LMFDB - Embedded newform 930.2.d.d.559.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [930,2,Mod(559,930)] 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("930.559"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(930, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,0,-2,4,-2,0,0,-2,2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.42608738798$
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			559.2
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	930.559
Dual form			930.2.d.d.559.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} -1.00000 q^{6} -2.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(1.00000 + 2.00000i) q^{10} -1.00000i q^{12} -2.00000i q^{13} +2.00000 q^{14} +(1.00000 + 2.00000i) q^{15} +1.00000 q^{16} -1.00000i q^{18} +4.00000 q^{19} +(-2.00000 + 1.00000i) q^{20} +2.00000 q^{21} -2.00000i q^{23} +1.00000 q^{24} +(3.00000 - 4.00000i) q^{25} +2.00000 q^{26} -1.00000i q^{27} +2.00000i q^{28} +10.0000 q^{29} +(-2.00000 + 1.00000i) q^{30} -1.00000 q^{31} +1.00000i q^{32} +(-2.00000 - 4.00000i) q^{35} +1.00000 q^{36} -2.00000i q^{37} +4.00000i q^{38} +2.00000 q^{39} +(-1.00000 - 2.00000i) q^{40} +2.00000 q^{41} +2.00000i q^{42} -4.00000i q^{43} +(-2.00000 + 1.00000i) q^{45} +2.00000 q^{46} +4.00000i q^{47} +1.00000i q^{48} +3.00000 q^{49} +(4.00000 + 3.00000i) q^{50} +2.00000i q^{52} -2.00000i q^{53} +1.00000 q^{54} -2.00000 q^{56} +4.00000i q^{57} +10.0000i q^{58} +6.00000 q^{59} +(-1.00000 - 2.00000i) q^{60} -8.00000 q^{61} -1.00000i q^{62} +2.00000i q^{63} -1.00000 q^{64} +(-2.00000 - 4.00000i) q^{65} +8.00000i q^{67} +2.00000 q^{69} +(4.00000 - 2.00000i) q^{70} -8.00000 q^{71} +1.00000i q^{72} +10.0000i q^{73} +2.00000 q^{74} +(4.00000 + 3.00000i) q^{75} -4.00000 q^{76} +2.00000i q^{78} -12.0000 q^{79} +(2.00000 - 1.00000i) q^{80} +1.00000 q^{81} +2.00000i q^{82} -4.00000i q^{83} -2.00000 q^{84} +4.00000 q^{86} +10.0000i q^{87} +14.0000 q^{89} +(-1.00000 - 2.00000i) q^{90} -4.00000 q^{91} +2.00000i q^{92} -1.00000i q^{93} -4.00000 q^{94} +(8.00000 - 4.00000i) q^{95} -1.00000 q^{96} -4.00000i q^{97} +3.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{9} + 2 q^{10} + 4 q^{14} + 2 q^{15} + 2 q^{16} + 8 q^{19} - 4 q^{20} + 4 q^{21} + 2 q^{24} + 6 q^{25} + 4 q^{26} + 20 q^{29} - 4 q^{30} - 2 q^{31} - 4 q^{35} + 2 q^{36}+ \cdots - 2 q^{96}+O(q^{100}) $ 2 * q - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^9 + 2 * q^10 + 4 * q^14 + 2 * q^15 + 2 * q^16 + 8 * q^19 - 4 * q^20 + 4 * q^21 + 2 * q^24 + 6 * q^25 + 4 * q^26 + 20 * q^29 - 4 * q^30 - 2 * q^31 - 4 * q^35 + 2 * q^36 + 4 * q^39 - 2 * q^40 + 4 * q^41 - 4 * q^45 + 4 * q^46 + 6 * q^49 + 8 * q^50 + 2 * q^54 - 4 * q^56 + 12 * q^59 - 2 * q^60 - 16 * q^61 - 2 * q^64 - 4 * q^65 + 4 * q^69 + 8 * q^70 - 16 * q^71 + 4 * q^74 + 8 * q^75 - 8 * q^76 - 24 * q^79 + 4 * q^80 + 2 * q^81 - 4 * q^84 + 8 * q^86 + 28 * q^89 - 2 * q^90 - 8 * q^91 - 8 * q^94 + 16 * q^95 - 2 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.00000			−0.500000
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$6$	−1.00000			−0.408248
$7$		−	2.00000i		−	0.755929i	−0.925820	−	0.377964i	$-0.876624\pi$
$7$		−	2.00000i		−	0.755929i	0.925820	−	0.377964i	$-0.123376\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	1.00000	+	2.00000i	0.316228	+	0.632456i
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$		−	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	$-0.0894562\pi$
$14$	2.00000			0.534522
$15$	1.00000	+	2.00000i	0.258199	+	0.516398i
$16$	1.00000			0.250000
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$		−	1.00000i		−	0.235702i
$19$	4.00000			0.917663			0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000			0.917663			0.458831	+	0.888523i	$0.348268\pi$
$20$	−2.00000	+	1.00000i	−0.447214	+	0.223607i
$21$	2.00000			0.436436
$22$		0			0
$23$		−	2.00000i		−	0.417029i	−0.978019	−	0.208514i	$-0.933137\pi$
$23$		−	2.00000i		−	0.417029i	0.978019	−	0.208514i	$-0.0668628\pi$
$24$	1.00000			0.204124
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$	2.00000			0.392232
$27$		−	1.00000i		−	0.192450i
$28$			2.00000i			0.377964i
$29$	10.0000			1.85695			0.928477	−	0.371391i	$-0.121119\pi$
$29$	10.0000			1.85695			0.928477	+	0.371391i	$0.121119\pi$
$30$	−2.00000	+	1.00000i	−0.365148	+	0.182574i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$			1.00000i			0.176777i
$33$		0			0
$34$		0			0
$35$	−2.00000	−	4.00000i	−0.338062	−	0.676123i
$36$	1.00000			0.166667
$37$		−	2.00000i		−	0.328798i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$		−	2.00000i		−	0.328798i	0.986394	−	0.164399i	$-0.0525685\pi$
$38$			4.00000i			0.648886i
$39$	2.00000			0.320256
$40$	−1.00000	−	2.00000i	−0.158114	−	0.316228i
$41$	2.00000			0.312348			0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000			0.312348			0.156174	+	0.987730i	$0.450084\pi$
$42$			2.00000i			0.308607i
$43$		−	4.00000i		−	0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$		0			0
$45$	−2.00000	+	1.00000i	−0.298142	+	0.149071i
$46$	2.00000			0.294884
$47$			4.00000i			0.583460i	0.956501	+	0.291730i	$0.0942309\pi$
$47$			4.00000i			0.583460i	−0.956501	+	0.291730i	$0.905769\pi$
$48$			1.00000i			0.144338i
$49$	3.00000			0.428571
$50$	4.00000	+	3.00000i	0.565685	+	0.424264i
$51$		0			0
$52$			2.00000i			0.277350i
$53$		−	2.00000i		−	0.274721i	−0.990521	−	0.137361i	$-0.956138\pi$
$53$		−	2.00000i		−	0.274721i	0.990521	−	0.137361i	$-0.0438619\pi$
$54$	1.00000			0.136083
$55$		0			0
$56$	−2.00000			−0.267261
$57$			4.00000i			0.529813i
$58$			10.0000i			1.31306i
$59$	6.00000			0.781133			0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000			0.781133			0.390567	+	0.920575i	$0.372279\pi$
$60$	−1.00000	−	2.00000i	−0.129099	−	0.258199i
$61$	−8.00000			−1.02430			−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000			−1.02430			−0.512148	+	0.858898i	$0.671150\pi$
$62$		−	1.00000i		−	0.127000i
$63$			2.00000i			0.251976i
$64$	−1.00000			−0.125000
$65$	−2.00000	−	4.00000i	−0.248069	−	0.496139i
$66$		0			0
$67$			8.00000i			0.977356i	0.872464	+	0.488678i	$0.162521\pi$
$67$			8.00000i			0.977356i	−0.872464	+	0.488678i	$0.837479\pi$
$68$		0			0
$69$	2.00000			0.240772
$70$	4.00000	−	2.00000i	0.478091	−	0.239046i
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$			1.00000i			0.117851i
$73$			10.0000i			1.17041i	0.810885	+	0.585206i	$0.198986\pi$
$73$			10.0000i			1.17041i	−0.810885	+	0.585206i	$0.801014\pi$
$74$	2.00000			0.232495
$75$	4.00000	+	3.00000i	0.461880	+	0.346410i
$76$	−4.00000			−0.458831
$77$		0			0
$78$			2.00000i			0.226455i
$79$	−12.0000			−1.35011			−0.675053	−	0.737769i	$-0.735879\pi$
$79$	−12.0000			−1.35011			−0.675053	+	0.737769i	$0.735879\pi$
$80$	2.00000	−	1.00000i	0.223607	−	0.111803i
$81$	1.00000			0.111111
$82$			2.00000i			0.220863i
$83$		−	4.00000i		−	0.439057i	−0.975606	−	0.219529i	$-0.929548\pi$
$83$		−	4.00000i		−	0.439057i	0.975606	−	0.219529i	$-0.0704519\pi$
$84$	−2.00000			−0.218218
$85$		0			0
$86$	4.00000			0.431331
$87$			10.0000i			1.07211i
$88$		0			0
$89$	14.0000			1.48400			0.741999	−	0.670402i	$-0.233878\pi$
$89$	14.0000			1.48400			0.741999	+	0.670402i	$0.233878\pi$
$90$	−1.00000	−	2.00000i	−0.105409	−	0.210819i
$91$	−4.00000			−0.419314
$92$			2.00000i			0.208514i
$93$		−	1.00000i		−	0.103695i
$94$	−4.00000			−0.412568
$95$	8.00000	−	4.00000i	0.820783	−	0.410391i
$96$	−1.00000			−0.102062
$97$		−	4.00000i		−	0.406138i	−0.979164	−	0.203069i	$-0.934908\pi$
$97$		−	4.00000i		−	0.406138i	0.979164	−	0.203069i	$-0.0650917\pi$
$98$			3.00000i			0.303046i
$99$		0			0
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$		0			0
$103$			18.0000i			1.77359i	0.462160	+	0.886796i	$0.347074\pi$
$103$			18.0000i			1.77359i	−0.462160	+	0.886796i	$0.652926\pi$
$104$	−2.00000			−0.196116
$105$	4.00000	−	2.00000i	0.390360	−	0.195180i
$106$	2.00000			0.194257
$107$			4.00000i			0.386695i	0.981130	+	0.193347i	$0.0619344\pi$
$107$			4.00000i			0.386695i	−0.981130	+	0.193347i	$0.938066\pi$
$108$			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	$0.530535\pi$
$110$		0			0
$111$	2.00000			0.189832
$112$		−	2.00000i		−	0.188982i
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$	−4.00000			−0.374634
$115$	−2.00000	−	4.00000i	−0.186501	−	0.373002i
$116$	−10.0000			−0.928477
$117$			2.00000i			0.184900i
$118$			6.00000i			0.552345i
$119$		0			0
$120$	2.00000	−	1.00000i	0.182574	−	0.0912871i
$121$	−11.0000			−1.00000
$122$		−	8.00000i		−	0.724286i
$123$			2.00000i			0.180334i
$124$	1.00000			0.0898027
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$	−2.00000			−0.178174
$127$			8.00000i			0.709885i	0.934888	+	0.354943i	$0.115500\pi$
$127$			8.00000i			0.709885i	−0.934888	+	0.354943i	$0.884500\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	4.00000			0.352180
$130$	4.00000	−	2.00000i	0.350823	−	0.175412i
$131$	−2.00000			−0.174741			−0.0873704	−	0.996176i	$-0.527846\pi$
$131$	−2.00000			−0.174741			−0.0873704	+	0.996176i	$0.527846\pi$
$132$		0			0
$133$		−	8.00000i		−	0.693688i
$134$	−8.00000			−0.691095
$135$	−1.00000	−	2.00000i	−0.0860663	−	0.172133i
$136$		0			0
$137$		−	16.0000i		−	1.36697i	−0.729964	−	0.683486i	$-0.760463\pi$
$137$		−	16.0000i		−	1.36697i	0.729964	−	0.683486i	$-0.239537\pi$
$138$			2.00000i			0.170251i
$139$	−10.0000			−0.848189			−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000			−0.848189			−0.424094	+	0.905618i	$0.639408\pi$
$140$	2.00000	+	4.00000i	0.169031	+	0.338062i
$141$	−4.00000			−0.336861
$142$		−	8.00000i		−	0.671345i
$143$		0			0
$144$	−1.00000			−0.0833333
$145$	20.0000	−	10.0000i	1.66091	−	0.830455i
$146$	−10.0000			−0.827606
$147$			3.00000i			0.247436i
$148$			2.00000i			0.164399i
$149$	12.0000			0.983078			0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000			0.983078			0.491539	+	0.870855i	$0.336434\pi$
$150$	−3.00000	+	4.00000i	−0.244949	+	0.326599i
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$		−	4.00000i		−	0.324443i
$153$		0			0
$154$		0			0
$155$	−2.00000	+	1.00000i	−0.160644	+	0.0803219i
$156$	−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	$-0.255069\pi$
$158$		−	12.0000i		−	0.954669i
$159$	2.00000			0.158610
$160$	1.00000	+	2.00000i	0.0790569	+	0.158114i
$161$	−4.00000			−0.315244
$162$			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
$165$		0			0
$166$	4.00000			0.310460
$167$		−	18.0000i		−	1.39288i	−0.717614	−	0.696441i	$-0.754766\pi$
$167$		−	18.0000i		−	1.39288i	0.717614	−	0.696441i	$-0.245234\pi$
$168$		−	2.00000i		−	0.154303i
$169$	9.00000			0.692308
$170$		0			0
$171$	−4.00000			−0.305888
$172$			4.00000i			0.304997i
$173$			2.00000i			0.152057i	0.997106	+	0.0760286i	$0.0242240\pi$
$173$			2.00000i			0.152057i	−0.997106	+	0.0760286i	$0.975776\pi$
$174$	−10.0000			−0.758098
$175$	−8.00000	−	6.00000i	−0.604743	−	0.453557i
$176$		0			0
$177$			6.00000i			0.450988i
$178$			14.0000i			1.04934i
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$	2.00000	−	1.00000i	0.149071	−	0.0745356i
$181$	−20.0000			−1.48659			−0.743294	−	0.668965i	$-0.766738\pi$
$181$	−20.0000			−1.48659			−0.743294	+	0.668965i	$0.766738\pi$
$182$		−	4.00000i		−	0.296500i
$183$		−	8.00000i		−	0.591377i
$184$	−2.00000			−0.147442
$185$	−2.00000	−	4.00000i	−0.147043	−	0.294086i
$186$	1.00000			0.0733236
$187$		0			0
$188$		−	4.00000i		−	0.291730i
$189$	−2.00000			−0.145479
$190$	4.00000	+	8.00000i	0.290191	+	0.580381i
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$		−	1.00000i		−	0.0721688i
$193$			16.0000i			1.15171i	0.817554	+	0.575853i	$0.195330\pi$
$193$			16.0000i			1.15171i	−0.817554	+	0.575853i	$0.804670\pi$
$194$	4.00000			0.287183
$195$	4.00000	−	2.00000i	0.286446	−	0.143223i
$196$	−3.00000			−0.214286
$197$			6.00000i			0.427482i	0.976890	+	0.213741i	$0.0685649\pi$
$197$			6.00000i			0.427482i	−0.976890	+	0.213741i	$0.931435\pi$
$198$		0			0
$199$	−24.0000			−1.70131			−0.850657	−	0.525720i	$-0.823796\pi$
$199$	−24.0000			−1.70131			−0.850657	+	0.525720i	$0.823796\pi$
$200$	−4.00000	−	3.00000i	−0.282843	−	0.212132i
$201$	−8.00000			−0.564276
$202$		0			0
$203$		−	20.0000i		−	1.40372i
$204$		0			0
$205$	4.00000	−	2.00000i	0.279372	−	0.139686i
$206$	−18.0000			−1.25412
$207$			2.00000i			0.139010i
$208$		−	2.00000i		−	0.138675i
$209$		0			0
$210$	2.00000	+	4.00000i	0.138013	+	0.276026i
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$			2.00000i			0.137361i
$213$		−	8.00000i		−	0.548151i
$214$	−4.00000			−0.273434
$215$	−4.00000	−	8.00000i	−0.272798	−	0.545595i
$216$	−1.00000			−0.0680414
$217$			2.00000i			0.135769i
$218$		−	2.00000i		−	0.135457i
$219$	−10.0000			−0.675737
$220$		0			0
$221$		0			0
$222$			2.00000i			0.134231i
$223$		−	4.00000i		−	0.267860i	−0.990991	−	0.133930i	$-0.957240\pi$
$223$		−	4.00000i		−	0.267860i	0.990991	−	0.133930i	$-0.0427597\pi$
$224$	2.00000			0.133631
$225$	−3.00000	+	4.00000i	−0.200000	+	0.266667i
$226$	6.00000			0.399114
$227$			12.0000i			0.796468i	0.917284	+	0.398234i	$0.130377\pi$
$227$			12.0000i			0.796468i	−0.917284	+	0.398234i	$0.869623\pi$
$228$		−	4.00000i		−	0.264906i
$229$		0			0			−	1.00000i	$-0.5\pi$
$229$		0			0				1.00000i	$0.5\pi$
$230$	4.00000	−	2.00000i	0.263752	−	0.131876i
$231$		0			0
$232$		−	10.0000i		−	0.656532i
$233$			6.00000i			0.393073i	0.980497	+	0.196537i	$0.0629694\pi$
$233$			6.00000i			0.393073i	−0.980497	+	0.196537i	$0.937031\pi$
$234$	−2.00000			−0.130744
$235$	4.00000	+	8.00000i	0.260931	+	0.521862i
$236$	−6.00000			−0.390567
$237$		−	12.0000i		−	0.779484i
$238$		0			0
$239$	8.00000			0.517477			0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000			0.517477			0.258738	+	0.965947i	$0.416693\pi$
$240$	1.00000	+	2.00000i	0.0645497	+	0.129099i
$241$	18.0000			1.15948			0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000			1.15948			0.579741	+	0.814801i	$0.303154\pi$
$242$		−	11.0000i		−	0.707107i
$243$			1.00000i			0.0641500i
$244$	8.00000			0.512148
$245$	6.00000	−	3.00000i	0.383326	−	0.191663i
$246$	−2.00000			−0.127515
$247$		−	8.00000i		−	0.509028i
$248$			1.00000i			0.0635001i
$249$	4.00000			0.253490
$250$	11.0000	+	2.00000i	0.695701	+	0.126491i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		−	2.00000i		−	0.125988i
$253$		0			0
$254$	−8.00000			−0.501965
$255$		0			0
$256$	1.00000			0.0625000
$257$			14.0000i			0.873296i	0.899632	+	0.436648i	$0.143834\pi$
$257$			14.0000i			0.873296i	−0.899632	+	0.436648i	$0.856166\pi$
$258$			4.00000i			0.249029i
$259$	−4.00000			−0.248548
$260$	2.00000	+	4.00000i	0.124035	+	0.248069i
$261$	−10.0000			−0.618984
$262$		−	2.00000i		−	0.123560i
$263$			6.00000i			0.369976i	0.982741	+	0.184988i	$0.0592246\pi$
$263$			6.00000i			0.369976i	−0.982741	+	0.184988i	$0.940775\pi$
$264$		0			0
$265$	−2.00000	−	4.00000i	−0.122859	−	0.245718i
$266$	8.00000			0.490511
$267$			14.0000i			0.856786i
$268$		−	8.00000i		−	0.488678i
$269$	−14.0000			−0.853595			−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−14.0000			−0.853595			−0.426798	+	0.904347i	$0.640358\pi$
$270$	2.00000	−	1.00000i	0.121716	−	0.0608581i
$271$	−12.0000			−0.728948			−0.364474	−	0.931214i	$-0.618751\pi$
$271$	−12.0000			−0.728948			−0.364474	+	0.931214i	$0.618751\pi$
$272$		0			0
$273$		−	4.00000i		−	0.242091i
$274$	16.0000			0.966595
$275$		0			0
$276$	−2.00000			−0.120386
$277$		−	22.0000i		−	1.32185i	−0.750451	−	0.660926i	$-0.770164\pi$
$277$		−	22.0000i		−	1.32185i	0.750451	−	0.660926i	$-0.229836\pi$
$278$		−	10.0000i		−	0.599760i
$279$	1.00000			0.0598684
$280$	−4.00000	+	2.00000i	−0.239046	+	0.119523i
$281$	−2.00000			−0.119310			−0.0596550	−	0.998219i	$-0.519000\pi$
$281$	−2.00000			−0.119310			−0.0596550	+	0.998219i	$0.519000\pi$
$282$		−	4.00000i		−	0.238197i
$283$			4.00000i			0.237775i	0.992908	+	0.118888i	$0.0379328\pi$
$283$			4.00000i			0.237775i	−0.992908	+	0.118888i	$0.962067\pi$
$284$	8.00000			0.474713
$285$	4.00000	+	8.00000i	0.236940	+	0.473879i
$286$		0			0
$287$		−	4.00000i		−	0.236113i
$288$		−	1.00000i		−	0.0589256i
$289$	17.0000			1.00000
$290$	10.0000	+	20.0000i	0.587220	+	1.17444i
$291$	4.00000			0.234484
$292$		−	10.0000i		−	0.585206i
$293$		−	6.00000i		−	0.350524i	−0.984522	−	0.175262i	$-0.943923\pi$
$293$		−	6.00000i		−	0.350524i	0.984522	−	0.175262i	$-0.0560772\pi$
$294$	−3.00000			−0.174964
$295$	12.0000	−	6.00000i	0.698667	−	0.349334i
$296$	−2.00000			−0.116248
$297$		0			0
$298$			12.0000i			0.695141i
$299$	−4.00000			−0.231326
$300$	−4.00000	−	3.00000i	−0.230940	−	0.173205i
$301$	−8.00000			−0.461112
$302$		−	16.0000i		−	0.920697i
$303$		0			0
$304$	4.00000			0.229416
$305$	−16.0000	+	8.00000i	−0.916157	+	0.458079i
$306$		0			0
$307$		−	4.00000i		−	0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$		−	4.00000i		−	0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$		0			0
$309$	−18.0000			−1.02398
$310$	−1.00000	−	2.00000i	−0.0567962	−	0.113592i
$311$	−20.0000			−1.13410			−0.567048	−	0.823685i	$-0.691915\pi$
$311$	−20.0000			−1.13410			−0.567048	+	0.823685i	$0.691915\pi$
$312$		−	2.00000i		−	0.113228i
$313$		−	6.00000i		−	0.339140i	−0.985518	−	0.169570i	$-0.945762\pi$
$313$		−	6.00000i		−	0.339140i	0.985518	−	0.169570i	$-0.0542379\pi$
$314$	18.0000			1.01580
$315$	2.00000	+	4.00000i	0.112687	+	0.225374i
$316$	12.0000			0.675053
$317$			30.0000i			1.68497i	0.538721	+	0.842484i	$0.318908\pi$
$317$			30.0000i			1.68497i	−0.538721	+	0.842484i	$0.681092\pi$
$318$			2.00000i			0.112154i
$319$		0			0
$320$	−2.00000	+	1.00000i	−0.111803	+	0.0559017i
$321$	−4.00000			−0.223258
$322$		−	4.00000i		−	0.222911i
$323$		0			0
$324$	−1.00000			−0.0555556
$325$	−8.00000	−	6.00000i	−0.443760	−	0.332820i
$326$	−4.00000			−0.221540
$327$		−	2.00000i		−	0.110600i
$328$		−	2.00000i		−	0.110432i
$329$	8.00000			0.441054
$330$		0			0
$331$	14.0000			0.769510			0.384755	−	0.923019i	$-0.374286\pi$
$331$	14.0000			0.769510			0.384755	+	0.923019i	$0.374286\pi$
$332$			4.00000i			0.219529i
$333$			2.00000i			0.109599i
$334$	18.0000			0.984916
$335$	8.00000	+	16.0000i	0.437087	+	0.874173i
$336$	2.00000			0.109109
$337$			2.00000i			0.108947i	0.998515	+	0.0544735i	$0.0173480\pi$
$337$			2.00000i			0.108947i	−0.998515	+	0.0544735i	$0.982652\pi$
$338$			9.00000i			0.489535i
$339$	6.00000			0.325875
$340$		0			0
$341$		0			0
$342$		−	4.00000i		−	0.216295i
$343$		−	20.0000i		−	1.07990i
$344$	−4.00000			−0.215666
$345$	4.00000	−	2.00000i	0.215353	−	0.107676i
$346$	−2.00000			−0.107521
$347$			32.0000i			1.71785i	0.512101	+	0.858925i	$0.328867\pi$
$347$			32.0000i			1.71785i	−0.512101	+	0.858925i	$0.671133\pi$
$348$		−	10.0000i		−	0.536056i
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$	6.00000	−	8.00000i	0.320713	−	0.427618i
$351$	−2.00000			−0.106752
$352$		0			0
$353$		−	12.0000i		−	0.638696i	−0.947638	−	0.319348i	$-0.896536\pi$
$353$		−	12.0000i		−	0.638696i	0.947638	−	0.319348i	$-0.103464\pi$
$354$	−6.00000			−0.318896
$355$	−16.0000	+	8.00000i	−0.849192	+	0.424596i
$356$	−14.0000			−0.741999
$357$		0			0
$358$			12.0000i			0.634220i
$359$	−24.0000			−1.26667			−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$	1.00000	+	2.00000i	0.0527046	+	0.105409i
$361$	−3.00000			−0.157895
$362$		−	20.0000i		−	1.05118i
$363$		−	11.0000i		−	0.577350i
$364$	4.00000			0.209657
$365$	10.0000	+	20.0000i	0.523424	+	1.04685i
$366$	8.00000			0.418167
$367$			32.0000i			1.67039i	0.549957	+	0.835193i	$0.314644\pi$
$367$			32.0000i			1.67039i	−0.549957	+	0.835193i	$0.685356\pi$
$368$		−	2.00000i		−	0.104257i
$369$	−2.00000			−0.104116
$370$	4.00000	−	2.00000i	0.207950	−	0.103975i
$371$	−4.00000			−0.207670
$372$			1.00000i			0.0518476i
$373$			26.0000i			1.34623i	0.739538	+	0.673114i	$0.235044\pi$
$373$			26.0000i			1.34623i	−0.739538	+	0.673114i	$0.764956\pi$
$374$		0			0
$375$	11.0000	+	2.00000i	0.568038	+	0.103280i
$376$	4.00000			0.206284
$377$		−	20.0000i		−	1.03005i
$378$		−	2.00000i		−	0.102869i
$379$	−24.0000			−1.23280			−0.616399	−	0.787434i	$-0.711409\pi$
$379$	−24.0000			−1.23280			−0.616399	+	0.787434i	$0.711409\pi$
$380$	−8.00000	+	4.00000i	−0.410391	+	0.205196i
$381$	−8.00000			−0.409852
$382$			8.00000i			0.409316i
$383$			38.0000i			1.94171i	0.239669	+	0.970855i	$0.422961\pi$
$383$			38.0000i			1.94171i	−0.239669	+	0.970855i	$0.577039\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−16.0000			−0.814379
$387$			4.00000i			0.203331i
$388$			4.00000i			0.203069i
$389$	−14.0000			−0.709828			−0.354914	−	0.934899i	$-0.615490\pi$
$389$	−14.0000			−0.709828			−0.354914	+	0.934899i	$0.615490\pi$
$390$	2.00000	+	4.00000i	0.101274	+	0.202548i
$391$		0			0
$392$		−	3.00000i		−	0.151523i
$393$		−	2.00000i		−	0.100887i
$394$	−6.00000			−0.302276
$395$	−24.0000	+	12.0000i	−1.20757	+	0.603786i
$396$		0			0
$397$			26.0000i			1.30490i	0.757831	+	0.652451i	$0.226259\pi$
$397$			26.0000i			1.30490i	−0.757831	+	0.652451i	$0.773741\pi$
$398$		−	24.0000i		−	1.20301i
$399$	8.00000			0.400501
$400$	3.00000	−	4.00000i	0.150000	−	0.200000i
$401$	2.00000			0.0998752			0.0499376	−	0.998752i	$-0.484098\pi$
$401$	2.00000			0.0998752			0.0499376	+	0.998752i	$0.484098\pi$
$402$		−	8.00000i		−	0.399004i
$403$			2.00000i			0.0996271i
$404$		0			0
$405$	2.00000	−	1.00000i	0.0993808	−	0.0496904i
$406$	20.0000			0.992583
$407$		0			0
$408$		0			0
$409$	2.00000			0.0988936			0.0494468	−	0.998777i	$-0.484254\pi$
$409$	2.00000			0.0988936			0.0494468	+	0.998777i	$0.484254\pi$
$410$	2.00000	+	4.00000i	0.0987730	+	0.197546i
$411$	16.0000			0.789222
$412$		−	18.0000i		−	0.886796i
$413$		−	12.0000i		−	0.590481i
$414$	−2.00000			−0.0982946
$415$	−4.00000	−	8.00000i	−0.196352	−	0.392705i
$416$	2.00000			0.0980581
$417$		−	10.0000i		−	0.489702i
$418$		0			0
$419$	18.0000			0.879358			0.439679	−	0.898155i	$-0.355092\pi$
$419$	18.0000			0.879358			0.439679	+	0.898155i	$0.355092\pi$
$420$	−4.00000	+	2.00000i	−0.195180	+	0.0975900i
$421$	−14.0000			−0.682318			−0.341159	−	0.940006i	$-0.610819\pi$
$421$	−14.0000			−0.682318			−0.341159	+	0.940006i	$0.610819\pi$
$422$			4.00000i			0.194717i
$423$		−	4.00000i		−	0.194487i
$424$	−2.00000			−0.0971286
$425$		0			0
$426$	8.00000			0.387601
$427$			16.0000i			0.774294i
$428$		−	4.00000i		−	0.193347i
$429$		0			0
$430$	8.00000	−	4.00000i	0.385794	−	0.192897i
$431$	24.0000			1.15604			0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000			1.15604			0.578020	+	0.816023i	$0.303826\pi$
$432$		−	1.00000i		−	0.0481125i
$433$			2.00000i			0.0961139i	0.998845	+	0.0480569i	$0.0153029\pi$
$433$			2.00000i			0.0961139i	−0.998845	+	0.0480569i	$0.984697\pi$
$434$	−2.00000			−0.0960031
$435$	10.0000	+	20.0000i	0.479463	+	0.958927i
$436$	2.00000			0.0957826
$437$		−	8.00000i		−	0.382692i
$438$		−	10.0000i		−	0.477818i
$439$	16.0000			0.763638			0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000			0.763638			0.381819	+	0.924237i	$0.375298\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$		0			0
$443$		−	20.0000i		−	0.950229i	−0.879924	−	0.475114i	$-0.842407\pi$
$443$		−	20.0000i		−	0.950229i	0.879924	−	0.475114i	$-0.157593\pi$
$444$	−2.00000			−0.0949158
$445$	28.0000	−	14.0000i	1.32733	−	0.663664i
$446$	4.00000			0.189405
$447$			12.0000i			0.567581i
$448$			2.00000i			0.0944911i
$449$	−2.00000			−0.0943858			−0.0471929	−	0.998886i	$-0.515028\pi$
$449$	−2.00000			−0.0943858			−0.0471929	+	0.998886i	$0.515028\pi$
$450$	−4.00000	−	3.00000i	−0.188562	−	0.141421i
$451$		0			0
$452$			6.00000i			0.282216i
$453$		−	16.0000i		−	0.751746i
$454$	−12.0000			−0.563188
$455$	−8.00000	+	4.00000i	−0.375046	+	0.187523i
$456$	4.00000			0.187317
$457$		−	18.0000i		−	0.842004i	−0.907060	−	0.421002i	$-0.861678\pi$
$457$		−	18.0000i		−	0.842004i	0.907060	−	0.421002i	$-0.138322\pi$
$458$		0			0
$459$		0			0
$460$	2.00000	+	4.00000i	0.0932505	+	0.186501i
$461$	10.0000			0.465746			0.232873	−	0.972507i	$-0.425187\pi$
$461$	10.0000			0.465746			0.232873	+	0.972507i	$0.425187\pi$
$462$		0			0
$463$			8.00000i			0.371792i	0.982569	+	0.185896i	$0.0595187\pi$
$463$			8.00000i			0.371792i	−0.982569	+	0.185896i	$0.940481\pi$
$464$	10.0000			0.464238
$465$	−1.00000	−	2.00000i	−0.0463739	−	0.0927478i
$466$	−6.00000			−0.277945
$467$			4.00000i			0.185098i	0.995708	+	0.0925490i	$0.0295015\pi$
$467$			4.00000i			0.185098i	−0.995708	+	0.0925490i	$0.970499\pi$
$468$		−	2.00000i		−	0.0924500i
$469$	16.0000			0.738811
$470$	−8.00000	+	4.00000i	−0.369012	+	0.184506i
$471$	18.0000			0.829396
$472$		−	6.00000i		−	0.276172i
$473$		0			0
$474$	12.0000			0.551178
$475$	12.0000	−	16.0000i	0.550598	−	0.734130i
$476$		0			0
$477$			2.00000i			0.0915737i
$478$			8.00000i			0.365911i
$479$	4.00000			0.182765			0.0913823	−	0.995816i	$-0.470871\pi$
$479$	4.00000			0.182765			0.0913823	+	0.995816i	$0.470871\pi$
$480$	−2.00000	+	1.00000i	−0.0912871	+	0.0456435i
$481$	−4.00000			−0.182384
$482$			18.0000i			0.819878i
$483$		−	4.00000i		−	0.182006i
$484$	11.0000			0.500000
$485$	−4.00000	−	8.00000i	−0.181631	−	0.363261i
$486$	−1.00000			−0.0453609
$487$		−	4.00000i		−	0.181257i	−0.995885	−	0.0906287i	$-0.971112\pi$
$487$		−	4.00000i		−	0.181257i	0.995885	−	0.0906287i	$-0.0288876\pi$
$488$			8.00000i			0.362143i
$489$	−4.00000			−0.180886
$490$	3.00000	+	6.00000i	0.135526	+	0.271052i
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$		−	2.00000i		−	0.0901670i
$493$		0			0
$494$	8.00000			0.359937
$495$		0			0
$496$	−1.00000			−0.0449013
$497$			16.0000i			0.717698i
$498$			4.00000i			0.179244i
$499$	14.0000			0.626726			0.313363	−	0.949633i	$-0.398544\pi$
$499$	14.0000			0.626726			0.313363	+	0.949633i	$0.398544\pi$
$500$	−2.00000	+	11.0000i	−0.0894427	+	0.491935i
$501$	18.0000			0.804181
$502$		−	12.0000i		−	0.535586i
$503$			16.0000i			0.713405i	0.934218	+	0.356702i	$0.116099\pi$
$503$			16.0000i			0.713405i	−0.934218	+	0.356702i	$0.883901\pi$
$504$	2.00000			0.0890871
$505$		0			0
$506$		0			0
$507$			9.00000i			0.399704i
$508$		−	8.00000i		−	0.354943i
$509$	−26.0000			−1.15243			−0.576215	−	0.817298i	$-0.695471\pi$
$509$	−26.0000			−1.15243			−0.576215	+	0.817298i	$0.695471\pi$
$510$		0			0
$511$	20.0000			0.884748
$512$			1.00000i			0.0441942i
$513$		−	4.00000i		−	0.176604i
$514$	−14.0000			−0.617514
$515$	18.0000	+	36.0000i	0.793175	+	1.58635i
$516$	−4.00000			−0.176090
$517$		0			0
$518$		−	4.00000i		−	0.175750i
$519$	−2.00000			−0.0877903
$520$	−4.00000	+	2.00000i	−0.175412	+	0.0877058i
$521$	30.0000			1.31432			0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000			1.31432			0.657162	+	0.753749i	$0.271757\pi$
$522$		−	10.0000i		−	0.437688i
$523$			20.0000i			0.874539i	0.899331	+	0.437269i	$0.144054\pi$
$523$			20.0000i			0.874539i	−0.899331	+	0.437269i	$0.855946\pi$
$524$	2.00000			0.0873704
$525$	6.00000	−	8.00000i	0.261861	−	0.349149i
$526$	−6.00000			−0.261612
$527$		0			0
$528$		0			0
$529$	19.0000			0.826087
$530$	4.00000	−	2.00000i	0.173749	−	0.0868744i
$531$	−6.00000			−0.260378
$532$			8.00000i			0.346844i
$533$		−	4.00000i		−	0.173259i
$534$	−14.0000			−0.605839
$535$	4.00000	+	8.00000i	0.172935	+	0.345870i
$536$	8.00000			0.345547
$537$			12.0000i			0.517838i
$538$		−	14.0000i		−	0.603583i
$539$		0			0
$540$	1.00000	+	2.00000i	0.0430331	+	0.0860663i
$541$	−30.0000			−1.28980			−0.644900	−	0.764267i	$-0.723101\pi$
$541$	−30.0000			−1.28980			−0.644900	+	0.764267i	$0.723101\pi$
$542$		−	12.0000i		−	0.515444i
$543$		−	20.0000i		−	0.858282i
$544$		0			0
$545$	−4.00000	+	2.00000i	−0.171341	+	0.0856706i
$546$	4.00000			0.171184
$547$		−	8.00000i		−	0.342055i	−0.985266	−	0.171028i	$-0.945291\pi$
$547$		−	8.00000i		−	0.342055i	0.985266	−	0.171028i	$-0.0547087\pi$
$548$			16.0000i			0.683486i
$549$	8.00000			0.341432
$550$		0			0
$551$	40.0000			1.70406
$552$		−	2.00000i		−	0.0851257i
$553$			24.0000i			1.02058i
$554$	22.0000			0.934690
$555$	4.00000	−	2.00000i	0.169791	−	0.0848953i
$556$	10.0000			0.424094
$557$			30.0000i			1.27114i	0.772043	+	0.635570i	$0.219235\pi$
$557$			30.0000i			1.27114i	−0.772043	+	0.635570i	$0.780765\pi$
$558$			1.00000i			0.0423334i
$559$	−8.00000			−0.338364
$560$	−2.00000	−	4.00000i	−0.0845154	−	0.169031i
$561$		0			0
$562$		−	2.00000i		−	0.0843649i
$563$			12.0000i			0.505740i	0.967500	+	0.252870i	$0.0813744\pi$
$563$			12.0000i			0.505740i	−0.967500	+	0.252870i	$0.918626\pi$
$564$	4.00000			0.168430
$565$	−6.00000	−	12.0000i	−0.252422	−	0.504844i
$566$	−4.00000			−0.168133
$567$		−	2.00000i		−	0.0839921i
$568$			8.00000i			0.335673i
$569$	−6.00000			−0.251533			−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000			−0.251533			−0.125767	+	0.992060i	$0.540139\pi$
$570$	−8.00000	+	4.00000i	−0.335083	+	0.167542i
$571$	−22.0000			−0.920671			−0.460336	−	0.887745i	$-0.652271\pi$
$571$	−22.0000			−0.920671			−0.460336	+	0.887745i	$0.652271\pi$
$572$		0			0
$573$			8.00000i			0.334205i
$574$	4.00000			0.166957
$575$	−8.00000	−	6.00000i	−0.333623	−	0.250217i
$576$	1.00000			0.0416667
$577$			32.0000i			1.33218i	0.745873	+	0.666089i	$0.232033\pi$
$577$			32.0000i			1.33218i	−0.745873	+	0.666089i	$0.767967\pi$
$578$			17.0000i			0.707107i
$579$	−16.0000			−0.664937
$580$	−20.0000	+	10.0000i	−0.830455	+	0.415227i
$581$	−8.00000			−0.331896
$582$			4.00000i			0.165805i
$583$		0			0
$584$	10.0000			0.413803
$585$	2.00000	+	4.00000i	0.0826898	+	0.165380i
$586$	6.00000			0.247858
$587$			12.0000i			0.495293i	0.968850	+	0.247647i	$0.0796572\pi$
$587$			12.0000i			0.495293i	−0.968850	+	0.247647i	$0.920343\pi$
$588$		−	3.00000i		−	0.123718i
$589$	−4.00000			−0.164817
$590$	6.00000	+	12.0000i	0.247016	+	0.494032i
$591$	−6.00000			−0.246807
$592$		−	2.00000i		−	0.0821995i
$593$		−	18.0000i		−	0.739171i	−0.929197	−	0.369586i	$-0.879500\pi$
$593$		−	18.0000i		−	0.739171i	0.929197	−	0.369586i	$-0.120500\pi$
$594$		0			0
$595$		0			0
$596$	−12.0000			−0.491539
$597$		−	24.0000i		−	0.982255i
$598$		−	4.00000i		−	0.163572i
$599$	32.0000			1.30748			0.653742	−	0.756717i	$-0.273198\pi$
$599$	32.0000			1.30748			0.653742	+	0.756717i	$0.273198\pi$
$600$	3.00000	−	4.00000i	0.122474	−	0.163299i
$601$	−2.00000			−0.0815817			−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000			−0.0815817			−0.0407909	+	0.999168i	$0.512988\pi$
$602$		−	8.00000i		−	0.326056i
$603$		−	8.00000i		−	0.325785i
$604$	16.0000			0.651031
$605$	−22.0000	+	11.0000i	−0.894427	+	0.447214i
$606$		0			0
$607$			6.00000i			0.243532i	0.992559	+	0.121766i	$0.0388558\pi$
$607$			6.00000i			0.243532i	−0.992559	+	0.121766i	$0.961144\pi$
$608$			4.00000i			0.162221i
$609$	20.0000			0.810441
$610$	−8.00000	−	16.0000i	−0.323911	−	0.647821i
$611$	8.00000			0.323645
$612$		0			0
$613$			6.00000i			0.242338i	0.992632	+	0.121169i	$0.0386643\pi$
$613$			6.00000i			0.242338i	−0.992632	+	0.121169i	$0.961336\pi$
$614$	4.00000			0.161427
$615$	2.00000	+	4.00000i	0.0806478	+	0.161296i
$616$		0			0
$617$			38.0000i			1.52982i	0.644136	+	0.764911i	$0.277217\pi$
$617$			38.0000i			1.52982i	−0.644136	+	0.764911i	$0.722783\pi$
$618$		−	18.0000i		−	0.724066i
$619$	30.0000			1.20580			0.602901	−	0.797816i	$-0.294011\pi$
$619$	30.0000			1.20580			0.602901	+	0.797816i	$0.294011\pi$
$620$	2.00000	−	1.00000i	0.0803219	−	0.0401610i
$621$	−2.00000			−0.0802572
$622$		−	20.0000i		−	0.801927i
$623$		−	28.0000i		−	1.12180i
$624$	2.00000			0.0800641
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	6.00000			0.239808
$627$		0			0
$628$			18.0000i			0.718278i
$629$		0			0
$630$	−4.00000	+	2.00000i	−0.159364	+	0.0796819i
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$			12.0000i			0.477334i
$633$			4.00000i			0.158986i
$634$	−30.0000			−1.19145
$635$	8.00000	+	16.0000i	0.317470	+	0.634941i
$636$	−2.00000			−0.0793052
$637$		−	6.00000i		−	0.237729i
$638$		0			0
$639$	8.00000			0.316475
$640$	−1.00000	−	2.00000i	−0.0395285	−	0.0790569i
$641$	−10.0000			−0.394976			−0.197488	−	0.980305i	$-0.563278\pi$
$641$	−10.0000			−0.394976			−0.197488	+	0.980305i	$0.563278\pi$
$642$		−	4.00000i		−	0.157867i
$643$		−	44.0000i		−	1.73519i	−0.497271	−	0.867595i	$-0.665665\pi$
$643$		−	44.0000i		−	1.73519i	0.497271	−	0.867595i	$-0.334335\pi$
$644$	4.00000			0.157622
$645$	8.00000	−	4.00000i	0.315000	−	0.157500i
$646$		0			0
$647$			34.0000i			1.33668i	0.743857	+	0.668339i	$0.232994\pi$
$647$			34.0000i			1.33668i	−0.743857	+	0.668339i	$0.767006\pi$
$648$		−	1.00000i		−	0.0392837i
$649$		0			0
$650$	6.00000	−	8.00000i	0.235339	−	0.313786i
$651$	−2.00000			−0.0783862
$652$		−	4.00000i		−	0.156652i
$653$		−	42.0000i		−	1.64359i	−0.569785	−	0.821794i	$-0.692974\pi$
$653$		−	42.0000i		−	1.64359i	0.569785	−	0.821794i	$-0.307026\pi$
$654$	2.00000			0.0782062
$655$	−4.00000	+	2.00000i	−0.156293	+	0.0781465i
$656$	2.00000			0.0780869
$657$		−	10.0000i		−	0.390137i
$658$			8.00000i			0.311872i
$659$	−6.00000			−0.233727			−0.116863	−	0.993148i	$-0.537284\pi$
$659$	−6.00000			−0.233727			−0.116863	+	0.993148i	$0.537284\pi$
$660$		0			0
$661$	42.0000			1.63361			0.816805	−	0.576913i	$-0.195743\pi$
$661$	42.0000			1.63361			0.816805	+	0.576913i	$0.195743\pi$
$662$			14.0000i			0.544125i
$663$		0			0
$664$	−4.00000			−0.155230
$665$	−8.00000	−	16.0000i	−0.310227	−	0.620453i
$666$	−2.00000			−0.0774984
$667$		−	20.0000i		−	0.774403i
$668$			18.0000i			0.696441i
$669$	4.00000			0.154649
$670$	−16.0000	+	8.00000i	−0.618134	+	0.309067i
$671$		0			0
$672$			2.00000i			0.0771517i
$673$			6.00000i			0.231283i	0.993291	+	0.115642i	$0.0368924\pi$
$673$			6.00000i			0.231283i	−0.993291	+	0.115642i	$0.963108\pi$
$674$	−2.00000			−0.0770371
$675$	−4.00000	−	3.00000i	−0.153960	−	0.115470i
$676$	−9.00000			−0.346154
$677$		−	26.0000i		−	0.999261i	−0.866239	−	0.499631i	$-0.833469\pi$
$677$		−	26.0000i		−	0.999261i	0.866239	−	0.499631i	$-0.166531\pi$
$678$			6.00000i			0.230429i
$679$	−8.00000			−0.307012
$680$		0			0
$681$	−12.0000			−0.459841
$682$		0			0
$683$			28.0000i			1.07139i	0.844411	+	0.535695i	$0.179950\pi$
$683$			28.0000i			1.07139i	−0.844411	+	0.535695i	$0.820050\pi$
$684$	4.00000			0.152944
$685$	−16.0000	−	32.0000i	−0.611329	−	1.22266i
$686$	20.0000			0.763604
$687$		0			0
$688$		−	4.00000i		−	0.152499i
$689$	−4.00000			−0.152388
$690$	2.00000	+	4.00000i	0.0761387	+	0.152277i
$691$	−8.00000			−0.304334			−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000			−0.304334			−0.152167	+	0.988355i	$0.548625\pi$
$692$		−	2.00000i		−	0.0760286i
$693$		0			0
$694$	−32.0000			−1.21470
$695$	−20.0000	+	10.0000i	−0.758643	+	0.379322i
$696$	10.0000			0.379049
$697$		0			0
$698$			10.0000i			0.378506i
$699$	−6.00000			−0.226941
$700$	8.00000	+	6.00000i	0.302372	+	0.226779i
$701$	−20.0000			−0.755390			−0.377695	−	0.925930i	$-0.623283\pi$
$701$	−20.0000			−0.755390			−0.377695	+	0.925930i	$0.623283\pi$
$702$		−	2.00000i		−	0.0754851i
$703$		−	8.00000i		−	0.301726i
$704$		0			0
$705$	−8.00000	+	4.00000i	−0.301297	+	0.150649i
$706$	12.0000			0.451626
$707$		0			0
$708$		−	6.00000i		−	0.225494i
$709$	−20.0000			−0.751116			−0.375558	−	0.926799i	$-0.622549\pi$
$709$	−20.0000			−0.751116			−0.375558	+	0.926799i	$0.622549\pi$
$710$	−8.00000	−	16.0000i	−0.300235	−	0.600469i
$711$	12.0000			0.450035
$712$		−	14.0000i		−	0.524672i
$713$			2.00000i			0.0749006i
$714$		0			0
$715$		0			0
$716$	−12.0000			−0.448461
$717$			8.00000i			0.298765i
$718$		−	24.0000i		−	0.895672i
$719$	8.00000			0.298350			0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000			0.298350			0.149175	+	0.988811i	$0.452338\pi$
$720$	−2.00000	+	1.00000i	−0.0745356	+	0.0372678i
$721$	36.0000			1.34071
$722$		−	3.00000i		−	0.111648i
$723$			18.0000i			0.669427i
$724$	20.0000			0.743294
$725$	30.0000	−	40.0000i	1.11417	−	1.48556i
$726$	11.0000			0.408248
$727$		−	26.0000i		−	0.964287i	−0.876092	−	0.482143i	$-0.839858\pi$
$727$		−	26.0000i		−	0.964287i	0.876092	−	0.482143i	$-0.160142\pi$
$728$			4.00000i			0.148250i
$729$	−1.00000			−0.0370370
$730$	−20.0000	+	10.0000i	−0.740233	+	0.370117i
$731$		0			0
$732$			8.00000i			0.295689i
$733$			22.0000i			0.812589i	0.913742	+	0.406294i	$0.133179\pi$
$733$			22.0000i			0.812589i	−0.913742	+	0.406294i	$0.866821\pi$
$734$	−32.0000			−1.18114
$735$	3.00000	+	6.00000i	0.110657	+	0.221313i
$736$	2.00000			0.0737210
$737$		0			0
$738$		−	2.00000i		−	0.0736210i
$739$	−54.0000			−1.98642			−0.993211	−	0.116326i	$-0.962888\pi$
$739$	−54.0000			−1.98642			−0.993211	+	0.116326i	$0.962888\pi$
$740$	2.00000	+	4.00000i	0.0735215	+	0.147043i
$741$	8.00000			0.293887
$742$		−	4.00000i		−	0.146845i
$743$		−	30.0000i		−	1.10059i	−0.834969	−	0.550297i	$-0.814515\pi$
$743$		−	30.0000i		−	1.10059i	0.834969	−	0.550297i	$-0.185485\pi$
$744$	−1.00000			−0.0366618
$745$	24.0000	−	12.0000i	0.879292	−	0.439646i
$746$	−26.0000			−0.951928
$747$			4.00000i			0.146352i
$748$		0			0
$749$	8.00000			0.292314
$750$	−2.00000	+	11.0000i	−0.0730297	+	0.401663i
$751$	−32.0000			−1.16770			−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000			−1.16770			−0.583848	+	0.811863i	$0.698454\pi$
$752$			4.00000i			0.145865i
$753$		−	12.0000i		−	0.437304i
$754$	20.0000			0.728357
$755$	−32.0000	+	16.0000i	−1.16460	+	0.582300i
$756$	2.00000			0.0727393
$757$		−	22.0000i		−	0.799604i	−0.916602	−	0.399802i	$-0.869079\pi$
$757$		−	22.0000i		−	0.799604i	0.916602	−	0.399802i	$-0.130921\pi$
$758$		−	24.0000i		−	0.871719i
$759$		0			0
$760$	−4.00000	−	8.00000i	−0.145095	−	0.290191i
$761$	−6.00000			−0.217500			−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000			−0.217500			−0.108750	+	0.994069i	$0.534685\pi$
$762$		−	8.00000i		−	0.289809i
$763$			4.00000i			0.144810i
$764$	−8.00000			−0.289430
$765$		0			0
$766$	−38.0000			−1.37300
$767$		−	12.0000i		−	0.433295i
$768$			1.00000i			0.0360844i
$769$	−6.00000			−0.216366			−0.108183	−	0.994131i	$-0.534503\pi$
$769$	−6.00000			−0.216366			−0.108183	+	0.994131i	$0.534503\pi$
$770$		0			0
$771$	−14.0000			−0.504198
$772$		−	16.0000i		−	0.575853i
$773$			14.0000i			0.503545i	0.967786	+	0.251773i	$0.0810135\pi$
$773$			14.0000i			0.503545i	−0.967786	+	0.251773i	$0.918987\pi$
$774$	−4.00000			−0.143777
$775$	−3.00000	+	4.00000i	−0.107763	+	0.143684i
$776$	−4.00000			−0.143592
$777$		−	4.00000i		−	0.143499i
$778$		−	14.0000i		−	0.501924i
$779$	8.00000			0.286630
$780$	−4.00000	+	2.00000i	−0.143223	+	0.0716115i
$781$		0			0
$782$		0			0
$783$		−	10.0000i		−	0.357371i
$784$	3.00000			0.107143
$785$	−18.0000	−	36.0000i	−0.642448	−	1.28490i
$786$	2.00000			0.0713376
$787$			12.0000i			0.427754i	0.976861	+	0.213877i	$0.0686091\pi$
$787$			12.0000i			0.427754i	−0.976861	+	0.213877i	$0.931391\pi$
$788$		−	6.00000i		−	0.213741i
$789$	−6.00000			−0.213606
$790$	−12.0000	−	24.0000i	−0.426941	−	0.853882i
$791$	−12.0000			−0.426671
$792$		0			0
$793$			16.0000i			0.568177i
$794$	−26.0000			−0.922705
$795$	4.00000	−	2.00000i	0.141865	−	0.0709327i
$796$	24.0000			0.850657
$797$			2.00000i			0.0708436i	0.999372	+	0.0354218i	$0.0112775\pi$
$797$			2.00000i			0.0708436i	−0.999372	+	0.0354218i	$0.988723\pi$
$798$			8.00000i			0.283197i
$799$		0			0
$800$	4.00000	+	3.00000i	0.141421	+	0.106066i
$801$	−14.0000			−0.494666
$802$			2.00000i			0.0706225i
$803$		0			0
$804$	8.00000			0.282138
$805$	−8.00000	+	4.00000i	−0.281963	+	0.140981i
$806$	−2.00000			−0.0704470
$807$		−	14.0000i		−	0.492823i
$808$		0			0
$809$	−42.0000			−1.47664			−0.738321	−	0.674450i	$-0.764381\pi$
$809$	−42.0000			−1.47664			−0.738321	+	0.674450i	$0.764381\pi$
$810$	1.00000	+	2.00000i	0.0351364	+	0.0702728i
$811$	−40.0000			−1.40459			−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000			−1.40459			−0.702295	+	0.711886i	$0.747841\pi$
$812$			20.0000i			0.701862i
$813$		−	12.0000i		−	0.420858i
$814$		0			0
$815$	4.00000	+	8.00000i	0.140114	+	0.280228i
$816$		0			0
$817$		−	16.0000i		−	0.559769i
$818$			2.00000i			0.0699284i
$819$	4.00000			0.139771
$820$	−4.00000	+	2.00000i	−0.139686	+	0.0698430i
$821$	30.0000			1.04701			0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000			1.04701			0.523504	+	0.852023i	$0.324625\pi$
$822$			16.0000i			0.558064i
$823$		−	36.0000i		−	1.25488i	−0.778664	−	0.627441i	$-0.784103\pi$
$823$		−	36.0000i		−	1.25488i	0.778664	−	0.627441i	$-0.215897\pi$
$824$	18.0000			0.627060
$825$		0			0
$826$	12.0000			0.417533
$827$			32.0000i			1.11275i	0.830932	+	0.556375i	$0.187808\pi$
$827$			32.0000i			1.11275i	−0.830932	+	0.556375i	$0.812192\pi$
$828$		−	2.00000i		−	0.0695048i
$829$	4.00000			0.138926			0.0694629	−	0.997585i	$-0.477871\pi$
$829$	4.00000			0.138926			0.0694629	+	0.997585i	$0.477871\pi$
$830$	8.00000	−	4.00000i	0.277684	−	0.138842i
$831$	22.0000			0.763172
$832$			2.00000i			0.0693375i
$833$		0			0
$834$	10.0000			0.346272
$835$	−18.0000	−	36.0000i	−0.622916	−	1.24583i
$836$		0			0
$837$			1.00000i			0.0345651i
$838$			18.0000i			0.621800i
$839$	−24.0000			−0.828572			−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000			−0.828572			−0.414286	+	0.910147i	$0.635969\pi$
$840$	−2.00000	−	4.00000i	−0.0690066	−	0.138013i
$841$	71.0000			2.44828
$842$		−	14.0000i		−	0.482472i
$843$		−	2.00000i		−	0.0688837i
$844$	−4.00000			−0.137686
$845$	18.0000	−	9.00000i	0.619219	−	0.309609i
$846$	4.00000			0.137523
$847$			22.0000i			0.755929i
$848$		−	2.00000i		−	0.0686803i
$849$	−4.00000			−0.137280
$850$		0			0
$851$	−4.00000			−0.137118
$852$			8.00000i			0.274075i
$853$		−	26.0000i		−	0.890223i	−0.895475	−	0.445112i	$-0.853164\pi$
$853$		−	26.0000i		−	0.890223i	0.895475	−	0.445112i	$-0.146836\pi$
$854$	−16.0000			−0.547509
$855$	−8.00000	+	4.00000i	−0.273594	+	0.136797i
$856$	4.00000			0.136717
$857$		−	22.0000i		−	0.751506i	−0.926720	−	0.375753i	$-0.877384\pi$
$857$		−	22.0000i		−	0.751506i	0.926720	−	0.375753i	$-0.122616\pi$
$858$		0			0
$859$	−22.0000			−0.750630			−0.375315	−	0.926897i	$-0.622466\pi$
$859$	−22.0000			−0.750630			−0.375315	+	0.926897i	$0.622466\pi$
$860$	4.00000	+	8.00000i	0.136399	+	0.272798i
$861$	4.00000			0.136320
$862$			24.0000i			0.817443i
$863$		−	46.0000i		−	1.56586i	−0.622111	−	0.782929i	$-0.713725\pi$
$863$		−	46.0000i		−	1.56586i	0.622111	−	0.782929i	$-0.286275\pi$
$864$	1.00000			0.0340207
$865$	2.00000	+	4.00000i	0.0680020	+	0.136004i
$866$	−2.00000			−0.0679628
$867$			17.0000i			0.577350i
$868$		−	2.00000i		−	0.0678844i
$869$		0			0
$870$	−20.0000	+	10.0000i	−0.678064	+	0.339032i
$871$	16.0000			0.542139
$872$			2.00000i			0.0677285i
$873$			4.00000i			0.135379i
$874$	8.00000			0.270604
$875$	−22.0000	−	4.00000i	−0.743736	−	0.135225i
$876$	10.0000			0.337869
$877$			54.0000i			1.82345i	0.410801	+	0.911725i	$0.365249\pi$
$877$			54.0000i			1.82345i	−0.410801	+	0.911725i	$0.634751\pi$
$878$			16.0000i			0.539974i
$879$	6.00000			0.202375
$880$		0			0
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		−	3.00000i		−	0.101015i
$883$			44.0000i			1.48072i	0.672212	+	0.740359i	$0.265344\pi$
$883$			44.0000i			1.48072i	−0.672212	+	0.740359i	$0.734656\pi$
$884$		0			0
$885$	6.00000	+	12.0000i	0.201688	+	0.403376i
$886$	20.0000			0.671913
$887$		−	48.0000i		−	1.61168i	−0.592132	−	0.805841i	$-0.701714\pi$
$887$		−	48.0000i		−	1.61168i	0.592132	−	0.805841i	$-0.298286\pi$
$888$		−	2.00000i		−	0.0671156i
$889$	16.0000			0.536623
$890$	14.0000	+	28.0000i	0.469281	+	0.938562i
$891$		0			0
$892$			4.00000i			0.133930i
$893$			16.0000i			0.535420i
$894$	−12.0000			−0.401340
$895$	24.0000	−	12.0000i	0.802232	−	0.401116i
$896$	−2.00000			−0.0668153
$897$		−	4.00000i		−	0.133556i
$898$		−	2.00000i		−	0.0667409i
$899$	−10.0000			−0.333519
$900$	3.00000	−	4.00000i	0.100000	−	0.133333i
$901$		0			0
$902$		0			0
$903$		−	8.00000i		−	0.266223i
$904$	−6.00000			−0.199557
$905$	−40.0000	+	20.0000i	−1.32964	+	0.664822i
$906$	16.0000			0.531564
$907$		−	12.0000i		−	0.398453i	−0.979953	−	0.199227i	$-0.936157\pi$
$907$		−	12.0000i		−	0.398453i	0.979953	−	0.199227i	$-0.0638430\pi$
$908$		−	12.0000i		−	0.398234i
$909$		0			0
$910$	−4.00000	−	8.00000i	−0.132599	−	0.265197i
$911$	32.0000			1.06021			0.530104	−	0.847933i	$-0.322153\pi$
$911$	32.0000			1.06021			0.530104	+	0.847933i	$0.322153\pi$
$912$			4.00000i			0.132453i
$913$		0			0
$914$	18.0000			0.595387
$915$	−8.00000	−	16.0000i	−0.264472	−	0.528944i
$916$		0			0
$917$			4.00000i			0.132092i
$918$		0			0
$919$	−8.00000			−0.263896			−0.131948	−	0.991257i	$-0.542123\pi$
$919$	−8.00000			−0.263896			−0.131948	+	0.991257i	$0.542123\pi$
$920$	−4.00000	+	2.00000i	−0.131876	+	0.0659380i
$921$	4.00000			0.131804
$922$			10.0000i			0.329332i
$923$			16.0000i			0.526646i
$924$		0			0
$925$	−8.00000	−	6.00000i	−0.263038	−	0.197279i
$926$	−8.00000			−0.262896
$927$		−	18.0000i		−	0.591198i
$928$			10.0000i			0.328266i
$929$	34.0000			1.11550			0.557752	−	0.830008i	$-0.311664\pi$
$929$	34.0000			1.11550			0.557752	+	0.830008i	$0.311664\pi$
$930$	2.00000	−	1.00000i	0.0655826	−	0.0327913i
$931$	12.0000			0.393284
$932$		−	6.00000i		−	0.196537i
$933$		−	20.0000i		−	0.654771i
$934$	−4.00000			−0.130884
$935$		0			0
$936$	2.00000			0.0653720
$937$		−	20.0000i		−	0.653372i	−0.945133	−	0.326686i	$-0.894068\pi$
$937$		−	20.0000i		−	0.653372i	0.945133	−	0.326686i	$-0.105932\pi$
$938$			16.0000i			0.522419i
$939$	6.00000			0.195803
$940$	−4.00000	−	8.00000i	−0.130466	−	0.260931i
$941$	−50.0000			−1.62995			−0.814977	−	0.579494i	$-0.803250\pi$
$941$	−50.0000			−1.62995			−0.814977	+	0.579494i	$0.803250\pi$
$942$			18.0000i			0.586472i
$943$		−	4.00000i		−	0.130258i
$944$	6.00000			0.195283
$945$	−4.00000	+	2.00000i	−0.130120	+	0.0650600i
$946$		0			0
$947$			52.0000i			1.68977i	0.534946	+	0.844886i	$0.320332\pi$
$947$			52.0000i			1.68977i	−0.534946	+	0.844886i	$0.679668\pi$
$948$			12.0000i			0.389742i
$949$	20.0000			0.649227
$950$	16.0000	+	12.0000i	0.519109	+	0.389331i
$951$	−30.0000			−0.972817
$952$		0			0
$953$		−	8.00000i		−	0.259145i	−0.991570	−	0.129573i	$-0.958639\pi$
$953$		−	8.00000i		−	0.259145i	0.991570	−	0.129573i	$-0.0413606\pi$
$954$	−2.00000			−0.0647524
$955$	16.0000	−	8.00000i	0.517748	−	0.258874i
$956$	−8.00000			−0.258738
$957$		0			0
$958$			4.00000i			0.129234i
$959$	−32.0000			−1.03333
$960$	−1.00000	−	2.00000i	−0.0322749	−	0.0645497i
$961$	1.00000			0.0322581
$962$		−	4.00000i		−	0.128965i
$963$		−	4.00000i		−	0.128898i
$964$	−18.0000			−0.579741
$965$	16.0000	+	32.0000i	0.515058	+	1.03012i
$966$	4.00000			0.128698
$967$		−	32.0000i		−	1.02905i	−0.857475	−	0.514525i	$-0.827968\pi$
$967$		−	32.0000i		−	1.02905i	0.857475	−	0.514525i	$-0.172032\pi$
$968$			11.0000i			0.353553i
$969$		0			0
$970$	8.00000	−	4.00000i	0.256865	−	0.128432i
$971$	18.0000			0.577647			0.288824	−	0.957382i	$-0.406736\pi$
$971$	18.0000			0.577647			0.288824	+	0.957382i	$0.406736\pi$
$972$		−	1.00000i		−	0.0320750i
$973$			20.0000i			0.641171i
$974$	4.00000			0.128168
$975$	6.00000	−	8.00000i	0.192154	−	0.256205i
$976$	−8.00000			−0.256074
$977$		−	42.0000i		−	1.34370i	−0.740688	−	0.671850i	$-0.765500\pi$
$977$		−	42.0000i		−	1.34370i	0.740688	−	0.671850i	$-0.234500\pi$
$978$		−	4.00000i		−	0.127906i
$979$		0			0
$980$	−6.00000	+	3.00000i	−0.191663	+	0.0958315i
$981$	2.00000			0.0638551
$982$		0			0
$983$		−	6.00000i		−	0.191370i	−0.995412	−	0.0956851i	$-0.969496\pi$
$983$		−	6.00000i		−	0.191370i	0.995412	−	0.0956851i	$-0.0305042\pi$
$984$	2.00000			0.0637577
$985$	6.00000	+	12.0000i	0.191176	+	0.382352i
$986$		0			0
$987$			8.00000i			0.254643i
$988$			8.00000i			0.254514i
$989$	−8.00000			−0.254385
$990$		0			0
$991$	40.0000			1.27064			0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000			1.27064			0.635321	+	0.772248i	$0.280868\pi$
$992$		−	1.00000i		−	0.0317500i
$993$			14.0000i			0.444277i
$994$	−16.0000			−0.507489
$995$	−48.0000	+	24.0000i	−1.52170	+	0.760851i
$996$	−4.00000			−0.126745
$997$		−	42.0000i		−	1.33015i	−0.746775	−	0.665077i	$-0.768399\pi$
$997$		−	42.0000i		−	1.33015i	0.746775	−	0.665077i	$-0.231601\pi$
$998$			14.0000i			0.443162i
$999$	−2.00000			−0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.d.d.559.2	yes	2
3.2	odd	2		2790.2.d.d.559.1		2
5.2	odd	4		4650.2.a.u.1.1		1
5.3	odd	4		4650.2.a.z.1.1		1
5.4	even	2	inner	930.2.d.d.559.1	✓	2
15.14	odd	2		2790.2.d.d.559.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.d.d.559.1	✓	2	5.4	even	2	inner
930.2.d.d.559.2	yes	2	1.1	even	1	trivial
2790.2.d.d.559.1		2	3.2	odd	2
2790.2.d.d.559.2		2	15.14	odd	2
4650.2.a.u.1.1		1	5.2	odd	4
4650.2.a.z.1.1		1	5.3	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} -1.00000 q^{6} -2.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(1.00000 + 2.00000i) q^{10} -1.00000i q^{12} -2.00000i q^{13} +2.00000 q^{14} +(1.00000 + 2.00000i) q^{15} +1.00000 q^{16} -1.00000i q^{18} +4.00000 q^{19} +(-2.00000 + 1.00000i) q^{20} +2.00000 q^{21} -2.00000i q^{23} +1.00000 q^{24} +(3.00000 - 4.00000i) q^{25} +2.00000 q^{26} -1.00000i q^{27} +2.00000i q^{28} +10.0000 q^{29} +(-2.00000 + 1.00000i) q^{30} -1.00000 q^{31} +1.00000i q^{32} +(-2.00000 - 4.00000i) q^{35} +1.00000 q^{36} -2.00000i q^{37} +4.00000i q^{38} +2.00000 q^{39} +(-1.00000 - 2.00000i) q^{40} +2.00000 q^{41} +2.00000i q^{42} -4.00000i q^{43} +(-2.00000 + 1.00000i) q^{45} +2.00000 q^{46} +4.00000i q^{47} +1.00000i q^{48} +3.00000 q^{49} +(4.00000 + 3.00000i) q^{50} +2.00000i q^{52} -2.00000i q^{53} +1.00000 q^{54} -2.00000 q^{56} +4.00000i q^{57} +10.0000i q^{58} +6.00000 q^{59} +(-1.00000 - 2.00000i) q^{60} -8.00000 q^{61} -1.00000i q^{62} +2.00000i q^{63} -1.00000 q^{64} +(-2.00000 - 4.00000i) q^{65} +8.00000i q^{67} +2.00000 q^{69} +(4.00000 - 2.00000i) q^{70} -8.00000 q^{71} +1.00000i q^{72} +10.0000i q^{73} +2.00000 q^{74} +(4.00000 + 3.00000i) q^{75} -4.00000 q^{76} +2.00000i q^{78} -12.0000 q^{79} +(2.00000 - 1.00000i) q^{80} +1.00000 q^{81} +2.00000i q^{82} -4.00000i q^{83} -2.00000 q^{84} +4.00000 q^{86} +10.0000i q^{87} +14.0000 q^{89} +(-1.00000 - 2.00000i) q^{90} -4.00000 q^{91} +2.00000i q^{92} -1.00000i q^{93} -4.00000 q^{94} +(8.00000 - 4.00000i) q^{95} -1.00000 q^{96} -4.00000i q^{97} +3.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{9} + 2 q^{10} + 4 q^{14} + 2 q^{15} + 2 q^{16} + 8 q^{19} - 4 q^{20} + 4 q^{21} + 2 q^{24} + 6 q^{25} + 4 q^{26} + 20 q^{29} - 4 q^{30} - 2 q^{31} - 4 q^{35} + 2 q^{36}+ \cdots - 2 q^{96}+O(q^{100}) \) 2 * q - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^9 + 2 * q^10 + 4 * q^14 + 2 * q^15 + 2 * q^16 + 8 * q^19 - 4 * q^20 + 4 * q^21 + 2 * q^24 + 6 * q^25 + 4 * q^26 + 20 * q^29 - 4 * q^30 - 2 * q^31 - 4 * q^35 + 2 * q^36 + 4 * q^39 - 2 * q^40 + 4 * q^41 - 4 * q^45 + 4 * q^46 + 6 * q^49 + 8 * q^50 + 2 * q^54 - 4 * q^56 + 12 * q^59 - 2 * q^60 - 16 * q^61 - 2 * q^64 - 4 * q^65 + 4 * q^69 + 8 * q^70 - 16 * q^71 + 4 * q^74 + 8 * q^75 - 8 * q^76 - 24 * q^79 + 4 * q^80 + 2 * q^81 - 4 * q^84 + 8 * q^86 + 28 * q^89 - 2 * q^90 - 8 * q^91 - 8 * q^94 + 16 * q^95 - 2 * q^96

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