LMFDB - Embedded newform 1470.2.b.c.881.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(881,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("1470.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 16x^{13} + 2x^{12} + 96x^{10} - 80x^{9} + 2x^{8} - 240x^{7} + 864x^{6} + 162x^{4} - 3888x^{3} + 6561 $ x^16 - 16x^13 + 2x^12 + 96x^10 - 80x^9 + 2x^8 - 240x^7 + 864x^6 + 162x^4 - 3888*x^3 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			881.14
Root			$-0.519068 - 1.65244i$ of defining polynomial
Character	$\chi$	$=$	1470.881
Dual form			1470.2.b.c.881.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.152807 - 1.72530i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.72530 + 0.152807i) q^{6} -1.00000i q^{8} +(-2.95330 - 0.527274i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.152807 - 1.72530i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.72530 + 0.152807i) q^{6} -1.00000i q^{8} +(-2.95330 - 0.527274i) q^{9} -1.00000i q^{10} -0.476459i q^{11} +(-0.152807 + 1.72530i) q^{12} +4.96165i q^{13} +(-0.152807 + 1.72530i) q^{15} +1.00000 q^{16} +5.31590 q^{17} +(0.527274 - 2.95330i) q^{18} +5.18049i q^{19} +1.00000 q^{20} +0.476459 q^{22} -3.71381i q^{23} +(-1.72530 - 0.152807i) q^{24} +1.00000 q^{25} -4.96165 q^{26} +(-1.36099 + 5.01475i) q^{27} -4.80278i q^{29} +(-1.72530 - 0.152807i) q^{30} -2.47917i q^{31} +1.00000i q^{32} +(-0.822034 - 0.0728062i) q^{33} +5.31590i q^{34} +(2.95330 + 0.527274i) q^{36} +2.38410 q^{37} -5.18049 q^{38} +(8.56033 + 0.758174i) q^{39} +1.00000i q^{40} +11.4897 q^{41} +1.38323 q^{43} +0.476459i q^{44} +(2.95330 + 0.527274i) q^{45} +3.71381 q^{46} +11.8319 q^{47} +(0.152807 - 1.72530i) q^{48} +1.00000i q^{50} +(0.812306 - 9.17151i) q^{51} -4.96165i q^{52} +0.305714i q^{53} +(-5.01475 - 1.36099i) q^{54} +0.476459i q^{55} +(8.93788 + 0.791613i) q^{57} +4.80278 q^{58} -0.441038 q^{59} +(0.152807 - 1.72530i) q^{60} +12.2202i q^{61} +2.47917 q^{62} -1.00000 q^{64} -4.96165i q^{65} +(0.0728062 - 0.822034i) q^{66} +3.11989 q^{67} -5.31590 q^{68} +(-6.40743 - 0.567495i) q^{69} -8.78061i q^{71} +(-0.527274 + 2.95330i) q^{72} -15.0920i q^{73} +2.38410i q^{74} +(0.152807 - 1.72530i) q^{75} -5.18049i q^{76} +(-0.758174 + 8.56033i) q^{78} +1.77425 q^{79} -1.00000 q^{80} +(8.44396 + 3.11440i) q^{81} +11.4897i q^{82} -14.2002 q^{83} -5.31590 q^{85} +1.38323i q^{86} +(-8.28621 - 0.733896i) q^{87} -0.476459 q^{88} +5.22255 q^{89} +(-0.527274 + 2.95330i) q^{90} +3.71381i q^{92} +(-4.27730 - 0.378833i) q^{93} +11.8319i q^{94} -5.18049i q^{95} +(1.72530 + 0.152807i) q^{96} -8.50932i q^{97} +(-0.251225 + 1.40713i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} - 16 q^{4} - 16 q^{5} + 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 - 16 * q^4 - 16 * q^5 + 8 * q^9	$ 16 q - 8 q^{3} - 16 q^{4} - 16 q^{5} + 8 q^{9} + 8 q^{12} + 8 q^{15} + 16 q^{16} + 48 q^{17} + 16 q^{20} + 16 q^{25} - 16 q^{26} - 8 q^{27} - 8 q^{36} + 16 q^{41} + 16 q^{43} - 8 q^{45} - 16 q^{46} + 32 q^{47} - 8 q^{48} + 16 q^{51} + 32 q^{57} + 16 q^{58} + 32 q^{59} - 8 q^{60} + 16 q^{62} - 16 q^{64} + 16 q^{67} - 48 q^{68} - 8 q^{75} - 32 q^{78} - 48 q^{79} - 16 q^{80} + 8 q^{81} + 48 q^{83} - 48 q^{85} + 16 q^{89} - 64 q^{93} - 8 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 - 16 * q^4 - 16 * q^5 + 8 * q^9 + 8 * q^12 + 8 * q^15 + 16 * q^16 + 48 * q^17 + 16 * q^20 + 16 * q^25 - 16 * q^26 - 8 * q^27 - 8 * q^36 + 16 * q^41 + 16 * q^43 - 8 * q^45 - 16 * q^46 + 32 * q^47 - 8 * q^48 + 16 * q^51 + 32 * q^57 + 16 * q^58 + 32 * q^59 - 8 * q^60 + 16 * q^62 - 16 * q^64 + 16 * q^67 - 48 * q^68 - 8 * q^75 - 32 * q^78 - 48 * q^79 - 16 * q^80 + 8 * q^81 + 48 * q^83 - 48 * q^85 + 16 * q^89 - 64 * q^93 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.152807	−	1.72530i	0.0882230	−	0.996101i
$3$	0.152807	−	1.72530i	0.0882230	−	0.996101i
$4$	−1.00000			−0.500000
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.72530	+	0.152807i	0.704350	+	0.0623831i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−2.95330	−	0.527274i	−0.984433	−	0.175758i
$10$		−	1.00000i		−	0.316228i
$11$		−	0.476459i		−	0.143658i	−0.997417	−	0.0718290i	$-0.977116\pi$
$11$		−	0.476459i		−	0.143658i	0.997417	−	0.0718290i	$-0.0228836\pi$
$12$	−0.152807	+	1.72530i	−0.0441115	+	0.498050i
$13$			4.96165i			1.37611i	0.725656	+	0.688057i	$0.241536\pi$
$13$			4.96165i			1.37611i	−0.725656	+	0.688057i	$0.758464\pi$
$14$		0			0
$15$	−0.152807	+	1.72530i	−0.0394545	+	0.445470i
$16$	1.00000			0.250000
$17$	5.31590			1.28930			0.644648	−	0.764479i	$-0.277004\pi$
$17$	5.31590			1.28930			0.644648	+	0.764479i	$0.277004\pi$
$18$	0.527274	−	2.95330i	0.124280	−	0.696100i
$19$			5.18049i			1.18849i	0.804286	+	0.594243i	$0.202548\pi$
$19$			5.18049i			1.18849i	−0.804286	+	0.594243i	$0.797452\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	0.476459			0.101581
$23$		−	3.71381i		−	0.774383i	−0.921999	−	0.387191i	$-0.873445\pi$
$23$		−	3.71381i		−	0.774383i	0.921999	−	0.387191i	$-0.126555\pi$
$24$	−1.72530	−	0.152807i	−0.352175	−	0.0311915i
$25$	1.00000			0.200000
$26$	−4.96165			−0.973060
$27$	−1.36099	+	5.01475i	−0.261922	+	0.965089i
$28$		0			0
$29$		−	4.80278i		−	0.891853i	−0.895070	−	0.445926i	$-0.852874\pi$
$29$		−	4.80278i		−	0.891853i	0.895070	−	0.445926i	$-0.147126\pi$
$30$	−1.72530	−	0.152807i	−0.314995	−	0.0278986i
$31$		−	2.47917i		−	0.445271i	−0.974902	−	0.222636i	$-0.928534\pi$
$31$		−	2.47917i		−	0.445271i	0.974902	−	0.222636i	$-0.0714660\pi$
$32$			1.00000i			0.176777i
$33$	−0.822034	−	0.0728062i	−0.143098	−	0.0126739i
$34$			5.31590i			0.911670i
$35$		0			0
$36$	2.95330	+	0.527274i	0.492217	+	0.0878790i
$37$	2.38410			0.391943			0.195972	−	0.980610i	$-0.437214\pi$
$37$	2.38410			0.391943			0.195972	+	0.980610i	$0.437214\pi$
$38$	−5.18049			−0.840386
$39$	8.56033	+	0.758174i	1.37075	+	0.121405i
$40$			1.00000i			0.158114i
$41$	11.4897			1.79439			0.897194	−	0.441636i	$-0.145602\pi$
$41$	11.4897			1.79439			0.897194	+	0.441636i	$0.145602\pi$
$42$		0			0
$43$	1.38323			0.210940			0.105470	−	0.994422i	$-0.466365\pi$
$43$	1.38323			0.210940			0.105470	+	0.994422i	$0.466365\pi$
$44$			0.476459i			0.0718290i
$45$	2.95330	+	0.527274i	0.440252	+	0.0786013i
$46$	3.71381			0.547571
$47$	11.8319			1.72585			0.862927	−	0.505329i	$-0.168629\pi$
$47$	11.8319			1.72585			0.862927	+	0.505329i	$0.168629\pi$
$48$	0.152807	−	1.72530i	0.0220557	−	0.249025i
$49$		0			0
$50$			1.00000i			0.141421i
$51$	0.812306	−	9.17151i	0.113746	−	1.28427i
$52$		−	4.96165i		−	0.688057i
$53$			0.305714i			0.0419931i	0.999780	+	0.0209965i	$0.00668390\pi$
$53$			0.305714i			0.0419931i	−0.999780	+	0.0209965i	$0.993316\pi$
$54$	−5.01475	−	1.36099i	−0.682421	−	0.185207i
$55$			0.476459i			0.0642458i
$56$		0			0
$57$	8.93788	+	0.791613i	1.18385	+	0.104852i
$58$	4.80278			0.630635
$59$	−0.441038			−0.0574182			−0.0287091	−	0.999588i	$-0.509140\pi$
$59$	−0.441038			−0.0574182			−0.0287091	+	0.999588i	$0.509140\pi$
$60$	0.152807	−	1.72530i	0.0197273	−	0.222735i
$61$			12.2202i			1.56463i	0.622881	+	0.782317i	$0.285962\pi$
$61$			12.2202i			1.56463i	−0.622881	+	0.782317i	$0.714038\pi$
$62$	2.47917			0.314854
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	4.96165i		−	0.615417i
$66$	0.0728062	−	0.822034i	0.00896182	−	0.101185i
$67$	3.11989			0.381155			0.190577	−	0.981672i	$-0.438964\pi$
$67$	3.11989			0.381155			0.190577	+	0.981672i	$0.438964\pi$
$68$	−5.31590			−0.644648
$69$	−6.40743	−	0.567495i	−0.771363	−	0.0683184i
$70$		0			0
$71$		−	8.78061i		−	1.04207i	−0.853536	−	0.521033i	$-0.825547\pi$
$71$		−	8.78061i		−	1.04207i	0.853536	−	0.521033i	$-0.174453\pi$
$72$	−0.527274	+	2.95330i	−0.0621398	+	0.348050i
$73$		−	15.0920i		−	1.76639i	−0.469009	−	0.883193i	$-0.655389\pi$
$73$		−	15.0920i		−	1.76639i	0.469009	−	0.883193i	$-0.344611\pi$
$74$			2.38410i			0.277146i
$75$	0.152807	−	1.72530i	0.0176446	−	0.199220i
$76$		−	5.18049i		−	0.594243i
$77$		0			0
$78$	−0.758174	+	8.56033i	−0.0858463	+	0.969266i
$79$	1.77425			0.199618			0.0998091	−	0.995007i	$-0.468177\pi$
$79$	1.77425			0.199618			0.0998091	+	0.995007i	$0.468177\pi$
$80$	−1.00000			−0.111803
$81$	8.44396	+	3.11440i	0.938218	+	0.346044i
$82$			11.4897i			1.26882i
$83$	−14.2002			−1.55867			−0.779335	−	0.626607i	$-0.784443\pi$
$83$	−14.2002			−1.55867			−0.779335	+	0.626607i	$0.784443\pi$
$84$		0			0
$85$	−5.31590			−0.576591
$86$			1.38323i			0.149157i
$87$	−8.28621	−	0.733896i	−0.888375	−	0.0786819i
$88$	−0.476459			−0.0507907
$89$	5.22255			0.553590			0.276795	−	0.960929i	$-0.410728\pi$
$89$	5.22255			0.553590			0.276795	+	0.960929i	$0.410728\pi$
$90$	−0.527274	+	2.95330i	−0.0555795	+	0.311305i
$91$		0			0
$92$			3.71381i			0.387191i
$93$	−4.27730	−	0.378833i	−0.443535	−	0.0392832i
$94$			11.8319i			1.22036i
$95$		−	5.18049i		−	0.531507i
$96$	1.72530	+	0.152807i	0.176087	+	0.0155958i
$97$		−	8.50932i		−	0.863991i	−0.901876	−	0.431995i	$-0.857810\pi$
$97$		−	8.50932i		−	0.863991i	0.901876	−	0.431995i	$-0.142190\pi$
$98$		0			0
$99$	−0.251225	+	1.40713i	−0.0252490	+	0.141422i
$100$	−1.00000			−0.100000
$101$	16.8555			1.67719			0.838593	−	0.544759i	$-0.183379\pi$
$101$	16.8555			1.67719			0.838593	+	0.544759i	$0.183379\pi$
$102$	9.17151	+	0.812306i	0.908115	+	0.0804302i
$103$			8.84632i			0.871654i	0.900030	+	0.435827i	$0.143544\pi$
$103$			8.84632i			0.871654i	−0.900030	+	0.435827i	$0.856456\pi$
$104$	4.96165			0.486530
$105$		0			0
$106$	−0.305714			−0.0296936
$107$			12.0789i			1.16771i	0.811859	+	0.583853i	$0.198456\pi$
$107$			12.0789i			1.16771i	−0.811859	+	0.583853i	$0.801544\pi$
$108$	1.36099	−	5.01475i	0.130961	−	0.482544i
$109$	17.0390			1.63204			0.816021	−	0.578023i	$-0.196176\pi$
$109$	17.0390			1.63204			0.816021	+	0.578023i	$0.196176\pi$
$110$	−0.476459			−0.0454286
$111$	0.364306	−	4.11328i	0.0345784	−	0.390415i
$112$		0			0
$113$			5.63769i			0.530349i	0.964200	+	0.265175i	$0.0854296\pi$
$113$			5.63769i			0.530349i	−0.964200	+	0.265175i	$0.914570\pi$
$114$	−0.791613	+	8.93788i	−0.0741414	+	0.837110i
$115$			3.71381i			0.346315i
$116$			4.80278i			0.445926i
$117$	2.61615	−	14.6533i	0.241863	−	1.35469i
$118$		−	0.441038i		−	0.0406008i
$119$		0			0
$120$	1.72530	+	0.152807i	0.157497	+	0.0139493i
$121$	10.7730			0.979362
$122$	−12.2202			−1.10636
$123$	1.75570	−	19.8231i	0.158306	−	1.78739i
$124$			2.47917i			0.222636i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−8.02146			−0.711789			−0.355895	−	0.934526i	$-0.615824\pi$
$127$	−8.02146			−0.711789			−0.355895	+	0.934526i	$0.615824\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	0.211366	−	2.38648i	0.0186098	−	0.210118i
$130$	4.96165			0.435166
$131$	0.177016			0.0154660			0.00773298	−	0.999970i	$-0.497538\pi$
$131$	0.177016			0.0154660			0.00773298	+	0.999970i	$0.497538\pi$
$132$	0.822034	+	0.0728062i	0.0715489	+	0.00633696i
$133$		0			0
$134$			3.11989i			0.269517i
$135$	1.36099	−	5.01475i	0.117135	−	0.431601i
$136$		−	5.31590i		−	0.455835i
$137$			17.5798i			1.50194i	0.660334	+	0.750972i	$0.270415\pi$
$137$			17.5798i			1.50194i	−0.660334	+	0.750972i	$0.729585\pi$
$138$	0.567495	−	6.40743i	0.0483084	−	0.545436i
$139$			10.6911i			0.906811i	0.891304	+	0.453406i	$0.149791\pi$
$139$			10.6911i			0.906811i	−0.891304	+	0.453406i	$0.850209\pi$
$140$		0			0
$141$	1.80799	−	20.4135i	0.152260	−	1.71912i
$142$	8.78061			0.736853
$143$	2.36403			0.197690
$144$	−2.95330	−	0.527274i	−0.246108	−	0.0439395i
$145$			4.80278i			0.398849i
$146$	15.0920			1.24902
$147$		0			0
$148$	−2.38410			−0.195972
$149$			18.1696i			1.48851i	0.667895	+	0.744256i	$0.267196\pi$
$149$			18.1696i			1.48851i	−0.667895	+	0.744256i	$0.732804\pi$
$150$	1.72530	+	0.152807i	0.140870	+	0.0124766i
$151$	−18.2521			−1.48533			−0.742665	−	0.669663i	$-0.766439\pi$
$151$	−18.2521			−1.48533			−0.742665	+	0.669663i	$0.766439\pi$
$152$	5.18049			0.420193
$153$	−15.6995	−	2.80294i	−1.26923	−	0.226604i
$154$		0			0
$155$			2.47917i			0.199131i
$156$	−8.56033	−	0.758174i	−0.685375	−	0.0607025i
$157$			4.46872i			0.356643i	0.983972	+	0.178321i	$0.0570666\pi$
$157$			4.46872i			0.356643i	−0.983972	+	0.178321i	$0.942933\pi$
$158$			1.77425i			0.141151i
$159$	0.527448	+	0.0467152i	0.0418293	+	0.00370475i
$160$		−	1.00000i		−	0.0790569i
$161$		0			0
$162$	−3.11440	+	8.44396i	−0.244690	+	0.663421i
$163$	20.9070			1.63756			0.818780	−	0.574107i	$-0.194651\pi$
$163$	20.9070			1.63756			0.818780	+	0.574107i	$0.194651\pi$
$164$	−11.4897			−0.897194
$165$	0.822034	+	0.0728062i	0.0639953	+	0.00566795i
$166$		−	14.2002i		−	1.10215i
$167$	−8.40082			−0.650075			−0.325038	−	0.945701i	$-0.605377\pi$
$167$	−8.40082			−0.650075			−0.325038	+	0.945701i	$0.605377\pi$
$168$		0			0
$169$	−11.6180			−0.893692
$170$		−	5.31590i		−	0.407711i
$171$	2.73154	−	15.2995i	0.208886	−	1.16999i
$172$	−1.38323			−0.105470
$173$	−4.69254			−0.356767			−0.178383	−	0.983961i	$-0.557087\pi$
$173$	−4.69254			−0.356767			−0.178383	+	0.983961i	$0.557087\pi$
$174$	0.733896	−	8.28621i	0.0556365	−	0.628176i
$175$		0			0
$176$		−	0.476459i		−	0.0359145i
$177$	−0.0673935	+	0.760921i	−0.00506561	+	0.0571943i
$178$			5.22255i			0.391447i
$179$		−	21.6928i		−	1.62140i	−0.585462	−	0.810700i	$-0.699087\pi$
$179$		−	21.6928i		−	1.62140i	0.585462	−	0.810700i	$-0.300913\pi$
$180$	−2.95330	−	0.527274i	−0.220126	−	0.0393007i
$181$			8.38421i			0.623193i	0.950214	+	0.311597i	$0.100864\pi$
$181$			8.38421i			0.623193i	−0.950214	+	0.311597i	$0.899136\pi$
$182$		0			0
$183$	21.0834	+	1.86732i	1.55853	+	0.138037i
$184$	−3.71381			−0.273786
$185$	−2.38410			−0.175282
$186$	0.378833	−	4.27730i	0.0277774	−	0.313627i
$187$		−	2.53281i		−	0.185218i
$188$	−11.8319			−0.862927
$189$		0			0
$190$	5.18049			0.375832
$191$			8.58536i			0.621215i	0.950538	+	0.310607i	$0.100532\pi$
$191$			8.58536i			0.621215i	−0.950538	+	0.310607i	$0.899468\pi$
$192$	−0.152807	+	1.72530i	−0.0110279	+	0.124513i
$193$	−11.9098			−0.857289			−0.428644	−	0.903473i	$-0.641009\pi$
$193$	−11.9098			−0.857289			−0.428644	+	0.903473i	$0.641009\pi$
$194$	8.50932			0.610934
$195$	−8.56033	−	0.758174i	−0.613018	−	0.0542939i
$196$		0			0
$197$		−	18.0983i		−	1.28945i	−0.764413	−	0.644726i	$-0.776971\pi$
$197$		−	18.0983i		−	1.28945i	0.764413	−	0.644726i	$-0.223029\pi$
$198$	−1.40713	−	0.251225i	−0.100000	−	0.0178538i
$199$			10.6113i			0.752218i	0.926575	+	0.376109i	$0.122738\pi$
$199$			10.6113i			0.752218i	−0.926575	+	0.376109i	$0.877262\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	0.476740	−	5.38273i	0.0336266	−	0.379669i
$202$			16.8555i			1.18595i
$203$		0			0
$204$	−0.812306	+	9.17151i	−0.0568728	+	0.642134i
$205$	−11.4897			−0.802475
$206$	−8.84632			−0.616353
$207$	−1.95819	+	10.9680i	−0.136104	+	0.762328i
$208$			4.96165i			0.344029i
$209$	2.46829			0.170735
$210$		0			0
$211$	−13.8286			−0.952000			−0.476000	−	0.879445i	$-0.657914\pi$
$211$	−13.8286			−0.952000			−0.476000	+	0.879445i	$0.657914\pi$
$212$		−	0.305714i		−	0.0209965i
$213$	−15.1492	−	1.34174i	−1.03800	−	0.0919342i
$214$	−12.0789			−0.825693
$215$	−1.38323			−0.0943353
$216$	5.01475	+	1.36099i	0.341210	+	0.0926035i
$217$		0			0
$218$			17.0390i			1.15403i
$219$	−26.0382	−	2.30616i	−1.75950	−	0.155836i
$220$		−	0.476459i		−	0.0321229i
$221$			26.3757i			1.77422i
$222$	4.11328	+	0.364306i	0.276065	+	0.0244506i
$223$			1.39419i			0.0933618i	0.998910	+	0.0466809i	$0.0148644\pi$
$223$			1.39419i			0.0933618i	−0.998910	+	0.0466809i	$0.985136\pi$
$224$		0			0
$225$	−2.95330	−	0.527274i	−0.196887	−	0.0351516i
$226$	−5.63769			−0.375014
$227$	4.57266			0.303498			0.151749	−	0.988419i	$-0.451509\pi$
$227$	4.57266			0.303498			0.151749	+	0.988419i	$0.451509\pi$
$228$	−8.93788	−	0.791613i	−0.591926	−	0.0524259i
$229$		−	3.35629i		−	0.221790i	−0.993832	−	0.110895i	$-0.964628\pi$
$229$		−	3.35629i		−	0.221790i	0.993832	−	0.110895i	$-0.0353717\pi$
$230$	−3.71381			−0.244881
$231$		0			0
$232$	−4.80278			−0.315318
$233$		−	8.18807i		−	0.536418i	−0.963361	−	0.268209i	$-0.913568\pi$
$233$		−	8.18807i		−	0.536418i	0.963361	−	0.268209i	$-0.0864318\pi$
$234$	14.6533	+	2.61615i	0.957913	+	0.171023i
$235$	−11.8319			−0.771825
$236$	0.441038			0.0287091
$237$	0.271117	−	3.06110i	0.0176109	−	0.198840i
$238$		0			0
$239$		−	14.1670i		−	0.916387i	−0.888853	−	0.458193i	$-0.848497\pi$
$239$		−	14.1670i		−	0.916387i	0.888853	−	0.458193i	$-0.151503\pi$
$240$	−0.152807	+	1.72530i	−0.00986363	+	0.111367i
$241$			17.2184i			1.10914i	0.832139	+	0.554568i	$0.187116\pi$
$241$			17.2184i			1.10914i	−0.832139	+	0.554568i	$0.812884\pi$
$242$			10.7730i			0.692514i
$243$	6.66355	−	14.0924i	0.427467	−	0.904031i
$244$		−	12.2202i		−	0.782317i
$245$		0			0
$246$	19.8231	+	1.75570i	1.26388	+	0.111939i
$247$	−25.7038			−1.63549
$248$	−2.47917			−0.157427
$249$	−2.16988	+	24.4995i	−0.137511	+	1.55259i
$250$		−	1.00000i		−	0.0632456i
$251$	28.2916			1.78575			0.892875	−	0.450304i	$-0.148684\pi$
$251$	28.2916			1.78575			0.892875	+	0.450304i	$0.148684\pi$
$252$		0			0
$253$	−1.76948			−0.111246
$254$		−	8.02146i		−	0.503311i
$255$	−0.812306	+	9.17151i	−0.0508686	+	0.574342i
$256$	1.00000			0.0625000
$257$	−9.66976			−0.603183			−0.301591	−	0.953437i	$-0.597518\pi$
$257$	−9.66976			−0.603183			−0.301591	+	0.953437i	$0.597518\pi$
$258$	2.38648	+	0.211366i	0.148576	+	0.0131591i
$259$		0			0
$260$			4.96165i			0.307709i
$261$	−2.53238	+	14.1840i	−0.156750	+	0.877970i
$262$			0.177016i			0.0109361i
$263$		−	28.8130i		−	1.77668i	−0.459183	−	0.888342i	$-0.651858\pi$
$263$		−	28.8130i		−	1.77668i	0.459183	−	0.888342i	$-0.348142\pi$
$264$	−0.0728062	+	0.822034i	−0.00448091	+	0.0505927i
$265$		−	0.305714i		−	0.0187799i
$266$		0			0
$267$	0.798041	−	9.01046i	0.0488393	−	0.551431i
$268$	−3.11989			−0.190577
$269$	8.09812			0.493751			0.246876	−	0.969047i	$-0.420596\pi$
$269$	8.09812			0.493751			0.246876	+	0.969047i	$0.420596\pi$
$270$	5.01475	+	1.36099i	0.305188	+	0.0828271i
$271$			9.70895i			0.589777i	0.955532	+	0.294888i	$0.0952825\pi$
$271$			9.70895i			0.589777i	−0.955532	+	0.294888i	$0.904718\pi$
$272$	5.31590			0.322324
$273$		0			0
$274$	−17.5798			−1.06203
$275$		−	0.476459i		−	0.0287316i
$276$	6.40743	+	0.567495i	0.385682	+	0.0341592i
$277$	−30.2568			−1.81795			−0.908977	−	0.416846i	$-0.863135\pi$
$277$	−30.2568			−1.81795			−0.908977	+	0.416846i	$0.863135\pi$
$278$	−10.6911			−0.641212
$279$	−1.30720	+	7.32172i	−0.0782600	+	0.438340i
$280$		0			0
$281$			7.61243i			0.454120i	0.973881	+	0.227060i	$0.0729113\pi$
$281$			7.61243i			0.454120i	−0.973881	+	0.227060i	$0.927089\pi$
$282$	20.4135	+	1.80799i	1.21560	+	0.107664i
$283$			20.9933i			1.24792i	0.781456	+	0.623960i	$0.214477\pi$
$283$			20.9933i			1.24792i	−0.781456	+	0.623960i	$0.785523\pi$
$284$			8.78061i			0.521033i
$285$	−8.93788	−	0.791613i	−0.529435	−	0.0468911i
$286$			2.36403i			0.139788i
$287$		0			0
$288$	0.527274	−	2.95330i	0.0310699	−	0.174025i
$289$	11.2588			0.662285
$290$	−4.80278			−0.282029
$291$	−14.6811	−	1.30028i	−0.860622	−	0.0762239i
$292$			15.0920i			0.883193i
$293$	−30.8856			−1.80435			−0.902177	−	0.431365i	$-0.858032\pi$
$293$	−30.8856			−1.80435			−0.902177	+	0.431365i	$0.858032\pi$
$294$		0			0
$295$	0.441038			0.0256782
$296$		−	2.38410i		−	0.138573i
$297$	2.38932	+	0.648456i	0.138643	+	0.0376272i
$298$	−18.1696			−1.05254
$299$	18.4266			1.06564
$300$	−0.152807	+	1.72530i	−0.00882230	+	0.0996101i
$301$		0			0
$302$		−	18.2521i		−	1.05029i
$303$	2.57563	−	29.0808i	0.147966	−	1.67065i
$304$			5.18049i			0.297121i
$305$		−	12.2202i		−	0.699725i
$306$	2.80294	−	15.6995i	0.160233	−	0.897478i
$307$		−	24.0737i		−	1.37396i	−0.726678	−	0.686979i	$-0.758937\pi$
$307$		−	24.0737i		−	1.37396i	0.726678	−	0.686979i	$-0.241063\pi$
$308$		0			0
$309$	15.2625	+	1.35178i	0.868255	+	0.0768999i
$310$	−2.47917			−0.140807
$311$	−12.3799			−0.702000			−0.351000	−	0.936375i	$-0.614158\pi$
$311$	−12.3799			−0.702000			−0.351000	+	0.936375i	$0.614158\pi$
$312$	0.758174	−	8.56033i	0.0429231	−	0.484633i
$313$		−	8.19263i		−	0.463075i	−0.972826	−	0.231538i	$-0.925624\pi$
$313$		−	8.19263i		−	0.463075i	0.972826	−	0.231538i	$-0.0743756\pi$
$314$	−4.46872			−0.252184
$315$		0			0
$316$	−1.77425			−0.0998091
$317$			6.33601i			0.355866i	0.984043	+	0.177933i	$0.0569410\pi$
$317$			6.33601i			0.355866i	−0.984043	+	0.177933i	$0.943059\pi$
$318$	−0.0467152	+	0.527448i	−0.00261966	+	0.0295778i
$319$	−2.28833			−0.128122
$320$	1.00000			0.0559017
$321$	20.8396	+	1.84573i	1.16315	+	0.103019i
$322$		0			0
$323$			27.5390i			1.53231i
$324$	−8.44396	−	3.11440i	−0.469109	−	0.173022i
$325$			4.96165i			0.275223i
$326$			20.9070i			1.15793i
$327$	2.60367	−	29.3974i	0.143984	−	1.62568i
$328$		−	11.4897i		−	0.634412i
$329$		0			0
$330$	−0.0728062	+	0.822034i	−0.00400785	+	0.0452515i
$331$	15.6010			0.857508			0.428754	−	0.903421i	$-0.358953\pi$
$331$	15.6010			0.857508			0.428754	+	0.903421i	$0.358953\pi$
$332$	14.2002			0.779335
$333$	−7.04096	−	1.25707i	−0.385842	−	0.0688872i
$334$		−	8.40082i		−	0.459673i
$335$	−3.11989			−0.170458
$336$		0			0
$337$	2.76611			0.150679			0.0753397	−	0.997158i	$-0.475996\pi$
$337$	2.76611			0.150679			0.0753397	+	0.997158i	$0.475996\pi$
$338$		−	11.6180i		−	0.631936i
$339$	9.72669	+	0.861477i	0.528281	+	0.0467890i
$340$	5.31590			0.288295
$341$	−1.18122			−0.0639667
$342$	15.2995	+	2.73154i	0.827305	+	0.147705i
$343$		0			0
$344$		−	1.38323i		−	0.0745786i
$345$	6.40743	+	0.567495i	0.344964	+	0.0305529i
$346$		−	4.69254i		−	0.252272i
$347$		−	31.4496i		−	1.68830i	−0.536106	−	0.844151i	$-0.680105\pi$
$347$		−	31.4496i		−	1.68830i	0.536106	−	0.844151i	$-0.319895\pi$
$348$	8.28621	+	0.733896i	0.444188	+	0.0393410i
$349$			6.51210i			0.348585i	0.984694	+	0.174292i	$0.0557638\pi$
$349$			6.51210i			0.348585i	−0.984694	+	0.174292i	$0.944236\pi$
$350$		0			0
$351$	−24.8814	−	6.75275i	−1.32807	−	0.360435i
$352$	0.476459			0.0253954
$353$	33.0035			1.75660			0.878299	−	0.478111i	$-0.158678\pi$
$353$	33.0035			1.75660			0.878299	+	0.478111i	$0.158678\pi$
$354$	−0.760921	−	0.0673935i	−0.0404425	−	0.00358192i
$355$			8.78061i			0.466026i
$356$	−5.22255			−0.276795
$357$		0			0
$358$	21.6928			1.14650
$359$		−	21.2601i		−	1.12207i	−0.827793	−	0.561033i	$-0.810404\pi$
$359$		−	21.2601i		−	1.12207i	0.827793	−	0.561033i	$-0.189596\pi$
$360$	0.527274	−	2.95330i	0.0277898	−	0.155653i
$361$	−7.83748			−0.412499
$362$	−8.38421			−0.440664
$363$	1.64618	−	18.5866i	0.0864023	−	0.975544i
$364$		0			0
$365$			15.0920i			0.789952i
$366$	−1.86732	+	21.0834i	−0.0976066	+	1.10205i
$367$		−	0.576702i		−	0.0301036i	−0.999887	−	0.0150518i	$-0.995209\pi$
$367$		−	0.576702i		−	0.0301036i	0.999887	−	0.0150518i	$-0.00479132\pi$
$368$		−	3.71381i		−	0.193596i
$369$	−33.9325	−	6.05821i	−1.76646	−	0.315378i
$370$		−	2.38410i		−	0.123943i
$371$		0			0
$372$	4.27730	+	0.378833i	0.221768	+	0.0196416i
$373$	−11.2196			−0.580929			−0.290465	−	0.956886i	$-0.593810\pi$
$373$	−11.2196			−0.580929			−0.290465	+	0.956886i	$0.593810\pi$
$374$	2.53281			0.130969
$375$	−0.152807	+	1.72530i	−0.00789090	+	0.0890940i
$376$		−	11.8319i		−	0.610181i
$377$	23.8297			1.22729
$378$		0			0
$379$	13.4189			0.689283			0.344641	−	0.938734i	$-0.388000\pi$
$379$	13.4189			0.689283			0.344641	+	0.938734i	$0.388000\pi$
$380$			5.18049i			0.265754i
$381$	−1.22573	+	13.8394i	−0.0627962	+	0.709014i
$382$	−8.58536			−0.439265
$383$	−27.0366			−1.38151			−0.690754	−	0.723090i	$-0.742721\pi$
$383$	−27.0366			−1.38151			−0.690754	+	0.723090i	$0.742721\pi$
$384$	−1.72530	−	0.152807i	−0.0880437	−	0.00779788i
$385$		0			0
$386$		−	11.9098i		−	0.606195i
$387$	−4.08509	−	0.729340i	−0.207657	−	0.0370744i
$388$			8.50932i			0.431995i
$389$			1.50672i			0.0763938i	0.999270	+	0.0381969i	$0.0121614\pi$
$389$			1.50672i			0.0763938i	−0.999270	+	0.0381969i	$0.987839\pi$
$390$	0.758174	−	8.56033i	0.0383916	−	0.433469i
$391$		−	19.7423i		−	0.998409i
$392$		0			0
$393$	0.0270492	−	0.305405i	0.00136445	−	0.0154057i
$394$	18.0983			0.911781
$395$	−1.77425			−0.0892720
$396$	0.251225	−	1.40713i	0.0126245	−	0.0707108i
$397$		−	17.3237i		−	0.869449i	−0.900563	−	0.434725i	$-0.856846\pi$
$397$		−	17.3237i		−	0.869449i	0.900563	−	0.434725i	$-0.143154\pi$
$398$	−10.6113			−0.531899
$399$		0			0
$400$	1.00000			0.0500000
$401$			12.6888i			0.633647i	0.948485	+	0.316823i	$0.102616\pi$
$401$			12.6888i			0.633647i	−0.948485	+	0.316823i	$0.897384\pi$
$402$	5.38273	+	0.476740i	0.268466	+	0.0237776i
$403$	12.3008			0.612744
$404$	−16.8555			−0.838593
$405$	−8.44396	−	3.11440i	−0.419584	−	0.154756i
$406$		0			0
$407$		−	1.13593i		−	0.0563058i
$408$	−9.17151	−	0.812306i	−0.454058	−	0.0402151i
$409$			20.8434i			1.03064i	0.856998	+	0.515320i	$0.172327\pi$
$409$			20.8434i			1.03064i	−0.856998	+	0.515320i	$0.827673\pi$
$410$		−	11.4897i		−	0.567435i
$411$	30.3304	+	2.68631i	1.49609	+	0.132506i
$412$		−	8.84632i		−	0.435827i
$413$		0			0
$414$	−10.9680	−	1.95819i	−0.539048	−	0.0962400i
$415$	14.2002			0.697058
$416$	−4.96165			−0.243265
$417$	18.4454	+	1.63368i	0.903275	+	0.0800016i
$418$			2.46829i			0.120728i
$419$	29.3248			1.43261			0.716306	−	0.697787i	$-0.245832\pi$
$419$	29.3248			1.43261			0.716306	+	0.697787i	$0.245832\pi$
$420$		0			0
$421$	−19.3254			−0.941861			−0.470931	−	0.882170i	$-0.656082\pi$
$421$	−19.3254			−0.941861			−0.470931	+	0.882170i	$0.656082\pi$
$422$		−	13.8286i		−	0.673166i
$423$	−34.9430	−	6.23863i	−1.69899	−	0.303332i
$424$	0.305714			0.0148468
$425$	5.31590			0.257859
$426$	1.34174	−	15.1492i	0.0650073	−	0.733979i
$427$		0			0
$428$		−	12.0789i		−	0.583853i
$429$	0.361239	−	4.07865i	0.0174408	−	0.196919i
$430$		−	1.38323i		−	0.0667052i
$431$			17.9318i			0.863743i	0.901935	+	0.431871i	$0.142147\pi$
$431$			17.9318i			0.863743i	−0.901935	+	0.431871i	$0.857853\pi$
$432$	−1.36099	+	5.01475i	−0.0654806	+	0.241272i
$433$		−	2.79305i		−	0.134225i	−0.997745	−	0.0671127i	$-0.978621\pi$
$433$		−	2.79305i		−	0.134225i	0.997745	−	0.0671127i	$-0.0213787\pi$
$434$		0			0
$435$	8.28621	+	0.733896i	0.397294	+	0.0351876i
$436$	−17.0390			−0.816021
$437$	19.2394			0.920343
$438$	2.30616	−	26.0382i	0.110193	−	1.24415i
$439$		−	15.1652i		−	0.723795i	−0.932218	−	0.361898i	$-0.882129\pi$
$439$		−	15.1652i		−	0.723795i	0.932218	−	0.361898i	$-0.117871\pi$
$440$	0.476459			0.0227143
$441$		0			0
$442$	−26.3757			−1.25456
$443$		−	5.62647i		−	0.267322i	−0.991027	−	0.133661i	$-0.957327\pi$
$443$		−	5.62647i		−	0.267322i	0.991027	−	0.133661i	$-0.0426733\pi$
$444$	−0.364306	+	4.11328i	−0.0172892	+	0.195208i
$445$	−5.22255			−0.247573
$446$	−1.39419			−0.0660168
$447$	31.3480	+	2.77644i	1.48271	+	0.131321i
$448$		0			0
$449$			13.6625i			0.644775i	0.946608	+	0.322388i	$0.104485\pi$
$449$			13.6625i			0.644775i	−0.946608	+	0.322388i	$0.895515\pi$
$450$	0.527274	−	2.95330i	0.0248559	−	0.139220i
$451$		−	5.47437i		−	0.257778i
$452$		−	5.63769i		−	0.265175i
$453$	−2.78904	+	31.4902i	−0.131040	+	1.47954i
$454$			4.57266i			0.214606i
$455$		0			0
$456$	0.791613	−	8.93788i	0.0370707	−	0.418555i
$457$	−3.70391			−0.173262			−0.0866309	−	0.996240i	$-0.527610\pi$
$457$	−3.70391			−0.173262			−0.0866309	+	0.996240i	$0.527610\pi$
$458$	3.35629			0.156829
$459$	−7.23488	+	26.6579i	−0.337695	+	1.24429i
$460$		−	3.71381i		−	0.173157i
$461$	−23.6183			−1.10001			−0.550007	−	0.835160i	$-0.685375\pi$
$461$	−23.6183			−1.10001			−0.550007	+	0.835160i	$0.685375\pi$
$462$		0			0
$463$	−24.8440			−1.15460			−0.577298	−	0.816533i	$-0.695893\pi$
$463$	−24.8440			−1.15460			−0.577298	+	0.816533i	$0.695893\pi$
$464$		−	4.80278i		−	0.222963i
$465$	4.27730	+	0.378833i	0.198355	+	0.0175680i
$466$	8.18807			0.379305
$467$	−18.2254			−0.843369			−0.421685	−	0.906743i	$-0.638561\pi$
$467$	−18.2254			−0.843369			−0.421685	+	0.906743i	$0.638561\pi$
$468$	−2.61615	+	14.6533i	−0.120932	+	0.677347i
$469$		0			0
$470$		−	11.8319i		−	0.545763i
$471$	7.70987	+	0.682850i	0.355252	+	0.0314641i
$472$			0.441038i			0.0203004i
$473$		−	0.659052i		−	0.0303032i
$474$	3.06110	+	0.271117i	0.140601	+	0.0124528i
$475$			5.18049i			0.237697i
$476$		0			0
$477$	0.161195	−	0.902866i	0.00738062	−	0.0413394i
$478$	14.1670			0.647983
$479$	−31.2048			−1.42578			−0.712891	−	0.701275i	$-0.752614\pi$
$479$	−31.2048			−1.42578			−0.712891	+	0.701275i	$0.752614\pi$
$480$	−1.72530	−	0.152807i	−0.0787487	−	0.00697464i
$481$			11.8291i			0.539359i
$482$	−17.2184			−0.784277
$483$		0			0
$484$	−10.7730			−0.489681
$485$			8.50932i			0.386389i
$486$	14.0924	+	6.66355i	0.639246	+	0.302265i
$487$	4.62293			0.209485			0.104743	−	0.994499i	$-0.466598\pi$
$487$	4.62293			0.209485			0.104743	+	0.994499i	$0.466598\pi$
$488$	12.2202			0.553181
$489$	3.19472	−	36.0707i	0.144470	−	1.63118i
$490$		0			0
$491$		−	14.9468i		−	0.674540i	−0.941408	−	0.337270i	$-0.890496\pi$
$491$		−	14.9468i		−	0.674540i	0.941408	−	0.337270i	$-0.109504\pi$
$492$	−1.75570	+	19.8231i	−0.0791531	+	0.893696i
$493$		−	25.5311i		−	1.14986i
$494$		−	25.7038i		−	1.15647i
$495$	0.251225	−	1.40713i	0.0112917	−	0.0632457i
$496$		−	2.47917i		−	0.111318i
$497$		0			0
$498$	−24.4995	−	2.16988i	−1.09785	−	0.0972346i
$499$	−12.5355			−0.561166			−0.280583	−	0.959830i	$-0.590528\pi$
$499$	−12.5355			−0.561166			−0.280583	+	0.959830i	$0.590528\pi$
$500$	1.00000			0.0447214
$501$	−1.28370	+	14.4939i	−0.0573516	+	0.647541i
$502$			28.2916i			1.26272i
$503$	−26.5310			−1.18296			−0.591479	−	0.806320i	$-0.701456\pi$
$503$	−26.5310			−1.18296			−0.591479	+	0.806320i	$0.701456\pi$
$504$		0			0
$505$	−16.8555			−0.750060
$506$		−	1.76948i		−	0.0786630i
$507$	−1.77531	+	20.0445i	−0.0788442	+	0.890208i
$508$	8.02146			0.355895
$509$	25.8107			1.14404			0.572020	−	0.820240i	$-0.306160\pi$
$509$	25.8107			1.14404			0.572020	+	0.820240i	$0.306160\pi$
$510$	−9.17151	−	0.812306i	−0.406121	−	0.0359695i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	−25.9789	−	7.05058i	−1.14699	−	0.311291i
$514$		−	9.66976i		−	0.426515i
$515$		−	8.84632i		−	0.389816i
$516$	−0.211366	+	2.38648i	−0.00930489	+	0.105059i
$517$		−	5.63740i		−	0.247933i
$518$		0			0
$519$	−0.717051	+	8.09602i	−0.0314750	+	0.355376i
$520$	−4.96165			−0.217583
$521$	7.06140			0.309366			0.154683	−	0.987964i	$-0.450564\pi$
$521$	7.06140			0.309366			0.154683	+	0.987964i	$0.450564\pi$
$522$	−14.1840	−	2.53238i	−0.620818	−	0.110839i
$523$		−	37.2776i		−	1.63003i	−0.579437	−	0.815017i	$-0.696727\pi$
$523$		−	37.2776i		−	1.63003i	0.579437	−	0.815017i	$-0.303273\pi$
$524$	−0.177016			−0.00773298
$525$		0			0
$526$	28.8130			1.25630
$527$		−	13.1790i		−	0.574087i
$528$	−0.822034	−	0.0728062i	−0.0357744	−	0.00316848i
$529$	9.20762			0.400331
$530$	0.305714			0.0132794
$531$	1.30252	+	0.232548i	0.0565244	+	0.0100917i
$532$		0			0
$533$			57.0079i			2.46928i
$534$	9.01046	+	0.798041i	0.389921	+	0.0345346i
$535$		−	12.0789i		−	0.522214i
$536$		−	3.11989i		−	0.134759i
$537$	−37.4266	−	3.31481i	−1.61508	−	0.143045i
$538$			8.09812i			0.349135i
$539$		0			0
$540$	−1.36099	+	5.01475i	−0.0585676	+	0.215800i
$541$	35.2331			1.51479			0.757395	−	0.652957i	$-0.226472\pi$
$541$	35.2331			1.51479			0.757395	+	0.652957i	$0.226472\pi$
$542$	−9.70895			−0.417035
$543$	14.4652	+	1.28116i	0.620763	+	0.0549799i
$544$			5.31590i			0.227918i
$545$	−17.0390			−0.729871
$546$		0			0
$547$	35.3886			1.51311			0.756554	−	0.653932i	$-0.226882\pi$
$547$	35.3886			1.51311			0.756554	+	0.653932i	$0.226882\pi$
$548$		−	17.5798i		−	0.750972i
$549$	6.44338	−	36.0899i	0.274997	−	1.54028i
$550$	0.476459			0.0203163
$551$	24.8807			1.05995
$552$	−0.567495	+	6.40743i	−0.0241542	+	0.272718i
$553$		0			0
$554$		−	30.2568i		−	1.28549i
$555$	−0.364306	+	4.11328i	−0.0154639	+	0.174599i
$556$		−	10.6911i		−	0.453406i
$557$			29.1977i			1.23715i	0.785727	+	0.618574i	$0.212289\pi$
$557$			29.1977i			1.23715i	−0.785727	+	0.618574i	$0.787711\pi$
$558$	−7.32172	−	1.30720i	−0.309953	−	0.0553382i
$559$			6.86310i			0.290278i
$560$		0			0
$561$	−4.36985	−	0.387031i	−0.184495	−	0.0163404i
$562$	−7.61243			−0.321111
$563$	−2.62310			−0.110551			−0.0552753	−	0.998471i	$-0.517604\pi$
$563$	−2.62310			−0.110551			−0.0552753	+	0.998471i	$0.517604\pi$
$564$	−1.80799	+	20.4135i	−0.0761300	+	0.859562i
$565$		−	5.63769i		−	0.237179i
$566$	−20.9933			−0.882412
$567$		0			0
$568$	−8.78061			−0.368426
$569$		−	35.1149i		−	1.47209i	−0.676931	−	0.736046i	$-0.736691\pi$
$569$		−	35.1149i		−	1.47209i	0.676931	−	0.736046i	$-0.263309\pi$
$570$	0.791613	−	8.93788i	0.0331570	−	0.374367i
$571$	27.9169			1.16829			0.584143	−	0.811651i	$-0.301431\pi$
$571$	27.9169			1.16829			0.584143	+	0.811651i	$0.301431\pi$
$572$	−2.36403			−0.0988449
$573$	14.8123	+	1.31190i	0.618792	+	0.0548054i
$574$		0			0
$575$		−	3.71381i		−	0.154877i
$576$	2.95330	+	0.527274i	0.123054	+	0.0219697i
$577$		−	29.2752i		−	1.21874i	−0.792884	−	0.609372i	$-0.791422\pi$
$577$		−	29.2752i		−	1.21874i	0.792884	−	0.609372i	$-0.208578\pi$
$578$			11.2588i			0.468306i
$579$	−1.81990	+	20.5480i	−0.0756326	+	0.853946i
$580$		−	4.80278i		−	0.199424i
$581$		0			0
$582$	1.30028	−	14.6811i	0.0538984	−	0.608552i
$583$	0.145660			0.00603264
$584$	−15.0920			−0.624512
$585$	−2.61615	+	14.6533i	−0.108164	+	0.605837i
$586$		−	30.8856i		−	1.27587i
$587$	32.6568			1.34789			0.673944	−	0.738782i	$-0.264599\pi$
$587$	32.6568			1.34789			0.673944	+	0.738782i	$0.264599\pi$
$588$		0			0
$589$	12.8433			0.529199
$590$			0.441038i			0.0181572i
$591$	−31.2250	−	2.76555i	−1.28442	−	0.113759i
$592$	2.38410			0.0979858
$593$	−29.8459			−1.22562			−0.612812	−	0.790228i	$-0.709962\pi$
$593$	−29.8459			−1.22562			−0.612812	+	0.790228i	$0.709962\pi$
$594$	−0.648456	+	2.38932i	−0.0266065	+	0.0980352i
$595$		0			0
$596$		−	18.1696i		−	0.744256i
$597$	18.3077	+	1.62148i	0.749285	+	0.0663630i
$598$			18.4266i			0.753521i
$599$		−	38.9952i		−	1.59330i	−0.604441	−	0.796650i	$-0.706604\pi$
$599$		−	38.9952i		−	1.59330i	0.604441	−	0.796650i	$-0.293396\pi$
$600$	−1.72530	−	0.152807i	−0.0704350	−	0.00623831i
$601$			12.0833i			0.492890i	0.969157	+	0.246445i	$0.0792624\pi$
$601$			12.0833i			0.492890i	−0.969157	+	0.246445i	$0.920738\pi$
$602$		0			0
$603$	−9.21396	−	1.64503i	−0.375222	−	0.0669910i
$604$	18.2521			0.742665
$605$	−10.7730			−0.437984
$606$	29.0808	+	2.57563i	1.18132	+	0.104628i
$607$			9.81922i			0.398550i	0.979944	+	0.199275i	$0.0638587\pi$
$607$			9.81922i			0.398550i	−0.979944	+	0.199275i	$0.936141\pi$
$608$	−5.18049			−0.210097
$609$		0			0
$610$	12.2202			0.494781
$611$			58.7056i			2.37497i
$612$	15.6995	+	2.80294i	0.634613	+	0.113302i
$613$	−9.51280			−0.384218			−0.192109	−	0.981374i	$-0.561533\pi$
$613$	−9.51280			−0.384218			−0.192109	+	0.981374i	$0.561533\pi$
$614$	24.0737			0.971534
$615$	−1.75570	+	19.8231i	−0.0707967	+	0.799346i
$616$		0			0
$617$			29.8611i			1.20216i	0.799188	+	0.601081i	$0.205263\pi$
$617$			29.8611i			1.20216i	−0.799188	+	0.601081i	$0.794737\pi$
$618$	−1.35178	+	15.2625i	−0.0543765	+	0.613949i
$619$		−	39.2407i		−	1.57722i	−0.614895	−	0.788609i	$-0.710802\pi$
$619$		−	39.2407i		−	1.57722i	0.614895	−	0.788609i	$-0.289198\pi$
$620$		−	2.47917i		−	0.0995657i
$621$	18.6238	+	5.05445i	0.747348	+	0.202828i
$622$		−	12.3799i		−	0.496389i
$623$		0			0
$624$	8.56033	+	0.758174i	0.342687	+	0.0303512i
$625$	1.00000			0.0400000
$626$	8.19263			0.327443
$627$	0.377172	−	4.25854i	0.0150628	−	0.170070i
$628$		−	4.46872i		−	0.178321i
$629$	12.6736			0.505331
$630$		0			0
$631$	19.6654			0.782868			0.391434	−	0.920206i	$-0.371979\pi$
$631$	19.6654			0.782868			0.391434	+	0.920206i	$0.371979\pi$
$632$		−	1.77425i		−	0.0705757i
$633$	−2.11310	+	23.8585i	−0.0839883	+	0.948288i
$634$	−6.33601			−0.251635
$635$	8.02146			0.318322
$636$	−0.527448	−	0.0467152i	−0.0209147	−	0.00185238i
$637$		0			0
$638$		−	2.28833i		−	0.0905958i
$639$	−4.62979	+	25.9318i	−0.183152	+	1.02585i
$640$			1.00000i			0.0395285i
$641$			14.8980i			0.588435i	0.955739	+	0.294217i	$0.0950590\pi$
$641$			14.8980i			0.588435i	−0.955739	+	0.294217i	$0.904941\pi$
$642$	−1.84573	+	20.8396i	−0.0728451	+	0.822474i
$643$			46.9493i			1.85150i	0.378134	+	0.925751i	$0.376566\pi$
$643$			46.9493i			1.85150i	−0.378134	+	0.925751i	$0.623434\pi$
$644$		0			0
$645$	−0.211366	+	2.38648i	−0.00832254	+	0.0939675i
$646$	−27.5390			−1.08351
$647$	−9.56306			−0.375963			−0.187981	−	0.982173i	$-0.560194\pi$
$647$	−9.56306			−0.375963			−0.187981	+	0.982173i	$0.560194\pi$
$648$	3.11440	−	8.44396i	0.122345	−	0.331710i
$649$			0.210137i			0.00824858i
$650$	−4.96165			−0.194612
$651$		0			0
$652$	−20.9070			−0.818780
$653$			7.62005i			0.298195i	0.988822	+	0.149098i	$0.0476369\pi$
$653$			7.62005i			0.298195i	−0.988822	+	0.149098i	$0.952363\pi$
$654$	29.3974	+	2.60367i	1.14953	+	0.101812i
$655$	−0.177016			−0.00691659
$656$	11.4897			0.448597
$657$	−7.95762	+	44.5712i	−0.310456	+	1.73889i
$658$		0			0
$659$			19.0410i			0.741731i	0.928686	+	0.370866i	$0.120939\pi$
$659$			19.0410i			0.741731i	−0.928686	+	0.370866i	$0.879061\pi$
$660$	−0.822034	−	0.0728062i	−0.0319976	−	0.00283398i
$661$			37.8335i			1.47155i	0.677224	+	0.735777i	$0.263183\pi$
$661$			37.8335i			1.47155i	−0.677224	+	0.735777i	$0.736817\pi$
$662$			15.6010i			0.606349i
$663$	45.5059	+	4.03038i	1.76730	+	0.156527i
$664$			14.2002i			0.551073i
$665$		0			0
$666$	1.25707	−	7.04096i	0.0487106	−	0.272832i
$667$	−17.8366			−0.690636
$668$	8.40082			0.325038
$669$	2.40539	+	0.213041i	0.0929978	+	0.00823666i
$670$		−	3.11989i		−	0.120532i
$671$	5.82242			0.224772
$672$		0			0
$673$	22.8824			0.882052			0.441026	−	0.897494i	$-0.354615\pi$
$673$	22.8824			0.882052			0.441026	+	0.897494i	$0.354615\pi$
$674$			2.76611i			0.106546i
$675$	−1.36099	+	5.01475i	−0.0523845	+	0.193018i
$676$	11.6180			0.446846
$677$	11.0909			0.426257			0.213128	−	0.977024i	$-0.431635\pi$
$677$	11.0909			0.426257			0.213128	+	0.977024i	$0.431635\pi$
$678$	−0.861477	+	9.72669i	−0.0330848	+	0.373551i
$679$		0			0
$680$			5.31590i			0.203856i
$681$	0.698734	−	7.88920i	0.0267755	−	0.302315i
$682$		−	1.18122i		−	0.0452313i
$683$			6.84051i			0.261745i	0.991399	+	0.130873i	$0.0417779\pi$
$683$			6.84051i			0.261745i	−0.991399	+	0.130873i	$0.958222\pi$
$684$	−2.73154	+	15.2995i	−0.104443	+	0.584993i
$685$		−	17.5798i		−	0.671690i
$686$		0			0
$687$	−5.79059	−	0.512863i	−0.220925	−	0.0195669i
$688$	1.38323			0.0527351
$689$	−1.51685			−0.0577873
$690$	−0.567495	+	6.40743i	−0.0216042	+	0.243927i
$691$			44.5919i			1.69635i	0.529713	+	0.848177i	$0.322300\pi$
$691$			44.5919i			1.69635i	−0.529713	+	0.848177i	$0.677700\pi$
$692$	4.69254			0.178383
$693$		0			0
$694$	31.4496			1.19381
$695$		−	10.6911i		−	0.405538i
$696$	−0.733896	+	8.28621i	−0.0278183	+	0.314088i
$697$	61.0781			2.31350
$698$	−6.51210			−0.246487
$699$	−14.1268	−	1.25119i	−0.534326	−	0.0473244i
$700$		0			0
$701$			30.2838i			1.14380i	0.820323	+	0.571901i	$0.193794\pi$
$701$			30.2838i			1.14380i	−0.820323	+	0.571901i	$0.806206\pi$
$702$	6.75275	−	24.8814i	0.254866	−	0.939090i
$703$			12.3508i			0.465819i
$704$			0.476459i			0.0179572i
$705$	−1.80799	+	20.4135i	−0.0680927	+	0.768816i
$706$			33.0035i			1.24210i
$707$		0			0
$708$	0.0673935	−	0.760921i	0.00253280	−	0.0285972i
$709$	8.53467			0.320526			0.160263	−	0.987074i	$-0.448766\pi$
$709$	8.53467			0.320526			0.160263	+	0.987074i	$0.448766\pi$
$710$	−8.78061			−0.329530
$711$	−5.23988	−	0.935513i	−0.196511	−	0.0350845i
$712$		−	5.22255i		−	0.195723i
$713$	−9.20715			−0.344810
$714$		0			0
$715$	−2.36403			−0.0884096
$716$			21.6928i			0.810700i
$717$	−24.4423	−	2.16481i	−0.912813	−	0.0808464i
$718$	21.2601			0.793421
$719$	4.23143			0.157806			0.0789029	−	0.996882i	$-0.474858\pi$
$719$	4.23143			0.157806			0.0789029	+	0.996882i	$0.474858\pi$
$720$	2.95330	+	0.527274i	0.110063	+	0.0196503i
$721$		0			0
$722$		−	7.83748i		−	0.291681i
$723$	29.7069	+	2.63109i	1.10481	+	0.0978512i
$724$		−	8.38421i		−	0.311597i
$725$		−	4.80278i		−	0.178371i
$726$	18.5866	+	1.64618i	0.689814	+	0.0610956i
$727$		−	5.91343i		−	0.219317i	−0.993969	−	0.109658i	$-0.965024\pi$
$727$		−	5.91343i		−	0.219317i	0.993969	−	0.109658i	$-0.0349757\pi$
$728$		0			0
$729$	−23.2954	−	13.6500i	−0.862793	−	0.505557i
$730$	−15.0920			−0.558580
$731$	7.35311			0.271964
$732$	−21.0834	−	1.86732i	−0.779266	−	0.0690183i
$733$			33.5690i			1.23990i	0.784642	+	0.619949i	$0.212847\pi$
$733$			33.5690i			1.23990i	−0.784642	+	0.619949i	$0.787153\pi$
$734$	0.576702			0.0212865
$735$		0			0
$736$	3.71381			0.136893
$737$		−	1.48650i		−	0.0547559i
$738$	6.05821	−	33.9325i	0.223006	−	1.24907i
$739$	−40.3871			−1.48566			−0.742831	−	0.669479i	$-0.766517\pi$
$739$	−40.3871			−1.48566			−0.742831	+	0.669479i	$0.766517\pi$
$740$	2.38410			0.0876412
$741$	−3.92771	+	44.3467i	−0.144288	+	1.62912i
$742$		0			0
$743$		−	23.9431i		−	0.878386i	−0.898393	−	0.439193i	$-0.855264\pi$
$743$		−	23.9431i		−	0.878386i	0.898393	−	0.439193i	$-0.144736\pi$
$744$	−0.378833	+	4.27730i	−0.0138887	+	0.156813i
$745$		−	18.1696i		−	0.665683i
$746$		−	11.2196i		−	0.410779i
$747$	41.9373	+	7.48737i	1.53441	+	0.273949i
$748$			2.53281i			0.0926088i
$749$		0			0
$750$	−1.72530	−	0.152807i	−0.0629989	−	0.00557971i
$751$	−25.5556			−0.932535			−0.466268	−	0.884644i	$-0.654402\pi$
$751$	−25.5556			−0.932535			−0.466268	+	0.884644i	$0.654402\pi$
$752$	11.8319			0.431463
$753$	4.32315	−	48.8114i	0.157544	−	1.77879i
$754$			23.8297i			0.867827i
$755$	18.2521			0.664260
$756$		0			0
$757$	44.0619			1.60146			0.800728	−	0.599028i	$-0.204446\pi$
$757$	44.0619			1.60146			0.800728	+	0.599028i	$0.204446\pi$
$758$			13.4189i			0.487397i
$759$	−0.270388	+	3.05288i	−0.00981447	+	0.110812i
$760$	−5.18049			−0.187916
$761$	−38.9175			−1.41076			−0.705380	−	0.708830i	$-0.749224\pi$
$761$	−38.9175			−1.41076			−0.705380	+	0.708830i	$0.749224\pi$
$762$	−13.8394	−	1.22573i	−0.501348	−	0.0444036i
$763$		0			0
$764$		−	8.58536i		−	0.310607i
$765$	15.6995	+	2.80294i	0.567615	+	0.101340i
$766$		−	27.0366i		−	0.976873i
$767$		−	2.18828i		−	0.0790141i
$768$	0.152807	−	1.72530i	0.00551394	−	0.0622563i
$769$		−	11.2174i		−	0.404508i	−0.979333	−	0.202254i	$-0.935173\pi$
$769$		−	11.2174i		−	0.404508i	0.979333	−	0.202254i	$-0.0648267\pi$
$770$		0			0
$771$	−1.47760	+	16.6832i	−0.0532146	+	0.600831i
$772$	11.9098			0.428644
$773$	−15.9211			−0.572642			−0.286321	−	0.958134i	$-0.592432\pi$
$773$	−15.9211			−0.572642			−0.286321	+	0.958134i	$0.592432\pi$
$774$	0.729340	−	4.08509i	0.0262156	−	0.146835i
$775$		−	2.47917i		−	0.0890543i
$776$	−8.50932			−0.305467
$777$		0			0
$778$	−1.50672			−0.0540186
$779$			59.5222i			2.13261i
$780$	8.56033	+	0.758174i	0.306509	+	0.0271470i
$781$	−4.18360			−0.149701
$782$	19.7423			0.705982
$783$	24.0847	+	6.53652i	0.860717	+	0.233596i
$784$		0			0
$785$		−	4.46872i		−	0.159495i
$786$	0.305405	+	0.0270492i	0.0108934	+	0.000964815i
$787$		−	14.9125i		−	0.531574i	−0.964032	−	0.265787i	$-0.914368\pi$
$787$		−	14.9125i		−	0.531574i	0.964032	−	0.265787i	$-0.0856318\pi$
$788$			18.0983i			0.644726i
$789$	−49.7109	−	4.40281i	−1.76976	−	0.156744i
$790$		−	1.77425i		−	0.0631248i
$791$		0			0
$792$	1.40713	+	0.251225i	0.0500001	+	0.00892688i
$793$	−60.6323			−2.15312
$794$	17.3237			0.614794
$795$	−0.527448	−	0.0467152i	−0.0187066	−	0.00165682i
$796$		−	10.6113i		−	0.376109i
$797$	−32.9042			−1.16553			−0.582763	−	0.812642i	$-0.698028\pi$
$797$	−32.9042			−1.16553			−0.582763	+	0.812642i	$0.698028\pi$
$798$		0			0
$799$	62.8970			2.22514
$800$			1.00000i			0.0353553i
$801$	−15.4238	−	2.75372i	−0.544972	−	0.0972978i
$802$	−12.6888			−0.448056
$803$	−7.19073			−0.253755
$804$	−0.476740	+	5.38273i	−0.0168133	+	0.189834i
$805$		0			0
$806$			12.3008i			0.433276i
$807$	1.23745	−	13.9717i	0.0435602	−	0.491826i
$808$		−	16.8555i		−	0.592975i
$809$		−	18.8026i		−	0.661065i	−0.943795	−	0.330533i	$-0.892772\pi$
$809$		−	18.8026i		−	0.661065i	0.943795	−	0.330533i	$-0.107228\pi$
$810$	3.11440	−	8.44396i	0.109429	−	0.296691i
$811$		−	24.4435i		−	0.858328i	−0.903227	−	0.429164i	$-0.858808\pi$
$811$		−	24.4435i		−	0.858328i	0.903227	−	0.429164i	$-0.141192\pi$
$812$		0			0
$813$	16.7508	+	1.48359i	0.587477	+	0.0520319i
$814$	1.13593			0.0398142
$815$	−20.9070			−0.732339
$816$	0.812306	−	9.17151i	0.0284364	−	0.321067i
$817$			7.16580i			0.250700i
$818$	−20.8434			−0.728772
$819$		0			0
$820$	11.4897			0.401237
$821$		−	2.67349i		−	0.0933054i	−0.998911	−	0.0466527i	$-0.985145\pi$
$821$		−	2.67349i		−	0.0933054i	0.998911	−	0.0466527i	$-0.0148554\pi$
$822$	−2.68631	+	30.3304i	−0.0936959	+	1.05789i
$823$	38.5503			1.34378			0.671890	−	0.740651i	$-0.265483\pi$
$823$	38.5503			1.34378			0.671890	+	0.740651i	$0.265483\pi$
$824$	8.84632			0.308176
$825$	−0.822034	−	0.0728062i	−0.0286196	−	0.00253479i
$826$		0			0
$827$		−	32.9672i		−	1.14638i	−0.819422	−	0.573190i	$-0.805706\pi$
$827$		−	32.9672i		−	1.14638i	0.819422	−	0.573190i	$-0.194294\pi$
$828$	1.95819	−	10.9680i	0.0680520	−	0.381164i
$829$		−	41.6039i		−	1.44496i	−0.691389	−	0.722482i	$-0.743001\pi$
$829$		−	41.6039i		−	1.44496i	0.691389	−	0.722482i	$-0.256999\pi$
$830$			14.2002i			0.492895i
$831$	−4.62344	+	52.2019i	−0.160385	+	1.81087i
$832$		−	4.96165i		−	0.172014i
$833$		0			0
$834$	−1.63368	+	18.4454i	−0.0565697	+	0.638712i
$835$	8.40082			0.290723
$836$	−2.46829			−0.0853677
$837$	12.4324	+	3.37411i	0.429726	+	0.116626i
$838$			29.3248i			1.01301i
$839$	20.1022			0.694006			0.347003	−	0.937864i	$-0.387199\pi$
$839$	20.1022			0.694006			0.347003	+	0.937864i	$0.387199\pi$
$840$		0			0
$841$	5.93335			0.204598
$842$		−	19.3254i		−	0.665996i
$843$	13.1337	+	1.16323i	0.452349	+	0.0400638i
$844$	13.8286			0.476000
$845$	11.6180			0.399671
$846$	6.23863	−	34.9430i	0.214488	−	1.20137i
$847$		0			0
$848$			0.305714i			0.0104983i
$849$	36.2196	+	3.20791i	1.24305	+	0.110095i
$850$			5.31590i			0.182334i
$851$		−	8.85409i		−	0.303514i
$852$	15.1492	+	1.34174i	0.519002	+	0.0459671i
$853$			19.5492i			0.669351i	0.942333	+	0.334676i	$0.108627\pi$
$853$			19.5492i			0.669351i	−0.942333	+	0.334676i	$0.891373\pi$
$854$		0			0
$855$	−2.73154	+	15.2995i	−0.0934166	+	0.523233i
$856$	12.0789			0.412847
$857$	−0.558864			−0.0190904			−0.00954522	−	0.999954i	$-0.503038\pi$
$857$	−0.558864			−0.0190904			−0.00954522	+	0.999954i	$0.503038\pi$
$858$	4.07865	+	0.361239i	0.139243	+	0.0123325i
$859$		−	38.8641i		−	1.32603i	−0.748608	−	0.663013i	$-0.769278\pi$
$859$		−	38.8641i		−	1.32603i	0.748608	−	0.663013i	$-0.230722\pi$
$860$	1.38323			0.0471677
$861$		0			0
$862$	−17.9318			−0.610758
$863$			30.6717i			1.04408i	0.852922	+	0.522038i	$0.174828\pi$
$863$			30.6717i			1.04408i	−0.852922	+	0.522038i	$0.825172\pi$
$864$	−5.01475	−	1.36099i	−0.170605	−	0.0463018i
$865$	4.69254			0.159551
$866$	2.79305			0.0949117
$867$	1.72043	−	19.4248i	0.0584287	−	0.659702i
$868$		0			0
$869$		−	0.845356i		−	0.0286767i
$870$	−0.733896	+	8.28621i	−0.0248814	+	0.280929i
$871$			15.4798i			0.524513i
$872$		−	17.0390i		−	0.577014i
$873$	−4.48674	+	25.1306i	−0.151853	+	0.850542i
$874$			19.2394i			0.650781i
$875$		0			0
$876$	26.0382	+	2.30616i	0.879750	+	0.0779179i
$877$	−38.9520			−1.31532			−0.657658	−	0.753317i	$-0.728453\pi$
$877$	−38.9520			−1.31532			−0.657658	+	0.753317i	$0.728453\pi$
$878$	15.1652			0.511801
$879$	−4.71952	+	53.2868i	−0.159186	+	1.79732i
$880$			0.476459i			0.0160614i
$881$	3.74997			0.126340			0.0631698	−	0.998003i	$-0.479879\pi$
$881$	3.74997			0.126340			0.0631698	+	0.998003i	$0.479879\pi$
$882$		0			0
$883$	−33.0043			−1.11068			−0.555342	−	0.831622i	$-0.687413\pi$
$883$	−33.0043			−1.11068			−0.555342	+	0.831622i	$0.687413\pi$
$884$		−	26.3757i		−	0.887110i
$885$	0.0673935	−	0.760921i	0.00226541	−	0.0255781i
$886$	5.62647			0.189025
$887$	−17.3301			−0.581889			−0.290944	−	0.956740i	$-0.593969\pi$
$887$	−17.3301			−0.581889			−0.290944	+	0.956740i	$0.593969\pi$
$888$	−4.11328	−	0.364306i	−0.138033	−	0.0122253i
$889$		0			0
$890$		−	5.22255i		−	0.175060i
$891$	1.48388	−	4.02321i	0.0497120	−	0.134782i
$892$		−	1.39419i		−	0.0466809i
$893$			61.2948i			2.05115i
$894$	−2.77644	+	31.3480i	−0.0928579	+	1.04843i
$895$			21.6928i			0.725112i
$896$		0			0
$897$	2.81571	−	31.7914i	0.0940139	−	1.06148i
$898$	−13.6625			−0.455925
$899$	−11.9069			−0.397117
$900$	2.95330	+	0.527274i	0.0984433	+	0.0175758i
$901$			1.62515i			0.0541415i
$902$	5.47437			0.182277
$903$		0			0
$904$	5.63769			0.187507
$905$		−	8.38421i		−	0.278700i
$906$	−31.4902	−	2.78904i	−1.04619	−	0.0926595i
$907$	34.4274			1.14314			0.571572	−	0.820552i	$-0.306334\pi$
$907$	34.4274			1.14314			0.571572	+	0.820552i	$0.306334\pi$
$908$	−4.57266			−0.151749
$909$	−49.7794	−	8.88747i	−1.65108	−	0.294779i
$910$		0			0
$911$			5.90076i			0.195501i	0.995211	+	0.0977505i	$0.0311647\pi$
$911$			5.90076i			0.195501i	−0.995211	+	0.0977505i	$0.968835\pi$
$912$	8.93788	+	0.791613i	0.295963	+	0.0262129i
$913$			6.76580i			0.223915i
$914$		−	3.70391i		−	0.122515i
$915$	−21.0834	−	1.86732i	−0.696997	−	0.0617319i
$916$			3.35629i			0.110895i
$917$		0			0
$918$	−26.6579	−	7.23488i	−0.879843	−	0.238787i
$919$	29.8749			0.985481			0.492741	−	0.870176i	$-0.335995\pi$
$919$	29.8749			0.985481			0.492741	+	0.870176i	$0.335995\pi$
$920$	3.71381			0.122441
$921$	−41.5342	−	3.67862i	−1.36860	−	0.121215i
$922$		−	23.6183i		−	0.777827i
$923$	43.5663			1.43400
$924$		0			0
$925$	2.38410			0.0783887
$926$		−	24.8440i		−	0.816423i
$927$	4.66443	−	26.1258i	0.153200	−	0.858085i
$928$	4.80278			0.157659
$929$	−15.7278			−0.516011			−0.258006	−	0.966143i	$-0.583065\pi$
$929$	−15.7278			−0.516011			−0.258006	+	0.966143i	$0.583065\pi$
$930$	−0.378833	+	4.27730i	−0.0124224	+	0.140258i
$931$		0			0
$932$			8.18807i			0.268209i
$933$	−1.89173	+	21.3590i	−0.0619325	+	0.699263i
$934$		−	18.2254i		−	0.596352i
$935$			2.53281i			0.0828318i
$936$	−14.6533	−	2.61615i	−0.478957	−	0.0855115i
$937$			19.1459i			0.625469i	0.949841	+	0.312735i	$0.101245\pi$
$937$			19.1459i			0.625469i	−0.949841	+	0.312735i	$0.898755\pi$
$938$		0			0
$939$	−14.1347	−	1.25189i	−0.461269	−	0.0408539i
$940$	11.8319			0.385913
$941$	2.89249			0.0942926			0.0471463	−	0.998888i	$-0.484987\pi$
$941$	2.89249			0.0942926			0.0471463	+	0.998888i	$0.484987\pi$
$942$	−0.682850	+	7.70987i	−0.0222485	+	0.251201i
$943$		−	42.6705i		−	1.38954i
$944$	−0.441038			−0.0143546
$945$		0			0
$946$	0.659052			0.0214276
$947$			7.90756i			0.256961i	0.991712	+	0.128481i	$0.0410100\pi$
$947$			7.90756i			0.256961i	−0.991712	+	0.128481i	$0.958990\pi$
$948$	−0.271117	+	3.06110i	−0.00880546	+	0.0994199i
$949$	74.8813			2.43075
$950$	−5.18049			−0.168077
$951$	10.9315	+	0.968185i	0.354478	+	0.0313956i
$952$		0			0
$953$		−	35.2895i		−	1.14314i	−0.820554	−	0.571569i	$-0.806335\pi$
$953$		−	35.2895i		−	1.14314i	0.820554	−	0.571569i	$-0.193665\pi$
$954$	0.902866	+	0.161195i	0.0292314	+	0.00521888i
$955$		−	8.58536i		−	0.277816i
$956$			14.1670i			0.458193i
$957$	−0.349672	+	3.94804i	−0.0113033	+	0.127622i
$958$		−	31.2048i		−	1.00818i
$959$		0			0
$960$	0.152807	−	1.72530i	0.00493181	−	0.0556837i
$961$	24.8537			0.801733
$962$	−11.8291			−0.381384
$963$	6.36886	−	35.6725i	0.205234	−	1.14953i
$964$		−	17.2184i		−	0.554568i
$965$	11.9098			0.383391
$966$		0			0
$967$	−11.4327			−0.367650			−0.183825	−	0.982959i	$-0.558848\pi$
$967$	−11.4327			−0.367650			−0.183825	+	0.982959i	$0.558848\pi$
$968$		−	10.7730i		−	0.346257i
$969$	47.5129	+	4.20814i	1.52634	+	0.135185i
$970$	−8.50932			−0.273218
$971$	−14.7667			−0.473885			−0.236942	−	0.971524i	$-0.576145\pi$
$971$	−14.7667			−0.473885			−0.236942	+	0.971524i	$0.576145\pi$
$972$	−6.66355	+	14.0924i	−0.213734	+	0.452015i
$973$		0			0
$974$			4.62293i			0.148128i
$975$	8.56033	+	0.758174i	0.274150	+	0.0242810i
$976$			12.2202i			0.391158i
$977$		−	25.5402i		−	0.817102i	−0.912736	−	0.408551i	$-0.866034\pi$
$977$		−	25.5402i		−	0.817102i	0.912736	−	0.408551i	$-0.133966\pi$
$978$	36.0707	+	3.19472i	1.15341	+	0.102156i
$979$		−	2.48834i		−	0.0795275i
$980$		0			0
$981$	−50.3213	−	8.98422i	−1.60664	−	0.286844i
$982$	14.9468			0.476972
$983$	−1.63102			−0.0520214			−0.0260107	−	0.999662i	$-0.508280\pi$
$983$	−1.63102			−0.0520214			−0.0260107	+	0.999662i	$0.508280\pi$
$984$	−19.8231	−	1.75570i	−0.631938	−	0.0559697i
$985$			18.0983i			0.576661i
$986$	25.5311			0.813076
$987$		0			0
$988$	25.7038			0.817747
$989$		−	5.13704i		−	0.163349i
$990$	1.40713	+	0.251225i	0.0447215	+	0.00798444i
$991$	27.2180			0.864607			0.432304	−	0.901728i	$-0.357701\pi$
$991$	27.2180			0.864607			0.432304	+	0.901728i	$0.357701\pi$
$992$	2.47917			0.0787136
$993$	2.38393	−	26.9163i	0.0756519	−	0.854164i
$994$		0			0
$995$		−	10.6113i		−	0.336402i
$996$	2.16988	−	24.4995i	0.0687553	−	0.776296i
$997$			11.7113i			0.370901i	0.982654	+	0.185451i	$0.0593745\pi$
$997$			11.7113i			0.370901i	−0.982654	+	0.185451i	$0.940625\pi$
$998$		−	12.5355i		−	0.396804i
$999$	−3.24473	+	11.9557i	−0.102659	+	0.378260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.b.c.881.14	yes	16
3.2	odd	2		1470.2.b.d.881.3	yes	16
7.6	odd	2		1470.2.b.d.881.11	yes	16
21.20	even	2	inner	1470.2.b.c.881.6	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.b.c.881.6	✓	16	21.20	even	2	inner
1470.2.b.c.881.14	yes	16	1.1	even	1	trivial
1470.2.b.d.881.3	yes	16	3.2	odd	2
1470.2.b.d.881.11	yes	16	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.152807 - 1.72530i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.72530 + 0.152807i) q^{6} -1.00000i q^{8} +(-2.95330 - 0.527274i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.152807 - 1.72530i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.72530 + 0.152807i) q^{6} -1.00000i q^{8} +(-2.95330 - 0.527274i) q^{9} -1.00000i q^{10} -0.476459i q^{11} +(-0.152807 + 1.72530i) q^{12} +4.96165i q^{13} +(-0.152807 + 1.72530i) q^{15} +1.00000 q^{16} +5.31590 q^{17} +(0.527274 - 2.95330i) q^{18} +5.18049i q^{19} +1.00000 q^{20} +0.476459 q^{22} -3.71381i q^{23} +(-1.72530 - 0.152807i) q^{24} +1.00000 q^{25} -4.96165 q^{26} +(-1.36099 + 5.01475i) q^{27} -4.80278i q^{29} +(-1.72530 - 0.152807i) q^{30} -2.47917i q^{31} +1.00000i q^{32} +(-0.822034 - 0.0728062i) q^{33} +5.31590i q^{34} +(2.95330 + 0.527274i) q^{36} +2.38410 q^{37} -5.18049 q^{38} +(8.56033 + 0.758174i) q^{39} +1.00000i q^{40} +11.4897 q^{41} +1.38323 q^{43} +0.476459i q^{44} +(2.95330 + 0.527274i) q^{45} +3.71381 q^{46} +11.8319 q^{47} +(0.152807 - 1.72530i) q^{48} +1.00000i q^{50} +(0.812306 - 9.17151i) q^{51} -4.96165i q^{52} +0.305714i q^{53} +(-5.01475 - 1.36099i) q^{54} +0.476459i q^{55} +(8.93788 + 0.791613i) q^{57} +4.80278 q^{58} -0.441038 q^{59} +(0.152807 - 1.72530i) q^{60} +12.2202i q^{61} +2.47917 q^{62} -1.00000 q^{64} -4.96165i q^{65} +(0.0728062 - 0.822034i) q^{66} +3.11989 q^{67} -5.31590 q^{68} +(-6.40743 - 0.567495i) q^{69} -8.78061i q^{71} +(-0.527274 + 2.95330i) q^{72} -15.0920i q^{73} +2.38410i q^{74} +(0.152807 - 1.72530i) q^{75} -5.18049i q^{76} +(-0.758174 + 8.56033i) q^{78} +1.77425 q^{79} -1.00000 q^{80} +(8.44396 + 3.11440i) q^{81} +11.4897i q^{82} -14.2002 q^{83} -5.31590 q^{85} +1.38323i q^{86} +(-8.28621 - 0.733896i) q^{87} -0.476459 q^{88} +5.22255 q^{89} +(-0.527274 + 2.95330i) q^{90} +3.71381i q^{92} +(-4.27730 - 0.378833i) q^{93} +11.8319i q^{94} -5.18049i q^{95} +(1.72530 + 0.152807i) q^{96} -8.50932i q^{97} +(-0.251225 + 1.40713i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} - 16 q^{4} - 16 q^{5} + 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 - 16 * q^4 - 16 * q^5 + 8 * q^9	\( 16 q - 8 q^{3} - 16 q^{4} - 16 q^{5} + 8 q^{9} + 8 q^{12} + 8 q^{15} + 16 q^{16} + 48 q^{17} + 16 q^{20} + 16 q^{25} - 16 q^{26} - 8 q^{27} - 8 q^{36} + 16 q^{41} + 16 q^{43} - 8 q^{45} - 16 q^{46} + 32 q^{47} - 8 q^{48} + 16 q^{51} + 32 q^{57} + 16 q^{58} + 32 q^{59} - 8 q^{60} + 16 q^{62} - 16 q^{64} + 16 q^{67} - 48 q^{68} - 8 q^{75} - 32 q^{78} - 48 q^{79} - 16 q^{80} + 8 q^{81} + 48 q^{83} - 48 q^{85} + 16 q^{89} - 64 q^{93} - 8 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 - 16 * q^4 - 16 * q^5 + 8 * q^9 + 8 * q^12 + 8 * q^15 + 16 * q^16 + 48 * q^17 + 16 * q^20 + 16 * q^25 - 16 * q^26 - 8 * q^27 - 8 * q^36 + 16 * q^41 + 16 * q^43 - 8 * q^45 - 16 * q^46 + 32 * q^47 - 8 * q^48 + 16 * q^51 + 32 * q^57 + 16 * q^58 + 32 * q^59 - 8 * q^60 + 16 * q^62 - 16 * q^64 + 16 * q^67 - 48 * q^68 - 8 * q^75 - 32 * q^78 - 48 * q^79 - 16 * q^80 + 8 * q^81 + 48 * q^83 - 48 * q^85 + 16 * q^89 - 64 * q^93 - 8 * q^99

Introduction

L-functions

Modular forms

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Database

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