LMFDB - Embedded newform 588.3.g.a.295.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,3,Mod(295,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.295"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	588.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-2,0,-4,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$16.0218395444$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			295.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	588.295
Dual form			588.3.g.a.295.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.73205i) q^{2} -1.73205i q^{3} +(-2.00000 + 3.46410i) q^{4} -5.00000 q^{5} +(-3.00000 + 1.73205i) q^{6} +8.00000 q^{8} -3.00000 q^{9} +(5.00000 + 8.66025i) q^{10} -5.19615i q^{11} +(6.00000 + 3.46410i) q^{12} -16.0000 q^{13} +8.66025i q^{15} +(-8.00000 - 13.8564i) q^{16} +4.00000 q^{17} +(3.00000 + 5.19615i) q^{18} +27.7128i q^{19} +(10.0000 - 17.3205i) q^{20} +(-9.00000 + 5.19615i) q^{22} +20.7846i q^{23} -13.8564i q^{24} +(16.0000 + 27.7128i) q^{26} +5.19615i q^{27} +37.0000 q^{29} +(15.0000 - 8.66025i) q^{30} -19.0526i q^{31} +(-16.0000 + 27.7128i) q^{32} -9.00000 q^{33} +(-4.00000 - 6.92820i) q^{34} +(6.00000 - 10.3923i) q^{36} +68.0000 q^{37} +(48.0000 - 27.7128i) q^{38} +27.7128i q^{39} -40.0000 q^{40} +40.0000 q^{41} -24.2487i q^{43} +(18.0000 + 10.3923i) q^{44} +15.0000 q^{45} +(36.0000 - 20.7846i) q^{46} -45.0333i q^{47} +(-24.0000 + 13.8564i) q^{48} -6.92820i q^{51} +(32.0000 - 55.4256i) q^{52} +73.0000 q^{53} +(9.00000 - 5.19615i) q^{54} +25.9808i q^{55} +48.0000 q^{57} +(-37.0000 - 64.0859i) q^{58} +29.4449i q^{59} +(-30.0000 - 17.3205i) q^{60} -82.0000 q^{61} +(-33.0000 + 19.0526i) q^{62} +64.0000 q^{64} +80.0000 q^{65} +(9.00000 + 15.5885i) q^{66} +79.6743i q^{67} +(-8.00000 + 13.8564i) q^{68} +36.0000 q^{69} -72.7461i q^{71} -24.0000 q^{72} -94.0000 q^{73} +(-68.0000 - 117.779i) q^{74} +(-96.0000 - 55.4256i) q^{76} +(48.0000 - 27.7128i) q^{78} +8.66025i q^{79} +(40.0000 + 69.2820i) q^{80} +9.00000 q^{81} +(-40.0000 - 69.2820i) q^{82} +133.368i q^{83} -20.0000 q^{85} +(-42.0000 + 24.2487i) q^{86} -64.0859i q^{87} -41.5692i q^{88} +58.0000 q^{89} +(-15.0000 - 25.9808i) q^{90} +(-72.0000 - 41.5692i) q^{92} -33.0000 q^{93} +(-78.0000 + 45.0333i) q^{94} -138.564i q^{95} +(48.0000 + 27.7128i) q^{96} +47.0000 q^{97} +15.5885i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 4 q^{4} - 10 q^{5} - 6 q^{6} + 16 q^{8} - 6 q^{9} + 10 q^{10} + 12 q^{12} - 32 q^{13} - 16 q^{16} + 8 q^{17} + 6 q^{18} + 20 q^{20} - 18 q^{22} + 32 q^{26} + 74 q^{29} + 30 q^{30} - 32 q^{32}+ \cdots + 94 q^{97}+O(q^{100}) $ 2 * q - 2 * q^2 - 4 * q^4 - 10 * q^5 - 6 * q^6 + 16 * q^8 - 6 * q^9 + 10 * q^10 + 12 * q^12 - 32 * q^13 - 16 * q^16 + 8 * q^17 + 6 * q^18 + 20 * q^20 - 18 * q^22 + 32 * q^26 + 74 * q^29 + 30 * q^30 - 32 * q^32 - 18 * q^33 - 8 * q^34 + 12 * q^36 + 136 * q^37 + 96 * q^38 - 80 * q^40 + 80 * q^41 + 36 * q^44 + 30 * q^45 + 72 * q^46 - 48 * q^48 + 64 * q^52 + 146 * q^53 + 18 * q^54 + 96 * q^57 - 74 * q^58 - 60 * q^60 - 164 * q^61 - 66 * q^62 + 128 * q^64 + 160 * q^65 + 18 * q^66 - 16 * q^68 + 72 * q^69 - 48 * q^72 - 188 * q^73 - 136 * q^74 - 192 * q^76 + 96 * q^78 + 80 * q^80 + 18 * q^81 - 80 * q^82 - 40 * q^85 - 84 * q^86 + 116 * q^89 - 30 * q^90 - 144 * q^92 - 66 * q^93 - 156 * q^94 + 96 * q^96 + 94 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$2$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$5$	−5.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$5$	−5.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$6$	−3.00000	+	1.73205i	−0.500000	+	0.288675i
$7$		0			0
$7$		0			0
$8$	8.00000			1.00000
$9$	−3.00000			−0.333333
$10$	5.00000	+	8.66025i	0.500000	+	0.866025i
$11$		−	5.19615i		−	0.472377i	−0.971707	−	0.236189i	$-0.924102\pi$
$11$		−	5.19615i		−	0.472377i	0.971707	−	0.236189i	$-0.0758984\pi$
$12$	6.00000	+	3.46410i	0.500000	+	0.288675i
$13$	−16.0000			−1.23077			−0.615385	−	0.788227i	$-0.710999\pi$
$13$	−16.0000			−1.23077			−0.615385	+	0.788227i	$0.710999\pi$
$14$		0			0
$15$			8.66025i			0.577350i
$16$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$17$	4.00000			0.235294			0.117647	−	0.993055i	$-0.462465\pi$
$17$	4.00000			0.235294			0.117647	+	0.993055i	$0.462465\pi$
$18$	3.00000	+	5.19615i	0.166667	+	0.288675i
$19$			27.7128i			1.45857i	0.684211	+	0.729285i	$0.260147\pi$
$19$			27.7128i			1.45857i	−0.684211	+	0.729285i	$0.739853\pi$
$20$	10.0000	−	17.3205i	0.500000	−	0.866025i
$21$		0			0
$22$	−9.00000	+	5.19615i	−0.409091	+	0.236189i
$23$			20.7846i			0.903679i	0.892099	+	0.451839i	$0.149232\pi$
$23$			20.7846i			0.903679i	−0.892099	+	0.451839i	$0.850768\pi$
$24$		−	13.8564i		−	0.577350i
$25$		0			0
$26$	16.0000	+	27.7128i	0.615385	+	1.06588i
$27$			5.19615i			0.192450i
$28$		0			0
$29$	37.0000			1.27586			0.637931	−	0.770093i	$-0.279790\pi$
$29$	37.0000			1.27586			0.637931	+	0.770093i	$0.279790\pi$
$30$	15.0000	−	8.66025i	0.500000	−	0.288675i
$31$		−	19.0526i		−	0.614599i	−0.951613	−	0.307299i	$-0.900575\pi$
$31$		−	19.0526i		−	0.614599i	0.951613	−	0.307299i	$-0.0994253\pi$
$32$	−16.0000	+	27.7128i	−0.500000	+	0.866025i
$33$	−9.00000			−0.272727
$34$	−4.00000	−	6.92820i	−0.117647	−	0.203771i
$35$		0			0
$36$	6.00000	−	10.3923i	0.166667	−	0.288675i
$37$	68.0000			1.83784			0.918919	−	0.394446i	$-0.129064\pi$
$37$	68.0000			1.83784			0.918919	+	0.394446i	$0.129064\pi$
$38$	48.0000	−	27.7128i	1.26316	−	0.729285i
$39$			27.7128i			0.710585i
$40$	−40.0000			−1.00000
$41$	40.0000			0.975610			0.487805	−	0.872953i	$-0.337798\pi$
$41$	40.0000			0.975610			0.487805	+	0.872953i	$0.337798\pi$
$42$		0			0
$43$		−	24.2487i		−	0.563924i	−0.959426	−	0.281962i	$-0.909015\pi$
$43$		−	24.2487i		−	0.563924i	0.959426	−	0.281962i	$-0.0909851\pi$
$44$	18.0000	+	10.3923i	0.409091	+	0.236189i
$45$	15.0000			0.333333
$46$	36.0000	−	20.7846i	0.782609	−	0.451839i
$47$		−	45.0333i		−	0.958156i	−0.877772	−	0.479078i	$-0.840971\pi$
$47$		−	45.0333i		−	0.958156i	0.877772	−	0.479078i	$-0.159029\pi$
$48$	−24.0000	+	13.8564i	−0.500000	+	0.288675i
$49$		0			0
$50$		0			0
$51$		−	6.92820i		−	0.135847i
$52$	32.0000	−	55.4256i	0.615385	−	1.06588i
$53$	73.0000			1.37736			0.688679	−	0.725066i	$-0.258191\pi$
$53$	73.0000			1.37736			0.688679	+	0.725066i	$0.258191\pi$
$54$	9.00000	−	5.19615i	0.166667	−	0.0962250i
$55$			25.9808i			0.472377i
$56$		0			0
$57$	48.0000			0.842105
$58$	−37.0000	−	64.0859i	−0.637931	−	1.10493i
$59$			29.4449i			0.499065i	0.968366	+	0.249533i	$0.0802770\pi$
$59$			29.4449i			0.499065i	−0.968366	+	0.249533i	$0.919723\pi$
$60$	−30.0000	−	17.3205i	−0.500000	−	0.288675i
$61$	−82.0000			−1.34426			−0.672131	−	0.740432i	$-0.734621\pi$
$61$	−82.0000			−1.34426			−0.672131	+	0.740432i	$0.734621\pi$
$62$	−33.0000	+	19.0526i	−0.532258	+	0.307299i
$63$		0			0
$64$	64.0000			1.00000
$65$	80.0000			1.23077
$66$	9.00000	+	15.5885i	0.136364	+	0.236189i
$67$			79.6743i			1.18917i	0.804033	+	0.594585i	$0.202683\pi$
$67$			79.6743i			1.18917i	−0.804033	+	0.594585i	$0.797317\pi$
$68$	−8.00000	+	13.8564i	−0.117647	+	0.203771i
$69$	36.0000			0.521739
$70$		0			0
$71$		−	72.7461i		−	1.02459i	−0.858809	−	0.512297i	$-0.828795\pi$
$71$		−	72.7461i		−	1.02459i	0.858809	−	0.512297i	$-0.171205\pi$
$72$	−24.0000			−0.333333
$73$	−94.0000			−1.28767			−0.643836	−	0.765164i	$-0.722658\pi$
$73$	−94.0000			−1.28767			−0.643836	+	0.765164i	$0.722658\pi$
$74$	−68.0000	−	117.779i	−0.918919	−	1.59161i
$75$		0			0
$76$	−96.0000	−	55.4256i	−1.26316	−	0.729285i
$77$		0			0
$78$	48.0000	−	27.7128i	0.615385	−	0.355292i
$79$			8.66025i			0.109623i	0.998497	+	0.0548117i	$0.0174559\pi$
$79$			8.66025i			0.109623i	−0.998497	+	0.0548117i	$0.982544\pi$
$80$	40.0000	+	69.2820i	0.500000	+	0.866025i
$81$	9.00000			0.111111
$82$	−40.0000	−	69.2820i	−0.487805	−	0.844903i
$83$			133.368i			1.60684i	0.595411	+	0.803421i	$0.296989\pi$
$83$			133.368i			1.60684i	−0.595411	+	0.803421i	$0.703011\pi$
$84$		0			0
$85$	−20.0000			−0.235294
$86$	−42.0000	+	24.2487i	−0.488372	+	0.281962i
$87$		−	64.0859i		−	0.736619i
$88$		−	41.5692i		−	0.472377i
$89$	58.0000			0.651685			0.325843	−	0.945424i	$-0.394352\pi$
$89$	58.0000			0.651685			0.325843	+	0.945424i	$0.394352\pi$
$90$	−15.0000	−	25.9808i	−0.166667	−	0.288675i
$91$		0			0
$92$	−72.0000	−	41.5692i	−0.782609	−	0.451839i
$93$	−33.0000			−0.354839
$94$	−78.0000	+	45.0333i	−0.829787	+	0.479078i
$95$		−	138.564i		−	1.45857i
$96$	48.0000	+	27.7128i	0.500000	+	0.288675i
$97$	47.0000			0.484536			0.242268	−	0.970209i	$-0.422109\pi$
$97$	47.0000			0.484536			0.242268	+	0.970209i	$0.422109\pi$
$98$		0			0
$99$			15.5885i			0.157459i
$100$		0			0
$101$	130.000			1.28713			0.643564	−	0.765392i	$-0.277455\pi$
$101$	130.000			1.28713			0.643564	+	0.765392i	$0.277455\pi$
$102$	−12.0000	+	6.92820i	−0.117647	+	0.0679236i
$103$		−	20.7846i		−	0.201792i	−0.994897	−	0.100896i	$-0.967829\pi$
$103$		−	20.7846i		−	0.201792i	0.994897	−	0.100896i	$-0.0321710\pi$
$104$	−128.000			−1.23077
$105$		0			0
$106$	−73.0000	−	126.440i	−0.688679	−	1.19283i
$107$			81.4064i			0.760807i	0.924821	+	0.380404i	$0.124215\pi$
$107$			81.4064i			0.760807i	−0.924821	+	0.380404i	$0.875785\pi$
$108$	−18.0000	−	10.3923i	−0.166667	−	0.0962250i
$109$	122.000			1.11927			0.559633	−	0.828741i	$-0.310942\pi$
$109$	122.000			1.11927			0.559633	+	0.828741i	$0.310942\pi$
$110$	45.0000	−	25.9808i	0.409091	−	0.236189i
$111$		−	117.779i		−	1.06108i
$112$		0			0
$113$	16.0000			0.141593			0.0707965	−	0.997491i	$-0.477446\pi$
$113$	16.0000			0.141593			0.0707965	+	0.997491i	$0.477446\pi$
$114$	−48.0000	−	83.1384i	−0.421053	−	0.729285i
$115$		−	103.923i		−	0.903679i
$116$	−74.0000	+	128.172i	−0.637931	+	1.10493i
$117$	48.0000			0.410256
$118$	51.0000	−	29.4449i	0.432203	−	0.249533i
$119$		0			0
$120$			69.2820i			0.577350i
$121$	94.0000			0.776860
$122$	82.0000	+	142.028i	0.672131	+	1.16417i
$123$		−	69.2820i		−	0.563269i
$124$	66.0000	+	38.1051i	0.532258	+	0.307299i
$125$	125.000			1.00000
$126$		0			0
$127$			109.119i			0.859206i	0.903018	+	0.429603i	$0.141347\pi$
$127$			109.119i			0.859206i	−0.903018	+	0.429603i	$0.858653\pi$
$128$	−64.0000	−	110.851i	−0.500000	−	0.866025i
$129$	−42.0000			−0.325581
$130$	−80.0000	−	138.564i	−0.615385	−	1.06588i
$131$			15.5885i			0.118996i	0.998228	+	0.0594979i	$0.0189500\pi$
$131$			15.5885i			0.118996i	−0.998228	+	0.0594979i	$0.981050\pi$
$132$	18.0000	−	31.1769i	0.136364	−	0.236189i
$133$		0			0
$134$	138.000	−	79.6743i	1.02985	−	0.594585i
$135$		−	25.9808i		−	0.192450i
$136$	32.0000			0.235294
$137$	−74.0000			−0.540146			−0.270073	−	0.962840i	$-0.587048\pi$
$137$	−74.0000			−0.540146			−0.270073	+	0.962840i	$0.587048\pi$
$138$	−36.0000	−	62.3538i	−0.260870	−	0.451839i
$139$			169.741i			1.22116i	0.791955	+	0.610579i	$0.209063\pi$
$139$			169.741i			1.22116i	−0.791955	+	0.610579i	$0.790937\pi$
$140$		0			0
$141$	−78.0000			−0.553191
$142$	−126.000	+	72.7461i	−0.887324	+	0.512297i
$143$			83.1384i			0.581388i
$144$	24.0000	+	41.5692i	0.166667	+	0.288675i
$145$	−185.000			−1.27586
$146$	94.0000	+	162.813i	0.643836	+	1.11516i
$147$		0			0
$148$	−136.000	+	235.559i	−0.918919	+	1.59161i
$149$	166.000			1.11409			0.557047	−	0.830481i	$-0.311934\pi$
$149$	166.000			1.11409			0.557047	+	0.830481i	$0.311934\pi$
$150$		0			0
$151$			140.296i			0.929113i	0.885543	+	0.464557i	$0.153786\pi$
$151$			140.296i			0.929113i	−0.885543	+	0.464557i	$0.846214\pi$
$152$			221.703i			1.45857i
$153$	−12.0000			−0.0784314
$154$		0			0
$155$			95.2628i			0.614599i
$156$	−96.0000	−	55.4256i	−0.615385	−	0.355292i
$157$	−52.0000			−0.331210			−0.165605	−	0.986192i	$-0.552958\pi$
$157$	−52.0000			−0.331210			−0.165605	+	0.986192i	$0.552958\pi$
$158$	15.0000	−	8.66025i	0.0949367	−	0.0548117i
$159$		−	126.440i		−	0.795218i
$160$	80.0000	−	138.564i	0.500000	−	0.866025i
$161$		0			0
$162$	−9.00000	−	15.5885i	−0.0555556	−	0.0962250i
$163$		−	76.2102i		−	0.467547i	−0.972291	−	0.233774i	$-0.924893\pi$
$163$		−	76.2102i		−	0.467547i	0.972291	−	0.233774i	$-0.0751075\pi$
$164$	−80.0000	+	138.564i	−0.487805	+	0.844903i
$165$	45.0000			0.272727
$166$	231.000	−	133.368i	1.39157	−	0.803421i
$167$		−	169.741i		−	1.01641i	−0.861235	−	0.508207i	$-0.830309\pi$
$167$		−	169.741i		−	1.01641i	0.861235	−	0.508207i	$-0.169691\pi$
$168$		0			0
$169$	87.0000			0.514793
$170$	20.0000	+	34.6410i	0.117647	+	0.203771i
$171$		−	83.1384i		−	0.486190i
$172$	84.0000	+	48.4974i	0.488372	+	0.281962i
$173$	−26.0000			−0.150289			−0.0751445	−	0.997173i	$-0.523942\pi$
$173$	−26.0000			−0.150289			−0.0751445	+	0.997173i	$0.523942\pi$
$174$	−111.000	+	64.0859i	−0.637931	+	0.368310i
$175$		0			0
$176$	−72.0000	+	41.5692i	−0.409091	+	0.236189i
$177$	51.0000			0.288136
$178$	−58.0000	−	100.459i	−0.325843	−	0.564376i
$179$			297.913i			1.66432i	0.554538	+	0.832158i	$0.312895\pi$
$179$			297.913i			1.66432i	−0.554538	+	0.832158i	$0.687105\pi$
$180$	−30.0000	+	51.9615i	−0.166667	+	0.288675i
$181$	−16.0000			−0.0883978			−0.0441989	−	0.999023i	$-0.514074\pi$
$181$	−16.0000			−0.0883978			−0.0441989	+	0.999023i	$0.514074\pi$
$182$		0			0
$183$			142.028i			0.776110i
$184$			166.277i			0.903679i
$185$	−340.000			−1.83784
$186$	33.0000	+	57.1577i	0.177419	+	0.307299i
$187$		−	20.7846i		−	0.111148i
$188$	156.000	+	90.0666i	0.829787	+	0.479078i
$189$		0			0
$190$	−240.000	+	138.564i	−1.26316	+	0.729285i
$191$			360.267i			1.88621i	0.332492	+	0.943106i	$0.392111\pi$
$191$			360.267i			1.88621i	−0.332492	+	0.943106i	$0.607889\pi$
$192$		−	110.851i		−	0.577350i
$193$	−151.000			−0.782383			−0.391192	−	0.920309i	$-0.627937\pi$
$193$	−151.000			−0.782383			−0.391192	+	0.920309i	$0.627937\pi$
$194$	−47.0000	−	81.4064i	−0.242268	−	0.419621i
$195$		−	138.564i		−	0.710585i
$196$		0			0
$197$	−278.000			−1.41117			−0.705584	−	0.708627i	$-0.749315\pi$
$197$	−278.000			−1.41117			−0.705584	+	0.708627i	$0.749315\pi$
$198$	27.0000	−	15.5885i	0.136364	−	0.0787296i
$199$			138.564i			0.696302i	0.937438	+	0.348151i	$0.113190\pi$
$199$			138.564i			0.696302i	−0.937438	+	0.348151i	$0.886810\pi$
$200$		0			0
$201$	138.000			0.686567
$202$	−130.000	−	225.167i	−0.643564	−	1.11469i
$203$		0			0
$204$	24.0000	+	13.8564i	0.117647	+	0.0679236i
$205$	−200.000			−0.975610
$206$	−36.0000	+	20.7846i	−0.174757	+	0.100896i
$207$		−	62.3538i		−	0.301226i
$208$	128.000	+	221.703i	0.615385	+	1.06588i
$209$	144.000			0.688995
$210$		0			0
$211$		−	121.244i		−	0.574614i	−0.957839	−	0.287307i	$-0.907240\pi$
$211$		−	121.244i		−	0.574614i	0.957839	−	0.287307i	$-0.0927600\pi$
$212$	−146.000	+	252.879i	−0.688679	+	1.19283i
$213$	−126.000			−0.591549
$214$	141.000	−	81.4064i	0.658879	−	0.380404i
$215$			121.244i			0.563924i
$216$			41.5692i			0.192450i
$217$		0			0
$218$	−122.000	−	211.310i	−0.559633	−	0.969313i
$219$			162.813i			0.743437i
$220$	−90.0000	−	51.9615i	−0.409091	−	0.236189i
$221$	−64.0000			−0.289593
$222$	−204.000	+	117.779i	−0.918919	+	0.530538i
$223$			12.1244i			0.0543693i	0.999630	+	0.0271847i	$0.00865421\pi$
$223$			12.1244i			0.0543693i	−0.999630	+	0.0271847i	$0.991346\pi$
$224$		0			0
$225$		0			0
$226$	−16.0000	−	27.7128i	−0.0707965	−	0.122623i
$227$			150.688i			0.663826i	0.943310	+	0.331913i	$0.107694\pi$
$227$			150.688i			0.663826i	−0.943310	+	0.331913i	$0.892306\pi$
$228$	−96.0000	+	166.277i	−0.421053	+	0.729285i
$229$	212.000			0.925764			0.462882	−	0.886420i	$-0.346815\pi$
$229$	212.000			0.925764			0.462882	+	0.886420i	$0.346815\pi$
$230$	−180.000	+	103.923i	−0.782609	+	0.451839i
$231$		0			0
$232$	296.000			1.27586
$233$	−212.000			−0.909871			−0.454936	−	0.890524i	$-0.650338\pi$
$233$	−212.000			−0.909871			−0.454936	+	0.890524i	$0.650338\pi$
$234$	−48.0000	−	83.1384i	−0.205128	−	0.355292i
$235$			225.167i			0.958156i
$236$	−102.000	−	58.8897i	−0.432203	−	0.249533i
$237$	15.0000			0.0632911
$238$		0			0
$239$			48.4974i			0.202918i	0.994840	+	0.101459i	$0.0323511\pi$
$239$			48.4974i			0.202918i	−0.994840	+	0.101459i	$0.967649\pi$
$240$	120.000	−	69.2820i	0.500000	−	0.288675i
$241$	11.0000			0.0456432			0.0228216	−	0.999740i	$-0.492735\pi$
$241$	11.0000			0.0456432			0.0228216	+	0.999740i	$0.492735\pi$
$242$	−94.0000	−	162.813i	−0.388430	−	0.672780i
$243$		−	15.5885i		−	0.0641500i
$244$	164.000	−	284.056i	0.672131	−	1.16417i
$245$		0			0
$246$	−120.000	+	69.2820i	−0.487805	+	0.281634i
$247$		−	443.405i		−	1.79516i
$248$		−	152.420i		−	0.614599i
$249$	231.000			0.927711
$250$	−125.000	−	216.506i	−0.500000	−	0.866025i
$251$			36.3731i			0.144913i	0.997372	+	0.0724563i	$0.0230838\pi$
$251$			36.3731i			0.144913i	−0.997372	+	0.0724563i	$0.976916\pi$
$252$		0			0
$253$	108.000			0.426877
$254$	189.000	−	109.119i	0.744094	−	0.429603i
$255$			34.6410i			0.135847i
$256$	−128.000	+	221.703i	−0.500000	+	0.866025i
$257$	58.0000			0.225681			0.112840	−	0.993613i	$-0.464005\pi$
$257$	58.0000			0.225681			0.112840	+	0.993613i	$0.464005\pi$
$258$	42.0000	+	72.7461i	0.162791	+	0.281962i
$259$		0			0
$260$	−160.000	+	277.128i	−0.615385	+	1.06588i
$261$	−111.000			−0.425287
$262$	27.0000	−	15.5885i	0.103053	−	0.0594979i
$263$		−	405.300i		−	1.54106i	−0.637401	−	0.770532i	$-0.719991\pi$
$263$		−	405.300i		−	1.54106i	0.637401	−	0.770532i	$-0.280009\pi$
$264$	−72.0000			−0.272727
$265$	−365.000			−1.37736
$266$		0			0
$267$		−	100.459i		−	0.376251i
$268$	−276.000	−	159.349i	−1.02985	−	0.594585i
$269$	445.000			1.65428			0.827138	−	0.562000i	$-0.189968\pi$
$269$	445.000			1.65428			0.827138	+	0.562000i	$0.189968\pi$
$270$	−45.0000	+	25.9808i	−0.166667	+	0.0962250i
$271$			355.070i			1.31022i	0.755532	+	0.655111i	$0.227378\pi$
$271$			355.070i			1.31022i	−0.755532	+	0.655111i	$0.772622\pi$
$272$	−32.0000	−	55.4256i	−0.117647	−	0.203771i
$273$		0			0
$274$	74.0000	+	128.172i	0.270073	+	0.467780i
$275$		0			0
$276$	−72.0000	+	124.708i	−0.260870	+	0.451839i
$277$	−256.000			−0.924188			−0.462094	−	0.886831i	$-0.652902\pi$
$277$	−256.000			−0.924188			−0.462094	+	0.886831i	$0.652902\pi$
$278$	294.000	−	169.741i	1.05755	−	0.610579i
$279$			57.1577i			0.204866i
$280$		0			0
$281$	−278.000			−0.989324			−0.494662	−	0.869085i	$-0.664708\pi$
$281$	−278.000			−0.989324			−0.494662	+	0.869085i	$0.664708\pi$
$282$	78.0000	+	135.100i	0.276596	+	0.479078i
$283$			17.3205i			0.0612032i	0.999532	+	0.0306016i	$0.00974231\pi$
$283$			17.3205i			0.0612032i	−0.999532	+	0.0306016i	$0.990258\pi$
$284$	252.000	+	145.492i	0.887324	+	0.512297i
$285$	−240.000			−0.842105
$286$	144.000	−	83.1384i	0.503497	−	0.290694i
$287$		0			0
$288$	48.0000	−	83.1384i	0.166667	−	0.288675i
$289$	−273.000			−0.944637
$290$	185.000	+	320.429i	0.637931	+	1.10493i
$291$		−	81.4064i		−	0.279747i
$292$	188.000	−	325.626i	0.643836	−	1.11516i
$293$	61.0000			0.208191			0.104096	−	0.994567i	$-0.466805\pi$
$293$	61.0000			0.208191			0.104096	+	0.994567i	$0.466805\pi$
$294$		0			0
$295$		−	147.224i		−	0.499065i
$296$	544.000			1.83784
$297$	27.0000			0.0909091
$298$	−166.000	−	287.520i	−0.557047	−	0.964834i
$299$		−	332.554i		−	1.11222i
$300$		0			0
$301$		0			0
$302$	243.000	−	140.296i	0.804636	−	0.464557i
$303$		−	225.167i		−	0.743124i
$304$	384.000	−	221.703i	1.26316	−	0.729285i
$305$	410.000			1.34426
$306$	12.0000	+	20.7846i	0.0392157	+	0.0679236i
$307$			436.477i			1.42175i	0.703319	+	0.710874i	$0.251701\pi$
$307$			436.477i			1.42175i	−0.703319	+	0.710874i	$0.748299\pi$
$308$		0			0
$309$	−36.0000			−0.116505
$310$	165.000	−	95.2628i	0.532258	−	0.307299i
$311$		−	152.420i		−	0.490098i	−0.969511	−	0.245049i	$-0.921196\pi$
$311$		−	152.420i		−	0.490098i	0.969511	−	0.245049i	$-0.0788040\pi$
$312$			221.703i			0.710585i
$313$	233.000			0.744409			0.372204	−	0.928151i	$-0.378602\pi$
$313$	233.000			0.744409			0.372204	+	0.928151i	$0.378602\pi$
$314$	52.0000	+	90.0666i	0.165605	+	0.286836i
$315$		0			0
$316$	−30.0000	−	17.3205i	−0.0949367	−	0.0548117i
$317$	−107.000			−0.337539			−0.168770	−	0.985656i	$-0.553979\pi$
$317$	−107.000			−0.337539			−0.168770	+	0.985656i	$0.553979\pi$
$318$	−219.000	+	126.440i	−0.688679	+	0.397609i
$319$		−	192.258i		−	0.602689i
$320$	−320.000			−1.00000
$321$	141.000			0.439252
$322$		0			0
$323$			110.851i			0.343193i
$324$	−18.0000	+	31.1769i	−0.0555556	+	0.0962250i
$325$		0			0
$326$	−132.000	+	76.2102i	−0.404908	+	0.233774i
$327$		−	211.310i		−	0.646209i
$328$	320.000			0.975610
$329$		0			0
$330$	−45.0000	−	77.9423i	−0.136364	−	0.236189i
$331$			408.764i			1.23494i	0.786596	+	0.617468i	$0.211842\pi$
$331$			408.764i			1.23494i	−0.786596	+	0.617468i	$0.788158\pi$
$332$	−462.000	−	266.736i	−1.39157	−	0.803421i
$333$	−204.000			−0.612613
$334$	−294.000	+	169.741i	−0.880240	+	0.508207i
$335$		−	398.372i		−	1.18917i
$336$		0			0
$337$	149.000			0.442136			0.221068	−	0.975258i	$-0.429046\pi$
$337$	149.000			0.442136			0.221068	+	0.975258i	$0.429046\pi$
$338$	−87.0000	−	150.688i	−0.257396	−	0.445824i
$339$		−	27.7128i		−	0.0817487i
$340$	40.0000	−	69.2820i	0.117647	−	0.203771i
$341$	−99.0000			−0.290323
$342$	−144.000	+	83.1384i	−0.421053	+	0.243095i
$343$		0			0
$344$		−	193.990i		−	0.563924i
$345$	−180.000			−0.521739
$346$	26.0000	+	45.0333i	0.0751445	+	0.130154i
$347$		−	381.051i		−	1.09813i	−0.835780	−	0.549065i	$-0.814984\pi$
$347$		−	381.051i		−	1.09813i	0.835780	−	0.549065i	$-0.185016\pi$
$348$	222.000	+	128.172i	0.637931	+	0.368310i
$349$	−394.000			−1.12894			−0.564470	−	0.825454i	$-0.690919\pi$
$349$	−394.000			−1.12894			−0.564470	+	0.825454i	$0.690919\pi$
$350$		0			0
$351$		−	83.1384i		−	0.236862i
$352$	144.000	+	83.1384i	0.409091	+	0.236189i
$353$	256.000			0.725212			0.362606	−	0.931942i	$-0.381887\pi$
$353$	256.000			0.725212			0.362606	+	0.931942i	$0.381887\pi$
$354$	−51.0000	−	88.3346i	−0.144068	−	0.249533i
$355$			363.731i			1.02459i
$356$	−116.000	+	200.918i	−0.325843	+	0.564376i
$357$		0			0
$358$	516.000	−	297.913i	1.44134	−	0.832158i
$359$		−	391.443i		−	1.09037i	−0.838315	−	0.545186i	$-0.816459\pi$
$359$		−	391.443i		−	1.09037i	0.838315	−	0.545186i	$-0.183541\pi$
$360$	120.000			0.333333
$361$	−407.000			−1.12742
$362$	16.0000	+	27.7128i	0.0441989	+	0.0765547i
$363$		−	162.813i		−	0.448520i
$364$		0			0
$365$	470.000			1.28767
$366$	246.000	−	142.028i	0.672131	−	0.388055i
$367$			296.181i			0.807032i	0.914973	+	0.403516i	$0.132212\pi$
$367$			296.181i			0.807032i	−0.914973	+	0.403516i	$0.867788\pi$
$368$	288.000	−	166.277i	0.782609	−	0.451839i
$369$	−120.000			−0.325203
$370$	340.000	+	588.897i	0.918919	+	1.59161i
$371$		0			0
$372$	66.0000	−	114.315i	0.177419	−	0.307299i
$373$	656.000			1.75871			0.879357	−	0.476164i	$-0.157973\pi$
$373$	656.000			1.75871			0.879357	+	0.476164i	$0.157973\pi$
$374$	−36.0000	+	20.7846i	−0.0962567	+	0.0555738i
$375$		−	216.506i		−	0.577350i
$376$		−	360.267i		−	0.958156i
$377$	−592.000			−1.57029
$378$		0			0
$379$		−	290.985i		−	0.767769i	−0.923381	−	0.383885i	$-0.874586\pi$
$379$		−	290.985i		−	0.767769i	0.923381	−	0.383885i	$-0.125414\pi$
$380$	480.000	+	277.128i	1.26316	+	0.729285i
$381$	189.000			0.496063
$382$	624.000	−	360.267i	1.63351	−	0.943106i
$383$			197.454i			0.515545i	0.966206	+	0.257773i	$0.0829885\pi$
$383$			197.454i			0.515545i	−0.966206	+	0.257773i	$0.917011\pi$
$384$	−192.000	+	110.851i	−0.500000	+	0.288675i
$385$		0			0
$386$	151.000	+	261.540i	0.391192	+	0.677564i
$387$			72.7461i			0.187975i
$388$	−94.0000	+	162.813i	−0.242268	+	0.419621i
$389$	−410.000			−1.05398			−0.526992	−	0.849870i	$-0.676680\pi$
$389$	−410.000			−1.05398			−0.526992	+	0.849870i	$0.676680\pi$
$390$	−240.000	+	138.564i	−0.615385	+	0.355292i
$391$			83.1384i			0.212630i
$392$		0			0
$393$	27.0000			0.0687023
$394$	278.000	+	481.510i	0.705584	+	1.22211i
$395$		−	43.3013i		−	0.109623i
$396$	−54.0000	−	31.1769i	−0.136364	−	0.0787296i
$397$	212.000			0.534005			0.267003	−	0.963696i	$-0.413967\pi$
$397$	212.000			0.534005			0.267003	+	0.963696i	$0.413967\pi$
$398$	240.000	−	138.564i	0.603015	−	0.348151i
$399$		0			0
$400$		0			0
$401$	−464.000			−1.15711			−0.578554	−	0.815644i	$-0.696383\pi$
$401$	−464.000			−1.15711			−0.578554	+	0.815644i	$0.696383\pi$
$402$	−138.000	−	239.023i	−0.343284	−	0.594585i
$403$			304.841i			0.756429i
$404$	−260.000	+	450.333i	−0.643564	+	1.11469i
$405$	−45.0000			−0.111111
$406$		0			0
$407$		−	353.338i		−	0.868153i
$408$		−	55.4256i		−	0.135847i
$409$	515.000			1.25917			0.629584	−	0.776932i	$-0.283225\pi$
$409$	515.000			1.25917			0.629584	+	0.776932i	$0.283225\pi$
$410$	200.000	+	346.410i	0.487805	+	0.844903i
$411$			128.172i			0.311853i
$412$	72.0000	+	41.5692i	0.174757	+	0.100896i
$413$		0			0
$414$	−108.000	+	62.3538i	−0.260870	+	0.150613i
$415$		−	666.840i		−	1.60684i
$416$	256.000	−	443.405i	0.615385	−	1.06588i
$417$	294.000			0.705036
$418$	−144.000	−	249.415i	−0.344498	−	0.596687i
$419$		−	96.9948i		−	0.231491i	−0.993279	−	0.115746i	$-0.963074\pi$
$419$		−	96.9948i		−	0.231491i	0.993279	−	0.115746i	$-0.0369257\pi$
$420$		0			0
$421$	170.000			0.403800			0.201900	−	0.979406i	$-0.435288\pi$
$421$	170.000			0.403800			0.201900	+	0.979406i	$0.435288\pi$
$422$	−210.000	+	121.244i	−0.497630	+	0.287307i
$423$			135.100i			0.319385i
$424$	584.000			1.37736
$425$		0			0
$426$	126.000	+	218.238i	0.295775	+	0.512297i
$427$		0			0
$428$	−282.000	−	162.813i	−0.658879	−	0.380404i
$429$	144.000			0.335664
$430$	210.000	−	121.244i	0.488372	−	0.281962i
$431$			6.92820i			0.0160747i	0.999968	+	0.00803736i	$0.00255840\pi$
$431$			6.92820i			0.0160747i	−0.999968	+	0.00803736i	$0.997442\pi$
$432$	72.0000	−	41.5692i	0.166667	−	0.0962250i
$433$	−226.000			−0.521940			−0.260970	−	0.965347i	$-0.584042\pi$
$433$	−226.000			−0.521940			−0.260970	+	0.965347i	$0.584042\pi$
$434$		0			0
$435$			320.429i			0.736619i
$436$	−244.000	+	422.620i	−0.559633	+	0.969313i
$437$	−576.000			−1.31808
$438$	282.000	−	162.813i	0.643836	−	0.371719i
$439$		−	178.401i		−	0.406381i	−0.979139	−	0.203190i	$-0.934869\pi$
$439$		−	178.401i		−	0.406381i	0.979139	−	0.203190i	$-0.0651311\pi$
$440$			207.846i			0.472377i
$441$		0			0
$442$	64.0000	+	110.851i	0.144796	+	0.250795i
$443$		−	621.806i		−	1.40363i	−0.712361	−	0.701813i	$-0.752374\pi$
$443$		−	621.806i		−	1.40363i	0.712361	−	0.701813i	$-0.247626\pi$
$444$	408.000	+	235.559i	0.918919	+	0.530538i
$445$	−290.000			−0.651685
$446$	21.0000	−	12.1244i	0.0470852	−	0.0271847i
$447$		−	287.520i		−	0.643222i
$448$		0			0
$449$	520.000			1.15813			0.579065	−	0.815282i	$-0.303418\pi$
$449$	520.000			1.15813			0.579065	+	0.815282i	$0.303418\pi$
$450$		0			0
$451$		−	207.846i		−	0.460856i
$452$	−32.0000	+	55.4256i	−0.0707965	+	0.122623i
$453$	243.000			0.536424
$454$	261.000	−	150.688i	0.574890	−	0.331913i
$455$		0			0
$456$	384.000			0.842105
$457$	−37.0000			−0.0809628			−0.0404814	−	0.999180i	$-0.512889\pi$
$457$	−37.0000			−0.0809628			−0.0404814	+	0.999180i	$0.512889\pi$
$458$	−212.000	−	367.195i	−0.462882	−	0.801735i
$459$			20.7846i			0.0452824i
$460$	360.000	+	207.846i	0.782609	+	0.451839i
$461$	250.000			0.542299			0.271150	−	0.962537i	$-0.412596\pi$
$461$	250.000			0.542299			0.271150	+	0.962537i	$0.412596\pi$
$462$		0			0
$463$		−	339.482i		−	0.733222i	−0.930374	−	0.366611i	$-0.880518\pi$
$463$		−	339.482i		−	0.733222i	0.930374	−	0.366611i	$-0.119482\pi$
$464$	−296.000	−	512.687i	−0.637931	−	1.10493i
$465$	165.000			0.354839
$466$	212.000	+	367.195i	0.454936	+	0.787972i
$467$		−	796.743i		−	1.70609i	−0.521839	−	0.853044i	$-0.674754\pi$
$467$		−	796.743i		−	1.70609i	0.521839	−	0.853044i	$-0.325246\pi$
$468$	−96.0000	+	166.277i	−0.205128	+	0.355292i
$469$		0			0
$470$	390.000	−	225.167i	0.829787	−	0.479078i
$471$			90.0666i			0.191224i
$472$			235.559i			0.499065i
$473$	−126.000			−0.266385
$474$	−15.0000	−	25.9808i	−0.0316456	−	0.0548117i
$475$		0			0
$476$		0			0
$477$	−219.000			−0.459119
$478$	84.0000	−	48.4974i	0.175732	−	0.101459i
$479$		−	176.669i		−	0.368829i	−0.982849	−	0.184415i	$-0.940961\pi$
$479$		−	176.669i		−	0.368829i	0.982849	−	0.184415i	$-0.0590389\pi$
$480$	−240.000	−	138.564i	−0.500000	−	0.288675i
$481$	−1088.00			−2.26195
$482$	−11.0000	−	19.0526i	−0.0228216	−	0.0395281i
$483$		0			0
$484$	−188.000	+	325.626i	−0.388430	+	0.672780i
$485$	−235.000			−0.484536
$486$	−27.0000	+	15.5885i	−0.0555556	+	0.0320750i
$487$			310.037i			0.636626i	0.947986	+	0.318313i	$0.103116\pi$
$487$			310.037i			0.636626i	−0.947986	+	0.318313i	$0.896884\pi$
$488$	−656.000			−1.34426
$489$	−132.000			−0.269939
$490$		0			0
$491$			230.363i			0.469171i	0.972096	+	0.234585i	$0.0753732\pi$
$491$			230.363i			0.469171i	−0.972096	+	0.234585i	$0.924627\pi$
$492$	240.000	+	138.564i	0.487805	+	0.281634i
$493$	148.000			0.300203
$494$	−768.000	+	443.405i	−1.55466	+	0.897581i
$495$		−	77.9423i		−	0.157459i
$496$	−264.000	+	152.420i	−0.532258	+	0.307299i
$497$		0			0
$498$	−231.000	−	400.104i	−0.463855	−	0.803421i
$499$			239.023i			0.479004i	0.970896	+	0.239502i	$0.0769842\pi$
$499$			239.023i			0.479004i	−0.970896	+	0.239502i	$0.923016\pi$
$500$	−250.000	+	433.013i	−0.500000	+	0.866025i
$501$	−294.000			−0.586826
$502$	63.0000	−	36.3731i	0.125498	−	0.0724563i
$503$		−	872.954i		−	1.73549i	−0.497006	−	0.867747i	$-0.665567\pi$
$503$		−	872.954i		−	1.73549i	0.497006	−	0.867747i	$-0.334433\pi$
$504$		0			0
$505$	−650.000			−1.28713
$506$	−108.000	−	187.061i	−0.213439	−	0.369687i
$507$		−	150.688i		−	0.297216i
$508$	−378.000	−	218.238i	−0.744094	−	0.429603i
$509$	541.000			1.06287			0.531434	−	0.847100i	$-0.321653\pi$
$509$	541.000			1.06287			0.531434	+	0.847100i	$0.321653\pi$
$510$	60.0000	−	34.6410i	0.117647	−	0.0679236i
$511$		0			0
$512$	512.000			1.00000
$513$	−144.000			−0.280702
$514$	−58.0000	−	100.459i	−0.112840	−	0.195445i
$515$			103.923i			0.201792i
$516$	84.0000	−	145.492i	0.162791	−	0.281962i
$517$	−234.000			−0.452611
$518$		0			0
$519$			45.0333i			0.0867694i
$520$	640.000			1.23077
$521$	550.000			1.05566			0.527831	−	0.849349i	$-0.323005\pi$
$521$	550.000			1.05566			0.527831	+	0.849349i	$0.323005\pi$
$522$	111.000	+	192.258i	0.212644	+	0.368310i
$523$			609.682i			1.16574i	0.812566	+	0.582870i	$0.198070\pi$
$523$			609.682i			1.16574i	−0.812566	+	0.582870i	$0.801930\pi$
$524$	−54.0000	−	31.1769i	−0.103053	−	0.0594979i
$525$		0			0
$526$	−702.000	+	405.300i	−1.33460	+	0.770532i
$527$		−	76.2102i		−	0.144611i
$528$	72.0000	+	124.708i	0.136364	+	0.236189i
$529$	97.0000			0.183365
$530$	365.000	+	632.199i	0.688679	+	1.19283i
$531$		−	88.3346i		−	0.166355i
$532$		0			0
$533$	−640.000			−1.20075
$534$	−174.000	+	100.459i	−0.325843	+	0.188125i
$535$		−	407.032i		−	0.760807i
$536$			637.395i			1.18917i
$537$	516.000			0.960894
$538$	−445.000	−	770.763i	−0.827138	−	1.43264i
$539$		0			0
$540$	90.0000	+	51.9615i	0.166667	+	0.0962250i
$541$	−310.000			−0.573013			−0.286506	−	0.958078i	$-0.592494\pi$
$541$	−310.000			−0.573013			−0.286506	+	0.958078i	$0.592494\pi$
$542$	615.000	−	355.070i	1.13469	−	0.655111i
$543$			27.7128i			0.0510365i
$544$	−64.0000	+	110.851i	−0.117647	+	0.203771i
$545$	−610.000			−1.11927
$546$		0			0
$547$			630.466i			1.15259i	0.817242	+	0.576295i	$0.195502\pi$
$547$			630.466i			1.15259i	−0.817242	+	0.576295i	$0.804498\pi$
$548$	148.000	−	256.344i	0.270073	−	0.467780i
$549$	246.000			0.448087
$550$		0			0
$551$			1025.37i			1.86093i
$552$	288.000			0.521739
$553$		0			0
$554$	256.000	+	443.405i	0.462094	+	0.800370i
$555$			588.897i			1.06108i
$556$	−588.000	−	339.482i	−1.05755	−	0.610579i
$557$	535.000			0.960503			0.480251	−	0.877131i	$-0.340545\pi$
$557$	535.000			0.960503			0.480251	+	0.877131i	$0.340545\pi$
$558$	99.0000	−	57.1577i	0.177419	−	0.102433i
$559$			387.979i			0.694060i
$560$		0			0
$561$	−36.0000			−0.0641711
$562$	278.000	+	481.510i	0.494662	+	0.856780i
$563$		−	698.016i		−	1.23982i	−0.784674	−	0.619908i	$-0.787170\pi$
$563$		−	698.016i		−	1.23982i	0.784674	−	0.619908i	$-0.212830\pi$
$564$	156.000	−	270.200i	0.276596	−	0.479078i
$565$	−80.0000			−0.141593
$566$	30.0000	−	17.3205i	0.0530035	−	0.0306016i
$567$		0			0
$568$		−	581.969i		−	1.02459i
$569$	712.000			1.25132			0.625659	−	0.780097i	$-0.284830\pi$
$569$	712.000			1.25132			0.625659	+	0.780097i	$0.284830\pi$
$570$	240.000	+	415.692i	0.421053	+	0.729285i
$571$		−	65.8179i		−	0.115268i	−0.998338	−	0.0576339i	$-0.981644\pi$
$571$		−	65.8179i		−	0.115268i	0.998338	−	0.0576339i	$-0.0183556\pi$
$572$	−288.000	−	166.277i	−0.503497	−	0.290694i
$573$	624.000			1.08901
$574$		0			0
$575$		0			0
$576$	−192.000			−0.333333
$577$	−157.000			−0.272097			−0.136049	−	0.990702i	$-0.543440\pi$
$577$	−157.000			−0.272097			−0.136049	+	0.990702i	$0.543440\pi$
$578$	273.000	+	472.850i	0.472318	+	0.818079i
$579$			261.540i			0.451709i
$580$	370.000	−	640.859i	0.637931	−	1.10493i
$581$		0			0
$582$	−141.000	+	81.4064i	−0.242268	+	0.139874i
$583$		−	379.319i		−	0.650633i
$584$	−752.000			−1.28767
$585$	−240.000			−0.410256
$586$	−61.0000	−	105.655i	−0.104096	−	0.180299i
$587$			788.083i			1.34256i	0.741204	+	0.671280i	$0.234255\pi$
$587$			788.083i			1.34256i	−0.741204	+	0.671280i	$0.765745\pi$
$588$		0			0
$589$	528.000			0.896435
$590$	−255.000	+	147.224i	−0.432203	+	0.249533i
$591$			481.510i			0.814738i
$592$	−544.000	−	942.236i	−0.918919	−	1.59161i
$593$	−68.0000			−0.114671			−0.0573356	−	0.998355i	$-0.518260\pi$
$593$	−68.0000			−0.114671			−0.0573356	+	0.998355i	$0.518260\pi$
$594$	−27.0000	−	46.7654i	−0.0454545	−	0.0787296i
$595$		0			0
$596$	−332.000	+	575.041i	−0.557047	+	0.964834i
$597$	240.000			0.402010
$598$	−576.000	+	332.554i	−0.963211	+	0.556110i
$599$			273.664i			0.456868i	0.973559	+	0.228434i	$0.0733605\pi$
$599$			273.664i			0.456868i	−0.973559	+	0.228434i	$0.926639\pi$
$600$		0			0
$601$	971.000			1.61564			0.807820	−	0.589429i	$-0.200647\pi$
$601$	971.000			1.61564			0.807820	+	0.589429i	$0.200647\pi$
$602$		0			0
$603$		−	239.023i		−	0.396390i
$604$	−486.000	−	280.592i	−0.804636	−	0.464557i
$605$	−470.000			−0.776860
$606$	−390.000	+	225.167i	−0.643564	+	0.371562i
$607$			88.3346i			0.145527i	0.997349	+	0.0727633i	$0.0231818\pi$
$607$			88.3346i			0.145527i	−0.997349	+	0.0727633i	$0.976818\pi$
$608$	−768.000	−	443.405i	−1.26316	−	0.729285i
$609$		0			0
$610$	−410.000	−	710.141i	−0.672131	−	1.16417i
$611$			720.533i			1.17927i
$612$	24.0000	−	41.5692i	0.0392157	−	0.0679236i
$613$	836.000			1.36378			0.681892	−	0.731453i	$-0.261157\pi$
$613$	836.000			1.36378			0.681892	+	0.731453i	$0.261157\pi$
$614$	756.000	−	436.477i	1.23127	−	0.710874i
$615$			346.410i			0.563269i
$616$		0			0
$617$	394.000			0.638574			0.319287	−	0.947658i	$-0.396557\pi$
$617$	394.000			0.638574			0.319287	+	0.947658i	$0.396557\pi$
$618$	36.0000	+	62.3538i	0.0582524	+	0.100896i
$619$			696.284i			1.12485i	0.826847	+	0.562427i	$0.190132\pi$
$619$			696.284i			1.12485i	−0.826847	+	0.562427i	$0.809868\pi$
$620$	−330.000	−	190.526i	−0.532258	−	0.307299i
$621$	−108.000			−0.173913
$622$	−264.000	+	152.420i	−0.424437	+	0.245049i
$623$		0			0
$624$	384.000	−	221.703i	0.615385	−	0.355292i
$625$	−625.000			−1.00000
$626$	−233.000	−	403.568i	−0.372204	−	0.644677i
$627$		−	249.415i		−	0.397792i
$628$	104.000	−	180.133i	0.165605	−	0.286836i
$629$	272.000			0.432432
$630$		0			0
$631$			254.611i			0.403505i	0.979437	+	0.201752i	$0.0646636\pi$
$631$			254.611i			0.403505i	−0.979437	+	0.201752i	$0.935336\pi$
$632$			69.2820i			0.109623i
$633$	−210.000			−0.331754
$634$	107.000	+	185.329i	0.168770	+	0.292318i
$635$		−	545.596i		−	0.859206i
$636$	438.000	+	252.879i	0.688679	+	0.397609i
$637$		0			0
$638$	−333.000	+	192.258i	−0.521944	+	0.301344i
$639$			218.238i			0.341531i
$640$	320.000	+	554.256i	0.500000	+	0.866025i
$641$	178.000			0.277691			0.138846	−	0.990314i	$-0.455661\pi$
$641$	178.000			0.277691			0.138846	+	0.990314i	$0.455661\pi$
$642$	−141.000	−	244.219i	−0.219626	−	0.380404i
$643$		−	266.736i		−	0.414830i	−0.978253	−	0.207415i	$-0.933495\pi$
$643$		−	266.736i		−	0.414830i	0.978253	−	0.207415i	$-0.0665051\pi$
$644$		0			0
$645$	210.000			0.325581
$646$	192.000	−	110.851i	0.297214	−	0.171596i
$647$			17.3205i			0.0267705i	0.999910	+	0.0133852i	$0.00426078\pi$
$647$			17.3205i			0.0267705i	−0.999910	+	0.0133852i	$0.995739\pi$
$648$	72.0000			0.111111
$649$	153.000			0.235747
$650$		0			0
$651$		0			0
$652$	264.000	+	152.420i	0.404908	+	0.233774i
$653$	−737.000			−1.12864			−0.564319	−	0.825557i	$-0.690861\pi$
$653$	−737.000			−1.12864			−0.564319	+	0.825557i	$0.690861\pi$
$654$	−366.000	+	211.310i	−0.559633	+	0.323104i
$655$		−	77.9423i		−	0.118996i
$656$	−320.000	−	554.256i	−0.487805	−	0.844903i
$657$	282.000			0.429224
$658$		0			0
$659$			678.964i			1.03029i	0.857102	+	0.515147i	$0.172263\pi$
$659$			678.964i			1.03029i	−0.857102	+	0.515147i	$0.827737\pi$
$660$	−90.0000	+	155.885i	−0.136364	+	0.236189i
$661$	−682.000			−1.03177			−0.515885	−	0.856658i	$-0.672537\pi$
$661$	−682.000			−1.03177			−0.515885	+	0.856658i	$0.672537\pi$
$662$	708.000	−	408.764i	1.06949	−	0.617468i
$663$			110.851i			0.167196i
$664$			1066.94i			1.60684i
$665$		0			0
$666$	204.000	+	353.338i	0.306306	+	0.530538i
$667$			769.031i			1.15297i
$668$	588.000	+	339.482i	0.880240	+	0.508207i
$669$	21.0000			0.0313901
$670$	−690.000	+	398.372i	−1.02985	+	0.594585i
$671$			426.084i			0.634999i
$672$		0			0
$673$	−1027.00			−1.52600			−0.763001	−	0.646397i	$-0.776275\pi$
$673$	−1027.00			−1.52600			−0.763001	+	0.646397i	$0.776275\pi$
$674$	−149.000	−	258.076i	−0.221068	−	0.382901i
$675$		0			0
$676$	−174.000	+	301.377i	−0.257396	+	0.445824i
$677$	331.000			0.488922			0.244461	−	0.969659i	$-0.421389\pi$
$677$	331.000			0.488922			0.244461	+	0.969659i	$0.421389\pi$
$678$	−48.0000	+	27.7128i	−0.0707965	+	0.0408744i
$679$		0			0
$680$	−160.000			−0.235294
$681$	261.000			0.383260
$682$	99.0000	+	171.473i	0.145161	+	0.251427i
$683$			261.540i			0.382928i	0.981500	+	0.191464i	$0.0613235\pi$
$683$			261.540i			0.382928i	−0.981500	+	0.191464i	$0.938677\pi$
$684$	288.000	+	166.277i	0.421053	+	0.243095i
$685$	370.000			0.540146
$686$		0			0
$687$		−	367.195i		−	0.534490i
$688$	−336.000	+	193.990i	−0.488372	+	0.281962i
$689$	−1168.00			−1.69521
$690$	180.000	+	311.769i	0.260870	+	0.451839i
$691$		−	1233.22i		−	1.78469i	−0.451355	−	0.892345i	$-0.649059\pi$
$691$		−	1233.22i		−	1.78469i	0.451355	−	0.892345i	$-0.350941\pi$
$692$	52.0000	−	90.0666i	0.0751445	−	0.130154i
$693$		0			0
$694$	−660.000	+	381.051i	−0.951009	+	0.549065i
$695$		−	848.705i		−	1.22116i
$696$		−	512.687i		−	0.736619i
$697$	160.000			0.229555
$698$	394.000	+	682.428i	0.564470	+	0.977691i
$699$			367.195i			0.525314i
$700$		0			0
$701$	−467.000			−0.666191			−0.333096	−	0.942893i	$-0.608093\pi$
$701$	−467.000			−0.666191			−0.333096	+	0.942893i	$0.608093\pi$
$702$	−144.000	+	83.1384i	−0.205128	+	0.118431i
$703$			1884.47i			2.68061i
$704$		−	332.554i		−	0.472377i
$705$	390.000			0.553191
$706$	−256.000	−	443.405i	−0.362606	−	0.628052i
$707$		0			0
$708$	−102.000	+	176.669i	−0.144068	+	0.249533i
$709$	530.000			0.747532			0.373766	−	0.927523i	$-0.378066\pi$
$709$	530.000			0.747532			0.373766	+	0.927523i	$0.378066\pi$
$710$	630.000	−	363.731i	0.887324	−	0.512297i
$711$		−	25.9808i		−	0.0365412i
$712$	464.000			0.651685
$713$	396.000			0.555400
$714$		0			0
$715$		−	415.692i		−	0.581388i
$716$	−1032.00	−	595.825i	−1.44134	−	0.832158i
$717$	84.0000			0.117155
$718$	−678.000	+	391.443i	−0.944290	+	0.545186i
$719$		−	723.997i		−	1.00695i	−0.864010	−	0.503475i	$-0.832055\pi$
$719$		−	723.997i		−	1.00695i	0.864010	−	0.503475i	$-0.167945\pi$
$720$	−120.000	−	207.846i	−0.166667	−	0.288675i
$721$		0			0
$722$	407.000	+	704.945i	0.563712	+	0.976378i
$723$		−	19.0526i		−	0.0263521i
$724$	32.0000	−	55.4256i	0.0441989	−	0.0765547i
$725$		0			0
$726$	−282.000	+	162.813i	−0.388430	+	0.224260i
$727$		−	60.6218i		−	0.0833862i	−0.999130	−	0.0416931i	$-0.986725\pi$
$727$		−	60.6218i		−	0.0833862i	0.999130	−	0.0416931i	$-0.0132752\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$	−470.000	−	814.064i	−0.643836	−	1.11516i
$731$		−	96.9948i		−	0.132688i
$732$	−492.000	−	284.056i	−0.672131	−	0.388055i
$733$	−586.000			−0.799454			−0.399727	−	0.916634i	$-0.630895\pi$
$733$	−586.000			−0.799454			−0.399727	+	0.916634i	$0.630895\pi$
$734$	513.000	−	296.181i	0.698910	−	0.403516i
$735$		0			0
$736$	−576.000	−	332.554i	−0.782609	−	0.451839i
$737$	414.000			0.561737
$738$	120.000	+	207.846i	0.162602	+	0.281634i
$739$			128.172i			0.173439i	0.996233	+	0.0867197i	$0.0276385\pi$
$739$			128.172i			0.173439i	−0.996233	+	0.0867197i	$0.972362\pi$
$740$	680.000	−	1177.79i	0.918919	−	1.59161i
$741$	−768.000			−1.03644
$742$		0			0
$743$		−	24.2487i		−	0.0326362i	−0.999867	−	0.0163181i	$-0.994806\pi$
$743$		−	24.2487i		−	0.0326362i	0.999867	−	0.0163181i	$-0.00519445\pi$
$744$	−264.000			−0.354839
$745$	−830.000			−1.11409
$746$	−656.000	−	1136.23i	−0.879357	−	1.52309i
$747$		−	400.104i		−	0.535614i
$748$	72.0000	+	41.5692i	0.0962567	+	0.0555738i
$749$		0			0
$750$	−375.000	+	216.506i	−0.500000	+	0.288675i
$751$			566.381i			0.754169i	0.926179	+	0.377084i	$0.123073\pi$
$751$			566.381i			0.754169i	−0.926179	+	0.377084i	$0.876927\pi$
$752$	−624.000	+	360.267i	−0.829787	+	0.479078i
$753$	63.0000			0.0836653
$754$	592.000	+	1025.37i	0.785146	+	1.35991i
$755$		−	701.481i		−	0.929113i
$756$		0			0
$757$	−250.000			−0.330251			−0.165125	−	0.986273i	$-0.552803\pi$
$757$	−250.000			−0.330251			−0.165125	+	0.986273i	$0.552803\pi$
$758$	−504.000	+	290.985i	−0.664908	+	0.383885i
$759$		−	187.061i		−	0.246458i
$760$		−	1108.51i		−	1.45857i
$761$	−320.000			−0.420499			−0.210250	−	0.977648i	$-0.567428\pi$
$761$	−320.000			−0.420499			−0.210250	+	0.977648i	$0.567428\pi$
$762$	−189.000	−	327.358i	−0.248031	−	0.429603i
$763$		0			0
$764$	−1248.00	−	720.533i	−1.63351	−	0.943106i
$765$	60.0000			0.0784314
$766$	342.000	−	197.454i	0.446475	−	0.257773i
$767$		−	471.118i		−	0.614234i
$768$	384.000	+	221.703i	0.500000	+	0.288675i
$769$	425.000			0.552666			0.276333	−	0.961062i	$-0.410881\pi$
$769$	425.000			0.552666			0.276333	+	0.961062i	$0.410881\pi$
$770$		0			0
$771$		−	100.459i		−	0.130297i
$772$	302.000	−	523.079i	0.391192	−	0.677564i
$773$	130.000			0.168176			0.0840880	−	0.996458i	$-0.473202\pi$
$773$	130.000			0.168176			0.0840880	+	0.996458i	$0.473202\pi$
$774$	126.000	−	72.7461i	0.162791	−	0.0939873i
$775$		0			0
$776$	376.000			0.484536
$777$		0			0
$778$	410.000	+	710.141i	0.526992	+	0.912777i
$779$			1108.51i			1.42299i
$780$	480.000	+	277.128i	0.615385	+	0.355292i
$781$	−378.000			−0.483995
$782$	144.000	−	83.1384i	0.184143	−	0.106315i
$783$			192.258i			0.245540i
$784$		0			0
$785$	260.000			0.331210
$786$	−27.0000	−	46.7654i	−0.0343511	−	0.0594979i
$787$		−	1001.13i		−	1.27208i	−0.771657	−	0.636039i	$-0.780572\pi$
$787$		−	1001.13i		−	1.27208i	0.771657	−	0.636039i	$-0.219428\pi$
$788$	556.000	−	963.020i	0.705584	−	1.22211i
$789$	−702.000			−0.889734
$790$	−75.0000	+	43.3013i	−0.0949367	+	0.0548117i
$791$		0			0
$792$			124.708i			0.157459i
$793$	1312.00			1.65448
$794$	−212.000	−	367.195i	−0.267003	−	0.462462i
$795$			632.199i			0.795218i
$796$	−480.000	−	277.128i	−0.603015	−	0.348151i
$797$	439.000			0.550816			0.275408	−	0.961327i	$-0.411187\pi$
$797$	439.000			0.550816			0.275408	+	0.961327i	$0.411187\pi$
$798$		0			0
$799$		−	180.133i		−	0.225448i
$800$		0			0
$801$	−174.000			−0.217228
$802$	464.000	+	803.672i	0.578554	+	1.00208i
$803$			488.438i			0.608267i
$804$	−276.000	+	478.046i	−0.343284	+	0.594585i
$805$		0			0
$806$	528.000	−	304.841i	0.655087	−	0.378215i
$807$		−	770.763i		−	0.955096i
$808$	1040.00			1.28713
$809$	−1040.00			−1.28554			−0.642769	−	0.766060i	$-0.722214\pi$
$809$	−1040.00			−1.28554			−0.642769	+	0.766060i	$0.722214\pi$
$810$	45.0000	+	77.9423i	0.0555556	+	0.0962250i
$811$			1236.68i			1.52489i	0.647054	+	0.762444i	$0.276001\pi$
$811$			1236.68i			1.52489i	−0.647054	+	0.762444i	$0.723999\pi$
$812$		0			0
$813$	615.000			0.756458
$814$	−612.000	+	353.338i	−0.751843	+	0.434077i
$815$			381.051i			0.467547i
$816$	−96.0000	+	55.4256i	−0.117647	+	0.0679236i
$817$	672.000			0.822521
$818$	−515.000	−	892.006i	−0.629584	−	1.09047i
$819$		0			0
$820$	400.000	−	692.820i	0.487805	−	0.844903i
$821$	145.000			0.176614			0.0883069	−	0.996093i	$-0.471854\pi$
$821$	145.000			0.176614			0.0883069	+	0.996093i	$0.471854\pi$
$822$	222.000	−	128.172i	0.270073	−	0.155927i
$823$		−	1447.99i		−	1.75941i	−0.475520	−	0.879705i	$-0.657740\pi$
$823$		−	1447.99i		−	1.75941i	0.475520	−	0.879705i	$-0.342260\pi$
$824$		−	166.277i		−	0.201792i
$825$		0			0
$826$		0			0
$827$		−	545.596i		−	0.659729i	−0.944028	−	0.329865i	$-0.892997\pi$
$827$		−	545.596i		−	0.659729i	0.944028	−	0.329865i	$-0.107003\pi$
$828$	216.000	+	124.708i	0.260870	+	0.150613i
$829$	368.000			0.443908			0.221954	−	0.975057i	$-0.428756\pi$
$829$	368.000			0.443908			0.221954	+	0.975057i	$0.428756\pi$
$830$	−1155.00	+	666.840i	−1.39157	+	0.803421i
$831$			443.405i			0.533580i
$832$	−1024.00			−1.23077
$833$		0			0
$834$	−294.000	−	509.223i	−0.352518	−	0.610579i
$835$			848.705i			1.01641i
$836$	−288.000	+	498.831i	−0.344498	+	0.596687i
$837$	99.0000			0.118280
$838$	−168.000	+	96.9948i	−0.200477	+	0.115746i
$839$		−	921.451i		−	1.09827i	−0.835733	−	0.549136i	$-0.814957\pi$
$839$		−	921.451i		−	1.09827i	0.835733	−	0.549136i	$-0.185043\pi$
$840$		0			0
$841$	528.000			0.627824
$842$	−170.000	−	294.449i	−0.201900	−	0.349701i
$843$			481.510i			0.571186i
$844$	420.000	+	242.487i	0.497630	+	0.287307i
$845$	−435.000			−0.514793
$846$	234.000	−	135.100i	0.276596	−	0.159693i
$847$		0			0
$848$	−584.000	−	1011.52i	−0.688679	−	1.19283i
$849$	30.0000			0.0353357
$850$		0			0
$851$			1413.35i			1.66081i
$852$	252.000	−	436.477i	0.295775	−	0.512297i
$853$	−1150.00			−1.34818			−0.674091	−	0.738648i	$-0.735465\pi$
$853$	−1150.00			−1.34818			−0.674091	+	0.738648i	$0.735465\pi$
$854$		0			0
$855$			415.692i			0.486190i
$856$			651.251i			0.760807i
$857$	214.000			0.249708			0.124854	−	0.992175i	$-0.460154\pi$
$857$	214.000			0.249708			0.124854	+	0.992175i	$0.460154\pi$
$858$	−144.000	−	249.415i	−0.167832	−	0.290694i
$859$		−	820.992i		−	0.955753i	−0.878427	−	0.477877i	$-0.841407\pi$
$859$		−	820.992i		−	0.955753i	0.878427	−	0.477877i	$-0.158593\pi$
$860$	−420.000	−	242.487i	−0.488372	−	0.281962i
$861$		0			0
$862$	12.0000	−	6.92820i	0.0139211	−	0.00803736i
$863$		−	391.443i		−	0.453585i	−0.973943	−	0.226792i	$-0.927176\pi$
$863$		−	391.443i		−	0.453585i	0.973943	−	0.226792i	$-0.0728239\pi$
$864$	−144.000	−	83.1384i	−0.166667	−	0.0962250i
$865$	130.000			0.150289
$866$	226.000	+	391.443i	0.260970	+	0.452013i
$867$			472.850i			0.545386i
$868$		0			0
$869$	45.0000			0.0517837
$870$	555.000	−	320.429i	0.637931	−	0.368310i
$871$		−	1274.79i		−	1.46359i
$872$	976.000			1.11927
$873$	−141.000			−0.161512
$874$	576.000	+	997.661i	0.659039	+	1.14149i
$875$		0			0
$876$	−564.000	−	325.626i	−0.643836	−	0.371719i
$877$	320.000			0.364880			0.182440	−	0.983217i	$-0.441600\pi$
$877$	320.000			0.364880			0.182440	+	0.983217i	$0.441600\pi$
$878$	−309.000	+	178.401i	−0.351936	+	0.203190i
$879$		−	105.655i		−	0.120199i
$880$	360.000	−	207.846i	0.409091	−	0.236189i
$881$	502.000			0.569807			0.284904	−	0.958556i	$-0.408038\pi$
$881$	502.000			0.569807			0.284904	+	0.958556i	$0.408038\pi$
$882$		0			0
$883$			290.985i			0.329541i	0.986332	+	0.164770i	$0.0526883\pi$
$883$			290.985i			0.329541i	−0.986332	+	0.164770i	$0.947312\pi$
$884$	128.000	−	221.703i	0.144796	−	0.250795i
$885$	−255.000			−0.288136
$886$	−1077.00	+	621.806i	−1.21558	+	0.701813i
$887$			270.200i			0.304622i	0.988333	+	0.152311i	$0.0486716\pi$
$887$			270.200i			0.304622i	−0.988333	+	0.152311i	$0.951328\pi$
$888$		−	942.236i		−	1.06108i
$889$		0			0
$890$	290.000	+	502.295i	0.325843	+	0.564376i
$891$		−	46.7654i		−	0.0524864i
$892$	−42.0000	−	24.2487i	−0.0470852	−	0.0271847i
$893$	1248.00			1.39754
$894$	−498.000	+	287.520i	−0.557047	+	0.321611i
$895$		−	1489.56i		−	1.66432i
$896$		0			0
$897$	−576.000			−0.642140
$898$	−520.000	−	900.666i	−0.579065	−	1.00297i
$899$		−	704.945i		−	0.784143i
$900$		0			0
$901$	292.000			0.324084
$902$	−360.000	+	207.846i	−0.399113	+	0.230428i
$903$		0			0
$904$	128.000			0.141593
$905$	80.0000			0.0883978
$906$	−243.000	−	420.888i	−0.268212	−	0.464557i
$907$		−	187.061i		−	0.206242i	−0.994669	−	0.103121i	$-0.967117\pi$
$907$		−	187.061i		−	0.206242i	0.994669	−	0.103121i	$-0.0328829\pi$
$908$	−522.000	−	301.377i	−0.574890	−	0.331913i
$909$	−390.000			−0.429043
$910$		0			0
$911$			1624.66i			1.78338i	0.452642	+	0.891692i	$0.350482\pi$
$911$			1624.66i			1.78338i	−0.452642	+	0.891692i	$0.649518\pi$
$912$	−384.000	−	665.108i	−0.421053	−	0.729285i
$913$	693.000			0.759036
$914$	37.0000	+	64.0859i	0.0404814	+	0.0701158i
$915$		−	710.141i		−	0.776110i
$916$	−424.000	+	734.390i	−0.462882	+	0.801735i
$917$		0			0
$918$	36.0000	−	20.7846i	0.0392157	−	0.0226412i
$919$		−	76.2102i		−	0.0829274i	−0.999140	−	0.0414637i	$-0.986798\pi$
$919$		−	76.2102i		−	0.0829274i	0.999140	−	0.0414637i	$-0.0132021\pi$
$920$		−	831.384i		−	0.903679i
$921$	756.000			0.820847
$922$	−250.000	−	433.013i	−0.271150	−	0.469645i
$923$			1163.94i			1.26104i
$924$		0			0
$925$		0			0
$926$	−588.000	+	339.482i	−0.634989	+	0.366611i
$927$			62.3538i			0.0672641i
$928$	−592.000	+	1025.37i	−0.637931	+	1.10493i
$929$	−1286.00			−1.38428			−0.692142	−	0.721761i	$-0.743333\pi$
$929$	−1286.00			−1.38428			−0.692142	+	0.721761i	$0.743333\pi$
$930$	−165.000	−	285.788i	−0.177419	−	0.307299i
$931$		0			0
$932$	424.000	−	734.390i	0.454936	−	0.787972i
$933$	−264.000			−0.282958
$934$	−1380.00	+	796.743i	−1.47752	+	0.853044i
$935$			103.923i			0.111148i
$936$	384.000			0.410256
$937$	1727.00			1.84312			0.921558	−	0.388240i	$-0.126917\pi$
$937$	1727.00			1.84312			0.921558	+	0.388240i	$0.126917\pi$
$938$		0			0
$939$		−	403.568i		−	0.429785i
$940$	−780.000	−	450.333i	−0.829787	−	0.479078i
$941$	403.000			0.428268			0.214134	−	0.976804i	$-0.431307\pi$
$941$	403.000			0.428268			0.214134	+	0.976804i	$0.431307\pi$
$942$	156.000	−	90.0666i	0.165605	−	0.0956121i
$943$			831.384i			0.881638i
$944$	408.000	−	235.559i	0.432203	−	0.249533i
$945$		0			0
$946$	126.000	+	218.238i	0.133192	+	0.230696i
$947$			942.236i			0.994969i	0.867473	+	0.497484i	$0.165743\pi$
$947$			942.236i			0.994969i	−0.867473	+	0.497484i	$0.834257\pi$
$948$	−30.0000	+	51.9615i	−0.0316456	+	0.0548117i
$949$	1504.00			1.58483
$950$		0			0
$951$			185.329i			0.194878i
$952$		0			0
$953$	730.000			0.766002			0.383001	−	0.923748i	$-0.374891\pi$
$953$	730.000			0.766002			0.383001	+	0.923748i	$0.374891\pi$
$954$	219.000	+	379.319i	0.229560	+	0.397609i
$955$		−	1801.33i		−	1.88621i
$956$	−168.000	−	96.9948i	−0.175732	−	0.101459i
$957$	−333.000			−0.347962
$958$	−306.000	+	176.669i	−0.319415	+	0.184415i
$959$		0			0
$960$			554.256i			0.577350i
$961$	598.000			0.622268
$962$	1088.00	+	1884.47i	1.13098	+	1.95891i
$963$		−	244.219i		−	0.253602i
$964$	−22.0000	+	38.1051i	−0.0228216	+	0.0395281i
$965$	755.000			0.782383
$966$		0			0
$967$		−	157.617i		−	0.162995i	−0.996674	−	0.0814977i	$-0.974030\pi$
$967$		−	157.617i		−	0.162995i	0.996674	−	0.0814977i	$-0.0259703\pi$
$968$	752.000			0.776860
$969$	192.000			0.198142
$970$	235.000	+	407.032i	0.242268	+	0.419621i
$971$			912.791i			0.940052i	0.882652	+	0.470026i	$0.155756\pi$
$971$			912.791i			0.940052i	−0.882652	+	0.470026i	$0.844244\pi$
$972$	54.0000	+	31.1769i	0.0555556	+	0.0320750i
$973$		0			0
$974$	537.000	−	310.037i	0.551335	−	0.318313i
$975$		0			0
$976$	656.000	+	1136.23i	0.672131	+	1.16417i
$977$	346.000			0.354145			0.177073	−	0.984198i	$-0.443337\pi$
$977$	346.000			0.354145			0.177073	+	0.984198i	$0.443337\pi$
$978$	132.000	+	228.631i	0.134969	+	0.233774i
$979$		−	301.377i		−	0.307842i
$980$		0			0
$981$	−366.000			−0.373089
$982$	399.000	−	230.363i	0.406314	−	0.234585i
$983$			769.031i			0.782330i	0.920321	+	0.391165i	$0.127928\pi$
$983$			769.031i			0.782330i	−0.920321	+	0.391165i	$0.872072\pi$
$984$		−	554.256i		−	0.563269i
$985$	1390.00			1.41117
$986$	−148.000	−	256.344i	−0.150101	−	0.259983i
$987$		0			0
$988$	1536.00	+	886.810i	1.55466	+	0.897581i
$989$	504.000			0.509606
$990$	−135.000	+	77.9423i	−0.136364	+	0.0787296i
$991$			1110.24i			1.12033i	0.828382	+	0.560164i	$0.189262\pi$
$991$			1110.24i			1.12033i	−0.828382	+	0.560164i	$0.810738\pi$
$992$	528.000	+	304.841i	0.532258	+	0.307299i
$993$	708.000			0.712991
$994$		0			0
$995$		−	692.820i		−	0.696302i
$996$	−462.000	+	800.207i	−0.463855	+	0.803421i
$997$	−430.000			−0.431294			−0.215647	−	0.976471i	$-0.569186\pi$
$997$	−430.000			−0.431294			−0.215647	+	0.976471i	$0.569186\pi$
$998$	414.000	−	239.023i	0.414830	−	0.239502i
$999$			353.338i			0.353692i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.3.g.a.295.1		2
4.3	odd	2	inner	588.3.g.a.295.2		2
7.2	even	3		84.3.l.a.67.1	✓	2
7.4	even	3		84.3.l.b.79.1	yes	2
7.6	odd	2		588.3.g.c.295.1		2
21.2	odd	6		252.3.y.b.235.1		2
21.11	odd	6		252.3.y.a.163.1		2
28.11	odd	6		84.3.l.a.79.1	yes	2
28.23	odd	6		84.3.l.b.67.1	yes	2
28.27	even	2		588.3.g.c.295.2		2
84.11	even	6		252.3.y.b.163.1		2
84.23	even	6		252.3.y.a.235.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.3.l.a.67.1	✓	2	7.2	even	3
84.3.l.a.79.1	yes	2	28.11	odd	6
84.3.l.b.67.1	yes	2	28.23	odd	6
84.3.l.b.79.1	yes	2	7.4	even	3
252.3.y.a.163.1		2	21.11	odd	6
252.3.y.a.235.1		2	84.23	even	6
252.3.y.b.163.1		2	84.11	even	6
252.3.y.b.235.1		2	21.2	odd	6
588.3.g.a.295.1		2	1.1	even	1	trivial
588.3.g.a.295.2		2	4.3	odd	2	inner
588.3.g.c.295.1		2	7.6	odd	2
588.3.g.c.295.2		2	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	588.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} -1.73205i q^{3} +(-2.00000 + 3.46410i) q^{4} -5.00000 q^{5} +(-3.00000 + 1.73205i) q^{6} +8.00000 q^{8} -3.00000 q^{9} +(5.00000 + 8.66025i) q^{10} -5.19615i q^{11} +(6.00000 + 3.46410i) q^{12} -16.0000 q^{13} +8.66025i q^{15} +(-8.00000 - 13.8564i) q^{16} +4.00000 q^{17} +(3.00000 + 5.19615i) q^{18} +27.7128i q^{19} +(10.0000 - 17.3205i) q^{20} +(-9.00000 + 5.19615i) q^{22} +20.7846i q^{23} -13.8564i q^{24} +(16.0000 + 27.7128i) q^{26} +5.19615i q^{27} +37.0000 q^{29} +(15.0000 - 8.66025i) q^{30} -19.0526i q^{31} +(-16.0000 + 27.7128i) q^{32} -9.00000 q^{33} +(-4.00000 - 6.92820i) q^{34} +(6.00000 - 10.3923i) q^{36} +68.0000 q^{37} +(48.0000 - 27.7128i) q^{38} +27.7128i q^{39} -40.0000 q^{40} +40.0000 q^{41} -24.2487i q^{43} +(18.0000 + 10.3923i) q^{44} +15.0000 q^{45} +(36.0000 - 20.7846i) q^{46} -45.0333i q^{47} +(-24.0000 + 13.8564i) q^{48} -6.92820i q^{51} +(32.0000 - 55.4256i) q^{52} +73.0000 q^{53} +(9.00000 - 5.19615i) q^{54} +25.9808i q^{55} +48.0000 q^{57} +(-37.0000 - 64.0859i) q^{58} +29.4449i q^{59} +(-30.0000 - 17.3205i) q^{60} -82.0000 q^{61} +(-33.0000 + 19.0526i) q^{62} +64.0000 q^{64} +80.0000 q^{65} +(9.00000 + 15.5885i) q^{66} +79.6743i q^{67} +(-8.00000 + 13.8564i) q^{68} +36.0000 q^{69} -72.7461i q^{71} -24.0000 q^{72} -94.0000 q^{73} +(-68.0000 - 117.779i) q^{74} +(-96.0000 - 55.4256i) q^{76} +(48.0000 - 27.7128i) q^{78} +8.66025i q^{79} +(40.0000 + 69.2820i) q^{80} +9.00000 q^{81} +(-40.0000 - 69.2820i) q^{82} +133.368i q^{83} -20.0000 q^{85} +(-42.0000 + 24.2487i) q^{86} -64.0859i q^{87} -41.5692i q^{88} +58.0000 q^{89} +(-15.0000 - 25.9808i) q^{90} +(-72.0000 - 41.5692i) q^{92} -33.0000 q^{93} +(-78.0000 + 45.0333i) q^{94} -138.564i q^{95} +(48.0000 + 27.7128i) q^{96} +47.0000 q^{97} +15.5885i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 4 q^{4} - 10 q^{5} - 6 q^{6} + 16 q^{8} - 6 q^{9} + 10 q^{10} + 12 q^{12} - 32 q^{13} - 16 q^{16} + 8 q^{17} + 6 q^{18} + 20 q^{20} - 18 q^{22} + 32 q^{26} + 74 q^{29} + 30 q^{30} - 32 q^{32}+ \cdots + 94 q^{97}+O(q^{100}) \) 2 * q - 2 * q^2 - 4 * q^4 - 10 * q^5 - 6 * q^6 + 16 * q^8 - 6 * q^9 + 10 * q^10 + 12 * q^12 - 32 * q^13 - 16 * q^16 + 8 * q^17 + 6 * q^18 + 20 * q^20 - 18 * q^22 + 32 * q^26 + 74 * q^29 + 30 * q^30 - 32 * q^32 - 18 * q^33 - 8 * q^34 + 12 * q^36 + 136 * q^37 + 96 * q^38 - 80 * q^40 + 80 * q^41 + 36 * q^44 + 30 * q^45 + 72 * q^46 - 48 * q^48 + 64 * q^52 + 146 * q^53 + 18 * q^54 + 96 * q^57 - 74 * q^58 - 60 * q^60 - 164 * q^61 - 66 * q^62 + 128 * q^64 + 160 * q^65 + 18 * q^66 - 16 * q^68 + 72 * q^69 - 48 * q^72 - 188 * q^73 - 136 * q^74 - 192 * q^76 + 96 * q^78 + 80 * q^80 + 18 * q^81 - 80 * q^82 - 40 * q^85 - 84 * q^86 + 116 * q^89 - 30 * q^90 - 144 * q^92 - 66 * q^93 - 156 * q^94 + 96 * q^96 + 94 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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