0.999758i	$-0.506999\pi$
$823$	−1.26153			−0.0439742			−0.0219871	+	0.999758i	$0.506999\pi$
$824$	−15.8943			−0.553704
$825$	1.50869	−	1.15938i	0.0525259	−	0.0403646i
$826$		0			0
$827$			46.4126i			1.61392i	0.590604	+	0.806961i	$0.298889\pi$
$827$			46.4126i			1.61392i	−0.590604	+	0.806961i	$0.701111\pi$
$828$	4.38591	+	1.16845i	0.152421	+	0.0406063i
$829$		−	6.90224i		−	0.239725i	−0.992791	−	0.119862i	$-0.961755\pi$
$829$		−	6.90224i		−	0.239725i	0.992791	−	0.119862i	$-0.0382453\pi$
$830$		−	15.3788i		−	0.533807i
$831$	−15.4003	−	20.0402i	−0.534229	−	0.695186i
$832$			3.66110i			0.126926i
$833$		0			0
$834$	9.05543	+	11.7837i	0.313564	+	0.408037i
$835$	11.9700			0.414240
$836$	−5.05053			−0.174676
$837$	8.69400	+	20.8618i	0.300509	+	0.721089i
$838$		−	17.7909i		−	0.614575i
$839$	47.3930			1.63619			0.818093	−	0.575085i	$-0.195031\pi$
$839$	47.3930			1.63619			0.818093	+	0.575085i	$0.195031\pi$
$840$		0			0
$841$	25.5590			0.881346
$842$			12.4583i			0.429343i
$843$	−40.4295	+	31.0689i	−1.39247	+	1.07007i
$844$	−9.64158			−0.331877
$845$	−0.403652			−0.0138861
$846$	−14.8922	−	3.96741i	−0.512004	−	0.136402i
$847$		0			0
$848$		−	11.5604i		−	0.396986i
$849$	−36.0201	+	27.6804i	−1.23621	+	0.949987i
$850$		−	4.39664i		−	0.150804i
$851$		−	17.7770i		−	0.609388i
$852$	−3.08054	+	2.36730i	−0.105538	+	0.0811024i
$853$			43.4138i			1.48646i	0.669035	+	0.743231i	$0.266708\pi$
$853$			43.4138i			1.48646i	−0.669035	+	0.743231i	$0.733292\pi$
$854$		0			0
$855$	13.3277	+	3.55062i	0.455798	+	0.121429i
$856$	−6.61505			−0.226098
$857$	−30.2475			−1.03324			−0.516618	−	0.856216i	$-0.672809\pi$
$857$	−30.2475			−1.03324			−0.516618	+	0.856216i	$0.672809\pi$
$858$	5.52348	−	4.24462i	0.188568	−	0.144909i
$859$		−	0.923617i		−	0.0315134i	−0.999876	−	0.0157567i	$-0.994984\pi$
$859$		−	0.923617i		−	0.0315134i	0.999876	−	0.0157567i	$-0.00501572\pi$
$860$	1.89061			0.0644692
$861$		0			0
$862$	−30.1606			−1.02727
$863$			28.1393i			0.957872i	0.877850	+	0.478936i	$0.158977\pi$
$863$			28.1393i			0.957872i	−0.877850	+	0.478936i	$0.841023\pi$
$864$	1.99883	+	4.79632i	0.0680016	+	0.163174i
$865$	−23.6045			−0.802579
$866$	−11.8201			−0.401664
$867$	−2.45955	−	3.20058i	−0.0835306	−	0.108697i
$868$		0			0
$869$		−	16.3726i		−	0.555404i
$870$	−1.95774	−	2.54758i	−0.0663735	−	0.0863710i
$871$			44.6923i			1.51434i
$872$		−	10.9297i		−	0.370127i
$873$	24.9492	+	6.64668i	0.844402	+	0.224956i
$874$			6.95588i			0.235286i
$875$		0			0
$876$	9.19141	−	7.06332i	0.310549	−	0.238648i
$877$	34.0947			1.15130			0.575648	−	0.817698i	$-0.304750\pi$
$877$	34.0947			1.15130			0.575648	+	0.817698i	$0.304750\pi$
$878$	15.2453			0.514503
$879$	17.9254	+	23.3261i	0.604608	+	0.786769i
$880$			1.09853i			0.0370316i
$881$	−57.8642			−1.94950			−0.974748	−	0.223308i	$-0.928314\pi$
$881$	−57.8642			−1.94950			−0.974748	+	0.223308i	$0.928314\pi$
$882$		0			0
$883$	−42.6657			−1.43582			−0.717908	−	0.696138i	$-0.754900\pi$
$883$	−42.6657			−1.43582			−0.717908	+	0.696138i	$0.754900\pi$
$884$		−	16.0965i		−	0.541385i
$885$	9.31694	+	12.1240i	0.313186	+	0.407545i
$886$	6.21871			0.208922
$887$	34.1357			1.14617			0.573083	−	0.819497i	$-0.305747\pi$
$887$	34.1357			1.14617			0.573083	+	0.819497i	$0.305747\pi$
$888$	16.1368	−	12.4007i	0.541516	−	0.416139i
$889$		0			0
$890$			1.22806i			0.0411646i
$891$	4.91876	−	8.57640i	0.164785	−	0.287320i
$892$			9.34880i			0.313021i
$893$		−	23.6184i		−	0.790360i
$894$	−10.6005	−	13.7944i	−0.354535	−	0.461352i
$895$			15.5223i			0.518853i
$896$		0			0
$897$	−5.84593	−	7.60724i	−0.195190	−	0.253998i
$898$	18.1053			0.604182
$899$	8.06833			0.269094
$900$	0.772290	−	2.89889i	0.0257430	−	0.0966297i
$901$			50.8270i			1.69329i
$902$	−6.68731			−0.222663
$903$		0			0
$904$	17.0903			0.568415
$905$			20.4343i			0.679258i
$906$	−11.7099	+	8.99871i	−0.389036	+	0.298962i
$907$	−3.41434			−0.113371			−0.0566857	−	0.998392i	$-0.518053\pi$
$907$	−3.41434			−0.113371			−0.0566857	+	0.998392i	$0.518053\pi$
$908$	1.90274			0.0631446
$909$	7.38496	−	27.7204i	0.244944	−	0.919429i
$910$		0			0
$911$		−	32.7643i		−	1.08553i	−0.839885	−	0.542765i	$-0.817377\pi$
$911$		−	32.7643i		−	1.08553i	0.839885	−	0.542765i	$-0.182623\pi$
$912$	−6.31410	+	4.85220i	−0.209081	+	0.160672i
$913$		−	16.8942i		−	0.559115i
$914$		−	25.2516i		−	0.835248i
$915$	−15.7365	+	12.0930i	−0.520234	+	0.399784i
$916$			5.81373i			0.192091i
$917$		0			0
$918$	−8.78814	−	21.0877i	−0.290052	−	0.695998i
$919$	−37.9819			−1.25291			−0.626454	−	0.779458i	$-0.715494\pi$
$919$	−37.9819			−1.25291			−0.626454	+	0.779458i	$0.715494\pi$
$920$	1.51296			0.0498809
$921$	3.72562	−	2.86303i	0.122763	−	0.0943399i
$922$		−	0.942963i		−	0.0310548i
$923$	8.21203			0.270302
$924$		0			0
$925$	−11.7498			−0.386331
$926$		−	8.47895i		−	0.278636i
$927$	46.0758	+	12.2750i	1.51333	+	0.403164i
$928$	1.85498			0.0608929
$929$	15.2617			0.500721			0.250361	−	0.968153i	$-0.419451\pi$
$929$	15.2617			0.500721			0.250361	+	0.968153i	$0.419451\pi$
$930$	4.59048	+	5.97353i	0.150528	+	0.195880i
$931$		0			0
$932$			12.6237i			0.413503i
$933$	−22.8737	−	29.7653i	−0.748852	−	0.974471i
$934$		−	9.23547i		−	0.302194i
$935$		−	4.82986i		−	0.157953i
$936$	2.82743	−	10.6131i	0.0924174	−	0.346901i
$937$			6.90130i			0.225456i	0.993626	+	0.112728i	$0.0359588\pi$
$937$			6.90130i			0.225456i	−0.993626	+	0.112728i	$0.964041\pi$
$938$		0			0
$939$	6.40106	−	4.91902i	0.208891	−	0.160526i
$940$	−5.13720			−0.167557
$941$	−20.5328			−0.669350			−0.334675	−	0.942334i	$-0.608627\pi$
$941$	−20.5328			−0.669350			−0.334675	+	0.942334i	$0.608627\pi$
$942$	−19.2735	−	25.0803i	−0.627964	−	0.817162i
$943$			9.21014i			0.299923i
$944$	−8.82794			−0.287325
$945$		0			0
$946$	2.07690			0.0675257
$947$		−	3.19324i		−	0.103766i	−0.998653	−	0.0518832i	$-0.983478\pi$
$947$		−	3.19324i		−	0.103766i	0.998653	−	0.0518832i	$-0.0165224\pi$
$948$	−15.7297	−	20.4688i	−0.510876	−	0.664797i
$949$	−24.5023			−0.795377
$950$	4.59752			0.149163
$951$	9.80510	−	7.53492i	0.317952	−	0.244337i
$952$		0			0
$953$			2.71901i			0.0880775i	0.999030	+	0.0440388i	$0.0140225\pi$
$953$			2.71901i			0.0880775i	−0.999030	+	0.0440388i	$0.985977\pi$
$954$	−8.92799	+	33.5124i	−0.289054	+	1.08500i
$955$			9.13497i			0.295601i
$956$		−	2.59987i		−	0.0840857i
$957$	−2.15064	−	2.79860i	−0.0695204	−	0.0904660i
$958$			4.39627i			0.142037i
$959$		0			0
$960$	1.05539	+	1.37337i	0.0340627	+	0.0443253i
$961$	12.0815			0.389725
$962$	−43.0172			−1.38693
$963$	19.1763	+	5.10874i	0.617948	+	0.164627i
$964$			5.59136i			0.180086i
$965$	18.8039			0.605320
$966$		0			0
$967$	−31.9095			−1.02614			−0.513071	−	0.858346i	$-0.671492\pi$
$967$	−31.9095			−1.02614			−0.513071	+	0.858346i	$0.671492\pi$
$968$		−	9.79322i		−	0.314766i
$969$	27.7608	−	21.3334i	0.891807	−	0.685327i
$970$	8.60646			0.276337
$971$	−24.3055			−0.779999			−0.390000	−	0.920815i	$-0.627525\pi$
$971$	−24.3055			−0.779999			−0.390000	+	0.920815i	$0.627525\pi$
$972$	−2.09024	−	15.4477i	−0.0670446	−	0.495485i
$973$		0			0
$974$			18.8932i			0.605378i
$975$	−5.02804	+	3.86390i	−0.161026	+	0.123744i
$976$		−	11.4583i		−	0.366772i
$977$			23.2233i			0.742979i	0.928437	+	0.371490i	$0.121153\pi$
$977$			23.2233i			0.742979i	−0.928437	+	0.371490i	$0.878847\pi$
$978$	9.36958	−	7.20024i	0.299606	−	0.230238i
$979$			1.34906i			0.0431163i
$980$		0			0
$981$	−8.44092	+	31.6841i	−0.269498	+	1.01159i
$982$	0.828339			0.0264334
$983$	−26.9225			−0.858696			−0.429348	−	0.903139i	$-0.641257\pi$
$983$	−26.9225			−0.858696			−0.429348	+	0.903139i	$0.641257\pi$
$984$	−8.36037	+	6.42469i	−0.266519	+	0.204812i
$985$		−	2.95703i		−	0.0942188i
$986$	−8.15570			−0.259730
$987$		0			0
$988$	16.8320			0.535497
$989$		−	2.86042i		−	0.0909560i
$990$	0.848386	−	3.18453i	0.0269635	−	0.101211i
$991$	18.0900			0.574646			0.287323	−	0.957834i	$-0.407235\pi$
$991$	18.0900			0.574646			0.287323	+	0.957834i	$0.407235\pi$
$992$	−4.34954			−0.138098
$993$	6.93717	+	9.02725i	0.220144	+	0.286471i
$994$		0			0
$995$			13.3017i			0.421693i
$996$	−16.2307	−	21.1208i	−0.514290	−	0.669239i
$997$			15.2244i			0.482161i	0.970505	+	0.241080i	$0.0775017\pi$
$997$			15.2244i			0.482161i	−0.970505	+	0.241080i	$0.922498\pi$
$998$			32.7999i			1.03826i
$999$	−56.3558	+	23.4859i	−1.78302	+	0.743060i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.05539 - 1.37337i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(1.37337 - 1.05539i) q^{6} -1.00000i q^{8} +(-0.772290 + 2.89889i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-1.05539 - 1.37337i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(1.37337 - 1.05539i) q^{6} -1.00000i q^{8} +(-0.772290 + 2.89889i) q^{9} +1.00000i q^{10} +1.09853i q^{11} +(1.05539 + 1.37337i) q^{12} -3.66110i q^{13} +(-1.05539 - 1.37337i) q^{15} +1.00000 q^{16} -4.39664 q^{17} +(-2.89889 - 0.772290i) q^{18} -4.59752i q^{19} -1.00000 q^{20} -1.09853 q^{22} +1.51296i q^{23} +(-1.37337 + 1.05539i) q^{24} +1.00000 q^{25} +3.66110 q^{26} +(4.79632 - 1.99883i) q^{27} -1.85498i q^{29} +(1.37337 - 1.05539i) q^{30} +4.34954i q^{31} +1.00000i q^{32} +(1.50869 - 1.15938i) q^{33} -4.39664i q^{34} +(0.772290 - 2.89889i) q^{36} -11.7498 q^{37} +4.59752 q^{38} +(-5.02804 + 3.86390i) q^{39} -1.00000i q^{40} +6.08749 q^{41} -1.89061 q^{43} -1.09853i q^{44} +(-0.772290 + 2.89889i) q^{45} -1.51296 q^{46} +5.13720 q^{47} +(-1.05539 - 1.37337i) q^{48} +1.00000i q^{50} +(4.64019 + 6.03822i) q^{51} +3.66110i q^{52} -11.5604i q^{53} +(1.99883 + 4.79632i) q^{54} +1.09853i q^{55} +(-6.31410 + 4.85220i) q^{57} +1.85498 q^{58} -8.82794 q^{59} +(1.05539 + 1.37337i) q^{60} -11.4583i q^{61} -4.34954 q^{62} -1.00000 q^{64} -3.66110i q^{65} +(1.15938 + 1.50869i) q^{66} -12.2073 q^{67} +4.39664 q^{68} +(2.07786 - 1.59677i) q^{69} +2.24305i q^{71} +(2.89889 + 0.772290i) q^{72} -6.69260i q^{73} -11.7498i q^{74} +(-1.05539 - 1.37337i) q^{75} +4.59752i q^{76} +(-3.86390 - 5.02804i) q^{78} -14.9041 q^{79} +1.00000 q^{80} +(-7.80714 - 4.47757i) q^{81} +6.08749i q^{82} -15.3788 q^{83} -4.39664 q^{85} -1.89061i q^{86} +(-2.54758 + 1.95774i) q^{87} +1.09853 q^{88} +1.22806 q^{89} +(-2.89889 - 0.772290i) q^{90} -1.51296i q^{92} +(5.97353 - 4.59048i) q^{93} +5.13720i q^{94} -4.59752i q^{95} +(1.37337 - 1.05539i) q^{96} -8.60646i q^{97} +(-3.18453 - 0.848386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} - 16 q^{4} + 16 q^{5} + 8 q^{9}+O(q^{10}) \) 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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