LMFDB - Embedded newform 675.2.f.i.593.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(107,675)] 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("675.107"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,4,0,0,0,0,0,4,0,0,-4,0,0,0,0,0,-4,0,0,0,0,0,44,0, 0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(31)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.12745506816.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 23x^{4} + 1 $ x^8 + 23*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			593.1
Root			$-1.54779 - 1.54779i$ of defining polynomial
Character	$\chi$	$=$	675.593
Dual form			675.2.f.i.107.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.54779 - 1.54779i) q^{2} +2.79129i q^{4} +(2.79129 - 2.79129i) q^{7} +(1.22474 - 1.22474i) q^{8} -1.80341i q^{11} +(2.79129 + 2.79129i) q^{13} -8.64064 q^{14} +1.79129 q^{16} +(1.87083 + 1.87083i) q^{17} +3.00000i q^{19} +(-2.79129 + 2.79129i) q^{22} +(0.578661 - 0.578661i) q^{23} -8.64064i q^{26} +(7.79129 + 7.79129i) q^{28} +6.83723 q^{29} -1.00000 q^{31} +(-5.22202 - 5.22202i) q^{32} -5.79129i q^{34} +(5.00000 - 5.00000i) q^{37} +(4.64336 - 4.64336i) q^{38} -1.80341i q^{41} +(-7.79129 - 7.79129i) q^{43} +5.03383 q^{44} -1.79129 q^{46} +(3.09557 + 3.09557i) q^{47} -8.58258i q^{49} +(-7.79129 + 7.79129i) q^{52} +(7.41589 - 7.41589i) q^{53} -6.83723i q^{56} +(-10.5826 - 10.5826i) q^{58} -6.83723 q^{59} -1.00000 q^{61} +(1.54779 + 1.54779i) q^{62} +12.5826i q^{64} +(0.582576 - 0.582576i) q^{67} +(-5.22202 + 5.22202i) q^{68} -1.80341i q^{71} +(-3.37386 - 3.37386i) q^{73} -15.4779 q^{74} -8.37386 q^{76} +(-5.03383 - 5.03383i) q^{77} -1.41742i q^{79} +(-2.79129 + 2.79129i) q^{82} +(-6.25857 + 6.25857i) q^{83} +24.1185i q^{86} +(-2.20871 - 2.20871i) q^{88} +5.41022 q^{89} +15.5826 q^{91} +(1.61521 + 1.61521i) q^{92} -9.58258i q^{94} +(-5.58258 + 5.58258i) q^{97} +(-13.2840 + 13.2840i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{7} + 4 q^{13} - 4 q^{16} - 4 q^{22} + 44 q^{28} - 8 q^{31} + 40 q^{37} - 44 q^{43} + 4 q^{46} - 44 q^{52} - 48 q^{58} - 8 q^{61} - 32 q^{67} + 28 q^{73} - 12 q^{76} - 4 q^{82} - 36 q^{88} + 88 q^{91}+ \cdots - 8 q^{97}+O(q^{100}) $ 8 * q + 4 * q^7 + 4 * q^13 - 4 * q^16 - 4 * q^22 + 44 * q^28 - 8 * q^31 + 40 * q^37 - 44 * q^43 + 4 * q^46 - 44 * q^52 - 48 * q^58 - 8 * q^61 - 32 * q^67 + 28 * q^73 - 12 * q^76 - 4 * q^82 - 36 * q^88 + 88 * q^91 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.54779	−	1.54779i	−1.09445	−	1.09445i	−0.995047	−	0.0994033i	$-0.968307\pi$
$2$	−1.54779	−	1.54779i	−1.09445	−	1.09445i	−0.0994033	−	0.995047i	$-0.531693\pi$
$3$		0			0
$3$		0			0
$4$			2.79129i			1.39564i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.79129	−	2.79129i	1.05501	−	1.05501i	0.0566113	−	0.998396i	$-0.481970\pi$
$7$	2.79129	−	2.79129i	1.05501	−	1.05501i	0.998396	−	0.0566113i	$-0.0180296\pi$
$8$	1.22474	−	1.22474i	0.433013	−	0.433013i
$9$		0			0
$10$		0			0
$11$		−	1.80341i		−	0.543747i	−0.962333	−	0.271874i	$-0.912357\pi$
$11$		−	1.80341i		−	0.543747i	0.962333	−	0.271874i	$-0.0876433\pi$
$12$		0			0
$13$	2.79129	+	2.79129i	0.774164	+	0.774164i	0.978832	−	0.204668i	$-0.0656113\pi$
$13$	2.79129	+	2.79129i	0.774164	+	0.774164i	−0.204668	+	0.978832i	$0.565611\pi$
$14$	−8.64064			−2.30931
$15$		0			0
$16$	1.79129			0.447822
$17$	1.87083	+	1.87083i	0.453743	+	0.453743i	0.896595	−	0.442852i	$-0.146033\pi$
$17$	1.87083	+	1.87083i	0.453743	+	0.453743i	−0.442852	+	0.896595i	$0.646033\pi$
$18$		0			0
$19$			3.00000i			0.688247i	0.938924	+	0.344124i	$0.111824\pi$
$19$			3.00000i			0.688247i	−0.938924	+	0.344124i	$0.888176\pi$
$20$		0			0
$21$		0			0
$22$	−2.79129	+	2.79129i	−0.595105	+	0.595105i
$23$	0.578661	−	0.578661i	0.120659	−	0.120659i	−0.644199	−	0.764858i	$-0.722809\pi$
$23$	0.578661	−	0.578661i	0.120659	−	0.120659i	0.764858	+	0.644199i	$0.222809\pi$
$24$		0			0
$25$		0			0
$26$		−	8.64064i		−	1.69457i
$27$		0			0
$28$	7.79129	+	7.79129i	1.47242	+	1.47242i
$29$	6.83723			1.26964			0.634821	−	0.772659i	$-0.281074\pi$
$29$	6.83723			1.26964			0.634821	+	0.772659i	$0.281074\pi$
$30$		0			0
$31$	−1.00000			−0.179605			−0.0898027	−	0.995960i	$-0.528624\pi$
$31$	−1.00000			−0.179605			−0.0898027	+	0.995960i	$0.528624\pi$
$32$	−5.22202	−	5.22202i	−0.923132	−	0.923132i
$33$		0			0
$34$		−	5.79129i		−	0.993198i
$35$		0			0
$36$		0			0
$37$	5.00000	−	5.00000i	0.821995	−	0.821995i	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	5.00000	−	5.00000i	0.821995	−	0.821995i	0.986394	+	0.164399i	$0.0525685\pi$
$38$	4.64336	−	4.64336i	0.753253	−	0.753253i
$39$		0			0
$40$		0			0
$41$		−	1.80341i		−	0.281645i	−0.990035	−	0.140822i	$-0.955025\pi$
$41$		−	1.80341i		−	0.281645i	0.990035	−	0.140822i	$-0.0449746\pi$
$42$		0			0
$43$	−7.79129	−	7.79129i	−1.18816	−	1.18816i	−0.977576	−	0.210585i	$-0.932463\pi$
$43$	−7.79129	−	7.79129i	−1.18816	−	1.18816i	−0.210585	−	0.977576i	$-0.567537\pi$
$44$	5.03383			0.758878
$45$		0			0
$46$	−1.79129			−0.264111
$47$	3.09557	+	3.09557i	0.451536	+	0.451536i	0.895864	−	0.444328i	$-0.146558\pi$
$47$	3.09557	+	3.09557i	0.451536	+	0.451536i	−0.444328	+	0.895864i	$0.646558\pi$
$48$		0			0
$49$		−	8.58258i		−	1.22608i
$50$		0			0
$51$		0			0
$52$	−7.79129	+	7.79129i	−1.08046	+	1.08046i
$53$	7.41589	−	7.41589i	1.01865	−	1.01865i	0.0188284	−	0.999823i	$-0.494006\pi$
$53$	7.41589	−	7.41589i	1.01865	−	1.01865i	0.999823	−	0.0188284i	$-0.00599361\pi$
$54$		0			0
$55$		0			0
$56$		−	6.83723i		−	0.913663i
$57$		0			0
$58$	−10.5826	−	10.5826i	−1.38956	−	1.38956i
$59$	−6.83723			−0.890132			−0.445066	−	0.895498i	$-0.646820\pi$
$59$	−6.83723			−0.890132			−0.445066	+	0.895498i	$0.646820\pi$
$60$		0			0
$61$	−1.00000			−0.128037			−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	−1.00000			−0.128037			−0.0640184	+	0.997949i	$0.520392\pi$
$62$	1.54779	+	1.54779i	0.196569	+	0.196569i
$63$		0			0
$64$			12.5826i			1.57282i
$65$		0			0
$66$		0			0
$67$	0.582576	−	0.582576i	0.0711729	−	0.0711729i	−0.670624	−	0.741797i	$-0.733974\pi$
$67$	0.582576	−	0.582576i	0.0711729	−	0.0711729i	0.741797	+	0.670624i	$0.233974\pi$
$68$	−5.22202	+	5.22202i	−0.633263	+	0.633263i
$69$		0			0
$70$		0			0
$71$		−	1.80341i		−	0.214025i	−0.994258	−	0.107012i	$-0.965872\pi$
$71$		−	1.80341i		−	0.214025i	0.994258	−	0.107012i	$-0.0341285\pi$
$72$		0			0
$73$	−3.37386	−	3.37386i	−0.394881	−	0.394881i	0.481542	−	0.876423i	$-0.340077\pi$
$73$	−3.37386	−	3.37386i	−0.394881	−	0.394881i	−0.876423	+	0.481542i	$0.840077\pi$
$74$	−15.4779			−1.79927
$75$		0			0
$76$	−8.37386			−0.960548
$77$	−5.03383	−	5.03383i	−0.573658	−	0.573658i
$78$		0			0
$79$		−	1.41742i		−	0.159473i	−0.996816	−	0.0797363i	$-0.974592\pi$
$79$		−	1.41742i		−	0.159473i	0.996816	−	0.0797363i	$-0.0254078\pi$
$80$		0			0
$81$		0			0
$82$	−2.79129	+	2.79129i	−0.308246	+	0.308246i
$83$	−6.25857	+	6.25857i	−0.686967	+	0.686967i	−0.961560	−	0.274593i	$-0.911457\pi$
$83$	−6.25857	+	6.25857i	−0.686967	+	0.686967i	0.274593	+	0.961560i	$0.411457\pi$
$84$		0			0
$85$		0			0
$86$			24.1185i			2.60077i
$87$		0			0
$88$	−2.20871	−	2.20871i	−0.235450	−	0.235450i
$89$	5.41022			0.573482			0.286741	−	0.958008i	$-0.407428\pi$
$89$	5.41022			0.573482			0.286741	+	0.958008i	$0.407428\pi$
$90$		0			0
$91$	15.5826			1.63350
$92$	1.61521	+	1.61521i	0.168397	+	0.168397i
$93$		0			0
$94$		−	9.58258i		−	0.988367i
$95$		0			0
$96$		0			0
$97$	−5.58258	+	5.58258i	−0.566825	+	0.566825i	−0.931238	−	0.364413i	$-0.881270\pi$
$97$	−5.58258	+	5.58258i	−0.566825	+	0.566825i	0.364413	+	0.931238i	$0.381270\pi$
$98$	−13.2840	+	13.2840i	−1.34189	+	1.34189i
$99$		0			0
$100$		0			0
$101$			3.60681i			0.358891i	0.983768	+	0.179446i	$0.0574304\pi$
$101$			3.60681i			0.358891i	−0.983768	+	0.179446i	$0.942570\pi$
$102$		0			0
$103$	−5.58258	−	5.58258i	−0.550068	−	0.550068i	0.376393	−	0.926460i	$-0.377164\pi$
$103$	−5.58258	−	5.58258i	−0.550068	−	0.550068i	−0.926460	+	0.376393i	$0.877164\pi$
$104$	6.83723			0.670446
$105$		0			0
$106$	−22.9564			−2.22973
$107$	−3.74166	−	3.74166i	−0.361720	−	0.361720i	0.502726	−	0.864446i	$-0.332330\pi$
$107$	−3.74166	−	3.74166i	−0.361720	−	0.361720i	−0.864446	+	0.502726i	$0.832330\pi$
$108$		0			0
$109$		−	13.7477i		−	1.31679i	−0.752671	−	0.658397i	$-0.771235\pi$
$109$		−	13.7477i		−	1.31679i	0.752671	−	0.658397i	$-0.228765\pi$
$110$		0			0
$111$		0			0
$112$	5.00000	−	5.00000i	0.472456	−	0.472456i
$113$	−1.15732	+	1.15732i	−0.108872	+	0.108872i	−0.759444	−	0.650572i	$-0.774529\pi$
$113$	−1.15732	+	1.15732i	−0.108872	+	0.108872i	0.650572	+	0.759444i	$0.274529\pi$
$114$		0			0
$115$		0			0
$116$			19.0847i			1.77197i
$117$		0			0
$118$	10.5826	+	10.5826i	0.974205	+	0.974205i
$119$	10.4440			0.957404
$120$		0			0
$121$	7.74773			0.704339
$122$	1.54779	+	1.54779i	0.140130	+	0.140130i
$123$		0			0
$124$		−	2.79129i		−	0.250665i
$125$		0			0
$126$		0			0
$127$	5.00000	−	5.00000i	0.443678	−	0.443678i	−0.449568	−	0.893246i	$-0.648422\pi$
$127$	5.00000	−	5.00000i	0.443678	−	0.443678i	0.893246	+	0.449568i	$0.148422\pi$
$128$	9.03110	−	9.03110i	0.798244	−	0.798244i
$129$		0			0
$130$		0			0
$131$		−	22.3151i		−	1.94968i	−0.222907	−	0.974840i	$-0.571555\pi$
$131$		−	22.3151i		−	1.94968i	0.222907	−	0.974840i	$-0.428445\pi$
$132$		0			0
$133$	8.37386	+	8.37386i	0.726106	+	0.726106i
$134$	−1.80341			−0.155791
$135$		0			0
$136$	4.58258			0.392953
$137$	14.1183	+	14.1183i	1.20621	+	1.20621i	0.972246	+	0.233959i	$0.0751683\pi$
$137$	14.1183	+	14.1183i	1.20621	+	1.20621i	0.233959	+	0.972246i	$0.424832\pi$
$138$		0			0
$139$			15.1652i			1.28629i	0.765744	+	0.643146i	$0.222371\pi$
$139$			15.1652i			1.28629i	−0.765744	+	0.643146i	$0.777629\pi$
$140$		0			0
$141$		0			0
$142$	−2.79129	+	2.79129i	−0.234240	+	0.234240i
$143$	5.03383	−	5.03383i	0.420950	−	0.420950i
$144$		0			0
$145$		0			0
$146$			10.4440i			0.864355i
$147$		0			0
$148$	13.9564	+	13.9564i	1.14721	+	1.14721i
$149$	19.0847			1.56348			0.781739	−	0.623606i	$-0.214333\pi$
$149$	19.0847			1.56348			0.781739	+	0.623606i	$0.214333\pi$
$150$		0			0
$151$	2.00000			0.162758			0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000			0.162758			0.0813788	+	0.996683i	$0.474068\pi$
$152$	3.67423	+	3.67423i	0.298020	+	0.298020i
$153$		0			0
$154$			15.5826i			1.25568i
$155$		0			0
$156$		0			0
$157$	−7.79129	+	7.79129i	−0.621812	+	0.621812i	−0.945995	−	0.324182i	$-0.894911\pi$
$157$	−7.79129	+	7.79129i	−0.621812	+	0.621812i	0.324182	+	0.945995i	$0.394911\pi$
$158$	−2.19387	+	2.19387i	−0.174535	+	0.174535i
$159$		0			0
$160$		0			0
$161$		−	3.23042i		−	0.254593i
$162$		0			0
$163$	5.00000	+	5.00000i	0.391630	+	0.391630i	0.875268	−	0.483638i	$-0.160685\pi$
$163$	5.00000	+	5.00000i	0.391630	+	0.391630i	−0.483638	+	0.875268i	$0.660685\pi$
$164$	5.03383			0.393076
$165$		0			0
$166$	19.3739			1.50370
$167$	15.5453	+	15.5453i	1.20293	+	1.20293i	0.973271	+	0.229660i	$0.0737613\pi$
$167$	15.5453	+	15.5453i	1.20293	+	1.20293i	0.229660	+	0.973271i	$0.426239\pi$
$168$		0			0
$169$			2.58258i			0.198660i
$170$		0			0
$171$		0			0
$172$	21.7477	−	21.7477i	1.65825	−	1.65825i
$173$	−11.6688	+	11.6688i	−0.887161	+	0.887161i	−0.994250	−	0.107088i	$-0.965847\pi$
$173$	−11.6688	+	11.6688i	−0.887161	+	0.887161i	0.107088	+	0.994250i	$0.465847\pi$
$174$		0			0
$175$		0			0
$176$		−	3.23042i		−	0.243502i
$177$		0			0
$178$	−8.37386	−	8.37386i	−0.627648	−	0.627648i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$	−17.7477			−1.31918			−0.659589	−	0.751626i	$-0.729270\pi$
$181$	−17.7477			−1.31918			−0.659589	+	0.751626i	$0.729270\pi$
$182$	−24.1185	−	24.1185i	−1.78778	−	1.78778i
$183$		0			0
$184$		−	1.41742i		−	0.104494i
$185$		0			0
$186$		0			0
$187$	3.37386	−	3.37386i	0.246721	−	0.246721i
$188$	−8.64064	+	8.64064i	−0.630183	+	0.630183i
$189$		0			0
$190$		0			0
$191$			18.7083i			1.35368i	0.736128	+	0.676842i	$0.236652\pi$
$191$			18.7083i			1.35368i	−0.736128	+	0.676842i	$0.763348\pi$
$192$		0			0
$193$	2.79129	+	2.79129i	0.200921	+	0.200921i	0.800395	−	0.599473i	$-0.204623\pi$
$193$	2.79129	+	2.79129i	0.200921	+	0.200921i	−0.599473	+	0.800395i	$0.704623\pi$
$194$	17.2813			1.24072
$195$		0			0
$196$	23.9564			1.71117
$197$	1.87083	+	1.87083i	0.133291	+	0.133291i	0.770605	−	0.637314i	$-0.219954\pi$
$197$	1.87083	+	1.87083i	0.133291	+	0.133291i	−0.637314	+	0.770605i	$0.719954\pi$
$198$		0			0
$199$			10.7477i			0.761886i	0.924598	+	0.380943i	$0.124401\pi$
$199$			10.7477i			0.761886i	−0.924598	+	0.380943i	$0.875599\pi$
$200$		0			0
$201$		0			0
$202$	5.58258	−	5.58258i	0.392789	−	0.392789i
$203$	19.0847	−	19.0847i	1.33948	−	1.33948i
$204$		0			0
$205$		0			0
$206$			17.2813i			1.20404i
$207$		0			0
$208$	5.00000	+	5.00000i	0.346688	+	0.346688i
$209$	5.41022			0.374233
$210$		0			0
$211$	−17.7477			−1.22180			−0.610902	−	0.791706i	$-0.709193\pi$
$211$	−17.7477			−1.22180			−0.610902	+	0.791706i	$0.709193\pi$
$212$	20.6999	+	20.6999i	1.42167	+	1.42167i
$213$		0			0
$214$			11.5826i			0.791769i
$215$		0			0
$216$		0			0
$217$	−2.79129	+	2.79129i	−0.189485	+	0.189485i
$218$	−21.2786	+	21.2786i	−1.44117	+	1.44117i
$219$		0			0
$220$		0			0
$221$			10.4440i			0.702542i
$222$		0			0
$223$	0.582576	+	0.582576i	0.0390122	+	0.0390122i	0.726344	−	0.687332i	$-0.241218\pi$
$223$	0.582576	+	0.582576i	0.0390122	+	0.0390122i	−0.687332	+	0.726344i	$0.741218\pi$
$224$	−29.1523			−1.94782
$225$		0			0
$226$	3.58258			0.238309
$227$	−11.8036	−	11.8036i	−0.783435	−	0.783435i	0.196974	−	0.980409i	$-0.436889\pi$
$227$	−11.8036	−	11.8036i	−0.783435	−	0.783435i	−0.980409	+	0.196974i	$0.936889\pi$
$228$		0			0
$229$			24.1652i			1.59688i	0.602076	+	0.798439i	$0.294341\pi$
$229$			24.1652i			1.59688i	−0.602076	+	0.798439i	$0.705659\pi$
$230$		0			0
$231$		0			0
$232$	8.37386	−	8.37386i	0.549771	−	0.549771i
$233$	−9.42157	+	9.42157i	−0.617227	+	0.617227i	−0.944819	−	0.327592i	$-0.893763\pi$
$233$	−9.42157	+	9.42157i	−0.617227	+	0.617227i	0.327592	+	0.944819i	$0.393763\pi$
$234$		0			0
$235$		0			0
$236$		−	19.0847i		−	1.24231i
$237$		0			0
$238$	−16.1652	−	16.1652i	−1.04783	−	1.04783i
$239$	−12.2474			−0.792222			−0.396111	−	0.918203i	$-0.629640\pi$
$239$	−12.2474			−0.792222			−0.396111	+	0.918203i	$0.629640\pi$
$240$		0			0
$241$	15.7477			1.01440			0.507200	−	0.861828i	$-0.330680\pi$
$241$	15.7477			1.01440			0.507200	+	0.861828i	$0.330680\pi$
$242$	−11.9918	−	11.9918i	−0.770864	−	0.770864i
$243$		0			0
$244$		−	2.79129i		−	0.178694i
$245$		0			0
$246$		0			0
$247$	−8.37386	+	8.37386i	−0.532816	+	0.532816i
$248$	−1.22474	+	1.22474i	−0.0777714	+	0.0777714i
$249$		0			0
$250$		0			0
$251$		−	7.21362i		−	0.455320i	−0.973741	−	0.227660i	$-0.926893\pi$
$251$		−	7.21362i		−	0.455320i	0.973741	−	0.227660i	$-0.0731075\pi$
$252$		0			0
$253$	−1.04356	−	1.04356i	−0.0656081	−	0.0656081i
$254$	−15.4779			−0.971168
$255$		0			0
$256$	−2.79129			−0.174455
$257$	−4.96640	−	4.96640i	−0.309796	−	0.309796i	0.535035	−	0.844830i	$-0.320299\pi$
$257$	−4.96640	−	4.96640i	−0.309796	−	0.309796i	−0.844830	+	0.535035i	$0.820299\pi$
$258$		0			0
$259$		−	27.9129i		−	1.73442i
$260$		0			0
$261$		0			0
$262$	−34.5390	+	34.5390i	−2.13383	+	2.13383i
$263$	17.9274	−	17.9274i	1.10545	−	1.10545i	0.111707	−	0.993741i	$-0.464368\pi$
$263$	17.9274	−	17.9274i	1.10545	−	1.10545i	0.993741	−	0.111707i	$-0.0356318\pi$
$264$		0			0
$265$		0			0
$266$		−	25.9219i		−	1.58937i
$267$		0			0
$268$	1.62614	+	1.62614i	0.0993321	+	0.0993321i
$269$	−25.9219			−1.58049			−0.790243	−	0.612793i	$-0.790046\pi$
$269$	−25.9219			−1.58049			−0.790243	+	0.612793i	$0.790046\pi$
$270$		0			0
$271$	−1.00000			−0.0607457			−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	−1.00000			−0.0607457			−0.0303728	+	0.999539i	$0.509669\pi$
$272$	3.35119	+	3.35119i	0.203196	+	0.203196i
$273$		0			0
$274$		−	43.7042i		−	2.64027i
$275$		0			0
$276$		0			0
$277$	17.7913	−	17.7913i	1.06897	−	1.06897i	0.0715369	−	0.997438i	$-0.477210\pi$
$277$	17.7913	−	17.7913i	1.06897	−	1.06897i	0.997438	−	0.0715369i	$-0.0227904\pi$
$278$	23.4724	−	23.4724i	1.40778	−	1.40778i
$279$		0			0
$280$		0			0
$281$			24.1185i			1.43879i	0.694602	+	0.719395i	$0.255581\pi$
$281$			24.1185i			1.43879i	−0.694602	+	0.719395i	$0.744419\pi$
$282$		0			0
$283$	17.7913	+	17.7913i	1.05758	+	1.05758i	0.998238	+	0.0593447i	$0.0189011\pi$
$283$	17.7913	+	17.7913i	1.05758	+	1.05758i	0.0593447	+	0.998238i	$0.481099\pi$
$284$	5.03383			0.298703
$285$		0			0
$286$	−15.5826			−0.921417
$287$	−5.03383	−	5.03383i	−0.297137	−	0.297137i
$288$		0			0
$289$		−	10.0000i		−	0.588235i
$290$		0			0
$291$		0			0
$292$	9.41742	−	9.41742i	0.551113	−	0.551113i
$293$	−4.83156	+	4.83156i	−0.282263	+	0.282263i	−0.834011	−	0.551748i	$-0.813961\pi$
$293$	−4.83156	+	4.83156i	−0.282263	+	0.282263i	0.551748	+	0.834011i	$0.313961\pi$
$294$		0			0
$295$		0			0
$296$		−	12.2474i		−	0.711868i
$297$		0			0
$298$	−29.5390	−	29.5390i	−1.71115	−	1.71115i
$299$	3.23042			0.186820
$300$		0			0
$301$	−43.4955			−2.50704
$302$	−3.09557	−	3.09557i	−0.178130	−	0.178130i
$303$		0			0
$304$			5.37386i			0.308212i
$305$		0			0
$306$		0			0
$307$	−11.7477	+	11.7477i	−0.670478	+	0.670478i	−0.957826	−	0.287348i	$-0.907226\pi$
$307$	−11.7477	+	11.7477i	−0.670478	+	0.670478i	0.287348	+	0.957826i	$0.407226\pi$
$308$	14.0509	−	14.0509i	0.800622	−	0.800622i
$309$		0			0
$310$		0			0
$311$		−	27.7253i		−	1.57216i	−0.618126	−	0.786079i	$-0.712108\pi$
$311$		−	27.7253i		−	1.57216i	0.618126	−	0.786079i	$-0.287892\pi$
$312$		0			0
$313$	−1.16515	−	1.16515i	−0.0658583	−	0.0658583i	0.673411	−	0.739269i	$-0.264829\pi$
$313$	−1.16515	−	1.16515i	−0.0658583	−	0.0658583i	−0.739269	+	0.673411i	$0.764829\pi$
$314$	24.1185			1.36109
$315$		0			0
$316$	3.95644			0.222567
$317$	3.29784	+	3.29784i	0.185225	+	0.185225i	0.793628	−	0.608403i	$-0.208190\pi$
$317$	3.29784	+	3.29784i	0.185225	+	0.185225i	−0.608403	+	0.793628i	$0.708190\pi$
$318$		0			0
$319$		−	12.3303i		−	0.690364i
$320$		0			0
$321$		0			0
$322$	−5.00000	+	5.00000i	−0.278639	+	0.278639i
$323$	−5.61249	+	5.61249i	−0.312287	+	0.312287i
$324$		0			0
$325$		0			0
$326$		−	15.4779i		−	0.857240i
$327$		0			0
$328$	−2.20871	−	2.20871i	−0.121956	−	0.121956i
$329$	17.2813			0.952747
$330$		0			0
$331$	−14.7477			−0.810608			−0.405304	−	0.914182i	$-0.632834\pi$
$331$	−14.7477			−0.810608			−0.405304	+	0.914182i	$0.632834\pi$
$332$	−17.4695	−	17.4695i	−0.958762	−	0.958762i
$333$		0			0
$334$		−	48.1216i		−	2.63310i
$335$		0			0
$336$		0			0
$337$	−22.7913	+	22.7913i	−1.24152	+	1.24152i	−0.282150	+	0.959370i	$0.591048\pi$
$337$	−22.7913	+	22.7913i	−1.24152	+	1.24152i	−0.959370	+	0.282150i	$0.908952\pi$
$338$	3.99728	−	3.99728i	0.217423	−	0.217423i
$339$		0			0
$340$		0			0
$341$			1.80341i			0.0976599i
$342$		0			0
$343$	−4.41742	−	4.41742i	−0.238518	−	0.238518i
$344$	−19.0847			−1.02898
$345$		0			0
$346$	36.1216			1.94191
$347$	−15.9891	−	15.9891i	−0.858340	−	0.858340i	0.132802	−	0.991143i	$-0.457602\pi$
$347$	−15.9891	−	15.9891i	−0.858340	−	0.858340i	−0.991143	+	0.132802i	$0.957602\pi$
$348$		0			0
$349$			28.5826i			1.52999i	0.644036	+	0.764995i	$0.277259\pi$
$349$			28.5826i			1.52999i	−0.644036	+	0.764995i	$0.722741\pi$
$350$		0			0
$351$		0			0
$352$	−9.41742	+	9.41742i	−0.501950	+	0.501950i
$353$	−2.58434	+	2.58434i	−0.137550	+	0.137550i	−0.772529	−	0.634979i	$-0.781009\pi$
$353$	−2.58434	+	2.58434i	−0.137550	+	0.137550i	0.634979	+	0.772529i	$0.281009\pi$
$354$		0			0
$355$		0			0
$356$			15.1015i			0.800377i
$357$		0			0
$358$		0			0
$359$	15.1015			0.797025			0.398513	−	0.917163i	$-0.369526\pi$
$359$	15.1015			0.797025			0.398513	+	0.917163i	$0.369526\pi$
$360$		0			0
$361$	10.0000			0.526316
$362$	27.4697	+	27.4697i	1.44378	+	1.44378i
$363$		0			0
$364$			43.4955i			2.27978i
$365$		0			0
$366$		0			0
$367$	−13.9564	+	13.9564i	−0.728520	+	0.728520i	−0.970325	−	0.241805i	$-0.922261\pi$
$367$	−13.9564	+	13.9564i	−0.728520	+	0.728520i	0.241805	+	0.970325i	$0.422261\pi$
$368$	1.03655	−	1.03655i	0.0540338	−	0.0540338i
$369$		0			0
$370$		0			0
$371$		−	41.3998i		−	2.14937i
$372$		0			0
$373$	−5.58258	−	5.58258i	−0.289055	−	0.289055i	0.547652	−	0.836706i	$-0.315522\pi$
$373$	−5.58258	−	5.58258i	−0.289055	−	0.289055i	−0.836706	+	0.547652i	$0.815522\pi$
$374$	−10.4440			−0.540049
$375$		0			0
$376$	7.58258			0.391041
$377$	19.0847	+	19.0847i	0.982911	+	0.982911i
$378$		0			0
$379$			19.7477i			1.01437i	0.861836	+	0.507186i	$0.169314\pi$
$379$			19.7477i			1.01437i	−0.861836	+	0.507186i	$0.830686\pi$
$380$		0			0
$381$		0			0
$382$	28.9564	−	28.9564i	1.48154	−	1.48154i
$383$	5.98888	−	5.98888i	0.306017	−	0.306017i	−0.537345	−	0.843362i	$-0.680573\pi$
$383$	5.98888	−	5.98888i	0.306017	−	0.306017i	0.843362	+	0.537345i	$0.180573\pi$
$384$		0			0
$385$		0			0
$386$		−	8.64064i		−	0.439797i
$387$		0			0
$388$	−15.5826	−	15.5826i	−0.791085	−	0.791085i
$389$	−19.0847			−0.967632			−0.483816	−	0.875170i	$-0.660750\pi$
$389$	−19.0847			−0.967632			−0.483816	+	0.875170i	$0.660750\pi$
$390$		0			0
$391$	2.16515			0.109496
$392$	−10.5115	−	10.5115i	−0.530909	−	0.530909i
$393$		0			0
$394$		−	5.79129i		−	0.291761i
$395$		0			0
$396$		0			0
$397$	15.1216	−	15.1216i	0.758931	−	0.758931i	−0.217197	−	0.976128i	$-0.569691\pi$
$397$	15.1216	−	15.1216i	0.758931	−	0.758931i	0.976128	+	0.217197i	$0.0696914\pi$
$398$	16.6352	−	16.6352i	0.833847	−	0.833847i
$399$		0			0
$400$		0			0
$401$			18.7083i			0.934247i	0.884192	+	0.467124i	$0.154710\pi$
$401$			18.7083i			0.934247i	−0.884192	+	0.467124i	$0.845290\pi$
$402$		0			0
$403$	−2.79129	−	2.79129i	−0.139044	−	0.139044i
$404$	−10.0677			−0.500884
$405$		0			0
$406$	−59.0780			−2.93199
$407$	−9.01703	−	9.01703i	−0.446958	−	0.446958i
$408$		0			0
$409$		−	5.83485i		−	0.288515i	−0.989540	−	0.144257i	$-0.953921\pi$
$409$		−	5.83485i		−	0.288515i	0.989540	−	0.144257i	$-0.0460793\pi$
$410$		0			0
$411$		0			0
$412$	15.5826	−	15.5826i	0.767698	−	0.767698i
$413$	−19.0847	+	19.0847i	−0.939096	+	0.939096i
$414$		0			0
$415$		0			0
$416$		−	29.1523i		−	1.42931i
$417$		0			0
$418$	−8.37386	−	8.37386i	−0.409579	−	0.409579i
$419$	−32.7591			−1.60039			−0.800194	−	0.599741i	$-0.795270\pi$
$419$	−32.7591			−1.60039			−0.800194	+	0.599741i	$0.795270\pi$
$420$		0			0
$421$	12.2523			0.597139			0.298570	−	0.954388i	$-0.403490\pi$
$421$	12.2523			0.597139			0.298570	+	0.954388i	$0.403490\pi$
$422$	27.4697	+	27.4697i	1.33720	+	1.33720i
$423$		0			0
$424$		−	18.1652i		−	0.882178i
$425$		0			0
$426$		0			0
$427$	−2.79129	+	2.79129i	−0.135080	+	0.135080i
$428$	10.4440	−	10.4440i	0.504832	−	0.504832i
$429$		0			0
$430$		0			0
$431$		−	27.7253i		−	1.33548i	−0.744394	−	0.667741i	$-0.767261\pi$
$431$		−	27.7253i		−	1.33548i	0.744394	−	0.667741i	$-0.232739\pi$
$432$		0			0
$433$	−18.3739	−	18.3739i	−0.882992	−	0.882992i	0.110846	−	0.993838i	$-0.464644\pi$
$433$	−18.3739	−	18.3739i	−0.882992	−	0.882992i	−0.993838	+	0.110846i	$0.964644\pi$
$434$	8.64064			0.414764
$435$		0			0
$436$	38.3739			1.83777
$437$	1.73598	+	1.73598i	0.0830433	+	0.0830433i
$438$		0			0
$439$		−	1.41742i		−	0.0676500i	−0.999428	−	0.0338250i	$-0.989231\pi$
$439$		−	1.41742i		−	0.0676500i	0.999428	−	0.0338250i	$-0.0107689\pi$
$440$		0			0
$441$		0			0
$442$	16.1652	−	16.1652i	0.768898	−	0.768898i
$443$	−11.6688	+	11.6688i	−0.554401	+	0.554401i	−0.927708	−	0.373307i	$-0.878224\pi$
$443$	−11.6688	+	11.6688i	−0.554401	+	0.554401i	0.373307	+	0.927708i	$0.378224\pi$
$444$		0			0
$445$		0			0
$446$		−	1.80341i		−	0.0853937i
$447$		0			0
$448$	35.1216	+	35.1216i	1.65934	+	1.65934i
$449$	20.5117			0.968007			0.484003	−	0.875066i	$-0.339182\pi$
$449$	20.5117			0.968007			0.484003	+	0.875066i	$0.339182\pi$
$450$		0			0
$451$	−3.25227			−0.153144
$452$	−3.23042	−	3.23042i	−0.151946	−	0.151946i
$453$		0			0
$454$			36.5390i			1.71486i
$455$		0			0
$456$		0			0
$457$	−5.58258	+	5.58258i	−0.261142	+	0.261142i	−0.825518	−	0.564376i	$-0.809117\pi$
$457$	−5.58258	+	5.58258i	−0.261142	+	0.261142i	0.564376	+	0.825518i	$0.309117\pi$
$458$	37.4025	−	37.4025i	1.74770	−	1.74770i
$459$		0			0
$460$		0			0
$461$			29.5287i			1.37529i	0.726047	+	0.687645i	$0.241355\pi$
$461$			29.5287i			1.37529i	−0.726047	+	0.687645i	$0.758645\pi$
$462$		0			0
$463$	26.1652	+	26.1652i	1.21600	+	1.21600i	0.969022	+	0.246976i	$0.0794369\pi$
$463$	26.1652	+	26.1652i	1.21600	+	1.21600i	0.246976	+	0.969022i	$0.420563\pi$
$464$	12.2474			0.568574
$465$		0			0
$466$	29.1652			1.35105
$467$	−24.0511	−	24.0511i	−1.11295	−	1.11295i	−0.992749	−	0.120202i	$-0.961646\pi$
$467$	−24.0511	−	24.0511i	−1.11295	−	1.11295i	−0.120202	−	0.992749i	$-0.538354\pi$
$468$		0			0
$469$		−	3.25227i		−	0.150176i
$470$		0			0
$471$		0			0
$472$	−8.37386	+	8.37386i	−0.385438	+	0.385438i
$473$	−14.0509	+	14.0509i	−0.646059	+	0.646059i
$474$		0			0
$475$		0			0
$476$			29.1523i			1.33619i
$477$		0			0
$478$	18.9564	+	18.9564i	0.867047	+	0.867047i
$479$	−19.0847			−0.872001			−0.436001	−	0.899946i	$-0.643605\pi$
$479$	−19.0847			−0.872001			−0.436001	+	0.899946i	$0.643605\pi$
$480$		0			0
$481$	27.9129			1.27272
$482$	−24.3741	−	24.3741i	−1.11021	−	1.11021i
$483$		0			0
$484$			21.6261i			0.983006i
$485$		0			0
$486$		0			0
$487$	13.3739	−	13.3739i	0.606028	−	0.606028i	−0.335878	−	0.941906i	$-0.609033\pi$
$487$	13.3739	−	13.3739i	0.606028	−	0.606028i	0.941906	+	0.335878i	$0.109033\pi$
$488$	−1.22474	+	1.22474i	−0.0554416	+	0.0554416i
$489$		0			0
$490$		0			0
$491$			29.5287i			1.33261i	0.745678	+	0.666306i	$0.232126\pi$
$491$			29.5287i			1.33261i	−0.745678	+	0.666306i	$0.767874\pi$
$492$		0			0
$493$	12.7913	+	12.7913i	0.576091	+	0.576091i
$494$	25.9219			1.16628
$495$		0			0
$496$	−1.79129			−0.0804312
$497$	−5.03383	−	5.03383i	−0.225798	−	0.225798i
$498$		0			0
$499$		−	9.33030i		−	0.417682i	−0.977950	−	0.208841i	$-0.933031\pi$
$499$		−	9.33030i		−	0.417682i	0.977950	−	0.208841i	$-0.0669691\pi$
$500$		0			0
$501$		0			0
$502$	−11.1652	+	11.1652i	−0.498325	+	0.498325i
$503$	12.8261	−	12.8261i	0.571888	−	0.571888i	−0.360768	−	0.932656i	$-0.617485\pi$
$503$	12.8261	−	12.8261i	0.571888	−	0.571888i	0.932656	+	0.360768i	$0.117485\pi$
$504$		0			0
$505$		0			0
$506$			3.23042i			0.143610i
$507$		0			0
$508$	13.9564	+	13.9564i	0.619217	+	0.619217i
$509$	−27.3489			−1.21222			−0.606110	−	0.795381i	$-0.707271\pi$
$509$	−27.3489			−1.21222			−0.606110	+	0.795381i	$0.707271\pi$
$510$		0			0
$511$	−18.8348			−0.833205
$512$	−13.7419	−	13.7419i	−0.607311	−	0.607311i
$513$		0			0
$514$			15.3739i			0.678112i
$515$		0			0
$516$		0			0
$517$	5.58258	−	5.58258i	0.245521	−	0.245521i
$518$	−43.2032	+	43.2032i	−1.89824	+	1.89824i
$519$		0			0
$520$		0			0
$521$			9.01703i			0.395043i	0.980299	+	0.197522i	$0.0632893\pi$
$521$			9.01703i			0.395043i	−0.980299	+	0.197522i	$0.936711\pi$
$522$		0			0
$523$	−1.62614	−	1.62614i	−0.0711060	−	0.0711060i	0.670659	−	0.741765i	$-0.266011\pi$
$523$	−1.62614	−	1.62614i	−0.0711060	−	0.0711060i	−0.741765	+	0.670659i	$0.766011\pi$
$524$	62.2879			2.72106
$525$		0			0
$526$	−55.4955			−2.41972
$527$	−1.87083	−	1.87083i	−0.0814946	−	0.0814946i
$528$		0			0
$529$			22.3303i			0.970883i
$530$		0			0
$531$		0			0
$532$	−23.3739	+	23.3739i	−1.01339	+	1.01339i
$533$	5.03383	−	5.03383i	0.218039	−	0.218039i
$534$		0			0
$535$		0			0
$536$		−	1.42701i		−	0.0616376i
$537$		0			0
$538$	40.1216	+	40.1216i	1.72976	+	1.72976i
$539$	−15.4779			−0.666679
$540$		0			0
$541$	35.4955			1.52607			0.763034	−	0.646358i	$-0.223709\pi$
$541$	35.4955			1.52607			0.763034	+	0.646358i	$0.223709\pi$
$542$	1.54779	+	1.54779i	0.0664831	+	0.0664831i
$543$		0			0
$544$		−	19.5390i		−	0.837728i
$545$		0			0
$546$		0			0
$547$	1.04356	−	1.04356i	0.0446194	−	0.0446194i	−0.684445	−	0.729064i	$-0.739955\pi$
$547$	1.04356	−	1.04356i	0.0446194	−	0.0446194i	0.729064	+	0.684445i	$0.239955\pi$
$548$	−39.4082	+	39.4082i	−1.68343	+	1.68343i
$549$		0			0
$550$		0			0
$551$			20.5117i			0.873827i
$552$		0			0
$553$	−3.95644	−	3.95644i	−0.168245	−	0.168245i
$554$	−55.0742			−2.33988
$555$		0			0
$556$	−42.3303			−1.79520
$557$	11.3598	+	11.3598i	0.481331	+	0.481331i	0.905557	−	0.424226i	$-0.139454\pi$
$557$	11.3598	+	11.3598i	0.481331	+	0.481331i	−0.424226	+	0.905557i	$0.639454\pi$
$558$		0			0
$559$		−	43.4955i		−	1.83966i
$560$		0			0
$561$		0			0
$562$	37.3303	−	37.3303i	1.57468	−	1.57468i
$563$	−1.15732	+	1.15732i	−0.0487753	+	0.0487753i	−0.731074	−	0.682298i	$-0.760980\pi$
$563$	−1.15732	+	1.15732i	−0.0487753	+	0.0487753i	0.682298	+	0.731074i	$0.260980\pi$
$564$		0			0
$565$		0			0
$566$		−	55.0742i		−	2.31494i
$567$		0			0
$568$	−2.20871	−	2.20871i	−0.0926755	−	0.0926755i
$569$	17.6577			0.740248			0.370124	−	0.928982i	$-0.379315\pi$
$569$	17.6577			0.740248			0.370124	+	0.928982i	$0.379315\pi$
$570$		0			0
$571$	32.4955			1.35989			0.679946	−	0.733262i	$-0.262003\pi$
$571$	32.4955			1.35989			0.679946	+	0.733262i	$0.262003\pi$
$572$	14.0509	+	14.0509i	0.587496	+	0.587496i
$573$		0			0
$574$			15.5826i			0.650404i
$575$		0			0
$576$		0			0
$577$	−3.37386	+	3.37386i	−0.140456	+	0.140456i	−0.773839	−	0.633383i	$-0.781666\pi$
$577$	−3.37386	+	3.37386i	−0.140456	+	0.140456i	0.633383	+	0.773839i	$0.281666\pi$
$578$	−15.4779	+	15.4779i	−0.643794	+	0.643794i
$579$		0			0
$580$		0			0
$581$			34.9389i			1.44951i
$582$		0			0
$583$	−13.3739	−	13.3739i	−0.553889	−	0.553889i
$584$	−8.26424			−0.341977
$585$		0			0
$586$	14.9564			0.617845
$587$	19.5285	+	19.5285i	0.806027	+	0.806027i	0.984030	−	0.178003i	$-0.0569636\pi$
$587$	19.5285	+	19.5285i	0.806027	+	0.806027i	−0.178003	+	0.984030i	$0.556964\pi$
$588$		0			0
$589$		−	3.00000i		−	0.123613i
$590$		0			0
$591$		0			0
$592$	8.95644	−	8.95644i	0.368107	−	0.368107i
$593$	22.5174	−	22.5174i	0.924677	−	0.924677i	−0.0726780	−	0.997355i	$-0.523155\pi$
$593$	22.5174	−	22.5174i	0.924677	−	0.924677i	0.997355	+	0.0726780i	$0.0231545\pi$
$594$		0			0
$595$		0			0
$596$			53.2708i			2.18206i
$597$		0			0
$598$	−5.00000	−	5.00000i	−0.204465	−	0.204465i
$599$	−17.6577			−0.721473			−0.360736	−	0.932668i	$-0.617475\pi$
$599$	−17.6577			−0.721473			−0.360736	+	0.932668i	$0.617475\pi$
$600$		0			0
$601$	12.2523			0.499781			0.249890	−	0.968274i	$-0.419605\pi$
$601$	12.2523			0.499781			0.249890	+	0.968274i	$0.419605\pi$
$602$	67.3217	+	67.3217i	2.74383	+	2.74383i
$603$		0			0
$604$			5.58258i			0.227152i
$605$		0			0
$606$		0			0
$607$	8.95644	−	8.95644i	0.363531	−	0.363531i	−0.501580	−	0.865111i	$-0.667248\pi$
$607$	8.95644	−	8.95644i	0.363531	−	0.363531i	0.865111	+	0.501580i	$0.167248\pi$
$608$	15.6661	−	15.6661i	0.635343	−	0.635343i
$609$		0			0
$610$		0			0
$611$			17.2813i			0.699126i
$612$		0			0
$613$	−10.0000	−	10.0000i	−0.403896	−	0.403896i	0.475707	−	0.879604i	$-0.342192\pi$
$613$	−10.0000	−	10.0000i	−0.403896	−	0.403896i	−0.879604	+	0.475707i	$0.842192\pi$
$614$	36.3660			1.46761
$615$		0			0
$616$	−12.3303			−0.496802
$617$	−10.3766	−	10.3766i	−0.417747	−	0.417747i	0.466680	−	0.884427i	$-0.345450\pi$
$617$	−10.3766	−	10.3766i	−0.417747	−	0.417747i	−0.884427	+	0.466680i	$0.845450\pi$
$618$		0			0
$619$		−	10.4174i		−	0.418712i	−0.977840	−	0.209356i	$-0.932863\pi$
$619$		−	10.4174i		−	0.418712i	0.977840	−	0.209356i	$-0.0671367\pi$
$620$		0			0
$621$		0			0
$622$	−42.9129	+	42.9129i	−1.72065	+	1.72065i
$623$	15.1015	−	15.1015i	0.605028	−	0.605028i
$624$		0			0
$625$		0			0
$626$			3.60681i			0.144157i
$627$		0			0
$628$	−21.7477	−	21.7477i	−0.867829	−	0.867829i
$629$	18.7083			0.745948
$630$		0			0
$631$	12.2523			0.487755			0.243878	−	0.969806i	$-0.421580\pi$
$631$	12.2523			0.487755			0.243878	+	0.969806i	$0.421580\pi$
$632$	−1.73598	−	1.73598i	−0.0690537	−	0.0690537i
$633$		0			0
$634$		−	10.2087i		−	0.405440i
$635$		0			0
$636$		0			0
$637$	23.9564	−	23.9564i	0.949189	−	0.949189i
$638$	−19.0847	+	19.0847i	−0.755570	+	0.755570i
$639$		0			0
$640$		0			0
$641$		−	37.4166i		−	1.47787i	−0.673779	−	0.738933i	$-0.735330\pi$
$641$		−	37.4166i		−	1.47787i	0.673779	−	0.738933i	$-0.264670\pi$
$642$		0			0
$643$	2.79129	+	2.79129i	0.110078	+	0.110078i	0.760000	−	0.649923i	$-0.225199\pi$
$643$	2.79129	+	2.79129i	0.110078	+	0.110078i	−0.649923	+	0.760000i	$0.725199\pi$
$644$	9.01703			0.355321
$645$		0			0
$646$	17.3739			0.683566
$647$	−3.53939	−	3.53939i	−0.139148	−	0.139148i	0.634102	−	0.773250i	$-0.281370\pi$
$647$	−3.53939	−	3.53939i	−0.139148	−	0.139148i	−0.773250	+	0.634102i	$0.781370\pi$
$648$		0			0
$649$			12.3303i			0.484007i
$650$		0			0
$651$		0			0
$652$	−13.9564	+	13.9564i	−0.546576	+	0.546576i
$653$	−19.9330	+	19.9330i	−0.780040	+	0.780040i	−0.979837	−	0.199797i	$-0.935972\pi$
$653$	−19.9330	+	19.9330i	−0.780040	+	0.780040i	0.199797	+	0.979837i	$0.435972\pi$
$654$		0			0
$655$		0			0
$656$		−	3.23042i		−	0.126127i
$657$		0			0
$658$	−26.7477	−	26.7477i	−1.04273	−	1.04273i
$659$	−3.98320			−0.155164			−0.0775818	−	0.996986i	$-0.524720\pi$
$659$	−3.98320			−0.155164			−0.0775818	+	0.996986i	$0.524720\pi$
$660$		0			0
$661$	−31.4955			−1.22503			−0.612516	−	0.790459i	$-0.709842\pi$
$661$	−31.4955			−1.22503			−0.612516	+	0.790459i	$0.709842\pi$
$662$	22.8263	+	22.8263i	0.887171	+	0.887171i
$663$		0			0
$664$			15.3303i			0.594931i
$665$		0			0
$666$		0			0
$667$	3.95644	−	3.95644i	0.153194	−	0.153194i
$668$	−43.3914	+	43.3914i	−1.67886	+	1.67886i
$669$		0			0
$670$		0			0
$671$			1.80341i			0.0696197i
$672$		0			0
$673$	−9.53901	−	9.53901i	−0.367702	−	0.367702i	0.498937	−	0.866639i	$-0.333724\pi$
$673$	−9.53901	−	9.53901i	−0.367702	−	0.367702i	−0.866639	+	0.498937i	$0.833724\pi$
$674$	70.5521			2.71757
$675$		0			0
$676$	−7.20871			−0.277258
$677$	−17.4161	−	17.4161i	−0.669356	−	0.669356i	0.288211	−	0.957567i	$-0.406940\pi$
$677$	−17.4161	−	17.4161i	−0.669356	−	0.669356i	−0.957567	+	0.288211i	$0.906940\pi$
$678$		0			0
$679$			31.1652i			1.19601i
$680$		0			0
$681$		0			0
$682$	2.79129	−	2.79129i	0.106884	−	0.106884i
$683$	7.41589	−	7.41589i	0.283761	−	0.283761i	−0.550846	−	0.834607i	$-0.685695\pi$
$683$	7.41589	−	7.41589i	0.283761	−	0.283761i	0.834607	+	0.550846i	$0.185695\pi$
$684$		0			0
$685$		0			0
$686$			13.6745i			0.522093i
$687$		0			0
$688$	−13.9564	−	13.9564i	−0.532084	−	0.532084i
$689$	41.3998			1.57721
$690$		0			0
$691$	15.7477			0.599072			0.299536	−	0.954085i	$-0.403168\pi$
$691$	15.7477			0.599072			0.299536	+	0.954085i	$0.403168\pi$
$692$	−32.5709	−	32.5709i	−1.23816	−	1.23816i
$693$		0			0
$694$			49.4955i			1.87882i
$695$		0			0
$696$		0			0
$697$	3.37386	−	3.37386i	0.127794	−	0.127794i
$698$	44.2397	−	44.2397i	1.67450	−	1.67450i
$699$		0			0
$700$		0			0
$701$			40.3492i			1.52397i	0.647597	+	0.761983i	$0.275774\pi$
$701$			40.3492i			1.52397i	−0.647597	+	0.761983i	$0.724226\pi$
$702$		0			0
$703$	15.0000	+	15.0000i	0.565736	+	0.565736i
$704$	22.6915			0.855218
$705$		0			0
$706$	8.00000			0.301084
$707$	10.0677	+	10.0677i	0.378633	+	0.378633i
$708$		0			0
$709$		−	30.6606i		−	1.15148i	−0.817632	−	0.575742i	$-0.804713\pi$
$709$		−	30.6606i		−	1.15148i	0.817632	−	0.575742i	$-0.195287\pi$
$710$		0			0
$711$		0			0
$712$	6.62614	−	6.62614i	0.248325	−	0.248325i
$713$	−0.578661	+	0.578661i	−0.0216710	+	0.0216710i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$	−23.3739	−	23.3739i	−0.872305	−	0.872305i
$719$	−15.1015			−0.563190			−0.281595	−	0.959533i	$-0.590863\pi$
$719$	−15.1015			−0.563190			−0.281595	+	0.959533i	$0.590863\pi$
$720$		0			0
$721$	−31.1652			−1.16065
$722$	−15.4779	−	15.4779i	−0.576027	−	0.576027i
$723$		0			0
$724$		−	49.5390i		−	1.84110i
$725$		0			0
$726$		0			0
$727$	−18.8348	+	18.8348i	−0.698546	+	0.698546i	−0.964097	−	0.265551i	$-0.914446\pi$
$727$	−18.8348	+	18.8348i	−0.698546	+	0.698546i	0.265551	+	0.964097i	$0.414446\pi$
$728$	19.0847	−	19.0847i	0.707325	−	0.707325i
$729$		0			0
$730$		0			0
$731$		−	29.1523i		−	1.07824i
$732$		0			0
$733$	−35.5826	−	35.5826i	−1.31427	−	1.31427i	−0.918234	−	0.396039i	$-0.870385\pi$
$733$	−35.5826	−	35.5826i	−1.31427	−	1.31427i	−0.396039	−	0.918234i	$-0.629615\pi$
$734$	43.2032			1.59466
$735$		0			0
$736$	−6.04356			−0.222769
$737$	−1.05062	−	1.05062i	−0.0387001	−	0.0387001i
$738$		0			0
$739$		−	30.4955i		−	1.12179i	−0.827886	−	0.560897i	$-0.810456\pi$
$739$		−	30.4955i		−	1.12179i	0.827886	−	0.560897i	$-0.189544\pi$
$740$		0			0
$741$		0			0
$742$	−64.0780	+	64.0780i	−2.35238	+	2.35238i
$743$	−27.0792	+	27.0792i	−0.993441	+	0.993441i	−0.999979	−	0.00653793i	$-0.997919\pi$
$743$	−27.0792	+	27.0792i	−0.993441	+	0.993441i	0.00653793	+	0.999979i	$0.497919\pi$
$744$		0			0
$745$		0			0
$746$			17.2813i			0.632712i
$747$		0			0
$748$	9.41742	+	9.41742i	0.344335	+	0.344335i
$749$	−20.8881			−0.763234
$750$		0			0
$751$	−17.7477			−0.647624			−0.323812	−	0.946121i	$-0.604964\pi$
$751$	−17.7477			−0.647624			−0.323812	+	0.946121i	$0.604964\pi$
$752$	5.54506	+	5.54506i	0.202208	+	0.202208i
$753$		0			0
$754$		−	59.0780i		−	2.15149i
$755$		0			0
$756$		0			0
$757$	5.00000	−	5.00000i	0.181728	−	0.181728i	−0.610380	−	0.792108i	$-0.708983\pi$
$757$	5.00000	−	5.00000i	0.181728	−	0.181728i	0.792108	+	0.610380i	$0.208983\pi$
$758$	30.5653	−	30.5653i	1.11018	−	1.11018i
$759$		0			0
$760$		0			0
$761$		−	27.7253i		−	1.00504i	−0.864565	−	0.502521i	$-0.832406\pi$
$761$		−	27.7253i		−	1.00504i	0.864565	−	0.502521i	$-0.167594\pi$
$762$		0			0
$763$	−38.3739	−	38.3739i	−1.38923	−	1.38923i
$764$	−52.2202			−1.88926
$765$		0			0
$766$	−18.5390			−0.669842
$767$	−19.0847	−	19.0847i	−0.689108	−	0.689108i
$768$		0			0
$769$		−	9.33030i		−	0.336459i	−0.985748	−	0.168230i	$-0.946195\pi$
$769$		−	9.33030i		−	0.336459i	0.985748	−	0.168230i	$-0.0538050\pi$
$770$		0			0
$771$		0			0
$772$	−7.79129	+	7.79129i	−0.280415	+	0.280415i
$773$	−29.3265	+	29.3265i	−1.05480	+	1.05480i	−0.0563904	+	0.998409i	$0.517959\pi$
$773$	−29.3265	+	29.3265i	−1.05480	+	1.05480i	−0.998409	+	0.0563904i	$0.982041\pi$
$774$		0			0
$775$		0			0
$776$			13.6745i			0.490885i
$777$		0			0
$778$	29.5390	+	29.5390i	1.05902	+	1.05902i
$779$	5.41022			0.193841
$780$		0			0
$781$	−3.25227			−0.116375
$782$	−3.35119	−	3.35119i	−0.119838	−	0.119838i
$783$		0			0
$784$		−	15.3739i		−	0.549067i
$785$		0			0
$786$		0			0
$787$	5.46099	−	5.46099i	0.194663	−	0.194663i	−0.603044	−	0.797708i	$-0.706046\pi$
$787$	5.46099	−	5.46099i	0.194663	−	0.194663i	0.797708	+	0.603044i	$0.206046\pi$
$788$	−5.22202	+	5.22202i	−0.186027	+	0.186027i
$789$		0			0
$790$		0			0
$791$			6.46084i			0.229721i
$792$		0			0
$793$	−2.79129	−	2.79129i	−0.0991215	−	0.0991215i
$794$	−46.8100			−1.66122
$795$		0			0
$796$	−30.0000			−1.06332
$797$	−4.96640	−	4.96640i	−0.175919	−	0.175919i	0.613655	−	0.789574i	$-0.289699\pi$
$797$	−4.96640	−	4.96640i	−0.175919	−	0.175919i	−0.789574	+	0.613655i	$0.789699\pi$
$798$		0			0
$799$			11.5826i			0.409762i
$800$		0			0
$801$		0			0
$802$	28.9564	−	28.9564i	1.02249	−	1.02249i
$803$	−6.08445	+	6.08445i	−0.214715	+	0.214715i
$804$		0			0
$805$		0			0
$806$			8.64064i			0.304353i
$807$		0			0
$808$	4.41742	+	4.41742i	0.155404	+	0.155404i
$809$	−35.6132			−1.25209			−0.626046	−	0.779786i	$-0.715328\pi$
$809$	−35.6132			−1.25209			−0.626046	+	0.779786i	$0.715328\pi$
$810$		0			0
$811$	−31.4955			−1.10595			−0.552977	−	0.833196i	$-0.686508\pi$
$811$	−31.4955			−1.10595			−0.552977	+	0.833196i	$0.686508\pi$
$812$	53.2708	+	53.2708i	1.86944	+	1.86944i
$813$		0			0
$814$			27.9129i			0.978346i
$815$		0			0
$816$		0			0
$817$	23.3739	−	23.3739i	0.817748	−	0.817748i
$818$	−9.03110	+	9.03110i	−0.315765	+	0.315765i
$819$		0			0
$820$		0			0
$821$		−	22.3151i		−	0.778802i	−0.921068	−	0.389401i	$-0.872682\pi$
$821$		−	22.3151i		−	0.778802i	0.921068	−	0.389401i	$-0.127318\pi$
$822$		0			0
$823$	1.04356	+	1.04356i	0.0363762	+	0.0363762i	0.725061	−	0.688685i	$-0.241812\pi$
$823$	1.04356	+	1.04356i	0.0363762	+	0.0363762i	−0.688685	+	0.725061i	$0.741812\pi$
$824$	−13.6745			−0.476372
$825$		0			0
$826$	59.0780			2.05559
$827$	16.9723	+	16.9723i	0.590185	+	0.590185i	0.937681	−	0.347496i	$-0.112968\pi$
$827$	16.9723	+	16.9723i	0.590185	+	0.590185i	−0.347496	+	0.937681i	$0.612968\pi$
$828$		0			0
$829$			7.25227i			0.251882i	0.992038	+	0.125941i	$0.0401950\pi$
$829$			7.25227i			0.251882i	−0.992038	+	0.125941i	$0.959805\pi$
$830$		0			0
$831$		0			0
$832$	−35.1216	+	35.1216i	−1.21762	+	1.21762i
$833$	16.0565	−	16.0565i	0.556326	−	0.556326i
$834$		0			0
$835$		0			0
$836$			15.1015i			0.522295i
$837$		0			0
$838$	50.7042	+	50.7042i	1.75155	+	1.75155i
$839$	−54.6978			−1.88838			−0.944190	−	0.329402i	$-0.893153\pi$
$839$	−54.6978			−1.88838			−0.944190	+	0.329402i	$0.893153\pi$
$840$		0			0
$841$	17.7477			0.611991
$842$	−18.9639	−	18.9639i	−0.653539	−	0.653539i
$843$		0			0
$844$		−	49.5390i		−	1.70520i
$845$		0			0
$846$		0			0
$847$	21.6261	−	21.6261i	0.743083	−	0.743083i
$848$	13.2840	−	13.2840i	0.456174	−	0.456174i
$849$		0			0
$850$		0			0
$851$		−	5.78661i		−	0.198362i
$852$		0			0
$853$	32.3303	+	32.3303i	1.10697	+	1.10697i	0.993547	+	0.113422i	$0.0361811\pi$
$853$	32.3303	+	32.3303i	1.10697	+	1.10697i	0.113422	+	0.993547i	$0.463819\pi$
$854$	8.64064			0.295677
$855$		0			0
$856$	−9.16515			−0.313258
$857$	8.70806	+	8.70806i	0.297462	+	0.297462i	0.840019	−	0.542557i	$-0.182544\pi$
$857$	8.70806	+	8.70806i	0.297462	+	0.297462i	−0.542557	+	0.840019i	$0.682544\pi$
$858$		0			0
$859$			27.6606i			0.943768i	0.881661	+	0.471884i	$0.156426\pi$
$859$			27.6606i			0.943768i	−0.881661	+	0.471884i	$0.843574\pi$
$860$		0			0
$861$		0			0
$862$	−42.9129	+	42.9129i	−1.46162	+	1.46162i
$863$	−33.6075	+	33.6075i	−1.14401	+	1.14401i	−0.156303	+	0.987709i	$0.549958\pi$
$863$	−33.6075	+	33.6075i	−1.14401	+	1.14401i	−0.987709	+	0.156303i	$0.950042\pi$
$864$		0			0
$865$		0			0
$866$			56.8776i			1.93278i
$867$		0			0
$868$	−7.79129	−	7.79129i	−0.264454	−	0.264454i
$869$	−2.55619			−0.0867129
$870$		0			0
$871$	3.25227			0.110199
$872$	−16.8375	−	16.8375i	−0.570188	−	0.570188i
$873$		0			0
$874$		−	5.37386i		−	0.181774i
$875$		0			0
$876$		0			0
$877$	−7.79129	+	7.79129i	−0.263093	+	0.263093i	−0.826309	−	0.563216i	$-0.809564\pi$
$877$	−7.79129	+	7.79129i	−0.263093	+	0.263093i	0.563216	+	0.826309i	$0.309564\pi$
$878$	−2.19387	+	2.19387i	−0.0740395	+	0.0740395i
$879$		0			0
$880$		0			0
$881$			13.2981i			0.448023i	0.974586	+	0.224012i	$0.0719154\pi$
$881$			13.2981i			0.448023i	−0.974586	+	0.224012i	$0.928085\pi$
$882$		0			0
$883$	11.6261	+	11.6261i	0.391251	+	0.391251i	0.875133	−	0.483882i	$-0.160774\pi$
$883$	11.6261	+	11.6261i	0.391251	+	0.391251i	−0.483882	+	0.875133i	$0.660774\pi$
$884$	−29.1523			−0.980499
$885$		0			0
$886$	36.1216			1.21353
$887$	5.85403	+	5.85403i	0.196559	+	0.196559i	0.798523	−	0.601964i	$-0.205615\pi$
$887$	5.85403	+	5.85403i	0.196559	+	0.196559i	−0.601964	+	0.798523i	$0.705615\pi$
$888$		0			0
$889$		−	27.9129i		−	0.936168i
$890$		0			0
$891$		0			0
$892$	−1.62614	+	1.62614i	−0.0544471	+	0.0544471i
$893$	−9.28672	+	9.28672i	−0.310768	+	0.310768i
$894$		0			0
$895$		0			0
$896$		−	50.4168i		−	1.68431i
$897$		0			0
$898$	−31.7477	−	31.7477i	−1.05944	−	1.05944i
$899$	−6.83723			−0.228034
$900$		0			0
$901$	27.7477			0.924411
$902$	5.03383	+	5.03383i	0.167608	+	0.167608i
$903$		0			0
$904$			2.83485i			0.0942857i
$905$		0			0
$906$		0			0
$907$	27.9129	−	27.9129i	0.926832	−	0.926832i	−0.0706680	−	0.997500i	$-0.522513\pi$
$907$	27.9129	−	27.9129i	0.926832	−	0.926832i	0.997500	+	0.0706680i	$0.0225131\pi$
$908$	32.9473	−	32.9473i	1.09340	−	1.09340i
$909$		0			0
$910$		0			0
$911$		−	16.9049i		−	0.560084i	−0.959988	−	0.280042i	$-0.909652\pi$
$911$		−	16.9049i		−	0.560084i	0.959988	−	0.280042i	$-0.0903483\pi$
$912$		0			0
$913$	11.2867	+	11.2867i	0.373537	+	0.373537i
$914$	17.2813			0.571614
$915$		0			0
$916$	−67.4519			−2.22867
$917$	−62.2879	−	62.2879i	−2.05693	−	2.05693i
$918$		0			0
$919$			24.0000i			0.791687i	0.918318	+	0.395843i	$0.129548\pi$
$919$			24.0000i			0.791687i	−0.918318	+	0.395843i	$0.870452\pi$
$920$		0			0
$921$		0			0
$922$	45.7042	−	45.7042i	1.50519	−	1.50519i
$923$	5.03383	−	5.03383i	0.165690	−	0.165690i
$924$		0			0
$925$		0			0
$926$		−	80.9962i		−	2.66170i
$927$		0			0
$928$	−35.7042	−	35.7042i	−1.17205	−	1.17205i
$929$	32.7591			1.07479			0.537396	−	0.843330i	$-0.319408\pi$
$929$	32.7591			1.07479			0.537396	+	0.843330i	$0.319408\pi$
$930$		0			0
$931$	25.7477			0.843848
$932$	−26.2983	−	26.2983i	−0.861430	−	0.861430i
$933$		0			0
$934$			74.4519i			2.43614i
$935$		0			0
$936$		0			0
$937$	−26.7477	+	26.7477i	−0.873810	+	0.873810i	−0.992885	−	0.119075i	$-0.962007\pi$
$937$	−26.7477	+	26.7477i	−0.873810	+	0.873810i	0.119075	+	0.992885i	$0.462007\pi$
$938$	−5.03383	+	5.03383i	−0.164360	+	0.164360i
$939$		0			0
$940$		0			0
$941$			29.5287i			0.962609i	0.876554	+	0.481304i	$0.159837\pi$
$941$			29.5287i			0.962609i	−0.876554	+	0.481304i	$0.840163\pi$
$942$		0			0
$943$	−1.04356	−	1.04356i	−0.0339830	−	0.0339830i
$944$	−12.2474			−0.398621
$945$		0			0
$946$	43.4955			1.41416
$947$	−17.2139	−	17.2139i	−0.559375	−	0.559375i	0.369754	−	0.929129i	$-0.379442\pi$
$947$	−17.2139	−	17.2139i	−0.559375	−	0.559375i	−0.929129	+	0.369754i	$0.879442\pi$
$948$		0			0
$949$		−	18.8348i		−	0.611405i
$950$		0			0
$951$		0			0
$952$	12.7913	−	12.7913i	0.414568	−	0.414568i
$953$	16.5003	−	16.5003i	0.534499	−	0.534499i	−0.387409	−	0.921908i	$-0.626630\pi$
$953$	16.5003	−	16.5003i	0.534499	−	0.534499i	0.921908	+	0.387409i	$0.126630\pi$
$954$		0			0
$955$		0			0
$956$		−	34.1862i		−	1.10566i
$957$		0			0
$958$	29.5390	+	29.5390i	0.954362	+	0.954362i
$959$	78.8164			2.54511
$960$		0			0
$961$	−30.0000			−0.967742
$962$	−43.2032	−	43.2032i	−1.39293	−	1.39293i
$963$		0			0
$964$			43.9564i			1.41574i
$965$		0			0
$966$		0			0
$967$	17.3303	−	17.3303i	0.557305	−	0.557305i	−0.371234	−	0.928539i	$-0.621065\pi$
$967$	17.3303	−	17.3303i	0.557305	−	0.557305i	0.928539	+	0.371234i	$0.121065\pi$
$968$	9.48899	−	9.48899i	0.304988	−	0.304988i
$969$		0			0
$970$		0			0
$971$			18.7083i			0.600377i	0.953880	+	0.300189i	$0.0970497\pi$
$971$			18.7083i			0.600377i	−0.953880	+	0.300189i	$0.902950\pi$
$972$		0			0
$973$	42.3303	+	42.3303i	1.35705	+	1.35705i
$974$	−41.3998			−1.32653
$975$		0			0
$976$	−1.79129			−0.0573377
$977$	35.8547	+	35.8547i	1.14709	+	1.14709i	0.987121	+	0.159972i	$0.0511406\pi$
$977$	35.8547	+	35.8547i	1.14709	+	1.14709i	0.159972	+	0.987121i	$0.448859\pi$
$978$		0			0
$979$		−	9.75682i		−	0.311829i
$980$		0			0
$981$		0			0
$982$	45.7042	−	45.7042i	1.45848	−	1.45848i
$983$	19.6633	−	19.6633i	0.627163	−	0.627163i	−0.320190	−	0.947353i	$-0.603747\pi$
$983$	19.6633	−	19.6633i	0.627163	−	0.627163i	0.947353	+	0.320190i	$0.103747\pi$
$984$		0			0
$985$		0			0
$986$		−	39.5964i		−	1.26101i
$987$		0			0
$988$	−23.3739	−	23.3739i	−0.743622	−	0.743622i
$989$	−9.01703			−0.286725
$990$		0			0
$991$	45.7477			1.45322			0.726612	−	0.687048i	$-0.241094\pi$
$991$	45.7477			1.45322			0.726612	+	0.687048i	$0.241094\pi$
$992$	5.22202	+	5.22202i	0.165799	+	0.165799i
$993$		0			0
$994$			15.5826i			0.494249i
$995$		0			0
$996$		0			0
$997$	−12.2087	+	12.2087i	−0.386654	+	0.386654i	−0.873492	−	0.486838i	$-0.838150\pi$
$997$	−12.2087	+	12.2087i	−0.386654	+	0.386654i	0.486838	+	0.873492i	$0.338150\pi$
$998$	−14.4413	+	14.4413i	−0.457132	+	0.457132i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.f.i.593.1		8
3.2	odd	2	inner	675.2.f.i.593.4		8
5.2	odd	4	inner	675.2.f.i.107.4		8
5.3	odd	4		135.2.f.a.107.1	yes	8
5.4	even	2		135.2.f.a.53.4	yes	8
15.2	even	4	inner	675.2.f.i.107.1		8
15.8	even	4		135.2.f.a.107.4	yes	8
15.14	odd	2		135.2.f.a.53.1	✓	8
20.3	even	4		2160.2.w.d.1457.1		8
20.19	odd	2		2160.2.w.d.593.3		8
45.4	even	6		405.2.m.c.188.1		16
45.13	odd	12		405.2.m.c.107.1		16
45.14	odd	6		405.2.m.c.188.4		16
45.23	even	12		405.2.m.c.107.4		16
45.29	odd	6		405.2.m.c.53.1		16
45.34	even	6		405.2.m.c.53.4		16
45.38	even	12		405.2.m.c.377.1		16
45.43	odd	12		405.2.m.c.377.4		16
60.23	odd	4		2160.2.w.d.1457.4		8
60.59	even	2		2160.2.w.d.593.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.f.a.53.1	✓	8	15.14	odd	2
135.2.f.a.53.4	yes	8	5.4	even	2
135.2.f.a.107.1	yes	8	5.3	odd	4
135.2.f.a.107.4	yes	8	15.8	even	4
405.2.m.c.53.1		16	45.29	odd	6
405.2.m.c.53.4		16	45.34	even	6
405.2.m.c.107.1		16	45.13	odd	12
405.2.m.c.107.4		16	45.23	even	12
405.2.m.c.188.1		16	45.4	even	6
405.2.m.c.188.4		16	45.14	odd	6
405.2.m.c.377.1		16	45.38	even	12
405.2.m.c.377.4		16	45.43	odd	12
675.2.f.i.107.1		8	15.2	even	4	inner
675.2.f.i.107.4		8	5.2	odd	4	inner
675.2.f.i.593.1		8	1.1	even	1	trivial
675.2.f.i.593.4		8	3.2	odd	2	inner
2160.2.w.d.593.2		8	60.59	even	2
2160.2.w.d.593.3		8	20.19	odd	2
2160.2.w.d.1457.1		8	20.3	even	4
2160.2.w.d.1457.4		8	60.23	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.54779 - 1.54779i) q^{2} +2.79129i q^{4} +(2.79129 - 2.79129i) q^{7} +(1.22474 - 1.22474i) q^{8} -1.80341i q^{11} +(2.79129 + 2.79129i) q^{13} -8.64064 q^{14} +1.79129 q^{16} +(1.87083 + 1.87083i) q^{17} +3.00000i q^{19} +(-2.79129 + 2.79129i) q^{22} +(0.578661 - 0.578661i) q^{23} -8.64064i q^{26} +(7.79129 + 7.79129i) q^{28} +6.83723 q^{29} -1.00000 q^{31} +(-5.22202 - 5.22202i) q^{32} -5.79129i q^{34} +(5.00000 - 5.00000i) q^{37} +(4.64336 - 4.64336i) q^{38} -1.80341i q^{41} +(-7.79129 - 7.79129i) q^{43} +5.03383 q^{44} -1.79129 q^{46} +(3.09557 + 3.09557i) q^{47} -8.58258i q^{49} +(-7.79129 + 7.79129i) q^{52} +(7.41589 - 7.41589i) q^{53} -6.83723i q^{56} +(-10.5826 - 10.5826i) q^{58} -6.83723 q^{59} -1.00000 q^{61} +(1.54779 + 1.54779i) q^{62} +12.5826i q^{64} +(0.582576 - 0.582576i) q^{67} +(-5.22202 + 5.22202i) q^{68} -1.80341i q^{71} +(-3.37386 - 3.37386i) q^{73} -15.4779 q^{74} -8.37386 q^{76} +(-5.03383 - 5.03383i) q^{77} -1.41742i q^{79} +(-2.79129 + 2.79129i) q^{82} +(-6.25857 + 6.25857i) q^{83} +24.1185i q^{86} +(-2.20871 - 2.20871i) q^{88} +5.41022 q^{89} +15.5826 q^{91} +(1.61521 + 1.61521i) q^{92} -9.58258i q^{94} +(-5.58258 + 5.58258i) q^{97} +(-13.2840 + 13.2840i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{7} + 4 q^{13} - 4 q^{16} - 4 q^{22} + 44 q^{28} - 8 q^{31} + 40 q^{37} - 44 q^{43} + 4 q^{46} - 44 q^{52} - 48 q^{58} - 8 q^{61} - 32 q^{67} + 28 q^{73} - 12 q^{76} - 4 q^{82} - 36 q^{88} + 88 q^{91}+ \cdots - 8 q^{97}+O(q^{100}) \) 8 * q + 4 * q^7 + 4 * q^13 - 4 * q^16 - 4 * q^22 + 44 * q^28 - 8 * q^31 + 40 * q^37 - 44 * q^43 + 4 * q^46 - 44 * q^52 - 48 * q^58 - 8 * q^61 - 32 * q^67 + 28 * q^73 - 12 * q^76 - 4 * q^82 - 36 * q^88 + 88 * q^91 - 8 * q^97

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