LMFDB - Embedded newform 435.2.f.a.289.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [435,2,Mod(289,435)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("435.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(435, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	435.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-4,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.47349248793$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			289.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	435.289
Dual form			435.2.f.a.289.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{2} +1.00000 q^{3} +2.00000 q^{4} +(2.00000 - 1.00000i) q^{5} -2.00000 q^{6} -4.00000i q^{7} +1.00000 q^{9} +(-4.00000 + 2.00000i) q^{10} -1.00000i q^{11} +2.00000 q^{12} -2.00000i q^{13} +8.00000i q^{14} +(2.00000 - 1.00000i) q^{15} -4.00000 q^{16} -6.00000 q^{17} -2.00000 q^{18} -4.00000i q^{19} +(4.00000 - 2.00000i) q^{20} -4.00000i q^{21} +2.00000i q^{22} +9.00000i q^{23} +(3.00000 - 4.00000i) q^{25} +4.00000i q^{26} +1.00000 q^{27} -8.00000i q^{28} +(-2.00000 + 5.00000i) q^{29} +(-4.00000 + 2.00000i) q^{30} -2.00000i q^{31} +8.00000 q^{32} -1.00000i q^{33} +12.0000 q^{34} +(-4.00000 - 8.00000i) q^{35} +2.00000 q^{36} -1.00000 q^{37} +8.00000i q^{38} -2.00000i q^{39} -9.00000i q^{41} +8.00000i q^{42} -1.00000 q^{43} -2.00000i q^{44} +(2.00000 - 1.00000i) q^{45} -18.0000i q^{46} +8.00000 q^{47} -4.00000 q^{48} -9.00000 q^{49} +(-6.00000 + 8.00000i) q^{50} -6.00000 q^{51} -4.00000i q^{52} -9.00000i q^{53} -2.00000 q^{54} +(-1.00000 - 2.00000i) q^{55} -4.00000i q^{57} +(4.00000 - 10.0000i) q^{58} +8.00000 q^{59} +(4.00000 - 2.00000i) q^{60} -6.00000i q^{61} +4.00000i q^{62} -4.00000i q^{63} -8.00000 q^{64} +(-2.00000 - 4.00000i) q^{65} +2.00000i q^{66} +12.0000i q^{67} -12.0000 q^{68} +9.00000i q^{69} +(8.00000 + 16.0000i) q^{70} +2.00000 q^{71} +15.0000 q^{73} +2.00000 q^{74} +(3.00000 - 4.00000i) q^{75} -8.00000i q^{76} -4.00000 q^{77} +4.00000i q^{78} +4.00000i q^{79} +(-8.00000 + 4.00000i) q^{80} +1.00000 q^{81} +18.0000i q^{82} +7.00000i q^{83} -8.00000i q^{84} +(-12.0000 + 6.00000i) q^{85} +2.00000 q^{86} +(-2.00000 + 5.00000i) q^{87} +2.00000i q^{89} +(-4.00000 + 2.00000i) q^{90} -8.00000 q^{91} +18.0000i q^{92} -2.00000i q^{93} -16.0000 q^{94} +(-4.00000 - 8.00000i) q^{95} +8.00000 q^{96} +11.0000 q^{97} +18.0000 q^{98} -1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} + 2 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} + 2 q^{9} - 8 q^{10} + 4 q^{12} + 4 q^{15} - 8 q^{16} - 12 q^{17} - 4 q^{18} + 8 q^{20} + 6 q^{25} + 2 q^{27} - 4 q^{29} - 8 q^{30} + 16 q^{32} + 24 q^{34}+ \cdots + 36 q^{98}+O(q^{100}) $ 2 * q - 4 * q^2 + 2 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 + 2 * q^9 - 8 * q^10 + 4 * q^12 + 4 * q^15 - 8 * q^16 - 12 * q^17 - 4 * q^18 + 8 * q^20 + 6 * q^25 + 2 * q^27 - 4 * q^29 - 8 * q^30 + 16 * q^32 + 24 * q^34 - 8 * q^35 + 4 * q^36 - 2 * q^37 - 2 * q^43 + 4 * q^45 + 16 * q^47 - 8 * q^48 - 18 * q^49 - 12 * q^50 - 12 * q^51 - 4 * q^54 - 2 * q^55 + 8 * q^58 + 16 * q^59 + 8 * q^60 - 16 * q^64 - 4 * q^65 - 24 * q^68 + 16 * q^70 + 4 * q^71 + 30 * q^73 + 4 * q^74 + 6 * q^75 - 8 * q^77 - 16 * q^80 + 2 * q^81 - 24 * q^85 + 4 * q^86 - 4 * q^87 - 8 * q^90 - 16 * q^91 - 32 * q^94 - 8 * q^95 + 16 * q^96 + 22 * q^97 + 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/435\mathbb{Z}\right)^\times$.

$n$	$31$	$146$	$262$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−2.00000			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$2$	−2.00000			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	2.00000			1.00000
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$6$	−2.00000			−0.816497
$7$		−	4.00000i		−	1.51186i	−0.654654	−	0.755929i	$-0.727186\pi$
$7$		−	4.00000i		−	1.51186i	0.654654	−	0.755929i	$-0.272814\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$	−4.00000	+	2.00000i	−1.26491	+	0.632456i
$11$		−	1.00000i		−	0.301511i	−0.988571	−	0.150756i	$-0.951829\pi$
$11$		−	1.00000i		−	0.301511i	0.988571	−	0.150756i	$-0.0481707\pi$
$12$	2.00000			0.577350
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$			8.00000i			2.13809i
$15$	2.00000	−	1.00000i	0.516398	−	0.258199i
$16$	−4.00000			−1.00000
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$	−2.00000			−0.471405
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$	4.00000	−	2.00000i	0.894427	−	0.447214i
$21$		−	4.00000i		−	0.872872i
$22$			2.00000i			0.426401i
$23$			9.00000i			1.87663i	0.345782	+	0.938315i	$0.387614\pi$
$23$			9.00000i			1.87663i	−0.345782	+	0.938315i	$0.612386\pi$
$24$		0			0
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$			4.00000i			0.784465i
$27$	1.00000			0.192450
$28$		−	8.00000i		−	1.51186i
$29$	−2.00000	+	5.00000i	−0.371391	+	0.928477i
$29$	−2.00000	+	5.00000i	−0.371391	+	0.928477i
$30$	−4.00000	+	2.00000i	−0.730297	+	0.365148i
$31$		−	2.00000i		−	0.359211i	−0.983739	−	0.179605i	$-0.942518\pi$
$31$		−	2.00000i		−	0.359211i	0.983739	−	0.179605i	$-0.0574821\pi$
$32$	8.00000			1.41421
$33$		−	1.00000i		−	0.174078i
$34$	12.0000			2.05798
$35$	−4.00000	−	8.00000i	−0.676123	−	1.35225i
$36$	2.00000			0.333333
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$			8.00000i			1.29777i
$39$		−	2.00000i		−	0.320256i
$40$		0			0
$41$		−	9.00000i		−	1.40556i	−0.711405	−	0.702782i	$-0.751941\pi$
$41$		−	9.00000i		−	1.40556i	0.711405	−	0.702782i	$-0.248059\pi$
$42$			8.00000i			1.23443i
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$		−	2.00000i		−	0.301511i
$45$	2.00000	−	1.00000i	0.298142	−	0.149071i
$46$		−	18.0000i		−	2.65396i
$47$	8.00000			1.16692			0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000			1.16692			0.583460	+	0.812142i	$0.301699\pi$
$48$	−4.00000			−0.577350
$49$	−9.00000			−1.28571
$50$	−6.00000	+	8.00000i	−0.848528	+	1.13137i
$51$	−6.00000			−0.840168
$52$		−	4.00000i		−	0.554700i
$53$		−	9.00000i		−	1.23625i	−0.786082	−	0.618123i	$-0.787894\pi$
$53$		−	9.00000i		−	1.23625i	0.786082	−	0.618123i	$-0.212106\pi$
$54$	−2.00000			−0.272166
$55$	−1.00000	−	2.00000i	−0.134840	−	0.269680i
$56$		0			0
$57$		−	4.00000i		−	0.529813i
$58$	4.00000	−	10.0000i	0.525226	−	1.31306i
$59$	8.00000			1.04151			0.520756	−	0.853706i	$-0.325650\pi$
$59$	8.00000			1.04151			0.520756	+	0.853706i	$0.325650\pi$
$60$	4.00000	−	2.00000i	0.516398	−	0.258199i
$61$		−	6.00000i		−	0.768221i	−0.923287	−	0.384111i	$-0.874508\pi$
$61$		−	6.00000i		−	0.768221i	0.923287	−	0.384111i	$-0.125492\pi$
$62$			4.00000i			0.508001i
$63$		−	4.00000i		−	0.503953i
$64$	−8.00000			−1.00000
$65$	−2.00000	−	4.00000i	−0.248069	−	0.496139i
$66$			2.00000i			0.246183i
$67$			12.0000i			1.46603i	0.680211	+	0.733017i	$0.261888\pi$
$67$			12.0000i			1.46603i	−0.680211	+	0.733017i	$0.738112\pi$
$68$	−12.0000			−1.45521
$69$			9.00000i			1.08347i
$70$	8.00000	+	16.0000i	0.956183	+	1.91237i
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$		0			0
$73$	15.0000			1.75562			0.877809	−	0.479012i	$-0.159005\pi$
$73$	15.0000			1.75562			0.877809	+	0.479012i	$0.159005\pi$
$74$	2.00000			0.232495
$75$	3.00000	−	4.00000i	0.346410	−	0.461880i
$76$		−	8.00000i		−	0.917663i
$77$	−4.00000			−0.455842
$78$			4.00000i			0.452911i
$79$			4.00000i			0.450035i	0.974355	+	0.225018i	$0.0722440\pi$
$79$			4.00000i			0.450035i	−0.974355	+	0.225018i	$0.927756\pi$
$80$	−8.00000	+	4.00000i	−0.894427	+	0.447214i
$81$	1.00000			0.111111
$82$			18.0000i			1.98777i
$83$			7.00000i			0.768350i	0.923260	+	0.384175i	$0.125514\pi$
$83$			7.00000i			0.768350i	−0.923260	+	0.384175i	$0.874486\pi$
$84$		−	8.00000i		−	0.872872i
$85$	−12.0000	+	6.00000i	−1.30158	+	0.650791i
$86$	2.00000			0.215666
$87$	−2.00000	+	5.00000i	−0.214423	+	0.536056i
$88$		0			0
$89$			2.00000i			0.212000i	0.994366	+	0.106000i	$0.0338043\pi$
$89$			2.00000i			0.212000i	−0.994366	+	0.106000i	$0.966196\pi$
$90$	−4.00000	+	2.00000i	−0.421637	+	0.210819i
$91$	−8.00000			−0.838628
$92$			18.0000i			1.87663i
$93$		−	2.00000i		−	0.207390i
$94$	−16.0000			−1.65027
$95$	−4.00000	−	8.00000i	−0.410391	−	0.820783i
$96$	8.00000			0.816497
$97$	11.0000			1.11688			0.558440	−	0.829545i	$-0.311400\pi$
$97$	11.0000			1.11688			0.558440	+	0.829545i	$0.311400\pi$
$98$	18.0000			1.81827
$99$		−	1.00000i		−	0.100504i
$100$	6.00000	−	8.00000i	0.600000	−	0.800000i
$101$			3.00000i			0.298511i	0.988799	+	0.149256i	$0.0476877\pi$
$101$			3.00000i			0.298511i	−0.988799	+	0.149256i	$0.952312\pi$
$102$	12.0000			1.18818
$103$			6.00000i			0.591198i	0.955312	+	0.295599i	$0.0955191\pi$
$103$			6.00000i			0.591198i	−0.955312	+	0.295599i	$0.904481\pi$
$104$		0			0
$105$	−4.00000	−	8.00000i	−0.390360	−	0.780720i
$106$			18.0000i			1.74831i
$107$		−	4.00000i		−	0.386695i	−0.981130	−	0.193347i	$-0.938066\pi$
$107$		−	4.00000i		−	0.386695i	0.981130	−	0.193347i	$-0.0619344\pi$
$108$	2.00000			0.192450
$109$	−1.00000			−0.0957826			−0.0478913	−	0.998853i	$-0.515250\pi$
$109$	−1.00000			−0.0957826			−0.0478913	+	0.998853i	$0.515250\pi$
$110$	2.00000	+	4.00000i	0.190693	+	0.381385i
$111$	−1.00000			−0.0949158
$112$			16.0000i			1.51186i
$113$	−8.00000			−0.752577			−0.376288	−	0.926503i	$-0.622800\pi$
$113$	−8.00000			−0.752577			−0.376288	+	0.926503i	$0.622800\pi$
$114$			8.00000i			0.749269i
$115$	9.00000	+	18.0000i	0.839254	+	1.67851i
$116$	−4.00000	+	10.0000i	−0.371391	+	0.928477i
$117$		−	2.00000i		−	0.184900i
$118$	−16.0000			−1.47292
$119$			24.0000i			2.20008i
$120$		0			0
$121$	10.0000			0.909091
$122$			12.0000i			1.08643i
$123$		−	9.00000i		−	0.811503i
$124$		−	4.00000i		−	0.359211i
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$			8.00000i			0.712697i
$127$	7.00000			0.621150			0.310575	−	0.950549i	$-0.399478\pi$
$127$	7.00000			0.621150			0.310575	+	0.950549i	$0.399478\pi$
$128$		0			0
$129$	−1.00000			−0.0880451
$130$	4.00000	+	8.00000i	0.350823	+	0.701646i
$131$			20.0000i			1.74741i	0.486458	+	0.873704i	$0.338289\pi$
$131$			20.0000i			1.74741i	−0.486458	+	0.873704i	$0.661711\pi$
$132$		−	2.00000i		−	0.174078i
$133$	−16.0000			−1.38738
$134$		−	24.0000i		−	2.07328i
$135$	2.00000	−	1.00000i	0.172133	−	0.0860663i
$136$		0			0
$137$	−16.0000			−1.36697			−0.683486	−	0.729964i	$-0.739537\pi$
$137$	−16.0000			−1.36697			−0.683486	+	0.729964i	$0.739537\pi$
$138$		−	18.0000i		−	1.53226i
$139$	11.0000			0.933008			0.466504	−	0.884519i	$-0.345513\pi$
$139$	11.0000			0.933008			0.466504	+	0.884519i	$0.345513\pi$
$140$	−8.00000	−	16.0000i	−0.676123	−	1.35225i
$141$	8.00000			0.673722
$142$	−4.00000			−0.335673
$143$	−2.00000			−0.167248
$144$	−4.00000			−0.333333
$145$	1.00000	+	12.0000i	0.0830455	+	0.996546i
$146$	−30.0000			−2.48282
$147$	−9.00000			−0.742307
$148$	−2.00000			−0.164399
$149$	14.0000			1.14692			0.573462	−	0.819232i	$-0.305600\pi$
$149$	14.0000			1.14692			0.573462	+	0.819232i	$0.305600\pi$
$150$	−6.00000	+	8.00000i	−0.489898	+	0.653197i
$151$	−17.0000			−1.38344			−0.691720	−	0.722166i	$-0.743147\pi$
$151$	−17.0000			−1.38344			−0.691720	+	0.722166i	$0.743147\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$	8.00000			0.644658
$155$	−2.00000	−	4.00000i	−0.160644	−	0.321288i
$156$		−	4.00000i		−	0.320256i
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$		−	8.00000i		−	0.636446i
$159$		−	9.00000i		−	0.713746i
$160$	16.0000	−	8.00000i	1.26491	−	0.632456i
$161$	36.0000			2.83720
$162$	−2.00000			−0.157135
$163$	−13.0000			−1.01824			−0.509119	−	0.860696i	$-0.670029\pi$
$163$	−13.0000			−1.01824			−0.509119	+	0.860696i	$0.670029\pi$
$164$		−	18.0000i		−	1.40556i
$165$	−1.00000	−	2.00000i	−0.0778499	−	0.155700i
$166$		−	14.0000i		−	1.08661i
$167$		−	24.0000i		−	1.85718i	−0.371113	−	0.928588i	$-0.621024\pi$
$167$		−	24.0000i		−	1.85718i	0.371113	−	0.928588i	$-0.378976\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$	24.0000	−	12.0000i	1.84072	−	0.920358i
$171$		−	4.00000i		−	0.305888i
$172$	−2.00000			−0.152499
$173$			21.0000i			1.59660i	0.602260	+	0.798300i	$0.294267\pi$
$173$			21.0000i			1.59660i	−0.602260	+	0.798300i	$0.705733\pi$
$174$	4.00000	−	10.0000i	0.303239	−	0.758098i
$175$	−16.0000	−	12.0000i	−1.20949	−	0.907115i
$176$			4.00000i			0.301511i
$177$	8.00000			0.601317
$178$		−	4.00000i		−	0.299813i
$179$	6.00000			0.448461			0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000			0.448461			0.224231	+	0.974536i	$0.428013\pi$
$180$	4.00000	−	2.00000i	0.298142	−	0.149071i
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$	16.0000			1.18600
$183$		−	6.00000i		−	0.443533i
$184$		0			0
$185$	−2.00000	+	1.00000i	−0.147043	+	0.0735215i
$186$			4.00000i			0.293294i
$187$			6.00000i			0.438763i
$188$	16.0000			1.16692
$189$		−	4.00000i		−	0.290957i
$190$	8.00000	+	16.0000i	0.580381	+	1.16076i
$191$			3.00000i			0.217072i	0.994092	+	0.108536i	$0.0346163\pi$
$191$			3.00000i			0.217072i	−0.994092	+	0.108536i	$0.965384\pi$
$192$	−8.00000			−0.577350
$193$	6.00000			0.431889			0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000			0.431889			0.215945	+	0.976406i	$0.430717\pi$
$194$	−22.0000			−1.57951
$195$	−2.00000	−	4.00000i	−0.143223	−	0.286446i
$196$	−18.0000			−1.28571
$197$		−	23.0000i		−	1.63868i	−0.573306	−	0.819341i	$-0.694340\pi$
$197$		−	23.0000i		−	1.63868i	0.573306	−	0.819341i	$-0.305660\pi$
$198$			2.00000i			0.142134i
$199$	−19.0000			−1.34687			−0.673437	−	0.739244i	$-0.735183\pi$
$199$	−19.0000			−1.34687			−0.673437	+	0.739244i	$0.735183\pi$
$200$		0			0
$201$			12.0000i			0.846415i
$202$		−	6.00000i		−	0.422159i
$203$	20.0000	+	8.00000i	1.40372	+	0.561490i
$204$	−12.0000			−0.840168
$205$	−9.00000	−	18.0000i	−0.628587	−	1.25717i
$206$		−	12.0000i		−	0.836080i
$207$			9.00000i			0.625543i
$208$			8.00000i			0.554700i
$209$	−4.00000			−0.276686
$210$	8.00000	+	16.0000i	0.552052	+	1.10410i
$211$			2.00000i			0.137686i	0.997628	+	0.0688428i	$0.0219307\pi$
$211$			2.00000i			0.137686i	−0.997628	+	0.0688428i	$0.978069\pi$
$212$		−	18.0000i		−	1.23625i
$213$	2.00000			0.137038
$214$			8.00000i			0.546869i
$215$	−2.00000	+	1.00000i	−0.136399	+	0.0681994i
$216$		0			0
$217$	−8.00000			−0.543075
$218$	2.00000			0.135457
$219$	15.0000			1.01361
$220$	−2.00000	−	4.00000i	−0.134840	−	0.269680i
$221$			12.0000i			0.807207i
$222$	2.00000			0.134231
$223$		−	4.00000i		−	0.267860i	−0.990991	−	0.133930i	$-0.957240\pi$
$223$		−	4.00000i		−	0.267860i	0.990991	−	0.133930i	$-0.0427597\pi$
$224$		−	32.0000i		−	2.13809i
$225$	3.00000	−	4.00000i	0.200000	−	0.266667i
$226$	16.0000			1.06430
$227$			7.00000i			0.464606i	0.972643	+	0.232303i	$0.0746261\pi$
$227$			7.00000i			0.464606i	−0.972643	+	0.232303i	$0.925374\pi$
$228$		−	8.00000i		−	0.529813i
$229$		−	4.00000i		−	0.264327i	−0.991228	−	0.132164i	$-0.957808\pi$
$229$		−	4.00000i		−	0.264327i	0.991228	−	0.132164i	$-0.0421925\pi$
$230$	−18.0000	−	36.0000i	−1.18688	−	2.37377i
$231$	−4.00000			−0.263181
$232$		0			0
$233$			1.00000i			0.0655122i	0.999463	+	0.0327561i	$0.0104285\pi$
$233$			1.00000i			0.0655122i	−0.999463	+	0.0327561i	$0.989572\pi$
$234$			4.00000i			0.261488i
$235$	16.0000	−	8.00000i	1.04372	−	0.521862i
$236$	16.0000			1.04151
$237$			4.00000i			0.259828i
$238$		−	48.0000i		−	3.11138i
$239$	−26.0000			−1.68180			−0.840900	−	0.541190i	$-0.817974\pi$
$239$	−26.0000			−1.68180			−0.840900	+	0.541190i	$0.817974\pi$
$240$	−8.00000	+	4.00000i	−0.516398	+	0.258199i
$241$	11.0000			0.708572			0.354286	−	0.935137i	$-0.384724\pi$
$241$	11.0000			0.708572			0.354286	+	0.935137i	$0.384724\pi$
$242$	−20.0000			−1.28565
$243$	1.00000			0.0641500
$244$		−	12.0000i		−	0.768221i
$245$	−18.0000	+	9.00000i	−1.14998	+	0.574989i
$246$			18.0000i			1.14764i
$247$	−8.00000			−0.509028
$248$		0			0
$249$			7.00000i			0.443607i
$250$	−4.00000	+	22.0000i	−0.252982	+	1.39140i
$251$		−	12.0000i		−	0.757433i	−0.925513	−	0.378717i	$-0.876365\pi$
$251$		−	12.0000i		−	0.757433i	0.925513	−	0.378717i	$-0.123635\pi$
$252$		−	8.00000i		−	0.503953i
$253$	9.00000			0.565825
$254$	−14.0000			−0.878438
$255$	−12.0000	+	6.00000i	−0.751469	+	0.375735i
$256$	16.0000			1.00000
$257$			15.0000i			0.935674i	0.883815	+	0.467837i	$0.154967\pi$
$257$			15.0000i			0.935674i	−0.883815	+	0.467837i	$0.845033\pi$
$258$	2.00000			0.124515
$259$			4.00000i			0.248548i
$260$	−4.00000	−	8.00000i	−0.248069	−	0.496139i
$261$	−2.00000	+	5.00000i	−0.123797	+	0.309492i
$262$		−	40.0000i		−	2.47121i
$263$	26.0000			1.60323			0.801614	−	0.597841i	$-0.203975\pi$
$263$	26.0000			1.60323			0.801614	+	0.597841i	$0.203975\pi$
$264$		0			0
$265$	−9.00000	−	18.0000i	−0.552866	−	1.10573i
$266$	32.0000			1.96205
$267$			2.00000i			0.122398i
$268$			24.0000i			1.46603i
$269$			10.0000i			0.609711i	0.952399	+	0.304855i	$0.0986081\pi$
$269$			10.0000i			0.609711i	−0.952399	+	0.304855i	$0.901392\pi$
$270$	−4.00000	+	2.00000i	−0.243432	+	0.121716i
$271$		−	2.00000i		−	0.121491i	−0.998153	−	0.0607457i	$-0.980652\pi$
$271$		−	2.00000i		−	0.121491i	0.998153	−	0.0607457i	$-0.0193479\pi$
$272$	24.0000			1.45521
$273$	−8.00000			−0.484182
$274$	32.0000			1.93319
$275$	−4.00000	−	3.00000i	−0.241209	−	0.180907i
$276$			18.0000i			1.08347i
$277$			2.00000i			0.120168i	0.998193	+	0.0600842i	$0.0191369\pi$
$277$			2.00000i			0.120168i	−0.998193	+	0.0600842i	$0.980863\pi$
$278$	−22.0000			−1.31947
$279$		−	2.00000i		−	0.119737i
$280$		0			0
$281$	−24.0000			−1.43172			−0.715860	−	0.698244i	$-0.753965\pi$
$281$	−24.0000			−1.43172			−0.715860	+	0.698244i	$0.753965\pi$
$282$	−16.0000			−0.952786
$283$			22.0000i			1.30776i	0.756596	+	0.653882i	$0.226861\pi$
$283$			22.0000i			1.30776i	−0.756596	+	0.653882i	$0.773139\pi$
$284$	4.00000			0.237356
$285$	−4.00000	−	8.00000i	−0.236940	−	0.473879i
$286$	4.00000			0.236525
$287$	−36.0000			−2.12501
$288$	8.00000			0.471405
$289$	19.0000			1.11765
$290$	−2.00000	−	24.0000i	−0.117444	−	1.40933i
$291$	11.0000			0.644831
$292$	30.0000			1.75562
$293$	2.00000			0.116841			0.0584206	−	0.998292i	$-0.481394\pi$
$293$	2.00000			0.116841			0.0584206	+	0.998292i	$0.481394\pi$
$294$	18.0000			1.04978
$295$	16.0000	−	8.00000i	0.931556	−	0.465778i
$296$		0			0
$297$		−	1.00000i		−	0.0580259i
$298$	−28.0000			−1.62200
$299$	18.0000			1.04097
$300$	6.00000	−	8.00000i	0.346410	−	0.461880i
$301$			4.00000i			0.230556i
$302$	34.0000			1.95648
$303$			3.00000i			0.172345i
$304$			16.0000i			0.917663i
$305$	−6.00000	−	12.0000i	−0.343559	−	0.687118i
$306$	12.0000			0.685994
$307$	15.0000			0.856095			0.428048	−	0.903756i	$-0.359202\pi$
$307$	15.0000			0.856095			0.428048	+	0.903756i	$0.359202\pi$
$308$	−8.00000			−0.455842
$309$			6.00000i			0.341328i
$310$	4.00000	+	8.00000i	0.227185	+	0.454369i
$311$			23.0000i			1.30421i	0.758129	+	0.652105i	$0.226114\pi$
$311$			23.0000i			1.30421i	−0.758129	+	0.652105i	$0.773886\pi$
$312$		0			0
$313$		−	8.00000i		−	0.452187i	−0.974106	−	0.226093i	$-0.927405\pi$
$313$		−	8.00000i		−	0.452187i	0.974106	−	0.226093i	$-0.0725954\pi$
$314$	−28.0000			−1.58013
$315$	−4.00000	−	8.00000i	−0.225374	−	0.450749i
$316$			8.00000i			0.450035i
$317$	−12.0000			−0.673987			−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000			−0.673987			−0.336994	+	0.941507i	$0.609410\pi$
$318$			18.0000i			1.00939i
$319$	5.00000	+	2.00000i	0.279946	+	0.111979i
$320$	−16.0000	+	8.00000i	−0.894427	+	0.447214i
$321$		−	4.00000i		−	0.223258i
$322$	−72.0000			−4.01240
$323$			24.0000i			1.33540i
$324$	2.00000			0.111111
$325$	−8.00000	−	6.00000i	−0.443760	−	0.332820i
$326$	26.0000			1.44001
$327$	−1.00000			−0.0553001
$328$		0			0
$329$		−	32.0000i		−	1.76422i
$330$	2.00000	+	4.00000i	0.110096	+	0.220193i
$331$			32.0000i			1.75888i	0.476011	+	0.879440i	$0.342082\pi$
$331$			32.0000i			1.75888i	−0.476011	+	0.879440i	$0.657918\pi$
$332$			14.0000i			0.768350i
$333$	−1.00000			−0.0547997
$334$			48.0000i			2.62644i
$335$	12.0000	+	24.0000i	0.655630	+	1.31126i
$336$			16.0000i			0.872872i
$337$	−10.0000			−0.544735			−0.272367	−	0.962193i	$-0.587807\pi$
$337$	−10.0000			−0.544735			−0.272367	+	0.962193i	$0.587807\pi$
$338$	−18.0000			−0.979071
$339$	−8.00000			−0.434500
$340$	−24.0000	+	12.0000i	−1.30158	+	0.650791i
$341$	−2.00000			−0.108306
$342$			8.00000i			0.432590i
$343$			8.00000i			0.431959i
$344$		0			0
$345$	9.00000	+	18.0000i	0.484544	+	0.969087i
$346$		−	42.0000i		−	2.25793i
$347$		−	19.0000i		−	1.01997i	−0.860182	−	0.509987i	$-0.829650\pi$
$347$		−	19.0000i		−	1.01997i	0.860182	−	0.509987i	$-0.170350\pi$
$348$	−4.00000	+	10.0000i	−0.214423	+	0.536056i
$349$	−11.0000			−0.588817			−0.294408	−	0.955680i	$-0.595123\pi$
$349$	−11.0000			−0.588817			−0.294408	+	0.955680i	$0.595123\pi$
$350$	32.0000	+	24.0000i	1.71047	+	1.28285i
$351$		−	2.00000i		−	0.106752i
$352$		−	8.00000i		−	0.426401i
$353$			18.0000i			0.958043i	0.877803	+	0.479022i	$0.159008\pi$
$353$			18.0000i			0.958043i	−0.877803	+	0.479022i	$0.840992\pi$
$354$	−16.0000			−0.850390
$355$	4.00000	−	2.00000i	0.212298	−	0.106149i
$356$			4.00000i			0.212000i
$357$			24.0000i			1.27021i
$358$	−12.0000			−0.634220
$359$			21.0000i			1.10834i	0.832404	+	0.554169i	$0.186964\pi$
$359$			21.0000i			1.10834i	−0.832404	+	0.554169i	$0.813036\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	14.0000			0.735824
$363$	10.0000			0.524864
$364$	−16.0000			−0.838628
$365$	30.0000	−	15.0000i	1.57027	−	0.785136i
$366$			12.0000i			0.627250i
$367$	27.0000			1.40939			0.704694	−	0.709511i	$-0.251084\pi$
$367$	27.0000			1.40939			0.704694	+	0.709511i	$0.251084\pi$
$368$		−	36.0000i		−	1.87663i
$369$		−	9.00000i		−	0.468521i
$370$	4.00000	−	2.00000i	0.207950	−	0.103975i
$371$	−36.0000			−1.86903
$372$		−	4.00000i		−	0.207390i
$373$			2.00000i			0.103556i	0.998659	+	0.0517780i	$0.0164888\pi$
$373$			2.00000i			0.103556i	−0.998659	+	0.0517780i	$0.983511\pi$
$374$		−	12.0000i		−	0.620505i
$375$	2.00000	−	11.0000i	0.103280	−	0.568038i
$376$		0			0
$377$	10.0000	+	4.00000i	0.515026	+	0.206010i
$378$			8.00000i			0.411476i
$379$			22.0000i			1.13006i	0.825069	+	0.565032i	$0.191136\pi$
$379$			22.0000i			1.13006i	−0.825069	+	0.565032i	$0.808864\pi$
$380$	−8.00000	−	16.0000i	−0.410391	−	0.820783i
$381$	7.00000			0.358621
$382$		−	6.00000i		−	0.306987i
$383$			27.0000i			1.37964i	0.723983	+	0.689818i	$0.242309\pi$
$383$			27.0000i			1.37964i	−0.723983	+	0.689818i	$0.757691\pi$
$384$		0			0
$385$	−8.00000	+	4.00000i	−0.407718	+	0.203859i
$386$	−12.0000			−0.610784
$387$	−1.00000			−0.0508329
$388$	22.0000			1.11688
$389$		−	3.00000i		−	0.152106i	−0.997104	−	0.0760530i	$-0.975768\pi$
$389$		−	3.00000i		−	0.152106i	0.997104	−	0.0760530i	$-0.0242318\pi$
$390$	4.00000	+	8.00000i	0.202548	+	0.405096i
$391$		−	54.0000i		−	2.73090i
$392$		0			0
$393$			20.0000i			1.00887i
$394$			46.0000i			2.31745i
$395$	4.00000	+	8.00000i	0.201262	+	0.402524i
$396$		−	2.00000i		−	0.100504i
$397$		−	16.0000i		−	0.803017i	−0.915855	−	0.401508i	$-0.868486\pi$
$397$		−	16.0000i		−	0.803017i	0.915855	−	0.401508i	$-0.131514\pi$
$398$	38.0000			1.90477
$399$	−16.0000			−0.801002
$400$	−12.0000	+	16.0000i	−0.600000	+	0.800000i
$401$	−12.0000			−0.599251			−0.299626	−	0.954057i	$-0.596862\pi$
$401$	−12.0000			−0.599251			−0.299626	+	0.954057i	$0.596862\pi$
$402$		−	24.0000i		−	1.19701i
$403$	−4.00000			−0.199254
$404$			6.00000i			0.298511i
$405$	2.00000	−	1.00000i	0.0993808	−	0.0496904i
$406$	−40.0000	−	16.0000i	−1.98517	−	0.794067i
$407$			1.00000i			0.0495682i
$408$		0			0
$409$		−	14.0000i		−	0.692255i	−0.938187	−	0.346128i	$-0.887496\pi$
$409$		−	14.0000i		−	0.692255i	0.938187	−	0.346128i	$-0.112504\pi$
$410$	18.0000	+	36.0000i	0.888957	+	1.77791i
$411$	−16.0000			−0.789222
$412$			12.0000i			0.591198i
$413$		−	32.0000i		−	1.57462i
$414$		−	18.0000i		−	0.884652i
$415$	7.00000	+	14.0000i	0.343616	+	0.687233i
$416$		−	16.0000i		−	0.784465i
$417$	11.0000			0.538672
$418$	8.00000			0.391293
$419$	30.0000			1.46560			0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000			1.46560			0.732798	+	0.680446i	$0.238214\pi$
$420$	−8.00000	−	16.0000i	−0.390360	−	0.780720i
$421$		−	22.0000i		−	1.07221i	−0.844150	−	0.536107i	$-0.819894\pi$
$421$		−	22.0000i		−	1.07221i	0.844150	−	0.536107i	$-0.180106\pi$
$422$		−	4.00000i		−	0.194717i
$423$	8.00000			0.388973
$424$		0			0
$425$	−18.0000	+	24.0000i	−0.873128	+	1.16417i
$426$	−4.00000			−0.193801
$427$	−24.0000			−1.16144
$428$		−	8.00000i		−	0.386695i
$429$	−2.00000			−0.0965609
$430$	4.00000	−	2.00000i	0.192897	−	0.0964486i
$431$	−6.00000			−0.289010			−0.144505	−	0.989504i	$-0.546159\pi$
$431$	−6.00000			−0.289010			−0.144505	+	0.989504i	$0.546159\pi$
$432$	−4.00000			−0.192450
$433$	7.00000			0.336399			0.168199	−	0.985753i	$-0.446205\pi$
$433$	7.00000			0.336399			0.168199	+	0.985753i	$0.446205\pi$
$434$	16.0000			0.768025
$435$	1.00000	+	12.0000i	0.0479463	+	0.575356i
$436$	−2.00000			−0.0957826
$437$	36.0000			1.72211
$438$	−30.0000			−1.43346
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		0			0
$441$	−9.00000			−0.428571
$442$		−	24.0000i		−	1.14156i
$443$	4.00000			0.190046			0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000			0.190046			0.0950229	+	0.995475i	$0.469708\pi$
$444$	−2.00000			−0.0949158
$445$	2.00000	+	4.00000i	0.0948091	+	0.189618i
$446$			8.00000i			0.378811i
$447$	14.0000			0.662177
$448$			32.0000i			1.51186i
$449$		−	15.0000i		−	0.707894i	−0.935266	−	0.353947i	$-0.884839\pi$
$449$		−	15.0000i		−	0.707894i	0.935266	−	0.353947i	$-0.115161\pi$
$450$	−6.00000	+	8.00000i	−0.282843	+	0.377124i
$451$	−9.00000			−0.423793
$452$	−16.0000			−0.752577
$453$	−17.0000			−0.798730
$454$		−	14.0000i		−	0.657053i
$455$	−16.0000	+	8.00000i	−0.750092	+	0.375046i
$456$		0			0
$457$			10.0000i			0.467780i	0.972263	+	0.233890i	$0.0751456\pi$
$457$			10.0000i			0.467780i	−0.972263	+	0.233890i	$0.924854\pi$
$458$			8.00000i			0.373815i
$459$	−6.00000			−0.280056
$460$	18.0000	+	36.0000i	0.839254	+	1.67851i
$461$		−	33.0000i		−	1.53696i	−0.639872	−	0.768482i	$-0.721013\pi$
$461$		−	33.0000i		−	1.53696i	0.639872	−	0.768482i	$-0.278987\pi$
$462$	8.00000			0.372194
$463$			2.00000i			0.0929479i	0.998920	+	0.0464739i	$0.0147984\pi$
$463$			2.00000i			0.0929479i	−0.998920	+	0.0464739i	$0.985202\pi$
$464$	8.00000	−	20.0000i	0.371391	−	0.928477i
$465$	−2.00000	−	4.00000i	−0.0927478	−	0.185496i
$466$		−	2.00000i		−	0.0926482i
$467$	−18.0000			−0.832941			−0.416470	−	0.909149i	$-0.636733\pi$
$467$	−18.0000			−0.832941			−0.416470	+	0.909149i	$0.636733\pi$
$468$		−	4.00000i		−	0.184900i
$469$	48.0000			2.21643
$470$	−32.0000	+	16.0000i	−1.47605	+	0.738025i
$471$	14.0000			0.645086
$472$		0			0
$473$			1.00000i			0.0459800i
$474$		−	8.00000i		−	0.367452i
$475$	−16.0000	−	12.0000i	−0.734130	−	0.550598i
$476$			48.0000i			2.20008i
$477$		−	9.00000i		−	0.412082i
$478$	52.0000			2.37842
$479$		0			0		1.00000			$0$
$479$		0			0		−1.00000			$\pi$
$480$	16.0000	−	8.00000i	0.730297	−	0.365148i
$481$			2.00000i			0.0911922i
$482$	−22.0000			−1.00207
$483$	36.0000			1.63806
$484$	20.0000			0.909091
$485$	22.0000	−	11.0000i	0.998969	−	0.499484i
$486$	−2.00000			−0.0907218
$487$			4.00000i			0.181257i	0.995885	+	0.0906287i	$0.0288876\pi$
$487$			4.00000i			0.181257i	−0.995885	+	0.0906287i	$0.971112\pi$
$488$		0			0
$489$	−13.0000			−0.587880
$490$	36.0000	−	18.0000i	1.62631	−	0.813157i
$491$			8.00000i			0.361035i	0.983572	+	0.180517i	$0.0577772\pi$
$491$			8.00000i			0.361035i	−0.983572	+	0.180517i	$0.942223\pi$
$492$		−	18.0000i		−	0.811503i
$493$	12.0000	−	30.0000i	0.540453	−	1.35113i
$494$	16.0000			0.719874
$495$	−1.00000	−	2.00000i	−0.0449467	−	0.0898933i
$496$			8.00000i			0.359211i
$497$		−	8.00000i		−	0.358849i
$498$		−	14.0000i		−	0.627355i
$499$	−12.0000			−0.537194			−0.268597	−	0.963253i	$-0.586560\pi$
$499$	−12.0000			−0.537194			−0.268597	+	0.963253i	$0.586560\pi$
$500$	4.00000	−	22.0000i	0.178885	−	0.983870i
$501$		−	24.0000i		−	1.07224i
$502$			24.0000i			1.07117i
$503$	−8.00000			−0.356702			−0.178351	−	0.983967i	$-0.557076\pi$
$503$	−8.00000			−0.356702			−0.178351	+	0.983967i	$0.557076\pi$
$504$		0			0
$505$	3.00000	+	6.00000i	0.133498	+	0.266996i
$506$	−18.0000			−0.800198
$507$	9.00000			0.399704
$508$	14.0000			0.621150
$509$	−28.0000			−1.24108			−0.620539	−	0.784176i	$-0.713086\pi$
$509$	−28.0000			−1.24108			−0.620539	+	0.784176i	$0.713086\pi$
$510$	24.0000	−	12.0000i	1.06274	−	0.531369i
$511$		−	60.0000i		−	2.65424i
$512$	−32.0000			−1.41421
$513$		−	4.00000i		−	0.176604i
$514$		−	30.0000i		−	1.32324i
$515$	6.00000	+	12.0000i	0.264392	+	0.528783i
$516$	−2.00000			−0.0880451
$517$		−	8.00000i		−	0.351840i
$518$		−	8.00000i		−	0.351500i
$519$			21.0000i			0.921798i
$520$		0			0
$521$	−8.00000			−0.350486			−0.175243	−	0.984525i	$-0.556071\pi$
$521$	−8.00000			−0.350486			−0.175243	+	0.984525i	$0.556071\pi$
$522$	4.00000	−	10.0000i	0.175075	−	0.437688i
$523$			2.00000i			0.0874539i	0.999044	+	0.0437269i	$0.0139232\pi$
$523$			2.00000i			0.0874539i	−0.999044	+	0.0437269i	$0.986077\pi$
$524$			40.0000i			1.74741i
$525$	−16.0000	−	12.0000i	−0.698297	−	0.523723i
$526$	−52.0000			−2.26731
$527$			12.0000i			0.522728i
$528$			4.00000i			0.174078i
$529$	−58.0000			−2.52174
$530$	18.0000	+	36.0000i	0.781870	+	1.56374i
$531$	8.00000			0.347170
$532$	−32.0000			−1.38738
$533$	−18.0000			−0.779667
$534$		−	4.00000i		−	0.173097i
$535$	−4.00000	−	8.00000i	−0.172935	−	0.345870i
$536$		0			0
$537$	6.00000			0.258919
$538$		−	20.0000i		−	0.862261i
$539$			9.00000i			0.387657i
$540$	4.00000	−	2.00000i	0.172133	−	0.0860663i
$541$			32.0000i			1.37579i	0.725811	+	0.687894i	$0.241464\pi$
$541$			32.0000i			1.37579i	−0.725811	+	0.687894i	$0.758536\pi$
$542$			4.00000i			0.171815i
$543$	−7.00000			−0.300399
$544$	−48.0000			−2.05798
$545$	−2.00000	+	1.00000i	−0.0856706	+	0.0428353i
$546$	16.0000			0.684737
$547$		−	26.0000i		−	1.11168i	−0.831289	−	0.555840i	$-0.812397\pi$
$547$		−	26.0000i		−	1.11168i	0.831289	−	0.555840i	$-0.187603\pi$
$548$	−32.0000			−1.36697
$549$		−	6.00000i		−	0.256074i
$550$	8.00000	+	6.00000i	0.341121	+	0.255841i
$551$	20.0000	+	8.00000i	0.852029	+	0.340811i
$552$		0			0
$553$	16.0000			0.680389
$554$		−	4.00000i		−	0.169944i
$555$	−2.00000	+	1.00000i	−0.0848953	+	0.0424476i
$556$	22.0000			0.933008
$557$		−	45.0000i		−	1.90671i	−0.301849	−	0.953356i	$-0.597604\pi$
$557$		−	45.0000i		−	1.90671i	0.301849	−	0.953356i	$-0.402396\pi$
$558$			4.00000i			0.169334i
$559$			2.00000i			0.0845910i
$560$	16.0000	+	32.0000i	0.676123	+	1.35225i
$561$			6.00000i			0.253320i
$562$	48.0000			2.02476
$563$	−36.0000			−1.51722			−0.758610	−	0.651546i	$-0.774121\pi$
$563$	−36.0000			−1.51722			−0.758610	+	0.651546i	$0.774121\pi$
$564$	16.0000			0.673722
$565$	−16.0000	+	8.00000i	−0.673125	+	0.336563i
$566$		−	44.0000i		−	1.84946i
$567$		−	4.00000i		−	0.167984i
$568$		0			0
$569$			38.0000i			1.59304i	0.604610	+	0.796521i	$0.293329\pi$
$569$			38.0000i			1.59304i	−0.604610	+	0.796521i	$0.706671\pi$
$570$	8.00000	+	16.0000i	0.335083	+	0.670166i
$571$	−23.0000			−0.962520			−0.481260	−	0.876578i	$-0.659821\pi$
$571$	−23.0000			−0.962520			−0.481260	+	0.876578i	$0.659821\pi$
$572$	−4.00000			−0.167248
$573$			3.00000i			0.125327i
$574$	72.0000			3.00522
$575$	36.0000	+	27.0000i	1.50130	+	1.12598i
$576$	−8.00000			−0.333333
$577$	−34.0000			−1.41544			−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000			−1.41544			−0.707719	+	0.706494i	$0.750276\pi$
$578$	−38.0000			−1.58059
$579$	6.00000			0.249351
$580$	2.00000	+	24.0000i	0.0830455	+	0.996546i
$581$	28.0000			1.16164
$582$	−22.0000			−0.911929
$583$	−9.00000			−0.372742
$584$		0			0
$585$	−2.00000	−	4.00000i	−0.0826898	−	0.165380i
$586$	−4.00000			−0.165238
$587$			12.0000i			0.495293i	0.968850	+	0.247647i	$0.0796572\pi$
$587$			12.0000i			0.495293i	−0.968850	+	0.247647i	$0.920343\pi$
$588$	−18.0000			−0.742307
$589$	−8.00000			−0.329634
$590$	−32.0000	+	16.0000i	−1.31742	+	0.658710i
$591$		−	23.0000i		−	0.946094i
$592$	4.00000			0.164399
$593$		−	14.0000i		−	0.574911i	−0.957794	−	0.287456i	$-0.907191\pi$
$593$		−	14.0000i		−	0.574911i	0.957794	−	0.287456i	$-0.0928094\pi$
$594$			2.00000i			0.0820610i
$595$	24.0000	+	48.0000i	0.983904	+	1.96781i
$596$	28.0000			1.14692
$597$	−19.0000			−0.777618
$598$	−36.0000			−1.47215
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$		0			0
$601$			26.0000i			1.06056i	0.847822	+	0.530281i	$0.177914\pi$
$601$			26.0000i			1.06056i	−0.847822	+	0.530281i	$0.822086\pi$
$602$		−	8.00000i		−	0.326056i
$603$			12.0000i			0.488678i
$604$	−34.0000			−1.38344
$605$	20.0000	−	10.0000i	0.813116	−	0.406558i
$606$		−	6.00000i		−	0.243733i
$607$	40.0000			1.62355			0.811775	−	0.583970i	$-0.198502\pi$
$607$	40.0000			1.62355			0.811775	+	0.583970i	$0.198502\pi$
$608$		−	32.0000i		−	1.29777i
$609$	20.0000	+	8.00000i	0.810441	+	0.324176i
$610$	12.0000	+	24.0000i	0.485866	+	0.971732i
$611$		−	16.0000i		−	0.647291i
$612$	−12.0000			−0.485071
$613$			6.00000i			0.242338i	0.992632	+	0.121169i	$0.0386643\pi$
$613$			6.00000i			0.242338i	−0.992632	+	0.121169i	$0.961336\pi$
$614$	−30.0000			−1.21070
$615$	−9.00000	−	18.0000i	−0.362915	−	0.725830i
$616$		0			0
$617$	36.0000			1.44931			0.724653	−	0.689114i	$-0.242000\pi$
$617$	36.0000			1.44931			0.724653	+	0.689114i	$0.242000\pi$
$618$		−	12.0000i		−	0.482711i
$619$		−	10.0000i		−	0.401934i	−0.979598	−	0.200967i	$-0.935592\pi$
$619$		−	10.0000i		−	0.401934i	0.979598	−	0.200967i	$-0.0644084\pi$
$620$	−4.00000	−	8.00000i	−0.160644	−	0.321288i
$621$			9.00000i			0.361158i
$622$		−	46.0000i		−	1.84443i
$623$	8.00000			0.320513
$624$			8.00000i			0.320256i
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$			16.0000i			0.639489i
$627$	−4.00000			−0.159745
$628$	28.0000			1.11732
$629$	6.00000			0.239236
$630$	8.00000	+	16.0000i	0.318728	+	0.637455i
$631$	32.0000			1.27390			0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000			1.27390			0.636950	+	0.770905i	$0.280196\pi$
$632$		0			0
$633$			2.00000i			0.0794929i
$634$	24.0000			0.953162
$635$	14.0000	−	7.00000i	0.555573	−	0.277787i
$636$		−	18.0000i		−	0.713746i
$637$			18.0000i			0.713186i
$638$	−10.0000	−	4.00000i	−0.395904	−	0.158362i
$639$	2.00000			0.0791188
$640$		0			0
$641$		−	33.0000i		−	1.30342i	−0.758468	−	0.651711i	$-0.774052\pi$
$641$		−	33.0000i		−	1.30342i	0.758468	−	0.651711i	$-0.225948\pi$
$642$			8.00000i			0.315735i
$643$			24.0000i			0.946468i	0.880937	+	0.473234i	$0.156913\pi$
$643$			24.0000i			0.946468i	−0.880937	+	0.473234i	$0.843087\pi$
$644$	72.0000			2.83720
$645$	−2.00000	+	1.00000i	−0.0787499	+	0.0393750i
$646$		−	48.0000i		−	1.88853i
$647$		−	17.0000i		−	0.668339i	−0.942513	−	0.334169i	$-0.891544\pi$
$647$		−	17.0000i		−	0.668339i	0.942513	−	0.334169i	$-0.108456\pi$
$648$		0			0
$649$		−	8.00000i		−	0.314027i
$650$	16.0000	+	12.0000i	0.627572	+	0.470679i
$651$	−8.00000			−0.313545
$652$	−26.0000			−1.01824
$653$	−24.0000			−0.939193			−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000			−0.939193			−0.469596	+	0.882881i	$0.655601\pi$
$654$	2.00000			0.0782062
$655$	20.0000	+	40.0000i	0.781465	+	1.56293i
$656$			36.0000i			1.40556i
$657$	15.0000			0.585206
$658$			64.0000i			2.49498i
$659$			29.0000i			1.12968i	0.825201	+	0.564840i	$0.191062\pi$
$659$			29.0000i			1.12968i	−0.825201	+	0.564840i	$0.808938\pi$
$660$	−2.00000	−	4.00000i	−0.0778499	−	0.155700i
$661$	−5.00000			−0.194477			−0.0972387	−	0.995261i	$-0.531001\pi$
$661$	−5.00000			−0.194477			−0.0972387	+	0.995261i	$0.531001\pi$
$662$		−	64.0000i		−	2.48743i
$663$			12.0000i			0.466041i
$664$		0			0
$665$	−32.0000	+	16.0000i	−1.24091	+	0.620453i
$666$	2.00000			0.0774984
$667$	−45.0000	−	18.0000i	−1.74241	−	0.696963i
$668$		−	48.0000i		−	1.85718i
$669$		−	4.00000i		−	0.154649i
$670$	−24.0000	−	48.0000i	−0.927201	−	1.85440i
$671$	−6.00000			−0.231627
$672$		−	32.0000i		−	1.23443i
$673$			32.0000i			1.23351i	0.787155	+	0.616755i	$0.211553\pi$
$673$			32.0000i			1.23351i	−0.787155	+	0.616755i	$0.788447\pi$
$674$	20.0000			0.770371
$675$	3.00000	−	4.00000i	0.115470	−	0.153960i
$676$	18.0000			0.692308
$677$	−18.0000			−0.691796			−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000			−0.691796			−0.345898	+	0.938272i	$0.612426\pi$
$678$	16.0000			0.614476
$679$		−	44.0000i		−	1.68857i
$680$		0			0
$681$			7.00000i			0.268241i
$682$	4.00000			0.153168
$683$			9.00000i			0.344375i	0.985064	+	0.172188i	$0.0550836\pi$
$683$			9.00000i			0.344375i	−0.985064	+	0.172188i	$0.944916\pi$
$684$		−	8.00000i		−	0.305888i
$685$	−32.0000	+	16.0000i	−1.22266	+	0.611329i
$686$		−	16.0000i		−	0.610883i
$687$		−	4.00000i		−	0.152610i
$688$	4.00000			0.152499
$689$	−18.0000			−0.685745
$690$	−18.0000	−	36.0000i	−0.685248	−	1.37050i
$691$	20.0000			0.760836			0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000			0.760836			0.380418	+	0.924815i	$0.375780\pi$
$692$			42.0000i			1.59660i
$693$	−4.00000			−0.151947
$694$			38.0000i			1.44246i
$695$	22.0000	−	11.0000i	0.834508	−	0.417254i
$696$		0			0
$697$			54.0000i			2.04540i
$698$	22.0000			0.832712
$699$			1.00000i			0.0378235i
$700$	−32.0000	−	24.0000i	−1.20949	−	0.907115i
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$			4.00000i			0.150970i
$703$			4.00000i			0.150863i
$704$			8.00000i			0.301511i
$705$	16.0000	−	8.00000i	0.602595	−	0.301297i
$706$		−	36.0000i		−	1.35488i
$707$	12.0000			0.451306
$708$	16.0000			0.601317
$709$	19.0000			0.713560			0.356780	−	0.934188i	$-0.383875\pi$
$709$	19.0000			0.713560			0.356780	+	0.934188i	$0.383875\pi$
$710$	−8.00000	+	4.00000i	−0.300235	+	0.150117i
$711$			4.00000i			0.150012i
$712$		0			0
$713$	18.0000			0.674105
$714$		−	48.0000i		−	1.79635i
$715$	−4.00000	+	2.00000i	−0.149592	+	0.0747958i
$716$	12.0000			0.448461
$717$	−26.0000			−0.970988
$718$		−	42.0000i		−	1.56743i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$	−8.00000	+	4.00000i	−0.298142	+	0.149071i
$721$	24.0000			0.893807
$722$	−6.00000			−0.223297
$723$	11.0000			0.409094
$724$	−14.0000			−0.520306
$725$	14.0000	+	23.0000i	0.519947	+	0.854199i
$726$	−20.0000			−0.742270
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−60.0000	+	30.0000i	−2.22070	+	1.11035i
$731$	6.00000			0.221918
$732$		−	12.0000i		−	0.443533i
$733$	2.00000			0.0738717			0.0369358	−	0.999318i	$-0.488240\pi$
$733$	2.00000			0.0738717			0.0369358	+	0.999318i	$0.488240\pi$
$734$	−54.0000			−1.99318
$735$	−18.0000	+	9.00000i	−0.663940	+	0.331970i
$736$			72.0000i			2.65396i
$737$	12.0000			0.442026
$738$			18.0000i			0.662589i
$739$			10.0000i			0.367856i	0.982940	+	0.183928i	$0.0588813\pi$
$739$			10.0000i			0.367856i	−0.982940	+	0.183928i	$0.941119\pi$
$740$	−4.00000	+	2.00000i	−0.147043	+	0.0735215i
$741$	−8.00000			−0.293887
$742$	72.0000			2.64320
$743$	6.00000			0.220119			0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000			0.220119			0.110059	+	0.993925i	$0.464896\pi$
$744$		0			0
$745$	28.0000	−	14.0000i	1.02584	−	0.512920i
$746$		−	4.00000i		−	0.146450i
$747$			7.00000i			0.256117i
$748$			12.0000i			0.438763i
$749$	−16.0000			−0.584627
$750$	−4.00000	+	22.0000i	−0.146059	+	0.803326i
$751$			28.0000i			1.02173i	0.859660	+	0.510867i	$0.170676\pi$
$751$			28.0000i			1.02173i	−0.859660	+	0.510867i	$0.829324\pi$
$752$	−32.0000			−1.16692
$753$		−	12.0000i		−	0.437304i
$754$	−20.0000	−	8.00000i	−0.728357	−	0.291343i
$755$	−34.0000	+	17.0000i	−1.23739	+	0.618693i
$756$		−	8.00000i		−	0.290957i
$757$	−33.0000			−1.19941			−0.599703	−	0.800223i	$-0.704714\pi$
$757$	−33.0000			−1.19941			−0.599703	+	0.800223i	$0.704714\pi$
$758$		−	44.0000i		−	1.59815i
$759$	9.00000			0.326679
$760$		0			0
$761$	−34.0000			−1.23250			−0.616250	−	0.787551i	$-0.711349\pi$
$761$	−34.0000			−1.23250			−0.616250	+	0.787551i	$0.711349\pi$
$762$	−14.0000			−0.507166
$763$			4.00000i			0.144810i
$764$			6.00000i			0.217072i
$765$	−12.0000	+	6.00000i	−0.433861	+	0.216930i
$766$		−	54.0000i		−	1.95110i
$767$		−	16.0000i		−	0.577727i
$768$	16.0000			0.577350
$769$		−	14.0000i		−	0.504853i	−0.967616	−	0.252426i	$-0.918771\pi$
$769$		−	14.0000i		−	0.504853i	0.967616	−	0.252426i	$-0.0812286\pi$
$770$	16.0000	−	8.00000i	0.576600	−	0.288300i
$771$			15.0000i			0.540212i
$772$	12.0000			0.431889
$773$	24.0000			0.863220			0.431610	−	0.902060i	$-0.357946\pi$
$773$	24.0000			0.863220			0.431610	+	0.902060i	$0.357946\pi$
$774$	2.00000			0.0718885
$775$	−8.00000	−	6.00000i	−0.287368	−	0.215526i
$776$		0			0
$777$			4.00000i			0.143499i
$778$			6.00000i			0.215110i
$779$	−36.0000			−1.28983
$780$	−4.00000	−	8.00000i	−0.143223	−	0.286446i
$781$		−	2.00000i		−	0.0715656i
$782$			108.000i			3.86207i
$783$	−2.00000	+	5.00000i	−0.0714742	+	0.178685i
$784$	36.0000			1.28571
$785$	28.0000	−	14.0000i	0.999363	−	0.499681i
$786$		−	40.0000i		−	1.42675i
$787$		−	42.0000i		−	1.49714i	−0.663057	−	0.748569i	$-0.730741\pi$
$787$		−	42.0000i		−	1.49714i	0.663057	−	0.748569i	$-0.269259\pi$
$788$		−	46.0000i		−	1.63868i
$789$	26.0000			0.925625
$790$	−8.00000	−	16.0000i	−0.284627	−	0.569254i
$791$			32.0000i			1.13779i
$792$		0			0
$793$	−12.0000			−0.426132
$794$			32.0000i			1.13564i
$795$	−9.00000	−	18.0000i	−0.319197	−	0.638394i
$796$	−38.0000			−1.34687
$797$	−16.0000			−0.566749			−0.283375	−	0.959009i	$-0.591454\pi$
$797$	−16.0000			−0.566749			−0.283375	+	0.959009i	$0.591454\pi$
$798$	32.0000			1.13279
$799$	−48.0000			−1.69812
$800$	24.0000	−	32.0000i	0.848528	−	1.13137i
$801$			2.00000i			0.0706665i
$802$	24.0000			0.847469
$803$		−	15.0000i		−	0.529339i
$804$			24.0000i			0.846415i
$805$	72.0000	−	36.0000i	2.53767	−	1.26883i
$806$	8.00000			0.281788
$807$			10.0000i			0.352017i
$808$		0			0
$809$		−	51.0000i		−	1.79306i	−0.442978	−	0.896532i	$-0.646078\pi$
$809$		−	51.0000i		−	1.79306i	0.442978	−	0.896532i	$-0.353922\pi$
$810$	−4.00000	+	2.00000i	−0.140546	+	0.0702728i
$811$	1.00000			0.0351147			0.0175574	−	0.999846i	$-0.494411\pi$
$811$	1.00000			0.0351147			0.0175574	+	0.999846i	$0.494411\pi$
$812$	40.0000	+	16.0000i	1.40372	+	0.561490i
$813$		−	2.00000i		−	0.0701431i
$814$		−	2.00000i		−	0.0701000i
$815$	−26.0000	+	13.0000i	−0.910740	+	0.455370i
$816$	24.0000			0.840168
$817$			4.00000i			0.139942i
$818$			28.0000i			0.978997i
$819$	−8.00000			−0.279543
$820$	−18.0000	−	36.0000i	−0.628587	−	1.25717i
$821$	44.0000			1.53561			0.767805	−	0.640683i	$-0.221349\pi$
$821$	44.0000			1.53561			0.767805	+	0.640683i	$0.221349\pi$
$822$	32.0000			1.11613
$823$	8.00000			0.278862			0.139431	−	0.990232i	$-0.455473\pi$
$823$	8.00000			0.278862			0.139431	+	0.990232i	$0.455473\pi$
$824$		0			0
$825$	−4.00000	−	3.00000i	−0.139262	−	0.104447i
$826$			64.0000i			2.22684i
$827$	−42.0000			−1.46048			−0.730242	−	0.683189i	$-0.760592\pi$
$827$	−42.0000			−1.46048			−0.730242	+	0.683189i	$0.760592\pi$
$828$			18.0000i			0.625543i
$829$		−	34.0000i		−	1.18087i	−0.807086	−	0.590434i	$-0.798956\pi$
$829$		−	34.0000i		−	1.18087i	0.807086	−	0.590434i	$-0.201044\pi$
$830$	−14.0000	−	28.0000i	−0.485947	−	0.971894i
$831$			2.00000i			0.0693792i
$832$			16.0000i			0.554700i
$833$	54.0000			1.87099
$834$	−22.0000			−0.761798
$835$	−24.0000	−	48.0000i	−0.830554	−	1.66111i
$836$	−8.00000			−0.276686
$837$		−	2.00000i		−	0.0691301i
$838$	−60.0000			−2.07267
$839$		−	28.0000i		−	0.966667i	−0.875436	−	0.483334i	$-0.839426\pi$
$839$		−	28.0000i		−	0.966667i	0.875436	−	0.483334i	$-0.160574\pi$
$840$		0			0
$841$	−21.0000	−	20.0000i	−0.724138	−	0.689655i
$842$			44.0000i			1.51634i
$843$	−24.0000			−0.826604
$844$			4.00000i			0.137686i
$845$	18.0000	−	9.00000i	0.619219	−	0.309609i
$846$	−16.0000			−0.550091
$847$		−	40.0000i		−	1.37442i
$848$			36.0000i			1.23625i
$849$			22.0000i			0.755038i
$850$	36.0000	−	48.0000i	1.23479	−	1.64639i
$851$		−	9.00000i		−	0.308516i
$852$	4.00000			0.137038
$853$	−21.0000			−0.719026			−0.359513	−	0.933140i	$-0.617057\pi$
$853$	−21.0000			−0.719026			−0.359513	+	0.933140i	$0.617057\pi$
$854$	48.0000			1.64253
$855$	−4.00000	−	8.00000i	−0.136797	−	0.273594i
$856$		0			0
$857$		−	7.00000i		−	0.239115i	−0.992827	−	0.119558i	$-0.961852\pi$
$857$		−	7.00000i		−	0.239115i	0.992827	−	0.119558i	$-0.0381477\pi$
$858$	4.00000			0.136558
$859$		−	44.0000i		−	1.50126i	−0.660722	−	0.750630i	$-0.729750\pi$
$859$		−	44.0000i		−	1.50126i	0.660722	−	0.750630i	$-0.270250\pi$
$860$	−4.00000	+	2.00000i	−0.136399	+	0.0681994i
$861$	−36.0000			−1.22688
$862$	12.0000			0.408722
$863$			20.0000i			0.680808i	0.940279	+	0.340404i	$0.110564\pi$
$863$			20.0000i			0.680808i	−0.940279	+	0.340404i	$0.889436\pi$
$864$	8.00000			0.272166
$865$	21.0000	+	42.0000i	0.714021	+	1.42804i
$866$	−14.0000			−0.475739
$867$	19.0000			0.645274
$868$	−16.0000			−0.543075
$869$	4.00000			0.135691
$870$	−2.00000	−	24.0000i	−0.0678064	−	0.813676i
$871$	24.0000			0.813209
$872$		0			0
$873$	11.0000			0.372294
$874$	−72.0000			−2.43544
$875$	−44.0000	−	8.00000i	−1.48747	−	0.270449i
$876$	30.0000			1.01361
$877$			8.00000i			0.270141i	0.990836	+	0.135070i	$0.0431261\pi$
$877$			8.00000i			0.270141i	−0.990836	+	0.135070i	$0.956874\pi$
$878$		0			0
$879$	2.00000			0.0674583
$880$	4.00000	+	8.00000i	0.134840	+	0.269680i
$881$			15.0000i			0.505363i	0.967550	+	0.252681i	$0.0813125\pi$
$881$			15.0000i			0.505363i	−0.967550	+	0.252681i	$0.918688\pi$
$882$	18.0000			0.606092
$883$		−	2.00000i		−	0.0673054i	−0.999434	−	0.0336527i	$-0.989286\pi$
$883$		−	2.00000i		−	0.0673054i	0.999434	−	0.0336527i	$-0.0107140\pi$
$884$			24.0000i			0.807207i
$885$	16.0000	−	8.00000i	0.537834	−	0.268917i
$886$	−8.00000			−0.268765
$887$	−30.0000			−1.00730			−0.503651	−	0.863907i	$-0.668010\pi$
$887$	−30.0000			−1.00730			−0.503651	+	0.863907i	$0.668010\pi$
$888$		0			0
$889$		−	28.0000i		−	0.939090i
$890$	−4.00000	−	8.00000i	−0.134080	−	0.268161i
$891$		−	1.00000i		−	0.0335013i
$892$		−	8.00000i		−	0.267860i
$893$		−	32.0000i		−	1.07084i
$894$	−28.0000			−0.936460
$895$	12.0000	−	6.00000i	0.401116	−	0.200558i
$896$		0			0
$897$	18.0000			0.601003
$898$			30.0000i			1.00111i
$899$	10.0000	+	4.00000i	0.333519	+	0.133407i
$900$	6.00000	−	8.00000i	0.200000	−	0.266667i
$901$			54.0000i			1.79900i
$902$	18.0000			0.599334
$903$			4.00000i			0.133112i
$904$		0			0
$905$	−14.0000	+	7.00000i	−0.465376	+	0.232688i
$906$	34.0000			1.12957
$907$	41.0000			1.36138			0.680691	−	0.732570i	$-0.261680\pi$
$907$	41.0000			1.36138			0.680691	+	0.732570i	$0.261680\pi$
$908$			14.0000i			0.464606i
$909$			3.00000i			0.0995037i
$910$	32.0000	−	16.0000i	1.06079	−	0.530395i
$911$		−	21.0000i		−	0.695761i	−0.937539	−	0.347881i	$-0.886901\pi$
$911$		−	21.0000i		−	0.695761i	0.937539	−	0.347881i	$-0.113099\pi$
$912$			16.0000i			0.529813i
$913$	7.00000			0.231666
$914$		−	20.0000i		−	0.661541i
$915$	−6.00000	−	12.0000i	−0.198354	−	0.396708i
$916$		−	8.00000i		−	0.264327i
$917$	80.0000			2.64183
$918$	12.0000			0.396059
$919$	24.0000			0.791687			0.395843	−	0.918318i	$-0.370452\pi$
$919$	24.0000			0.791687			0.395843	+	0.918318i	$0.370452\pi$
$920$		0			0
$921$	15.0000			0.494267
$922$			66.0000i			2.17359i
$923$		−	4.00000i		−	0.131662i
$924$	−8.00000			−0.263181
$925$	−3.00000	+	4.00000i	−0.0986394	+	0.131519i
$926$		−	4.00000i		−	0.131448i
$927$			6.00000i			0.197066i
$928$	−16.0000	+	40.0000i	−0.525226	+	1.31306i
$929$	46.0000			1.50921			0.754606	−	0.656179i	$-0.227828\pi$
$929$	46.0000			1.50921			0.754606	+	0.656179i	$0.227828\pi$
$930$	4.00000	+	8.00000i	0.131165	+	0.262330i
$931$			36.0000i			1.17985i
$932$			2.00000i			0.0655122i
$933$			23.0000i			0.752986i
$934$	36.0000			1.17796
$935$	6.00000	+	12.0000i	0.196221	+	0.392442i
$936$		0			0
$937$		−	8.00000i		−	0.261349i	−0.991425	−	0.130674i	$-0.958286\pi$
$937$		−	8.00000i		−	0.261349i	0.991425	−	0.130674i	$-0.0417142\pi$
$938$	−96.0000			−3.13451
$939$		−	8.00000i		−	0.261070i
$940$	32.0000	−	16.0000i	1.04372	−	0.521862i
$941$	−24.0000			−0.782378			−0.391189	−	0.920310i	$-0.627936\pi$
$941$	−24.0000			−0.782378			−0.391189	+	0.920310i	$0.627936\pi$
$942$	−28.0000			−0.912289
$943$	81.0000			2.63772
$944$	−32.0000			−1.04151
$945$	−4.00000	−	8.00000i	−0.130120	−	0.260240i
$946$		−	2.00000i		−	0.0650256i
$947$	−6.00000			−0.194974			−0.0974869	−	0.995237i	$-0.531080\pi$
$947$	−6.00000			−0.194974			−0.0974869	+	0.995237i	$0.531080\pi$
$948$			8.00000i			0.259828i
$949$		−	30.0000i		−	0.973841i
$950$	32.0000	+	24.0000i	1.03822	+	0.778663i
$951$	−12.0000			−0.389127
$952$		0			0
$953$		−	2.00000i		−	0.0647864i	−0.999475	−	0.0323932i	$-0.989687\pi$
$953$		−	2.00000i		−	0.0647864i	0.999475	−	0.0323932i	$-0.0103129\pi$
$954$			18.0000i			0.582772i
$955$	3.00000	+	6.00000i	0.0970777	+	0.194155i
$956$	−52.0000			−1.68180
$957$	5.00000	+	2.00000i	0.161627	+	0.0646508i
$958$		0			0
$959$			64.0000i			2.06667i
$960$	−16.0000	+	8.00000i	−0.516398	+	0.258199i
$961$	27.0000			0.870968
$962$		−	4.00000i		−	0.128965i
$963$		−	4.00000i		−	0.128898i
$964$	22.0000			0.708572
$965$	12.0000	−	6.00000i	0.386294	−	0.193147i
$966$	−72.0000			−2.31656
$967$	−31.0000			−0.996893			−0.498446	−	0.866921i	$-0.666096\pi$
$967$	−31.0000			−0.996893			−0.498446	+	0.866921i	$0.666096\pi$
$968$		0			0
$969$			24.0000i			0.770991i
$970$	−44.0000	+	22.0000i	−1.41275	+	0.706377i
$971$			51.0000i			1.63667i	0.574743	+	0.818334i	$0.305102\pi$
$971$			51.0000i			1.63667i	−0.574743	+	0.818334i	$0.694898\pi$
$972$	2.00000			0.0641500
$973$		−	44.0000i		−	1.41058i
$974$		−	8.00000i		−	0.256337i
$975$	−8.00000	−	6.00000i	−0.256205	−	0.192154i
$976$			24.0000i			0.768221i
$977$			29.0000i			0.927792i	0.885890	+	0.463896i	$0.153549\pi$
$977$			29.0000i			0.927792i	−0.885890	+	0.463896i	$0.846451\pi$
$978$	26.0000			0.831388
$979$	2.00000			0.0639203
$980$	−36.0000	+	18.0000i	−1.14998	+	0.574989i
$981$	−1.00000			−0.0319275
$982$		−	16.0000i		−	0.510581i
$983$	−54.0000			−1.72233			−0.861166	−	0.508323i	$-0.830265\pi$
$983$	−54.0000			−1.72233			−0.861166	+	0.508323i	$0.830265\pi$
$984$		0			0
$985$	−23.0000	−	46.0000i	−0.732841	−	1.46568i
$986$	−24.0000	+	60.0000i	−0.764316	+	1.91079i
$987$		−	32.0000i		−	1.01857i
$988$	−16.0000			−0.509028
$989$		−	9.00000i		−	0.286183i
$990$	2.00000	+	4.00000i	0.0635642	+	0.127128i
$991$	−47.0000			−1.49300			−0.746502	−	0.665383i	$-0.768268\pi$
$991$	−47.0000			−1.49300			−0.746502	+	0.665383i	$0.768268\pi$
$992$		−	16.0000i		−	0.508001i
$993$			32.0000i			1.01549i
$994$			16.0000i			0.507489i
$995$	−38.0000	+	19.0000i	−1.20468	+	0.602340i
$996$			14.0000i			0.443607i
$997$	−55.0000			−1.74187			−0.870934	−	0.491400i	$-0.836485\pi$
$997$	−55.0000			−1.74187			−0.870934	+	0.491400i	$0.836485\pi$
$998$	24.0000			0.759707
$999$	−1.00000			−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.2.f.a.289.1	✓	2
3.2	odd	2		1305.2.f.d.289.2		2
5.2	odd	4		2175.2.d.b.376.1		2
5.3	odd	4		2175.2.d.a.376.2		2
5.4	even	2		435.2.f.d.289.2	yes	2
15.14	odd	2		1305.2.f.a.289.1		2
29.28	even	2		435.2.f.d.289.1	yes	2
87.86	odd	2		1305.2.f.a.289.2		2
145.28	odd	4		2175.2.d.a.376.1		2
145.57	odd	4		2175.2.d.b.376.2		2
145.144	even	2	inner	435.2.f.a.289.2	yes	2
435.434	odd	2		1305.2.f.d.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.f.a.289.1	✓	2	1.1	even	1	trivial
435.2.f.a.289.2	yes	2	145.144	even	2	inner
435.2.f.d.289.1	yes	2	29.28	even	2
435.2.f.d.289.2	yes	2	5.4	even	2
1305.2.f.a.289.1		2	15.14	odd	2
1305.2.f.a.289.2		2	87.86	odd	2
1305.2.f.d.289.1		2	435.434	odd	2
1305.2.f.d.289.2		2	3.2	odd	2
2175.2.d.a.376.1		2	145.28	odd	4
2175.2.d.a.376.2		2	5.3	odd	4
2175.2.d.b.376.1		2	5.2	odd	4
2175.2.d.b.376.2		2	145.57	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +1.00000 q^{3} +2.00000 q^{4} +(2.00000 - 1.00000i) q^{5} -2.00000 q^{6} -4.00000i q^{7} +1.00000 q^{9} +(-4.00000 + 2.00000i) q^{10} -1.00000i q^{11} +2.00000 q^{12} -2.00000i q^{13} +8.00000i q^{14} +(2.00000 - 1.00000i) q^{15} -4.00000 q^{16} -6.00000 q^{17} -2.00000 q^{18} -4.00000i q^{19} +(4.00000 - 2.00000i) q^{20} -4.00000i q^{21} +2.00000i q^{22} +9.00000i q^{23} +(3.00000 - 4.00000i) q^{25} +4.00000i q^{26} +1.00000 q^{27} -8.00000i q^{28} +(-2.00000 + 5.00000i) q^{29} +(-4.00000 + 2.00000i) q^{30} -2.00000i q^{31} +8.00000 q^{32} -1.00000i q^{33} +12.0000 q^{34} +(-4.00000 - 8.00000i) q^{35} +2.00000 q^{36} -1.00000 q^{37} +8.00000i q^{38} -2.00000i q^{39} -9.00000i q^{41} +8.00000i q^{42} -1.00000 q^{43} -2.00000i q^{44} +(2.00000 - 1.00000i) q^{45} -18.0000i q^{46} +8.00000 q^{47} -4.00000 q^{48} -9.00000 q^{49} +(-6.00000 + 8.00000i) q^{50} -6.00000 q^{51} -4.00000i q^{52} -9.00000i q^{53} -2.00000 q^{54} +(-1.00000 - 2.00000i) q^{55} -4.00000i q^{57} +(4.00000 - 10.0000i) q^{58} +8.00000 q^{59} +(4.00000 - 2.00000i) q^{60} -6.00000i q^{61} +4.00000i q^{62} -4.00000i q^{63} -8.00000 q^{64} +(-2.00000 - 4.00000i) q^{65} +2.00000i q^{66} +12.0000i q^{67} -12.0000 q^{68} +9.00000i q^{69} +(8.00000 + 16.0000i) q^{70} +2.00000 q^{71} +15.0000 q^{73} +2.00000 q^{74} +(3.00000 - 4.00000i) q^{75} -8.00000i q^{76} -4.00000 q^{77} +4.00000i q^{78} +4.00000i q^{79} +(-8.00000 + 4.00000i) q^{80} +1.00000 q^{81} +18.0000i q^{82} +7.00000i q^{83} -8.00000i q^{84} +(-12.0000 + 6.00000i) q^{85} +2.00000 q^{86} +(-2.00000 + 5.00000i) q^{87} +2.00000i q^{89} +(-4.00000 + 2.00000i) q^{90} -8.00000 q^{91} +18.0000i q^{92} -2.00000i q^{93} -16.0000 q^{94} +(-4.00000 - 8.00000i) q^{95} +8.00000 q^{96} +11.0000 q^{97} +18.0000 q^{98} -1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} + 2 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} + 2 q^{9} - 8 q^{10} + 4 q^{12} + 4 q^{15} - 8 q^{16} - 12 q^{17} - 4 q^{18} + 8 q^{20} + 6 q^{25} + 2 q^{27} - 4 q^{29} - 8 q^{30} + 16 q^{32} + 24 q^{34}+ \cdots + 36 q^{98}+O(q^{100}) \) 2 * q - 4 * q^2 + 2 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 + 2 * q^9 - 8 * q^10 + 4 * q^12 + 4 * q^15 - 8 * q^16 - 12 * q^17 - 4 * q^18 + 8 * q^20 + 6 * q^25 + 2 * q^27 - 4 * q^29 - 8 * q^30 + 16 * q^32 + 24 * q^34 - 8 * q^35 + 4 * q^36 - 2 * q^37 - 2 * q^43 + 4 * q^45 + 16 * q^47 - 8 * q^48 - 18 * q^49 - 12 * q^50 - 12 * q^51 - 4 * q^54 - 2 * q^55 + 8 * q^58 + 16 * q^59 + 8 * q^60 - 16 * q^64 - 4 * q^65 - 24 * q^68 + 16 * q^70 + 4 * q^71 + 30 * q^73 + 4 * q^74 + 6 * q^75 - 8 * q^77 - 16 * q^80 + 2 * q^81 - 24 * q^85 + 4 * q^86 - 4 * q^87 - 8 * q^90 - 16 * q^91 - 32 * q^94 - 8 * q^95 + 16 * q^96 + 22 * q^97 + 36 * q^98

Introduction

L-functions

Modular forms

Varieties

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