LMFDB - Embedded newform 1470.2.b.d.881.6

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			881.6
Root			$-1.11192 - 1.32802i$ of defining polynomial
Character	$\chi$	$=$	1470.881
Dual form			1470.2.b.d.881.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.53549 + 0.801418i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(0.801418 - 1.53549i) q^{6} +1.00000i q^{8} +(1.71546 + 2.46114i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.53549 + 0.801418i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(0.801418 - 1.53549i) q^{6} +1.00000i q^{8} +(1.71546 + 2.46114i) q^{9} -1.00000i q^{10} -5.48447i q^{11} +(-1.53549 - 0.801418i) q^{12} -4.37587i q^{13} +(1.53549 + 0.801418i) q^{15} +1.00000 q^{16} -6.99274 q^{17} +(2.46114 - 1.71546i) q^{18} -4.64816i q^{19} -1.00000 q^{20} -5.48447 q^{22} -7.99511i q^{23} +(-0.801418 + 1.53549i) q^{24} +1.00000 q^{25} -4.37587 q^{26} +(0.661673 + 5.15385i) q^{27} +3.40414i q^{29} +(0.801418 - 1.53549i) q^{30} +3.85766i q^{31} -1.00000i q^{32} +(4.39535 - 8.42134i) q^{33} +6.99274i q^{34} +(-1.71546 - 2.46114i) q^{36} +9.25252 q^{37} -4.64816 q^{38} +(3.50690 - 6.71910i) q^{39} +1.00000i q^{40} +4.36516 q^{41} +1.48092 q^{43} +5.48447i q^{44} +(1.71546 + 2.46114i) q^{45} -7.99511 q^{46} +7.51483 q^{47} +(1.53549 + 0.801418i) q^{48} -1.00000i q^{50} +(-10.7373 - 5.60410i) q^{51} +4.37587i q^{52} -4.68750i q^{53} +(5.15385 - 0.661673i) q^{54} -5.48447i q^{55} +(3.72512 - 7.13721i) q^{57} +3.40414 q^{58} +6.00852 q^{59} +(-1.53549 - 0.801418i) q^{60} +6.75039i q^{61} +3.85766 q^{62} -1.00000 q^{64} -4.37587i q^{65} +(-8.42134 - 4.39535i) q^{66} -5.98178 q^{67} +6.99274 q^{68} +(6.40743 - 12.2764i) q^{69} -4.42464i q^{71} +(-2.46114 + 1.71546i) q^{72} +10.7067i q^{73} -9.25252i q^{74} +(1.53549 + 0.801418i) q^{75} +4.64816i q^{76} +(-6.71910 - 3.50690i) q^{78} +4.87263 q^{79} +1.00000 q^{80} +(-3.11440 + 8.44396i) q^{81} -4.36516i q^{82} -9.22718 q^{83} -6.99274 q^{85} -1.48092i q^{86} +(-2.72814 + 5.22703i) q^{87} +5.48447 q^{88} +0.525443 q^{89} +(2.46114 - 1.71546i) q^{90} +7.99511i q^{92} +(-3.09160 + 5.92340i) q^{93} -7.51483i q^{94} -4.64816i q^{95} +(0.801418 - 1.53549i) q^{96} +2.60272i q^{97} +(13.4980 - 9.40838i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.53549	+	0.801418i	0.886516	+	0.462699i
$3$	1.53549	+	0.801418i	0.886516	+	0.462699i
$4$	−1.00000			−0.500000
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	0.801418	−	1.53549i	0.327177	−	0.626861i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	1.71546	+	2.46114i	0.571820	+	0.820379i
$10$		−	1.00000i		−	0.316228i
$11$		−	5.48447i		−	1.65363i	−0.562475	−	0.826815i	$-0.690151\pi$
$11$		−	5.48447i		−	1.65363i	0.562475	−	0.826815i	$-0.309849\pi$
$12$	−1.53549	−	0.801418i	−0.443258	−	0.231349i
$13$		−	4.37587i		−	1.21365i	−0.794837	−	0.606824i	$-0.792443\pi$
$13$		−	4.37587i		−	1.21365i	0.794837	−	0.606824i	$-0.207557\pi$
$14$		0			0
$15$	1.53549	+	0.801418i	0.396462	+	0.206925i
$16$	1.00000			0.250000
$17$	−6.99274			−1.69599			−0.847994	−	0.530005i	$-0.822190\pi$
$17$	−6.99274			−1.69599			−0.847994	+	0.530005i	$0.822190\pi$
$18$	2.46114	−	1.71546i	0.580096	−	0.404338i
$19$		−	4.64816i		−	1.06636i	−0.846001	−	0.533181i	$-0.820996\pi$
$19$		−	4.64816i		−	1.06636i	0.846001	−	0.533181i	$-0.179004\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	−5.48447			−1.16929
$23$		−	7.99511i		−	1.66710i	−0.552447	−	0.833548i	$-0.686306\pi$
$23$		−	7.99511i		−	1.66710i	0.552447	−	0.833548i	$-0.313694\pi$
$24$	−0.801418	+	1.53549i	−0.163589	+	0.313431i
$25$	1.00000			0.200000
$26$	−4.37587			−0.858178
$27$	0.661673	+	5.15385i	0.127339	+	0.991859i
$28$		0			0
$29$			3.40414i			0.632134i	0.948737	+	0.316067i	$0.102362\pi$
$29$			3.40414i			0.632134i	−0.948737	+	0.316067i	$0.897638\pi$
$30$	0.801418	−	1.53549i	0.146318	−	0.280341i
$31$			3.85766i			0.692856i	0.938077	+	0.346428i	$0.112605\pi$
$31$			3.85766i			0.692856i	−0.938077	+	0.346428i	$0.887395\pi$
$32$		−	1.00000i		−	0.176777i
$33$	4.39535	−	8.42134i	0.765132	−	1.46597i
$34$			6.99274i			1.19925i
$35$		0			0
$36$	−1.71546	−	2.46114i	−0.285910	−	0.410190i
$37$	9.25252			1.52111			0.760553	−	0.649276i	$-0.224928\pi$
$37$	9.25252			1.52111			0.760553	+	0.649276i	$0.224928\pi$
$38$	−4.64816			−0.754032
$39$	3.50690	−	6.71910i	0.561553	−	1.07592i
$40$			1.00000i			0.158114i
$41$	4.36516			0.681724			0.340862	−	0.940113i	$-0.389281\pi$
$41$	4.36516			0.681724			0.340862	+	0.940113i	$0.389281\pi$
$42$		0			0
$43$	1.48092			0.225838			0.112919	−	0.993604i	$-0.463980\pi$
$43$	1.48092			0.225838			0.112919	+	0.993604i	$0.463980\pi$
$44$			5.48447i			0.826815i
$45$	1.71546	+	2.46114i	0.255726	+	0.366885i
$46$	−7.99511			−1.17882
$47$	7.51483			1.09615			0.548075	−	0.836429i	$-0.315361\pi$
$47$	7.51483			1.09615			0.548075	+	0.836429i	$0.315361\pi$
$48$	1.53549	+	0.801418i	0.221629	+	0.115675i
$49$		0			0
$50$		−	1.00000i		−	0.141421i
$51$	−10.7373	−	5.60410i	−1.50352	−	0.784732i
$52$			4.37587i			0.606824i
$53$		−	4.68750i		−	0.643877i	−0.946761	−	0.321939i	$-0.895666\pi$
$53$		−	4.68750i		−	0.643877i	0.946761	−	0.321939i	$-0.104334\pi$
$54$	5.15385	−	0.661673i	0.701350	−	0.0900422i
$55$		−	5.48447i		−	0.739525i
$56$		0			0
$57$	3.72512	−	7.13721i	0.493404	−	0.945346i
$58$	3.40414			0.446986
$59$	6.00852			0.782243			0.391122	−	0.920339i	$-0.372087\pi$
$59$	6.00852			0.782243			0.391122	+	0.920339i	$0.372087\pi$
$60$	−1.53549	−	0.801418i	−0.198231	−	0.103463i
$61$			6.75039i			0.864298i	0.901802	+	0.432149i	$0.142245\pi$
$61$			6.75039i			0.864298i	−0.901802	+	0.432149i	$0.857755\pi$
$62$	3.85766			0.489923
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	4.37587i		−	0.542759i
$66$	−8.42134	−	4.39535i	−1.03660	−	0.541030i
$67$	−5.98178			−0.730791			−0.365396	−	0.930852i	$-0.619066\pi$
$67$	−5.98178			−0.730791			−0.365396	+	0.930852i	$0.619066\pi$
$68$	6.99274			0.847994
$69$	6.40743	−	12.2764i	0.771363	−	1.47791i
$70$		0			0
$71$		−	4.42464i		−	0.525108i	−0.964917	−	0.262554i	$-0.915435\pi$
$71$		−	4.42464i		−	0.525108i	0.964917	−	0.262554i	$-0.0845647\pi$
$72$	−2.46114	+	1.71546i	−0.290048	+	0.202169i
$73$			10.7067i			1.25313i	0.779370	+	0.626564i	$0.215539\pi$
$73$			10.7067i			1.25313i	−0.779370	+	0.626564i	$0.784461\pi$
$74$		−	9.25252i		−	1.07558i
$75$	1.53549	+	0.801418i	0.177303	+	0.0925397i
$76$			4.64816i			0.533181i
$77$		0			0
$78$	−6.71910	−	3.50690i	−0.760788	−	0.397078i
$79$	4.87263			0.548214			0.274107	−	0.961699i	$-0.411618\pi$
$79$	4.87263			0.548214			0.274107	+	0.961699i	$0.411618\pi$
$80$	1.00000			0.111803
$81$	−3.11440	+	8.44396i	−0.346044	+	0.938218i
$82$		−	4.36516i		−	0.482052i
$83$	−9.22718			−1.01281			−0.506407	−	0.862294i	$-0.669027\pi$
$83$	−9.22718			−1.01281			−0.506407	+	0.862294i	$0.669027\pi$
$84$		0			0
$85$	−6.99274			−0.758469
$86$		−	1.48092i		−	0.159692i
$87$	−2.72814	+	5.22703i	−0.292487	+	0.560396i
$88$	5.48447			0.584646
$89$	0.525443			0.0556969			0.0278484	−	0.999612i	$-0.491134\pi$
$89$	0.525443			0.0556969			0.0278484	+	0.999612i	$0.491134\pi$
$90$	2.46114	−	1.71546i	0.259427	−	0.180825i
$91$		0			0
$92$			7.99511i			0.833548i
$93$	−3.09160	+	5.92340i	−0.320583	+	0.614228i
$94$		−	7.51483i		−	0.775096i
$95$		−	4.64816i		−	0.476892i
$96$	0.801418	−	1.53549i	0.0817943	−	0.156715i
$97$			2.60272i			0.264267i	0.991232	+	0.132133i	$0.0421827\pi$
$97$			2.60272i			0.264267i	−0.991232	+	0.132133i	$0.957817\pi$
$98$		0			0
$99$	13.4980	−	9.40838i	1.35660	−	0.945578i
$100$	−1.00000			−0.100000
$101$	−1.59753			−0.158960			−0.0794799	−	0.996836i	$-0.525326\pi$
$101$	−1.59753			−0.158960			−0.0794799	+	0.996836i	$0.525326\pi$
$102$	−5.60410	+	10.7373i	−0.554889	+	1.06315i
$103$			9.40273i			0.926479i	0.886233	+	0.463239i	$0.153313\pi$
$103$			9.40273i			0.926479i	−0.886233	+	0.463239i	$0.846687\pi$
$104$	4.37587			0.429089
$105$		0			0
$106$	−4.68750			−0.455290
$107$			5.31279i			0.513607i	0.966464	+	0.256804i	$0.0826693\pi$
$107$			5.31279i			0.513607i	−0.966464	+	0.256804i	$0.917331\pi$
$108$	−0.661673	−	5.15385i	−0.0636695	−	0.495930i
$109$	−14.5402			−1.39269			−0.696347	−	0.717705i	$-0.745192\pi$
$109$	−14.5402			−1.39269			−0.696347	+	0.717705i	$0.745192\pi$
$110$	−5.48447			−0.522923
$111$	14.2072	+	7.41513i	1.34848	+	0.703813i
$112$		0			0
$113$		−	14.2482i		−	1.34036i	−0.742198	−	0.670180i	$-0.766217\pi$
$113$		−	14.2482i		−	1.34036i	0.742198	−	0.670180i	$-0.233783\pi$
$114$	−7.13721	−	3.72512i	−0.668461	−	0.348889i
$115$		−	7.99511i		−	0.745548i
$116$		−	3.40414i		−	0.316067i
$117$	10.7696	−	7.50662i	0.995651	−	0.693988i
$118$		−	6.00852i		−	0.553129i
$119$		0			0
$120$	−0.801418	+	1.53549i	−0.0731591	+	0.140170i
$121$	−19.0794			−1.73449
$122$	6.75039			0.611151
$123$	6.70267	+	3.49832i	0.604359	+	0.315433i
$124$		−	3.85766i		−	0.346428i
$125$	1.00000			0.0894427
$126$		0			0
$127$	4.88266			0.433266			0.216633	−	0.976253i	$-0.430492\pi$
$127$	4.88266			0.433266			0.216633	+	0.976253i	$0.430492\pi$
$128$			1.00000i			0.0883883i
$129$	2.27394	+	1.18684i	0.200209	+	0.104495i
$130$	−4.37587			−0.383789
$131$	14.3521			1.25395			0.626974	−	0.779040i	$-0.284293\pi$
$131$	14.3521			1.25395			0.626974	+	0.779040i	$0.284293\pi$
$132$	−4.39535	+	8.42134i	−0.382566	+	0.732984i
$133$		0			0
$134$			5.98178i			0.516747i
$135$	0.661673	+	5.15385i	0.0569477	+	0.443573i
$136$		−	6.99274i		−	0.599623i
$137$		−	5.65795i		−	0.483392i	−0.970352	−	0.241696i	$-0.922296\pi$
$137$		−	5.65795i		−	0.483392i	0.970352	−	0.241696i	$-0.0777036\pi$
$138$	−12.2764	−	6.40743i	−1.04504	−	0.545436i
$139$			8.20450i			0.695897i	0.937514	+	0.347949i	$0.113122\pi$
$139$			8.20450i			0.695897i	−0.937514	+	0.347949i	$0.886878\pi$
$140$		0			0
$141$	11.5389	+	6.02252i	0.971755	+	0.507187i
$142$	−4.42464			−0.371307
$143$	−23.9993			−2.00692
$144$	1.71546	+	2.46114i	0.142955	+	0.205095i
$145$			3.40414i			0.282699i
$146$	10.7067			0.886095
$147$		0			0
$148$	−9.25252			−0.760553
$149$			10.5894i			0.867516i	0.901029	+	0.433758i	$0.142813\pi$
$149$			10.5894i			0.867516i	−0.901029	+	0.433758i	$0.857187\pi$
$150$	0.801418	−	1.53549i	0.0654355	−	0.125372i
$151$	−16.4546			−1.33906			−0.669528	−	0.742787i	$-0.733504\pi$
$151$	−16.4546			−1.33906			−0.669528	+	0.742787i	$0.733504\pi$
$152$	4.64816			0.377016
$153$	−11.9958	−	17.2101i	−0.969800	−	1.39135i
$154$		0			0
$155$			3.85766i			0.309855i
$156$	−3.50690	+	6.71910i	−0.280776	+	0.537959i
$157$			8.65512i			0.690754i	0.938464	+	0.345377i	$0.112249\pi$
$157$			8.65512i			0.690754i	−0.938464	+	0.345377i	$0.887751\pi$
$158$		−	4.87263i		−	0.387646i
$159$	3.75664	−	7.19761i	0.297921	−	0.570807i
$160$		−	1.00000i		−	0.0790569i
$161$		0			0
$162$	8.44396	+	3.11440i	0.663421	+	0.244690i
$163$	19.1573			1.50051			0.750256	−	0.661148i	$-0.229930\pi$
$163$	19.1573			1.50051			0.750256	+	0.661148i	$0.229930\pi$
$164$	−4.36516			−0.340862
$165$	4.39535	−	8.42134i	0.342177	−	0.655601i
$166$			9.22718i			0.716168i
$167$	−3.99462			−0.309113			−0.154556	−	0.987984i	$-0.549395\pi$
$167$	−3.99462			−0.309113			−0.154556	+	0.987984i	$0.549395\pi$
$168$		0			0
$169$	−6.14821			−0.472939
$170$			6.99274i			0.536319i
$171$	11.4398	−	7.97374i	0.874821	−	0.609767i
$172$	−1.48092			−0.112919
$173$	−18.7253			−1.42366			−0.711830	−	0.702352i	$-0.752133\pi$
$173$	−18.7253			−1.42366			−0.711830	+	0.702352i	$0.752133\pi$
$174$	5.22703	+	2.72814i	0.396260	+	0.206820i
$175$		0			0
$176$		−	5.48447i		−	0.413407i
$177$	9.22603	+	4.81534i	0.693471	+	0.361943i
$178$		−	0.525443i		−	0.0393836i
$179$			10.9143i			0.815776i	0.913032	+	0.407888i	$0.133735\pi$
$179$			10.9143i			0.815776i	−0.913032	+	0.407888i	$0.866265\pi$
$180$	−1.71546	−	2.46114i	−0.127863	−	0.183442i
$181$		−	11.1025i		−	0.825244i	−0.910902	−	0.412622i	$-0.864613\pi$
$181$		−	11.1025i		−	0.825244i	0.910902	−	0.412622i	$-0.135387\pi$
$182$		0			0
$183$	−5.40988	+	10.3651i	−0.399910	+	0.766214i
$184$	7.99511			0.589408
$185$	9.25252			0.680259
$186$	5.92340	+	3.09160i	0.434324	+	0.226687i
$187$			38.3515i			2.80454i
$188$	−7.51483			−0.548075
$189$		0			0
$190$	−4.64816			−0.337213
$191$		−	18.3911i		−	1.33073i	−0.746517	−	0.665366i	$-0.768275\pi$
$191$		−	18.3911i		−	1.33073i	0.746517	−	0.665366i	$-0.231725\pi$
$192$	−1.53549	−	0.801418i	−0.110814	−	0.0578373i
$193$	23.3665			1.68196			0.840978	−	0.541070i	$-0.181980\pi$
$193$	23.3665			1.68196			0.840978	+	0.541070i	$0.181980\pi$
$194$	2.60272			0.186865
$195$	3.50690	−	6.71910i	0.251134	−	0.481165i
$196$		0			0
$197$		−	6.30178i		−	0.448983i	−0.974476	−	0.224492i	$-0.927928\pi$
$197$		−	6.30178i		−	0.448983i	0.974476	−	0.224492i	$-0.0720722\pi$
$198$	−9.40838	−	13.4980i	−0.668625	−	0.959263i
$199$			11.0277i			0.781734i	0.920447	+	0.390867i	$0.127825\pi$
$199$			11.0277i			0.781734i	−0.920447	+	0.390867i	$0.872175\pi$
$200$			1.00000i			0.0707107i
$201$	−9.18497	−	4.79391i	−0.647858	−	0.338136i
$202$			1.59753i			0.112402i
$203$		0			0
$204$	10.7373	+	5.60410i	0.751760	+	0.392366i
$205$	4.36516			0.304876
$206$	9.40273			0.655119
$207$	19.6771	−	13.7153i	1.36765	−	0.953279i
$208$		−	4.37587i		−	0.303412i
$209$	−25.4927			−1.76337
$210$		0			0
$211$	16.4672			1.13365			0.566823	−	0.823840i	$-0.308172\pi$
$211$	16.4672			1.13365			0.566823	+	0.823840i	$0.308172\pi$
$212$			4.68750i			0.321939i
$213$	3.54598	−	6.79398i	0.242967	−	0.465516i
$214$	5.31279			0.363175
$215$	1.48092			0.100998
$216$	−5.15385	+	0.661673i	−0.350675	+	0.0450211i
$217$		0			0
$218$			14.5402i			0.984783i
$219$	−8.58056	+	16.4401i	−0.579821	+	1.11092i
$220$			5.48447i			0.369763i
$221$			30.5993i			2.05833i
$222$	7.41513	−	14.2072i	0.497671	−	0.953522i
$223$		−	13.5203i		−	0.905387i	−0.891666	−	0.452693i	$-0.850463\pi$
$223$		−	13.5203i		−	0.905387i	0.891666	−	0.452693i	$-0.149537\pi$
$224$		0			0
$225$	1.71546	+	2.46114i	0.114364	+	0.164076i
$226$	−14.2482			−0.947778
$227$	−5.57785			−0.370215			−0.185108	−	0.982718i	$-0.559263\pi$
$227$	−5.57785			−0.370215			−0.185108	+	0.982718i	$0.559263\pi$
$228$	−3.72512	+	7.13721i	−0.246702	+	0.472673i
$229$			11.6640i			0.770776i	0.922755	+	0.385388i	$0.125932\pi$
$229$			11.6640i			0.770776i	−0.922755	+	0.385388i	$0.874068\pi$
$230$	−7.99511			−0.527182
$231$		0			0
$232$	−3.40414			−0.223493
$233$		−	22.7275i		−	1.48893i	−0.667663	−	0.744464i	$-0.732705\pi$
$233$		−	22.7275i		−	1.48893i	0.667663	−	0.744464i	$-0.267295\pi$
$234$	−7.50662	−	10.7696i	−0.490723	−	0.704031i
$235$	7.51483			0.490213
$236$	−6.00852			−0.391122
$237$	7.48188	+	3.90501i	0.486000	+	0.253658i
$238$		0			0
$239$			5.34353i			0.345644i	0.984953	+	0.172822i	$0.0552886\pi$
$239$			5.34353i			0.345644i	−0.984953	+	0.172822i	$0.944711\pi$
$240$	1.53549	+	0.801418i	0.0991155	+	0.0517313i
$241$			14.8146i			0.954292i	0.878824	+	0.477146i	$0.158329\pi$
$241$			14.8146i			0.954292i	−0.878824	+	0.477146i	$0.841671\pi$
$242$			19.0794i			1.22647i
$243$	−11.5493	+	10.4697i	−0.740886	+	0.671631i
$244$		−	6.75039i		−	0.432149i
$245$		0			0
$246$	3.49832	−	6.70267i	0.223045	−	0.427346i
$247$	−20.3397			−1.29419
$248$	−3.85766			−0.244962
$249$	−14.1682	−	7.39483i	−0.897876	−	0.468628i
$250$		−	1.00000i		−	0.0632456i
$251$	−11.9052			−0.751446			−0.375723	−	0.926732i	$-0.622606\pi$
$251$	−11.9052			−0.751446			−0.375723	+	0.926732i	$0.622606\pi$
$252$		0			0
$253$	−43.8489			−2.75676
$254$		−	4.88266i		−	0.306366i
$255$	−10.7373	−	5.60410i	−0.672395	−	0.350943i
$256$	1.00000			0.0625000
$257$	−23.1928			−1.44673			−0.723364	−	0.690467i	$-0.757405\pi$
$257$	−23.1928			−1.44673			−0.723364	+	0.690467i	$0.757405\pi$
$258$	1.18684	−	2.27394i	0.0738892	−	0.141569i
$259$		0			0
$260$			4.37587i			0.271380i
$261$	−8.37807	+	5.83967i	−0.518589	+	0.361467i
$262$		−	14.3521i		−	0.886675i
$263$		−	9.86287i		−	0.608171i	−0.952645	−	0.304085i	$-0.901649\pi$
$263$		−	9.86287i		−	0.608171i	0.952645	−	0.304085i	$-0.0983508\pi$
$264$	8.42134	+	4.39535i	0.518298	+	0.270515i
$265$		−	4.68750i		−	0.287951i
$266$		0			0
$267$	0.806813	+	0.421099i	0.0493762	+	0.0257709i
$268$	5.98178			0.365396
$269$	20.3827			1.24275			0.621376	−	0.783512i	$-0.286574\pi$
$269$	20.3827			1.24275			0.621376	+	0.783512i	$0.286574\pi$
$270$	5.15385	−	0.661673i	0.313653	−	0.0402681i
$271$			20.2646i			1.23099i	0.788142	+	0.615493i	$0.211043\pi$
$271$			20.2646i			1.23099i	−0.788142	+	0.615493i	$0.788957\pi$
$272$	−6.99274			−0.423997
$273$		0			0
$274$	−5.65795			−0.341810
$275$		−	5.48447i		−	0.330726i
$276$	−6.40743	+	12.2764i	−0.385682	+	0.738954i
$277$	−19.8717			−1.19398			−0.596988	−	0.802250i	$-0.703636\pi$
$277$	−19.8717			−1.19398			−0.596988	+	0.802250i	$0.703636\pi$
$278$	8.20450			0.492073
$279$	−9.49423	+	6.61766i	−0.568405	+	0.396189i
$280$		0			0
$281$		−	20.8001i		−	1.24083i	−0.784273	−	0.620416i	$-0.786964\pi$
$281$		−	20.8001i		−	1.24083i	0.784273	−	0.620416i	$-0.213036\pi$
$282$	6.02252	−	11.5389i	0.358636	−	0.687134i
$283$		−	8.58090i		−	0.510082i	−0.966930	−	0.255041i	$-0.917911\pi$
$283$		−	8.58090i		−	0.510082i	0.966930	−	0.255041i	$-0.0820889\pi$
$284$			4.42464i			0.262554i
$285$	3.72512	−	7.13721i	0.220657	−	0.422772i
$286$			23.9993i			1.41911i
$287$		0			0
$288$	2.46114	−	1.71546i	0.145024	−	0.101084i
$289$	31.8984			1.87638
$290$	3.40414			0.199898
$291$	−2.08587	+	3.99646i	−0.122276	+	0.234276i
$292$		−	10.7067i		−	0.626564i
$293$	2.72492			0.159192			0.0795958	−	0.996827i	$-0.474637\pi$
$293$	2.72492			0.159192			0.0795958	+	0.996827i	$0.474637\pi$
$294$		0			0
$295$	6.00852			0.349830
$296$			9.25252i			0.537792i
$297$	28.2661	−	3.62892i	1.64017	−	0.210571i
$298$	10.5894			0.613426
$299$	−34.9856			−2.02327
$300$	−1.53549	−	0.801418i	−0.0886516	−	0.0462699i
$301$		0			0
$302$			16.4546i			0.946856i
$303$	−2.45298	−	1.28029i	−0.140920	−	0.0735505i
$304$		−	4.64816i		−	0.266590i
$305$			6.75039i			0.386526i
$306$	−17.2101	+	11.9958i	−0.983836	+	0.685752i
$307$			25.3383i			1.44613i	0.690778	+	0.723067i	$0.257268\pi$
$307$			25.3383i			1.44613i	−0.690778	+	0.723067i	$0.742732\pi$
$308$		0			0
$309$	−7.53552	+	14.4378i	−0.428680	+	0.821338i
$310$	3.85766			0.219100
$311$	3.05993			0.173513			0.0867563	−	0.996230i	$-0.472350\pi$
$311$	3.05993			0.173513			0.0867563	+	0.996230i	$0.472350\pi$
$312$	6.71910	+	3.50690i	0.380394	+	0.198539i
$313$		−	32.4069i		−	1.83174i	−0.401470	−	0.915872i	$-0.631501\pi$
$313$		−	32.4069i		−	1.83174i	0.401470	−	0.915872i	$-0.368499\pi$
$314$	8.65512			0.488437
$315$		0			0
$316$	−4.87263			−0.274107
$317$			12.8954i			0.724280i	0.932124	+	0.362140i	$0.117954\pi$
$317$			12.8954i			0.724280i	−0.932124	+	0.362140i	$0.882046\pi$
$318$	−7.19761	−	3.75664i	−0.403622	−	0.210662i
$319$	18.6699			1.04531
$320$	−1.00000			−0.0559017
$321$	−4.25777	+	8.15774i	−0.237645	+	0.455321i
$322$		0			0
$323$			32.5034i			1.80854i
$324$	3.11440	−	8.44396i	0.173022	−	0.469109i
$325$		−	4.37587i		−	0.242729i
$326$		−	19.1573i		−	1.06102i
$327$	−22.3263	−	11.6527i	−1.23464	−	0.644398i
$328$			4.36516i			0.241026i
$329$		0			0
$330$	−8.42134	−	4.39535i	−0.463580	−	0.241956i
$331$	34.4890			1.89568			0.947842	−	0.318740i	$-0.103260\pi$
$331$	34.4890			1.89568			0.947842	+	0.318740i	$0.103260\pi$
$332$	9.22718			0.506407
$333$	15.8723	+	22.7717i	0.869798	+	1.24788i
$334$			3.99462i			0.218576i
$335$	−5.98178			−0.326820
$336$		0			0
$337$	1.05685			0.0575704			0.0287852	−	0.999586i	$-0.490836\pi$
$337$	1.05685			0.0575704			0.0287852	+	0.999586i	$0.490836\pi$
$338$			6.14821i			0.334419i
$339$	11.4188	−	21.8780i	0.620183	−	1.18825i
$340$	6.99274			0.379235
$341$	21.1572			1.14573
$342$	−7.97374	−	11.4398i	−0.431170	−	0.618592i
$343$		0			0
$344$			1.48092i			0.0798459i
$345$	6.40743	−	12.2764i	0.344964	−	0.660940i
$346$			18.7253i			1.00668i
$347$			2.51957i			0.135258i	0.997711	+	0.0676288i	$0.0215433\pi$
$347$			2.51957i			0.135258i	−0.997711	+	0.0676288i	$0.978457\pi$
$348$	2.72814	−	5.22703i	0.146244	−	0.280198i
$349$			4.67230i			0.250102i	0.992150	+	0.125051i	$0.0399095\pi$
$349$			4.67230i			0.250102i	−0.992150	+	0.125051i	$0.960090\pi$
$350$		0			0
$351$	22.5526	−	2.89539i	1.20377	−	0.154545i
$352$	−5.48447			−0.292323
$353$	17.3565			0.923791			0.461895	−	0.886934i	$-0.347170\pi$
$353$	17.3565			0.923791			0.461895	+	0.886934i	$0.347170\pi$
$354$	4.81534	−	9.22603i	0.255932	−	0.490358i
$355$		−	4.42464i		−	0.234835i
$356$	−0.525443			−0.0278484
$357$		0			0
$358$	10.9143			0.576841
$359$			7.07262i			0.373279i	0.982429	+	0.186639i	$0.0597596\pi$
$359$			7.07262i			0.373279i	−0.982429	+	0.186639i	$0.940240\pi$
$360$	−2.46114	+	1.71546i	−0.129713	+	0.0904127i
$361$	−2.60543			−0.137128
$362$	−11.1025			−0.583536
$363$	−29.2962	−	15.2905i	−1.53765	−	0.802546i
$364$		0			0
$365$			10.7067i			0.560416i
$366$	10.3651	+	5.40988i	0.541795	+	0.282779i
$367$		−	8.54263i		−	0.445922i	−0.974827	−	0.222961i	$-0.928428\pi$
$367$		−	8.54263i		−	0.445922i	0.974827	−	0.222961i	$-0.0715722\pi$
$368$		−	7.99511i		−	0.416774i
$369$	7.48826	+	10.7433i	0.389823	+	0.559272i
$370$		−	9.25252i		−	0.481016i
$371$		0			0
$372$	3.09160	−	5.92340i	0.160292	−	0.307114i
$373$	19.8185			1.02616			0.513081	−	0.858340i	$-0.328504\pi$
$373$	19.8185			1.02616			0.513081	+	0.858340i	$0.328504\pi$
$374$	38.3515			1.98311
$375$	1.53549	+	0.801418i	0.0792924	+	0.0413850i
$376$			7.51483i			0.387548i
$377$	14.8961			0.767187
$378$		0			0
$379$	12.4542			0.639728			0.319864	−	0.947463i	$-0.396363\pi$
$379$	12.4542			0.639728			0.319864	+	0.947463i	$0.396363\pi$
$380$			4.64816i			0.238446i
$381$	7.49728	+	3.91305i	0.384097	+	0.200472i
$382$	−18.3911			−0.940970
$383$	27.5102			1.40571			0.702853	−	0.711335i	$-0.251909\pi$
$383$	27.5102			1.40571			0.702853	+	0.711335i	$0.251909\pi$
$384$	−0.801418	+	1.53549i	−0.0408972	+	0.0783577i
$385$		0			0
$386$		−	23.3665i		−	1.18932i
$387$	2.54046	+	3.64475i	0.129139	+	0.185273i
$388$		−	2.60272i		−	0.132133i
$389$			30.6518i			1.55411i	0.629435	+	0.777053i	$0.283286\pi$
$389$			30.6518i			1.55411i	−0.629435	+	0.777053i	$0.716714\pi$
$390$	−6.71910	−	3.50690i	−0.340235	−	0.177579i
$391$			55.9078i			2.82738i
$392$		0			0
$393$	22.0375	+	11.5020i	1.11164	+	0.580200i
$394$	−6.30178			−0.317479
$395$	4.87263			0.245169
$396$	−13.4980	+	9.40838i	−0.678301	+	0.472789i
$397$			5.68732i			0.285439i	0.989763	+	0.142719i	$0.0455846\pi$
$397$			5.68732i			0.285439i	−0.989763	+	0.142719i	$0.954415\pi$
$398$	11.0277			0.552769
$399$		0			0
$400$	1.00000			0.0500000
$401$			12.7853i			0.638467i	0.947676	+	0.319234i	$0.103425\pi$
$401$			12.7853i			0.638467i	−0.947676	+	0.319234i	$0.896575\pi$
$402$	−4.79391	+	9.18497i	−0.239098	+	0.458105i
$403$	16.8806			0.840883
$404$	1.59753			0.0794799
$405$	−3.11440	+	8.44396i	−0.154756	+	0.419584i
$406$		0			0
$407$		−	50.7451i		−	2.51534i
$408$	5.60410	−	10.7373i	0.277445	−	0.531575i
$409$			14.6466i			0.724228i	0.932134	+	0.362114i	$0.117945\pi$
$409$			14.6466i			0.724228i	−0.932134	+	0.362114i	$0.882055\pi$
$410$		−	4.36516i		−	0.215580i
$411$	4.53438	−	8.68773i	0.223665	−	0.428534i
$412$		−	9.40273i		−	0.463239i
$413$		0			0
$414$	−13.7153	−	19.6771i	−0.674070	−	0.967076i
$415$	−9.22718			−0.452945
$416$	−4.37587			−0.214545
$417$	−6.57523	+	12.5979i	−0.321991	+	0.616924i
$418$			25.4927i			1.24689i
$419$	38.2058			1.86647			0.933237	−	0.359261i	$-0.116971\pi$
$419$	38.2058			1.86647			0.933237	+	0.359261i	$0.116971\pi$
$420$		0			0
$421$	13.5971			0.662681			0.331341	−	0.943511i	$-0.392499\pi$
$421$	13.5971			0.662681			0.331341	+	0.943511i	$0.392499\pi$
$422$		−	16.4672i		−	0.801609i
$423$	12.8914	+	18.4950i	0.626801	+	0.899259i
$424$	4.68750			0.227645
$425$	−6.99274			−0.339198
$426$	−6.79398	−	3.54598i	−0.329170	−	0.171803i
$427$		0			0
$428$		−	5.31279i		−	0.256804i
$429$	−36.8507	−	19.2335i	−1.77917	−	0.928600i
$430$		−	1.48092i		−	0.0714163i
$431$			24.8072i			1.19492i	0.801899	+	0.597460i	$0.203823\pi$
$431$			24.8072i			1.19492i	−0.801899	+	0.597460i	$0.796177\pi$
$432$	0.661673	+	5.15385i	0.0318347	+	0.247965i
$433$		−	10.5514i		−	0.507069i	−0.967326	−	0.253535i	$-0.918407\pi$
$433$		−	10.5514i		−	0.507069i	0.967326	−	0.253535i	$-0.0815932\pi$
$434$		0			0
$435$	−2.72814	+	5.22703i	−0.130804	+	0.250617i
$436$	14.5402			0.696347
$437$	−37.1626			−1.77773
$438$	16.4401	+	8.58056i	0.785537	+	0.409995i
$439$			11.2224i			0.535615i	0.963472	+	0.267807i	$0.0862991\pi$
$439$			11.2224i			0.535615i	−0.963472	+	0.267807i	$0.913701\pi$
$440$	5.48447			0.261462
$441$		0			0
$442$	30.5993			1.45546
$443$			14.1488i			0.672230i	0.941821	+	0.336115i	$0.109113\pi$
$443$			14.1488i			0.672230i	−0.941821	+	0.336115i	$0.890887\pi$
$444$	−14.2072	−	7.41513i	−0.674242	−	0.351907i
$445$	0.525443			0.0249084
$446$	−13.5203			−0.640205
$447$	−8.48652	+	16.2599i	−0.401398	+	0.769066i
$448$		0			0
$449$			1.16231i			0.0548527i	0.999624	+	0.0274264i	$0.00873118\pi$
$449$			1.16231i			0.0548527i	−0.999624	+	0.0274264i	$0.991269\pi$
$450$	2.46114	−	1.71546i	0.116019	−	0.0808675i
$451$		−	23.9406i		−	1.12732i
$452$			14.2482i			0.670180i
$453$	−25.2659	−	13.1870i	−1.18709	−	0.619580i
$454$			5.57785i			0.261782i
$455$		0			0
$456$	7.13721	+	3.72512i	0.334230	+	0.174445i
$457$	−27.8911			−1.30469			−0.652345	−	0.757922i	$-0.726215\pi$
$457$	−27.8911			−1.30469			−0.652345	+	0.757922i	$0.726215\pi$
$458$	11.6640			0.545021
$459$	−4.62690	−	36.0395i	−0.215965	−	1.68218i
$460$			7.99511i			0.372774i
$461$	17.1662			0.799511			0.399755	−	0.916622i	$-0.369095\pi$
$461$	17.1662			0.799511			0.399755	+	0.916622i	$0.369095\pi$
$462$		0			0
$463$	−39.1372			−1.81886			−0.909430	−	0.415856i	$-0.863482\pi$
$463$	−39.1372			−1.81886			−0.909430	+	0.415856i	$0.863482\pi$
$464$			3.40414i			0.158033i
$465$	−3.09160	+	5.92340i	−0.143369	+	0.274691i
$466$	−22.7275			−1.05283
$467$	5.33074			0.246677			0.123339	−	0.992365i	$-0.460640\pi$
$467$	5.33074			0.246677			0.123339	+	0.992365i	$0.460640\pi$
$468$	−10.7696	+	7.50662i	−0.497825	+	0.346994i
$469$		0			0
$470$		−	7.51483i		−	0.346633i
$471$	−6.93636	+	13.2898i	−0.319611	+	0.612364i
$472$			6.00852i			0.276565i
$473$		−	8.12206i		−	0.373453i
$474$	3.90501	−	7.48188i	0.179363	−	0.343654i
$475$		−	4.64816i		−	0.213272i
$476$		0			0
$477$	11.5366	−	8.04121i	0.528224	−	0.368182i
$478$	5.34353			0.244407
$479$	−6.57119			−0.300245			−0.150123	−	0.988667i	$-0.547967\pi$
$479$	−6.57119			−0.300245			−0.150123	+	0.988667i	$0.547967\pi$
$480$	0.801418	−	1.53549i	0.0365795	−	0.0700852i
$481$		−	40.4878i		−	1.84608i
$482$	14.8146			0.674786
$483$		0			0
$484$	19.0794			0.867244
$485$			2.60272i			0.118184i
$486$	10.4697	+	11.5493i	0.474915	+	0.523885i
$487$	26.0143			1.17882			0.589410	−	0.807834i	$-0.299360\pi$
$487$	26.0143			1.17882			0.589410	+	0.807834i	$0.299360\pi$
$488$	−6.75039			−0.305576
$489$	29.4158	+	15.3530i	1.33023	+	0.694285i
$490$		0			0
$491$			30.2128i			1.36349i	0.731591	+	0.681743i	$0.238778\pi$
$491$			30.2128i			1.36349i	−0.731591	+	0.681743i	$0.761222\pi$
$492$	−6.70267	−	3.49832i	−0.302180	−	0.157716i
$493$		−	23.8043i		−	1.07209i
$494$			20.3397i			0.915128i
$495$	13.4980	−	9.40838i	0.606691	−	0.422875i
$496$			3.85766i			0.173214i
$497$		0			0
$498$	−7.39483	+	14.1682i	−0.331370	+	0.634894i
$499$	−9.86296			−0.441527			−0.220763	−	0.975327i	$-0.570855\pi$
$499$	−9.86296			−0.441527			−0.220763	+	0.975327i	$0.570855\pi$
$500$	−1.00000			−0.0447214
$501$	−6.13370	−	3.20136i	−0.274033	−	0.143026i
$502$			11.9052i			0.531353i
$503$	−2.92257			−0.130311			−0.0651554	−	0.997875i	$-0.520754\pi$
$503$	−2.92257			−0.130311			−0.0651554	+	0.997875i	$0.520754\pi$
$504$		0			0
$505$	−1.59753			−0.0710890
$506$			43.8489i			1.94932i
$507$	−9.44052	−	4.92728i	−0.419268	−	0.218828i
$508$	−4.88266			−0.216633
$509$	−34.1660			−1.51438			−0.757190	−	0.653194i	$-0.773428\pi$
$509$	−34.1660			−1.51438			−0.757190	+	0.653194i	$0.773428\pi$
$510$	−5.60410	+	10.7373i	−0.248154	+	0.475455i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	23.9559	−	3.07556i	1.05768	−	0.135789i
$514$			23.1928i			1.02299i
$515$			9.40273i			0.414334i
$516$	−2.27394	−	1.18684i	−0.100105	−	0.0522475i
$517$		−	41.2148i		−	1.81263i
$518$		0			0
$519$	−28.7525	−	15.0068i	−1.26210	−	0.658725i
$520$	4.37587			0.191894
$521$	−14.5920			−0.639286			−0.319643	−	0.947538i	$-0.603563\pi$
$521$	−14.5920			−0.639286			−0.319643	+	0.947538i	$0.603563\pi$
$522$	5.83967	+	8.37807i	0.255596	+	0.366698i
$523$		−	5.13396i		−	0.224492i	−0.993680	−	0.112246i	$-0.964196\pi$
$523$		−	5.13396i		−	0.224492i	0.993680	−	0.112246i	$-0.0358045\pi$
$524$	−14.3521			−0.626974
$525$		0			0
$526$	−9.86287			−0.430042
$527$		−	26.9756i		−	1.17508i
$528$	4.39535	−	8.42134i	0.191283	−	0.366492i
$529$	−40.9219			−1.77921
$530$	−4.68750			−0.203612
$531$	10.3074	+	14.7878i	0.447302	+	0.641736i
$532$		0			0
$533$		−	19.1014i		−	0.827372i
$534$	0.421099	−	0.806813i	0.0182228	−	0.0349142i
$535$			5.31279i			0.229692i
$536$		−	5.98178i		−	0.258374i
$537$	−8.74694	+	16.7589i	−0.377458	+	0.723198i
$538$		−	20.3827i		−	0.878759i
$539$		0			0
$540$	−0.661673	−	5.15385i	−0.0284739	−	0.221786i
$541$	−30.8179			−1.32497			−0.662483	−	0.749077i	$-0.730497\pi$
$541$	−30.8179			−1.32497			−0.662483	+	0.749077i	$0.730497\pi$
$542$	20.2646			0.870439
$543$	8.89776	−	17.0478i	0.381839	−	0.731592i
$544$			6.99274i			0.299811i
$545$	−14.5402			−0.622832
$546$		0			0
$547$	−9.79462			−0.418788			−0.209394	−	0.977831i	$-0.567149\pi$
$547$	−9.79462			−0.418788			−0.209394	+	0.977831i	$0.567149\pi$
$548$			5.65795i			0.241696i
$549$	−16.6136	+	11.5800i	−0.709052	+	0.494223i
$550$	−5.48447			−0.233858
$551$	15.8230			0.674083
$552$	12.2764	+	6.40743i	0.522519	+	0.272718i
$553$		0			0
$554$			19.8717i			0.844268i
$555$	14.2072	+	7.41513i	0.603060	+	0.314755i
$556$		−	8.20450i		−	0.347949i
$557$		−	2.19574i		−	0.0930365i	−0.998917	−	0.0465183i	$-0.985187\pi$
$557$		−	2.19574i		−	0.0930365i	0.998917	−	0.0465183i	$-0.0148126\pi$
$558$	6.61766	+	9.49423i	0.280148	+	0.401923i
$559$		−	6.48031i		−	0.274088i
$560$		0			0
$561$	−30.7355	+	58.8883i	−1.29765	+	2.48626i
$562$	−20.8001			−0.877401
$563$	−22.7822			−0.960155			−0.480078	−	0.877226i	$-0.659392\pi$
$563$	−22.7822			−0.960155			−0.480078	+	0.877226i	$0.659392\pi$
$564$	−11.5389	−	6.02252i	−0.485877	−	0.253594i
$565$		−	14.2482i		−	0.599427i
$566$	−8.58090			−0.360682
$567$		0			0
$568$	4.42464			0.185654
$569$		−	7.00282i		−	0.293573i	−0.989168	−	0.146787i	$-0.953107\pi$
$569$		−	7.00282i		−	0.293573i	0.989168	−	0.146787i	$-0.0468931\pi$
$570$	−7.13721	−	3.72512i	−0.298945	−	0.156028i
$571$	20.4402			0.855397			0.427698	−	0.903921i	$-0.359325\pi$
$571$	20.4402			0.855397			0.427698	+	0.903921i	$0.359325\pi$
$572$	23.9993			1.00346
$573$	14.7389	−	28.2393i	0.615728	−	1.17972i
$574$		0			0
$575$		−	7.99511i		−	0.333419i
$576$	−1.71546	−	2.46114i	−0.0714775	−	0.102547i
$577$		−	27.2878i		−	1.13601i	−0.823027	−	0.568003i	$-0.807716\pi$
$577$		−	27.2878i		−	1.13601i	0.823027	−	0.568003i	$-0.192284\pi$
$578$		−	31.8984i		−	1.32680i
$579$	35.8790	+	18.7263i	1.49108	+	0.778239i
$580$		−	3.40414i		−	0.141349i
$581$		0			0
$582$	3.99646	+	2.08587i	0.165658	+	0.0864620i
$583$	−25.7084			−1.06473
$584$	−10.7067			−0.443048
$585$	10.7696	−	7.50662i	0.445269	−	0.310361i
$586$		−	2.72492i		−	0.112565i
$587$	40.1596			1.65757			0.828783	−	0.559570i	$-0.189034\pi$
$587$	40.1596			1.65757			0.828783	+	0.559570i	$0.189034\pi$
$588$		0			0
$589$	17.9310			0.738835
$590$		−	6.00852i		−	0.247367i
$591$	5.05036	−	9.67632i	0.207744	−	0.398031i
$592$	9.25252			0.380276
$593$	−2.62320			−0.107722			−0.0538609	−	0.998548i	$-0.517153\pi$
$593$	−2.62320			−0.107722			−0.0538609	+	0.998548i	$0.517153\pi$
$594$	−3.62892	−	28.2661i	−0.148896	−	1.15977i
$595$		0			0
$596$		−	10.5894i		−	0.433758i
$597$	−8.83780	+	16.9329i	−0.361707	+	0.693019i
$598$			34.9856i			1.43067i
$599$			41.8523i			1.71004i	0.518595	+	0.855020i	$0.326455\pi$
$599$			41.8523i			1.71004i	−0.518595	+	0.855020i	$0.673545\pi$
$600$	−0.801418	+	1.53549i	−0.0327177	+	0.0626861i
$601$			31.5777i			1.28808i	0.764992	+	0.644040i	$0.222743\pi$
$601$			31.5777i			1.28808i	−0.764992	+	0.644040i	$0.777257\pi$
$602$		0			0
$603$	−10.2615	−	14.7220i	−0.417881	−	0.599526i
$604$	16.4546			0.669528
$605$	−19.0794			−0.775687
$606$	−1.28029	+	2.45298i	−0.0520080	+	0.0996457i
$607$			6.41971i			0.260568i	0.991477	+	0.130284i	$0.0415889\pi$
$607$			6.41971i			0.260568i	−0.991477	+	0.130284i	$0.958411\pi$
$608$	−4.64816			−0.188508
$609$		0			0
$610$	6.75039			0.273315
$611$		−	32.8839i		−	1.33034i
$612$	11.9958	+	17.2101i	0.484900	+	0.695677i
$613$	−38.0165			−1.53547			−0.767736	−	0.640766i	$-0.778617\pi$
$613$	−38.0165			−1.53547			−0.767736	+	0.640766i	$0.778617\pi$
$614$	25.3383			1.02257
$615$	6.70267	+	3.49832i	0.270278	+	0.141066i
$616$		0			0
$617$			33.5160i			1.34930i	0.738136	+	0.674652i	$0.235706\pi$
$617$			33.5160i			1.34930i	−0.738136	+	0.674652i	$0.764294\pi$
$618$	14.4378	+	7.53552i	0.580774	+	0.303123i
$619$			0.791382i			0.0318083i	0.999874	+	0.0159042i	$0.00506266\pi$
$619$			0.791382i			0.0318083i	−0.999874	+	0.0159042i	$0.994937\pi$
$620$		−	3.85766i		−	0.154927i
$621$	41.2056	−	5.29015i	1.65353	−	0.212286i
$622$		−	3.05993i		−	0.122692i
$623$		0			0
$624$	3.50690	−	6.71910i	0.140388	−	0.268979i
$625$	1.00000			0.0400000
$626$	−32.4069			−1.29524
$627$	−39.1438	−	20.4303i	−1.56325	−	0.815908i
$628$		−	8.65512i		−	0.345377i
$629$	−64.7005			−2.57978
$630$		0			0
$631$	31.5697			1.25677			0.628386	−	0.777902i	$-0.283716\pi$
$631$	31.5697			1.25677			0.628386	+	0.777902i	$0.283716\pi$
$632$			4.87263i			0.193823i
$633$	25.2852	+	13.1971i	1.00499	+	0.524537i
$634$	12.8954			0.512143
$635$	4.88266			0.193763
$636$	−3.75664	+	7.19761i	−0.148961	+	0.285404i
$637$		0			0
$638$		−	18.6699i		−	0.739149i
$639$	10.8896	−	7.59028i	0.430787	−	0.300267i
$640$			1.00000i			0.0395285i
$641$			3.80187i			0.150165i	0.997177	+	0.0750824i	$0.0239220\pi$
$641$			3.80187i			0.150165i	−0.997177	+	0.0750824i	$0.976078\pi$
$642$	8.15774	+	4.25777i	0.321960	+	0.168041i
$643$			4.78358i			0.188646i	0.995542	+	0.0943230i	$0.0300686\pi$
$643$			4.78358i			0.188646i	−0.995542	+	0.0943230i	$0.969931\pi$
$644$		0			0
$645$	2.27394	+	1.18684i	0.0895362	+	0.0467316i
$646$	32.5034			1.27883
$647$	16.5620			0.651121			0.325560	−	0.945521i	$-0.394447\pi$
$647$	16.5620			0.651121			0.325560	+	0.945521i	$0.394447\pi$
$648$	−8.44396	−	3.11440i	−0.331710	−	0.122345i
$649$		−	32.9535i		−	1.29354i
$650$	−4.37587			−0.171636
$651$		0			0
$652$	−19.1573			−0.750256
$653$		−	8.09175i		−	0.316655i	−0.987387	−	0.158327i	$-0.949390\pi$
$653$		−	8.09175i		−	0.316655i	0.987387	−	0.158327i	$-0.0506101\pi$
$654$	−11.6527	+	22.3263i	−0.455658	+	0.873026i
$655$	14.3521			0.560783
$656$	4.36516			0.170431
$657$	−26.3507	+	18.3670i	−1.02804	+	0.716564i
$658$		0			0
$659$		−	33.3747i		−	1.30009i	−0.759894	−	0.650047i	$-0.774749\pi$
$659$		−	33.3747i		−	1.30009i	0.759894	−	0.650047i	$-0.225251\pi$
$660$	−4.39535	+	8.42134i	−0.171089	+	0.327800i
$661$			26.5081i			1.03105i	0.856876	+	0.515523i	$0.172402\pi$
$661$			26.5081i			1.03105i	−0.856876	+	0.515523i	$0.827598\pi$
$662$		−	34.4890i		−	1.34045i
$663$	−24.5228	+	46.9849i	−0.952387	+	1.82474i
$664$		−	9.22718i		−	0.358084i
$665$		0			0
$666$	22.7717	−	15.8723i	0.882387	−	0.615040i
$667$	27.2165			1.05383
$668$	3.99462			0.154556
$669$	10.8354	−	20.7603i	0.418921	−	0.802640i
$670$			5.98178i			0.231096i
$671$	37.0223			1.42923
$672$		0			0
$673$	15.9621			0.615295			0.307648	−	0.951500i	$-0.400458\pi$
$673$	15.9621			0.615295			0.307648	+	0.951500i	$0.400458\pi$
$674$		−	1.05685i		−	0.0407085i
$675$	0.661673	+	5.15385i	0.0254678	+	0.198372i
$676$	6.14821			0.236470
$677$	−11.3672			−0.436877			−0.218438	−	0.975851i	$-0.570096\pi$
$677$	−11.3672			−0.436877			−0.218438	+	0.975851i	$0.570096\pi$
$678$	−21.8780	−	11.4188i	−0.840220	−	0.438536i
$679$		0			0
$680$		−	6.99274i		−	0.268159i
$681$	−8.56474	−	4.47019i	−0.328201	−	0.171298i
$682$		−	21.1572i		−	0.810151i
$683$		−	45.1270i		−	1.72674i	−0.504574	−	0.863369i	$-0.668350\pi$
$683$		−	45.1270i		−	1.72674i	0.504574	−	0.863369i	$-0.331650\pi$
$684$	−11.4398	+	7.97374i	−0.437411	+	0.304883i
$685$		−	5.65795i		−	0.216179i
$686$		0			0
$687$	−9.34770	+	17.9099i	−0.356637	+	0.683305i
$688$	1.48092			0.0564596
$689$	−20.5119			−0.781440
$690$	−12.2764	−	6.40743i	−0.467355	−	0.243927i
$691$		−	32.0881i		−	1.22069i	−0.792135	−	0.610345i	$-0.791031\pi$
$691$		−	32.0881i		−	1.22069i	0.792135	−	0.610345i	$-0.208969\pi$
$692$	18.7253			0.711830
$693$		0			0
$694$	2.51957			0.0956415
$695$			8.20450i			0.311215i
$696$	−5.22703	−	2.72814i	−0.198130	−	0.103410i
$697$	−30.5245			−1.15620
$698$	4.67230			0.176849
$699$	18.2142	−	34.8978i	0.688925	−	1.31996i
$700$		0			0
$701$			8.71262i			0.329071i	0.986371	+	0.164536i	$0.0526125\pi$
$701$			8.71262i			0.329071i	−0.986371	+	0.164536i	$0.947387\pi$
$702$	−2.89539	−	22.5526i	−0.109279	−	0.851192i
$703$		−	43.0072i		−	1.62205i
$704$			5.48447i			0.206704i
$705$	11.5389	+	6.02252i	0.434582	+	0.226821i
$706$		−	17.3565i		−	0.653219i
$707$		0			0
$708$	−9.22603	−	4.81534i	−0.346735	−	0.180971i
$709$	−22.5339			−0.846279			−0.423140	−	0.906064i	$-0.639072\pi$
$709$	−22.5339			−0.846279			−0.423140	+	0.906064i	$0.639072\pi$
$710$	−4.42464			−0.166054
$711$	8.35881	+	11.9922i	0.313480	+	0.449744i
$712$			0.525443i			0.0196918i
$713$	30.8424			1.15506
$714$		0			0
$715$	−23.9993			−0.897523
$716$		−	10.9143i		−	0.407888i
$717$	−4.28240	+	8.20494i	−0.159929	+	0.306419i
$718$	7.07262			0.263948
$719$	5.46856			0.203943			0.101971	−	0.994787i	$-0.467485\pi$
$719$	5.46856			0.203943			0.101971	+	0.994787i	$0.467485\pi$
$720$	1.71546	+	2.46114i	0.0639314	+	0.0917212i
$721$		0			0
$722$			2.60543i			0.0969639i
$723$	−11.8727	+	22.7477i	−0.441550	+	0.845995i
$724$			11.1025i			0.412622i
$725$			3.40414i			0.126427i
$726$	−15.2905	+	29.2962i	−0.567485	+	1.08728i
$727$		−	37.3430i		−	1.38498i	−0.721429	−	0.692488i	$-0.756514\pi$
$727$		−	37.3430i		−	1.38498i	0.721429	−	0.692488i	$-0.243486\pi$
$728$		0			0
$729$	−26.1244	+	6.82032i	−0.967570	+	0.252605i
$730$	10.7067			0.396274
$731$	−10.3557			−0.383019
$732$	5.40988	−	10.3651i	0.199955	−	0.383107i
$733$		−	5.62093i		−	0.207614i	−0.994597	−	0.103807i	$-0.966898\pi$
$733$		−	5.62093i		−	0.207614i	0.994597	−	0.103807i	$-0.0331024\pi$
$734$	−8.54263			−0.315314
$735$		0			0
$736$	−7.99511			−0.294704
$737$			32.8069i			1.20846i
$738$	10.7433	−	7.48826i	0.395465	−	0.275647i
$739$	24.3382			0.895296			0.447648	−	0.894210i	$-0.352262\pi$
$739$	24.3382			0.895296			0.447648	+	0.894210i	$0.352262\pi$
$740$	−9.25252			−0.340129
$741$	−31.2315	−	16.3006i	−1.14732	−	0.598819i
$742$		0			0
$743$		−	8.46882i		−	0.310691i	−0.987860	−	0.155345i	$-0.950351\pi$
$743$		−	8.46882i		−	0.310691i	0.987860	−	0.155345i	$-0.0496491\pi$
$744$	−5.92340	−	3.09160i	−0.217162	−	0.113343i
$745$			10.5894i			0.387965i
$746$		−	19.8185i		−	0.725605i
$747$	−15.8289	−	22.7094i	−0.579148	−	0.830892i
$748$		−	38.3515i		−	1.40227i
$749$		0			0
$750$	0.801418	−	1.53549i	0.0292636	−	0.0560682i
$751$	−30.1044			−1.09853			−0.549263	−	0.835650i	$-0.685091\pi$
$751$	−30.1044			−1.09853			−0.549263	+	0.835650i	$0.685091\pi$
$752$	7.51483			0.274038
$753$	−18.2802	−	9.54100i	−0.666169	−	0.347693i
$754$		−	14.8961i		−	0.542483i
$755$	−16.4546			−0.598844
$756$		0			0
$757$	−24.3263			−0.884154			−0.442077	−	0.896977i	$-0.645758\pi$
$757$	−24.3263			−0.884154			−0.442077	+	0.896977i	$0.645758\pi$
$758$		−	12.4542i		−	0.452356i
$759$	−67.3296	−	35.1413i	−2.44391	−	1.27555i
$760$	4.64816			0.168607
$761$	49.5903			1.79765			0.898824	−	0.438311i	$-0.144423\pi$
$761$	49.5903			1.79765			0.898824	+	0.438311i	$0.144423\pi$
$762$	3.91305	−	7.49728i	0.141755	−	0.271598i
$763$		0			0
$764$			18.3911i			0.665366i
$765$	−11.9958	−	17.2101i	−0.433708	−	0.622232i
$766$		−	27.5102i		−	0.993985i
$767$		−	26.2925i		−	0.949367i
$768$	1.53549	+	0.801418i	0.0554072	+	0.0289187i
$769$			24.0765i			0.868221i	0.900860	+	0.434110i	$0.142937\pi$
$769$			24.0765i			0.868221i	−0.900860	+	0.434110i	$0.857063\pi$
$770$		0			0
$771$	−35.6123	−	18.5871i	−1.28255	−	0.669399i
$772$	−23.3665			−0.840978
$773$	−33.3050			−1.19790			−0.598949	−	0.800787i	$-0.704415\pi$
$773$	−33.3050			−1.19790			−0.598949	+	0.800787i	$0.704415\pi$
$774$	3.64475	−	2.54046i	0.131008	−	0.0913149i
$775$			3.85766i			0.138571i
$776$	−2.60272			−0.0934323
$777$		0			0
$778$	30.6518			1.09892
$779$		−	20.2900i		−	0.726965i
$780$	−3.50690	+	6.71910i	−0.125567	+	0.240582i
$781$	−24.2668			−0.868333
$782$	55.9078			1.99926
$783$	−17.5445	+	2.25243i	−0.626988	+	0.0804952i
$784$		0			0
$785$			8.65512i			0.308914i
$786$	11.5020	−	22.0375i	0.410263	−	0.786051i
$787$		−	1.98548i		−	0.0707748i	−0.999374	−	0.0353874i	$-0.988733\pi$
$787$		−	1.98548i		−	0.0707748i	0.999374	−	0.0353874i	$-0.0112665\pi$
$788$			6.30178i			0.224492i
$789$	7.90428	−	15.1443i	0.281400	−	0.539153i
$790$		−	4.87263i		−	0.173361i
$791$		0			0
$792$	9.40838	+	13.4980i	0.334312	+	0.479632i
$793$	29.5388			1.04895
$794$	5.68732			0.201836
$795$	3.75664	−	7.19761i	0.133234	−	0.255273i
$796$		−	11.0277i		−	0.390867i
$797$	−39.2292			−1.38957			−0.694785	−	0.719218i	$-0.744500\pi$
$797$	−39.2292			−1.38957			−0.694785	+	0.719218i	$0.744500\pi$
$798$		0			0
$799$	−52.5493			−1.85906
$800$		−	1.00000i		−	0.0353553i
$801$	0.901377	+	1.29319i	0.0318486	+	0.0456926i
$802$	12.7853			0.451465
$803$	58.7207			2.07221
$804$	9.18497	+	4.79391i	0.323929	+	0.169068i
$805$		0			0
$806$		−	16.8806i		−	0.594594i
$807$	31.2974	+	16.3350i	1.10172	+	0.575020i
$808$		−	1.59753i		−	0.0562008i
$809$		−	43.0358i		−	1.51306i	−0.653961	−	0.756529i	$-0.726894\pi$
$809$		−	43.0358i		−	1.51306i	0.653961	−	0.756529i	$-0.273106\pi$
$810$	8.44396	+	3.11440i	0.296691	+	0.109429i
$811$		−	46.2399i		−	1.62370i	−0.583865	−	0.811850i	$-0.698460\pi$
$811$		−	46.2399i		−	1.62370i	0.583865	−	0.811850i	$-0.301540\pi$
$812$		0			0
$813$	−16.2404	+	31.1161i	−0.569576	+	1.09129i
$814$	−50.7451			−1.77862
$815$	19.1573			0.671049
$816$	−10.7373	−	5.60410i	−0.375880	−	0.196183i
$817$		−	6.88356i		−	0.240825i
$818$	14.6466			0.512107
$819$		0			0
$820$	−4.36516			−0.152438
$821$			40.9505i			1.42918i	0.699542	+	0.714591i	$0.253387\pi$
$821$			40.9505i			1.42918i	−0.699542	+	0.714591i	$0.746613\pi$
$822$	−8.68773	−	4.53438i	−0.303019	−	0.158155i
$823$	8.93572			0.311480			0.155740	−	0.987798i	$-0.450224\pi$
$823$	8.93572			0.311480			0.155740	+	0.987798i	$0.450224\pi$
$824$	−9.40273			−0.327560
$825$	4.39535	−	8.42134i	0.153026	−	0.293194i
$826$		0			0
$827$			4.48639i			0.156007i	0.996953	+	0.0780036i	$0.0248546\pi$
$827$			4.48639i			0.156007i	−0.996953	+	0.0780036i	$0.975145\pi$
$828$	−19.6771	+	13.7153i	−0.683826	+	0.476640i
$829$		−	38.5514i		−	1.33895i	−0.742837	−	0.669473i	$-0.766520\pi$
$829$		−	38.5514i		−	1.33895i	0.742837	−	0.669473i	$-0.233480\pi$
$830$			9.22718i			0.320280i
$831$	−30.5128	−	15.9255i	−1.05848	−	0.552451i
$832$			4.37587i			0.151706i
$833$		0			0
$834$	12.5979	+	6.57523i	0.436231	+	0.227682i
$835$	−3.99462			−0.138239
$836$	25.4927			0.881683
$837$	−19.8818	+	2.55251i	−0.687216	+	0.0882275i
$838$		−	38.2058i		−	1.31980i
$839$	21.0084			0.725290			0.362645	−	0.931927i	$-0.381874\pi$
$839$	21.0084			0.725290			0.362645	+	0.931927i	$0.381874\pi$
$840$		0			0
$841$	17.4118			0.600407
$842$		−	13.5971i		−	0.468586i
$843$	16.6696	−	31.9384i	0.574131	−	1.10002i
$844$	−16.4672			−0.566823
$845$	−6.14821			−0.211505
$846$	18.4950	−	12.8914i	0.635872	−	0.443215i
$847$		0			0
$848$		−	4.68750i		−	0.160969i
$849$	6.87688	−	13.1759i	0.236014	−	0.452195i
$850$			6.99274i			0.239849i
$851$		−	73.9750i		−	2.53583i
$852$	−3.54598	+	6.79398i	−0.121483	+	0.232758i
$853$			36.7293i			1.25759i	0.777572	+	0.628794i	$0.216451\pi$
$853$			36.7293i			1.25759i	−0.777572	+	0.628794i	$0.783549\pi$
$854$		0			0
$855$	11.4398	−	7.97374i	0.391232	−	0.272696i
$856$	−5.31279			−0.181588
$857$	13.3707			0.456733			0.228367	−	0.973575i	$-0.426661\pi$
$857$	13.3707			0.456733			0.228367	+	0.973575i	$0.426661\pi$
$858$	−19.2335	+	36.8507i	−0.656619	+	1.25806i
$859$		−	1.51210i		−	0.0515923i	−0.999667	−	0.0257962i	$-0.991788\pi$
$859$		−	1.51210i		−	0.0515923i	0.999667	−	0.0257962i	$-0.00821208\pi$
$860$	−1.48092			−0.0504990
$861$		0			0
$862$	24.8072			0.844936
$863$		−	1.38300i		−	0.0470777i	−0.999723	−	0.0235389i	$-0.992507\pi$
$863$		−	1.38300i		−	0.0470777i	0.999723	−	0.0235389i	$-0.00749334\pi$
$864$	5.15385	−	0.661673i	0.175338	−	0.0225106i
$865$	−18.7253			−0.636680
$866$	−10.5514			−0.358552
$867$	48.9797	+	25.5639i	1.66344	+	0.868197i
$868$		0			0
$869$		−	26.7238i		−	0.906543i
$870$	5.22703	+	2.72814i	0.177213	+	0.0924927i
$871$			26.1755i			0.886922i
$872$		−	14.5402i		−	0.492392i
$873$	−6.40566	+	4.46487i	−0.216799	+	0.151113i
$874$			37.1626i			1.25704i
$875$		0			0
$876$	8.58056	−	16.4401i	0.289910	−	0.555459i
$877$	−55.9731			−1.89008			−0.945039	−	0.326957i	$-0.893977\pi$
$877$	−55.9731			−1.89008			−0.945039	+	0.326957i	$0.893977\pi$
$878$	11.2224			0.378737
$879$	4.18409	+	2.18380i	0.141126	+	0.0736578i
$880$		−	5.48447i		−	0.184881i
$881$	10.5177			0.354350			0.177175	−	0.984179i	$-0.443304\pi$
$881$	10.5177			0.354350			0.177175	+	0.984179i	$0.443304\pi$
$882$		0			0
$883$	49.6637			1.67132			0.835658	−	0.549251i	$-0.185087\pi$
$883$	49.6637			1.67132			0.835658	+	0.549251i	$0.185087\pi$
$884$		−	30.5993i		−	1.02917i
$885$	9.22603	+	4.81534i	0.310130	+	0.161866i
$886$	14.1488			0.475339
$887$	−19.1044			−0.641463			−0.320732	−	0.947170i	$-0.603929\pi$
$887$	−19.1044			−0.641463			−0.320732	+	0.947170i	$0.603929\pi$
$888$	−7.41513	+	14.2072i	−0.248836	+	0.476761i
$889$		0			0
$890$		−	0.525443i		−	0.0176129i
$891$	46.3106	+	17.0808i	1.55146	+	0.572228i
$892$			13.5203i			0.452693i
$893$		−	34.9302i		−	1.16889i
$894$	16.2599	+	8.48652i	0.543812	+	0.283832i
$895$			10.9143i			0.364826i
$896$		0			0
$897$	−53.7200	−	28.0380i	−1.79366	−	0.936163i
$898$	1.16231			0.0387867
$899$	−13.1320			−0.437978
$900$	−1.71546	−	2.46114i	−0.0571820	−	0.0820379i
$901$			32.7784i			1.09201i
$902$	−23.9406			−0.797135
$903$		0			0
$904$	14.2482			0.473889
$905$		−	11.1025i		−	0.369060i
$906$	−13.1870	+	25.2659i	−0.438109	+	0.839403i
$907$	−18.2459			−0.605846			−0.302923	−	0.953015i	$-0.597962\pi$
$907$	−18.2459			−0.605846			−0.302923	+	0.953015i	$0.597962\pi$
$908$	5.57785			0.185108
$909$	−2.74049	−	3.93173i	−0.0908964	−	0.130407i
$910$		0			0
$911$			36.6428i			1.21403i	0.794690	+	0.607015i	$0.207633\pi$
$911$			36.6428i			1.21403i	−0.794690	+	0.607015i	$0.792367\pi$
$912$	3.72512	−	7.13721i	0.123351	−	0.236337i
$913$			50.6062i			1.67482i
$914$			27.8911i			0.922556i
$915$	−5.40988	+	10.3651i	−0.178845	+	0.342661i
$916$		−	11.6640i		−	0.385388i
$917$		0			0
$918$	−36.0395	+	4.62690i	−1.18948	+	0.152711i
$919$	7.12268			0.234955			0.117478	−	0.993076i	$-0.462519\pi$
$919$	7.12268			0.234955			0.117478	+	0.993076i	$0.462519\pi$
$920$	7.99511			0.263591
$921$	−20.3066	+	38.9067i	−0.669124	+	1.28202i
$922$		−	17.1662i		−	0.565340i
$923$	−19.3616			−0.637295
$924$		0			0
$925$	9.25252			0.304221
$926$			39.1372i			1.28613i
$927$	−23.1414	+	16.1300i	−0.760064	+	0.529779i
$928$	3.40414			0.111747
$929$	−59.7337			−1.95980			−0.979899	−	0.199493i	$-0.936070\pi$
$929$	−59.7337			−1.95980			−0.979899	+	0.199493i	$0.936070\pi$
$930$	5.92340	+	3.09160i	0.194236	+	0.101377i
$931$		0			0
$932$			22.7275i			0.744464i
$933$	4.69849	+	2.45228i	0.153822	+	0.0802840i
$934$		−	5.33074i		−	0.174427i
$935$			38.3515i			1.25423i
$936$	7.50662	+	10.7696i	0.245362	+	0.352016i
$937$			1.86949i			0.0610737i	0.999534	+	0.0305369i	$0.00972170\pi$
$937$			1.86949i			0.0610737i	−0.999534	+	0.0305369i	$0.990278\pi$
$938$		0			0
$939$	25.9714	−	49.7604i	0.847545	−	1.62387i
$940$	−7.51483			−0.245107
$941$	29.6514			0.966608			0.483304	−	0.875453i	$-0.339437\pi$
$941$	29.6514			0.966608			0.483304	+	0.875453i	$0.339437\pi$
$942$	13.2898	+	6.93636i	0.433007	+	0.225999i
$943$		−	34.9000i		−	1.13650i
$944$	6.00852			0.195561
$945$		0			0
$946$	−8.12206			−0.264071
$947$			3.19911i			0.103957i	0.998648	+	0.0519785i	$0.0165527\pi$
$947$			3.19911i			0.103957i	−0.998648	+	0.0519785i	$0.983447\pi$
$948$	−7.48188	−	3.90501i	−0.243000	−	0.126829i
$949$	46.8512			1.52086
$950$	−4.64816			−0.150806
$951$	−10.3346	+	19.8008i	−0.335123	+	0.642085i
$952$		0			0
$953$		−	7.78715i		−	0.252250i	−0.992014	−	0.126125i	$-0.959746\pi$
$953$		−	7.78715i		−	0.252250i	0.992014	−	0.126125i	$-0.0402541\pi$
$954$	−8.04121	−	11.5366i	−0.260344	−	0.373510i
$955$		−	18.3911i		−	0.595122i
$956$		−	5.34353i		−	0.172822i
$957$	28.6675	+	14.9624i	0.926688	+	0.483666i
$958$			6.57119i			0.212305i
$959$		0			0
$960$	−1.53549	−	0.801418i	−0.0495577	−	0.0258656i
$961$	16.1185			0.519951
$962$	−40.4878			−1.30538
$963$	−13.0755	+	9.11388i	−0.421353	+	0.293691i
$964$		−	14.8146i		−	0.477146i
$965$	23.3665			0.752193
$966$		0			0
$967$	4.08407			0.131335			0.0656674	−	0.997842i	$-0.479082\pi$
$967$	4.08407			0.131335			0.0656674	+	0.997842i	$0.479082\pi$
$968$		−	19.0794i		−	0.613234i
$969$	−26.0488	+	49.9086i	−0.836808	+	1.60330i
$970$	2.60272			0.0835684
$971$	0.634482			0.0203615			0.0101808	−	0.999948i	$-0.496759\pi$
$971$	0.634482			0.0203615			0.0101808	+	0.999948i	$0.496759\pi$
$972$	11.5493	−	10.4697i	0.370443	−	0.335816i
$973$		0			0
$974$		−	26.0143i		−	0.833552i
$975$	3.50690	−	6.71910i	0.112311	−	0.215183i
$976$			6.75039i			0.216075i
$977$			13.8771i			0.443967i	0.975050	+	0.221983i	$0.0712531\pi$
$977$			13.8771i			0.443967i	−0.975050	+	0.221983i	$0.928747\pi$
$978$	15.3530	−	29.4158i	0.490933	−	0.940613i
$979$		−	2.88178i		−	0.0921020i
$980$		0			0
$981$	−24.9430	−	35.7853i	−0.796370	−	1.14254i
$982$	30.2128			0.964131
$983$	−36.3583			−1.15965			−0.579825	−	0.814741i	$-0.696879\pi$
$983$	−36.3583			−1.15965			−0.579825	+	0.814741i	$0.696879\pi$
$984$	−3.49832	+	6.70267i	−0.111522	+	0.213673i
$985$		−	6.30178i		−	0.200791i
$986$	−23.8043			−0.758083
$987$		0			0
$988$	20.3397			0.647093
$989$		−	11.8401i		−	0.376494i
$990$	−9.40838	−	13.4980i	−0.299018	−	0.428995i
$991$	12.3858			0.393449			0.196725	−	0.980459i	$-0.436969\pi$
$991$	12.3858			0.393449			0.196725	+	0.980459i	$0.436969\pi$
$992$	3.85766			0.122481
$993$	52.9574	+	27.6401i	1.68055	+	0.877131i
$994$		0			0
$995$			11.0277i			0.349602i
$996$	14.1682	+	7.39483i	0.448938	+	0.234314i
$997$			26.3408i			0.834221i	0.908856	+	0.417111i	$0.136957\pi$
$997$			26.3408i			0.834221i	−0.908856	+	0.417111i	$0.863043\pi$
$998$			9.86296i			0.312207i
$999$	6.12214	+	47.6861i	0.193696	+	1.50872i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.53549 + 0.801418i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(0.801418 - 1.53549i) q^{6} +1.00000i q^{8} +(1.71546 + 2.46114i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.53549 + 0.801418i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(0.801418 - 1.53549i) q^{6} +1.00000i q^{8} +(1.71546 + 2.46114i) q^{9} -1.00000i q^{10} -5.48447i q^{11} +(-1.53549 - 0.801418i) q^{12} -4.37587i q^{13} +(1.53549 + 0.801418i) q^{15} +1.00000 q^{16} -6.99274 q^{17} +(2.46114 - 1.71546i) q^{18} -4.64816i q^{19} -1.00000 q^{20} -5.48447 q^{22} -7.99511i q^{23} +(-0.801418 + 1.53549i) q^{24} +1.00000 q^{25} -4.37587 q^{26} +(0.661673 + 5.15385i) q^{27} +3.40414i q^{29} +(0.801418 - 1.53549i) q^{30} +3.85766i q^{31} -1.00000i q^{32} +(4.39535 - 8.42134i) q^{33} +6.99274i q^{34} +(-1.71546 - 2.46114i) q^{36} +9.25252 q^{37} -4.64816 q^{38} +(3.50690 - 6.71910i) q^{39} +1.00000i q^{40} +4.36516 q^{41} +1.48092 q^{43} +5.48447i q^{44} +(1.71546 + 2.46114i) q^{45} -7.99511 q^{46} +7.51483 q^{47} +(1.53549 + 0.801418i) q^{48} -1.00000i q^{50} +(-10.7373 - 5.60410i) q^{51} +4.37587i q^{52} -4.68750i q^{53} +(5.15385 - 0.661673i) q^{54} -5.48447i q^{55} +(3.72512 - 7.13721i) q^{57} +3.40414 q^{58} +6.00852 q^{59} +(-1.53549 - 0.801418i) q^{60} +6.75039i q^{61} +3.85766 q^{62} -1.00000 q^{64} -4.37587i q^{65} +(-8.42134 - 4.39535i) q^{66} -5.98178 q^{67} +6.99274 q^{68} +(6.40743 - 12.2764i) q^{69} -4.42464i q^{71} +(-2.46114 + 1.71546i) q^{72} +10.7067i q^{73} -9.25252i q^{74} +(1.53549 + 0.801418i) q^{75} +4.64816i q^{76} +(-6.71910 - 3.50690i) q^{78} +4.87263 q^{79} +1.00000 q^{80} +(-3.11440 + 8.44396i) q^{81} -4.36516i q^{82} -9.22718 q^{83} -6.99274 q^{85} -1.48092i q^{86} +(-2.72814 + 5.22703i) q^{87} +5.48447 q^{88} +0.525443 q^{89} +(2.46114 - 1.71546i) q^{90} +7.99511i q^{92} +(-3.09160 + 5.92340i) q^{93} -7.51483i q^{94} -4.64816i q^{95} +(0.801418 - 1.53549i) q^{96} +2.60272i q^{97} +(13.4980 - 9.40838i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} - 16 q^{4} + 16 q^{5} + 8 q^{9}+O(q^{10}) \) 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

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