LMFDB - Embedded newform 1260.2.c.d.811.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,2,Mod(811,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 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("1260.811");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.c (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:	$10.0611506547$
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} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 3x^14 - 4x^13 + 3x^12 + 2x^11 - 7x^10 + 12x^9 - 28x^8 + 24x^7 - 28x^6 + 16x^5 + 48x^4 - 128x^3 + 192x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			811.6
Root			$1.07312 + 0.921096i$ of defining polynomial
Character	$\chi$	$=$	1260.811
Dual form			1260.2.c.d.811.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07312 + 0.921096i) q^{2} +(0.303166 - 1.97689i) q^{4} +1.00000i q^{5} +(-1.82575 + 1.91485i) q^{7} +(1.49557 + 2.40068i) q^{8} +O(q^{10})$	\(q+(-1.07312 + 0.921096i) q^{2} +(0.303166 - 1.97689i) q^{4} +1.00000i q^{5} +(-1.82575 + 1.91485i) q^{7} +(1.49557 + 2.40068i) q^{8} +(-0.921096 - 1.07312i) q^{10} +6.24043i q^{11} -2.40312i q^{13} +(0.195481 - 3.73655i) q^{14} +(-3.81618 - 1.19865i) q^{16} +1.30768i q^{17} -3.94796 q^{19} +(1.97689 + 0.303166i) q^{20} +(-5.74803 - 6.69672i) q^{22} -3.55648i q^{23} -1.00000 q^{25} +(2.21350 + 2.57883i) q^{26} +(3.23194 + 4.18981i) q^{28} -1.44221 q^{29} +10.9517 q^{31} +(5.19929 - 2.22877i) q^{32} +(-1.20450 - 1.40329i) q^{34} +(-1.91485 - 1.82575i) q^{35} -5.06265 q^{37} +(4.23663 - 3.63645i) q^{38} +(-2.40068 + 1.49557i) q^{40} -1.26175i q^{41} +2.19850i q^{43} +(12.3366 + 1.89189i) q^{44} +(3.27586 + 3.81652i) q^{46} -11.6743 q^{47} +(-0.333303 - 6.99206i) q^{49} +(1.07312 - 0.921096i) q^{50} +(-4.75070 - 0.728544i) q^{52} -11.7545 q^{53} -6.24043 q^{55} +(-7.32748 - 1.51924i) q^{56} +(1.54766 - 1.32842i) q^{58} -0.415368 q^{59} -12.6848i q^{61} +(-11.7524 + 10.0875i) q^{62} +(-3.52653 + 7.18078i) q^{64} +2.40312 q^{65} +3.10097i q^{67} +(2.58513 + 0.396443i) q^{68} +(3.73655 + 0.195481i) q^{70} +10.4762i q^{71} -1.64141i q^{73} +(5.43282 - 4.66319i) q^{74} +(-1.19689 + 7.80468i) q^{76} +(-11.9495 - 11.3934i) q^{77} +9.18952i q^{79} +(1.19865 - 3.81618i) q^{80} +(1.16219 + 1.35401i) q^{82} -7.39922 q^{83} -1.30768 q^{85} +(-2.02502 - 2.35925i) q^{86} +(-14.9813 + 9.33301i) q^{88} -11.4448i q^{89} +(4.60162 + 4.38749i) q^{91} +(-7.03076 - 1.07820i) q^{92} +(12.5279 - 10.7531i) q^{94} -3.94796i q^{95} +12.4433i q^{97} +(6.79803 + 7.19630i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 2 q^{4} - 4 q^{7} - 2 q^{8}+O(q^{10}) $ 16 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 - 2 * q^8	$ 16 q - 2 q^{2} - 2 q^{4} - 4 q^{7} - 2 q^{8} + 2 q^{14} + 6 q^{16} - 24 q^{19} - 12 q^{22} - 16 q^{25} + 12 q^{26} + 14 q^{28} - 16 q^{29} + 8 q^{31} + 18 q^{32} + 24 q^{34} + 24 q^{37} - 28 q^{38} + 12 q^{40} + 8 q^{44} - 20 q^{46} - 16 q^{47} - 16 q^{49} + 2 q^{50} - 20 q^{52} + 32 q^{53} - 2 q^{56} - 32 q^{58} - 8 q^{59} - 16 q^{62} - 2 q^{64} + 8 q^{65} - 4 q^{68} + 4 q^{74} + 16 q^{76} + 8 q^{77} + 16 q^{80} - 4 q^{82} - 8 q^{83} - 64 q^{86} - 52 q^{88} + 16 q^{91} - 64 q^{92} + 16 q^{94} + 86 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 - 2 * q^8 + 2 * q^14 + 6 * q^16 - 24 * q^19 - 12 * q^22 - 16 * q^25 + 12 * q^26 + 14 * q^28 - 16 * q^29 + 8 * q^31 + 18 * q^32 + 24 * q^34 + 24 * q^37 - 28 * q^38 + 12 * q^40 + 8 * q^44 - 20 * q^46 - 16 * q^47 - 16 * q^49 + 2 * q^50 - 20 * q^52 + 32 * q^53 - 2 * q^56 - 32 * q^58 - 8 * q^59 - 16 * q^62 - 2 * q^64 + 8 * q^65 - 4 * q^68 + 4 * q^74 + 16 * q^76 + 8 * q^77 + 16 * q^80 - 4 * q^82 - 8 * q^83 - 64 * q^86 - 52 * q^88 + 16 * q^91 - 64 * q^92 + 16 * q^94 + 86 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$1$	$-1$	$1$	$-1$

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 $

$2$	−1.07312	+	0.921096i	−0.758809	+	0.651313i
$2$	−1.07312	+	0.921096i	−0.758809	+	0.651313i
$3$		0			0
$3$		0			0
$4$	0.303166	−	1.97689i	0.151583	−	0.988445i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	−1.82575	+	1.91485i	−0.690067	+	0.723745i
$7$	−1.82575	+	1.91485i	−0.690067	+	0.723745i
$8$	1.49557	+	2.40068i	0.528764	+	0.848769i
$9$		0			0
$10$	−0.921096	−	1.07312i	−0.291276	−	0.339350i
$11$			6.24043i			1.88156i	0.339016	+	0.940780i	$0.389906\pi$
$11$			6.24043i			1.88156i	−0.339016	+	0.940780i	$0.610094\pi$
$12$		0			0
$13$		−	2.40312i		−	0.666506i	−0.942837	−	0.333253i	$-0.891854\pi$
$13$		−	2.40312i		−	0.666506i	0.942837	−	0.333253i	$-0.108146\pi$
$14$	0.195481	−	3.73655i	0.0522446	−	0.998634i
$15$		0			0
$16$	−3.81618	−	1.19865i	−0.954045	−	0.299663i
$17$			1.30768i			0.317159i	0.987346	+	0.158579i	$0.0506913\pi$
$17$			1.30768i			0.317159i	−0.987346	+	0.158579i	$0.949309\pi$
$18$		0			0
$19$	−3.94796			−0.905724			−0.452862	−	0.891581i	$-0.649597\pi$
$19$	−3.94796			−0.905724			−0.452862	+	0.891581i	$0.649597\pi$
$20$	1.97689	+	0.303166i	0.442046	+	0.0677899i
$21$		0			0
$22$	−5.74803	−	6.69672i	−1.22548	−	1.42775i
$23$		−	3.55648i		−	0.741577i	−0.928717	−	0.370788i	$-0.879088\pi$
$23$		−	3.55648i		−	0.741577i	0.928717	−	0.370788i	$-0.120912\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	2.21350	+	2.57883i	0.434104	+	0.505751i
$27$		0			0
$28$	3.23194	+	4.18981i	0.610780	+	0.791801i
$29$	−1.44221			−0.267812			−0.133906	−	0.990994i	$-0.542752\pi$
$29$	−1.44221			−0.267812			−0.133906	+	0.990994i	$0.542752\pi$
$30$		0			0
$31$	10.9517			1.96698			0.983488	−	0.180974i	$-0.0579249\pi$
$31$	10.9517			1.96698			0.983488	+	0.180974i	$0.0579249\pi$
$32$	5.19929	−	2.22877i	0.919112	−	0.393995i
$33$		0			0
$34$	−1.20450	−	1.40329i	−0.206569	−	0.240663i
$35$	−1.91485	−	1.82575i	−0.323669	−	0.308607i
$36$		0			0
$37$	−5.06265			−0.832295			−0.416147	−	0.909297i	$-0.636620\pi$
$37$	−5.06265			−0.832295			−0.416147	+	0.909297i	$0.636620\pi$
$38$	4.23663	−	3.63645i	0.687272	−	0.589910i
$39$		0			0
$40$	−2.40068	+	1.49557i	−0.379581	+	0.236471i
$41$		−	1.26175i		−	0.197052i	−0.995134	−	0.0985260i	$-0.968587\pi$
$41$		−	1.26175i		−	0.197052i	0.995134	−	0.0985260i	$-0.0314128\pi$
$42$		0			0
$43$			2.19850i			0.335267i	0.985849	+	0.167634i	$0.0536126\pi$
$43$			2.19850i			0.335267i	−0.985849	+	0.167634i	$0.946387\pi$
$44$	12.3366	+	1.89189i	1.85982	+	0.285212i
$45$		0			0
$46$	3.27586	+	3.81652i	0.482999	+	0.562715i
$47$	−11.6743			−1.70287			−0.851434	−	0.524462i	$-0.824267\pi$
$47$	−11.6743			−1.70287			−0.851434	+	0.524462i	$0.824267\pi$
$48$		0			0
$49$	−0.333303	−	6.99206i	−0.0476147	−	0.998866i
$50$	1.07312	−	0.921096i	0.151762	−	0.130263i
$51$		0			0
$52$	−4.75070	−	0.728544i	−0.658804	−	0.101031i
$53$	−11.7545			−1.61461			−0.807303	−	0.590137i	$-0.799074\pi$
$53$	−11.7545			−1.61461			−0.807303	+	0.590137i	$0.799074\pi$
$54$		0			0
$55$	−6.24043			−0.841460
$56$	−7.32748	−	1.51924i	−0.979175	−	0.203017i
$57$		0			0
$58$	1.54766	−	1.32842i	0.203218	−	0.174430i
$59$	−0.415368			−0.0540763			−0.0270382	−	0.999634i	$-0.508608\pi$
$59$	−0.415368			−0.0540763			−0.0270382	+	0.999634i	$0.508608\pi$
$60$		0			0
$61$		−	12.6848i		−	1.62412i	−0.583574	−	0.812060i	$-0.698346\pi$
$61$		−	12.6848i		−	1.62412i	0.583574	−	0.812060i	$-0.301654\pi$
$62$	−11.7524	+	10.0875i	−1.49256	+	1.28112i
$63$		0			0
$64$	−3.52653	+	7.18078i	−0.440817	+	0.897597i
$65$	2.40312			0.298070
$66$		0			0
$67$			3.10097i			0.378844i	0.981896	+	0.189422i	$0.0606614\pi$
$67$			3.10097i			0.378844i	−0.981896	+	0.189422i	$0.939339\pi$
$68$	2.58513	+	0.396443i	0.313494	+	0.0480758i
$69$		0			0
$70$	3.73655	+	0.195481i	0.446603	+	0.0233645i
$71$			10.4762i			1.24330i	0.783296	+	0.621649i	$0.213537\pi$
$71$			10.4762i			1.24330i	−0.783296	+	0.621649i	$0.786463\pi$
$72$		0			0
$73$		−	1.64141i		−	0.192112i	−0.995376	−	0.0960562i	$-0.969377\pi$
$73$		−	1.64141i		−	0.192112i	0.995376	−	0.0960562i	$-0.0306229\pi$
$74$	5.43282	−	4.66319i	0.631553	−	0.542084i
$75$		0			0
$76$	−1.19689	+	7.80468i	−0.137292	+	0.895258i
$77$	−11.9495	−	11.3934i	−1.36177	−	1.29840i
$78$		0			0
$79$			9.18952i			1.03390i	0.856015	+	0.516951i	$0.172933\pi$
$79$			9.18952i			1.03390i	−0.856015	+	0.516951i	$0.827067\pi$
$80$	1.19865	−	3.81618i	0.134013	−	0.426662i
$81$		0			0
$82$	1.16219	+	1.35401i	0.128343	+	0.149525i
$83$	−7.39922			−0.812170			−0.406085	−	0.913835i	$-0.633106\pi$
$83$	−7.39922			−0.812170			−0.406085	+	0.913835i	$0.633106\pi$
$84$		0			0
$85$	−1.30768			−0.141838
$86$	−2.02502	−	2.35925i	−0.218364	−	0.254404i
$87$		0			0
$88$	−14.9813	+	9.33301i	−1.59701	+	0.994902i
$89$		−	11.4448i		−	1.21314i	−0.795028	−	0.606572i	$-0.792544\pi$
$89$		−	11.4448i		−	1.21314i	0.795028	−	0.606572i	$-0.207456\pi$
$90$		0			0
$91$	4.60162	+	4.38749i	0.482380	+	0.459934i
$92$	−7.03076	−	1.07820i	−0.733008	−	0.112410i
$93$		0			0
$94$	12.5279	−	10.7531i	1.29215	−	1.10910i
$95$		−	3.94796i		−	0.405052i
$96$		0			0
$97$			12.4433i			1.26343i	0.775202	+	0.631714i	$0.217648\pi$
$97$			12.4433i			1.26343i	−0.775202	+	0.631714i	$0.782352\pi$
$98$	6.79803	+	7.19630i	0.686705	+	0.726936i
$99$		0			0
$100$	−0.303166	+	1.97689i	−0.0303166	+	0.197689i
$101$			4.25585i			0.423473i	0.977327	+	0.211737i	$0.0679119\pi$
$101$			4.25585i			0.423473i	−0.977327	+	0.211737i	$0.932088\pi$
$102$		0			0
$103$	−15.3254			−1.51006			−0.755029	−	0.655691i	$-0.772377\pi$
$103$	−15.3254			−1.51006			−0.755029	+	0.655691i	$0.772377\pi$
$104$	5.76913	−	3.59404i	0.565709	−	0.352424i
$105$		0			0
$106$	12.6140	−	10.8270i	1.22518	−	1.05161i
$107$		−	4.83844i		−	0.467750i	−0.972267	−	0.233875i	$-0.924859\pi$
$107$		−	4.83844i		−	0.467750i	0.972267	−	0.233875i	$-0.0751406\pi$
$108$		0			0
$109$	8.77146			0.840153			0.420077	−	0.907489i	$-0.362003\pi$
$109$	8.77146			0.840153			0.420077	+	0.907489i	$0.362003\pi$
$110$	6.69672	−	5.74803i	0.638507	−	0.548054i
$111$		0			0
$112$	9.26261	−	5.11898i	0.875235	−	0.483699i
$113$	−4.09511			−0.385236			−0.192618	−	0.981274i	$-0.561698\pi$
$113$	−4.09511			−0.385236			−0.192618	+	0.981274i	$0.561698\pi$
$114$		0			0
$115$	3.55648			0.331643
$116$	−0.437230	+	2.85109i	−0.0405957	+	0.264717i
$117$		0			0
$118$	0.445739	−	0.382594i	0.0410336	−	0.0352206i
$119$	−2.50401	−	2.38749i	−0.229542	−	0.218861i
$120$		0			0
$121$	−27.9430			−2.54027
$122$	11.6839	+	13.6123i	1.05781	+	1.23240i
$123$		0			0
$124$	3.32017	−	21.6502i	0.298160	−	1.94425i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$		−	6.68595i		−	0.593282i	−0.954989	−	0.296641i	$-0.904134\pi$
$127$		−	6.68595i		−	0.593282i	0.954989	−	0.296641i	$-0.0958664\pi$
$128$	−2.82979	−	10.9541i	−0.250121	−	0.968215i
$129$		0			0
$130$	−2.57883	+	2.21350i	−0.226179	+	0.194137i
$131$	−13.3308			−1.16472			−0.582360	−	0.812931i	$-0.697871\pi$
$131$	−13.3308			−1.16472			−0.582360	+	0.812931i	$0.697871\pi$
$132$		0			0
$133$	7.20797	−	7.55975i	0.625010	−	0.655513i
$134$	−2.85629	−	3.32771i	−0.246746	−	0.287470i
$135$		0			0
$136$	−3.13932	+	1.95573i	−0.269194	+	0.167702i
$137$	−5.59837			−0.478301			−0.239151	−	0.970982i	$-0.576869\pi$
$137$	−5.59837			−0.478301			−0.239151	+	0.970982i	$0.576869\pi$
$138$		0			0
$139$	−6.13537			−0.520395			−0.260198	−	0.965555i	$-0.583788\pi$
$139$	−6.13537			−0.520395			−0.260198	+	0.965555i	$0.583788\pi$
$140$	−4.18981	+	3.23194i	−0.354104	+	0.273149i
$141$		0			0
$142$	−9.64959	−	11.2422i	−0.809776	−	0.943425i
$143$	14.9965			1.25407
$144$		0			0
$145$		−	1.44221i		−	0.119769i
$146$	1.51189	+	1.76143i	0.125125	+	0.145777i
$147$		0			0
$148$	−1.53482	+	10.0083i	−0.126162	+	0.822677i
$149$	12.3505			1.01179			0.505895	−	0.862595i	$-0.331162\pi$
$149$	12.3505			1.01179			0.505895	+	0.862595i	$0.331162\pi$
$150$		0			0
$151$		−	15.9654i		−	1.29924i	−0.760258	−	0.649621i	$-0.774928\pi$
$151$		−	15.9654i		−	1.29924i	0.760258	−	0.649621i	$-0.225072\pi$
$152$	−5.90445	−	9.47779i	−0.478914	−	0.768750i
$153$		0			0
$154$	23.3177	+	1.21989i	1.87899	+	0.0983014i
$155$			10.9517i			0.879658i
$156$		0			0
$157$		−	5.15966i		−	0.411786i	−0.978575	−	0.205893i	$-0.933990\pi$
$157$		−	5.15966i		−	0.411786i	0.978575	−	0.205893i	$-0.0660098\pi$
$158$	−8.46443	−	9.86144i	−0.673394	−	0.784534i
$159$		0			0
$160$	2.22877	+	5.19929i	0.176200	+	0.411040i
$161$	6.81012	+	6.49322i	0.536713	+	0.511738i
$162$		0			0
$163$		−	1.27295i		−	0.0997052i	−0.998757	−	0.0498526i	$-0.984125\pi$
$163$		−	1.27295i		−	0.0997052i	0.998757	−	0.0498526i	$-0.0158751\pi$
$164$	−2.49434	−	0.382519i	−0.194775	−	0.0298697i
$165$		0			0
$166$	7.94023	−	6.81539i	0.616282	−	0.528977i
$167$	21.6628			1.67632			0.838158	−	0.545428i	$-0.183633\pi$
$167$	21.6628			1.67632			0.838158	+	0.545428i	$0.183633\pi$
$168$		0			0
$169$	7.22501			0.555770
$170$	1.40329	−	1.20450i	0.107628	−	0.0923807i
$171$		0			0
$172$	4.34618	+	0.666509i	0.331393	+	0.0508208i
$173$		−	12.9769i		−	0.986617i	−0.869855	−	0.493308i	$-0.835787\pi$
$173$		−	12.9769i		−	0.986617i	0.869855	−	0.493308i	$-0.164213\pi$
$174$		0			0
$175$	1.82575	−	1.91485i	0.138013	−	0.144749i
$176$	7.48010	−	23.8146i	0.563833	−	1.79509i
$177$		0			0
$178$	10.5417	+	12.2816i	0.790137	+	0.920545i
$179$			15.1508i			1.13242i	0.824261	+	0.566210i	$0.191591\pi$
$179$			15.1508i			1.13242i	−0.824261	+	0.566210i	$0.808409\pi$
$180$		0			0
$181$			2.92356i			0.217307i	0.994080	+	0.108653i	$0.0346538\pi$
$181$			2.92356i			0.217307i	−0.994080	+	0.108653i	$0.965346\pi$
$182$	−8.97937	−	0.469765i	−0.665596	−	0.0348213i
$183$		0			0
$184$	8.53797	−	5.31896i	0.629427	−	0.392119i
$185$		−	5.06265i		−	0.372214i
$186$		0			0
$187$	−8.16048			−0.596753
$188$	−3.53924	+	23.0788i	−0.258126	+	1.68319i
$189$		0			0
$190$	3.63645	+	4.23663i	0.263816	+	0.307357i
$191$			13.9477i			1.00922i	0.863348	+	0.504608i	$0.168363\pi$
$191$			13.9477i			1.00922i	−0.863348	+	0.504608i	$0.831637\pi$
$192$		0			0
$193$	−13.3869			−0.963607			−0.481803	−	0.876279i	$-0.660018\pi$
$193$	−13.3869			−0.963607			−0.481803	+	0.876279i	$0.660018\pi$
$194$	−11.4615	−	13.3532i	−0.822887	−	0.958701i
$195$		0			0
$196$	−13.9236	−	1.46085i	−0.994541	−	0.104346i
$197$	−4.07989			−0.290680			−0.145340	−	0.989382i	$-0.546428\pi$
$197$	−4.07989			−0.290680			−0.145340	+	0.989382i	$0.546428\pi$
$198$		0			0
$199$	3.66884			0.260077			0.130039	−	0.991509i	$-0.458490\pi$
$199$	3.66884			0.260077			0.130039	+	0.991509i	$0.458490\pi$
$200$	−1.49557	−	2.40068i	−0.105753	−	0.169754i
$201$		0			0
$202$	−3.92005	−	4.56703i	−0.275814	−	0.321335i
$203$	2.63311	−	2.76162i	0.184808	−	0.193828i
$204$		0			0
$205$	1.26175			0.0881244
$206$	16.4460	−	14.1162i	1.14585	−	0.983521i
$207$		0			0
$208$	−2.88050	+	9.17074i	−0.199727	+	0.635877i
$209$		−	24.6370i		−	1.70417i
$210$		0			0
$211$			5.67817i			0.390901i	0.980714	+	0.195451i	$0.0626170\pi$
$211$			5.67817i			0.390901i	−0.980714	+	0.195451i	$0.937383\pi$
$212$	−3.56357	+	23.2374i	−0.244747	+	1.59595i
$213$		0			0
$214$	4.45667	+	5.19222i	0.304651	+	0.354933i
$215$	−2.19850			−0.149936
$216$		0			0
$217$	−19.9949	+	20.9708i	−1.35735	+	1.42359i
$218$	−9.41281	+	8.07935i	−0.637516	+	0.547203i
$219$		0			0
$220$	−1.89189	+	12.3366i	−0.127551	+	0.831736i
$221$	3.14251			0.211388
$222$		0			0
$223$	3.97664			0.266296			0.133148	−	0.991096i	$-0.457491\pi$
$223$	3.97664			0.266296			0.133148	+	0.991096i	$0.457491\pi$
$224$	−5.22481	+	14.0250i	−0.349097	+	0.937087i
$225$		0			0
$226$	4.39454	−	3.77199i	0.292321	−	0.250909i
$227$	2.54691			0.169045			0.0845223	−	0.996422i	$-0.473064\pi$
$227$	2.54691			0.169045			0.0845223	+	0.996422i	$0.473064\pi$
$228$		0			0
$229$			10.6638i			0.704681i	0.935872	+	0.352341i	$0.114614\pi$
$229$			10.6638i			0.704681i	−0.935872	+	0.352341i	$0.885386\pi$
$230$	−3.81652	+	3.27586i	−0.251654	+	0.216004i
$231$		0			0
$232$	−2.15693	−	3.46229i	−0.141609	−	0.227311i
$233$	20.4421			1.33921			0.669605	−	0.742718i	$-0.266464\pi$
$233$	20.4421			1.33921			0.669605	+	0.742718i	$0.266464\pi$
$234$		0			0
$235$		−	11.6743i		−	0.761546i
$236$	−0.125925	+	0.821137i	−0.00819705	+	0.0534515i
$237$		0			0
$238$	4.88620	+	0.255627i	0.316725	+	0.0165698i
$239$		−	4.38800i		−	0.283836i	−0.989878	−	0.141918i	$-0.954673\pi$
$239$		−	4.38800i		−	0.283836i	0.989878	−	0.141918i	$-0.0453270\pi$
$240$		0			0
$241$			22.5909i			1.45521i	0.685996	+	0.727605i	$0.259367\pi$
$241$			22.5909i			1.45521i	−0.685996	+	0.727605i	$0.740633\pi$
$242$	29.9861	−	25.7382i	1.92758	−	1.65451i
$243$		0			0
$244$	−25.0764	−	3.84559i	−1.60535	−	0.246189i
$245$	6.99206	−	0.333303i	0.446706	−	0.0212940i
$246$		0			0
$247$			9.48742i			0.603670i
$248$	16.3790	+	26.2914i	1.04007	+	1.66951i
$249$		0			0
$250$	0.921096	+	1.07312i	0.0582552	+	0.0678700i
$251$	−12.0822			−0.762624			−0.381312	−	0.924446i	$-0.624528\pi$
$251$	−12.0822			−0.762624			−0.381312	+	0.924446i	$0.624528\pi$
$252$		0			0
$253$	22.1940			1.39532
$254$	6.15840	+	7.17481i	0.386412	+	0.450188i
$255$		0			0
$256$	13.1265	+	9.14853i	0.820405	+	0.571783i
$257$			14.1869i			0.884957i	0.896779	+	0.442478i	$0.145901\pi$
$257$			14.1869i			0.884957i	−0.896779	+	0.442478i	$0.854099\pi$
$258$		0			0
$259$	9.24311	−	9.69422i	0.574339	−	0.602369i
$260$	0.728544	−	4.75070i	0.0451824	−	0.294626i
$261$		0			0
$262$	14.3056	−	12.2790i	0.883801	−	0.758598i
$263$			13.5093i			0.833021i	0.909131	+	0.416511i	$0.136747\pi$
$263$			13.5093i			0.833021i	−0.909131	+	0.416511i	$0.863253\pi$
$264$		0			0
$265$		−	11.7545i		−	0.722074i
$266$	−0.771752	+	14.7517i	−0.0473192	+	0.904487i
$267$		0			0
$268$	6.13027	+	0.940108i	0.374466	+	0.0574262i
$269$			9.57770i			0.583963i	0.956424	+	0.291981i	$0.0943145\pi$
$269$			9.57770i			0.583963i	−0.956424	+	0.291981i	$0.905685\pi$
$270$		0			0
$271$	7.20379			0.437599			0.218800	−	0.975770i	$-0.429786\pi$
$271$	7.20379			0.437599			0.218800	+	0.975770i	$0.429786\pi$
$272$	1.56745	−	4.99034i	0.0950406	−	0.302584i
$273$		0			0
$274$	6.00771	−	5.15663i	0.362939	−	0.311524i
$275$		−	6.24043i		−	0.376312i
$276$		0			0
$277$	22.2563			1.33725			0.668627	−	0.743598i	$-0.266882\pi$
$277$	22.2563			1.33725			0.668627	+	0.743598i	$0.266882\pi$
$278$	6.58398	−	5.65126i	0.394881	−	0.338940i
$279$		0			0
$280$	1.51924	−	7.32748i	0.0907919	−	0.437900i
$281$	−27.2215			−1.62390			−0.811950	−	0.583727i	$-0.801594\pi$
$281$	−27.2215			−1.62390			−0.811950	+	0.583727i	$0.801594\pi$
$282$		0			0
$283$	−18.6312			−1.10751			−0.553754	−	0.832680i	$-0.686805\pi$
$283$	−18.6312			−1.10751			−0.553754	+	0.832680i	$0.686805\pi$
$284$	20.7103	+	3.17603i	1.22893	+	0.188463i
$285$		0			0
$286$	−16.0930	+	13.8132i	−0.951601	+	0.816793i
$287$	2.41606	+	2.30363i	0.142616	+	0.135979i
$288$		0			0
$289$	15.2900			0.899410
$290$	1.32842	+	1.54766i	0.0780073	+	0.0908820i
$291$		0			0
$292$	−3.24488	−	0.497619i	−0.189892	−	0.0291210i
$293$			15.4578i			0.903057i	0.892257	+	0.451528i	$0.149121\pi$
$293$			15.4578i			0.903057i	−0.892257	+	0.451528i	$0.850879\pi$
$294$		0			0
$295$		−	0.415368i		−	0.0241837i
$296$	−7.57155	−	12.1538i	−0.440088	−	0.706426i
$297$		0			0
$298$	−13.2535	+	11.3760i	−0.767756	+	0.658992i
$299$	−8.54664			−0.494265
$300$		0			0
$301$	−4.20979	−	4.01389i	−0.242648	−	0.231357i
$302$	14.7056	+	17.1327i	0.846213	+	0.985877i
$303$		0			0
$304$	15.0661	+	4.73222i	0.864101	+	0.271412i
$305$	12.6848			0.726329
$306$		0			0
$307$	−30.4225			−1.73630			−0.868151	−	0.496299i	$-0.834692\pi$
$307$	−30.4225			−1.73630			−0.868151	+	0.496299i	$0.834692\pi$
$308$	−26.1463	+	20.1687i	−1.48982	+	1.14922i
$309$		0			0
$310$	−10.0875	−	11.7524i	−0.572933	−	0.667493i
$311$	6.24557			0.354154			0.177077	−	0.984197i	$-0.443336\pi$
$311$	6.24557			0.354154			0.177077	+	0.984197i	$0.443336\pi$
$312$		0			0
$313$			14.5063i			0.819945i	0.912098	+	0.409973i	$0.134462\pi$
$313$			14.5063i			0.819945i	−0.912098	+	0.409973i	$0.865538\pi$
$314$	4.75254	+	5.53692i	0.268201	+	0.312467i
$315$		0			0
$316$	18.1667	+	2.78595i	1.02195	+	0.156722i
$317$	−2.29755			−0.129043			−0.0645215	−	0.997916i	$-0.520552\pi$
$317$	−2.29755			−0.129043			−0.0645215	+	0.997916i	$0.520552\pi$
$318$		0			0
$319$		−	9.00003i		−	0.503905i
$320$	−7.18078	−	3.52653i	−0.401418	−	0.197139i
$321$		0			0
$322$	−13.2889	−	0.695225i	−0.740564	−	0.0387434i
$323$		−	5.16266i		−	0.287258i
$324$		0			0
$325$			2.40312i			0.133301i
$326$	1.17251	+	1.36603i	0.0649393	+	0.0756572i
$327$		0			0
$328$	3.02906	−	1.88704i	0.167252	−	0.104194i
$329$	21.3143	−	22.3545i	1.17509	−	1.23244i
$330$		0			0
$331$			23.4483i			1.28884i	0.764673	+	0.644419i	$0.222901\pi$
$331$			23.4483i			1.28884i	−0.764673	+	0.644419i	$0.777099\pi$
$332$	−2.24319	+	14.6274i	−0.123111	+	0.802785i
$333$		0			0
$334$	−23.2467	+	19.9535i	−1.27200	+	1.09181i
$335$	−3.10097			−0.169424
$336$		0			0
$337$	14.6709			0.799174			0.399587	−	0.916695i	$-0.369153\pi$
$337$	14.6709			0.799174			0.399587	+	0.916695i	$0.369153\pi$
$338$	−7.75329	+	6.65493i	−0.421723	+	0.361980i
$339$		0			0
$340$	−0.396443	+	2.58513i	−0.0215002	+	0.140199i
$341$			68.3431i			3.70099i
$342$		0			0
$343$	13.9973	+	12.1275i	0.755782	+	0.654823i
$344$	−5.27789	+	3.28801i	−0.284565	+	0.177277i
$345$		0			0
$346$	11.9530	+	13.9258i	0.642596	+	0.748654i
$347$			21.6099i			1.16008i	0.814587	+	0.580041i	$0.196964\pi$
$347$			21.6099i			1.16008i	−0.814587	+	0.580041i	$0.803036\pi$
$348$		0			0
$349$			0.885917i			0.0474220i	0.999719	+	0.0237110i	$0.00754816\pi$
$349$			0.885917i			0.0474220i	−0.999719	+	0.0237110i	$0.992452\pi$
$350$	−0.195481	+	3.73655i	−0.0104489	+	0.199727i
$351$		0			0
$352$	13.9085	+	32.4458i	0.741326	+	1.72937i
$353$			14.2476i			0.758325i	0.925330	+	0.379163i	$0.123788\pi$
$353$			14.2476i			0.758325i	−0.925330	+	0.379163i	$0.876212\pi$
$354$		0			0
$355$	−10.4762			−0.556019
$356$	−22.6251	−	3.46967i	−1.19913	−	0.183892i
$357$		0			0
$358$	−13.9553	−	16.2586i	−0.737560	−	0.859291i
$359$		−	23.9005i		−	1.26142i	−0.776018	−	0.630710i	$-0.782764\pi$
$359$		−	23.9005i		−	1.26142i	0.776018	−	0.630710i	$-0.217236\pi$
$360$		0			0
$361$	−3.41362			−0.179664
$362$	−2.69288	−	3.13733i	−0.141535	−	0.164894i
$363$		0			0
$364$	10.0686	−	7.76675i	0.527740	−	0.407088i
$365$	1.64141			0.0859153
$366$		0			0
$367$	32.8358			1.71401			0.857007	−	0.515304i	$-0.172321\pi$
$367$	32.8358			1.71401			0.857007	+	0.515304i	$0.172321\pi$
$368$	−4.26297	+	13.5722i	−0.222223	+	0.707498i
$369$		0			0
$370$	4.66319	+	5.43282i	0.242427	+	0.282439i
$371$	21.4608	−	22.5081i	1.11419	−	1.16856i
$372$		0			0
$373$	11.9520			0.618852			0.309426	−	0.950923i	$-0.399863\pi$
$373$	11.9520			0.618852			0.309426	+	0.950923i	$0.399863\pi$
$374$	8.75716	−	7.51658i	0.452822	−	0.388673i
$375$		0			0
$376$	−17.4597	−	28.0262i	−0.900416	−	1.44534i
$377$			3.46581i			0.178498i
$378$		0			0
$379$			21.9351i			1.12673i	0.826208	+	0.563366i	$0.190494\pi$
$379$			21.9351i			1.12673i	−0.826208	+	0.563366i	$0.809506\pi$
$380$	−7.80468	−	1.19689i	−0.400371	−	0.0613990i
$381$		0			0
$382$	−12.8471	−	14.9675i	−0.657316	−	0.765803i
$383$	−28.3845			−1.45038			−0.725190	−	0.688549i	$-0.758248\pi$
$383$	−28.3845			−1.45038			−0.725190	+	0.688549i	$0.758248\pi$
$384$		0			0
$385$	11.3934	−	11.9495i	0.580664	−	0.609003i
$386$	14.3657	−	12.3306i	0.731194	−	0.627610i
$387$		0			0
$388$	24.5991	+	3.77239i	1.24883	+	0.191514i
$389$	−22.0568			−1.11832			−0.559162	−	0.829058i	$-0.688877\pi$
$389$	−22.0568			−1.11832			−0.559162	+	0.829058i	$0.688877\pi$
$390$		0			0
$391$	4.65073			0.235197
$392$	16.2872	−	11.2573i	0.822629	−	0.568578i
$393$		0			0
$394$	4.37821	−	3.75797i	0.220571	−	0.189324i
$395$	−9.18952			−0.462375
$396$		0			0
$397$			37.0058i			1.85727i	0.370997	+	0.928634i	$0.379016\pi$
$397$			37.0058i			1.85727i	−0.370997	+	0.928634i	$0.620984\pi$
$398$	−3.93710	+	3.37935i	−0.197349	+	0.169392i
$399$		0			0
$400$	3.81618	+	1.19865i	0.190809	+	0.0599325i
$401$	1.70729			0.0852580			0.0426290	−	0.999091i	$-0.486427\pi$
$401$	1.70729			0.0852580			0.0426290	+	0.999091i	$0.486427\pi$
$402$		0			0
$403$		−	26.3182i		−	1.31100i
$404$	8.41335	+	1.29023i	0.418580	+	0.0641913i
$405$		0			0
$406$	−0.281926	+	5.38890i	−0.0139917	+	0.267446i
$407$		−	31.5931i		−	1.56601i
$408$		0			0
$409$		−	26.3062i		−	1.30076i	−0.759609	−	0.650379i	$-0.774610\pi$
$409$		−	26.3062i		−	1.30076i	0.759609	−	0.650379i	$-0.225390\pi$
$410$	−1.35401	+	1.16219i	−0.0668696	+	0.0573965i
$411$		0			0
$412$	−4.64614	+	30.2967i	−0.228899	+	1.49261i
$413$	0.758357	−	0.795368i	0.0373163	−	0.0391375i
$414$		0			0
$415$		−	7.39922i		−	0.363213i
$416$	−5.35601	−	12.4945i	−0.262600	−	0.612594i
$417$		0			0
$418$	22.6930	+	26.4384i	1.10995	+	1.29314i
$419$	−5.33293			−0.260531			−0.130265	−	0.991479i	$-0.541583\pi$
$419$	−5.33293			−0.260531			−0.130265	+	0.991479i	$0.541583\pi$
$420$		0			0
$421$	−14.7096			−0.716903			−0.358451	−	0.933548i	$-0.616695\pi$
$421$	−14.7096			−0.716903			−0.358451	+	0.933548i	$0.616695\pi$
$422$	−5.23014	−	6.09335i	−0.254599	−	0.296620i
$423$		0			0
$424$	−17.5797	−	28.2188i	−0.853746	−	1.37043i
$425$		−	1.30768i		−	0.0634317i
$426$		0			0
$427$	24.2895	+	23.1592i	1.17545	+	1.12075i
$428$	−9.56506	−	1.46685i	−0.462345	−	0.0709029i
$429$		0			0
$430$	2.35925	−	2.02502i	0.113773	−	0.0976554i
$431$		−	20.0200i		−	0.964331i	−0.876080	−	0.482166i	$-0.839850\pi$
$431$		−	20.0200i		−	0.964331i	0.876080	−	0.482166i	$-0.160150\pi$
$432$		0			0
$433$		−	8.87770i		−	0.426635i	−0.976983	−	0.213317i	$-0.931573\pi$
$433$		−	8.87770i		−	0.426635i	0.976983	−	0.213317i	$-0.0684268\pi$
$434$	2.14084	−	40.9214i	0.102764	−	1.96429i
$435$		0			0
$436$	2.65921	−	17.3402i	0.127353	−	0.830445i
$437$			14.0408i			0.671664i
$438$		0			0
$439$	25.3037			1.20768			0.603841	−	0.797105i	$-0.293636\pi$
$439$	25.3037			1.20768			0.603841	+	0.797105i	$0.293636\pi$
$440$	−9.33301	−	14.9813i	−0.444934	−	0.714205i
$441$		0			0
$442$	−3.37228	+	2.89455i	−0.160403	+	0.137680i
$443$		−	27.9709i		−	1.32894i	−0.747317	−	0.664468i	$-0.768658\pi$
$443$		−	27.9709i		−	1.32894i	0.747317	−	0.664468i	$-0.231342\pi$
$444$		0			0
$445$	11.4448			0.542535
$446$	−4.26741	+	3.66287i	−0.202068	+	0.173442i
$447$		0			0
$448$	−7.31156	−	19.8631i	−0.345439	−	0.938441i
$449$	36.0790			1.70267			0.851337	−	0.524619i	$-0.175792\pi$
$449$	36.0790			1.70267			0.851337	+	0.524619i	$0.175792\pi$
$450$		0			0
$451$	7.87386			0.370765
$452$	−1.24150	+	8.09559i	−0.0583952	+	0.380784i
$453$		0			0
$454$	−2.73314	+	2.34595i	−0.128273	+	0.110101i
$455$	−4.38749	+	4.60162i	−0.205689	+	0.215727i
$456$		0			0
$457$	−4.26370			−0.199448			−0.0997238	−	0.995015i	$-0.531796\pi$
$457$	−4.26370			−0.199448			−0.0997238	+	0.995015i	$0.531796\pi$
$458$	−9.82235	−	11.4435i	−0.458968	−	0.534719i
$459$		0			0
$460$	1.07820	−	7.03076i	0.0502714	−	0.327811i
$461$		−	18.7953i		−	0.875386i	−0.899124	−	0.437693i	$-0.855796\pi$
$461$		−	18.7953i		−	0.875386i	0.899124	−	0.437693i	$-0.144204\pi$
$462$		0			0
$463$		−	38.2151i		−	1.77601i	−0.459836	−	0.888004i	$-0.652092\pi$
$463$		−	38.2151i		−	1.77601i	0.459836	−	0.888004i	$-0.347908\pi$
$464$	5.50374	+	1.72871i	0.255505	+	0.0802533i
$465$		0			0
$466$	−21.9368	+	18.8292i	−1.01620	+	0.872244i
$467$	15.7945			0.730882			0.365441	−	0.930834i	$-0.380918\pi$
$467$	15.7945			0.730882			0.365441	+	0.930834i	$0.380918\pi$
$468$		0			0
$469$	−5.93789	−	5.66158i	−0.274186	−	0.261428i
$470$	10.7531	+	12.5279i	0.496005	+	0.577868i
$471$		0			0
$472$	−0.621213	−	0.997166i	−0.0285936	−	0.0458983i
$473$	−13.7196			−0.630826
$474$		0			0
$475$	3.94796			0.181145
$476$	−5.47893	+	4.22634i	−0.251126	+	0.193714i
$477$		0			0
$478$	4.04177	+	4.70885i	0.184866	+	0.215378i
$479$	33.1809			1.51608			0.758038	−	0.652210i	$-0.226158\pi$
$479$	33.1809			1.51608			0.758038	+	0.652210i	$0.226158\pi$
$480$		0			0
$481$			12.1662i			0.554729i
$482$	−20.8084	−	24.2428i	−0.947798	−	1.10423i
$483$		0			0
$484$	−8.47136	+	55.2402i	−0.385062	+	2.51092i
$485$	−12.4433			−0.565022
$486$		0			0
$487$			18.8854i			0.855781i	0.903831	+	0.427891i	$0.140743\pi$
$487$			18.8854i			0.855781i	−0.903831	+	0.427891i	$0.859257\pi$
$488$	30.4521	−	18.9710i	1.37850	−	0.858777i
$489$		0			0
$490$	−7.19630	+	6.79803i	−0.325096	+	0.307104i
$491$			1.14336i			0.0515989i	0.999667	+	0.0257995i	$0.00821314\pi$
$491$			1.14336i			0.0515989i	−0.999667	+	0.0257995i	$0.991787\pi$
$492$		0			0
$493$		−	1.88595i		−	0.0849389i
$494$	−8.73882	−	10.1811i	−0.393178	−	0.458070i
$495$		0			0
$496$	−41.7935	−	13.1272i	−1.87658	−	0.589429i
$497$	−20.0604	−	19.1269i	−0.899831	−	0.857959i
$498$		0			0
$499$			18.8734i			0.844890i	0.906389	+	0.422445i	$0.138828\pi$
$499$			18.8734i			0.844890i	−0.906389	+	0.422445i	$0.861172\pi$
$500$	−1.97689	−	0.303166i	−0.0884092	−	0.0135580i
$501$		0			0
$502$	12.9657	−	11.1289i	0.578686	−	0.496707i
$503$	−18.8624			−0.841035			−0.420517	−	0.907284i	$-0.638151\pi$
$503$	−18.8624			−0.841035			−0.420517	+	0.907284i	$0.638151\pi$
$504$		0			0
$505$	−4.25585			−0.189383
$506$	−23.8167	+	20.4428i	−1.05878	+	0.908791i
$507$		0			0
$508$	−13.2174	−	2.02695i	−0.586426	−	0.0899314i
$509$			24.1765i			1.07160i	0.844344	+	0.535801i	$0.179990\pi$
$509$			24.1765i			1.07160i	−0.844344	+	0.535801i	$0.820010\pi$
$510$		0			0
$511$	3.14305	+	2.99680i	0.139040	+	0.132570i
$512$	−22.5129	+	2.27328i	−0.994941	+	0.100466i
$513$		0			0
$514$	−13.0675	−	15.2243i	−0.576384	−	0.671513i
$515$		−	15.3254i		−	0.675319i
$516$		0			0
$517$		−	72.8525i		−	3.20405i
$518$	−0.989654	+	18.9168i	−0.0434829	+	0.831158i
$519$		0			0
$520$	3.59404	+	5.76913i	0.157609	+	0.252993i
$521$		−	17.2367i		−	0.755152i	−0.925979	−	0.377576i	$-0.876758\pi$
$521$		−	17.2367i		−	0.755152i	0.925979	−	0.377576i	$-0.123242\pi$
$522$		0			0
$523$	−14.1555			−0.618975			−0.309487	−	0.950904i	$-0.600157\pi$
$523$	−14.1555			−0.618975			−0.309487	+	0.950904i	$0.600157\pi$
$524$	−4.04145	+	26.3536i	−0.176552	+	1.15126i
$525$		0			0
$526$	−12.4434	−	14.4971i	−0.542557	−	0.632104i
$527$			14.3212i			0.623843i
$528$		0			0
$529$	10.3515			0.450064
$530$	10.8270	+	12.6140i	0.470296	+	0.547916i
$531$		0			0
$532$	−12.7596	−	16.5412i	−0.553198	−	0.717153i
$533$	−3.03213			−0.131336
$534$		0			0
$535$	4.83844			0.209184
$536$	−7.44444	+	4.63772i	−0.321551	+	0.200319i
$537$		0			0
$538$	−8.82198	−	10.2780i	−0.380342	−	0.443116i
$539$	43.6335	−	2.07996i	1.87943	−	0.0895900i
$540$		0			0
$541$	20.6842			0.889283			0.444642	−	0.895709i	$-0.353331\pi$
$541$	20.6842			0.889283			0.444642	+	0.895709i	$0.353331\pi$
$542$	−7.73052	+	6.63538i	−0.332054	+	0.285014i
$543$		0			0
$544$	2.91452	+	6.79899i	0.124959	+	0.291504i
$545$			8.77146i			0.375728i
$546$		0			0
$547$		−	14.1854i		−	0.606526i	−0.952907	−	0.303263i	$-0.901924\pi$
$547$		−	14.1854i		−	0.606526i	0.952907	−	0.303263i	$-0.0980760\pi$
$548$	−1.69723	+	11.0674i	−0.0725023	+	0.472774i
$549$		0			0
$550$	5.74803	+	6.69672i	0.245097	+	0.285549i
$551$	5.69380			0.242564
$552$		0			0
$553$	−17.5966	−	16.7777i	−0.748282	−	0.713462i
$554$	−23.8837	+	20.5002i	−1.01472	+	0.870971i
$555$		0			0
$556$	−1.86003	+	12.1289i	−0.0788830	+	0.514382i
$557$	23.5297			0.996987			0.498494	−	0.866893i	$-0.333887\pi$
$557$	23.5297			0.996987			0.498494	+	0.866893i	$0.333887\pi$
$558$		0			0
$559$	5.28325			0.223458
$560$	5.11898	+	9.26261i	0.216317	+	0.391417i
$561$		0			0
$562$	29.2119	−	25.0736i	1.23223	−	1.05767i
$563$	−30.5742			−1.28855			−0.644275	−	0.764794i	$-0.722841\pi$
$563$	−30.5742			−1.28855			−0.644275	+	0.764794i	$0.722841\pi$
$564$		0			0
$565$		−	4.09511i		−	0.172283i
$566$	19.9935	−	17.1611i	0.840388	−	0.721335i
$567$		0			0
$568$	−25.1500	+	15.6679i	−1.05527	+	0.657411i
$569$	−12.0943			−0.507018			−0.253509	−	0.967333i	$-0.581585\pi$
$569$	−12.0943			−0.507018			−0.253509	+	0.967333i	$0.581585\pi$
$570$		0			0
$571$			20.1686i			0.844029i	0.906589	+	0.422015i	$0.138677\pi$
$571$			20.1686i			0.844029i	−0.906589	+	0.422015i	$0.861323\pi$
$572$	4.54643	−	29.6464i	0.190096	−	1.23958i
$573$		0			0
$574$	−4.71458	−	0.246648i	−0.196783	−	0.0102949i
$575$			3.55648i			0.148315i
$576$		0			0
$577$			2.82405i			0.117567i	0.998271	+	0.0587834i	$0.0187221\pi$
$577$			2.82405i			0.117567i	−0.998271	+	0.0587834i	$0.981278\pi$
$578$	−16.4080	+	14.0835i	−0.682481	+	0.585798i
$579$		0			0
$580$	−2.85109	−	0.437230i	−0.118385	−	0.0181550i
$581$	13.5091	−	14.1684i	0.560451	−	0.587804i
$582$		0			0
$583$		−	73.3532i		−	3.03798i
$584$	3.94050	−	2.45484i	0.163059	−	0.101582i
$585$		0			0
$586$	−14.2381	−	16.5881i	−0.588172	−	0.685248i
$587$	0.0213868			0.000882727			0.000441363	−	1.00000i	$-0.499860\pi$
$587$	0.0213868			0.000882727			0.000441363		1.00000i	$0.499860\pi$
$588$		0			0
$589$	−43.2367			−1.78154
$590$	0.382594	+	0.445739i	0.0157511	+	0.0183508i
$591$		0			0
$592$	19.3200	+	6.06835i	0.794047	+	0.249408i
$593$			31.7082i			1.30210i	0.759036	+	0.651049i	$0.225671\pi$
$593$			31.7082i			1.30210i	−0.759036	+	0.651049i	$0.774329\pi$
$594$		0			0
$595$	2.38749	−	2.50401i	0.0978775	−	0.102654i
$596$	3.74424	−	24.4155i	0.153370	−	1.00010i
$597$		0			0
$598$	9.17156	−	7.87228i	0.375053	−	0.321921i
$599$		−	17.4804i		−	0.714229i	−0.934061	−	0.357114i	$-0.883761\pi$
$599$		−	17.4804i		−	0.714229i	0.934061	−	0.357114i	$-0.116239\pi$
$600$		0			0
$601$			45.4399i			1.85353i	0.375637	+	0.926767i	$0.377424\pi$
$601$			45.4399i			1.85353i	−0.375637	+	0.926767i	$0.622576\pi$
$602$	8.21478	+	0.429765i	0.334810	+	0.0175159i
$603$		0			0
$604$	−31.5617	−	4.84015i	−1.28423	−	0.196943i
$605$		−	27.9430i		−	1.13604i
$606$		0			0
$607$	−12.3160			−0.499893			−0.249946	−	0.968260i	$-0.580413\pi$
$607$	−12.3160			−0.499893			−0.249946	+	0.968260i	$0.580413\pi$
$608$	−20.5266	+	8.79911i	−0.832462	+	0.356851i
$609$		0			0
$610$	−13.6123	+	11.6839i	−0.551145	+	0.473067i
$611$			28.0547i			1.13497i
$612$		0			0
$613$	27.3548			1.10485			0.552424	−	0.833563i	$-0.313703\pi$
$613$	27.3548			1.10485			0.552424	+	0.833563i	$0.313703\pi$
$614$	32.6469	−	28.0220i	1.31752	−	1.13088i
$615$		0			0
$616$	9.48070	−	45.7266i	0.381988	−	1.84238i
$617$	44.5457			1.79334			0.896671	−	0.442698i	$-0.145979\pi$
$617$	44.5457			1.79334			0.896671	+	0.442698i	$0.145979\pi$
$618$		0			0
$619$	−23.1713			−0.931334			−0.465667	−	0.884960i	$-0.654185\pi$
$619$	−23.1713			−0.931334			−0.465667	+	0.884960i	$0.654185\pi$
$620$	21.6502	+	3.32017i	0.869494	+	0.133341i
$621$		0			0
$622$	−6.70223	+	5.75276i	−0.268735	+	0.230665i
$623$	21.9150	+	20.8953i	0.878008	+	0.837151i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−13.3617	−	15.5670i	−0.534041	−	0.622182i
$627$		0			0
$628$	−10.2001	−	1.56423i	−0.407027	−	0.0624197i
$629$		−	6.62032i		−	0.263969i
$630$		0			0
$631$			10.4615i			0.416464i	0.978079	+	0.208232i	$0.0667709\pi$
$631$			10.4615i			0.416464i	−0.978079	+	0.208232i	$0.933229\pi$
$632$	−22.0611	+	13.7436i	−0.877543	+	0.546690i
$633$		0			0
$634$	2.46554	−	2.11626i	0.0979190	−	0.0840474i
$635$	6.68595			0.265324
$636$		0			0
$637$	−16.8028	+	0.800968i	−0.665750	+	0.0317355i
$638$	8.28989	+	9.65810i	0.328200	+	0.382368i
$639$		0			0
$640$	10.9541	−	2.82979i	0.432999	−	0.111857i
$641$	−21.4122			−0.845731			−0.422866	−	0.906192i	$-0.638976\pi$
$641$	−21.4122			−0.845731			−0.422866	+	0.906192i	$0.638976\pi$
$642$		0			0
$643$	−26.2531			−1.03532			−0.517661	−	0.855586i	$-0.673197\pi$
$643$	−26.2531			−1.03532			−0.517661	+	0.855586i	$0.673197\pi$
$644$	14.9010	−	11.4943i	0.587181	−	0.452940i
$645$		0			0
$646$	4.75530	+	5.54014i	0.187095	+	0.217974i
$647$	6.99553			0.275023			0.137511	−	0.990500i	$-0.456090\pi$
$647$	6.99553			0.275023			0.137511	+	0.990500i	$0.456090\pi$
$648$		0			0
$649$		−	2.59208i		−	0.101748i
$650$	−2.21350	−	2.57883i	−0.0868208	−	0.101150i
$651$		0			0
$652$	−2.51648	−	0.385915i	−0.0985530	−	0.0151136i
$653$	−21.1729			−0.828559			−0.414280	−	0.910150i	$-0.635966\pi$
$653$	−21.1729			−0.828559			−0.414280	+	0.910150i	$0.635966\pi$
$654$		0			0
$655$		−	13.3308i		−	0.520879i
$656$	−1.51240	+	4.81506i	−0.0590491	+	0.187997i
$657$		0			0
$658$	−2.28210	+	43.6215i	−0.0889656	+	1.70054i
$659$			21.4552i			0.835774i	0.908499	+	0.417887i	$0.137229\pi$
$659$			21.4552i			0.835774i	−0.908499	+	0.417887i	$0.862771\pi$
$660$		0			0
$661$			19.5116i			0.758914i	0.925209	+	0.379457i	$0.123889\pi$
$661$			19.5116i			0.758914i	−0.925209	+	0.379457i	$0.876111\pi$
$662$	−21.5982	−	25.1628i	−0.839437	−	0.977982i
$663$		0			0
$664$	−11.0661	−	17.7632i	−0.429446	−	0.689344i
$665$	7.55975	+	7.20797i	0.293155	+	0.279513i
$666$		0			0
$667$			5.12920i			0.198603i
$668$	6.56741	−	42.8249i	0.254101	−	1.65695i
$669$		0			0
$670$	3.32771	−	2.85629i	0.128561	−	0.110348i
$671$	79.1585			3.05588
$672$		0			0
$673$	2.26978			0.0874936			0.0437468	−	0.999043i	$-0.486071\pi$
$673$	2.26978			0.0874936			0.0437468	+	0.999043i	$0.486071\pi$
$674$	−15.7436	+	13.5133i	−0.606421	+	0.520513i
$675$		0			0
$676$	2.19038	−	14.2830i	0.0842452	−	0.549348i
$677$		−	17.8761i		−	0.687035i	−0.939146	−	0.343518i	$-0.888381\pi$
$677$		−	17.8761i		−	0.687035i	0.939146	−	0.343518i	$-0.111619\pi$
$678$		0			0
$679$	−23.8271	−	22.7183i	−0.914400	−	0.871850i
$680$	−1.95573	−	3.13932i	−0.0749986	−	0.120387i
$681$		0			0
$682$	−62.9505	−	73.3402i	−2.41050	−	2.80834i
$683$		−	4.47109i		−	0.171081i	−0.996335	−	0.0855407i	$-0.972738\pi$
$683$		−	4.47109i		−	0.171081i	0.996335	−	0.0855407i	$-0.0272618\pi$
$684$		0			0
$685$		−	5.59837i		−	0.213903i
$686$	−26.1913	−	0.121414i	−0.999989	−	0.00463560i
$687$		0			0
$688$	2.63523	−	8.38986i	0.100467	−	0.319860i
$689$			28.2475i			1.07614i
$690$		0			0
$691$	2.13713			0.0813003			0.0406502	−	0.999173i	$-0.487057\pi$
$691$	2.13713			0.0813003			0.0406502	+	0.999173i	$0.487057\pi$
$692$	−25.6539	−	3.93416i	−0.975216	−	0.149554i
$693$		0			0
$694$	−19.9048	−	23.1900i	−0.755577	−	0.880281i
$695$		−	6.13537i		−	0.232728i
$696$		0			0
$697$	1.64996			0.0624967
$698$	−0.816014	−	0.950694i	−0.0308866	−	0.0359843i
$699$		0			0
$700$	−3.23194	−	4.18981i	−0.122156	−	0.158360i
$701$	−2.37715			−0.0897836			−0.0448918	−	0.998992i	$-0.514294\pi$
$701$	−2.37715			−0.0897836			−0.0448918	+	0.998992i	$0.514294\pi$
$702$		0			0
$703$	19.9871			0.753829
$704$	−44.8111	−	22.0071i	−1.68888	−	0.829424i
$705$		0			0
$706$	−13.1234	−	15.2894i	−0.493907	−	0.575424i
$707$	−8.14932	−	7.77011i	−0.306487	−	0.292225i
$708$		0			0
$709$	−11.2074			−0.420904			−0.210452	−	0.977604i	$-0.567494\pi$
$709$	−11.2074			−0.420904			−0.210452	+	0.977604i	$0.567494\pi$
$710$	11.2422	−	9.64959i	0.421913	−	0.362143i
$711$		0			0
$712$	27.4753	−	17.1165i	1.02968	−	0.641467i
$713$		−	38.9493i		−	1.45866i
$714$		0			0
$715$			14.9965i			0.560838i
$716$	29.9514	+	4.59319i	1.11934	+	0.171656i
$717$		0			0
$718$	22.0147	+	25.6481i	0.821580	+	0.957178i
$719$	−43.4702			−1.62116			−0.810582	−	0.585624i	$-0.800849\pi$
$719$	−43.4702			−1.62116			−0.810582	+	0.585624i	$0.800849\pi$
$720$		0			0
$721$	27.9803	−	29.3459i	1.04204	−	1.09290i
$722$	3.66322	−	3.14427i	0.136331	−	0.117018i
$723$		0			0
$724$	5.77956	+	0.886324i	0.214795	+	0.0329400i
$725$	1.44221			0.0535624
$726$		0			0
$727$	8.53645			0.316599			0.158300	−	0.987391i	$-0.449399\pi$
$727$	8.53645			0.316599			0.158300	+	0.987391i	$0.449399\pi$
$728$	−3.65091	+	17.6088i	−0.135312	+	0.652626i
$729$		0			0
$730$	−1.76143	+	1.51189i	−0.0651933	+	0.0559577i
$731$	−2.87492			−0.106333
$732$		0			0
$733$			12.7274i			0.470098i	0.971984	+	0.235049i	$0.0755250\pi$
$733$			12.7274i			0.470098i	−0.971984	+	0.235049i	$0.924475\pi$
$734$	−35.2367	+	30.2449i	−1.30061	+	1.11636i
$735$		0			0
$736$	−7.92658	−	18.4911i	−0.292178	−	0.681592i
$737$	−19.3514			−0.712818
$738$		0			0
$739$		−	17.6922i		−	0.650817i	−0.945573	−	0.325409i	$-0.894498\pi$
$739$		−	17.6922i		−	0.650817i	0.945573	−	0.325409i	$-0.105502\pi$
$740$	−10.0083	−	1.53482i	−0.367912	−	0.0564212i
$741$		0			0
$742$	−2.29779	+	43.9213i	−0.0843544	+	1.61240i
$743$		−	11.0428i		−	0.405122i	−0.979270	−	0.202561i	$-0.935074\pi$
$743$		−	11.0428i		−	0.405122i	0.979270	−	0.202561i	$-0.0649265\pi$
$744$		0			0
$745$			12.3505i			0.452486i
$746$	−12.8259	+	11.0090i	−0.469591	+	0.403066i
$747$		0			0
$748$	−2.47398	+	16.1324i	−0.0904576	+	0.589857i
$749$	9.26489	+	8.83376i	0.338532	+	0.322779i
$750$		0			0
$751$			18.4917i			0.674771i	0.941367	+	0.337385i	$0.109543\pi$
$751$			18.4917i			0.674771i	−0.941367	+	0.337385i	$0.890457\pi$
$752$	44.5512	+	13.9934i	1.62461	+	0.510286i
$753$		0			0
$754$	−3.19234	−	3.71923i	−0.116258	−	0.135446i
$755$	15.9654			0.581039
$756$		0			0
$757$	−20.2498			−0.735992			−0.367996	−	0.929827i	$-0.619956\pi$
$757$	−20.2498			−0.735992			−0.367996	+	0.929827i	$0.619956\pi$
$758$	−20.2043	−	23.5390i	−0.733855	−	0.854974i
$759$		0			0
$760$	9.47779	−	5.90445i	0.343795	−	0.214177i
$761$		−	25.4306i		−	0.921857i	−0.887437	−	0.460928i	$-0.847516\pi$
$761$		−	25.4306i		−	0.921857i	0.887437	−	0.460928i	$-0.152484\pi$
$762$		0			0
$763$	−16.0145	+	16.7960i	−0.579762	+	0.608057i
$764$	27.5730	+	4.22845i	0.997555	+	0.152980i
$765$		0			0
$766$	30.4599	−	26.1448i	1.10056	−	0.944651i
$767$			0.998180i			0.0360422i
$768$		0			0
$769$			31.4563i			1.13434i	0.823600	+	0.567172i	$0.191962\pi$
$769$			31.4563i			1.13434i	−0.823600	+	0.567172i	$0.808038\pi$
$770$	−1.21989	+	23.3177i	−0.0439617	+	0.840310i
$771$		0			0
$772$	−4.05844	+	26.4643i	−0.146066	+	0.952472i
$773$		−	9.51127i		−	0.342097i	−0.985263	−	0.171048i	$-0.945285\pi$
$773$		−	9.51127i		−	0.342097i	0.985263	−	0.171048i	$-0.0547154\pi$
$774$		0			0
$775$	−10.9517			−0.393395
$776$	−29.8724	+	18.6099i	−1.07236	+	0.668055i
$777$		0			0
$778$	23.6696	−	20.3164i	0.848595	−	0.728379i
$779$			4.98133i			0.178475i
$780$		0			0
$781$	−65.3761			−2.33934
$782$	−4.99078	+	4.28376i	−0.178470	+	0.153187i
$783$		0			0
$784$	−7.10909	+	27.0825i	−0.253896	+	0.967231i
$785$	5.15966			0.184156
$786$		0			0
$787$	23.8141			0.848880			0.424440	−	0.905456i	$-0.360471\pi$
$787$	23.8141			0.848880			0.424440	+	0.905456i	$0.360471\pi$
$788$	−1.23688	+	8.06550i	−0.0440622	+	0.287321i
$789$		0			0
$790$	9.86144	−	8.46443i	0.350854	−	0.301151i
$791$	7.47664	−	7.84153i	0.265839	−	0.278813i
$792$		0			0
$793$	−30.4831			−1.08249
$794$	−34.0859	−	39.7116i	−1.20966	−	1.40931i
$795$		0			0
$796$	1.11227	−	7.25289i	0.0394233	−	0.257072i
$797$			38.0855i			1.34906i	0.738248	+	0.674529i	$0.235653\pi$
$797$			38.0855i			1.34906i	−0.738248	+	0.674529i	$0.764347\pi$
$798$		0			0
$799$		−	15.2662i		−	0.540079i
$800$	−5.19929	+	2.22877i	−0.183822	+	0.0787990i
$801$		0			0
$802$	−1.83212	+	1.57258i	−0.0646945	+	0.0555296i
$803$	10.2431			0.361471
$804$		0			0
$805$	−6.49322	+	6.81012i	−0.228856	+	0.240025i
$806$	24.2415	+	28.2425i	0.853872	+	0.994800i
$807$		0			0
$808$	−10.2169	+	6.36493i	−0.359431	+	0.223917i
$809$	−0.368855			−0.0129682			−0.00648412	−	0.999979i	$-0.502064\pi$
$809$	−0.368855			−0.0129682			−0.00648412	+	0.999979i	$0.502064\pi$
$810$		0			0
$811$	−4.21418			−0.147980			−0.0739900	−	0.997259i	$-0.523573\pi$
$811$	−4.21418			−0.147980			−0.0739900	+	0.997259i	$0.523573\pi$
$812$	−4.66115	−	6.04260i	−0.163574	−	0.212054i
$813$		0			0
$814$	29.1003	+	33.9032i	1.01996	+	1.18831i
$815$	1.27295			0.0445895
$816$		0			0
$817$		−	8.67957i		−	0.303660i
$818$	24.2305	+	28.2297i	0.847201	+	0.987028i
$819$		0			0
$820$	0.382519	−	2.49434i	0.0133581	−	0.0871060i
$821$	5.15654			0.179964			0.0899822	−	0.995943i	$-0.471319\pi$
$821$	5.15654			0.179964			0.0899822	+	0.995943i	$0.471319\pi$
$822$		0			0
$823$			53.4133i			1.86187i	0.365185	+	0.930935i	$0.381006\pi$
$823$			53.4133i			1.86187i	−0.365185	+	0.930935i	$0.618994\pi$
$824$	−22.9203	−	36.7914i	−0.798465	−	1.28169i
$825$		0			0
$826$	−0.0811967	+	1.55204i	−0.00282520	+	0.0540025i
$827$			13.7009i			0.476426i	0.971213	+	0.238213i	$0.0765617\pi$
$827$			13.7009i			0.476426i	−0.971213	+	0.238213i	$0.923438\pi$
$828$		0			0
$829$			19.5764i			0.679915i	0.940441	+	0.339958i	$0.110413\pi$
$829$			19.5764i			0.679915i	−0.940441	+	0.339958i	$0.889587\pi$
$830$	6.81539	+	7.94023i	0.236565	+	0.275610i
$831$		0			0
$832$	17.2563	+	8.47469i	0.598254	+	0.293807i
$833$	9.14336	−	0.435853i	0.316799	−	0.0151014i
$834$		0			0
$835$			21.6628i			0.749671i
$836$	−48.7045	−	7.46909i	−1.68448	−	0.258324i
$837$		0			0
$838$	5.72286	−	4.91214i	0.197693	−	0.169687i
$839$	−48.5281			−1.67537			−0.837687	−	0.546150i	$-0.816093\pi$
$839$	−48.5281			−1.67537			−0.837687	+	0.546150i	$0.816093\pi$
$840$		0			0
$841$	−26.9200			−0.928277
$842$	15.7852	−	13.5490i	0.543993	−	0.466928i
$843$		0			0
$844$	11.2251	+	1.72143i	0.386384	+	0.0592540i
$845$			7.22501i			0.248548i
$846$		0			0
$847$	51.0168	−	53.5066i	1.75296	−	1.83851i
$848$	44.8574	+	14.0896i	1.54041	+	0.483837i
$849$		0			0
$850$	1.20450	+	1.40329i	0.0413139	+	0.0481326i
$851$			18.0052i			0.617210i
$852$		0			0
$853$		−	2.55438i		−	0.0874603i	−0.999043	−	0.0437302i	$-0.986076\pi$
$853$		−	2.55438i		−	0.0874603i	0.999043	−	0.0437302i	$-0.0139242\pi$
$854$	−47.3973	−	2.47964i	−1.62190	−	0.0848515i
$855$		0			0
$856$	11.6155	−	7.23623i	0.397011	−	0.247329i
$857$			17.1530i			0.585937i	0.956122	+	0.292968i	$0.0946430\pi$
$857$			17.1530i			0.585937i	−0.956122	+	0.292968i	$0.905357\pi$
$858$		0			0
$859$	−43.1437			−1.47204			−0.736022	−	0.676958i	$-0.763298\pi$
$859$	−43.1437			−1.47204			−0.736022	+	0.676958i	$0.763298\pi$
$860$	−0.666509	+	4.34618i	−0.0227278	+	0.148204i
$861$		0			0
$862$	18.4404	+	21.4839i	0.628082	+	0.731744i
$863$		−	36.5532i		−	1.24429i	−0.782904	−	0.622143i	$-0.786262\pi$
$863$		−	36.5532i		−	1.24429i	0.782904	−	0.622143i	$-0.213738\pi$
$864$		0			0
$865$	12.9769			0.441228
$866$	8.17721	+	9.52682i	0.277873	+	0.323734i
$867$		0			0
$868$	35.3951	+	45.8854i	1.20139	+	1.55745i
$869$	−57.3466			−1.94535
$870$		0			0
$871$	7.45200			0.252502
$872$	13.1183	+	21.0575i	0.444243	+	0.713096i
$873$		0			0
$874$	−12.9329	−	15.0675i	−0.437463	−	0.509665i
$875$	1.91485	+	1.82575i	0.0647338	+	0.0617215i
$876$		0			0
$877$	−14.8376			−0.501031			−0.250515	−	0.968113i	$-0.580600\pi$
$877$	−14.8376			−0.501031			−0.250515	+	0.968113i	$0.580600\pi$
$878$	−27.1539	+	23.3072i	−0.916400	+	0.786579i
$879$		0			0
$880$	23.8146	+	7.48010i	0.802791	+	0.252154i
$881$		−	9.84229i		−	0.331595i	−0.986160	−	0.165798i	$-0.946980\pi$
$881$		−	9.84229i		−	0.331595i	0.986160	−	0.165798i	$-0.0530198\pi$
$882$		0			0
$883$			0.749575i			0.0252252i	0.999920	+	0.0126126i	$0.00401482\pi$
$883$			0.749575i			0.0252252i	−0.999920	+	0.0126126i	$0.995985\pi$
$884$	0.952701	−	6.21239i	0.0320428	−	0.208945i
$885$		0			0
$886$	25.7638	+	30.0161i	0.865553	+	1.00841i
$887$	−26.2358			−0.880913			−0.440456	−	0.897774i	$-0.645183\pi$
$887$	−26.2358			−0.880913			−0.440456	+	0.897774i	$0.645183\pi$
$888$		0			0
$889$	12.8026	+	12.2068i	0.429385	+	0.409404i
$890$	−12.2816	+	10.5417i	−0.411680	+	0.353360i
$891$		0			0
$892$	1.20558	−	7.86138i	0.0403659	−	0.263219i
$893$	46.0896			1.54233
$894$		0			0
$895$	−15.1508			−0.506434
$896$	26.1419	+	14.5808i	0.873341	+	0.487109i
$897$		0			0
$898$	−38.7170	+	33.2322i	−1.29200	+	1.10897i
$899$	−15.7946			−0.526780
$900$		0			0
$901$		−	15.3711i		−	0.512086i
$902$	−8.44958	+	7.25258i	−0.281340	+	0.241484i
$903$		0			0
$904$	−6.12453	−	9.83106i	−0.203699	−	0.326976i
$905$	−2.92356			−0.0971825
$906$		0			0
$907$			12.6248i			0.419201i	0.977787	+	0.209601i	$0.0672164\pi$
$907$			12.6248i			0.419201i	−0.977787	+	0.209601i	$0.932784\pi$
$908$	0.772137	−	5.03496i	0.0256243	−	0.167091i
$909$		0			0
$910$	0.469765	−	8.97937i	0.0155726	−	0.297663i
$911$		−	25.1171i		−	0.832167i	−0.909326	−	0.416084i	$-0.863402\pi$
$911$		−	25.1171i		−	0.832167i	0.909326	−	0.416084i	$-0.136598\pi$
$912$		0			0
$913$		−	46.1743i		−	1.52815i
$914$	4.57546	−	3.92728i	0.151343	−	0.129903i
$915$		0			0
$916$	21.0811	+	3.23289i	0.696539	+	0.106818i
$917$	24.3387	−	25.5266i	0.803735	−	0.842961i
$918$		0			0
$919$		−	53.9495i		−	1.77963i	−0.456323	−	0.889814i	$-0.650834\pi$
$919$		−	53.9495i		−	1.77963i	0.456323	−	0.889814i	$-0.349166\pi$
$920$	5.31896	+	8.53797i	0.175361	+	0.281488i
$921$		0			0
$922$	17.3123	+	20.1696i	0.570150	+	0.664251i
$923$	25.1756			0.828665
$924$		0			0
$925$	5.06265			0.166459
$926$	35.1998	+	41.0094i	1.15674	+	1.34765i
$927$		0			0
$928$	−7.49847	+	3.21437i	−0.246149	+	0.105517i
$929$			21.0953i			0.692116i	0.938213	+	0.346058i	$0.112480\pi$
$929$			21.0953i			0.692116i	−0.938213	+	0.346058i	$0.887520\pi$
$930$		0			0
$931$	1.31587	+	27.6044i	0.0431258	+	0.904696i
$932$	6.19736	−	40.4118i	0.203001	−	1.32373i
$933$		0			0
$934$	−16.9494	+	14.5482i	−0.554600	+	0.476033i
$935$		−	8.16048i		−	0.266876i
$936$		0			0
$937$		−	4.64561i		−	0.151765i	−0.997117	−	0.0758827i	$-0.975823\pi$
$937$		−	4.64561i		−	0.151765i	0.997117	−	0.0758827i	$-0.0241774\pi$
$938$	11.5869	+	0.606182i	0.378326	+	0.0197925i
$939$		0			0
$940$	−23.0788	−	3.53924i	−0.752746	−	0.115437i
$941$		−	28.8306i		−	0.939849i	−0.882707	−	0.469925i	$-0.844281\pi$
$941$		−	28.8306i		−	0.939849i	0.882707	−	0.469925i	$-0.155719\pi$
$942$		0			0
$943$	−4.48738			−0.146129
$944$	1.58512	+	0.497881i	0.0515913	+	0.0162047i
$945$		0			0
$946$	14.7227	−	12.6370i	0.478677	−	0.410865i
$947$			18.9318i			0.615200i	0.951516	+	0.307600i	$0.0995259\pi$
$947$			18.9318i			0.615200i	−0.951516	+	0.307600i	$0.900474\pi$
$948$		0			0
$949$	−3.94450			−0.128044
$950$	−4.23663	+	3.63645i	−0.137454	+	0.117982i
$951$		0			0
$952$	1.98667	−	9.58198i	0.0643885	−	0.310554i
$953$	57.1800			1.85224			0.926122	−	0.377225i	$-0.123122\pi$
$953$	57.1800			1.85224			0.926122	+	0.377225i	$0.123122\pi$
$954$		0			0
$955$	−13.9477			−0.451336
$956$	−8.67460	−	1.33029i	−0.280557	−	0.0430248i
$957$		0			0
$958$	−35.6071	+	30.5628i	−1.15041	+	0.987440i
$959$	10.2212	−	10.7200i	0.330060	−	0.346168i
$960$		0			0
$961$	88.9388			2.86899
$962$	−11.2062	−	13.0557i	−0.361302	−	0.420934i
$963$		0			0
$964$	44.6598	+	6.84880i	1.43840	+	0.220585i
$965$		−	13.3869i		−	0.430938i
$966$		0			0
$967$			31.9569i			1.02767i	0.857890	+	0.513833i	$0.171775\pi$
$967$			31.9569i			1.02767i	−0.857890	+	0.513833i	$0.828225\pi$
$968$	−41.7907	−	67.0822i	−1.34320	−	2.15610i
$969$		0			0
$970$	13.3532	−	11.4615i	0.428744	−	0.368006i
$971$	−7.21917			−0.231674			−0.115837	−	0.993268i	$-0.536955\pi$
$971$	−7.21917			−0.231674			−0.115837	+	0.993268i	$0.536955\pi$
$972$		0			0
$973$	11.2016	−	11.7483i	0.359108	−	0.376634i
$974$	−17.3953	−	20.2663i	−0.557381	−	0.649375i
$975$		0			0
$976$	−15.2046	+	48.4074i	−0.486688	+	1.54948i
$977$	14.2131			0.454716			0.227358	−	0.973811i	$-0.426991\pi$
$977$	14.2131			0.454716			0.227358	+	0.973811i	$0.426991\pi$
$978$		0			0
$979$	71.4204			2.28261
$980$	1.46085	−	13.9236i	0.0466652	−	0.444772i
$981$		0			0
$982$	−1.05314	−	1.22696i	−0.0336071	−	0.0391538i
$983$	23.1081			0.737034			0.368517	−	0.929621i	$-0.379866\pi$
$983$	23.1081			0.737034			0.368517	+	0.929621i	$0.379866\pi$
$984$		0			0
$985$		−	4.07989i		−	0.129996i
$986$	1.73714	+	2.02385i	0.0553218	+	0.0644524i
$987$		0			0
$988$	18.7556	+	2.87626i	0.596694	+	0.0915061i
$989$	7.81890			0.248627
$990$		0			0
$991$			11.3485i			0.360497i	0.983621	+	0.180248i	$0.0576902\pi$
$991$			11.3485i			0.360497i	−0.983621	+	0.180248i	$0.942310\pi$
$992$	56.9408	−	24.4088i	1.80787	−	0.774979i
$993$		0			0
$994$	39.1449	+	2.04790i	1.24160	+	0.0649555i
$995$			3.66884i			0.116310i
$996$		0			0
$997$		−	10.4798i		−	0.331900i	−0.986134	−	0.165950i	$-0.946931\pi$
$997$		−	10.4798i		−	0.331900i	0.986134	−	0.165950i	$-0.0530690\pi$
$998$	−17.3842	−	20.2534i	−0.550288	−	0.641110i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.c.d.811.6		16
3.2	odd	2		420.2.c.a.391.11	✓	16
4.3	odd	2		1260.2.c.e.811.5		16
7.6	odd	2		1260.2.c.e.811.6		16
12.11	even	2		420.2.c.b.391.12	yes	16
21.20	even	2		420.2.c.b.391.11	yes	16
28.27	even	2	inner	1260.2.c.d.811.5		16
84.83	odd	2		420.2.c.a.391.12	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.c.a.391.11	✓	16	3.2	odd	2
420.2.c.a.391.12	yes	16	84.83	odd	2
420.2.c.b.391.11	yes	16	21.20	even	2
420.2.c.b.391.12	yes	16	12.11	even	2
1260.2.c.d.811.5		16	28.27	even	2	inner
1260.2.c.d.811.6		16	1.1	even	1	trivial
1260.2.c.e.811.5		16	4.3	odd	2
1260.2.c.e.811.6		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:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07312 + 0.921096i) q^{2} +(0.303166 - 1.97689i) q^{4} +1.00000i q^{5} +(-1.82575 + 1.91485i) q^{7} +(1.49557 + 2.40068i) q^{8} +O(q^{10})\)	\(q+(-1.07312 + 0.921096i) q^{2} +(0.303166 - 1.97689i) q^{4} +1.00000i q^{5} +(-1.82575 + 1.91485i) q^{7} +(1.49557 + 2.40068i) q^{8} +(-0.921096 - 1.07312i) q^{10} +6.24043i q^{11} -2.40312i q^{13} +(0.195481 - 3.73655i) q^{14} +(-3.81618 - 1.19865i) q^{16} +1.30768i q^{17} -3.94796 q^{19} +(1.97689 + 0.303166i) q^{20} +(-5.74803 - 6.69672i) q^{22} -3.55648i q^{23} -1.00000 q^{25} +(2.21350 + 2.57883i) q^{26} +(3.23194 + 4.18981i) q^{28} -1.44221 q^{29} +10.9517 q^{31} +(5.19929 - 2.22877i) q^{32} +(-1.20450 - 1.40329i) q^{34} +(-1.91485 - 1.82575i) q^{35} -5.06265 q^{37} +(4.23663 - 3.63645i) q^{38} +(-2.40068 + 1.49557i) q^{40} -1.26175i q^{41} +2.19850i q^{43} +(12.3366 + 1.89189i) q^{44} +(3.27586 + 3.81652i) q^{46} -11.6743 q^{47} +(-0.333303 - 6.99206i) q^{49} +(1.07312 - 0.921096i) q^{50} +(-4.75070 - 0.728544i) q^{52} -11.7545 q^{53} -6.24043 q^{55} +(-7.32748 - 1.51924i) q^{56} +(1.54766 - 1.32842i) q^{58} -0.415368 q^{59} -12.6848i q^{61} +(-11.7524 + 10.0875i) q^{62} +(-3.52653 + 7.18078i) q^{64} +2.40312 q^{65} +3.10097i q^{67} +(2.58513 + 0.396443i) q^{68} +(3.73655 + 0.195481i) q^{70} +10.4762i q^{71} -1.64141i q^{73} +(5.43282 - 4.66319i) q^{74} +(-1.19689 + 7.80468i) q^{76} +(-11.9495 - 11.3934i) q^{77} +9.18952i q^{79} +(1.19865 - 3.81618i) q^{80} +(1.16219 + 1.35401i) q^{82} -7.39922 q^{83} -1.30768 q^{85} +(-2.02502 - 2.35925i) q^{86} +(-14.9813 + 9.33301i) q^{88} -11.4448i q^{89} +(4.60162 + 4.38749i) q^{91} +(-7.03076 - 1.07820i) q^{92} +(12.5279 - 10.7531i) q^{94} -3.94796i q^{95} +12.4433i q^{97} +(6.79803 + 7.19630i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 2 q^{4} - 4 q^{7} - 2 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 - 2 * q^8	\( 16 q - 2 q^{2} - 2 q^{4} - 4 q^{7} - 2 q^{8} + 2 q^{14} + 6 q^{16} - 24 q^{19} - 12 q^{22} - 16 q^{25} + 12 q^{26} + 14 q^{28} - 16 q^{29} + 8 q^{31} + 18 q^{32} + 24 q^{34} + 24 q^{37} - 28 q^{38} + 12 q^{40} + 8 q^{44} - 20 q^{46} - 16 q^{47} - 16 q^{49} + 2 q^{50} - 20 q^{52} + 32 q^{53} - 2 q^{56} - 32 q^{58} - 8 q^{59} - 16 q^{62} - 2 q^{64} + 8 q^{65} - 4 q^{68} + 4 q^{74} + 16 q^{76} + 8 q^{77} + 16 q^{80} - 4 q^{82} - 8 q^{83} - 64 q^{86} - 52 q^{88} + 16 q^{91} - 64 q^{92} + 16 q^{94} + 86 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 - 2 * q^8 + 2 * q^14 + 6 * q^16 - 24 * q^19 - 12 * q^22 - 16 * q^25 + 12 * q^26 + 14 * q^28 - 16 * q^29 + 8 * q^31 + 18 * q^32 + 24 * q^34 + 24 * q^37 - 28 * q^38 + 12 * q^40 + 8 * q^44 - 20 * q^46 - 16 * q^47 - 16 * q^49 + 2 * q^50 - 20 * q^52 + 32 * q^53 - 2 * q^56 - 32 * q^58 - 8 * q^59 - 16 * q^62 - 2 * q^64 + 8 * q^65 - 4 * q^68 + 4 * q^74 + 16 * q^76 + 8 * q^77 + 16 * q^80 - 4 * q^82 - 8 * q^83 - 64 * q^86 - 52 * q^88 + 16 * q^91 - 64 * q^92 + 16 * q^94 + 86 * q^98

Introduction

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