LMFDB - Embedded newform 1650.2.f.a.1649.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1650,2,Mod(1649,1650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1650, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1650.1649"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1650.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,-4,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$13.1753163335$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1649.3
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1650.1649
Dual form			1650.2.f.a.1649.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +(-1.41421 + 1.00000i) q^{3} -1.00000 q^{4} +(-1.00000 - 1.41421i) q^{6} -4.24264 q^{7} -1.00000i q^{8} +(1.00000 - 2.82843i) q^{9} +(-3.00000 + 1.41421i) q^{11} +(1.41421 - 1.00000i) q^{12} -4.24264 q^{13} -4.24264i q^{14} +1.00000 q^{16} +(2.82843 + 1.00000i) q^{18} +(6.00000 - 4.24264i) q^{21} +(-1.41421 - 3.00000i) q^{22} -1.41421 q^{23} +(1.00000 + 1.41421i) q^{24} -4.24264i q^{26} +(1.41421 + 5.00000i) q^{27} +4.24264 q^{28} +6.00000 q^{29} -4.00000 q^{31} +1.00000i q^{32} +(2.82843 - 5.00000i) q^{33} +(-1.00000 + 2.82843i) q^{36} +2.00000i q^{37} +(6.00000 - 4.24264i) q^{39} +6.00000 q^{41} +(4.24264 + 6.00000i) q^{42} -8.48528 q^{43} +(3.00000 - 1.41421i) q^{44} -1.41421i q^{46} +9.89949 q^{47} +(-1.41421 + 1.00000i) q^{48} +11.0000 q^{49} +4.24264 q^{52} +7.07107 q^{53} +(-5.00000 + 1.41421i) q^{54} +4.24264i q^{56} +6.00000i q^{58} -11.3137i q^{59} +4.24264i q^{61} -4.00000i q^{62} +(-4.24264 + 12.0000i) q^{63} -1.00000 q^{64} +(5.00000 + 2.82843i) q^{66} -4.00000i q^{67} +(2.00000 - 1.41421i) q^{69} +7.07107i q^{71} +(-2.82843 - 1.00000i) q^{72} -2.00000 q^{74} +(12.7279 - 6.00000i) q^{77} +(4.24264 + 6.00000i) q^{78} -4.24264i q^{79} +(-7.00000 - 5.65685i) q^{81} +6.00000i q^{82} -12.0000i q^{83} +(-6.00000 + 4.24264i) q^{84} -8.48528i q^{86} +(-8.48528 + 6.00000i) q^{87} +(1.41421 + 3.00000i) q^{88} +5.65685i q^{89} +18.0000 q^{91} +1.41421 q^{92} +(5.65685 - 4.00000i) q^{93} +9.89949i q^{94} +(-1.00000 - 1.41421i) q^{96} +8.00000i q^{97} +11.0000i q^{98} +(1.00000 + 9.89949i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 4 q^{6} + 4 q^{9} - 12 q^{11} + 4 q^{16} + 24 q^{21} + 4 q^{24} + 24 q^{29} - 16 q^{31} - 4 q^{36} + 24 q^{39} + 24 q^{41} + 12 q^{44} + 44 q^{49} - 20 q^{54} - 4 q^{64} + 20 q^{66} + 8 q^{69}+ \cdots + 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 - 4 * q^6 + 4 * q^9 - 12 * q^11 + 4 * q^16 + 24 * q^21 + 4 * q^24 + 24 * q^29 - 16 * q^31 - 4 * q^36 + 24 * q^39 + 24 * q^41 + 12 * q^44 + 44 * q^49 - 20 * q^54 - 4 * q^64 + 20 * q^66 + 8 * q^69 - 8 * q^74 - 28 * q^81 - 24 * q^84 + 72 * q^91 - 4 * q^96 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1650\mathbb{Z}\right)^\times$.

$n$	$551$	$727$	$1201$
$\chi(n)$	$-1$	$-1$	$-1$

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
$3$	−1.41421	+	1.00000i	−0.816497	+	0.577350i
$3$	−1.41421	+	1.00000i	−0.816497	+	0.577350i
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−1.00000	−	1.41421i	−0.408248	−	0.577350i
$7$	−4.24264			−1.60357			−0.801784	−	0.597614i	$-0.796115\pi$
$7$	−4.24264			−1.60357			−0.801784	+	0.597614i	$0.796115\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.00000	−	2.82843i	0.333333	−	0.942809i
$10$		0			0
$11$	−3.00000	+	1.41421i	−0.904534	+	0.426401i
$11$	−3.00000	+	1.41421i	−0.904534	+	0.426401i
$12$	1.41421	−	1.00000i	0.408248	−	0.288675i
$13$	−4.24264			−1.17670			−0.588348	−	0.808608i	$-0.700222\pi$
$13$	−4.24264			−1.17670			−0.588348	+	0.808608i	$0.700222\pi$
$14$		−	4.24264i		−	1.13389i
$15$		0			0
$16$	1.00000			0.250000
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$	2.82843	+	1.00000i	0.666667	+	0.235702i
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$		0			0
$21$	6.00000	−	4.24264i	1.30931	−	0.925820i
$22$	−1.41421	−	3.00000i	−0.301511	−	0.639602i
$23$	−1.41421			−0.294884			−0.147442	−	0.989071i	$-0.547104\pi$
$23$	−1.41421			−0.294884			−0.147442	+	0.989071i	$0.547104\pi$
$24$	1.00000	+	1.41421i	0.204124	+	0.288675i
$25$		0			0
$26$		−	4.24264i		−	0.832050i
$27$	1.41421	+	5.00000i	0.272166	+	0.962250i
$28$	4.24264			0.801784
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$			1.00000i			0.176777i
$33$	2.82843	−	5.00000i	0.492366	−	0.870388i
$34$		0			0
$35$		0			0
$36$	−1.00000	+	2.82843i	−0.166667	+	0.471405i
$37$			2.00000i			0.328798i	0.986394	+	0.164399i	$0.0525685\pi$
$37$			2.00000i			0.328798i	−0.986394	+	0.164399i	$0.947432\pi$
$38$		0			0
$39$	6.00000	−	4.24264i	0.960769	−	0.679366i
$40$		0			0
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$	4.24264	+	6.00000i	0.654654	+	0.925820i
$43$	−8.48528			−1.29399			−0.646997	−	0.762493i	$-0.723975\pi$
$43$	−8.48528			−1.29399			−0.646997	+	0.762493i	$0.723975\pi$
$44$	3.00000	−	1.41421i	0.452267	−	0.213201i
$45$		0			0
$46$		−	1.41421i		−	0.208514i
$47$	9.89949			1.44399			0.721995	−	0.691898i	$-0.243225\pi$
$47$	9.89949			1.44399			0.721995	+	0.691898i	$0.243225\pi$
$48$	−1.41421	+	1.00000i	−0.204124	+	0.144338i
$49$	11.0000			1.57143
$50$		0			0
$51$		0			0
$52$	4.24264			0.588348
$53$	7.07107			0.971286			0.485643	−	0.874157i	$-0.338586\pi$
$53$	7.07107			0.971286			0.485643	+	0.874157i	$0.338586\pi$
$54$	−5.00000	+	1.41421i	−0.680414	+	0.192450i
$55$		0			0
$56$			4.24264i			0.566947i
$57$		0			0
$58$			6.00000i			0.787839i
$59$		−	11.3137i		−	1.47292i	−0.676481	−	0.736460i	$-0.736496\pi$
$59$		−	11.3137i		−	1.47292i	0.676481	−	0.736460i	$-0.263504\pi$
$60$		0			0
$61$			4.24264i			0.543214i	0.962408	+	0.271607i	$0.0875552\pi$
$61$			4.24264i			0.543214i	−0.962408	+	0.271607i	$0.912445\pi$
$62$		−	4.00000i		−	0.508001i
$63$	−4.24264	+	12.0000i	−0.534522	+	1.51186i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	5.00000	+	2.82843i	0.615457	+	0.348155i
$67$		−	4.00000i		−	0.488678i	−0.969690	−	0.244339i	$-0.921429\pi$
$67$		−	4.00000i		−	0.488678i	0.969690	−	0.244339i	$-0.0785709\pi$
$68$		0			0
$69$	2.00000	−	1.41421i	0.240772	−	0.170251i
$70$		0			0
$71$			7.07107i			0.839181i	0.907713	+	0.419591i	$0.137826\pi$
$71$			7.07107i			0.839181i	−0.907713	+	0.419591i	$0.862174\pi$
$72$	−2.82843	−	1.00000i	−0.333333	−	0.117851i
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$	−2.00000			−0.232495
$75$		0			0
$76$		0			0
$77$	12.7279	−	6.00000i	1.45048	−	0.683763i
$78$	4.24264	+	6.00000i	0.480384	+	0.679366i
$79$		−	4.24264i		−	0.477334i	−0.971101	−	0.238667i	$-0.923290\pi$
$79$		−	4.24264i		−	0.477334i	0.971101	−	0.238667i	$-0.0767105\pi$
$80$		0			0
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$			6.00000i			0.662589i
$83$		−	12.0000i		−	1.31717i	−0.752506	−	0.658586i	$-0.771155\pi$
$83$		−	12.0000i		−	1.31717i	0.752506	−	0.658586i	$-0.228845\pi$
$84$	−6.00000	+	4.24264i	−0.654654	+	0.462910i
$85$		0			0
$86$		−	8.48528i		−	0.914991i
$87$	−8.48528	+	6.00000i	−0.909718	+	0.643268i
$88$	1.41421	+	3.00000i	0.150756	+	0.319801i
$89$			5.65685i			0.599625i	0.953998	+	0.299813i	$0.0969242\pi$
$89$			5.65685i			0.599625i	−0.953998	+	0.299813i	$0.903076\pi$
$90$		0			0
$91$	18.0000			1.88691
$92$	1.41421			0.147442
$93$	5.65685	−	4.00000i	0.586588	−	0.414781i
$94$			9.89949i			1.02105i
$95$		0			0
$96$	−1.00000	−	1.41421i	−0.102062	−	0.144338i
$97$			8.00000i			0.812277i	0.913812	+	0.406138i	$0.133125\pi$
$97$			8.00000i			0.812277i	−0.913812	+	0.406138i	$0.866875\pi$
$98$			11.0000i			1.11117i
$99$	1.00000	+	9.89949i	0.100504	+	0.994937i
$100$		0			0
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$		0			0
$103$			4.00000i			0.394132i	0.980390	+	0.197066i	$0.0631413\pi$
$103$			4.00000i			0.394132i	−0.980390	+	0.197066i	$0.936859\pi$
$104$			4.24264i			0.416025i
$105$		0			0
$106$			7.07107i			0.686803i
$107$			18.0000i			1.74013i	0.492941	+	0.870063i	$0.335922\pi$
$107$			18.0000i			1.74013i	−0.492941	+	0.870063i	$0.664078\pi$
$108$	−1.41421	−	5.00000i	−0.136083	−	0.481125i
$109$		−	12.7279i		−	1.21911i	−0.792742	−	0.609557i	$-0.791347\pi$
$109$		−	12.7279i		−	1.21911i	0.792742	−	0.609557i	$-0.208653\pi$
$110$		0			0
$111$	−2.00000	−	2.82843i	−0.189832	−	0.268462i
$112$	−4.24264			−0.400892
$113$	11.3137			1.06430			0.532152	−	0.846649i	$-0.321383\pi$
$113$	11.3137			1.06430			0.532152	+	0.846649i	$0.321383\pi$
$114$		0			0
$115$		0			0
$116$	−6.00000			−0.557086
$117$	−4.24264	+	12.0000i	−0.392232	+	1.10940i
$118$	11.3137			1.04151
$119$		0			0
$120$		0			0
$121$	7.00000	−	8.48528i	0.636364	−	0.771389i
$122$	−4.24264			−0.384111
$123$	−8.48528	+	6.00000i	−0.765092	+	0.541002i
$124$	4.00000			0.359211
$125$		0			0
$126$	−12.0000	−	4.24264i	−1.06904	−	0.377964i
$127$	12.7279			1.12942			0.564710	−	0.825289i	$-0.308988\pi$
$127$	12.7279			1.12942			0.564710	+	0.825289i	$0.308988\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	12.0000	−	8.48528i	1.05654	−	0.747087i
$130$		0			0
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$	−2.82843	+	5.00000i	−0.246183	+	0.435194i
$133$		0			0
$134$	4.00000			0.345547
$135$		0			0
$136$		0			0
$137$	−2.82843			−0.241649			−0.120824	−	0.992674i	$-0.538554\pi$
$137$	−2.82843			−0.241649			−0.120824	+	0.992674i	$0.538554\pi$
$138$	1.41421	+	2.00000i	0.120386	+	0.170251i
$139$			16.9706i			1.43942i	0.694273	+	0.719712i	$0.255726\pi$
$139$			16.9706i			1.43942i	−0.694273	+	0.719712i	$0.744274\pi$
$140$		0			0
$141$	−14.0000	+	9.89949i	−1.17901	+	0.833688i
$142$	−7.07107			−0.593391
$143$	12.7279	−	6.00000i	1.06436	−	0.501745i
$144$	1.00000	−	2.82843i	0.0833333	−	0.235702i
$145$		0			0
$146$		0			0
$147$	−15.5563	+	11.0000i	−1.28307	+	0.907265i
$148$		−	2.00000i		−	0.164399i
$149$	−6.00000			−0.491539			−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000			−0.491539			−0.245770	+	0.969328i	$0.579041\pi$
$150$		0			0
$151$			4.24264i			0.345261i	0.984987	+	0.172631i	$0.0552267\pi$
$151$			4.24264i			0.345261i	−0.984987	+	0.172631i	$0.944773\pi$
$152$		0			0
$153$		0			0
$154$	6.00000	+	12.7279i	0.483494	+	1.02565i
$155$		0			0
$156$	−6.00000	+	4.24264i	−0.480384	+	0.339683i
$157$		−	22.0000i		−	1.75579i	−0.478852	−	0.877896i	$-0.658947\pi$
$157$		−	22.0000i		−	1.75579i	0.478852	−	0.877896i	$-0.341053\pi$
$158$	4.24264			0.337526
$159$	−10.0000	+	7.07107i	−0.793052	+	0.560772i
$160$		0			0
$161$	6.00000			0.472866
$162$	5.65685	−	7.00000i	0.444444	−	0.549972i
$163$		−	2.00000i		−	0.156652i	−0.996928	−	0.0783260i	$-0.975042\pi$
$163$		−	2.00000i		−	0.156652i	0.996928	−	0.0783260i	$-0.0249575\pi$
$164$	−6.00000			−0.468521
$165$		0			0
$166$	12.0000			0.931381
$167$		−	12.0000i		−	0.928588i	−0.885681	−	0.464294i	$-0.846308\pi$
$167$		−	12.0000i		−	0.928588i	0.885681	−	0.464294i	$-0.153692\pi$
$168$	−4.24264	−	6.00000i	−0.327327	−	0.462910i
$169$	5.00000			0.384615
$170$		0			0
$171$		0			0
$172$	8.48528			0.646997
$173$			6.00000i			0.456172i	0.973641	+	0.228086i	$0.0732467\pi$
$173$			6.00000i			0.456172i	−0.973641	+	0.228086i	$0.926753\pi$
$174$	−6.00000	−	8.48528i	−0.454859	−	0.643268i
$175$		0			0
$176$	−3.00000	+	1.41421i	−0.226134	+	0.106600i
$177$	11.3137	+	16.0000i	0.850390	+	1.20263i
$178$	−5.65685			−0.423999
$179$			5.65685i			0.422813i	0.977398	+	0.211407i	$0.0678044\pi$
$179$			5.65685i			0.422813i	−0.977398	+	0.211407i	$0.932196\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$			18.0000i			1.33425i
$183$	−4.24264	−	6.00000i	−0.313625	−	0.443533i
$184$			1.41421i			0.104257i
$185$		0			0
$186$	4.00000	+	5.65685i	0.293294	+	0.414781i
$187$		0			0
$188$	−9.89949			−0.721995
$189$	−6.00000	−	21.2132i	−0.436436	−	1.54303i
$190$		0			0
$191$		−	9.89949i		−	0.716302i	−0.933664	−	0.358151i	$-0.883407\pi$
$191$		−	9.89949i		−	0.716302i	0.933664	−	0.358151i	$-0.116593\pi$
$192$	1.41421	−	1.00000i	0.102062	−	0.0721688i
$193$	8.48528			0.610784			0.305392	−	0.952227i	$-0.401213\pi$
$193$	8.48528			0.610784			0.305392	+	0.952227i	$0.401213\pi$
$194$	−8.00000			−0.574367
$195$		0			0
$196$	−11.0000			−0.785714
$197$		−	18.0000i		−	1.28245i	−0.767354	−	0.641223i	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$	−9.89949	+	1.00000i	−0.703526	+	0.0710669i
$199$	16.0000			1.13421			0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000			1.13421			0.567105	+	0.823646i	$0.308063\pi$
$200$		0			0
$201$	4.00000	+	5.65685i	0.282138	+	0.399004i
$202$		−	6.00000i		−	0.422159i
$203$	−25.4558			−1.78665
$204$		0			0
$205$		0			0
$206$	−4.00000			−0.278693
$207$	−1.41421	+	4.00000i	−0.0982946	+	0.278019i
$208$	−4.24264			−0.294174
$209$		0			0
$210$		0			0
$211$			8.48528i			0.584151i	0.956395	+	0.292075i	$0.0943458\pi$
$211$			8.48528i			0.584151i	−0.956395	+	0.292075i	$0.905654\pi$
$212$	−7.07107			−0.485643
$213$	−7.07107	−	10.0000i	−0.484502	−	0.685189i
$214$	−18.0000			−1.23045
$215$		0			0
$216$	5.00000	−	1.41421i	0.340207	−	0.0962250i
$217$	16.9706			1.15204
$218$	12.7279			0.862044
$219$		0			0
$220$		0			0
$221$		0			0
$222$	2.82843	−	2.00000i	0.189832	−	0.134231i
$223$		−	8.00000i		−	0.535720i	−0.963458	−	0.267860i	$-0.913684\pi$
$223$		−	8.00000i		−	0.535720i	0.963458	−	0.267860i	$-0.0863164\pi$
$224$		−	4.24264i		−	0.283473i
$225$		0			0
$226$			11.3137i			0.752577i
$227$		−	6.00000i		−	0.398234i	−0.979976	−	0.199117i	$-0.936193\pi$
$227$		−	6.00000i		−	0.398234i	0.979976	−	0.199117i	$-0.0638074\pi$
$228$		0			0
$229$	−14.0000			−0.925146			−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000			−0.925146			−0.462573	+	0.886581i	$0.653074\pi$
$230$		0			0
$231$	−12.0000	+	21.2132i	−0.789542	+	1.39573i
$232$		−	6.00000i		−	0.393919i
$233$		−	18.0000i		−	1.17922i	−0.807688	−	0.589610i	$-0.799282\pi$
$233$		−	18.0000i		−	1.17922i	0.807688	−	0.589610i	$-0.200718\pi$
$234$	−12.0000	−	4.24264i	−0.784465	−	0.277350i
$235$		0			0
$236$			11.3137i			0.736460i
$237$	4.24264	+	6.00000i	0.275589	+	0.389742i
$238$		0			0
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$		−	8.48528i		−	0.546585i	−0.961931	−	0.273293i	$-0.911887\pi$
$241$		−	8.48528i		−	0.546585i	0.961931	−	0.273293i	$-0.0881127\pi$
$242$	8.48528	+	7.00000i	0.545455	+	0.449977i
$243$	15.5563	+	1.00000i	0.997940	+	0.0641500i
$244$		−	4.24264i		−	0.271607i
$245$		0			0
$246$	−6.00000	−	8.48528i	−0.382546	−	0.541002i
$247$		0			0
$248$			4.00000i			0.254000i
$249$	12.0000	+	16.9706i	0.760469	+	1.07547i
$250$		0			0
$251$		−	5.65685i		−	0.357057i	−0.983935	−	0.178529i	$-0.942866\pi$
$251$		−	5.65685i		−	0.357057i	0.983935	−	0.178529i	$-0.0571337\pi$
$252$	4.24264	−	12.0000i	0.267261	−	0.755929i
$253$	4.24264	−	2.00000i	0.266733	−	0.125739i
$254$			12.7279i			0.798621i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−11.3137			−0.705730			−0.352865	−	0.935674i	$-0.614792\pi$
$257$	−11.3137			−0.705730			−0.352865	+	0.935674i	$0.614792\pi$
$258$	8.48528	+	12.0000i	0.528271	+	0.747087i
$259$		−	8.48528i		−	0.527250i
$260$		0			0
$261$	6.00000	−	16.9706i	0.371391	−	1.05045i
$262$		−	12.0000i		−	0.741362i
$263$		−	12.0000i		−	0.739952i	−0.929041	−	0.369976i	$-0.879366\pi$
$263$		−	12.0000i		−	0.739952i	0.929041	−	0.369976i	$-0.120634\pi$
$264$	−5.00000	−	2.82843i	−0.307729	−	0.174078i
$265$		0			0
$266$		0			0
$267$	−5.65685	−	8.00000i	−0.346194	−	0.489592i
$268$			4.00000i			0.244339i
$269$		−	7.07107i		−	0.431131i	−0.976489	−	0.215565i	$-0.930841\pi$
$269$		−	7.07107i		−	0.431131i	0.976489	−	0.215565i	$-0.0691594\pi$
$270$		0			0
$271$			12.7279i			0.773166i	0.922255	+	0.386583i	$0.126345\pi$
$271$			12.7279i			0.773166i	−0.922255	+	0.386583i	$0.873655\pi$
$272$		0			0
$273$	−25.4558	+	18.0000i	−1.54066	+	1.08941i
$274$		−	2.82843i		−	0.170872i
$275$		0			0
$276$	−2.00000	+	1.41421i	−0.120386	+	0.0851257i
$277$	21.2132			1.27458			0.637289	−	0.770625i	$-0.280056\pi$
$277$	21.2132			1.27458			0.637289	+	0.770625i	$0.280056\pi$
$278$	−16.9706			−1.01783
$279$	−4.00000	+	11.3137i	−0.239474	+	0.677334i
$280$		0			0
$281$	12.0000			0.715860			0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000			0.715860			0.357930	+	0.933748i	$0.383483\pi$
$282$	−9.89949	−	14.0000i	−0.589506	−	0.833688i
$283$	8.48528			0.504398			0.252199	−	0.967675i	$-0.418846\pi$
$283$	8.48528			0.504398			0.252199	+	0.967675i	$0.418846\pi$
$284$		−	7.07107i		−	0.419591i
$285$		0			0
$286$	6.00000	+	12.7279i	0.354787	+	0.752618i
$287$	−25.4558			−1.50261
$288$	2.82843	+	1.00000i	0.166667	+	0.0589256i
$289$	17.0000			1.00000
$290$		0			0
$291$	−8.00000	−	11.3137i	−0.468968	−	0.663221i
$292$		0			0
$293$		−	6.00000i		−	0.350524i	−0.984522	−	0.175262i	$-0.943923\pi$
$293$		−	6.00000i		−	0.350524i	0.984522	−	0.175262i	$-0.0560772\pi$
$294$	−11.0000	−	15.5563i	−0.641533	−	0.907265i
$295$		0			0
$296$	2.00000			0.116248
$297$	−11.3137	−	13.0000i	−0.656488	−	0.754337i
$298$		−	6.00000i		−	0.347571i
$299$	6.00000			0.346989
$300$		0			0
$301$	36.0000			2.07501
$302$	−4.24264			−0.244137
$303$	8.48528	−	6.00000i	0.487467	−	0.344691i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$	−12.7279	+	6.00000i	−0.725241	+	0.341882i
$309$	−4.00000	−	5.65685i	−0.227552	−	0.321807i
$310$		0			0
$311$		−	26.8701i		−	1.52366i	−0.647776	−	0.761831i	$-0.724301\pi$
$311$		−	26.8701i		−	1.52366i	0.647776	−	0.761831i	$-0.275699\pi$
$312$	−4.24264	−	6.00000i	−0.240192	−	0.339683i
$313$			10.0000i			0.565233i	0.959233	+	0.282617i	$0.0912024\pi$
$313$			10.0000i			0.565233i	−0.959233	+	0.282617i	$0.908798\pi$
$314$	22.0000			1.24153
$315$		0			0
$316$			4.24264i			0.238667i
$317$	9.89949			0.556011			0.278006	−	0.960579i	$-0.410327\pi$
$317$	9.89949			0.556011			0.278006	+	0.960579i	$0.410327\pi$
$318$	−7.07107	−	10.0000i	−0.396526	−	0.560772i
$319$	−18.0000	+	8.48528i	−1.00781	+	0.475085i
$320$		0			0
$321$	−18.0000	−	25.4558i	−1.00466	−	1.42081i
$322$			6.00000i			0.334367i
$323$		0			0
$324$	7.00000	+	5.65685i	0.388889	+	0.314270i
$325$		0			0
$326$	2.00000			0.110770
$327$	12.7279	+	18.0000i	0.703856	+	0.995402i
$328$		−	6.00000i		−	0.331295i
$329$	−42.0000			−2.31553
$330$		0			0
$331$	−10.0000			−0.549650			−0.274825	−	0.961494i	$-0.588620\pi$
$331$	−10.0000			−0.549650			−0.274825	+	0.961494i	$0.588620\pi$
$332$			12.0000i			0.658586i
$333$	5.65685	+	2.00000i	0.309994	+	0.109599i
$334$	12.0000			0.656611
$335$		0			0
$336$	6.00000	−	4.24264i	0.327327	−	0.231455i
$337$	−33.9411			−1.84889			−0.924445	−	0.381314i	$-0.875472\pi$
$337$	−33.9411			−1.84889			−0.924445	+	0.381314i	$0.875472\pi$
$338$			5.00000i			0.271964i
$339$	−16.0000	+	11.3137i	−0.869001	+	0.614476i
$340$		0			0
$341$	12.0000	−	5.65685i	0.649836	−	0.306336i
$342$		0			0
$343$	−16.9706			−0.916324
$344$			8.48528i			0.457496i
$345$		0			0
$346$	−6.00000			−0.322562
$347$		−	12.0000i		−	0.644194i	−0.946707	−	0.322097i	$-0.895612\pi$
$347$		−	12.0000i		−	0.644194i	0.946707	−	0.322097i	$-0.104388\pi$
$348$	8.48528	−	6.00000i	0.454859	−	0.321634i
$349$		−	29.6985i		−	1.58972i	−0.606791	−	0.794862i	$-0.707543\pi$
$349$		−	29.6985i		−	1.58972i	0.606791	−	0.794862i	$-0.292457\pi$
$350$		0			0
$351$	−6.00000	−	21.2132i	−0.320256	−	1.13228i
$352$	−1.41421	−	3.00000i	−0.0753778	−	0.159901i
$353$	−22.6274			−1.20434			−0.602168	−	0.798369i	$-0.705696\pi$
$353$	−22.6274			−1.20434			−0.602168	+	0.798369i	$0.705696\pi$
$354$	−16.0000	+	11.3137i	−0.850390	+	0.601317i
$355$		0			0
$356$		−	5.65685i		−	0.299813i
$357$		0			0
$358$	−5.65685			−0.298974
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	19.0000			1.00000
$362$			2.00000i			0.105118i
$363$	−1.41421	+	19.0000i	−0.0742270	+	0.997241i
$364$	−18.0000			−0.943456
$365$		0			0
$366$	6.00000	−	4.24264i	0.313625	−	0.221766i
$367$		−	28.0000i		−	1.46159i	−0.682598	−	0.730794i	$-0.739150\pi$
$367$		−	28.0000i		−	1.46159i	0.682598	−	0.730794i	$-0.260850\pi$
$368$	−1.41421			−0.0737210
$369$	6.00000	−	16.9706i	0.312348	−	0.883452i
$370$		0			0
$371$	−30.0000			−1.55752
$372$	−5.65685	+	4.00000i	−0.293294	+	0.207390i
$373$	−29.6985			−1.53773			−0.768865	−	0.639412i	$-0.779178\pi$
$373$	−29.6985			−1.53773			−0.768865	+	0.639412i	$0.779178\pi$
$374$		0			0
$375$		0			0
$376$		−	9.89949i		−	0.510527i
$377$	−25.4558			−1.31104
$378$	21.2132	−	6.00000i	1.09109	−	0.308607i
$379$	−2.00000			−0.102733			−0.0513665	−	0.998680i	$-0.516358\pi$
$379$	−2.00000			−0.102733			−0.0513665	+	0.998680i	$0.516358\pi$
$380$		0			0
$381$	−18.0000	+	12.7279i	−0.922168	+	0.652071i
$382$	9.89949			0.506502
$383$	−1.41421			−0.0722629			−0.0361315	−	0.999347i	$-0.511504\pi$
$383$	−1.41421			−0.0722629			−0.0361315	+	0.999347i	$0.511504\pi$
$384$	1.00000	+	1.41421i	0.0510310	+	0.0721688i
$385$		0			0
$386$			8.48528i			0.431889i
$387$	−8.48528	+	24.0000i	−0.431331	+	1.21999i
$388$		−	8.00000i		−	0.406138i
$389$			9.89949i			0.501924i	0.967997	+	0.250962i	$0.0807470\pi$
$389$			9.89949i			0.501924i	−0.967997	+	0.250962i	$0.919253\pi$
$390$		0			0
$391$		0			0
$392$		−	11.0000i		−	0.555584i
$393$	16.9706	−	12.0000i	0.856052	−	0.605320i
$394$	18.0000			0.906827
$395$		0			0
$396$	−1.00000	−	9.89949i	−0.0502519	−	0.497468i
$397$		−	34.0000i		−	1.70641i	−0.521575	−	0.853206i	$-0.674655\pi$
$397$		−	34.0000i		−	1.70641i	0.521575	−	0.853206i	$-0.325345\pi$
$398$			16.0000i			0.802008i
$399$		0			0
$400$		0			0
$401$			36.7696i			1.83618i	0.396368	+	0.918092i	$0.370271\pi$
$401$			36.7696i			1.83618i	−0.396368	+	0.918092i	$0.629729\pi$
$402$	−5.65685	+	4.00000i	−0.282138	+	0.199502i
$403$	16.9706			0.845364
$404$	6.00000			0.298511
$405$		0			0
$406$		−	25.4558i		−	1.26335i
$407$	−2.82843	−	6.00000i	−0.140200	−	0.297409i
$408$		0			0
$409$		−	8.48528i		−	0.419570i	−0.977748	−	0.209785i	$-0.932724\pi$
$409$		−	8.48528i		−	0.419570i	0.977748	−	0.209785i	$-0.0672764\pi$
$410$		0			0
$411$	4.00000	−	2.82843i	0.197305	−	0.139516i
$412$		−	4.00000i		−	0.197066i
$413$			48.0000i			2.36193i
$414$	−4.00000	−	1.41421i	−0.196589	−	0.0695048i
$415$		0			0
$416$		−	4.24264i		−	0.208013i
$417$	−16.9706	−	24.0000i	−0.831052	−	1.17529i
$418$		0			0
$419$		−	11.3137i		−	0.552711i	−0.961056	−	0.276355i	$-0.910873\pi$
$419$		−	11.3137i		−	0.552711i	0.961056	−	0.276355i	$-0.0891267\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	−8.48528			−0.413057
$423$	9.89949	−	28.0000i	0.481330	−	1.36141i
$424$		−	7.07107i		−	0.343401i
$425$		0			0
$426$	10.0000	−	7.07107i	0.484502	−	0.342594i
$427$		−	18.0000i		−	0.871081i
$428$		−	18.0000i		−	0.870063i
$429$	−12.0000	+	21.2132i	−0.579365	+	1.02418i
$430$		0			0
$431$	36.0000			1.73406			0.867029	−	0.498257i	$-0.166026\pi$
$431$	36.0000			1.73406			0.867029	+	0.498257i	$0.166026\pi$
$432$	1.41421	+	5.00000i	0.0680414	+	0.240563i
$433$		−	2.00000i		−	0.0961139i	−0.998845	−	0.0480569i	$-0.984697\pi$
$433$		−	2.00000i		−	0.0961139i	0.998845	−	0.0480569i	$-0.0153029\pi$
$434$			16.9706i			0.814613i
$435$		0			0
$436$			12.7279i			0.609557i
$437$		0			0
$438$		0			0
$439$			21.2132i			1.01245i	0.862401	+	0.506225i	$0.168960\pi$
$439$			21.2132i			1.01245i	−0.862401	+	0.506225i	$0.831040\pi$
$440$		0			0
$441$	11.0000	−	31.1127i	0.523810	−	1.48156i
$442$		0			0
$443$	28.2843			1.34383			0.671913	−	0.740630i	$-0.265473\pi$
$443$	28.2843			1.34383			0.671913	+	0.740630i	$0.265473\pi$
$444$	2.00000	+	2.82843i	0.0949158	+	0.134231i
$445$		0			0
$446$	8.00000			0.378811
$447$	8.48528	−	6.00000i	0.401340	−	0.283790i
$448$	4.24264			0.200446
$449$			31.1127i			1.46830i	0.678988	+	0.734150i	$0.262419\pi$
$449$			31.1127i			1.46830i	−0.678988	+	0.734150i	$0.737581\pi$
$450$		0			0
$451$	−18.0000	+	8.48528i	−0.847587	+	0.399556i
$452$	−11.3137			−0.532152
$453$	−4.24264	−	6.00000i	−0.199337	−	0.281905i
$454$	6.00000			0.281594
$455$		0			0
$456$		0			0
$457$	8.48528			0.396925			0.198462	−	0.980109i	$-0.436405\pi$
$457$	8.48528			0.396925			0.198462	+	0.980109i	$0.436405\pi$
$458$		−	14.0000i		−	0.654177i
$459$		0			0
$460$		0			0
$461$	30.0000			1.39724			0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000			1.39724			0.698620	+	0.715493i	$0.253798\pi$
$462$	−21.2132	−	12.0000i	−0.986928	−	0.558291i
$463$		−	32.0000i		−	1.48717i	−0.668644	−	0.743583i	$-0.733125\pi$
$463$		−	32.0000i		−	1.48717i	0.668644	−	0.743583i	$-0.266875\pi$
$464$	6.00000			0.278543
$465$		0			0
$466$	18.0000			0.833834
$467$	31.1127			1.43972			0.719862	−	0.694117i	$-0.244205\pi$
$467$	31.1127			1.43972			0.719862	+	0.694117i	$0.244205\pi$
$468$	4.24264	−	12.0000i	0.196116	−	0.554700i
$469$			16.9706i			0.783628i
$470$		0			0
$471$	22.0000	+	31.1127i	1.01371	+	1.43360i
$472$	−11.3137			−0.520756
$473$	25.4558	−	12.0000i	1.17046	−	0.551761i
$474$	−6.00000	+	4.24264i	−0.275589	+	0.194871i
$475$		0			0
$476$		0			0
$477$	7.07107	−	20.0000i	0.323762	−	0.915737i
$478$			12.0000i			0.548867i
$479$	−12.0000			−0.548294			−0.274147	−	0.961688i	$-0.588395\pi$
$479$	−12.0000			−0.548294			−0.274147	+	0.961688i	$0.588395\pi$
$480$		0			0
$481$		−	8.48528i		−	0.386896i
$482$	8.48528			0.386494
$483$	−8.48528	+	6.00000i	−0.386094	+	0.273009i
$484$	−7.00000	+	8.48528i	−0.318182	+	0.385695i
$485$		0			0
$486$	−1.00000	+	15.5563i	−0.0453609	+	0.705650i
$487$			20.0000i			0.906287i	0.891438	+	0.453143i	$0.149697\pi$
$487$			20.0000i			0.906287i	−0.891438	+	0.453143i	$0.850303\pi$
$488$	4.24264			0.192055
$489$	2.00000	+	2.82843i	0.0904431	+	0.127906i
$490$		0			0
$491$	6.00000			0.270776			0.135388	−	0.990793i	$-0.456772\pi$
$491$	6.00000			0.270776			0.135388	+	0.990793i	$0.456772\pi$
$492$	8.48528	−	6.00000i	0.382546	−	0.270501i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−4.00000			−0.179605
$497$		−	30.0000i		−	1.34568i
$498$	−16.9706	+	12.0000i	−0.760469	+	0.537733i
$499$	−14.0000			−0.626726			−0.313363	−	0.949633i	$-0.601456\pi$
$499$	−14.0000			−0.626726			−0.313363	+	0.949633i	$0.601456\pi$
$500$		0			0
$501$	12.0000	+	16.9706i	0.536120	+	0.758189i
$502$	5.65685			0.252478
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$	12.0000	+	4.24264i	0.534522	+	0.188982i
$505$		0			0
$506$	2.00000	+	4.24264i	0.0889108	+	0.188608i
$507$	−7.07107	+	5.00000i	−0.314037	+	0.222058i
$508$	−12.7279			−0.564710
$509$			1.41421i			0.0626839i	0.999509	+	0.0313420i	$0.00997809\pi$
$509$			1.41421i			0.0626839i	−0.999509	+	0.0313420i	$0.990022\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		0			0
$514$		−	11.3137i		−	0.499026i
$515$		0			0
$516$	−12.0000	+	8.48528i	−0.528271	+	0.373544i
$517$	−29.6985	+	14.0000i	−1.30614	+	0.615719i
$518$	8.48528			0.372822
$519$	−6.00000	−	8.48528i	−0.263371	−	0.372463i
$520$		0			0
$521$			19.7990i			0.867409i	0.901055	+	0.433705i	$0.142794\pi$
$521$			19.7990i			0.867409i	−0.901055	+	0.433705i	$0.857206\pi$
$522$	16.9706	+	6.00000i	0.742781	+	0.262613i
$523$	25.4558			1.11311			0.556553	−	0.830812i	$-0.312124\pi$
$523$	25.4558			1.11311			0.556553	+	0.830812i	$0.312124\pi$
$524$	12.0000			0.524222
$525$		0			0
$526$	12.0000			0.523225
$527$		0			0
$528$	2.82843	−	5.00000i	0.123091	−	0.217597i
$529$	−21.0000			−0.913043
$530$		0			0
$531$	−32.0000	−	11.3137i	−1.38868	−	0.490973i
$532$		0			0
$533$	−25.4558			−1.10262
$534$	8.00000	−	5.65685i	0.346194	−	0.244796i
$535$		0			0
$536$	−4.00000			−0.172774
$537$	−5.65685	−	8.00000i	−0.244111	−	0.345225i
$538$	7.07107			0.304855
$539$	−33.0000	+	15.5563i	−1.42141	+	0.670059i
$540$		0			0
$541$			12.7279i			0.547216i	0.961841	+	0.273608i	$0.0882171\pi$
$541$			12.7279i			0.547216i	−0.961841	+	0.273608i	$0.911783\pi$
$542$	−12.7279			−0.546711
$543$	−2.82843	+	2.00000i	−0.121379	+	0.0858282i
$544$		0			0
$545$		0			0
$546$	−18.0000	−	25.4558i	−0.770329	−	1.08941i
$547$	33.9411			1.45122			0.725609	−	0.688107i	$-0.241558\pi$
$547$	33.9411			1.45122			0.725609	+	0.688107i	$0.241558\pi$
$548$	2.82843			0.120824
$549$	12.0000	+	4.24264i	0.512148	+	0.181071i
$550$		0			0
$551$		0			0
$552$	−1.41421	−	2.00000i	−0.0601929	−	0.0851257i
$553$			18.0000i			0.765438i
$554$			21.2132i			0.901263i
$555$		0			0
$556$		−	16.9706i		−	0.719712i
$557$		−	18.0000i		−	0.762684i	−0.924434	−	0.381342i	$-0.875462\pi$
$557$		−	18.0000i		−	0.762684i	0.924434	−	0.381342i	$-0.124538\pi$
$558$	−11.3137	−	4.00000i	−0.478947	−	0.169334i
$559$	36.0000			1.52264
$560$		0			0
$561$		0			0
$562$			12.0000i			0.506189i
$563$			30.0000i			1.26435i	0.774826	+	0.632175i	$0.217837\pi$
$563$			30.0000i			1.26435i	−0.774826	+	0.632175i	$0.782163\pi$
$564$	14.0000	−	9.89949i	0.589506	−	0.416844i
$565$		0			0
$566$			8.48528i			0.356663i
$567$	29.6985	+	24.0000i	1.24722	+	1.00791i
$568$	7.07107			0.296695
$569$	24.0000			1.00613			0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000			1.00613			0.503066	+	0.864248i	$0.332205\pi$
$570$		0			0
$571$			33.9411i			1.42039i	0.704004	+	0.710196i	$0.251394\pi$
$571$			33.9411i			1.42039i	−0.704004	+	0.710196i	$0.748606\pi$
$572$	−12.7279	+	6.00000i	−0.532181	+	0.250873i
$573$	9.89949	+	14.0000i	0.413557	+	0.584858i
$574$		−	25.4558i		−	1.06251i
$575$		0			0
$576$	−1.00000	+	2.82843i	−0.0416667	+	0.117851i
$577$			20.0000i			0.832611i	0.909225	+	0.416305i	$0.136675\pi$
$577$			20.0000i			0.832611i	−0.909225	+	0.416305i	$0.863325\pi$
$578$			17.0000i			0.707107i
$579$	−12.0000	+	8.48528i	−0.498703	+	0.352636i
$580$		0			0
$581$			50.9117i			2.11217i
$582$	11.3137	−	8.00000i	0.468968	−	0.331611i
$583$	−21.2132	+	10.0000i	−0.878561	+	0.414158i
$584$		0			0
$585$		0			0
$586$	6.00000			0.247858
$587$	−28.2843			−1.16742			−0.583708	−	0.811963i	$-0.698399\pi$
$587$	−28.2843			−1.16742			−0.583708	+	0.811963i	$0.698399\pi$
$588$	15.5563	−	11.0000i	0.641533	−	0.453632i
$589$		0			0
$590$		0			0
$591$	18.0000	+	25.4558i	0.740421	+	1.04711i
$592$			2.00000i			0.0821995i
$593$			36.0000i			1.47834i	0.673517	+	0.739171i	$0.264783\pi$
$593$			36.0000i			1.47834i	−0.673517	+	0.739171i	$0.735217\pi$
$594$	13.0000	−	11.3137i	0.533396	−	0.464207i
$595$		0			0
$596$	6.00000			0.245770
$597$	−22.6274	+	16.0000i	−0.926079	+	0.654836i
$598$			6.00000i			0.245358i
$599$		−	24.0416i		−	0.982314i	−0.871071	−	0.491157i	$-0.836574\pi$
$599$		−	24.0416i		−	0.982314i	0.871071	−	0.491157i	$-0.163426\pi$
$600$		0			0
$601$		−	33.9411i		−	1.38449i	−0.721664	−	0.692244i	$-0.756622\pi$
$601$		−	33.9411i		−	1.38449i	0.721664	−	0.692244i	$-0.243378\pi$
$602$			36.0000i			1.46725i
$603$	−11.3137	−	4.00000i	−0.460730	−	0.162893i
$604$		−	4.24264i		−	0.172631i
$605$		0			0
$606$	6.00000	+	8.48528i	0.243733	+	0.344691i
$607$	4.24264			0.172203			0.0861017	−	0.996286i	$-0.472559\pi$
$607$	4.24264			0.172203			0.0861017	+	0.996286i	$0.472559\pi$
$608$		0			0
$609$	36.0000	−	25.4558i	1.45879	−	1.03152i
$610$		0			0
$611$	−42.0000			−1.69914
$612$		0			0
$613$	12.7279			0.514076			0.257038	−	0.966401i	$-0.417253\pi$
$613$	12.7279			0.514076			0.257038	+	0.966401i	$0.417253\pi$
$614$		0			0
$615$		0			0
$616$	−6.00000	−	12.7279i	−0.241747	−	0.512823i
$617$	39.5980			1.59415			0.797077	−	0.603877i	$-0.206378\pi$
$617$	39.5980			1.59415			0.797077	+	0.603877i	$0.206378\pi$
$618$	5.65685	−	4.00000i	0.227552	−	0.160904i
$619$	−44.0000			−1.76851			−0.884255	−	0.467005i	$-0.845333\pi$
$619$	−44.0000			−1.76851			−0.884255	+	0.467005i	$0.845333\pi$
$620$		0			0
$621$	−2.00000	−	7.07107i	−0.0802572	−	0.283752i
$622$	26.8701			1.07739
$623$		−	24.0000i		−	0.961540i
$624$	6.00000	−	4.24264i	0.240192	−	0.169842i
$625$		0			0
$626$	−10.0000			−0.399680
$627$		0			0
$628$			22.0000i			0.877896i
$629$		0			0
$630$		0			0
$631$	20.0000			0.796187			0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000			0.796187			0.398094	+	0.917345i	$0.369672\pi$
$632$	−4.24264			−0.168763
$633$	−8.48528	−	12.0000i	−0.337260	−	0.476957i
$634$			9.89949i			0.393159i
$635$		0			0
$636$	10.0000	−	7.07107i	0.396526	−	0.280386i
$637$	−46.6690			−1.84909
$638$	−8.48528	−	18.0000i	−0.335936	−	0.712627i
$639$	20.0000	+	7.07107i	0.791188	+	0.279727i
$640$		0			0
$641$		−	48.0833i		−	1.89917i	−0.313503	−	0.949587i	$-0.601502\pi$
$641$		−	48.0833i		−	1.89917i	0.313503	−	0.949587i	$-0.398498\pi$
$642$	25.4558	−	18.0000i	1.00466	−	0.710403i
$643$			4.00000i			0.157745i	0.996885	+	0.0788723i	$0.0251319\pi$
$643$			4.00000i			0.157745i	−0.996885	+	0.0788723i	$0.974868\pi$
$644$	−6.00000			−0.236433
$645$		0			0
$646$		0			0
$647$	−7.07107			−0.277992			−0.138996	−	0.990293i	$-0.544388\pi$
$647$	−7.07107			−0.277992			−0.138996	+	0.990293i	$0.544388\pi$
$648$	−5.65685	+	7.00000i	−0.222222	+	0.274986i
$649$	16.0000	+	33.9411i	0.628055	+	1.33231i
$650$		0			0
$651$	−24.0000	+	16.9706i	−0.940634	+	0.665129i
$652$			2.00000i			0.0783260i
$653$	−26.8701			−1.05151			−0.525753	−	0.850637i	$-0.676216\pi$
$653$	−26.8701			−1.05151			−0.525753	+	0.850637i	$0.676216\pi$
$654$	−18.0000	+	12.7279i	−0.703856	+	0.497701i
$655$		0			0
$656$	6.00000			0.234261
$657$		0			0
$658$		−	42.0000i		−	1.63733i
$659$	−30.0000			−1.16863			−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000			−1.16863			−0.584317	+	0.811525i	$0.698638\pi$
$660$		0			0
$661$	−22.0000			−0.855701			−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000			−0.855701			−0.427850	+	0.903850i	$0.640729\pi$
$662$		−	10.0000i		−	0.388661i
$663$		0			0
$664$	−12.0000			−0.465690
$665$		0			0
$666$	−2.00000	+	5.65685i	−0.0774984	+	0.219199i
$667$	−8.48528			−0.328551
$668$			12.0000i			0.464294i
$669$	8.00000	+	11.3137i	0.309298	+	0.437413i
$670$		0			0
$671$	−6.00000	−	12.7279i	−0.231627	−	0.491356i
$672$	4.24264	+	6.00000i	0.163663	+	0.231455i
$673$	42.4264			1.63542			0.817709	−	0.575632i	$-0.195244\pi$
$673$	42.4264			1.63542			0.817709	+	0.575632i	$0.195244\pi$
$674$		−	33.9411i		−	1.30736i
$675$		0			0
$676$	−5.00000			−0.192308
$677$			30.0000i			1.15299i	0.817099	+	0.576497i	$0.195581\pi$
$677$			30.0000i			1.15299i	−0.817099	+	0.576497i	$0.804419\pi$
$678$	−11.3137	−	16.0000i	−0.434500	−	0.614476i
$679$		−	33.9411i		−	1.30254i
$680$		0			0
$681$	6.00000	+	8.48528i	0.229920	+	0.325157i
$682$	5.65685	+	12.0000i	0.216612	+	0.459504i
$683$	−5.65685			−0.216454			−0.108227	−	0.994126i	$-0.534517\pi$
$683$	−5.65685			−0.216454			−0.108227	+	0.994126i	$0.534517\pi$
$684$		0			0
$685$		0			0
$686$		−	16.9706i		−	0.647939i
$687$	19.7990	−	14.0000i	0.755379	−	0.534133i
$688$	−8.48528			−0.323498
$689$	−30.0000			−1.14291
$690$		0			0
$691$	−28.0000			−1.06517			−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000			−1.06517			−0.532585	+	0.846376i	$0.678779\pi$
$692$		−	6.00000i		−	0.228086i
$693$	−4.24264	−	42.0000i	−0.161165	−	1.59545i
$694$	12.0000			0.455514
$695$		0			0
$696$	6.00000	+	8.48528i	0.227429	+	0.321634i
$697$		0			0
$698$	29.6985			1.12410
$699$	18.0000	+	25.4558i	0.680823	+	0.962828i
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$	21.2132	−	6.00000i	0.800641	−	0.226455i
$703$		0			0
$704$	3.00000	−	1.41421i	0.113067	−	0.0533002i
$705$		0			0
$706$		−	22.6274i		−	0.851594i
$707$	25.4558			0.957366
$708$	−11.3137	−	16.0000i	−0.425195	−	0.601317i
$709$	10.0000			0.375558			0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000			0.375558			0.187779	+	0.982211i	$0.439871\pi$
$710$		0			0
$711$	−12.0000	−	4.24264i	−0.450035	−	0.159111i
$712$	5.65685			0.212000
$713$	5.65685			0.211851
$714$		0			0
$715$		0			0
$716$		−	5.65685i		−	0.211407i
$717$	−16.9706	+	12.0000i	−0.633777	+	0.448148i
$718$		0			0
$719$		−	32.5269i		−	1.21305i	−0.795065	−	0.606525i	$-0.792563\pi$
$719$		−	32.5269i		−	1.21305i	0.795065	−	0.606525i	$-0.207437\pi$
$720$		0			0
$721$		−	16.9706i		−	0.632017i
$722$			19.0000i			0.707107i
$723$	8.48528	+	12.0000i	0.315571	+	0.446285i
$724$	−2.00000			−0.0743294
$725$		0			0
$726$	−19.0000	−	1.41421i	−0.705156	−	0.0524864i
$727$			44.0000i			1.63187i	0.578144	+	0.815935i	$0.303777\pi$
$727$			44.0000i			1.63187i	−0.578144	+	0.815935i	$0.696223\pi$
$728$		−	18.0000i		−	0.667124i
$729$	−23.0000	+	14.1421i	−0.851852	+	0.523783i
$730$		0			0
$731$		0			0
$732$	4.24264	+	6.00000i	0.156813	+	0.221766i
$733$	−4.24264			−0.156706			−0.0783528	−	0.996926i	$-0.524966\pi$
$733$	−4.24264			−0.156706			−0.0783528	+	0.996926i	$0.524966\pi$
$734$	28.0000			1.03350
$735$		0			0
$736$		−	1.41421i		−	0.0521286i
$737$	5.65685	+	12.0000i	0.208373	+	0.442026i
$738$	16.9706	+	6.00000i	0.624695	+	0.220863i
$739$			25.4558i			0.936408i	0.883620	+	0.468204i	$0.155099\pi$
$739$			25.4558i			0.936408i	−0.883620	+	0.468204i	$0.844901\pi$
$740$		0			0
$741$		0			0
$742$		−	30.0000i		−	1.10133i
$743$		−	24.0000i		−	0.880475i	−0.897881	−	0.440237i	$-0.854894\pi$
$743$		−	24.0000i		−	0.880475i	0.897881	−	0.440237i	$-0.145106\pi$
$744$	−4.00000	−	5.65685i	−0.146647	−	0.207390i
$745$		0			0
$746$		−	29.6985i		−	1.08734i
$747$	−33.9411	−	12.0000i	−1.24184	−	0.439057i
$748$		0			0
$749$		−	76.3675i		−	2.79041i
$750$		0			0
$751$	−40.0000			−1.45962			−0.729810	−	0.683650i	$-0.760392\pi$
$751$	−40.0000			−1.45962			−0.729810	+	0.683650i	$0.760392\pi$
$752$	9.89949			0.360997
$753$	5.65685	+	8.00000i	0.206147	+	0.291536i
$754$		−	25.4558i		−	0.927047i
$755$		0			0
$756$	6.00000	+	21.2132i	0.218218	+	0.771517i
$757$			2.00000i			0.0726912i	0.999339	+	0.0363456i	$0.0115717\pi$
$757$			2.00000i			0.0726912i	−0.999339	+	0.0363456i	$0.988428\pi$
$758$		−	2.00000i		−	0.0726433i
$759$	−4.00000	+	7.07107i	−0.145191	+	0.256664i
$760$		0			0
$761$	24.0000			0.869999			0.435000	−	0.900431i	$-0.356748\pi$
$761$	24.0000			0.869999			0.435000	+	0.900431i	$0.356748\pi$
$762$	−12.7279	−	18.0000i	−0.461084	−	0.652071i
$763$			54.0000i			1.95493i
$764$			9.89949i			0.358151i
$765$		0			0
$766$		−	1.41421i		−	0.0510976i
$767$			48.0000i			1.73318i
$768$	−1.41421	+	1.00000i	−0.0510310	+	0.0360844i
$769$			42.4264i			1.52994i	0.644069	+	0.764968i	$0.277245\pi$
$769$			42.4264i			1.52994i	−0.644069	+	0.764968i	$0.722755\pi$
$770$		0			0
$771$	16.0000	−	11.3137i	0.576226	−	0.407453i
$772$	−8.48528			−0.305392
$773$	−18.3848			−0.661254			−0.330627	−	0.943761i	$-0.607260\pi$
$773$	−18.3848			−0.661254			−0.330627	+	0.943761i	$0.607260\pi$
$774$	−24.0000	−	8.48528i	−0.862662	−	0.304997i
$775$		0			0
$776$	8.00000			0.287183
$777$	8.48528	+	12.0000i	0.304408	+	0.430498i
$778$	−9.89949			−0.354914
$779$		0			0
$780$		0			0
$781$	−10.0000	−	21.2132i	−0.357828	−	0.759068i
$782$		0			0
$783$	8.48528	+	30.0000i	0.303239	+	1.07211i
$784$	11.0000			0.392857
$785$		0			0
$786$	12.0000	+	16.9706i	0.428026	+	0.605320i
$787$	42.4264			1.51234			0.756169	−	0.654376i	$-0.227069\pi$
$787$	42.4264			1.51234			0.756169	+	0.654376i	$0.227069\pi$
$788$			18.0000i			0.641223i
$789$	12.0000	+	16.9706i	0.427211	+	0.604168i
$790$		0			0
$791$	−48.0000			−1.70668
$792$	9.89949	−	1.00000i	0.351763	−	0.0355335i
$793$		−	18.0000i		−	0.639199i
$794$	34.0000			1.20661
$795$		0			0
$796$	−16.0000			−0.567105
$797$	1.41421			0.0500940			0.0250470	−	0.999686i	$-0.492026\pi$
$797$	1.41421			0.0500940			0.0250470	+	0.999686i	$0.492026\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	16.0000	+	5.65685i	0.565332	+	0.199875i
$802$	−36.7696			−1.29838
$803$		0			0
$804$	−4.00000	−	5.65685i	−0.141069	−	0.199502i
$805$		0			0
$806$			16.9706i			0.597763i
$807$	7.07107	+	10.0000i	0.248913	+	0.352017i
$808$			6.00000i			0.211079i
$809$	54.0000			1.89854			0.949269	−	0.314464i	$-0.101825\pi$
$809$	54.0000			1.89854			0.949269	+	0.314464i	$0.101825\pi$
$810$		0			0
$811$			25.4558i			0.893876i	0.894565	+	0.446938i	$0.147485\pi$
$811$			25.4558i			0.893876i	−0.894565	+	0.446938i	$0.852515\pi$
$812$	25.4558			0.893325
$813$	−12.7279	−	18.0000i	−0.446388	−	0.631288i
$814$	6.00000	−	2.82843i	0.210300	−	0.0991363i
$815$		0			0
$816$		0			0
$817$		0			0
$818$	8.48528			0.296681
$819$	18.0000	−	50.9117i	0.628971	−	1.77900i
$820$		0			0
$821$	30.0000			1.04701			0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000			1.04701			0.523504	+	0.852023i	$0.324625\pi$
$822$	2.82843	+	4.00000i	0.0986527	+	0.139516i
$823$			40.0000i			1.39431i	0.716919	+	0.697156i	$0.245552\pi$
$823$			40.0000i			1.39431i	−0.716919	+	0.697156i	$0.754448\pi$
$824$	4.00000			0.139347
$825$		0			0
$826$	−48.0000			−1.67013
$827$			36.0000i			1.25184i	0.779886	+	0.625921i	$0.215277\pi$
$827$			36.0000i			1.25184i	−0.779886	+	0.625921i	$0.784723\pi$
$828$	1.41421	−	4.00000i	0.0491473	−	0.139010i
$829$	−2.00000			−0.0694629			−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000			−0.0694629			−0.0347314	+	0.999397i	$0.511058\pi$
$830$		0			0
$831$	−30.0000	+	21.2132i	−1.04069	+	0.735878i
$832$	4.24264			0.147087
$833$		0			0
$834$	24.0000	−	16.9706i	0.831052	−	0.587643i
$835$		0			0
$836$		0			0
$837$	−5.65685	−	20.0000i	−0.195529	−	0.691301i
$838$	11.3137			0.390826
$839$		−	15.5563i		−	0.537065i	−0.963271	−	0.268532i	$-0.913461\pi$
$839$		−	15.5563i		−	0.537065i	0.963271	−	0.268532i	$-0.0865386\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		−	10.0000i		−	0.344623i
$843$	−16.9706	+	12.0000i	−0.584497	+	0.413302i
$844$		−	8.48528i		−	0.292075i
$845$		0			0
$846$	28.0000	+	9.89949i	0.962660	+	0.340352i
$847$	−29.6985	+	36.0000i	−1.02045	+	1.23697i
$848$	7.07107			0.242821
$849$	−12.0000	+	8.48528i	−0.411839	+	0.291214i
$850$		0			0
$851$		−	2.82843i		−	0.0969572i
$852$	7.07107	+	10.0000i	0.242251	+	0.342594i
$853$	−21.2132			−0.726326			−0.363163	−	0.931726i	$-0.618303\pi$
$853$	−21.2132			−0.726326			−0.363163	+	0.931726i	$0.618303\pi$
$854$	18.0000			0.615947
$855$		0			0
$856$	18.0000			0.615227
$857$		−	6.00000i		−	0.204956i	−0.994735	−	0.102478i	$-0.967323\pi$
$857$		−	6.00000i		−	0.204956i	0.994735	−	0.102478i	$-0.0326771\pi$
$858$	−21.2132	−	12.0000i	−0.724207	−	0.409673i
$859$	22.0000			0.750630			0.375315	−	0.926897i	$-0.377534\pi$
$859$	22.0000			0.750630			0.375315	+	0.926897i	$0.377534\pi$
$860$		0			0
$861$	36.0000	−	25.4558i	1.22688	−	0.867533i
$862$			36.0000i			1.22616i
$863$	7.07107			0.240702			0.120351	−	0.992731i	$-0.461598\pi$
$863$	7.07107			0.240702			0.120351	+	0.992731i	$0.461598\pi$
$864$	−5.00000	+	1.41421i	−0.170103	+	0.0481125i
$865$		0			0
$866$	2.00000			0.0679628
$867$	−24.0416	+	17.0000i	−0.816497	+	0.577350i
$868$	−16.9706			−0.576018
$869$	6.00000	+	12.7279i	0.203536	+	0.431765i
$870$		0			0
$871$			16.9706i			0.575026i
$872$	−12.7279			−0.431022
$873$	22.6274	+	8.00000i	0.765822	+	0.270759i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	29.6985			1.00285			0.501423	−	0.865202i	$-0.332810\pi$
$877$	29.6985			1.00285			0.501423	+	0.865202i	$0.332810\pi$
$878$	−21.2132			−0.715911
$879$	6.00000	+	8.48528i	0.202375	+	0.286201i
$880$		0			0
$881$		−	5.65685i		−	0.190584i	−0.995449	−	0.0952921i	$-0.969621\pi$
$881$		−	5.65685i		−	0.190584i	0.995449	−	0.0952921i	$-0.0303785\pi$
$882$	31.1127	+	11.0000i	1.04762	+	0.370389i
$883$		−	20.0000i		−	0.673054i	−0.941674	−	0.336527i	$-0.890748\pi$
$883$		−	20.0000i		−	0.673054i	0.941674	−	0.336527i	$-0.109252\pi$
$884$		0			0
$885$		0			0
$886$			28.2843i			0.950229i
$887$		−	48.0000i		−	1.61168i	−0.592132	−	0.805841i	$-0.701714\pi$
$887$		−	48.0000i		−	1.61168i	0.592132	−	0.805841i	$-0.298286\pi$
$888$	−2.82843	+	2.00000i	−0.0949158	+	0.0671156i
$889$	−54.0000			−1.81110
$890$		0			0
$891$	29.0000	+	7.07107i	0.971537	+	0.236890i
$892$			8.00000i			0.267860i
$893$		0			0
$894$	6.00000	+	8.48528i	0.200670	+	0.283790i
$895$		0			0
$896$			4.24264i			0.141737i
$897$	−8.48528	+	6.00000i	−0.283315	+	0.200334i
$898$	−31.1127			−1.03824
$899$	−24.0000			−0.800445
$900$		0			0
$901$		0			0
$902$	−8.48528	−	18.0000i	−0.282529	−	0.599334i
$903$	−50.9117	+	36.0000i	−1.69423	+	1.19800i
$904$		−	11.3137i		−	0.376288i
$905$		0			0
$906$	6.00000	−	4.24264i	0.199337	−	0.140952i
$907$			44.0000i			1.46100i	0.682915	+	0.730498i	$0.260712\pi$
$907$			44.0000i			1.46100i	−0.682915	+	0.730498i	$0.739288\pi$
$908$			6.00000i			0.199117i
$909$	−6.00000	+	16.9706i	−0.199007	+	0.562878i
$910$		0			0
$911$		−	9.89949i		−	0.327985i	−0.986462	−	0.163992i	$-0.947563\pi$
$911$		−	9.89949i		−	0.327985i	0.986462	−	0.163992i	$-0.0524373\pi$
$912$		0			0
$913$	16.9706	+	36.0000i	0.561644	+	1.19143i
$914$			8.48528i			0.280668i
$915$		0			0
$916$	14.0000			0.462573
$917$	50.9117			1.68125
$918$		0			0
$919$		−	38.1838i		−	1.25957i	−0.776771	−	0.629783i	$-0.783144\pi$
$919$		−	38.1838i		−	1.25957i	0.776771	−	0.629783i	$-0.216856\pi$
$920$		0			0
$921$		0			0
$922$			30.0000i			0.987997i
$923$		−	30.0000i		−	0.987462i
$924$	12.0000	−	21.2132i	0.394771	−	0.697863i
$925$		0			0
$926$	32.0000			1.05159
$927$	11.3137	+	4.00000i	0.371591	+	0.131377i
$928$			6.00000i			0.196960i
$929$		−	2.82843i		−	0.0927977i	−0.998923	−	0.0463988i	$-0.985225\pi$
$929$		−	2.82843i		−	0.0927977i	0.998923	−	0.0463988i	$-0.0147745\pi$
$930$		0			0
$931$		0			0
$932$			18.0000i			0.589610i
$933$	26.8701	+	38.0000i	0.879686	+	1.24406i
$934$			31.1127i			1.01804i
$935$		0			0
$936$	12.0000	+	4.24264i	0.392232	+	0.138675i
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$	−16.9706			−0.554109
$939$	−10.0000	−	14.1421i	−0.326338	−	0.461511i
$940$		0			0
$941$	42.0000			1.36916			0.684580	−	0.728937i	$-0.259985\pi$
$941$	42.0000			1.36916			0.684580	+	0.728937i	$0.259985\pi$
$942$	−31.1127	+	22.0000i	−1.01371	+	0.716799i
$943$	−8.48528			−0.276319
$944$		−	11.3137i		−	0.368230i
$945$		0			0
$946$	12.0000	+	25.4558i	0.390154	+	0.827641i
$947$	48.0833			1.56250			0.781248	−	0.624221i	$-0.214583\pi$
$947$	48.0833			1.56250			0.781248	+	0.624221i	$0.214583\pi$
$948$	−4.24264	−	6.00000i	−0.137795	−	0.194871i
$949$		0			0
$950$		0			0
$951$	−14.0000	+	9.89949i	−0.453981	+	0.321013i
$952$		0			0
$953$			54.0000i			1.74923i	0.484817	+	0.874616i	$0.338886\pi$
$953$			54.0000i			1.74923i	−0.484817	+	0.874616i	$0.661114\pi$
$954$	20.0000	+	7.07107i	0.647524	+	0.228934i
$955$		0			0
$956$	−12.0000			−0.388108
$957$	16.9706	−	30.0000i	0.548580	−	0.969762i
$958$		−	12.0000i		−	0.387702i
$959$	12.0000			0.387500
$960$		0			0
$961$	−15.0000			−0.483871
$962$	8.48528			0.273576
$963$	50.9117	+	18.0000i	1.64061	+	0.580042i
$964$			8.48528i			0.273293i
$965$		0			0
$966$	−6.00000	−	8.48528i	−0.193047	−	0.273009i
$967$	4.24264			0.136434			0.0682171	−	0.997671i	$-0.478269\pi$
$967$	4.24264			0.136434			0.0682171	+	0.997671i	$0.478269\pi$
$968$	−8.48528	−	7.00000i	−0.272727	−	0.224989i
$969$		0			0
$970$		0			0
$971$			45.2548i			1.45230i	0.687538	+	0.726148i	$0.258691\pi$
$971$			45.2548i			1.45230i	−0.687538	+	0.726148i	$0.741309\pi$
$972$	−15.5563	−	1.00000i	−0.498970	−	0.0320750i
$973$		−	72.0000i		−	2.30821i
$974$	−20.0000			−0.640841
$975$		0			0
$976$			4.24264i			0.135804i
$977$	14.1421			0.452447			0.226224	−	0.974075i	$-0.427362\pi$
$977$	14.1421			0.452447			0.226224	+	0.974075i	$0.427362\pi$
$978$	−2.82843	+	2.00000i	−0.0904431	+	0.0639529i
$979$	−8.00000	−	16.9706i	−0.255681	−	0.542382i
$980$		0			0
$981$	−36.0000	−	12.7279i	−1.14939	−	0.406371i
$982$			6.00000i			0.191468i
$983$	−9.89949			−0.315745			−0.157872	−	0.987460i	$-0.550463\pi$
$983$	−9.89949			−0.315745			−0.157872	+	0.987460i	$0.550463\pi$
$984$	6.00000	+	8.48528i	0.191273	+	0.270501i
$985$		0			0
$986$		0			0
$987$	59.3970	−	42.0000i	1.89063	−	1.33687i
$988$		0			0
$989$	12.0000			0.381578
$990$		0			0
$991$	20.0000			0.635321			0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000			0.635321			0.317660	+	0.948205i	$0.397103\pi$
$992$		−	4.00000i		−	0.127000i
$993$	14.1421	−	10.0000i	0.448787	−	0.317340i
$994$	30.0000			0.951542
$995$		0			0
$996$	−12.0000	−	16.9706i	−0.380235	−	0.537733i
$997$	−29.6985			−0.940560			−0.470280	−	0.882517i	$-0.655847\pi$
$997$	−29.6985			−0.940560			−0.470280	+	0.882517i	$0.655847\pi$
$998$		−	14.0000i		−	0.443162i
$999$	−10.0000	+	2.82843i	−0.316386	+	0.0894875i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1650.2.f.a.1649.3		4
3.2	odd	2		1650.2.f.b.1649.2		4
5.2	odd	4		1650.2.d.a.1451.2		2
5.3	odd	4		66.2.b.b.65.1	yes	2
5.4	even	2	inner	1650.2.f.a.1649.2		4
11.10	odd	2		1650.2.f.b.1649.1		4
15.2	even	4		1650.2.d.b.1451.1		2
15.8	even	4		66.2.b.a.65.2	yes	2
15.14	odd	2		1650.2.f.b.1649.3		4
20.3	even	4		528.2.b.c.65.2		2
33.32	even	2	inner	1650.2.f.a.1649.4		4
40.3	even	4		2112.2.b.b.65.1		2
40.13	odd	4		2112.2.b.i.65.2		2
45.13	odd	12		1782.2.i.c.593.1		4
45.23	even	12		1782.2.i.f.593.2		4
45.38	even	12		1782.2.i.f.1187.1		4
45.43	odd	12		1782.2.i.c.1187.2		4
55.3	odd	20		726.2.h.e.233.2		8
55.8	even	20		726.2.h.i.233.2		8
55.13	even	20		726.2.h.i.161.1		8
55.18	even	20		726.2.h.i.215.1		8
55.28	even	20		726.2.h.i.239.2		8
55.32	even	4		1650.2.d.b.1451.2		2
55.38	odd	20		726.2.h.e.239.2		8
55.43	even	4		66.2.b.a.65.1	✓	2
55.48	odd	20		726.2.h.e.215.1		8
55.53	odd	20		726.2.h.e.161.1		8
55.54	odd	2		1650.2.f.b.1649.4		4
60.23	odd	4		528.2.b.b.65.1		2
120.53	even	4		2112.2.b.g.65.1		2
120.83	odd	4		2112.2.b.d.65.2		2
165.8	odd	20		726.2.h.e.233.1		8
165.32	odd	4		1650.2.d.a.1451.1		2
165.38	even	20		726.2.h.i.239.1		8
165.53	even	20		726.2.h.i.161.2		8
165.68	odd	20		726.2.h.e.161.2		8
165.83	odd	20		726.2.h.e.239.1		8
165.98	odd	4		66.2.b.b.65.2	yes	2
165.113	even	20		726.2.h.i.233.1		8
165.128	odd	20		726.2.h.e.215.2		8
165.158	even	20		726.2.h.i.215.2		8
165.164	even	2	inner	1650.2.f.a.1649.1		4
220.43	odd	4		528.2.b.b.65.2		2
440.43	odd	4		2112.2.b.d.65.1		2
440.373	even	4		2112.2.b.g.65.2		2
495.43	even	12		1782.2.i.f.1187.2		4
495.263	odd	12		1782.2.i.c.1187.1		4
495.373	even	12		1782.2.i.f.593.1		4
495.428	odd	12		1782.2.i.c.593.2		4
660.263	even	4		528.2.b.c.65.1		2
1320.923	even	4		2112.2.b.b.65.2		2
1320.1253	odd	4		2112.2.b.i.65.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.b.a.65.1	✓	2	55.43	even	4
66.2.b.a.65.2	yes	2	15.8	even	4
66.2.b.b.65.1	yes	2	5.3	odd	4
66.2.b.b.65.2	yes	2	165.98	odd	4
528.2.b.b.65.1		2	60.23	odd	4
528.2.b.b.65.2		2	220.43	odd	4
528.2.b.c.65.1		2	660.263	even	4
528.2.b.c.65.2		2	20.3	even	4
726.2.h.e.161.1		8	55.53	odd	20
726.2.h.e.161.2		8	165.68	odd	20
726.2.h.e.215.1		8	55.48	odd	20
726.2.h.e.215.2		8	165.128	odd	20
726.2.h.e.233.1		8	165.8	odd	20
726.2.h.e.233.2		8	55.3	odd	20
726.2.h.e.239.1		8	165.83	odd	20
726.2.h.e.239.2		8	55.38	odd	20
726.2.h.i.161.1		8	55.13	even	20
726.2.h.i.161.2		8	165.53	even	20
726.2.h.i.215.1		8	55.18	even	20
726.2.h.i.215.2		8	165.158	even	20
726.2.h.i.233.1		8	165.113	even	20
726.2.h.i.233.2		8	55.8	even	20
726.2.h.i.239.1		8	165.38	even	20
726.2.h.i.239.2		8	55.28	even	20
1650.2.d.a.1451.1		2	165.32	odd	4
1650.2.d.a.1451.2		2	5.2	odd	4
1650.2.d.b.1451.1		2	15.2	even	4
1650.2.d.b.1451.2		2	55.32	even	4
1650.2.f.a.1649.1		4	165.164	even	2	inner
1650.2.f.a.1649.2		4	5.4	even	2	inner
1650.2.f.a.1649.3		4	1.1	even	1	trivial
1650.2.f.a.1649.4		4	33.32	even	2	inner
1650.2.f.b.1649.1		4	11.10	odd	2
1650.2.f.b.1649.2		4	3.2	odd	2
1650.2.f.b.1649.3		4	15.14	odd	2
1650.2.f.b.1649.4		4	55.54	odd	2
1782.2.i.c.593.1		4	45.13	odd	12
1782.2.i.c.593.2		4	495.428	odd	12
1782.2.i.c.1187.1		4	495.263	odd	12
1782.2.i.c.1187.2		4	45.43	odd	12
1782.2.i.f.593.1		4	495.373	even	12
1782.2.i.f.593.2		4	45.23	even	12
1782.2.i.f.1187.1		4	45.38	even	12
1782.2.i.f.1187.2		4	495.43	even	12
2112.2.b.b.65.1		2	40.3	even	4
2112.2.b.b.65.2		2	1320.923	even	4
2112.2.b.d.65.1		2	440.43	odd	4
2112.2.b.d.65.2		2	120.83	odd	4
2112.2.b.g.65.1		2	120.53	even	4
2112.2.b.g.65.2		2	440.373	even	4
2112.2.b.i.65.1		2	1320.1253	odd	4
2112.2.b.i.65.2		2	40.13	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:	\( N \)	\(=\)	\( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1650.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.41421 + 1.00000i) q^{3} -1.00000 q^{4} +(-1.00000 - 1.41421i) q^{6} -4.24264 q^{7} -1.00000i q^{8} +(1.00000 - 2.82843i) q^{9} +(-3.00000 + 1.41421i) q^{11} +(1.41421 - 1.00000i) q^{12} -4.24264 q^{13} -4.24264i q^{14} +1.00000 q^{16} +(2.82843 + 1.00000i) q^{18} +(6.00000 - 4.24264i) q^{21} +(-1.41421 - 3.00000i) q^{22} -1.41421 q^{23} +(1.00000 + 1.41421i) q^{24} -4.24264i q^{26} +(1.41421 + 5.00000i) q^{27} +4.24264 q^{28} +6.00000 q^{29} -4.00000 q^{31} +1.00000i q^{32} +(2.82843 - 5.00000i) q^{33} +(-1.00000 + 2.82843i) q^{36} +2.00000i q^{37} +(6.00000 - 4.24264i) q^{39} +6.00000 q^{41} +(4.24264 + 6.00000i) q^{42} -8.48528 q^{43} +(3.00000 - 1.41421i) q^{44} -1.41421i q^{46} +9.89949 q^{47} +(-1.41421 + 1.00000i) q^{48} +11.0000 q^{49} +4.24264 q^{52} +7.07107 q^{53} +(-5.00000 + 1.41421i) q^{54} +4.24264i q^{56} +6.00000i q^{58} -11.3137i q^{59} +4.24264i q^{61} -4.00000i q^{62} +(-4.24264 + 12.0000i) q^{63} -1.00000 q^{64} +(5.00000 + 2.82843i) q^{66} -4.00000i q^{67} +(2.00000 - 1.41421i) q^{69} +7.07107i q^{71} +(-2.82843 - 1.00000i) q^{72} -2.00000 q^{74} +(12.7279 - 6.00000i) q^{77} +(4.24264 + 6.00000i) q^{78} -4.24264i q^{79} +(-7.00000 - 5.65685i) q^{81} +6.00000i q^{82} -12.0000i q^{83} +(-6.00000 + 4.24264i) q^{84} -8.48528i q^{86} +(-8.48528 + 6.00000i) q^{87} +(1.41421 + 3.00000i) q^{88} +5.65685i q^{89} +18.0000 q^{91} +1.41421 q^{92} +(5.65685 - 4.00000i) q^{93} +9.89949i q^{94} +(-1.00000 - 1.41421i) q^{96} +8.00000i q^{97} +11.0000i q^{98} +(1.00000 + 9.89949i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 4 q^{6} + 4 q^{9} - 12 q^{11} + 4 q^{16} + 24 q^{21} + 4 q^{24} + 24 q^{29} - 16 q^{31} - 4 q^{36} + 24 q^{39} + 24 q^{41} + 12 q^{44} + 44 q^{49} - 20 q^{54} - 4 q^{64} + 20 q^{66} + 8 q^{69}+ \cdots + 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 - 4 * q^6 + 4 * q^9 - 12 * q^11 + 4 * q^16 + 24 * q^21 + 4 * q^24 + 24 * q^29 - 16 * q^31 - 4 * q^36 + 24 * q^39 + 24 * q^41 + 12 * q^44 + 44 * q^49 - 20 * q^54 - 4 * q^64 + 20 * q^66 + 8 * q^69 - 8 * q^74 - 28 * q^81 - 24 * q^84 + 72 * q^91 - 4 * q^96 + 4 * q^99

Introduction

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