LMFDB - Embedded newform 1470.2.b.c.881.16

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			881.16
Root			$1.11836 + 1.32260i$ of defining polynomial
Character	$\chi$	$=$	1470.881
Dual form			1470.2.b.c.881.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(1.64990 - 0.527098i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(0.527098 + 1.64990i) q^{6} -1.00000i q^{8} +(2.44434 - 1.73932i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(1.64990 - 0.527098i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(0.527098 + 1.64990i) q^{6} -1.00000i q^{8} +(2.44434 - 1.73932i) q^{9} -1.00000i q^{10} -0.183234i q^{11} +(-1.64990 + 0.527098i) q^{12} +2.22106i q^{13} +(-1.64990 + 0.527098i) q^{15} +1.00000 q^{16} +5.92858 q^{17} +(1.73932 + 2.44434i) q^{18} -2.74533i q^{19} +1.00000 q^{20} +0.183234 q^{22} -1.86609i q^{23} +(-0.527098 - 1.64990i) q^{24} +1.00000 q^{25} -2.22106 q^{26} +(3.11612 - 4.15810i) q^{27} +10.0295i q^{29} +(-0.527098 - 1.64990i) q^{30} -8.13368i q^{31} +1.00000i q^{32} +(-0.0965821 - 0.302317i) q^{33} +5.92858i q^{34} +(-2.44434 + 1.73932i) q^{36} +8.64068 q^{37} +2.74533 q^{38} +(1.17072 + 3.66453i) q^{39} +1.00000i q^{40} +5.35770 q^{41} -2.74103 q^{43} +0.183234i q^{44} +(-2.44434 + 1.73932i) q^{45} +1.86609 q^{46} +3.00263 q^{47} +(1.64990 - 0.527098i) q^{48} +1.00000i q^{50} +(9.78156 - 3.12494i) q^{51} -2.22106i q^{52} -1.72832i q^{53} +(4.15810 + 3.11612i) q^{54} +0.183234i q^{55} +(-1.44706 - 4.52952i) q^{57} -10.0295 q^{58} +11.8401 q^{59} +(1.64990 - 0.527098i) q^{60} -5.73054i q^{61} +8.13368 q^{62} -1.00000 q^{64} -2.22106i q^{65} +(0.302317 - 0.0965821i) q^{66} -3.79196 q^{67} -5.92858 q^{68} +(-0.983611 - 3.07886i) q^{69} +11.3992i q^{71} +(-1.73932 - 2.44434i) q^{72} +8.37048i q^{73} +8.64068i q^{74} +(1.64990 - 0.527098i) q^{75} +2.74533i q^{76} +(-3.66453 + 1.17072i) q^{78} -8.97002 q^{79} -1.00000 q^{80} +(2.94956 - 8.50295i) q^{81} +5.35770i q^{82} +9.25852 q^{83} -5.92858 q^{85} -2.74103i q^{86} +(5.28652 + 16.5476i) q^{87} -0.183234 q^{88} +12.1711 q^{89} +(-1.73932 - 2.44434i) q^{90} +1.86609i q^{92} +(-4.28724 - 13.4198i) q^{93} +3.00263i q^{94} +2.74533i q^{95} +(0.527098 + 1.64990i) q^{96} +7.23005i q^{97} +(-0.318701 - 0.447885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} - 16 q^{4} - 16 q^{5} + 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 - 16 * q^4 - 16 * q^5 + 8 * q^9	$ 16 q - 8 q^{3} - 16 q^{4} - 16 q^{5} + 8 q^{9} + 8 q^{12} + 8 q^{15} + 16 q^{16} + 48 q^{17} + 16 q^{20} + 16 q^{25} - 16 q^{26} - 8 q^{27} - 8 q^{36} + 16 q^{41} + 16 q^{43} - 8 q^{45} - 16 q^{46} + 32 q^{47} - 8 q^{48} + 16 q^{51} + 32 q^{57} + 16 q^{58} + 32 q^{59} - 8 q^{60} + 16 q^{62} - 16 q^{64} + 16 q^{67} - 48 q^{68} - 8 q^{75} - 32 q^{78} - 48 q^{79} - 16 q^{80} + 8 q^{81} + 48 q^{83} - 48 q^{85} + 16 q^{89} - 64 q^{93} - 8 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 - 16 * q^4 - 16 * q^5 + 8 * q^9 + 8 * q^12 + 8 * q^15 + 16 * q^16 + 48 * q^17 + 16 * q^20 + 16 * q^25 - 16 * q^26 - 8 * q^27 - 8 * q^36 + 16 * q^41 + 16 * q^43 - 8 * q^45 - 16 * q^46 + 32 * q^47 - 8 * q^48 + 16 * q^51 + 32 * q^57 + 16 * q^58 + 32 * q^59 - 8 * q^60 + 16 * q^62 - 16 * q^64 + 16 * q^67 - 48 * q^68 - 8 * q^75 - 32 * q^78 - 48 * q^79 - 16 * q^80 + 8 * q^81 + 48 * q^83 - 48 * q^85 + 16 * q^89 - 64 * q^93 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.64990	−	0.527098i	0.952570	−	0.304320i
$3$	1.64990	−	0.527098i	0.952570	−	0.304320i
$4$	−1.00000			−0.500000
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.527098	+	1.64990i	0.215187	+	0.673569i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	2.44434	−	1.73932i	0.814779	−	0.579772i
$10$		−	1.00000i		−	0.316228i
$11$		−	0.183234i		−	0.0552471i	−0.999618	−	0.0276235i	$-0.991206\pi$
$11$		−	0.183234i		−	0.0552471i	0.999618	−	0.0276235i	$-0.00879396\pi$
$12$	−1.64990	+	0.527098i	−0.476285	+	0.152160i
$13$			2.22106i			0.616011i	0.951385	+	0.308006i	$0.0996615\pi$
$13$			2.22106i			0.616011i	−0.951385	+	0.308006i	$0.900338\pi$
$14$		0			0
$15$	−1.64990	+	0.527098i	−0.426002	+	0.136096i
$16$	1.00000			0.250000
$17$	5.92858			1.43789			0.718946	−	0.695066i	$-0.244625\pi$
$17$	5.92858			1.43789			0.718946	+	0.695066i	$0.244625\pi$
$18$	1.73932	+	2.44434i	0.409961	+	0.576135i
$19$		−	2.74533i		−	0.629823i	−0.949121	−	0.314911i	$-0.898025\pi$
$19$		−	2.74533i		−	0.629823i	0.949121	−	0.314911i	$-0.101975\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	0.183234			0.0390656
$23$		−	1.86609i		−	0.389106i	−0.980892	−	0.194553i	$-0.937674\pi$
$23$		−	1.86609i		−	0.389106i	0.980892	−	0.194553i	$-0.0623257\pi$
$24$	−0.527098	−	1.64990i	−0.107593	−	0.336784i
$25$	1.00000			0.200000
$26$	−2.22106			−0.435586
$27$	3.11612	−	4.15810i	0.599697	−	0.800227i
$28$		0			0
$29$			10.0295i			1.86243i	0.364473	+	0.931214i	$0.381249\pi$
$29$			10.0295i			1.86243i	−0.364473	+	0.931214i	$0.618751\pi$
$30$	−0.527098	−	1.64990i	−0.0962344	−	0.301229i
$31$		−	8.13368i		−	1.46085i	−0.682992	−	0.730426i	$-0.739322\pi$
$31$		−	8.13368i		−	1.46085i	0.682992	−	0.730426i	$-0.260678\pi$
$32$			1.00000i			0.176777i
$33$	−0.0965821	−	0.302317i	−0.0168128	−	0.0526267i
$34$			5.92858i			1.01674i
$35$		0			0
$36$	−2.44434	+	1.73932i	−0.407389	+	0.289886i
$37$	8.64068			1.42052			0.710260	−	0.703940i	$-0.248577\pi$
$37$	8.64068			1.42052			0.710260	+	0.703940i	$0.248577\pi$
$38$	2.74533			0.445352
$39$	1.17072	+	3.66453i	0.187465	+	0.586794i
$40$			1.00000i			0.158114i
$41$	5.35770			0.836732			0.418366	−	0.908278i	$-0.362603\pi$
$41$	5.35770			0.836732			0.418366	+	0.908278i	$0.362603\pi$
$42$		0			0
$43$	−2.74103			−0.418004			−0.209002	−	0.977915i	$-0.567021\pi$
$43$	−2.74103			−0.418004			−0.209002	+	0.977915i	$0.567021\pi$
$44$			0.183234i			0.0276235i
$45$	−2.44434	+	1.73932i	−0.364380	+	0.259282i
$46$	1.86609			0.275140
$47$	3.00263			0.437979			0.218989	−	0.975727i	$-0.429724\pi$
$47$	3.00263			0.437979			0.218989	+	0.975727i	$0.429724\pi$
$48$	1.64990	−	0.527098i	0.238142	−	0.0760800i
$49$		0			0
$50$			1.00000i			0.141421i
$51$	9.78156	−	3.12494i	1.36969	−	0.437579i
$52$		−	2.22106i		−	0.308006i
$53$		−	1.72832i		−	0.237403i	−0.992930	−	0.118701i	$-0.962127\pi$
$53$		−	1.72832i		−	0.237403i	0.992930	−	0.118701i	$-0.0378731\pi$
$54$	4.15810	+	3.11612i	0.565846	+	0.424050i
$55$			0.183234i			0.0247072i
$56$		0			0
$57$	−1.44706	−	4.52952i	−0.191668	−	0.599950i
$58$	−10.0295			−1.31694
$59$	11.8401			1.54146			0.770728	−	0.637165i	$-0.219893\pi$
$59$	11.8401			1.54146			0.770728	+	0.637165i	$0.219893\pi$
$60$	1.64990	−	0.527098i	0.213001	−	0.0680480i
$61$		−	5.73054i		−	0.733720i	−0.930276	−	0.366860i	$-0.880433\pi$
$61$		−	5.73054i		−	0.733720i	0.930276	−	0.366860i	$-0.119567\pi$
$62$	8.13368			1.03298
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	2.22106i		−	0.275489i
$66$	0.302317	−	0.0965821i	0.0372127	−	0.0118884i
$67$	−3.79196			−0.463262			−0.231631	−	0.972804i	$-0.574406\pi$
$67$	−3.79196			−0.463262			−0.231631	+	0.972804i	$0.574406\pi$
$68$	−5.92858			−0.718946
$69$	−0.983611	−	3.07886i	−0.118413	−	0.370651i
$70$		0			0
$71$			11.3992i			1.35283i	0.736519	+	0.676417i	$0.236468\pi$
$71$			11.3992i			1.35283i	−0.736519	+	0.676417i	$0.763532\pi$
$72$	−1.73932	−	2.44434i	−0.204980	−	0.288068i
$73$			8.37048i			0.979690i	0.871809	+	0.489845i	$0.162947\pi$
$73$			8.37048i			0.979690i	−0.871809	+	0.489845i	$0.837053\pi$
$74$			8.64068i			1.00446i
$75$	1.64990	−	0.527098i	0.190514	−	0.0608640i
$76$			2.74533i			0.314911i
$77$		0			0
$78$	−3.66453	+	1.17072i	−0.414926	+	0.132557i
$79$	−8.97002			−1.00921			−0.504603	−	0.863351i	$-0.668361\pi$
$79$	−8.97002			−1.00921			−0.504603	+	0.863351i	$0.668361\pi$
$80$	−1.00000			−0.111803
$81$	2.94956	−	8.50295i	0.327728	−	0.944772i
$82$			5.35770i			0.591659i
$83$	9.25852			1.01625			0.508127	−	0.861282i	$-0.330338\pi$
$83$	9.25852			1.01625			0.508127	+	0.861282i	$0.330338\pi$
$84$		0			0
$85$	−5.92858			−0.643045
$86$		−	2.74103i		−	0.295573i
$87$	5.28652	+	16.5476i	0.566774	+	1.77409i
$88$	−0.183234			−0.0195328
$89$	12.1711			1.29013			0.645066	−	0.764127i	$-0.276830\pi$
$89$	12.1711			1.29013			0.645066	+	0.764127i	$0.276830\pi$
$90$	−1.73932	−	2.44434i	−0.183340	−	0.257656i
$91$		0			0
$92$			1.86609i			0.194553i
$93$	−4.28724	−	13.4198i	−0.444567	−	1.39156i
$94$			3.00263i			0.309698i
$95$			2.74533i			0.281665i
$96$	0.527098	+	1.64990i	0.0537967	+	0.168392i
$97$			7.23005i			0.734100i	0.930201	+	0.367050i	$0.119632\pi$
$97$			7.23005i			0.734100i	−0.930201	+	0.367050i	$0.880368\pi$
$98$		0			0
$99$	−0.318701	−	0.447885i	−0.0320307	−	0.0450141i
$100$	−1.00000			−0.100000
$101$	−7.98749			−0.794785			−0.397393	−	0.917649i	$-0.630085\pi$
$101$	−7.98749			−0.794785			−0.397393	+	0.917649i	$0.630085\pi$
$102$	3.12494	+	9.78156i	0.309415	+	0.968518i
$103$		−	15.2633i		−	1.50393i	−0.659200	−	0.751967i	$-0.729105\pi$
$103$		−	15.2633i		−	1.50393i	0.659200	−	0.751967i	$-0.270895\pi$
$104$	2.22106			0.217793
$105$		0			0
$106$	1.72832			0.167869
$107$			6.18268i			0.597702i	0.954300	+	0.298851i	$0.0966034\pi$
$107$			6.18268i			0.597702i	−0.954300	+	0.298851i	$0.903397\pi$
$108$	−3.11612	+	4.15810i	−0.299849	+	0.400113i
$109$	−18.5699			−1.77868			−0.889338	−	0.457251i	$-0.848834\pi$
$109$	−18.5699			−1.77868			−0.889338	+	0.457251i	$0.848834\pi$
$110$	−0.183234			−0.0174707
$111$	14.2563	−	4.55448i	1.35314	−	0.432293i
$112$		0			0
$113$		−	8.96035i		−	0.842919i	−0.906847	−	0.421459i	$-0.861518\pi$
$113$		−	8.96035i		−	0.842919i	0.906847	−	0.421459i	$-0.138482\pi$
$114$	4.52952	−	1.44706i	0.424229	−	0.135530i
$115$			1.86609i			0.174014i
$116$		−	10.0295i		−	0.931214i
$117$	3.86313	+	5.42902i	0.357146	+	0.501913i
$118$			11.8401i			1.08997i
$119$		0			0
$120$	0.527098	+	1.64990i	0.0481172	+	0.150615i
$121$	10.9664			0.996948
$122$	5.73054			0.518818
$123$	8.83967	−	2.82403i	0.797046	−	0.254634i
$124$			8.13368i			0.730426i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	9.46529			0.839908			0.419954	−	0.907545i	$-0.362046\pi$
$127$	9.46529			0.839908			0.419954	+	0.907545i	$0.362046\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−4.52243	+	1.44479i	−0.398178	+	0.127207i
$130$	2.22106			0.194800
$131$	−18.0259			−1.57493			−0.787467	−	0.616357i	$-0.788608\pi$
$131$	−18.0259			−1.57493			−0.787467	+	0.616357i	$0.788608\pi$
$132$	0.0965821	+	0.302317i	0.00840639	+	0.0263133i
$133$		0			0
$134$		−	3.79196i		−	0.327576i
$135$	−3.11612	+	4.15810i	−0.268193	+	0.357872i
$136$		−	5.92858i		−	0.508371i
$137$			1.58312i			0.135255i	0.997711	+	0.0676275i	$0.0215429\pi$
$137$			1.58312i			0.135255i	−0.997711	+	0.0676275i	$0.978457\pi$
$138$	3.07886	−	0.983611i	0.262090	−	0.0837305i
$139$		−	8.23768i		−	0.698711i	−0.936990	−	0.349356i	$-0.886401\pi$
$139$		−	8.23768i		−	0.698711i	0.936990	−	0.349356i	$-0.113599\pi$
$140$		0			0
$141$	4.95404	−	1.58268i	0.417205	−	0.133286i
$142$	−11.3992			−0.956598
$143$	0.406973			0.0340328
$144$	2.44434	−	1.73932i	0.203695	−	0.144943i
$145$		−	10.0295i		−	0.832903i
$146$	−8.37048			−0.692746
$147$		0			0
$148$	−8.64068			−0.710260
$149$		−	9.35407i		−	0.766315i	−0.923683	−	0.383158i	$-0.874837\pi$
$149$		−	9.35407i		−	0.766315i	0.923683	−	0.383158i	$-0.125163\pi$
$150$	0.527098	+	1.64990i	0.0430374	+	0.134714i
$151$	−14.2685			−1.16115			−0.580575	−	0.814207i	$-0.697172\pi$
$151$	−14.2685			−1.16115			−0.580575	+	0.814207i	$0.697172\pi$
$152$	−2.74533			−0.222676
$153$	14.4914	−	10.3117i	1.17156	−	0.833649i
$154$		0			0
$155$			8.13368i			0.653313i
$156$	−1.17072	−	3.66453i	−0.0937323	−	0.293397i
$157$		−	5.01925i		−	0.400580i	−0.979737	−	0.200290i	$-0.935812\pi$
$157$		−	5.01925i		−	0.400580i	0.979737	−	0.200290i	$-0.0641884\pi$
$158$		−	8.97002i		−	0.713616i
$159$	−0.910992	−	2.85155i	−0.0722464	−	0.226143i
$160$		−	1.00000i		−	0.0790569i
$161$		0			0
$162$	8.50295	+	2.94956i	0.668055	+	0.231739i
$163$	−23.9391			−1.87505			−0.937526	−	0.347916i	$-0.886889\pi$
$163$	−23.9391			−1.87505			−0.937526	+	0.347916i	$0.886889\pi$
$164$	−5.35770			−0.418366
$165$	0.0965821	+	0.302317i	0.00751891	+	0.0235354i
$166$			9.25852i			0.718601i
$167$	−12.2295			−0.946349			−0.473174	−	0.880969i	$-0.656892\pi$
$167$	−12.2295			−0.946349			−0.473174	+	0.880969i	$0.656892\pi$
$168$		0			0
$169$	8.06689			0.620530
$170$		−	5.92858i		−	0.454701i
$171$	−4.77500	−	6.71052i	−0.365154	−	0.513166i
$172$	2.74103			0.209002
$173$	−2.75498			−0.209457			−0.104729	−	0.994501i	$-0.533397\pi$
$173$	−2.75498			−0.209457			−0.104729	+	0.994501i	$0.533397\pi$
$174$	−16.5476	+	5.28652i	−1.25447	+	0.400770i
$175$		0			0
$176$		−	0.183234i		−	0.0138118i
$177$	19.5350	−	6.24091i	1.46834	−	0.469096i
$178$			12.1711i			0.912261i
$179$			5.15274i			0.385134i	0.981284	+	0.192567i	$0.0616812\pi$
$179$			5.15274i			0.385134i	−0.981284	+	0.192567i	$0.938319\pi$
$180$	2.44434	−	1.73932i	0.182190	−	0.129641i
$181$			18.1045i			1.34569i	0.739781	+	0.672847i	$0.234929\pi$
$181$			18.1045i			1.34569i	−0.739781	+	0.672847i	$0.765071\pi$
$182$		0			0
$183$	−3.02055	−	9.45481i	−0.223286	−	0.698919i
$184$	−1.86609			−0.137570
$185$	−8.64068			−0.635276
$186$	13.4198	−	4.28724i	0.983984	−	0.314356i
$187$		−	1.08632i		−	0.0794393i
$188$	−3.00263			−0.218989
$189$		0			0
$190$	−2.74533			−0.199167
$191$			15.0739i			1.09071i	0.838206	+	0.545353i	$0.183604\pi$
$191$			15.0739i			1.09071i	−0.838206	+	0.545353i	$0.816396\pi$
$192$	−1.64990	+	0.527098i	−0.119071	+	0.0380400i
$193$	−24.3119			−1.75001			−0.875004	−	0.484115i	$-0.839142\pi$
$193$	−24.3119			−1.75001			−0.875004	+	0.484115i	$0.839142\pi$
$194$	−7.23005			−0.519087
$195$	−1.17072	−	3.66453i	−0.0838367	−	0.262422i
$196$		0			0
$197$			0.763219i			0.0543771i	0.999630	+	0.0271885i	$0.00865545\pi$
$197$			0.763219i			0.0543771i	−0.999630	+	0.0271885i	$0.991345\pi$
$198$	0.447885	−	0.318701i	0.0318298	−	0.0226491i
$199$		−	7.53057i		−	0.533828i	−0.963720	−	0.266914i	$-0.913996\pi$
$199$		−	7.53057i		−	0.533828i	0.963720	−	0.266914i	$-0.0860040\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	−6.25636	+	1.99874i	−0.441289	+	0.140980i
$202$		−	7.98749i		−	0.561998i
$203$		0			0
$204$	−9.78156	+	3.12494i	−0.684846	+	0.218790i
$205$	−5.35770			−0.374198
$206$	15.2633			1.06344
$207$	−3.24572	−	4.56135i	−0.225593	−	0.317036i
$208$			2.22106i			0.154003i
$209$	−0.503038			−0.0347959
$210$		0			0
$211$	13.9076			0.957438			0.478719	−	0.877968i	$-0.341101\pi$
$211$	13.9076			0.957438			0.478719	+	0.877968i	$0.341101\pi$
$212$			1.72832i			0.118701i
$213$	6.00848	+	18.8075i	0.411694	+	1.28867i
$214$	−6.18268			−0.422639
$215$	2.74103			0.186937
$216$	−4.15810	−	3.11612i	−0.282923	−	0.212025i
$217$		0			0
$218$		−	18.5699i		−	1.25771i
$219$	4.41206	+	13.8104i	0.298139	+	0.933223i
$220$		−	0.183234i		−	0.0123536i
$221$			13.1677i			0.885757i
$222$	4.55448	+	14.2563i	0.305677	+	0.956817i
$223$		−	18.8741i		−	1.26390i	−0.775009	−	0.631951i	$-0.782255\pi$
$223$		−	18.8741i		−	1.26390i	0.775009	−	0.631951i	$-0.217745\pi$
$224$		0			0
$225$	2.44434	−	1.73932i	0.162956	−	0.115954i
$226$	8.96035			0.596034
$227$	−3.61611			−0.240009			−0.120005	−	0.992773i	$-0.538291\pi$
$227$	−3.61611			−0.240009			−0.120005	+	0.992773i	$0.538291\pi$
$228$	1.44706	+	4.52952i	0.0958338	+	0.299975i
$229$			20.4388i			1.35063i	0.737528	+	0.675317i	$0.235993\pi$
$229$			20.4388i			1.35063i	−0.737528	+	0.675317i	$0.764007\pi$
$230$	−1.86609			−0.123046
$231$		0			0
$232$	10.0295			0.658468
$233$			13.8804i			0.909333i	0.890662	+	0.454667i	$0.150242\pi$
$233$			13.8804i			0.909333i	−0.890662	+	0.454667i	$0.849758\pi$
$234$	−5.42902	+	3.86313i	−0.354906	+	0.252540i
$235$	−3.00263			−0.195870
$236$	−11.8401			−0.770728
$237$	−14.7996	+	4.72808i	−0.961339	+	0.307122i
$238$		0			0
$239$			25.8786i			1.67395i	0.547243	+	0.836974i	$0.315677\pi$
$239$			25.8786i			1.67395i	−0.547243	+	0.836974i	$0.684323\pi$
$240$	−1.64990	+	0.527098i	−0.106501	+	0.0340240i
$241$		−	26.2005i		−	1.68772i	−0.536561	−	0.843862i	$-0.680277\pi$
$241$		−	26.2005i		−	1.68772i	0.536561	−	0.843862i	$-0.319723\pi$
$242$			10.9664i			0.704949i
$243$	0.384586	−	15.5837i	0.0246712	−	0.999696i
$244$			5.73054i			0.366860i
$245$		0			0
$246$	2.82403	+	8.83967i	0.180054	+	0.563597i
$247$	6.09755			0.387978
$248$	−8.13368			−0.516489
$249$	15.2756	−	4.88015i	0.968053	−	0.309267i
$250$		−	1.00000i		−	0.0632456i
$251$	−17.1154			−1.08031			−0.540156	−	0.841565i	$-0.681635\pi$
$251$	−17.1154			−1.08031			−0.540156	+	0.841565i	$0.681635\pi$
$252$		0			0
$253$	−0.341930			−0.0214970
$254$			9.46529i			0.593905i
$255$	−9.78156	+	3.12494i	−0.612545	+	0.195691i
$256$	1.00000			0.0625000
$257$	16.1541			1.00766			0.503832	−	0.863802i	$-0.331923\pi$
$257$	16.1541			1.00766			0.503832	+	0.863802i	$0.331923\pi$
$258$	−1.44479	−	4.52243i	−0.0899488	−	0.281554i
$259$		0			0
$260$			2.22106i			0.137744i
$261$	17.4444	+	24.5154i	1.07978	+	1.51747i
$262$		−	18.0259i		−	1.11365i
$263$		−	3.79029i		−	0.233719i	−0.993148	−	0.116860i	$-0.962717\pi$
$263$		−	3.79029i		−	0.233719i	0.993148	−	0.116860i	$-0.0372828\pi$
$264$	−0.302317	+	0.0965821i	−0.0186063	+	0.00594422i
$265$			1.72832i			0.106170i
$266$		0			0
$267$	20.0811	−	6.41535i	1.22894	−	0.392613i
$268$	3.79196			0.231631
$269$	−1.67131			−0.101901			−0.0509507	−	0.998701i	$-0.516225\pi$
$269$	−1.67131			−0.101901			−0.0509507	+	0.998701i	$0.516225\pi$
$270$	−4.15810	−	3.11612i	−0.253054	−	0.189641i
$271$			27.8686i			1.69290i	0.532469	+	0.846449i	$0.321264\pi$
$271$			27.8686i			1.69290i	−0.532469	+	0.846449i	$0.678736\pi$
$272$	5.92858			0.359473
$273$		0			0
$274$	−1.58312			−0.0956397
$275$		−	0.183234i		−	0.0110494i
$276$	0.983611	+	3.07886i	0.0592064	+	0.185326i
$277$	−2.08837			−0.125478			−0.0627389	−	0.998030i	$-0.519984\pi$
$277$	−2.08837			−0.125478			−0.0627389	+	0.998030i	$0.519984\pi$
$278$	8.23768			0.494063
$279$	−14.1470	−	19.8814i	−0.846961	−	1.19027i
$280$		0			0
$281$		−	19.4447i		−	1.15997i	−0.814625	−	0.579987i	$-0.803057\pi$
$281$		−	19.4447i		−	1.15997i	0.814625	−	0.579987i	$-0.196943\pi$
$282$	1.58268	+	4.95404i	0.0942472	+	0.295009i
$283$			1.11859i			0.0664931i	0.999447	+	0.0332465i	$0.0105847\pi$
$283$			1.11859i			0.0664931i	−0.999447	+	0.0332465i	$0.989415\pi$
$284$		−	11.3992i		−	0.676417i
$285$	1.44706	+	4.52952i	0.0857164	+	0.268306i
$286$			0.406973i			0.0240648i
$287$		0			0
$288$	1.73932	+	2.44434i	0.102490	+	0.144034i
$289$	18.1480			1.06753
$290$	10.0295			0.588951
$291$	3.81094	+	11.9289i	0.223401	+	0.699282i
$292$		−	8.37048i		−	0.489845i
$293$	−25.9736			−1.51739			−0.758697	−	0.651444i	$-0.774164\pi$
$293$	−25.9736			−1.51739			−0.758697	+	0.651444i	$0.774164\pi$
$294$		0			0
$295$	−11.8401			−0.689360
$296$		−	8.64068i		−	0.502229i
$297$	−0.761904	−	0.570978i	−0.0442102	−	0.0331315i
$298$	9.35407			0.541867
$299$	4.14469			0.239694
$300$	−1.64990	+	0.527098i	−0.0952570	+	0.0304320i
$301$		0			0
$302$		−	14.2685i		−	0.821057i
$303$	−13.1786	+	4.21019i	−0.757089	+	0.241869i
$304$		−	2.74533i		−	0.157456i
$305$			5.73054i			0.328130i
$306$	10.3117	+	14.4914i	0.589479	+	0.828420i
$307$			14.8678i			0.848548i	0.905534	+	0.424274i	$0.139471\pi$
$307$			14.8678i			0.848548i	−0.905534	+	0.424274i	$0.860529\pi$
$308$		0			0
$309$	−8.04524	−	25.1829i	−0.457677	−	1.43260i
$310$	−8.13368			−0.461962
$311$	−10.1085			−0.573201			−0.286600	−	0.958050i	$-0.592525\pi$
$311$	−10.1085			−0.573201			−0.286600	+	0.958050i	$0.592525\pi$
$312$	3.66453	−	1.17072i	0.207463	−	0.0662787i
$313$		−	30.7635i		−	1.73886i	−0.494058	−	0.869429i	$-0.664487\pi$
$313$		−	30.7635i		−	1.73886i	0.494058	−	0.869429i	$-0.335513\pi$
$314$	5.01925			0.283253
$315$		0			0
$316$	8.97002			0.504603
$317$			15.3849i			0.864102i	0.901849	+	0.432051i	$0.142210\pi$
$317$			15.3849i			0.864102i	−0.901849	+	0.432051i	$0.857790\pi$
$318$	2.85155	−	0.910992i	0.159907	−	0.0510859i
$319$	1.83774			0.102894
$320$	1.00000			0.0559017
$321$	3.25888	+	10.2008i	0.181893	+	0.569353i
$322$		0			0
$323$		−	16.2759i		−	0.905617i
$324$	−2.94956	+	8.50295i	−0.163864	+	0.472386i
$325$			2.22106i			0.123202i
$326$		−	23.9391i		−	1.32586i
$327$	−30.6385	+	9.78816i	−1.69431	+	0.541287i
$328$		−	5.35770i		−	0.295830i
$329$		0			0
$330$	−0.302317	+	0.0965821i	−0.0166420	+	0.00531667i
$331$	−11.3036			−0.621300			−0.310650	−	0.950524i	$-0.600547\pi$
$331$	−11.3036			−0.621300			−0.310650	+	0.950524i	$0.600547\pi$
$332$	−9.25852			−0.508127
$333$	21.1207	−	15.0289i	1.15741	−	0.823578i
$334$		−	12.2295i		−	0.669170i
$335$	3.79196			0.207177
$336$		0			0
$337$	−35.2334			−1.91929			−0.959643	−	0.281221i	$-0.909261\pi$
$337$	−35.2334			−1.91929			−0.959643	+	0.281221i	$0.909261\pi$
$338$			8.06689i			0.438781i
$339$	−4.72298	−	14.7837i	−0.256517	−	0.802939i
$340$	5.92858			0.321522
$341$	−1.49036			−0.0807078
$342$	6.71052	−	4.77500i	0.362863	−	0.258203i
$343$		0			0
$344$			2.74103i			0.147787i
$345$	0.983611	+	3.07886i	0.0529558	+	0.165760i
$346$		−	2.75498i		−	0.148109i
$347$		−	36.4627i		−	1.95742i	−0.205243	−	0.978711i	$-0.565799\pi$
$347$		−	36.4627i		−	1.95742i	0.205243	−	0.978711i	$-0.434201\pi$
$348$	−5.28652	−	16.5476i	−0.283387	−	0.887046i
$349$			5.80210i			0.310580i	0.987869	+	0.155290i	$0.0496311\pi$
$349$			5.80210i			0.310580i	−0.987869	+	0.155290i	$0.950369\pi$
$350$		0			0
$351$	9.23539	+	6.92109i	0.492949	+	0.369420i
$352$	0.183234			0.00976639
$353$	−36.8540			−1.96154			−0.980770	−	0.195167i	$-0.937475\pi$
$353$	−36.8540			−1.96154			−0.980770	+	0.195167i	$0.937475\pi$
$354$	6.24091	+	19.5350i	0.331701	+	1.03828i
$355$		−	11.3992i		−	0.605006i
$356$	−12.1711			−0.645066
$357$		0			0
$358$	−5.15274			−0.272331
$359$		−	14.6764i		−	0.774589i	−0.921956	−	0.387294i	$-0.873410\pi$
$359$		−	14.6764i		−	0.774589i	0.921956	−	0.387294i	$-0.126590\pi$
$360$	1.73932	+	2.44434i	0.0916700	+	0.128828i
$361$	11.4631			0.603323
$362$	−18.1045			−0.951550
$363$	18.0935	−	5.78038i	0.949662	−	0.303391i
$364$		0			0
$365$		−	8.37048i		−	0.438131i
$366$	9.45481	−	3.02055i	0.494211	−	0.157887i
$367$		−	28.9944i		−	1.51350i	−0.653707	−	0.756748i	$-0.726787\pi$
$367$		−	28.9944i		−	1.51350i	0.653707	−	0.756748i	$-0.273213\pi$
$368$		−	1.86609i		−	0.0972766i
$369$	13.0960	−	9.31874i	0.681752	−	0.485114i
$370$		−	8.64068i		−	0.449208i
$371$		0			0
$372$	4.28724	+	13.4198i	0.222283	+	0.695782i
$373$	−27.5619			−1.42710			−0.713552	−	0.700603i	$-0.752915\pi$
$373$	−27.5619			−1.42710			−0.713552	+	0.700603i	$0.752915\pi$
$374$	1.08632			0.0561720
$375$	−1.64990	+	0.527098i	−0.0852004	+	0.0272192i
$376$		−	3.00263i		−	0.154849i
$377$	−22.2761			−1.14728
$378$		0			0
$379$	25.9475			1.33283			0.666417	−	0.745580i	$-0.267827\pi$
$379$	25.9475			1.33283			0.666417	+	0.745580i	$0.267827\pi$
$380$		−	2.74533i		−	0.140833i
$381$	15.6168	−	4.98913i	0.800071	−	0.255601i
$382$	−15.0739			−0.771246
$383$	36.5542			1.86783			0.933917	−	0.357491i	$-0.116368\pi$
$383$	36.5542			1.86783			0.933917	+	0.357491i	$0.116368\pi$
$384$	−0.527098	−	1.64990i	−0.0268983	−	0.0841961i
$385$		0			0
$386$		−	24.3119i		−	1.23744i
$387$	−6.70001	+	4.76752i	−0.340580	+	0.242347i
$388$		−	7.23005i		−	0.367050i
$389$			19.5029i			0.988839i	0.869224	+	0.494419i	$0.164619\pi$
$389$			19.5029i			0.988839i	−0.869224	+	0.494419i	$0.835381\pi$
$390$	3.66453	−	1.17072i	0.185560	−	0.0592815i
$391$		−	11.0633i		−	0.559493i
$392$		0			0
$393$	−29.7410	+	9.50143i	−1.50023	+	0.479284i
$394$	−0.763219			−0.0384504
$395$	8.97002			0.451331
$396$	0.318701	+	0.447885i	0.0160154	+	0.0225071i
$397$		−	8.12748i		−	0.407907i	−0.978981	−	0.203953i	$-0.934621\pi$
$397$		−	8.12748i		−	0.407907i	0.978981	−	0.203953i	$-0.0653791\pi$
$398$	7.53057			0.377473
$399$		0			0
$400$	1.00000			0.0500000
$401$			19.8417i			0.990845i	0.868652	+	0.495422i	$0.164987\pi$
$401$			19.8417i			0.990845i	−0.868652	+	0.495422i	$0.835013\pi$
$402$	−1.99874	−	6.25636i	−0.0996878	−	0.312039i
$403$	18.0654			0.899901
$404$	7.98749			0.397393
$405$	−2.94956	+	8.50295i	−0.146565	+	0.422515i
$406$		0			0
$407$		−	1.58326i		−	0.0784795i
$408$	−3.12494	−	9.78156i	−0.154708	−	0.484259i
$409$			3.20599i			0.158526i	0.996854	+	0.0792629i	$0.0252567\pi$
$409$			3.20599i			0.158526i	−0.996854	+	0.0792629i	$0.974743\pi$
$410$		−	5.35770i		−	0.264598i
$411$	0.834458	+	2.61199i	0.0411608	+	0.128840i
$412$			15.2633i			0.751967i
$413$		0			0
$414$	4.56135	−	3.24572i	0.224178	−	0.159518i
$415$	−9.25852			−0.454483
$416$	−2.22106			−0.108896
$417$	−4.34206	−	13.5913i	−0.212632	−	0.665571i
$418$		−	0.503038i		−	0.0246044i
$419$	6.99137			0.341551			0.170775	−	0.985310i	$-0.445373\pi$
$419$	6.99137			0.341551			0.170775	+	0.985310i	$0.445373\pi$
$420$		0			0
$421$	17.7534			0.865246			0.432623	−	0.901575i	$-0.357588\pi$
$421$	17.7534			0.865246			0.432623	+	0.901575i	$0.357588\pi$
$422$			13.9076i			0.677011i
$423$	7.33944	−	5.22253i	0.356856	−	0.253928i
$424$	−1.72832			−0.0839345
$425$	5.92858			0.287578
$426$	−18.8075	+	6.00848i	−0.911226	+	0.291112i
$427$		0			0
$428$		−	6.18268i		−	0.298851i
$429$	0.671465	−	0.214515i	0.0324186	−	0.0103569i
$430$			2.74103i			0.132184i
$431$			21.5466i			1.03786i	0.854816	+	0.518931i	$0.173670\pi$
$431$			21.5466i			1.03786i	−0.854816	+	0.518931i	$0.826330\pi$
$432$	3.11612	−	4.15810i	0.149924	−	0.200057i
$433$			2.22339i			0.106850i	0.998572	+	0.0534248i	$0.0170137\pi$
$433$			2.22339i			0.106850i	−0.998572	+	0.0534248i	$0.982986\pi$
$434$		0			0
$435$	−5.28652	−	16.5476i	−0.253469	−	0.793398i
$436$	18.5699			0.889338
$437$	−5.12304			−0.245068
$438$	−13.8104	+	4.41206i	−0.659889	+	0.210816i
$439$			1.07643i			0.0513751i	0.999670	+	0.0256876i	$0.00817750\pi$
$439$			1.07643i			0.0513751i	−0.999670	+	0.0256876i	$0.991822\pi$
$440$	0.183234			0.00873533
$441$		0			0
$442$	−13.1677			−0.626325
$443$		−	22.1450i		−	1.05214i	−0.850442	−	0.526070i	$-0.823665\pi$
$443$		−	22.1450i		−	1.05214i	0.850442	−	0.526070i	$-0.176335\pi$
$444$	−14.2563	+	4.55448i	−0.676572	+	0.216146i
$445$	−12.1711			−0.576964
$446$	18.8741			0.893713
$447$	−4.93051	−	15.4333i	−0.233205	−	0.729969i
$448$		0			0
$449$			2.54766i			0.120231i	0.998191	+	0.0601157i	$0.0191470\pi$
$449$			2.54766i			0.120231i	−0.998191	+	0.0601157i	$0.980853\pi$
$450$	1.73932	+	2.44434i	0.0819922	+	0.115227i
$451$		−	0.981712i		−	0.0462270i
$452$			8.96035i			0.421459i
$453$	−23.5415	+	7.52087i	−1.10608	+	0.353361i
$454$		−	3.61611i		−	0.169712i
$455$		0			0
$456$	−4.52952	+	1.44706i	−0.212114	+	0.0677648i
$457$	4.69058			0.219416			0.109708	−	0.993964i	$-0.465008\pi$
$457$	4.69058			0.219416			0.109708	+	0.993964i	$0.465008\pi$
$458$	−20.4388			−0.955042
$459$	18.4742	−	24.6516i	0.862300	−	1.15064i
$460$		−	1.86609i		−	0.0870068i
$461$	5.10979			0.237986			0.118993	−	0.992895i	$-0.462033\pi$
$461$	5.10979			0.237986			0.118993	+	0.992895i	$0.462033\pi$
$462$		0			0
$463$	−20.6740			−0.960804			−0.480402	−	0.877048i	$-0.659509\pi$
$463$	−20.6740			−0.960804			−0.480402	+	0.877048i	$0.659509\pi$
$464$			10.0295i			0.465607i
$465$	4.28724	+	13.4198i	0.198816	+	0.622326i
$466$	−13.8804			−0.642996
$467$	2.10185			0.0972621			0.0486310	−	0.998817i	$-0.484514\pi$
$467$	2.10185			0.0972621			0.0486310	+	0.998817i	$0.484514\pi$
$468$	−3.86313	−	5.42902i	−0.178573	−	0.250956i
$469$		0			0
$470$		−	3.00263i		−	0.138501i
$471$	−2.64564	−	8.28126i	−0.121904	−	0.381580i
$472$		−	11.8401i		−	0.544987i
$473$			0.502250i			0.0230935i
$474$	−4.72808	−	14.7996i	−0.217168	−	0.679769i
$475$		−	2.74533i		−	0.125965i
$476$		0			0
$477$	−3.00609	−	4.22459i	−0.137639	−	0.193431i
$478$	−25.8786			−1.18366
$479$	10.7574			0.491517			0.245759	−	0.969331i	$-0.420963\pi$
$479$	10.7574			0.491517			0.245759	+	0.969331i	$0.420963\pi$
$480$	−0.527098	−	1.64990i	−0.0240586	−	0.0753073i
$481$			19.1915i			0.875056i
$482$	26.2005			1.19340
$483$		0			0
$484$	−10.9664			−0.498474
$485$		−	7.23005i		−	0.328300i
$486$	15.5837	+	0.384586i	0.706892	+	0.0174452i
$487$	27.2491			1.23477			0.617386	−	0.786660i	$-0.288192\pi$
$487$	27.2491			1.23477			0.617386	+	0.786660i	$0.288192\pi$
$488$	−5.73054			−0.259409
$489$	−39.4970	+	12.6182i	−1.78612	+	0.570616i
$490$		0			0
$491$		−	9.39148i		−	0.423831i	−0.977288	−	0.211916i	$-0.932030\pi$
$491$		−	9.39148i		−	0.423831i	0.977288	−	0.211916i	$-0.0679702\pi$
$492$	−8.83967	+	2.82403i	−0.398523	+	0.127317i
$493$			59.4605i			2.67797i
$494$			6.09755i			0.274342i
$495$	0.318701	+	0.447885i	0.0143246	+	0.0201309i
$496$		−	8.13368i		−	0.365213i
$497$		0			0
$498$	4.88015	+	15.2756i	0.218685	+	0.684517i
$499$	−23.4355			−1.04912			−0.524558	−	0.851374i	$-0.675770\pi$
$499$	−23.4355			−1.04912			−0.524558	+	0.851374i	$0.675770\pi$
$500$	1.00000			0.0447214
$501$	−20.1775	+	6.44615i	−0.901463	+	0.287993i
$502$		−	17.1154i		−	0.763896i
$503$	−33.0002			−1.47140			−0.735702	−	0.677305i	$-0.763148\pi$
$503$	−33.0002			−1.47140			−0.735702	+	0.677305i	$0.763148\pi$
$504$		0			0
$505$	7.98749			0.355439
$506$		−	0.341930i		−	0.0152007i
$507$	13.3096	−	4.25204i	0.591098	−	0.188840i
$508$	−9.46529			−0.419954
$509$	−6.56393			−0.290941			−0.145471	−	0.989363i	$-0.546470\pi$
$509$	−6.56393			−0.290941			−0.145471	+	0.989363i	$0.546470\pi$
$510$	−3.12494	−	9.78156i	−0.138375	−	0.433135i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	−11.4154	−	8.55478i	−0.504001	−	0.377703i
$514$			16.1541i			0.712526i
$515$			15.2633i			0.672580i
$516$	4.52243	−	1.44479i	0.199089	−	0.0636034i
$517$		−	0.550183i		−	0.0241970i
$518$		0			0
$519$	−4.54544	+	1.45214i	−0.199523	+	0.0637421i
$520$	−2.22106			−0.0973999
$521$	4.70072			0.205942			0.102971	−	0.994684i	$-0.467165\pi$
$521$	4.70072			0.205942			0.102971	+	0.994684i	$0.467165\pi$
$522$	−24.5154	+	17.4444i	−1.07301	+	0.763522i
$523$		−	3.39241i		−	0.148340i	−0.997246	−	0.0741700i	$-0.976369\pi$
$523$		−	3.39241i		−	0.148340i	0.997246	−	0.0741700i	$-0.0236307\pi$
$524$	18.0259			0.787467
$525$		0			0
$526$	3.79029			0.165265
$527$		−	48.2212i		−	2.10055i
$528$	−0.0965821	−	0.302317i	−0.00420320	−	0.0131567i
$529$	19.5177			0.848596
$530$	−1.72832			−0.0750733
$531$	28.9413	−	20.5938i	1.25594	−	0.893693i
$532$		0			0
$533$			11.8998i			0.515436i
$534$	6.41535	+	20.0811i	0.277619	+	0.868992i
$535$		−	6.18268i		−	0.267301i
$536$			3.79196i			0.163788i
$537$	2.71600	+	8.50150i	0.117204	+	0.366867i
$538$		−	1.67131i		−	0.0720552i
$539$		0			0
$540$	3.11612	−	4.15810i	0.134096	−	0.178936i
$541$	25.7143			1.10555			0.552773	−	0.833332i	$-0.313570\pi$
$541$	25.7143			1.10555			0.552773	+	0.833332i	$0.313570\pi$
$542$	−27.8686			−1.19706
$543$	9.54282	+	29.8705i	0.409522	+	1.28187i
$544$			5.92858i			0.254186i
$545$	18.5699			0.795448
$546$		0			0
$547$	2.86827			0.122638			0.0613192	−	0.998118i	$-0.480469\pi$
$547$	2.86827			0.122638			0.0613192	+	0.998118i	$0.480469\pi$
$548$		−	1.58312i		−	0.0676275i
$549$	−9.96722	−	14.0074i	−0.425390	−	0.597819i
$550$	0.183234			0.00781311
$551$	27.5343			1.17300
$552$	−3.07886	+	0.983611i	−0.131045	+	0.0418653i
$553$		0			0
$554$		−	2.08837i		−	0.0887262i
$555$	−14.2563	+	4.55448i	−0.605144	+	0.193327i
$556$			8.23768i			0.349356i
$557$		−	23.1881i		−	0.982511i	−0.871015	−	0.491256i	$-0.836538\pi$
$557$		−	23.1881i		−	0.982511i	0.871015	−	0.491256i	$-0.163462\pi$
$558$	19.8814	−	14.1470i	0.841649	−	0.598892i
$559$		−	6.08800i		−	0.257495i
$560$		0			0
$561$	−0.572595	−	1.79231i	−0.0241750	−	0.0756714i
$562$	19.4447			0.820226
$563$	5.87313			0.247523			0.123761	−	0.992312i	$-0.460504\pi$
$563$	5.87313			0.247523			0.123761	+	0.992312i	$0.460504\pi$
$564$	−4.95404	+	1.58268i	−0.208603	+	0.0666429i
$565$			8.96035i			0.376965i
$566$	−1.11859			−0.0470177
$567$		0			0
$568$	11.3992			0.478299
$569$		−	31.9287i		−	1.33852i	−0.743028	−	0.669261i	$-0.766611\pi$
$569$		−	31.9287i		−	1.33852i	0.743028	−	0.669261i	$-0.233389\pi$
$570$	−4.52952	+	1.44706i	−0.189721	+	0.0606106i
$571$	−18.5344			−0.775640			−0.387820	−	0.921735i	$-0.626772\pi$
$571$	−18.5344			−0.775640			−0.387820	+	0.921735i	$0.626772\pi$
$572$	−0.406973			−0.0170164
$573$	7.94540	+	24.8704i	0.331924	+	1.03897i
$574$		0			0
$575$		−	1.86609i		−	0.0778213i
$576$	−2.44434	+	1.73932i	−0.101847	+	0.0724715i
$577$		−	15.3847i		−	0.640474i	−0.947337	−	0.320237i	$-0.896237\pi$
$577$		−	15.3847i		−	0.640474i	0.947337	−	0.320237i	$-0.103763\pi$
$578$			18.1480i			0.754859i
$579$	−40.1122	+	12.8147i	−1.66701	+	0.532563i
$580$			10.0295i			0.416451i
$581$		0			0
$582$	−11.9289	+	3.81094i	−0.494467	+	0.157969i
$583$	−0.316686			−0.0131158
$584$	8.37048			0.346373
$585$	−3.86313	−	5.42902i	−0.159721	−	0.224462i
$586$		−	25.9736i		−	1.07296i
$587$	−3.04776			−0.125795			−0.0628973	−	0.998020i	$-0.520034\pi$
$587$	−3.04776			−0.125795			−0.0628973	+	0.998020i	$0.520034\pi$
$588$		0			0
$589$	−22.3297			−0.920078
$590$		−	11.8401i		−	0.487451i
$591$	0.402291	+	1.25923i	0.0165480	+	0.0517980i
$592$	8.64068			0.355130
$593$	−7.74576			−0.318080			−0.159040	−	0.987272i	$-0.550840\pi$
$593$	−7.74576			−0.318080			−0.159040	+	0.987272i	$0.550840\pi$
$594$	0.570978	−	0.761904i	0.0234275	−	0.0312613i
$595$		0			0
$596$			9.35407i			0.383158i
$597$	−3.96935	−	12.4247i	−0.162455	−	0.508508i
$598$			4.14469i			0.169489i
$599$		−	33.6603i		−	1.37532i	−0.726032	−	0.687661i	$-0.758638\pi$
$599$		−	33.6603i		−	1.37532i	0.726032	−	0.687661i	$-0.241362\pi$
$600$	−0.527098	−	1.64990i	−0.0215187	−	0.0673569i
$601$			38.9597i			1.58920i	0.607134	+	0.794600i	$0.292319\pi$
$601$			38.9597i			1.58920i	−0.607134	+	0.794600i	$0.707681\pi$
$602$		0			0
$603$	−9.26883	+	6.59542i	−0.377456	+	0.268586i
$604$	14.2685			0.580575
$605$	−10.9664			−0.445849
$606$	−4.21019	−	13.1786i	−0.171027	−	0.535342i
$607$			23.5510i			0.955906i	0.878386	+	0.477953i	$0.158621\pi$
$607$			23.5510i			0.955906i	−0.878386	+	0.477953i	$0.841379\pi$
$608$	2.74533			0.111338
$609$		0			0
$610$	−5.73054			−0.232023
$611$			6.66902i			0.269800i
$612$	−14.4914	+	10.3117i	−0.585782	+	0.416825i
$613$	4.95160			0.199993			0.0999966	−	0.994988i	$-0.468117\pi$
$613$	4.95160			0.199993			0.0999966	+	0.994988i	$0.468117\pi$
$614$	−14.8678			−0.600014
$615$	−8.83967	+	2.82403i	−0.356450	+	0.113876i
$616$		0			0
$617$			32.5086i			1.30875i	0.756172	+	0.654373i	$0.227067\pi$
$617$			32.5086i			1.30875i	−0.756172	+	0.654373i	$0.772933\pi$
$618$	25.1829	−	8.04524i	1.01300	−	0.323627i
$619$			28.1229i			1.13035i	0.824970	+	0.565177i	$0.191192\pi$
$619$			28.1229i			1.13035i	−0.824970	+	0.565177i	$0.808808\pi$
$620$		−	8.13368i		−	0.326656i
$621$	−7.75939	−	5.81495i	−0.311373	−	0.233346i
$622$		−	10.1085i		−	0.405314i
$623$		0			0
$624$	1.17072	+	3.66453i	0.0468661	+	0.146698i
$625$	1.00000			0.0400000
$626$	30.7635			1.22956
$627$	−0.829962	+	0.265150i	−0.0331455	+	0.0105891i
$628$			5.01925i			0.200290i
$629$	51.2270			2.04255
$630$		0			0
$631$	22.5082			0.896038			0.448019	−	0.894024i	$-0.352130\pi$
$631$	22.5082			0.896038			0.448019	+	0.894024i	$0.352130\pi$
$632$			8.97002i			0.356808i
$633$	22.9461	−	7.33066i	0.912026	−	0.291367i
$634$	−15.3849			−0.611012
$635$	−9.46529			−0.375618
$636$	0.910992	+	2.85155i	0.0361232	+	0.113071i
$637$		0			0
$638$			1.83774i			0.0727568i
$639$	19.8268	+	27.8634i	0.784335	+	1.10226i
$640$			1.00000i			0.0395285i
$641$			48.5107i			1.91606i	0.286670	+	0.958029i	$0.407452\pi$
$641$			48.5107i			1.91606i	−0.286670	+	0.958029i	$0.592548\pi$
$642$	−10.2008	+	3.25888i	−0.402593	+	0.128618i
$643$		−	18.4380i		−	0.727123i	−0.931570	−	0.363561i	$-0.881561\pi$
$643$		−	18.4380i		−	0.727123i	0.931570	−	0.363561i	$-0.118439\pi$
$644$		0			0
$645$	4.52243	−	1.44479i	0.178070	−	0.0568886i
$646$	16.2759			0.640368
$647$	16.2081			0.637208			0.318604	−	0.947888i	$-0.396786\pi$
$647$	16.2081			0.637208			0.318604	+	0.947888i	$0.396786\pi$
$648$	−8.50295	−	2.94956i	−0.334027	−	0.115870i
$649$		−	2.16951i		−	0.0851609i
$650$	−2.22106			−0.0871171
$651$		0			0
$652$	23.9391			0.937526
$653$			10.1843i			0.398544i	0.979944	+	0.199272i	$0.0638578\pi$
$653$			10.1843i			0.398544i	−0.979944	+	0.199272i	$0.936142\pi$
$654$	−9.78816	−	30.6385i	−0.382747	−	1.19806i
$655$	18.0259			0.704332
$656$	5.35770			0.209183
$657$	14.5589	+	20.4603i	0.567997	+	0.798231i
$658$		0			0
$659$			11.7903i			0.459287i	0.973275	+	0.229643i	$0.0737560\pi$
$659$			11.7903i			0.459287i	−0.973275	+	0.229643i	$0.926244\pi$
$660$	−0.0965821	−	0.302317i	−0.00375945	−	0.0117677i
$661$			26.8096i			1.04277i	0.853320	+	0.521387i	$0.174585\pi$
$661$			26.8096i			1.04277i	−0.853320	+	0.521387i	$0.825415\pi$
$662$		−	11.3036i		−	0.439326i
$663$	6.94068	+	21.7254i	0.269554	+	0.843746i
$664$		−	9.25852i		−	0.359300i
$665$		0			0
$666$	15.0289	+	21.1207i	0.582357	+	0.818412i
$667$	18.7159			0.724682
$668$	12.2295			0.473174
$669$	−9.94848	−	31.1403i	−0.384630	−	1.20395i
$670$			3.79196i			0.146496i
$671$	−1.05003			−0.0405359
$672$		0			0
$673$	−5.41415			−0.208700			−0.104350	−	0.994541i	$-0.533276\pi$
$673$	−5.41415			−0.208700			−0.104350	+	0.994541i	$0.533276\pi$
$674$		−	35.2334i		−	1.35714i
$675$	3.11612	−	4.15810i	0.119939	−	0.160045i
$676$	−8.06689			−0.310265
$677$	−27.7636			−1.06704			−0.533521	−	0.845787i	$-0.679131\pi$
$677$	−27.7636			−1.06704			−0.533521	+	0.845787i	$0.679131\pi$
$678$	14.7837	−	4.72298i	0.567764	−	0.181385i
$679$		0			0
$680$			5.92858i			0.227351i
$681$	−5.96621	+	1.90604i	−0.228626	+	0.0730397i
$682$		−	1.49036i		−	0.0570690i
$683$			0.877923i			0.0335928i	0.999859	+	0.0167964i	$0.00534671\pi$
$683$			0.877923i			0.0335928i	−0.999859	+	0.0167964i	$0.994653\pi$
$684$	4.77500	+	6.71052i	0.182577	+	0.256583i
$685$		−	1.58312i		−	0.0604879i
$686$		0			0
$687$	10.7732	+	33.7220i	0.411025	+	1.28657i
$688$	−2.74103			−0.104501
$689$	3.83870			0.146243
$690$	−3.07886	+	0.983611i	−0.117210	+	0.0374454i
$691$			34.2334i			1.30230i	0.758949	+	0.651151i	$0.225713\pi$
$691$			34.2334i			1.30230i	−0.758949	+	0.651151i	$0.774287\pi$
$692$	2.75498			0.104729
$693$		0			0
$694$	36.4627			1.38411
$695$			8.23768i			0.312473i
$696$	16.5476	−	5.28652i	0.627236	−	0.200385i
$697$	31.7635			1.20313
$698$	−5.80210			−0.219613
$699$	7.31631	+	22.9012i	0.276728	+	0.866203i
$700$		0			0
$701$			16.9235i			0.639191i	0.947554	+	0.319596i	$0.103547\pi$
$701$			16.9235i			0.639191i	−0.947554	+	0.319596i	$0.896453\pi$
$702$	−6.92109	+	9.23539i	−0.261220	+	0.348567i
$703$		−	23.7216i		−	0.894675i
$704$			0.183234i			0.00690588i
$705$	−4.95404	+	1.58268i	−0.186580	+	0.0596072i
$706$		−	36.8540i		−	1.38702i
$707$		0			0
$708$	−19.5350	+	6.24091i	−0.734172	+	0.234548i
$709$	6.85139			0.257310			0.128655	−	0.991689i	$-0.458934\pi$
$709$	6.85139			0.257310			0.128655	+	0.991689i	$0.458934\pi$
$710$	11.3992			0.427804
$711$	−21.9257	+	15.6017i	−0.822280	+	0.585110i
$712$		−	12.1711i		−	0.456130i
$713$	−15.1782			−0.568427
$714$		0			0
$715$	−0.406973			−0.0152199
$716$		−	5.15274i		−	0.192567i
$717$	13.6406	+	42.6971i	0.509416	+	1.59455i
$718$	14.6764			0.547717
$719$	−22.2069			−0.828179			−0.414089	−	0.910236i	$-0.635900\pi$
$719$	−22.2069			−0.828179			−0.414089	+	0.910236i	$0.635900\pi$
$720$	−2.44434	+	1.73932i	−0.0910950	+	0.0648205i
$721$		0			0
$722$			11.4631i			0.426614i
$723$	−13.8102	−	43.2282i	−0.513608	−	1.60767i
$724$		−	18.1045i		−	0.672847i
$725$			10.0295i			0.372486i
$726$	5.78038	+	18.0935i	0.214530	+	0.671513i
$727$		−	7.00749i		−	0.259894i	−0.991521	−	0.129947i	$-0.958519\pi$
$727$		−	7.00749i		−	0.259894i	0.991521	−	0.129947i	$-0.0414806\pi$
$728$		0			0
$729$	−7.57961	−	25.9143i	−0.280726	−	0.959788i
$730$	8.37048			0.309805
$731$	−16.2504			−0.601044
$732$	3.02055	+	9.45481i	0.111643	+	0.349460i
$733$			36.7024i			1.35563i	0.735231	+	0.677816i	$0.237074\pi$
$733$			36.7024i			1.35563i	−0.735231	+	0.677816i	$0.762926\pi$
$734$	28.9944			1.07020
$735$		0			0
$736$	1.86609			0.0687849
$737$			0.694816i			0.0255939i
$738$	9.31874	+	13.0960i	0.343027	+	0.482071i
$739$	20.6386			0.759203			0.379602	−	0.925150i	$-0.376061\pi$
$739$	20.6386			0.759203			0.379602	+	0.925150i	$0.376061\pi$
$740$	8.64068			0.317638
$741$	10.0603	−	3.21401i	0.369576	−	0.118069i
$742$		0			0
$743$		−	8.62699i		−	0.316494i	−0.987400	−	0.158247i	$-0.949416\pi$
$743$		−	8.62699i		−	0.316494i	0.987400	−	0.158247i	$-0.0505842\pi$
$744$	−13.4198	+	4.28724i	−0.491992	+	0.157178i
$745$			9.35407i			0.342707i
$746$		−	27.5619i		−	1.00911i
$747$	22.6309	−	16.1035i	0.828023	−	0.589196i
$748$			1.08632i			0.0397196i
$749$		0			0
$750$	−0.527098	−	1.64990i	−0.0192469	−	0.0602458i
$751$	−4.16116			−0.151843			−0.0759214	−	0.997114i	$-0.524190\pi$
$751$	−4.16116			−0.151843			−0.0759214	+	0.997114i	$0.524190\pi$
$752$	3.00263			0.109495
$753$	−28.2386	+	9.02147i	−1.02907	+	0.328761i
$754$		−	22.2761i		−	0.811247i
$755$	14.2685			0.519282
$756$		0			0
$757$	19.4589			0.707244			0.353622	−	0.935388i	$-0.384950\pi$
$757$	19.4589			0.707244			0.353622	+	0.935388i	$0.384950\pi$
$758$			25.9475i			0.942455i
$759$	−0.564151	+	0.180231i	−0.0204774	+	0.00654196i
$760$	2.74533			0.0995837
$761$	−2.91036			−0.105500			−0.0527502	−	0.998608i	$-0.516799\pi$
$761$	−2.91036			−0.105500			−0.0527502	+	0.998608i	$0.516799\pi$
$762$	4.98913	+	15.6168i	0.180737	+	0.565736i
$763$		0			0
$764$		−	15.0739i		−	0.545353i
$765$	−14.4914	+	10.3117i	−0.523939	+	0.372819i
$766$			36.5542i			1.32076i
$767$			26.2977i			0.949554i
$768$	1.64990	−	0.527098i	0.0595356	−	0.0190200i
$769$			13.9115i			0.501661i	0.968031	+	0.250830i	$0.0807036\pi$
$769$			13.9115i			0.501661i	−0.968031	+	0.250830i	$0.919296\pi$
$770$		0			0
$771$	26.6526	−	8.51478i	0.959870	−	0.306652i
$772$	24.3119			0.875004
$773$	−8.15536			−0.293328			−0.146664	−	0.989186i	$-0.546854\pi$
$773$	−8.15536			−0.293328			−0.146664	+	0.989186i	$0.546854\pi$
$774$	−4.76752	−	6.70001i	−0.171365	−	0.240827i
$775$		−	8.13368i		−	0.292170i
$776$	7.23005			0.259544
$777$		0			0
$778$	−19.5029			−0.699214
$779$		−	14.7087i		−	0.526993i
$780$	1.17072	+	3.66453i	0.0419183	+	0.131211i
$781$	2.08871			0.0747401
$782$	11.0633			0.395621
$783$	41.7036	+	31.2530i	1.49036	+	1.11689i
$784$		0			0
$785$			5.01925i			0.179145i
$786$	−9.50143	−	29.7410i	−0.338905	−	1.06083i
$787$			1.35697i			0.0483707i	0.999707	+	0.0241854i	$0.00769919\pi$
$787$			1.35697i			0.0483707i	−0.999707	+	0.0241854i	$0.992301\pi$
$788$		−	0.763219i		−	0.0271885i
$789$	−1.99785	−	6.25360i	−0.0711255	−	0.222634i
$790$			8.97002i			0.319139i
$791$		0			0
$792$	−0.447885	+	0.318701i	−0.0159149	+	0.0113246i
$793$	12.7279			0.451980
$794$	8.12748			0.288434
$795$	0.910992	+	2.85155i	0.0323096	+	0.101134i
$796$			7.53057i			0.266914i
$797$	−11.4530			−0.405688			−0.202844	−	0.979211i	$-0.565018\pi$
$797$	−11.4530			−0.405688			−0.202844	+	0.979211i	$0.565018\pi$
$798$		0			0
$799$	17.8013			0.629766
$800$			1.00000i			0.0353553i
$801$	29.7502	−	21.1694i	1.05117	−	0.747983i
$802$	−19.8417			−0.700633
$803$	1.53375			0.0541250
$804$	6.25636	−	1.99874i	0.220645	−	0.0704899i
$805$		0			0
$806$			18.0654i			0.636326i
$807$	−2.75749	+	0.880942i	−0.0970682	+	0.0310106i
$808$			7.98749i			0.280999i
$809$		−	6.10324i		−	0.214579i	−0.994228	−	0.107289i	$-0.965783\pi$
$809$		−	6.10324i		−	0.214579i	0.994228	−	0.107289i	$-0.0342171\pi$
$810$	−8.50295	−	2.94956i	−0.298763	−	0.103637i
$811$			32.4705i			1.14019i	0.821578	+	0.570097i	$0.193094\pi$
$811$			32.4705i			1.14019i	−0.821578	+	0.570097i	$0.806906\pi$
$812$		0			0
$813$	14.6895	+	45.9804i	0.515183	+	1.61260i
$814$	1.58326			0.0554934
$815$	23.9391			0.838548
$816$	9.78156	−	3.12494i	0.342423	−	0.109395i
$817$			7.52505i			0.263268i
$818$	−3.20599			−0.112095
$819$		0			0
$820$	5.35770			0.187099
$821$			36.7165i			1.28142i	0.767785	+	0.640708i	$0.221359\pi$
$821$			36.7165i			1.28142i	−0.767785	+	0.640708i	$0.778641\pi$
$822$	−2.61199	+	0.834458i	−0.0911035	+	0.0291051i
$823$	−10.6302			−0.370545			−0.185273	−	0.982687i	$-0.559317\pi$
$823$	−10.6302			−0.370545			−0.185273	+	0.982687i	$0.559317\pi$
$824$	−15.2633			−0.531721
$825$	−0.0965821	−	0.302317i	−0.00336256	−	0.0105253i
$826$		0			0
$827$			18.9955i			0.660537i	0.943887	+	0.330269i	$0.107139\pi$
$827$			18.9955i			0.660537i	−0.943887	+	0.330269i	$0.892861\pi$
$828$	3.24572	+	4.56135i	0.112797	+	0.158518i
$829$			29.1165i			1.01126i	0.862751	+	0.505628i	$0.168739\pi$
$829$			29.1165i			1.01126i	−0.862751	+	0.505628i	$0.831261\pi$
$830$		−	9.25852i		−	0.321368i
$831$	−3.44560	+	1.10077i	−0.119526	+	0.0381854i
$832$		−	2.22106i		−	0.0770014i
$833$		0			0
$834$	13.5913	−	4.34206i	0.470630	−	0.150353i
$835$	12.2295			0.423220
$836$	0.503038			0.0173979
$837$	−33.8207	−	25.3455i	−1.16901	−	0.876069i
$838$			6.99137i			0.241513i
$839$	37.0577			1.27937			0.639687	−	0.768636i	$-0.279064\pi$
$839$	37.0577			1.27937			0.639687	+	0.768636i	$0.279064\pi$
$840$		0			0
$841$	−71.5905			−2.46864
$842$			17.7534i			0.611822i
$843$	−10.2493	−	32.0818i	−0.353004	−	1.10496i
$844$	−13.9076			−0.478719
$845$	−8.06689			−0.277510
$846$	5.22253	+	7.33944i	0.179554	+	0.252335i
$847$		0			0
$848$		−	1.72832i		−	0.0593506i
$849$	0.589605	+	1.84556i	0.0202352	+	0.0633393i
$850$			5.92858i			0.203349i
$851$		−	16.1243i		−	0.552733i
$852$	−6.00848	−	18.8075i	−0.205847	−	0.644334i
$853$			0.176745i			0.00605163i	0.999995	+	0.00302581i	$0.000963148\pi$
$853$			0.176745i			0.00605163i	−0.999995	+	0.00302581i	$0.999037\pi$
$854$		0			0
$855$	4.77500	+	6.71052i	0.163302	+	0.229495i
$856$	6.18268			0.211320
$857$	14.9114			0.509365			0.254682	−	0.967025i	$-0.418029\pi$
$857$	14.9114			0.509365			0.254682	+	0.967025i	$0.418029\pi$
$858$	0.214515	+	0.671465i	0.00732341	+	0.0229234i
$859$			22.9969i			0.784646i	0.919828	+	0.392323i	$0.128328\pi$
$859$			22.9969i			0.784646i	−0.919828	+	0.392323i	$0.871672\pi$
$860$	−2.74103			−0.0934684
$861$		0			0
$862$	−21.5466			−0.733879
$863$		−	23.1453i		−	0.787877i	−0.919137	−	0.393938i	$-0.871112\pi$
$863$		−	23.1453i		−	0.787877i	0.919137	−	0.393938i	$-0.128888\pi$
$864$	4.15810	+	3.11612i	0.141461	+	0.106013i
$865$	2.75498			0.0936722
$866$	−2.22339			−0.0755540
$867$	29.9424	−	9.56579i	1.01690	−	0.324871i
$868$		0			0
$869$			1.64361i			0.0557557i
$870$	16.5476	−	5.28652i	0.561017	−	0.179230i
$871$		−	8.42218i		−	0.285375i
$872$			18.5699i			0.628857i
$873$	12.5753	+	17.6727i	0.425611	+	0.598129i
$874$		−	5.12304i		−	0.173289i
$875$		0			0
$876$	−4.41206	−	13.8104i	−0.149070	−	0.466612i
$877$	7.97467			0.269286			0.134643	−	0.990894i	$-0.457011\pi$
$877$	7.97467			0.269286			0.134643	+	0.990894i	$0.457011\pi$
$878$	−1.07643			−0.0363277
$879$	−42.8538	+	13.6906i	−1.44542	+	0.461773i
$880$			0.183234i			0.00617681i
$881$	2.54981			0.0859054			0.0429527	−	0.999077i	$-0.486324\pi$
$881$	2.54981			0.0859054			0.0429527	+	0.999077i	$0.486324\pi$
$882$		0			0
$883$	23.8728			0.803384			0.401692	−	0.915775i	$-0.368422\pi$
$883$	23.8728			0.803384			0.401692	+	0.915775i	$0.368422\pi$
$884$		−	13.1677i		−	0.442879i
$885$	−19.5350	+	6.24091i	−0.656663	+	0.209786i
$886$	22.1450			0.743975
$887$	37.5185			1.25975			0.629874	−	0.776697i	$-0.283106\pi$
$887$	37.5185			1.25975			0.629874	+	0.776697i	$0.283106\pi$
$888$	−4.55448	−	14.2563i	−0.152838	−	0.478409i
$889$		0			0
$890$		−	12.1711i		−	0.407976i
$891$	−1.55803	−	0.540458i	−0.0521959	−	0.0181060i
$892$			18.8741i			0.631951i
$893$		−	8.24323i		−	0.275849i
$894$	15.4333	−	4.93051i	0.516166	−	0.164901i
$895$		−	5.15274i		−	0.172237i
$896$		0			0
$897$	6.83833	−	2.18466i	0.228325	−	0.0729437i
$898$	−2.54766			−0.0850164
$899$	81.5766			2.72073
$900$	−2.44434	+	1.73932i	−0.0814779	+	0.0579772i
$901$		−	10.2465i		−	0.341359i
$902$	0.981712			0.0326874
$903$		0			0
$904$	−8.96035			−0.298017
$905$		−	18.1045i		−	0.601813i
$906$	−7.52087	−	23.5415i	−0.249864	−	0.782114i
$907$	29.2619			0.971625			0.485813	−	0.874063i	$-0.338524\pi$
$907$	29.2619			0.971625			0.485813	+	0.874063i	$0.338524\pi$
$908$	3.61611			0.120005
$909$	−19.5241	+	13.8928i	−0.647574	+	0.460794i
$910$		0			0
$911$			22.2195i			0.736164i	0.929793	+	0.368082i	$0.119985\pi$
$911$			22.2195i			0.736164i	−0.929793	+	0.368082i	$0.880015\pi$
$912$	−1.44706	−	4.52952i	−0.0479169	−	0.149988i
$913$		−	1.69647i		−	0.0561451i
$914$			4.69058i			0.155150i
$915$	3.02055	+	9.45481i	0.0998564	+	0.312566i
$916$		−	20.4388i		−	0.675317i
$917$		0			0
$918$	24.6516	+	18.4742i	0.813625	+	0.609738i
$919$	−16.3855			−0.540508			−0.270254	−	0.962789i	$-0.587108\pi$
$919$	−16.3855			−0.540508			−0.270254	+	0.962789i	$0.587108\pi$
$920$	1.86609			0.0615231
$921$	7.83677	+	24.5303i	0.258230	+	0.808302i
$922$			5.10979i			0.168282i
$923$	−25.3183			−0.833361
$924$		0			0
$925$	8.64068			0.284104
$926$		−	20.6740i		−	0.679391i
$927$	−26.5477	−	37.3086i	−0.871939	−	1.22537i
$928$	−10.0295			−0.329234
$929$	−3.74333			−0.122815			−0.0614073	−	0.998113i	$-0.519559\pi$
$929$	−3.74333			−0.122815			−0.0614073	+	0.998113i	$0.519559\pi$
$930$	−13.4198	+	4.28724i	−0.440051	+	0.140584i
$931$		0			0
$932$		−	13.8804i		−	0.454667i
$933$	−16.6780	+	5.32817i	−0.546014	+	0.174436i
$934$			2.10185i			0.0687747i
$935$			1.08632i			0.0355263i
$936$	5.42902	−	3.86313i	0.177453	−	0.126270i
$937$		−	6.53832i		−	0.213598i	−0.994281	−	0.106799i	$-0.965940\pi$
$937$		−	6.53832i		−	0.213598i	0.994281	−	0.106799i	$-0.0340601\pi$
$938$		0			0
$939$	−16.2154	−	50.7567i	−0.529169	−	1.65638i
$940$	3.00263			0.0979350
$941$	−15.2301			−0.496487			−0.248244	−	0.968698i	$-0.579853\pi$
$941$	−15.2301			−0.496487			−0.248244	+	0.968698i	$0.579853\pi$
$942$	8.28126	−	2.64564i	0.269818	−	0.0861995i
$943$		−	9.99794i		−	0.325578i
$944$	11.8401			0.385364
$945$		0			0
$946$	−0.502250			−0.0163295
$947$		−	42.7603i		−	1.38952i	−0.719241	−	0.694761i	$-0.755510\pi$
$947$		−	42.7603i		−	1.38952i	0.719241	−	0.694761i	$-0.244490\pi$
$948$	14.7996	−	4.72808i	0.480670	−	0.153561i
$949$	−18.5913			−0.603500
$950$	2.74533			0.0890704
$951$	8.10934	+	25.3835i	0.262963	+	0.823117i
$952$		0			0
$953$			25.9458i			0.840466i	0.907416	+	0.420233i	$0.138052\pi$
$953$			25.9458i			0.840466i	−0.907416	+	0.420233i	$0.861948\pi$
$954$	4.22459	−	3.00609i	0.136776	−	0.0973258i
$955$		−	15.0739i		−	0.487779i
$956$		−	25.8786i		−	0.836974i
$957$	3.03208	−	0.968668i	0.0980134	−	0.0313126i
$958$			10.7574i			0.347555i
$959$		0			0
$960$	1.64990	−	0.527098i	0.0532503	−	0.0170120i
$961$	−35.1568			−1.13409
$962$	−19.1915			−0.618758
$963$	10.7536	+	15.1125i	0.346531	+	0.486995i
$964$			26.2005i			0.843862i
$965$	24.3119			0.782628
$966$		0			0
$967$	−41.1260			−1.32252			−0.661262	−	0.750155i	$-0.729979\pi$
$967$	−41.1260			−1.32252			−0.661262	+	0.750155i	$0.729979\pi$
$968$		−	10.9664i		−	0.352474i
$969$	−8.57900	−	26.8536i	−0.275597	−	0.862663i
$970$	7.23005			0.232143
$971$	−13.8976			−0.445996			−0.222998	−	0.974819i	$-0.571584\pi$
$971$	−13.8976			−0.445996			−0.222998	+	0.974819i	$0.571584\pi$
$972$	−0.384586	+	15.5837i	−0.0123356	+	0.499848i
$973$		0			0
$974$			27.2491i			0.873116i
$975$	1.17072	+	3.66453i	0.0374929	+	0.117359i
$976$		−	5.73054i		−	0.183430i
$977$			47.6237i			1.52362i	0.647801	+	0.761809i	$0.275689\pi$
$977$			47.6237i			1.52362i	−0.647801	+	0.761809i	$0.724311\pi$
$978$	−12.6182	−	39.4970i	−0.403486	−	1.26298i
$979$		−	2.23015i		−	0.0712760i
$980$		0			0
$981$	−45.3911	+	32.2990i	−1.44923	+	1.03123i
$982$	9.39148			0.299694
$983$	−39.7344			−1.26733			−0.633665	−	0.773607i	$-0.718450\pi$
$983$	−39.7344			−1.26733			−0.633665	+	0.773607i	$0.718450\pi$
$984$	−2.82403	−	8.83967i	−0.0900268	−	0.281798i
$985$		−	0.763219i		−	0.0243182i
$986$	−59.4605			−1.89361
$987$		0			0
$988$	−6.09755			−0.193989
$989$			5.11501i			0.162648i
$990$	−0.447885	+	0.318701i	−0.0142347	+	0.0101290i
$991$	35.1681			1.11715			0.558576	−	0.829454i	$-0.311348\pi$
$991$	35.1681			1.11715			0.558576	+	0.829454i	$0.311348\pi$
$992$	8.13368			0.258245
$993$	−18.6498	+	5.95809i	−0.591832	+	0.189074i
$994$		0			0
$995$			7.53057i			0.238735i
$996$	−15.2756	+	4.88015i	−0.484027	+	0.154633i
$997$			20.2745i			0.642101i	0.947062	+	0.321050i	$0.104036\pi$
$997$			20.2745i			0.642101i	−0.947062	+	0.321050i	$0.895964\pi$
$998$		−	23.4355i		−	0.741838i
$999$	26.9254	−	35.9288i	0.851882	−	1.13674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.b.c.881.16	yes	16
3.2	odd	2		1470.2.b.d.881.1	yes	16
7.6	odd	2		1470.2.b.d.881.9	yes	16
21.20	even	2	inner	1470.2.b.c.881.8	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.b.c.881.8	✓	16	21.20	even	2	inner
1470.2.b.c.881.16	yes	16	1.1	even	1	trivial
1470.2.b.d.881.1	yes	16	3.2	odd	2
1470.2.b.d.881.9	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.64990 - 0.527098i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(0.527098 + 1.64990i) q^{6} -1.00000i q^{8} +(2.44434 - 1.73932i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(1.64990 - 0.527098i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(0.527098 + 1.64990i) q^{6} -1.00000i q^{8} +(2.44434 - 1.73932i) q^{9} -1.00000i q^{10} -0.183234i q^{11} +(-1.64990 + 0.527098i) q^{12} +2.22106i q^{13} +(-1.64990 + 0.527098i) q^{15} +1.00000 q^{16} +5.92858 q^{17} +(1.73932 + 2.44434i) q^{18} -2.74533i q^{19} +1.00000 q^{20} +0.183234 q^{22} -1.86609i q^{23} +(-0.527098 - 1.64990i) q^{24} +1.00000 q^{25} -2.22106 q^{26} +(3.11612 - 4.15810i) q^{27} +10.0295i q^{29} +(-0.527098 - 1.64990i) q^{30} -8.13368i q^{31} +1.00000i q^{32} +(-0.0965821 - 0.302317i) q^{33} +5.92858i q^{34} +(-2.44434 + 1.73932i) q^{36} +8.64068 q^{37} +2.74533 q^{38} +(1.17072 + 3.66453i) q^{39} +1.00000i q^{40} +5.35770 q^{41} -2.74103 q^{43} +0.183234i q^{44} +(-2.44434 + 1.73932i) q^{45} +1.86609 q^{46} +3.00263 q^{47} +(1.64990 - 0.527098i) q^{48} +1.00000i q^{50} +(9.78156 - 3.12494i) q^{51} -2.22106i q^{52} -1.72832i q^{53} +(4.15810 + 3.11612i) q^{54} +0.183234i q^{55} +(-1.44706 - 4.52952i) q^{57} -10.0295 q^{58} +11.8401 q^{59} +(1.64990 - 0.527098i) q^{60} -5.73054i q^{61} +8.13368 q^{62} -1.00000 q^{64} -2.22106i q^{65} +(0.302317 - 0.0965821i) q^{66} -3.79196 q^{67} -5.92858 q^{68} +(-0.983611 - 3.07886i) q^{69} +11.3992i q^{71} +(-1.73932 - 2.44434i) q^{72} +8.37048i q^{73} +8.64068i q^{74} +(1.64990 - 0.527098i) q^{75} +2.74533i q^{76} +(-3.66453 + 1.17072i) q^{78} -8.97002 q^{79} -1.00000 q^{80} +(2.94956 - 8.50295i) q^{81} +5.35770i q^{82} +9.25852 q^{83} -5.92858 q^{85} -2.74103i q^{86} +(5.28652 + 16.5476i) q^{87} -0.183234 q^{88} +12.1711 q^{89} +(-1.73932 - 2.44434i) q^{90} +1.86609i q^{92} +(-4.28724 - 13.4198i) q^{93} +3.00263i q^{94} +2.74533i q^{95} +(0.527098 + 1.64990i) q^{96} +7.23005i q^{97} +(-0.318701 - 0.447885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} - 16 q^{4} - 16 q^{5} + 8 q^{9}+O(q^{10}) \) 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

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