LMFDB - Embedded newform 1470.2.b.d.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			$-0.793941 - 1.53937i$ of defining polynomial
Character	$\chi$	$=$	1470.881
Dual form			1470.2.b.d.881.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(1.72602 - 0.144414i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(0.144414 + 1.72602i) q^{6} -1.00000i q^{8} +(2.95829 - 0.498524i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(1.72602 - 0.144414i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(0.144414 + 1.72602i) q^{6} -1.00000i q^{8} +(2.95829 - 0.498524i) q^{9} +1.00000i q^{10} -5.90717i q^{11} +(-1.72602 + 0.144414i) q^{12} -1.19315i q^{13} +(1.72602 - 0.144414i) q^{15} +1.00000 q^{16} -0.519764 q^{17} +(0.498524 + 2.95829i) q^{18} -5.46018i q^{19} -1.00000 q^{20} +5.90717 q^{22} +6.81104i q^{23} +(-0.144414 - 1.72602i) q^{24} +1.00000 q^{25} +1.19315 q^{26} +(5.03407 - 1.28768i) q^{27} -6.27090i q^{29} +(0.144414 + 1.72602i) q^{30} -3.20353i q^{31} +1.00000i q^{32} +(-0.853079 - 10.1959i) q^{33} -0.519764i q^{34} +(-2.95829 + 0.498524i) q^{36} -4.15021 q^{37} +5.46018 q^{38} +(-0.172308 - 2.05941i) q^{39} -1.00000i q^{40} +11.7294 q^{41} +3.42854 q^{43} +5.90717i q^{44} +(2.95829 - 0.498524i) q^{45} -6.81104 q^{46} -5.45825 q^{47} +(1.72602 - 0.144414i) q^{48} +1.00000i q^{50} +(-0.897122 + 0.0750613i) q^{51} +1.19315i q^{52} +4.12614i q^{53} +(1.28768 + 5.03407i) q^{54} -5.90717i q^{55} +(-0.788529 - 9.42439i) q^{57} +6.27090 q^{58} -2.16108 q^{59} +(-1.72602 + 0.144414i) q^{60} +9.24003i q^{61} +3.20353 q^{62} -1.00000 q^{64} -1.19315i q^{65} +(10.1959 - 0.853079i) q^{66} -7.37539 q^{67} +0.519764 q^{68} +(0.983611 + 11.7560i) q^{69} +9.94550i q^{71} +(-0.498524 - 2.95829i) q^{72} +9.04250i q^{73} -4.15021i q^{74} +(1.72602 - 0.144414i) q^{75} +5.46018i q^{76} +(2.05941 - 0.172308i) q^{78} -13.1097 q^{79} +1.00000 q^{80} +(8.50295 - 2.94956i) q^{81} +11.7294i q^{82} +15.8037 q^{83} -0.519764 q^{85} +3.42854i q^{86} +(-0.905608 - 10.8237i) q^{87} -5.90717 q^{88} +2.22998 q^{89} +(0.498524 + 2.95829i) q^{90} -6.81104i q^{92} +(-0.462636 - 5.52936i) q^{93} -5.45825i q^{94} -5.46018i q^{95} +(0.144414 + 1.72602i) q^{96} -9.01872i q^{97} +(-2.94486 - 17.4751i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.72602	−	0.144414i	0.996518	−	0.0833776i
$3$	1.72602	−	0.144414i	0.996518	−	0.0833776i
$4$	−1.00000			−0.500000
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	0.144414	+	1.72602i	0.0589569	+	0.704645i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	2.95829	−	0.498524i	0.986096	−	0.166175i
$10$			1.00000i			0.316228i
$11$		−	5.90717i		−	1.78108i	−0.454907	−	0.890539i	$-0.650328\pi$
$11$		−	5.90717i		−	1.78108i	0.454907	−	0.890539i	$-0.349672\pi$
$12$	−1.72602	+	0.144414i	−0.498259	+	0.0416888i
$13$		−	1.19315i		−	0.330921i	−0.986216	−	0.165461i	$-0.947089\pi$
$13$		−	1.19315i		−	0.330921i	0.986216	−	0.165461i	$-0.0529111\pi$
$14$		0			0
$15$	1.72602	−	0.144414i	0.445656	−	0.0372876i
$16$	1.00000			0.250000
$17$	−0.519764			−0.126061			−0.0630306	−	0.998012i	$-0.520077\pi$
$17$	−0.519764			−0.126061			−0.0630306	+	0.998012i	$0.520077\pi$
$18$	0.498524	+	2.95829i	0.117503	+	0.697275i
$19$		−	5.46018i		−	1.25265i	−0.779561	−	0.626326i	$-0.784558\pi$
$19$		−	5.46018i		−	1.25265i	0.779561	−	0.626326i	$-0.215442\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	5.90717			1.25941
$23$			6.81104i			1.42020i	0.704101	+	0.710100i	$0.251350\pi$
$23$			6.81104i			1.42020i	−0.704101	+	0.710100i	$0.748650\pi$
$24$	−0.144414	−	1.72602i	−0.0294785	−	0.352322i
$25$	1.00000			0.200000
$26$	1.19315			0.233997
$27$	5.03407	−	1.28768i	0.968808	−	0.247814i
$28$		0			0
$29$		−	6.27090i		−	1.16448i	−0.813018	−	0.582239i	$-0.802177\pi$
$29$		−	6.27090i		−	1.16448i	0.813018	−	0.582239i	$-0.197823\pi$
$30$	0.144414	+	1.72602i	0.0263663	+	0.315127i
$31$		−	3.20353i		−	0.575371i	−0.957725	−	0.287685i	$-0.907114\pi$
$31$		−	3.20353i		−	0.575371i	0.957725	−	0.287685i	$-0.0928858\pi$
$32$			1.00000i			0.176777i
$33$	−0.853079	−	10.1959i	−0.148502	−	1.77488i
$34$		−	0.519764i		−	0.0891387i
$35$		0			0
$36$	−2.95829	+	0.498524i	−0.493048	+	0.0830873i
$37$	−4.15021			−0.682290			−0.341145	−	0.940011i	$-0.610815\pi$
$37$	−4.15021			−0.682290			−0.341145	+	0.940011i	$0.610815\pi$
$38$	5.46018			0.885759
$39$	−0.172308	−	2.05941i	−0.0275914	−	0.329769i
$40$		−	1.00000i		−	0.158114i
$41$	11.7294			1.83183			0.915913	−	0.401378i	$-0.131469\pi$
$41$	11.7294			1.83183			0.915913	+	0.401378i	$0.131469\pi$
$42$		0			0
$43$	3.42854			0.522848			0.261424	−	0.965224i	$-0.415808\pi$
$43$	3.42854			0.522848			0.261424	+	0.965224i	$0.415808\pi$
$44$			5.90717i			0.890539i
$45$	2.95829	−	0.498524i	0.440996	−	0.0743156i
$46$	−6.81104			−1.00423
$47$	−5.45825			−0.796168			−0.398084	−	0.917349i	$-0.630325\pi$
$47$	−5.45825			−0.796168			−0.398084	+	0.917349i	$0.630325\pi$
$48$	1.72602	−	0.144414i	0.249130	−	0.0208444i
$49$		0			0
$50$			1.00000i			0.141421i
$51$	−0.897122	+	0.0750613i	−0.125622	+	0.0105107i
$52$			1.19315i			0.165461i
$53$			4.12614i			0.566769i	0.959006	+	0.283385i	$0.0914573\pi$
$53$			4.12614i			0.566769i	−0.959006	+	0.283385i	$0.908543\pi$
$54$	1.28768	+	5.03407i	0.175231	+	0.685050i
$55$		−	5.90717i		−	0.796522i
$56$		0			0
$57$	−0.788529	−	9.42439i	−0.104443	−	1.24829i
$58$	6.27090			0.823410
$59$	−2.16108			−0.281348			−0.140674	−	0.990056i	$-0.544927\pi$
$59$	−2.16108			−0.281348			−0.140674	+	0.990056i	$0.544927\pi$
$60$	−1.72602	+	0.144414i	−0.222828	+	0.0186438i
$61$			9.24003i			1.18306i	0.806281	+	0.591532i	$0.201477\pi$
$61$			9.24003i			1.18306i	−0.806281	+	0.591532i	$0.798523\pi$
$62$	3.20353			0.406849
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	1.19315i		−	0.147993i
$66$	10.1959	−	0.853079i	1.25503	−	0.105007i
$67$	−7.37539			−0.901047			−0.450524	−	0.892764i	$-0.648763\pi$
$67$	−7.37539			−0.901047			−0.450524	+	0.892764i	$0.648763\pi$
$68$	0.519764			0.0630306
$69$	0.983611	+	11.7560i	0.118413	+	1.41525i
$70$		0			0
$71$			9.94550i			1.18031i	0.807289	+	0.590157i	$0.200934\pi$
$71$			9.94550i			1.18031i	−0.807289	+	0.590157i	$0.799066\pi$
$72$	−0.498524	−	2.95829i	−0.0587516	−	0.348638i
$73$			9.04250i			1.05834i	0.848514	+	0.529172i	$0.177497\pi$
$73$			9.04250i			1.05834i	−0.848514	+	0.529172i	$0.822503\pi$
$74$		−	4.15021i		−	0.482452i
$75$	1.72602	−	0.144414i	0.199304	−	0.0166755i
$76$			5.46018i			0.626326i
$77$		0			0
$78$	2.05941	−	0.172308i	0.233182	−	0.0195101i
$79$	−13.1097			−1.47496			−0.737481	−	0.675368i	$-0.763985\pi$
$79$	−13.1097			−1.47496			−0.737481	+	0.675368i	$0.763985\pi$
$80$	1.00000			0.111803
$81$	8.50295	−	2.94956i	0.944772	−	0.327728i
$82$			11.7294i			1.29530i
$83$	15.8037			1.73468			0.867339	−	0.497717i	$-0.165828\pi$
$83$	15.8037			1.73468			0.867339	+	0.497717i	$0.165828\pi$
$84$		0			0
$85$	−0.519764			−0.0563763
$86$			3.42854i			0.369709i
$87$	−0.905608	−	10.8237i	−0.0970914	−	1.16042i
$88$	−5.90717			−0.629706
$89$	2.22998			0.236377			0.118189	−	0.992991i	$-0.462291\pi$
$89$	2.22998			0.236377			0.118189	+	0.992991i	$0.462291\pi$
$90$	0.498524	+	2.95829i	0.0525490	+	0.311831i
$91$		0			0
$92$		−	6.81104i		−	0.710100i
$93$	−0.462636	−	5.52936i	−0.0479731	−	0.573367i
$94$		−	5.45825i		−	0.562976i
$95$		−	5.46018i		−	0.560203i
$96$	0.144414	+	1.72602i	0.0147392	+	0.176161i
$97$		−	9.01872i		−	0.915712i	−0.889026	−	0.457856i	$-0.848617\pi$
$97$		−	9.01872i		−	0.915712i	0.889026	−	0.457856i	$-0.151383\pi$
$98$		0			0
$99$	−2.94486	−	17.4751i	−0.295970	−	1.75631i
$100$	−1.00000			−0.100000
$101$	18.1861			1.80959			0.904794	−	0.425849i	$-0.140024\pi$
$101$	18.1861			1.80959			0.904794	+	0.425849i	$0.140024\pi$
$102$	−0.0750613	−	0.897122i	−0.00743218	−	0.0888283i
$103$		−	6.51986i		−	0.642421i	−0.947008	−	0.321211i	$-0.895910\pi$
$103$		−	6.51986i		−	0.642421i	0.947008	−	0.321211i	$-0.104090\pi$
$104$	−1.19315			−0.116998
$105$		0			0
$106$	−4.12614			−0.400766
$107$			14.1211i			1.36513i	0.730823	+	0.682567i	$0.239136\pi$
$107$			14.1211i			1.36513i	−0.730823	+	0.682567i	$0.760864\pi$
$108$	−5.03407	+	1.28768i	−0.484404	+	0.123907i
$109$	9.28898			0.889723			0.444862	−	0.895599i	$-0.353253\pi$
$109$	9.28898			0.889723			0.444862	+	0.895599i	$0.353253\pi$
$110$	5.90717			0.563226
$111$	−7.16334	+	0.599349i	−0.679914	+	0.0568877i
$112$		0			0
$113$			3.85650i			0.362789i	0.983410	+	0.181395i	$0.0580611\pi$
$113$			3.85650i			0.362789i	−0.983410	+	0.181395i	$0.941939\pi$
$114$	9.42439	−	0.788529i	0.882675	−	0.0738525i
$115$			6.81104i			0.635132i
$116$			6.27090i			0.582239i
$117$	−0.594816	−	3.52969i	−0.0549907	−	0.326320i
$118$		−	2.16108i		−	0.198943i
$119$		0			0
$120$	−0.144414	−	1.72602i	−0.0131832	−	0.157563i
$121$	−23.8946			−2.17224
$122$	−9.24003			−0.836553
$123$	20.2452	−	1.69389i	1.82545	−	0.152733i
$124$			3.20353i			0.287685i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−20.4494			−1.81459			−0.907297	−	0.420491i	$-0.861858\pi$
$127$	−20.4494			−1.81459			−0.907297	+	0.420491i	$0.861858\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	5.91773	−	0.495131i	0.521027	−	0.0435938i
$130$	1.19315			0.104647
$131$	11.6718			1.01977			0.509884	−	0.860243i	$-0.329688\pi$
$131$	11.6718			1.01977			0.509884	+	0.860243i	$0.329688\pi$
$132$	0.853079	+	10.1959i	0.0742510	+	0.887438i
$133$		0			0
$134$		−	7.37539i		−	0.637137i
$135$	5.03407	−	1.28768i	0.433264	−	0.110826i
$136$			0.519764i			0.0445694i
$137$			13.0310i			1.11331i	0.830743	+	0.556656i	$0.187916\pi$
$137$			13.0310i			1.11331i	−0.830743	+	0.556656i	$0.812084\pi$
$138$	−11.7560	+	0.983611i	−1.00074	+	0.0837305i
$139$		−	10.4077i		−	0.882767i	−0.897319	−	0.441383i	$-0.854488\pi$
$139$		−	10.4077i		−	0.882767i	0.897319	−	0.441383i	$-0.145512\pi$
$140$		0			0
$141$	−9.42105	+	0.788250i	−0.793396	+	0.0663826i
$142$	−9.94550			−0.834608
$143$	−7.04816			−0.589396
$144$	2.95829	−	0.498524i	0.246524	−	0.0415437i
$145$		−	6.27090i		−	0.520770i
$146$	−9.04250			−0.748363
$147$		0			0
$148$	4.15021			0.341145
$149$			3.47353i			0.284563i	0.989826	+	0.142282i	$0.0454438\pi$
$149$			3.47353i			0.284563i	−0.989826	+	0.142282i	$0.954556\pi$
$150$	0.144414	+	1.72602i	0.0117914	+	0.140929i
$151$	4.06178			0.330543			0.165271	−	0.986248i	$-0.447150\pi$
$151$	4.06178			0.330543			0.165271	+	0.986248i	$0.447150\pi$
$152$	−5.46018			−0.442879
$153$	−1.53761	+	0.259115i	−0.124308	+	0.0209482i
$154$		0			0
$155$		−	3.20353i		−	0.257314i
$156$	0.172308	+	2.05941i	0.0137957	+	0.164885i
$157$			11.5039i			0.918115i	0.888407	+	0.459057i	$0.151813\pi$
$157$			11.5039i			0.918115i	−0.888407	+	0.459057i	$0.848187\pi$
$158$		−	13.1097i		−	1.04296i
$159$	0.595874	+	7.12180i	0.0472559	+	0.564796i
$160$			1.00000i			0.0790569i
$161$		0			0
$162$	2.94956	+	8.50295i	0.231739	+	0.668055i
$163$	21.2114			1.66141			0.830703	−	0.556716i	$-0.187939\pi$
$163$	21.2114			1.66141			0.830703	+	0.556716i	$0.187939\pi$
$164$	−11.7294			−0.915913
$165$	−0.853079	−	10.1959i	−0.0664121	−	0.793749i
$166$			15.8037i			1.22660i
$167$	0.446666			0.0345641			0.0172820	−	0.999851i	$-0.494499\pi$
$167$	0.446666			0.0345641			0.0172820	+	0.999851i	$0.494499\pi$
$168$		0			0
$169$	11.5764			0.890491
$170$		−	0.519764i		−	0.0398641i
$171$	−2.72203	−	16.1528i	−0.208159	−	1.23524i
$172$	−3.42854			−0.261424
$173$	−14.5993			−1.10996			−0.554981	−	0.831863i	$-0.687274\pi$
$173$	−14.5993			−1.10996			−0.554981	+	0.831863i	$0.687274\pi$
$174$	10.8237	−	0.905608i	0.820543	−	0.0686540i
$175$		0			0
$176$		−	5.90717i		−	0.445269i
$177$	−3.73006	+	0.312090i	−0.280368	+	0.0234581i
$178$			2.22998i			0.167144i
$179$			3.32735i			0.248698i	0.992239	+	0.124349i	$0.0396842\pi$
$179$			3.32735i			0.248698i	−0.992239	+	0.124349i	$0.960316\pi$
$180$	−2.95829	+	0.498524i	−0.220498	+	0.0371578i
$181$		−	0.943424i		−	0.0701242i	−0.999385	−	0.0350621i	$-0.988837\pi$
$181$		−	0.943424i		−	0.0701242i	0.999385	−	0.0350621i	$-0.0111629\pi$
$182$		0			0
$183$	1.33439	+	15.9485i	0.0986411	+	1.17894i
$184$	6.81104			0.502116
$185$	−4.15021			−0.305129
$186$	5.52936	−	0.462636i	0.405432	−	0.0339221i
$187$			3.07033i			0.224525i
$188$	5.45825			0.398084
$189$		0			0
$190$	5.46018			0.396123
$191$		−	10.7011i		−	0.774306i	−0.922015	−	0.387153i	$-0.873459\pi$
$191$		−	10.7011i		−	0.774306i	0.922015	−	0.387153i	$-0.126541\pi$
$192$	−1.72602	+	0.144414i	−0.124565	+	0.0104222i
$193$	−21.0803			−1.51739			−0.758697	−	0.651444i	$-0.774164\pi$
$193$	−21.0803			−1.51739			−0.758697	+	0.651444i	$0.774164\pi$
$194$	9.01872			0.647506
$195$	−0.172308	−	2.05941i	−0.0123393	−	0.147477i
$196$		0			0
$197$		−	0.349379i		−	0.0248922i	−0.999923	−	0.0124461i	$-0.996038\pi$
$197$		−	0.349379i		−	0.0248922i	0.999923	−	0.0124461i	$-0.00396182\pi$
$198$	17.4751	−	2.94486i	1.24190	−	0.209282i
$199$			5.36410i			0.380251i	0.981760	+	0.190126i	$0.0608895\pi$
$199$			5.36410i			0.380251i	−0.981760	+	0.190126i	$0.939110\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	−12.7301	+	1.06511i	−0.897910	+	0.0751272i
$202$			18.1861i			1.27957i
$203$		0			0
$204$	0.897122	−	0.0750613i	0.0628111	−	0.00525534i
$205$	11.7294			0.819217
$206$	6.51986			0.454260
$207$	3.39546	+	20.1490i	0.236001	+	1.40045i
$208$		−	1.19315i		−	0.0827303i
$209$	−32.2542			−2.23107
$210$		0			0
$211$	−23.9455			−1.64848			−0.824238	−	0.566243i	$-0.808396\pi$
$211$	−23.9455			−1.64848			−0.824238	+	0.566243i	$0.808396\pi$
$212$		−	4.12614i		−	0.283385i
$213$	1.43627	+	17.1661i	0.0984118	+	1.17620i
$214$	−14.1211			−0.965295
$215$	3.42854			0.233825
$216$	−1.28768	−	5.03407i	−0.0876156	−	0.342525i
$217$		0			0
$218$			9.28898i			0.629129i
$219$	1.30587	+	15.6075i	0.0882423	+	1.05466i
$220$			5.90717i			0.398261i
$221$			0.620158i			0.0417163i
$222$	−0.599349	−	7.16334i	−0.0402257	−	0.480772i
$223$		−	12.8354i		−	0.859522i	−0.902943	−	0.429761i	$-0.858598\pi$
$223$		−	12.8354i		−	0.859522i	0.902943	−	0.429761i	$-0.141402\pi$
$224$		0			0
$225$	2.95829	−	0.498524i	0.197219	−	0.0332349i
$226$	−3.85650			−0.256531
$227$	4.51349			0.299571			0.149785	−	0.988719i	$-0.452142\pi$
$227$	4.51349			0.299571			0.149785	+	0.988719i	$0.452142\pi$
$228$	0.788529	+	9.42439i	0.0522216	+	0.624145i
$229$		−	4.85121i		−	0.320577i	−0.987070	−	0.160288i	$-0.948758\pi$
$229$		−	4.85121i		−	0.320577i	0.987070	−	0.160288i	$-0.0512424\pi$
$230$	−6.81104			−0.449106
$231$		0			0
$232$	−6.27090			−0.411705
$233$			0.485207i			0.0317870i	0.999874	+	0.0158935i	$0.00505927\pi$
$233$			0.485207i			0.0317870i	−0.999874	+	0.0158935i	$0.994941\pi$
$234$	3.52969	−	0.594816i	0.230743	−	0.0388843i
$235$	−5.45825			−0.356057
$236$	2.16108			0.140674
$237$	−22.6277	+	1.89324i	−1.46983	+	0.122979i
$238$		0			0
$239$			18.5705i			1.20122i	0.799541	+	0.600612i	$0.205076\pi$
$239$			18.5705i			1.20122i	−0.799541	+	0.600612i	$0.794924\pi$
$240$	1.72602	−	0.144414i	0.111414	−	0.00932190i
$241$			9.00275i			0.579918i	0.957039	+	0.289959i	$0.0936417\pi$
$241$			9.00275i			0.579918i	−0.957039	+	0.289959i	$0.906358\pi$
$242$		−	23.8946i		−	1.53600i
$243$	14.2503	−	6.31894i	0.914157	−	0.405360i
$244$		−	9.24003i		−	0.591532i
$245$		0			0
$246$	1.69389	+	20.2452i	0.107999	+	1.29079i
$247$	−6.51484			−0.414529
$248$	−3.20353			−0.203424
$249$	27.2775	−	2.28228i	1.72864	−	0.144633i
$250$			1.00000i			0.0632456i
$251$	10.0744			0.635889			0.317944	−	0.948109i	$-0.397007\pi$
$251$	10.0744			0.635889			0.317944	+	0.948109i	$0.397007\pi$
$252$		0			0
$253$	40.2339			2.52948
$254$		−	20.4494i		−	1.28311i
$255$	−0.897122	+	0.0750613i	−0.0561800	+	0.00470052i
$256$	1.00000			0.0625000
$257$	1.71064			0.106707			0.0533534	−	0.998576i	$-0.483009\pi$
$257$	1.71064			0.106707			0.0533534	+	0.998576i	$0.483009\pi$
$258$	0.495131	+	5.91773i	0.0308255	+	0.368422i
$259$		0			0
$260$			1.19315i			0.0739963i
$261$	−3.12619	−	18.5511i	−0.193507	−	1.14829i
$262$			11.6718i			0.721085i
$263$			23.7626i			1.46527i	0.680624	+	0.732633i	$0.261709\pi$
$263$			23.7626i			1.46527i	−0.680624	+	0.732633i	$0.738291\pi$
$264$	−10.1959	+	0.853079i	−0.627513	+	0.0525034i
$265$			4.12614i			0.253467i
$266$		0			0
$267$	3.84899	−	0.322041i	0.235554	−	0.0197086i
$268$	7.37539			0.450524
$269$	−22.0479			−1.34428			−0.672141	−	0.740423i	$-0.734625\pi$
$269$	−22.0479			−1.34428			−0.672141	+	0.740423i	$0.734625\pi$
$270$	1.28768	+	5.03407i	0.0783658	+	0.306364i
$271$		−	7.87416i		−	0.478321i	−0.970980	−	0.239161i	$-0.923128\pi$
$271$		−	7.87416i		−	0.478321i	0.970980	−	0.239161i	$-0.0768723\pi$
$272$	−0.519764			−0.0315153
$273$		0			0
$274$	−13.0310			−0.787231
$275$		−	5.90717i		−	0.356216i
$276$	−0.983611	−	11.7560i	−0.0592064	−	0.707627i
$277$	11.4892			0.690322			0.345161	−	0.938544i	$-0.387824\pi$
$277$	11.4892			0.690322			0.345161	+	0.938544i	$0.387824\pi$
$278$	10.4077			0.624210
$279$	−1.59704	−	9.47697i	−0.0956121	−	0.567371i
$280$		0			0
$281$			11.5657i			0.689954i	0.938611	+	0.344977i	$0.112113\pi$
$281$			11.5657i			0.689954i	−0.938611	+	0.344977i	$0.887887\pi$
$282$	−0.788250	−	9.42105i	−0.0469396	−	0.561016i
$283$			22.8509i			1.35834i	0.733979	+	0.679172i	$0.237661\pi$
$283$			22.8509i			1.35834i	−0.733979	+	0.679172i	$0.762339\pi$
$284$		−	9.94550i		−	0.590157i
$285$	−0.788529	−	9.42439i	−0.0467084	−	0.558252i
$286$		−	7.04816i		−	0.416766i
$287$		0			0
$288$	0.498524	+	2.95829i	0.0293758	+	0.174319i
$289$	−16.7298			−0.984109
$290$	6.27090			0.368240
$291$	−1.30243	−	15.5665i	−0.0763499	−	0.912524i
$292$		−	9.04250i		−	0.529172i
$293$	−6.67909			−0.390197			−0.195098	−	0.980784i	$-0.562503\pi$
$293$	−6.67909			−0.390197			−0.195098	+	0.980784i	$0.562503\pi$
$294$		0			0
$295$	−2.16108			−0.125823
$296$			4.15021i			0.241226i
$297$	−7.60655	−	29.7371i	−0.441377	−	1.72552i
$298$	−3.47353			−0.201216
$299$	8.12661			0.469974
$300$	−1.72602	+	0.144414i	−0.0996518	+	0.00833776i
$301$		0			0
$302$			4.06178i			0.233729i
$303$	31.3896	−	2.62634i	1.80329	−	0.150879i
$304$		−	5.46018i		−	0.313163i
$305$			9.24003i			0.529082i
$306$	−0.259115	−	1.53761i	−0.0148126	−	0.0878994i
$307$		−	27.1482i		−	1.54943i	−0.632311	−	0.774715i	$-0.717894\pi$
$307$		−	27.1482i		−	1.54943i	0.632311	−	0.774715i	$-0.282106\pi$
$308$		0			0
$309$	−0.941561	−	11.2534i	−0.0535636	−	0.640184i
$310$	3.20353			0.181948
$311$	−23.3835			−1.32596			−0.662980	−	0.748637i	$-0.730708\pi$
$311$	−23.3835			−1.32596			−0.662980	+	0.748637i	$0.730708\pi$
$312$	−2.05941	+	0.172308i	−0.116591	+	0.00975505i
$313$		−	25.1047i		−	1.41900i	−0.704706	−	0.709500i	$-0.748921\pi$
$313$		−	25.1047i		−	1.41900i	0.704706	−	0.709500i	$-0.251079\pi$
$314$	−11.5039			−0.649205
$315$		0			0
$316$	13.1097			0.737481
$317$		−	8.45405i		−	0.474827i	−0.971409	−	0.237413i	$-0.923700\pi$
$317$		−	8.45405i		−	0.474827i	0.971409	−	0.237413i	$-0.0762996\pi$
$318$	−7.12180	+	0.595874i	−0.399371	+	0.0334150i
$319$	−37.0433			−2.07402
$320$	−1.00000			−0.0559017
$321$	2.03928	+	24.3732i	0.113822	+	1.36038i
$322$		0			0
$323$			2.83800i			0.157911i
$324$	−8.50295	+	2.94956i	−0.472386	+	0.163864i
$325$		−	1.19315i		−	0.0661843i
$326$			21.2114i			1.17479i
$327$	16.0330	−	1.34146i	0.886625	−	0.0741830i
$328$		−	11.7294i		−	0.647648i
$329$		0			0
$330$	10.1959	−	0.853079i	0.561265	−	0.0469605i
$331$	−29.3727			−1.61447			−0.807236	−	0.590229i	$-0.799038\pi$
$331$	−29.3727			−1.61447			−0.807236	+	0.590229i	$0.799038\pi$
$332$	−15.8037			−0.867339
$333$	−12.2775	+	2.06898i	−0.672803	+	0.113379i
$334$			0.446666i			0.0244405i
$335$	−7.37539			−0.402961
$336$		0			0
$337$	−4.97762			−0.271148			−0.135574	−	0.990767i	$-0.543288\pi$
$337$	−4.97762			−0.271148			−0.135574	+	0.990767i	$0.543288\pi$
$338$			11.5764i			0.629672i
$339$	0.556934	+	6.65640i	0.0302485	+	0.361526i
$340$	0.519764			0.0281881
$341$	−18.9238			−1.02478
$342$	16.1528	−	2.72203i	0.873443	−	0.147191i
$343$		0			0
$344$		−	3.42854i		−	0.184855i
$345$	0.983611	+	11.7560i	0.0529558	+	0.632921i
$346$		−	14.5993i		−	0.784862i
$347$		−	2.15190i		−	0.115520i	−0.998330	−	0.0577601i	$-0.981604\pi$
$347$		−	2.15190i		−	0.115520i	0.998330	−	0.0577601i	$-0.0183958\pi$
$348$	0.905608	+	10.8237i	0.0485457	+	0.580211i
$349$			25.9752i			1.39042i	0.718806	+	0.695211i	$0.244689\pi$
$349$			25.9752i			1.39042i	−0.718806	+	0.695211i	$0.755311\pi$
$350$		0			0
$351$	−1.53640	−	6.00642i	−0.0820071	−	0.320599i
$352$	5.90717			0.314853
$353$	27.1728			1.44626			0.723131	−	0.690711i	$-0.242702\pi$
$353$	27.1728			1.44626			0.723131	+	0.690711i	$0.242702\pi$
$354$	−0.312090	−	3.73006i	−0.0165874	−	0.198250i
$355$			9.94550i			0.527852i
$356$	−2.22998			−0.118189
$357$		0			0
$358$	−3.32735			−0.175856
$359$		−	34.5969i		−	1.82595i	−0.408011	−	0.912977i	$-0.633778\pi$
$359$		−	34.5969i		−	1.82595i	0.408011	−	0.912977i	$-0.366222\pi$
$360$	−0.498524	−	2.95829i	−0.0262745	−	0.155916i
$361$	−10.8136			−0.569137
$362$	0.943424			0.0495853
$363$	−41.2426	+	3.45072i	−2.16467	+	0.181116i
$364$		0			0
$365$			9.04250i			0.473306i
$366$	−15.9485	+	1.33439i	−0.833640	+	0.0697498i
$367$		−	28.5579i		−	1.49071i	−0.666667	−	0.745355i	$-0.732280\pi$
$367$		−	28.5579i		−	1.49071i	0.666667	−	0.745355i	$-0.267720\pi$
$368$			6.81104i			0.355050i
$369$	34.6990	−	5.84739i	1.80636	−	0.304403i
$370$		−	4.15021i		−	0.215759i
$371$		0			0
$372$	0.462636	+	5.52936i	0.0239865	+	0.286684i
$373$	11.1237			0.575964			0.287982	−	0.957636i	$-0.407016\pi$
$373$	11.1237			0.575964			0.287982	+	0.957636i	$0.407016\pi$
$374$	−3.07033			−0.158763
$375$	1.72602	−	0.144414i	0.0891313	−	0.00745752i
$376$			5.45825i			0.281488i
$377$	−7.48215			−0.385350
$378$		0			0
$379$	11.9502			0.613840			0.306920	−	0.951735i	$-0.400702\pi$
$379$	11.9502			0.613840			0.306920	+	0.951735i	$0.400702\pi$
$380$			5.46018i			0.280102i
$381$	−35.2961	+	2.95319i	−1.80827	+	0.151297i
$382$	10.7011			0.547517
$383$	−13.3235			−0.680799			−0.340400	−	0.940281i	$-0.610562\pi$
$383$	−13.3235			−0.680799			−0.340400	+	0.940281i	$0.610562\pi$
$384$	−0.144414	−	1.72602i	−0.00736961	−	0.0880806i
$385$		0			0
$386$		−	21.0803i		−	1.07296i
$387$	10.1426	−	1.70921i	0.515578	−	0.0868841i
$388$			9.01872i			0.457856i
$389$			8.00925i			0.406085i	0.979170	+	0.203042i	$0.0650829\pi$
$389$			8.00925i			0.406085i	−0.979170	+	0.203042i	$0.934917\pi$
$390$	2.05941	−	0.172308i	0.104282	−	0.00872518i
$391$		−	3.54013i		−	0.179032i
$392$		0			0
$393$	20.1457	−	1.68557i	1.01622	−	0.0850258i
$394$	0.349379			0.0176015
$395$	−13.1097			−0.659623
$396$	2.94486	+	17.4751i	0.147985	+	0.878157i
$397$			35.3561i			1.77447i	0.461314	+	0.887237i	$0.347378\pi$
$397$			35.3561i			1.77447i	−0.461314	+	0.887237i	$0.652622\pi$
$398$	−5.36410			−0.268878
$399$		0			0
$400$	1.00000			0.0500000
$401$		−	30.8568i		−	1.54091i	−0.637492	−	0.770457i	$-0.720028\pi$
$401$		−	30.8568i		−	1.54091i	0.637492	−	0.770457i	$-0.279972\pi$
$402$	−1.06511	−	12.7301i	−0.0531230	−	0.634918i
$403$	−3.82230			−0.190402
$404$	−18.1861			−0.904794
$405$	8.50295	−	2.94956i	0.422515	−	0.146565i
$406$		0			0
$407$			24.5160i			1.21521i
$408$	0.0750613	+	0.897122i	0.00371609	+	0.0444142i
$409$		−	11.4854i		−	0.567919i	−0.958836	−	0.283959i	$-0.908352\pi$
$409$		−	11.4854i		−	0.567919i	0.958836	−	0.283959i	$-0.0916481\pi$
$410$			11.7294i			0.579274i
$411$	1.88186	+	22.4917i	0.0928253	+	1.10944i
$412$			6.51986i			0.321211i
$413$		0			0
$414$	−20.1490	+	3.39546i	−0.990270	+	0.166878i
$415$	15.8037			0.775772
$416$	1.19315			0.0584992
$417$	−1.50302	−	17.9638i	−0.0736030	−	0.879693i
$418$		−	32.2542i		−	1.57761i
$419$	−14.4383			−0.705356			−0.352678	−	0.935745i	$-0.614729\pi$
$419$	−14.4383			−0.705356			−0.352678	+	0.935745i	$0.614729\pi$
$420$		0			0
$421$	−19.1284			−0.932261			−0.466130	−	0.884716i	$-0.654352\pi$
$421$	−19.1284			−0.932261			−0.466130	+	0.884716i	$0.654352\pi$
$422$		−	23.9455i		−	1.16565i
$423$	−16.1471	+	2.72107i	−0.785098	+	0.132303i
$424$	4.12614			0.200383
$425$	−0.519764			−0.0252122
$426$	−17.1661	+	1.43627i	−0.831702	+	0.0695876i
$427$		0			0
$428$		−	14.1211i		−	0.682567i
$429$	−12.1653	+	1.01785i	−0.587344	+	0.0491425i
$430$			3.42854i			0.165339i
$431$		−	15.8639i		−	0.764137i	−0.924134	−	0.382068i	$-0.875212\pi$
$431$		−	15.8639i		−	0.764137i	0.924134	−	0.382068i	$-0.124788\pi$
$432$	5.03407	−	1.28768i	0.242202	−	0.0619536i
$433$			10.3829i			0.498970i	0.968379	+	0.249485i	$0.0802614\pi$
$433$			10.3829i			0.498970i	−0.968379	+	0.249485i	$0.919739\pi$
$434$		0			0
$435$	−0.905608	−	10.8237i	−0.0434206	−	0.518957i
$436$	−9.28898			−0.444862
$437$	37.1895			1.77902
$438$	−15.6075	+	1.30587i	−0.745757	+	0.0623967i
$439$			19.4004i			0.925930i	0.886376	+	0.462965i	$0.153215\pi$
$439$			19.4004i			0.925930i	−0.886376	+	0.462965i	$0.846785\pi$
$440$	−5.90717			−0.281613
$441$		0			0
$442$	−0.620158			−0.0294979
$443$			13.6242i			0.647306i	0.946176	+	0.323653i	$0.104911\pi$
$443$			13.6242i			0.647306i	−0.946176	+	0.323653i	$0.895089\pi$
$444$	7.16334	−	0.599349i	0.339957	−	0.0284439i
$445$	2.22998			0.105711
$446$	12.8354			0.607774
$447$	0.501628	+	5.99539i	0.0237262	+	0.283572i
$448$		0			0
$449$			30.4744i			1.43818i	0.694919	+	0.719088i	$0.255440\pi$
$449$			30.4744i			1.43818i	−0.694919	+	0.719088i	$0.744560\pi$
$450$	0.498524	+	2.95829i	0.0235006	+	0.139455i
$451$		−	69.2875i		−	3.26262i
$452$		−	3.85650i		−	0.181395i
$453$	7.01071	−	0.586579i	0.329392	−	0.0275599i
$454$			4.51349i			0.211828i
$455$		0			0
$456$	−9.42439	+	0.788529i	−0.441337	+	0.0369262i
$457$	−14.3218			−0.669946			−0.334973	−	0.942228i	$-0.608727\pi$
$457$	−14.3218			−0.669946			−0.334973	+	0.942228i	$0.608727\pi$
$458$	4.85121			0.226682
$459$	−2.61653	+	0.669290i	−0.122129	+	0.0312398i
$460$		−	6.81104i		−	0.317566i
$461$	9.84757			0.458647			0.229324	−	0.973350i	$-0.426349\pi$
$461$	9.84757			0.458647			0.229324	+	0.973350i	$0.426349\pi$
$462$		0			0
$463$	−16.8754			−0.784266			−0.392133	−	0.919908i	$-0.628263\pi$
$463$	−16.8754			−0.784266			−0.392133	+	0.919908i	$0.628263\pi$
$464$		−	6.27090i		−	0.291119i
$465$	−0.462636	−	5.52936i	−0.0214542	−	0.256418i
$466$	−0.485207			−0.0224768
$467$	−14.6036			−0.675773			−0.337887	−	0.941187i	$-0.609712\pi$
$467$	−14.6036			−0.675773			−0.337887	+	0.941187i	$0.609712\pi$
$468$	0.594816	+	3.52969i	0.0274954	+	0.163160i
$469$		0			0
$470$		−	5.45825i		−	0.251770i
$471$	1.66133	+	19.8560i	0.0765503	+	0.914918i
$472$			2.16108i			0.0994716i
$473$		−	20.2530i		−	0.931233i
$474$	−1.89324	−	22.6277i	−0.0869592	−	1.03932i
$475$		−	5.46018i		−	0.250530i
$476$		0			0
$477$	2.05698	+	12.2063i	0.0941827	+	0.558889i
$478$	−18.5705			−0.849393
$479$	25.3810			1.15969			0.579843	−	0.814728i	$-0.303114\pi$
$479$	25.3810			1.15969			0.579843	+	0.814728i	$0.303114\pi$
$480$	0.144414	+	1.72602i	0.00659158	+	0.0787817i
$481$			4.95183i			0.225784i
$482$	−9.00275			−0.410064
$483$		0			0
$484$	23.8946			1.08612
$485$		−	9.01872i		−	0.409519i
$486$	6.31894	+	14.2503i	0.286633	+	0.646407i
$487$	26.4935			1.20053			0.600267	−	0.799800i	$-0.295061\pi$
$487$	26.4935			1.20053			0.600267	+	0.799800i	$0.295061\pi$
$488$	9.24003			0.418276
$489$	36.6113	−	3.06323i	1.65562	−	0.138524i
$490$		0			0
$491$		−	29.5424i		−	1.33323i	−0.745402	−	0.666616i	$-0.767742\pi$
$491$		−	29.5424i		−	1.33323i	0.745402	−	0.666616i	$-0.232258\pi$
$492$	−20.2452	+	1.69389i	−0.912723	+	0.0763666i
$493$			3.25939i			0.146795i
$494$		−	6.51484i		−	0.293116i
$495$	−2.94486	−	17.4751i	−0.132362	−	0.785448i
$496$		−	3.20353i		−	0.143843i
$497$		0			0
$498$	2.28228	+	27.2775i	0.102271	+	1.22233i
$499$	12.6748			0.567400			0.283700	−	0.958913i	$-0.408438\pi$
$499$	12.6748			0.567400			0.283700	+	0.958913i	$0.408438\pi$
$500$	−1.00000			−0.0447214
$501$	0.770955	−	0.0645050i	0.0344437	−	0.00288187i
$502$			10.0744i			0.449641i
$503$	32.7697			1.46113			0.730565	−	0.682843i	$-0.239257\pi$
$503$	32.7697			1.46113			0.730565	+	0.682843i	$0.239257\pi$
$504$		0			0
$505$	18.1861			0.809273
$506$			40.2339i			1.78862i
$507$	19.9811	−	1.67180i	0.887390	−	0.0742471i
$508$	20.4494			0.907297
$509$	−12.9308			−0.573149			−0.286574	−	0.958058i	$-0.592517\pi$
$509$	−12.9308			−0.573149			−0.286574	+	0.958058i	$0.592517\pi$
$510$	−0.0750613	−	0.897122i	−0.00332377	−	0.0397252i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	−7.03098	−	27.4870i	−0.310425	−	1.21358i
$514$			1.71064i			0.0754531i
$515$		−	6.51986i		−	0.287299i
$516$	−5.91773	+	0.495131i	−0.260514	+	0.0217969i
$517$			32.2428i			1.41804i
$518$		0			0
$519$	−25.1986	+	2.10834i	−1.10610	+	0.0925460i
$520$	−1.19315			−0.0523233
$521$	−29.8148			−1.30621			−0.653106	−	0.757267i	$-0.726534\pi$
$521$	−29.8148			−1.30621			−0.653106	+	0.757267i	$0.726534\pi$
$522$	18.5511	−	3.12619i	0.811961	−	0.136830i
$523$		−	0.484121i		−	0.0211691i	−0.999944	−	0.0105846i	$-0.996631\pi$
$523$		−	0.484121i		−	0.0211691i	0.999944	−	0.0105846i	$-0.00336924\pi$
$524$	−11.6718			−0.509884
$525$		0			0
$526$	−23.7626			−1.03610
$527$			1.66508i			0.0725319i
$528$	−0.853079	−	10.1959i	−0.0371255	−	0.443719i
$529$	−23.3902			−1.01697
$530$	−4.12614			−0.179228
$531$	−6.39309	+	1.07735i	−0.277436	+	0.0467529i
$532$		0			0
$533$		−	13.9950i		−	0.606190i
$534$	0.322041	+	3.84899i	0.0139361	+	0.166562i
$535$			14.1211i			0.610506i
$536$			7.37539i			0.318568i
$537$	0.480517	+	5.74307i	0.0207358	+	0.247832i
$538$		−	22.0479i		−	0.950551i
$539$		0			0
$540$	−5.03407	+	1.28768i	−0.216632	+	0.0554130i
$541$	−12.9285			−0.555840			−0.277920	−	0.960604i	$-0.589645\pi$
$541$	−12.9285			−0.555840			−0.277920	+	0.960604i	$0.589645\pi$
$542$	7.87416			0.338224
$543$	−0.136244	−	1.62837i	−0.00584679	−	0.0698800i
$544$		−	0.519764i		−	0.0222847i
$545$	9.28898			0.397896
$546$		0			0
$547$	−2.44976			−0.104744			−0.0523721	−	0.998628i	$-0.516678\pi$
$547$	−2.44976			−0.104744			−0.0523721	+	0.998628i	$0.516678\pi$
$548$		−	13.0310i		−	0.556656i
$549$	4.60638	+	27.3347i	0.196595	+	1.16662i
$550$	5.90717			0.251882
$551$	−34.2403			−1.45868
$552$	11.7560	−	0.983611i	0.500368	−	0.0418653i
$553$		0			0
$554$			11.4892i			0.488131i
$555$	−7.16334	+	0.599349i	−0.304067	+	0.0254410i
$556$			10.4077i			0.441383i
$557$			22.8644i			0.968796i	0.874848	+	0.484398i	$0.160961\pi$
$557$			22.8644i			0.968796i	−0.874848	+	0.484398i	$0.839039\pi$
$558$	9.47697	−	1.59704i	0.401192	−	0.0676079i
$559$		−	4.09078i		−	0.173022i
$560$		0			0
$561$	0.443400	+	5.29945i	0.0187203	+	0.223743i
$562$	−11.5657			−0.487871
$563$	−3.86315			−0.162812			−0.0814061	−	0.996681i	$-0.525941\pi$
$563$	−3.86315			−0.162812			−0.0814061	+	0.996681i	$0.525941\pi$
$564$	9.42105	−	0.788250i	0.396698	−	0.0331913i
$565$			3.85650i			0.162244i
$566$	−22.8509			−0.960494
$567$		0			0
$568$	9.94550			0.417304
$569$			33.3926i			1.39989i	0.714197	+	0.699945i	$0.246792\pi$
$569$			33.3926i			1.39989i	−0.714197	+	0.699945i	$0.753208\pi$
$570$	9.42439	−	0.788529i	0.394744	−	0.0330278i
$571$	1.44273			0.0603765			0.0301882	−	0.999544i	$-0.490389\pi$
$571$	1.44273			0.0603765			0.0301882	+	0.999544i	$0.490389\pi$
$572$	7.04816			0.294698
$573$	−1.54540	−	18.4704i	−0.0645598	−	0.771610i
$574$		0			0
$575$			6.81104i			0.284040i
$576$	−2.95829	+	0.498524i	−0.123262	+	0.0207718i
$577$			34.7490i			1.44662i	0.690525	+	0.723309i	$0.257380\pi$
$577$			34.7490i			1.44662i	−0.690525	+	0.723309i	$0.742620\pi$
$578$		−	16.7298i		−	0.695870i
$579$	−36.3850	+	3.04430i	−1.51211	+	0.126517i
$580$			6.27090i			0.260385i
$581$		0			0
$582$	15.5665	−	1.30243i	0.645252	−	0.0539876i
$583$	24.3738			1.00946
$584$	9.04250			0.374181
$585$	−0.594816	−	3.52969i	−0.0245926	−	0.145935i
$586$		−	6.67909i		−	0.275911i
$587$	−27.3035			−1.12694			−0.563468	−	0.826138i	$-0.690533\pi$
$587$	−27.3035			−1.12694			−0.563468	+	0.826138i	$0.690533\pi$
$588$		0			0
$589$	−17.4919			−0.720739
$590$		−	2.16108i		−	0.0889701i
$591$	−0.0504553	−	0.603035i	−0.00207545	−	0.0248055i
$592$	−4.15021			−0.170572
$593$	10.2075			0.419171			0.209585	−	0.977790i	$-0.432789\pi$
$593$	10.2075			0.419171			0.209585	+	0.977790i	$0.432789\pi$
$594$	29.7371	−	7.60655i	1.22013	−	0.312100i
$595$		0			0
$596$		−	3.47353i		−	0.142282i
$597$	0.774653	+	9.25855i	0.0317044	+	0.378927i
$598$			8.12661i			0.332322i
$599$			17.9575i			0.733725i	0.930275	+	0.366863i	$0.119568\pi$
$599$			17.9575i			0.733725i	−0.930275	+	0.366863i	$0.880432\pi$
$600$	−0.144414	−	1.72602i	−0.00589569	−	0.0704645i
$601$			14.6375i			0.597075i	0.954398	+	0.298537i	$0.0964988\pi$
$601$			14.6375i			0.597075i	−0.954398	+	0.298537i	$0.903501\pi$
$602$		0			0
$603$	−21.8185	+	3.67681i	−0.888520	+	0.149731i
$604$	−4.06178			−0.165271
$605$	−23.8946			−0.971454
$606$	2.62634	+	31.3896i	0.106688	+	1.27512i
$607$			0.770307i			0.0312658i	0.999878	+	0.0156329i	$0.00497631\pi$
$607$			0.770307i			0.0312658i	−0.999878	+	0.0156329i	$0.995024\pi$
$608$	5.46018			0.221440
$609$		0			0
$610$	−9.24003			−0.374118
$611$			6.51254i			0.263469i
$612$	1.53761	−	0.259115i	0.0621542	−	0.0104741i
$613$	11.1013			0.448377			0.224189	−	0.974546i	$-0.428027\pi$
$613$	11.1013			0.448377			0.224189	+	0.974546i	$0.428027\pi$
$614$	27.1482			1.09561
$615$	20.2452	−	1.69389i	0.816365	−	0.0683044i
$616$		0			0
$617$		−	22.3928i		−	0.901499i	−0.892650	−	0.450750i	$-0.851157\pi$
$617$		−	22.3928i		−	0.901499i	0.892650	−	0.450750i	$-0.148843\pi$
$618$	11.2534	−	0.941561i	0.452679	−	0.0378752i
$619$		−	25.9283i		−	1.04215i	−0.853512	−	0.521073i	$-0.825532\pi$
$619$		−	25.9283i		−	1.04215i	0.853512	−	0.521073i	$-0.174468\pi$
$620$			3.20353i			0.128657i
$621$	8.77045	+	34.2872i	0.351946	+	1.37590i
$622$		−	23.3835i		−	0.937595i
$623$		0			0
$624$	−0.172308	−	2.05941i	−0.00689786	−	0.0824423i
$625$	1.00000			0.0400000
$626$	25.1047			1.00338
$627$	−55.6714	+	4.65797i	−2.22330	+	0.186021i
$628$		−	11.5039i		−	0.459057i
$629$	2.15713			0.0860102
$630$		0			0
$631$	43.5245			1.73268			0.866341	−	0.499452i	$-0.166465\pi$
$631$	43.5245			1.73268			0.866341	+	0.499452i	$0.166465\pi$
$632$			13.1097i			0.521478i
$633$	−41.3304	+	3.45807i	−1.64274	+	0.137446i
$634$	8.45405			0.335753
$635$	−20.4494			−0.811511
$636$	−0.595874	−	7.12180i	−0.0236279	−	0.282398i
$637$		0			0
$638$		−	37.0433i		−	1.46656i
$639$	4.95807	+	29.4217i	0.196138	+	1.16390i
$640$		−	1.00000i		−	0.0395285i
$641$			0.543684i			0.0214742i	0.999942	+	0.0107371i	$0.00341780\pi$
$641$			0.543684i			0.0214742i	−0.999942	+	0.0107371i	$0.996582\pi$
$642$	−24.3732	+	2.03928i	−0.961934	+	0.0804841i
$643$		−	1.89361i		−	0.0746768i	−0.999303	−	0.0373384i	$-0.988112\pi$
$643$		−	1.89361i		−	0.0746768i	0.999303	−	0.0373384i	$-0.0118879\pi$
$644$		0			0
$645$	5.91773	−	0.495131i	0.233011	−	0.0194958i
$646$	−2.83800			−0.111660
$647$	33.0341			1.29870			0.649352	−	0.760488i	$-0.275040\pi$
$647$	33.0341			1.29870			0.649352	+	0.760488i	$0.275040\pi$
$648$	−2.94956	−	8.50295i	−0.115870	−	0.334027i
$649$			12.7658i			0.501103i
$650$	1.19315			0.0467993
$651$		0			0
$652$	−21.2114			−0.830703
$653$			5.07330i			0.198534i	0.995061	+	0.0992668i	$0.0316497\pi$
$653$			5.07330i			0.198534i	−0.995061	+	0.0992668i	$0.968350\pi$
$654$	1.34146	+	16.0330i	0.0524553	+	0.626939i
$655$	11.6718			0.456054
$656$	11.7294			0.457956
$657$	4.50790	+	26.7503i	0.175870	+	1.04363i
$658$		0			0
$659$		−	6.90298i		−	0.268902i	−0.990920	−	0.134451i	$-0.957073\pi$
$659$		−	6.90298i		−	0.268902i	0.990920	−	0.134451i	$-0.0429270\pi$
$660$	0.853079	+	10.1959i	0.0332061	+	0.396874i
$661$			35.5646i			1.38330i	0.722232	+	0.691650i	$0.243116\pi$
$661$			35.5646i			1.38330i	−0.722232	+	0.691650i	$0.756884\pi$
$662$		−	29.3727i		−	1.14160i
$663$	0.0895597	+	1.07040i	0.00347821	+	0.0415711i
$664$		−	15.8037i		−	0.613302i
$665$		0			0
$666$	−2.06898	−	12.2775i	−0.0801712	−	0.475744i
$667$	42.7113			1.65379
$668$	−0.446666			−0.0172820
$669$	−1.85362	−	22.1542i	−0.0716649	−	0.856529i
$670$		−	7.37539i		−	0.284936i
$671$	54.5824			2.10713
$672$		0			0
$673$	36.3461			1.40104			0.700519	−	0.713633i	$-0.252952\pi$
$673$	36.3461			1.40104			0.700519	+	0.713633i	$0.252952\pi$
$674$		−	4.97762i		−	0.191731i
$675$	5.03407	−	1.28768i	0.193762	−	0.0495629i
$676$	−11.5764			−0.445246
$677$	45.2138			1.73771			0.868854	−	0.495069i	$-0.164857\pi$
$677$	45.2138			1.73771			0.868854	+	0.495069i	$0.164857\pi$
$678$	−6.65640	+	0.556934i	−0.255638	+	0.0213889i
$679$		0			0
$680$			0.519764i			0.0199320i
$681$	7.79037	−	0.651812i	0.298527	−	0.0249775i
$682$		−	18.9238i		−	0.724629i
$683$		−	48.6162i		−	1.86025i	−0.367245	−	0.930124i	$-0.619699\pi$
$683$		−	48.6162i		−	1.86025i	0.367245	−	0.930124i	$-0.380301\pi$
$684$	2.72203	+	16.1528i	0.104080	+	0.617618i
$685$			13.0310i			0.497888i
$686$		0			0
$687$	−0.700584	−	8.37328i	−0.0267289	−	0.319460i
$688$	3.42854			0.130712
$689$	4.92312			0.187556
$690$	−11.7560	+	0.983611i	−0.447543	+	0.0374454i
$691$			25.3838i			0.965645i	0.875718	+	0.482823i	$0.160388\pi$
$691$			25.3838i			0.965645i	−0.875718	+	0.482823i	$0.839612\pi$
$692$	14.5993			0.554981
$693$		0			0
$694$	2.15190			0.0816851
$695$		−	10.4077i		−	0.394785i
$696$	−10.8237	+	0.905608i	−0.410271	+	0.0343270i
$697$	−6.09652			−0.230922
$698$	−25.9752			−0.983176
$699$	0.0700709	+	0.837477i	0.00265032	+	0.0316763i
$700$		0			0
$701$		−	34.9681i		−	1.32073i	−0.750947	−	0.660363i	$-0.770403\pi$
$701$		−	34.9681i		−	1.32073i	0.750947	−	0.660363i	$-0.229597\pi$
$702$	6.00642	−	1.53640i	0.226698	−	0.0579878i
$703$			22.6609i			0.854672i
$704$			5.90717i			0.222635i
$705$	−9.42105	+	0.788250i	−0.354817	+	0.0296872i
$706$			27.1728i			1.02266i
$707$		0			0
$708$	3.73006	−	0.312090i	0.140184	−	0.0117291i
$709$	21.3545			0.801985			0.400992	−	0.916081i	$-0.368665\pi$
$709$	21.3545			0.801985			0.400992	+	0.916081i	$0.368665\pi$
$710$	−9.94550			−0.373248
$711$	−38.7824	+	6.53552i	−1.45445	+	0.245101i
$712$		−	2.22998i		−	0.0835719i
$713$	21.8194			0.817141
$714$		0			0
$715$	−7.04816			−0.263586
$716$		−	3.32735i		−	0.124349i
$717$	2.68184	+	32.0530i	0.100155	+	1.19704i
$718$	34.5969			1.29114
$719$	−19.6899			−0.734311			−0.367155	−	0.930160i	$-0.619668\pi$
$719$	−19.6899			−0.734311			−0.367155	+	0.930160i	$0.619668\pi$
$720$	2.95829	−	0.498524i	0.110249	−	0.0185789i
$721$		0			0
$722$		−	10.8136i		−	0.402441i
$723$	1.30013	+	15.5389i	0.0483522	+	0.577899i
$724$			0.943424i			0.0350621i
$725$		−	6.27090i		−	0.232895i
$726$	−3.45072	−	41.2426i	−0.128068	−	1.53066i
$727$			1.94837i			0.0722612i	0.999347	+	0.0361306i	$0.0115032\pi$
$727$			1.94837i			0.0722612i	−0.999347	+	0.0361306i	$0.988497\pi$
$728$		0			0
$729$	23.6838	−	12.9646i	0.877176	−	0.480169i
$730$	−9.04250			−0.334678
$731$	−1.78203			−0.0659108
$732$	−1.33439	−	15.9485i	−0.0493206	−	0.589472i
$733$		−	0.813417i		−	0.0300442i	−0.999887	−	0.0150221i	$-0.995218\pi$
$733$		−	0.813417i		−	0.0300442i	0.999887	−	0.0150221i	$-0.00478187\pi$
$734$	28.5579			1.05409
$735$		0			0
$736$	−6.81104			−0.251058
$737$			43.5677i			1.60484i
$738$	5.84739	+	34.6990i	0.215245	+	1.27729i
$739$	35.8402			1.31840			0.659201	−	0.751967i	$-0.270895\pi$
$739$	35.8402			1.31840			0.659201	+	0.751967i	$0.270895\pi$
$740$	4.15021			0.152565
$741$	−11.2447	+	0.940836i	−0.413086	+	0.0345625i
$742$		0			0
$743$		−	32.1530i		−	1.17958i	−0.807558	−	0.589789i	$-0.799211\pi$
$743$		−	32.1530i		−	1.17958i	0.807558	−	0.589789i	$-0.200789\pi$
$744$	−5.52936	+	0.462636i	−0.202716	+	0.0169610i
$745$			3.47353i			0.127260i
$746$			11.1237i			0.407268i
$747$	46.7518	−	7.87851i	1.71056	−	0.288260i
$748$		−	3.07033i		−	0.112262i
$749$		0			0
$750$	0.144414	+	1.72602i	0.00527327	+	0.0630253i
$751$	45.2483			1.65113			0.825567	−	0.564304i	$-0.190855\pi$
$751$	45.2483			1.65113			0.825567	+	0.564304i	$0.190855\pi$
$752$	−5.45825			−0.199042
$753$	17.3886	−	1.45488i	0.633675	−	0.0530189i
$754$		−	7.48215i		−	0.272484i
$755$	4.06178			0.147823
$756$		0			0
$757$	−23.3384			−0.848249			−0.424125	−	0.905604i	$-0.639418\pi$
$757$	−23.3384			−0.848249			−0.424125	+	0.905604i	$0.639418\pi$
$758$			11.9502i			0.434051i
$759$	69.4445	−	5.81035i	2.52068	−	0.210903i
$760$	−5.46018			−0.198062
$761$	−15.0369			−0.545087			−0.272544	−	0.962143i	$-0.587865\pi$
$761$	−15.0369			−0.545087			−0.272544	+	0.962143i	$0.587865\pi$
$762$	−2.95319	−	35.2961i	−0.106983	−	1.27864i
$763$		0			0
$764$			10.7011i			0.387153i
$765$	−1.53761	+	0.259115i	−0.0555924	+	0.00936831i
$766$		−	13.3235i		−	0.481398i
$767$			2.57850i			0.0931041i
$768$	1.72602	−	0.144414i	0.0622824	−	0.00521110i
$769$			15.3211i			0.552492i	0.961087	+	0.276246i	$0.0890905\pi$
$769$			15.3211i			0.552492i	−0.961087	+	0.276246i	$0.910910\pi$
$770$		0			0
$771$	2.95260	−	0.247041i	0.106335	−	0.00889697i
$772$	21.0803			0.758697
$773$	50.6305			1.82105			0.910527	−	0.413450i	$-0.135676\pi$
$773$	50.6305			1.82105			0.910527	+	0.413450i	$0.135676\pi$
$774$	1.70921	+	10.1426i	0.0614363	+	0.364569i
$775$		−	3.20353i		−	0.115074i
$776$	−9.01872			−0.323753
$777$		0			0
$778$	−8.00925			−0.287145
$779$		−	64.0447i		−	2.29464i
$780$	0.172308	+	2.05941i	0.00616963	+	0.0737386i
$781$	58.7497			2.10223
$782$	3.54013			0.126595
$783$	−8.07492	−	31.5682i	−0.288574	−	1.12815i
$784$		0			0
$785$			11.5039i			0.410593i
$786$	1.68557	+	20.1457i	0.0601223	+	0.718574i
$787$			10.9883i			0.391690i	0.980635	+	0.195845i	$0.0627449\pi$
$787$			10.9883i			0.391690i	−0.980635	+	0.195845i	$0.937255\pi$
$788$			0.349379i			0.0124461i
$789$	3.43166	+	41.0147i	0.122170	+	1.46016i
$790$		−	13.1097i		−	0.466424i
$791$		0			0
$792$	−17.4751	+	2.94486i	−0.620951	+	0.104641i
$793$	11.0248			0.391501
$794$	−35.3561			−1.25474
$795$	0.595874	+	7.12180i	0.0211335	+	0.252584i
$796$		−	5.36410i		−	0.190126i
$797$	23.2182			0.822430			0.411215	−	0.911538i	$-0.365105\pi$
$797$	23.2182			0.822430			0.411215	+	0.911538i	$0.365105\pi$
$798$		0			0
$799$	2.83700			0.100366
$800$			1.00000i			0.0353553i
$801$	6.59692	−	1.11170i	0.233091	−	0.0392799i
$802$	30.8568			1.08959
$803$	53.4156			1.88499
$804$	12.7301	−	1.06511i	0.448955	−	0.0375636i
$805$		0			0
$806$		−	3.82230i		−	0.134635i
$807$	−38.0551	+	3.18403i	−1.33960	+	0.112083i
$808$		−	18.1861i		−	0.639786i
$809$			45.4818i			1.59906i	0.600629	+	0.799528i	$0.294917\pi$
$809$			45.4818i			1.59906i	−0.600629	+	0.799528i	$0.705083\pi$
$810$	2.94956	+	8.50295i	0.103637	+	0.298763i
$811$		−	16.9849i		−	0.596422i	−0.954500	−	0.298211i	$-0.903610\pi$
$811$		−	16.9849i		−	0.596422i	0.954500	−	0.298211i	$-0.0963899\pi$
$812$		0			0
$813$	−1.13714	−	13.5910i	−0.0398813	−	0.476656i
$814$	−24.5160			−0.859284
$815$	21.2114			0.743003
$816$	−0.897122	+	0.0750613i	−0.0314056	+	0.00262767i
$817$		−	18.7205i		−	0.654947i
$818$	11.4854			0.401579
$819$		0			0
$820$	−11.7294			−0.409609
$821$			43.7943i			1.52843i	0.644962	+	0.764215i	$0.276873\pi$
$821$			43.7943i			1.52843i	−0.644962	+	0.764215i	$0.723127\pi$
$822$	−22.4917	+	1.88186i	−0.784489	+	0.0656374i
$823$	−19.7050			−0.686873			−0.343436	−	0.939176i	$-0.611591\pi$
$823$	−19.7050			−0.686873			−0.343436	+	0.939176i	$0.611591\pi$
$824$	−6.51986			−0.227130
$825$	−0.853079	−	10.1959i	−0.0297004	−	0.354975i
$826$		0			0
$827$		−	4.72370i		−	0.164259i	−0.996622	−	0.0821296i	$-0.973828\pi$
$827$		−	4.72370i		−	0.164259i	0.996622	−	0.0821296i	$-0.0261722\pi$
$828$	−3.39546	−	20.1490i	−0.118001	−	0.700227i
$829$			10.1622i			0.352947i	0.984305	+	0.176474i	$0.0564691\pi$
$829$			10.1622i			0.352947i	−0.984305	+	0.176474i	$0.943531\pi$
$830$			15.8037i			0.548554i
$831$	19.8307	−	1.65921i	0.687918	−	0.0575574i
$832$			1.19315i			0.0413652i
$833$		0			0
$834$	17.9638	−	1.50302i	0.622037	−	0.0520452i
$835$	0.446666			0.0154575
$836$	32.2542			1.11554
$837$	−4.12513	−	16.1268i	−0.142585	−	0.557424i
$838$		−	14.4383i		−	0.498762i
$839$	0.819210			0.0282823			0.0141411	−	0.999900i	$-0.495499\pi$
$839$	0.819210			0.0282823			0.0141411	+	0.999900i	$0.495499\pi$
$840$		0			0
$841$	−10.3242			−0.356007
$842$		−	19.1284i		−	0.659208i
$843$	1.67026	+	19.9627i	0.0575268	+	0.687552i
$844$	23.9455			0.824238
$845$	11.5764			0.398240
$846$	−2.72107	−	16.1471i	−0.0935523	−	0.555148i
$847$		0			0
$848$			4.12614i			0.141692i
$849$	3.29999	+	39.4411i	0.113256	+	1.35361i
$850$		−	0.519764i		−	0.0178277i
$851$		−	28.2672i		−	0.968987i
$852$	−1.43627	−	17.1661i	−0.0492059	−	0.588102i
$853$			40.0054i			1.36976i	0.728657	+	0.684879i	$0.240145\pi$
$853$			40.0054i			1.36976i	−0.728657	+	0.684879i	$0.759855\pi$
$854$		0			0
$855$	−2.72203	−	16.1528i	−0.0930915	−	0.552414i
$856$	14.1211			0.482648
$857$	−0.962108			−0.0328650			−0.0164325	−	0.999865i	$-0.505231\pi$
$857$	−0.962108			−0.0328650			−0.0164325	+	0.999865i	$0.505231\pi$
$858$	−1.01785	−	12.1653i	−0.0347490	−	0.415315i
$859$		−	55.4503i		−	1.89194i	−0.324253	−	0.945970i	$-0.605113\pi$
$859$		−	55.4503i		−	1.89194i	0.324253	−	0.945970i	$-0.394887\pi$
$860$	−3.42854			−0.116912
$861$		0			0
$862$	15.8639			0.540326
$863$			42.1521i			1.43488i	0.696623	+	0.717438i	$0.254685\pi$
$863$			42.1521i			1.43488i	−0.696623	+	0.717438i	$0.745315\pi$
$864$	1.28768	+	5.03407i	0.0438078	+	0.171263i
$865$	−14.5993			−0.496390
$866$	−10.3829			−0.352825
$867$	−28.8760	+	2.41603i	−0.980682	+	0.0820527i
$868$		0			0
$869$			77.4414i			2.62702i
$870$	10.8237	−	0.905608i	0.366958	−	0.0307030i
$871$			8.79998i			0.298176i
$872$		−	9.28898i		−	0.314565i
$873$	−4.49605	−	26.6800i	−0.152168	−	0.902980i
$874$			37.1895i			1.25795i
$875$		0			0
$876$	−1.30587	−	15.6075i	−0.0441211	−	0.527330i
$877$	−17.0594			−0.576056			−0.288028	−	0.957622i	$-0.593000\pi$
$877$	−17.0594			−0.576056			−0.288028	+	0.957622i	$0.593000\pi$
$878$	−19.4004			−0.654732
$879$	−11.5282	+	0.964556i	−0.388838	+	0.0325337i
$880$		−	5.90717i		−	0.199131i
$881$	16.1634			0.544558			0.272279	−	0.962218i	$-0.412223\pi$
$881$	16.1634			0.544558			0.272279	+	0.962218i	$0.412223\pi$
$882$		0			0
$883$	2.88552			0.0971055			0.0485527	−	0.998821i	$-0.484539\pi$
$883$	2.88552			0.0971055			0.0485527	+	0.998821i	$0.484539\pi$
$884$		−	0.620158i		−	0.0208582i
$885$	−3.73006	+	0.312090i	−0.125385	+	0.0104908i
$886$	−13.6242			−0.457714
$887$	−38.7448			−1.30092			−0.650461	−	0.759539i	$-0.725424\pi$
$887$	−38.7448			−1.30092			−0.650461	+	0.759539i	$0.725424\pi$
$888$	0.599349	+	7.16334i	0.0201128	+	0.240386i
$889$		0			0
$890$			2.22998i			0.0747490i
$891$	−17.4235	−	50.2283i	−0.583710	−	1.68271i
$892$			12.8354i			0.429761i
$893$			29.8031i			0.997322i
$894$	−5.99539	+	0.501628i	−0.200516	+	0.0167770i
$895$			3.32735i			0.111221i
$896$		0			0
$897$	14.0267	−	1.17360i	0.468338	−	0.0391853i
$898$	−30.4744			−1.01694
$899$	−20.0890			−0.670006
$900$	−2.95829	+	0.498524i	−0.0986096	+	0.0166175i
$901$		−	2.14462i		−	0.0714476i
$902$	69.2875			2.30702
$903$		0			0
$904$	3.85650			0.128265
$905$		−	0.943424i		−	0.0313605i
$906$	0.586579	+	7.01071i	0.0194878	+	0.232915i
$907$	−16.0649			−0.533428			−0.266714	−	0.963776i	$-0.585938\pi$
$907$	−16.0649			−0.533428			−0.266714	+	0.963776i	$0.585938\pi$
$908$	−4.51349			−0.149785
$909$	53.7999	−	9.06623i	1.78443	−	0.300708i
$910$		0			0
$911$		−	2.85184i		−	0.0944856i	−0.998883	−	0.0472428i	$-0.984957\pi$
$911$		−	2.85184i		−	0.0944856i	0.998883	−	0.0472428i	$-0.0150434\pi$
$912$	−0.788529	−	9.42439i	−0.0261108	−	0.312073i
$913$		−	93.3549i		−	3.08960i
$914$		−	14.3218i		−	0.473724i
$915$	1.33439	+	15.9485i	0.0441136	+	0.527240i
$916$			4.85121i			0.160288i
$917$		0			0
$918$	−0.669290	−	2.61653i	−0.0220899	−	0.0863583i
$919$	25.8571			0.852947			0.426474	−	0.904500i	$-0.359756\pi$
$919$	25.8571			0.852947			0.426474	+	0.904500i	$0.359756\pi$
$920$	6.81104			0.224553
$921$	−3.92059	−	46.8583i	−0.129188	−	1.54403i
$922$			9.84757i			0.324312i
$923$	11.8665			0.390591
$924$		0			0
$925$	−4.15021			−0.136458
$926$		−	16.8754i		−	0.554560i
$927$	−3.25031	−	19.2876i	−0.106754	−	0.633489i
$928$	6.27090			0.205852
$929$	3.81424			0.125141			0.0625706	−	0.998041i	$-0.480070\pi$
$929$	3.81424			0.125141			0.0625706	+	0.998041i	$0.480070\pi$
$930$	5.52936	−	0.462636i	0.181315	−	0.0151704i
$931$		0			0
$932$		−	0.485207i		−	0.0158935i
$933$	−40.3605	+	3.37692i	−1.32134	+	0.110555i
$934$		−	14.6036i		−	0.477844i
$935$			3.07033i			0.100411i
$936$	−3.52969	+	0.594816i	−0.115372	+	0.0194422i
$937$			24.8945i			0.813268i	0.913591	+	0.406634i	$0.133298\pi$
$937$			24.8945i			0.813268i	−0.913591	+	0.406634i	$0.866702\pi$
$938$		0			0
$939$	−3.62547	−	43.3312i	−0.118313	−	1.41406i
$940$	5.45825			0.178029
$941$	1.36851			0.0446120			0.0223060	−	0.999751i	$-0.492899\pi$
$941$	1.36851			0.0446120			0.0223060	+	0.999751i	$0.492899\pi$
$942$	−19.8560	+	1.66133i	−0.646945	+	0.0541292i
$943$			79.8894i			2.60156i
$944$	−2.16108			−0.0703370
$945$		0			0
$946$	20.2530			0.658481
$947$			5.48468i			0.178228i	0.996021	+	0.0891141i	$0.0284036\pi$
$947$			5.48468i			0.178228i	−0.996021	+	0.0891141i	$0.971596\pi$
$948$	22.6277	−	1.89324i	0.734913	−	0.0614894i
$949$	10.7891			0.350229
$950$	5.46018			0.177152
$951$	−1.22089	−	14.5919i	−0.0395899	−	0.473173i
$952$		0			0
$953$		−	25.4797i		−	0.825370i	−0.910874	−	0.412685i	$-0.864591\pi$
$953$		−	25.4797i		−	0.825370i	0.910874	−	0.412685i	$-0.135409\pi$
$954$	−12.2063	+	2.05698i	−0.395194	+	0.0665972i
$955$		−	10.7011i		−	0.346280i
$956$		−	18.5705i		−	0.600612i
$957$	−63.9374	+	5.34958i	−2.06680	+	0.172927i
$958$			25.3810i			0.820022i
$959$		0			0
$960$	−1.72602	+	0.144414i	−0.0557071	+	0.00466095i
$961$	20.7374			0.668948
$962$	−4.95183			−0.159654
$963$	7.03968	+	41.7742i	0.226851	+	1.34615i
$964$		−	9.00275i		−	0.289959i
$965$	−21.0803			−0.678599
$966$		0			0
$967$	−15.9134			−0.511741			−0.255871	−	0.966711i	$-0.582362\pi$
$967$	−15.9134			−0.511741			−0.255871	+	0.966711i	$0.582362\pi$
$968$			23.8946i			0.768002i
$969$	0.409849	+	4.89845i	0.0131662	+	0.157361i
$970$	9.01872			0.289574
$971$	26.5406			0.851729			0.425865	−	0.904787i	$-0.359970\pi$
$971$	26.5406			0.851729			0.425865	+	0.904787i	$0.359970\pi$
$972$	−14.2503	+	6.31894i	−0.457079	+	0.202680i
$973$		0			0
$974$			26.4935i			0.848905i
$975$	−0.172308	−	2.05941i	−0.00551829	−	0.0659538i
$976$			9.24003i			0.295766i
$977$			21.1619i			0.677030i	0.940961	+	0.338515i	$0.109925\pi$
$977$			21.1619i			0.677030i	−0.940961	+	0.338515i	$0.890075\pi$
$978$	3.06323	+	36.6113i	0.0979514	+	1.17070i
$979$		−	13.1728i		−	0.421006i
$980$		0			0
$981$	27.4795	−	4.63078i	0.877353	−	0.147849i
$982$	29.5424			0.942737
$983$	15.2872			0.487587			0.243794	−	0.969827i	$-0.421608\pi$
$983$	15.2872			0.487587			0.243794	+	0.969827i	$0.421608\pi$
$984$	−1.69389	−	20.2452i	−0.0539994	−	0.645393i
$985$		−	0.349379i		−	0.0111321i
$986$	−3.25939			−0.103800
$987$		0			0
$988$	6.51484			0.207265
$989$			23.3519i			0.742548i
$990$	17.4751	−	2.94486i	0.555395	−	0.0935939i
$991$	−15.2805			−0.485402			−0.242701	−	0.970101i	$-0.578033\pi$
$991$	−15.2805			−0.485402			−0.242701	+	0.970101i	$0.578033\pi$
$992$	3.20353			0.101712
$993$	−50.6979	+	4.24185i	−1.60885	+	0.134611i
$994$		0			0
$995$			5.36410i			0.170053i
$996$	−27.2775	+	2.28228i	−0.864319	+	0.0723167i
$997$			19.9914i			0.633133i	0.948570	+	0.316567i	$0.102530\pi$
$997$			19.9914i			0.633133i	−0.948570	+	0.316567i	$0.897470\pi$
$998$			12.6748i			0.401212i
$999$	−20.8924	+	5.34414i	−0.661007	+	0.169081i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.72602 - 0.144414i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(0.144414 + 1.72602i) q^{6} -1.00000i q^{8} +(2.95829 - 0.498524i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(1.72602 - 0.144414i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(0.144414 + 1.72602i) q^{6} -1.00000i q^{8} +(2.95829 - 0.498524i) q^{9} +1.00000i q^{10} -5.90717i q^{11} +(-1.72602 + 0.144414i) q^{12} -1.19315i q^{13} +(1.72602 - 0.144414i) q^{15} +1.00000 q^{16} -0.519764 q^{17} +(0.498524 + 2.95829i) q^{18} -5.46018i q^{19} -1.00000 q^{20} +5.90717 q^{22} +6.81104i q^{23} +(-0.144414 - 1.72602i) q^{24} +1.00000 q^{25} +1.19315 q^{26} +(5.03407 - 1.28768i) q^{27} -6.27090i q^{29} +(0.144414 + 1.72602i) q^{30} -3.20353i q^{31} +1.00000i q^{32} +(-0.853079 - 10.1959i) q^{33} -0.519764i q^{34} +(-2.95829 + 0.498524i) q^{36} -4.15021 q^{37} +5.46018 q^{38} +(-0.172308 - 2.05941i) q^{39} -1.00000i q^{40} +11.7294 q^{41} +3.42854 q^{43} +5.90717i q^{44} +(2.95829 - 0.498524i) q^{45} -6.81104 q^{46} -5.45825 q^{47} +(1.72602 - 0.144414i) q^{48} +1.00000i q^{50} +(-0.897122 + 0.0750613i) q^{51} +1.19315i q^{52} +4.12614i q^{53} +(1.28768 + 5.03407i) q^{54} -5.90717i q^{55} +(-0.788529 - 9.42439i) q^{57} +6.27090 q^{58} -2.16108 q^{59} +(-1.72602 + 0.144414i) q^{60} +9.24003i q^{61} +3.20353 q^{62} -1.00000 q^{64} -1.19315i q^{65} +(10.1959 - 0.853079i) q^{66} -7.37539 q^{67} +0.519764 q^{68} +(0.983611 + 11.7560i) q^{69} +9.94550i q^{71} +(-0.498524 - 2.95829i) q^{72} +9.04250i q^{73} -4.15021i q^{74} +(1.72602 - 0.144414i) q^{75} +5.46018i q^{76} +(2.05941 - 0.172308i) q^{78} -13.1097 q^{79} +1.00000 q^{80} +(8.50295 - 2.94956i) q^{81} +11.7294i q^{82} +15.8037 q^{83} -0.519764 q^{85} +3.42854i q^{86} +(-0.905608 - 10.8237i) q^{87} -5.90717 q^{88} +2.22998 q^{89} +(0.498524 + 2.95829i) q^{90} -6.81104i q^{92} +(-0.462636 - 5.52936i) q^{93} -5.45825i q^{94} -5.46018i q^{95} +(0.144414 + 1.72602i) q^{96} -9.01872i q^{97} +(-2.94486 - 17.4751i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} - 16 q^{4} + 16 q^{5} + 8 q^{9}+O(q^{10}) \) 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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