LMFDB - Embedded newform 147.6.e.l.67.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [147,6,Mod(67,147)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(147, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("147.67"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$N$	$=$	$147 = 3 \cdot 7^{2}$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	147.e (of order $3$ , degree $2$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [4,3,-18,-65,-33] 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:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-83})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} - x^{3} - 20x^{2} - 21x + 441$ x^4 - x^3 - 20x^2 - 21x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$3$
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$4.19493 + 1.84460i$ of defining polynomial
Character	$\chi$	$=$	147.67
Dual form			147.6.e.l.79.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.19493 - 5.53379i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-4.41520 + 7.64735i) q^{4} +(19.3645 + 33.5404i) q^{5} +57.5088 q^{6} -148.051 q^{8} +(-40.5000 - 70.1481i) q^{9} +(123.737 - 214.318i) q^{10} +(288.195 - 499.168i) q^{11} +(-39.7368 - 68.8262i) q^{12} -391.491 q^{13} -348.562 q^{15} +(614.298 + 1064.00i) q^{16} +(-664.850 + 1151.55i) q^{17} +(-258.790 + 448.237i) q^{18} +(471.237 + 816.206i) q^{19} -341.993 q^{20} -3683.05 q^{22} +(816.040 + 1413.42i) q^{23} +(666.228 - 1153.94i) q^{24} +(812.530 - 1407.34i) q^{25} +(1250.79 + 2166.43i) q^{26} +729.000 q^{27} -1463.54 q^{29} +(1113.63 + 1928.87i) q^{30} +(-1956.21 + 3388.25i) q^{31} +(1556.47 - 2695.89i) q^{32} +(2593.75 + 4492.51i) q^{33} +8496.61 q^{34} +715.262 q^{36} +(8150.17 + 14116.5i) q^{37} +(3011.14 - 5215.45i) q^{38} +(1761.71 - 3051.37i) q^{39} +(-2866.93 - 4965.67i) q^{40} +13103.8 q^{41} +14733.5 q^{43} +(2544.88 + 4407.86i) q^{44} +(1568.53 - 2716.77i) q^{45} +(5214.38 - 9031.58i) q^{46} +(-3407.26 - 5901.55i) q^{47} -11057.4 q^{48} -10383.9 q^{50} +(-5983.65 - 10364.0i) q^{51} +(1728.51 - 2993.87i) q^{52} +(1005.67 - 1741.87i) q^{53} +(-2329.11 - 4034.13i) q^{54} +22323.0 q^{55} -8482.26 q^{57} +(4675.93 + 8098.94i) q^{58} +(25726.6 - 44559.7i) q^{59} +(1538.97 - 2665.57i) q^{60} +(20548.9 + 35591.8i) q^{61} +24999.8 q^{62} +19423.8 q^{64} +(-7581.04 - 13130.8i) q^{65} +(16573.7 - 28706.6i) q^{66} +(-25289.1 + 43802.0i) q^{67} +(-5870.89 - 10168.7i) q^{68} -14688.7 q^{69} +39970.6 q^{71} +(5996.05 + 10385.5i) q^{72} +(-27843.3 + 48226.0i) q^{73} +(52078.5 - 90202.6i) q^{74} +(7312.77 + 12666.1i) q^{75} -8322.42 q^{76} -22514.2 q^{78} +(31575.7 + 54690.7i) q^{79} +(-23791.2 + 41207.6i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-41865.9 - 72513.8i) q^{82} -45572.4 q^{83} -51498.1 q^{85} +(-47072.5 - 81532.0i) q^{86} +(6585.95 - 11407.2i) q^{87} +(-42667.5 + 73902.2i) q^{88} +(7843.34 + 13585.1i) q^{89} -20045.4 q^{90} -14411.9 q^{92} +(-17605.9 - 30494.3i) q^{93} +(-21771.9 + 37710.1i) q^{94} +(-18250.6 + 31610.9i) q^{95} +(14008.3 + 24263.0i) q^{96} -3128.49 q^{97} -46687.6 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q + 3 q^{2} - 18 q^{3} - 65 q^{4} - 33 q^{5} - 54 q^{6} - 750 q^{8} - 162 q^{9} + 921 q^{10} + 1137 q^{11} - 585 q^{12} - 1850 q^{13} + 594 q^{15} + 895 q^{16} - 324 q^{17} + 243 q^{18} + 2311 q^{19}+ \cdots - 184194 q^{99}+O(q^{100})$ 4 * q + 3 * q^2 - 18 * q^3 - 65 * q^4 - 33 * q^5 - 54 * q^6 - 750 * q^8 - 162 * q^9 + 921 * q^10 + 1137 * q^11 - 585 * q^12 - 1850 * q^13 + 594 * q^15 + 895 * q^16 - 324 * q^17 + 243 * q^18 + 2311 * q^19 + 7374 * q^20 + 3162 * q^22 - 1596 * q^23 + 3375 * q^24 - 395 * q^25 - 2508 * q^26 + 2916 * q^27 - 4434 * q^29 + 8289 * q^30 + 4294 * q^31 - 1017 * q^32 + 10233 * q^33 + 35880 * q^34 + 10530 * q^36 + 19109 * q^37 - 6828 * q^38 + 8325 * q^39 + 10545 * q^40 + 25716 * q^41 - 5542 * q^43 + 36579 * q^44 - 2673 * q^45 + 40740 * q^46 - 23160 * q^47 - 16110 * q^48 - 58704 * q^50 - 2916 * q^51 + 33424 * q^52 + 31653 * q^53 + 2187 * q^54 - 35778 * q^55 - 41598 * q^57 + 2277 * q^58 + 41097 * q^59 - 33183 * q^60 + 42052 * q^61 + 204114 * q^62 - 60062 * q^64 + 23106 * q^65 - 14229 * q^66 - 30763 * q^67 + 44748 * q^68 + 28728 * q^69 + 204192 * q^71 + 30375 * q^72 - 28577 * q^73 + 77784 * q^74 - 3555 * q^75 - 170384 * q^76 + 45144 * q^78 + 18464 * q^79 - 71511 * q^80 - 13122 * q^81 - 86040 * q^82 - 122358 * q^83 - 247272 * q^85 - 258510 * q^86 + 19953 * q^87 - 212565 * q^88 + 29322 * q^89 - 149202 * q^90 + 333816 * q^92 + 38646 * q^93 + 109938 * q^94 + 61662 * q^95 - 9153 * q^96 + 19582 * q^97 - 184194 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$ .

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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

)

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

$2$	−3.19493	−	5.53379i	−0.564790	−	0.978245i	−0.997069	−	0.0765049i	$-0.975624\pi$
$2$	−3.19493	−	5.53379i	−0.564790	−	0.978245i	0.432279	−	0.901740i	$-0.357709\pi$
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$4$	−4.41520	+	7.64735i	−0.137975	+	0.238980i
$5$	19.3645	+	33.5404i	0.346403	+	0.599988i	0.985608	−	0.169049i	$-0.0540695\pi$
$5$	19.3645	+	33.5404i	0.346403	+	0.599988i	−0.639204	+	0.769037i	$0.720736\pi$
$6$	57.5088			0.652163
$7$		0			0
$7$		0			0
$8$	−148.051			−0.817872
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$	123.737	−	214.318i	0.391290	−	0.677734i
$11$	288.195	−	499.168i	0.718133	−	1.24384i	−0.243606	−	0.969874i	$-0.578330\pi$
$11$	288.195	−	499.168i	0.718133	−	1.24384i	0.961739	−	0.273968i	$-0.0883362\pi$
$12$	−39.7368	−	68.8262i	−0.0796599	−	0.137975i
$13$	−391.491			−0.642486			−0.321243	−	0.946997i	$-0.604101\pi$
$13$	−391.491			−0.642486			−0.321243	+	0.946997i	$0.604101\pi$
$14$		0			0
$15$	−348.562			−0.399992
$16$	614.298	+	1064.00i	0.599901	+	1.03906i
$17$	−664.850	+	1151.55i	−0.557958	+	0.966412i	0.439709	+	0.898140i	$0.355082\pi$
$17$	−664.850	+	1151.55i	−0.557958	+	0.966412i	−0.997667	+	0.0682711i	$0.978252\pi$
$18$	−258.790	+	448.237i	−0.188263	+	0.326082i
$19$	471.237	+	816.206i	0.299471	+	0.518699i	0.976015	−	0.217703i	$-0.0698564\pi$
$19$	471.237	+	816.206i	0.299471	+	0.518699i	−0.676544	+	0.736402i	$0.736523\pi$
$20$	−341.993			−0.191180
$21$		0			0
$22$	−3683.05			−1.62238
$23$	816.040	+	1413.42i	0.321656	+	0.557124i	0.980830	−	0.194866i	$-0.0624272\pi$
$23$	816.040	+	1413.42i	0.321656	+	0.557124i	−0.659174	+	0.751991i	$0.729094\pi$
$24$	666.228	−	1153.94i	0.236099	−	0.408936i
$25$	812.530	−	1407.34i	0.260009	−	0.450350i
$26$	1250.79	+	2166.43i	0.362869	+	0.628508i
$27$	729.000			0.192450
$28$		0			0
$29$	−1463.54			−0.323155			−0.161577	−	0.986860i	$-0.551658\pi$
$29$	−1463.54			−0.323155			−0.161577	+	0.986860i	$0.551658\pi$
$30$	1113.63	+	1928.87i	0.225911	+	0.391290i
$31$	−1956.21	+	3388.25i	−0.365604	+	0.633245i	−0.988873	−	0.148763i	$-0.952471\pi$
$31$	−1956.21	+	3388.25i	−0.365604	+	0.633245i	0.623269	+	0.782008i	$0.285804\pi$
$32$	1556.47	−	2695.89i	0.268700	−	0.465401i
$33$	2593.75	+	4492.51i	0.414614	+	0.718133i
$34$	8496.61			1.26052
$35$		0			0
$36$	715.262			0.0919833
$37$	8150.17	+	14116.5i	0.978729	+	1.69521i	0.667038	+	0.745024i	$0.267562\pi$
$37$	8150.17	+	14116.5i	0.978729	+	1.69521i	0.311691	+	0.950184i	$0.399105\pi$
$38$	3011.14	−	5215.45i	0.338277	−	0.585912i
$39$	1761.71	−	3051.37i	0.185470	−	0.321243i
$40$	−2866.93	−	4965.67i	−0.283314	−	0.490714i
$41$	13103.8			1.21741			0.608707	−	0.793395i	$-0.291688\pi$
$41$	13103.8			1.21741			0.608707	+	0.793395i	$0.291688\pi$
$42$		0			0
$43$	14733.5			1.21516			0.607582	−	0.794257i	$-0.292140\pi$
$43$	14733.5			1.21516			0.607582	+	0.794257i	$0.292140\pi$
$44$	2544.88	+	4407.86i	0.198169	+	0.343238i
$45$	1568.53	−	2716.77i	0.115468	−	0.199996i
$46$	5214.38	−	9031.58i	0.363336	−	0.629316i
$47$	−3407.26	−	5901.55i	−0.224989	−	0.389692i	0.731327	−	0.682027i	$-0.238901\pi$
$47$	−3407.26	−	5901.55i	−0.224989	−	0.389692i	−0.956316	+	0.292335i	$0.905568\pi$
$48$	−11057.4			−0.692706
$49$		0			0
$50$	−10383.9			−0.587403
$51$	−5983.65	−	10364.0i	−0.322137	−	0.557958i
$52$	1728.51	−	2993.87i	0.0886470	−	0.153541i
$53$	1005.67	−	1741.87i	0.0491775	−	0.0851779i	−0.840389	−	0.541984i	$-0.817673\pi$
$53$	1005.67	−	1741.87i	0.0491775	−	0.0851779i	0.889566	+	0.456806i	$0.151007\pi$
$54$	−2329.11	−	4034.13i	−0.108694	−	0.188263i
$55$	22323.0			0.995054
$56$		0			0
$57$	−8482.26			−0.345800
$58$	4675.93	+	8098.94i	0.182515	+	0.316125i
$59$	25726.6	−	44559.7i	0.962170	−	1.66653i	0.245135	−	0.969489i	$-0.421168\pi$
$59$	25726.6	−	44559.7i	0.962170	−	1.66653i	0.717035	−	0.697037i	$-0.245499\pi$
$60$	1538.97	−	2665.57i	0.0551889	−	0.0955900i
$61$	20548.9	+	35591.8i	0.707073	+	1.22469i	0.965938	+	0.258773i	$0.0833181\pi$
$61$	20548.9	+	35591.8i	0.707073	+	1.22469i	−0.258865	+	0.965913i	$0.583349\pi$
$62$	24999.8			0.825958
$63$		0			0
$64$	19423.8			0.592766
$65$	−7581.04	−	13130.8i	−0.222559	−	0.385484i
$66$	16573.7	−	28706.6i	0.468340	−	0.811188i
$67$	−25289.1	+	43802.0i	−0.688250	+	1.19208i	0.284153	+	0.958779i	$0.408288\pi$
$67$	−25289.1	+	43802.0i	−0.688250	+	1.19208i	−0.972404	+	0.233305i	$0.925046\pi$
$68$	−5870.89	−	10168.7i	−0.153968	−	0.266681i
$69$	−14688.7			−0.371416
$70$		0			0
$71$	39970.6			0.941012			0.470506	−	0.882397i	$-0.344071\pi$
$71$	39970.6			0.941012			0.470506	+	0.882397i	$0.344071\pi$
$72$	5996.05	+	10385.5i	0.136312	+	0.236099i
$73$	−27843.3	+	48226.0i	−0.611524	+	1.05919i	0.379459	+	0.925208i	$0.376110\pi$
$73$	−27843.3	+	48226.0i	−0.611524	+	1.05919i	−0.990984	+	0.133983i	$0.957223\pi$
$74$	52078.5	−	90202.6i	1.10555	−	1.91487i
$75$	7312.77	+	12666.1i	0.150117	+	0.260009i
$76$	−8322.42			−0.165278
$77$		0			0
$78$	−22514.2			−0.419006
$79$	31575.7	+	54690.7i	0.569226	+	0.985929i	0.996643	+	0.0818739i	$0.0260905\pi$
$79$	31575.7	+	54690.7i	0.569226	+	0.985929i	−0.427416	+	0.904055i	$0.640576\pi$
$80$	−23791.2	+	41207.6i	−0.415615	+	0.719867i
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$	−41865.9	−	72513.8i	−0.687583	−	1.19093i
$83$	−45572.4			−0.726116			−0.363058	−	0.931766i	$-0.618267\pi$
$83$	−45572.4			−0.726116			−0.363058	+	0.931766i	$0.618267\pi$
$84$		0			0
$85$	−51498.1			−0.773114
$86$	−47072.5	−	81532.0i	−0.686312	−	1.18873i
$87$	6585.95	−	11407.2i	0.0932868	−	0.161577i
$88$	−42667.5	+	73902.2i	−0.587341	+	1.01730i
$89$	7843.34	+	13585.1i	0.104961	+	0.181797i	0.913722	−	0.406340i	$-0.133195\pi$
$89$	7843.34	+	13585.1i	0.104961	+	0.181797i	−0.808762	+	0.588137i	$0.799862\pi$
$90$	−20045.4			−0.260860
$91$		0			0
$92$	−14411.9			−0.177522
$93$	−17605.9	−	30494.3i	−0.211082	−	0.365604i
$94$	−21771.9	+	37710.1i	−0.254143	+	0.440188i
$95$	−18250.6	+	31610.9i	−0.207476	+	0.359358i
$96$	14008.3	+	24263.0i	0.155134	+	0.268700i
$97$	−3128.49			−0.0337603			−0.0168801	−	0.999858i	$-0.505373\pi$
$97$	−3128.49			−0.0337603			−0.0168801	+	0.999858i	$0.505373\pi$
$98$		0			0
$99$	−46687.6			−0.478755
$100$	7174.96	+	12427.4i	0.0717496	+	0.124274i
$101$	−84505.5	+	146368.i	−0.824292	+	1.42772i	0.0781663	+	0.996940i	$0.475093\pi$
$101$	−84505.5	+	146368.i	−0.824292	+	1.42772i	−0.902459	+	0.430776i	$0.858240\pi$
$102$	−38234.7	+	66224.5i	−0.363880	+	0.630258i
$103$	56410.1	+	97705.1i	0.523918	+	0.907453i	0.999612	+	0.0278422i	$0.00886360\pi$
$103$	56410.1	+	97705.1i	0.523918	+	0.907453i	−0.475694	+	0.879611i	$0.657803\pi$
$104$	57960.5			0.525471
$105$		0			0
$106$	−12852.2			−0.111100
$107$	11154.7	+	19320.6i	0.0941890	+	0.163140i	0.909270	−	0.416207i	$-0.136641\pi$
$107$	11154.7	+	19320.6i	0.0941890	+	0.163140i	−0.815081	+	0.579347i	$0.803308\pi$
$108$	−3218.68	+	5574.92i	−0.0265533	+	0.0459917i
$109$	41909.8	−	72589.8i	0.337869	−	0.585207i	−0.646162	−	0.763200i	$-0.723627\pi$
$109$	41909.8	−	72589.8i	0.337869	−	0.585207i	0.984032	+	0.177993i	$0.0569604\pi$
$110$	−71320.6	−	123531.i	−0.561996	−	0.973406i
$111$	−146703.			−1.13014
$112$		0			0
$113$	−40928.4			−0.301529			−0.150764	−	0.988570i	$-0.548174\pi$
$113$	−40928.4			−0.301529			−0.150764	+	0.988570i	$0.548174\pi$
$114$	27100.3	+	46939.0i	0.195304	+	0.338277i
$115$	−31604.4	+	54740.5i	−0.222845	+	0.385980i
$116$	6461.84	−	11192.2i	0.0445873	−	0.0772275i
$117$	15855.4	+	27462.3i	0.107081	+	0.185470i
$118$	−328779.			−2.17369
$119$		0			0
$120$	51604.8			0.327142
$121$	−85587.1	−	148241.i	−0.531429	−	0.920462i
$122$	131305.	−	227427.i	0.798695	−	1.38338i
$123$	−58967.2	+	102134.i	−0.351437	+	0.608707i
$124$	−17274.1	−	29919.6i	−0.100888	−	0.174744i
$125$	183965.			1.05308
$126$		0			0
$127$	83270.1			0.458120			0.229060	−	0.973412i	$-0.426435\pi$
$127$	83270.1			0.458120			0.229060	+	0.973412i	$0.426435\pi$
$128$	−111865.	−	193756.i	−0.603488	−	1.04527i
$129$	−66300.7	+	114836.i	−0.350788	+	0.607582i
$130$	−48441.9	+	83903.8i	−0.251398	+	0.435435i
$131$	−83437.4	−	144518.i	−0.424798	−	0.735772i	0.571603	−	0.820530i	$-0.306322\pi$
$131$	−83437.4	−	144518.i	−0.424798	−	0.735772i	−0.996402	+	0.0847580i	$0.972988\pi$
$132$	−45807.8			−0.228825
$133$		0			0
$134$	323188.			1.55487
$135$	14116.7	+	24450.9i	0.0666653	+	0.115468i
$136$	98431.5	−	170488.i	0.456338	−	0.790401i
$137$	−19111.9	+	33102.9i	−0.0869969	+	0.150683i	−0.906240	−	0.422763i	$-0.861060\pi$
$137$	−19111.9	+	33102.9i	−0.0869969	+	0.150683i	0.819244	+	0.573446i	$0.194394\pi$
$138$	46929.5	+	81284.2i	0.209772	+	0.363336i
$139$	−106263.			−0.466492			−0.233246	−	0.972418i	$-0.574935\pi$
$139$	−106263.			−0.466492			−0.233246	+	0.972418i	$0.574935\pi$
$140$		0			0
$141$	61330.7			0.259795
$142$	−127703.	−	221189.i	−0.531474	−	0.920540i
$143$	−112826.	+	195420.i	−0.461390	+	0.799151i
$144$	49758.2	−	86183.7i	0.199967	−	0.346353i
$145$	−28340.8	−	49087.8i	−0.111942	−	0.193889i
$146$	355830.			1.38153
$147$		0			0
$148$	−143938.			−0.540160
$149$	−96277.8	−	166758.i	−0.355271	−	0.615348i	0.631893	−	0.775056i	$-0.282278\pi$
$149$	−96277.8	−	166758.i	−0.355271	−	0.615348i	−0.987164	+	0.159708i	$0.948945\pi$
$150$	46727.6	−	80934.6i	0.169569	−	0.293701i
$151$	−70849.3	+	122715.i	−0.252868	+	0.437980i	−0.964314	−	0.264761i	$-0.914707\pi$
$151$	−70849.3	+	122715.i	−0.252868	+	0.437980i	0.711447	+	0.702740i	$0.248040\pi$
$152$	−69766.9	−	120840.i	−0.244929	−	0.424230i
$153$	107706.			0.371972
$154$		0			0
$155$	−151524.			−0.506586
$156$	15556.6	+	26944.8i	0.0511804	+	0.0886470i
$157$	282885.	−	489972.i	0.915928	−	1.58643i	0.110392	−	0.993888i	$-0.464789\pi$
$157$	282885.	−	489972.i	0.915928	−	1.58643i	0.805536	−	0.592546i	$-0.201877\pi$
$158$	201764.	−	349466.i	0.642986	−	1.11368i
$159$	9051.04	+	15676.9i	0.0283926	+	0.0491775i
$160$	120562.			0.372314
$161$		0			0
$162$	41923.9			0.125509
$163$	215101.	+	372565.i	0.634121	+	1.09833i	0.986701	+	0.162549i	$0.0519714\pi$
$163$	215101.	+	372565.i	0.634121	+	1.09833i	−0.352579	+	0.935782i	$0.614695\pi$
$164$	−57856.0	+	100210.i	−0.167973	+	0.290937i
$165$	−100454.	+	173991.i	−0.287247	+	0.497527i
$166$	145601.	+	252188.i	0.410103	+	0.710319i
$167$	240265.			0.666653			0.333327	−	0.942811i	$-0.391829\pi$
$167$	240265.			0.666653			0.333327	+	0.942811i	$0.391829\pi$
$168$		0			0
$169$	−218028.			−0.587212
$170$	164533.	+	284979.i	0.436647	+	0.756295i
$171$	38170.2	−	66112.7i	0.0998238	−	0.172900i
$172$	−65051.3	+	112672.i	−0.167662	+	0.290399i
$173$	−89650.1	−	155279.i	−0.227738	−	0.394454i	0.729399	−	0.684088i	$-0.239800\pi$
$173$	−89650.1	−	155279.i	−0.227738	−	0.394454i	−0.957137	+	0.289634i	$0.906466\pi$
$174$	−84166.7			−0.210750
$175$		0			0
$176$	708151.			1.72323
$177$	231539.	+	401037.i	0.555509	+	0.962170i
$178$	50117.9	−	86806.8i	0.118561	−	0.205354i
$179$	287780.	−	498449.i	0.671317	−	1.16275i	−0.306214	−	0.951963i	$-0.599062\pi$
$179$	287780.	−	498449.i	0.671317	−	1.16275i	0.977531	−	0.210792i	$-0.0676043\pi$
$180$	13850.7	+	23990.2i	0.0318633	+	0.0551889i
$181$	−581006.			−1.31821			−0.659105	−	0.752051i	$-0.729065\pi$
$181$	−581006.			−1.31821			−0.659105	+	0.752051i	$0.729065\pi$
$182$		0			0
$183$	−369880.			−0.816458
$184$	−120815.	−	209258.i	−0.263073	−	0.455657i
$185$	−315648.	+	546719.i	−0.678070	+	1.17445i
$186$	−112499.	+	194854.i	−0.238433	+	0.412979i
$187$	383213.	+	663744.i	0.801376	+	1.38802i
$188$	60174.9			0.124171
$189$		0			0
$190$	233237.			0.468721
$191$	330280.	+	572062.i	0.655087	+	1.13464i	0.981872	+	0.189545i	$0.0607013\pi$
$191$	330280.	+	572062.i	0.655087	+	1.13464i	−0.326785	+	0.945099i	$0.605965\pi$
$192$	−87407.0	+	151393.i	−0.171117	+	0.296383i
$193$	278655.	−	482645.i	0.538485	−	0.932684i	−0.460501	−	0.887659i	$-0.652330\pi$
$193$	278655.	−	482645.i	0.538485	−	0.932684i	0.998986	−	0.0450243i	$-0.0143365\pi$
$194$	9995.33	+	17312.4i	0.0190675	+	0.0330258i
$195$	136459.			0.256989
$196$		0			0
$197$	−761400.			−1.39781			−0.698904	−	0.715216i	$-0.746328\pi$
$197$	−761400.			−1.39781			−0.698904	+	0.715216i	$0.746328\pi$
$198$	149164.	+	258359.i	0.270396	+	0.468340i
$199$	−67929.9	+	117658.i	−0.121598	+	0.210615i	−0.920398	−	0.390982i	$-0.872135\pi$
$199$	−67929.9	+	117658.i	−0.121598	+	0.210615i	0.798800	+	0.601597i	$0.205469\pi$
$200$	−120296.	+	208358.i	−0.212655	+	0.368328i
$201$	−227602.	−	394218.i	−0.397361	−	0.688250i
$202$	1.07996e6			1.86221
$203$		0			0
$204$	105676.			0.177787
$205$	253750.	+	439507.i	0.421716	+	0.730434i
$206$	360453.	−	624323.i	0.591807	−	1.02504i
$207$	66099.2	−	114487.i	0.107219	−	0.185708i
$208$	−240492.	−	416545.i	−0.385428	−	0.667581i
$209$	543232.			0.860240
$210$		0			0
$211$	−991157.			−1.53263			−0.766313	−	0.642467i	$-0.777911\pi$
$211$	−991157.			−1.53263			−0.766313	+	0.642467i	$0.777911\pi$
$212$	8880.48	+	15381.4i	0.0135705	+	0.0235048i
$213$	−179868.	+	311540.i	−0.271647	+	0.470506i
$214$	71277.3	−	123456.i	0.106394	−	0.184280i
$215$	285307.	+	494167.i	0.420937	+	0.729084i
$216$	−107929.			−0.157400
$217$		0			0
$218$	−535596.			−0.763301
$219$	−250590.	−	434034.i	−0.353064	−	0.611524i
$220$	−98560.7	+	170712.i	−0.137293	+	0.237798i
$221$	260283.	−	450823.i	0.358480	−	0.620906i
$222$	468706.	+	811823.i	0.638291	+	1.10555i
$223$	−543344.			−0.731666			−0.365833	−	0.930681i	$-0.619216\pi$
$223$	−543344.			−0.731666			−0.365833	+	0.930681i	$0.619216\pi$
$224$		0			0
$225$	−131630.			−0.173340
$226$	130764.	+	226489.i	0.170300	+	0.294969i
$227$	8.16704	−	14.1457i	1.05196e−5	−	1.82205e-5i	−0.866020	−	0.500009i	$-0.833330\pi$
$227$	8.16704	−	14.1457i	1.05196e−5	−	1.82205e-5i	0.866031	+	0.499991i	$0.166663\pi$
$228$	37450.9	−	64866.8i	0.0477117	−	0.0826391i
$229$	−38689.5	−	67012.2i	−0.0487534	−	0.0844433i	0.840619	−	0.541627i	$-0.182192\pi$
$229$	−38689.5	−	67012.2i	−0.0487534	−	0.0844433i	−0.889372	+	0.457184i	$0.848858\pi$
$230$	403896.			0.503443
$231$		0			0
$232$	216679.			0.264299
$233$	51828.6	+	89769.9i	0.0625432	+	0.108328i	0.895602	−	0.444857i	$-0.146746\pi$
$233$	51828.6	+	89769.9i	0.0625432	+	0.108328i	−0.833058	+	0.553185i	$0.813412\pi$
$234$	101314.	−	175481.i	0.120956	−	0.209503i
$235$	131960.	−	228561.i	0.155874	−	0.269981i
$236$	227176.	+	393480.i	0.265511	+	0.459878i
$237$	−568362.			−0.657286
$238$		0			0
$239$	689109.			0.780356			0.390178	−	0.920739i	$-0.372413\pi$
$239$	689109.			0.780356			0.390178	+	0.920739i	$0.372413\pi$
$240$	−214121.	−	370868.i	−0.239956	−	0.415615i
$241$	110148.	−	190782.i	0.122161	−	0.211590i	−0.798458	−	0.602050i	$-0.794351\pi$
$241$	110148.	−	190782.i	0.122161	−	0.211590i	0.920620	+	0.390460i	$0.127684\pi$
$242$	−546890.	+	947242.i	−0.600291	+	1.03973i
$243$	−29524.5	−	51137.9i	−0.0320750	−	0.0555556i
$244$	−362910.			−0.390234
$245$		0			0
$246$	753585.			0.793953
$247$	−184485.	−	319537.i	−0.192406	−	0.333257i
$248$	289618.	−	501633.i	0.299017	−	0.517913i
$249$	205076.	−	355201.i	0.209612	−	0.363058i
$250$	−587757.	−	1.01803e6i	−0.594768	−	1.03017i
$251$	−1.43641e6			−1.43912			−0.719558	−	0.694433i	$-0.755655\pi$
$251$	−1.43641e6			−1.43912			−0.719558	+	0.694433i	$0.755655\pi$
$252$		0			0
$253$	940714.			0.923966
$254$	−266042.	−	460799.i	−0.258742	−	0.448154i
$255$	231741.	−	401388.i	0.223179	−	0.386557i
$256$	−404021.	+	699785.i	−0.385305	+	0.667367i
$257$	−454598.	−	787388.i	−0.429334	−	0.743628i	0.567480	−	0.823387i	$-0.307918\pi$
$257$	−454598.	−	787388.i	−0.429334	−	0.743628i	−0.996814	+	0.0797589i	$0.974585\pi$
$258$	847306.			0.792485
$259$		0			0
$260$	133887.			0.122830
$261$	59273.5	+	102665.i	0.0538592	+	0.0932868i
$262$	−533154.	+	923450.i	−0.479843	+	0.831113i
$263$	−374528.	+	648702.i	−0.333884	+	0.578304i	−0.983270	−	0.182155i	$-0.941693\pi$
$263$	−374528.	+	648702.i	−0.333884	+	0.578304i	0.649386	+	0.760459i	$0.275026\pi$
$264$	−384007.	−	665120.i	−0.339101	−	0.587341i
$265$	77897.4			0.0681410
$266$		0			0
$267$	−141180.			−0.121198
$268$	−223313.	−	386789.i	−0.189923	−	0.328956i
$269$	334972.	−	580189.i	0.282246	−	0.488865i	−0.689691	−	0.724104i	$-0.742254\pi$
$269$	334972.	−	580189.i	0.282246	−	0.488865i	0.971938	+	0.235238i	$0.0755871\pi$
$270$	90204.1	−	156238.i	0.0753038	−	0.130430i
$271$	270330.	+	468225.i	0.223599	+	0.387285i	0.955898	−	0.293698i	$-0.0948860\pi$
$271$	270330.	+	468225.i	0.223599	+	0.387285i	−0.732299	+	0.680983i	$0.761553\pi$
$272$	−1.63367e6			−1.33888
$273$		0			0
$274$	244246.			0.196540
$275$	−468334.	−	811178.i	−0.373443	−	0.646821i
$276$	64853.6	−	112330.i	0.0512462	−	0.0887610i
$277$	200955.	−	348064.i	0.157362	−	0.272558i	−0.776555	−	0.630050i	$-0.783035\pi$
$277$	200955.	−	348064.i	0.157362	−	0.272558i	0.933916	+	0.357491i	$0.116368\pi$
$278$	339502.	+	588035.i	0.263470	+	0.456343i
$279$	316906.			0.243736
$280$		0			0
$281$	−429139.			−0.324214			−0.162107	−	0.986773i	$-0.551829\pi$
$281$	−429139.			−0.324214			−0.162107	+	0.986773i	$0.551829\pi$
$282$	−195947.	−	339391.i	−0.146729	−	0.254143i
$283$	−170463.	+	295251.i	−0.126522	+	0.219142i	−0.922327	−	0.386411i	$-0.873715\pi$
$283$	−170463.	+	295251.i	−0.126522	+	0.219142i	0.795805	+	0.605553i	$0.207048\pi$
$284$	−176478.	+	305669.i	−0.129836	+	0.224883i
$285$	−164255.	−	284498.i	−0.119786	−	0.207476i
$286$	1.44188e6			1.04235
$287$		0			0
$288$	−252149.			−0.179133
$289$	−174123.	−	301590.i	−0.122634	−	0.212409i
$290$	−181094.	+	313664.i	−0.126447	+	0.219013i
$291$	14078.2	−	24384.2i	0.00974575	−	0.0168801i
$292$	−245868.	−	425855.i	−0.168750	−	0.292284i
$293$	388847.			0.264612			0.132306	−	0.991209i	$-0.457762\pi$
$293$	388847.			0.264612			0.132306	+	0.991209i	$0.457762\pi$
$294$		0			0
$295$	1.99273e6			1.33319
$296$	−1.20664e6	−	2.08996e6i	−0.800475	−	1.38646i
$297$	210094.	−	363894.i	0.138205	−	0.239378i
$298$	−615202.	+	1.06556e6i	−0.401307	+	0.695085i
$299$	−319472.	−	553342.i	−0.206659	−	0.357945i
$300$	−129149.			−0.0828493
$301$		0			0
$302$	905435.			0.571268
$303$	−760549.	−	1.31731e6i	−0.475905	−	0.824292i
$304$	−578960.	+	1.00279e6i	−0.359306	+	0.622336i
$305$	−795840.	+	1.37844e6i	−0.489865	+	0.848471i
$306$	−344113.	−	596021.i	−0.210086	−	0.363880i
$307$	2.35747e6			1.42758			0.713789	−	0.700361i	$-0.246978\pi$
$307$	2.35747e6			1.42758			0.713789	+	0.700361i	$0.246978\pi$
$308$		0			0
$309$	−1.01538e6			−0.604969
$310$	484110.	+	838503.i	0.286114	+	0.495565i
$311$	−718314.	+	1.24416e6i	−0.421127	+	0.729414i	−0.996050	−	0.0887939i	$-0.971699\pi$
$311$	−718314.	+	1.24416e6i	−0.421127	+	0.729414i	0.574923	+	0.818208i	$0.305032\pi$
$312$	−260822.	+	451758.i	−0.151691	+	0.262736i
$313$	−411400.	−	712566.i	−0.237358	−	0.411116i	0.722598	−	0.691269i	$-0.242948\pi$
$313$	−411400.	−	712566.i	−0.237358	−	0.411116i	−0.959955	+	0.280153i	$0.909615\pi$
$314$	−3.61520e6			−2.06923
$315$		0			0
$316$	−557652.			−0.314156
$317$	883467.	+	1.53021e6i	0.493790	+	0.855269i	0.999974	−	0.00715584i	$-0.00227779\pi$
$317$	883467.	+	1.53021e6i	0.493790	+	0.855269i	−0.506184	+	0.862425i	$0.668944\pi$
$318$	57835.0	−	100173.i	0.0320718	−	0.0555499i
$319$	−421786.	+	730555.i	−0.232068	+	0.401954i
$320$	376132.	+	651480.i	0.205336	+	0.355653i
$321$	−200785.			−0.108760
$322$		0			0
$323$	−1.25321e6			−0.668370
$324$	−28968.1	−	50174.3i	−0.0153306	−	0.0265533i
$325$	−318098.	+	550962.i	−0.167052	+	0.289343i
$326$	1.37446e6	−	2.38064e6i	0.716291	−	1.24065i
$327$	377188.	+	653309.i	0.195069	+	0.337869i
$328$	−1.94003e6			−0.995689
$329$		0			0
$330$	1.28377e6			0.648937
$331$	1526.14	+	2643.35i	0.000765638	+	0.00132612i	0.866408	−	0.499337i	$-0.166423\pi$
$331$	1526.14	+	2643.35i	0.000765638	+	0.00132612i	−0.865642	+	0.500663i	$0.833090\pi$
$332$	201211.	−	348508.i	0.100186	−	0.173527i
$333$	660164.	−	1.14344e6i	0.326243	−	0.565069i
$334$	−767632.	−	1.32958e6i	−0.376519	−	0.652150i
$335$	−1.95885e6			−0.953649
$336$		0			0
$337$	2.02939e6			0.973398			0.486699	−	0.873570i	$-0.338201\pi$
$337$	2.02939e6			0.973398			0.486699	+	0.873570i	$0.338201\pi$
$338$	696584.	+	1.20652e6i	0.331651	+	0.574437i
$339$	184178.	−	319006.i	0.0870439	−	0.150764i
$340$	227374.	−	393824.i	0.106670	−	0.184759i
$341$	1.12754e6	+	1.95295e6i	0.525104	+	0.909507i
$342$	−487805.			−0.225518
$343$		0			0
$344$	−2.18130e6			−0.993848
$345$	−284440.	−	492665.i	−0.128660	−	0.222845i
$346$	−572852.	+	992209.i	−0.257248	+	0.445567i
$347$	−1.89109e6	+	3.27547e6i	−0.843119	+	1.46033i	0.0441252	+	0.999026i	$0.485950\pi$
$347$	−1.89109e6	+	3.27547e6i	−0.843119	+	1.46033i	−0.887245	+	0.461299i	$0.847383\pi$
$348$	58156.6	+	100730.i	0.0257425	+	0.0445873i
$349$	−291147.			−0.127953			−0.0639763	−	0.997951i	$-0.520378\pi$
$349$	−291147.			−0.127953			−0.0639763	+	0.997951i	$0.520378\pi$
$350$		0			0
$351$	−285397.			−0.123646
$352$	−897136.	−	1.55389e6i	−0.385924	−	0.668440i
$353$	192538.	−	333486.i	0.0822394	−	0.142443i	−0.821972	−	0.569528i	$-0.807126\pi$
$353$	192538.	−	333486.i	0.0822394	−	0.142443i	0.904212	+	0.427085i	$0.140459\pi$
$354$	1.47950e6	−	2.56257e6i	0.627491	−	1.08685i
$355$	774013.	+	1.34063e6i	0.325970	+	0.564596i
$356$	−138520.			−0.0579277
$357$		0			0
$358$	−3.67775e6			−1.51661
$359$	1.61507e6	+	2.79738e6i	0.661385	+	1.14555i	0.980252	+	0.197753i	$0.0633645\pi$
$359$	1.61507e6	+	2.79738e6i	0.661385	+	1.14555i	−0.318866	+	0.947800i	$0.603302\pi$
$360$	−232222.	+	402219.i	−0.0944379	+	0.163571i
$361$	793921.	−	1.37511e6i	0.320634	−	0.555354i
$362$	1.85628e6	+	3.21517e6i	0.744511	+	1.28953i
$363$	1.54057e6			0.613641
$364$		0			0
$365$	−2.15669e6			−0.847336
$366$	1.18174e6	+	2.04684e6i	0.461127	+	0.798695i
$367$	−239779.	+	415310.i	−0.0929280	+	0.160956i	−0.908742	−	0.417358i	$-0.862956\pi$
$367$	−239779.	+	415310.i	−0.0929280	+	0.160956i	0.815814	+	0.578314i	$0.196289\pi$
$368$	−1.00258e6	+	1.73653e6i	−0.385923	+	0.668439i
$369$	−530705.	−	919208.i	−0.202902	−	0.351437i
$370$	4.03390e6			1.53187
$371$		0			0
$372$	310934.			0.116496
$373$	−436333.	−	755751.i	−0.162385	−	0.281259i	0.773339	−	0.633993i	$-0.218585\pi$
$373$	−436333.	−	755751.i	−0.162385	−	0.281259i	−0.935724	+	0.352734i	$0.885252\pi$
$374$	2.44868e6	−	4.24124e6i	0.905217	−	1.56788i
$375$	−827844.	+	1.43387e6i	−0.303998	+	0.526540i
$376$	504447.	+	873728.i	0.184012	+	0.318718i
$377$	572965.			0.207622
$378$		0			0
$379$	−2.43493e6			−0.870742			−0.435371	−	0.900251i	$-0.643383\pi$
$379$	−2.43493e6			−0.870742			−0.435371	+	0.900251i	$0.643383\pi$
$380$	−161160.	−	279137.i	−0.0572529	−	0.0991650i
$381$	−374715.	+	649026.i	−0.132248	+	0.229060i
$382$	2.11044e6	−	3.65540e6i	0.739973	−	1.28167i
$383$	−1.80584e6	−	3.12781e6i	−0.629047	−	1.08954i	−0.987743	−	0.156087i	$-0.950112\pi$
$383$	−1.80584e6	−	3.12781e6i	−0.629047	−	1.08954i	0.358696	−	0.933454i	$-0.383222\pi$
$384$	2.01357e6			0.696848
$385$		0			0
$386$	−3.56114e6			−1.21652
$387$	−596707.	−	1.03353e6i	−0.202527	−	0.350788i
$388$	13812.9	−	23924.7i	0.00465807	−	0.00806802i
$389$	87616.2	−	151756.i	0.0293569	−	0.0508477i	−0.850974	−	0.525208i	$-0.823987\pi$
$389$	87616.2	−	151756.i	0.0293569	−	0.0508477i	0.880331	+	0.474361i	$0.157321\pi$
$390$	−435977.	−	755134.i	−0.145145	−	0.251398i
$391$	−2.17018e6			−0.717882
$392$		0			0
$393$	1.50187e6			0.490515
$394$	2.43262e6	+	4.21343e6i	0.789467	+	1.36740i
$395$	−1.22290e6	+	2.11812e6i	−0.394364	+	0.683058i
$396$	206135.	−	357036.i	0.0660562	−	0.114413i
$397$	942577.	+	1.63259e6i	0.300152	+	0.519878i	0.976170	−	0.217007i	$-0.0696294\pi$
$397$	942577.	+	1.63259e6i	0.300152	+	0.519878i	−0.676019	+	0.736885i	$0.736296\pi$
$398$	868126.			0.274710
$399$		0			0
$400$	1.99654e6			0.623920
$401$	−669915.	−	1.16033e6i	−0.208046	−	0.360346i	0.743053	−	0.669232i	$-0.233377\pi$
$401$	−669915.	−	1.16033e6i	−0.208046	−	0.360346i	−0.951099	+	0.308887i	$0.900044\pi$
$402$	−1.45435e6	+	2.51900e6i	−0.448851	+	0.777433i
$403$	765839.	−	1.32647e6i	0.234895	−	0.406851i
$404$	−746217.	−	1.29249e6i	−0.227463	−	0.393978i
$405$	−254101.			−0.0769785
$406$		0			0
$407$	9.39535e6			2.81143
$408$	885884.	+	1.53440e6i	0.263467	+	0.456338i
$409$	3.29314e6	−	5.70388e6i	0.973423	−	1.68602i	0.288381	−	0.957516i	$-0.406883\pi$
$409$	3.29314e6	−	5.70388e6i	0.973423	−	1.68602i	0.685043	−	0.728503i	$-0.259783\pi$
$410$	1.62143e6	−	2.80839e6i	0.476362	−	0.825084i
$411$	−172008.	−	297926.i	−0.0502277	−	0.0869969i
$412$	−996247.			−0.289150
$413$		0			0
$414$	−844730.			−0.242224
$415$	−882487.	−	1.52851e6i	−0.251529	−	0.435661i
$416$	−609346.	+	1.05542e6i	−0.172636	+	0.299014i
$417$	478182.	−	828236.i	0.134665	−	0.233246i
$418$	−1.73559e6	−	3.00613e6i	−0.485855	−	0.841525i
$419$	6.96869e6			1.93917			0.969585	−	0.244754i	$-0.0787071\pi$
$419$	6.96869e6			1.93917			0.969585	+	0.244754i	$0.0787071\pi$
$420$		0			0
$421$	3.84041e6			1.05602			0.528010	−	0.849238i	$-0.322938\pi$
$421$	3.84041e6			1.05602			0.528010	+	0.849238i	$0.322938\pi$
$422$	3.16668e6	+	5.48485e6i	0.865612	+	1.49928i
$423$	−275988.	+	478025.i	−0.0749962	+	0.129897i
$424$	−148890.	+	257886.i	−0.0402209	+	0.0696647i
$425$	1.08042e6	+	1.87134e6i	0.290149	+	0.502552i
$426$	2.29866e6			0.613693
$427$		0			0
$428$	−197002.			−0.0519829
$429$	−1.01543e6	−	1.75878e6i	−0.266384	−	0.461390i
$430$	1.82308e6	−	3.15766e6i	0.475481	−	0.823558i
$431$	−1.51818e6	+	2.62957e6i	−0.393668	+	0.681854i	−0.992930	−	0.118699i	$-0.962128\pi$
$431$	−1.51818e6	+	2.62957e6i	−0.393668	+	0.681854i	0.599262	+	0.800553i	$0.295461\pi$
$432$	447824.	+	775653.i	0.115451	+	0.199967i
$433$	941529.			0.241332			0.120666	−	0.992693i	$-0.461497\pi$
$433$	941529.			0.241332			0.120666	+	0.992693i	$0.461497\pi$
$434$		0			0
$435$	510135.			0.129259
$436$	370080.	+	640997.i	0.0932351	+	0.161488i
$437$	−769096.	+	1.33211e6i	−0.192653	+	0.333686i
$438$	−1.60124e6	+	2.77342e6i	−0.398814	+	0.690765i
$439$	670546.	+	1.16142e6i	0.166061	+	0.287626i	0.937031	−	0.349245i	$-0.113562\pi$
$439$	670546.	+	1.16142e6i	0.166061	+	0.287626i	−0.770971	+	0.636871i	$0.780229\pi$
$440$	−3.30494e6			−0.813827
$441$		0			0
$442$	−3.32635e6			−0.809864
$443$	386171.	+	668867.i	0.0934910	+	0.161931i	0.908978	−	0.416844i	$-0.136864\pi$
$443$	386171.	+	668867.i	0.0934910	+	0.161931i	−0.815487	+	0.578776i	$0.803531\pi$
$444$	647723.	−	1.12189e6i	0.155931	−	0.270080i
$445$	−303765.	+	526137.i	−0.0727174	+	0.125950i
$446$	1.73595e6	+	3.00675e6i	0.413238	+	0.715748i
$447$	1.73300e6			0.410232
$448$		0			0
$449$	2.25684e6			0.528304			0.264152	−	0.964481i	$-0.414908\pi$
$449$	2.25684e6			0.528304			0.264152	+	0.964481i	$0.414908\pi$
$450$	420548.	+	728411.i	0.0979005	+	0.169569i
$451$	3.77646e6	−	6.54101e6i	0.874265	−	1.51427i
$452$	180707.	−	312994.i	0.0416034	−	0.0720593i
$453$	−637644.	−	1.10443e6i	−0.145993	−	0.252868i
$454$	−104.373			−2.37655e−5
$455$		0			0
$456$	1.25580e6			0.282820
$457$	−2.14235e6	−	3.71066e6i	−0.479844	−	0.831114i	0.519889	−	0.854234i	$-0.325973\pi$
$457$	−2.14235e6	−	3.71066e6i	−0.479844	−	0.831114i	−0.999733	+	0.0231196i	$0.992640\pi$
$458$	−247221.	+	428199.i	−0.0550708	+	0.0953854i
$459$	−484676.	+	839483.i	−0.107379	+	0.185986i
$460$	−279080.	−	483381.i	−0.0614942	−	0.106511i
$461$	3.10462e6			0.680387			0.340193	−	0.940355i	$-0.389507\pi$
$461$	3.10462e6			0.680387			0.340193	+	0.940355i	$0.389507\pi$
$462$		0			0
$463$	−3.53386e6			−0.766121			−0.383060	−	0.923723i	$-0.625130\pi$
$463$	−3.53386e6			−0.766121			−0.383060	+	0.923723i	$0.625130\pi$
$464$	−899053.	−	1.55721e6i	−0.193861	−	0.335777i
$465$	681859.	−	1.18102e6i	0.146239	−	0.253293i
$466$	331178.	−	573617.i	0.0706475	−	0.122365i
$467$	1.36230e6	+	2.35957e6i	0.289054	+	0.500657i	0.973584	−	0.228328i	$-0.0733258\pi$
$467$	1.36230e6	+	2.35957e6i	0.289054	+	0.500657i	−0.684530	+	0.728985i	$0.739993\pi$
$468$	−280019.			−0.0590980
$469$		0			0
$470$	−1.68641e6			−0.352143
$471$	2.54597e6	+	4.40975e6i	0.528812	+	0.915928i
$472$	−3.80883e6	+	6.59709e6i	−0.786932	+	1.36301i
$473$	4.24612e6	−	7.35449e6i	0.872649	−	1.51147i
$474$	1.81588e6	+	3.14520e6i	0.371228	+	0.642986i
$475$	1.53158e6			0.311461
$476$		0			0
$477$	−162919.			−0.0327850
$478$	−2.20166e6	−	3.81338e6i	−0.440737	−	0.763379i
$479$	489342.	−	847566.i	0.0974482	−	0.168785i	−0.813180	−	0.582013i	$-0.802265\pi$
$479$	489342.	−	847566.i	0.0974482	−	0.168785i	0.910628	+	0.413228i	$0.135599\pi$
$480$	−542527.	+	939685.i	−0.107478	+	0.186157i
$481$	−3.19072e6	−	5.52649e6i	−0.628819	−	1.08915i
$482$	−1.40766e6			−0.275982
$483$		0			0
$484$	1.51154e6			0.293296
$485$	−60581.8	−	104931.i	−0.0116947	−	0.0202558i
$486$	−188658.	+	326765.i	−0.0362313	+	0.0627544i
$487$	−1.96372e6	+	3.40126e6i	−0.375195	+	0.649857i	−0.990356	−	0.138544i	$-0.955758\pi$
$487$	−1.96372e6	+	3.40126e6i	−0.375195	+	0.649857i	0.615161	+	0.788401i	$0.289091\pi$
$488$	−3.04228e6	−	5.26938e6i	−0.578295	−	1.00164i
$489$	−3.87181e6			−0.732220
$490$		0			0
$491$	2.63241e6			0.492777			0.246388	−	0.969171i	$-0.420756\pi$
$491$	2.63241e6			0.492777			0.246388	+	0.969171i	$0.420756\pi$
$492$	−520704.	−	901886.i	−0.0969791	−	0.167973i
$493$	973037.	−	1.68535e6i	0.180307	−	0.312301i
$494$	−1.17883e6	+	2.04180e6i	−0.217338	+	0.376440i
$495$	−904083.	−	1.56592e6i	−0.165842	−	0.287247i
$496$	−4.80678e6			−0.877305
$497$		0			0
$498$	−2.62081e6			−0.473546
$499$	−1.06272e6	−	1.84069e6i	−0.191059	−	0.330924i	0.754542	−	0.656251i	$-0.227859\pi$
$499$	−1.06272e6	−	1.84069e6i	−0.191059	−	0.330924i	−0.945601	+	0.325327i	$0.894526\pi$
$500$	−812244.	+	1.40685e6i	−0.145299	+	0.251665i
$501$	−1.08119e6	+	1.87268e6i	−0.192446	+	0.333327i
$502$	4.58925e6	+	7.94881e6i	0.812798	+	1.40781i
$503$	−2.60929e6			−0.459835			−0.229917	−	0.973210i	$-0.573846\pi$
$503$	−2.60929e6			−0.459835			−0.229917	+	0.973210i	$0.573846\pi$
$504$		0			0
$505$	−6.54564e6			−1.14215
$506$	−3.00552e6	−	5.20571e6i	−0.521847	−	0.903865i
$507$	981124.	−	1.69936e6i	0.169513	−	0.293606i
$508$	−367654.	+	636795.i	−0.0632092	+	0.109481i
$509$	−5.00911e6	−	8.67603e6i	−0.856970	−	1.48432i	−0.874805	−	0.484475i	$-0.839011\pi$
$509$	−5.00911e6	−	8.67603e6i	−0.856970	−	1.48432i	0.0178348	−	0.999841i	$-0.494323\pi$
$510$	−2.96159e6			−0.504196
$511$		0			0
$512$	−1.99607e6			−0.336512
$513$	343532.	+	595014.i	0.0576333	+	0.0998238i
$514$	−2.90482e6	+	5.03130e6i	−0.484967	+	0.839987i
$515$	−2.18471e6	+	3.78403e6i	−0.362974	+	0.628689i
$516$	−585462.	−	1.01405e6i	−0.0967998	−	0.167662i
$517$	−3.92782e6			−0.646287
$518$		0			0
$519$	1.61370e6			0.262969
$520$	1.12238e6	+	1.94402e6i	0.182025	+	0.315277i
$521$	−2.08970e6	+	3.61947e6i	−0.337280	+	0.584186i	−0.983920	−	0.178609i	$-0.942840\pi$
$521$	−2.08970e6	+	3.61947e6i	−0.337280	+	0.584186i	0.646640	+	0.762795i	$0.276174\pi$
$522$	378750.	−	656014.i	0.0608382	−	0.105375i
$523$	1.80263e6	+	3.12224e6i	0.288172	+	0.499128i	0.973373	−	0.229225i	$-0.0736193\pi$
$523$	1.80263e6	+	3.12224e6i	0.288172	+	0.499128i	−0.685202	+	0.728353i	$0.740286\pi$
$524$	1.47357e6			0.234446
$525$		0			0
$526$	4.78637e6			0.754297
$527$	−2.60117e6	−	4.50536e6i	−0.407983	−	0.706648i
$528$	−3.18668e6	+	5.51949e6i	−0.497455	+	0.861617i
$529$	1.88633e6	−	3.26722e6i	0.293075	−	0.507621i
$530$	−248877.	−	431068.i	−0.0384853	−	0.0666586i
$531$	−4.16770e6			−0.641446
$532$		0			0
$533$	−5.13003e6			−0.782172
$534$	451061.	+	781261.i	0.0684514	+	0.118561i
$535$	−432013.	+	748268.i	−0.0652547	+	0.113025i
$536$	3.74407e6	−	6.48492e6i	0.562901	−	0.974972i
$537$	2.59002e6	+	4.48604e6i	0.387585	+	0.671317i
$538$	−4.28086e6			−0.637640
$539$		0			0
$540$	−249313.			−0.0367926
$541$	3.34083e6	+	5.78648e6i	0.490751	+	0.850005i	0.999943	−	0.0106475i	$-0.00338926\pi$
$541$	3.34083e6	+	5.78648e6i	0.490751	+	0.850005i	−0.509193	+	0.860653i	$0.670056\pi$
$542$	1.72737e6	−	2.99189e6i	0.252573	−	0.437470i
$543$	2.61453e6	−	4.52850e6i	0.380534	−	0.659105i
$544$	2.06964e6	+	3.58473e6i	0.299846	+	0.519349i
$545$	3.24625e6			0.468156
$546$		0			0
$547$	8.69076e6			1.24191			0.620954	−	0.783847i	$-0.286745\pi$
$547$	8.69076e6			1.24191			0.620954	+	0.783847i	$0.286745\pi$
$548$	−168766.	−	292312.i	−0.0240068	−	0.0415810i
$549$	1.66446e6	−	2.88293e6i	0.235691	−	0.408229i
$550$	−2.99259e6	+	5.18332e6i	−0.421833	+	0.730636i
$551$	−689676.	−	1.19455e6i	−0.0967756	−	0.167620i
$552$	2.17467e6			0.303771
$553$		0			0
$554$	−2.56815e6			−0.355505
$555$	−2.84084e6	−	4.92047e6i	−0.391484	−	0.678070i
$556$	469171.	−	812628.i	0.0643642	−	0.111482i
$557$	−3.12371e6	+	5.41042e6i	−0.426612	+	0.738913i	−0.996569	−	0.0827611i	$-0.973626\pi$
$557$	−3.12371e6	+	5.41042e6i	−0.426612	+	0.738913i	0.569958	+	0.821674i	$0.306960\pi$
$558$	−1.01249e6	−	1.75369e6i	−0.137660	−	0.238433i
$559$	−5.76803e6			−0.780725
$560$		0			0
$561$	−6.89783e6			−0.925349
$562$	1.37107e6	+	2.37476e6i	0.183113	+	0.317161i
$563$	−5.95223e6	+	1.03096e7i	−0.791423	+	1.37078i	0.133663	+	0.991027i	$0.457326\pi$
$563$	−5.95223e6	+	1.03096e7i	−0.791423	+	1.37078i	−0.925086	+	0.379758i	$0.876007\pi$
$564$	−270787.	+	469017.i	−0.0358451	+	0.0620856i
$565$	−792560.	−	1.37275e6i	−0.104451	−	0.180914i
$566$	2.17848e6			0.285833
$567$		0			0
$568$	−5.91768e6			−0.769627
$569$	−10707.2	−	18545.4i	−0.00138642	−	0.00240135i	0.865331	−	0.501200i	$-0.167108\pi$
$569$	−10707.2	−	18545.4i	−0.00138642	−	0.00240135i	−0.866718	+	0.498799i	$0.833775\pi$
$570$	−1.04957e6	+	1.81791e6i	−0.135308	+	0.234360i
$571$	−3.55823e6	+	6.16304e6i	−0.456714	+	0.791051i	−0.998785	−	0.0492811i	$-0.984307\pi$
$571$	−3.55823e6	+	6.16304e6i	−0.456714	+	0.791051i	0.542071	+	0.840333i	$0.317640\pi$
$572$	−996297.	−	1.72564e6i	−0.127321	−	0.220526i
$573$	−5.94504e6			−0.756429
$574$		0			0
$575$	2.65223e6			0.334534
$576$	−786663.	−	1.36254e6i	−0.0987944	−	0.171117i
$577$	−5.33259e6	+	9.23632e6i	−0.666805	+	1.15494i	0.311988	+	0.950086i	$0.399005\pi$
$577$	−5.33259e6	+	9.23632e6i	−0.666805	+	1.15494i	−0.978793	+	0.204854i	$0.934328\pi$
$578$	−1.11262e6	+	1.92712e6i	−0.138525	+	0.239932i
$579$	2.50790e6	+	4.34380e6i	0.310895	+	0.538485i
$580$	500522.			0.0617808
$581$		0			0
$582$	−179916.			−0.0220172
$583$	−579659.	−	1.00400e6i	−0.0706319	−	0.122338i
$584$	4.12222e6	−	7.13990e6i	0.500149	−	0.866283i
$585$	−614065.	+	1.06359e6i	−0.0741864	+	0.128495i
$586$	−1.24234e6	−	2.15180e6i	−0.149450	−	0.258856i
$587$	1.30101e7			1.55843			0.779213	−	0.626759i	$-0.215619\pi$
$587$	1.30101e7			1.55843			0.779213	+	0.626759i	$0.215619\pi$
$588$		0			0
$589$	−3.68735e6			−0.437952
$590$	−6.36664e6	−	1.10273e7i	−0.752975	−	1.30419i
$591$	3.42630e6	−	5.93453e6i	0.403512	−	0.698904i
$592$	−1.00133e7	+	1.73435e7i	−1.17428	+	2.03391i
$593$	2.13043e6	+	3.69002e6i	0.248789	+	0.430915i	0.963190	−	0.268821i	$-0.0866342\pi$
$593$	2.13043e6	+	3.69002e6i	0.248789	+	0.430915i	−0.714401	+	0.699736i	$0.753301\pi$
$594$	−2.68495e6			−0.312226
$595$		0			0
$596$	1.70034e6			0.196074
$597$	−611369.	−	1.05892e6i	−0.0702049	−	0.121598i
$598$	−2.04139e6	+	3.53578e6i	−0.233438	+	0.404327i
$599$	6.89790e6	−	1.19475e7i	0.785507	−	1.36054i	−0.143189	−	0.989695i	$-0.545736\pi$
$599$	6.89790e6	−	1.19475e7i	0.785507	−	1.36054i	0.928696	−	0.370842i	$-0.120931\pi$
$600$	−1.08266e6	−	1.87522e6i	−0.122776	−	0.212655i
$601$	−4.99695e6			−0.564311			−0.282155	−	0.959369i	$-0.591049\pi$
$601$	−4.99695e6			−0.564311			−0.282155	+	0.959369i	$0.591049\pi$
$602$		0			0
$603$	4.09683e6			0.458833
$604$	−625628.	−	1.08362e6i	−0.0697788	−	0.120860i
$605$	3.31471e6	−	5.74125e6i	0.368177	−	0.637702i
$606$	−4.85981e6	+	8.41743e6i	−0.537573	+	0.931104i
$607$	−1.52473e6	−	2.64091e6i	−0.167966	−	0.290926i	0.769739	−	0.638359i	$-0.220387\pi$
$607$	−1.52473e6	−	2.64091e6i	−0.167966	−	0.290926i	−0.937705	+	0.347434i	$0.887053\pi$
$608$	2.93387e6			0.321871
$609$		0			0
$610$	1.01706e7			1.10668
$611$	1.33391e6	+	2.31040e6i	0.144552	+	0.250372i
$612$	−475542.	+	823663.i	−0.0513228	+	0.0888937i
$613$	3.51813e6	−	6.09357e6i	0.378147	−	0.654969i	−0.612646	−	0.790357i	$-0.709895\pi$
$613$	3.51813e6	−	6.09357e6i	0.378147	−	0.654969i	0.990793	+	0.135388i	$0.0432282\pi$
$614$	−7.53195e6	−	1.30457e7i	−0.806281	−	1.39652i
$615$	−4.56749e6			−0.486956
$616$		0			0
$617$	1.00066e7			1.05822			0.529108	−	0.848554i	$-0.322527\pi$
$617$	1.00066e7			1.05822			0.529108	+	0.848554i	$0.322527\pi$
$618$	3.24408e6	+	5.61890e6i	0.341680	+	0.591807i
$619$	−3.27533e6	+	5.67304e6i	−0.343581	+	0.595099i	−0.985095	−	0.172012i	$-0.944973\pi$
$619$	−3.27533e6	+	5.67304e6i	−0.343581	+	0.595099i	0.641514	+	0.767111i	$0.278307\pi$
$620$	669010.	−	1.15876e6i	0.0698962	−	0.121064i
$621$	594893.	+	1.03038e6i	0.0619027	+	0.107219i
$622$	9.17986e6			0.951393
$623$		0			0
$624$	4.32886e6			0.445054
$625$	1.02325e6	+	1.77232e6i	0.104781	+	0.181485i
$626$	−2.62879e6	+	4.55320e6i	−0.268114	+	0.464388i
$627$	−2.44455e6	+	4.23408e6i	−0.248330	+	0.430120i
$628$	2.49799e6	+	4.32665e6i	0.252750	+	0.437777i
$629$	−2.16746e7			−2.18436
$630$		0			0
$631$	2.22672e6			0.222635			0.111317	−	0.993785i	$-0.464493\pi$
$631$	2.22672e6			0.222635			0.111317	+	0.993785i	$0.464493\pi$
$632$	−4.67480e6	−	8.09699e6i	−0.465554	−	0.806364i
$633$	4.46021e6	−	7.72531e6i	0.442431	−	0.766313i
$634$	5.64524e6	−	9.77784e6i	0.557775	−	0.966095i
$635$	1.61249e6	+	2.79291e6i	0.158694	+	0.274867i
$636$	−159849.			−0.0156699
$637$		0			0
$638$	5.39031e6			0.524279
$639$	−1.61881e6	−	2.80386e6i	−0.156835	−	0.271647i
$640$	4.33242e6	−	7.50397e6i	0.418101	−	0.724171i
$641$	7.96698e6	−	1.37992e7i	0.765859	−	1.32651i	−0.173932	−	0.984758i	$-0.555647\pi$
$641$	7.96698e6	−	1.37992e7i	0.765859	−	1.32651i	0.939791	−	0.341749i	$-0.111019\pi$
$642$	641496.	+	1.11110e6i	0.0614266	+	0.106394i
$643$	1.49933e7			1.43011			0.715056	−	0.699067i	$-0.246401\pi$
$643$	1.49933e7			1.43011			0.715056	+	0.699067i	$0.246401\pi$
$644$		0			0
$645$	−5.13553e6			−0.486056
$646$	4.00391e6	+	6.93498e6i	0.377488	+	0.653829i
$647$	6.49027e6	−	1.12415e7i	0.609540	−	1.05575i	−0.381776	−	0.924255i	$-0.624687\pi$
$647$	6.49027e6	−	1.12415e7i	0.609540	−	1.05575i	0.991316	−	0.131500i	$-0.0419792\pi$
$648$	485680.	−	841223.i	0.0454373	−	0.0786998i
$649$	−1.48285e7	−	2.56838e7i	−1.38193	−	2.39357i
$650$	4.06521e6			0.377398
$651$		0			0
$652$	−3.79885e6			−0.349972
$653$	8.27460e6	+	1.43320e7i	0.759389	+	1.31530i	0.943163	+	0.332332i	$0.107835\pi$
$653$	8.27460e6	+	1.43320e7i	0.759389	+	1.31530i	−0.183774	+	0.982969i	$0.558831\pi$
$654$	2.41018e6	−	4.17455e6i	0.220346	−	0.381650i
$655$	3.23145e6	−	5.59704e6i	0.294303	−	0.509748i
$656$	8.04966e6	+	1.39424e7i	0.730328	+	1.26497i
$657$	4.51062e6			0.407683
$658$		0			0
$659$	5.86879e6			0.526423			0.263212	−	0.964738i	$-0.415218\pi$
$659$	5.86879e6			0.526423			0.263212	+	0.964738i	$0.415218\pi$
$660$	−887046.	−	1.53641e6i	−0.0792659	−	0.137293i
$661$	3.63843e6	−	6.30195e6i	0.323900	−	0.561011i	−0.657389	−	0.753551i	$-0.728339\pi$
$661$	3.63843e6	−	6.30195e6i	0.323900	−	0.561011i	0.981289	+	0.192540i	$0.0616726\pi$
$662$	9751.81	−	16890.6i	0.000864849	−	0.00149796i
$663$	2.34255e6	+	4.05741e6i	0.206969	+	0.358480i
$664$	6.74702e6			0.593870
$665$		0			0
$666$	−8.43672e6			−0.737035
$667$	−1.19431e6	−	2.06861e6i	−0.103945	−	0.180038i
$668$	−1.06082e6	+	1.83739e6i	−0.0919815	+	0.159317i
$669$	2.44505e6	−	4.23495e6i	0.211214	−	0.365833i
$670$	6.25838e6	+	1.08398e7i	0.538611	+	0.932902i
$671$	2.36884e7			2.03109
$672$		0			0
$673$	−1.82417e7			−1.55248			−0.776241	−	0.630437i	$-0.782876\pi$
$673$	−1.82417e7			−1.55248			−0.776241	+	0.630437i	$0.782876\pi$
$674$	−6.48376e6	−	1.12302e7i	−0.549765	−	0.952222i
$675$	592334.	−	1.02595e6i	0.0500388	−	0.0866698i
$676$	962636.	−	1.66733e6i	0.0810205	−	0.140332i
$677$	−3.88203e6	−	6.72387e6i	−0.325527	−	0.563829i	0.656092	−	0.754681i	$-0.272208\pi$
$677$	−3.88203e6	−	6.72387e6i	−0.325527	−	0.563829i	−0.981619	+	0.190852i	$0.938875\pi$
$678$	−2.35374e6			−0.196646
$679$		0			0
$680$	7.62432e6			0.632308
$681$	73.5034	+	127.312i	6.07351e−6	+	1.05196e-5i
$682$	7.20482e6	−	1.24791e7i	0.593147	−	1.02736i
$683$	−4.28162e6	+	7.41598e6i	−0.351201	+	0.608299i	−0.986460	−	0.164001i	$-0.947560\pi$
$683$	−4.28162e6	+	7.41598e6i	−0.351201	+	0.608299i	0.635259	+	0.772299i	$0.280893\pi$
$684$	337058.	+	583801.i	0.0275464	+	0.0477117i
$685$	−1.48038e6			−0.120544
$686$		0			0
$687$	696411.			0.0562955
$688$	9.05076e6	+	1.56764e7i	0.728978	+	1.26263i
$689$	−393712.	+	681928.i	−0.0315959	+	0.0547256i
$690$	−1.81753e6	+	3.14806e6i	−0.145332	+	0.251722i
$691$	8.22547e6	+	1.42469e7i	0.655338	+	1.13508i	0.981809	+	0.189872i	$0.0608071\pi$
$691$	8.22547e6	+	1.42469e7i	0.655338	+	1.13508i	−0.326471	+	0.945207i	$0.605860\pi$
$692$	1.58329e6			0.125689
$693$		0			0
$694$	2.41677e7			1.90474
$695$	−2.05773e6	−	3.56409e6i	−0.161594	−	0.279890i
$696$	−975054.	+	1.68884e6i	−0.0762967	+	0.132150i
$697$	−8.71208e6	+	1.50898e7i	−0.679266	+	1.17652i
$698$	930197.	+	1.61115e6i	0.0722664	+	0.125169i
$699$	−932916.			−0.0722187
$700$		0			0
$701$	−1.66928e7			−1.28302			−0.641512	−	0.767113i	$-0.721693\pi$
$701$	−1.66928e7			−1.28302			−0.641512	+	0.767113i	$0.721693\pi$
$702$	911825.	+	1.57933e6i	0.0698343	+	0.120956i
$703$	−7.68132e6	+	1.33044e7i	−0.586202	+	1.01533i
$704$	5.59783e6	−	9.69573e6i	0.425685	−	0.737308i
$705$	1.18764e6	+	2.05705e6i	0.0899937	+	0.155874i
$706$	−2.46059e6			−0.185792
$707$		0			0
$708$	−4.08916e6			−0.306585
$709$	−2.80890e6	−	4.86515e6i	−0.209855	−	0.363480i	0.741813	−	0.670606i	$-0.233966\pi$
$709$	−2.80890e6	−	4.86515e6i	−0.209855	−	0.363480i	−0.951669	+	0.307126i	$0.900633\pi$
$710$	4.94584e6	−	8.56644e6i	0.368209	−	0.637756i
$711$	2.55763e6	−	4.42994e6i	0.189742	−	0.328643i
$712$	−1.16121e6	−	2.01128e6i	−0.0858443	−	0.148687i
$713$	−6.38537e6			−0.470395
$714$		0			0
$715$	−8.73927e6			−0.639308
$716$	2.54121e6	+	4.40150e6i	0.185250	+	0.320862i
$717$	−3.10099e6	+	5.37107e6i	−0.225269	+	0.390178i
$718$	1.03201e7	−	1.78749e7i	0.747087	−	1.29399i
$719$	5.18592e6	+	8.98227e6i	0.374113	+	0.647983i	0.990194	−	0.139700i	$-0.0446138\pi$
$719$	5.18592e6	+	8.98227e6i	0.374113	+	0.647983i	−0.616081	+	0.787683i	$0.711280\pi$
$720$	3.85418e6			0.277077
$721$		0			0
$722$	−1.01461e7			−0.724363
$723$	991332.	+	1.71704e6i	0.0705299	+	0.122161i
$724$	2.56526e6	−	4.44316e6i	0.181880	−	0.315025i
$725$	−1.18917e6	+	2.05971e6i	−0.0840233	+	0.145533i
$726$	−4.92201e6	−	8.52518e6i	−0.346578	−	0.600291i
$727$	−1.15369e7			−0.809565			−0.404783	−	0.914413i	$-0.632653\pi$
$727$	−1.15369e7			−0.809565			−0.404783	+	0.914413i	$0.632653\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	6.89049e6	+	1.19347e7i	0.478567	+	0.828902i
$731$	−9.79557e6	+	1.69664e7i	−0.678010	+	1.17435i
$732$	1.63310e6	−	2.82860e6i	0.112651	−	0.195117i
$733$	7.47349e6	+	1.29445e7i	0.513764	+	0.889865i	0.999873	+	0.0159667i	$0.00508258\pi$
$733$	7.47349e6	+	1.29445e7i	0.513764	+	0.889865i	−0.486109	+	0.873898i	$0.661584\pi$
$734$	3.06432e6			0.209939
$735$		0			0
$736$	5.08058e6			0.345715
$737$	1.45764e7	+	2.52470e7i	0.988510	+	1.71215i
$738$	−3.39113e6	+	5.87362e6i	−0.229194	+	0.396976i
$739$	−4.50682e6	+	7.80604e6i	−0.303570	+	0.525799i	−0.976942	−	0.213505i	$-0.931512\pi$
$739$	−4.50682e6	+	7.80604e6i	−0.303570	+	0.525799i	0.673372	+	0.739304i	$0.264845\pi$
$740$	−2.78730e6	−	4.82775e6i	−0.187113	−	0.324090i
$741$	3.32073e6			0.222171
$742$		0			0
$743$	−2.10239e7			−1.39714			−0.698571	−	0.715541i	$-0.746180\pi$
$743$	−2.10239e7			−1.39714			−0.698571	+	0.715541i	$0.746180\pi$
$744$	2.60656e6	+	4.51470e6i	0.172638	+	0.299017i
$745$	3.72875e6	−	6.45838e6i	0.246134	−	0.426317i
$746$	−2.78811e6	+	4.82915e6i	−0.183427	+	0.317705i
$747$	1.84568e6	+	3.19681e6i	0.121019	+	0.209612i
$748$	−6.76785e6			−0.442279
$749$		0			0
$750$	1.05796e7			0.686779
$751$	−2.02110e6	−	3.50064e6i	−0.130764	−	0.226489i	0.793207	−	0.608952i	$-0.208410\pi$
$751$	−2.02110e6	−	3.50064e6i	−0.130764	−	0.226489i	−0.923971	+	0.382462i	$0.875076\pi$
$752$	4.18615e6	−	7.25062e6i	0.269942	−	0.467553i
$753$	6.46387e6	−	1.11957e7i	0.415437	−	0.719558i
$754$	−1.83058e6	−	3.17066e6i	−0.117263	−	0.203106i
$755$	−5.48786e6			−0.350377
$756$		0			0
$757$	−1.82059e7			−1.15471			−0.577353	−	0.816495i	$-0.695914\pi$
$757$	−1.82059e7			−1.15471			−0.577353	+	0.816495i	$0.695914\pi$
$758$	7.77945e6	+	1.34744e7i	0.491786	+	0.851798i
$759$	−4.23321e6	+	7.33214e6i	−0.266726	+	0.461983i
$760$	2.70201e6	−	4.68001e6i	0.169689	−	0.293909i
$761$	−9.45999e6	−	1.63852e7i	−0.592146	−	1.02563i	−0.993943	−	0.109898i	$-0.964947\pi$
$761$	−9.45999e6	−	1.63852e7i	−0.592146	−	1.02563i	0.401797	−	0.915729i	$-0.368386\pi$
$762$	4.78876e6			0.298769
$763$		0			0
$764$	−5.83301e6			−0.361542
$765$	2.08567e6	+	3.61249e6i	0.128852	+	0.223179i
$766$	−1.15391e7	+	1.99863e7i	−0.710559	+	1.23072i
$767$	−1.00717e7	+	1.74447e7i	−0.618180	+	1.07072i
$768$	−3.63619e6	−	6.29807e6i	−0.222456	−	0.385305i
$769$	1.12831e7			0.688037			0.344019	−	0.938963i	$-0.388212\pi$
$769$	1.12831e7			0.688037			0.344019	+	0.938963i	$0.388212\pi$
$770$		0			0
$771$	8.18277e6			0.495752
$772$	2.46064e6	+	4.26195e6i	0.148595	+	0.257374i
$773$	−1.84282e6	+	3.19186e6i	−0.110926	+	0.192130i	−0.916144	−	0.400849i	$-0.868715\pi$
$773$	−1.84282e6	+	3.19186e6i	−0.110926	+	0.192130i	0.805218	+	0.592979i	$0.202048\pi$
$774$	−3.81288e6	+	6.60410e6i	−0.228771	+	0.396242i
$775$	3.17896e6	+	5.50611e6i	0.190121	+	0.329299i
$776$	463176.			0.0276116
$777$		0			0
$778$	−1.11971e6			−0.0663219
$779$	6.17501e6	+	1.06954e7i	0.364581	+	0.631472i
$780$	−602493.	+	1.04355e6i	−0.0354581	+	0.0614152i
$781$	1.15193e7	−	1.99521e7i	0.675771	−	1.17047i
$782$	6.93357e6	+	1.20093e7i	0.405452	+	0.702264i
$783$	−1.06692e6			−0.0621912
$784$		0			0
$785$	2.19118e7			1.26912
$786$	−4.79839e6	−	8.31105e6i	−0.277038	−	0.479843i
$787$	−7.03741e6	+	1.21891e7i	−0.405019	+	0.701514i	−0.994324	−	0.106397i	$-0.966069\pi$
$787$	−7.03741e6	+	1.21891e7i	−0.405019	+	0.701514i	0.589304	+	0.807911i	$0.299402\pi$
$788$	3.36173e6	−	5.82269e6i	0.192862	−	0.334048i
$789$	−3.37076e6	−	5.83832e6i	−0.192768	−	0.333884i
$790$	1.56283e7			0.890930
$791$		0			0
$792$	6.91213e6			0.391560
$793$	−8.04472e6	−	1.39339e7i	−0.454284	−	0.786844i
$794$	6.02294e6	−	1.04320e7i	0.339045	−	0.587243i
$795$	−350538.	+	607150.i	−0.0196706	+	0.0340705i
$796$	−599848.	−	1.03897e6i	−0.0335551	−	0.0581191i
$797$	1.75191e7			0.976937			0.488469	−	0.872582i	$-0.337556\pi$
$797$	1.75191e7			0.976937			0.488469	+	0.872582i	$0.337556\pi$
$798$		0			0
$799$	9.06127e6			0.502137
$800$	−2.52936e6	−	4.38099e6i	−0.139729	−	0.242018i
$801$	635311.	−	1.10039e6i	0.0349869	−	0.0605990i
$802$	−4.28067e6	+	7.41433e6i	−0.235004	+	0.407039i
$803$	1.60486e7	+	2.77970e7i	0.878311	+	1.52128i
$804$	4.01963e6			0.219304
$805$		0			0
$806$	−9.78721e6			−0.530666
$807$	3.01475e6	+	5.22170e6i	0.162955	+	0.282246i
$808$	1.25111e7	−	2.16698e7i	0.674166	−	1.16769i
$809$	−407261.	+	705396.i	−0.0218777	+	0.0378932i	−0.876757	−	0.480934i	$-0.840298\pi$
$809$	−407261.	+	705396.i	−0.0218777	+	0.0378932i	0.854879	+	0.518827i	$0.173631\pi$
$810$	811837.	+	1.40614e6i	0.0434767	+	0.0753038i
$811$	−1.26533e7			−0.675540			−0.337770	−	0.941229i	$-0.609673\pi$
$811$	−1.26533e7			−0.675540			−0.337770	+	0.941229i	$0.609673\pi$
$812$		0			0
$813$	−4.86593e6			−0.258190
$814$	−3.00175e7	−	5.19919e7i	−1.58787	−	2.75026i
$815$	−8.33064e6	+	1.44291e7i	−0.439324	+	0.760931i
$816$	7.35150e6	−	1.27332e7i	0.386501	−	0.669439i
$817$	6.94297e6	+	1.20256e7i	0.363907	+	0.630305i
$818$	−4.20854e7			−2.19912
$819$		0			0
$820$	−4.48142e6			−0.232745
$821$	−2.13697e6	−	3.70133e6i	−0.110647	−	0.191646i	0.805384	−	0.592753i	$-0.201959\pi$
$821$	−2.13697e6	−	3.70133e6i	−0.110647	−	0.191646i	−0.916031	+	0.401107i	$0.868626\pi$
$822$	−1.09911e6	+	1.90371e6i	−0.0567361	+	0.0982699i
$823$	−8.52317e6	+	1.47626e7i	−0.438633	+	0.759735i	−0.997584	−	0.0694656i	$-0.977871\pi$
$823$	−8.52317e6	+	1.47626e7i	−0.438633	+	0.759735i	0.558951	+	0.829201i	$0.311204\pi$
$824$	−8.35155e6	−	1.44653e7i	−0.428498	−	0.742180i
$825$	8.43001e6			0.431214
$826$		0			0
$827$	2.60828e6			0.132614			0.0663071	−	0.997799i	$-0.478878\pi$
$827$	2.60828e6			0.132614			0.0663071	+	0.997799i	$0.478878\pi$
$828$	583682.	+	1.01097e6i	0.0295870	+	0.0512462i
$829$	1.06932e7	−	1.85212e7i	0.540409	−	0.936016i	−0.458471	−	0.888709i	$-0.651603\pi$
$829$	1.06932e7	−	1.85212e7i	0.540409	−	0.936016i	0.998880	−	0.0473066i	$-0.0150638\pi$
$830$	−5.63898e6	+	9.76700e6i	−0.284122	+	0.492114i
$831$	1.80859e6	+	3.13257e6i	0.0908528	+	0.157362i
$832$	−7.60423e6			−0.380844
$833$		0			0
$834$	−6.11104e6			−0.304229
$835$	4.65263e6	+	8.05859e6i	0.230931	+	0.399984i
$836$	−2.39848e6	+	4.15429e6i	−0.118692	+	0.205580i
$837$	−1.42608e6	+	2.47004e6i	−0.0703605	+	0.121868i
$838$	−2.22645e7	−	3.85632e7i	−1.09522	−	1.89698i
$839$	−771393.			−0.0378330			−0.0189165	−	0.999821i	$-0.506022\pi$
$839$	−771393.			−0.0378330			−0.0189165	+	0.999821i	$0.506022\pi$
$840$		0			0
$841$	−1.83692e7			−0.895571
$842$	−1.22699e7	−	2.12520e7i	−0.596430	−	1.03305i
$843$	1.93112e6	−	3.34480e6i	0.0935925	−	0.162107i
$844$	4.37616e6	−	7.57973e6i	0.211464	−	0.366267i
$845$	−4.22200e6	−	7.31272e6i	−0.203412	−	0.352320i
$846$	3.52705e6			0.169428
$847$		0			0
$848$	2.47113e6			0.118006
$849$	−1.53417e6	−	2.65726e6i	−0.0730474	−	0.126522i
$850$	6.90375e6	−	1.19576e7i	0.327746	−	0.567673i
$851$	−1.33017e7	+	2.30393e7i	−0.629628	+	1.09055i
$852$	−1.58830e6	−	2.75102e6i	−0.0749609	−	0.129836i
$853$	−2.94032e7			−1.38364			−0.691818	−	0.722072i	$-0.743190\pi$
$853$	−2.94032e7			−1.38364			−0.691818	+	0.722072i	$0.743190\pi$
$854$		0			0
$855$	2.95659e6			0.138317
$856$	−1.65147e6	−	2.86042e6i	−0.0770345	−	0.133428i
$857$	−1.32505e7	+	2.29505e7i	−0.616283	+	1.06743i	0.373875	+	0.927479i	$0.378029\pi$
$857$	−1.32505e7	+	2.29505e7i	−0.616283	+	1.06743i	−0.990158	+	0.139954i	$0.955304\pi$
$858$	−6.48848e6	+	1.12384e7i	−0.300902	+	0.521177i
$859$	−1.83759e7	−	3.18281e7i	−0.849702	−	1.47173i	−0.881475	−	0.472232i	$-0.843449\pi$
$859$	−1.83759e7	−	3.18281e7i	−0.849702	−	1.47173i	0.0317727	−	0.999495i	$-0.489885\pi$
$860$	−5.03876e6			−0.232315
$861$		0			0
$862$	1.94020e7			0.889360
$863$	−5.90946e6	−	1.02355e7i	−0.270098	−	0.467823i	0.698789	−	0.715328i	$-0.253723\pi$
$863$	−5.90946e6	−	1.02355e7i	−0.270098	−	0.467823i	−0.968887	+	0.247505i	$0.920389\pi$
$864$	1.13467e6	−	1.96531e6i	0.0517113	−	0.0895665i
$865$	3.47207e6	−	6.01379e6i	0.157778	−	0.273280i
$866$	−3.00812e6	−	5.21022e6i	−0.136302	−	0.236081i
$867$	3.13421e6			0.141606
$868$		0			0
$869$	3.63998e7			1.63512
$870$	−1.62985e6	−	2.82298e6i	−0.0730044	−	0.126447i
$871$	9.90046e6	−	1.71481e7i	0.442191	−	0.765897i
$872$	−6.20477e6	+	1.07470e7i	−0.276334	+	0.478625i
$873$	126704.	+	219458.i	0.00562671	+	0.00974575i
$874$	9.82884e6			0.435235
$875$		0			0
$876$	4.42562e6			0.194856
$877$	−3.96754e6	−	6.87199e6i	−0.174190	−	0.301706i	0.765691	−	0.643209i	$-0.222397\pi$
$877$	−3.96754e6	−	6.87199e6i	−0.174190	−	0.301706i	−0.939881	+	0.341503i	$0.889064\pi$
$878$	4.28470e6	−	7.42131e6i	0.187579	−	0.324896i
$879$	−1.74981e6	+	3.03077e6i	−0.0763870	+	0.132306i
$880$	1.37130e7	+	2.37516e7i	0.596934	+	1.03392i
$881$	−4.20152e7			−1.82375			−0.911877	−	0.410464i	$-0.865367\pi$
$881$	−4.20152e7			−1.82375			−0.911877	+	0.410464i	$0.865367\pi$
$882$		0			0
$883$	2.12461e7			0.917016			0.458508	−	0.888690i	$-0.348384\pi$
$883$	2.12461e7			0.917016			0.458508	+	0.888690i	$0.348384\pi$
$884$	2.29840e6	+	3.98095e6i	0.0989226	+	0.171339i
$885$	−8.96729e6	+	1.55318e7i	−0.384860	+	0.666597i
$886$	2.46758e6	−	4.27397e6i	0.105606	−	0.182914i
$887$	9.42452e6	+	1.63238e7i	0.402208	+	0.696644i	0.993992	−	0.109452i	$-0.0349097\pi$
$887$	9.42452e6	+	1.63238e7i	0.402208	+	0.696644i	−0.591784	+	0.806096i	$0.701576\pi$
$888$	2.17195e7			0.924309
$889$		0			0
$890$	3.88204e6			0.164280
$891$	1.89085e6	+	3.27504e6i	0.0797925	+	0.138205i
$892$	2.39897e6	−	4.15514e6i	0.100952	−	0.174853i
$893$	3.21125e6	−	5.56205e6i	0.134755	−	0.233403i
$894$	−5.53682e6	−	9.59005e6i	−0.231695	−	0.401307i
$895$	2.22909e7			0.930186
$896$		0			0
$897$	5.75050e6			0.238630
$898$	−7.21044e6	−	1.24889e7i	−0.298381	−	0.516811i
$899$	2.86300e6	−	4.95886e6i	0.118147	−	0.204636i
$900$	581172.	−	1.00662e6i	0.0239165	−	0.0414247i
$901$	1.33724e6	+	2.31617e6i	0.0548780	+	0.0950514i
$902$	−4.82621e7			−1.97510
$903$		0			0
$904$	6.05948e6			0.246612
$905$	−1.12509e7	−	1.94872e7i	−0.456632	−	0.790910i
$906$	−4.07446e6	+	7.05717e6i	−0.164911	+	0.285634i
$907$	3.09723e6	−	5.36456e6i	0.125013	−	0.216529i	−0.796725	−	0.604342i	$-0.793436\pi$
$907$	3.09723e6	−	5.36456e6i	0.125013	−	0.216529i	0.921738	+	0.387813i	$0.126769\pi$
$908$	72.1183	+	124.912i	2.90289e−6	+	5.02795e-6i
$909$	1.36899e7			0.549528
$910$		0			0
$911$	−2.50171e7			−0.998712			−0.499356	−	0.866397i	$-0.666430\pi$
$911$	−2.50171e7			−0.998712			−0.499356	+	0.866397i	$0.666430\pi$
$912$	−5.21064e6	−	9.02509e6i	−0.207445	−	0.359306i
$913$	−1.31337e7	+	2.27483e7i	−0.521448	+	0.903174i
$914$	−1.36893e7	+	2.37106e7i	−0.542022	+	0.938810i
$915$	−7.16256e6	−	1.24059e7i	−0.282824	−	0.489865i
$916$	683288.			0.0269070
$917$		0			0
$918$	6.19403e6			0.242586
$919$	−7.74961e6	−	1.34227e7i	−0.302685	−	0.524266i	0.674058	−	0.738678i	$-0.264550\pi$
$919$	−7.74961e6	−	1.34227e7i	−0.302685	−	0.524266i	−0.976743	+	0.214412i	$0.931216\pi$
$920$	4.67906e6	−	8.10437e6i	0.182259	−	0.315682i
$921$	−1.06086e7	+	1.83746e7i	−0.412106	+	0.713789i
$922$	−9.91905e6	−	1.71803e7i	−0.384276	−	0.665585i
$923$	−1.56481e7			−0.604587
$924$		0			0
$925$	2.64890e7			1.01791
$926$	1.12905e7	+	1.95556e7i	0.432697	+	0.749453i
$927$	4.56921e6	−	7.91411e6i	0.174639	−	0.302484i
$928$	−2.27797e6	+	3.94556e6i	−0.0868316	+	0.150397i
$929$	1.87643e7	+	3.25007e7i	0.713333	+	1.23553i	0.963599	+	0.267352i	$0.0861485\pi$
$929$	1.87643e7	+	3.25007e7i	0.713333	+	1.23553i	−0.250266	+	0.968177i	$0.580518\pi$
$930$	−8.71398e6			−0.330377
$931$		0			0
$932$	−915335.			−0.0345176
$933$	−6.46483e6	−	1.11974e7i	−0.243138	−	0.421127i
$934$	8.70489e6	−	1.50773e7i	0.326510	−	0.565532i
$935$	−1.48415e7	+	2.57062e7i	−0.555198	+	0.961632i
$936$	−2.34740e6	−	4.06582e6i	−0.0875786	−	0.151691i
$937$	1.08298e7			0.402969			0.201485	−	0.979492i	$-0.435423\pi$
$937$	1.08298e7			0.402969			0.201485	+	0.979492i	$0.435423\pi$
$938$		0			0
$939$	7.40520e6			0.274077
$940$	1.16526e6	+	2.01829e6i	0.0430133	+	0.0745013i
$941$	1.62295e7	−	2.81104e7i	0.597492	−	1.03489i	−0.395699	−	0.918380i	$-0.629497\pi$
$941$	1.62295e7	−	2.81104e7i	0.597492	−	1.03489i	0.993190	−	0.116505i	$-0.0371692\pi$
$942$	1.62684e7	−	2.81777e7i	0.597335	−	1.03461i
$943$	1.06932e7	+	1.85212e7i	0.391589	+	0.678251i
$944$	6.32151e7			2.30883
$945$		0			0
$946$	−5.42643e7			−1.97145
$947$	−3.76939e6	−	6.52877e6i	−0.136583	−	0.236568i	0.789618	−	0.613598i	$-0.210279\pi$
$947$	−3.76939e6	−	6.52877e6i	−0.136583	−	0.236568i	−0.926201	+	0.377030i	$0.876945\pi$
$948$	2.50943e6	−	4.34646e6i	0.0906890	−	0.157078i
$949$	1.09004e7	−	1.88801e7i	0.392896	−	0.680516i
$950$	−4.89328e6	−	8.47541e6i	−0.175910	−	0.304686i
$951$	−1.59024e7			−0.570180
$952$		0			0
$953$	−3.01356e7			−1.07485			−0.537424	−	0.843312i	$-0.680602\pi$
$953$	−3.01356e7			−1.07485			−0.537424	+	0.843312i	$0.680602\pi$
$954$	520515.	+	901558.i	0.0185166	+	0.0320718i
$955$	−1.27914e7	+	2.21554e7i	−0.453848	+	0.786089i
$956$	−3.04255e6	+	5.26986e6i	−0.107670	+	0.186489i
$957$	−3.79607e6	−	6.57499e6i	−0.133985	−	0.232068i
$958$	−6.25366e6			−0.220151
$959$		0			0
$960$	−6.77038e6			−0.237102
$961$	6.66107e6	+	1.15373e7i	0.232667	+	0.402992i
$962$	−2.03883e7	+	3.53135e7i	−0.710301	+	1.23028i
$963$	903534.	−	1.56497e6i	0.0313963	−	0.0543800i
$964$	972650.	+	1.68468e6i	0.0337104	+	0.0583882i
$965$	2.15841e7			0.746132
$966$		0			0
$967$	2.88021e6			0.0990509			0.0495255	−	0.998773i	$-0.484229\pi$
$967$	2.88021e6			0.0990509			0.0495255	+	0.998773i	$0.484229\pi$
$968$	1.26712e7	+	2.19472e7i	0.434641	+	0.752820i
$969$	5.63943e6	−	9.76779e6i	0.192942	−	0.334185i
$970$	−387110.	+	670494.i	−0.0132101	+	0.0228805i
$971$	−1.37245e7	−	2.37715e7i	−0.467142	−	0.809113i	0.532154	−	0.846648i	$-0.321383\pi$
$971$	−1.37245e7	−	2.37715e7i	−0.467142	−	0.809113i	−0.999295	+	0.0375347i	$0.988050\pi$
$972$	521426.			0.0177022
$973$		0			0
$974$	2.50958e7			0.847626
$975$	−2.86288e6	−	4.95866e6i	−0.0964478	−	0.167052i
$976$	−2.52463e7	+	4.37279e7i	−0.848347	+	1.46938i
$977$	2.94262e7	−	5.09676e7i	0.986274	−	1.70828i	0.350141	−	0.936697i	$-0.386134\pi$
$977$	2.94262e7	−	5.09676e7i	0.986274	−	1.70828i	0.636133	−	0.771579i	$-0.280533\pi$
$978$	1.23702e7	+	2.14258e7i	0.413551	+	0.716291i
$979$	9.04164e6			0.301502
$980$		0			0
$981$	−6.78938e6			−0.225246
$982$	−8.41039e6	−	1.45672e7i	−0.278315	−	0.482056i
$983$	9.30384e6	−	1.61147e7i	0.307099	−	0.531911i	−0.670627	−	0.741794i	$-0.733975\pi$
$983$	9.30384e6	−	1.61147e7i	0.307099	−	0.531911i	0.977726	+	0.209883i	$0.0673084\pi$
$984$	8.73014e6	−	1.51210e7i	0.287431	−	0.497845i
$985$	−1.47442e7	−	2.55376e7i	−0.484205	−	0.838668i
$986$	−1.24352e7			−0.407342
$987$		0			0
$988$	3.25815e6			0.106189
$989$	1.20231e7	+	2.08246e7i	0.390865	+	0.676997i
$990$	−5.77697e6	+	1.00060e7i	−0.187332	+	0.324469i
$991$	−1.23577e7	+	2.14041e7i	−0.399718	+	0.692331i	−0.993691	−	0.112154i	$-0.964225\pi$
$991$	−1.23577e7	+	2.14041e7i	−0.399718	+	0.692331i	0.593973	+	0.804485i	$0.297558\pi$
$992$	6.08958e6	+	1.05475e7i	0.196475	+	0.340305i
$993$	−27470.5			−0.000884083
$994$		0			0
$995$	−5.26172e6			−0.168488
$996$	1.81090e6	+	3.13657e6i	0.0578424	+	0.100186i
$997$	−8.97906e6	+	1.55522e7i	−0.286084	+	0.495511i	−0.972871	−	0.231347i	$-0.925687\pi$
$997$	−8.97906e6	+	1.55522e7i	−0.286084	+	0.495511i	0.686788	+	0.726858i	$0.259020\pi$
$998$	−6.79064e6	+	1.17617e7i	−0.215816	+	0.373805i
$999$	5.94147e6	+	1.02909e7i	0.188356	+	0.326243i

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	147.6.e.l.67.1		4
7.2	even	3	inner	147.6.e.l.79.1		4
7.3	odd	6		147.6.a.i.1.2		2
7.4	even	3		147.6.a.k.1.2		2
7.5	odd	6		21.6.e.b.16.1	yes	4
7.6	odd	2		21.6.e.b.4.1	✓	4
21.5	even	6		63.6.e.c.37.2		4
21.11	odd	6		441.6.a.s.1.1		2
21.17	even	6		441.6.a.t.1.1		2
21.20	even	2		63.6.e.c.46.2		4
28.19	even	6		336.6.q.e.289.1		4
28.27	even	2		336.6.q.e.193.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.b.4.1	✓	4	7.6	odd	2
21.6.e.b.16.1	yes	4	7.5	odd	6
63.6.e.c.37.2		4	21.5	even	6
63.6.e.c.46.2		4	21.20	even	2
147.6.a.i.1.2		2	7.3	odd	6
147.6.a.k.1.2		2	7.4	even	3
147.6.e.l.67.1		4	1.1	even	1	trivial
147.6.e.l.79.1		4	7.2	even	3	inner
336.6.q.e.193.1		4	28.27	even	2
336.6.q.e.289.1		4	28.19	even	6
441.6.a.s.1.1		2	21.11	odd	6
441.6.a.t.1.1		2	21.17	even	6

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

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	147.6.e.l.67.1

Level	$147$
Weight	$6$
Character	147.67
Analytic conductor	$23.576$
Analytic rank	$0$
Dimension	$4$
Inner twists	$2$