LMFDB - Embedded newform 1260.2.c.e.811.9

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			811.9
Root			$-0.102186 - 1.41052i$ of defining polynomial
Character	$\chi$	$=$	1260.811
Dual form			1260.2.c.e.811.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.102186 - 1.41052i) q^{2} +(-1.97912 - 0.288270i) q^{4} +1.00000i q^{5} +(0.178143 - 2.63975i) q^{7} +(-0.608847 + 2.76212i) q^{8} +O(q^{10})$	\(q+(0.102186 - 1.41052i) q^{2} +(-1.97912 - 0.288270i) q^{4} +1.00000i q^{5} +(0.178143 - 2.63975i) q^{7} +(-0.608847 + 2.76212i) q^{8} +(1.41052 + 0.102186i) q^{10} +5.22855i q^{11} -4.52534i q^{13} +(-3.70520 - 0.521019i) q^{14} +(3.83380 + 1.14104i) q^{16} -6.70156i q^{17} -2.81981 q^{19} +(0.288270 - 1.97912i) q^{20} +(7.37496 + 0.534284i) q^{22} -0.858617i q^{23} -1.00000 q^{25} +(-6.38308 - 0.462426i) q^{26} +(-1.11353 + 5.17301i) q^{28} -6.47333 q^{29} -2.60723 q^{31} +(2.00121 - 5.29104i) q^{32} +(-9.45266 - 0.684805i) q^{34} +(2.63975 + 0.178143i) q^{35} +2.13976 q^{37} +(-0.288144 + 3.97738i) q^{38} +(-2.76212 - 0.608847i) q^{40} -8.71476i q^{41} -7.42042i q^{43} +(1.50723 - 10.3479i) q^{44} +(-1.21109 - 0.0877385i) q^{46} -9.82671 q^{47} +(-6.93653 - 0.940508i) q^{49} +(-0.102186 + 1.41052i) q^{50} +(-1.30452 + 8.95618i) q^{52} -3.69301 q^{53} -5.22855 q^{55} +(7.18284 + 2.09926i) q^{56} +(-0.661483 + 9.13075i) q^{58} +4.27962 q^{59} +10.7054i q^{61} +(-0.266423 + 3.67755i) q^{62} +(-7.25861 - 3.36342i) q^{64} +4.52534 q^{65} +4.52269i q^{67} +(-1.93186 + 13.2632i) q^{68} +(0.521019 - 3.70520i) q^{70} +7.23513i q^{71} -9.24697i q^{73} +(0.218653 - 3.01816i) q^{74} +(5.58072 + 0.812865i) q^{76} +(13.8020 + 0.931432i) q^{77} +2.68314i q^{79} +(-1.14104 + 3.83380i) q^{80} +(-12.2923 - 0.890525i) q^{82} -16.2812 q^{83} +6.70156 q^{85} +(-10.4666 - 0.758262i) q^{86} +(-14.4419 - 3.18339i) q^{88} -8.53516i q^{89} +(-11.9458 - 0.806161i) q^{91} +(-0.247513 + 1.69930i) q^{92} +(-1.00415 + 13.8607i) q^{94} -2.81981i q^{95} -10.5209i q^{97} +(-2.03542 + 9.68799i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 10 q^{14} + 6 q^{16} + 24 q^{19} - 12 q^{22} - 16 q^{25} - 12 q^{26} - 22 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} - 20 q^{70} + 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} - 2 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8 - 10 * q^14 + 6 * q^16 + 24 * q^19 - 12 * q^22 - 16 * q^25 - 12 * q^26 - 22 * 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 - 20 * q^70 + 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 - 2 * 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 $

$2$	0.102186	−	1.41052i	0.0722563	−	0.997386i
$2$	0.102186	−	1.41052i	0.0722563	−	0.997386i
$3$		0			0
$3$		0			0
$4$	−1.97912	−	0.288270i	−0.989558	−	0.144135i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	0.178143	−	2.63975i	0.0673319	−	0.997731i
$7$	0.178143	−	2.63975i	0.0673319	−	0.997731i
$8$	−0.608847	+	2.76212i	−0.215260	+	0.976557i
$9$		0			0
$10$	1.41052	+	0.102186i	0.446045	+	0.0323140i
$11$			5.22855i			1.57647i	0.615376	+	0.788234i	$0.289004\pi$
$11$			5.22855i			1.57647i	−0.615376	+	0.788234i	$0.710996\pi$
$12$		0			0
$13$		−	4.52534i		−	1.25510i	−0.778574	−	0.627552i	$-0.784057\pi$
$13$		−	4.52534i		−	1.25510i	0.778574	−	0.627552i	$-0.215943\pi$
$14$	−3.70520	−	0.521019i	−0.990258	−	0.139248i
$15$		0			0
$16$	3.83380	+	1.14104i	0.958450	+	0.285260i
$17$		−	6.70156i		−	1.62537i	−0.582705	−	0.812684i	$-0.698006\pi$
$17$		−	6.70156i		−	1.62537i	0.582705	−	0.812684i	$-0.301994\pi$
$18$		0			0
$19$	−2.81981			−0.646908			−0.323454	−	0.946244i	$-0.604844\pi$
$19$	−2.81981			−0.646908			−0.323454	+	0.946244i	$0.604844\pi$
$20$	0.288270	−	1.97912i	0.0644591	−	0.442544i
$21$		0			0
$22$	7.37496	+	0.534284i	1.57235	+	0.113910i
$23$		−	0.858617i		−	0.179034i	−0.995985	−	0.0895170i	$-0.971468\pi$
$23$		−	0.858617i		−	0.179034i	0.995985	−	0.0895170i	$-0.0285323\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−6.38308	−	0.462426i	−1.25182	−	0.0906893i
$27$		0			0
$28$	−1.11353	+	5.17301i	−0.210437	+	0.977607i
$29$	−6.47333			−1.20207			−0.601034	−	0.799224i	$-0.705244\pi$
$29$	−6.47333			−1.20207			−0.601034	+	0.799224i	$0.705244\pi$
$30$		0			0
$31$	−2.60723			−0.468273			−0.234137	−	0.972204i	$-0.575226\pi$
$31$	−2.60723			−0.468273			−0.234137	+	0.972204i	$0.575226\pi$
$32$	2.00121	−	5.29104i	0.353768	−	0.935333i
$33$		0			0
$34$	−9.45266	−	0.684805i	−1.62112	−	0.117443i
$35$	2.63975	+	0.178143i	0.446199	+	0.0301117i
$36$		0			0
$37$	2.13976			0.351774			0.175887	−	0.984410i	$-0.443721\pi$
$37$	2.13976			0.351774			0.175887	+	0.984410i	$0.443721\pi$
$38$	−0.288144	+	3.97738i	−0.0467432	+	0.645217i
$39$		0			0
$40$	−2.76212	−	0.608847i	−0.436729	−	0.0962672i
$41$		−	8.71476i		−	1.36102i	−0.732740	−	0.680508i	$-0.761759\pi$
$41$		−	8.71476i		−	1.36102i	0.732740	−	0.680508i	$-0.238241\pi$
$42$		0			0
$43$		−	7.42042i		−	1.13160i	−0.824541	−	0.565802i	$-0.808567\pi$
$43$		−	7.42042i		−	1.13160i	0.824541	−	0.565802i	$-0.191433\pi$
$44$	1.50723	−	10.3479i	0.227224	−	1.56001i
$45$		0			0
$46$	−1.21109	−	0.0877385i	−0.178566	−	0.0129363i
$47$	−9.82671			−1.43337			−0.716686	−	0.697396i	$-0.754342\pi$
$47$	−9.82671			−1.43337			−0.716686	+	0.697396i	$0.754342\pi$
$48$		0			0
$49$	−6.93653	−	0.940508i	−0.990933	−	0.134358i
$50$	−0.102186	+	1.41052i	−0.0144513	+	0.199477i
$51$		0			0
$52$	−1.30452	+	8.95618i	−0.180904	+	1.24200i
$53$	−3.69301			−0.507274			−0.253637	−	0.967299i	$-0.581627\pi$
$53$	−3.69301			−0.507274			−0.253637	+	0.967299i	$0.581627\pi$
$54$		0			0
$55$	−5.22855			−0.705018
$56$	7.18284	+	2.09926i	0.959847	+	0.280525i
$57$		0			0
$58$	−0.661483	+	9.13075i	−0.0868570	+	1.19893i
$59$	4.27962			0.557159			0.278579	−	0.960413i	$-0.410136\pi$
$59$	4.27962			0.557159			0.278579	+	0.960413i	$0.410136\pi$
$60$		0			0
$61$			10.7054i			1.37069i	0.728221	+	0.685343i	$0.240347\pi$
$61$			10.7054i			1.37069i	−0.728221	+	0.685343i	$0.759653\pi$
$62$	−0.266423	+	3.67755i	−0.0338357	+	0.467049i
$63$		0			0
$64$	−7.25861	−	3.36342i	−0.907326	−	0.420427i
$65$	4.52534			0.561300
$66$		0			0
$67$			4.52269i			0.552534i	0.961081	+	0.276267i	$0.0890975\pi$
$67$			4.52269i			0.552534i	−0.961081	+	0.276267i	$0.910903\pi$
$68$	−1.93186	+	13.2632i	−0.234272	+	1.60840i
$69$		0			0
$70$	0.521019	−	3.70520i	0.0622737	−	0.442857i
$71$			7.23513i			0.858652i	0.903150	+	0.429326i	$0.141249\pi$
$71$			7.23513i			0.858652i	−0.903150	+	0.429326i	$0.858751\pi$
$72$		0			0
$73$		−	9.24697i		−	1.08228i	−0.840934	−	0.541138i	$-0.817994\pi$
$73$		−	9.24697i		−	1.08228i	0.840934	−	0.541138i	$-0.182006\pi$
$74$	0.218653	−	3.01816i	0.0254179	−	0.350854i
$75$		0			0
$76$	5.58072	+	0.812865i	0.640153	+	0.0932420i
$77$	13.8020	+	0.931432i	1.57289	+	0.106147i
$78$		0			0
$79$			2.68314i			0.301877i	0.988543	+	0.150938i	$0.0482295\pi$
$79$			2.68314i			0.301877i	−0.988543	+	0.150938i	$0.951770\pi$
$80$	−1.14104	+	3.83380i	−0.127572	+	0.428632i
$81$		0			0
$82$	−12.2923	−	0.890525i	−1.35746	−	0.0983421i
$83$	−16.2812			−1.78710			−0.893548	−	0.448967i	$-0.851792\pi$
$83$	−16.2812			−1.78710			−0.893548	+	0.448967i	$0.851792\pi$
$84$		0			0
$85$	6.70156			0.726886
$86$	−10.4666	−	0.758262i	−1.12865	−	0.0817655i
$87$		0			0
$88$	−14.4419	−	3.18339i	−1.53951	−	0.339350i
$89$		−	8.53516i		−	0.904725i	−0.891834	−	0.452362i	$-0.850581\pi$
$89$		−	8.53516i		−	0.904725i	0.891834	−	0.452362i	$-0.149419\pi$
$90$		0			0
$91$	−11.9458	−	0.806161i	−1.25226	−	0.0845086i
$92$	−0.247513	+	1.69930i	−0.0258051	+	0.177165i
$93$		0			0
$94$	−1.00415	+	13.8607i	−0.103570	+	1.42963i
$95$		−	2.81981i		−	0.289306i
$96$		0			0
$97$		−	10.5209i		−	1.06824i	−0.845410	−	0.534118i	$-0.820644\pi$
$97$		−	10.5209i		−	1.06824i	0.845410	−	0.534118i	$-0.179356\pi$
$98$	−2.03542	+	9.68799i	−0.205608	+	0.978634i
$99$		0			0
$100$	1.97912	+	0.288270i	0.197912	+	0.0288270i
$101$		−	3.97836i		−	0.395861i	−0.980216	−	0.197931i	$-0.936578\pi$
$101$		−	3.97836i		−	0.395861i	0.980216	−	0.197931i	$-0.0634221\pi$
$102$		0			0
$103$	−3.78934			−0.373375			−0.186688	−	0.982419i	$-0.559775\pi$
$103$	−3.78934			−0.373375			−0.186688	+	0.982419i	$0.559775\pi$
$104$	12.4995	+	2.75524i	1.22568	+	0.270174i
$105$		0			0
$106$	−0.377374	+	5.20906i	−0.0366538	+	0.505948i
$107$		−	2.38868i		−	0.230922i	−0.993312	−	0.115461i	$-0.963165\pi$
$107$		−	2.38868i		−	0.230922i	0.993312	−	0.115461i	$-0.0368346\pi$
$108$		0			0
$109$	5.79748			0.555298			0.277649	−	0.960683i	$-0.410445\pi$
$109$	5.79748			0.555298			0.277649	+	0.960683i	$0.410445\pi$
$110$	−0.534284	+	7.37496i	−0.0509420	+	0.703175i
$111$		0			0
$112$	3.69502	−	9.91700i	0.349147	−	0.937068i
$113$	6.86598			0.645897			0.322948	−	0.946417i	$-0.395326\pi$
$113$	6.86598			0.645897			0.322948	+	0.946417i	$0.395326\pi$
$114$		0			0
$115$	0.858617			0.0800665
$116$	12.8115	+	1.86607i	1.18952	+	0.173260i
$117$		0			0
$118$	0.437316	−	6.03647i	0.0402582	−	0.555702i
$119$	−17.6904	−	1.19384i	−1.62168	−	0.109439i
$120$		0			0
$121$	−16.3377			−1.48525
$122$	15.1001	+	1.09394i	1.36710	+	0.0990407i
$123$		0			0
$124$	5.16002	+	0.751587i	0.463384	+	0.0674945i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$		−	10.4834i		−	0.930250i	−0.885245	−	0.465125i	$-0.846009\pi$
$127$		−	10.4834i		−	0.930250i	0.885245	−	0.465125i	$-0.153991\pi$
$128$	−5.48588	+	9.89470i	−0.484888	+	0.874576i
$129$		0			0
$130$	0.462426	−	6.38308i	0.0405575	−	0.559833i
$131$	19.0936			1.66821			0.834106	−	0.551604i	$-0.185984\pi$
$131$	19.0936			1.66821			0.834106	+	0.551604i	$0.185984\pi$
$132$		0			0
$133$	−0.502330	+	7.44358i	−0.0435576	+	0.645440i
$134$	6.37933	+	0.462155i	0.551090	+	0.0399241i
$135$		0			0
$136$	18.5105	+	4.08023i	1.58726	+	0.349876i
$137$	−5.47214			−0.467516			−0.233758	−	0.972295i	$-0.575102\pi$
$137$	−5.47214			−0.467516			−0.233758	+	0.972295i	$0.575102\pi$
$138$		0			0
$139$	2.83943			0.240838			0.120419	−	0.992723i	$-0.461576\pi$
$139$	2.83943			0.240838			0.120419	+	0.992723i	$0.461576\pi$
$140$	−5.17301	−	1.11353i	−0.437199	−	0.0941101i
$141$		0			0
$142$	10.2053	+	0.739328i	0.856407	+	0.0620430i
$143$	23.6610			1.97863
$144$		0			0
$145$		−	6.47333i		−	0.537581i
$146$	−13.0430	−	0.944910i	−1.07945	−	0.0782013i
$147$		0			0
$148$	−4.23483	−	0.616827i	−0.348101	−	0.0507029i
$149$	−1.72856			−0.141609			−0.0708045	−	0.997490i	$-0.522557\pi$
$149$	−1.72856			−0.141609			−0.0708045	+	0.997490i	$0.522557\pi$
$150$		0			0
$151$			14.9532i			1.21687i	0.793603	+	0.608436i	$0.208203\pi$
$151$			14.9532i			1.21687i	−0.793603	+	0.608436i	$0.791797\pi$
$152$	1.71683	−	7.78864i	0.139253	−	0.631742i
$153$		0			0
$154$	2.72418	−	19.3728i	0.219520	−	1.56111i
$155$		−	2.60723i		−	0.209418i
$156$		0			0
$157$			11.0383i			0.880953i	0.897764	+	0.440476i	$0.145190\pi$
$157$			11.0383i			0.880953i	−0.897764	+	0.440476i	$0.854810\pi$
$158$	3.78461	+	0.274179i	0.301088	+	0.0218125i
$159$		0			0
$160$	5.29104	+	2.00121i	0.418294	+	0.158210i
$161$	−2.26653	−	0.152957i	−0.178628	−	0.0120547i
$162$		0			0
$163$			18.7969i			1.47229i	0.676826	+	0.736143i	$0.263355\pi$
$163$			18.7969i			1.47229i	−0.676826	+	0.736143i	$0.736645\pi$
$164$	−2.51220	+	17.2475i	−0.196170	+	1.34681i
$165$		0			0
$166$	−1.66371	+	22.9649i	−0.129129	+	1.78243i
$167$	−1.89315			−0.146496			−0.0732481	−	0.997314i	$-0.523337\pi$
$167$	−1.89315			−0.146496			−0.0732481	+	0.997314i	$0.523337\pi$
$168$		0			0
$169$	−7.47874			−0.575288
$170$	0.684805	−	9.45266i	0.0525221	−	0.724986i
$171$		0			0
$172$	−2.13908	+	14.6859i	−0.163104	+	1.11979i
$173$			9.43306i			0.717182i	0.933495	+	0.358591i	$0.116743\pi$
$173$			9.43306i			0.717182i	−0.933495	+	0.358591i	$0.883257\pi$
$174$		0			0
$175$	−0.178143	+	2.63975i	−0.0134664	+	0.199546i
$176$	−5.96598	+	20.0452i	−0.449703	+	1.51097i
$177$		0			0
$178$	−12.0390	−	0.872173i	−0.902360	−	0.0653721i
$179$		−	21.4618i		−	1.60413i	−0.597239	−	0.802063i	$-0.703736\pi$
$179$		−	21.4618i		−	1.60413i	0.597239	−	0.802063i	$-0.296264\pi$
$180$		0			0
$181$		−	24.1736i		−	1.79681i	−0.439171	−	0.898403i	$-0.644728\pi$
$181$		−	24.1736i		−	1.79681i	0.439171	−	0.898403i	$-0.355272\pi$
$182$	−2.35779	+	16.7673i	−0.174771	+	1.24288i
$183$		0			0
$184$	2.37160	+	0.522767i	0.174837	+	0.0385389i
$185$			2.13976i			0.157318i
$186$		0			0
$187$	35.0394			2.56234
$188$	19.4482	+	2.83274i	1.41841	+	0.206599i
$189$		0			0
$190$	−3.97738	−	0.288144i	−0.288550	−	0.0209042i
$191$		−	18.9822i		−	1.37350i	−0.726892	−	0.686751i	$-0.759036\pi$
$191$		−	18.9822i		−	1.37350i	0.726892	−	0.686751i	$-0.240964\pi$
$192$		0			0
$193$	26.5854			1.91366			0.956828	−	0.290654i	$-0.0938728\pi$
$193$	26.5854			1.91366			0.956828	+	0.290654i	$0.0938728\pi$
$194$	−14.8399	−	1.07509i	−1.06544	−	0.0771868i
$195$		0			0
$196$	13.4571	+	3.86097i	0.961220	+	0.275783i
$197$	−23.2008			−1.65299			−0.826494	−	0.562945i	$-0.809668\pi$
$197$	−23.2008			−1.65299			−0.826494	+	0.562945i	$0.809668\pi$
$198$		0			0
$199$	19.8867			1.40973			0.704866	−	0.709341i	$-0.251007\pi$
$199$	19.8867			1.40973			0.704866	+	0.709341i	$0.251007\pi$
$200$	0.608847	−	2.76212i	0.0430520	−	0.195311i
$201$		0			0
$202$	−5.61154	−	0.406532i	−0.394827	−	0.0286035i
$203$	−1.15318	+	17.0880i	−0.0809375	+	1.19934i
$204$		0			0
$205$	8.71476			0.608665
$206$	−0.387217	+	5.34493i	−0.0269787	+	0.372399i
$207$		0			0
$208$	5.16359	−	17.3493i	0.358031	−	1.20296i
$209$		−	14.7435i		−	1.01983i
$210$		0			0
$211$			2.51318i			0.173014i	0.996251	+	0.0865072i	$0.0275706\pi$
$211$			2.51318i			0.173014i	−0.996251	+	0.0865072i	$0.972429\pi$
$212$	7.30890	+	1.06458i	0.501977	+	0.0731159i
$213$		0			0
$214$	−3.36927	−	0.244089i	−0.230319	−	0.0166856i
$215$	7.42042			0.506068
$216$		0			0
$217$	−0.464462	+	6.88244i	−0.0315297	+	0.467211i
$218$	0.592420	−	8.17744i	0.0401238	−	0.553846i
$219$		0			0
$220$	10.3479	+	1.50723i	0.697656	+	0.101618i
$221$	−30.3269			−2.04001
$222$		0			0
$223$	1.23567			0.0827463			0.0413732	−	0.999144i	$-0.486827\pi$
$223$	1.23567			0.0827463			0.0413732	+	0.999144i	$0.486827\pi$
$224$	−13.6105	−	6.22527i	−0.909391	−	0.415943i
$225$		0			0
$226$	0.701606	−	9.68458i	0.0466701	−	0.644208i
$227$	1.76552			0.117182			0.0585909	−	0.998282i	$-0.481339\pi$
$227$	1.76552			0.117182			0.0585909	+	0.998282i	$0.481339\pi$
$228$		0			0
$229$		−	8.94803i		−	0.591302i	−0.955296	−	0.295651i	$-0.904463\pi$
$229$		−	8.94803i		−	0.591302i	0.955296	−	0.295651i	$-0.0955366\pi$
$230$	0.0877385	−	1.21109i	0.00578531	−	0.0798572i
$231$		0			0
$232$	3.94127	−	17.8801i	0.258757	−	1.17389i
$233$	21.8087			1.42874			0.714368	−	0.699770i	$-0.246714\pi$
$233$	21.8087			1.42874			0.714368	+	0.699770i	$0.246714\pi$
$234$		0			0
$235$		−	9.82671i		−	0.641024i
$236$	−8.46986	−	1.23368i	−0.551341	−	0.0803060i
$237$		0			0
$238$	−3.49164	+	24.8306i	−0.226330	+	1.60953i
$239$		−	14.7558i		−	0.954471i	−0.878776	−	0.477235i	$-0.841639\pi$
$239$		−	14.7558i		−	0.954471i	0.878776	−	0.477235i	$-0.158361\pi$
$240$		0			0
$241$			15.3302i			0.987503i	0.869603	+	0.493751i	$0.164375\pi$
$241$			15.3302i			0.987503i	−0.869603	+	0.493751i	$0.835625\pi$
$242$	−1.66949	+	23.0447i	−0.107319	+	1.48137i
$243$		0			0
$244$	3.08604	−	21.1872i	0.197564	−	1.35637i
$245$	0.940508	−	6.93653i	0.0600868	−	0.443159i
$246$		0			0
$247$			12.7606i			0.811937i
$248$	1.58741	−	7.20149i	0.100800	−	0.457295i
$249$		0			0
$250$	−1.41052	−	0.102186i	−0.0892089	−	0.00646280i
$251$	15.4063			0.972435			0.486218	−	0.873838i	$-0.338376\pi$
$251$	15.4063			0.972435			0.486218	+	0.873838i	$0.338376\pi$
$252$		0			0
$253$	4.48932			0.282241
$254$	−14.7870	−	1.07125i	−0.927818	−	0.0672164i
$255$		0			0
$256$	13.3961	+	8.74903i	0.837254	+	0.546814i
$257$		−	11.6114i		−	0.724298i	−0.932120	−	0.362149i	$-0.882043\pi$
$257$		−	11.6114i		−	0.724298i	0.932120	−	0.362149i	$-0.117957\pi$
$258$		0			0
$259$	0.381184	−	5.64842i	0.0236856	−	0.350976i
$260$	−8.95618	−	1.30452i	−0.555439	−	0.0809029i
$261$		0			0
$262$	1.95109	−	26.9318i	0.120539	−	1.66385i
$263$			14.4160i			0.888927i	0.895797	+	0.444463i	$0.146606\pi$
$263$			14.4160i			0.888927i	−0.895797	+	0.444463i	$0.853394\pi$
$264$		0			0
$265$		−	3.69301i		−	0.226860i
$266$	10.4480	+	1.46917i	0.640605	+	0.0900808i
$267$		0			0
$268$	1.30375	−	8.95093i	0.0796395	−	0.546765i
$269$			10.8482i			0.661425i	0.943732	+	0.330712i	$0.107289\pi$
$269$			10.8482i			0.661425i	−0.943732	+	0.330712i	$0.892711\pi$
$270$		0			0
$271$	−18.9758			−1.15270			−0.576349	−	0.817204i	$-0.695523\pi$
$271$	−18.9758			−1.15270			−0.576349	+	0.817204i	$0.695523\pi$
$272$	7.64674	−	25.6924i	0.463652	−	1.55783i
$273$		0			0
$274$	−0.559175	+	7.71854i	−0.0337810	+	0.466294i
$275$		−	5.22855i		−	0.315293i
$276$		0			0
$277$	11.0960			0.666692			0.333346	−	0.942804i	$-0.391822\pi$
$277$	11.0960			0.666692			0.333346	+	0.942804i	$0.391822\pi$
$278$	0.290150	−	4.00507i	0.0174020	−	0.240208i
$279$		0			0
$280$	−2.09926	+	7.18284i	−0.125455	+	0.429257i
$281$	26.1397			1.55937			0.779683	−	0.626175i	$-0.215380\pi$
$281$	26.1397			1.55937			0.779683	+	0.626175i	$0.215380\pi$
$282$		0			0
$283$	15.0023			0.891793			0.445897	−	0.895084i	$-0.352885\pi$
$283$	15.0023			0.891793			0.445897	+	0.895084i	$0.352885\pi$
$284$	2.08567	−	14.3192i	0.123762	−	0.849686i
$285$		0			0
$286$	2.41782	−	33.3742i	0.142969	−	1.97346i
$287$	−23.0048	−	1.55248i	−1.35793	−	0.0916399i
$288$		0			0
$289$	−27.9109			−1.64182
$290$	−9.13075	−	0.661483i	−0.536176	−	0.0388436i
$291$		0			0
$292$	−2.66562	+	18.3008i	−0.155994	+	1.07097i
$293$		−	30.1766i		−	1.76293i	−0.472245	−	0.881467i	$-0.656556\pi$
$293$		−	30.1766i		−	1.76293i	0.472245	−	0.881467i	$-0.343444\pi$
$294$		0			0
$295$			4.27962i			0.249169i
$296$	−1.30278	+	5.91026i	−0.0757228	+	0.343527i
$297$		0			0
$298$	−0.176634	+	2.43816i	−0.0102321	+	0.141239i
$299$	−3.88554			−0.224706
$300$		0			0
$301$	−19.5880	−	1.32190i	−1.12904	−	0.0761930i
$302$	21.0917	+	1.52800i	1.21369	+	0.0879267i
$303$		0			0
$304$	−10.8106	−	3.21751i	−0.620029	−	0.184537i
$305$	−10.7054			−0.612989
$306$		0			0
$307$	−6.17458			−0.352402			−0.176201	−	0.984354i	$-0.556381\pi$
$307$	−6.17458			−0.352402			−0.176201	+	0.984354i	$0.556381\pi$
$308$	−27.0474	−	5.82213i	−1.54117	−	0.331746i
$309$		0			0
$310$	−3.67755	−	0.266423i	−0.208871	−	0.0151318i
$311$	−3.80564			−0.215798			−0.107899	−	0.994162i	$-0.534412\pi$
$311$	−3.80564			−0.215798			−0.107899	+	0.994162i	$0.534412\pi$
$312$		0			0
$313$		−	16.5774i		−	0.937011i	−0.883461	−	0.468506i	$-0.844793\pi$
$313$		−	16.5774i		−	0.937011i	0.883461	−	0.468506i	$-0.155207\pi$
$314$	15.5697	+	1.12796i	0.878650	+	0.0636544i
$315$		0			0
$316$	0.773468	−	5.31025i	0.0435110	−	0.298725i
$317$	11.1118			0.624098			0.312049	−	0.950066i	$-0.398985\pi$
$317$	11.1118			0.624098			0.312049	+	0.950066i	$0.398985\pi$
$318$		0			0
$319$		−	33.8461i		−	1.89502i
$320$	3.36342	−	7.25861i	0.188021	−	0.405769i
$321$		0			0
$322$	−0.447356	+	3.18135i	−0.0249302	+	0.177290i
$323$			18.8971i			1.05146i
$324$		0			0
$325$			4.52534i			0.251021i
$326$	26.5133	+	1.92078i	1.46844	+	0.106382i
$327$		0			0
$328$	24.0712	+	5.30596i	1.32911	+	0.292972i
$329$	−1.75056	+	25.9400i	−0.0965117	+	1.43012i
$330$		0			0
$331$		−	22.4709i		−	1.23511i	−0.786526	−	0.617557i	$-0.788123\pi$
$331$		−	22.4709i		−	1.23511i	0.786526	−	0.617557i	$-0.211877\pi$
$332$	32.2224	+	4.69339i	1.76844	+	0.257583i
$333$		0			0
$334$	−0.193453	+	2.67032i	−0.0105853	+	0.146113i
$335$	−4.52269			−0.247101
$336$		0			0
$337$	−6.02729			−0.328328			−0.164164	−	0.986433i	$-0.552493\pi$
$337$	−6.02729			−0.328328			−0.164164	+	0.986433i	$0.552493\pi$
$338$	−0.764222	+	10.5489i	−0.0415682	+	0.573784i
$339$		0			0
$340$	−13.2632	−	1.93186i	−0.719296	−	0.104770i
$341$		−	13.6321i		−	0.738217i
$342$		0			0
$343$	−3.71840	+	18.1431i	−0.200775	+	0.979637i
$344$	20.4961	+	4.51790i	1.10508	+	0.243589i
$345$		0			0
$346$	13.3055	+	0.963925i	0.715307	+	0.0518209i
$347$			9.57093i			0.513794i	0.966439	+	0.256897i	$0.0827001\pi$
$347$			9.57093i			0.513794i	−0.966439	+	0.256897i	$0.917300\pi$
$348$		0			0
$349$			12.9442i			0.692884i	0.938071	+	0.346442i	$0.112610\pi$
$349$			12.9442i			0.692884i	−0.938071	+	0.346442i	$0.887390\pi$
$350$	3.70520	+	0.521019i	0.198052	+	0.0278497i
$351$		0			0
$352$	27.6645	+	10.4635i	1.47452	+	0.557704i
$353$			11.6209i			0.618520i	0.950978	+	0.309260i	$0.100081\pi$
$353$			11.6209i			0.618520i	−0.950978	+	0.309260i	$0.899919\pi$
$354$		0			0
$355$	−7.23513			−0.384001
$356$	−2.46043	+	16.8921i	−0.130402	+	0.895278i
$357$		0			0
$358$	−30.2722	−	2.19309i	−1.59993	−	0.115908i
$359$			5.42483i			0.286312i	0.989700	+	0.143156i	$0.0457250\pi$
$359$			5.42483i			0.286312i	−0.989700	+	0.143156i	$0.954275\pi$
$360$		0			0
$361$	−11.0487			−0.581510
$362$	−34.0972	−	2.47020i	−1.79211	−	0.129831i
$363$		0			0
$364$	23.4097	+	5.03909i	1.22700	+	0.264120i
$365$	9.24697			0.484009
$366$		0			0
$367$	−28.4203			−1.48353			−0.741763	−	0.670662i	$-0.766010\pi$
$367$	−28.4203			−1.48353			−0.741763	+	0.670662i	$0.766010\pi$
$368$	0.979715	−	3.29177i	0.0510712	−	0.171595i
$369$		0			0
$370$	3.01816	+	0.218653i	0.156907	+	0.0113672i
$371$	−0.657886	+	9.74862i	−0.0341557	+	0.506123i
$372$		0			0
$373$	23.0923			1.19568			0.597838	−	0.801617i	$-0.296027\pi$
$373$	23.0923			1.19568			0.597838	+	0.801617i	$0.296027\pi$
$374$	3.58054	−	49.4237i	0.185145	−	2.55564i
$375$		0			0
$376$	5.98296	−	27.1425i	0.308548	−	1.39977i
$377$			29.2941i			1.50872i
$378$		0			0
$379$			12.0804i			0.620527i	0.950651	+	0.310263i	$0.100417\pi$
$379$			12.0804i			0.620527i	−0.950651	+	0.310263i	$0.899583\pi$
$380$	−0.812865	+	5.58072i	−0.0416991	+	0.286285i
$381$		0			0
$382$	−26.7747	−	1.93971i	−1.36991	−	0.0992443i
$383$	4.05602			0.207253			0.103626	−	0.994616i	$-0.466955\pi$
$383$	4.05602			0.207253			0.103626	+	0.994616i	$0.466955\pi$
$384$		0			0
$385$	−0.931432	+	13.8020i	−0.0474702	+	0.703418i
$386$	2.71665	−	37.4991i	0.138274	−	1.90865i
$387$		0			0
$388$	−3.03286	+	20.8221i	−0.153970	+	1.05708i
$389$	−5.28804			−0.268114			−0.134057	−	0.990974i	$-0.542801\pi$
$389$	−5.28804			−0.268114			−0.134057	+	0.990974i	$0.542801\pi$
$390$		0			0
$391$	−5.75407			−0.290996
$392$	6.82108	−	18.5869i	0.344517	−	0.938780i
$393$		0			0
$394$	−2.37079	+	32.7251i	−0.119439	+	1.64867i
$395$	−2.68314			−0.135003
$396$		0			0
$397$		−	15.0058i		−	0.753121i	−0.926392	−	0.376561i	$-0.877107\pi$
$397$		−	15.0058i		−	0.753121i	0.926392	−	0.376561i	$-0.122893\pi$
$398$	2.03214	−	28.0505i	0.101862	−	1.40605i
$399$		0			0
$400$	−3.83380	−	1.14104i	−0.191690	−	0.0570519i
$401$	−19.3630			−0.966942			−0.483471	−	0.875360i	$-0.660624\pi$
$401$	−19.3630			−0.966942			−0.483471	+	0.875360i	$0.660624\pi$
$402$		0			0
$403$			11.7986i			0.587732i
$404$	−1.14684	+	7.87363i	−0.0570574	+	0.391728i
$405$		0			0
$406$	23.9850	+	3.37273i	1.19036	+	0.167386i
$407$			11.1878i			0.554560i
$408$		0			0
$409$		−	0.432474i		−	0.0213845i	−0.999943	−	0.0106922i	$-0.996596\pi$
$409$		−	0.432474i		−	0.0213845i	0.999943	−	0.0106922i	$-0.00340351\pi$
$410$	0.890525	−	12.2923i	0.0439799	−	0.607074i
$411$		0			0
$412$	7.49955	+	1.09235i	0.369476	+	0.0538164i
$413$	0.762386	−	11.2971i	0.0375146	−	0.555894i
$414$		0			0
$415$		−	16.2812i		−	0.799214i
$416$	−23.9438	−	9.05619i	−1.17394	−	0.444016i
$417$		0			0
$418$	−20.7960	−	1.50658i	−1.01716	−	0.0736891i
$419$	−5.56216			−0.271729			−0.135865	−	0.990727i	$-0.543381\pi$
$419$	−5.56216			−0.271729			−0.135865	+	0.990727i	$0.543381\pi$
$420$		0			0
$421$	−1.97874			−0.0964379			−0.0482190	−	0.998837i	$-0.515355\pi$
$421$	−1.97874			−0.0964379			−0.0482190	+	0.998837i	$0.515355\pi$
$422$	3.54488	+	0.256811i	0.172562	+	0.0125014i
$423$		0			0
$424$	2.24848	−	10.2005i	0.109196	−	0.495382i
$425$			6.70156i			0.325073i
$426$		0			0
$427$	28.2595	+	1.90710i	1.36757	+	0.0922908i
$428$	−0.688584	+	4.72747i	−0.0332840	+	0.228511i
$429$		0			0
$430$	0.758262	−	10.4666i	0.0365666	−	0.504746i
$431$			14.0974i			0.679048i	0.940597	+	0.339524i	$0.110266\pi$
$431$			14.0974i			0.679048i	−0.940597	+	0.339524i	$0.889734\pi$
$432$		0			0
$433$			18.3496i			0.881826i	0.897550	+	0.440913i	$0.145345\pi$
$433$			18.3496i			0.881826i	−0.897550	+	0.440913i	$0.854655\pi$
$434$	9.66034	+	1.35842i	0.463711	+	0.0652062i
$435$		0			0
$436$	−11.4739	−	1.67124i	−0.549499	−	0.0800378i
$437$			2.42113i			0.115819i
$438$		0			0
$439$	8.36492			0.399236			0.199618	−	0.979874i	$-0.436030\pi$
$439$	8.36492			0.399236			0.199618	+	0.979874i	$0.436030\pi$
$440$	3.18339	−	14.4419i	0.151762	−	0.688490i
$441$		0			0
$442$	−3.09898	+	42.7766i	−0.147403	+	2.03467i
$443$			1.47488i			0.0700737i	0.999386	+	0.0350368i	$0.0111549\pi$
$443$			1.47488i			0.0700737i	−0.999386	+	0.0350368i	$0.988845\pi$
$444$		0			0
$445$	8.53516			0.404605
$446$	0.126268	−	1.74293i	0.00597895	−	0.0825300i
$447$		0			0
$448$	−10.1716	+	18.5617i	−0.480565	+	0.876959i
$449$	16.1871			0.763918			0.381959	−	0.924179i	$-0.375250\pi$
$449$	16.1871			0.763918			0.381959	+	0.924179i	$0.375250\pi$
$450$		0			0
$451$	45.5656			2.14560
$452$	−13.5886	−	1.97925i	−0.639152	−	0.0930963i
$453$		0			0
$454$	0.180411	−	2.49030i	0.00846713	−	0.116876i
$455$	0.806161	−	11.9458i	0.0377934	−	0.560026i
$456$		0			0
$457$	−26.6551			−1.24687			−0.623435	−	0.781875i	$-0.714264\pi$
$457$	−26.6551			−1.24687			−0.623435	+	0.781875i	$0.714264\pi$
$458$	−12.6213	−	0.914362i	−0.589757	−	0.0427253i
$459$		0			0
$460$	−1.69930	−	0.247513i	−0.0792304	−	0.0115404i
$461$			34.3308i			1.59895i	0.600703	+	0.799473i	$0.294888\pi$
$461$			34.3308i			1.59895i	−0.600703	+	0.799473i	$0.705112\pi$
$462$		0			0
$463$		−	16.8787i		−	0.784421i	−0.919875	−	0.392210i	$-0.871710\pi$
$463$		−	16.8787i		−	0.784421i	0.919875	−	0.392210i	$-0.128290\pi$
$464$	−24.8175	−	7.38632i	−1.15212	−	0.342902i
$465$		0			0
$466$	2.22854	−	30.7615i	0.103235	−	1.42500i
$467$	33.4884			1.54966			0.774829	−	0.632171i	$-0.217836\pi$
$467$	33.4884			1.54966			0.774829	+	0.632171i	$0.217836\pi$
$468$		0			0
$469$	11.9388	+	0.805688i	0.551280	+	0.0372032i
$470$	−13.8607	−	1.00415i	−0.639348	−	0.0463180i
$471$		0			0
$472$	−2.60563	+	11.8208i	−0.119934	+	0.544097i
$473$	38.7980			1.78394
$474$		0			0
$475$	2.81981			0.129382
$476$	34.6673	+	7.46236i	1.58897	+	0.342037i
$477$		0			0
$478$	−20.8132	−	1.50783i	−0.951976	−	0.0689665i
$479$	21.1342			0.965644			0.482822	−	0.875718i	$-0.339612\pi$
$479$	21.1342			0.965644			0.482822	+	0.875718i	$0.339612\pi$
$480$		0			0
$481$		−	9.68314i		−	0.441513i
$482$	21.6235	+	1.56653i	0.984921	+	0.0713533i
$483$		0			0
$484$	32.3343	+	4.70968i	1.46974	+	0.214076i
$485$	10.5209			0.477730
$486$		0			0
$487$		−	13.3600i		−	0.605399i	−0.953086	−	0.302699i	$-0.902112\pi$
$487$		−	13.3600i		−	0.605399i	0.953086	−	0.302699i	$-0.0978878\pi$
$488$	−29.5696	−	6.51795i	−1.33855	−	0.295054i
$489$		0			0
$490$	−9.68799	−	2.03542i	−0.437659	−	0.0919508i
$491$		−	10.6077i		−	0.478717i	−0.970931	−	0.239359i	$-0.923063\pi$
$491$		−	10.6077i		−	0.478717i	0.970931	−	0.239359i	$-0.0769372\pi$
$492$		0			0
$493$			43.3814i			1.95380i
$494$	17.9990	+	1.30395i	0.809815	+	0.0586676i
$495$		0			0
$496$	−9.99562	−	2.97496i	−0.448817	−	0.133579i
$497$	19.0989	+	1.28889i	0.856703	+	0.0578147i
$498$		0			0
$499$		−	22.9131i		−	1.02573i	−0.858470	−	0.512865i	$-0.828584\pi$
$499$		−	22.9131i		−	1.02573i	0.858470	−	0.512865i	$-0.171416\pi$
$500$	−0.288270	+	1.97912i	−0.0128918	+	0.0885088i
$501$		0			0
$502$	1.57430	−	21.7308i	0.0702646	−	0.969893i
$503$	−15.2517			−0.680040			−0.340020	−	0.940418i	$-0.610434\pi$
$503$	−15.2517			−0.680040			−0.340020	+	0.940418i	$0.610434\pi$
$504$		0			0
$505$	3.97836			0.177035
$506$	0.458745	−	6.33227i	0.0203937	−	0.281504i
$507$		0			0
$508$	−3.02204	+	20.7478i	−0.134081	+	0.920536i
$509$			6.06153i			0.268673i	0.990936	+	0.134336i	$0.0428902\pi$
$509$			6.06153i			0.268673i	−0.990936	+	0.134336i	$0.957110\pi$
$510$		0			0
$511$	−24.4097	−	1.64729i	−1.07982	−	0.0728717i
$512$	13.7095	−	18.0013i	0.605882	−	0.795555i
$513$		0			0
$514$	−16.3781	−	1.18652i	−0.722405	−	0.0523351i
$515$		−	3.78934i		−	0.166978i
$516$		0			0
$517$		−	51.3794i		−	2.25967i
$518$	−7.92824	−	1.11485i	−0.348347	−	0.0489839i
$519$		0			0
$520$	−2.75524	+	12.4995i	−0.120825	+	0.548141i
$521$			33.7238i			1.47747i	0.673998	+	0.738733i	$0.264576\pi$
$521$			33.7238i			1.47747i	−0.673998	+	0.738733i	$0.735424\pi$
$522$		0			0
$523$	17.5830			0.768852			0.384426	−	0.923156i	$-0.374399\pi$
$523$	17.5830			0.768852			0.384426	+	0.923156i	$0.374399\pi$
$524$	−37.7884	−	5.50410i	−1.65079	−	0.240448i
$525$		0			0
$526$	20.3340	+	1.47311i	0.886603	+	0.0642306i
$527$			17.4725i			0.761116i
$528$		0			0
$529$	22.2628			0.967947
$530$	−5.20906	−	0.377374i	−0.226267	−	0.0163921i
$531$		0			0
$532$	3.13993	−	14.5869i	0.136133	−	0.632422i
$533$	−39.4373			−1.70822
$534$		0			0
$535$	2.38868			0.103272
$536$	−12.4922	−	2.75363i	−0.539581	−	0.118939i
$537$		0			0
$538$	15.3015	+	1.10853i	0.659696	+	0.0477921i
$539$	4.91749	−	36.2680i	0.211811	−	1.56217i
$540$		0			0
$541$	−22.7960			−0.980079			−0.490039	−	0.871700i	$-0.663018\pi$
$541$	−22.7960			−0.980079			−0.490039	+	0.871700i	$0.663018\pi$
$542$	−1.93906	+	26.7657i	−0.0832897	+	1.14968i
$543$		0			0
$544$	−35.4582	−	13.4113i	−1.52026	−	0.575003i
$545$			5.79748i			0.248337i
$546$		0			0
$547$			14.4784i			0.619053i	0.950891	+	0.309527i	$0.100171\pi$
$547$			14.4784i			0.619053i	−0.950891	+	0.309527i	$0.899829\pi$
$548$	10.8300	+	1.57745i	0.462635	+	0.0673854i
$549$		0			0
$550$	−7.37496	−	0.534284i	−0.314469	−	0.0227819i
$551$	18.2535			0.777627
$552$		0			0
$553$	7.08281	+	0.477984i	0.301192	+	0.0203259i
$554$	1.13385	−	15.6511i	0.0481727	−	0.664950i
$555$		0			0
$556$	−5.61957	−	0.818523i	−0.238323	−	0.0347131i
$557$	−14.9697			−0.634288			−0.317144	−	0.948377i	$-0.602724\pi$
$557$	−14.9697			−0.634288			−0.317144	+	0.948377i	$0.602724\pi$
$558$		0			0
$559$	−33.5800			−1.42028
$560$	9.91700	+	3.69502i	0.419070	+	0.156143i
$561$		0			0
$562$	2.67111	−	36.8705i	0.112674	−	1.55529i
$563$	−6.81282			−0.287126			−0.143563	−	0.989641i	$-0.545856\pi$
$563$	−6.81282			−0.287126			−0.143563	+	0.989641i	$0.545856\pi$
$564$		0			0
$565$			6.86598i			0.288854i
$566$	1.53302	−	21.1610i	0.0644377	−	0.889462i
$567$		0			0
$568$	−19.9843	−	4.40509i	−0.838522	−	0.184833i
$569$	−15.3819			−0.644841			−0.322421	−	0.946597i	$-0.604497\pi$
$569$	−15.3819			−0.644841			−0.322421	+	0.946597i	$0.604497\pi$
$570$		0			0
$571$			33.9875i			1.42233i	0.703024	+	0.711167i	$0.251833\pi$
$571$			33.9875i			1.42233i	−0.703024	+	0.711167i	$0.748167\pi$
$572$	−46.8278	−	6.82075i	−1.95797	−	0.285190i
$573$		0			0
$574$	−4.54056	+	32.2900i	−0.189519	+	1.34776i
$575$			0.858617i			0.0358068i
$576$		0			0
$577$			41.9819i			1.74773i	0.486170	+	0.873864i	$0.338394\pi$
$577$			41.9819i			1.74773i	−0.486170	+	0.873864i	$0.661606\pi$
$578$	−2.85210	+	39.3688i	−0.118632	+	1.63753i
$579$		0			0
$580$	−1.86607	+	12.8115i	−0.0774842	+	0.531968i
$581$	−2.90039	+	42.9783i	−0.120329	+	1.78304i
$582$		0			0
$583$		−	19.3091i		−	0.799701i
$584$	25.5412	+	5.62999i	1.05690	+	0.232971i
$585$		0			0
$586$	−42.5646	−	3.08362i	−1.75833	−	0.127383i
$587$	−12.5442			−0.517756			−0.258878	−	0.965910i	$-0.583353\pi$
$587$	−12.5442			−0.517756			−0.258878	+	0.965910i	$0.583353\pi$
$588$		0			0
$589$	7.35190			0.302930
$590$	6.03647	+	0.437316i	0.248518	+	0.0180040i
$591$		0			0
$592$	8.20340	+	2.44155i	0.337158	+	0.100347i
$593$			9.26081i			0.380296i	0.981755	+	0.190148i	$0.0608968\pi$
$593$			9.26081i			0.380296i	−0.981755	+	0.190148i	$0.939103\pi$
$594$		0			0
$595$	1.19384	−	17.6904i	0.0489426	−	0.725237i
$596$	3.42102	+	0.498291i	0.140130	+	0.0204108i
$597$		0			0
$598$	−0.397047	+	5.48062i	−0.0162365	+	0.224119i
$599$			15.8991i			0.649618i	0.945780	+	0.324809i	$0.105300\pi$
$599$			15.8991i			0.649618i	−0.945780	+	0.324809i	$0.894700\pi$
$600$		0			0
$601$			31.4061i			1.28108i	0.767925	+	0.640540i	$0.221289\pi$
$601$			31.4061i			1.28108i	−0.767925	+	0.640540i	$0.778711\pi$
$602$	−3.86618	+	27.4942i	−0.157574	+	1.12058i
$603$		0			0
$604$	4.31055	−	29.5941i	0.175394	−	1.20417i
$605$		−	16.3377i		−	0.664223i
$606$		0			0
$607$	−14.6628			−0.595147			−0.297573	−	0.954699i	$-0.596177\pi$
$607$	−14.6628			−0.595147			−0.297573	+	0.954699i	$0.596177\pi$
$608$	−5.64304	+	14.9197i	−0.228855	+	0.605074i
$609$		0			0
$610$	−1.09394	+	15.1001i	−0.0442923	+	0.611387i
$611$			44.4692i			1.79903i
$612$		0			0
$613$	35.6120			1.43836			0.719178	−	0.694826i	$-0.244519\pi$
$613$	35.6120			1.43836			0.719178	+	0.694826i	$0.244519\pi$
$614$	−0.630955	+	8.70935i	−0.0254633	+	0.351481i
$615$		0			0
$616$	−10.9761	+	37.5558i	−0.442238	+	1.51317i
$617$	−22.0702			−0.888513			−0.444256	−	0.895900i	$-0.646532\pi$
$617$	−22.0702			−0.888513			−0.444256	+	0.895900i	$0.646532\pi$
$618$		0			0
$619$	−29.1671			−1.17232			−0.586162	−	0.810194i	$-0.699362\pi$
$619$	−29.1671			−1.17232			−0.586162	+	0.810194i	$0.699362\pi$
$620$	−0.751587	+	5.16002i	−0.0301845	+	0.207231i
$621$		0			0
$622$	−0.388882	+	5.36792i	−0.0155928	+	0.215234i
$623$	−22.5307	−	1.52048i	−0.902672	−	0.0609169i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−23.3827	−	1.69398i	−0.934562	−	0.0677050i
$627$		0			0
$628$	3.18201	−	21.8461i	0.126976	−	0.871754i
$629$		−	14.3397i		−	0.571762i
$630$		0			0
$631$		−	0.162149i		−	0.00645504i	−0.999995	−	0.00322752i	$-0.998973\pi$
$631$		−	0.162149i		−	0.00645504i	0.999995	−	0.00322752i	$-0.00102735\pi$
$632$	−7.41115	−	1.63362i	−0.294800	−	0.0649820i
$633$		0			0
$634$	1.13546	−	15.6733i	0.0450950	−	0.622467i
$635$	10.4834			0.416020
$636$		0			0
$637$	−4.25612	+	31.3902i	−0.168634	+	1.24372i
$638$	−47.7406	−	3.45860i	−1.89007	−	0.136927i
$639$		0			0
$640$	−9.89470	−	5.48588i	−0.391122	−	0.216849i
$641$	−12.4758			−0.492766			−0.246383	−	0.969173i	$-0.579242\pi$
$641$	−12.4758			−0.492766			−0.246383	+	0.969173i	$0.579242\pi$
$642$		0			0
$643$	−28.4881			−1.12346			−0.561731	−	0.827320i	$-0.689864\pi$
$643$	−28.4881			−1.12346			−0.561731	+	0.827320i	$0.689864\pi$
$644$	4.44164	+	0.956093i	0.175025	+	0.0376753i
$645$		0			0
$646$	26.6547	+	1.93102i	1.04871	+	0.0759748i
$647$	24.4328			0.960554			0.480277	−	0.877117i	$-0.340536\pi$
$647$	24.4328			0.960554			0.480277	+	0.877117i	$0.340536\pi$
$648$		0			0
$649$			22.3762i			0.878342i
$650$	6.38308	+	0.462426i	0.250365	+	0.0181379i
$651$		0			0
$652$	5.41858	−	37.2012i	0.212208	−	1.45691i
$653$	39.9022			1.56149			0.780746	−	0.624848i	$-0.214839\pi$
$653$	39.9022			1.56149			0.780746	+	0.624848i	$0.214839\pi$
$654$		0			0
$655$			19.0936i			0.746047i
$656$	9.94388	−	33.4107i	0.388243	−	1.30447i
$657$		0			0
$658$	36.4100	+	5.11990i	1.41941	+	0.199595i
$659$		−	2.24981i		−	0.0876403i	−0.999039	−	0.0438202i	$-0.986047\pi$
$659$		−	2.24981i		−	0.0876403i	0.999039	−	0.0438202i	$-0.0139529\pi$
$660$		0			0
$661$		−	26.0267i		−	1.01232i	−0.862439	−	0.506162i	$-0.831064\pi$
$661$		−	26.0267i		−	1.01232i	0.862439	−	0.506162i	$-0.168936\pi$
$662$	−31.6956	−	2.29621i	−1.23188	−	0.0892447i
$663$		0			0
$664$	9.91278	−	44.9707i	0.384690	−	1.74520i
$665$	−7.44358	−	0.502330i	−0.288650	−	0.0194795i
$666$		0			0
$667$			5.55812i			0.215211i
$668$	3.74676	+	0.545738i	0.144967	+	0.0211152i
$669$		0			0
$670$	−0.462155	+	6.37933i	−0.0178546	+	0.246455i
$671$	−55.9737			−2.16084
$672$		0			0
$673$	34.4184			1.32673			0.663365	−	0.748296i	$-0.269127\pi$
$673$	34.4184			1.32673			0.663365	+	0.748296i	$0.269127\pi$
$674$	−0.615904	+	8.50160i	−0.0237237	+	0.327469i
$675$		0			0
$676$	14.8013	+	2.15590i	0.569281	+	0.0829191i
$677$			37.6392i			1.44659i	0.690538	+	0.723296i	$0.257374\pi$
$677$			37.6392i			1.44659i	−0.690538	+	0.723296i	$0.742626\pi$
$678$		0			0
$679$	−27.7725	−	1.87423i	−1.06581	−	0.0719264i
$680$	−4.08023	+	18.5105i	−0.156470	+	0.709846i
$681$		0			0
$682$	−19.2282	−	1.39300i	−0.736288	−	0.0533409i
$683$		−	25.5973i		−	0.979454i	−0.871876	−	0.489727i	$-0.837096\pi$
$683$		−	25.5973i		−	0.979454i	0.871876	−	0.489727i	$-0.162904\pi$
$684$		0			0
$685$		−	5.47214i		−	0.209080i
$686$	25.2112	+	7.09884i	0.962570	+	0.271035i
$687$		0			0
$688$	8.46699	−	28.4484i	0.322801	−	1.08459i
$689$			16.7122i			0.636682i
$690$		0			0
$691$	20.4140			0.776585			0.388293	−	0.921536i	$-0.373065\pi$
$691$	20.4140			0.776585			0.388293	+	0.921536i	$0.373065\pi$
$692$	2.71927	−	18.6691i	0.103371	−	0.709693i
$693$		0			0
$694$	13.5000	+	0.978013i	0.512451	+	0.0371249i
$695$			2.83943i			0.107706i
$696$		0			0
$697$	−58.4025			−2.21215
$698$	18.2579	+	1.32271i	0.691073	+	0.0500653i
$699$		0			0
$700$	1.11353	−	5.17301i	0.0420873	−	0.195521i
$701$	7.73141			0.292011			0.146006	−	0.989284i	$-0.453358\pi$
$701$	7.73141			0.292011			0.146006	+	0.989284i	$0.453358\pi$
$702$		0			0
$703$	−6.03370			−0.227565
$704$	17.5858	−	37.9520i	0.662790	−	1.43037i
$705$		0			0
$706$	16.3915	+	1.18750i	0.616903	+	0.0446920i
$707$	−10.5019	−	0.708718i	−0.394963	−	0.0266541i
$708$		0			0
$709$	29.7793			1.11839			0.559193	−	0.829038i	$-0.311111\pi$
$709$	29.7793			1.11839			0.559193	+	0.829038i	$0.311111\pi$
$710$	−0.739328	+	10.2053i	−0.0277465	+	0.382997i
$711$		0			0
$712$	23.5751	+	5.19661i	0.883515	+	0.194751i
$713$			2.23862i			0.0838369i
$714$		0			0
$715$			23.6610i			0.884871i
$716$	−6.18677	+	42.4753i	−0.231211	+	1.58738i
$717$		0			0
$718$	7.65182	+	0.554341i	0.285563	+	0.0206878i
$719$	18.4203			0.686963			0.343481	−	0.939160i	$-0.388394\pi$
$719$	18.4203			0.686963			0.343481	+	0.939160i	$0.388394\pi$
$720$		0			0
$721$	−0.675047	+	10.0029i	−0.0251401	+	0.372528i
$722$	−1.12902	+	15.5844i	−0.0420178	+	0.579990i
$723$		0			0
$724$	−6.96851	+	47.8423i	−0.258983	+	1.77804i
$725$	6.47333			0.240414
$726$		0			0
$727$	−30.7292			−1.13968			−0.569842	−	0.821754i	$-0.692996\pi$
$727$	−30.7292			−1.13968			−0.569842	+	0.821754i	$0.692996\pi$
$728$	9.49986	−	32.5048i	0.352088	−	1.20471i
$729$		0			0
$730$	0.944910	−	13.0430i	0.0349727	−	0.482743i
$731$	−49.7284			−1.83927
$732$		0			0
$733$		−	5.09061i		−	0.188026i	−0.995571	−	0.0940130i	$-0.970030\pi$
$733$		−	5.09061i		−	0.188026i	0.995571	−	0.0940130i	$-0.0299695\pi$
$734$	−2.90415	+	40.0873i	−0.107194	+	1.47965i
$735$		0			0
$736$	−4.54298	−	1.71828i	−0.167456	−	0.0633365i
$737$	−23.6471			−0.871052
$738$		0			0
$739$		−	15.1154i		−	0.556030i	−0.960577	−	0.278015i	$-0.910323\pi$
$739$		−	15.1154i		−	0.556030i	0.960577	−	0.278015i	$-0.0896765\pi$
$740$	0.616827	−	4.23483i	0.0226750	−	0.155675i
$741$		0			0
$742$	13.6834	+	1.92413i	0.502332	+	0.0706370i
$743$		−	42.0496i		−	1.54265i	−0.636440	−	0.771326i	$-0.719594\pi$
$743$		−	42.0496i		−	1.54265i	0.636440	−	0.771326i	$-0.280406\pi$
$744$		0			0
$745$		−	1.72856i		−	0.0633295i
$746$	2.35971	−	32.5721i	0.0863951	−	1.19255i
$747$		0			0
$748$	−69.3471	−	10.1008i	−2.53558	−	0.369322i
$749$	−6.30551	−	0.425527i	−0.230398	−	0.0155484i
$750$		0			0
$751$			24.8965i			0.908487i	0.890877	+	0.454244i	$0.150090\pi$
$751$			24.8965i			0.908487i	−0.890877	+	0.454244i	$0.849910\pi$
$752$	−37.6736	−	11.2127i	−1.37382	−	0.408884i
$753$		0			0
$754$	41.3198	+	2.99344i	1.50478	+	0.109015i
$755$	−14.9532			−0.544202
$756$		0			0
$757$	−39.7946			−1.44636			−0.723179	−	0.690661i	$-0.757320\pi$
$757$	−39.7946			−1.44636			−0.723179	+	0.690661i	$0.757320\pi$
$758$	17.0396	+	1.23444i	0.618905	+	0.0448370i
$759$		0			0
$760$	7.78864	+	1.71683i	0.282524	+	0.0622760i
$761$		−	27.5663i		−	0.999279i	−0.866234	−	0.499639i	$-0.833466\pi$
$761$		−	27.5663i		−	0.999279i	0.866234	−	0.499639i	$-0.166534\pi$
$762$		0			0
$763$	1.03278	−	15.3039i	0.0373893	−	0.554038i
$764$	−5.47199	+	37.5680i	−0.197970	+	1.35916i
$765$		0			0
$766$	0.414468	−	5.72108i	0.0149753	−	0.206711i
$767$		−	19.3667i		−	0.699292i
$768$		0			0
$769$		−	5.38100i		−	0.194044i	−0.995282	−	0.0970219i	$-0.969068\pi$
$769$		−	5.38100i		−	0.194044i	0.995282	−	0.0970219i	$-0.0309317\pi$
$770$	19.3728	+	2.72418i	0.698149	+	0.0981725i
$771$		0			0
$772$	−52.6155	−	7.66376i	−1.89367	−	0.275825i
$773$			18.8696i			0.678693i	0.940661	+	0.339347i	$0.110206\pi$
$773$			18.8696i			0.678693i	−0.940661	+	0.339347i	$0.889794\pi$
$774$		0			0
$775$	2.60723			0.0936546
$776$	29.0600	+	6.40563i	1.04319	+	0.229949i
$777$		0			0
$778$	−0.540363	+	7.45887i	−0.0193730	+	0.267413i
$779$			24.5739i			0.880453i
$780$		0			0
$781$	−37.8292			−1.35364
$782$	−0.587985	+	8.11622i	−0.0210263	+	0.290235i
$783$		0			0
$784$	−25.5201	−	11.5206i	−0.911433	−	0.411449i
$785$	−11.0383			−0.393974
$786$		0			0
$787$	−36.8177			−1.31241			−0.656204	−	0.754583i	$-0.727839\pi$
$787$	−36.8177			−1.31241			−0.656204	+	0.754583i	$0.727839\pi$
$788$	45.9171	+	6.68809i	1.63573	+	0.238253i
$789$		0			0
$790$	−0.274179	+	3.78461i	−0.00975485	+	0.134651i
$791$	1.22313	−	18.1244i	0.0434895	−	0.644431i
$792$		0			0
$793$	48.4456			1.72035
$794$	−21.1660	−	1.53338i	−0.751153	−	0.0544178i
$795$		0			0
$796$	−39.3581	−	5.73274i	−1.39501	−	0.203191i
$797$			26.2324i			0.929200i	0.885521	+	0.464600i	$0.153802\pi$
$797$			26.2324i			0.929200i	−0.885521	+	0.464600i	$0.846198\pi$
$798$		0			0
$799$			65.8543i			2.32976i
$800$	−2.00121	+	5.29104i	−0.0707536	+	0.187067i
$801$		0			0
$802$	−1.97862	+	27.3118i	−0.0698676	+	0.964414i
$803$	48.3482			1.70617
$804$		0			0
$805$	0.152957	−	2.26653i	0.00539103	−	0.0798848i
$806$	16.6422	+	1.20565i	0.586196	+	0.0424673i
$807$		0			0
$808$	10.9887	+	2.42221i	0.386581	+	0.0852131i
$809$	38.8484			1.36584			0.682919	−	0.730494i	$-0.260710\pi$
$809$	38.8484			1.36584			0.682919	+	0.730494i	$0.260710\pi$
$810$		0			0
$811$	5.18833			0.182187			0.0910935	−	0.995842i	$-0.470964\pi$
$811$	5.18833			0.182187			0.0910935	+	0.995842i	$0.470964\pi$
$812$	7.20823	−	33.4866i	0.252959	−	1.17515i
$813$		0			0
$814$	15.7806	+	1.14324i	0.553110	+	0.0400705i
$815$	−18.7969			−0.658427
$816$		0			0
$817$			20.9242i			0.732043i
$818$	−0.610013	−	0.0441928i	−0.0213286	−	0.00154516i
$819$		0			0
$820$	−17.2475	−	2.51220i	−0.602310	−	0.0877299i
$821$	−19.2600			−0.672178			−0.336089	−	0.941830i	$-0.609104\pi$
$821$	−19.2600			−0.672178			−0.336089	+	0.941830i	$0.609104\pi$
$822$		0			0
$823$			7.22802i			0.251953i	0.992033	+	0.125976i	$0.0402064\pi$
$823$			7.22802i			0.251953i	−0.992033	+	0.125976i	$0.959794\pi$
$824$	2.30713	−	10.4666i	0.0803727	−	0.364622i
$825$		0			0
$826$	−15.8569	−	2.22976i	−0.551730	−	0.0775834i
$827$		−	48.2236i		−	1.67690i	−0.544979	−	0.838449i	$-0.683463\pi$
$827$		−	48.2236i		−	1.67690i	0.544979	−	0.838449i	$-0.316537\pi$
$828$		0			0
$829$		−	38.5326i		−	1.33829i	−0.743130	−	0.669147i	$-0.766660\pi$
$829$		−	38.5326i		−	1.33829i	0.743130	−	0.669147i	$-0.233340\pi$
$830$	−22.9649	−	1.66371i	−0.797125	−	0.0577483i
$831$		0			0
$832$	−15.2206	+	32.8477i	−0.527680	+	1.13879i
$833$	−6.30287	+	46.4856i	−0.218381	+	1.61063i
$834$		0			0
$835$		−	1.89315i		−	0.0655151i
$836$	−4.25011	+	29.1791i	−0.146993	+	1.00918i
$837$		0			0
$838$	−0.568374	+	7.84552i	−0.0196342	+	0.271019i
$839$	−36.5920			−1.26330			−0.631649	−	0.775255i	$-0.717622\pi$
$839$	−36.5920			−1.26330			−0.631649	+	0.775255i	$0.717622\pi$
$840$		0			0
$841$	12.9040			0.444967
$842$	−0.202199	+	2.79105i	−0.00696825	+	0.0961858i
$843$		0			0
$844$	0.724474	−	4.97387i	0.0249374	−	0.171208i
$845$		−	7.47874i		−	0.257277i
$846$		0			0
$847$	−2.91046	+	43.1275i	−0.100005	+	1.48188i
$848$	−14.1583	−	4.21387i	−0.486197	−	0.144705i
$849$		0			0
$850$	9.45266	+	0.684805i	0.324224	+	0.0234886i
$851$		−	1.83723i		−	0.0629795i
$852$		0			0
$853$			11.8256i			0.404901i	0.979292	+	0.202451i	$0.0648906\pi$
$853$			11.8256i			0.404901i	−0.979292	+	0.202451i	$0.935109\pi$
$854$	5.57772	−	39.6657i	0.190865	−	1.35733i
$855$		0			0
$856$	6.59781	+	1.45434i	0.225509	+	0.0497083i
$857$		−	44.9795i		−	1.53647i	−0.640167	−	0.768235i	$-0.721135\pi$
$857$		−	44.9795i		−	1.53647i	0.640167	−	0.768235i	$-0.278865\pi$
$858$		0			0
$859$	54.7905			1.86943			0.934713	−	0.355402i	$-0.115656\pi$
$859$	54.7905			1.86943			0.934713	+	0.355402i	$0.115656\pi$
$860$	−14.6859	−	2.13908i	−0.500784	−	0.0729421i
$861$		0			0
$862$	19.8846	+	1.44056i	0.677273	+	0.0490655i
$863$		−	12.9172i		−	0.439708i	−0.975533	−	0.219854i	$-0.929442\pi$
$863$		−	12.9172i		−	0.439708i	0.975533	−	0.219854i	$-0.0705580\pi$
$864$		0			0
$865$	−9.43306			−0.320734
$866$	25.8824	+	1.87507i	0.879521	+	0.0637175i
$867$		0			0
$868$	2.90322	−	13.4873i	0.0985418	−	0.457787i
$869$	−14.0289			−0.475899
$870$		0			0
$871$	20.4667			0.693489
$872$	−3.52978	+	16.0133i	−0.119533	+	0.542280i
$873$		0			0
$874$	3.41505	+	0.247406i	0.115516	+	0.00836862i
$875$	−2.63975	−	0.178143i	−0.0892397	−	0.00602235i
$876$		0			0
$877$	−1.64568			−0.0555706			−0.0277853	−	0.999614i	$-0.508845\pi$
$877$	−1.64568			−0.0555706			−0.0277853	+	0.999614i	$0.508845\pi$
$878$	0.854777	−	11.7989i	0.0288473	−	0.398192i
$879$		0			0
$880$	−20.0452	−	5.96598i	−0.675724	−	0.201113i
$881$		−	38.0777i		−	1.28287i	−0.767177	−	0.641435i	$-0.778339\pi$
$881$		−	38.0777i		−	1.28287i	0.767177	−	0.641435i	$-0.221661\pi$
$882$		0			0
$883$		−	7.08731i		−	0.238507i	−0.992864	−	0.119253i	$-0.961950\pi$
$883$		−	7.08731i		−	0.238507i	0.992864	−	0.119253i	$-0.0380501\pi$
$884$	60.0204	+	8.74232i	2.01870	+	0.294036i
$885$		0			0
$886$	2.08034	+	0.150712i	0.0698905	+	0.00506327i
$887$	14.6383			0.491506			0.245753	−	0.969333i	$-0.420965\pi$
$887$	14.6383			0.491506			0.245753	+	0.969333i	$0.420965\pi$
$888$		0			0
$889$	−27.6735	−	1.86755i	−0.928139	−	0.0626355i
$890$	0.872173	−	12.0390i	0.0292353	−	0.403548i
$891$		0			0
$892$	−2.44553	−	0.356205i	−0.0818823	−	0.0119266i
$893$	27.7094			0.927260
$894$		0			0
$895$	21.4618			0.717387
$896$	25.1422	+	16.2440i	0.839943	+	0.542675i
$897$		0			0
$898$	1.65410	−	22.8322i	0.0551979	−	0.761921i
$899$	16.8775			0.562896
$900$		0			0
$901$			24.7489i			0.824507i
$902$	4.65616	−	64.2710i	0.155033	−	2.13999i
$903$		0			0
$904$	−4.18033	+	18.9646i	−0.139036	+	0.630755i
$905$	24.1736			0.803556
$906$		0			0
$907$		−	32.1062i		−	1.06607i	−0.846094	−	0.533034i	$-0.821052\pi$
$907$		−	32.1062i		−	1.06607i	0.846094	−	0.533034i	$-0.178948\pi$
$908$	−3.49417	−	0.508947i	−0.115958	−	0.0168900i
$909$		0			0
$910$	−16.7673	−	2.35779i	−0.555831	−	0.0781600i
$911$		−	1.73881i		−	0.0576092i	−0.999585	−	0.0288046i	$-0.990830\pi$
$911$		−	1.73881i		−	0.0576092i	0.999585	−	0.0288046i	$-0.00917006\pi$
$912$		0			0
$913$		−	85.1272i		−	2.81730i
$914$	−2.72377	+	37.5974i	−0.0900943	+	1.24361i
$915$		0			0
$916$	−2.57945	+	17.7092i	−0.0852273	+	0.585128i
$917$	3.40139	−	50.4022i	0.112324	−	1.66443i
$918$		0			0
$919$			40.8342i			1.34700i	0.739189	+	0.673498i	$0.235209\pi$
$919$			40.8342i			1.34700i	−0.739189	+	0.673498i	$0.764791\pi$
$920$	−0.522767	+	2.37160i	−0.0172351	+	0.0781894i
$921$		0			0
$922$	48.4242	+	3.50812i	1.59477	+	0.115534i
$923$	32.7415			1.07770
$924$		0			0
$925$	−2.13976			−0.0703548
$926$	−23.8077	−	1.72477i	−0.782371	−	0.0566794i
$927$		0			0
$928$	−12.9545	+	34.2507i	−0.425253	+	1.12433i
$929$			0.604846i			0.0198444i	0.999951	+	0.00992218i	$0.00315838\pi$
$929$			0.604846i			0.0198444i	−0.999951	+	0.00992218i	$0.996842\pi$
$930$		0			0
$931$	19.5597	+	2.65205i	0.641042	+	0.0869174i
$932$	−43.1620	−	6.28679i	−1.41382	−	0.205931i
$933$		0			0
$934$	3.42204	−	47.2359i	0.111973	−	1.54561i
$935$			35.0394i			1.14591i
$936$		0			0
$937$		−	21.4792i		−	0.701694i	−0.936433	−	0.350847i	$-0.885894\pi$
$937$		−	21.4792i		−	0.701694i	0.936433	−	0.350847i	$-0.114106\pi$
$938$	2.35641	−	16.7575i	0.0769394	−	0.547151i
$939$		0			0
$940$	−2.83274	+	19.4482i	−0.0923939	+	0.634330i
$941$		−	20.4286i		−	0.665953i	−0.942935	−	0.332976i	$-0.891947\pi$
$941$		−	20.4286i		−	0.665953i	0.942935	−	0.332976i	$-0.108053\pi$
$942$		0			0
$943$	−7.48264			−0.243668
$944$	16.4072	+	4.88321i	0.534009	+	0.158935i
$945$		0			0
$946$	3.96461	−	54.7253i	0.128901	−	1.77927i
$947$			2.74440i			0.0891810i	0.999005	+	0.0445905i	$0.0141983\pi$
$947$			2.74440i			0.0891810i	−0.999005	+	0.0445905i	$0.985802\pi$
$948$		0			0
$949$	−41.8457			−1.35837
$950$	0.288144	−	3.97738i	0.00934864	−	0.129043i
$951$		0			0
$952$	14.0683	−	48.1362i	0.455956	−	1.56010i
$953$	17.4001			0.563644			0.281822	−	0.959467i	$-0.409061\pi$
$953$	17.4001			0.563644			0.281822	+	0.959467i	$0.409061\pi$
$954$		0			0
$955$	18.9822			0.614249
$956$	−4.25364	+	29.2034i	−0.137573	+	0.944504i
$957$		0			0
$958$	2.15961	−	29.8101i	0.0697739	−	0.963120i
$959$	−0.974826	+	14.4451i	−0.0314788	+	0.466455i
$960$		0			0
$961$	−24.2023			−0.780720
$962$	−13.6582	−	0.989480i	−0.440359	−	0.0319021i
$963$		0			0
$964$	4.41922	−	30.3402i	0.142334	−	0.977191i
$965$			26.5854i			0.855813i
$966$		0			0
$967$		−	29.1327i		−	0.936845i	−0.883505	−	0.468422i	$-0.844823\pi$
$967$		−	29.1327i		−	0.936845i	0.883505	−	0.468422i	$-0.155177\pi$
$968$	9.94718	−	45.1268i	0.319715	−	1.45043i
$969$		0			0
$970$	1.07509	−	14.8399i	0.0345190	−	0.476481i
$971$	42.2191			1.35487			0.677437	−	0.735581i	$-0.263091\pi$
$971$	42.2191			1.35487			0.677437	+	0.735581i	$0.263091\pi$
$972$		0			0
$973$	0.505827	−	7.49539i	0.0162161	−	0.240291i
$974$	−18.8445	−	1.36520i	−0.603816	−	0.0437439i
$975$		0			0
$976$	−12.2153	+	41.0423i	−0.391001	+	1.31373i
$977$	−44.1167			−1.41142			−0.705710	−	0.708501i	$-0.749372\pi$
$977$	−44.1167			−1.41142			−0.705710	+	0.708501i	$0.749372\pi$
$978$		0			0
$979$	44.6265			1.42627
$980$	−3.86097	+	13.4571i	−0.123334	+	0.429871i
$981$		0			0
$982$	−14.9623	−	1.08395i	−0.477466	−	0.0345904i
$983$	−34.2931			−1.09378			−0.546890	−	0.837204i	$-0.684189\pi$
$983$	−34.2931			−1.09378			−0.546890	+	0.837204i	$0.684189\pi$
$984$		0			0
$985$		−	23.2008i		−	0.739239i
$986$	61.1902	+	4.43297i	1.94869	+	0.141175i
$987$		0			0
$988$	3.67849	−	25.2547i	0.117029	−	0.803459i
$989$	−6.37130			−0.202596
$990$		0			0
$991$		−	34.2121i		−	1.08678i	−0.839479	−	0.543392i	$-0.817140\pi$
$991$		−	34.2121i		−	1.08678i	0.839479	−	0.543392i	$-0.182860\pi$
$992$	−5.21764	+	13.7950i	−0.165660	+	0.437991i
$993$		0			0
$994$	3.76964	−	26.8076i	0.119566	−	0.850287i
$995$			19.8867i			0.630451i
$996$		0			0
$997$			30.2000i			0.956443i	0.878239	+	0.478221i	$0.158718\pi$
$997$			30.2000i			0.956443i	−0.878239	+	0.478221i	$0.841282\pi$
$998$	−32.3192	−	2.34139i	−1.02305	−	0.0741154i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.c.e.811.9		16
3.2	odd	2		420.2.c.b.391.8	yes	16
4.3	odd	2		1260.2.c.d.811.10		16
7.6	odd	2		1260.2.c.d.811.9		16
12.11	even	2		420.2.c.a.391.7	✓	16
21.20	even	2		420.2.c.a.391.8	yes	16
28.27	even	2	inner	1260.2.c.e.811.10		16
84.83	odd	2		420.2.c.b.391.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.c.a.391.7	✓	16	12.11	even	2
420.2.c.a.391.8	yes	16	21.20	even	2
420.2.c.b.391.7	yes	16	84.83	odd	2
420.2.c.b.391.8	yes	16	3.2	odd	2
1260.2.c.d.811.9		16	7.6	odd	2
1260.2.c.d.811.10		16	4.3	odd	2
1260.2.c.e.811.9		16	1.1	even	1	trivial
1260.2.c.e.811.10		16	28.27	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.102186 - 1.41052i) q^{2} +(-1.97912 - 0.288270i) q^{4} +1.00000i q^{5} +(0.178143 - 2.63975i) q^{7} +(-0.608847 + 2.76212i) q^{8} +O(q^{10})\)	\(q+(0.102186 - 1.41052i) q^{2} +(-1.97912 - 0.288270i) q^{4} +1.00000i q^{5} +(0.178143 - 2.63975i) q^{7} +(-0.608847 + 2.76212i) q^{8} +(1.41052 + 0.102186i) q^{10} +5.22855i q^{11} -4.52534i q^{13} +(-3.70520 - 0.521019i) q^{14} +(3.83380 + 1.14104i) q^{16} -6.70156i q^{17} -2.81981 q^{19} +(0.288270 - 1.97912i) q^{20} +(7.37496 + 0.534284i) q^{22} -0.858617i q^{23} -1.00000 q^{25} +(-6.38308 - 0.462426i) q^{26} +(-1.11353 + 5.17301i) q^{28} -6.47333 q^{29} -2.60723 q^{31} +(2.00121 - 5.29104i) q^{32} +(-9.45266 - 0.684805i) q^{34} +(2.63975 + 0.178143i) q^{35} +2.13976 q^{37} +(-0.288144 + 3.97738i) q^{38} +(-2.76212 - 0.608847i) q^{40} -8.71476i q^{41} -7.42042i q^{43} +(1.50723 - 10.3479i) q^{44} +(-1.21109 - 0.0877385i) q^{46} -9.82671 q^{47} +(-6.93653 - 0.940508i) q^{49} +(-0.102186 + 1.41052i) q^{50} +(-1.30452 + 8.95618i) q^{52} -3.69301 q^{53} -5.22855 q^{55} +(7.18284 + 2.09926i) q^{56} +(-0.661483 + 9.13075i) q^{58} +4.27962 q^{59} +10.7054i q^{61} +(-0.266423 + 3.67755i) q^{62} +(-7.25861 - 3.36342i) q^{64} +4.52534 q^{65} +4.52269i q^{67} +(-1.93186 + 13.2632i) q^{68} +(0.521019 - 3.70520i) q^{70} +7.23513i q^{71} -9.24697i q^{73} +(0.218653 - 3.01816i) q^{74} +(5.58072 + 0.812865i) q^{76} +(13.8020 + 0.931432i) q^{77} +2.68314i q^{79} +(-1.14104 + 3.83380i) q^{80} +(-12.2923 - 0.890525i) q^{82} -16.2812 q^{83} +6.70156 q^{85} +(-10.4666 - 0.758262i) q^{86} +(-14.4419 - 3.18339i) q^{88} -8.53516i q^{89} +(-11.9458 - 0.806161i) q^{91} +(-0.247513 + 1.69930i) q^{92} +(-1.00415 + 13.8607i) q^{94} -2.81981i q^{95} -10.5209i q^{97} +(-2.03542 + 9.68799i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8	\( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} - 10 q^{14} + 6 q^{16} + 24 q^{19} - 12 q^{22} - 16 q^{25} - 12 q^{26} - 22 q^{28} - 16 q^{29} - 8 q^{31} + 18 q^{32} - 24 q^{34} + 24 q^{37} + 28 q^{38} - 12 q^{40} + 8 q^{44} - 20 q^{46} + 16 q^{47} - 16 q^{49} + 2 q^{50} + 20 q^{52} + 32 q^{53} + 2 q^{56} - 32 q^{58} + 8 q^{59} + 16 q^{62} - 2 q^{64} + 8 q^{65} + 4 q^{68} - 20 q^{70} + 4 q^{74} - 16 q^{76} + 8 q^{77} - 16 q^{80} + 4 q^{82} + 8 q^{83} - 64 q^{86} - 52 q^{88} - 16 q^{91} - 64 q^{92} - 16 q^{94} - 2 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8 - 10 * q^14 + 6 * q^16 + 24 * q^19 - 12 * q^22 - 16 * q^25 - 12 * q^26 - 22 * 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 - 20 * q^70 + 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 - 2 * q^98

Introduction

L-functions

Modular forms

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