LMFDB - Embedded newform 416.3.x.a.303.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [416,3,Mod(303,416)] 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("416.303"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(416, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 3, names="a")

Level:	$N$	$=$	$416 = 2^{5} \cdot 13$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	416.x (of order $6$ , degree $2$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,1,0,-4] 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:	$11.3351789974$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			303.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	416.303
Dual form			416.3.x.a.335.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} -2.00000 q^{5} +(-2.50000 - 4.33013i) q^{7} +(4.00000 + 6.92820i) q^{9} +(-10.5000 - 6.06218i) q^{11} -13.0000 q^{13} +(-1.00000 + 1.73205i) q^{15} +(12.5000 + 21.6506i) q^{17} +(-10.5000 + 6.06218i) q^{19} -5.00000 q^{21} +(-7.50000 - 4.33013i) q^{23} -21.0000 q^{25} +17.0000 q^{27} +(-19.5000 - 11.2583i) q^{29} -10.0000 q^{31} +(-10.5000 + 6.06218i) q^{33} +(5.00000 + 8.66025i) q^{35} +(-30.5000 + 52.8275i) q^{37} +(-6.50000 + 11.2583i) q^{39} +(1.50000 + 0.866025i) q^{41} +(20.5000 + 35.5070i) q^{43} +(-8.00000 - 13.8564i) q^{45} -82.0000 q^{47} +(12.0000 - 20.7846i) q^{49} +25.0000 q^{51} -41.5692i q^{53} +(21.0000 + 12.1244i) q^{55} +12.1244i q^{57} +(-46.5000 + 26.8468i) q^{59} +(52.5000 - 30.3109i) q^{61} +(20.0000 - 34.6410i) q^{63} +26.0000 q^{65} +(-10.5000 - 6.06218i) q^{67} +(-7.50000 + 4.33013i) q^{69} +(-14.5000 - 25.1147i) q^{71} -41.5692i q^{73} +(-10.5000 + 18.1865i) q^{75} +60.6218i q^{77} +124.708i q^{79} +(-27.5000 + 47.6314i) q^{81} +(-25.0000 - 43.3013i) q^{85} +(-19.5000 + 11.2583i) q^{87} +(-34.5000 - 19.9186i) q^{89} +(32.5000 + 56.2917i) q^{91} +(-5.00000 + 8.66025i) q^{93} +(21.0000 - 12.1244i) q^{95} +(1.50000 - 0.866025i) q^{97} -96.9948i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q + q^{3} - 4 q^{5} - 5 q^{7} + 8 q^{9} - 21 q^{11} - 26 q^{13} - 2 q^{15} + 25 q^{17} - 21 q^{19} - 10 q^{21} - 15 q^{23} - 42 q^{25} + 34 q^{27} - 39 q^{29} - 20 q^{31} - 21 q^{33} + 10 q^{35} - 61 q^{37}+ \cdots + 3 q^{97}+O(q^{100})$ 2 * q + q^3 - 4 * q^5 - 5 * q^7 + 8 * q^9 - 21 * q^11 - 26 * q^13 - 2 * q^15 + 25 * q^17 - 21 * q^19 - 10 * q^21 - 15 * q^23 - 42 * q^25 + 34 * q^27 - 39 * q^29 - 20 * q^31 - 21 * q^33 + 10 * q^35 - 61 * q^37 - 13 * q^39 + 3 * q^41 + 41 * q^43 - 16 * q^45 - 164 * q^47 + 24 * q^49 + 50 * q^51 + 42 * q^55 - 93 * q^59 + 105 * q^61 + 40 * q^63 + 52 * q^65 - 21 * q^67 - 15 * q^69 - 29 * q^71 - 21 * q^75 - 55 * q^81 - 50 * q^85 - 39 * q^87 - 69 * q^89 + 65 * q^91 - 10 * q^93 + 42 * q^95 + 3 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$ .

$n$	$261$	$287$	$353$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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

)

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

$2$		0			0
$2$		0			0
$3$	0.500000	−	0.866025i	0.166667	−	0.288675i	−0.770579	−	0.637344i	$-0.780033\pi$
$3$	0.500000	−	0.866025i	0.166667	−	0.288675i	0.937246	+	0.348669i	$0.113366\pi$
$4$		0			0
$5$	−2.00000			−0.400000			−0.200000	−	0.979796i	$-0.564094\pi$
$5$	−2.00000			−0.400000			−0.200000	+	0.979796i	$0.564094\pi$
$6$		0			0
$7$	−2.50000	−	4.33013i	−0.357143	−	0.618590i	0.630339	−	0.776320i	$-0.282916\pi$
$7$	−2.50000	−	4.33013i	−0.357143	−	0.618590i	−0.987482	+	0.157730i	$0.949582\pi$
$8$		0			0
$9$	4.00000	+	6.92820i	0.444444	+	0.769800i
$10$		0			0
$11$	−10.5000	−	6.06218i	−0.954545	−	0.551107i	−0.0600555	−	0.998195i	$-0.519128\pi$
$11$	−10.5000	−	6.06218i	−0.954545	−	0.551107i	−0.894490	+	0.447088i	$0.852461\pi$
$12$		0			0
$13$	−13.0000			−1.00000
$13$	−13.0000			−1.00000
$14$		0			0
$15$	−1.00000	+	1.73205i	−0.0666667	+	0.115470i
$16$		0			0
$17$	12.5000	+	21.6506i	0.735294	+	1.27357i	0.954594	+	0.297909i	$0.0962893\pi$
$17$	12.5000	+	21.6506i	0.735294	+	1.27357i	−0.219300	+	0.975657i	$0.570377\pi$
$18$		0			0
$19$	−10.5000	+	6.06218i	−0.552632	+	0.319062i	−0.750183	−	0.661231i	$-0.770034\pi$
$19$	−10.5000	+	6.06218i	−0.552632	+	0.319062i	0.197551	+	0.980293i	$0.436701\pi$
$20$		0			0
$21$	−5.00000			−0.238095
$22$		0			0
$23$	−7.50000	−	4.33013i	−0.326087	−	0.188266i	0.328016	−	0.944672i	$-0.393620\pi$
$23$	−7.50000	−	4.33013i	−0.326087	−	0.188266i	−0.654102	+	0.756406i	$0.726954\pi$
$24$		0			0
$25$	−21.0000			−0.840000
$26$		0			0
$27$	17.0000			0.629630
$28$		0			0
$29$	−19.5000	−	11.2583i	−0.672414	−	0.388218i	0.124577	−	0.992210i	$-0.460243\pi$
$29$	−19.5000	−	11.2583i	−0.672414	−	0.388218i	−0.796991	+	0.603992i	$0.793576\pi$
$30$		0			0
$31$	−10.0000			−0.322581			−0.161290	−	0.986907i	$-0.551566\pi$
$31$	−10.0000			−0.322581			−0.161290	+	0.986907i	$0.551566\pi$
$32$		0			0
$33$	−10.5000	+	6.06218i	−0.318182	+	0.183702i
$34$		0			0
$35$	5.00000	+	8.66025i	0.142857	+	0.247436i
$36$		0			0
$37$	−30.5000	+	52.8275i	−0.824324	+	1.42777i	0.0781103	+	0.996945i	$0.475111\pi$
$37$	−30.5000	+	52.8275i	−0.824324	+	1.42777i	−0.902435	+	0.430827i	$0.858222\pi$
$38$		0			0
$39$	−6.50000	+	11.2583i	−0.166667	+	0.288675i
$40$		0			0
$41$	1.50000	+	0.866025i	0.0365854	+	0.0211226i	0.518181	−	0.855271i	$-0.326609\pi$
$41$	1.50000	+	0.866025i	0.0365854	+	0.0211226i	−0.481596	+	0.876393i	$0.659943\pi$
$42$		0			0
$43$	20.5000	+	35.5070i	0.476744	+	0.825745i	0.999645	−	0.0266485i	$-0.00848347\pi$
$43$	20.5000	+	35.5070i	0.476744	+	0.825745i	−0.522901	+	0.852394i	$0.675150\pi$
$44$		0			0
$45$	−8.00000	−	13.8564i	−0.177778	−	0.307920i
$46$		0			0
$47$	−82.0000			−1.74468			−0.872340	−	0.488899i	$-0.837399\pi$
$47$	−82.0000			−1.74468			−0.872340	+	0.488899i	$0.837399\pi$
$48$		0			0
$49$	12.0000	−	20.7846i	0.244898	−	0.424176i
$50$		0			0
$51$	25.0000			0.490196
$52$		0			0
$53$		−	41.5692i		−	0.784325i	−0.919896	−	0.392162i	$-0.871727\pi$
$53$		−	41.5692i		−	0.784325i	0.919896	−	0.392162i	$-0.128273\pi$
$54$		0			0
$55$	21.0000	+	12.1244i	0.381818	+	0.220443i
$56$		0			0
$57$			12.1244i			0.212708i
$58$		0			0
$59$	−46.5000	+	26.8468i	−0.788136	+	0.455030i	−0.839306	−	0.543660i	$-0.817038\pi$
$59$	−46.5000	+	26.8468i	−0.788136	+	0.455030i	0.0511702	+	0.998690i	$0.483705\pi$
$60$		0			0
$61$	52.5000	−	30.3109i	0.860656	−	0.496900i	−0.00357609	−	0.999994i	$-0.501138\pi$
$61$	52.5000	−	30.3109i	0.860656	−	0.496900i	0.864232	+	0.503094i	$0.167805\pi$
$62$		0			0
$63$	20.0000	−	34.6410i	0.317460	−	0.549857i
$64$		0			0
$65$	26.0000			0.400000
$66$		0			0
$67$	−10.5000	−	6.06218i	−0.156716	−	0.0904803i	0.419591	−	0.907713i	$-0.362174\pi$
$67$	−10.5000	−	6.06218i	−0.156716	−	0.0904803i	−0.576307	+	0.817233i	$0.695507\pi$
$68$		0			0
$69$	−7.50000	+	4.33013i	−0.108696	+	0.0627555i
$70$		0			0
$71$	−14.5000	−	25.1147i	−0.204225	−	0.353729i	0.745660	−	0.666326i	$-0.232134\pi$
$71$	−14.5000	−	25.1147i	−0.204225	−	0.353729i	−0.949886	+	0.312598i	$0.898801\pi$
$72$		0			0
$73$		−	41.5692i		−	0.569441i	−0.958611	−	0.284721i	$-0.908099\pi$
$73$		−	41.5692i		−	0.569441i	0.958611	−	0.284721i	$-0.0919009\pi$
$74$		0			0
$75$	−10.5000	+	18.1865i	−0.140000	+	0.242487i
$76$		0			0
$77$			60.6218i			0.787296i
$78$		0			0
$79$			124.708i			1.57858i	0.614022	+	0.789289i	$0.289551\pi$
$79$			124.708i			1.57858i	−0.614022	+	0.789289i	$0.710449\pi$
$80$		0			0
$81$	−27.5000	+	47.6314i	−0.339506	+	0.588042i
$82$		0			0
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$		0			0
$85$	−25.0000	−	43.3013i	−0.294118	−	0.509427i
$86$		0			0
$87$	−19.5000	+	11.2583i	−0.224138	+	0.129406i
$88$		0			0
$89$	−34.5000	−	19.9186i	−0.387640	−	0.223804i	0.293497	−	0.955960i	$-0.405181\pi$
$89$	−34.5000	−	19.9186i	−0.387640	−	0.223804i	−0.681137	+	0.732156i	$0.738514\pi$
$90$		0			0
$91$	32.5000	+	56.2917i	0.357143	+	0.618590i
$92$		0			0
$93$	−5.00000	+	8.66025i	−0.0537634	+	0.0931210i
$94$		0			0
$95$	21.0000	−	12.1244i	0.221053	−	0.127625i
$96$		0			0
$97$	1.50000	−	0.866025i	0.0154639	−	0.00892810i	−0.492248	−	0.870455i	$-0.663825\pi$
$97$	1.50000	−	0.866025i	0.0154639	−	0.00892810i	0.507712	+	0.861527i	$0.330491\pi$
$98$		0			0
$99$		−	96.9948i		−	0.979746i
$100$		0			0
$101$	52.5000	+	30.3109i	0.519802	+	0.300108i	0.736854	−	0.676052i	$-0.236311\pi$
$101$	52.5000	+	30.3109i	0.519802	+	0.300108i	−0.217052	+	0.976160i	$0.569644\pi$
$102$		0			0
$103$		−	166.277i		−	1.61434i	−0.590320	−	0.807169i	$-0.700998\pi$
$103$		−	166.277i		−	1.61434i	0.590320	−	0.807169i	$-0.299002\pi$
$104$		0			0
$105$	10.0000			0.0952381
$106$		0			0
$107$	44.5000	−	77.0763i	0.415888	−	0.720339i	−0.579633	−	0.814877i	$-0.696804\pi$
$107$	44.5000	−	77.0763i	0.415888	−	0.720339i	0.995521	+	0.0945385i	$0.0301375\pi$
$108$		0			0
$109$	94.0000			0.862385			0.431193	−	0.902260i	$-0.358093\pi$
$109$	94.0000			0.862385			0.431193	+	0.902260i	$0.358093\pi$
$110$		0			0
$111$	30.5000	+	52.8275i	0.274775	+	0.475924i
$112$		0			0
$113$	−83.5000	−	144.626i	−0.738938	−	1.27988i	−0.952974	−	0.303052i	$-0.901994\pi$
$113$	−83.5000	−	144.626i	−0.738938	−	1.27988i	0.214036	−	0.976826i	$-0.431339\pi$
$114$		0			0
$115$	15.0000	+	8.66025i	0.130435	+	0.0753066i
$116$		0			0
$117$	−52.0000	−	90.0666i	−0.444444	−	0.769800i
$118$		0			0
$119$	62.5000	−	108.253i	0.525210	−	0.909691i
$120$		0			0
$121$	13.0000	+	22.5167i	0.107438	+	0.186088i
$122$		0			0
$123$	1.50000	−	0.866025i	0.0121951	−	0.00704086i
$124$		0			0
$125$	92.0000			0.736000
$126$		0			0
$127$	208.500	+	120.378i	1.64173	+	0.947855i	0.980218	+	0.197922i	$0.0634194\pi$
$127$	208.500	+	120.378i	1.64173	+	0.947855i	0.661515	+	0.749932i	$0.269914\pi$
$128$		0			0
$129$	41.0000			0.317829
$130$		0			0
$131$	−110.000			−0.839695			−0.419847	−	0.907595i	$-0.637916\pi$
$131$	−110.000			−0.839695			−0.419847	+	0.907595i	$0.637916\pi$
$132$		0			0
$133$	52.5000	+	30.3109i	0.394737	+	0.227901i
$134$		0			0
$135$	−34.0000			−0.251852
$136$		0			0
$137$	109.500	−	63.2199i	0.799270	−	0.461459i	−0.0439458	−	0.999034i	$-0.513993\pi$
$137$	109.500	−	63.2199i	0.799270	−	0.461459i	0.843216	+	0.537575i	$0.180660\pi$
$138$		0			0
$139$	−63.5000	−	109.985i	−0.456835	−	0.791261i	0.541957	−	0.840406i	$-0.317684\pi$
$139$	−63.5000	−	109.985i	−0.456835	−	0.791261i	−0.998792	+	0.0491455i	$0.984350\pi$
$140$		0			0
$141$	−41.0000	+	71.0141i	−0.290780	+	0.503646i
$142$		0			0
$143$	136.500	+	78.8083i	0.954545	+	0.551107i
$144$		0			0
$145$	39.0000	+	22.5167i	0.268966	+	0.155287i
$146$		0			0
$147$	−12.0000	−	20.7846i	−0.0816327	−	0.141392i
$148$		0			0
$149$	29.5000	+	51.0955i	0.197987	+	0.342923i	0.947875	−	0.318641i	$-0.103226\pi$
$149$	29.5000	+	51.0955i	0.197987	+	0.342923i	−0.749889	+	0.661564i	$0.769893\pi$
$150$		0			0
$151$	−10.0000			−0.0662252			−0.0331126	−	0.999452i	$-0.510542\pi$
$151$	−10.0000			−0.0662252			−0.0331126	+	0.999452i	$0.510542\pi$
$152$		0			0
$153$	−100.000	+	173.205i	−0.653595	+	1.13206i
$154$		0			0
$155$	20.0000			0.129032
$156$		0			0
$157$		−	41.5692i		−	0.264772i	−0.991198	−	0.132386i	$-0.957736\pi$
$157$		−	41.5692i		−	0.264772i	0.991198	−	0.132386i	$-0.0422639\pi$
$158$		0			0
$159$	−36.0000	−	20.7846i	−0.226415	−	0.130721i
$160$		0			0
$161$			43.3013i			0.268952i
$162$		0			0
$163$	241.500	−	139.430i	1.48160	−	0.855399i	0.481813	−	0.876274i	$-0.339978\pi$
$163$	241.500	−	139.430i	1.48160	−	0.855399i	0.999782	+	0.0208747i	$0.00664512\pi$
$164$		0			0
$165$	21.0000	−	12.1244i	0.127273	−	0.0734809i
$166$		0			0
$167$	69.5000	−	120.378i	0.416168	−	0.720824i	−0.579383	−	0.815056i	$-0.696706\pi$
$167$	69.5000	−	120.378i	0.416168	−	0.720824i	0.995550	+	0.0942322i	$0.0300396\pi$
$168$		0			0
$169$	169.000			1.00000
$170$		0			0
$171$	−84.0000	−	48.4974i	−0.491228	−	0.283611i
$172$		0			0
$173$	52.5000	−	30.3109i	0.303468	−	0.175207i	−0.340532	−	0.940233i	$-0.610607\pi$
$173$	52.5000	−	30.3109i	0.303468	−	0.175207i	0.644000	+	0.765026i	$0.277274\pi$
$174$		0			0
$175$	52.5000	+	90.9327i	0.300000	+	0.519615i
$176$		0			0
$177$			53.6936i			0.303354i
$178$		0			0
$179$	−111.500	+	193.124i	−0.622905	+	1.07890i	0.366037	+	0.930600i	$0.380714\pi$
$179$	−111.500	+	193.124i	−0.622905	+	1.07890i	−0.988942	+	0.148303i	$0.952619\pi$
$180$		0			0
$181$			290.985i			1.60765i	0.594866	+	0.803825i	$0.297205\pi$
$181$			290.985i			1.60765i	−0.594866	+	0.803825i	$0.702795\pi$
$182$		0			0
$183$		−	60.6218i		−	0.331267i
$184$		0			0
$185$	61.0000	−	105.655i	0.329730	−	0.571109i
$186$		0			0
$187$		−	303.109i		−	1.62090i
$188$		0			0
$189$	−42.5000	−	73.6122i	−0.224868	−	0.389482i
$190$		0			0
$191$	−115.500	+	66.6840i	−0.604712	+	0.349131i	−0.770893	−	0.636965i	$-0.780190\pi$
$191$	−115.500	+	66.6840i	−0.604712	+	0.349131i	0.166181	+	0.986095i	$0.446856\pi$
$192$		0			0
$193$	−178.500	−	103.057i	−0.924870	−	0.533974i	−0.0396849	−	0.999212i	$-0.512635\pi$
$193$	−178.500	−	103.057i	−0.924870	−	0.533974i	−0.885186	+	0.465238i	$0.845969\pi$
$194$		0			0
$195$	13.0000	−	22.5167i	0.0666667	−	0.115470i
$196$		0			0
$197$	77.5000	−	134.234i	0.393401	−	0.681391i	−0.599495	−	0.800379i	$-0.704632\pi$
$197$	77.5000	−	134.234i	0.393401	−	0.681391i	0.992896	+	0.118988i	$0.0379651\pi$
$198$		0			0
$199$	100.500	−	58.0237i	0.505025	−	0.291576i	−0.225761	−	0.974183i	$-0.572487\pi$
$199$	100.500	−	58.0237i	0.505025	−	0.291576i	0.730786	+	0.682606i	$0.239154\pi$
$200$		0			0
$201$	−10.5000	+	6.06218i	−0.0522388	+	0.0301601i
$202$		0			0
$203$			112.583i			0.554598i
$204$		0			0
$205$	−3.00000	−	1.73205i	−0.0146341	−	0.00844903i
$206$		0			0
$207$		−	69.2820i		−	0.334696i
$208$		0			0
$209$	147.000			0.703349
$210$		0			0
$211$	−63.5000	+	109.985i	−0.300948	+	0.521257i	−0.976351	−	0.216192i	$-0.930636\pi$
$211$	−63.5000	+	109.985i	−0.300948	+	0.521257i	0.675403	+	0.737449i	$0.263970\pi$
$212$		0			0
$213$	−29.0000			−0.136150
$214$		0			0
$215$	−41.0000	−	71.0141i	−0.190698	−	0.330298i
$216$		0			0
$217$	25.0000	+	43.3013i	0.115207	+	0.199545i
$218$		0			0
$219$	−36.0000	−	20.7846i	−0.164384	−	0.0949069i
$220$		0			0
$221$	−162.500	−	281.458i	−0.735294	−	1.27357i
$222$		0			0
$223$	−182.500	+	316.099i	−0.818386	+	1.41749i	0.0884855	+	0.996077i	$0.471797\pi$
$223$	−182.500	+	316.099i	−0.818386	+	1.41749i	−0.906871	+	0.421408i	$0.861536\pi$
$224$		0			0
$225$	−84.0000	−	145.492i	−0.373333	−	0.646632i
$226$		0			0
$227$	−298.500	+	172.339i	−1.31498	+	0.759203i	−0.982916	−	0.184055i	$-0.941078\pi$
$227$	−298.500	+	172.339i	−1.31498	+	0.759203i	−0.332062	+	0.943258i	$0.607744\pi$
$228$		0			0
$229$	−2.00000			−0.00873362			−0.00436681	−	0.999990i	$-0.501390\pi$
$229$	−2.00000			−0.00873362			−0.00436681	+	0.999990i	$0.501390\pi$
$230$		0			0
$231$	52.5000	+	30.3109i	0.227273	+	0.131216i
$232$		0			0
$233$	−310.000			−1.33047			−0.665236	−	0.746633i	$-0.731669\pi$
$233$	−310.000			−1.33047			−0.665236	+	0.746633i	$0.731669\pi$
$234$		0			0
$235$	164.000			0.697872
$236$		0			0
$237$	108.000	+	62.3538i	0.455696	+	0.263096i
$238$		0			0
$239$	−394.000			−1.64854			−0.824268	−	0.566200i	$-0.808413\pi$
$239$	−394.000			−1.64854			−0.824268	+	0.566200i	$0.808413\pi$
$240$		0			0
$241$	109.500	−	63.2199i	0.454357	−	0.262323i	−0.255312	−	0.966859i	$-0.582178\pi$
$241$	109.500	−	63.2199i	0.454357	−	0.262323i	0.709668	+	0.704536i	$0.248845\pi$
$242$		0			0
$243$	104.000	+	180.133i	0.427984	+	0.741289i
$244$		0			0
$245$	−24.0000	+	41.5692i	−0.0979592	+	0.169670i
$246$		0			0
$247$	136.500	−	78.8083i	0.552632	−	0.319062i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	188.500	+	326.492i	0.750996	+	1.30076i	0.947340	+	0.320228i	$0.103760\pi$
$251$	188.500	+	326.492i	0.750996	+	1.30076i	−0.196344	+	0.980535i	$0.562907\pi$
$252$		0			0
$253$	52.5000	+	90.9327i	0.207510	+	0.359418i
$254$		0			0
$255$	−50.0000			−0.196078
$256$		0			0
$257$	−107.500	+	186.195i	−0.418288	+	0.724496i	−0.995767	−	0.0919093i	$-0.970703\pi$
$257$	−107.500	+	186.195i	−0.418288	+	0.724496i	0.577479	+	0.816405i	$0.304036\pi$
$258$		0			0
$259$	305.000			1.17761
$260$		0			0
$261$		−	180.133i		−	0.690166i
$262$		0			0
$263$	−367.500	−	212.176i	−1.39734	−	0.806754i	−0.403225	−	0.915101i	$-0.632111\pi$
$263$	−367.500	−	212.176i	−1.39734	−	0.806754i	−0.994113	+	0.108347i	$0.965444\pi$
$264$		0			0
$265$			83.1384i			0.313730i
$266$		0			0
$267$	−34.5000	+	19.9186i	−0.129213	+	0.0746014i
$268$		0			0
$269$	−415.500	+	239.889i	−1.54461	+	0.891781i	−0.546071	+	0.837739i	$0.683877\pi$
$269$	−415.500	+	239.889i	−1.54461	+	0.891781i	−0.998539	+	0.0540419i	$0.982790\pi$
$270$		0			0
$271$	−158.500	+	274.530i	−0.584871	+	1.01303i	0.410021	+	0.912076i	$0.365521\pi$
$271$	−158.500	+	274.530i	−0.584871	+	1.01303i	−0.994892	+	0.100950i	$0.967812\pi$
$272$		0			0
$273$	65.0000			0.238095
$274$		0			0
$275$	220.500	+	127.306i	0.801818	+	0.462930i
$276$		0			0
$277$	−163.500	+	94.3968i	−0.590253	+	0.340783i	−0.765197	−	0.643796i	$-0.777359\pi$
$277$	−163.500	+	94.3968i	−0.590253	+	0.340783i	0.174945	+	0.984578i	$0.444025\pi$
$278$		0			0
$279$	−40.0000	−	69.2820i	−0.143369	−	0.248323i
$280$		0			0
$281$		−	290.985i		−	1.03553i	−0.855522	−	0.517766i	$-0.826764\pi$
$281$		−	290.985i		−	1.03553i	0.855522	−	0.517766i	$-0.173236\pi$
$282$		0			0
$283$	−195.500	+	338.616i	−0.690813	+	1.19652i	0.280759	+	0.959778i	$0.409414\pi$
$283$	−195.500	+	338.616i	−0.690813	+	1.19652i	−0.971572	+	0.236744i	$0.923920\pi$
$284$		0			0
$285$		−	24.2487i		−	0.0850832i
$286$		0			0
$287$		−	8.66025i		−	0.0301751i
$288$		0			0
$289$	−168.000	+	290.985i	−0.581315	+	1.00687i
$290$		0			0
$291$		−	1.73205i		−	0.00595206i
$292$		0			0
$293$	−90.5000	−	156.751i	−0.308874	−	0.534985i	0.669243	−	0.743044i	$-0.266619\pi$
$293$	−90.5000	−	156.751i	−0.308874	−	0.534985i	−0.978116	+	0.208059i	$0.933285\pi$
$294$		0			0
$295$	93.0000	−	53.6936i	0.315254	−	0.182012i
$296$		0			0
$297$	−178.500	−	103.057i	−0.601010	−	0.346993i
$298$		0			0
$299$	97.5000	+	56.2917i	0.326087	+	0.188266i
$300$		0			0
$301$	102.500	−	177.535i	0.340532	−	0.589818i
$302$		0			0
$303$	52.5000	−	30.3109i	0.173267	−	0.100036i
$304$		0			0
$305$	−105.000	+	60.6218i	−0.344262	+	0.198760i
$306$		0			0
$307$		−	581.969i		−	1.89566i	−0.318769	−	0.947832i	$-0.603269\pi$
$307$		−	581.969i		−	1.89566i	0.318769	−	0.947832i	$-0.396731\pi$
$308$		0			0
$309$	−144.000	−	83.1384i	−0.466019	−	0.269056i
$310$		0			0
$311$		−	249.415i		−	0.801979i	−0.916083	−	0.400989i	$-0.868666\pi$
$311$		−	249.415i		−	0.801979i	0.916083	−	0.400989i	$-0.131334\pi$
$312$		0			0
$313$	26.0000			0.0830671			0.0415335	−	0.999137i	$-0.486776\pi$
$313$	26.0000			0.0830671			0.0415335	+	0.999137i	$0.486776\pi$
$314$		0			0
$315$	−40.0000	+	69.2820i	−0.126984	+	0.219943i
$316$		0			0
$317$	166.000			0.523659			0.261830	−	0.965114i	$-0.415674\pi$
$317$	166.000			0.523659			0.261830	+	0.965114i	$0.415674\pi$
$318$		0			0
$319$	136.500	+	236.425i	0.427900	+	0.741144i
$320$		0			0
$321$	−44.5000	−	77.0763i	−0.138629	−	0.240113i
$322$		0			0
$323$	−262.500	−	151.554i	−0.812693	−	0.469209i
$324$		0			0
$325$	273.000			0.840000
$326$		0			0
$327$	47.0000	−	81.4064i	0.143731	−	0.248949i
$328$		0			0
$329$	205.000	+	355.070i	0.623100	+	1.07924i
$330$		0			0
$331$	−10.5000	+	6.06218i	−0.0317221	+	0.0183147i	−0.515777	−	0.856723i	$-0.672497\pi$
$331$	−10.5000	+	6.06218i	−0.0317221	+	0.0183147i	0.484055	+	0.875038i	$0.339163\pi$
$332$		0			0
$333$	−488.000			−1.46547
$334$		0			0
$335$	21.0000	+	12.1244i	0.0626866	+	0.0361921i
$336$		0			0
$337$	506.000			1.50148			0.750742	−	0.660596i	$-0.229696\pi$
$337$	506.000			1.50148			0.750742	+	0.660596i	$0.229696\pi$
$338$		0			0
$339$	−167.000			−0.492625
$340$		0			0
$341$	105.000	+	60.6218i	0.307918	+	0.177776i
$342$		0			0
$343$	−365.000			−1.06414
$344$		0			0
$345$	15.0000	−	8.66025i	0.0434783	−	0.0251022i
$346$		0			0
$347$	−243.500	−	421.754i	−0.701729	−	1.21543i	−0.967859	−	0.251493i	$-0.919078\pi$
$347$	−243.500	−	421.754i	−0.701729	−	1.21543i	0.266130	−	0.963937i	$-0.414255\pi$
$348$		0			0
$349$	−258.500	+	447.735i	−0.740688	+	1.28291i	0.211495	+	0.977379i	$0.432167\pi$
$349$	−258.500	+	447.735i	−0.740688	+	1.28291i	−0.952183	+	0.305530i	$0.901167\pi$
$350$		0			0
$351$	−221.000			−0.629630
$352$		0			0
$353$	577.500	+	333.420i	1.63598	+	0.944532i	0.982198	+	0.187846i	$0.0601507\pi$
$353$	577.500	+	333.420i	1.63598	+	0.944532i	0.653779	+	0.756686i	$0.273183\pi$
$354$		0			0
$355$	29.0000	+	50.2295i	0.0816901	+	0.141491i
$356$		0			0
$357$	−62.5000	−	108.253i	−0.175070	−	0.303230i
$358$		0			0
$359$	−250.000			−0.696379			−0.348189	−	0.937424i	$-0.613203\pi$
$359$	−250.000			−0.696379			−0.348189	+	0.937424i	$0.613203\pi$
$360$		0			0
$361$	−107.000	+	185.329i	−0.296399	+	0.513378i
$362$		0			0
$363$	26.0000			0.0716253
$364$		0			0
$365$			83.1384i			0.227777i
$366$		0			0
$367$	388.500	+	224.301i	1.05858	+	0.611173i	0.925040	−	0.379870i	$-0.124031\pi$
$367$	388.500	+	224.301i	1.05858	+	0.611173i	0.133543	+	0.991043i	$0.457365\pi$
$368$		0			0
$369$			13.8564i			0.0375512i
$370$		0			0
$371$	−180.000	+	103.923i	−0.485175	+	0.280116i
$372$		0			0
$373$	−451.500	+	260.674i	−1.21046	+	0.698857i	−0.962859	−	0.270006i	$-0.912974\pi$
$373$	−451.500	+	260.674i	−1.21046	+	0.698857i	−0.247597	+	0.968863i	$0.579641\pi$
$374$		0			0
$375$	46.0000	−	79.6743i	0.122667	−	0.212465i
$376$		0			0
$377$	253.500	+	146.358i	0.672414	+	0.388218i
$378$		0			0
$379$	61.5000	+	35.5070i	0.162269	+	0.0936861i	0.578935	−	0.815373i	$-0.303468\pi$
$379$	61.5000	+	35.5070i	0.162269	+	0.0936861i	−0.416666	+	0.909059i	$0.636802\pi$
$380$		0			0
$381$	208.500	−	120.378i	0.547244	−	0.315952i
$382$		0			0
$383$	369.500	+	639.993i	0.964752	+	1.67100i	0.710280	+	0.703919i	$0.248568\pi$
$383$	369.500	+	639.993i	0.964752	+	1.67100i	0.254472	+	0.967080i	$0.418098\pi$
$384$		0			0
$385$		−	121.244i		−	0.314918i
$386$		0			0
$387$	−164.000	+	284.056i	−0.423773	+	0.733996i
$388$		0			0
$389$		−	332.554i		−	0.854894i	−0.904040	−	0.427447i	$-0.859413\pi$
$389$		−	332.554i		−	0.854894i	0.904040	−	0.427447i	$-0.140587\pi$
$390$		0			0
$391$		−	216.506i		−	0.553725i
$392$		0			0
$393$	−55.0000	+	95.2628i	−0.139949	+	0.242399i
$394$		0			0
$395$		−	249.415i		−	0.631431i
$396$		0			0
$397$	197.500	+	342.080i	0.497481	+	0.861663i	0.999996	−	0.00290613i	$-0.000925050\pi$
$397$	197.500	+	342.080i	0.497481	+	0.861663i	−0.502515	+	0.864569i	$0.667592\pi$
$398$		0			0
$399$	52.5000	−	30.3109i	0.131579	−	0.0759671i
$400$		0			0
$401$	−538.500	−	310.903i	−1.34289	−	0.775320i	−0.355662	−	0.934615i	$-0.615744\pi$
$401$	−538.500	−	310.903i	−1.34289	−	0.775320i	−0.987231	+	0.159295i	$0.949078\pi$
$402$		0			0
$403$	130.000			0.322581
$404$		0			0
$405$	55.0000	−	95.2628i	0.135802	−	0.235217i
$406$		0			0
$407$	640.500	−	369.793i	1.57371	−	0.908582i
$408$		0			0
$409$	−142.500	+	82.2724i	−0.348411	+	0.201155i	−0.663985	−	0.747746i	$-0.731136\pi$
$409$	−142.500	+	82.2724i	−0.348411	+	0.201155i	0.315574	+	0.948901i	$0.397803\pi$
$410$		0			0
$411$		−	126.440i		−	0.307639i
$412$		0			0
$413$	232.500	+	134.234i	0.562954	+	0.325022i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−127.000			−0.304556
$418$		0			0
$419$	188.500	−	326.492i	0.449881	−	0.779216i	−0.548497	−	0.836152i	$-0.684800\pi$
$419$	188.500	−	326.492i	0.449881	−	0.779216i	0.998378	+	0.0569363i	$0.0181332\pi$
$420$		0			0
$421$	478.000			1.13539			0.567696	−	0.823238i	$-0.307835\pi$
$421$	478.000			1.13539			0.567696	+	0.823238i	$0.307835\pi$
$422$		0			0
$423$	−328.000	−	568.113i	−0.775414	−	1.34306i
$424$		0			0
$425$	−262.500	−	454.663i	−0.617647	−	1.06980i
$426$		0			0
$427$	−262.500	−	151.554i	−0.614754	−	0.354928i
$428$		0			0
$429$	136.500	−	78.8083i	0.318182	−	0.183702i
$430$		0			0
$431$	21.5000	−	37.2391i	0.0498840	−	0.0864016i	−0.840005	−	0.542578i	$-0.817448\pi$
$431$	21.5000	−	37.2391i	0.0498840	−	0.0864016i	0.889889	+	0.456177i	$0.150782\pi$
$432$		0			0
$433$	84.5000	+	146.358i	0.195150	+	0.338010i	0.946950	−	0.321382i	$-0.104147\pi$
$433$	84.5000	+	146.358i	0.195150	+	0.338010i	−0.751800	+	0.659392i	$0.770814\pi$
$434$		0			0
$435$	39.0000	−	22.5167i	0.0896552	−	0.0517624i
$436$		0			0
$437$	105.000			0.240275
$438$		0			0
$439$	244.500	+	141.162i	0.556948	+	0.321554i	0.751919	−	0.659255i	$-0.229128\pi$
$439$	244.500	+	141.162i	0.556948	+	0.321554i	−0.194972	+	0.980809i	$0.562462\pi$
$440$		0			0
$441$	192.000			0.435374
$442$		0			0
$443$	226.000			0.510158			0.255079	−	0.966920i	$-0.417899\pi$
$443$	226.000			0.510158			0.255079	+	0.966920i	$0.417899\pi$
$444$		0			0
$445$	69.0000	+	39.8372i	0.155056	+	0.0895217i
$446$		0			0
$447$	59.0000			0.131991
$448$		0			0
$449$	−250.500	+	144.626i	−0.557906	+	0.322107i	−0.752305	−	0.658815i	$-0.771058\pi$
$449$	−250.500	+	144.626i	−0.557906	+	0.322107i	0.194398	+	0.980923i	$0.437725\pi$
$450$		0			0
$451$	−10.5000	−	18.1865i	−0.0232816	−	0.0403249i
$452$		0			0
$453$	−5.00000	+	8.66025i	−0.0110375	+	0.0191176i
$454$		0			0
$455$	−65.0000	−	112.583i	−0.142857	−	0.247436i
$456$		0			0
$457$	−34.5000	−	19.9186i	−0.0754923	−	0.0435855i	0.461779	−	0.886995i	$-0.347211\pi$
$457$	−34.5000	−	19.9186i	−0.0754923	−	0.0435855i	−0.537271	+	0.843410i	$0.680545\pi$
$458$		0			0
$459$	212.500	+	368.061i	0.462963	+	0.801875i
$460$		0			0
$461$	−258.500	−	447.735i	−0.560738	−	0.971226i	−0.997432	−	0.0716161i	$-0.977184\pi$
$461$	−258.500	−	447.735i	−0.560738	−	0.971226i	0.436695	−	0.899610i	$-0.356149\pi$
$462$		0			0
$463$	278.000			0.600432			0.300216	−	0.953871i	$-0.402941\pi$
$463$	278.000			0.600432			0.300216	+	0.953871i	$0.402941\pi$
$464$		0			0
$465$	10.0000	−	17.3205i	0.0215054	−	0.0372484i
$466$		0			0
$467$	394.000			0.843683			0.421842	−	0.906670i	$-0.361384\pi$
$467$	394.000			0.843683			0.421842	+	0.906670i	$0.361384\pi$
$468$		0			0
$469$			60.6218i			0.129258i
$470$		0			0
$471$	−36.0000	−	20.7846i	−0.0764331	−	0.0441287i
$472$		0			0
$473$		−	497.099i		−	1.05095i
$474$		0			0
$475$	220.500	−	127.306i	0.464211	−	0.268012i
$476$		0			0
$477$	288.000	−	166.277i	0.603774	−	0.348589i
$478$		0			0
$479$	−146.500	+	253.745i	−0.305846	+	0.529740i	−0.977449	−	0.211171i	$-0.932272\pi$
$479$	−146.500	+	253.745i	−0.305846	+	0.529740i	0.671604	+	0.740911i	$0.265606\pi$
$480$		0			0
$481$	396.500	−	686.758i	0.824324	−	1.42777i
$482$		0			0
$483$	37.5000	+	21.6506i	0.0776398	+	0.0448253i
$484$		0			0
$485$	−3.00000	+	1.73205i	−0.00618557	+	0.00357124i
$486$		0			0
$487$	225.500	+	390.577i	0.463039	+	0.802007i	0.999111	−	0.0421654i	$-0.0134256\pi$
$487$	225.500	+	390.577i	0.463039	+	0.802007i	−0.536072	+	0.844172i	$0.680092\pi$
$488$		0			0
$489$		−	278.860i		−	0.570266i
$490$		0			0
$491$	−63.5000	+	109.985i	−0.129328	+	0.224002i	−0.923416	−	0.383800i	$-0.874615\pi$
$491$	−63.5000	+	109.985i	−0.129328	+	0.224002i	0.794088	+	0.607802i	$0.207949\pi$
$492$		0			0
$493$		−	562.917i		−	1.14182i
$494$		0			0
$495$			193.990i			0.391898i
$496$		0			0
$497$	−72.5000	+	125.574i	−0.145875	+	0.252663i
$498$		0			0
$499$		−	166.277i		−	0.333220i	−0.986023	−	0.166610i	$-0.946718\pi$
$499$		−	166.277i		−	0.333220i	0.986023	−	0.166610i	$-0.0532821\pi$
$500$		0			0
$501$	−69.5000	−	120.378i	−0.138723	−	0.240275i
$502$		0			0
$503$	208.500	−	120.378i	0.414513	−	0.239319i	−0.278214	−	0.960519i	$-0.589742\pi$
$503$	208.500	−	120.378i	0.414513	−	0.239319i	0.692727	+	0.721200i	$0.256409\pi$
$504$		0			0
$505$	−105.000	−	60.6218i	−0.207921	−	0.120043i
$506$		0			0
$507$	84.5000	−	146.358i	0.166667	−	0.288675i
$508$		0			0
$509$	−114.500	+	198.320i	−0.224951	+	0.389626i	−0.956305	−	0.292372i	$-0.905555\pi$
$509$	−114.500	+	198.320i	−0.224951	+	0.389626i	0.731354	+	0.681998i	$0.238889\pi$
$510$		0			0
$511$	−180.000	+	103.923i	−0.352250	+	0.203372i
$512$		0			0
$513$	−178.500	+	103.057i	−0.347953	+	0.200891i
$514$		0			0
$515$			332.554i			0.645735i
$516$		0			0
$517$	861.000	+	497.099i	1.66538	+	0.961506i
$518$		0			0
$519$		−	60.6218i		−	0.116805i
$520$		0			0
$521$	122.000			0.234165			0.117083	−	0.993122i	$-0.462646\pi$
$521$	122.000			0.234165			0.117083	+	0.993122i	$0.462646\pi$
$522$		0			0
$523$	−207.500	+	359.401i	−0.396750	+	0.687190i	−0.993323	−	0.115368i	$-0.963195\pi$
$523$	−207.500	+	359.401i	−0.396750	+	0.687190i	0.596573	+	0.802559i	$0.296529\pi$
$524$		0			0
$525$	105.000			0.200000
$526$		0			0
$527$	−125.000	−	216.506i	−0.237192	−	0.410828i
$528$		0			0
$529$	−227.000	−	393.176i	−0.429112	−	0.743243i
$530$		0			0
$531$	−372.000	−	214.774i	−0.700565	−	0.404471i
$532$		0			0
$533$	−19.5000	−	11.2583i	−0.0365854	−	0.0211226i
$534$		0			0
$535$	−89.0000	+	154.153i	−0.166355	+	0.288136i
$536$		0			0
$537$	111.500	+	193.124i	0.207635	+	0.359634i
$538$		0			0
$539$	−252.000	+	145.492i	−0.467532	+	0.269930i
$540$		0			0
$541$	166.000			0.306839			0.153420	−	0.988161i	$-0.450971\pi$
$541$	166.000			0.306839			0.153420	+	0.988161i	$0.450971\pi$
$542$		0			0
$543$	252.000	+	145.492i	0.464088	+	0.267942i
$544$		0			0
$545$	−188.000			−0.344954
$546$		0			0
$547$	82.0000			0.149909			0.0749543	−	0.997187i	$-0.476119\pi$
$547$	82.0000			0.149909			0.0749543	+	0.997187i	$0.476119\pi$
$548$		0			0
$549$	420.000	+	242.487i	0.765027	+	0.441689i
$550$		0			0
$551$	273.000			0.495463
$552$		0			0
$553$	540.000	−	311.769i	0.976492	−	0.563778i
$554$		0			0
$555$	−61.0000	−	105.655i	−0.109910	−	0.190370i
$556$		0			0
$557$	41.5000	−	71.8801i	0.0745063	−	0.129049i	−0.826365	−	0.563135i	$-0.809595\pi$
$557$	41.5000	−	71.8801i	0.0745063	−	0.129049i	0.900871	+	0.434086i	$0.142929\pi$
$558$		0			0
$559$	−266.500	−	461.592i	−0.476744	−	0.825745i
$560$		0			0
$561$	−262.500	−	151.554i	−0.467914	−	0.270151i
$562$		0			0
$563$	−243.500	−	421.754i	−0.432504	−	0.749120i	0.564584	−	0.825376i	$-0.309037\pi$
$563$	−243.500	−	421.754i	−0.432504	−	0.749120i	−0.997088	+	0.0762561i	$0.975703\pi$
$564$		0			0
$565$	167.000	+	289.252i	0.295575	+	0.511951i
$566$		0			0
$567$	275.000			0.485009
$568$		0			0
$569$	−443.500	+	768.165i	−0.779438	+	1.35003i	0.152829	+	0.988253i	$0.451162\pi$
$569$	−443.500	+	768.165i	−0.779438	+	1.35003i	−0.932266	+	0.361773i	$0.882172\pi$
$570$		0			0
$571$	466.000			0.816112			0.408056	−	0.912957i	$-0.366207\pi$
$571$	466.000			0.816112			0.408056	+	0.912957i	$0.366207\pi$
$572$		0			0
$573$			133.368i			0.232754i
$574$		0			0
$575$	157.500	+	90.9327i	0.273913	+	0.158144i
$576$		0			0
$577$		−	623.538i		−	1.08066i	−0.841455	−	0.540328i	$-0.818300\pi$
$577$		−	623.538i		−	1.08066i	0.841455	−	0.540328i	$-0.181700\pi$
$578$		0			0
$579$	−178.500	+	103.057i	−0.308290	+	0.177991i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−252.000	+	436.477i	−0.432247	+	0.748674i
$584$		0			0
$585$	104.000	+	180.133i	0.177778	+	0.307920i
$586$		0			0
$587$	−190.500	−	109.985i	−0.324532	−	0.187368i	0.328879	−	0.944372i	$-0.393329\pi$
$587$	−190.500	−	109.985i	−0.324532	−	0.187368i	−0.653411	+	0.757004i	$0.726662\pi$
$588$		0			0
$589$	105.000	−	60.6218i	0.178268	−	0.102923i
$590$		0			0
$591$	−77.5000	−	134.234i	−0.131134	−	0.227130i
$592$		0			0
$593$			457.261i			0.771099i	0.922687	+	0.385549i	$0.125988\pi$
$593$			457.261i			0.771099i	−0.922687	+	0.385549i	$0.874012\pi$
$594$		0			0
$595$	−125.000	+	216.506i	−0.210084	+	0.363876i
$596$		0			0
$597$		−	116.047i		−	0.194384i
$598$		0			0
$599$			41.5692i			0.0693977i	0.999398	+	0.0346988i	$0.0110472\pi$
$599$			41.5692i			0.0693977i	−0.999398	+	0.0346988i	$0.988953\pi$
$600$		0			0
$601$	168.500	−	291.851i	0.280366	−	0.485608i	−0.691109	−	0.722751i	$-0.742877\pi$
$601$	168.500	−	291.851i	0.280366	−	0.485608i	0.971475	+	0.237142i	$0.0762108\pi$
$602$		0			0
$603$		−	96.9948i		−	0.160854i
$604$		0			0
$605$	−26.0000	−	45.0333i	−0.0429752	−	0.0744352i
$606$		0			0
$607$	136.500	−	78.8083i	0.224876	−	0.129832i	−0.383330	−	0.923612i	$-0.625223\pi$
$607$	136.500	−	78.8083i	0.224876	−	0.129832i	0.608206	+	0.793779i	$0.291889\pi$
$608$		0			0
$609$	97.5000	+	56.2917i	0.160099	+	0.0924329i
$610$		0			0
$611$	1066.00			1.74468
$612$		0			0
$613$	377.500	−	653.849i	0.615824	−	1.06664i	−0.374416	−	0.927261i	$-0.622157\pi$
$613$	377.500	−	653.849i	0.615824	−	1.06664i	0.990239	−	0.139377i	$-0.0445100\pi$
$614$		0			0
$615$	−3.00000	+	1.73205i	−0.00487805	+	0.00281634i
$616$		0			0
$617$	−250.500	+	144.626i	−0.405997	+	0.234402i	−0.689068	−	0.724696i	$-0.741980\pi$
$617$	−250.500	+	144.626i	−0.405997	+	0.234402i	0.283071	+	0.959099i	$0.408647\pi$
$618$		0			0
$619$			332.554i			0.537244i	0.963246	+	0.268622i	$0.0865682\pi$
$619$			332.554i			0.537244i	−0.963246	+	0.268622i	$0.913432\pi$
$620$		0			0
$621$	−127.500	−	73.6122i	−0.205314	−	0.118538i
$622$		0			0
$623$			199.186i			0.319720i
$624$		0			0
$625$	341.000			0.545600
$626$		0			0
$627$	73.5000	−	127.306i	0.117225	−	0.203039i
$628$		0			0
$629$	−1525.00			−2.42448
$630$		0			0
$631$	−14.5000	−	25.1147i	−0.0229794	−	0.0398015i	0.854307	−	0.519769i	$-0.173982\pi$
$631$	−14.5000	−	25.1147i	−0.0229794	−	0.0398015i	−0.877286	+	0.479967i	$0.840649\pi$
$632$		0			0
$633$	63.5000	+	109.985i	0.100316	+	0.173752i
$634$		0			0
$635$	−417.000	−	240.755i	−0.656693	−	0.379142i
$636$		0			0
$637$	−156.000	+	270.200i	−0.244898	+	0.424176i
$638$		0			0
$639$	116.000	−	200.918i	0.181534	−	0.314425i
$640$		0			0
$641$	12.5000	+	21.6506i	0.0195008	+	0.0337763i	0.875611	−	0.483017i	$-0.160459\pi$
$641$	12.5000	+	21.6506i	0.0195008	+	0.0337763i	−0.856110	+	0.516793i	$0.827126\pi$
$642$		0			0
$643$	−694.500	+	400.970i	−1.08009	+	0.623592i	−0.930922	−	0.365219i	$-0.880994\pi$
$643$	−694.500	+	400.970i	−1.08009	+	0.623592i	−0.149172	+	0.988811i	$0.547661\pi$
$644$		0			0
$645$	−82.0000			−0.127132
$646$		0			0
$647$	−115.500	−	66.6840i	−0.178516	−	0.103066i	0.408079	−	0.912947i	$-0.366199\pi$
$647$	−115.500	−	66.6840i	−0.178516	−	0.103066i	−0.586595	+	0.809880i	$0.699532\pi$
$648$		0			0
$649$	651.000			1.00308
$650$		0			0
$651$	50.0000			0.0768049
$652$		0			0
$653$	−55.5000	−	32.0429i	−0.0849923	−	0.0490704i	0.456901	−	0.889517i	$-0.348959\pi$
$653$	−55.5000	−	32.0429i	−0.0849923	−	0.0490704i	−0.541894	+	0.840447i	$0.682293\pi$
$654$		0			0
$655$	220.000			0.335878
$656$		0			0
$657$	288.000	−	166.277i	0.438356	−	0.253085i
$658$		0			0
$659$	−399.500	−	691.954i	−0.606222	−	1.05001i	−0.991857	−	0.127355i	$-0.959351\pi$
$659$	−399.500	−	691.954i	−0.606222	−	1.05001i	0.385636	−	0.922651i	$-0.373982\pi$
$660$		0			0
$661$	−294.500	+	510.089i	−0.445537	+	0.771693i	−0.998089	−	0.0617853i	$-0.980321\pi$
$661$	−294.500	+	510.089i	−0.445537	+	0.771693i	0.552552	+	0.833478i	$0.313654\pi$
$662$		0			0
$663$	−325.000			−0.490196
$664$		0			0
$665$	−105.000	−	60.6218i	−0.157895	−	0.0911606i
$666$		0			0
$667$	97.5000	+	168.875i	0.146177	+	0.253186i
$668$		0			0
$669$	182.500	+	316.099i	0.272795	+	0.472495i
$670$		0			0
$671$	−735.000			−1.09538
$672$		0			0
$673$	−335.500	+	581.103i	−0.498514	+	0.863452i	−0.999999	−	0.00171490i	$-0.999454\pi$
$673$	−335.500	+	581.103i	−0.498514	+	0.863452i	0.501484	+	0.865167i	$0.332787\pi$
$674$		0			0
$675$	−357.000			−0.528889
$676$		0			0
$677$		−	124.708i		−	0.184206i	−0.995749	−	0.0921031i	$-0.970641\pi$
$677$		−	124.708i		−	0.184206i	0.995749	−	0.0921031i	$-0.0293590\pi$
$678$		0			0
$679$	−7.50000	−	4.33013i	−0.0110457	−	0.00637721i
$680$		0			0
$681$			344.678i			0.506135i
$682$		0			0
$683$	961.500	−	555.122i	1.40776	−	0.812771i	0.412588	−	0.910918i	$-0.364625\pi$
$683$	961.500	−	555.122i	1.40776	−	0.812771i	0.995172	+	0.0981472i	$0.0312916\pi$
$684$		0			0
$685$	−219.000	+	126.440i	−0.319708	+	0.184584i
$686$		0			0
$687$	−1.00000	+	1.73205i	−0.00145560	+	0.00252118i
$688$		0			0
$689$			540.400i			0.784325i
$690$		0			0
$691$	1105.50	+	638.261i	1.59986	+	0.923677i	0.991514	+	0.130001i	$0.0414982\pi$
$691$	1105.50	+	638.261i	1.59986	+	0.923677i	0.608341	+	0.793675i	$0.291835\pi$
$692$		0			0
$693$	−420.000	+	242.487i	−0.606061	+	0.349909i
$694$		0			0
$695$	127.000	+	219.970i	0.182734	+	0.316504i
$696$		0			0
$697$			43.3013i			0.0621252i
$698$		0			0
$699$	−155.000	+	268.468i	−0.221745	+	0.384074i
$700$		0			0
$701$		−	290.985i		−	0.415099i	−0.978224	−	0.207550i	$-0.933451\pi$
$701$		−	290.985i		−	0.415099i	0.978224	−	0.207550i	$-0.0665488\pi$
$702$		0			0
$703$		−	739.586i		−	1.05204i
$704$		0			0
$705$	82.0000	−	142.028i	0.116312	−	0.201458i
$706$		0			0
$707$		−	303.109i		−	0.428725i
$708$		0			0
$709$	−390.500	−	676.366i	−0.550776	−	0.953972i	−0.998219	−	0.0596591i	$-0.980999\pi$
$709$	−390.500	−	676.366i	−0.550776	−	0.953972i	0.447443	−	0.894312i	$-0.352335\pi$
$710$		0			0
$711$	−864.000	+	498.831i	−1.21519	+	0.701590i
$712$		0			0
$713$	75.0000	+	43.3013i	0.105189	+	0.0607311i
$714$		0			0
$715$	−273.000	−	157.617i	−0.381818	−	0.220443i
$716$		0			0
$717$	−197.000	+	341.214i	−0.274756	+	0.475891i
$718$		0			0
$719$	−619.500	+	357.668i	−0.861613	+	0.497453i	−0.864552	−	0.502543i	$-0.832398\pi$
$719$	−619.500	+	357.668i	−0.861613	+	0.497453i	0.00293887	+	0.999996i	$0.499065\pi$
$720$		0			0
$721$	−720.000	+	415.692i	−0.998613	+	0.576550i
$722$		0			0
$723$		−	126.440i		−	0.174882i
$724$		0			0
$725$	409.500	+	236.425i	0.564828	+	0.326103i
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	−287.000			−0.393690
$730$		0			0
$731$	−512.500	+	887.676i	−0.701094	+	1.21433i
$732$		0			0
$733$	−506.000			−0.690314			−0.345157	−	0.938545i	$-0.612174\pi$
$733$	−506.000			−0.690314			−0.345157	+	0.938545i	$0.612174\pi$
$734$		0			0
$735$	24.0000	+	41.5692i	0.0326531	+	0.0565568i
$736$		0			0
$737$	73.5000	+	127.306i	0.0997286	+	0.172735i
$738$		0			0
$739$	−10.5000	−	6.06218i	−0.0142084	−	0.00820322i	0.492879	−	0.870098i	$-0.335945\pi$
$739$	−10.5000	−	6.06218i	−0.0142084	−	0.00820322i	−0.507087	+	0.861895i	$0.669278\pi$
$740$		0			0
$741$		−	157.617i		−	0.212708i
$742$		0			0
$743$	657.500	−	1138.82i	0.884926	−	1.53274i	0.0391275	−	0.999234i	$-0.487542\pi$
$743$	657.500	−	1138.82i	0.884926	−	1.53274i	0.845798	−	0.533503i	$-0.179125\pi$
$744$		0			0
$745$	−59.0000	−	102.191i	−0.0791946	−	0.137169i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−445.000			−0.594126
$750$		0			0
$751$	244.500	+	141.162i	0.325566	+	0.187966i	0.653871	−	0.756606i	$-0.273144\pi$
$751$	244.500	+	141.162i	0.325566	+	0.187966i	−0.328305	+	0.944572i	$0.606477\pi$
$752$		0			0
$753$	377.000			0.500664
$754$		0			0
$755$	20.0000			0.0264901
$756$		0			0
$757$	−1027.50	−	593.227i	−1.35733	−	0.783656i	−0.368068	−	0.929799i	$-0.619981\pi$
$757$	−1027.50	−	593.227i	−1.35733	−	0.783656i	−0.989263	+	0.146143i	$0.953314\pi$
$758$		0			0
$759$	105.000			0.138340
$760$		0			0
$761$	−430.500	+	248.549i	−0.565703	+	0.326609i	−0.755431	−	0.655228i	$-0.772573\pi$
$761$	−430.500	+	248.549i	−0.565703	+	0.326609i	0.189728	+	0.981837i	$0.439239\pi$
$762$		0			0
$763$	−235.000	−	407.032i	−0.307995	−	0.533463i
$764$		0			0
$765$	200.000	−	346.410i	0.261438	−	0.452824i
$766$		0			0
$767$	604.500	−	349.008i	0.788136	−	0.455030i
$768$		0			0
$769$	757.500	+	437.343i	0.985046	+	0.568716i	0.903790	−	0.427977i	$-0.140774\pi$
$769$	757.500	+	437.343i	0.985046	+	0.568716i	0.0812559	+	0.996693i	$0.474107\pi$
$770$		0			0
$771$	107.500	+	186.195i	0.139429	+	0.241499i
$772$		0			0
$773$	257.500	+	446.003i	0.333118	+	0.576977i	0.983121	−	0.182954i	$-0.0585660\pi$
$773$	257.500	+	446.003i	0.333118	+	0.576977i	−0.650004	+	0.759931i	$0.725233\pi$
$774$		0			0
$775$	210.000			0.270968
$776$		0			0
$777$	152.500	−	264.138i	0.196268	−	0.339946i
$778$		0			0
$779$	−21.0000			−0.0269576
$780$		0			0
$781$			351.606i			0.450200i
$782$		0			0
$783$	−331.500	−	191.392i	−0.423372	−	0.244434i
$784$		0			0
$785$			83.1384i			0.105909i
$786$		0			0
$787$	−550.500	+	317.831i	−0.699492	+	0.403852i	−0.807158	−	0.590335i	$-0.798996\pi$
$787$	−550.500	+	317.831i	−0.699492	+	0.403852i	0.107666	+	0.994187i	$0.465662\pi$
$788$		0			0
$789$	−367.500	+	212.176i	−0.465779	+	0.268918i
$790$		0			0
$791$	−417.500	+	723.131i	−0.527813	+	0.914199i
$792$		0			0
$793$	−682.500	+	394.042i	−0.860656	+	0.496900i
$794$		0			0
$795$	72.0000	+	41.5692i	0.0905660	+	0.0522883i
$796$		0			0
$797$	988.500	−	570.711i	1.24028	−	0.716074i	0.271126	−	0.962544i	$-0.412604\pi$
$797$	988.500	−	570.711i	1.24028	−	0.716074i	0.969150	+	0.246470i	$0.0792708\pi$
$798$		0			0
$799$	−1025.00	−	1775.35i	−1.28285	−	2.22197i
$800$		0			0
$801$		−	318.697i		−	0.397874i
$802$		0			0
$803$	−252.000	+	436.477i	−0.313823	+	0.543558i
$804$		0			0
$805$		−	86.6025i		−	0.107581i
$806$		0			0
$807$			479.778i			0.594521i
$808$		0			0
$809$	−455.500	+	788.949i	−0.563041	+	0.975215i	0.434188	+	0.900822i	$0.357035\pi$
$809$	−455.500	+	788.949i	−0.563041	+	0.975215i	−0.997229	+	0.0743931i	$0.976298\pi$
$810$		0			0
$811$			872.954i			1.07639i	0.842820	+	0.538196i	$0.180894\pi$
$811$			872.954i			1.07639i	−0.842820	+	0.538196i	$0.819106\pi$
$812$		0			0
$813$	158.500	+	274.530i	0.194957	+	0.337675i
$814$		0			0
$815$	−483.000	+	278.860i	−0.592638	+	0.342160i
$816$		0			0
$817$	−430.500	−	248.549i	−0.526928	−	0.304222i
$818$		0			0
$819$	−260.000	+	450.333i	−0.317460	+	0.549857i
$820$		0			0
$821$	−618.500	+	1071.27i	−0.753350	+	1.30484i	0.192841	+	0.981230i	$0.438230\pi$
$821$	−618.500	+	1071.27i	−0.753350	+	1.30484i	−0.946191	+	0.323610i	$0.895104\pi$
$822$		0			0
$823$	−1411.50	+	814.930i	−1.71507	+	0.990194i	−0.787685	+	0.616078i	$0.788720\pi$
$823$	−1411.50	+	814.930i	−1.71507	+	0.990194i	−0.927382	+	0.374116i	$0.877946\pi$
$824$		0			0
$825$	220.500	−	127.306i	0.267273	−	0.154310i
$826$		0			0
$827$		−	1163.94i		−	1.40742i	−0.710486	−	0.703711i	$-0.751525\pi$
$827$		−	1163.94i		−	1.40742i	0.710486	−	0.703711i	$-0.248475\pi$
$828$		0			0
$829$	−451.500	−	260.674i	−0.544632	−	0.314443i	0.202322	−	0.979319i	$-0.435151\pi$
$829$	−451.500	−	260.674i	−0.544632	−	0.314443i	−0.746954	+	0.664876i	$0.768485\pi$
$830$		0			0
$831$			188.794i			0.227188i
$832$		0			0
$833$	600.000			0.720288
$834$		0			0
$835$	−139.000	+	240.755i	−0.166467	+	0.288329i
$836$		0			0
$837$	−170.000			−0.203106
$838$		0			0
$839$	489.500	+	847.839i	0.583433	+	1.01054i	0.995069	+	0.0991867i	$0.0316241\pi$
$839$	489.500	+	847.839i	0.583433	+	1.01054i	−0.411636	+	0.911348i	$0.635043\pi$
$840$		0			0
$841$	−167.000	−	289.252i	−0.198573	−	0.343939i
$842$		0			0
$843$	−252.000	−	145.492i	−0.298932	−	0.172589i
$844$		0			0
$845$	−338.000			−0.400000
$846$		0			0
$847$	65.0000	−	112.583i	0.0767414	−	0.132920i
$848$		0			0
$849$	195.500	+	338.616i	0.230271	+	0.398841i
$850$		0			0
$851$	457.500	−	264.138i	0.537603	−	0.310385i
$852$		0			0
$853$	−530.000			−0.621336			−0.310668	−	0.950518i	$-0.600553\pi$
$853$	−530.000			−0.621336			−0.310668	+	0.950518i	$0.600553\pi$
$854$		0			0
$855$	168.000	+	96.9948i	0.196491	+	0.113444i
$856$		0			0
$857$	1130.00			1.31855			0.659277	−	0.751901i	$-0.270863\pi$
$857$	1130.00			1.31855			0.659277	+	0.751901i	$0.270863\pi$
$858$		0			0
$859$	226.000			0.263097			0.131548	−	0.991310i	$-0.458005\pi$
$859$	226.000			0.263097			0.131548	+	0.991310i	$0.458005\pi$
$860$		0			0
$861$	−7.50000	−	4.33013i	−0.00871080	−	0.00502918i
$862$		0			0
$863$	86.0000			0.0996524			0.0498262	−	0.998758i	$-0.484133\pi$
$863$	86.0000			0.0996524			0.0498262	+	0.998758i	$0.484133\pi$
$864$		0			0
$865$	−105.000	+	60.6218i	−0.121387	+	0.0700830i
$866$		0			0
$867$	168.000	+	290.985i	0.193772	+	0.335622i
$868$		0			0
$869$	756.000	−	1309.43i	0.869965	−	1.50682i
$870$		0			0
$871$	136.500	+	78.8083i	0.156716	+	0.0904803i
$872$		0			0
$873$	12.0000	+	6.92820i	0.0137457	+	0.00793609i
$874$		0			0
$875$	−230.000	−	398.372i	−0.262857	−	0.455282i
$876$		0			0
$877$	449.500	+	778.557i	0.512543	+	0.887750i	0.999894	+	0.0145442i	$0.00462973\pi$
$877$	449.500	+	778.557i	0.512543	+	0.887750i	−0.487351	+	0.873206i	$0.662037\pi$
$878$		0			0
$879$	−181.000			−0.205916
$880$		0			0
$881$	84.5000	−	146.358i	0.0959137	−	0.166127i	−0.814076	−	0.580759i	$-0.802756\pi$
$881$	84.5000	−	146.358i	0.0959137	−	0.166127i	0.909990	+	0.414631i	$0.136089\pi$
$882$		0			0
$883$	−590.000			−0.668177			−0.334088	−	0.942542i	$-0.608428\pi$
$883$	−590.000			−0.668177			−0.334088	+	0.942542i	$0.608428\pi$
$884$		0			0
$885$		−	107.387i		−	0.121341i
$886$		0			0
$887$	748.500	+	432.147i	0.843856	+	0.487200i	0.858573	−	0.512691i	$-0.171351\pi$
$887$	748.500	+	432.147i	0.843856	+	0.487200i	−0.0147173	+	0.999892i	$0.504685\pi$
$888$		0			0
$889$		−	1203.78i		−	1.35408i
$890$		0			0
$891$	577.500	−	333.420i	0.648148	−	0.374209i
$892$		0			0
$893$	861.000	−	497.099i	0.964166	−	0.556661i
$894$		0			0
$895$	223.000	−	386.247i	0.249162	−	0.431561i
$896$		0			0
$897$	97.5000	−	56.2917i	0.108696	−	0.0627555i
$898$		0			0
$899$	195.000	+	112.583i	0.216908	+	0.125232i
$900$		0			0
$901$	900.000	−	519.615i	0.998890	−	0.576709i
$902$		0			0
$903$	−102.500	−	177.535i	−0.113511	−	0.196606i
$904$		0			0
$905$		−	581.969i		−	0.643060i
$906$		0			0
$907$	308.500	−	534.338i	0.340132	−	0.589126i	−0.644325	−	0.764752i	$-0.722861\pi$
$907$	308.500	−	534.338i	0.340132	−	0.589126i	0.984457	+	0.175626i	$0.0561948\pi$
$908$		0			0
$909$			484.974i			0.533525i
$910$		0			0
$911$		−	581.969i		−	0.638824i	−0.947616	−	0.319412i	$-0.896515\pi$
$911$		−	581.969i		−	0.638824i	0.947616	−	0.319412i	$-0.103485\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$			121.244i			0.132507i
$916$		0			0
$917$	275.000	+	476.314i	0.299891	+	0.519426i
$918$		0			0
$919$	−871.500	+	503.161i	−0.948313	+	0.547509i	−0.892557	−	0.450935i	$-0.851090\pi$
$919$	−871.500	+	503.161i	−0.948313	+	0.547509i	−0.0557568	+	0.998444i	$0.517757\pi$
$920$		0			0
$921$	−504.000	−	290.985i	−0.547231	−	0.315944i
$922$		0			0
$923$	188.500	+	326.492i	0.204225	+	0.353729i
$924$		0			0
$925$	640.500	−	1109.38i	0.692432	−	1.19933i
$926$		0			0
$927$	1152.00	−	665.108i	1.24272	−	0.717484i
$928$		0			0
$929$	829.500	−	478.912i	0.892896	−	0.515514i	0.0180071	−	0.999838i	$-0.494268\pi$
$929$	829.500	−	478.912i	0.892896	−	0.515514i	0.874889	+	0.484324i	$0.160935\pi$
$930$		0			0
$931$			290.985i			0.312551i
$932$		0			0
$933$	−216.000	−	124.708i	−0.231511	−	0.133663i
$934$		0			0
$935$			606.218i			0.648361i
$936$		0			0
$937$	−502.000			−0.535752			−0.267876	−	0.963453i	$-0.586322\pi$
$937$	−502.000			−0.535752			−0.267876	+	0.963453i	$0.586322\pi$
$938$		0			0
$939$	13.0000	−	22.5167i	0.0138445	−	0.0239794i
$940$		0			0
$941$	−1082.00			−1.14984			−0.574920	−	0.818209i	$-0.694967\pi$
$941$	−1082.00			−1.14984			−0.574920	+	0.818209i	$0.694967\pi$
$942$		0			0
$943$	−7.50000	−	12.9904i	−0.00795334	−	0.0137756i
$944$		0			0
$945$	85.0000	+	147.224i	0.0899471	+	0.155793i
$946$		0			0
$947$	601.500	+	347.276i	0.635164	+	0.366712i	0.782749	−	0.622337i	$-0.213817\pi$
$947$	601.500	+	347.276i	0.635164	+	0.366712i	−0.147585	+	0.989049i	$0.547150\pi$
$948$		0			0
$949$			540.400i			0.569441i
$950$		0			0
$951$	83.0000	−	143.760i	0.0872766	−	0.151167i
$952$		0			0
$953$	84.5000	+	146.358i	0.0886674	+	0.153576i	0.906948	−	0.421242i	$-0.138406\pi$
$953$	84.5000	+	146.358i	0.0886674	+	0.153576i	−0.818281	+	0.574819i	$0.805073\pi$
$954$		0			0
$955$	231.000	−	133.368i	0.241885	−	0.139652i
$956$		0			0
$957$	273.000			0.285266
$958$		0			0
$959$	−547.500	−	316.099i	−0.570907	−	0.329613i
$960$		0			0
$961$	−861.000			−0.895942
$962$		0			0
$963$	712.000			0.739356
$964$		0			0
$965$	357.000	+	206.114i	0.369948	+	0.213590i
$966$		0			0
$967$	614.000			0.634953			0.317477	−	0.948266i	$-0.397164\pi$
$967$	614.000			0.634953			0.317477	+	0.948266i	$0.397164\pi$
$968$		0			0
$969$	−262.500	+	151.554i	−0.270898	+	0.156403i
$970$		0			0
$971$	572.500	+	991.599i	0.589598	+	1.02121i	0.994285	+	0.106759i	$0.0340473\pi$
$971$	572.500	+	991.599i	0.589598	+	1.02121i	−0.404687	+	0.914455i	$0.632619\pi$
$972$		0			0
$973$	−317.500	+	549.926i	−0.326310	+	0.565186i
$974$		0			0
$975$	136.500	−	236.425i	0.140000	−	0.242487i
$976$		0			0
$977$	−1438.50	−	830.518i	−1.47236	−	0.850070i	−0.472847	−	0.881144i	$-0.656774\pi$
$977$	−1438.50	−	830.518i	−1.47236	−	0.850070i	−0.999517	+	0.0310744i	$0.990107\pi$
$978$		0			0
$979$	241.500	+	418.290i	0.246680	+	0.427263i
$980$		0			0
$981$	376.000	+	651.251i	0.383282	+	0.663865i
$982$		0			0
$983$	−10.0000			−0.0101729			−0.00508647	−	0.999987i	$-0.501619\pi$
$983$	−10.0000			−0.0101729			−0.00508647	+	0.999987i	$0.501619\pi$
$984$		0			0
$985$	−155.000	+	268.468i	−0.157360	+	0.272556i
$986$		0			0
$987$	410.000			0.415400
$988$		0			0
$989$		−	355.070i		−	0.359020i
$990$		0			0
$991$	1144.50	+	660.777i	1.15489	+	0.666778i	0.950075	−	0.312021i	$-0.101006\pi$
$991$	1144.50	+	660.777i	1.15489	+	0.666778i	0.204819	+	0.978800i	$0.434339\pi$
$992$		0			0
$993$			12.1244i			0.0122098i
$994$		0			0
$995$	−201.000	+	116.047i	−0.202010	+	0.116631i
$996$		0			0
$997$	1600.50	−	924.049i	1.60532	−	0.926830i	0.614917	−	0.788592i	$-0.289190\pi$
$997$	1600.50	−	924.049i	1.60532	−	0.926830i	0.990399	−	0.138238i	$-0.0441438\pi$
$998$		0			0
$999$	−518.500	+	898.068i	−0.519019	+	0.898967i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.3.x.a.303.1		2
4.3	odd	2		104.3.p.b.43.1	yes	2
8.3	odd	2		416.3.x.b.303.1		2
8.5	even	2		104.3.p.a.43.1	✓	2
13.10	even	6		416.3.x.b.335.1		2
52.23	odd	6		104.3.p.a.75.1	yes	2
104.75	odd	6	inner	416.3.x.a.335.1		2
104.101	even	6		104.3.p.b.75.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.3.p.a.43.1	✓	2	8.5	even	2
104.3.p.a.75.1	yes	2	52.23	odd	6
104.3.p.b.43.1	yes	2	4.3	odd	2
104.3.p.b.75.1	yes	2	104.101	even	6
416.3.x.a.303.1		2	1.1	even	1	trivial
416.3.x.a.335.1		2	104.75	odd	6	inner
416.3.x.b.303.1		2	8.3	odd	2
416.3.x.b.335.1		2	13.10	even	6

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

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$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	416.3.x.a.303.1

Level	$416$
Weight	$3$
Character	416.303
Analytic conductor	$11.335$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$