LMFDB - Embedded newform 680.2.z.a.89.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(89,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.89"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.z (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			89.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	680.89
Dual form			680.2.z.a.489.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.00000i) q^{3} +(1.00000 + 2.00000i) q^{5} +(-1.00000 + 1.00000i) q^{7} -1.00000i q^{9} +(-1.00000 - 1.00000i) q^{11} +4.00000i q^{13} +(1.00000 - 3.00000i) q^{15} +(1.00000 + 4.00000i) q^{17} +2.00000i q^{19} +2.00000 q^{21} +(-1.00000 + 1.00000i) q^{23} +(-3.00000 + 4.00000i) q^{25} +(-4.00000 + 4.00000i) q^{27} +(-1.00000 + 1.00000i) q^{29} +(3.00000 - 3.00000i) q^{31} +2.00000i q^{33} +(-3.00000 - 1.00000i) q^{35} +(3.00000 + 3.00000i) q^{37} +(4.00000 - 4.00000i) q^{39} +(1.00000 + 1.00000i) q^{41} -4.00000 q^{43} +(2.00000 - 1.00000i) q^{45} +10.0000i q^{47} +5.00000i q^{49} +(3.00000 - 5.00000i) q^{51} +6.00000 q^{53} +(1.00000 - 3.00000i) q^{55} +(2.00000 - 2.00000i) q^{57} +10.0000i q^{59} +(7.00000 + 7.00000i) q^{61} +(1.00000 + 1.00000i) q^{63} +(-8.00000 + 4.00000i) q^{65} +2.00000i q^{67} +2.00000 q^{69} +(11.0000 - 11.0000i) q^{71} +(-7.00000 - 7.00000i) q^{73} +(7.00000 - 1.00000i) q^{75} +2.00000 q^{77} +(-7.00000 - 7.00000i) q^{79} +5.00000 q^{81} +12.0000 q^{83} +(-7.00000 + 6.00000i) q^{85} +2.00000 q^{87} -10.0000 q^{89} +(-4.00000 - 4.00000i) q^{91} -6.00000 q^{93} +(-4.00000 + 2.00000i) q^{95} +(-3.00000 - 3.00000i) q^{97} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + 2 q^{5} - 2 q^{7} - 2 q^{11} + 2 q^{15} + 2 q^{17} + 4 q^{21} - 2 q^{23} - 6 q^{25} - 8 q^{27} - 2 q^{29} + 6 q^{31} - 6 q^{35} + 6 q^{37} + 8 q^{39} + 2 q^{41} - 8 q^{43} + 4 q^{45} + 6 q^{51}+ \cdots - 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 + 2 * q^5 - 2 * q^7 - 2 * q^11 + 2 * q^15 + 2 * q^17 + 4 * q^21 - 2 * q^23 - 6 * q^25 - 8 * q^27 - 2 * q^29 + 6 * q^31 - 6 * q^35 + 6 * q^37 + 8 * q^39 + 2 * q^41 - 8 * q^43 + 4 * q^45 + 6 * q^51 + 12 * q^53 + 2 * q^55 + 4 * q^57 + 14 * q^61 + 2 * q^63 - 16 * q^65 + 4 * q^69 + 22 * q^71 - 14 * q^73 + 14 * q^75 + 4 * q^77 - 14 * q^79 + 10 * q^81 + 24 * q^83 - 14 * q^85 + 4 * q^87 - 20 * q^89 - 8 * q^91 - 12 * q^93 - 8 * q^95 - 6 * q^97 - 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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	−	1.00000i	−0.577350	−	0.577350i	0.356822	−	0.934172i	$-0.383860\pi$
$3$	−1.00000	−	1.00000i	−0.577350	−	0.577350i	−0.934172	+	0.356822i	$0.883860\pi$
$4$		0			0
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$6$		0			0
$7$	−1.00000	+	1.00000i	−0.377964	+	0.377964i	−0.870367	−	0.492403i	$-0.836119\pi$
$7$	−1.00000	+	1.00000i	−0.377964	+	0.377964i	0.492403	+	0.870367i	$0.336119\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−1.00000	−	1.00000i	−0.301511	−	0.301511i	0.540094	−	0.841605i	$-0.318389\pi$
$11$	−1.00000	−	1.00000i	−0.301511	−	0.301511i	−0.841605	+	0.540094i	$0.818389\pi$
$12$		0			0
$13$			4.00000i			1.10940i	0.832050	+	0.554700i	$0.187167\pi$
$13$			4.00000i			1.10940i	−0.832050	+	0.554700i	$0.812833\pi$
$14$		0			0
$15$	1.00000	−	3.00000i	0.258199	−	0.774597i
$16$		0			0
$17$	1.00000	+	4.00000i	0.242536	+	0.970143i
$17$	1.00000	+	4.00000i	0.242536	+	0.970143i
$18$		0			0
$19$			2.00000i			0.458831i	0.973329	+	0.229416i	$0.0736815\pi$
$19$			2.00000i			0.458831i	−0.973329	+	0.229416i	$0.926318\pi$
$20$		0			0
$21$	2.00000			0.436436
$22$		0			0
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	−0.803636	−	0.595121i	$-0.797104\pi$
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	0.595121	+	0.803636i	$0.297104\pi$
$24$		0			0
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$		0			0
$27$	−4.00000	+	4.00000i	−0.769800	+	0.769800i
$28$		0			0
$29$	−1.00000	+	1.00000i	−0.185695	+	0.185695i	−0.793832	−	0.608137i	$-0.791917\pi$
$29$	−1.00000	+	1.00000i	−0.185695	+	0.185695i	0.608137	+	0.793832i	$0.291917\pi$
$30$		0			0
$31$	3.00000	−	3.00000i	0.538816	−	0.538816i	−0.384365	−	0.923181i	$-0.625580\pi$
$31$	3.00000	−	3.00000i	0.538816	−	0.538816i	0.923181	+	0.384365i	$0.125580\pi$
$32$		0			0
$33$			2.00000i			0.348155i
$34$		0			0
$35$	−3.00000	−	1.00000i	−0.507093	−	0.169031i
$36$		0			0
$37$	3.00000	+	3.00000i	0.493197	+	0.493197i	0.909312	−	0.416115i	$-0.136609\pi$
$37$	3.00000	+	3.00000i	0.493197	+	0.493197i	−0.416115	+	0.909312i	$0.636609\pi$
$38$		0			0
$39$	4.00000	−	4.00000i	0.640513	−	0.640513i
$40$		0			0
$41$	1.00000	+	1.00000i	0.156174	+	0.156174i	0.780869	−	0.624695i	$-0.214777\pi$
$41$	1.00000	+	1.00000i	0.156174	+	0.156174i	−0.624695	+	0.780869i	$0.714777\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$	2.00000	−	1.00000i	0.298142	−	0.149071i
$46$		0			0
$47$			10.0000i			1.45865i	0.684167	+	0.729325i	$0.260166\pi$
$47$			10.0000i			1.45865i	−0.684167	+	0.729325i	$0.739834\pi$
$48$		0			0
$49$			5.00000i			0.714286i
$50$		0			0
$51$	3.00000	−	5.00000i	0.420084	−	0.700140i
$52$		0			0
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$		0			0
$55$	1.00000	−	3.00000i	0.134840	−	0.404520i
$56$		0			0
$57$	2.00000	−	2.00000i	0.264906	−	0.264906i
$58$		0			0
$59$			10.0000i			1.30189i	0.759125	+	0.650945i	$0.225627\pi$
$59$			10.0000i			1.30189i	−0.759125	+	0.650945i	$0.774373\pi$
$60$		0			0
$61$	7.00000	+	7.00000i	0.896258	+	0.896258i	0.995103	−	0.0988447i	$-0.0315147\pi$
$61$	7.00000	+	7.00000i	0.896258	+	0.896258i	−0.0988447	+	0.995103i	$0.531515\pi$
$62$		0			0
$63$	1.00000	+	1.00000i	0.125988	+	0.125988i
$64$		0			0
$65$	−8.00000	+	4.00000i	−0.992278	+	0.496139i
$66$		0			0
$67$			2.00000i			0.244339i	0.992509	+	0.122169i	$0.0389851\pi$
$67$			2.00000i			0.244339i	−0.992509	+	0.122169i	$0.961015\pi$
$68$		0			0
$69$	2.00000			0.240772
$70$		0			0
$71$	11.0000	−	11.0000i	1.30546	−	1.30546i	0.380804	−	0.924656i	$-0.375647\pi$
$71$	11.0000	−	11.0000i	1.30546	−	1.30546i	0.924656	−	0.380804i	$-0.124353\pi$
$72$		0			0
$73$	−7.00000	−	7.00000i	−0.819288	−	0.819288i	0.166717	−	0.986005i	$-0.446683\pi$
$73$	−7.00000	−	7.00000i	−0.819288	−	0.819288i	−0.986005	+	0.166717i	$0.946683\pi$
$74$		0			0
$75$	7.00000	−	1.00000i	0.808290	−	0.115470i
$76$		0			0
$77$	2.00000			0.227921
$78$		0			0
$79$	−7.00000	−	7.00000i	−0.787562	−	0.787562i	0.193532	−	0.981094i	$-0.438006\pi$
$79$	−7.00000	−	7.00000i	−0.787562	−	0.787562i	−0.981094	+	0.193532i	$0.938006\pi$
$80$		0			0
$81$	5.00000			0.555556
$82$		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
$85$	−7.00000	+	6.00000i	−0.759257	+	0.650791i
$86$		0			0
$87$	2.00000			0.214423
$88$		0			0
$89$	−10.0000			−1.06000			−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000			−1.06000			−0.529999	+	0.847998i	$0.677808\pi$
$90$		0			0
$91$	−4.00000	−	4.00000i	−0.419314	−	0.419314i
$92$		0			0
$93$	−6.00000			−0.622171
$94$		0			0
$95$	−4.00000	+	2.00000i	−0.410391	+	0.205196i
$96$		0			0
$97$	−3.00000	−	3.00000i	−0.304604	−	0.304604i	0.538208	−	0.842812i	$-0.319101\pi$
$97$	−3.00000	−	3.00000i	−0.304604	−	0.304604i	−0.842812	+	0.538208i	$0.819101\pi$
$98$		0			0
$99$	−1.00000	+	1.00000i	−0.100504	+	0.100504i
$100$		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
$103$		−	6.00000i		−	0.591198i	−0.955312	−	0.295599i	$-0.904481\pi$
$103$		−	6.00000i		−	0.591198i	0.955312	−	0.295599i	$-0.0955191\pi$
$104$		0			0
$105$	2.00000	+	4.00000i	0.195180	+	0.390360i
$106$		0			0
$107$	−5.00000	−	5.00000i	−0.483368	−	0.483368i	0.422837	−	0.906206i	$-0.361034\pi$
$107$	−5.00000	−	5.00000i	−0.483368	−	0.483368i	−0.906206	+	0.422837i	$0.861034\pi$
$108$		0			0
$109$	−5.00000	−	5.00000i	−0.478913	−	0.478913i	0.425871	−	0.904784i	$-0.359968\pi$
$109$	−5.00000	−	5.00000i	−0.478913	−	0.478913i	−0.904784	+	0.425871i	$0.859968\pi$
$110$		0			0
$111$		−	6.00000i		−	0.569495i
$112$		0			0
$113$	5.00000	−	5.00000i	0.470360	−	0.470360i	−0.431671	−	0.902031i	$-0.642076\pi$
$113$	5.00000	−	5.00000i	0.470360	−	0.470360i	0.902031	+	0.431671i	$0.142076\pi$
$114$		0			0
$115$	−3.00000	−	1.00000i	−0.279751	−	0.0932505i
$116$		0			0
$117$	4.00000			0.369800
$118$		0			0
$119$	−5.00000	−	3.00000i	−0.458349	−	0.275010i
$120$		0			0
$121$		−	9.00000i		−	0.818182i
$122$		0			0
$123$		−	2.00000i		−	0.180334i
$124$		0			0
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$		0			0
$129$	4.00000	+	4.00000i	0.352180	+	0.352180i
$130$		0			0
$131$	1.00000	−	1.00000i	0.0873704	−	0.0873704i	−0.662071	−	0.749441i	$-0.730322\pi$
$131$	1.00000	−	1.00000i	0.0873704	−	0.0873704i	0.749441	+	0.662071i	$0.230322\pi$
$132$		0			0
$133$	−2.00000	−	2.00000i	−0.173422	−	0.173422i
$134$		0			0
$135$	−12.0000	−	4.00000i	−1.03280	−	0.344265i
$136$		0			0
$137$		−	12.0000i		−	1.02523i	−0.858619	−	0.512615i	$-0.828677\pi$
$137$		−	12.0000i		−	1.02523i	0.858619	−	0.512615i	$-0.171323\pi$
$138$		0			0
$139$	−3.00000	+	3.00000i	−0.254457	+	0.254457i	−0.822795	−	0.568338i	$-0.807586\pi$
$139$	−3.00000	+	3.00000i	−0.254457	+	0.254457i	0.568338	+	0.822795i	$0.307586\pi$
$140$		0			0
$141$	10.0000	−	10.0000i	0.842152	−	0.842152i
$142$		0			0
$143$	4.00000	−	4.00000i	0.334497	−	0.334497i
$144$		0			0
$145$	−3.00000	−	1.00000i	−0.249136	−	0.0830455i
$146$		0			0
$147$	5.00000	−	5.00000i	0.412393	−	0.412393i
$148$		0			0
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$		0			0
$151$			2.00000i			0.162758i	0.996683	+	0.0813788i	$0.0259324\pi$
$151$			2.00000i			0.162758i	−0.996683	+	0.0813788i	$0.974068\pi$
$152$		0			0
$153$	4.00000	−	1.00000i	0.323381	−	0.0808452i
$154$		0			0
$155$	9.00000	+	3.00000i	0.722897	+	0.240966i
$156$		0			0
$157$		−	8.00000i		−	0.638470i	−0.947676	−	0.319235i	$-0.896574\pi$
$157$		−	8.00000i		−	0.638470i	0.947676	−	0.319235i	$-0.103426\pi$
$158$		0			0
$159$	−6.00000	−	6.00000i	−0.475831	−	0.475831i
$160$		0			0
$161$		−	2.00000i		−	0.157622i
$162$		0			0
$163$	−7.00000	+	7.00000i	−0.548282	+	0.548282i	−0.925944	−	0.377661i	$-0.876728\pi$
$163$	−7.00000	+	7.00000i	−0.548282	+	0.548282i	0.377661	+	0.925944i	$0.376728\pi$
$164$		0			0
$165$	−4.00000	+	2.00000i	−0.311400	+	0.155700i
$166$		0			0
$167$	−7.00000	−	7.00000i	−0.541676	−	0.541676i	0.382344	−	0.924020i	$-0.375117\pi$
$167$	−7.00000	−	7.00000i	−0.541676	−	0.541676i	−0.924020	+	0.382344i	$0.875117\pi$
$168$		0			0
$169$	−3.00000			−0.230769
$170$		0			0
$171$	2.00000			0.152944
$172$		0			0
$173$	11.0000	+	11.0000i	0.836315	+	0.836315i	0.988372	−	0.152057i	$-0.0485898\pi$
$173$	11.0000	+	11.0000i	0.836315	+	0.836315i	−0.152057	+	0.988372i	$0.548590\pi$
$174$		0			0
$175$	−1.00000	−	7.00000i	−0.0755929	−	0.529150i
$176$		0			0
$177$	10.0000	−	10.0000i	0.751646	−	0.751646i
$178$		0			0
$179$			18.0000i			1.34538i	0.739923	+	0.672692i	$0.234862\pi$
$179$			18.0000i			1.34538i	−0.739923	+	0.672692i	$0.765138\pi$
$180$		0			0
$181$	3.00000	+	3.00000i	0.222988	+	0.222988i	0.809756	−	0.586767i	$-0.199600\pi$
$181$	3.00000	+	3.00000i	0.222988	+	0.222988i	−0.586767	+	0.809756i	$0.699600\pi$
$182$		0			0
$183$		−	14.0000i		−	1.03491i
$184$		0			0
$185$	−3.00000	+	9.00000i	−0.220564	+	0.661693i
$186$		0			0
$187$	3.00000	−	5.00000i	0.219382	−	0.365636i
$188$		0			0
$189$		−	8.00000i		−	0.581914i
$190$		0			0
$191$	16.0000			1.15772			0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000			1.15772			0.578860	+	0.815427i	$0.303498\pi$
$192$		0			0
$193$	−3.00000	+	3.00000i	−0.215945	+	0.215945i	−0.806787	−	0.590842i	$-0.798796\pi$
$193$	−3.00000	+	3.00000i	−0.215945	+	0.215945i	0.590842	+	0.806787i	$0.298796\pi$
$194$		0			0
$195$	12.0000	+	4.00000i	0.859338	+	0.286446i
$196$		0			0
$197$	19.0000	−	19.0000i	1.35369	−	1.35369i	0.472205	−	0.881489i	$-0.343458\pi$
$197$	19.0000	−	19.0000i	1.35369	−	1.35369i	0.881489	−	0.472205i	$-0.156542\pi$
$198$		0			0
$199$	−9.00000	+	9.00000i	−0.637993	+	0.637993i	−0.950060	−	0.312067i	$-0.898979\pi$
$199$	−9.00000	+	9.00000i	−0.637993	+	0.637993i	0.312067	+	0.950060i	$0.398979\pi$
$200$		0			0
$201$	2.00000	−	2.00000i	0.141069	−	0.141069i
$202$		0			0
$203$		−	2.00000i		−	0.140372i
$204$		0			0
$205$	−1.00000	+	3.00000i	−0.0698430	+	0.209529i
$206$		0			0
$207$	1.00000	+	1.00000i	0.0695048	+	0.0695048i
$208$		0			0
$209$	2.00000	−	2.00000i	0.138343	−	0.138343i
$210$		0			0
$211$	11.0000	+	11.0000i	0.757271	+	0.757271i	0.975825	−	0.218554i	$-0.0701339\pi$
$211$	11.0000	+	11.0000i	0.757271	+	0.757271i	−0.218554	+	0.975825i	$0.570134\pi$
$212$		0			0
$213$	−22.0000			−1.50742
$214$		0			0
$215$	−4.00000	−	8.00000i	−0.272798	−	0.545595i
$216$		0			0
$217$			6.00000i			0.407307i
$218$		0			0
$219$			14.0000i			0.946032i
$220$		0			0
$221$	−16.0000	+	4.00000i	−1.07628	+	0.269069i
$222$		0			0
$223$	8.00000			0.535720			0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000			0.535720			0.267860	+	0.963458i	$0.413684\pi$
$224$		0			0
$225$	4.00000	+	3.00000i	0.266667	+	0.200000i
$226$		0			0
$227$	−7.00000	+	7.00000i	−0.464606	+	0.464606i	−0.900162	−	0.435556i	$-0.856552\pi$
$227$	−7.00000	+	7.00000i	−0.464606	+	0.464606i	0.435556	+	0.900162i	$0.356552\pi$
$228$		0			0
$229$			20.0000i			1.32164i	0.750546	+	0.660819i	$0.229791\pi$
$229$			20.0000i			1.32164i	−0.750546	+	0.660819i	$0.770209\pi$
$230$		0			0
$231$	−2.00000	−	2.00000i	−0.131590	−	0.131590i
$232$		0			0
$233$	−7.00000	−	7.00000i	−0.458585	−	0.458585i	0.439606	−	0.898191i	$-0.355118\pi$
$233$	−7.00000	−	7.00000i	−0.458585	−	0.458585i	−0.898191	+	0.439606i	$0.855118\pi$
$234$		0			0
$235$	−20.0000	+	10.0000i	−1.30466	+	0.652328i
$236$		0			0
$237$			14.0000i			0.909398i
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		0			0
$241$	17.0000	−	17.0000i	1.09507	−	1.09507i	0.100088	−	0.994979i	$-0.468088\pi$
$241$	17.0000	−	17.0000i	1.09507	−	1.09507i	0.994979	−	0.100088i	$-0.0319123\pi$
$242$		0			0
$243$	7.00000	+	7.00000i	0.449050	+	0.449050i
$244$		0			0
$245$	−10.0000	+	5.00000i	−0.638877	+	0.319438i
$246$		0			0
$247$	−8.00000			−0.509028
$248$		0			0
$249$	−12.0000	−	12.0000i	−0.760469	−	0.760469i
$250$		0			0
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	2.00000			0.125739
$254$		0			0
$255$	13.0000	+	1.00000i	0.814092	+	0.0626224i
$256$		0			0
$257$	14.0000			0.873296			0.436648	−	0.899632i	$-0.356166\pi$
$257$	14.0000			0.873296			0.436648	+	0.899632i	$0.356166\pi$
$258$		0			0
$259$	−6.00000			−0.372822
$260$		0			0
$261$	1.00000	+	1.00000i	0.0618984	+	0.0618984i
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$		0			0
$265$	6.00000	+	12.0000i	0.368577	+	0.737154i
$266$		0			0
$267$	10.0000	+	10.0000i	0.611990	+	0.611990i
$268$		0			0
$269$	23.0000	−	23.0000i	1.40233	−	1.40233i	0.609711	−	0.792624i	$-0.291286\pi$
$269$	23.0000	−	23.0000i	1.40233	−	1.40233i	0.792624	−	0.609711i	$-0.208714\pi$
$270$		0			0
$271$	−16.0000			−0.971931			−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000			−0.971931			−0.485965	+	0.873978i	$0.661532\pi$
$272$		0			0
$273$			8.00000i			0.484182i
$274$		0			0
$275$	7.00000	−	1.00000i	0.422116	−	0.0603023i
$276$		0			0
$277$	−17.0000	−	17.0000i	−1.02143	−	1.02143i	−0.999765	−	0.0216657i	$-0.993103\pi$
$277$	−17.0000	−	17.0000i	−1.02143	−	1.02143i	−0.0216657	−	0.999765i	$-0.506897\pi$
$278$		0			0
$279$	−3.00000	−	3.00000i	−0.179605	−	0.179605i
$280$		0			0
$281$		−	32.0000i		−	1.90896i	−0.298275	−	0.954480i	$-0.596411\pi$
$281$		−	32.0000i		−	1.90896i	0.298275	−	0.954480i	$-0.403589\pi$
$282$		0			0
$283$	−3.00000	+	3.00000i	−0.178331	+	0.178331i	−0.790628	−	0.612297i	$-0.790246\pi$
$283$	−3.00000	+	3.00000i	−0.178331	+	0.178331i	0.612297	+	0.790628i	$0.290246\pi$
$284$		0			0
$285$	6.00000	+	2.00000i	0.355409	+	0.118470i
$286$		0			0
$287$	−2.00000			−0.118056
$288$		0			0
$289$	−15.0000	+	8.00000i	−0.882353	+	0.470588i
$290$		0			0
$291$			6.00000i			0.351726i
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$		0			0
$295$	−20.0000	+	10.0000i	−1.16445	+	0.582223i
$296$		0			0
$297$	8.00000			0.464207
$298$		0			0
$299$	−4.00000	−	4.00000i	−0.231326	−	0.231326i
$300$		0			0
$301$	4.00000	−	4.00000i	0.230556	−	0.230556i
$302$		0			0
$303$	6.00000	+	6.00000i	0.344691	+	0.344691i
$304$		0			0
$305$	−7.00000	+	21.0000i	−0.400819	+	1.20246i
$306$		0			0
$307$			10.0000i			0.570730i	0.958419	+	0.285365i	$0.0921148\pi$
$307$			10.0000i			0.570730i	−0.958419	+	0.285365i	$0.907885\pi$
$308$		0			0
$309$	−6.00000	+	6.00000i	−0.341328	+	0.341328i
$310$		0			0
$311$	15.0000	−	15.0000i	0.850572	−	0.850572i	−0.139632	−	0.990204i	$-0.544592\pi$
$311$	15.0000	−	15.0000i	0.850572	−	0.850572i	0.990204	+	0.139632i	$0.0445918\pi$
$312$		0			0
$313$	−19.0000	+	19.0000i	−1.07394	+	1.07394i	−0.0769051	+	0.997038i	$0.524504\pi$
$313$	−19.0000	+	19.0000i	−1.07394	+	1.07394i	−0.997038	+	0.0769051i	$0.975496\pi$
$314$		0			0
$315$	−1.00000	+	3.00000i	−0.0563436	+	0.169031i
$316$		0			0
$317$	−1.00000	+	1.00000i	−0.0561656	+	0.0561656i	−0.734632	−	0.678466i	$-0.762645\pi$
$317$	−1.00000	+	1.00000i	−0.0561656	+	0.0561656i	0.678466	+	0.734632i	$0.262645\pi$
$318$		0			0
$319$	2.00000			0.111979
$320$		0			0
$321$			10.0000i			0.558146i
$322$		0			0
$323$	−8.00000	+	2.00000i	−0.445132	+	0.111283i
$324$		0			0
$325$	−16.0000	−	12.0000i	−0.887520	−	0.665640i
$326$		0			0
$327$			10.0000i			0.553001i
$328$		0			0
$329$	−10.0000	−	10.0000i	−0.551318	−	0.551318i
$330$		0			0
$331$			26.0000i			1.42909i	0.699590	+	0.714545i	$0.253366\pi$
$331$			26.0000i			1.42909i	−0.699590	+	0.714545i	$0.746634\pi$
$332$		0			0
$333$	3.00000	−	3.00000i	0.164399	−	0.164399i
$334$		0			0
$335$	−4.00000	+	2.00000i	−0.218543	+	0.109272i
$336$		0			0
$337$	−3.00000	−	3.00000i	−0.163420	−	0.163420i	0.620660	−	0.784080i	$-0.286865\pi$
$337$	−3.00000	−	3.00000i	−0.163420	−	0.163420i	−0.784080	+	0.620660i	$0.786865\pi$
$338$		0			0
$339$	−10.0000			−0.543125
$340$		0			0
$341$	−6.00000			−0.324918
$342$		0			0
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$		0			0
$345$	2.00000	+	4.00000i	0.107676	+	0.215353i
$346$		0			0
$347$	1.00000	−	1.00000i	0.0536828	−	0.0536828i	−0.679756	−	0.733439i	$-0.737914\pi$
$347$	1.00000	−	1.00000i	0.0536828	−	0.0536828i	0.733439	+	0.679756i	$0.237914\pi$
$348$		0			0
$349$		−	24.0000i		−	1.28469i	−0.766415	−	0.642345i	$-0.777962\pi$
$349$		−	24.0000i		−	1.28469i	0.766415	−	0.642345i	$-0.222038\pi$
$350$		0			0
$351$	−16.0000	−	16.0000i	−0.854017	−	0.854017i
$352$		0			0
$353$			24.0000i			1.27739i	0.769460	+	0.638696i	$0.220526\pi$
$353$			24.0000i			1.27739i	−0.769460	+	0.638696i	$0.779474\pi$
$354$		0			0
$355$	33.0000	+	11.0000i	1.75146	+	0.583819i
$356$		0			0
$357$	2.00000	+	8.00000i	0.105851	+	0.423405i
$358$		0			0
$359$			18.0000i			0.950004i	0.879985	+	0.475002i	$0.157553\pi$
$359$			18.0000i			0.950004i	−0.879985	+	0.475002i	$0.842447\pi$
$360$		0			0
$361$	15.0000			0.789474
$362$		0			0
$363$	−9.00000	+	9.00000i	−0.472377	+	0.472377i
$364$		0			0
$365$	7.00000	−	21.0000i	0.366397	−	1.09919i
$366$		0			0
$367$	−21.0000	+	21.0000i	−1.09619	+	1.09619i	−0.101339	+	0.994852i	$0.532313\pi$
$367$	−21.0000	+	21.0000i	−1.09619	+	1.09619i	−0.994852	+	0.101339i	$0.967687\pi$
$368$		0			0
$369$	1.00000	−	1.00000i	0.0520579	−	0.0520579i
$370$		0			0
$371$	−6.00000	+	6.00000i	−0.311504	+	0.311504i
$372$		0			0
$373$			4.00000i			0.207112i	0.994624	+	0.103556i	$0.0330221\pi$
$373$			4.00000i			0.207112i	−0.994624	+	0.103556i	$0.966978\pi$
$374$		0			0
$375$	9.00000	+	13.0000i	0.464758	+	0.671317i
$376$		0			0
$377$	−4.00000	−	4.00000i	−0.206010	−	0.206010i
$378$		0			0
$379$	21.0000	−	21.0000i	1.07870	−	1.07870i	0.0820711	−	0.996626i	$-0.473847\pi$
$379$	21.0000	−	21.0000i	1.07870	−	1.07870i	0.996626	−	0.0820711i	$-0.0261534\pi$
$380$		0			0
$381$	16.0000	+	16.0000i	0.819705	+	0.819705i
$382$		0			0
$383$	24.0000			1.22634			0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000			1.22634			0.613171	+	0.789950i	$0.289894\pi$
$384$		0			0
$385$	2.00000	+	4.00000i	0.101929	+	0.203859i
$386$		0			0
$387$			4.00000i			0.203331i
$388$		0			0
$389$			28.0000i			1.41966i	0.704375	+	0.709828i	$0.251227\pi$
$389$			28.0000i			1.41966i	−0.704375	+	0.709828i	$0.748773\pi$
$390$		0			0
$391$	−5.00000	−	3.00000i	−0.252861	−	0.151717i
$392$		0			0
$393$	−2.00000			−0.100887
$394$		0			0
$395$	7.00000	−	21.0000i	0.352208	−	1.05662i
$396$		0			0
$397$	11.0000	−	11.0000i	0.552074	−	0.552074i	−0.374965	−	0.927039i	$-0.622345\pi$
$397$	11.0000	−	11.0000i	0.552074	−	0.552074i	0.927039	+	0.374965i	$0.122345\pi$
$398$		0			0
$399$			4.00000i			0.200250i
$400$		0			0
$401$	−3.00000	−	3.00000i	−0.149813	−	0.149813i	0.628222	−	0.778034i	$-0.283783\pi$
$401$	−3.00000	−	3.00000i	−0.149813	−	0.149813i	−0.778034	+	0.628222i	$0.783783\pi$
$402$		0			0
$403$	12.0000	+	12.0000i	0.597763	+	0.597763i
$404$		0			0
$405$	5.00000	+	10.0000i	0.248452	+	0.496904i
$406$		0			0
$407$		−	6.00000i		−	0.297409i
$408$		0			0
$409$	26.0000			1.28562			0.642809	−	0.766027i	$-0.277769\pi$
$409$	26.0000			1.28562			0.642809	+	0.766027i	$0.277769\pi$
$410$		0			0
$411$	−12.0000	+	12.0000i	−0.591916	+	0.591916i
$412$		0			0
$413$	−10.0000	−	10.0000i	−0.492068	−	0.492068i
$414$		0			0
$415$	12.0000	+	24.0000i	0.589057	+	1.17811i
$416$		0			0
$417$	6.00000			0.293821
$418$		0			0
$419$	7.00000	+	7.00000i	0.341972	+	0.341972i	0.857108	−	0.515136i	$-0.172259\pi$
$419$	7.00000	+	7.00000i	0.341972	+	0.341972i	−0.515136	+	0.857108i	$0.672259\pi$
$420$		0			0
$421$	−14.0000			−0.682318			−0.341159	−	0.940006i	$-0.610819\pi$
$421$	−14.0000			−0.682318			−0.341159	+	0.940006i	$0.610819\pi$
$422$		0			0
$423$	10.0000			0.486217
$424$		0			0
$425$	−19.0000	−	8.00000i	−0.921635	−	0.388057i
$426$		0			0
$427$	−14.0000			−0.677507
$428$		0			0
$429$	−8.00000			−0.386244
$430$		0			0
$431$	1.00000	+	1.00000i	0.0481683	+	0.0481683i	0.730781	−	0.682612i	$-0.239156\pi$
$431$	1.00000	+	1.00000i	0.0481683	+	0.0481683i	−0.682612	+	0.730781i	$0.739156\pi$
$432$		0			0
$433$	30.0000			1.44171			0.720854	−	0.693087i	$-0.243750\pi$
$433$	30.0000			1.44171			0.720854	+	0.693087i	$0.243750\pi$
$434$		0			0
$435$	2.00000	+	4.00000i	0.0958927	+	0.191785i
$436$		0			0
$437$	−2.00000	−	2.00000i	−0.0956730	−	0.0956730i
$438$		0			0
$439$	3.00000	−	3.00000i	0.143182	−	0.143182i	−0.631882	−	0.775064i	$-0.717717\pi$
$439$	3.00000	−	3.00000i	0.143182	−	0.143182i	0.775064	+	0.631882i	$0.217717\pi$
$440$		0			0
$441$	5.00000			0.238095
$442$		0			0
$443$			26.0000i			1.23530i	0.786454	+	0.617649i	$0.211915\pi$
$443$			26.0000i			1.23530i	−0.786454	+	0.617649i	$0.788085\pi$
$444$		0			0
$445$	−10.0000	−	20.0000i	−0.474045	−	0.948091i
$446$		0			0
$447$	−6.00000	−	6.00000i	−0.283790	−	0.283790i
$448$		0			0
$449$	21.0000	+	21.0000i	0.991051	+	0.991051i	0.999960	−	0.00890904i	$-0.00283587\pi$
$449$	21.0000	+	21.0000i	0.991051	+	0.991051i	−0.00890904	+	0.999960i	$0.502836\pi$
$450$		0			0
$451$		−	2.00000i		−	0.0941763i
$452$		0			0
$453$	2.00000	−	2.00000i	0.0939682	−	0.0939682i
$454$		0			0
$455$	4.00000	−	12.0000i	0.187523	−	0.562569i
$456$		0			0
$457$	−10.0000			−0.467780			−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000			−0.467780			−0.233890	+	0.972263i	$0.575146\pi$
$458$		0			0
$459$	−20.0000	−	12.0000i	−0.933520	−	0.560112i
$460$		0			0
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$		−	6.00000i		−	0.278844i	−0.990233	−	0.139422i	$-0.955476\pi$
$463$		−	6.00000i		−	0.278844i	0.990233	−	0.139422i	$-0.0445244\pi$
$464$		0			0
$465$	−6.00000	−	12.0000i	−0.278243	−	0.556487i
$466$		0			0
$467$	20.0000			0.925490			0.462745	−	0.886492i	$-0.346865\pi$
$467$	20.0000			0.925490			0.462745	+	0.886492i	$0.346865\pi$
$468$		0			0
$469$	−2.00000	−	2.00000i	−0.0923514	−	0.0923514i
$470$		0			0
$471$	−8.00000	+	8.00000i	−0.368621	+	0.368621i
$472$		0			0
$473$	4.00000	+	4.00000i	0.183920	+	0.183920i
$474$		0			0
$475$	−8.00000	−	6.00000i	−0.367065	−	0.275299i
$476$		0			0
$477$		−	6.00000i		−	0.274721i
$478$		0			0
$479$	15.0000	−	15.0000i	0.685367	−	0.685367i	−0.275837	−	0.961204i	$-0.588955\pi$
$479$	15.0000	−	15.0000i	0.685367	−	0.685367i	0.961204	+	0.275837i	$0.0889550\pi$
$480$		0			0
$481$	−12.0000	+	12.0000i	−0.547153	+	0.547153i
$482$		0			0
$483$	−2.00000	+	2.00000i	−0.0910032	+	0.0910032i
$484$		0			0
$485$	3.00000	−	9.00000i	0.136223	−	0.408669i
$486$		0			0
$487$	−29.0000	+	29.0000i	−1.31412	+	1.31412i	−0.395763	+	0.918353i	$0.629520\pi$
$487$	−29.0000	+	29.0000i	−1.31412	+	1.31412i	−0.918353	+	0.395763i	$0.870480\pi$
$488$		0			0
$489$	14.0000			0.633102
$490$		0			0
$491$			26.0000i			1.17336i	0.809818	+	0.586682i	$0.199566\pi$
$491$			26.0000i			1.17336i	−0.809818	+	0.586682i	$0.800434\pi$
$492$		0			0
$493$	−5.00000	−	3.00000i	−0.225189	−	0.135113i
$494$		0			0
$495$	−3.00000	−	1.00000i	−0.134840	−	0.0449467i
$496$		0			0
$497$			22.0000i			0.986835i
$498$		0			0
$499$	−5.00000	−	5.00000i	−0.223831	−	0.223831i	0.586279	−	0.810109i	$-0.300592\pi$
$499$	−5.00000	−	5.00000i	−0.223831	−	0.223831i	−0.810109	+	0.586279i	$0.800592\pi$
$500$		0			0
$501$			14.0000i			0.625474i
$502$		0			0
$503$	19.0000	−	19.0000i	0.847168	−	0.847168i	−0.142611	−	0.989779i	$-0.545550\pi$
$503$	19.0000	−	19.0000i	0.847168	−	0.847168i	0.989779	+	0.142611i	$0.0455497\pi$
$504$		0			0
$505$	−6.00000	−	12.0000i	−0.266996	−	0.533993i
$506$		0			0
$507$	3.00000	+	3.00000i	0.133235	+	0.133235i
$508$		0			0
$509$	−34.0000			−1.50702			−0.753512	−	0.657434i	$-0.771642\pi$
$509$	−34.0000			−1.50702			−0.753512	+	0.657434i	$0.771642\pi$
$510$		0			0
$511$	14.0000			0.619324
$512$		0			0
$513$	−8.00000	−	8.00000i	−0.353209	−	0.353209i
$514$		0			0
$515$	12.0000	−	6.00000i	0.528783	−	0.264392i
$516$		0			0
$517$	10.0000	−	10.0000i	0.439799	−	0.439799i
$518$		0			0
$519$		−	22.0000i		−	0.965693i
$520$		0			0
$521$	−11.0000	−	11.0000i	−0.481919	−	0.481919i	0.423825	−	0.905744i	$-0.360687\pi$
$521$	−11.0000	−	11.0000i	−0.481919	−	0.481919i	−0.905744	+	0.423825i	$0.860687\pi$
$522$		0			0
$523$		−	38.0000i		−	1.66162i	−0.556553	−	0.830812i	$-0.687876\pi$
$523$		−	38.0000i		−	1.66162i	0.556553	−	0.830812i	$-0.312124\pi$
$524$		0			0
$525$	−6.00000	+	8.00000i	−0.261861	+	0.349149i
$526$		0			0
$527$	15.0000	+	9.00000i	0.653410	+	0.392046i
$528$		0			0
$529$			21.0000i			0.913043i
$530$		0			0
$531$	10.0000			0.433963
$532$		0			0
$533$	−4.00000	+	4.00000i	−0.173259	+	0.173259i
$534$		0			0
$535$	5.00000	−	15.0000i	0.216169	−	0.648507i
$536$		0			0
$537$	18.0000	−	18.0000i	0.776757	−	0.776757i
$538$		0			0
$539$	5.00000	−	5.00000i	0.215365	−	0.215365i
$540$		0			0
$541$	−1.00000	+	1.00000i	−0.0429934	+	0.0429934i	−0.728277	−	0.685283i	$-0.759678\pi$
$541$	−1.00000	+	1.00000i	−0.0429934	+	0.0429934i	0.685283	+	0.728277i	$0.259678\pi$
$542$		0			0
$543$		−	6.00000i		−	0.257485i
$544$		0			0
$545$	5.00000	−	15.0000i	0.214176	−	0.642529i
$546$		0			0
$547$	−13.0000	−	13.0000i	−0.555840	−	0.555840i	0.372280	−	0.928120i	$-0.378576\pi$
$547$	−13.0000	−	13.0000i	−0.555840	−	0.555840i	−0.928120	+	0.372280i	$0.878576\pi$
$548$		0			0
$549$	7.00000	−	7.00000i	0.298753	−	0.298753i
$550$		0			0
$551$	−2.00000	−	2.00000i	−0.0852029	−	0.0852029i
$552$		0			0
$553$	14.0000			0.595341
$554$		0			0
$555$	12.0000	−	6.00000i	0.509372	−	0.254686i
$556$		0			0
$557$			28.0000i			1.18640i	0.805056	+	0.593199i	$0.202135\pi$
$557$			28.0000i			1.18640i	−0.805056	+	0.593199i	$0.797865\pi$
$558$		0			0
$559$		−	16.0000i		−	0.676728i
$560$		0			0
$561$	−8.00000	+	2.00000i	−0.337760	+	0.0844401i
$562$		0			0
$563$	−28.0000			−1.18006			−0.590030	−	0.807382i	$-0.700884\pi$
$563$	−28.0000			−1.18006			−0.590030	+	0.807382i	$0.700884\pi$
$564$		0			0
$565$	15.0000	+	5.00000i	0.631055	+	0.210352i
$566$		0			0
$567$	−5.00000	+	5.00000i	−0.209980	+	0.209980i
$568$		0			0
$569$			24.0000i			1.00613i	0.864248	+	0.503066i	$0.167795\pi$
$569$			24.0000i			1.00613i	−0.864248	+	0.503066i	$0.832205\pi$
$570$		0			0
$571$	7.00000	+	7.00000i	0.292941	+	0.292941i	0.838241	−	0.545300i	$-0.183584\pi$
$571$	7.00000	+	7.00000i	0.292941	+	0.292941i	−0.545300	+	0.838241i	$0.683584\pi$
$572$		0			0
$573$	−16.0000	−	16.0000i	−0.668410	−	0.668410i
$574$		0			0
$575$	−1.00000	−	7.00000i	−0.0417029	−	0.291920i
$576$		0			0
$577$		−	4.00000i		−	0.166522i	−0.996528	−	0.0832611i	$-0.973466\pi$
$577$		−	4.00000i		−	0.166522i	0.996528	−	0.0832611i	$-0.0265335\pi$
$578$		0			0
$579$	6.00000			0.249351
$580$		0			0
$581$	−12.0000	+	12.0000i	−0.497844	+	0.497844i
$582$		0			0
$583$	−6.00000	−	6.00000i	−0.248495	−	0.248495i
$584$		0			0
$585$	4.00000	+	8.00000i	0.165380	+	0.330759i
$586$		0			0
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	6.00000	+	6.00000i	0.247226	+	0.247226i
$590$		0			0
$591$	−38.0000			−1.56311
$592$		0			0
$593$	−6.00000			−0.246390			−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000			−0.246390			−0.123195	+	0.992382i	$0.539314\pi$
$594$		0			0
$595$	1.00000	−	13.0000i	0.0409960	−	0.532948i
$596$		0			0
$597$	18.0000			0.736691
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	−27.0000	−	27.0000i	−1.10135	−	1.10135i	−0.994248	−	0.107105i	$-0.965842\pi$
$601$	−27.0000	−	27.0000i	−1.10135	−	1.10135i	−0.107105	−	0.994248i	$-0.534158\pi$
$602$		0			0
$603$	2.00000			0.0814463
$604$		0			0
$605$	18.0000	−	9.00000i	0.731804	−	0.365902i
$606$		0			0
$607$	29.0000	+	29.0000i	1.17707	+	1.17707i	0.980486	+	0.196587i	$0.0629859\pi$
$607$	29.0000	+	29.0000i	1.17707	+	1.17707i	0.196587	+	0.980486i	$0.437014\pi$
$608$		0			0
$609$	−2.00000	+	2.00000i	−0.0810441	+	0.0810441i
$610$		0			0
$611$	−40.0000			−1.61823
$612$		0			0
$613$		−	16.0000i		−	0.646234i	−0.946359	−	0.323117i	$-0.895269\pi$
$613$		−	16.0000i		−	0.646234i	0.946359	−	0.323117i	$-0.104731\pi$
$614$		0			0
$615$	4.00000	−	2.00000i	0.161296	−	0.0806478i
$616$		0			0
$617$	5.00000	+	5.00000i	0.201292	+	0.201292i	0.800554	−	0.599261i	$-0.204539\pi$
$617$	5.00000	+	5.00000i	0.201292	+	0.201292i	−0.599261	+	0.800554i	$0.704539\pi$
$618$		0			0
$619$	−21.0000	−	21.0000i	−0.844061	−	0.844061i	0.145323	−	0.989384i	$-0.453578\pi$
$619$	−21.0000	−	21.0000i	−0.844061	−	0.844061i	−0.989384	+	0.145323i	$0.953578\pi$
$620$		0			0
$621$		−	8.00000i		−	0.321029i
$622$		0			0
$623$	10.0000	−	10.0000i	0.400642	−	0.400642i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$		0			0
$627$	−4.00000			−0.159745
$628$		0			0
$629$	−9.00000	+	15.0000i	−0.358854	+	0.598089i
$630$		0			0
$631$			10.0000i			0.398094i	0.979990	+	0.199047i	$0.0637846\pi$
$631$			10.0000i			0.398094i	−0.979990	+	0.199047i	$0.936215\pi$
$632$		0			0
$633$		−	22.0000i		−	0.874421i
$634$		0			0
$635$	−16.0000	−	32.0000i	−0.634941	−	1.26988i
$636$		0			0
$637$	−20.0000			−0.792429
$638$		0			0
$639$	−11.0000	−	11.0000i	−0.435153	−	0.435153i
$640$		0			0
$641$	−27.0000	+	27.0000i	−1.06644	+	1.06644i	−0.0688058	+	0.997630i	$0.521919\pi$
$641$	−27.0000	+	27.0000i	−1.06644	+	1.06644i	−0.997630	+	0.0688058i	$0.978081\pi$
$642$		0			0
$643$	−17.0000	−	17.0000i	−0.670415	−	0.670415i	0.287397	−	0.957812i	$-0.407210\pi$
$643$	−17.0000	−	17.0000i	−0.670415	−	0.670415i	−0.957812	+	0.287397i	$0.907210\pi$
$644$		0			0
$645$	−4.00000	+	12.0000i	−0.157500	+	0.472500i
$646$		0			0
$647$		−	38.0000i		−	1.49393i	−0.664861	−	0.746967i	$-0.731509\pi$
$647$		−	38.0000i		−	1.49393i	0.664861	−	0.746967i	$-0.268491\pi$
$648$		0			0
$649$	10.0000	−	10.0000i	0.392534	−	0.392534i
$650$		0			0
$651$	6.00000	−	6.00000i	0.235159	−	0.235159i
$652$		0			0
$653$	−1.00000	+	1.00000i	−0.0391330	+	0.0391330i	−0.726403	−	0.687270i	$-0.758809\pi$
$653$	−1.00000	+	1.00000i	−0.0391330	+	0.0391330i	0.687270	+	0.726403i	$0.258809\pi$
$654$		0			0
$655$	3.00000	+	1.00000i	0.117220	+	0.0390732i
$656$		0			0
$657$	−7.00000	+	7.00000i	−0.273096	+	0.273096i
$658$		0			0
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$		0			0
$661$			48.0000i			1.86698i	0.358599	+	0.933492i	$0.383255\pi$
$661$			48.0000i			1.86698i	−0.358599	+	0.933492i	$0.616745\pi$
$662$		0			0
$663$	20.0000	+	12.0000i	0.776736	+	0.466041i
$664$		0			0
$665$	2.00000	−	6.00000i	0.0775567	−	0.232670i
$666$		0			0
$667$		−	2.00000i		−	0.0774403i
$668$		0			0
$669$	−8.00000	−	8.00000i	−0.309298	−	0.309298i
$670$		0			0
$671$		−	14.0000i		−	0.540464i
$672$		0			0
$673$	17.0000	−	17.0000i	0.655302	−	0.655302i	−0.298963	−	0.954265i	$-0.596641\pi$
$673$	17.0000	−	17.0000i	0.655302	−	0.655302i	0.954265	+	0.298963i	$0.0966407\pi$
$674$		0			0
$675$	−4.00000	−	28.0000i	−0.153960	−	1.07772i
$676$		0			0
$677$	11.0000	+	11.0000i	0.422764	+	0.422764i	0.886154	−	0.463390i	$-0.153367\pi$
$677$	11.0000	+	11.0000i	0.422764	+	0.422764i	−0.463390	+	0.886154i	$0.653367\pi$
$678$		0			0
$679$	6.00000			0.230259
$680$		0			0
$681$	14.0000			0.536481
$682$		0			0
$683$	−17.0000	−	17.0000i	−0.650487	−	0.650487i	0.302623	−	0.953110i	$-0.402138\pi$
$683$	−17.0000	−	17.0000i	−0.650487	−	0.650487i	−0.953110	+	0.302623i	$0.902138\pi$
$684$		0			0
$685$	24.0000	−	12.0000i	0.916993	−	0.458496i
$686$		0			0
$687$	20.0000	−	20.0000i	0.763048	−	0.763048i
$688$		0			0
$689$			24.0000i			0.914327i
$690$		0			0
$691$	−17.0000	−	17.0000i	−0.646710	−	0.646710i	0.305486	−	0.952197i	$-0.401181\pi$
$691$	−17.0000	−	17.0000i	−0.646710	−	0.646710i	−0.952197	+	0.305486i	$0.901181\pi$
$692$		0			0
$693$		−	2.00000i		−	0.0759737i
$694$		0			0
$695$	−9.00000	−	3.00000i	−0.341389	−	0.113796i
$696$		0			0
$697$	−3.00000	+	5.00000i	−0.113633	+	0.189389i
$698$		0			0
$699$			14.0000i			0.529529i
$700$		0			0
$701$	−6.00000			−0.226617			−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000			−0.226617			−0.113308	+	0.993560i	$0.536145\pi$
$702$		0			0
$703$	−6.00000	+	6.00000i	−0.226294	+	0.226294i
$704$		0			0
$705$	30.0000	+	10.0000i	1.12987	+	0.376622i
$706$		0			0
$707$	6.00000	−	6.00000i	0.225653	−	0.225653i
$708$		0			0
$709$	7.00000	−	7.00000i	0.262891	−	0.262891i	−0.563337	−	0.826227i	$-0.690483\pi$
$709$	7.00000	−	7.00000i	0.262891	−	0.262891i	0.826227	+	0.563337i	$0.190483\pi$
$710$		0			0
$711$	−7.00000	+	7.00000i	−0.262521	+	0.262521i
$712$		0			0
$713$			6.00000i			0.224702i
$714$		0			0
$715$	12.0000	+	4.00000i	0.448775	+	0.149592i
$716$		0			0
$717$	−24.0000	−	24.0000i	−0.896296	−	0.896296i
$718$		0			0
$719$	27.0000	−	27.0000i	1.00693	−	1.00693i	0.00695427	−	0.999976i	$-0.497786\pi$
$719$	27.0000	−	27.0000i	1.00693	−	1.00693i	0.999976	−	0.00695427i	$-0.00221363\pi$
$720$		0			0
$721$	6.00000	+	6.00000i	0.223452	+	0.223452i
$722$		0			0
$723$	−34.0000			−1.26447
$724$		0			0
$725$	−1.00000	−	7.00000i	−0.0371391	−	0.259973i
$726$		0			0
$727$		−	14.0000i		−	0.519231i	−0.965712	−	0.259616i	$-0.916404\pi$
$727$		−	14.0000i		−	0.519231i	0.965712	−	0.259616i	$-0.0835959\pi$
$728$		0			0
$729$		−	29.0000i		−	1.07407i
$730$		0			0
$731$	−4.00000	−	16.0000i	−0.147945	−	0.591781i
$732$		0			0
$733$	14.0000			0.517102			0.258551	−	0.965998i	$-0.416755\pi$
$733$	14.0000			0.517102			0.258551	+	0.965998i	$0.416755\pi$
$734$		0			0
$735$	15.0000	+	5.00000i	0.553283	+	0.184428i
$736$		0			0
$737$	2.00000	−	2.00000i	0.0736709	−	0.0736709i
$738$		0			0
$739$			10.0000i			0.367856i	0.982940	+	0.183928i	$0.0588813\pi$
$739$			10.0000i			0.367856i	−0.982940	+	0.183928i	$0.941119\pi$
$740$		0			0
$741$	8.00000	+	8.00000i	0.293887	+	0.293887i
$742$		0			0
$743$	21.0000	+	21.0000i	0.770415	+	0.770415i	0.978179	−	0.207764i	$-0.0666185\pi$
$743$	21.0000	+	21.0000i	0.770415	+	0.770415i	−0.207764	+	0.978179i	$0.566619\pi$
$744$		0			0
$745$	6.00000	+	12.0000i	0.219823	+	0.439646i
$746$		0			0
$747$		−	12.0000i		−	0.439057i
$748$		0			0
$749$	10.0000			0.365392
$750$		0			0
$751$	−13.0000	+	13.0000i	−0.474377	+	0.474377i	−0.903328	−	0.428951i	$-0.858883\pi$
$751$	−13.0000	+	13.0000i	−0.474377	+	0.474377i	0.428951	+	0.903328i	$0.358883\pi$
$752$		0			0
$753$	−12.0000	−	12.0000i	−0.437304	−	0.437304i
$754$		0			0
$755$	−4.00000	+	2.00000i	−0.145575	+	0.0727875i
$756$		0			0
$757$	42.0000			1.52652			0.763258	−	0.646094i	$-0.223599\pi$
$757$	42.0000			1.52652			0.763258	+	0.646094i	$0.223599\pi$
$758$		0			0
$759$	−2.00000	−	2.00000i	−0.0725954	−	0.0725954i
$760$		0			0
$761$	−10.0000			−0.362500			−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000			−0.362500			−0.181250	+	0.983437i	$0.558014\pi$
$762$		0			0
$763$	10.0000			0.362024
$764$		0			0
$765$	6.00000	+	7.00000i	0.216930	+	0.253086i
$766$		0			0
$767$	−40.0000			−1.44432
$768$		0			0
$769$	−18.0000			−0.649097			−0.324548	−	0.945869i	$-0.605212\pi$
$769$	−18.0000			−0.649097			−0.324548	+	0.945869i	$0.605212\pi$
$770$		0			0
$771$	−14.0000	−	14.0000i	−0.504198	−	0.504198i
$772$		0			0
$773$	34.0000			1.22290			0.611448	−	0.791285i	$-0.290588\pi$
$773$	34.0000			1.22290			0.611448	+	0.791285i	$0.290588\pi$
$774$		0			0
$775$	3.00000	+	21.0000i	0.107763	+	0.754342i
$776$		0			0
$777$	6.00000	+	6.00000i	0.215249	+	0.215249i
$778$		0			0
$779$	−2.00000	+	2.00000i	−0.0716574	+	0.0716574i
$780$		0			0
$781$	−22.0000			−0.787222
$782$		0			0
$783$		−	8.00000i		−	0.285897i
$784$		0			0
$785$	16.0000	−	8.00000i	0.571064	−	0.285532i
$786$		0			0
$787$	−9.00000	−	9.00000i	−0.320815	−	0.320815i	0.528265	−	0.849080i	$-0.322843\pi$
$787$	−9.00000	−	9.00000i	−0.320815	−	0.320815i	−0.849080	+	0.528265i	$0.822843\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			10.0000i			0.355559i
$792$		0			0
$793$	−28.0000	+	28.0000i	−0.994309	+	0.994309i
$794$		0			0
$795$	6.00000	−	18.0000i	0.212798	−	0.638394i
$796$		0			0
$797$	−34.0000			−1.20434			−0.602171	−	0.798367i	$-0.705697\pi$
$797$	−34.0000			−1.20434			−0.602171	+	0.798367i	$0.705697\pi$
$798$		0			0
$799$	−40.0000	+	10.0000i	−1.41510	+	0.353775i
$800$		0			0
$801$			10.0000i			0.353333i
$802$		0			0
$803$			14.0000i			0.494049i
$804$		0			0
$805$	4.00000	−	2.00000i	0.140981	−	0.0704907i
$806$		0			0
$807$	−46.0000			−1.61928
$808$		0			0
$809$	−31.0000	−	31.0000i	−1.08990	−	1.08990i	−0.995538	−	0.0943642i	$-0.969918\pi$
$809$	−31.0000	−	31.0000i	−1.08990	−	1.08990i	−0.0943642	−	0.995538i	$-0.530082\pi$
$810$		0			0
$811$	17.0000	−	17.0000i	0.596951	−	0.596951i	−0.342549	−	0.939500i	$-0.611290\pi$
$811$	17.0000	−	17.0000i	0.596951	−	0.596951i	0.939500	+	0.342549i	$0.111290\pi$
$812$		0			0
$813$	16.0000	+	16.0000i	0.561144	+	0.561144i
$814$		0			0
$815$	−21.0000	−	7.00000i	−0.735598	−	0.245199i
$816$		0			0
$817$		−	8.00000i		−	0.279885i
$818$		0			0
$819$	−4.00000	+	4.00000i	−0.139771	+	0.139771i
$820$		0			0
$821$	−1.00000	+	1.00000i	−0.0349002	+	0.0349002i	−0.724342	−	0.689441i	$-0.757856\pi$
$821$	−1.00000	+	1.00000i	−0.0349002	+	0.0349002i	0.689441	+	0.724342i	$0.257856\pi$
$822$		0			0
$823$	15.0000	−	15.0000i	0.522867	−	0.522867i	−0.395569	−	0.918436i	$-0.629453\pi$
$823$	15.0000	−	15.0000i	0.522867	−	0.522867i	0.918436	+	0.395569i	$0.129453\pi$
$824$		0			0
$825$	−8.00000	−	6.00000i	−0.278524	−	0.208893i
$826$		0			0
$827$	−15.0000	+	15.0000i	−0.521601	+	0.521601i	−0.918055	−	0.396454i	$-0.870241\pi$
$827$	−15.0000	+	15.0000i	−0.521601	+	0.521601i	0.396454	+	0.918055i	$0.370241\pi$
$828$		0			0
$829$	14.0000			0.486240			0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000			0.486240			0.243120	+	0.969996i	$0.421829\pi$
$830$		0			0
$831$			34.0000i			1.17945i
$832$		0			0
$833$	−20.0000	+	5.00000i	−0.692959	+	0.173240i
$834$		0			0
$835$	7.00000	−	21.0000i	0.242245	−	0.726735i
$836$		0			0
$837$			24.0000i			0.829561i
$838$		0			0
$839$	33.0000	+	33.0000i	1.13929	+	1.13929i	0.988578	+	0.150708i	$0.0481554\pi$
$839$	33.0000	+	33.0000i	1.13929	+	1.13929i	0.150708	+	0.988578i	$0.451845\pi$
$840$		0			0
$841$			27.0000i			0.931034i
$842$		0			0
$843$	−32.0000	+	32.0000i	−1.10214	+	1.10214i
$844$		0			0
$845$	−3.00000	−	6.00000i	−0.103203	−	0.206406i
$846$		0			0
$847$	9.00000	+	9.00000i	0.309244	+	0.309244i
$848$		0			0
$849$	6.00000			0.205919
$850$		0			0
$851$	−6.00000			−0.205677
$852$		0			0
$853$	39.0000	+	39.0000i	1.33533	+	1.33533i	0.900520	+	0.434815i	$0.143186\pi$
$853$	39.0000	+	39.0000i	1.33533	+	1.33533i	0.434815	+	0.900520i	$0.356814\pi$
$854$		0			0
$855$	2.00000	+	4.00000i	0.0683986	+	0.136797i
$856$		0			0
$857$	21.0000	−	21.0000i	0.717346	−	0.717346i	−0.250715	−	0.968061i	$-0.580666\pi$
$857$	21.0000	−	21.0000i	0.717346	−	0.717346i	0.968061	+	0.250715i	$0.0806656\pi$
$858$		0			0
$859$		−	54.0000i		−	1.84246i	−0.389023	−	0.921228i	$-0.627187\pi$
$859$		−	54.0000i		−	1.84246i	0.389023	−	0.921228i	$-0.372813\pi$
$860$		0			0
$861$	2.00000	+	2.00000i	0.0681598	+	0.0681598i
$862$		0			0
$863$		−	54.0000i		−	1.83818i	−0.394046	−	0.919091i	$-0.628925\pi$
$863$		−	54.0000i		−	1.83818i	0.394046	−	0.919091i	$-0.371075\pi$
$864$		0			0
$865$	−11.0000	+	33.0000i	−0.374011	+	1.12203i
$866$		0			0
$867$	23.0000	+	7.00000i	0.781121	+	0.237732i
$868$		0			0
$869$			14.0000i			0.474917i
$870$		0			0
$871$	−8.00000			−0.271070
$872$		0			0
$873$	−3.00000	+	3.00000i	−0.101535	+	0.101535i
$874$		0			0
$875$	13.0000	−	9.00000i	0.439480	−	0.304256i
$876$		0			0
$877$	7.00000	−	7.00000i	0.236373	−	0.236373i	−0.578973	−	0.815347i	$-0.696546\pi$
$877$	7.00000	−	7.00000i	0.236373	−	0.236373i	0.815347	+	0.578973i	$0.196546\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−19.0000	+	19.0000i	−0.640126	+	0.640126i	−0.950586	−	0.310460i	$-0.899517\pi$
$881$	−19.0000	+	19.0000i	−0.640126	+	0.640126i	0.310460	+	0.950586i	$0.399517\pi$
$882$		0			0
$883$			34.0000i			1.14419i	0.820187	+	0.572096i	$0.193869\pi$
$883$			34.0000i			1.14419i	−0.820187	+	0.572096i	$0.806131\pi$
$884$		0			0
$885$	30.0000	+	10.0000i	1.00844	+	0.336146i
$886$		0			0
$887$	1.00000	+	1.00000i	0.0335767	+	0.0335767i	0.723696	−	0.690119i	$-0.242442\pi$
$887$	1.00000	+	1.00000i	0.0335767	+	0.0335767i	−0.690119	+	0.723696i	$0.742442\pi$
$888$		0			0
$889$	16.0000	−	16.0000i	0.536623	−	0.536623i
$890$		0			0
$891$	−5.00000	−	5.00000i	−0.167506	−	0.167506i
$892$		0			0
$893$	−20.0000			−0.669274
$894$		0			0
$895$	−36.0000	+	18.0000i	−1.20335	+	0.601674i
$896$		0			0
$897$			8.00000i			0.267112i
$898$		0			0
$899$			6.00000i			0.200111i
$900$		0			0
$901$	6.00000	+	24.0000i	0.199889	+	0.799556i
$902$		0			0
$903$	−8.00000			−0.266223
$904$		0			0
$905$	−3.00000	+	9.00000i	−0.0997234	+	0.299170i
$906$		0			0
$907$	37.0000	−	37.0000i	1.22856	−	1.22856i	0.264058	−	0.964507i	$-0.414939\pi$
$907$	37.0000	−	37.0000i	1.22856	−	1.22856i	0.964507	−	0.264058i	$-0.0850611\pi$
$908$		0			0
$909$			6.00000i			0.199007i
$910$		0			0
$911$	33.0000	+	33.0000i	1.09334	+	1.09334i	0.995170	+	0.0981690i	$0.0312986\pi$
$911$	33.0000	+	33.0000i	1.09334	+	1.09334i	0.0981690	+	0.995170i	$0.468701\pi$
$912$		0			0
$913$	−12.0000	−	12.0000i	−0.397142	−	0.397142i
$914$		0			0
$915$	28.0000	−	14.0000i	0.925651	−	0.462826i
$916$		0			0
$917$			2.00000i			0.0660458i
$918$		0			0
$919$	−24.0000			−0.791687			−0.395843	−	0.918318i	$-0.629548\pi$
$919$	−24.0000			−0.791687			−0.395843	+	0.918318i	$0.629548\pi$
$920$		0			0
$921$	10.0000	−	10.0000i	0.329511	−	0.329511i
$922$		0			0
$923$	44.0000	+	44.0000i	1.44828	+	1.44828i
$924$		0			0
$925$	−21.0000	+	3.00000i	−0.690476	+	0.0986394i
$926$		0			0
$927$	−6.00000			−0.197066
$928$		0			0
$929$	33.0000	+	33.0000i	1.08269	+	1.08269i	0.996257	+	0.0864376i	$0.0275483\pi$
$929$	33.0000	+	33.0000i	1.08269	+	1.08269i	0.0864376	+	0.996257i	$0.472452\pi$
$930$		0			0
$931$	−10.0000			−0.327737
$932$		0			0
$933$	−30.0000			−0.982156
$934$		0			0
$935$	13.0000	+	1.00000i	0.425145	+	0.0327035i
$936$		0			0
$937$	2.00000			0.0653372			0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000			0.0653372			0.0326686	+	0.999466i	$0.489599\pi$
$938$		0			0
$939$	38.0000			1.24008
$940$		0			0
$941$	−9.00000	−	9.00000i	−0.293392	−	0.293392i	0.545027	−	0.838419i	$-0.316519\pi$
$941$	−9.00000	−	9.00000i	−0.293392	−	0.293392i	−0.838419	+	0.545027i	$0.816519\pi$
$942$		0			0
$943$	−2.00000			−0.0651290
$944$		0			0
$945$	16.0000	−	8.00000i	0.520480	−	0.260240i
$946$		0			0
$947$	39.0000	+	39.0000i	1.26733	+	1.26733i	0.947462	+	0.319867i	$0.103638\pi$
$947$	39.0000	+	39.0000i	1.26733	+	1.26733i	0.319867	+	0.947462i	$0.396362\pi$
$948$		0			0
$949$	28.0000	−	28.0000i	0.908918	−	0.908918i
$950$		0			0
$951$	2.00000			0.0648544
$952$		0			0
$953$		−	44.0000i		−	1.42530i	−0.701520	−	0.712650i	$-0.747495\pi$
$953$		−	44.0000i		−	1.42530i	0.701520	−	0.712650i	$-0.252505\pi$
$954$		0			0
$955$	16.0000	+	32.0000i	0.517748	+	1.03550i
$956$		0			0
$957$	−2.00000	−	2.00000i	−0.0646508	−	0.0646508i
$958$		0			0
$959$	12.0000	+	12.0000i	0.387500	+	0.387500i
$960$		0			0
$961$			13.0000i			0.419355i
$962$		0			0
$963$	−5.00000	+	5.00000i	−0.161123	+	0.161123i
$964$		0			0
$965$	−9.00000	−	3.00000i	−0.289720	−	0.0965734i
$966$		0			0
$967$	48.0000			1.54358			0.771788	−	0.635880i	$-0.219363\pi$
$967$	48.0000			1.54358			0.771788	+	0.635880i	$0.219363\pi$
$968$		0			0
$969$	10.0000	+	6.00000i	0.321246	+	0.192748i
$970$		0			0
$971$		−	22.0000i		−	0.706014i	−0.935621	−	0.353007i	$-0.885159\pi$
$971$		−	22.0000i		−	0.706014i	0.935621	−	0.353007i	$-0.114841\pi$
$972$		0			0
$973$		−	6.00000i		−	0.192351i
$974$		0			0
$975$	4.00000	+	28.0000i	0.128103	+	0.896718i
$976$		0			0
$977$	−54.0000			−1.72761			−0.863807	−	0.503824i	$-0.831926\pi$
$977$	−54.0000			−1.72761			−0.863807	+	0.503824i	$0.831926\pi$
$978$		0			0
$979$	10.0000	+	10.0000i	0.319601	+	0.319601i
$980$		0			0
$981$	−5.00000	+	5.00000i	−0.159638	+	0.159638i
$982$		0			0
$983$	−3.00000	−	3.00000i	−0.0956851	−	0.0956851i	0.657644	−	0.753329i	$-0.271553\pi$
$983$	−3.00000	−	3.00000i	−0.0956851	−	0.0956851i	−0.753329	+	0.657644i	$0.771553\pi$
$984$		0			0
$985$	57.0000	+	19.0000i	1.81617	+	0.605390i
$986$		0			0
$987$			20.0000i			0.636607i
$988$		0			0
$989$	4.00000	−	4.00000i	0.127193	−	0.127193i
$990$		0			0
$991$	−5.00000	+	5.00000i	−0.158830	+	0.158830i	−0.782048	−	0.623218i	$-0.785825\pi$
$991$	−5.00000	+	5.00000i	−0.158830	+	0.158830i	0.623218	+	0.782048i	$0.285825\pi$
$992$		0			0
$993$	26.0000	−	26.0000i	0.825085	−	0.825085i
$994$		0			0
$995$	−27.0000	−	9.00000i	−0.855958	−	0.285319i
$996$		0			0
$997$	−21.0000	+	21.0000i	−0.665077	+	0.665077i	−0.956572	−	0.291496i	$-0.905847\pi$
$997$	−21.0000	+	21.0000i	−0.665077	+	0.665077i	0.291496	+	0.956572i	$0.405847\pi$
$998$		0			0
$999$	−24.0000			−0.759326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.z.a.89.1	✓	2
5.4	even	2		680.2.z.b.89.1	yes	2
17.13	even	4		680.2.z.b.489.1	yes	2
85.64	even	4	inner	680.2.z.a.489.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.z.a.89.1	✓	2	1.1	even	1	trivial
680.2.z.a.489.1	yes	2	85.64	even	4	inner
680.2.z.b.89.1	yes	2	5.4	even	2
680.2.z.b.489.1	yes	2	17.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.z (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{3} +(1.00000 + 2.00000i) q^{5} +(-1.00000 + 1.00000i) q^{7} -1.00000i q^{9} +(-1.00000 - 1.00000i) q^{11} +4.00000i q^{13} +(1.00000 - 3.00000i) q^{15} +(1.00000 + 4.00000i) q^{17} +2.00000i q^{19} +2.00000 q^{21} +(-1.00000 + 1.00000i) q^{23} +(-3.00000 + 4.00000i) q^{25} +(-4.00000 + 4.00000i) q^{27} +(-1.00000 + 1.00000i) q^{29} +(3.00000 - 3.00000i) q^{31} +2.00000i q^{33} +(-3.00000 - 1.00000i) q^{35} +(3.00000 + 3.00000i) q^{37} +(4.00000 - 4.00000i) q^{39} +(1.00000 + 1.00000i) q^{41} -4.00000 q^{43} +(2.00000 - 1.00000i) q^{45} +10.0000i q^{47} +5.00000i q^{49} +(3.00000 - 5.00000i) q^{51} +6.00000 q^{53} +(1.00000 - 3.00000i) q^{55} +(2.00000 - 2.00000i) q^{57} +10.0000i q^{59} +(7.00000 + 7.00000i) q^{61} +(1.00000 + 1.00000i) q^{63} +(-8.00000 + 4.00000i) q^{65} +2.00000i q^{67} +2.00000 q^{69} +(11.0000 - 11.0000i) q^{71} +(-7.00000 - 7.00000i) q^{73} +(7.00000 - 1.00000i) q^{75} +2.00000 q^{77} +(-7.00000 - 7.00000i) q^{79} +5.00000 q^{81} +12.0000 q^{83} +(-7.00000 + 6.00000i) q^{85} +2.00000 q^{87} -10.0000 q^{89} +(-4.00000 - 4.00000i) q^{91} -6.00000 q^{93} +(-4.00000 + 2.00000i) q^{95} +(-3.00000 - 3.00000i) q^{97} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + 2 q^{5} - 2 q^{7} - 2 q^{11} + 2 q^{15} + 2 q^{17} + 4 q^{21} - 2 q^{23} - 6 q^{25} - 8 q^{27} - 2 q^{29} + 6 q^{31} - 6 q^{35} + 6 q^{37} + 8 q^{39} + 2 q^{41} - 8 q^{43} + 4 q^{45} + 6 q^{51}+ \cdots - 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 + 2 * q^5 - 2 * q^7 - 2 * q^11 + 2 * q^15 + 2 * q^17 + 4 * q^21 - 2 * q^23 - 6 * q^25 - 8 * q^27 - 2 * q^29 + 6 * q^31 - 6 * q^35 + 6 * q^37 + 8 * q^39 + 2 * q^41 - 8 * q^43 + 4 * q^45 + 6 * q^51 + 12 * q^53 + 2 * q^55 + 4 * q^57 + 14 * q^61 + 2 * q^63 - 16 * q^65 + 4 * q^69 + 22 * q^71 - 14 * q^73 + 14 * q^75 + 4 * q^77 - 14 * q^79 + 10 * q^81 + 24 * q^83 - 14 * q^85 + 4 * q^87 - 20 * q^89 - 8 * q^91 - 12 * q^93 - 8 * q^95 - 6 * q^97 - 2 * q^99

Introduction

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