LMFDB - Embedded newform 105.2.d.a.64.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,2,Mod(64,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("105.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.838429221223$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	105.64
Dual form			105.2.d.a.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +1.00000i q^{3} +1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} -1.00000 q^{6} +1.00000i q^{7} +3.00000i q^{8} -1.00000 q^{9} +(2.00000 + 1.00000i) q^{10} -6.00000 q^{11} +1.00000i q^{12} -2.00000i q^{13} -1.00000 q^{14} +(2.00000 + 1.00000i) q^{15} -1.00000 q^{16} -4.00000i q^{17} -1.00000i q^{18} +6.00000 q^{19} +(1.00000 - 2.00000i) q^{20} -1.00000 q^{21} -6.00000i q^{22} -3.00000 q^{24} +(-3.00000 - 4.00000i) q^{25} +2.00000 q^{26} -1.00000i q^{27} +1.00000i q^{28} +2.00000 q^{29} +(-1.00000 + 2.00000i) q^{30} -10.0000 q^{31} +5.00000i q^{32} -6.00000i q^{33} +4.00000 q^{34} +(2.00000 + 1.00000i) q^{35} -1.00000 q^{36} +4.00000i q^{37} +6.00000i q^{38} +2.00000 q^{39} +(6.00000 + 3.00000i) q^{40} +2.00000 q^{41} -1.00000i q^{42} -4.00000i q^{43} -6.00000 q^{44} +(-1.00000 + 2.00000i) q^{45} -1.00000i q^{48} -1.00000 q^{49} +(4.00000 - 3.00000i) q^{50} +4.00000 q^{51} -2.00000i q^{52} +6.00000i q^{53} +1.00000 q^{54} +(-6.00000 + 12.0000i) q^{55} -3.00000 q^{56} +6.00000i q^{57} +2.00000i q^{58} +8.00000 q^{59} +(2.00000 + 1.00000i) q^{60} -2.00000 q^{61} -10.0000i q^{62} -1.00000i q^{63} -7.00000 q^{64} +(-4.00000 - 2.00000i) q^{65} +6.00000 q^{66} +16.0000i q^{67} -4.00000i q^{68} +(-1.00000 + 2.00000i) q^{70} +10.0000 q^{71} -3.00000i q^{72} -6.00000i q^{73} -4.00000 q^{74} +(4.00000 - 3.00000i) q^{75} +6.00000 q^{76} -6.00000i q^{77} +2.00000i q^{78} -4.00000 q^{79} +(-1.00000 + 2.00000i) q^{80} +1.00000 q^{81} +2.00000i q^{82} +8.00000i q^{83} -1.00000 q^{84} +(-8.00000 - 4.00000i) q^{85} +4.00000 q^{86} +2.00000i q^{87} -18.0000i q^{88} -6.00000 q^{89} +(-2.00000 - 1.00000i) q^{90} +2.00000 q^{91} -10.0000i q^{93} +(6.00000 - 12.0000i) q^{95} -5.00000 q^{96} +2.00000i q^{97} -1.00000i q^{98} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{9} + 4 q^{10} - 12 q^{11} - 2 q^{14} + 4 q^{15} - 2 q^{16} + 12 q^{19} + 2 q^{20} - 2 q^{21} - 6 q^{24} - 6 q^{25} + 4 q^{26} + 4 q^{29} - 2 q^{30} - 20 q^{31} + 8 q^{34}+ \cdots + 12 q^{99}+O(q^{100}) $ 2 * q + 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^9 + 4 * q^10 - 12 * q^11 - 2 * q^14 + 4 * q^15 - 2 * q^16 + 12 * q^19 + 2 * q^20 - 2 * q^21 - 6 * q^24 - 6 * q^25 + 4 * q^26 + 4 * q^29 - 2 * q^30 - 20 * q^31 + 8 * q^34 + 4 * q^35 - 2 * q^36 + 4 * q^39 + 12 * q^40 + 4 * q^41 - 12 * q^44 - 2 * q^45 - 2 * q^49 + 8 * q^50 + 8 * q^51 + 2 * q^54 - 12 * q^55 - 6 * q^56 + 16 * q^59 + 4 * q^60 - 4 * q^61 - 14 * q^64 - 8 * q^65 + 12 * q^66 - 2 * q^70 + 20 * q^71 - 8 * q^74 + 8 * q^75 + 12 * q^76 - 8 * q^79 - 2 * q^80 + 2 * q^81 - 2 * q^84 - 16 * q^85 + 8 * q^86 - 12 * q^89 - 4 * q^90 + 4 * q^91 + 12 * q^95 - 10 * q^96 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i	0.935414	+	0.353553i	$0.115027\pi$
$2$			1.00000i			0.707107i	−0.935414	+	0.353553i	$0.884973\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.00000			0.500000
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$6$	−1.00000			−0.408248
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$			3.00000i			1.06066i
$9$	−1.00000			−0.333333
$10$	2.00000	+	1.00000i	0.632456	+	0.316228i
$11$	−6.00000			−1.80907			−0.904534	−	0.426401i	$-0.859781\pi$
$11$	−6.00000			−1.80907			−0.904534	+	0.426401i	$0.859781\pi$
$12$			1.00000i			0.288675i
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$	−1.00000			−0.267261
$15$	2.00000	+	1.00000i	0.516398	+	0.258199i
$16$	−1.00000			−0.250000
$17$		−	4.00000i		−	0.970143i	−0.874475	−	0.485071i	$-0.838794\pi$
$17$		−	4.00000i		−	0.970143i	0.874475	−	0.485071i	$-0.161206\pi$
$18$		−	1.00000i		−	0.235702i
$19$	6.00000			1.37649			0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000			1.37649			0.688247	+	0.725476i	$0.258380\pi$
$20$	1.00000	−	2.00000i	0.223607	−	0.447214i
$21$	−1.00000			−0.218218
$22$		−	6.00000i		−	1.27920i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	−3.00000			−0.612372
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$	2.00000			0.392232
$27$		−	1.00000i		−	0.192450i
$28$			1.00000i			0.188982i
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$	−1.00000	+	2.00000i	−0.182574	+	0.365148i
$31$	−10.0000			−1.79605			−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−10.0000			−1.79605			−0.898027	+	0.439941i	$0.854999\pi$
$32$			5.00000i			0.883883i
$33$		−	6.00000i		−	1.04447i
$34$	4.00000			0.685994
$35$	2.00000	+	1.00000i	0.338062	+	0.169031i
$36$	−1.00000			−0.166667
$37$			4.00000i			0.657596i	0.944400	+	0.328798i	$0.106644\pi$
$37$			4.00000i			0.657596i	−0.944400	+	0.328798i	$0.893356\pi$
$38$			6.00000i			0.973329i
$39$	2.00000			0.320256
$40$	6.00000	+	3.00000i	0.948683	+	0.474342i
$41$	2.00000			0.312348			0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000			0.312348			0.156174	+	0.987730i	$0.450084\pi$
$42$		−	1.00000i		−	0.154303i
$43$		−	4.00000i		−	0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$	−6.00000			−0.904534
$45$	−1.00000	+	2.00000i	−0.149071	+	0.298142i
$46$		0			0
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−1.00000			−0.142857
$50$	4.00000	−	3.00000i	0.565685	−	0.424264i
$51$	4.00000			0.560112
$52$		−	2.00000i		−	0.277350i
$53$			6.00000i			0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$			6.00000i			0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$	1.00000			0.136083
$55$	−6.00000	+	12.0000i	−0.809040	+	1.61808i
$56$	−3.00000			−0.400892
$57$			6.00000i			0.794719i
$58$			2.00000i			0.262613i
$59$	8.00000			1.04151			0.520756	−	0.853706i	$-0.325650\pi$
$59$	8.00000			1.04151			0.520756	+	0.853706i	$0.325650\pi$
$60$	2.00000	+	1.00000i	0.258199	+	0.129099i
$61$	−2.00000			−0.256074			−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000			−0.256074			−0.128037	+	0.991769i	$0.540868\pi$
$62$		−	10.0000i		−	1.27000i
$63$		−	1.00000i		−	0.125988i
$64$	−7.00000			−0.875000
$65$	−4.00000	−	2.00000i	−0.496139	−	0.248069i
$66$	6.00000			0.738549
$67$			16.0000i			1.95471i	0.211604	+	0.977356i	$0.432131\pi$
$67$			16.0000i			1.95471i	−0.211604	+	0.977356i	$0.567869\pi$
$68$		−	4.00000i		−	0.485071i
$69$		0			0
$70$	−1.00000	+	2.00000i	−0.119523	+	0.239046i
$71$	10.0000			1.18678			0.593391	−	0.804914i	$-0.297789\pi$
$71$	10.0000			1.18678			0.593391	+	0.804914i	$0.297789\pi$
$72$		−	3.00000i		−	0.353553i
$73$		−	6.00000i		−	0.702247i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$		−	6.00000i		−	0.702247i	0.936329	−	0.351123i	$-0.114200\pi$
$74$	−4.00000			−0.464991
$75$	4.00000	−	3.00000i	0.461880	−	0.346410i
$76$	6.00000			0.688247
$77$		−	6.00000i		−	0.683763i
$78$			2.00000i			0.226455i
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	−1.00000	+	2.00000i	−0.111803	+	0.223607i
$81$	1.00000			0.111111
$82$			2.00000i			0.220863i
$83$			8.00000i			0.878114i	0.898459	+	0.439057i	$0.144687\pi$
$83$			8.00000i			0.878114i	−0.898459	+	0.439057i	$0.855313\pi$
$84$	−1.00000			−0.109109
$85$	−8.00000	−	4.00000i	−0.867722	−	0.433861i
$86$	4.00000			0.431331
$87$			2.00000i			0.214423i
$88$		−	18.0000i		−	1.91881i
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$	−2.00000	−	1.00000i	−0.210819	−	0.105409i
$91$	2.00000			0.209657
$92$		0			0
$93$		−	10.0000i		−	1.03695i
$94$		0			0
$95$	6.00000	−	12.0000i	0.615587	−	1.23117i
$96$	−5.00000			−0.510310
$97$			2.00000i			0.203069i	0.994832	+	0.101535i	$0.0323753\pi$
$97$			2.00000i			0.203069i	−0.994832	+	0.101535i	$0.967625\pi$
$98$		−	1.00000i		−	0.101015i
$99$	6.00000			0.603023
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$			4.00000i			0.396059i
$103$			8.00000i			0.788263i	0.919054	+	0.394132i	$0.128955\pi$
$103$			8.00000i			0.788263i	−0.919054	+	0.394132i	$0.871045\pi$
$104$	6.00000			0.588348
$105$	−1.00000	+	2.00000i	−0.0975900	+	0.195180i
$106$	−6.00000			−0.582772
$107$		−	4.00000i		−	0.386695i	−0.981130	−	0.193347i	$-0.938066\pi$
$107$		−	4.00000i		−	0.386695i	0.981130	−	0.193347i	$-0.0619344\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	−12.0000	−	6.00000i	−1.14416	−	0.572078i
$111$	−4.00000			−0.379663
$112$		−	1.00000i		−	0.0944911i
$113$			6.00000i			0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$			6.00000i			0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$	−6.00000			−0.561951
$115$		0			0
$116$	2.00000			0.185695
$117$			2.00000i			0.184900i
$118$			8.00000i			0.736460i
$119$	4.00000			0.366679
$120$	−3.00000	+	6.00000i	−0.273861	+	0.547723i
$121$	25.0000			2.27273
$122$		−	2.00000i		−	0.181071i
$123$			2.00000i			0.180334i
$124$	−10.0000			−0.898027
$125$	−11.0000	+	2.00000i	−0.983870	+	0.178885i
$126$	1.00000			0.0890871
$127$		−	20.0000i		−	1.77471i	−0.461084	−	0.887357i	$-0.652539\pi$
$127$		−	20.0000i		−	1.77471i	0.461084	−	0.887357i	$-0.347461\pi$
$128$			3.00000i			0.265165i
$129$	4.00000			0.352180
$130$	2.00000	−	4.00000i	0.175412	−	0.350823i
$131$	4.00000			0.349482			0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000			0.349482			0.174741	+	0.984614i	$0.444091\pi$
$132$		−	6.00000i		−	0.522233i
$133$			6.00000i			0.520266i
$134$	−16.0000			−1.38219
$135$	−2.00000	−	1.00000i	−0.172133	−	0.0860663i
$136$	12.0000			1.02899
$137$			6.00000i			0.512615i	0.966595	+	0.256307i	$0.0825059\pi$
$137$			6.00000i			0.512615i	−0.966595	+	0.256307i	$0.917494\pi$
$138$		0			0
$139$	−2.00000			−0.169638			−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000			−0.169638			−0.0848189	+	0.996396i	$0.527031\pi$
$140$	2.00000	+	1.00000i	0.169031	+	0.0845154i
$141$		0			0
$142$			10.0000i			0.839181i
$143$			12.0000i			1.00349i
$144$	1.00000			0.0833333
$145$	2.00000	−	4.00000i	0.166091	−	0.332182i
$146$	6.00000			0.496564
$147$		−	1.00000i		−	0.0824786i
$148$			4.00000i			0.328798i
$149$	14.0000			1.14692			0.573462	−	0.819232i	$-0.305600\pi$
$149$	14.0000			1.14692			0.573462	+	0.819232i	$0.305600\pi$
$150$	3.00000	+	4.00000i	0.244949	+	0.326599i
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$			18.0000i			1.45999i
$153$			4.00000i			0.323381i
$154$	6.00000			0.483494
$155$	−10.0000	+	20.0000i	−0.803219	+	1.60644i
$156$	2.00000			0.160128
$157$		−	18.0000i		−	1.43656i	−0.695756	−	0.718278i	$-0.744931\pi$
$157$		−	18.0000i		−	1.43656i	0.695756	−	0.718278i	$-0.255069\pi$
$158$		−	4.00000i		−	0.318223i
$159$	−6.00000			−0.475831
$160$	10.0000	+	5.00000i	0.790569	+	0.395285i
$161$		0			0
$162$			1.00000i			0.0785674i
$163$			4.00000i			0.313304i	0.987654	+	0.156652i	$0.0500701\pi$
$163$			4.00000i			0.313304i	−0.987654	+	0.156652i	$0.949930\pi$
$164$	2.00000			0.156174
$165$	−12.0000	−	6.00000i	−0.934199	−	0.467099i
$166$	−8.00000			−0.620920
$167$		−	12.0000i		−	0.928588i	−0.885681	−	0.464294i	$-0.846308\pi$
$167$		−	12.0000i		−	0.928588i	0.885681	−	0.464294i	$-0.153692\pi$
$168$		−	3.00000i		−	0.231455i
$169$	9.00000			0.692308
$170$	4.00000	−	8.00000i	0.306786	−	0.613572i
$171$	−6.00000			−0.458831
$172$		−	4.00000i		−	0.304997i
$173$		0			0		1.00000			$0$
$173$		0			0		−1.00000			$\pi$
$174$	−2.00000			−0.151620
$175$	4.00000	−	3.00000i	0.302372	−	0.226779i
$176$	6.00000			0.452267
$177$			8.00000i			0.601317i
$178$		−	6.00000i		−	0.449719i
$179$	14.0000			1.04641			0.523205	−	0.852207i	$-0.324736\pi$
$179$	14.0000			1.04641			0.523205	+	0.852207i	$0.324736\pi$
$180$	−1.00000	+	2.00000i	−0.0745356	+	0.149071i
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$			2.00000i			0.148250i
$183$		−	2.00000i		−	0.147844i
$184$		0			0
$185$	8.00000	+	4.00000i	0.588172	+	0.294086i
$186$	10.0000			0.733236
$187$			24.0000i			1.75505i
$188$		0			0
$189$	1.00000			0.0727393
$190$	12.0000	+	6.00000i	0.870572	+	0.435286i
$191$	−18.0000			−1.30243			−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000			−1.30243			−0.651217	+	0.758891i	$0.725741\pi$
$192$		−	7.00000i		−	0.505181i
$193$		−	8.00000i		−	0.575853i	−0.957653	−	0.287926i	$-0.907034\pi$
$193$		−	8.00000i		−	0.575853i	0.957653	−	0.287926i	$-0.0929658\pi$
$194$	−2.00000			−0.143592
$195$	2.00000	−	4.00000i	0.143223	−	0.286446i
$196$	−1.00000			−0.0714286
$197$		−	2.00000i		−	0.142494i	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$		−	2.00000i		−	0.142494i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$			6.00000i			0.426401i
$199$	−14.0000			−0.992434			−0.496217	−	0.868199i	$-0.665278\pi$
$199$	−14.0000			−0.992434			−0.496217	+	0.868199i	$0.665278\pi$
$200$	12.0000	−	9.00000i	0.848528	−	0.636396i
$201$	−16.0000			−1.12855
$202$		−	6.00000i		−	0.422159i
$203$			2.00000i			0.140372i
$204$	4.00000			0.280056
$205$	2.00000	−	4.00000i	0.139686	−	0.279372i
$206$	−8.00000			−0.557386
$207$		0			0
$208$			2.00000i			0.138675i
$209$	−36.0000			−2.49017
$210$	−2.00000	−	1.00000i	−0.138013	−	0.0690066i
$211$	−16.0000			−1.10149			−0.550743	−	0.834675i	$-0.685655\pi$
$211$	−16.0000			−1.10149			−0.550743	+	0.834675i	$0.685655\pi$
$212$			6.00000i			0.412082i
$213$			10.0000i			0.685189i
$214$	4.00000			0.273434
$215$	−8.00000	−	4.00000i	−0.545595	−	0.272798i
$216$	3.00000			0.204124
$217$		−	10.0000i		−	0.678844i
$218$		−	2.00000i		−	0.135457i
$219$	6.00000			0.405442
$220$	−6.00000	+	12.0000i	−0.404520	+	0.809040i
$221$	−8.00000			−0.538138
$222$		−	4.00000i		−	0.268462i
$223$		−	24.0000i		−	1.60716i	−0.595198	−	0.803579i	$-0.702926\pi$
$223$		−	24.0000i		−	1.60716i	0.595198	−	0.803579i	$-0.297074\pi$
$224$	−5.00000			−0.334077
$225$	3.00000	+	4.00000i	0.200000	+	0.266667i
$226$	−6.00000			−0.399114
$227$		−	8.00000i		−	0.530979i	−0.964114	−	0.265489i	$-0.914466\pi$
$227$		−	8.00000i		−	0.530979i	0.964114	−	0.265489i	$-0.0855335\pi$
$228$			6.00000i			0.397360i
$229$	10.0000			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$230$		0			0
$231$	6.00000			0.394771
$232$			6.00000i			0.393919i
$233$		−	26.0000i		−	1.70332i	−0.524097	−	0.851658i	$-0.675597\pi$
$233$		−	26.0000i		−	1.70332i	0.524097	−	0.851658i	$-0.324403\pi$
$234$	−2.00000			−0.130744
$235$		0			0
$236$	8.00000			0.520756
$237$		−	4.00000i		−	0.259828i
$238$			4.00000i			0.259281i
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$	−2.00000	−	1.00000i	−0.129099	−	0.0645497i
$241$	22.0000			1.41714			0.708572	−	0.705638i	$-0.249340\pi$
$241$	22.0000			1.41714			0.708572	+	0.705638i	$0.249340\pi$
$242$			25.0000i			1.60706i
$243$			1.00000i			0.0641500i
$244$	−2.00000			−0.128037
$245$	−1.00000	+	2.00000i	−0.0638877	+	0.127775i
$246$	−2.00000			−0.127515
$247$		−	12.0000i		−	0.763542i
$248$		−	30.0000i		−	1.90500i
$249$	−8.00000			−0.506979
$250$	−2.00000	−	11.0000i	−0.126491	−	0.695701i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		−	1.00000i		−	0.0629941i
$253$		0			0
$254$	20.0000			1.25491
$255$	4.00000	−	8.00000i	0.250490	−	0.500979i
$256$	−17.0000			−1.06250
$257$		−	16.0000i		−	0.998053i	−0.866587	−	0.499026i	$-0.833691\pi$
$257$		−	16.0000i		−	0.998053i	0.866587	−	0.499026i	$-0.166309\pi$
$258$			4.00000i			0.249029i
$259$	−4.00000			−0.248548
$260$	−4.00000	−	2.00000i	−0.248069	−	0.124035i
$261$	−2.00000			−0.123797
$262$			4.00000i			0.247121i
$263$		−	24.0000i		−	1.47990i	−0.672660	−	0.739952i	$-0.734848\pi$
$263$		−	24.0000i		−	1.47990i	0.672660	−	0.739952i	$-0.265152\pi$
$264$	18.0000			1.10782
$265$	12.0000	+	6.00000i	0.737154	+	0.368577i
$266$	−6.00000			−0.367884
$267$		−	6.00000i		−	0.367194i
$268$			16.0000i			0.977356i
$269$	14.0000			0.853595			0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000			0.853595			0.426798	+	0.904347i	$0.359642\pi$
$270$	1.00000	−	2.00000i	0.0608581	−	0.121716i
$271$	−14.0000			−0.850439			−0.425220	−	0.905090i	$-0.639803\pi$
$271$	−14.0000			−0.850439			−0.425220	+	0.905090i	$0.639803\pi$
$272$			4.00000i			0.242536i
$273$			2.00000i			0.121046i
$274$	−6.00000			−0.362473
$275$	18.0000	+	24.0000i	1.08544	+	1.44725i
$276$		0			0
$277$			28.0000i			1.68236i	0.540758	+	0.841178i	$0.318138\pi$
$277$			28.0000i			1.68236i	−0.540758	+	0.841178i	$0.681862\pi$
$278$		−	2.00000i		−	0.119952i
$279$	10.0000			0.598684
$280$	−3.00000	+	6.00000i	−0.179284	+	0.358569i
$281$	−2.00000			−0.119310			−0.0596550	−	0.998219i	$-0.519000\pi$
$281$	−2.00000			−0.119310			−0.0596550	+	0.998219i	$0.519000\pi$
$282$		0			0
$283$			20.0000i			1.18888i	0.804141	+	0.594438i	$0.202626\pi$
$283$			20.0000i			1.18888i	−0.804141	+	0.594438i	$0.797374\pi$
$284$	10.0000			0.593391
$285$	12.0000	+	6.00000i	0.710819	+	0.355409i
$286$	−12.0000			−0.709575
$287$			2.00000i			0.118056i
$288$		−	5.00000i		−	0.294628i
$289$	1.00000			0.0588235
$290$	4.00000	+	2.00000i	0.234888	+	0.117444i
$291$	−2.00000			−0.117242
$292$		−	6.00000i		−	0.351123i
$293$			24.0000i			1.40209i	0.713115	+	0.701047i	$0.247284\pi$
$293$			24.0000i			1.40209i	−0.713115	+	0.701047i	$0.752716\pi$
$294$	1.00000			0.0583212
$295$	8.00000	−	16.0000i	0.465778	−	0.931556i
$296$	−12.0000			−0.697486
$297$			6.00000i			0.348155i
$298$			14.0000i			0.810998i
$299$		0			0
$300$	4.00000	−	3.00000i	0.230940	−	0.173205i
$301$	4.00000			0.230556
$302$			8.00000i			0.460348i
$303$		−	6.00000i		−	0.344691i
$304$	−6.00000			−0.344124
$305$	−2.00000	+	4.00000i	−0.114520	+	0.229039i
$306$	−4.00000			−0.228665
$307$		−	4.00000i		−	0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$		−	4.00000i		−	0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$		−	6.00000i		−	0.341882i
$309$	−8.00000			−0.455104
$310$	−20.0000	−	10.0000i	−1.13592	−	0.567962i
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$			6.00000i			0.339683i
$313$			6.00000i			0.339140i	0.985518	+	0.169570i	$0.0542379\pi$
$313$			6.00000i			0.339140i	−0.985518	+	0.169570i	$0.945762\pi$
$314$	18.0000			1.01580
$315$	−2.00000	−	1.00000i	−0.112687	−	0.0563436i
$316$	−4.00000			−0.225018
$317$			18.0000i			1.01098i	0.862832	+	0.505490i	$0.168688\pi$
$317$			18.0000i			1.01098i	−0.862832	+	0.505490i	$0.831312\pi$
$318$		−	6.00000i		−	0.336463i
$319$	−12.0000			−0.671871
$320$	−7.00000	+	14.0000i	−0.391312	+	0.782624i
$321$	4.00000			0.223258
$322$		0			0
$323$		−	24.0000i		−	1.33540i
$324$	1.00000			0.0555556
$325$	−8.00000	+	6.00000i	−0.443760	+	0.332820i
$326$	−4.00000			−0.221540
$327$		−	2.00000i		−	0.110600i
$328$			6.00000i			0.331295i
$329$		0			0
$330$	6.00000	−	12.0000i	0.330289	−	0.660578i
$331$	−24.0000			−1.31916			−0.659580	−	0.751635i	$-0.729266\pi$
$331$	−24.0000			−1.31916			−0.659580	+	0.751635i	$0.729266\pi$
$332$			8.00000i			0.439057i
$333$		−	4.00000i		−	0.219199i
$334$	12.0000			0.656611
$335$	32.0000	+	16.0000i	1.74835	+	0.874173i
$336$	1.00000			0.0545545
$337$			24.0000i			1.30736i	0.756770	+	0.653682i	$0.226776\pi$
$337$			24.0000i			1.30736i	−0.756770	+	0.653682i	$0.773224\pi$
$338$			9.00000i			0.489535i
$339$	−6.00000			−0.325875
$340$	−8.00000	−	4.00000i	−0.433861	−	0.216930i
$341$	60.0000			3.24918
$342$		−	6.00000i		−	0.324443i
$343$		−	1.00000i		−	0.0539949i
$344$	12.0000			0.646997
$345$		0			0
$346$		0			0
$347$		−	12.0000i		−	0.644194i	−0.946707	−	0.322097i	$-0.895612\pi$
$347$		−	12.0000i		−	0.644194i	0.946707	−	0.322097i	$-0.104388\pi$
$348$			2.00000i			0.107211i
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$	3.00000	+	4.00000i	0.160357	+	0.213809i
$351$	−2.00000			−0.106752
$352$		−	30.0000i		−	1.59901i
$353$			20.0000i			1.06449i	0.846590	+	0.532246i	$0.178652\pi$
$353$			20.0000i			1.06449i	−0.846590	+	0.532246i	$0.821348\pi$
$354$	−8.00000			−0.425195
$355$	10.0000	−	20.0000i	0.530745	−	1.06149i
$356$	−6.00000			−0.317999
$357$			4.00000i			0.211702i
$358$			14.0000i			0.739923i
$359$	−22.0000			−1.16112			−0.580558	−	0.814219i	$-0.697165\pi$
$359$	−22.0000			−1.16112			−0.580558	+	0.814219i	$0.697165\pi$
$360$	−6.00000	−	3.00000i	−0.316228	−	0.158114i
$361$	17.0000			0.894737
$362$		−	6.00000i		−	0.315353i
$363$			25.0000i			1.31216i
$364$	2.00000			0.104828
$365$	−12.0000	−	6.00000i	−0.628109	−	0.314054i
$366$	2.00000			0.104542
$367$		0			0		1.00000			$0$
$367$		0			0		−1.00000			$\pi$
$368$		0			0
$369$	−2.00000			−0.104116
$370$	−4.00000	+	8.00000i	−0.207950	+	0.415900i
$371$	−6.00000			−0.311504
$372$		−	10.0000i		−	0.518476i
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$	−24.0000			−1.24101
$375$	−2.00000	−	11.0000i	−0.103280	−	0.568038i
$376$		0			0
$377$		−	4.00000i		−	0.206010i
$378$			1.00000i			0.0514344i
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$	6.00000	−	12.0000i	0.307794	−	0.615587i
$381$	20.0000			1.02463
$382$		−	18.0000i		−	0.920960i
$383$		−	20.0000i		−	1.02195i	−0.859595	−	0.510976i	$-0.829284\pi$
$383$		−	20.0000i		−	1.02195i	0.859595	−	0.510976i	$-0.170716\pi$
$384$	−3.00000			−0.153093
$385$	−12.0000	−	6.00000i	−0.611577	−	0.305788i
$386$	8.00000			0.407189
$387$			4.00000i			0.203331i
$388$			2.00000i			0.101535i
$389$	−26.0000			−1.31825			−0.659126	−	0.752032i	$-0.729074\pi$
$389$	−26.0000			−1.31825			−0.659126	+	0.752032i	$0.729074\pi$
$390$	4.00000	+	2.00000i	0.202548	+	0.101274i
$391$		0			0
$392$		−	3.00000i		−	0.151523i
$393$			4.00000i			0.201773i
$394$	2.00000			0.100759
$395$	−4.00000	+	8.00000i	−0.201262	+	0.402524i
$396$	6.00000			0.301511
$397$		−	22.0000i		−	1.10415i	−0.833795	−	0.552074i	$-0.813837\pi$
$397$		−	22.0000i		−	1.10415i	0.833795	−	0.552074i	$-0.186163\pi$
$398$		−	14.0000i		−	0.701757i
$399$	−6.00000			−0.300376
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$	−30.0000			−1.49813			−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000			−1.49813			−0.749064	+	0.662497i	$0.769497\pi$
$402$		−	16.0000i		−	0.798007i
$403$			20.0000i			0.996271i
$404$	−6.00000			−0.298511
$405$	1.00000	−	2.00000i	0.0496904	−	0.0993808i
$406$	−2.00000			−0.0992583
$407$		−	24.0000i		−	1.18964i
$408$			12.0000i			0.594089i
$409$	22.0000			1.08783			0.543915	−	0.839140i	$-0.316941\pi$
$409$	22.0000			1.08783			0.543915	+	0.839140i	$0.316941\pi$
$410$	4.00000	+	2.00000i	0.197546	+	0.0987730i
$411$	−6.00000			−0.295958
$412$			8.00000i			0.394132i
$413$			8.00000i			0.393654i
$414$		0			0
$415$	16.0000	+	8.00000i	0.785409	+	0.392705i
$416$	10.0000			0.490290
$417$		−	2.00000i		−	0.0979404i
$418$		−	36.0000i		−	1.76082i
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$	−1.00000	+	2.00000i	−0.0487950	+	0.0975900i
$421$	18.0000			0.877266			0.438633	−	0.898666i	$-0.355463\pi$
$421$	18.0000			0.877266			0.438633	+	0.898666i	$0.355463\pi$
$422$		−	16.0000i		−	0.778868i
$423$		0			0
$424$	−18.0000			−0.874157
$425$	−16.0000	+	12.0000i	−0.776114	+	0.582086i
$426$	−10.0000			−0.484502
$427$		−	2.00000i		−	0.0967868i
$428$		−	4.00000i		−	0.193347i
$429$	−12.0000			−0.579365
$430$	4.00000	−	8.00000i	0.192897	−	0.385794i
$431$	−14.0000			−0.674356			−0.337178	−	0.941441i	$-0.609472\pi$
$431$	−14.0000			−0.674356			−0.337178	+	0.941441i	$0.609472\pi$
$432$			1.00000i			0.0481125i
$433$		−	34.0000i		−	1.63394i	−0.576683	−	0.816968i	$-0.695653\pi$
$433$		−	34.0000i		−	1.63394i	0.576683	−	0.816968i	$-0.304347\pi$
$434$	10.0000			0.480015
$435$	4.00000	+	2.00000i	0.191785	+	0.0958927i
$436$	−2.00000			−0.0957826
$437$		0			0
$438$			6.00000i			0.286691i
$439$	−6.00000			−0.286364			−0.143182	−	0.989696i	$-0.545733\pi$
$439$	−6.00000			−0.286364			−0.143182	+	0.989696i	$0.545733\pi$
$440$	−36.0000	−	18.0000i	−1.71623	−	0.858116i
$441$	1.00000			0.0476190
$442$		−	8.00000i		−	0.380521i
$443$		−	4.00000i		−	0.190046i	−0.995475	−	0.0950229i	$-0.969708\pi$
$443$		−	4.00000i		−	0.190046i	0.995475	−	0.0950229i	$-0.0302924\pi$
$444$	−4.00000			−0.189832
$445$	−6.00000	+	12.0000i	−0.284427	+	0.568855i
$446$	24.0000			1.13643
$447$			14.0000i			0.662177i
$448$		−	7.00000i		−	0.330719i
$449$	−10.0000			−0.471929			−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000			−0.471929			−0.235965	+	0.971762i	$0.575825\pi$
$450$	−4.00000	+	3.00000i	−0.188562	+	0.141421i
$451$	−12.0000			−0.565058
$452$			6.00000i			0.282216i
$453$			8.00000i			0.375873i
$454$	8.00000			0.375459
$455$	2.00000	−	4.00000i	0.0937614	−	0.187523i
$456$	−18.0000			−0.842927
$457$			20.0000i			0.935561i	0.883845	+	0.467780i	$0.154946\pi$
$457$			20.0000i			0.935561i	−0.883845	+	0.467780i	$0.845054\pi$
$458$			10.0000i			0.467269i
$459$	−4.00000			−0.186704
$460$		0			0
$461$	30.0000			1.39724			0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000			1.39724			0.698620	+	0.715493i	$0.253798\pi$
$462$			6.00000i			0.279145i
$463$			36.0000i			1.67306i	0.547920	+	0.836531i	$0.315420\pi$
$463$			36.0000i			1.67306i	−0.547920	+	0.836531i	$0.684580\pi$
$464$	−2.00000			−0.0928477
$465$	−20.0000	−	10.0000i	−0.927478	−	0.463739i
$466$	26.0000			1.20443
$467$			24.0000i			1.11059i	0.831654	+	0.555294i	$0.187394\pi$
$467$			24.0000i			1.11059i	−0.831654	+	0.555294i	$0.812606\pi$
$468$			2.00000i			0.0924500i
$469$	−16.0000			−0.738811
$470$		0			0
$471$	18.0000			0.829396
$472$			24.0000i			1.10469i
$473$			24.0000i			1.10352i
$474$	4.00000			0.183726
$475$	−18.0000	−	24.0000i	−0.825897	−	1.10120i
$476$	4.00000			0.183340
$477$		−	6.00000i		−	0.274721i
$478$			6.00000i			0.274434i
$479$	−24.0000			−1.09659			−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000			−1.09659			−0.548294	+	0.836286i	$0.684723\pi$
$480$	−5.00000	+	10.0000i	−0.228218	+	0.456435i
$481$	8.00000			0.364769
$482$			22.0000i			1.00207i
$483$		0			0
$484$	25.0000			1.13636
$485$	4.00000	+	2.00000i	0.181631	+	0.0908153i
$486$	−1.00000			−0.0453609
$487$		−	12.0000i		−	0.543772i	−0.962329	−	0.271886i	$-0.912353\pi$
$487$		−	12.0000i		−	0.543772i	0.962329	−	0.271886i	$-0.0876473\pi$
$488$		−	6.00000i		−	0.271607i
$489$	−4.00000			−0.180886
$490$	−2.00000	−	1.00000i	−0.0903508	−	0.0451754i
$491$	10.0000			0.451294			0.225647	−	0.974209i	$-0.427550\pi$
$491$	10.0000			0.451294			0.225647	+	0.974209i	$0.427550\pi$
$492$			2.00000i			0.0901670i
$493$		−	8.00000i		−	0.360302i
$494$	12.0000			0.539906
$495$	6.00000	−	12.0000i	0.269680	−	0.539360i
$496$	10.0000			0.449013
$497$			10.0000i			0.448561i
$498$		−	8.00000i		−	0.358489i
$499$	−4.00000			−0.179065			−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000			−0.179065			−0.0895323	+	0.995984i	$0.528537\pi$
$500$	−11.0000	+	2.00000i	−0.491935	+	0.0894427i
$501$	12.0000			0.536120
$502$		0			0
$503$		−	36.0000i		−	1.60516i	−0.596544	−	0.802580i	$-0.703460\pi$
$503$		−	36.0000i		−	1.60516i	0.596544	−	0.802580i	$-0.296540\pi$
$504$	3.00000			0.133631
$505$	−6.00000	+	12.0000i	−0.266996	+	0.533993i
$506$		0			0
$507$			9.00000i			0.399704i
$508$		−	20.0000i		−	0.887357i
$509$	−30.0000			−1.32973			−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000			−1.32973			−0.664863	+	0.746965i	$0.731510\pi$
$510$	8.00000	+	4.00000i	0.354246	+	0.177123i
$511$	6.00000			0.265424
$512$		−	11.0000i		−	0.486136i
$513$		−	6.00000i		−	0.264906i
$514$	16.0000			0.705730
$515$	16.0000	+	8.00000i	0.705044	+	0.352522i
$516$	4.00000			0.176090
$517$		0			0
$518$		−	4.00000i		−	0.175750i
$519$		0			0
$520$	6.00000	−	12.0000i	0.263117	−	0.526235i
$521$	38.0000			1.66481			0.832405	−	0.554168i	$-0.186963\pi$
$521$	38.0000			1.66481			0.832405	+	0.554168i	$0.186963\pi$
$522$		−	2.00000i		−	0.0875376i
$523$			20.0000i			0.874539i	0.899331	+	0.437269i	$0.144054\pi$
$523$			20.0000i			0.874539i	−0.899331	+	0.437269i	$0.855946\pi$
$524$	4.00000			0.174741
$525$	3.00000	+	4.00000i	0.130931	+	0.174574i
$526$	24.0000			1.04645
$527$			40.0000i			1.74243i
$528$			6.00000i			0.261116i
$529$	23.0000			1.00000
$530$	−6.00000	+	12.0000i	−0.260623	+	0.521247i
$531$	−8.00000			−0.347170
$532$			6.00000i			0.260133i
$533$		−	4.00000i		−	0.173259i
$534$	6.00000			0.259645
$535$	−8.00000	−	4.00000i	−0.345870	−	0.172935i
$536$	−48.0000			−2.07328
$537$			14.0000i			0.604145i
$538$			14.0000i			0.603583i
$539$	6.00000			0.258438
$540$	−2.00000	−	1.00000i	−0.0860663	−	0.0430331i
$541$	6.00000			0.257960			0.128980	−	0.991647i	$-0.458830\pi$
$541$	6.00000			0.257960			0.128980	+	0.991647i	$0.458830\pi$
$542$		−	14.0000i		−	0.601351i
$543$		−	6.00000i		−	0.257485i
$544$	20.0000			0.857493
$545$	−2.00000	+	4.00000i	−0.0856706	+	0.171341i
$546$	−2.00000			−0.0855921
$547$			16.0000i			0.684111i	0.939680	+	0.342055i	$0.111123\pi$
$547$			16.0000i			0.684111i	−0.939680	+	0.342055i	$0.888877\pi$
$548$			6.00000i			0.256307i
$549$	2.00000			0.0853579
$550$	−24.0000	+	18.0000i	−1.02336	+	0.767523i
$551$	12.0000			0.511217
$552$		0			0
$553$		−	4.00000i		−	0.170097i
$554$	−28.0000			−1.18961
$555$	−4.00000	+	8.00000i	−0.169791	+	0.339581i
$556$	−2.00000			−0.0848189
$557$		−	38.0000i		−	1.61011i	−0.593199	−	0.805056i	$-0.702135\pi$
$557$		−	38.0000i		−	1.61011i	0.593199	−	0.805056i	$-0.297865\pi$
$558$			10.0000i			0.423334i
$559$	−8.00000			−0.338364
$560$	−2.00000	−	1.00000i	−0.0845154	−	0.0422577i
$561$	−24.0000			−1.01328
$562$		−	2.00000i		−	0.0843649i
$563$		−	36.0000i		−	1.51722i	−0.651546	−	0.758610i	$-0.725879\pi$
$563$		−	36.0000i		−	1.51722i	0.651546	−	0.758610i	$-0.274121\pi$
$564$		0			0
$565$	12.0000	+	6.00000i	0.504844	+	0.252422i
$566$	−20.0000			−0.840663
$567$			1.00000i			0.0419961i
$568$			30.0000i			1.25877i
$569$	30.0000			1.25767			0.628833	−	0.777541i	$-0.283533\pi$
$569$	30.0000			1.25767			0.628833	+	0.777541i	$0.283533\pi$
$570$	−6.00000	+	12.0000i	−0.251312	+	0.502625i
$571$	36.0000			1.50655			0.753277	−	0.657704i	$-0.228472\pi$
$571$	36.0000			1.50655			0.753277	+	0.657704i	$0.228472\pi$
$572$			12.0000i			0.501745i
$573$		−	18.0000i		−	0.751961i
$574$	−2.00000			−0.0834784
$575$		0			0
$576$	7.00000			0.291667
$577$		−	14.0000i		−	0.582828i	−0.956597	−	0.291414i	$-0.905874\pi$
$577$		−	14.0000i		−	0.582828i	0.956597	−	0.291414i	$-0.0941257\pi$
$578$			1.00000i			0.0415945i
$579$	8.00000			0.332469
$580$	2.00000	−	4.00000i	0.0830455	−	0.166091i
$581$	−8.00000			−0.331896
$582$		−	2.00000i		−	0.0829027i
$583$		−	36.0000i		−	1.49097i
$584$	18.0000			0.744845
$585$	4.00000	+	2.00000i	0.165380	+	0.0826898i
$586$	−24.0000			−0.991431
$587$			12.0000i			0.495293i	0.968850	+	0.247647i	$0.0796572\pi$
$587$			12.0000i			0.495293i	−0.968850	+	0.247647i	$0.920343\pi$
$588$		−	1.00000i		−	0.0412393i
$589$	−60.0000			−2.47226
$590$	16.0000	+	8.00000i	0.658710	+	0.329355i
$591$	2.00000			0.0822690
$592$		−	4.00000i		−	0.164399i
$593$			44.0000i			1.80686i	0.428732	+	0.903432i	$0.358960\pi$
$593$			44.0000i			1.80686i	−0.428732	+	0.903432i	$0.641040\pi$
$594$	−6.00000			−0.246183
$595$	4.00000	−	8.00000i	0.163984	−	0.327968i
$596$	14.0000			0.573462
$597$		−	14.0000i		−	0.572982i
$598$		0			0
$599$	2.00000			0.0817178			0.0408589	−	0.999165i	$-0.486991\pi$
$599$	2.00000			0.0817178			0.0408589	+	0.999165i	$0.486991\pi$
$600$	9.00000	+	12.0000i	0.367423	+	0.489898i
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$			4.00000i			0.163028i
$603$		−	16.0000i		−	0.651570i
$604$	8.00000			0.325515
$605$	25.0000	−	50.0000i	1.01639	−	2.03279i
$606$	6.00000			0.243733
$607$		−	24.0000i		−	0.974130i	−0.873366	−	0.487065i	$-0.838067\pi$
$607$		−	24.0000i		−	0.974130i	0.873366	−	0.487065i	$-0.161933\pi$
$608$			30.0000i			1.21666i
$609$	−2.00000			−0.0810441
$610$	−4.00000	−	2.00000i	−0.161955	−	0.0809776i
$611$		0			0
$612$			4.00000i			0.161690i
$613$			4.00000i			0.161558i	0.996732	+	0.0807792i	$0.0257409\pi$
$613$			4.00000i			0.161558i	−0.996732	+	0.0807792i	$0.974259\pi$
$614$	4.00000			0.161427
$615$	4.00000	+	2.00000i	0.161296	+	0.0806478i
$616$	18.0000			0.725241
$617$			26.0000i			1.04672i	0.852111	+	0.523360i	$0.175322\pi$
$617$			26.0000i			1.04672i	−0.852111	+	0.523360i	$0.824678\pi$
$618$		−	8.00000i		−	0.321807i
$619$	−10.0000			−0.401934			−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000			−0.401934			−0.200967	+	0.979598i	$0.564408\pi$
$620$	−10.0000	+	20.0000i	−0.401610	+	0.803219i
$621$		0			0
$622$		−	24.0000i		−	0.962312i
$623$		−	6.00000i		−	0.240385i
$624$	−2.00000			−0.0800641
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	−6.00000			−0.239808
$627$		−	36.0000i		−	1.43770i
$628$		−	18.0000i		−	0.718278i
$629$	16.0000			0.637962
$630$	1.00000	−	2.00000i	0.0398410	−	0.0796819i
$631$	−20.0000			−0.796187			−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000			−0.796187			−0.398094	+	0.917345i	$0.630328\pi$
$632$		−	12.0000i		−	0.477334i
$633$		−	16.0000i		−	0.635943i
$634$	−18.0000			−0.714871
$635$	−40.0000	−	20.0000i	−1.58735	−	0.793676i
$636$	−6.00000			−0.237915
$637$			2.00000i			0.0792429i
$638$		−	12.0000i		−	0.475085i
$639$	−10.0000			−0.395594
$640$	6.00000	+	3.00000i	0.237171	+	0.118585i
$641$	−2.00000			−0.0789953			−0.0394976	−	0.999220i	$-0.512576\pi$
$641$	−2.00000			−0.0789953			−0.0394976	+	0.999220i	$0.512576\pi$
$642$			4.00000i			0.157867i
$643$		−	20.0000i		−	0.788723i	−0.918955	−	0.394362i	$-0.870966\pi$
$643$		−	20.0000i		−	0.788723i	0.918955	−	0.394362i	$-0.129034\pi$
$644$		0			0
$645$	4.00000	−	8.00000i	0.157500	−	0.315000i
$646$	24.0000			0.944267
$647$			20.0000i			0.786281i	0.919478	+	0.393141i	$0.128611\pi$
$647$			20.0000i			0.786281i	−0.919478	+	0.393141i	$0.871389\pi$
$648$			3.00000i			0.117851i
$649$	−48.0000			−1.88416
$650$	−6.00000	−	8.00000i	−0.235339	−	0.313786i
$651$	10.0000			0.391931
$652$			4.00000i			0.156652i
$653$			2.00000i			0.0782660i	0.999234	+	0.0391330i	$0.0124596\pi$
$653$			2.00000i			0.0782660i	−0.999234	+	0.0391330i	$0.987540\pi$
$654$	2.00000			0.0782062
$655$	4.00000	−	8.00000i	0.156293	−	0.312586i
$656$	−2.00000			−0.0780869
$657$			6.00000i			0.234082i
$658$		0			0
$659$	18.0000			0.701180			0.350590	−	0.936529i	$-0.385981\pi$
$659$	18.0000			0.701180			0.350590	+	0.936529i	$0.385981\pi$
$660$	−12.0000	−	6.00000i	−0.467099	−	0.233550i
$661$	−18.0000			−0.700119			−0.350059	−	0.936727i	$-0.613839\pi$
$661$	−18.0000			−0.700119			−0.350059	+	0.936727i	$0.613839\pi$
$662$		−	24.0000i		−	0.932786i
$663$		−	8.00000i		−	0.310694i
$664$	−24.0000			−0.931381
$665$	12.0000	+	6.00000i	0.465340	+	0.232670i
$666$	4.00000			0.154997
$667$		0			0
$668$		−	12.0000i		−	0.464294i
$669$	24.0000			0.927894
$670$	−16.0000	+	32.0000i	−0.618134	+	1.23627i
$671$	12.0000			0.463255
$672$		−	5.00000i		−	0.192879i
$673$		−	36.0000i		−	1.38770i	−0.720121	−	0.693849i	$-0.755914\pi$
$673$		−	36.0000i		−	1.38770i	0.720121	−	0.693849i	$-0.244086\pi$
$674$	−24.0000			−0.924445
$675$	−4.00000	+	3.00000i	−0.153960	+	0.115470i
$676$	9.00000			0.346154
$677$		−	32.0000i		−	1.22986i	−0.788582	−	0.614930i	$-0.789184\pi$
$677$		−	32.0000i		−	1.22986i	0.788582	−	0.614930i	$-0.210816\pi$
$678$		−	6.00000i		−	0.230429i
$679$	−2.00000			−0.0767530
$680$	12.0000	−	24.0000i	0.460179	−	0.920358i
$681$	8.00000			0.306561
$682$			60.0000i			2.29752i
$683$			28.0000i			1.07139i	0.844411	+	0.535695i	$0.179950\pi$
$683$			28.0000i			1.07139i	−0.844411	+	0.535695i	$0.820050\pi$
$684$	−6.00000			−0.229416
$685$	12.0000	+	6.00000i	0.458496	+	0.229248i
$686$	1.00000			0.0381802
$687$			10.0000i			0.381524i
$688$			4.00000i			0.152499i
$689$	12.0000			0.457164
$690$		0			0
$691$	−50.0000			−1.90209			−0.951045	−	0.309053i	$-0.899988\pi$
$691$	−50.0000			−1.90209			−0.951045	+	0.309053i	$0.899988\pi$
$692$		0			0
$693$			6.00000i			0.227921i
$694$	12.0000			0.455514
$695$	−2.00000	+	4.00000i	−0.0758643	+	0.151729i
$696$	−6.00000			−0.227429
$697$		−	8.00000i		−	0.303022i
$698$			2.00000i			0.0757011i
$699$	26.0000			0.983410
$700$	4.00000	−	3.00000i	0.151186	−	0.113389i
$701$	−10.0000			−0.377695			−0.188847	−	0.982006i	$-0.560475\pi$
$701$	−10.0000			−0.377695			−0.188847	+	0.982006i	$0.560475\pi$
$702$		−	2.00000i		−	0.0754851i
$703$			24.0000i			0.905177i
$704$	42.0000			1.58293
$705$		0			0
$706$	−20.0000			−0.752710
$707$		−	6.00000i		−	0.225653i
$708$			8.00000i			0.300658i
$709$	−26.0000			−0.976450			−0.488225	−	0.872718i	$-0.662356\pi$
$709$	−26.0000			−0.976450			−0.488225	+	0.872718i	$0.662356\pi$
$710$	20.0000	+	10.0000i	0.750587	+	0.375293i
$711$	4.00000			0.150012
$712$		−	18.0000i		−	0.674579i
$713$		0			0
$714$	−4.00000			−0.149696
$715$	24.0000	+	12.0000i	0.897549	+	0.448775i
$716$	14.0000			0.523205
$717$			6.00000i			0.224074i
$718$		−	22.0000i		−	0.821033i
$719$	−12.0000			−0.447524			−0.223762	−	0.974644i	$-0.571834\pi$
$719$	−12.0000			−0.447524			−0.223762	+	0.974644i	$0.571834\pi$
$720$	1.00000	−	2.00000i	0.0372678	−	0.0745356i
$721$	−8.00000			−0.297936
$722$			17.0000i			0.632674i
$723$			22.0000i			0.818189i
$724$	−6.00000			−0.222988
$725$	−6.00000	−	8.00000i	−0.222834	−	0.297113i
$726$	−25.0000			−0.927837
$727$			40.0000i			1.48352i	0.670667	+	0.741759i	$0.266008\pi$
$727$			40.0000i			1.48352i	−0.670667	+	0.741759i	$0.733992\pi$
$728$			6.00000i			0.222375i
$729$	−1.00000			−0.0370370
$730$	6.00000	−	12.0000i	0.222070	−	0.444140i
$731$	−16.0000			−0.591781
$732$		−	2.00000i		−	0.0739221i
$733$			22.0000i			0.812589i	0.913742	+	0.406294i	$0.133179\pi$
$733$			22.0000i			0.812589i	−0.913742	+	0.406294i	$0.866821\pi$
$734$		0			0
$735$	−2.00000	−	1.00000i	−0.0737711	−	0.0368856i
$736$		0			0
$737$		−	96.0000i		−	3.53621i
$738$		−	2.00000i		−	0.0736210i
$739$	44.0000			1.61857			0.809283	−	0.587419i	$-0.199856\pi$
$739$	44.0000			1.61857			0.809283	+	0.587419i	$0.199856\pi$
$740$	8.00000	+	4.00000i	0.294086	+	0.147043i
$741$	12.0000			0.440831
$742$		−	6.00000i		−	0.220267i
$743$			40.0000i			1.46746i	0.679442	+	0.733729i	$0.262222\pi$
$743$			40.0000i			1.46746i	−0.679442	+	0.733729i	$0.737778\pi$
$744$	30.0000			1.09985
$745$	14.0000	−	28.0000i	0.512920	−	1.02584i
$746$		0			0
$747$		−	8.00000i		−	0.292705i
$748$			24.0000i			0.877527i
$749$	4.00000			0.146157
$750$	11.0000	−	2.00000i	0.401663	−	0.0730297i
$751$	−12.0000			−0.437886			−0.218943	−	0.975738i	$-0.570261\pi$
$751$	−12.0000			−0.437886			−0.218943	+	0.975738i	$0.570261\pi$
$752$		0			0
$753$		0			0
$754$	4.00000			0.145671
$755$	8.00000	−	16.0000i	0.291150	−	0.582300i
$756$	1.00000			0.0363696
$757$			40.0000i			1.45382i	0.686730	+	0.726912i	$0.259045\pi$
$757$			40.0000i			1.45382i	−0.686730	+	0.726912i	$0.740955\pi$
$758$			28.0000i			1.01701i
$759$		0			0
$760$	36.0000	+	18.0000i	1.30586	+	0.652929i
$761$	−22.0000			−0.797499			−0.398750	−	0.917060i	$-0.630556\pi$
$761$	−22.0000			−0.797499			−0.398750	+	0.917060i	$0.630556\pi$
$762$			20.0000i			0.724524i
$763$		−	2.00000i		−	0.0724049i
$764$	−18.0000			−0.651217
$765$	8.00000	+	4.00000i	0.289241	+	0.144620i
$766$	20.0000			0.722629
$767$		−	16.0000i		−	0.577727i
$768$		−	17.0000i		−	0.613435i
$769$	18.0000			0.649097			0.324548	−	0.945869i	$-0.394788\pi$
$769$	18.0000			0.649097			0.324548	+	0.945869i	$0.394788\pi$
$770$	6.00000	−	12.0000i	0.216225	−	0.432450i
$771$	16.0000			0.576226
$772$		−	8.00000i		−	0.287926i
$773$			24.0000i			0.863220i	0.902060	+	0.431610i	$0.142054\pi$
$773$			24.0000i			0.863220i	−0.902060	+	0.431610i	$0.857946\pi$
$774$	−4.00000			−0.143777
$775$	30.0000	+	40.0000i	1.07763	+	1.43684i
$776$	−6.00000			−0.215387
$777$		−	4.00000i		−	0.143499i
$778$		−	26.0000i		−	0.932145i
$779$	12.0000			0.429945
$780$	2.00000	−	4.00000i	0.0716115	−	0.143223i
$781$	−60.0000			−2.14697
$782$		0			0
$783$		−	2.00000i		−	0.0714742i
$784$	1.00000			0.0357143
$785$	−36.0000	−	18.0000i	−1.28490	−	0.642448i
$786$	−4.00000			−0.142675
$787$			4.00000i			0.142585i	0.997455	+	0.0712923i	$0.0227123\pi$
$787$			4.00000i			0.142585i	−0.997455	+	0.0712923i	$0.977288\pi$
$788$		−	2.00000i		−	0.0712470i
$789$	24.0000			0.854423
$790$	−8.00000	−	4.00000i	−0.284627	−	0.142314i
$791$	−6.00000			−0.213335
$792$			18.0000i			0.639602i
$793$			4.00000i			0.142044i
$794$	22.0000			0.780751
$795$	−6.00000	+	12.0000i	−0.212798	+	0.425596i
$796$	−14.0000			−0.496217
$797$			16.0000i			0.566749i	0.959009	+	0.283375i	$0.0914540\pi$
$797$			16.0000i			0.566749i	−0.959009	+	0.283375i	$0.908546\pi$
$798$		−	6.00000i		−	0.212398i
$799$		0			0
$800$	20.0000	−	15.0000i	0.707107	−	0.530330i
$801$	6.00000			0.212000
$802$		−	30.0000i		−	1.05934i
$803$			36.0000i			1.27041i
$804$	−16.0000			−0.564276
$805$		0			0
$806$	−20.0000			−0.704470
$807$			14.0000i			0.492823i
$808$		−	18.0000i		−	0.633238i
$809$	18.0000			0.632846			0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000			0.632846			0.316423	+	0.948618i	$0.397518\pi$
$810$	2.00000	+	1.00000i	0.0702728	+	0.0351364i
$811$	34.0000			1.19390			0.596951	−	0.802278i	$-0.296379\pi$
$811$	34.0000			1.19390			0.596951	+	0.802278i	$0.296379\pi$
$812$			2.00000i			0.0701862i
$813$		−	14.0000i		−	0.491001i
$814$	24.0000			0.841200
$815$	8.00000	+	4.00000i	0.280228	+	0.140114i
$816$	−4.00000			−0.140028
$817$		−	24.0000i		−	0.839654i
$818$			22.0000i			0.769212i
$819$	−2.00000			−0.0698857
$820$	2.00000	−	4.00000i	0.0698430	−	0.139686i
$821$	−2.00000			−0.0698005			−0.0349002	−	0.999391i	$-0.511111\pi$
$821$	−2.00000			−0.0698005			−0.0349002	+	0.999391i	$0.511111\pi$
$822$		−	6.00000i		−	0.209274i
$823$			44.0000i			1.53374i	0.641800	+	0.766872i	$0.278188\pi$
$823$			44.0000i			1.53374i	−0.641800	+	0.766872i	$0.721812\pi$
$824$	−24.0000			−0.836080
$825$	−24.0000	+	18.0000i	−0.835573	+	0.626680i
$826$	−8.00000			−0.278356
$827$			12.0000i			0.417281i	0.977992	+	0.208640i	$0.0669038\pi$
$827$			12.0000i			0.417281i	−0.977992	+	0.208640i	$0.933096\pi$
$828$		0			0
$829$	6.00000			0.208389			0.104194	−	0.994557i	$-0.466774\pi$
$829$	6.00000			0.208389			0.104194	+	0.994557i	$0.466774\pi$
$830$	−8.00000	+	16.0000i	−0.277684	+	0.555368i
$831$	−28.0000			−0.971309
$832$			14.0000i			0.485363i
$833$			4.00000i			0.138592i
$834$	2.00000			0.0692543
$835$	−24.0000	−	12.0000i	−0.830554	−	0.415277i
$836$	−36.0000			−1.24509
$837$			10.0000i			0.345651i
$838$			12.0000i			0.414533i
$839$	−12.0000			−0.414286			−0.207143	−	0.978311i	$-0.566417\pi$
$839$	−12.0000			−0.414286			−0.207143	+	0.978311i	$0.566417\pi$
$840$	−6.00000	−	3.00000i	−0.207020	−	0.103510i
$841$	−25.0000			−0.862069
$842$			18.0000i			0.620321i
$843$		−	2.00000i		−	0.0688837i
$844$	−16.0000			−0.550743
$845$	9.00000	−	18.0000i	0.309609	−	0.619219i
$846$		0			0
$847$			25.0000i			0.859010i
$848$		−	6.00000i		−	0.206041i
$849$	−20.0000			−0.686398
$850$	−12.0000	−	16.0000i	−0.411597	−	0.548795i
$851$		0			0
$852$			10.0000i			0.342594i
$853$			30.0000i			1.02718i	0.858036	+	0.513590i	$0.171685\pi$
$853$			30.0000i			1.02718i	−0.858036	+	0.513590i	$0.828315\pi$
$854$	2.00000			0.0684386
$855$	−6.00000	+	12.0000i	−0.205196	+	0.410391i
$856$	12.0000			0.410152
$857$			24.0000i			0.819824i	0.912125	+	0.409912i	$0.134441\pi$
$857$			24.0000i			0.819824i	−0.912125	+	0.409912i	$0.865559\pi$
$858$		−	12.0000i		−	0.409673i
$859$	26.0000			0.887109			0.443554	−	0.896248i	$-0.353717\pi$
$859$	26.0000			0.887109			0.443554	+	0.896248i	$0.353717\pi$
$860$	−8.00000	−	4.00000i	−0.272798	−	0.136399i
$861$	−2.00000			−0.0681598
$862$		−	14.0000i		−	0.476842i
$863$		−	24.0000i		−	0.816970i	−0.912765	−	0.408485i	$-0.866057\pi$
$863$		−	24.0000i		−	0.816970i	0.912765	−	0.408485i	$-0.133943\pi$
$864$	5.00000			0.170103
$865$		0			0
$866$	34.0000			1.15537
$867$			1.00000i			0.0339618i
$868$		−	10.0000i		−	0.339422i
$869$	24.0000			0.814144
$870$	−2.00000	+	4.00000i	−0.0678064	+	0.135613i
$871$	32.0000			1.08428
$872$		−	6.00000i		−	0.203186i
$873$		−	2.00000i		−	0.0676897i
$874$		0			0
$875$	−2.00000	−	11.0000i	−0.0676123	−	0.371868i
$876$	6.00000			0.202721
$877$			4.00000i			0.135070i	0.997717	+	0.0675352i	$0.0215135\pi$
$877$			4.00000i			0.135070i	−0.997717	+	0.0675352i	$0.978487\pi$
$878$		−	6.00000i		−	0.202490i
$879$	−24.0000			−0.809500
$880$	6.00000	−	12.0000i	0.202260	−	0.404520i
$881$	14.0000			0.471672			0.235836	−	0.971793i	$-0.424217\pi$
$881$	14.0000			0.471672			0.235836	+	0.971793i	$0.424217\pi$
$882$			1.00000i			0.0336718i
$883$		−	48.0000i		−	1.61533i	−0.589643	−	0.807664i	$-0.700731\pi$
$883$		−	48.0000i		−	1.61533i	0.589643	−	0.807664i	$-0.299269\pi$
$884$	−8.00000			−0.269069
$885$	16.0000	+	8.00000i	0.537834	+	0.268917i
$886$	4.00000			0.134383
$887$		−	8.00000i		−	0.268614i	−0.990940	−	0.134307i	$-0.957119\pi$
$887$		−	8.00000i		−	0.268614i	0.990940	−	0.134307i	$-0.0428808\pi$
$888$		−	12.0000i		−	0.402694i
$889$	20.0000			0.670778
$890$	−12.0000	−	6.00000i	−0.402241	−	0.201120i
$891$	−6.00000			−0.201008
$892$		−	24.0000i		−	0.803579i
$893$		0			0
$894$	−14.0000			−0.468230
$895$	14.0000	−	28.0000i	0.467968	−	0.935937i
$896$	−3.00000			−0.100223
$897$		0			0
$898$		−	10.0000i		−	0.333704i
$899$	−20.0000			−0.667037
$900$	3.00000	+	4.00000i	0.100000	+	0.133333i
$901$	24.0000			0.799556
$902$		−	12.0000i		−	0.399556i
$903$			4.00000i			0.133112i
$904$	−18.0000			−0.598671
$905$	−6.00000	+	12.0000i	−0.199447	+	0.398893i
$906$	−8.00000			−0.265782
$907$		−	16.0000i		−	0.531271i	−0.964073	−	0.265636i	$-0.914418\pi$
$907$		−	16.0000i		−	0.531271i	0.964073	−	0.265636i	$-0.0855818\pi$
$908$		−	8.00000i		−	0.265489i
$909$	6.00000			0.199007
$910$	4.00000	+	2.00000i	0.132599	+	0.0662994i
$911$	6.00000			0.198789			0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000			0.198789			0.0993944	+	0.995048i	$0.468309\pi$
$912$		−	6.00000i		−	0.198680i
$913$		−	48.0000i		−	1.58857i
$914$	−20.0000			−0.661541
$915$	−4.00000	−	2.00000i	−0.132236	−	0.0661180i
$916$	10.0000			0.330409
$917$			4.00000i			0.132092i
$918$		−	4.00000i		−	0.132020i
$919$	−28.0000			−0.923635			−0.461817	−	0.886975i	$-0.652802\pi$
$919$	−28.0000			−0.923635			−0.461817	+	0.886975i	$0.652802\pi$
$920$		0			0
$921$	4.00000			0.131804
$922$			30.0000i			0.987997i
$923$		−	20.0000i		−	0.658308i
$924$	6.00000			0.197386
$925$	16.0000	−	12.0000i	0.526077	−	0.394558i
$926$	−36.0000			−1.18303
$927$		−	8.00000i		−	0.262754i
$928$			10.0000i			0.328266i
$929$	14.0000			0.459325			0.229663	−	0.973270i	$-0.426238\pi$
$929$	14.0000			0.459325			0.229663	+	0.973270i	$0.426238\pi$
$930$	10.0000	−	20.0000i	0.327913	−	0.655826i
$931$	−6.00000			−0.196642
$932$		−	26.0000i		−	0.851658i
$933$		−	24.0000i		−	0.785725i
$934$	−24.0000			−0.785304
$935$	48.0000	+	24.0000i	1.56977	+	0.784884i
$936$	−6.00000			−0.196116
$937$		−	2.00000i		−	0.0653372i	−0.999466	−	0.0326686i	$-0.989599\pi$
$937$		−	2.00000i		−	0.0653372i	0.999466	−	0.0326686i	$-0.0104006\pi$
$938$		−	16.0000i		−	0.522419i
$939$	−6.00000			−0.195803
$940$		0			0
$941$	−42.0000			−1.36916			−0.684580	−	0.728937i	$-0.740015\pi$
$941$	−42.0000			−1.36916			−0.684580	+	0.728937i	$0.740015\pi$
$942$			18.0000i			0.586472i
$943$		0			0
$944$	−8.00000			−0.260378
$945$	1.00000	−	2.00000i	0.0325300	−	0.0650600i
$946$	−24.0000			−0.780307
$947$			36.0000i			1.16984i	0.811090	+	0.584921i	$0.198875\pi$
$947$			36.0000i			1.16984i	−0.811090	+	0.584921i	$0.801125\pi$
$948$		−	4.00000i		−	0.129914i
$949$	−12.0000			−0.389536
$950$	24.0000	−	18.0000i	0.778663	−	0.583997i
$951$	−18.0000			−0.583690
$952$			12.0000i			0.388922i
$953$			6.00000i			0.194359i	0.995267	+	0.0971795i	$0.0309821\pi$
$953$			6.00000i			0.194359i	−0.995267	+	0.0971795i	$0.969018\pi$
$954$	6.00000			0.194257
$955$	−18.0000	+	36.0000i	−0.582466	+	1.16493i
$956$	6.00000			0.194054
$957$		−	12.0000i		−	0.387905i
$958$		−	24.0000i		−	0.775405i
$959$	−6.00000			−0.193750
$960$	−14.0000	−	7.00000i	−0.451848	−	0.225924i
$961$	69.0000			2.22581
$962$			8.00000i			0.257930i
$963$			4.00000i			0.128898i
$964$	22.0000			0.708572
$965$	−16.0000	−	8.00000i	−0.515058	−	0.257529i
$966$		0			0
$967$		−	40.0000i		−	1.28631i	−0.765735	−	0.643157i	$-0.777624\pi$
$967$		−	40.0000i		−	1.28631i	0.765735	−	0.643157i	$-0.222376\pi$
$968$			75.0000i			2.41059i
$969$	24.0000			0.770991
$970$	−2.00000	+	4.00000i	−0.0642161	+	0.128432i
$971$	−8.00000			−0.256732			−0.128366	−	0.991727i	$-0.540973\pi$
$971$	−8.00000			−0.256732			−0.128366	+	0.991727i	$0.540973\pi$
$972$			1.00000i			0.0320750i
$973$		−	2.00000i		−	0.0641171i
$974$	12.0000			0.384505
$975$	−6.00000	−	8.00000i	−0.192154	−	0.256205i
$976$	2.00000			0.0640184
$977$		−	30.0000i		−	0.959785i	−0.877327	−	0.479893i	$-0.840676\pi$
$977$		−	30.0000i		−	0.959785i	0.877327	−	0.479893i	$-0.159324\pi$
$978$		−	4.00000i		−	0.127906i
$979$	36.0000			1.15056
$980$	−1.00000	+	2.00000i	−0.0319438	+	0.0638877i
$981$	2.00000			0.0638551
$982$			10.0000i			0.319113i
$983$			24.0000i			0.765481i	0.923856	+	0.382741i	$0.125020\pi$
$983$			24.0000i			0.765481i	−0.923856	+	0.382741i	$0.874980\pi$
$984$	−6.00000			−0.191273
$985$	−4.00000	−	2.00000i	−0.127451	−	0.0637253i
$986$	8.00000			0.254772
$987$		0			0
$988$		−	12.0000i		−	0.381771i
$989$		0			0
$990$	12.0000	+	6.00000i	0.381385	+	0.190693i
$991$	4.00000			0.127064			0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000			0.127064			0.0635321	+	0.997980i	$0.479763\pi$
$992$		−	50.0000i		−	1.58750i
$993$		−	24.0000i		−	0.761617i
$994$	−10.0000			−0.317181
$995$	−14.0000	+	28.0000i	−0.443830	+	0.887660i
$996$	−8.00000			−0.253490
$997$		−	14.0000i		−	0.443384i	−0.975117	−	0.221692i	$-0.928842\pi$
$997$		−	14.0000i		−	0.443384i	0.975117	−	0.221692i	$-0.0711580\pi$
$998$		−	4.00000i		−	0.126618i
$999$	4.00000			0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.d.a.64.2	yes	2
3.2	odd	2		315.2.d.c.64.1		2
4.3	odd	2		1680.2.t.f.1009.1		2
5.2	odd	4		525.2.a.b.1.1		1
5.3	odd	4		525.2.a.c.1.1		1
5.4	even	2	inner	105.2.d.a.64.1	✓	2
7.2	even	3		735.2.q.a.214.2		4
7.3	odd	6		735.2.q.b.79.1		4
7.4	even	3		735.2.q.a.79.1		4
7.5	odd	6		735.2.q.b.214.2		4
7.6	odd	2		735.2.d.a.589.2		2
12.11	even	2		5040.2.t.e.1009.2		2
15.2	even	4		1575.2.a.i.1.1		1
15.8	even	4		1575.2.a.e.1.1		1
15.14	odd	2		315.2.d.c.64.2		2
20.3	even	4		8400.2.a.ch.1.1		1
20.7	even	4		8400.2.a.bj.1.1		1
20.19	odd	2		1680.2.t.f.1009.2		2
21.20	even	2		2205.2.d.f.1324.1		2
35.4	even	6		735.2.q.a.79.2		4
35.9	even	6		735.2.q.a.214.1		4
35.13	even	4		3675.2.a.l.1.1		1
35.19	odd	6		735.2.q.b.214.1		4
35.24	odd	6		735.2.q.b.79.2		4
35.27	even	4		3675.2.a.d.1.1		1
35.34	odd	2		735.2.d.a.589.1		2
60.59	even	2		5040.2.t.e.1009.1		2
105.104	even	2		2205.2.d.f.1324.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.d.a.64.1	✓	2	5.4	even	2	inner
105.2.d.a.64.2	yes	2	1.1	even	1	trivial
315.2.d.c.64.1		2	3.2	odd	2
315.2.d.c.64.2		2	15.14	odd	2
525.2.a.b.1.1		1	5.2	odd	4
525.2.a.c.1.1		1	5.3	odd	4
735.2.d.a.589.1		2	35.34	odd	2
735.2.d.a.589.2		2	7.6	odd	2
735.2.q.a.79.1		4	7.4	even	3
735.2.q.a.79.2		4	35.4	even	6
735.2.q.a.214.1		4	35.9	even	6
735.2.q.a.214.2		4	7.2	even	3
735.2.q.b.79.1		4	7.3	odd	6
735.2.q.b.79.2		4	35.24	odd	6
735.2.q.b.214.1		4	35.19	odd	6
735.2.q.b.214.2		4	7.5	odd	6
1575.2.a.e.1.1		1	15.8	even	4
1575.2.a.i.1.1		1	15.2	even	4
1680.2.t.f.1009.1		2	4.3	odd	2
1680.2.t.f.1009.2		2	20.19	odd	2
2205.2.d.f.1324.1		2	21.20	even	2
2205.2.d.f.1324.2		2	105.104	even	2
3675.2.a.d.1.1		1	35.27	even	4
3675.2.a.l.1.1		1	35.13	even	4
5040.2.t.e.1009.1		2	60.59	even	2
5040.2.t.e.1009.2		2	12.11	even	2
8400.2.a.bj.1.1		1	20.7	even	4
8400.2.a.ch.1.1		1	20.3	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} +1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} -1.00000 q^{6} +1.00000i q^{7} +3.00000i q^{8} -1.00000 q^{9} +(2.00000 + 1.00000i) q^{10} -6.00000 q^{11} +1.00000i q^{12} -2.00000i q^{13} -1.00000 q^{14} +(2.00000 + 1.00000i) q^{15} -1.00000 q^{16} -4.00000i q^{17} -1.00000i q^{18} +6.00000 q^{19} +(1.00000 - 2.00000i) q^{20} -1.00000 q^{21} -6.00000i q^{22} -3.00000 q^{24} +(-3.00000 - 4.00000i) q^{25} +2.00000 q^{26} -1.00000i q^{27} +1.00000i q^{28} +2.00000 q^{29} +(-1.00000 + 2.00000i) q^{30} -10.0000 q^{31} +5.00000i q^{32} -6.00000i q^{33} +4.00000 q^{34} +(2.00000 + 1.00000i) q^{35} -1.00000 q^{36} +4.00000i q^{37} +6.00000i q^{38} +2.00000 q^{39} +(6.00000 + 3.00000i) q^{40} +2.00000 q^{41} -1.00000i q^{42} -4.00000i q^{43} -6.00000 q^{44} +(-1.00000 + 2.00000i) q^{45} -1.00000i q^{48} -1.00000 q^{49} +(4.00000 - 3.00000i) q^{50} +4.00000 q^{51} -2.00000i q^{52} +6.00000i q^{53} +1.00000 q^{54} +(-6.00000 + 12.0000i) q^{55} -3.00000 q^{56} +6.00000i q^{57} +2.00000i q^{58} +8.00000 q^{59} +(2.00000 + 1.00000i) q^{60} -2.00000 q^{61} -10.0000i q^{62} -1.00000i q^{63} -7.00000 q^{64} +(-4.00000 - 2.00000i) q^{65} +6.00000 q^{66} +16.0000i q^{67} -4.00000i q^{68} +(-1.00000 + 2.00000i) q^{70} +10.0000 q^{71} -3.00000i q^{72} -6.00000i q^{73} -4.00000 q^{74} +(4.00000 - 3.00000i) q^{75} +6.00000 q^{76} -6.00000i q^{77} +2.00000i q^{78} -4.00000 q^{79} +(-1.00000 + 2.00000i) q^{80} +1.00000 q^{81} +2.00000i q^{82} +8.00000i q^{83} -1.00000 q^{84} +(-8.00000 - 4.00000i) q^{85} +4.00000 q^{86} +2.00000i q^{87} -18.0000i q^{88} -6.00000 q^{89} +(-2.00000 - 1.00000i) q^{90} +2.00000 q^{91} -10.0000i q^{93} +(6.00000 - 12.0000i) q^{95} -5.00000 q^{96} +2.00000i q^{97} -1.00000i q^{98} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{9} + 4 q^{10} - 12 q^{11} - 2 q^{14} + 4 q^{15} - 2 q^{16} + 12 q^{19} + 2 q^{20} - 2 q^{21} - 6 q^{24} - 6 q^{25} + 4 q^{26} + 4 q^{29} - 2 q^{30} - 20 q^{31} + 8 q^{34}+ \cdots + 12 q^{99}+O(q^{100}) \) 2 * q + 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^9 + 4 * q^10 - 12 * q^11 - 2 * q^14 + 4 * q^15 - 2 * q^16 + 12 * q^19 + 2 * q^20 - 2 * q^21 - 6 * q^24 - 6 * q^25 + 4 * q^26 + 4 * q^29 - 2 * q^30 - 20 * q^31 + 8 * q^34 + 4 * q^35 - 2 * q^36 + 4 * q^39 + 12 * q^40 + 4 * q^41 - 12 * q^44 - 2 * q^45 - 2 * q^49 + 8 * q^50 + 8 * q^51 + 2 * q^54 - 12 * q^55 - 6 * q^56 + 16 * q^59 + 4 * q^60 - 4 * q^61 - 14 * q^64 - 8 * q^65 + 12 * q^66 - 2 * q^70 + 20 * q^71 - 8 * q^74 + 8 * q^75 + 12 * q^76 - 8 * q^79 - 2 * q^80 + 2 * q^81 - 2 * q^84 - 16 * q^85 + 8 * q^86 - 12 * q^89 - 4 * q^90 + 4 * q^91 + 12 * q^95 - 10 * q^96 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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