LMFDB - Embedded newform 2112.2.b.b.65.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2112,2,Mod(65,2112)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2112, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2112.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2112 = 2^{6} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2112.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.8644049069$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-2}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 2 $ x^2 + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			65.1
Root			$1.41421i$ of defining polynomial
Character	$\chi$	$=$	2112.65
Dual form			2112.2.b.b.65.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.41421i) q^{3} +1.41421i q^{5} -4.24264i q^{7} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})$	$q+(-1.00000 - 1.41421i) q^{3} +1.41421i q^{5} -4.24264i q^{7} +(-1.00000 + 2.82843i) q^{9} +(-3.00000 + 1.41421i) q^{11} +4.24264i q^{13} +(2.00000 - 1.41421i) q^{15} +(-6.00000 + 4.24264i) q^{21} +1.41421i q^{23} +3.00000 q^{25} +(5.00000 - 1.41421i) q^{27} +6.00000 q^{29} +4.00000 q^{31} +(5.00000 + 2.82843i) q^{33} +6.00000 q^{35} -2.00000 q^{37} +(6.00000 - 4.24264i) q^{39} +6.00000 q^{41} -8.48528i q^{43} +(-4.00000 - 1.41421i) q^{45} +9.89949i q^{47} -11.0000 q^{49} -7.07107i q^{53} +(-2.00000 - 4.24264i) q^{55} +11.3137i q^{59} -4.24264i q^{61} +(12.0000 + 4.24264i) q^{63} -6.00000 q^{65} -4.00000 q^{67} +(2.00000 - 1.41421i) q^{69} -7.07107i q^{71} +(-3.00000 - 4.24264i) q^{75} +(6.00000 + 12.7279i) q^{77} -4.24264i q^{79} +(-7.00000 - 5.65685i) q^{81} +12.0000 q^{83} +(-6.00000 - 8.48528i) q^{87} -5.65685i q^{89} +18.0000 q^{91} +(-4.00000 - 5.65685i) q^{93} +8.00000 q^{97} +(-1.00000 - 9.89949i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 - 2 * q^9	$ 2 q - 2 q^{3} - 2 q^{9} - 6 q^{11} + 4 q^{15} - 12 q^{21} + 6 q^{25} + 10 q^{27} + 12 q^{29} + 8 q^{31} + 10 q^{33} + 12 q^{35} - 4 q^{37} + 12 q^{39} + 12 q^{41} - 8 q^{45} - 22 q^{49} - 4 q^{55} + 24 q^{63} - 12 q^{65} - 8 q^{67} + 4 q^{69} - 6 q^{75} + 12 q^{77} - 14 q^{81} + 24 q^{83} - 12 q^{87} + 36 q^{91} - 8 q^{93} + 16 q^{97} - 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 - 2 * q^9 - 6 * q^11 + 4 * q^15 - 12 * q^21 + 6 * q^25 + 10 * q^27 + 12 * q^29 + 8 * q^31 + 10 * q^33 + 12 * q^35 - 4 * q^37 + 12 * q^39 + 12 * q^41 - 8 * q^45 - 22 * q^49 - 4 * q^55 + 24 * q^63 - 12 * q^65 - 8 * q^67 + 4 * q^69 - 6 * q^75 + 12 * q^77 - 14 * q^81 + 24 * q^83 - 12 * q^87 + 36 * q^91 - 8 * q^93 + 16 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2112\mathbb{Z}\right)^\times$.

$n$	$133$	$1409$	$1729$	$2047$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.00000	−	1.41421i	−0.577350	−	0.816497i
$3$	−1.00000	−	1.41421i	−0.577350	−	0.816497i
$4$		0			0
$5$			1.41421i			0.632456i	0.948683	+	0.316228i	$0.102416\pi$
$5$			1.41421i			0.632456i	−0.948683	+	0.316228i	$0.897584\pi$
$6$		0			0
$7$		−	4.24264i		−	1.60357i	−0.597614	−	0.801784i	$-0.703885\pi$
$7$		−	4.24264i		−	1.60357i	0.597614	−	0.801784i	$-0.296115\pi$
$8$		0			0
$9$	−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
$12$		0			0
$13$			4.24264i			1.17670i	0.808608	+	0.588348i	$0.200222\pi$
$13$			4.24264i			1.17670i	−0.808608	+	0.588348i	$0.799778\pi$
$14$		0			0
$15$	2.00000	−	1.41421i	0.516398	−	0.365148i
$16$		0			0
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$		0			0
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$		0			0
$21$	−6.00000	+	4.24264i	−1.30931	+	0.925820i
$22$		0			0
$23$			1.41421i			0.294884i	0.989071	+	0.147442i	$0.0471040\pi$
$23$			1.41421i			0.294884i	−0.989071	+	0.147442i	$0.952896\pi$
$24$		0			0
$25$	3.00000			0.600000
$26$		0			0
$27$	5.00000	−	1.41421i	0.962250	−	0.272166i
$28$		0			0
$29$	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	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$		0			0
$33$	5.00000	+	2.82843i	0.870388	+	0.492366i
$34$		0			0
$35$	6.00000			1.01419
$36$		0			0
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$		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	$0.344787\pi$
$42$		0			0
$43$		−	8.48528i		−	1.29399i	−0.762493	−	0.646997i	$-0.776025\pi$
$43$		−	8.48528i		−	1.29399i	0.762493	−	0.646997i	$-0.223975\pi$
$44$		0			0
$45$	−4.00000	−	1.41421i	−0.596285	−	0.210819i
$46$		0			0
$47$			9.89949i			1.44399i	0.691898	+	0.721995i	$0.256775\pi$
$47$			9.89949i			1.44399i	−0.691898	+	0.721995i	$0.743225\pi$
$48$		0			0
$49$	−11.0000			−1.57143
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	7.07107i		−	0.971286i	−0.874157	−	0.485643i	$-0.838586\pi$
$53$		−	7.07107i		−	0.971286i	0.874157	−	0.485643i	$-0.161414\pi$
$54$		0			0
$55$	−2.00000	−	4.24264i	−0.269680	−	0.572078i
$56$		0			0
$57$		0			0
$58$		0			0
$59$			11.3137i			1.47292i	0.676481	+	0.736460i	$0.263504\pi$
$59$			11.3137i			1.47292i	−0.676481	+	0.736460i	$0.736496\pi$
$60$		0			0
$61$		−	4.24264i		−	0.543214i	−0.962408	−	0.271607i	$-0.912445\pi$
$61$		−	4.24264i		−	0.543214i	0.962408	−	0.271607i	$-0.0875552\pi$
$62$		0			0
$63$	12.0000	+	4.24264i	1.51186	+	0.534522i
$64$		0			0
$65$	−6.00000			−0.744208
$66$		0			0
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$		0			0
$69$	2.00000	−	1.41421i	0.240772	−	0.170251i
$70$		0			0
$71$		−	7.07107i		−	0.839181i	−0.907713	−	0.419591i	$-0.862174\pi$
$71$		−	7.07107i		−	0.839181i	0.907713	−	0.419591i	$-0.137826\pi$
$72$		0			0
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$	−3.00000	−	4.24264i	−0.346410	−	0.489898i
$76$		0			0
$77$	6.00000	+	12.7279i	0.683763	+	1.45048i
$78$		0			0
$79$		−	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
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−6.00000	−	8.48528i	−0.643268	−	0.909718i
$88$		0			0
$89$		−	5.65685i		−	0.599625i	−0.953998	−	0.299813i	$-0.903076\pi$
$89$		−	5.65685i		−	0.599625i	0.953998	−	0.299813i	$-0.0969242\pi$
$90$		0			0
$91$	18.0000			1.88691
$92$		0			0
$93$	−4.00000	−	5.65685i	−0.414781	−	0.586588i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$		0			0
$99$	−1.00000	−	9.89949i	−0.100504	−	0.994937i
$100$		0			0
$101$	6.00000			0.597022			0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000			0.597022			0.298511	+	0.954406i	$0.403510\pi$
$102$		0			0
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$		0			0
$105$	−6.00000	−	8.48528i	−0.585540	−	0.828079i
$106$		0			0
$107$	18.0000			1.74013			0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000			1.74013			0.870063	+	0.492941i	$0.164078\pi$
$108$		0			0
$109$		−	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
$112$		0			0
$113$			11.3137i			1.06430i	0.846649	+	0.532152i	$0.178617\pi$
$113$			11.3137i			1.06430i	−0.846649	+	0.532152i	$0.821383\pi$
$114$		0			0
$115$	−2.00000			−0.186501
$116$		0			0
$117$	−12.0000	−	4.24264i	−1.10940	−	0.392232i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	7.00000	−	8.48528i	0.636364	−	0.771389i
$122$		0			0
$123$	−6.00000	−	8.48528i	−0.541002	−	0.765092i
$124$		0			0
$125$			11.3137i			1.01193i
$126$		0			0
$127$			12.7279i			1.12942i	0.825289	+	0.564710i	$0.191012\pi$
$127$			12.7279i			1.12942i	−0.825289	+	0.564710i	$0.808988\pi$
$128$		0			0
$129$	−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	$0.675644\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	2.00000	+	7.07107i	0.172133	+	0.608581i
$136$		0			0
$137$			2.82843i			0.241649i	0.992674	+	0.120824i	$0.0385538\pi$
$137$			2.82843i			0.241649i	−0.992674	+	0.120824i	$0.961446\pi$
$138$		0			0
$139$		−	16.9706i		−	1.43942i	−0.694273	−	0.719712i	$-0.744274\pi$
$139$		−	16.9706i		−	1.43942i	0.694273	−	0.719712i	$-0.255726\pi$
$140$		0			0
$141$	14.0000	−	9.89949i	1.17901	−	0.833688i
$142$		0			0
$143$	−6.00000	−	12.7279i	−0.501745	−	1.06436i
$144$		0			0
$145$			8.48528i			0.704664i
$146$		0			0
$147$	11.0000	+	15.5563i	0.907265	+	1.28307i
$148$		0			0
$149$	−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	$-0.944773\pi$
$151$		−	4.24264i		−	0.345261i	0.984987	−	0.172631i	$-0.0552267\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			5.65685i			0.454369i
$156$		0			0
$157$	22.0000			1.75579			0.877896	−	0.478852i	$-0.158947\pi$
$157$	22.0000			1.75579			0.877896	+	0.478852i	$0.158947\pi$
$158$		0			0
$159$	−10.0000	+	7.07107i	−0.793052	+	0.560772i
$160$		0			0
$161$	6.00000			0.472866
$162$		0			0
$163$	2.00000			0.156652			0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000			0.156652			0.0783260	+	0.996928i	$0.475042\pi$
$164$		0			0
$165$	−4.00000	+	7.07107i	−0.311400	+	0.550482i
$166$		0			0
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$		0			0
$169$	−5.00000			−0.384615
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$		0			0
$175$		−	12.7279i		−	0.962140i
$176$		0			0
$177$	16.0000	−	11.3137i	1.20263	−	0.850390i
$178$		0			0
$179$		−	5.65685i		−	0.422813i	−0.977398	−	0.211407i	$-0.932196\pi$
$179$		−	5.65685i		−	0.422813i	0.977398	−	0.211407i	$-0.0678044\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$	−6.00000	+	4.24264i	−0.443533	+	0.313625i
$184$		0			0
$185$		−	2.82843i		−	0.207950i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−6.00000	−	21.2132i	−0.436436	−	1.54303i
$190$		0			0
$191$			9.89949i			0.716302i	0.933664	+	0.358151i	$0.116593\pi$
$191$			9.89949i			0.716302i	−0.933664	+	0.358151i	$0.883407\pi$
$192$		0			0
$193$			8.48528i			0.610784i	0.952227	+	0.305392i	$0.0987875\pi$
$193$			8.48528i			0.610784i	−0.952227	+	0.305392i	$0.901213\pi$
$194$		0			0
$195$	6.00000	+	8.48528i	0.429669	+	0.607644i
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	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
$202$		0			0
$203$		−	25.4558i		−	1.78665i
$204$		0			0
$205$			8.48528i			0.592638i
$206$		0			0
$207$	−4.00000	−	1.41421i	−0.278019	−	0.0982946i
$208$		0			0
$209$		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	$0.905654\pi$
$212$		0			0
$213$	−10.0000	+	7.07107i	−0.685189	+	0.484502i
$214$		0			0
$215$	12.0000			0.818393
$216$		0			0
$217$		−	16.9706i		−	1.15204i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−8.00000			−0.535720			−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000			−0.535720			−0.267860	+	0.963458i	$0.586316\pi$
$224$		0			0
$225$	−3.00000	+	8.48528i	−0.200000	+	0.565685i
$226$		0			0
$227$	−6.00000			−0.398234			−0.199117	−	0.979976i	$-0.563807\pi$
$227$	−6.00000			−0.398234			−0.199117	+	0.979976i	$0.563807\pi$
$228$		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
$232$		0			0
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$		0			0
$235$	−14.0000			−0.913259
$236$		0			0
$237$	−6.00000	+	4.24264i	−0.389742	+	0.275589i
$238$		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	$-0.0881127\pi$
$242$		0			0
$243$	−1.00000	+	15.5563i	−0.0641500	+	0.997940i
$244$		0			0
$245$		−	15.5563i		−	0.993859i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−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	$-0.0571337\pi$
$252$		0			0
$253$	−2.00000	−	4.24264i	−0.125739	−	0.266733i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			11.3137i			0.705730i	0.935674	+	0.352865i	$0.114792\pi$
$257$			11.3137i			0.705730i	−0.935674	+	0.352865i	$0.885208\pi$
$258$		0			0
$259$			8.48528i			0.527250i
$260$		0			0
$261$	−6.00000	+	16.9706i	−0.371391	+	1.05045i
$262$		0			0
$263$	−12.0000			−0.739952			−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000			−0.739952			−0.369976	+	0.929041i	$0.620634\pi$
$264$		0			0
$265$	10.0000			0.614295
$266$		0			0
$267$	−8.00000	+	5.65685i	−0.489592	+	0.346194i
$268$		0			0
$269$		−	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	$-0.873655\pi$
$271$		−	12.7279i		−	0.773166i	0.922255	−	0.386583i	$-0.126345\pi$
$272$		0			0
$273$	−18.0000	−	25.4558i	−1.08941	−	1.54066i
$274$		0			0
$275$	−9.00000	+	4.24264i	−0.542720	+	0.255841i
$276$		0			0
$277$			21.2132i			1.27458i	0.770625	+	0.637289i	$0.219944\pi$
$277$			21.2132i			1.27458i	−0.770625	+	0.637289i	$0.780056\pi$
$278$		0			0
$279$	−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	$0.383483\pi$
$282$		0			0
$283$			8.48528i			0.504398i	0.967675	+	0.252199i	$0.0811537\pi$
$283$			8.48528i			0.504398i	−0.967675	+	0.252199i	$0.918846\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	25.4558i		−	1.50261i
$288$		0			0
$289$	−17.0000			−1.00000
$290$		0			0
$291$	−8.00000	−	11.3137i	−0.468968	−	0.663221i
$292$		0			0
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$		0			0
$295$	−16.0000			−0.931556
$296$		0			0
$297$	−13.0000	+	11.3137i	−0.754337	+	0.656488i
$298$		0			0
$299$	−6.00000			−0.346989
$300$		0			0
$301$	−36.0000			−2.07501
$302$		0			0
$303$	−6.00000	−	8.48528i	−0.344691	−	0.487467i
$304$		0			0
$305$	6.00000			0.343559
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$	−4.00000	−	5.65685i	−0.227552	−	0.321807i
$310$		0			0
$311$			26.8701i			1.52366i	0.647776	+	0.761831i	$0.275699\pi$
$311$			26.8701i			1.52366i	−0.647776	+	0.761831i	$0.724301\pi$
$312$		0			0
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$		0			0
$315$	−6.00000	+	16.9706i	−0.338062	+	0.956183i
$316$		0			0
$317$			9.89949i			0.556011i	0.960579	+	0.278006i	$0.0896734\pi$
$317$			9.89949i			0.556011i	−0.960579	+	0.278006i	$0.910327\pi$
$318$		0			0
$319$	−18.0000	+	8.48528i	−1.00781	+	0.475085i
$320$		0			0
$321$	−18.0000	−	25.4558i	−1.00466	−	1.42081i
$322$		0			0
$323$		0			0
$324$		0			0
$325$			12.7279i			0.706018i
$326$		0			0
$327$	−18.0000	+	12.7279i	−0.995402	+	0.703856i
$328$		0			0
$329$	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	$0.588620\pi$
$332$		0			0
$333$	2.00000	−	5.65685i	0.109599	−	0.309994i
$334$		0			0
$335$		−	5.65685i		−	0.309067i
$336$		0			0
$337$			33.9411i			1.84889i	0.381314	+	0.924445i	$0.375472\pi$
$337$			33.9411i			1.84889i	−0.381314	+	0.924445i	$0.624528\pi$
$338$		0			0
$339$	16.0000	−	11.3137i	0.869001	−	0.614476i
$340$		0			0
$341$	−12.0000	+	5.65685i	−0.649836	+	0.306336i
$342$		0			0
$343$			16.9706i			0.916324i
$344$		0			0
$345$	2.00000	+	2.82843i	0.107676	+	0.152277i
$346$		0			0
$347$	−12.0000			−0.644194			−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000			−0.644194			−0.322097	+	0.946707i	$0.604388\pi$
$348$		0			0
$349$		−	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
$352$		0			0
$353$		−	22.6274i		−	1.20434i	−0.798369	−	0.602168i	$-0.794304\pi$
$353$		−	22.6274i		−	1.20434i	0.798369	−	0.602168i	$-0.205696\pi$
$354$		0			0
$355$	10.0000			0.530745
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	19.0000			1.00000
$362$		0			0
$363$	−19.0000	−	1.41421i	−0.997241	−	0.0742270i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	28.0000			1.46159			0.730794	−	0.682598i	$-0.239150\pi$
$367$	28.0000			1.46159			0.730794	+	0.682598i	$0.239150\pi$
$368$		0			0
$369$	−6.00000	+	16.9706i	−0.312348	+	0.883452i
$370$		0			0
$371$	−30.0000			−1.55752
$372$		0			0
$373$			29.6985i			1.53773i	0.639412	+	0.768865i	$0.279178\pi$
$373$			29.6985i			1.53773i	−0.639412	+	0.768865i	$0.720822\pi$
$374$		0			0
$375$	16.0000	−	11.3137i	0.826236	−	0.584237i
$376$		0			0
$377$			25.4558i			1.31104i
$378$		0			0
$379$	2.00000			0.102733			0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000			0.102733			0.0513665	+	0.998680i	$0.483642\pi$
$380$		0			0
$381$	18.0000	−	12.7279i	0.922168	−	0.652071i
$382$		0			0
$383$			1.41421i			0.0722629i	0.999347	+	0.0361315i	$0.0115035\pi$
$383$			1.41421i			0.0722629i	−0.999347	+	0.0361315i	$0.988496\pi$
$384$		0			0
$385$	−18.0000	+	8.48528i	−0.917365	+	0.432450i
$386$		0			0
$387$	24.0000	+	8.48528i	1.21999	+	0.431331i
$388$		0			0
$389$			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
$392$		0			0
$393$	12.0000	+	16.9706i	0.605320	+	0.856052i
$394$		0			0
$395$	6.00000			0.301893
$396$		0			0
$397$	34.0000			1.70641			0.853206	−	0.521575i	$-0.174655\pi$
$397$	34.0000			1.70641			0.853206	+	0.521575i	$0.174655\pi$
$398$		0			0
$399$		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	$0.629729\pi$
$402$		0			0
$403$			16.9706i			0.845364i
$404$		0			0
$405$	8.00000	−	9.89949i	0.397523	−	0.491910i
$406$		0			0
$407$	6.00000	−	2.82843i	0.297409	−	0.140200i
$408$		0			0
$409$			8.48528i			0.419570i	0.977748	+	0.209785i	$0.0672764\pi$
$409$			8.48528i			0.419570i	−0.977748	+	0.209785i	$0.932724\pi$
$410$		0			0
$411$	4.00000	−	2.82843i	0.197305	−	0.139516i
$412$		0			0
$413$	48.0000			2.36193
$414$		0			0
$415$			16.9706i			0.833052i
$416$		0			0
$417$	−24.0000	+	16.9706i	−1.17529	+	0.831052i
$418$		0			0
$419$			11.3137i			0.552711i	0.961056	+	0.276355i	$0.0891267\pi$
$419$			11.3137i			0.552711i	−0.961056	+	0.276355i	$0.910873\pi$
$420$		0			0
$421$	10.0000			0.487370			0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000			0.487370			0.243685	+	0.969854i	$0.421644\pi$
$422$		0			0
$423$	−28.0000	−	9.89949i	−1.36141	−	0.481330i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−18.0000			−0.871081
$428$		0			0
$429$	−12.0000	+	21.2132i	−0.579365	+	1.02418i
$430$		0			0
$431$	−36.0000			−1.73406			−0.867029	−	0.498257i	$-0.833974\pi$
$431$	−36.0000			−1.73406			−0.867029	+	0.498257i	$0.833974\pi$
$432$		0			0
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$		0			0
$435$	12.0000	−	8.48528i	0.575356	−	0.406838i
$436$		0			0
$437$		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
$443$			28.2843i			1.34383i	0.740630	+	0.671913i	$0.234527\pi$
$443$			28.2843i			1.34383i	−0.740630	+	0.671913i	$0.765473\pi$
$444$		0			0
$445$	8.00000			0.379236
$446$		0			0
$447$	6.00000	+	8.48528i	0.283790	+	0.401340i
$448$		0			0
$449$		−	31.1127i		−	1.46830i	−0.678988	−	0.734150i	$-0.737581\pi$
$449$		−	31.1127i		−	1.46830i	0.678988	−	0.734150i	$-0.262419\pi$
$450$		0			0
$451$	−18.0000	+	8.48528i	−0.847587	+	0.399556i
$452$		0			0
$453$	−6.00000	+	4.24264i	−0.281905	+	0.199337i
$454$		0			0
$455$			25.4558i			1.19339i
$456$		0			0
$457$		−	8.48528i		−	0.396925i	−0.980109	−	0.198462i	$-0.936405\pi$
$457$		−	8.48528i		−	0.396925i	0.980109	−	0.198462i	$-0.0635948\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$		0			0
$463$	−32.0000			−1.48717			−0.743583	−	0.668644i	$-0.766875\pi$
$463$	−32.0000			−1.48717			−0.743583	+	0.668644i	$0.766875\pi$
$464$		0			0
$465$	8.00000	−	5.65685i	0.370991	−	0.262330i
$466$		0			0
$467$		−	31.1127i		−	1.43972i	−0.694117	−	0.719862i	$-0.744205\pi$
$467$		−	31.1127i		−	1.43972i	0.694117	−	0.719862i	$-0.255795\pi$
$468$		0			0
$469$			16.9706i			0.783628i
$470$		0			0
$471$	−22.0000	−	31.1127i	−1.01371	−	1.43360i
$472$		0			0
$473$	12.0000	+	25.4558i	0.551761	+	1.17046i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	20.0000	+	7.07107i	0.915737	+	0.323762i
$478$		0			0
$479$	−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
$482$		0			0
$483$	−6.00000	−	8.48528i	−0.273009	−	0.386094i
$484$		0			0
$485$			11.3137i			0.513729i
$486$		0			0
$487$	−20.0000			−0.906287			−0.453143	−	0.891438i	$-0.649697\pi$
$487$	−20.0000			−0.906287			−0.453143	+	0.891438i	$0.649697\pi$
$488$		0			0
$489$	−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	$0.456772\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	14.0000	−	1.41421i	0.629253	−	0.0635642i
$496$		0			0
$497$	−30.0000			−1.34568
$498$		0			0
$499$	14.0000			0.626726			0.313363	−	0.949633i	$-0.398544\pi$
$499$	14.0000			0.626726			0.313363	+	0.949633i	$0.398544\pi$
$500$		0			0
$501$	−12.0000	−	16.9706i	−0.536120	−	0.758189i
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$			8.48528i			0.377590i
$506$		0			0
$507$	5.00000	+	7.07107i	0.222058	+	0.314037i
$508$		0			0
$509$			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
$512$		0			0
$513$		0			0
$514$		0			0
$515$			5.65685i			0.249271i
$516$		0			0
$517$	−14.0000	−	29.6985i	−0.615719	−	1.30614i
$518$		0			0
$519$	−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	$0.857206\pi$
$522$		0			0
$523$			25.4558i			1.11311i	0.830812	+	0.556553i	$0.187876\pi$
$523$			25.4558i			1.11311i	−0.830812	+	0.556553i	$0.812124\pi$
$524$		0			0
$525$	−18.0000	+	12.7279i	−0.785584	+	0.555492i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	21.0000			0.913043
$530$		0			0
$531$	−32.0000	−	11.3137i	−1.38868	−	0.490973i
$532$		0			0
$533$			25.4558i			1.10262i
$534$		0			0
$535$			25.4558i			1.10055i
$536$		0			0
$537$	−8.00000	+	5.65685i	−0.345225	+	0.244111i
$538$		0			0
$539$	33.0000	−	15.5563i	1.42141	−	0.670059i
$540$		0			0
$541$		−	12.7279i		−	0.547216i	−0.961841	−	0.273608i	$-0.911783\pi$
$541$		−	12.7279i		−	0.547216i	0.961841	−	0.273608i	$-0.0882171\pi$
$542$		0			0
$543$	2.00000	+	2.82843i	0.0858282	+	0.121379i
$544$		0			0
$545$	18.0000			0.771035
$546$		0			0
$547$		−	33.9411i		−	1.45122i	−0.688107	−	0.725609i	$-0.741558\pi$
$547$		−	33.9411i		−	1.45122i	0.688107	−	0.725609i	$-0.258442\pi$
$548$		0			0
$549$	12.0000	+	4.24264i	0.512148	+	0.181071i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−18.0000			−0.765438
$554$		0			0
$555$	−4.00000	+	2.82843i	−0.169791	+	0.120060i
$556$		0			0
$557$	18.0000			0.762684			0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000			0.762684			0.381342	+	0.924434i	$0.375462\pi$
$558$		0			0
$559$	36.0000			1.52264
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−30.0000			−1.26435			−0.632175	−	0.774826i	$-0.717837\pi$
$563$	−30.0000			−1.26435			−0.632175	+	0.774826i	$0.717837\pi$
$564$		0			0
$565$	−16.0000			−0.673125
$566$		0			0
$567$	−24.0000	+	29.6985i	−1.00791	+	1.24722i
$568$		0			0
$569$	−24.0000			−1.00613			−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000			−1.00613			−0.503066	+	0.864248i	$0.667795\pi$
$570$		0			0
$571$			33.9411i			1.42039i	0.704004	+	0.710196i	$0.251394\pi$
$571$			33.9411i			1.42039i	−0.704004	+	0.710196i	$0.748606\pi$
$572$		0			0
$573$	14.0000	−	9.89949i	0.584858	−	0.413557i
$574$		0			0
$575$			4.24264i			0.176930i
$576$		0			0
$577$	20.0000			0.832611			0.416305	−	0.909225i	$-0.363325\pi$
$577$	20.0000			0.832611			0.416305	+	0.909225i	$0.363325\pi$
$578$		0			0
$579$	12.0000	−	8.48528i	0.498703	−	0.352636i
$580$		0			0
$581$		−	50.9117i		−	2.11217i
$582$		0			0
$583$	10.0000	+	21.2132i	0.414158	+	0.878561i
$584$		0			0
$585$	6.00000	−	16.9706i	0.248069	−	0.701646i
$586$		0			0
$587$			28.2843i			1.16742i	0.811963	+	0.583708i	$0.198399\pi$
$587$			28.2843i			1.16742i	−0.811963	+	0.583708i	$0.801601\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	−18.0000	−	25.4558i	−0.740421	−	1.04711i
$592$		0			0
$593$	−36.0000			−1.47834			−0.739171	−	0.673517i	$-0.764783\pi$
$593$	−36.0000			−1.47834			−0.739171	+	0.673517i	$0.764783\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−16.0000	−	22.6274i	−0.654836	−	0.926079i
$598$		0			0
$599$		−	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	$-0.243378\pi$
$602$		0			0
$603$	4.00000	−	11.3137i	0.162893	−	0.460730i
$604$		0			0
$605$	12.0000	+	9.89949i	0.487869	+	0.402472i
$606$		0			0
$607$			4.24264i			0.172203i	0.996286	+	0.0861017i	$0.0274410\pi$
$607$			4.24264i			0.172203i	−0.996286	+	0.0861017i	$0.972559\pi$
$608$		0			0
$609$	−36.0000	+	25.4558i	−1.45879	+	1.03152i
$610$		0			0
$611$	−42.0000			−1.69914
$612$		0			0
$613$		−	12.7279i		−	0.514076i	−0.966401	−	0.257038i	$-0.917253\pi$
$613$		−	12.7279i		−	0.514076i	0.966401	−	0.257038i	$-0.0827465\pi$
$614$		0			0
$615$	12.0000	−	8.48528i	0.483887	−	0.342160i
$616$		0			0
$617$		−	39.5980i		−	1.59415i	−0.603877	−	0.797077i	$-0.706378\pi$
$617$		−	39.5980i		−	1.59415i	0.603877	−	0.797077i	$-0.293622\pi$
$618$		0			0
$619$	44.0000			1.76851			0.884255	−	0.467005i	$-0.154667\pi$
$619$	44.0000			1.76851			0.884255	+	0.467005i	$0.154667\pi$
$620$		0			0
$621$	2.00000	+	7.07107i	0.0802572	+	0.283752i
$622$		0			0
$623$	−24.0000			−0.961540
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−20.0000			−0.796187			−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000			−0.796187			−0.398094	+	0.917345i	$0.630328\pi$
$632$		0			0
$633$	12.0000	−	8.48528i	0.476957	−	0.337260i
$634$		0			0
$635$	−18.0000			−0.714308
$636$		0			0
$637$		−	46.6690i		−	1.84909i
$638$		0			0
$639$	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	$-0.398498\pi$
$642$		0			0
$643$	−4.00000			−0.157745			−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000			−0.157745			−0.0788723	+	0.996885i	$0.525132\pi$
$644$		0			0
$645$	−12.0000	−	16.9706i	−0.472500	−	0.668215i
$646$		0			0
$647$		−	7.07107i		−	0.277992i	−0.990293	−	0.138996i	$-0.955612\pi$
$647$		−	7.07107i		−	0.277992i	0.990293	−	0.138996i	$-0.0443876\pi$
$648$		0			0
$649$	−16.0000	−	33.9411i	−0.628055	−	1.33231i
$650$		0			0
$651$	−24.0000	+	16.9706i	−0.940634	+	0.665129i
$652$		0			0
$653$			26.8701i			1.05151i	0.850637	+	0.525753i	$0.176216\pi$
$653$			26.8701i			1.05151i	−0.850637	+	0.525753i	$0.823784\pi$
$654$		0			0
$655$		−	16.9706i		−	0.663095i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	30.0000			1.16863			0.584317	−	0.811525i	$-0.301362\pi$
$659$	30.0000			1.16863			0.584317	+	0.811525i	$0.301362\pi$
$660$		0			0
$661$	22.0000			0.855701			0.427850	−	0.903850i	$-0.359271\pi$
$661$	22.0000			0.855701			0.427850	+	0.903850i	$0.359271\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$			8.48528i			0.328551i
$668$		0			0
$669$	8.00000	+	11.3137i	0.309298	+	0.437413i
$670$		0			0
$671$	6.00000	+	12.7279i	0.231627	+	0.491356i
$672$		0			0
$673$			42.4264i			1.63542i	0.575632	+	0.817709i	$0.304756\pi$
$673$			42.4264i			1.63542i	−0.575632	+	0.817709i	$0.695244\pi$
$674$		0			0
$675$	15.0000	−	4.24264i	0.577350	−	0.163299i
$676$		0			0
$677$	−30.0000			−1.15299			−0.576497	−	0.817099i	$-0.695581\pi$
$677$	−30.0000			−1.15299			−0.576497	+	0.817099i	$0.695581\pi$
$678$		0			0
$679$		−	33.9411i		−	1.30254i
$680$		0			0
$681$	6.00000	+	8.48528i	0.229920	+	0.325157i
$682$		0			0
$683$		−	5.65685i		−	0.216454i	−0.994126	−	0.108227i	$-0.965483\pi$
$683$		−	5.65685i		−	0.216454i	0.994126	−	0.108227i	$-0.0345173\pi$
$684$		0			0
$685$	−4.00000			−0.152832
$686$		0			0
$687$	14.0000	+	19.7990i	0.534133	+	0.755379i
$688$		0			0
$689$	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	$0.678779\pi$
$692$		0			0
$693$	−42.0000	+	4.24264i	−1.59545	+	0.161165i
$694$		0			0
$695$	24.0000			0.910372
$696$		0			0
$697$		0			0
$698$		0			0
$699$	−18.0000	−	25.4558i	−0.680823	−	0.962828i
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	14.0000	+	19.7990i	0.527271	+	0.745673i
$706$		0			0
$707$		−	25.4558i		−	0.957366i
$708$		0			0
$709$	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
$712$		0			0
$713$			5.65685i			0.211851i
$714$		0			0
$715$	18.0000	−	8.48528i	0.673162	−	0.317332i
$716$		0			0
$717$	−12.0000	−	16.9706i	−0.448148	−	0.633777i
$718$		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
$722$		0			0
$723$	−12.0000	+	8.48528i	−0.446285	+	0.315571i
$724$		0			0
$725$	18.0000			0.668503
$726$		0			0
$727$	−44.0000			−1.63187			−0.815935	−	0.578144i	$-0.803777\pi$
$727$	−44.0000			−1.63187			−0.815935	+	0.578144i	$0.803777\pi$
$728$		0			0
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$		0			0
$731$		0			0
$732$		0			0
$733$			4.24264i			0.156706i	0.996926	+	0.0783528i	$0.0249660\pi$
$733$			4.24264i			0.156706i	−0.996926	+	0.0783528i	$0.975034\pi$
$734$		0			0
$735$	−22.0000	+	15.5563i	−0.811482	+	0.573805i
$736$		0			0
$737$	12.0000	−	5.65685i	0.442026	−	0.208373i
$738$		0			0
$739$		−	25.4558i		−	0.936408i	−0.883620	−	0.468204i	$-0.844901\pi$
$739$		−	25.4558i		−	0.936408i	0.883620	−	0.468204i	$-0.155099\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−24.0000			−0.880475			−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000			−0.880475			−0.440237	+	0.897881i	$0.645106\pi$
$744$		0			0
$745$		−	8.48528i		−	0.310877i
$746$		0			0
$747$	−12.0000	+	33.9411i	−0.439057	+	1.24184i
$748$		0			0
$749$		−	76.3675i		−	2.79041i
$750$		0			0
$751$	40.0000			1.45962			0.729810	−	0.683650i	$-0.239608\pi$
$751$	40.0000			1.45962			0.729810	+	0.683650i	$0.239608\pi$
$752$		0			0
$753$	−8.00000	+	5.65685i	−0.291536	+	0.206147i
$754$		0			0
$755$	6.00000			0.218362
$756$		0			0
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$		0			0
$759$	−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	$0.356748\pi$
$762$		0			0
$763$	−54.0000			−1.95493
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−48.0000			−1.73318
$768$		0			0
$769$		−	42.4264i		−	1.52994i	−0.644069	−	0.764968i	$-0.722755\pi$
$769$		−	42.4264i		−	1.52994i	0.644069	−	0.764968i	$-0.277245\pi$
$770$		0			0
$771$	16.0000	−	11.3137i	0.576226	−	0.407453i
$772$		0			0
$773$			18.3848i			0.661254i	0.943761	+	0.330627i	$0.107260\pi$
$773$			18.3848i			0.661254i	−0.943761	+	0.330627i	$0.892740\pi$
$774$		0			0
$775$	12.0000			0.431053
$776$		0			0
$777$	12.0000	−	8.48528i	0.430498	−	0.304408i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	10.0000	+	21.2132i	0.357828	+	0.759068i
$782$		0			0
$783$	30.0000	−	8.48528i	1.07211	−	0.303239i
$784$		0			0
$785$			31.1127i			1.11046i
$786$		0			0
$787$		−	42.4264i		−	1.51234i	−0.654376	−	0.756169i	$-0.727069\pi$
$787$		−	42.4264i		−	1.51234i	0.654376	−	0.756169i	$-0.272931\pi$
$788$		0			0
$789$	12.0000	+	16.9706i	0.427211	+	0.604168i
$790$		0			0
$791$	48.0000			1.70668
$792$		0			0
$793$	18.0000			0.639199
$794$		0			0
$795$	−10.0000	−	14.1421i	−0.354663	−	0.501570i
$796$		0			0
$797$			1.41421i			0.0500940i	0.999686	+	0.0250470i	$0.00797354\pi$
$797$			1.41421i			0.0500940i	−0.999686	+	0.0250470i	$0.992026\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	16.0000	+	5.65685i	0.565332	+	0.199875i
$802$		0			0
$803$		0			0
$804$		0			0
$805$			8.48528i			0.299067i
$806$		0			0
$807$	−10.0000	+	7.07107i	−0.352017	+	0.248913i
$808$		0			0
$809$	−54.0000			−1.89854			−0.949269	−	0.314464i	$-0.898175\pi$
$809$	−54.0000			−1.89854			−0.949269	+	0.314464i	$0.898175\pi$
$810$		0			0
$811$			25.4558i			0.893876i	0.894565	+	0.446938i	$0.147485\pi$
$811$			25.4558i			0.893876i	−0.894565	+	0.446938i	$0.852515\pi$
$812$		0			0
$813$	−18.0000	+	12.7279i	−0.631288	+	0.446388i
$814$		0			0
$815$			2.82843i			0.0990755i
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−18.0000	+	50.9117i	−0.628971	+	1.77900i
$820$		0			0
$821$	−30.0000			−1.04701			−0.523504	−	0.852023i	$-0.675375\pi$
$821$	−30.0000			−1.04701			−0.523504	+	0.852023i	$0.675375\pi$
$822$		0			0
$823$	40.0000			1.39431			0.697156	−	0.716919i	$-0.254448\pi$
$823$	40.0000			1.39431			0.697156	+	0.716919i	$0.254448\pi$
$824$		0			0
$825$	15.0000	+	8.48528i	0.522233	+	0.295420i
$826$		0			0
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$		0			0
$829$	−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
$832$		0			0
$833$		0			0
$834$		0			0
$835$			16.9706i			0.587291i
$836$		0			0
$837$	20.0000	−	5.65685i	0.691301	−	0.195529i
$838$		0			0
$839$		−	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
$842$		0			0
$843$	−12.0000	−	16.9706i	−0.413302	−	0.584497i
$844$		0			0
$845$		−	7.07107i		−	0.243252i
$846$		0			0
$847$	−36.0000	−	29.6985i	−1.23697	−	1.02045i
$848$		0			0
$849$	12.0000	−	8.48528i	0.411839	−	0.291214i
$850$		0			0
$851$		−	2.82843i		−	0.0969572i
$852$		0			0
$853$			21.2132i			0.726326i	0.931726	+	0.363163i	$0.118303\pi$
$853$			21.2132i			0.726326i	−0.931726	+	0.363163i	$0.881697\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−6.00000			−0.204956			−0.102478	−	0.994735i	$-0.532677\pi$
$857$	−6.00000			−0.204956			−0.102478	+	0.994735i	$0.532677\pi$
$858$		0			0
$859$	−22.0000			−0.750630			−0.375315	−	0.926897i	$-0.622466\pi$
$859$	−22.0000			−0.750630			−0.375315	+	0.926897i	$0.622466\pi$
$860$		0			0
$861$	−36.0000	+	25.4558i	−1.22688	+	0.867533i
$862$		0			0
$863$		−	7.07107i		−	0.240702i	−0.992731	−	0.120351i	$-0.961598\pi$
$863$		−	7.07107i		−	0.240702i	0.992731	−	0.120351i	$-0.0384020\pi$
$864$		0			0
$865$			8.48528i			0.288508i
$866$		0			0
$867$	17.0000	+	24.0416i	0.577350	+	0.816497i
$868$		0			0
$869$	6.00000	+	12.7279i	0.203536	+	0.431765i
$870$		0			0
$871$		−	16.9706i		−	0.575026i
$872$		0			0
$873$	−8.00000	+	22.6274i	−0.270759	+	0.765822i
$874$		0			0
$875$	48.0000			1.62270
$876$		0			0
$877$			29.6985i			1.00285i	0.865202	+	0.501423i	$0.167190\pi$
$877$			29.6985i			1.00285i	−0.865202	+	0.501423i	$0.832810\pi$
$878$		0			0
$879$	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	$-0.0303785\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$		0			0
$885$	16.0000	+	22.6274i	0.537834	+	0.760612i
$886$		0			0
$887$	48.0000			1.61168			0.805841	−	0.592132i	$-0.201714\pi$
$887$	48.0000			1.61168			0.805841	+	0.592132i	$0.201714\pi$
$888$		0			0
$889$	54.0000			1.81110
$890$		0			0
$891$	29.0000	+	7.07107i	0.971537	+	0.236890i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	8.00000			0.267411
$896$		0			0
$897$	6.00000	+	8.48528i	0.200334	+	0.283315i
$898$		0			0
$899$	24.0000			0.800445
$900$		0			0
$901$		0			0
$902$		0			0
$903$	36.0000	+	50.9117i	1.19800	+	1.69423i
$904$		0			0
$905$		−	2.82843i		−	0.0940201i
$906$		0			0
$907$	44.0000			1.46100			0.730498	−	0.682915i	$-0.239288\pi$
$907$	44.0000			1.46100			0.730498	+	0.682915i	$0.239288\pi$
$908$		0			0
$909$	−6.00000	+	16.9706i	−0.199007	+	0.562878i
$910$		0			0
$911$			9.89949i			0.327985i	0.986462	+	0.163992i	$0.0524373\pi$
$911$			9.89949i			0.327985i	−0.986462	+	0.163992i	$0.947563\pi$
$912$		0			0
$913$	−36.0000	+	16.9706i	−1.19143	+	0.561644i
$914$		0			0
$915$	−6.00000	−	8.48528i	−0.198354	−	0.280515i
$916$		0			0
$917$			50.9117i			1.68125i
$918$		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
$922$		0			0
$923$	30.0000			0.987462
$924$		0			0
$925$	−6.00000			−0.197279
$926$		0			0
$927$	−4.00000	+	11.3137i	−0.131377	+	0.371591i
$928$		0			0
$929$			2.82843i			0.0927977i	0.998923	+	0.0463988i	$0.0147745\pi$
$929$			2.82843i			0.0927977i	−0.998923	+	0.0463988i	$0.985225\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	38.0000	−	26.8701i	1.24406	−	0.879686i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$	10.0000	+	14.1421i	0.326338	+	0.461511i
$940$		0			0
$941$	−42.0000			−1.36916			−0.684580	−	0.728937i	$-0.740015\pi$
$941$	−42.0000			−1.36916			−0.684580	+	0.728937i	$0.740015\pi$
$942$		0			0
$943$			8.48528i			0.276319i
$944$		0			0
$945$	30.0000	−	8.48528i	0.975900	−	0.276026i
$946$		0			0
$947$		−	48.0833i		−	1.56250i	−0.624221	−	0.781248i	$-0.714583\pi$
$947$		−	48.0833i		−	1.56250i	0.624221	−	0.781248i	$-0.285417\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	14.0000	−	9.89949i	0.453981	−	0.321013i
$952$		0			0
$953$	−54.0000			−1.74923			−0.874616	−	0.484817i	$-0.838886\pi$
$953$	−54.0000			−1.74923			−0.874616	+	0.484817i	$0.838886\pi$
$954$		0			0
$955$	−14.0000			−0.453029
$956$		0			0
$957$	30.0000	+	16.9706i	0.969762	+	0.548580i
$958$		0			0
$959$	12.0000			0.387500
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	−18.0000	+	50.9117i	−0.580042	+	1.64061i
$964$		0			0
$965$	−12.0000			−0.386294
$966$		0			0
$967$			4.24264i			0.136434i	0.997671	+	0.0682171i	$0.0217310\pi$
$967$			4.24264i			0.136434i	−0.997671	+	0.0682171i	$0.978269\pi$
$968$		0			0
$969$		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	$0.741309\pi$
$972$		0			0
$973$	−72.0000			−2.30821
$974$		0			0
$975$	18.0000	−	12.7279i	0.576461	−	0.407620i
$976$		0			0
$977$		−	14.1421i		−	0.452447i	−0.974075	−	0.226224i	$-0.927362\pi$
$977$		−	14.1421i		−	0.452447i	0.974075	−	0.226224i	$-0.0726380\pi$
$978$		0			0
$979$	8.00000	+	16.9706i	0.255681	+	0.542382i
$980$		0			0
$981$	36.0000	+	12.7279i	1.14939	+	0.406371i
$982$		0			0
$983$			9.89949i			0.315745i	0.987460	+	0.157872i	$0.0504635\pi$
$983$			9.89949i			0.315745i	−0.987460	+	0.157872i	$0.949537\pi$
$984$		0			0
$985$			25.4558i			0.811091i
$986$		0			0
$987$	−42.0000	−	59.3970i	−1.33687	−	1.89063i
$988$		0			0
$989$	12.0000			0.381578
$990$		0			0
$991$	−20.0000			−0.635321			−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000			−0.635321			−0.317660	+	0.948205i	$0.602897\pi$
$992$		0			0
$993$	10.0000	+	14.1421i	0.317340	+	0.448787i
$994$		0			0
$995$			22.6274i			0.717337i
$996$		0			0
$997$		−	29.6985i		−	0.940560i	−0.882517	−	0.470280i	$-0.844153\pi$
$997$		−	29.6985i		−	0.940560i	0.882517	−	0.470280i	$-0.155847\pi$
$998$		0			0
$999$	−10.0000	+	2.82843i	−0.316386	+	0.0894875i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2112.2.b.b.65.1		2
3.2	odd	2		2112.2.b.d.65.2		2
4.3	odd	2		2112.2.b.i.65.2		2
8.3	odd	2		66.2.b.b.65.1	yes	2
8.5	even	2		528.2.b.c.65.2		2
11.10	odd	2		2112.2.b.d.65.1		2
12.11	even	2		2112.2.b.g.65.1		2
24.5	odd	2		528.2.b.b.65.1		2
24.11	even	2		66.2.b.a.65.2	yes	2
33.32	even	2	inner	2112.2.b.b.65.2		2
40.3	even	4		1650.2.f.a.1649.2		4
40.19	odd	2		1650.2.d.a.1451.2		2
40.27	even	4		1650.2.f.a.1649.3		4
44.43	even	2		2112.2.b.g.65.2		2
72.11	even	6		1782.2.i.f.1187.1		4
72.43	odd	6		1782.2.i.c.1187.2		4
72.59	even	6		1782.2.i.f.593.2		4
72.67	odd	6		1782.2.i.c.593.1		4
88.3	odd	10		726.2.h.e.233.2		8
88.19	even	10		726.2.h.i.233.2		8
88.21	odd	2		528.2.b.b.65.2		2
88.27	odd	10		726.2.h.e.239.2		8
88.35	even	10		726.2.h.i.161.1		8
88.43	even	2		66.2.b.a.65.1	✓	2
88.51	even	10		726.2.h.i.215.1		8
88.59	odd	10		726.2.h.e.215.1		8
88.75	odd	10		726.2.h.e.161.1		8
88.83	even	10		726.2.h.i.239.2		8
120.59	even	2		1650.2.d.b.1451.1		2
120.83	odd	4		1650.2.f.b.1649.3		4
120.107	odd	4		1650.2.f.b.1649.2		4
132.131	odd	2		2112.2.b.i.65.1		2
264.35	odd	10		726.2.h.e.161.2		8
264.59	even	10		726.2.h.i.215.2		8
264.83	odd	10		726.2.h.e.239.1		8
264.107	odd	10		726.2.h.e.233.1		8
264.131	odd	2		66.2.b.b.65.2	yes	2
264.179	even	10		726.2.h.i.233.1		8
264.197	even	2		528.2.b.c.65.1		2
264.203	even	10		726.2.h.i.239.1		8
264.227	odd	10		726.2.h.e.215.2		8
264.251	even	10		726.2.h.i.161.2		8
440.43	odd	4		1650.2.f.b.1649.4		4
440.219	even	2		1650.2.d.b.1451.2		2
440.307	odd	4		1650.2.f.b.1649.1		4
792.43	even	6		1782.2.i.f.1187.2		4
792.131	odd	6		1782.2.i.c.593.2		4
792.571	even	6		1782.2.i.f.593.1		4
792.659	odd	6		1782.2.i.c.1187.1		4
1320.659	odd	2		1650.2.d.a.1451.1		2
1320.923	even	4		1650.2.f.a.1649.1		4
1320.1187	even	4		1650.2.f.a.1649.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.b.a.65.1	✓	2	88.43	even	2
66.2.b.a.65.2	yes	2	24.11	even	2
66.2.b.b.65.1	yes	2	8.3	odd	2
66.2.b.b.65.2	yes	2	264.131	odd	2
528.2.b.b.65.1		2	24.5	odd	2
528.2.b.b.65.2		2	88.21	odd	2
528.2.b.c.65.1		2	264.197	even	2
528.2.b.c.65.2		2	8.5	even	2
726.2.h.e.161.1		8	88.75	odd	10
726.2.h.e.161.2		8	264.35	odd	10
726.2.h.e.215.1		8	88.59	odd	10
726.2.h.e.215.2		8	264.227	odd	10
726.2.h.e.233.1		8	264.107	odd	10
726.2.h.e.233.2		8	88.3	odd	10
726.2.h.e.239.1		8	264.83	odd	10
726.2.h.e.239.2		8	88.27	odd	10
726.2.h.i.161.1		8	88.35	even	10
726.2.h.i.161.2		8	264.251	even	10
726.2.h.i.215.1		8	88.51	even	10
726.2.h.i.215.2		8	264.59	even	10
726.2.h.i.233.1		8	264.179	even	10
726.2.h.i.233.2		8	88.19	even	10
726.2.h.i.239.1		8	264.203	even	10
726.2.h.i.239.2		8	88.83	even	10
1650.2.d.a.1451.1		2	1320.659	odd	2
1650.2.d.a.1451.2		2	40.19	odd	2
1650.2.d.b.1451.1		2	120.59	even	2
1650.2.d.b.1451.2		2	440.219	even	2
1650.2.f.a.1649.1		4	1320.923	even	4
1650.2.f.a.1649.2		4	40.3	even	4
1650.2.f.a.1649.3		4	40.27	even	4
1650.2.f.a.1649.4		4	1320.1187	even	4
1650.2.f.b.1649.1		4	440.307	odd	4
1650.2.f.b.1649.2		4	120.107	odd	4
1650.2.f.b.1649.3		4	120.83	odd	4
1650.2.f.b.1649.4		4	440.43	odd	4
1782.2.i.c.593.1		4	72.67	odd	6
1782.2.i.c.593.2		4	792.131	odd	6
1782.2.i.c.1187.1		4	792.659	odd	6
1782.2.i.c.1187.2		4	72.43	odd	6
1782.2.i.f.593.1		4	792.571	even	6
1782.2.i.f.593.2		4	72.59	even	6
1782.2.i.f.1187.1		4	72.11	even	6
1782.2.i.f.1187.2		4	792.43	even	6
2112.2.b.b.65.1		2	1.1	even	1	trivial
2112.2.b.b.65.2		2	33.32	even	2	inner
2112.2.b.d.65.1		2	11.10	odd	2
2112.2.b.d.65.2		2	3.2	odd	2
2112.2.b.g.65.1		2	12.11	even	2
2112.2.b.g.65.2		2	44.43	even	2
2112.2.b.i.65.1		2	132.131	odd	2
2112.2.b.i.65.2		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2112 = 2^{6} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2112.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.41421i) q^{3} +1.41421i q^{5} -4.24264i q^{7} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.41421i) q^{3} +1.41421i q^{5} -4.24264i q^{7} +(-1.00000 + 2.82843i) q^{9} +(-3.00000 + 1.41421i) q^{11} +4.24264i q^{13} +(2.00000 - 1.41421i) q^{15} +(-6.00000 + 4.24264i) q^{21} +1.41421i q^{23} +3.00000 q^{25} +(5.00000 - 1.41421i) q^{27} +6.00000 q^{29} +4.00000 q^{31} +(5.00000 + 2.82843i) q^{33} +6.00000 q^{35} -2.00000 q^{37} +(6.00000 - 4.24264i) q^{39} +6.00000 q^{41} -8.48528i q^{43} +(-4.00000 - 1.41421i) q^{45} +9.89949i q^{47} -11.0000 q^{49} -7.07107i q^{53} +(-2.00000 - 4.24264i) q^{55} +11.3137i q^{59} -4.24264i q^{61} +(12.0000 + 4.24264i) q^{63} -6.00000 q^{65} -4.00000 q^{67} +(2.00000 - 1.41421i) q^{69} -7.07107i q^{71} +(-3.00000 - 4.24264i) q^{75} +(6.00000 + 12.7279i) q^{77} -4.24264i q^{79} +(-7.00000 - 5.65685i) q^{81} +12.0000 q^{83} +(-6.00000 - 8.48528i) q^{87} -5.65685i q^{89} +18.0000 q^{91} +(-4.00000 - 5.65685i) q^{93} +8.00000 q^{97} +(-1.00000 - 9.89949i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 - 2 * q^9	\( 2 q - 2 q^{3} - 2 q^{9} - 6 q^{11} + 4 q^{15} - 12 q^{21} + 6 q^{25} + 10 q^{27} + 12 q^{29} + 8 q^{31} + 10 q^{33} + 12 q^{35} - 4 q^{37} + 12 q^{39} + 12 q^{41} - 8 q^{45} - 22 q^{49} - 4 q^{55} + 24 q^{63} - 12 q^{65} - 8 q^{67} + 4 q^{69} - 6 q^{75} + 12 q^{77} - 14 q^{81} + 24 q^{83} - 12 q^{87} + 36 q^{91} - 8 q^{93} + 16 q^{97} - 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 - 2 * q^9 - 6 * q^11 + 4 * q^15 - 12 * q^21 + 6 * q^25 + 10 * q^27 + 12 * q^29 + 8 * q^31 + 10 * q^33 + 12 * q^35 - 4 * q^37 + 12 * q^39 + 12 * q^41 - 8 * q^45 - 22 * q^49 - 4 * q^55 + 24 * q^63 - 12 * q^65 - 8 * q^67 + 4 * q^69 - 6 * q^75 + 12 * q^77 - 14 * q^81 + 24 * q^83 - 12 * q^87 + 36 * q^91 - 8 * q^93 + 16 * q^97 - 2 * q^99

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