LMFDB - Embedded newform 2070.2.j.i.737.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2070,2,Mod(323,2070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2070, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2070.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2070.j (of order $4$, degree $2$, 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:	$16.5290332184$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} + 28x^{14} + 290x^{12} + 1396x^{10} + 3263x^{8} + 3508x^{6} + 1442x^{4} + 128x^{2} + 1 $ x^16 + 28x^14 + 290x^12 + 1396x^10 + 3263x^8 + 3508x^6 + 1442x^4 + 128*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.8
Root			$3.24374i$ of defining polynomial
Character	$\chi$	$=$	2070.737
Dual form			2070.2.j.i.323.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.43853 + 1.71191i) q^{5} +(3.17313 + 3.17313i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.43853 + 1.71191i) q^{5} +(3.17313 + 3.17313i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.22770 + 0.193306i) q^{10} +3.42382i q^{11} +(2.00000 - 2.00000i) q^{13} +4.48749 q^{14} -1.00000 q^{16} +(1.61043 - 1.61043i) q^{17} -6.45539i q^{19} +(1.71191 - 1.43853i) q^{20} +(2.42100 + 2.42100i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-0.861256 + 4.92527i) q^{25} -2.82843i q^{26} +(3.17313 - 3.17313i) q^{28} -3.94074 q^{29} -2.27749 q^{31} +(-0.707107 + 0.707107i) q^{32} -2.27749i q^{34} +(-0.867460 + 9.99677i) q^{35} +(1.24787 + 1.24787i) q^{37} +(-4.56465 - 4.56465i) q^{38} +(0.193306 - 2.22770i) q^{40} +11.1091i q^{41} +(-0.752131 + 0.752131i) q^{43} +3.42382 q^{44} +1.00000 q^{46} +(4.29128 - 4.29128i) q^{47} +13.1376i q^{49} +(2.87369 + 4.09169i) q^{50} +(-2.00000 - 2.00000i) q^{52} +(2.08676 + 2.08676i) q^{53} +(-5.86126 + 4.92527i) q^{55} -4.48749i q^{56} +(-2.78652 + 2.78652i) q^{58} +7.47024 q^{59} -3.89087 q^{61} +(-1.61043 + 1.61043i) q^{62} +1.00000i q^{64} +(6.30088 + 0.546753i) q^{65} +(8.93004 + 8.93004i) q^{67} +(-1.61043 - 1.61043i) q^{68} +(6.45539 + 7.68217i) q^{70} +10.4865i q^{71} +(6.06401 - 6.06401i) q^{73} +1.76475 q^{74} -6.45539 q^{76} +(-10.8642 + 10.8642i) q^{77} -11.3970i q^{79} +(-1.43853 - 1.71191i) q^{80} +(7.85530 + 7.85530i) q^{82} +(-9.32421 - 9.32421i) q^{83} +(5.07355 + 0.440253i) q^{85} +1.06367i q^{86} +(2.42100 - 2.42100i) q^{88} -8.03580 q^{89} +12.6925 q^{91} +(0.707107 - 0.707107i) q^{92} -6.06878i q^{94} +(11.0510 - 9.28628i) q^{95} +(-11.3510 - 11.3510i) q^{97} +(9.28966 + 9.28966i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 4 q^{10} + 32 q^{13} - 16 q^{16} - 24 q^{25} - 16 q^{31} + 32 q^{37} + 4 q^{40} + 16 q^{46} - 32 q^{52} - 104 q^{55} + 8 q^{58} - 40 q^{61} + 72 q^{67} + 24 q^{70} + 24 q^{73} - 24 q^{76} - 8 q^{82} - 8 q^{85} - 72 q^{97}+O(q^{100}) $ 16 * q - 4 * q^10 + 32 * q^13 - 16 * q^16 - 24 * q^25 - 16 * q^31 + 32 * q^37 + 4 * q^40 + 16 * q^46 - 32 * q^52 - 104 * q^55 + 8 * q^58 - 40 * q^61 + 72 * q^67 + 24 * q^70 + 24 * q^73 - 24 * q^76 - 8 * q^82 - 8 * q^85 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times$.

$n$	$461$	$1657$	$1891$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	1.43853	+	1.71191i	0.643331	+	0.765588i
$5$	1.43853	+	1.71191i	0.643331	+	0.765588i
$6$		0			0
$7$	3.17313	+	3.17313i	1.19933	+	1.19933i	0.974367	+	0.224965i	$0.0722268\pi$
$7$	3.17313	+	3.17313i	1.19933	+	1.19933i	0.224965	+	0.974367i	$0.427773\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	2.22770	+	0.193306i	0.704460	+	0.0611289i
$11$			3.42382i			1.03232i	0.856492	+	0.516160i	$0.172639\pi$
$11$			3.42382i			1.03232i	−0.856492	+	0.516160i	$0.827361\pi$
$12$		0			0
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	−0.373094	−	0.927794i	$-0.621703\pi$
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	0.927794	+	0.373094i	$0.121703\pi$
$14$	4.48749			1.19933
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.61043	−	1.61043i	0.390586	−	0.390586i	−0.484310	−	0.874896i	$-0.660929\pi$
$17$	1.61043	−	1.61043i	0.390586	−	0.390586i	0.874896	+	0.484310i	$0.160929\pi$
$18$		0			0
$19$		−	6.45539i		−	1.48097i	−0.672074	−	0.740484i	$-0.734596\pi$
$19$		−	6.45539i		−	1.48097i	0.672074	−	0.740484i	$-0.265404\pi$
$20$	1.71191	−	1.43853i	0.382794	−	0.321665i
$21$		0			0
$22$	2.42100	+	2.42100i	0.516160	+	0.516160i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$		0			0
$25$	−0.861256	+	4.92527i	−0.172251	+	0.985053i
$26$		−	2.82843i		−	0.554700i
$27$		0			0
$28$	3.17313	−	3.17313i	0.599666	−	0.599666i
$29$	−3.94074			−0.731776			−0.365888	−	0.930659i	$-0.619235\pi$
$29$	−3.94074			−0.731776			−0.365888	+	0.930659i	$0.619235\pi$
$30$		0			0
$31$	−2.27749			−0.409049			−0.204524	−	0.978861i	$-0.565565\pi$
$31$	−2.27749			−0.409049			−0.204524	+	0.978861i	$0.565565\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	2.27749i		−	0.390586i
$35$	−0.867460	+	9.99677i	−0.146628	+	1.68976i
$36$		0			0
$37$	1.24787	+	1.24787i	0.205148	+	0.205148i	0.802202	−	0.597053i	$-0.203662\pi$
$37$	1.24787	+	1.24787i	0.205148	+	0.205148i	−0.597053	+	0.802202i	$0.703662\pi$
$38$	−4.56465	−	4.56465i	−0.740484	−	0.740484i
$39$		0			0
$40$	0.193306	−	2.22770i	0.0305644	−	0.352230i
$41$			11.1091i			1.73495i	0.497484	+	0.867473i	$0.334257\pi$
$41$			11.1091i			1.73495i	−0.497484	+	0.867473i	$0.665743\pi$
$42$		0			0
$43$	−0.752131	+	0.752131i	−0.114699	+	0.114699i	−0.762127	−	0.647428i	$-0.775845\pi$
$43$	−0.752131	+	0.752131i	−0.114699	+	0.114699i	0.647428	+	0.762127i	$0.275845\pi$
$44$	3.42382			0.516160
$45$		0			0
$46$	1.00000			0.147442
$47$	4.29128	−	4.29128i	0.625947	−	0.625947i	−0.321099	−	0.947046i	$-0.604052\pi$
$47$	4.29128	−	4.29128i	0.625947	−	0.625947i	0.947046	+	0.321099i	$0.104052\pi$
$48$		0			0
$49$			13.1376i			1.87679i
$50$	2.87369	+	4.09169i	0.406401	+	0.578652i
$51$		0			0
$52$	−2.00000	−	2.00000i	−0.277350	−	0.277350i
$53$	2.08676	+	2.08676i	0.286639	+	0.286639i	0.835750	−	0.549111i	$-0.185033\pi$
$53$	2.08676	+	2.08676i	0.286639	+	0.286639i	−0.549111	+	0.835750i	$0.685033\pi$
$54$		0			0
$55$	−5.86126	+	4.92527i	−0.790332	+	0.664123i
$56$		−	4.48749i		−	0.599666i
$57$		0			0
$58$	−2.78652	+	2.78652i	−0.365888	+	0.365888i
$59$	7.47024			0.972543			0.486271	−	0.873808i	$-0.338357\pi$
$59$	7.47024			0.972543			0.486271	+	0.873808i	$0.338357\pi$
$60$		0			0
$61$	−3.89087			−0.498175			−0.249088	−	0.968481i	$-0.580131\pi$
$61$	−3.89087			−0.498175			−0.249088	+	0.968481i	$0.580131\pi$
$62$	−1.61043	+	1.61043i	−0.204524	+	0.204524i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	6.30088	+	0.546753i	0.781528	+	0.0678164i
$66$		0			0
$67$	8.93004	+	8.93004i	1.09098	+	1.09098i	0.995424	+	0.0955533i	$0.0304620\pi$
$67$	8.93004	+	8.93004i	1.09098	+	1.09098i	0.0955533	+	0.995424i	$0.469538\pi$
$68$	−1.61043	−	1.61043i	−0.195293	−	0.195293i
$69$		0			0
$70$	6.45539	+	7.68217i	0.771567	+	0.918195i
$71$			10.4865i			1.24451i	0.782813	+	0.622257i	$0.213784\pi$
$71$			10.4865i			1.24451i	−0.782813	+	0.622257i	$0.786216\pi$
$72$		0			0
$73$	6.06401	−	6.06401i	0.709739	−	0.709739i	−0.256742	−	0.966480i	$-0.582649\pi$
$73$	6.06401	−	6.06401i	0.709739	−	0.709739i	0.966480	+	0.256742i	$0.0826489\pi$
$74$	1.76475			0.205148
$75$		0			0
$76$	−6.45539			−0.740484
$77$	−10.8642	+	10.8642i	−1.23809	+	1.23809i
$78$		0			0
$79$		−	11.3970i		−	1.28226i	−0.767432	−	0.641130i	$-0.778466\pi$
$79$		−	11.3970i		−	1.28226i	0.767432	−	0.641130i	$-0.221534\pi$
$80$	−1.43853	−	1.71191i	−0.160833	−	0.191397i
$81$		0			0
$82$	7.85530	+	7.85530i	0.867473	+	0.867473i
$83$	−9.32421	−	9.32421i	−1.02347	−	1.02347i	−0.999718	−	0.0237475i	$-0.992440\pi$
$83$	−9.32421	−	9.32421i	−1.02347	−	1.02347i	−0.0237475	−	0.999718i	$-0.507560\pi$
$84$		0			0
$85$	5.07355	+	0.440253i	0.550304	+	0.0477521i
$86$			1.06367i			0.114699i
$87$		0			0
$88$	2.42100	−	2.42100i	0.258080	−	0.258080i
$89$	−8.03580			−0.851793			−0.425896	−	0.904772i	$-0.640041\pi$
$89$	−8.03580			−0.851793			−0.425896	+	0.904772i	$0.640041\pi$
$90$		0			0
$91$	12.6925			1.33054
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$		0			0
$94$		−	6.06878i		−	0.625947i
$95$	11.0510	−	9.28628i	1.13381	−	0.952753i
$96$		0			0
$97$	−11.3510	−	11.3510i	−1.15252	−	1.15252i	−0.986045	−	0.166478i	$-0.946760\pi$
$97$	−11.3510	−	11.3510i	−1.15252	−	1.15252i	−0.166478	−	0.986045i	$-0.553240\pi$
$98$	9.28966	+	9.28966i	0.938397	+	0.938397i
$99$		0			0
$100$	4.92527	+	0.861256i	0.492527	+	0.0861256i
$101$			1.50474i			0.149727i	0.997194	+	0.0748634i	$0.0238521\pi$
$101$			1.50474i			0.149727i	−0.997194	+	0.0748634i	$0.976148\pi$
$102$		0			0
$103$	−3.17313	+	3.17313i	−0.312658	+	0.312658i	−0.845939	−	0.533280i	$-0.820959\pi$
$103$	−3.17313	+	3.17313i	−0.312658	+	0.312658i	0.533280	+	0.845939i	$0.320959\pi$
$104$	−2.82843			−0.277350
$105$		0			0
$106$	2.95113			0.286639
$107$	−4.31980	+	4.31980i	−0.417611	+	0.417611i	−0.884380	−	0.466768i	$-0.845418\pi$
$107$	−4.31980	+	4.31980i	−0.417611	+	0.417611i	0.466768	+	0.884380i	$0.345418\pi$
$108$		0			0
$109$		−	13.9692i		−	1.33801i	−0.743259	−	0.669003i	$-0.766721\pi$
$109$		−	13.9692i		−	1.33801i	0.743259	−	0.669003i	$-0.233279\pi$
$110$	−0.661845	+	7.62722i	−0.0631045	+	0.727227i
$111$		0			0
$112$	−3.17313	−	3.17313i	−0.299833	−	0.299833i
$113$	9.02361	+	9.02361i	0.848870	+	0.848870i	0.989992	−	0.141122i	$-0.0450710\pi$
$113$	9.02361	+	9.02361i	0.848870	+	0.848870i	−0.141122	+	0.989992i	$0.545071\pi$
$114$		0			0
$115$	−0.193306	+	2.22770i	−0.0180259	+	0.207734i
$116$			3.94074i			0.365888i
$117$		0			0
$118$	5.28226	−	5.28226i	0.486271	−	0.486271i
$119$	10.2202			0.936884
$120$		0			0
$121$	−0.722512			−0.0656829
$122$	−2.75126	+	2.75126i	−0.249088	+	0.249088i
$123$		0			0
$124$			2.27749i			0.204524i
$125$	−9.67054	+	5.61076i	−0.864960	+	0.501841i
$126$		0			0
$127$	−15.6925	−	15.6925i	−1.39249	−	1.39249i	−0.819713	−	0.572774i	$-0.805867\pi$
$127$	−15.6925	−	15.6925i	−1.39249	−	1.39249i	−0.572774	−	0.819713i	$-0.694133\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	4.84201	−	4.06878i	0.424672	−	0.356856i
$131$		−	14.2582i		−	1.24575i	−0.782323	−	0.622873i	$-0.785965\pi$
$131$		−	14.2582i		−	1.24575i	0.782323	−	0.622873i	$-0.214035\pi$
$132$		0			0
$133$	20.4838	−	20.4838i	1.77617	−	1.77617i
$134$	12.6290			1.09098
$135$		0			0
$136$	−2.27749			−0.195293
$137$	−12.4747	+	12.4747i	−1.06578	+	1.06578i	−0.0681032	+	0.997678i	$0.521695\pi$
$137$	−12.4747	+	12.4747i	−1.06578	+	1.06578i	−0.997678	+	0.0681032i	$0.978305\pi$
$138$		0			0
$139$		−	10.7021i		−	0.907739i	−0.891068	−	0.453869i	$-0.850043\pi$
$139$		−	10.7021i		−	0.907739i	0.891068	−	0.453869i	$-0.149957\pi$
$140$	9.99677	+	0.867460i	0.844881	+	0.0733138i
$141$		0			0
$142$	7.41505	+	7.41505i	0.622257	+	0.622257i
$143$	6.84763	+	6.84763i	0.572628	+	0.572628i
$144$		0			0
$145$	−5.66887	−	6.74618i	−0.470774	−	0.560240i
$146$		−	8.57580i		−	0.709739i
$147$		0			0
$148$	1.24787	−	1.24787i	0.102574	−	0.102574i
$149$	6.15497			0.504235			0.252117	−	0.967697i	$-0.418873\pi$
$149$	6.15497			0.504235			0.252117	+	0.967697i	$0.418873\pi$
$150$		0			0
$151$	14.9796			1.21902			0.609510	−	0.792778i	$-0.291366\pi$
$151$	14.9796			1.21902			0.609510	+	0.792778i	$0.291366\pi$
$152$	−4.56465	+	4.56465i	−0.370242	+	0.370242i
$153$		0			0
$154$			15.3643i			1.23809i
$155$	−3.27624	−	3.89885i	−0.263154	−	0.313163i
$156$		0			0
$157$	4.53388	+	4.53388i	0.361843	+	0.361843i	0.864491	−	0.502648i	$-0.167641\pi$
$157$	4.53388	+	4.53388i	0.361843	+	0.361843i	−0.502648	+	0.864491i	$0.667641\pi$
$158$	−8.05888	−	8.05888i	−0.641130	−	0.641130i
$159$		0			0
$160$	−2.22770	−	0.193306i	−0.176115	−	0.0152822i
$161$			4.48749i			0.353664i
$162$		0			0
$163$	16.1376	−	16.1376i	1.26399	−	1.26399i	0.314850	−	0.949141i	$-0.398046\pi$
$163$	16.1376	−	16.1376i	1.26399	−	1.26399i	0.949141	−	0.314850i	$-0.101954\pi$
$164$	11.1091			0.867473
$165$		0			0
$166$	−13.1864			−1.02347
$167$	−8.53392	+	8.53392i	−0.660374	+	0.660374i	−0.955468	−	0.295094i	$-0.904649\pi$
$167$	−8.53392	+	8.53392i	−0.660374	+	0.660374i	0.295094	+	0.955468i	$0.404649\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$	3.89885	−	3.27624i	0.299028	−	0.251276i
$171$		0			0
$172$	0.752131	+	0.752131i	0.0573495	+	0.0573495i
$173$	5.90170	+	5.90170i	0.448698	+	0.448698i	0.894922	−	0.446223i	$-0.147231\pi$
$173$	5.90170	+	5.90170i	0.448698	+	0.448698i	−0.446223	+	0.894922i	$0.647231\pi$
$174$		0			0
$175$	−18.3614	+	12.8956i	−1.38799	+	0.974819i
$176$		−	3.42382i		−	0.258080i
$177$		0			0
$178$	−5.68217	+	5.68217i	−0.425896	+	0.425896i
$179$	−22.6890			−1.69586			−0.847929	−	0.530109i	$-0.822151\pi$
$179$	−22.6890			−1.69586			−0.847929	+	0.530109i	$0.822151\pi$
$180$		0			0
$181$	−5.68217			−0.422352			−0.211176	−	0.977448i	$-0.567729\pi$
$181$	−5.68217			−0.422352			−0.211176	+	0.977448i	$0.567729\pi$
$182$	8.97498	−	8.97498i	0.665270	−	0.665270i
$183$		0			0
$184$		−	1.00000i		−	0.0737210i
$185$	−0.341138	+	3.93133i	−0.0250810	+	0.289037i
$186$		0			0
$187$	5.51381	+	5.51381i	0.403209	+	0.403209i
$188$	−4.29128	−	4.29128i	−0.312973	−	0.312973i
$189$		0			0
$190$	1.24787	−	14.3807i	0.0905299	−	1.04328i
$191$			0.156935i			0.0113554i	0.999984	+	0.00567771i	$0.00180728\pi$
$191$			0.156935i			0.0113554i	−0.999984	+	0.00567771i	$0.998193\pi$
$192$		0			0
$193$	17.6238	−	17.6238i	1.26859	−	1.26859i	0.321767	−	0.946819i	$-0.395723\pi$
$193$	17.6238	−	17.6238i	1.26859	−	1.26859i	0.946819	−	0.321767i	$-0.104277\pi$
$194$	−16.0528			−1.15252
$195$		0			0
$196$	13.1376			0.938397
$197$	7.08987	−	7.08987i	0.505132	−	0.505132i	−0.407896	−	0.913028i	$-0.633737\pi$
$197$	7.08987	−	7.08987i	0.505132	−	0.505132i	0.913028	+	0.407896i	$0.133737\pi$
$198$		0			0
$199$			15.8601i			1.12429i	0.827038	+	0.562145i	$0.190024\pi$
$199$			15.8601i			1.12429i	−0.827038	+	0.562145i	$0.809976\pi$
$200$	4.09169	−	2.87369i	0.289326	−	0.203200i
$201$		0			0
$202$	1.06401	+	1.06401i	0.0748634	+	0.0748634i
$203$	−12.5045	−	12.5045i	−0.877643	−	0.877643i
$204$		0			0
$205$	−19.0177	+	15.9808i	−1.32825	+	1.11614i
$206$			4.48749i			0.312658i
$207$		0			0
$208$	−2.00000	+	2.00000i	−0.138675	+	0.138675i
$209$	22.1021			1.52883
$210$		0			0
$211$	1.68032			0.115678			0.0578391	−	0.998326i	$-0.481579\pi$
$211$	1.68032			0.115678			0.0578391	+	0.998326i	$0.481579\pi$
$212$	2.08676	−	2.08676i	0.143320	−	0.143320i
$213$		0			0
$214$			6.10913i			0.417611i
$215$	−2.36954	−	0.205615i	−0.161601	−	0.0140228i
$216$		0			0
$217$	−7.22677	−	7.22677i	−0.490585	−	0.490585i
$218$	−9.87771	−	9.87771i	−0.669003	−	0.669003i
$219$		0			0
$220$	4.92527	+	5.86126i	0.332061	+	0.395166i
$221$		−	6.44171i		−	0.433316i
$222$		0			0
$223$	−4.72627	+	4.72627i	−0.316494	+	0.316494i	−0.847419	−	0.530925i	$-0.821845\pi$
$223$	−4.72627	+	4.72627i	−0.316494	+	0.316494i	0.530925	+	0.847419i	$0.321845\pi$
$224$	−4.48749			−0.299833
$225$		0			0
$226$	12.7613			0.848870
$227$	9.14266	−	9.14266i	0.606820	−	0.606820i	−0.335294	−	0.942114i	$-0.608836\pi$
$227$	9.14266	−	9.14266i	0.606820	−	0.606820i	0.942114	+	0.335294i	$0.108836\pi$
$228$		0			0
$229$		−	4.98963i		−	0.329724i	−0.986317	−	0.164862i	$-0.947282\pi$
$229$		−	4.98963i		−	0.329724i	0.986317	−	0.164862i	$-0.0527179\pi$
$230$	1.43853	+	1.71191i	0.0948539	+	0.112880i
$231$		0			0
$232$	2.78652	+	2.78652i	0.182944	+	0.182944i
$233$	7.59060	+	7.59060i	0.497277	+	0.497277i	0.910589	−	0.413313i	$-0.135628\pi$
$233$	7.59060	+	7.59060i	0.497277	+	0.497277i	−0.413313	+	0.910589i	$0.635628\pi$
$234$		0			0
$235$	13.5194	+	1.17313i	0.881909	+	0.0765268i
$236$		−	7.47024i		−	0.486271i
$237$		0			0
$238$	7.22677	−	7.22677i	0.468442	−	0.468442i
$239$	20.3792			1.31822			0.659111	−	0.752046i	$-0.270933\pi$
$239$	20.3792			1.31822			0.659111	+	0.752046i	$0.270933\pi$
$240$		0			0
$241$	9.11949			0.587438			0.293719	−	0.955892i	$-0.405107\pi$
$241$	9.11949			0.587438			0.293719	+	0.955892i	$0.405107\pi$
$242$	−0.510893	+	0.510893i	−0.0328415	+	0.0328415i
$243$		0			0
$244$			3.89087i			0.249088i
$245$	−22.4903	+	18.8988i	−1.43685	+	1.20740i
$246$		0			0
$247$	−12.9108	−	12.9108i	−0.821494	−	0.821494i
$248$	1.61043	+	1.61043i	0.102262	+	0.102262i
$249$		0			0
$250$	−2.87070	+	10.8055i	−0.181559	+	0.683401i
$251$		−	10.5069i		−	0.663192i	−0.943421	−	0.331596i	$-0.892413\pi$
$251$		−	10.5069i		−	0.663192i	0.943421	−	0.331596i	$-0.107587\pi$
$252$		0			0
$253$	−2.42100	+	2.42100i	−0.152207	+	0.152207i
$254$	−22.1926			−1.39249
$255$		0			0
$256$	1.00000			0.0625000
$257$	7.17509	−	7.17509i	0.447570	−	0.447570i	−0.446976	−	0.894546i	$-0.647499\pi$
$257$	7.17509	−	7.17509i	0.447570	−	0.447570i	0.894546	+	0.446976i	$0.147499\pi$
$258$		0			0
$259$			7.91931i			0.492082i
$260$	0.546753	−	6.30088i	0.0339082	−	0.390764i
$261$		0			0
$262$	−10.0821	−	10.0821i	−0.622873	−	0.622873i
$263$	−8.26859	−	8.26859i	−0.509863	−	0.509863i	0.404621	−	0.914484i	$-0.367403\pi$
$263$	−8.26859	−	8.26859i	−0.509863	−	0.509863i	−0.914484	+	0.404621i	$0.867403\pi$
$264$		0			0
$265$	−0.570473	+	6.57423i	−0.0350439	+	0.403851i
$266$		−	28.9685i		−	1.77617i
$267$		0			0
$268$	8.93004	−	8.93004i	0.545489	−	0.545489i
$269$	−12.2878			−0.749200			−0.374600	−	0.927186i	$-0.622220\pi$
$269$	−12.2878			−0.749200			−0.374600	+	0.927186i	$0.622220\pi$
$270$		0			0
$271$	−21.2666			−1.29185			−0.645927	−	0.763399i	$-0.723529\pi$
$271$	−21.2666			−1.29185			−0.645927	+	0.763399i	$0.723529\pi$
$272$	−1.61043	+	1.61043i	−0.0976465	+	0.0976465i
$273$		0			0
$274$			17.6418i			1.06578i
$275$	−16.8632	−	2.94878i	−1.01689	−	0.177818i
$276$		0			0
$277$	7.64182	+	7.64182i	0.459153	+	0.459153i	0.898377	−	0.439225i	$-0.144747\pi$
$277$	7.64182	+	7.64182i	0.459153	+	0.459153i	−0.439225	+	0.898377i	$0.644747\pi$
$278$	−7.56751	−	7.56751i	−0.453869	−	0.453869i
$279$		0			0
$280$	7.68217	−	6.45539i	0.459097	−	0.385784i
$281$		−	26.4923i		−	1.58040i	−0.612850	−	0.790199i	$-0.709977\pi$
$281$		−	26.4923i		−	1.58040i	0.612850	−	0.790199i	$-0.290023\pi$
$282$		0			0
$283$	−1.20752	+	1.20752i	−0.0717799	+	0.0717799i	−0.742085	−	0.670305i	$-0.766163\pi$
$283$	−1.20752	+	1.20752i	−0.0717799	+	0.0717799i	0.670305	+	0.742085i	$0.266163\pi$
$284$	10.4865			0.622257
$285$		0			0
$286$	9.68401			0.572628
$287$	−35.2506	+	35.2506i	−2.08078	+	2.08078i
$288$		0			0
$289$			11.8130i			0.694885i
$290$	−8.77877	−	0.761770i	−0.515507	−	0.0447327i
$291$		0			0
$292$	−6.06401	−	6.06401i	−0.354869	−	0.354869i
$293$	1.04189	+	1.04189i	0.0608681	+	0.0608681i	0.736886	−	0.676017i	$-0.236296\pi$
$293$	1.04189	+	1.04189i	0.0608681	+	0.0608681i	−0.676017	+	0.736886i	$0.736296\pi$
$294$		0			0
$295$	10.7462	+	12.7884i	0.625667	+	0.744567i
$296$		−	1.76475i		−	0.102574i
$297$		0			0
$298$	4.35222	−	4.35222i	0.252117	−	0.252117i
$299$	2.82843			0.163572
$300$		0			0
$301$	−4.77323			−0.275124
$302$	10.5922	−	10.5922i	0.609510	−	0.609510i
$303$		0			0
$304$			6.45539i			0.370242i
$305$	−5.59714	−	6.66082i	−0.320492	−	0.381397i
$306$		0			0
$307$	−14.0303	−	14.0303i	−0.800750	−	0.800750i	0.182462	−	0.983213i	$-0.441593\pi$
$307$	−14.0303	−	14.0303i	−0.800750	−	0.800750i	−0.983213	+	0.182462i	$0.941593\pi$
$308$	10.8642	+	10.8642i	0.619047	+	0.619047i
$309$		0			0
$310$	−5.07355	−	0.440253i	−0.288158	−	0.0250047i
$311$		−	16.8256i		−	0.954092i	−0.878878	−	0.477046i	$-0.841708\pi$
$311$		−	16.8256i		−	0.954092i	0.878878	−	0.477046i	$-0.158292\pi$
$312$		0			0
$313$	−10.6466	+	10.6466i	−0.601781	+	0.601781i	−0.940785	−	0.339004i	$-0.889910\pi$
$313$	−10.6466	+	10.6466i	−0.601781	+	0.601781i	0.339004	+	0.940785i	$0.389910\pi$
$314$	6.41188			0.361843
$315$		0			0
$316$	−11.3970			−0.641130
$317$	−16.5143	+	16.5143i	−0.927537	+	0.927537i	−0.997546	−	0.0700090i	$-0.977697\pi$
$317$	−16.5143	+	16.5143i	−0.927537	+	0.927537i	0.0700090	+	0.997546i	$0.477697\pi$
$318$		0			0
$319$		−	13.4924i		−	0.755427i
$320$	−1.71191	+	1.43853i	−0.0956986	+	0.0804163i
$321$		0			0
$322$	3.17313	+	3.17313i	0.176832	+	0.176832i
$323$	−10.3959	−	10.3959i	−0.578446	−	0.578446i
$324$		0			0
$325$	8.12802	+	11.5730i	0.450861	+	0.641957i
$326$		−	22.8220i		−	1.26399i
$327$		0			0
$328$	7.85530	−	7.85530i	0.433736	−	0.433736i
$329$	27.2336			1.50144
$330$		0			0
$331$	6.20871			0.341261			0.170631	−	0.985335i	$-0.445419\pi$
$331$	6.20871			0.341261			0.170631	+	0.985335i	$0.445419\pi$
$332$	−9.32421	+	9.32421i	−0.511733	+	0.511733i
$333$		0			0
$334$			12.0688i			0.660374i
$335$	−2.44126	+	28.1335i	−0.133380	+	1.53710i
$336$		0			0
$337$	−14.0436	−	14.0436i	−0.765002	−	0.765002i	0.212220	−	0.977222i	$-0.431931\pi$
$337$	−14.0436	−	14.0436i	−0.765002	−	0.765002i	−0.977222	+	0.212220i	$0.931931\pi$
$338$	3.53553	+	3.53553i	0.192308	+	0.192308i
$339$		0			0
$340$	0.440253	−	5.07355i	0.0238761	−	0.275152i
$341$		−	7.79770i		−	0.422269i
$342$		0			0
$343$	−19.4753	+	19.4753i	−1.05157	+	1.05157i
$344$	1.06367			0.0573495
$345$		0			0
$346$	8.34627			0.448698
$347$	−21.8505	+	21.8505i	−1.17300	+	1.17300i	−0.191503	+	0.981492i	$0.561336\pi$
$347$	−21.8505	+	21.8505i	−1.17300	+	1.17300i	−0.981492	+	0.191503i	$0.938664\pi$
$348$		0			0
$349$			3.57304i			0.191261i	0.995417	+	0.0956303i	$0.0304867\pi$
$349$			3.57304i			0.191261i	−0.995417	+	0.0956303i	$0.969513\pi$
$350$	−3.86488	+	22.1021i	−0.206586	+	1.18141i
$351$		0			0
$352$	−2.42100	−	2.42100i	−0.129040	−	0.129040i
$353$	−16.1852	−	16.1852i	−0.861452	−	0.861452i	0.130055	−	0.991507i	$-0.458485\pi$
$353$	−16.1852	−	16.1852i	−0.861452	−	0.861452i	−0.991507	+	0.130055i	$0.958485\pi$
$354$		0			0
$355$	−17.9519	+	15.0851i	−0.952786	+	0.800634i
$356$			8.03580i			0.425896i
$357$		0			0
$358$	−16.0436	+	16.0436i	−0.847929	+	0.847929i
$359$	−17.8662			−0.942941			−0.471471	−	0.881882i	$-0.656277\pi$
$359$	−17.8662			−0.942941			−0.471471	+	0.881882i	$0.656277\pi$
$360$		0			0
$361$	−22.6721			−1.19327
$362$	−4.01790	+	4.01790i	−0.211176	+	0.211176i
$363$		0			0
$364$		−	12.6925i		−	0.665270i
$365$	19.1043	+	1.65776i	0.999964	+	0.0867710i
$366$		0			0
$367$	−5.13095	−	5.13095i	−0.267833	−	0.267833i	0.560393	−	0.828227i	$-0.310650\pi$
$367$	−5.13095	−	5.13095i	−0.267833	−	0.267833i	−0.828227	+	0.560393i	$0.810650\pi$
$368$	−0.707107	−	0.707107i	−0.0368605	−	0.0368605i
$369$		0			0
$370$	2.53865	+	3.02109i	0.131978	+	0.157059i
$371$			13.2432i			0.687551i
$372$		0			0
$373$	−19.3469	+	19.3469i	−1.00175	+	1.00175i	−0.00174761	+	0.999998i	$0.500556\pi$
$373$	−19.3469	+	19.3469i	−1.00175	+	1.00175i	−0.999998	+	0.00174761i	$0.999444\pi$
$374$	7.79770			0.403209
$375$		0			0
$376$	−6.06878			−0.312973
$377$	−7.88147	+	7.88147i	−0.405916	+	0.405916i
$378$		0			0
$379$		−	34.0261i		−	1.74780i	−0.486104	−	0.873901i	$-0.661582\pi$
$379$		−	34.0261i		−	1.74780i	0.486104	−	0.873901i	$-0.338418\pi$
$380$	−9.28628	−	11.0510i	−0.476376	−	0.566906i
$381$		0			0
$382$	0.110970	+	0.110970i	0.00567771	+	0.00567771i
$383$	−12.7426	−	12.7426i	−0.651116	−	0.651116i	0.302146	−	0.953262i	$-0.402297\pi$
$383$	−12.7426	−	12.7426i	−0.651116	−	0.651116i	−0.953262	+	0.302146i	$0.902297\pi$
$384$		0			0
$385$	−34.2271	−	2.97002i	−1.74437	−	0.151366i
$386$		−	24.9238i		−	1.26859i
$387$		0			0
$388$	−11.3510	+	11.3510i	−0.576262	+	0.576262i
$389$	29.5372			1.49759			0.748797	−	0.662799i	$-0.230632\pi$
$389$	29.5372			1.49759			0.748797	+	0.662799i	$0.230632\pi$
$390$		0			0
$391$	2.27749			0.115178
$392$	9.28966	−	9.28966i	0.469199	−	0.469199i
$393$		0			0
$394$		−	10.0266i		−	0.505132i
$395$	19.5106	−	16.3949i	0.981684	−	0.824918i
$396$		0			0
$397$	13.6840	+	13.6840i	0.686781	+	0.686781i	0.961519	−	0.274738i	$-0.0885912\pi$
$397$	13.6840	+	13.6840i	0.686781	+	0.686781i	−0.274738	+	0.961519i	$0.588591\pi$
$398$	11.2148	+	11.2148i	0.562145	+	0.562145i
$399$		0			0
$400$	0.861256	−	4.92527i	0.0430628	−	0.246263i
$401$			0.560249i			0.0279775i	0.999902	+	0.0139887i	$0.00445290\pi$
$401$			0.560249i			0.0279775i	−0.999902	+	0.0139887i	$0.995547\pi$
$402$		0			0
$403$	−4.55498	+	4.55498i	−0.226899	+	0.226899i
$404$	1.50474			0.0748634
$405$		0			0
$406$	−17.6840			−0.877643
$407$	−4.27247	+	4.27247i	−0.211779	+	0.211779i
$408$		0			0
$409$		−	6.90710i		−	0.341534i	−0.985311	−	0.170767i	$-0.945375\pi$
$409$		−	6.90710i		−	0.341534i	0.985311	−	0.170767i	$-0.0546245\pi$
$410$	−2.14746	+	24.7476i	−0.106055	+	1.22220i
$411$		0			0
$412$	3.17313	+	3.17313i	0.156329	+	0.156329i
$413$	23.7041	+	23.7041i	1.16640	+	1.16640i
$414$		0			0
$415$	2.54902	−	29.3754i	0.125127	−	1.44198i
$416$			2.82843i			0.138675i
$417$		0			0
$418$	15.6285	−	15.6285i	0.764416	−	0.764416i
$419$	7.98977			0.390326			0.195163	−	0.980771i	$-0.437476\pi$
$419$	7.98977			0.390326			0.195163	+	0.980771i	$0.437476\pi$
$420$		0			0
$421$	27.9862			1.36397			0.681983	−	0.731368i	$-0.261118\pi$
$421$	27.9862			1.36397			0.681983	+	0.731368i	$0.261118\pi$
$422$	1.18817	−	1.18817i	0.0578391	−	0.0578391i
$423$		0			0
$424$		−	2.95113i		−	0.143320i
$425$	6.54479	+	9.31877i	0.317469	+	0.452027i
$426$		0			0
$427$	−12.3463	−	12.3463i	−0.597478	−	0.597478i
$428$	4.31980	+	4.31980i	0.208806	+	0.208806i
$429$		0			0
$430$	−1.82091	+	1.53013i	−0.0878122	+	0.0737893i
$431$		−	11.1996i		−	0.539466i	−0.962935	−	0.269733i	$-0.913065\pi$
$431$		−	11.1996i		−	0.539466i	0.962935	−	0.269733i	$-0.0869354\pi$
$432$		0			0
$433$	−7.24376	+	7.24376i	−0.348113	+	0.348113i	−0.859406	−	0.511293i	$-0.829167\pi$
$433$	−7.24376	+	7.24376i	−0.348113	+	0.348113i	0.511293	+	0.859406i	$0.329167\pi$
$434$	−10.2202			−0.490585
$435$		0			0
$436$	−13.9692			−0.669003
$437$	4.56465	−	4.56465i	0.218357	−	0.218357i
$438$		0			0
$439$		−	37.9230i		−	1.80997i	−0.425448	−	0.904983i	$-0.639883\pi$
$439$		−	37.9230i		−	1.80997i	0.425448	−	0.904983i	$-0.360117\pi$
$440$	7.62722	+	0.661845i	0.363614	+	0.0315522i
$441$		0			0
$442$	−4.55498	−	4.55498i	−0.216658	−	0.216658i
$443$	−8.89120	−	8.89120i	−0.422434	−	0.422434i	0.463607	−	0.886041i	$-0.346555\pi$
$443$	−8.89120	−	8.89120i	−0.422434	−	0.422434i	−0.886041	+	0.463607i	$0.846555\pi$
$444$		0			0
$445$	−11.5597	−	13.7565i	−0.547985	−	0.652123i
$446$			6.68395i			0.316494i
$447$		0			0
$448$	−3.17313	+	3.17313i	−0.149916	+	0.149916i
$449$	40.7787			1.92446			0.962232	−	0.272231i	$-0.0877613\pi$
$449$	40.7787			1.92446			0.962232	+	0.272231i	$0.0877613\pi$
$450$		0			0
$451$	−38.0354			−1.79102
$452$	9.02361	−	9.02361i	0.424435	−	0.424435i
$453$		0			0
$454$		−	12.9297i		−	0.606820i
$455$	18.2586	+	21.7285i	0.855977	+	1.01865i
$456$		0			0
$457$	−7.73581	−	7.73581i	−0.361866	−	0.361866i	0.502634	−	0.864500i	$-0.332364\pi$
$457$	−7.73581	−	7.73581i	−0.361866	−	0.361866i	−0.864500	+	0.502634i	$0.832364\pi$
$458$	−3.52820	−	3.52820i	−0.164862	−	0.164862i
$459$		0			0
$460$	2.22770	+	0.193306i	0.103867	+	0.00901296i
$461$		−	21.7525i		−	1.01311i	−0.862207	−	0.506557i	$-0.830918\pi$
$461$		−	21.7525i		−	1.01311i	0.862207	−	0.506557i	$-0.169082\pi$
$462$		0			0
$463$	−26.5345	+	26.5345i	−1.23316	+	1.23316i	−0.270423	+	0.962742i	$0.587164\pi$
$463$	−26.5345	+	26.5345i	−1.23316	+	1.23316i	−0.962742	+	0.270423i	$0.912836\pi$
$464$	3.94074			0.182944
$465$		0			0
$466$	10.7347			0.497277
$467$	10.4936	−	10.4936i	0.485585	−	0.485585i	−0.421325	−	0.906910i	$-0.638435\pi$
$467$	10.4936	−	10.4936i	0.485585	−	0.485585i	0.906910	+	0.421325i	$0.138435\pi$
$468$		0			0
$469$			56.6724i			2.61689i
$470$	10.3892	−	8.73013i	0.479218	−	0.402691i
$471$		0			0
$472$	−5.28226	−	5.28226i	−0.243136	−	0.243136i
$473$	−2.57516	−	2.57516i	−0.118406	−	0.118406i
$474$		0			0
$475$	31.7945	+	5.55975i	1.45883	+	0.255099i
$476$		−	10.2202i		−	0.468442i
$477$		0			0
$478$	14.4103	−	14.4103i	0.659111	−	0.659111i
$479$	−8.73949			−0.399317			−0.199659	−	0.979866i	$-0.563983\pi$
$479$	−8.73949			−0.399317			−0.199659	+	0.979866i	$0.563983\pi$
$480$		0			0
$481$	4.99148			0.227592
$482$	6.44846	−	6.44846i	0.293719	−	0.293719i
$483$		0			0
$484$			0.722512i			0.0328415i
$485$	3.10311	−	35.7608i	0.140905	−	1.62381i
$486$		0			0
$487$	7.33673	+	7.33673i	0.332459	+	0.332459i	0.853520	−	0.521061i	$-0.174464\pi$
$487$	7.33673	+	7.33673i	0.332459	+	0.332459i	−0.521061	+	0.853520i	$0.674464\pi$
$488$	2.75126	+	2.75126i	0.124544	+	0.124544i
$489$		0			0
$490$	−2.53957	+	29.2665i	−0.114726	+	1.32213i
$491$			10.0738i			0.454624i	0.973822	+	0.227312i	$0.0729937\pi$
$491$			10.0738i			0.454624i	−0.973822	+	0.227312i	$0.927006\pi$
$492$		0			0
$493$	−6.34627	+	6.34627i	−0.285822	+	0.285822i
$494$	−18.2586			−0.821494
$495$		0			0
$496$	2.27749			0.102262
$497$	−33.2750	+	33.2750i	−1.49259	+	1.49259i
$498$		0			0
$499$			21.0483i			0.942253i	0.882066	+	0.471127i	$0.156153\pi$
$499$			21.0483i			0.942253i	−0.882066	+	0.471127i	$0.843847\pi$
$500$	5.61076	+	9.67054i	0.250921	+	0.432480i
$501$		0			0
$502$	−7.42953	−	7.42953i	−0.331596	−	0.331596i
$503$	−20.0585	−	20.0585i	−0.894364	−	0.894364i	0.100566	−	0.994930i	$-0.467935\pi$
$503$	−20.0585	−	20.0585i	−0.894364	−	0.894364i	−0.994930	+	0.100566i	$0.967935\pi$
$504$		0			0
$505$	−2.57597	+	2.16461i	−0.114629	+	0.0963239i
$506$			3.42382i			0.152207i
$507$		0			0
$508$	−15.6925	+	15.6925i	−0.696244	+	0.696244i
$509$	24.8896			1.10321			0.551605	−	0.834105i	$-0.314016\pi$
$509$	24.8896			1.10321			0.551605	+	0.834105i	$0.314016\pi$
$510$		0			0
$511$	38.4838			1.70242
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	10.1471i		−	0.447570i
$515$	−9.99677	−	0.867460i	−0.440510	−	0.0382249i
$516$		0			0
$517$	14.6925	+	14.6925i	0.646177	+	0.646177i
$518$	5.59980	+	5.59980i	0.246041	+	0.246041i
$519$		0			0
$520$	−4.06878	−	4.84201i	−0.178428	−	0.212336i
$521$		−	37.0211i		−	1.62193i	−0.585097	−	0.810963i	$-0.698944\pi$
$521$		−	37.0211i		−	1.62193i	0.585097	−	0.810963i	$-0.301056\pi$
$522$		0			0
$523$	7.83898	−	7.83898i	0.342775	−	0.342775i	−0.514635	−	0.857409i	$-0.672073\pi$
$523$	7.83898	−	7.83898i	0.342775	−	0.342775i	0.857409	+	0.514635i	$0.172073\pi$
$524$	−14.2582			−0.622873
$525$		0			0
$526$	−11.6936			−0.509863
$527$	−3.66773	+	3.66773i	−0.159769	+	0.159769i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$	4.24529	+	5.05206i	0.184404	+	0.219448i
$531$		0			0
$532$	−20.4838	−	20.4838i	−0.888087	−	0.888087i
$533$	22.2181	+	22.2181i	0.962375	+	0.962375i
$534$		0			0
$535$	−13.6093	−	1.18093i	−0.588380	−	0.0510562i
$536$		−	12.6290i		−	0.545489i
$537$		0			0
$538$	−8.68878	+	8.68878i	−0.374600	+	0.374600i
$539$	−44.9806			−1.93745
$540$		0			0
$541$	22.0000			0.945854			0.472927	−	0.881102i	$-0.343197\pi$
$541$	22.0000			0.945854			0.472927	+	0.881102i	$0.343197\pi$
$542$	−15.0378	+	15.0378i	−0.645927	+	0.645927i
$543$		0			0
$544$			2.27749i			0.0976465i
$545$	23.9140	−	20.0951i	1.02436	−	0.860781i
$546$		0			0
$547$	−11.3051	−	11.3051i	−0.483371	−	0.483371i	0.422835	−	0.906206i	$-0.361035\pi$
$547$	−11.3051	−	11.3051i	−0.483371	−	0.483371i	−0.906206	+	0.422835i	$0.861035\pi$
$548$	12.4747	+	12.4747i	0.532891	+	0.532891i
$549$		0			0
$550$	−14.0092	+	9.83898i	−0.597354	+	0.419535i
$551$			25.4390i			1.08374i
$552$		0			0
$553$	36.1642	−	36.1642i	1.53786	−	1.53786i
$554$	10.8072			0.459153
$555$		0			0
$556$	−10.7021			−0.453869
$557$	1.51810	−	1.51810i	0.0643238	−	0.0643238i	−0.674213	−	0.738537i	$-0.735517\pi$
$557$	1.51810	−	1.51810i	0.0643238	−	0.0643238i	0.738537	+	0.674213i	$0.235517\pi$
$558$		0			0
$559$			3.00852i			0.127247i
$560$	0.867460	−	9.99677i	0.0366569	−	0.422440i
$561$		0			0
$562$	−18.7329	−	18.7329i	−0.790199	−	0.790199i
$563$	−25.1468	−	25.1468i	−1.05981	−	1.05981i	−0.998094	−	0.0617187i	$-0.980342\pi$
$563$	−25.1468	−	25.1468i	−1.05981	−	1.05981i	−0.0617187	−	0.998094i	$-0.519658\pi$
$564$		0			0
$565$	−2.46684	+	28.4283i	−0.103781	+	1.19599i
$566$			1.70770i			0.0717799i
$567$		0			0
$568$	7.41505	−	7.41505i	0.311129	−	0.311129i
$569$	−22.6811			−0.950842			−0.475421	−	0.879758i	$-0.657704\pi$
$569$	−22.6811			−0.950842			−0.475421	+	0.879758i	$0.657704\pi$
$570$		0			0
$571$	12.2927			0.514433			0.257217	−	0.966354i	$-0.417195\pi$
$571$	12.2927			0.514433			0.257217	+	0.966354i	$0.417195\pi$
$572$	6.84763	−	6.84763i	0.286314	−	0.286314i
$573$		0			0
$574$			49.8519i			2.08078i
$575$	−4.09169	+	2.87369i	−0.170635	+	0.119841i
$576$		0			0
$577$	4.22302	+	4.22302i	0.175807	+	0.175807i	0.789525	−	0.613718i	$-0.210327\pi$
$577$	4.22302	+	4.22302i	0.175807	+	0.175807i	−0.613718	+	0.789525i	$0.710327\pi$
$578$	8.35309	+	8.35309i	0.347443	+	0.347443i
$579$		0			0
$580$	−6.74618	+	5.66887i	−0.280120	+	0.235387i
$581$		−	59.1740i		−	2.45495i
$582$		0			0
$583$	−7.14470	+	7.14470i	−0.295903	+	0.295903i
$584$	−8.57580			−0.354869
$585$		0			0
$586$	1.47346			0.0608681
$587$	4.19233	−	4.19233i	0.173036	−	0.173036i	−0.615276	−	0.788312i	$-0.710955\pi$
$587$	4.19233	−	4.19233i	0.173036	−	0.173036i	0.788312	+	0.615276i	$0.210955\pi$
$588$		0			0
$589$			14.7021i			0.605789i
$590$	16.6414	+	1.44405i	0.685117	+	0.0594504i
$591$		0			0
$592$	−1.24787	−	1.24787i	−0.0512871	−	0.0512871i
$593$	23.0815	+	23.0815i	0.947842	+	0.947842i	0.998706	−	0.0508632i	$-0.0161973\pi$
$593$	23.0815	+	23.0815i	0.947842	+	0.947842i	−0.0508632	+	0.998706i	$0.516197\pi$
$594$		0			0
$595$	14.7021	+	17.4960i	0.602727	+	0.717268i
$596$		−	6.15497i		−	0.252117i
$597$		0			0
$598$	2.00000	−	2.00000i	0.0817861	−	0.0817861i
$599$	15.1827			0.620349			0.310175	−	0.950680i	$-0.399612\pi$
$599$	15.1827			0.620349			0.310175	+	0.950680i	$0.399612\pi$
$600$		0			0
$601$	−27.1171			−1.10613			−0.553065	−	0.833138i	$-0.686542\pi$
$601$	−27.1171			−1.10613			−0.553065	+	0.833138i	$0.686542\pi$
$602$	−3.37518	+	3.37518i	−0.137562	+	0.137562i
$603$		0			0
$604$		−	14.9796i		−	0.609510i
$605$	−1.03936	−	1.23687i	−0.0422558	−	0.0502861i
$606$		0			0
$607$	10.2608	+	10.2608i	0.416473	+	0.416473i	0.883986	−	0.467513i	$-0.154850\pi$
$607$	10.2608	+	10.2608i	0.416473	+	0.416473i	−0.467513	+	0.883986i	$0.654850\pi$
$608$	4.56465	+	4.56465i	0.185121	+	0.185121i
$609$		0			0
$610$	−8.66769	−	0.752131i	−0.350944	−	0.0304529i
$611$		−	17.1651i		−	0.694426i
$612$		0			0
$613$	−34.2825	+	34.2825i	−1.38466	+	1.38466i	−0.548515	+	0.836141i	$0.684807\pi$
$613$	−34.2825	+	34.2825i	−1.38466	+	1.38466i	−0.836141	+	0.548515i	$0.815193\pi$
$614$	−19.8418			−0.800750
$615$		0			0
$616$	15.3643			0.619047
$617$	16.4180	−	16.4180i	0.660964	−	0.660964i	−0.294644	−	0.955607i	$-0.595201\pi$
$617$	16.4180	−	16.4180i	0.660964	−	0.660964i	0.955607	+	0.294644i	$0.0952009\pi$
$618$		0			0
$619$		−	38.4820i		−	1.54672i	−0.633966	−	0.773361i	$-0.718574\pi$
$619$		−	38.4820i		−	1.54672i	0.633966	−	0.773361i	$-0.281426\pi$
$620$	−3.89885	+	3.27624i	−0.156582	+	0.131577i
$621$		0			0
$622$	−11.8975	−	11.8975i	−0.477046	−	0.477046i
$623$	−25.4987	−	25.4987i	−1.02158	−	1.02158i
$624$		0			0
$625$	−23.5165	−	8.48383i	−0.940659	−	0.339353i
$626$			15.0566i			0.601781i
$627$		0			0
$628$	4.53388	−	4.53388i	0.180922	−	0.180922i
$629$	4.01920			0.160256
$630$		0			0
$631$	−2.89888			−0.115403			−0.0577013	−	0.998334i	$-0.518377\pi$
$631$	−2.89888			−0.115403			−0.0577013	+	0.998334i	$0.518377\pi$
$632$	−8.05888	+	8.05888i	−0.320565	+	0.320565i
$633$		0			0
$634$			23.3548i			0.927537i
$635$	4.28997	−	49.4384i	0.170242	−	1.96190i
$636$		0			0
$637$	26.2751	+	26.2751i	1.04106	+	1.04106i
$638$	−9.54053	−	9.54053i	−0.377713	−	0.377713i
$639$		0			0
$640$	−0.193306	+	2.22770i	−0.00764111	+	0.0880574i
$641$			31.0985i			1.22832i	0.789183	+	0.614158i	$0.210504\pi$
$641$			31.0985i			1.22832i	−0.789183	+	0.614158i	$0.789496\pi$
$642$		0			0
$643$	5.34745	−	5.34745i	0.210883	−	0.210883i	−0.593760	−	0.804642i	$-0.702357\pi$
$643$	5.34745	−	5.34745i	0.210883	−	0.210883i	0.804642	+	0.593760i	$0.202357\pi$
$644$	4.48749			0.176832
$645$		0			0
$646$	−14.7021			−0.578446
$647$	−1.72817	+	1.72817i	−0.0679415	+	0.0679415i	−0.740261	−	0.672320i	$-0.765298\pi$
$647$	−1.72817	+	1.72817i	−0.0679415	+	0.0679415i	0.672320	+	0.740261i	$0.265298\pi$
$648$		0			0
$649$			25.5767i			1.00397i
$650$	13.9308	+	2.43600i	0.546409	+	0.0955478i
$651$		0			0
$652$	−16.1376	−	16.1376i	−0.631996	−	0.631996i
$653$	−15.3048	−	15.3048i	−0.598921	−	0.598921i	0.341104	−	0.940025i	$-0.389199\pi$
$653$	−15.3048	−	15.3048i	−0.598921	−	0.598921i	−0.940025	+	0.341104i	$0.889199\pi$
$654$		0			0
$655$	24.4087	−	20.5109i	0.953728	−	0.801426i
$656$		−	11.1091i		−	0.433736i
$657$		0			0
$658$	19.2571	−	19.2571i	0.750718	−	0.750718i
$659$	18.0992			0.705045			0.352523	−	0.935803i	$-0.385324\pi$
$659$	18.0992			0.705045			0.352523	+	0.935803i	$0.385324\pi$
$660$		0			0
$661$	−4.87044			−0.189438			−0.0947191	−	0.995504i	$-0.530195\pi$
$661$	−4.87044			−0.189438			−0.0947191	+	0.995504i	$0.530195\pi$
$662$	4.39022	−	4.39022i	0.170631	−	0.170631i
$663$		0			0
$664$			13.1864i			0.511733i
$665$	64.5331	+	5.59980i	2.50248	+	0.217151i
$666$		0			0
$667$	−2.78652	−	2.78652i	−0.107895	−	0.107895i
$668$	8.53392	+	8.53392i	0.330187	+	0.330187i
$669$		0			0
$670$	18.1672	+	21.6196i	0.701859	+	0.835240i
$671$		−	13.3216i		−	0.514276i
$672$		0			0
$673$	−30.4886	+	30.4886i	−1.17525	+	1.17525i	−0.194309	+	0.980940i	$0.562246\pi$
$673$	−30.4886	+	30.4886i	−1.17525	+	1.17525i	−0.980940	+	0.194309i	$0.937754\pi$
$674$	−19.8606			−0.765002
$675$		0			0
$676$	5.00000			0.192308
$677$	−3.12903	+	3.12903i	−0.120258	+	0.120258i	−0.764675	−	0.644416i	$-0.777100\pi$
$677$	−3.12903	+	3.12903i	−0.120258	+	0.120258i	0.644416	+	0.764675i	$0.277100\pi$
$678$		0			0
$679$		−	72.0367i		−	2.76452i
$680$	−3.27624	−	3.89885i	−0.125638	−	0.149514i
$681$		0			0
$682$	−5.51381	−	5.51381i	−0.211135	−	0.211135i
$683$	−27.5040	−	27.5040i	−1.05241	−	1.05241i	−0.998548	−	0.0538625i	$-0.982847\pi$
$683$	−27.5040	−	27.5040i	−1.05241	−	1.05241i	−0.0538625	−	0.998548i	$-0.517153\pi$
$684$		0			0
$685$	−39.3006	−	3.41028i	−1.50160	−	0.130300i
$686$			27.5422i			1.05157i
$687$		0			0
$688$	0.752131	−	0.752131i	0.0286747	−	0.0286747i
$689$	8.34706			0.317998
$690$		0			0
$691$	21.6033			0.821829			0.410915	−	0.911674i	$-0.365209\pi$
$691$	21.6033			0.821829			0.410915	+	0.911674i	$0.365209\pi$
$692$	5.90170	−	5.90170i	0.224349	−	0.224349i
$693$		0			0
$694$			30.9012i			1.17300i
$695$	18.3210	−	15.3953i	0.694954	−	0.583976i
$696$		0			0
$697$	17.8904	+	17.8904i	0.677645	+	0.677645i
$698$	2.52652	+	2.52652i	0.0956303	+	0.0956303i
$699$		0			0
$700$	12.8956	+	18.3614i	0.487410	+	0.693996i
$701$			0.544287i			0.0205574i	0.999947	+	0.0102787i	$0.00327187\pi$
$701$			0.544287i			0.0205574i	−0.999947	+	0.0102787i	$0.996728\pi$
$702$		0			0
$703$	8.05548	−	8.05548i	0.303818	−	0.303818i
$704$	−3.42382			−0.129040
$705$		0			0
$706$	−22.8893			−0.861452
$707$	−4.77473	+	4.77473i	−0.179572	+	0.179572i
$708$		0			0
$709$		−	26.6848i		−	1.00217i	−0.865398	−	0.501085i	$-0.832934\pi$
$709$		−	26.6848i		−	1.00217i	0.865398	−	0.501085i	$-0.167066\pi$
$710$	−2.02710	+	23.3607i	−0.0760757	+	0.876710i
$711$		0			0
$712$	5.68217	+	5.68217i	0.212948	+	0.212948i
$713$	−1.61043	−	1.61043i	−0.0603110	−	0.0603110i
$714$		0			0
$715$	−1.87198	+	21.5730i	−0.0700081	+	0.806786i
$716$			22.6890i			0.847929i
$717$		0			0
$718$	−12.6333	+	12.6333i	−0.471471	+	0.471471i
$719$	−0.851266			−0.0317469			−0.0158734	−	0.999874i	$-0.505053\pi$
$719$	−0.851266			−0.0317469			−0.0158734	+	0.999874i	$0.505053\pi$
$720$		0			0
$721$	−20.1376			−0.749962
$722$	−16.0316	+	16.0316i	−0.596634	+	0.596634i
$723$		0			0
$724$			5.68217i			0.211176i
$725$	3.39398	−	19.4092i	0.126049	−	0.720839i
$726$		0			0
$727$	21.5858	+	21.5858i	0.800574	+	0.800574i	0.983185	−	0.182611i	$-0.0584550\pi$
$727$	21.5858	+	21.5858i	0.800574	+	0.800574i	−0.182611	+	0.983185i	$0.558455\pi$
$728$	−8.97498	−	8.97498i	−0.332635	−	0.332635i
$729$		0			0
$730$	14.6810	−	12.3366i	0.543368	−	0.456597i
$731$			2.42250i			0.0895996i
$732$		0			0
$733$	11.0410	−	11.0410i	0.407809	−	0.407809i	−0.473165	−	0.880974i	$-0.656889\pi$
$733$	11.0410	−	11.0410i	0.407809	−	0.407809i	0.880974	+	0.473165i	$0.156889\pi$
$734$	−7.25625			−0.267833
$735$		0			0
$736$	−1.00000			−0.0368605
$737$	−30.5748	+	30.5748i	−1.12624	+	1.12624i
$738$		0			0
$739$			46.0967i			1.69569i	0.530241	+	0.847847i	$0.322102\pi$
$739$			46.0967i			1.69569i	−0.530241	+	0.847847i	$0.677898\pi$
$740$	3.93133	+	0.341138i	0.144519	+	0.0125405i
$741$		0			0
$742$	9.36434	+	9.36434i	0.343776	+	0.343776i
$743$	−12.6723	−	12.6723i	−0.464902	−	0.464902i	0.435356	−	0.900258i	$-0.356622\pi$
$743$	−12.6723	−	12.6723i	−0.464902	−	0.464902i	−0.900258	+	0.435356i	$0.856622\pi$
$744$		0			0
$745$	8.85412	+	10.5367i	0.324390	+	0.386036i
$746$			27.3607i			1.00175i
$747$		0			0
$748$	5.51381	−	5.51381i	0.201605	−	0.201605i
$749$	−27.4146			−1.00171
$750$		0			0
$751$	−4.16652			−0.152038			−0.0760192	−	0.997106i	$-0.524221\pi$
$751$	−4.16652			−0.152038			−0.0760192	+	0.997106i	$0.524221\pi$
$752$	−4.29128	+	4.29128i	−0.156487	+	0.156487i
$753$		0			0
$754$			11.1461i			0.405916i
$755$	21.5486	+	25.6436i	0.784233	+	0.933268i
$756$		0			0
$757$	6.74443	+	6.74443i	0.245131	+	0.245131i	0.818969	−	0.573838i	$-0.194546\pi$
$757$	6.74443	+	6.74443i	0.245131	+	0.245131i	−0.573838	+	0.818969i	$0.694546\pi$
$758$	−24.0601	−	24.0601i	−0.873901	−	0.873901i
$759$		0			0
$760$	−14.3807	−	1.24787i	−0.521641	−	0.0452650i
$761$			6.87318i			0.249153i	0.992210	+	0.124576i	$0.0397572\pi$
$761$			6.87318i			0.249153i	−0.992210	+	0.124576i	$0.960243\pi$
$762$		0			0
$763$	44.3261	−	44.3261i	1.60471	−	1.60471i
$764$	0.156935			0.00567771
$765$		0			0
$766$	−18.0207			−0.651116
$767$	14.9405	−	14.9405i	0.539470	−	0.539470i
$768$		0			0
$769$			29.5826i			1.06678i	0.845871	+	0.533388i	$0.179081\pi$
$769$			29.5826i			1.06678i	−0.845871	+	0.533388i	$0.820919\pi$
$770$	−26.3023	+	22.1021i	−0.947870	+	0.796504i
$771$		0			0
$772$	−17.6238	−	17.6238i	−0.634293	−	0.634293i
$773$	−8.79887	−	8.79887i	−0.316473	−	0.316473i	0.530938	−	0.847411i	$-0.321840\pi$
$773$	−8.79887	−	8.79887i	−0.316473	−	0.316473i	−0.847411	+	0.530938i	$0.821840\pi$
$774$		0			0
$775$	1.96150	−	11.2172i	0.0704592	−	0.402935i
$776$			16.0528i			0.576262i
$777$		0			0
$778$	20.8859	−	20.8859i	0.748797	−	0.748797i
$779$	71.7134			2.56940
$780$		0			0
$781$	−35.9037			−1.28474
$782$	1.61043	−	1.61043i	0.0575888	−	0.0575888i
$783$		0			0
$784$		−	13.1376i		−	0.469199i
$785$	−1.23946	+	14.2837i	−0.0442381	+	0.509808i
$786$		0			0
$787$	−1.76250	−	1.76250i	−0.0628263	−	0.0628263i	0.674996	−	0.737822i	$-0.264146\pi$
$787$	−1.76250	−	1.76250i	−0.0628263	−	0.0628263i	−0.737822	+	0.674996i	$0.764146\pi$
$788$	−7.08987	−	7.08987i	−0.252566	−	0.252566i
$789$		0			0
$790$	2.20311	−	25.3890i	0.0783831	−	0.903301i
$791$			57.2663i			2.03615i
$792$		0			0
$793$	−7.78175	+	7.78175i	−0.276338	+	0.276338i
$794$	19.3521			0.686781
$795$		0			0
$796$	15.8601			0.562145
$797$	−15.3709	+	15.3709i	−0.544465	+	0.544465i	−0.924834	−	0.380370i	$-0.875797\pi$
$797$	−15.3709	+	15.3709i	−0.544465	+	0.544465i	0.380370	+	0.924834i	$0.375797\pi$
$798$		0			0
$799$		−	13.8216i		−	0.488972i
$800$	−2.87369	−	4.09169i	−0.101600	−	0.144663i
$801$		0			0
$802$	0.396156	+	0.396156i	0.0139887	+	0.0139887i
$803$	20.7620	+	20.7620i	0.732677	+	0.732677i
$804$		0			0
$805$	−7.68217	+	6.45539i	−0.270761	+	0.227523i
$806$			6.44171i			0.226899i
$807$		0			0
$808$	1.06401	−	1.06401i	0.0374317	−	0.0374317i
$809$	−46.8226			−1.64620			−0.823098	−	0.567899i	$-0.807756\pi$
$809$	−46.8226			−1.64620			−0.823098	+	0.567899i	$0.807756\pi$
$810$		0			0
$811$	43.1955			1.51680			0.758399	−	0.651791i	$-0.225982\pi$
$811$	43.1955			1.51680			0.758399	+	0.651791i	$0.225982\pi$
$812$	−12.5045	+	12.5045i	−0.438821	+	0.438821i
$813$		0			0
$814$			6.04219i			0.211779i
$815$	50.8404	+	4.41163i	1.78086	+	0.154533i
$816$		0			0
$817$	4.85530	+	4.85530i	0.169866	+	0.169866i
$818$	−4.88406	−	4.88406i	−0.170767	−	0.170767i
$819$		0			0
$820$	15.9808	+	19.0177i	0.558072	+	0.664127i
$821$			34.5656i			1.20635i	0.797610	+	0.603174i	$0.206098\pi$
$821$			34.5656i			1.20635i	−0.797610	+	0.603174i	$0.793902\pi$
$822$		0			0
$823$	10.4910	−	10.4910i	0.365692	−	0.365692i	−0.500211	−	0.865903i	$-0.666744\pi$
$823$	10.4910	−	10.4910i	0.365692	−	0.365692i	0.865903	+	0.500211i	$0.166744\pi$
$824$	4.48749			0.156329
$825$		0			0
$826$	33.5226			1.16640
$827$	−5.84595	+	5.84595i	−0.203284	+	0.203284i	−0.801405	−	0.598122i	$-0.795914\pi$
$827$	−5.84595	+	5.84595i	−0.203284	+	0.203284i	0.598122	+	0.801405i	$0.295914\pi$
$828$		0			0
$829$			20.7287i			0.719937i	0.932965	+	0.359968i	$0.117212\pi$
$829$			20.7287i			0.719937i	−0.932965	+	0.359968i	$0.882788\pi$
$830$	−18.9691	−	22.5740i	−0.658427	−	0.783553i
$831$		0			0
$832$	2.00000	+	2.00000i	0.0693375	+	0.0693375i
$833$	21.1571	+	21.1571i	0.733050	+	0.733050i
$834$		0			0
$835$	−26.8856	−	2.33297i	−0.930414	−	0.0807358i
$836$		−	22.1021i		−	0.764416i
$837$		0			0
$838$	5.64962	−	5.64962i	0.195163	−	0.195163i
$839$	−13.9495			−0.481589			−0.240795	−	0.970576i	$-0.577408\pi$
$839$	−13.9495			−0.481589			−0.240795	+	0.970576i	$0.577408\pi$
$840$		0			0
$841$	−13.4706			−0.464503
$842$	19.7893	−	19.7893i	0.681983	−	0.681983i
$843$		0			0
$844$		−	1.68032i		−	0.0578391i
$845$	−8.55954	+	7.19266i	−0.294457	+	0.247435i
$846$		0			0
$847$	−2.29263	−	2.29263i	−0.0787756	−	0.0787756i
$848$	−2.08676	−	2.08676i	−0.0716598	−	0.0716598i
$849$		0			0
$850$	11.2172	+	1.96150i	0.384748	+	0.0672789i
$851$			1.76475i			0.0604950i
$852$		0			0
$853$	−11.8890	+	11.8890i	−0.407073	+	0.407073i	−0.880716	−	0.473644i	$-0.842938\pi$
$853$	−11.8890	+	11.8890i	−0.407073	+	0.407073i	0.473644	+	0.880716i	$0.342938\pi$
$854$	−17.4603			−0.597478
$855$		0			0
$856$	6.10913			0.208806
$857$	5.82156	−	5.82156i	0.198861	−	0.198861i	−0.600651	−	0.799512i	$-0.705092\pi$
$857$	5.82156	−	5.82156i	0.198861	−	0.198861i	0.799512	+	0.600651i	$0.205092\pi$
$858$		0			0
$859$		−	7.91549i		−	0.270073i	−0.990841	−	0.135037i	$-0.956885\pi$
$859$		−	7.91549i		−	0.270073i	0.990841	−	0.135037i	$-0.0431152\pi$
$860$	−0.205615	+	2.36954i	−0.00701141	+	0.0808007i
$861$		0			0
$862$	−7.91931	−	7.91931i	−0.269733	−	0.269733i
$863$	−19.3695	−	19.3695i	−0.659345	−	0.659345i	0.295880	−	0.955225i	$-0.404387\pi$
$863$	−19.3695	−	19.3695i	−0.659345	−	0.659345i	−0.955225	+	0.295880i	$0.904387\pi$
$864$		0			0
$865$	−1.61339	+	18.5930i	−0.0548568	+	0.632179i
$866$			10.2442i			0.348113i
$867$		0			0
$868$	−7.22677	+	7.22677i	−0.245293	+	0.245293i
$869$	39.0212			1.32370
$870$		0			0
$871$	35.7201			1.21033
$872$	−9.87771	+	9.87771i	−0.334502	+	0.334502i
$873$		0			0
$874$		−	6.45539i		−	0.218357i
$875$	−48.4896	−	12.8822i	−1.63925	−	0.435499i
$876$		0			0
$877$	−26.2329	−	26.2329i	−0.885823	−	0.885823i	0.108296	−	0.994119i	$-0.465461\pi$
$877$	−26.2329	−	26.2329i	−0.885823	−	0.885823i	−0.994119	+	0.108296i	$0.965461\pi$
$878$	−26.8156	−	26.8156i	−0.904983	−	0.904983i
$879$		0			0
$880$	5.86126	−	4.92527i	0.197583	−	0.166031i
$881$			45.8820i			1.54580i	0.634525	+	0.772902i	$0.281196\pi$
$881$			45.8820i			1.54580i	−0.634525	+	0.772902i	$0.718804\pi$
$882$		0			0
$883$	18.8627	−	18.8627i	0.634782	−	0.634782i	−0.314482	−	0.949264i	$-0.601831\pi$
$883$	18.8627	−	18.8627i	0.634782	−	0.634782i	0.949264	+	0.314482i	$0.101831\pi$
$884$	−6.44171			−0.216658
$885$		0			0
$886$	−12.5741			−0.422434
$887$	15.4909	−	15.4909i	0.520133	−	0.520133i	−0.397479	−	0.917611i	$-0.630115\pi$
$887$	15.4909	−	15.4909i	0.520133	−	0.520133i	0.917611	+	0.397479i	$0.130115\pi$
$888$		0			0
$889$		−	99.5890i		−	3.34011i
$890$	−17.9013	−	1.55337i	−0.600054	−	0.0520691i
$891$		0			0
$892$	4.72627	+	4.72627i	0.158247	+	0.158247i
$893$	−27.7019	−	27.7019i	−0.927008	−	0.927008i
$894$		0			0
$895$	−32.6389	−	38.8415i	−1.09100	−	1.29833i
$896$			4.48749i			0.149916i
$897$		0			0
$898$	28.8349	−	28.8349i	0.962232	−	0.962232i
$899$	8.97498			0.299332
$900$		0			0
$901$	6.72117			0.223914
$902$	−26.8951	+	26.8951i	−0.895509	+	0.895509i
$903$		0			0
$904$		−	12.7613i		−	0.424435i
$905$	−8.17398	−	9.72735i	−0.271712	−	0.323348i
$906$		0			0
$907$	9.41571	+	9.41571i	0.312644	+	0.312644i	0.845933	−	0.533289i	$-0.179044\pi$
$907$	9.41571	+	9.41571i	0.312644	+	0.312644i	−0.533289	+	0.845933i	$0.679044\pi$
$908$	−9.14266	−	9.14266i	−0.303410	−	0.303410i
$909$		0			0
$910$	28.2751	+	2.45355i	0.937311	+	0.0813343i
$911$		−	24.2752i		−	0.804274i	−0.915580	−	0.402137i	$-0.868268\pi$
$911$		−	24.2752i		−	0.804274i	0.915580	−	0.402137i	$-0.131732\pi$
$912$		0			0
$913$	31.9244	−	31.9244i	1.05654	−	1.05654i
$914$	−10.9401			−0.361866
$915$		0			0
$916$	−4.98963			−0.164862
$917$	45.2432	−	45.2432i	1.49406	−	1.49406i
$918$		0			0
$919$			45.8495i			1.51244i	0.654320	+	0.756218i	$0.272955\pi$
$919$			45.8495i			1.51244i	−0.654320	+	0.756218i	$0.727045\pi$
$920$	1.71191	−	1.43853i	0.0564399	−	0.0474270i
$921$		0			0
$922$	−15.3813	−	15.3813i	−0.506557	−	0.506557i
$923$	20.9729	+	20.9729i	0.690332	+	0.690332i
$924$		0			0
$925$	−7.22082	+	5.07135i	−0.237419	+	0.166745i
$926$			37.5255i			1.23316i
$927$		0			0
$928$	2.78652	−	2.78652i	0.0914720	−	0.0914720i
$929$	51.5944			1.69276			0.846379	−	0.532582i	$-0.178778\pi$
$929$	51.5944			1.69276			0.846379	+	0.532582i	$0.178778\pi$
$930$		0			0
$931$	84.8081			2.77947
$932$	7.59060	−	7.59060i	0.248638	−	0.248638i
$933$		0			0
$934$		−	14.8402i		−	0.485585i
$935$	−1.50734	+	17.3709i	−0.0492955	+	0.568089i
$936$		0			0
$937$	−8.15455	−	8.15455i	−0.266397	−	0.266397i	0.561249	−	0.827647i	$-0.310321\pi$
$937$	−8.15455	−	8.15455i	−0.266397	−	0.266397i	−0.827647	+	0.561249i	$0.810321\pi$
$938$	40.0734	+	40.0734i	1.30844	+	1.30844i
$939$		0			0
$940$	1.17313	−	13.5194i	0.0382634	−	0.440954i
$941$		−	19.0545i		−	0.621159i	−0.950547	−	0.310579i	$-0.899477\pi$
$941$		−	19.0545i		−	0.621159i	0.950547	−	0.310579i	$-0.100523\pi$
$942$		0			0
$943$	−7.85530	+	7.85530i	−0.255804	+	0.255804i
$944$	−7.47024			−0.243136
$945$		0			0
$946$	−3.64182			−0.118406
$947$	−39.5188	+	39.5188i	−1.28419	+	1.28419i	−0.345926	+	0.938262i	$0.612435\pi$
$947$	−39.5188	+	39.5188i	−1.28419	+	1.28419i	−0.938262	+	0.345926i	$0.887565\pi$
$948$		0			0
$949$		−	24.2560i		−	0.787384i
$950$	26.4135	−	18.5508i	0.856966	−	0.601867i
$951$		0			0
$952$	−7.22677	−	7.22677i	−0.234221	−	0.234221i
$953$	−13.1971	−	13.1971i	−0.427497	−	0.427497i	0.460278	−	0.887775i	$-0.347750\pi$
$953$	−13.1971	−	13.1971i	−0.427497	−	0.427497i	−0.887775	+	0.460278i	$0.847750\pi$
$954$		0			0
$955$	−0.268658	+	0.225756i	−0.00869357	+	0.00730528i
$956$		−	20.3792i		−	0.659111i
$957$		0			0
$958$	−6.17975	+	6.17975i	−0.199659	+	0.199659i
$959$	−79.1675			−2.55645
$960$		0			0
$961$	−25.8130			−0.832679
$962$	3.52951	−	3.52951i	0.113796	−	0.113796i
$963$		0			0
$964$		−	9.11949i		−	0.293719i
$965$	55.5226	+	4.81792i	1.78733	+	0.155094i
$966$		0			0
$967$	−27.0265	−	27.0265i	−0.869115	−	0.869115i	0.123260	−	0.992374i	$-0.460665\pi$
$967$	−27.0265	−	27.0265i	−0.869115	−	0.869115i	−0.992374	+	0.123260i	$0.960665\pi$
$968$	0.510893	+	0.510893i	0.0164207	+	0.0164207i
$969$		0			0
$970$	−23.0924	−	27.4809i	−0.741454	−	0.882359i
$971$			23.1061i			0.741510i	0.928731	+	0.370755i	$0.120901\pi$
$971$			23.1061i			0.741510i	−0.928731	+	0.370755i	$0.879099\pi$
$972$		0			0
$973$	33.9591	−	33.9591i	1.08868	−	1.08868i
$974$	10.3757			0.332459
$975$		0			0
$976$	3.89087			0.124544
$977$	15.3977	−	15.3977i	0.492617	−	0.492617i	−0.416513	−	0.909130i	$-0.636748\pi$
$977$	15.3977	−	15.3977i	0.492617	−	0.492617i	0.909130	+	0.416513i	$0.136748\pi$
$978$		0			0
$979$		−	27.5131i		−	0.879322i
$980$	18.8988	+	22.4903i	0.603700	+	0.718426i
$981$		0			0
$982$	7.12325	+	7.12325i	0.227312	+	0.227312i
$983$	−10.6126	−	10.6126i	−0.338490	−	0.338490i	0.517309	−	0.855799i	$-0.326934\pi$
$983$	−10.6126	−	10.6126i	−0.338490	−	0.338490i	−0.855799	+	0.517309i	$0.826934\pi$
$984$		0			0
$985$	22.3362	+	1.93820i	0.711691	+	0.0617563i
$986$			8.97498i			0.285822i
$987$		0			0
$988$	−12.9108	+	12.9108i	−0.410747	+	0.410747i
$989$	−1.06367			−0.0338229
$990$		0			0
$991$	18.0072			0.572017			0.286008	−	0.958227i	$-0.407671\pi$
$991$	18.0072			0.572017			0.286008	+	0.958227i	$0.407671\pi$
$992$	1.61043	−	1.61043i	0.0511311	−	0.0511311i
$993$		0			0
$994$			47.0579i			1.49259i
$995$	−27.1510	+	22.8152i	−0.860744	+	0.723291i
$996$		0			0
$997$	−4.81541	−	4.81541i	−0.152506	−	0.152506i	0.626730	−	0.779236i	$-0.284393\pi$
$997$	−4.81541	−	4.81541i	−0.152506	−	0.152506i	−0.779236	+	0.626730i	$0.784393\pi$
$998$	14.8834	+	14.8834i	0.471127	+	0.471127i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.j.i.737.8	yes	16
3.2	odd	2	inner	2070.2.j.i.737.1	yes	16
5.3	odd	4	inner	2070.2.j.i.323.1	✓	16
15.8	even	4	inner	2070.2.j.i.323.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.j.i.323.1	✓	16	5.3	odd	4	inner
2070.2.j.i.323.8	yes	16	15.8	even	4	inner
2070.2.j.i.737.1	yes	16	3.2	odd	2	inner
2070.2.j.i.737.8	yes	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2070.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.43853 + 1.71191i) q^{5} +(3.17313 + 3.17313i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.43853 + 1.71191i) q^{5} +(3.17313 + 3.17313i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.22770 + 0.193306i) q^{10} +3.42382i q^{11} +(2.00000 - 2.00000i) q^{13} +4.48749 q^{14} -1.00000 q^{16} +(1.61043 - 1.61043i) q^{17} -6.45539i q^{19} +(1.71191 - 1.43853i) q^{20} +(2.42100 + 2.42100i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-0.861256 + 4.92527i) q^{25} -2.82843i q^{26} +(3.17313 - 3.17313i) q^{28} -3.94074 q^{29} -2.27749 q^{31} +(-0.707107 + 0.707107i) q^{32} -2.27749i q^{34} +(-0.867460 + 9.99677i) q^{35} +(1.24787 + 1.24787i) q^{37} +(-4.56465 - 4.56465i) q^{38} +(0.193306 - 2.22770i) q^{40} +11.1091i q^{41} +(-0.752131 + 0.752131i) q^{43} +3.42382 q^{44} +1.00000 q^{46} +(4.29128 - 4.29128i) q^{47} +13.1376i q^{49} +(2.87369 + 4.09169i) q^{50} +(-2.00000 - 2.00000i) q^{52} +(2.08676 + 2.08676i) q^{53} +(-5.86126 + 4.92527i) q^{55} -4.48749i q^{56} +(-2.78652 + 2.78652i) q^{58} +7.47024 q^{59} -3.89087 q^{61} +(-1.61043 + 1.61043i) q^{62} +1.00000i q^{64} +(6.30088 + 0.546753i) q^{65} +(8.93004 + 8.93004i) q^{67} +(-1.61043 - 1.61043i) q^{68} +(6.45539 + 7.68217i) q^{70} +10.4865i q^{71} +(6.06401 - 6.06401i) q^{73} +1.76475 q^{74} -6.45539 q^{76} +(-10.8642 + 10.8642i) q^{77} -11.3970i q^{79} +(-1.43853 - 1.71191i) q^{80} +(7.85530 + 7.85530i) q^{82} +(-9.32421 - 9.32421i) q^{83} +(5.07355 + 0.440253i) q^{85} +1.06367i q^{86} +(2.42100 - 2.42100i) q^{88} -8.03580 q^{89} +12.6925 q^{91} +(0.707107 - 0.707107i) q^{92} -6.06878i q^{94} +(11.0510 - 9.28628i) q^{95} +(-11.3510 - 11.3510i) q^{97} +(9.28966 + 9.28966i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 4 q^{10} + 32 q^{13} - 16 q^{16} - 24 q^{25} - 16 q^{31} + 32 q^{37} + 4 q^{40} + 16 q^{46} - 32 q^{52} - 104 q^{55} + 8 q^{58} - 40 q^{61} + 72 q^{67} + 24 q^{70} + 24 q^{73} - 24 q^{76} - 8 q^{82} - 8 q^{85} - 72 q^{97}+O(q^{100}) \) 16 * q - 4 * q^10 + 32 * q^13 - 16 * q^16 - 24 * q^25 - 16 * q^31 + 32 * q^37 + 4 * q^40 + 16 * q^46 - 32 * q^52 - 104 * q^55 + 8 * q^58 - 40 * q^61 + 72 * q^67 + 24 * q^70 + 24 * q^73 - 24 * q^76 - 8 * q^82 - 8 * q^85 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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