LMFDB - Embedded newform 1755.2.i.f.586.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1755,2,Mod(586,1755)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1755, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("1755.586");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1755 = 3^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1755.i (of order $3$, degree $2$, not 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:	$14.0137455547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
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} - 5 x^{15} + 20 x^{14} - 44 x^{13} + 96 x^{12} - 107 x^{11} + 178 x^{10} - 19 x^{9} + 231 x^{8} + \cdots + 268 $ x^16 - 5x^15 + 20x^14 - 44x^13 + 96x^12 - 107x^11 + 178x^10 - 19x^9 + 231x^8 + 326x^7 + 551x^6 + 859x^5 + 1118x^4 + 1215x^3 + 1103x^2 + 770*x + 268
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 585)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			586.3
Root			$0.466399 + 1.64781i$ of defining polynomial
Character	$\chi$	$=$	1755.586
Dual form			1755.2.i.f.1171.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0336011 - 0.0581988i) q^{2} +(0.997742 + 1.72814i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.23179 + 2.13352i) q^{7} +0.268505 q^{8} +O(q^{10})$	\(q+(0.0336011 - 0.0581988i) q^{2} +(0.997742 + 1.72814i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.23179 + 2.13352i) q^{7} +0.268505 q^{8} -0.0672022 q^{10} +(1.60607 - 2.78180i) q^{11} +(0.500000 + 0.866025i) q^{13} +(0.0827788 + 0.143377i) q^{14} +(-1.98646 + 3.44065i) q^{16} +4.77678 q^{17} -3.94903 q^{19} +(0.997742 - 1.72814i) q^{20} +(-0.107932 - 0.186943i) q^{22} +(2.13489 + 3.69773i) q^{23} +(-0.500000 + 0.866025i) q^{25} +0.0672022 q^{26} -4.91602 q^{28} +(-1.15314 + 1.99730i) q^{29} +(3.81652 + 6.61041i) q^{31} +(0.402000 + 0.696284i) q^{32} +(0.160505 - 0.278003i) q^{34} +2.46357 q^{35} +4.87293 q^{37} +(-0.132692 + 0.229829i) q^{38} +(-0.134253 - 0.232532i) q^{40} +(-1.26518 - 2.19136i) q^{41} +(2.28304 - 3.95433i) q^{43} +6.40978 q^{44} +0.286938 q^{46} +(-3.13284 + 5.42623i) q^{47} +(0.465404 + 0.806103i) q^{49} +(0.0336011 + 0.0581988i) q^{50} +(-0.997742 + 1.72814i) q^{52} -12.4968 q^{53} -3.21214 q^{55} +(-0.330741 + 0.572861i) q^{56} +(0.0774937 + 0.134223i) q^{58} +(1.42509 + 2.46833i) q^{59} +(-6.35000 + 10.9985i) q^{61} +0.512957 q^{62} -7.89182 q^{64} +(0.500000 - 0.866025i) q^{65} +(6.75359 + 11.6976i) q^{67} +(4.76599 + 8.25494i) q^{68} +(0.0827788 - 0.143377i) q^{70} -7.79224 q^{71} +2.26796 q^{73} +(0.163736 - 0.283599i) q^{74} +(-3.94012 - 6.82448i) q^{76} +(3.95668 + 6.85316i) q^{77} +(-4.56668 + 7.90972i) q^{79} +3.97292 q^{80} -0.170046 q^{82} +(5.25595 - 9.10356i) q^{83} +(-2.38839 - 4.13681i) q^{85} +(-0.153425 - 0.265740i) q^{86} +(0.431239 - 0.746927i) q^{88} -0.966612 q^{89} -2.46357 q^{91} +(-4.26013 + 7.37876i) q^{92} +(0.210533 + 0.364655i) q^{94} +(1.97452 + 3.41996i) q^{95} +(9.39020 - 16.2643i) q^{97} +0.0625523 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8}+O(q^{10}) $ 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8	$ 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8} - 6 q^{10} + 6 q^{11} + 8 q^{13} + 10 q^{14} - 11 q^{16} + 4 q^{17} - 20 q^{19} - 9 q^{20} - 3 q^{22} + 6 q^{23} - 8 q^{25} + 6 q^{26} - 68 q^{28} + 14 q^{29} + 31 q^{31} + q^{32} + 7 q^{34} - 22 q^{35} + 2 q^{37} + 9 q^{38} - 6 q^{40} - 12 q^{41} - 15 q^{43} - 32 q^{44} - 64 q^{46} - 18 q^{47} - 17 q^{49} + 3 q^{50} + 9 q^{52} - 4 q^{53} - 12 q^{55} + 16 q^{56} + 42 q^{58} + 24 q^{59} + 9 q^{61} + 40 q^{62} - 60 q^{64} + 8 q^{65} + 18 q^{67} - 14 q^{68} + 10 q^{70} - 20 q^{71} + 12 q^{73} - 37 q^{74} + 53 q^{76} - 34 q^{77} + 3 q^{79} + 22 q^{80} - 68 q^{82} - 10 q^{83} - 2 q^{85} + 60 q^{86} + 14 q^{88} + 26 q^{89} + 22 q^{91} + 5 q^{92} - 17 q^{94} + 10 q^{95} + 34 q^{97} + 60 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8 - 6 * q^10 + 6 * q^11 + 8 * q^13 + 10 * q^14 - 11 * q^16 + 4 * q^17 - 20 * q^19 - 9 * q^20 - 3 * q^22 + 6 * q^23 - 8 * q^25 + 6 * q^26 - 68 * q^28 + 14 * q^29 + 31 * q^31 + q^32 + 7 * q^34 - 22 * q^35 + 2 * q^37 + 9 * q^38 - 6 * q^40 - 12 * q^41 - 15 * q^43 - 32 * q^44 - 64 * q^46 - 18 * q^47 - 17 * q^49 + 3 * q^50 + 9 * q^52 - 4 * q^53 - 12 * q^55 + 16 * q^56 + 42 * q^58 + 24 * q^59 + 9 * q^61 + 40 * q^62 - 60 * q^64 + 8 * q^65 + 18 * q^67 - 14 * q^68 + 10 * q^70 - 20 * q^71 + 12 * q^73 - 37 * q^74 + 53 * q^76 - 34 * q^77 + 3 * q^79 + 22 * q^80 - 68 * q^82 - 10 * q^83 - 2 * q^85 + 60 * q^86 + 14 * q^88 + 26 * q^89 + 22 * q^91 + 5 * q^92 - 17 * q^94 + 10 * q^95 + 34 * q^97 + 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1755\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	0.0336011	−	0.0581988i	0.0237596	−	0.0411528i	−0.853901	−	0.520435i	$-0.825770\pi$
$2$	0.0336011	−	0.0581988i	0.0237596	−	0.0411528i	0.877661	+	0.479282i	$0.159103\pi$
$3$		0			0
$3$		0			0
$4$	0.997742	+	1.72814i	0.498871	+	0.864070i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−1.23179	+	2.13352i	−0.465572	+	0.806394i	−0.999227	−	0.0393083i	$-0.987485\pi$
$7$	−1.23179	+	2.13352i	−0.465572	+	0.806394i	0.533656	+	0.845702i	$0.320818\pi$
$8$	0.268505			0.0949309
$9$		0			0
$10$	−0.0672022			−0.0212512
$11$	1.60607	−	2.78180i	0.484249	−	0.838744i	−0.515587	−	0.856837i	$-0.672426\pi$
$11$	1.60607	−	2.78180i	0.484249	−	0.838744i	0.999836	+	0.0180933i	$0.00575960\pi$
$12$		0			0
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	0.0827788	+	0.143377i	0.0221236	+	0.0383191i
$15$		0			0
$16$	−1.98646	+	3.44065i	−0.496615	+	0.860163i
$17$	4.77678			1.15854			0.579269	−	0.815136i	$-0.303338\pi$
$17$	4.77678			1.15854			0.579269	+	0.815136i	$0.303338\pi$
$18$		0			0
$19$	−3.94903			−0.905970			−0.452985	−	0.891518i	$-0.649641\pi$
$19$	−3.94903			−0.905970			−0.452985	+	0.891518i	$0.649641\pi$
$20$	0.997742	−	1.72814i	0.223102	−	0.386424i
$21$		0			0
$22$	−0.107932	−	0.186943i	−0.0230111	−	0.0398564i
$23$	2.13489	+	3.69773i	0.445154	+	0.771030i	0.998063	−	0.0622118i	$-0.0198154\pi$
$23$	2.13489	+	3.69773i	0.445154	+	0.771030i	−0.552908	+	0.833242i	$0.686482\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.0672022			0.0131794
$27$		0			0
$28$	−4.91602			−0.929040
$29$	−1.15314	+	1.99730i	−0.214133	+	0.370890i	−0.953004	−	0.302957i	$-0.902026\pi$
$29$	−1.15314	+	1.99730i	−0.214133	+	0.370890i	0.738871	+	0.673847i	$0.235359\pi$
$30$		0			0
$31$	3.81652	+	6.61041i	0.685468	+	1.18726i	0.973290	+	0.229581i	$0.0737356\pi$
$31$	3.81652	+	6.61041i	0.685468	+	1.18726i	−0.287822	+	0.957684i	$0.592931\pi$
$32$	0.402000	+	0.696284i	0.0710642	+	0.123087i
$33$		0			0
$34$	0.160505	−	0.278003i	0.0275264	−	0.0476771i
$35$	2.46357			0.416420
$36$		0			0
$37$	4.87293			0.801105			0.400553	−	0.916274i	$-0.368818\pi$
$37$	4.87293			0.801105			0.400553	+	0.916274i	$0.368818\pi$
$38$	−0.132692	+	0.229829i	−0.0215255	+	0.0372832i
$39$		0			0
$40$	−0.134253	−	0.232532i	−0.0212272	−	0.0367666i
$41$	−1.26518	−	2.19136i	−0.197588	−	0.342233i	0.750158	−	0.661259i	$-0.229978\pi$
$41$	−1.26518	−	2.19136i	−0.197588	−	0.342233i	−0.947746	+	0.319026i	$0.896644\pi$
$42$		0			0
$43$	2.28304	−	3.95433i	0.348160	−	0.603030i	−0.637763	−	0.770233i	$-0.720140\pi$
$43$	2.28304	−	3.95433i	0.348160	−	0.603030i	0.985923	+	0.167202i	$0.0534734\pi$
$44$	6.40978			0.966311
$45$		0			0
$46$	0.286938			0.0423067
$47$	−3.13284	+	5.42623i	−0.456971	+	0.791497i	−0.998799	−	0.0489922i	$-0.984399\pi$
$47$	−3.13284	+	5.42623i	−0.456971	+	0.791497i	0.541828	+	0.840489i	$0.317732\pi$
$48$		0			0
$49$	0.465404	+	0.806103i	0.0664863	+	0.115158i
$50$	0.0336011	+	0.0581988i	0.00475191	+	0.00823055i
$51$		0			0
$52$	−0.997742	+	1.72814i	−0.138362	+	0.239650i
$53$	−12.4968			−1.71657			−0.858286	−	0.513172i	$-0.828470\pi$
$53$	−12.4968			−1.71657			−0.858286	+	0.513172i	$0.828470\pi$
$54$		0			0
$55$	−3.21214			−0.433125
$56$	−0.330741	+	0.572861i	−0.0441971	+	0.0765517i
$57$		0			0
$58$	0.0774937	+	0.134223i	0.0101754	+	0.0176244i
$59$	1.42509	+	2.46833i	0.185531	+	0.321350i	0.943755	−	0.330644i	$-0.107266\pi$
$59$	1.42509	+	2.46833i	0.185531	+	0.321350i	−0.758224	+	0.651994i	$0.773933\pi$
$60$		0			0
$61$	−6.35000	+	10.9985i	−0.813034	+	1.40822i	0.0976967	+	0.995216i	$0.468852\pi$
$61$	−6.35000	+	10.9985i	−0.813034	+	1.40822i	−0.910731	+	0.413000i	$0.864481\pi$
$62$	0.512957			0.0651457
$63$		0			0
$64$	−7.89182			−0.986477
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$		0			0
$67$	6.75359	+	11.6976i	0.825082	+	1.42908i	0.901856	+	0.432036i	$0.142205\pi$
$67$	6.75359	+	11.6976i	0.825082	+	1.42908i	−0.0767741	+	0.997049i	$0.524462\pi$
$68$	4.76599	+	8.25494i	0.577961	+	1.00106i
$69$		0			0
$70$	0.0827788	−	0.143377i	0.00989395	−	0.0171368i
$71$	−7.79224			−0.924769			−0.462384	−	0.886680i	$-0.653006\pi$
$71$	−7.79224			−0.924769			−0.462384	+	0.886680i	$0.653006\pi$
$72$		0			0
$73$	2.26796			0.265444			0.132722	−	0.991153i	$-0.457628\pi$
$73$	2.26796			0.265444			0.132722	+	0.991153i	$0.457628\pi$
$74$	0.163736	−	0.283599i	0.0190339	−	0.0329677i
$75$		0			0
$76$	−3.94012	−	6.82448i	−0.451962	−	0.782822i
$77$	3.95668	+	6.85316i	0.450905	+	0.780990i
$78$		0			0
$79$	−4.56668	+	7.90972i	−0.513791	+	0.889913i	0.486081	+	0.873914i	$0.338426\pi$
$79$	−4.56668	+	7.90972i	−0.513791	+	0.889913i	−0.999872	+	0.0159988i	$0.994907\pi$
$80$	3.97292			0.444186
$81$		0			0
$82$	−0.170046			−0.0187784
$83$	5.25595	−	9.10356i	0.576915	−	0.999246i	−0.418916	−	0.908025i	$-0.637590\pi$
$83$	5.25595	−	9.10356i	0.576915	−	0.999246i	0.995831	−	0.0912209i	$-0.0290769\pi$
$84$		0			0
$85$	−2.38839	−	4.13681i	−0.259057	−	0.448700i
$86$	−0.153425	−	0.265740i	−0.0165442	−	0.0286555i
$87$		0			0
$88$	0.431239	−	0.746927i	0.0459702	−	0.0796227i
$89$	−0.966612			−0.102461			−0.0512303	−	0.998687i	$-0.516314\pi$
$89$	−0.966612			−0.102461			−0.0512303	+	0.998687i	$0.516314\pi$
$90$		0			0
$91$	−2.46357			−0.258253
$92$	−4.26013	+	7.37876i	−0.444149	+	0.769289i
$93$		0			0
$94$	0.210533	+	0.364655i	0.0217149	+	0.0376113i
$95$	1.97452	+	3.41996i	0.202581	+	0.350881i
$96$		0			0
$97$	9.39020	−	16.2643i	0.953431	−	1.65139i	0.215511	−	0.976501i	$-0.430858\pi$
$97$	9.39020	−	16.2643i	0.953431	−	1.65139i	0.737919	−	0.674889i	$-0.235809\pi$
$98$	0.0625523			0.00631874
$99$		0			0
$100$	−1.99548			−0.199548
$101$	−9.27873	+	16.0712i	−0.923268	+	1.59915i	−0.128944	+	0.991652i	$0.541159\pi$
$101$	−9.27873	+	16.0712i	−0.923268	+	1.59915i	−0.794324	+	0.607495i	$0.792175\pi$
$102$		0			0
$103$	−5.12815	−	8.88222i	−0.505292	−	0.875191i	−0.999981	−	0.00612110i	$-0.998052\pi$
$103$	−5.12815	−	8.88222i	−0.505292	−	0.875191i	0.494690	−	0.869070i	$-0.335282\pi$
$104$	0.134253	+	0.232532i	0.0131646	+	0.0228017i
$105$		0			0
$106$	−0.419907	+	0.727300i	−0.0407850	+	0.0706417i
$107$	13.3729			1.29281			0.646403	−	0.762996i	$-0.276273\pi$
$107$	13.3729			1.29281			0.646403	+	0.762996i	$0.276273\pi$
$108$		0			0
$109$	−1.35788			−0.130061			−0.0650306	−	0.997883i	$-0.520715\pi$
$109$	−1.35788			−0.130061			−0.0650306	+	0.997883i	$0.520715\pi$
$110$	−0.107932	+	0.186943i	−0.0102909	+	0.0178243i
$111$		0			0
$112$	−4.89379	−	8.47630i	−0.462420	−	0.800935i
$113$	−3.67848	−	6.37132i	−0.346042	−	0.599363i	0.639500	−	0.768791i	$-0.279141\pi$
$113$	−3.67848	−	6.37132i	−0.346042	−	0.599363i	−0.985543	+	0.169428i	$0.945808\pi$
$114$		0			0
$115$	2.13489	−	3.69773i	0.199079	−	0.344815i
$116$	−4.60216			−0.427300
$117$		0			0
$118$	0.191539			0.0176326
$119$	−5.88397	+	10.1913i	−0.539383	+	0.934238i
$120$		0			0
$121$	0.341067	+	0.590745i	0.0310061	+	0.0537041i
$122$	0.426734	+	0.739125i	0.0386347	+	0.0669172i
$123$		0			0
$124$	−7.61581	+	13.1910i	−0.683920	+	1.18458i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−5.97693			−0.530367			−0.265183	−	0.964198i	$-0.585433\pi$
$127$	−5.97693			−0.530367			−0.265183	+	0.964198i	$0.585433\pi$
$128$	−1.06917	+	1.85186i	−0.0945025	+	0.163683i
$129$		0			0
$130$	−0.0336011	−	0.0581988i	−0.00294701	−	0.00510437i
$131$	8.93670	+	15.4788i	0.780803	+	1.35239i	0.931475	+	0.363806i	$0.118523\pi$
$131$	8.93670	+	15.4788i	0.780803	+	1.35239i	−0.150672	+	0.988584i	$0.548144\pi$
$132$		0			0
$133$	4.86436	−	8.42533i	0.421794	−	0.730568i
$134$	0.907712			0.0784144
$135$		0			0
$136$	1.28259			0.109981
$137$	5.24653	−	9.08726i	0.448241	−	0.776377i	−0.550030	−	0.835145i	$-0.685384\pi$
$137$	5.24653	−	9.08726i	0.448241	−	0.776377i	0.998272	+	0.0587679i	$0.0187172\pi$
$138$		0			0
$139$	5.35343	+	9.27241i	0.454072	+	0.786475i	0.998634	−	0.0522449i	$-0.0166376\pi$
$139$	5.35343	+	9.27241i	0.454072	+	0.786475i	−0.544563	+	0.838720i	$0.683304\pi$
$140$	2.45801	+	4.25740i	0.207740	+	0.359816i
$141$		0			0
$142$	−0.261828	+	0.453499i	−0.0219721	+	0.0380568i
$143$	3.21214			0.268613
$144$		0			0
$145$	2.30629			0.191527
$146$	0.0762058	−	0.131992i	0.00630684	−	0.0109238i
$147$		0			0
$148$	4.86193	+	8.42111i	0.399648	+	0.692211i
$149$	−10.1595	−	17.5968i	−0.832300	−	1.44159i	−0.896210	−	0.443631i	$-0.853690\pi$
$149$	−10.1595	−	17.5968i	−0.832300	−	1.44159i	0.0639091	−	0.997956i	$-0.479643\pi$
$150$		0			0
$151$	8.51099	−	14.7415i	0.692615	−	1.19964i	−0.278363	−	0.960476i	$-0.589792\pi$
$151$	8.51099	−	14.7415i	0.692615	−	1.19964i	0.970978	−	0.239168i	$-0.0768747\pi$
$152$	−1.06034			−0.0860046
$153$		0			0
$154$	0.531794			0.0428532
$155$	3.81652	−	6.61041i	0.306550	−	0.530961i
$156$		0			0
$157$	0.653935	+	1.13265i	0.0521897	+	0.0903952i	0.890940	−	0.454121i	$-0.150047\pi$
$157$	0.653935	+	1.13265i	0.0521897	+	0.0903952i	−0.838750	+	0.544516i	$0.816713\pi$
$158$	0.306891	+	0.531550i	0.0244149	+	0.0422879i
$159$		0			0
$160$	0.402000	−	0.696284i	0.0317809	−	0.0550461i
$161$	−10.5189			−0.829005
$162$		0			0
$163$	−9.81120			−0.768473			−0.384236	−	0.923235i	$-0.625535\pi$
$163$	−9.81120			−0.768473			−0.384236	+	0.923235i	$0.625535\pi$
$164$	2.52465	−	4.37282i	0.197142	−	0.341460i
$165$		0			0
$166$	−0.353211	−	0.611779i	−0.0274145	−	0.0474833i
$167$	4.08745	+	7.07968i	0.316297	+	0.547842i	0.979712	−	0.200409i	$-0.0642272\pi$
$167$	4.08745	+	7.07968i	0.316297	+	0.547842i	−0.663416	+	0.748251i	$0.730894\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−0.321010			−0.0246203
$171$		0			0
$172$	9.11152			0.694747
$173$	−3.19885	+	5.54058i	−0.243204	+	0.421242i	−0.961625	−	0.274366i	$-0.911532\pi$
$173$	−3.19885	+	5.54058i	−0.243204	+	0.421242i	0.718421	+	0.695609i	$0.244865\pi$
$174$		0			0
$175$	−1.23179	−	2.13352i	−0.0931143	−	0.161279i
$176$	6.38080	+	11.0519i	0.480971	+	0.833066i
$177$		0			0
$178$	−0.0324792	+	0.0562557i	−0.00243442	+	0.00421654i
$179$	15.6316			1.16836			0.584180	−	0.811624i	$-0.301416\pi$
$179$	15.6316			1.16836			0.584180	+	0.811624i	$0.301416\pi$
$180$		0			0
$181$	11.1033			0.825299			0.412650	−	0.910890i	$-0.364603\pi$
$181$	11.1033			0.825299			0.412650	+	0.910890i	$0.364603\pi$
$182$	−0.0827788	+	0.143377i	−0.00613597	+	0.0106278i
$183$		0			0
$184$	0.573228	+	0.992860i	0.0422589	+	0.0731946i
$185$	−2.43647	−	4.22008i	−0.179133	−	0.310267i
$186$		0			0
$187$	7.67185	−	13.2880i	0.561021	−	0.971717i
$188$	−12.5030			−0.911878
$189$		0			0
$190$	0.265384			0.0192530
$191$	7.79123	−	13.4948i	0.563753	−	0.976450i	−0.433411	−	0.901196i	$-0.642690\pi$
$191$	7.79123	−	13.4948i	0.563753	−	0.976450i	0.997164	−	0.0752533i	$-0.0239765\pi$
$192$		0			0
$193$	9.34800	+	16.1912i	0.672884	+	1.16547i	0.977083	+	0.212860i	$0.0682780\pi$
$193$	9.34800	+	16.1912i	0.672884	+	1.16547i	−0.304199	+	0.952609i	$0.598389\pi$
$194$	−0.631042	−	1.09300i	−0.0453062	−	0.0784726i
$195$		0			0
$196$	−0.928706	+	1.60857i	−0.0663362	+	0.114898i
$197$	10.2024			0.726893			0.363447	−	0.931615i	$-0.381600\pi$
$197$	10.2024			0.726893			0.363447	+	0.931615i	$0.381600\pi$
$198$		0			0
$199$	−16.4798			−1.16822			−0.584112	−	0.811673i	$-0.698557\pi$
$199$	−16.4798			−1.16822			−0.584112	+	0.811673i	$0.698557\pi$
$200$	−0.134253	+	0.232532i	−0.00949309	+	0.0164425i
$201$		0			0
$202$	0.623551	+	1.08002i	0.0438729	+	0.0759900i
$203$	−2.84085	−	4.92050i	−0.199389	−	0.345351i
$204$		0			0
$205$	−1.26518	+	2.19136i	−0.0883641	+	0.153051i
$206$	−0.689246			−0.0480220
$207$		0			0
$208$	−3.97292			−0.275473
$209$	−6.34243	+	10.9854i	−0.438715	+	0.759877i
$210$		0			0
$211$	12.5991	+	21.8223i	0.867359	+	1.50231i	0.864686	+	0.502313i	$0.167517\pi$
$211$	12.5991	+	21.8223i	0.867359	+	1.50231i	0.00267240	+	0.999996i	$0.499149\pi$
$212$	−12.4686	−	21.5963i	−0.856348	−	1.48324i
$213$		0			0
$214$	0.449344	−	0.778286i	0.0307165	−	0.0532025i
$215$	−4.56607			−0.311403
$216$		0			0
$217$	−18.8046			−1.27654
$218$	−0.0456262	+	0.0790270i	−0.00309020	+	0.00535238i
$219$		0			0
$220$	−3.20489	−	5.55103i	−0.216074	−	0.374251i
$221$	2.38839	+	4.13681i	0.160660	+	0.278272i
$222$		0			0
$223$	−3.79219	+	6.56827i	−0.253944	+	0.439844i	−0.964608	−	0.263688i	$-0.915061\pi$
$223$	−3.79219	+	6.56827i	−0.253944	+	0.439844i	0.710664	+	0.703531i	$0.248395\pi$
$224$	−1.98071			−0.132342
$225$		0			0
$226$	−0.494404			−0.0328873
$227$	0.150519	−	0.260706i	0.00999028	−	0.0173037i	−0.860987	−	0.508627i	$-0.830153\pi$
$227$	0.150519	−	0.260706i	0.00999028	−	0.0173037i	0.870977	+	0.491323i	$0.163487\pi$
$228$		0			0
$229$	2.31658	+	4.01244i	0.153084	+	0.265149i	0.932360	−	0.361532i	$-0.117746\pi$
$229$	2.31658	+	4.01244i	0.153084	+	0.265149i	−0.779276	+	0.626681i	$0.784413\pi$
$230$	−0.143469	−	0.248496i	−0.00946007	−	0.0163853i
$231$		0			0
$232$	−0.309625	+	0.536286i	−0.0203279	+	0.0352089i
$233$	−5.62440			−0.368466			−0.184233	−	0.982883i	$-0.558980\pi$
$233$	−5.62440			−0.368466			−0.184233	+	0.982883i	$0.558980\pi$
$234$		0			0
$235$	6.26567			0.408727
$236$	−2.84375	+	4.92552i	−0.185112	+	0.320624i
$237$		0			0
$238$	0.395416	+	0.684880i	0.0256310	+	0.0443942i
$239$	1.28093	+	2.21863i	0.0828562	+	0.143511i	0.904476	−	0.426525i	$-0.140262\pi$
$239$	1.28093	+	2.21863i	0.0828562	+	0.143511i	−0.821619	+	0.570036i	$0.806929\pi$
$240$		0			0
$241$	7.49149	−	12.9756i	0.482569	−	0.835835i	−0.517230	−	0.855846i	$-0.673037\pi$
$241$	7.49149	−	12.9756i	0.482569	−	0.835835i	0.999800	+	0.0200114i	$0.00637025\pi$
$242$	0.0458409			0.00294676
$243$		0			0
$244$	−25.3426			−1.62240
$245$	0.465404	−	0.806103i	0.0297336	−	0.0515001i
$246$		0			0
$247$	−1.97452	−	3.41996i	−0.125635	−	0.217607i
$248$	1.02476	+	1.77493i	0.0650721	+	0.112708i
$249$		0			0
$250$	0.0336011	−	0.0581988i	0.00212512	−	0.00368082i
$251$	7.27387			0.459123			0.229561	−	0.973294i	$-0.426271\pi$
$251$	7.27387			0.459123			0.229561	+	0.973294i	$0.426271\pi$
$252$		0			0
$253$	13.7151			0.862262
$254$	−0.200831	+	0.347850i	−0.0126013	+	0.0218261i
$255$		0			0
$256$	−7.81997	−	13.5446i	−0.488748	−	0.846536i
$257$	−4.53307	−	7.85150i	−0.282765	−	0.489763i	0.689300	−	0.724476i	$-0.257918\pi$
$257$	−4.53307	−	7.85150i	−0.282765	−	0.489763i	−0.972065	+	0.234713i	$0.924585\pi$
$258$		0			0
$259$	−6.00241	+	10.3965i	−0.372972	+	0.646006i
$260$	1.99548			0.123755
$261$		0			0
$262$	1.20113			0.0742061
$263$	13.7692	−	23.8490i	0.849045	−	1.47059i	−0.0330158	−	0.999455i	$-0.510511\pi$
$263$	13.7692	−	23.8490i	0.849045	−	1.47059i	0.882061	−	0.471135i	$-0.156156\pi$
$264$		0			0
$265$	6.24841	+	10.8226i	0.383837	+	0.664825i
$266$	−0.326896	−	0.566200i	−0.0200433	−	0.0347160i
$267$		0			0
$268$	−13.4767	+	23.3423i	−0.823219	+	1.42586i
$269$	6.82403			0.416069			0.208034	−	0.978122i	$-0.433293\pi$
$269$	6.82403			0.416069			0.208034	+	0.978122i	$0.433293\pi$
$270$		0			0
$271$	1.91734			0.116470			0.0582352	−	0.998303i	$-0.481453\pi$
$271$	1.91734			0.116470			0.0582352	+	0.998303i	$0.481453\pi$
$272$	−9.48889	+	16.4352i	−0.575348	+	0.996532i
$273$		0			0
$274$	−0.352578	−	0.610684i	−0.0213000	−	0.0368927i
$275$	1.60607	+	2.78180i	0.0968498	+	0.167749i
$276$		0			0
$277$	13.6495	−	23.6416i	0.820119	−	1.42049i	−0.0854740	−	0.996340i	$-0.527240\pi$
$277$	13.6495	−	23.6416i	0.820119	−	1.42049i	0.905593	−	0.424148i	$-0.139426\pi$
$278$	0.719524			0.0431542
$279$		0			0
$280$	0.661482			0.0395311
$281$	−0.328412	+	0.568826i	−0.0195914	+	0.0339333i	−0.875655	−	0.482937i	$-0.839570\pi$
$281$	−0.328412	+	0.568826i	−0.0195914	+	0.0339333i	0.856063	+	0.516871i	$0.172903\pi$
$282$		0			0
$283$	2.50989	+	4.34726i	0.149198	+	0.258418i	0.930931	−	0.365195i	$-0.118998\pi$
$283$	2.50989	+	4.34726i	0.149198	+	0.258418i	−0.781734	+	0.623613i	$0.785664\pi$
$284$	−7.77464	−	13.4661i	−0.461340	−	0.799065i
$285$		0			0
$286$	0.107932	−	0.186943i	0.00638213	−	0.0110542i
$287$	6.23373			0.367966
$288$		0			0
$289$	5.81760			0.342212
$290$	0.0774937	−	0.134223i	0.00455059	−	0.00788185i
$291$		0			0
$292$	2.26284	+	3.91935i	0.132422	+	0.229362i
$293$	−6.11183	−	10.5860i	−0.357057	−	0.618441i	0.630411	−	0.776262i	$-0.282887\pi$
$293$	−6.11183	−	10.5860i	−0.357057	−	0.618441i	−0.987468	+	0.157821i	$0.949553\pi$
$294$		0			0
$295$	1.42509	−	2.46833i	0.0829722	−	0.143712i
$296$	1.30841			0.0760497
$297$		0			0
$298$	−1.36548			−0.0791004
$299$	−2.13489	+	3.69773i	−0.123464	+	0.213845i
$300$		0			0
$301$	5.62443	+	9.74179i	0.324186	+	0.561507i
$302$	−0.571957	−	0.990659i	−0.0329124	−	0.0570060i
$303$		0			0
$304$	7.84460	−	13.5872i	0.449919	−	0.779282i
$305$	12.7000			0.727200
$306$		0			0
$307$	−1.01733			−0.0580619			−0.0290309	−	0.999579i	$-0.509242\pi$
$307$	−1.01733			−0.0580619			−0.0290309	+	0.999579i	$0.509242\pi$
$308$	−7.89548	+	13.6754i	−0.449887	+	0.779227i
$309$		0			0
$310$	−0.256479	−	0.444234i	−0.0145670	−	0.0252308i
$311$	−11.1446	−	19.3030i	−0.631952	−	1.09457i	−0.987152	−	0.159783i	$-0.948921\pi$
$311$	−11.1446	−	19.3030i	−0.631952	−	1.09457i	0.355200	−	0.934790i	$-0.384413\pi$
$312$		0			0
$313$	11.8874	−	20.5896i	0.671915	−	1.16379i	−0.305445	−	0.952210i	$-0.598805\pi$
$313$	11.8874	−	20.5896i	0.671915	−	1.16379i	0.977360	−	0.211581i	$-0.0678613\pi$
$314$	0.0878917			0.00496001
$315$		0			0
$316$	−18.2255			−1.02526
$317$	14.0187	−	24.2810i	0.787366	−	1.36376i	−0.140209	−	0.990122i	$-0.544777\pi$
$317$	14.0187	−	24.2810i	0.787366	−	1.36376i	0.927575	−	0.373637i	$-0.121889\pi$
$318$		0			0
$319$	3.70406	+	6.41562i	0.207388	+	0.359206i
$320$	3.94591	+	6.83451i	0.220583	+	0.382061i
$321$		0			0
$322$	−0.353446	+	0.612187i	−0.0196968	+	0.0341159i
$323$	−18.8636			−1.04960
$324$		0			0
$325$	−1.00000			−0.0554700
$326$	−0.329667	+	0.571000i	−0.0182586	+	0.0316248i
$327$		0			0
$328$	−0.339708	−	0.588391i	−0.0187572	−	0.0324885i
$329$	−7.71797	−	13.3679i	−0.425505	−	0.736997i
$330$		0			0
$331$	8.93018	−	15.4675i	0.490847	−	0.850172i	−0.509098	−	0.860709i	$-0.670021\pi$
$331$	8.93018	−	15.4675i	0.490847	−	0.850172i	0.999944	+	0.0105370i	$0.00335410\pi$
$332$	20.9763			1.15122
$333$		0			0
$334$	0.549372			0.0300603
$335$	6.75359	−	11.6976i	0.368988	−	0.639106i
$336$		0			0
$337$	−4.88581	−	8.46246i	−0.266147	−	0.460980i	0.701717	−	0.712456i	$-0.252417\pi$
$337$	−4.88581	−	8.46246i	−0.266147	−	0.460980i	−0.967863	+	0.251476i	$0.919084\pi$
$338$	0.0336011	+	0.0581988i	0.00182766	+	0.00316560i
$339$		0			0
$340$	4.76599	−	8.25494i	0.258472	−	0.447687i
$341$	24.5184			1.32775
$342$		0			0
$343$	−19.5381			−1.05496
$344$	0.613007	−	1.06176i	0.0330511	−	0.0572462i
$345$		0			0
$346$	0.214970	+	0.372339i	0.0115569	+	0.0200171i
$347$	10.5073	+	18.1991i	0.564059	+	0.976978i	0.997137	+	0.0756219i	$0.0240942\pi$
$347$	10.5073	+	18.1991i	0.564059	+	0.976978i	−0.433078	+	0.901357i	$0.642572\pi$
$348$		0			0
$349$	4.61976	−	8.00166i	0.247290	−	0.428319i	−0.715483	−	0.698630i	$-0.753793\pi$
$349$	4.61976	−	8.00166i	0.247290	−	0.428319i	0.962773	+	0.270311i	$0.0871266\pi$
$350$	−0.165558			−0.00884942
$351$		0			0
$352$	2.58256			0.137651
$353$	2.25362	−	3.90339i	0.119948	−	0.207756i	−0.799799	−	0.600268i	$-0.795060\pi$
$353$	2.25362	−	3.90339i	0.119948	−	0.207756i	0.919747	+	0.392512i	$0.128394\pi$
$354$		0			0
$355$	3.89612	+	6.74828i	0.206785	+	0.358161i
$356$	−0.964429	−	1.67044i	−0.0511146	−	0.0885332i
$357$		0			0
$358$	0.525239	−	0.909741i	0.0277597	−	0.0480813i
$359$	−25.2752			−1.33397			−0.666986	−	0.745070i	$-0.732416\pi$
$359$	−25.2752			−1.33397			−0.666986	+	0.745070i	$0.732416\pi$
$360$		0			0
$361$	−3.40514			−0.179218
$362$	0.373082	−	0.646197i	0.0196087	−	0.0339633i
$363$		0			0
$364$	−2.45801	−	4.25740i	−0.128835	−	0.223148i
$365$	−1.13398	−	1.96411i	−0.0593551	−	0.102806i
$366$		0			0
$367$	5.55336	−	9.61871i	0.289883	−	0.502092i	−0.683898	−	0.729577i	$-0.739717\pi$
$367$	5.55336	−	9.61871i	0.289883	−	0.502092i	0.973782	+	0.227485i	$0.0730502\pi$
$368$	−16.9635			−0.884282
$369$		0			0
$370$	−0.327472			−0.0170244
$371$	15.3934	−	26.6622i	0.799187	−	1.38423i
$372$		0			0
$373$	3.86823	+	6.69997i	0.200289	+	0.346911i	0.948622	−	0.316413i	$-0.102478\pi$
$373$	3.86823	+	6.69997i	0.200289	+	0.346911i	−0.748332	+	0.663324i	$0.769145\pi$
$374$	−0.515565	−	0.892985i	−0.0266592	−	0.0461751i
$375$		0			0
$376$	−0.841183	+	1.45697i	−0.0433807	+	0.0751376i
$377$	−2.30629			−0.118780
$378$		0			0
$379$	26.0870			1.34000			0.669999	−	0.742362i	$-0.266295\pi$
$379$	26.0870			1.34000			0.669999	+	0.742362i	$0.266295\pi$
$380$	−3.94012	+	6.82448i	−0.202124	+	0.350088i
$381$		0			0
$382$	−0.523588	−	0.906880i	−0.0267891	−	0.0464000i
$383$	−0.421284	−	0.729686i	−0.0215266	−	0.0372852i	0.855061	−	0.518527i	$-0.173519\pi$
$383$	−0.421284	−	0.729686i	−0.0215266	−	0.0372852i	−0.876588	+	0.481242i	$0.840186\pi$
$384$		0			0
$385$	3.95668	−	6.85316i	0.201651	−	0.349269i
$386$	1.25641			0.0639497
$387$		0			0
$388$	37.4760			1.90256
$389$	−4.37726	+	7.58163i	−0.221936	+	0.384404i	−0.955396	−	0.295329i	$-0.904571\pi$
$389$	−4.37726	+	7.58163i	−0.221936	+	0.384404i	0.733460	+	0.679733i	$0.237904\pi$
$390$		0			0
$391$	10.1979	+	17.6632i	0.515729	+	0.893268i
$392$	0.124963	+	0.216443i	0.00631161	+	0.0109320i
$393$		0			0
$394$	0.342813	−	0.593769i	0.0172707	−	0.0299137i
$395$	9.13335			0.459549
$396$		0			0
$397$	−6.72904			−0.337721			−0.168860	−	0.985640i	$-0.554009\pi$
$397$	−6.72904			−0.337721			−0.168860	+	0.985640i	$0.554009\pi$
$398$	−0.553740	+	0.959106i	−0.0277565	+	0.0480757i
$399$		0			0
$400$	−1.98646	−	3.44065i	−0.0993231	−	0.172033i
$401$	−14.4471	−	25.0231i	−0.721453	−	1.24959i	−0.960417	−	0.278565i	$-0.910141\pi$
$401$	−14.4471	−	25.0231i	−0.721453	−	1.24959i	0.238964	−	0.971028i	$-0.423192\pi$
$402$		0			0
$403$	−3.81652	+	6.61041i	−0.190115	+	0.329288i
$404$	−37.0311			−1.84237
$405$		0			0
$406$	−0.381823			−0.0189496
$407$	7.82628	−	13.5555i	0.387934	−	0.671922i
$408$		0			0
$409$	9.19426	+	15.9249i	0.454627	+	0.787437i	0.998667	−	0.0516225i	$-0.0164392\pi$
$409$	9.19426	+	15.9249i	0.454627	+	0.787437i	−0.544040	+	0.839059i	$0.683106\pi$
$410$	0.0850230	+	0.147264i	0.00419898	+	0.00727285i
$411$		0			0
$412$	10.2331	−	17.7243i	0.504151	−	0.873215i
$413$	−7.02164			−0.345513
$414$		0			0
$415$	−10.5119			−0.516008
$416$	−0.402000	+	0.696284i	−0.0197097	+	0.0341381i
$417$		0			0
$418$	0.426225	+	0.738244i	0.0208474	+	0.0361087i
$419$	−12.6003	−	21.8244i	−0.615567	−	1.06619i	−0.990285	−	0.139054i	$-0.955594\pi$
$419$	−12.6003	−	21.8244i	−0.615567	−	1.06619i	0.374718	−	0.927139i	$-0.377739\pi$
$420$		0			0
$421$	8.93227	−	15.4711i	0.435332	−	0.754017i	−0.561991	−	0.827144i	$-0.689964\pi$
$421$	8.93227	−	15.4711i	0.435332	−	0.754017i	0.997323	+	0.0731263i	$0.0232976\pi$
$422$	1.69338			0.0824322
$423$		0			0
$424$	−3.35546			−0.162956
$425$	−2.38839	+	4.13681i	−0.115854	+	0.200665i
$426$		0			0
$427$	−15.6437	−	27.0957i	−0.757051	−	1.31125i
$428$	13.3427	+	23.1102i	0.644943	+	1.11707i
$429$		0			0
$430$	−0.153425	+	0.265740i	−0.00739881	+	0.0128151i
$431$	−28.4290			−1.36937			−0.684687	−	0.728837i	$-0.740061\pi$
$431$	−28.4290			−1.36937			−0.684687	+	0.728837i	$0.740061\pi$
$432$		0			0
$433$	−20.4163			−0.981146			−0.490573	−	0.871400i	$-0.663212\pi$
$433$	−20.4163			−0.981146			−0.490573	+	0.871400i	$0.663212\pi$
$434$	−0.631854	+	1.09440i	−0.0303300	+	0.0525330i
$435$		0			0
$436$	−1.35481	−	2.34661i	−0.0648838	−	0.112382i
$437$	−8.43073	−	14.6025i	−0.403297	−	0.698530i
$438$		0			0
$439$	−4.91252	+	8.50874i	−0.234462	+	0.406100i	−0.959116	−	0.283013i	$-0.908666\pi$
$439$	−4.91252	+	8.50874i	−0.234462	+	0.406100i	0.724654	+	0.689113i	$0.241999\pi$
$440$	−0.862477			−0.0411170
$441$		0			0
$442$	0.321010			0.0152689
$443$	−9.82384	+	17.0154i	−0.466745	+	0.808425i	−0.999278	−	0.0379835i	$-0.987907\pi$
$443$	−9.82384	+	17.0154i	−0.466745	+	0.808425i	0.532534	+	0.846409i	$0.321240\pi$
$444$		0			0
$445$	0.483306	+	0.837110i	0.0229109	+	0.0396828i
$446$	0.254844	+	0.441402i	0.0120672	+	0.0209010i
$447$		0			0
$448$	9.72103	−	16.8373i	0.459276	−	0.795489i
$449$	−27.3713			−1.29173			−0.645866	−	0.763451i	$-0.723504\pi$
$449$	−27.3713			−1.29173			−0.645866	+	0.763451i	$0.723504\pi$
$450$		0			0
$451$	−8.12789			−0.382727
$452$	7.34035	−	12.7139i	0.345261	−	0.598010i
$453$		0			0
$454$	−0.0101152	−	0.0175200i	−0.000474729	−	0.000822255i
$455$	1.23179	+	2.13352i	0.0577470	+	0.100021i
$456$		0			0
$457$	12.2292	−	21.1815i	0.572056	−	0.990830i	−0.424299	−	0.905522i	$-0.639479\pi$
$457$	12.2292	−	21.1815i	0.572056	−	0.990830i	0.996355	−	0.0853077i	$-0.0271873\pi$
$458$	0.311359			0.0145488
$459$		0			0
$460$	8.52026			0.397259
$461$	4.38036	−	7.58701i	0.204014	−	0.353362i	−0.745804	−	0.666165i	$-0.767935\pi$
$461$	4.38036	−	7.58701i	0.204014	−	0.353362i	0.949818	+	0.312803i	$0.101268\pi$
$462$		0			0
$463$	−7.55160	−	13.0797i	−0.350952	−	0.607867i	0.635464	−	0.772130i	$-0.280809\pi$
$463$	−7.55160	−	13.0797i	−0.350952	−	0.607867i	−0.986417	+	0.164263i	$0.947475\pi$
$464$	−4.58135	−	7.93513i	−0.212684	−	0.368379i
$465$		0			0
$466$	−0.188986	+	0.327333i	−0.00875460	+	0.0151634i
$467$	19.5484			0.904591			0.452296	−	0.891868i	$-0.350605\pi$
$467$	19.5484			0.904591			0.452296	+	0.891868i	$0.350605\pi$
$468$		0			0
$469$	−33.2759			−1.53654
$470$	0.210533	−	0.364655i	0.00971118	−	0.0168203i
$471$		0			0
$472$	0.382645	+	0.662761i	0.0176127	+	0.0305060i
$473$	−7.33344	−	12.7019i	−0.337192	−	0.584033i
$474$		0			0
$475$	1.97452	−	3.41996i	0.0905970	−	0.156919i
$476$	−23.4827			−1.07633
$477$		0			0
$478$	0.172162			0.00787451
$479$	0.653565	−	1.13201i	0.0298621	−	0.0517227i	−0.850708	−	0.525638i	$-0.823827\pi$
$479$	0.653565	−	1.13201i	0.0298621	−	0.0517227i	0.880570	+	0.473916i	$0.157160\pi$
$480$		0			0
$481$	2.43647	+	4.22008i	0.111093	+	0.192419i
$482$	−0.503445	−	0.871992i	−0.0229313	−	0.0397181i
$483$		0			0
$484$	−0.680593	+	1.17882i	−0.0309361	+	0.0535828i
$485$	−18.7804			−0.852774
$486$		0			0
$487$	30.3533			1.37544			0.687719	−	0.725977i	$-0.258612\pi$
$487$	30.3533			1.37544			0.687719	+	0.725977i	$0.258612\pi$
$488$	−1.70501	+	2.95316i	−0.0771821	+	0.133683i
$489$		0			0
$490$	−0.0312762	−	0.0541719i	−0.00141291	−	0.00244724i
$491$	4.18858	+	7.25484i	0.189028	+	0.327406i	0.944926	−	0.327283i	$-0.106133\pi$
$491$	4.18858	+	7.25484i	0.189028	+	0.327406i	−0.755898	+	0.654689i	$0.772800\pi$
$492$		0			0
$493$	−5.50831	+	9.54067i	−0.248082	+	0.429690i
$494$	−0.265384			−0.0119402
$495$		0			0
$496$	−30.3255			−1.36166
$497$	9.59837	−	16.6249i	0.430546	−	0.745727i
$498$		0			0
$499$	−6.43013	−	11.1373i	−0.287852	−	0.498574i	0.685445	−	0.728125i	$-0.259608\pi$
$499$	−6.43013	−	11.1373i	−0.287852	−	0.498574i	−0.973297	+	0.229550i	$0.926274\pi$
$500$	0.997742	+	1.72814i	0.0446204	+	0.0772848i
$501$		0			0
$502$	0.244410	−	0.423331i	0.0109086	−	0.0188942i
$503$	−5.22447			−0.232947			−0.116474	−	0.993194i	$-0.537159\pi$
$503$	−5.22447			−0.232947			−0.116474	+	0.993194i	$0.537159\pi$
$504$		0			0
$505$	18.5575			0.825796
$506$	0.460843	−	0.798204i	0.0204870	−	0.0354845i
$507$		0			0
$508$	−5.96344	−	10.3290i	−0.264585	−	0.458274i
$509$	5.01119	+	8.67964i	0.222117	+	0.384718i	0.955451	−	0.295151i	$-0.0953699\pi$
$509$	5.01119	+	8.67964i	0.222117	+	0.384718i	−0.733334	+	0.679869i	$0.762037\pi$
$510$		0			0
$511$	−2.79364	+	4.83872i	−0.123583	+	0.214053i
$512$	−5.32773			−0.235455
$513$		0			0
$514$	−0.609264			−0.0268735
$515$	−5.12815	+	8.88222i	−0.225973	+	0.391397i
$516$		0			0
$517$	10.0631	+	17.4298i	0.442575	+	0.766563i
$518$	0.403375	+	0.698667i	0.0177233	+	0.0306976i
$519$		0			0
$520$	0.134253	−	0.232532i	0.00588737	−	0.0101972i
$521$	−20.3192			−0.890202			−0.445101	−	0.895480i	$-0.646832\pi$
$521$	−20.3192			−0.890202			−0.445101	+	0.895480i	$0.646832\pi$
$522$		0			0
$523$	−0.572523			−0.0250347			−0.0125173	−	0.999922i	$-0.503984\pi$
$523$	−0.572523			−0.0250347			−0.0125173	+	0.999922i	$0.503984\pi$
$524$	−17.8330	+	30.8877i	−0.779040	+	1.34934i
$525$		0			0
$526$	−0.925321	−	1.60270i	−0.0403459	−	0.0698811i
$527$	18.2307	+	31.5765i	0.794141	+	1.37549i
$528$		0			0
$529$	2.38452	−	4.13012i	0.103675	−	0.179570i
$530$	0.839814			0.0364792
$531$		0			0
$532$	19.4135			0.841683
$533$	1.26518	−	2.19136i	0.0548011	−	0.0949183i
$534$		0			0
$535$	−6.68644	−	11.5813i	−0.289080	−	0.500702i
$536$	1.81337	+	3.14086i	0.0783258	+	0.135664i
$537$		0			0
$538$	0.229295	−	0.397151i	0.00988561	−	0.0171224i
$539$	2.98989			0.128784
$540$		0			0
$541$	−23.5766			−1.01364			−0.506819	−	0.862052i	$-0.669179\pi$
$541$	−23.5766			−1.01364			−0.506819	+	0.862052i	$0.669179\pi$
$542$	0.0644248	−	0.111587i	0.00276728	−	0.00479308i
$543$		0			0
$544$	1.92026	+	3.32599i	0.0823306	+	0.142601i
$545$	0.678940	+	1.17596i	0.0290826	+	0.0503725i
$546$		0			0
$547$	1.87854	−	3.25373i	0.0803205	−	0.139119i	−0.823067	−	0.567944i	$-0.807739\pi$
$547$	1.87854	−	3.25373i	0.0803205	−	0.139119i	0.903388	+	0.428825i	$0.141072\pi$
$548$	20.9387			0.894458
$549$		0			0
$550$	0.215863			0.00920443
$551$	4.55380	−	7.88741i	0.193998	−	0.336015i
$552$		0			0
$553$	−11.2503	−	19.4862i	−0.478413	−	0.828636i
$554$	−0.917276	−	1.58877i	−0.0389713	−	0.0675003i
$555$		0			0
$556$	−10.6827	+	18.5029i	−0.453046	+	0.784699i
$557$	39.9225			1.69157			0.845785	−	0.533523i	$-0.179132\pi$
$557$	39.9225			1.69157			0.845785	+	0.533523i	$0.179132\pi$
$558$		0			0
$559$	4.56607			0.193124
$560$	−4.89379	+	8.47630i	−0.206801	+	0.358189i
$561$		0			0
$562$	0.0220700	+	0.0382264i	0.000930967	+	0.00161248i
$563$	16.7785	+	29.0612i	0.707130	+	1.22478i	0.965917	+	0.258850i	$0.0833437\pi$
$563$	16.7785	+	29.0612i	0.707130	+	1.22478i	−0.258788	+	0.965934i	$0.583323\pi$
$564$		0			0
$565$	−3.67848	+	6.37132i	−0.154755	+	0.268043i
$566$	0.337340			0.0141795
$567$		0			0
$568$	−2.09226			−0.0877892
$569$	7.71687	−	13.3660i	0.323508	−	0.560332i	−0.657701	−	0.753279i	$-0.728471\pi$
$569$	7.71687	−	13.3660i	0.323508	−	0.560332i	0.981209	+	0.192946i	$0.0618044\pi$
$570$		0			0
$571$	−19.9691	−	34.5875i	−0.835681	−	1.44744i	−0.893475	−	0.449114i	$-0.851740\pi$
$571$	−19.9691	−	34.5875i	−0.835681	−	1.44744i	0.0577933	−	0.998329i	$-0.481594\pi$
$572$	3.20489	+	5.55103i	0.134003	+	0.232100i
$573$		0			0
$574$	0.209460	−	0.362796i	0.00874270	−	0.0151428i
$575$	−4.26977			−0.178062
$576$		0			0
$577$	25.4359			1.05891			0.529455	−	0.848338i	$-0.322396\pi$
$577$	25.4359			1.05891			0.529455	+	0.848338i	$0.322396\pi$
$578$	0.195478	−	0.338578i	0.00813081	−	0.0140830i
$579$		0			0
$580$	2.30108	+	3.98558i	0.0955471	+	0.165492i
$581$	12.9484	+	22.4273i	0.537190	+	0.930441i
$582$		0			0
$583$	−20.0708	+	34.7637i	−0.831248	+	1.43976i
$584$	0.608958			0.0251989
$585$		0			0
$586$	−0.821457			−0.0339341
$587$	−20.4639	+	35.4446i	−0.844637	+	1.46295i	0.0412991	+	0.999147i	$0.486850\pi$
$587$	−20.4639	+	35.4446i	−0.844637	+	1.46295i	−0.885936	+	0.463807i	$0.846483\pi$
$588$		0			0
$589$	−15.0716	−	26.1047i	−0.621013	−	1.07563i
$590$	−0.0957694	−	0.165877i	−0.00394276	−	0.00682907i
$591$		0			0
$592$	−9.67990	+	16.7661i	−0.397841	+	0.689081i
$593$	1.00808			0.0413971			0.0206985	−	0.999786i	$-0.493411\pi$
$593$	1.00808			0.0413971			0.0206985	+	0.999786i	$0.493411\pi$
$594$		0			0
$595$	11.7679			0.482439
$596$	20.2732	−	35.1141i	0.830421	−	1.43833i
$597$		0			0
$598$	0.143469	+	0.248496i	0.00586688	+	0.0101617i
$599$	0.939758	+	1.62771i	0.0383975	+	0.0665064i	0.884585	−	0.466378i	$-0.154441\pi$
$599$	0.939758	+	1.62771i	0.0383975	+	0.0665064i	−0.846188	+	0.532884i	$0.821108\pi$
$600$		0			0
$601$	1.47264	−	2.55068i	0.0600702	−	0.104045i	−0.834426	−	0.551119i	$-0.814201\pi$
$601$	1.47264	−	2.55068i	0.0600702	−	0.104045i	0.894497	+	0.447075i	$0.147534\pi$
$602$	0.755947			0.0308101
$603$		0			0
$604$	33.9671			1.38210
$605$	0.341067	−	0.590745i	0.0138663	−	0.0240172i
$606$		0			0
$607$	−0.670347	−	1.16108i	−0.0272085	−	0.0471266i	0.852101	−	0.523378i	$-0.175328\pi$
$607$	−0.670347	−	1.16108i	−0.0272085	−	0.0471266i	−0.879309	+	0.476252i	$0.841995\pi$
$608$	−1.58751	−	2.74965i	−0.0643820	−	0.111513i
$609$		0			0
$610$	0.426734	−	0.739125i	0.0172780	−	0.0299263i
$611$	−6.26567			−0.253482
$612$		0			0
$613$	−20.1796			−0.815046			−0.407523	−	0.913195i	$-0.633607\pi$
$613$	−20.1796			−0.815046			−0.407523	+	0.913195i	$0.633607\pi$
$614$	−0.0341833	+	0.0592072i	−0.00137952	+	0.00238941i
$615$		0			0
$616$	1.06239	+	1.84011i	0.0428048	+	0.0741402i
$617$	−3.56739	−	6.17890i	−0.143618	−	0.248753i	0.785239	−	0.619193i	$-0.212540\pi$
$617$	−3.56739	−	6.17890i	−0.143618	−	0.248753i	−0.928856	+	0.370440i	$0.879207\pi$
$618$		0			0
$619$	15.4477	−	26.7562i	0.620895	−	1.07542i	−0.368424	−	0.929658i	$-0.620103\pi$
$619$	15.4477	−	26.7562i	0.620895	−	1.07542i	0.989319	−	0.145764i	$-0.0465640\pi$
$620$	15.2316			0.611717
$621$		0			0
$622$	−1.49788			−0.0600596
$623$	1.19066	−	2.06228i	0.0477028	−	0.0826236i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−0.798859	−	1.38366i	−0.0319288	−	0.0553023i
$627$		0			0
$628$	−1.30492	+	2.26018i	−0.0520718	+	0.0901910i
$629$	23.2769			0.928112
$630$		0			0
$631$	11.8799			0.472932			0.236466	−	0.971640i	$-0.424011\pi$
$631$	11.8799			0.472932			0.236466	+	0.971640i	$0.424011\pi$
$632$	−1.22618	+	2.12380i	−0.0487747	+	0.0844803i
$633$		0			0
$634$	−0.942085	−	1.63174i	−0.0374150	−	0.0648046i
$635$	2.98847	+	5.17618i	0.118594	+	0.205410i
$636$		0			0
$637$	−0.465404	+	0.806103i	−0.0184400	+	0.0319390i
$638$	0.497842			0.0197098
$639$		0			0
$640$	2.13835			0.0845256
$641$	12.5654	−	21.7639i	0.496302	−	0.859621i	−0.503689	−	0.863885i	$-0.668024\pi$
$641$	12.5654	−	21.7639i	0.496302	−	0.859621i	0.999991	+	0.00426452i	$0.00135744\pi$
$642$		0			0
$643$	18.9486	+	32.8199i	0.747258	+	1.29429i	0.949132	+	0.314877i	$0.101963\pi$
$643$	18.9486	+	32.8199i	0.747258	+	1.29429i	−0.201874	+	0.979411i	$0.564703\pi$
$644$	−10.4951	−	18.1781i	−0.413567	−	0.716318i
$645$		0			0
$646$	−0.633839	+	1.09784i	−0.0249381	+	0.0431940i
$647$	5.59065			0.219791			0.109896	−	0.993943i	$-0.464948\pi$
$647$	5.59065			0.219791			0.109896	+	0.993943i	$0.464948\pi$
$648$		0			0
$649$	9.15521			0.359373
$650$	−0.0336011	+	0.0581988i	−0.00131794	+	0.00228274i
$651$		0			0
$652$	−9.78905	−	16.9551i	−0.383369	−	0.664014i
$653$	−4.29248	−	7.43479i	−0.167978	−	0.290946i	0.769731	−	0.638368i	$-0.220390\pi$
$653$	−4.29248	−	7.43479i	−0.167978	−	0.290946i	−0.937709	+	0.347422i	$0.887057\pi$
$654$		0			0
$655$	8.93670	−	15.4788i	0.349186	−	0.604807i
$656$	10.0529			0.392501
$657$		0			0
$658$	−1.03733			−0.0404393
$659$	−9.85987	+	17.0778i	−0.384086	+	0.665257i	−0.991642	−	0.129020i	$-0.958817\pi$
$659$	−9.85987	+	17.0778i	−0.384086	+	0.665257i	0.607556	+	0.794277i	$0.292150\pi$
$660$		0			0
$661$	−17.6742	−	30.6127i	−0.687448	−	1.19069i	−0.972661	−	0.232230i	$-0.925398\pi$
$661$	−17.6742	−	30.6127i	−0.687448	−	1.19069i	0.285213	−	0.958464i	$-0.407936\pi$
$662$	−0.600127	−	1.03945i	−0.0233246	−	0.0403994i
$663$		0			0
$664$	1.41125	−	2.44436i	0.0547671	−	0.0948594i
$665$	−9.72873			−0.377264
$666$		0			0
$667$	−9.84732			−0.381290
$668$	−8.15645	+	14.1274i	−0.315582	+	0.546605i
$669$		0			0
$670$	−0.453856	−	0.786102i	−0.0175340	−	0.0303698i
$671$	20.3971	+	35.3288i	0.787422	+	1.36385i
$672$		0			0
$673$	−8.53274	+	14.7791i	−0.328913	+	0.569694i	−0.982296	−	0.187333i	$-0.940016\pi$
$673$	−8.53274	+	14.7791i	−0.328913	+	0.569694i	0.653383	+	0.757027i	$0.273349\pi$
$674$	−0.656674			−0.0252941
$675$		0			0
$676$	−1.99548			−0.0767494
$677$	−5.54423	+	9.60290i	−0.213082	+	0.369069i	−0.952678	−	0.303982i	$-0.901684\pi$
$677$	−5.54423	+	9.60290i	−0.213082	+	0.369069i	0.739595	+	0.673052i	$0.235017\pi$
$678$		0			0
$679$	23.1335	+	40.0683i	0.887780	+	1.53768i
$680$	−0.641295	−	1.11076i	−0.0245925	−	0.0425955i
$681$		0			0
$682$	0.823846	−	1.42694i	0.0315467	−	0.0546405i
$683$	42.5037			1.62636			0.813179	−	0.582014i	$-0.197735\pi$
$683$	42.5037			1.62636			0.813179	+	0.582014i	$0.197735\pi$
$684$		0			0
$685$	−10.4931			−0.400919
$686$	−0.656502	+	1.13710i	−0.0250654	+	0.0434145i
$687$		0			0
$688$	9.07033	+	15.7103i	0.345803	+	0.598948i
$689$	−6.24841	−	10.8226i	−0.238046	−	0.412307i
$690$		0			0
$691$	−0.656332	+	1.13680i	−0.0249681	+	0.0432460i	−0.878239	−	0.478221i	$-0.841282\pi$
$691$	−0.656332	+	1.13680i	−0.0249681	+	0.0432460i	0.853271	+	0.521467i	$0.174615\pi$
$692$	−12.7665			−0.485310
$693$		0			0
$694$	1.41222			0.0536072
$695$	5.35343	−	9.27241i	0.203067	−	0.351722i
$696$		0			0
$697$	−6.04349	−	10.4676i	−0.228914	−	0.396490i
$698$	−0.310458	−	0.537729i	−0.0117510	−	0.0203534i
$699$		0			0
$700$	2.45801	−	4.25740i	0.0929040	−	0.160915i
$701$	−21.2054			−0.800916			−0.400458	−	0.916315i	$-0.631149\pi$
$701$	−21.2054			−0.800916			−0.400458	+	0.916315i	$0.631149\pi$
$702$		0			0
$703$	−19.2434			−0.725778
$704$	−12.6748	+	21.9534i	−0.477700	+	0.827401i
$705$		0			0
$706$	−0.151448	−	0.262316i	−0.00569983	−	0.00987240i
$707$	−22.8588	−	39.5926i	−0.859694	−	1.48903i
$708$		0			0
$709$	−24.6030	+	42.6136i	−0.923985	+	1.60039i	−0.130799	+	0.991409i	$0.541754\pi$
$709$	−24.6030	+	42.6136i	−0.923985	+	1.60039i	−0.793186	+	0.608980i	$0.791579\pi$
$710$	0.523655			0.0196524
$711$		0			0
$712$	−0.259540			−0.00972669
$713$	−16.2957	+	28.2249i	−0.610278	+	1.05703i
$714$		0			0
$715$	−1.60607	−	2.78180i	−0.0600637	−	0.104033i
$716$	15.5963	+	27.0136i	0.582861	+	1.00955i
$717$		0			0
$718$	−0.849273	+	1.47098i	−0.0316946	+	0.0548966i
$719$	31.1080			1.16013			0.580067	−	0.814569i	$-0.303026\pi$
$719$	31.1080			1.16013			0.580067	+	0.814569i	$0.303026\pi$
$720$		0			0
$721$	25.2671			0.940998
$722$	−0.114417	+	0.198175i	−0.00425814	+	0.00737532i
$723$		0			0
$724$	11.0782	+	19.1880i	0.411718	+	0.713116i
$725$	−1.15314	−	1.99730i	−0.0428267	−	0.0741780i
$726$		0			0
$727$	−15.0470	+	26.0622i	−0.558062	+	0.966592i	0.439596	+	0.898196i	$0.355122\pi$
$727$	−15.0470	+	26.0622i	−0.558062	+	0.966592i	−0.997658	+	0.0683968i	$0.978212\pi$
$728$	−0.661482			−0.0245162
$729$		0			0
$730$	−0.152412			−0.00564101
$731$	10.9056	−	18.8890i	0.403356	−	0.698634i
$732$		0			0
$733$	6.49987	+	11.2581i	0.240078	+	0.415827i	0.960736	−	0.277463i	$-0.0894936\pi$
$733$	6.49987	+	11.2581i	0.240078	+	0.415827i	−0.720658	+	0.693290i	$0.756160\pi$
$734$	−0.373198	−	0.646398i	−0.0137750	−	0.0238590i
$735$		0			0
$736$	−1.71645	+	2.97297i	−0.0632691	+	0.109585i
$737$	43.3870			1.59818
$738$		0			0
$739$	43.9402			1.61637			0.808183	−	0.588932i	$-0.200451\pi$
$739$	43.9402			1.61637			0.808183	+	0.588932i	$0.200451\pi$
$740$	4.86193	−	8.42111i	0.178728	−	0.309566i
$741$		0			0
$742$	−1.03447	−	1.79176i	−0.0379767	−	0.0657775i
$743$	−24.4254	−	42.3061i	−0.896081	−	1.55206i	−0.832461	−	0.554084i	$-0.813069\pi$
$743$	−24.4254	−	42.3061i	−0.896081	−	1.55206i	−0.0636208	−	0.997974i	$-0.520265\pi$
$744$		0			0
$745$	−10.1595	+	17.5968i	−0.372216	+	0.644697i
$746$	0.519907			0.0190351
$747$		0			0
$748$	30.6181			1.11951
$749$	−16.4725	+	28.5313i	−0.601894	+	1.04251i
$750$		0			0
$751$	16.7071	+	28.9376i	0.609651	+	1.05595i	0.991298	+	0.131638i	$0.0420238\pi$
$751$	16.7071	+	28.9376i	0.609651	+	1.05595i	−0.381647	+	0.924308i	$0.624643\pi$
$752$	−12.4465	−	21.5580i	−0.453878	−	0.786139i
$753$		0			0
$754$	−0.0774937	+	0.134223i	−0.00282216	+	0.00488812i
$755$	−17.0220			−0.619493
$756$		0			0
$757$	45.6922			1.66071			0.830356	−	0.557233i	$-0.188137\pi$
$757$	45.6922			1.66071			0.830356	+	0.557233i	$0.188137\pi$
$758$	0.876551	−	1.51823i	0.0318378	−	0.0551446i
$759$		0			0
$760$	0.530168	+	0.918278i	0.0192312	+	0.0333094i
$761$	−2.43929	−	4.22497i	−0.0884242	−	0.153155i	0.818421	−	0.574619i	$-0.194850\pi$
$761$	−2.43929	−	4.22497i	−0.0884242	−	0.153155i	−0.906845	+	0.421464i	$0.861516\pi$
$762$		0			0
$763$	1.67262	−	2.89706i	0.0605528	−	0.104881i
$764$	31.0945			1.12496
$765$		0			0
$766$	−0.0566225			−0.00204585
$767$	−1.42509	+	2.46833i	−0.0514572	+	0.0891264i
$768$		0			0
$769$	−5.62978	−	9.75106i	−0.203015	−	0.351632i	0.746483	−	0.665404i	$-0.231741\pi$
$769$	−5.62978	−	9.75106i	−0.203015	−	0.351632i	−0.949498	+	0.313772i	$0.898407\pi$
$770$	−0.265897	−	0.460548i	−0.00958227	−	0.0165970i
$771$		0			0
$772$	−18.6538	+	32.3093i	−0.671364	+	1.16284i
$773$	−17.8461			−0.641880			−0.320940	−	0.947100i	$-0.603999\pi$
$773$	−17.8461			−0.641880			−0.320940	+	0.947100i	$0.603999\pi$
$774$		0			0
$775$	−7.63305			−0.274187
$776$	2.52132	−	4.36705i	0.0905101	−	0.156768i
$777$		0			0
$778$	0.294161	+	0.509502i	0.0105462	+	0.0182665i
$779$	4.99624	+	8.65375i	0.179009	+	0.310053i
$780$		0			0
$781$	−12.5149	+	21.6764i	−0.447818	+	0.775644i
$782$	1.37064			0.0490140
$783$		0			0
$784$	−3.69803			−0.132072
$785$	0.653935	−	1.13265i	0.0233399	−	0.0404259i
$786$		0			0
$787$	−12.3557	−	21.4006i	−0.440432	−	0.762850i	0.557290	−	0.830318i	$-0.311841\pi$
$787$	−12.3557	−	21.4006i	−0.440432	−	0.762850i	−0.997721	+	0.0674682i	$0.978508\pi$
$788$	10.1794	+	17.6312i	0.362626	+	0.628087i
$789$		0			0
$790$	0.306891	−	0.531550i	0.0109187	−	0.0189117i
$791$	18.1244			0.644430
$792$		0			0
$793$	−12.7000			−0.450990
$794$	−0.226103	+	0.391622i	−0.00802410	+	0.0138981i
$795$		0			0
$796$	−16.4426	−	28.4794i	−0.582793	−	1.00943i
$797$	19.8688	+	34.4139i	0.703791	+	1.21900i	0.967126	+	0.254297i	$0.0818440\pi$
$797$	19.8688	+	34.4139i	0.703791	+	1.21900i	−0.263336	+	0.964704i	$0.584823\pi$
$798$		0			0
$799$	−14.9649	+	25.9199i	−0.529419	+	0.916980i
$800$	−0.804000			−0.0284257
$801$		0			0
$802$	−1.94175			−0.0685657
$803$	3.64250	−	6.30900i	0.128541	−	0.222640i
$804$		0			0
$805$	5.25945	+	9.10963i	0.185371	+	0.321072i
$806$	0.256479	+	0.444234i	0.00903408	+	0.0156475i
$807$		0			0
$808$	−2.49139	+	4.31521i	−0.0876467	+	0.151808i
$809$	−40.0717			−1.40885			−0.704423	−	0.709780i	$-0.748794\pi$
$809$	−40.0717			−1.40885			−0.704423	+	0.709780i	$0.748794\pi$
$810$		0			0
$811$	49.6910			1.74489			0.872444	−	0.488714i	$-0.162534\pi$
$811$	49.6910			1.74489			0.872444	+	0.488714i	$0.162534\pi$
$812$	5.66887	−	9.81878i	0.198939	−	0.344572i
$813$		0			0
$814$	−0.525943	−	0.910960i	−0.0184343	−	0.0319291i
$815$	4.90560	+	8.49675i	0.171836	+	0.297628i
$816$		0			0
$817$	−9.01578	+	15.6158i	−0.315422	+	0.546327i
$818$	1.23575			0.0432070
$819$		0			0
$820$	−5.04930			−0.176329
$821$	9.44011	−	16.3507i	0.329462	−	0.570645i	−0.652943	−	0.757407i	$-0.726466\pi$
$821$	9.44011	−	16.3507i	0.329462	−	0.570645i	0.982405	+	0.186762i	$0.0597993\pi$
$822$		0			0
$823$	14.2363	+	24.6580i	0.496247	+	0.859525i	0.999991	−	0.00432845i	$-0.00137779\pi$
$823$	14.2363	+	24.6580i	0.496247	+	0.859525i	−0.503744	+	0.863853i	$0.668044\pi$
$824$	−1.37694	−	2.38492i	−0.0479678	−	0.0830827i
$825$		0			0
$826$	−0.235935	+	0.408651i	−0.00820923	+	0.0142188i
$827$	15.9961			0.556239			0.278120	−	0.960546i	$-0.410289\pi$
$827$	15.9961			0.556239			0.278120	+	0.960546i	$0.410289\pi$
$828$		0			0
$829$	20.7729			0.721474			0.360737	−	0.932668i	$-0.382525\pi$
$829$	20.7729			0.721474			0.360737	+	0.932668i	$0.382525\pi$
$830$	−0.353211	+	0.611779i	−0.0122601	+	0.0212352i
$831$		0			0
$832$	−3.94591	−	6.83451i	−0.136800	−	0.236944i
$833$	2.22313	+	3.85058i	0.0770269	+	0.133415i
$834$		0			0
$835$	4.08745	−	7.07968i	0.141452	−	0.245002i
$836$	−25.3124			−0.875449
$837$		0			0
$838$	−1.69354			−0.0585024
$839$	−8.59202	+	14.8818i	−0.296630	+	0.513777i	−0.975363	−	0.220608i	$-0.929196\pi$
$839$	−8.59202	+	14.8818i	−0.296630	+	0.513777i	0.678733	+	0.734385i	$0.262529\pi$
$840$		0			0
$841$	11.8405	+	20.5084i	0.408294	+	0.707186i
$842$	−0.600268	−	1.03969i	−0.0206866	−	0.0358302i
$843$		0			0
$844$	−25.1413	+	43.5460i	−0.865400	+	1.49892i
$845$	1.00000			0.0344010
$846$		0			0
$847$	−1.68049			−0.0577422
$848$	24.8245	−	42.9972i	0.852476	−	1.47653i
$849$		0			0
$850$	0.160505	+	0.278003i	0.00550527	+	0.00953542i
$851$	10.4032	+	18.0188i	0.356616	+	0.617676i
$852$		0			0
$853$	−16.5366	+	28.6423i	−0.566203	+	0.980693i	0.430733	+	0.902479i	$0.358255\pi$
$853$	−16.5366	+	28.6423i	−0.566203	+	0.980693i	−0.996937	+	0.0782138i	$0.975078\pi$
$854$	−2.10258			−0.0719488
$855$		0			0
$856$	3.59069			0.122727
$857$	−19.8148	+	34.3202i	−0.676859	+	1.17235i	0.299063	+	0.954233i	$0.403326\pi$
$857$	−19.8148	+	34.3202i	−0.676859	+	1.17235i	−0.975922	+	0.218121i	$0.930007\pi$
$858$		0			0
$859$	0.586442	+	1.01575i	0.0200091	+	0.0346569i	0.875857	−	0.482571i	$-0.160297\pi$
$859$	0.586442	+	1.01575i	0.0200091	+	0.0346569i	−0.855847	+	0.517228i	$0.826964\pi$
$860$	−4.55576	−	7.89081i	−0.155350	−	0.269074i
$861$		0			0
$862$	−0.955244	+	1.65453i	−0.0325357	+	0.0563536i
$863$	54.3303			1.84943			0.924713	−	0.380665i	$-0.124305\pi$
$863$	54.3303			1.84943			0.924713	+	0.380665i	$0.124305\pi$
$864$		0			0
$865$	6.39771			0.217529
$866$	−0.686011	+	1.18821i	−0.0233116	+	0.0403769i
$867$		0			0
$868$	−18.7621	−	32.4969i	−0.636827	−	1.10302i
$869$	14.6688	+	25.4071i	0.497606	+	0.861878i
$870$		0			0
$871$	−6.75359	+	11.6976i	−0.228837	+	0.396357i
$872$	−0.364598			−0.0123468
$873$		0			0
$874$	−1.13313			−0.0383286
$875$	−1.23179	+	2.13352i	−0.0416420	+	0.0721260i
$876$		0			0
$877$	−23.8867	−	41.3730i	−0.806597	−	1.39707i	−0.915207	−	0.402983i	$-0.867973\pi$
$877$	−23.8867	−	41.3730i	−0.806597	−	1.39707i	0.108610	−	0.994084i	$-0.465360\pi$
$878$	0.330132	+	0.571806i	0.0111414	+	0.0192975i
$879$		0			0
$880$	6.38080	−	11.0519i	0.215097	−	0.372558i
$881$	−28.0225			−0.944101			−0.472050	−	0.881572i	$-0.656486\pi$
$881$	−28.0225			−0.944101			−0.472050	+	0.881572i	$0.656486\pi$
$882$		0			0
$883$	−2.71952			−0.0915191			−0.0457595	−	0.998952i	$-0.514571\pi$
$883$	−2.71952			−0.0915191			−0.0457595	+	0.998952i	$0.514571\pi$
$884$	−4.76599	+	8.25494i	−0.160298	+	0.277644i
$885$		0			0
$886$	0.660183	+	1.14347i	0.0221793	+	0.0384157i
$887$	−2.38124	−	4.12442i	−0.0799541	−	0.138485i	0.823276	−	0.567642i	$-0.192144\pi$
$887$	−2.38124	−	4.12442i	−0.0799541	−	0.138485i	−0.903230	+	0.429157i	$0.858811\pi$
$888$		0			0
$889$	7.36230	−	12.7519i	0.246924	−	0.427685i
$890$	0.0649584			0.00217741
$891$		0			0
$892$	−15.1345			−0.506741
$893$	12.3717	−	21.4284i	0.414002	−	0.717073i
$894$		0			0
$895$	−7.81580	−	13.5374i	−0.261253	−	0.452504i
$896$	−2.63399	−	4.56220i	−0.0879953	−	0.152412i
$897$		0			0
$898$	−0.919706	+	1.59298i	−0.0306910	+	0.0531584i
$899$	−17.6040			−0.587126
$900$		0			0
$901$	−59.6946			−1.98871
$902$	−0.273106	+	0.473033i	−0.00909343	+	0.0157503i
$903$		0			0
$904$	−0.987692	−	1.71073i	−0.0328501	−	0.0568981i
$905$	−5.55163	−	9.61571i	−0.184543	−	0.319637i
$906$		0			0
$907$	11.5731	−	20.0452i	0.384278	−	0.665589i	−0.607391	−	0.794403i	$-0.707784\pi$
$907$	11.5731	−	20.0452i	0.384278	−	0.665589i	0.991669	+	0.128814i	$0.0411171\pi$
$908$	0.600715			0.0199354
$909$		0			0
$910$	0.165558			0.00548818
$911$	−5.77944	+	10.0103i	−0.191481	+	0.331655i	−0.945741	−	0.324920i	$-0.894662\pi$
$911$	−5.77944	+	10.0103i	−0.191481	+	0.331655i	0.754260	+	0.656576i	$0.227996\pi$
$912$		0			0
$913$	−16.8829	−	29.2420i	−0.558741	−	0.967768i
$914$	−0.821826	−	1.42344i	−0.0271836	−	0.0470834i
$915$		0			0
$916$	−4.62270	+	8.00676i	−0.152738	+	0.264551i
$917$	−44.0324			−1.45408
$918$		0			0
$919$	−45.9902			−1.51708			−0.758538	−	0.651629i	$-0.774086\pi$
$919$	−45.9902			−1.51708			−0.758538	+	0.651629i	$0.774086\pi$
$920$	0.573228	−	0.992860i	0.0188988	−	0.0327336i
$921$		0			0
$922$	−0.294370	−	0.509864i	−0.00969456	−	0.0167915i
$923$	−3.89612	−	6.74828i	−0.128242	−	0.222122i
$924$		0			0
$925$	−2.43647	+	4.22008i	−0.0801105	+	0.138756i
$926$	−1.01497			−0.0333539
$927$		0			0
$928$	−1.85425			−0.0608689
$929$	21.3396	−	36.9613i	0.700130	−	1.21266i	−0.268291	−	0.963338i	$-0.586459\pi$
$929$	21.3396	−	36.9613i	0.700130	−	1.21266i	0.968421	−	0.249322i	$-0.0802079\pi$
$930$		0			0
$931$	−1.83790	−	3.18333i	−0.0602346	−	0.104329i
$932$	−5.61169	−	9.71974i	−0.183817	−	0.318381i
$933$		0			0
$934$	0.656847	−	1.13769i	0.0214927	−	0.0372264i
$935$	−15.3437			−0.501792
$936$		0			0
$937$	−47.1687			−1.54093			−0.770467	−	0.637480i	$-0.779977\pi$
$937$	−47.1687			−1.54093			−0.770467	+	0.637480i	$0.779977\pi$
$938$	−1.11811	+	1.93662i	−0.0365075	+	0.0632328i
$939$		0			0
$940$	6.25152	+	10.8280i	0.203902	+	0.353169i
$941$	20.0891	+	34.7954i	0.654887	+	1.13430i	0.981922	+	0.189285i	$0.0606171\pi$
$941$	20.0891	+	34.7954i	0.654887	+	1.13430i	−0.327035	+	0.945012i	$0.606050\pi$
$942$		0			0
$943$	5.40204	−	9.35660i	0.175914	−	0.304693i
$944$	−11.3236			−0.368551
$945$		0			0
$946$	−0.985646			−0.0320461
$947$	−0.402966	+	0.697957i	−0.0130946	+	0.0226806i	−0.872498	−	0.488617i	$-0.837502\pi$
$947$	−0.402966	+	0.697957i	−0.0130946	+	0.0226806i	0.859404	+	0.511297i	$0.170835\pi$
$948$		0			0
$949$	1.13398	+	1.96411i	0.0368105	+	0.0637577i
$950$	−0.132692	−	0.229829i	−0.00430509	−	0.00745664i
$951$		0			0
$952$	−1.57988	+	2.73643i	−0.0512041	+	0.0886881i
$953$	8.33532			0.270007			0.135004	−	0.990845i	$-0.456895\pi$
$953$	8.33532			0.270007			0.135004	+	0.990845i	$0.456895\pi$
$954$		0			0
$955$	−15.5825			−0.504236
$956$	−2.55607	+	4.42724i	−0.0826691	+	0.143187i
$957$		0			0
$958$	−0.0439210	−	0.0760733i	−0.00141902	−	0.00245782i
$959$	12.9252	+	22.3871i	0.417377	+	0.722918i
$960$		0			0
$961$	−13.6317	+	23.6108i	−0.439732	+	0.761638i
$962$	0.327472			0.0105581
$963$		0			0
$964$	29.8983			0.962960
$965$	9.34800	−	16.1912i	0.300923	−	0.521214i
$966$		0			0
$967$	21.0963	+	36.5398i	0.678410	+	1.17504i	0.975459	+	0.220179i	$0.0706642\pi$
$967$	21.0963	+	36.5398i	0.678410	+	1.17504i	−0.297049	+	0.954862i	$0.596002\pi$
$968$	0.0915782	+	0.158618i	0.00294344	+	0.00509818i
$969$		0			0
$970$	−0.631042	+	1.09300i	−0.0202615	+	0.0350940i
$971$	−25.3293			−0.812856			−0.406428	−	0.913683i	$-0.633226\pi$
$971$	−25.3293			−0.812856			−0.406428	+	0.913683i	$0.633226\pi$
$972$		0			0
$973$	−26.3771			−0.845611
$974$	1.01990	−	1.76652i	0.0326798	−	0.0566031i
$975$		0			0
$976$	−25.2281	−	43.6963i	−0.807531	−	1.39868i
$977$	18.0466	+	31.2575i	0.577360	+	1.00002i	0.995781	+	0.0917641i	$0.0292506\pi$
$977$	18.0466	+	31.2575i	0.577360	+	1.00002i	−0.418420	+	0.908253i	$0.637416\pi$
$978$		0			0
$979$	−1.55245	+	2.68892i	−0.0496165	+	0.0859382i
$980$	1.85741			0.0593329
$981$		0			0
$982$	0.562964			0.0179649
$983$	−30.4781	+	52.7897i	−0.972102	+	1.68373i	−0.282916	+	0.959145i	$0.591302\pi$
$983$	−30.4781	+	52.7897i	−0.972102	+	1.68373i	−0.689186	+	0.724584i	$0.742032\pi$
$984$		0			0
$985$	−5.10122	−	8.83557i	−0.162538	−	0.281525i
$986$	0.370170	+	0.641154i	0.0117886	+	0.0204185i
$987$		0			0
$988$	3.94012	−	6.82448i	0.125352	−	0.217116i
$989$	19.4961			0.619939
$990$		0			0
$991$	56.5677			1.79693			0.898466	−	0.439042i	$-0.144682\pi$
$991$	56.5677			1.79693			0.898466	+	0.439042i	$0.144682\pi$
$992$	−3.06848	+	5.31477i	−0.0974244	+	0.168744i
$993$		0			0
$994$	−0.645032	−	1.11723i	−0.0204592	−	0.0354363i
$995$	8.23991	+	14.2719i	0.261223	+	0.452451i
$996$		0			0
$997$	1.18890	−	2.05924i	0.0376530	−	0.0652169i	−0.846585	−	0.532254i	$-0.821345\pi$
$997$	1.18890	−	2.05924i	0.0376530	−	0.0652169i	0.884238	+	0.467037i	$0.154679\pi$
$998$	−0.864237			−0.0273569
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1755.2.i.f.586.3		16
3.2	odd	2		585.2.i.e.196.6	✓	16
9.2	odd	6		5265.2.a.bf.1.3		8
9.4	even	3	inner	1755.2.i.f.1171.3		16
9.5	odd	6		585.2.i.e.391.6	yes	16
9.7	even	3		5265.2.a.ba.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.e.196.6	✓	16	3.2	odd	2
585.2.i.e.391.6	yes	16	9.5	odd	6
1755.2.i.f.586.3		16	1.1	even	1	trivial
1755.2.i.f.1171.3		16	9.4	even	3	inner
5265.2.a.ba.1.6		8	9.7	even	3
5265.2.a.bf.1.3		8	9.2	odd	6

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:	\( N \)	\(=\)	\( 1755 = 3^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1755.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0336011 - 0.0581988i) q^{2} +(0.997742 + 1.72814i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.23179 + 2.13352i) q^{7} +0.268505 q^{8} +O(q^{10})\)	\(q+(0.0336011 - 0.0581988i) q^{2} +(0.997742 + 1.72814i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.23179 + 2.13352i) q^{7} +0.268505 q^{8} -0.0672022 q^{10} +(1.60607 - 2.78180i) q^{11} +(0.500000 + 0.866025i) q^{13} +(0.0827788 + 0.143377i) q^{14} +(-1.98646 + 3.44065i) q^{16} +4.77678 q^{17} -3.94903 q^{19} +(0.997742 - 1.72814i) q^{20} +(-0.107932 - 0.186943i) q^{22} +(2.13489 + 3.69773i) q^{23} +(-0.500000 + 0.866025i) q^{25} +0.0672022 q^{26} -4.91602 q^{28} +(-1.15314 + 1.99730i) q^{29} +(3.81652 + 6.61041i) q^{31} +(0.402000 + 0.696284i) q^{32} +(0.160505 - 0.278003i) q^{34} +2.46357 q^{35} +4.87293 q^{37} +(-0.132692 + 0.229829i) q^{38} +(-0.134253 - 0.232532i) q^{40} +(-1.26518 - 2.19136i) q^{41} +(2.28304 - 3.95433i) q^{43} +6.40978 q^{44} +0.286938 q^{46} +(-3.13284 + 5.42623i) q^{47} +(0.465404 + 0.806103i) q^{49} +(0.0336011 + 0.0581988i) q^{50} +(-0.997742 + 1.72814i) q^{52} -12.4968 q^{53} -3.21214 q^{55} +(-0.330741 + 0.572861i) q^{56} +(0.0774937 + 0.134223i) q^{58} +(1.42509 + 2.46833i) q^{59} +(-6.35000 + 10.9985i) q^{61} +0.512957 q^{62} -7.89182 q^{64} +(0.500000 - 0.866025i) q^{65} +(6.75359 + 11.6976i) q^{67} +(4.76599 + 8.25494i) q^{68} +(0.0827788 - 0.143377i) q^{70} -7.79224 q^{71} +2.26796 q^{73} +(0.163736 - 0.283599i) q^{74} +(-3.94012 - 6.82448i) q^{76} +(3.95668 + 6.85316i) q^{77} +(-4.56668 + 7.90972i) q^{79} +3.97292 q^{80} -0.170046 q^{82} +(5.25595 - 9.10356i) q^{83} +(-2.38839 - 4.13681i) q^{85} +(-0.153425 - 0.265740i) q^{86} +(0.431239 - 0.746927i) q^{88} -0.966612 q^{89} -2.46357 q^{91} +(-4.26013 + 7.37876i) q^{92} +(0.210533 + 0.364655i) q^{94} +(1.97452 + 3.41996i) q^{95} +(9.39020 - 16.2643i) q^{97} +0.0625523 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8}+O(q^{10}) \) 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8	\( 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8} - 6 q^{10} + 6 q^{11} + 8 q^{13} + 10 q^{14} - 11 q^{16} + 4 q^{17} - 20 q^{19} - 9 q^{20} - 3 q^{22} + 6 q^{23} - 8 q^{25} + 6 q^{26} - 68 q^{28} + 14 q^{29} + 31 q^{31} + q^{32} + 7 q^{34} - 22 q^{35} + 2 q^{37} + 9 q^{38} - 6 q^{40} - 12 q^{41} - 15 q^{43} - 32 q^{44} - 64 q^{46} - 18 q^{47} - 17 q^{49} + 3 q^{50} + 9 q^{52} - 4 q^{53} - 12 q^{55} + 16 q^{56} + 42 q^{58} + 24 q^{59} + 9 q^{61} + 40 q^{62} - 60 q^{64} + 8 q^{65} + 18 q^{67} - 14 q^{68} + 10 q^{70} - 20 q^{71} + 12 q^{73} - 37 q^{74} + 53 q^{76} - 34 q^{77} + 3 q^{79} + 22 q^{80} - 68 q^{82} - 10 q^{83} - 2 q^{85} + 60 q^{86} + 14 q^{88} + 26 q^{89} + 22 q^{91} + 5 q^{92} - 17 q^{94} + 10 q^{95} + 34 q^{97} + 60 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8 - 6 * q^10 + 6 * q^11 + 8 * q^13 + 10 * q^14 - 11 * q^16 + 4 * q^17 - 20 * q^19 - 9 * q^20 - 3 * q^22 + 6 * q^23 - 8 * q^25 + 6 * q^26 - 68 * q^28 + 14 * q^29 + 31 * q^31 + q^32 + 7 * q^34 - 22 * q^35 + 2 * q^37 + 9 * q^38 - 6 * q^40 - 12 * q^41 - 15 * q^43 - 32 * q^44 - 64 * q^46 - 18 * q^47 - 17 * q^49 + 3 * q^50 + 9 * q^52 - 4 * q^53 - 12 * q^55 + 16 * q^56 + 42 * q^58 + 24 * q^59 + 9 * q^61 + 40 * q^62 - 60 * q^64 + 8 * q^65 + 18 * q^67 - 14 * q^68 + 10 * q^70 - 20 * q^71 + 12 * q^73 - 37 * q^74 + 53 * q^76 - 34 * q^77 + 3 * q^79 + 22 * q^80 - 68 * q^82 - 10 * q^83 - 2 * q^85 + 60 * q^86 + 14 * q^88 + 26 * q^89 + 22 * q^91 + 5 * q^92 - 17 * q^94 + 10 * q^95 + 34 * q^97 + 60 * q^98

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