LMFDB - Embedded newform 168.5.z.a.145.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,5,Mod(73,168)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("168.73");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	168.z (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$17.3661537981$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 99 x^{14} - 1810 x^{13} + 14212 x^{12} - 199882 x^{11} + 1800935 x^{10} + \cdots + 41390114348800 $ x^16 - 6x^15 + 99x^14 - 1810x^13 + 14212x^12 - 199882x^11 + 1800935x^10 - 9073270x^9 + 62016647x^8 - 13497916x^7 - 872612906x^6 + 8208467240x^5 + 11144877252x^4 - 185824445600x^3 + 3750935164160x^2 - 13970712492800*x + 41390114348800
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{36}\cdot 7^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.8
Root			$-7.54715 + 8.93193i$ of defining polynomial
Character	$\chi$	$=$	168.145
Dual form			168.5.z.a.73.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.50000 + 2.59808i) q^{3} +(36.1660 + 20.8805i) q^{5} +(45.8999 + 17.1523i) q^{7} +(13.5000 - 23.3827i) q^{9} +O(q^{10})$	\(q+(-4.50000 + 2.59808i) q^{3} +(36.1660 + 20.8805i) q^{5} +(45.8999 + 17.1523i) q^{7} +(13.5000 - 23.3827i) q^{9} +(-8.30491 - 14.3845i) q^{11} -2.70453i q^{13} -216.996 q^{15} +(290.132 - 167.508i) q^{17} +(-170.800 - 98.6116i) q^{19} +(-251.112 + 42.0659i) q^{21} +(-309.364 + 535.835i) q^{23} +(559.489 + 969.063i) q^{25} +140.296i q^{27} +1484.08 q^{29} +(-83.0093 + 47.9254i) q^{31} +(74.7442 + 43.1536i) q^{33} +(1301.87 + 1578.74i) q^{35} +(-923.145 + 1598.93i) q^{37} +(7.02658 + 12.1704i) q^{39} +2220.19i q^{41} +2347.27 q^{43} +(976.483 - 563.773i) q^{45} +(-2998.28 - 1731.06i) q^{47} +(1812.60 + 1574.58i) q^{49} +(-870.395 + 1507.57i) q^{51} +(-2028.09 - 3512.76i) q^{53} -693.642i q^{55} +1024.80 q^{57} +(-1888.74 + 1090.46i) q^{59} +(1348.51 + 778.561i) q^{61} +(1020.72 - 841.706i) q^{63} +(56.4719 - 97.8122i) q^{65} +(822.467 + 1424.55i) q^{67} -3215.01i q^{69} -5449.32 q^{71} +(6819.43 - 3937.20i) q^{73} +(-5035.40 - 2907.19i) q^{75} +(-134.466 - 802.697i) q^{77} +(-2668.17 + 4621.40i) q^{79} +(-364.500 - 631.333i) q^{81} -3205.42i q^{83} +13990.5 q^{85} +(-6678.37 + 3855.76i) q^{87} +(-1380.35 - 796.944i) q^{89} +(46.3890 - 124.138i) q^{91} +(249.028 - 431.329i) q^{93} +(-4118.11 - 7132.78i) q^{95} +8001.69i q^{97} -448.465 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 72 q^{3} + 12 q^{5} + 40 q^{7} + 216 q^{9}+O(q^{10}) $ 16 * q - 72 * q^3 + 12 * q^5 + 40 * q^7 + 216 * q^9	$ 16 q - 72 q^{3} + 12 q^{5} + 40 q^{7} + 216 q^{9} - 108 q^{11} - 72 q^{15} - 168 q^{17} + 948 q^{19} - 252 q^{21} - 768 q^{23} + 1908 q^{25} - 1608 q^{29} - 3216 q^{31} + 972 q^{33} + 696 q^{35} - 1820 q^{37} - 1188 q^{39} + 2888 q^{43} + 324 q^{45} + 744 q^{47} - 3784 q^{49} + 504 q^{51} + 4476 q^{53} - 5688 q^{57} - 4668 q^{59} + 17760 q^{61} + 1188 q^{63} + 8760 q^{65} + 1580 q^{67} + 48 q^{71} + 588 q^{73} - 17172 q^{75} - 17508 q^{77} - 3824 q^{79} - 5832 q^{81} + 11440 q^{85} + 7236 q^{87} - 360 q^{89} + 25860 q^{91} + 9648 q^{93} - 21792 q^{95} - 5832 q^{99}+O(q^{100}) $ 16 * q - 72 * q^3 + 12 * q^5 + 40 * q^7 + 216 * q^9 - 108 * q^11 - 72 * q^15 - 168 * q^17 + 948 * q^19 - 252 * q^21 - 768 * q^23 + 1908 * q^25 - 1608 * q^29 - 3216 * q^31 + 972 * q^33 + 696 * q^35 - 1820 * q^37 - 1188 * q^39 + 2888 * q^43 + 324 * q^45 + 744 * q^47 - 3784 * q^49 + 504 * q^51 + 4476 * q^53 - 5688 * q^57 - 4668 * q^59 + 17760 * q^61 + 1188 * q^63 + 8760 * q^65 + 1580 * q^67 + 48 * q^71 + 588 * q^73 - 17172 * q^75 - 17508 * q^77 - 3824 * q^79 - 5832 * q^81 + 11440 * q^85 + 7236 * q^87 - 360 * q^89 + 25860 * q^91 + 9648 * q^93 - 21792 * q^95 - 5832 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−4.50000	+	2.59808i	−0.500000	+	0.288675i
$3$	−4.50000	+	2.59808i	−0.500000	+	0.288675i
$4$		0			0
$5$	36.1660	+	20.8805i	1.44664	+	0.835219i	0.998280	−	0.0586329i	$-0.0186741\pi$
$5$	36.1660	+	20.8805i	1.44664	+	0.835219i	0.448362	+	0.893852i	$0.352007\pi$
$6$		0			0
$7$	45.8999	+	17.1523i	0.936732	+	0.350047i
$7$	45.8999	+	17.1523i	0.936732	+	0.350047i
$8$		0			0
$9$	13.5000	−	23.3827i	0.166667	−	0.288675i
$10$		0			0
$11$	−8.30491	−	14.3845i	−0.0686356	−	0.118880i	0.829665	−	0.558261i	$-0.188531\pi$
$11$	−8.30491	−	14.3845i	−0.0686356	−	0.118880i	−0.898301	+	0.439381i	$0.855198\pi$
$12$		0			0
$13$		−	2.70453i		−	0.0160031i	−0.999968	−	0.00800157i	$-0.997453\pi$
$13$		−	2.70453i		−	0.0160031i	0.999968	−	0.00800157i	$-0.00254701\pi$
$14$		0			0
$15$	−216.996			−0.964428
$16$		0			0
$17$	290.132	−	167.508i	1.00392	−	0.579611i	0.0945110	−	0.995524i	$-0.469871\pi$
$17$	290.132	−	167.508i	1.00392	−	0.579611i	0.909404	+	0.415913i	$0.136538\pi$
$18$		0			0
$19$	−170.800	−	98.6116i	−0.473131	−	0.273162i	0.244419	−	0.969670i	$-0.421403\pi$
$19$	−170.800	−	98.6116i	−0.473131	−	0.273162i	−0.717549	+	0.696508i	$0.754736\pi$
$20$		0			0
$21$	−251.112	+	42.0659i	−0.569416	+	0.0953875i
$22$		0			0
$23$	−309.364	+	535.835i	−0.584810	+	1.01292i	0.410089	+	0.912045i	$0.365498\pi$
$23$	−309.364	+	535.835i	−0.584810	+	1.01292i	−0.994899	+	0.100875i	$0.967836\pi$
$24$		0			0
$25$	559.489	+	969.063i	0.895182	+	1.55050i
$26$		0			0
$27$			140.296i			0.192450i
$28$		0			0
$29$	1484.08			1.76466			0.882332	−	0.470628i	$-0.155973\pi$
$29$	1484.08			1.76466			0.882332	+	0.470628i	$0.155973\pi$
$30$		0			0
$31$	−83.0093	+	47.9254i	−0.0863780	+	0.0498704i	−0.542567	−	0.840013i	$-0.682547\pi$
$31$	−83.0093	+	47.9254i	−0.0863780	+	0.0498704i	0.456189	+	0.889883i	$0.349214\pi$
$32$		0			0
$33$	74.7442	+	43.1536i	0.0686356	+	0.0396268i
$34$		0			0
$35$	1301.87	+	1578.74i	1.06275	+	1.28877i
$36$		0			0
$37$	−923.145	+	1598.93i	−0.674320	+	1.16796i	0.302347	+	0.953198i	$0.402230\pi$
$37$	−923.145	+	1598.93i	−0.674320	+	1.16796i	−0.976667	+	0.214759i	$0.931103\pi$
$38$		0			0
$39$	7.02658	+	12.1704i	0.00461971	+	0.00800157i
$40$		0			0
$41$			2220.19i			1.32075i	0.750934	+	0.660377i	$0.229603\pi$
$41$			2220.19i			1.32075i	−0.750934	+	0.660377i	$0.770397\pi$
$42$		0			0
$43$	2347.27			1.26948			0.634740	−	0.772726i	$-0.281107\pi$
$43$	2347.27			1.26948			0.634740	+	0.772726i	$0.281107\pi$
$44$		0			0
$45$	976.483	−	563.773i	0.482214	−	0.278406i
$46$		0			0
$47$	−2998.28	−	1731.06i	−1.35730	−	0.783638i	−0.368042	−	0.929809i	$-0.619972\pi$
$47$	−2998.28	−	1731.06i	−1.35730	−	0.783638i	−0.989259	+	0.146171i	$0.953305\pi$
$48$		0			0
$49$	1812.60	+	1574.58i	0.754934	+	0.655801i
$50$		0			0
$51$	−870.395	+	1507.57i	−0.334638	+	0.579611i
$52$		0			0
$53$	−2028.09	−	3512.76i	−0.721999	−	1.25054i	−0.960197	−	0.279322i	$-0.909890\pi$
$53$	−2028.09	−	3512.76i	−0.721999	−	1.25054i	0.238199	−	0.971216i	$-0.423443\pi$
$54$		0			0
$55$		−	693.642i		−	0.229303i
$56$		0			0
$57$	1024.80			0.315421
$58$		0			0
$59$	−1888.74	+	1090.46i	−0.542586	+	0.313262i	−0.746126	−	0.665805i	$-0.768088\pi$
$59$	−1888.74	+	1090.46i	−0.542586	+	0.313262i	0.203541	+	0.979066i	$0.434755\pi$
$60$		0			0
$61$	1348.51	+	778.561i	0.362405	+	0.209234i	0.670135	−	0.742239i	$-0.266236\pi$
$61$	1348.51	+	778.561i	0.362405	+	0.209234i	−0.307730	+	0.951474i	$0.599570\pi$
$62$		0			0
$63$	1020.72	−	841.706i	0.257172	−	0.212070i
$64$		0			0
$65$	56.4719	−	97.8122i	0.0133661	−	0.0231508i
$66$		0			0
$67$	822.467	+	1424.55i	0.183218	+	0.317343i	0.942975	−	0.332864i	$-0.108015\pi$
$67$	822.467	+	1424.55i	0.183218	+	0.317343i	−0.759756	+	0.650208i	$0.774682\pi$
$68$		0			0
$69$		−	3215.01i		−	0.675280i
$70$		0			0
$71$	−5449.32			−1.08100			−0.540500	−	0.841344i	$-0.681765\pi$
$71$	−5449.32			−1.08100			−0.540500	+	0.841344i	$0.681765\pi$
$72$		0			0
$73$	6819.43	−	3937.20i	1.27968	−	0.738825i	0.302892	−	0.953025i	$-0.402048\pi$
$73$	6819.43	−	3937.20i	1.27968	−	0.738825i	0.976790	+	0.214200i	$0.0687144\pi$
$74$		0			0
$75$	−5035.40	−	2907.19i	−0.895182	−	0.516833i
$76$		0			0
$77$	−134.466	−	802.697i	−0.0226794	−	0.135385i
$78$		0			0
$79$	−2668.17	+	4621.40i	−0.427522	+	0.740490i	−0.996652	−	0.0817574i	$-0.973947\pi$
$79$	−2668.17	+	4621.40i	−0.427522	+	0.740490i	0.569130	+	0.822247i	$0.307280\pi$
$80$		0			0
$81$	−364.500	−	631.333i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	3205.42i		−	0.465296i	−0.972561	−	0.232648i	$-0.925261\pi$
$83$		−	3205.42i		−	0.465296i	0.972561	−	0.232648i	$-0.0747390\pi$
$84$		0			0
$85$	13990.5			1.93641
$86$		0			0
$87$	−6678.37	+	3855.76i	−0.882332	+	0.509414i
$88$		0			0
$89$	−1380.35	−	796.944i	−0.174264	−	0.100612i	0.410331	−	0.911937i	$-0.365413\pi$
$89$	−1380.35	−	796.944i	−0.174264	−	0.100612i	−0.584595	+	0.811325i	$0.698747\pi$
$90$		0			0
$91$	46.3890	−	124.138i	0.00560186	−	0.0149907i
$92$		0			0
$93$	249.028	−	431.329i	0.0287927	−	0.0498704i
$94$		0			0
$95$	−4118.11	−	7132.78i	−0.456301	−	0.790336i
$96$		0			0
$97$			8001.69i			0.850429i	0.905093	+	0.425215i	$0.139801\pi$
$97$			8001.69i			0.850429i	−0.905093	+	0.425215i	$0.860199\pi$
$98$		0			0
$99$	−448.465			−0.0457571
$100$		0			0
$101$	−1083.43	+	625.517i	−0.106208	+	0.0613192i	−0.552163	−	0.833736i	$-0.686197\pi$
$101$	−1083.43	+	625.517i	−0.106208	+	0.0613192i	0.445955	+	0.895055i	$0.352864\pi$
$102$		0			0
$103$	−3298.98	−	1904.67i	−0.310960	−	0.179533i	0.336396	−	0.941721i	$-0.390792\pi$
$103$	−3298.98	−	1904.67i	−0.310960	−	0.179533i	−0.647356	+	0.762188i	$0.724125\pi$
$104$		0			0
$105$	−9960.10	−	3721.99i	−0.903410	−	0.337595i
$106$		0			0
$107$	10105.3	−	17503.0i	0.882640	−	1.52878i	0.0342450	−	0.999413i	$-0.489097\pi$
$107$	10105.3	−	17503.0i	0.882640	−	1.52878i	0.848395	−	0.529364i	$-0.177569\pi$
$108$		0			0
$109$	−6948.63	−	12035.4i	−0.584852	−	1.01299i	−0.994894	−	0.100927i	$-0.967819\pi$
$109$	−6948.63	−	12035.4i	−0.584852	−	1.01299i	0.410042	−	0.912067i	$-0.365514\pi$
$110$		0			0
$111$		−	9593.60i		−	0.778638i
$112$		0			0
$113$	−13063.0			−1.02303			−0.511513	−	0.859275i	$-0.670915\pi$
$113$	−13063.0			−1.02303			−0.511513	+	0.859275i	$0.670915\pi$
$114$		0			0
$115$	−22377.0	+	12919.4i	−1.69202	+	0.976889i
$116$		0			0
$117$	−63.2392	−	36.5112i	−0.00461971	−	0.00266719i
$118$		0			0
$119$	16190.1	−	2712.14i	1.14329	−	0.191522i
$120$		0			0
$121$	7182.56	−	12440.6i	0.490578	−	0.849707i
$122$		0			0
$123$	−5768.21	−	9990.84i	−0.381269	−	0.660377i
$124$		0			0
$125$			20629.0i			1.32025i
$126$		0			0
$127$	16817.4			1.04268			0.521341	−	0.853349i	$-0.325432\pi$
$127$	16817.4			1.04268			0.521341	+	0.853349i	$0.325432\pi$
$128$		0			0
$129$	−10562.7	+	6098.38i	−0.634740	+	0.366467i
$130$		0			0
$131$	−7014.54	−	4049.85i	−0.408749	−	0.235991i	0.281503	−	0.959560i	$-0.409167\pi$
$131$	−7014.54	−	4049.85i	−0.408749	−	0.235991i	−0.690252	+	0.723569i	$0.742500\pi$
$132$		0			0
$133$	−6148.29	−	7455.88i	−0.347577	−	0.421498i
$134$		0			0
$135$	−2929.45	+	5073.96i	−0.160738	+	0.278406i
$136$		0			0
$137$	−9531.62	−	16509.3i	−0.507839	−	0.879602i	−0.999959	−	0.00907502i	$-0.997111\pi$
$137$	−9531.62	−	16509.3i	−0.507839	−	0.879602i	0.492120	−	0.870527i	$-0.336222\pi$
$138$		0			0
$139$		−	11447.2i		−	0.592476i	−0.955114	−	0.296238i	$-0.904268\pi$
$139$		−	11447.2i		−	0.592476i	0.955114	−	0.296238i	$-0.0957321\pi$
$140$		0			0
$141$	17989.7			0.904867
$142$		0			0
$143$	−38.9034	+	22.4609i	−0.00190246	+	0.00109839i
$144$		0			0
$145$	53673.4	+	30988.3i	2.55284	+	1.47388i
$146$		0			0
$147$	−12247.6	−	2376.34i	−0.566780	−	0.109970i
$148$		0			0
$149$	10714.5	−	18558.0i	0.482611	−	0.835907i	−0.517190	−	0.855871i	$-0.673022\pi$
$149$	10714.5	−	18558.0i	0.482611	−	0.835907i	0.999801	+	0.0199638i	$0.00635510\pi$
$150$		0			0
$151$	21706.7	+	37597.2i	0.952008	+	1.64893i	0.741071	+	0.671427i	$0.234318\pi$
$151$	21706.7	+	37597.2i	0.952008	+	1.64893i	0.210937	+	0.977500i	$0.432348\pi$
$152$		0			0
$153$		−	9045.41i		−	0.386407i
$154$		0			0
$155$	−4002.82			−0.166611
$156$		0			0
$157$	−23716.3	+	13692.6i	−0.962162	+	0.555504i	−0.896838	−	0.442360i	$-0.854141\pi$
$157$	−23716.3	+	13692.6i	−0.962162	+	0.555504i	−0.0653240	+	0.997864i	$0.520808\pi$
$158$		0			0
$159$	18252.9	+	10538.3i	0.721999	+	0.416846i
$160$		0			0
$161$	−23390.6	+	19288.4i	−0.902380	+	0.744124i
$162$		0			0
$163$	9687.83	−	16779.8i	0.364629	−	0.631556i	−0.624087	−	0.781355i	$-0.714529\pi$
$163$	9687.83	−	16779.8i	0.364629	−	0.631556i	0.988717	+	0.149798i	$0.0478624\pi$
$164$		0			0
$165$	1802.14	+	3121.39i	0.0661941	+	0.114652i
$166$		0			0
$167$			46458.1i			1.66582i	0.553409	+	0.832910i	$0.313327\pi$
$167$			46458.1i			1.66582i	−0.553409	+	0.832910i	$0.686673\pi$
$168$		0			0
$169$	28553.7			0.999744
$170$		0			0
$171$	−4611.61	+	2662.51i	−0.157710	+	0.0910541i
$172$		0			0
$173$	462.105	+	266.796i	0.0154400	+	0.00891431i	0.507700	−	0.861534i	$-0.330496\pi$
$173$	462.105	+	266.796i	0.0154400	+	0.00891431i	−0.492260	+	0.870448i	$0.663829\pi$
$174$		0			0
$175$	9058.78	+	54076.4i	0.295797	+	1.76576i
$176$		0			0
$177$	5666.22	−	9814.18i	0.180862	−	0.313262i
$178$		0			0
$179$	−15650.1	−	27106.9i	−0.488441	−	0.846005i	0.511470	−	0.859301i	$-0.329101\pi$
$179$	−15650.1	−	27106.9i	−0.488441	−	0.846005i	−0.999912	+	0.0132958i	$0.995768\pi$
$180$		0			0
$181$		−	29684.7i		−	0.906100i	−0.891485	−	0.453050i	$-0.850336\pi$
$181$		−	29684.7i		−	0.906100i	0.891485	−	0.453050i	$-0.149664\pi$
$182$		0			0
$183$	−8091.04			−0.241603
$184$		0			0
$185$	−66773.0	+	38551.4i	−1.95100	+	1.12641i
$186$		0			0
$187$	−4819.04	−	2782.27i	−0.137809	−	0.0795639i
$188$		0			0
$189$	−2406.40	+	6439.57i	−0.0673667	+	0.180274i
$190$		0			0
$191$	13742.2	−	23802.2i	0.376695	−	0.652455i	−0.613884	−	0.789396i	$-0.710394\pi$
$191$	13742.2	−	23802.2i	0.376695	−	0.652455i	0.990579	+	0.136941i	$0.0437272\pi$
$192$		0			0
$193$	−3060.29	−	5300.58i	−0.0821576	−	0.142301i	0.822019	−	0.569460i	$-0.192848\pi$
$193$	−3060.29	−	5300.58i	−0.0821576	−	0.142301i	−0.904176	+	0.427159i	$0.859514\pi$
$194$		0			0
$195$			586.873i			0.0154339i
$196$		0			0
$197$	−37545.6			−0.967446			−0.483723	−	0.875221i	$-0.660716\pi$
$197$	−37545.6			−0.967446			−0.483723	+	0.875221i	$0.660716\pi$
$198$		0			0
$199$	40552.8	−	23413.2i	1.02403	−	0.591226i	0.108764	−	0.994068i	$-0.465311\pi$
$199$	40552.8	−	23413.2i	1.02403	−	0.591226i	0.915270	+	0.402841i	$0.131977\pi$
$200$		0			0
$201$	−7402.20	−	4273.66i	−0.183218	−	0.105781i
$202$		0			0
$203$	68119.2	+	25455.5i	1.65302	+	0.617716i
$204$		0			0
$205$	−46358.6	+	80295.4i	−1.10312	+	1.91066i
$206$		0			0
$207$	8352.84	+	14467.5i	0.194937	+	0.337640i
$208$		0			0
$209$			3275.84i			0.0749947i
$210$		0			0
$211$	35769.2			0.803423			0.401712	−	0.915766i	$-0.368415\pi$
$211$	35769.2			0.803423			0.401712	+	0.915766i	$0.368415\pi$
$212$		0			0
$213$	24522.0	−	14157.8i	0.540500	−	0.312058i
$214$		0			0
$215$	84891.4	+	49012.1i	1.83648	+	1.06029i
$216$		0			0
$217$	−4632.15	+	775.969i	−0.0983700	+	0.0164788i
$218$		0			0
$219$	−20458.3	+	35434.8i	−0.426561	+	0.738825i
$220$		0			0
$221$	−453.030	−	784.670i	−0.00927560	−	0.0160658i
$222$		0			0
$223$			12109.5i			0.243510i	0.992560	+	0.121755i	$0.0388522\pi$
$223$			12109.5i			0.243510i	−0.992560	+	0.121755i	$0.961148\pi$
$224$		0			0
$225$	30212.4			0.596788
$226$		0			0
$227$	30115.4	−	17387.2i	0.584437	−	0.337425i	−0.178458	−	0.983948i	$-0.557111\pi$
$227$	30115.4	−	17387.2i	0.584437	−	0.337425i	0.762895	+	0.646523i	$0.223778\pi$
$228$		0			0
$229$	−46895.9	−	27075.4i	−0.894260	−	0.516301i	−0.0189266	−	0.999821i	$-0.506025\pi$
$229$	−46895.9	−	27075.4i	−0.894260	−	0.516301i	−0.875334	+	0.483520i	$0.839358\pi$
$230$		0			0
$231$	2690.57	+	3262.78i	0.0504219	+	0.0611454i
$232$		0			0
$233$	22763.5	−	39427.5i	0.419302	−	0.726252i	−0.576568	−	0.817049i	$-0.695608\pi$
$233$	22763.5	−	39427.5i	0.419302	−	0.726252i	0.995869	+	0.0907977i	$0.0289417\pi$
$234$		0			0
$235$	−72290.6	−	125211.i	−1.30902	−	2.26729i
$236$		0			0
$237$		−	27728.4i		−	0.493660i
$238$		0			0
$239$	76686.6			1.34253			0.671265	−	0.741218i	$-0.265751\pi$
$239$	76686.6			1.34253			0.671265	+	0.741218i	$0.265751\pi$
$240$		0			0
$241$	−61108.3	+	35280.9i	−1.05212	+	0.607443i	−0.923243	−	0.384218i	$-0.874471\pi$
$241$	−61108.3	+	35280.9i	−1.05212	+	0.607443i	−0.128879	+	0.991660i	$0.541138\pi$
$242$		0			0
$243$	3280.50	+	1894.00i	0.0555556	+	0.0320750i
$244$		0			0
$245$	32676.5	+	94794.1i	0.544381	+	1.57924i
$246$		0			0
$247$	−266.698	+	461.935i	−0.00437146	+	0.00757158i
$248$		0			0
$249$	8327.94	+	14424.4i	0.134319	+	0.232648i
$250$		0			0
$251$		−	85852.8i		−	1.36272i	−0.731948	−	0.681360i	$-0.761389\pi$
$251$		−	85852.8i		−	1.36272i	0.731948	−	0.681360i	$-0.238611\pi$
$252$		0			0
$253$	10277.0			0.160555
$254$		0			0
$255$	−62957.5	+	36348.5i	−0.968204	+	0.558993i
$256$		0			0
$257$	−48366.2	−	27924.2i	−0.732277	−	0.422780i	0.0869775	−	0.996210i	$-0.472279\pi$
$257$	−48366.2	−	27924.2i	−0.732277	−	0.422780i	−0.819255	+	0.573430i	$0.805613\pi$
$258$		0			0
$259$	−69797.6	+	57556.8i	−1.04050	+	0.858019i
$260$		0			0
$261$	20035.1	−	34701.8i	0.294111	−	0.509414i
$262$		0			0
$263$	−53818.5	−	93216.3i	−0.778072	−	1.34766i	−0.933052	−	0.359743i	$-0.882865\pi$
$263$	−53818.5	−	93216.3i	−0.778072	−	1.34766i	0.154980	−	0.987918i	$-0.450469\pi$
$264$		0			0
$265$		−	169390.i		−	2.41211i
$266$		0			0
$267$	8282.08			0.116176
$268$		0			0
$269$	−31930.5	+	18435.1i	−0.441266	+	0.254765i	−0.704135	−	0.710067i	$-0.748665\pi$
$269$	−31930.5	+	18435.1i	−0.441266	+	0.254765i	0.262868	+	0.964832i	$0.415331\pi$
$270$		0			0
$271$	−121856.	−	70353.4i	−1.65923	−	0.957958i	−0.973070	−	0.230511i	$-0.925960\pi$
$271$	−121856.	−	70353.4i	−1.65923	−	0.957958i	−0.686163	−	0.727448i	$-0.740706\pi$
$272$		0			0
$273$	113.769	+	679.142i	0.00152650	+	0.00911245i
$274$		0			0
$275$	9293.01	−	16096.0i	0.122883	−	0.212839i
$276$		0			0
$277$	−52999.7	−	91798.2i	−0.690739	−	1.19639i	−0.971596	−	0.236645i	$-0.923952\pi$
$277$	−52999.7	−	91798.2i	−0.690739	−	1.19639i	0.280857	−	0.959750i	$-0.409381\pi$
$278$		0			0
$279$			2587.97i			0.0332469i
$280$		0			0
$281$	68418.5			0.866484			0.433242	−	0.901278i	$-0.357369\pi$
$281$	68418.5			0.866484			0.433242	+	0.901278i	$0.357369\pi$
$282$		0			0
$283$	−9845.78	+	5684.47i	−0.122936	+	0.0709769i	−0.560207	−	0.828353i	$-0.689278\pi$
$283$	−9845.78	+	5684.47i	−0.122936	+	0.0709769i	0.437271	+	0.899330i	$0.355945\pi$
$284$		0			0
$285$	37063.0	+	21398.3i	0.456301	+	0.263445i
$286$		0			0
$287$	−38081.4	+	101906.i	−0.462326	+	1.23719i
$288$		0			0
$289$	14357.1	−	24867.1i	0.171898	−	0.297735i
$290$		0			0
$291$	−20789.0	−	36007.6i	−0.245498	−	0.425215i
$292$		0			0
$293$		−	73401.8i		−	0.855011i	−0.904013	−	0.427506i	$-0.859392\pi$
$293$		−	73401.8i		−	0.855011i	0.904013	−	0.427506i	$-0.140608\pi$
$294$		0			0
$295$	−91077.7			−1.04657
$296$		0			0
$297$	2018.09	−	1165.15i	0.0228785	−	0.0132089i
$298$		0			0
$299$	1449.18	+	836.686i	0.0162099	+	0.00935880i
$300$		0			0
$301$	107739.	+	40261.1i	1.18916	+	0.444378i
$302$		0			0
$303$	3250.28	−	5629.66i	0.0354027	−	0.0613192i
$304$		0			0
$305$	32513.5	+	56314.9i	0.349513	+	0.605374i
$306$		0			0
$307$			81405.2i			0.863725i	0.901940	+	0.431862i	$0.142143\pi$
$307$			81405.2i			0.863725i	−0.901940	+	0.431862i	$0.857857\pi$
$308$		0			0
$309$	19793.9			0.207307
$310$		0			0
$311$	46862.8	−	27056.2i	0.484515	−	0.279735i	−0.237781	−	0.971319i	$-0.576420\pi$
$311$	46862.8	−	27056.2i	0.484515	−	0.279735i	0.722296	+	0.691584i	$0.243087\pi$
$312$		0			0
$313$	77477.8	+	44731.8i	0.790840	+	0.456592i	0.840258	−	0.542187i	$-0.182403\pi$
$313$	77477.8	+	44731.8i	0.790840	+	0.456592i	−0.0494183	+	0.998778i	$0.515737\pi$
$314$		0			0
$315$	54490.5	−	9128.14i	0.549161	−	0.0919944i
$316$		0			0
$317$	−57553.9	+	99686.3i	−0.572739	+	0.992012i	0.423545	+	0.905875i	$0.360786\pi$
$317$	−57553.9	+	99686.3i	−0.572739	+	0.992012i	−0.996283	+	0.0861371i	$0.972548\pi$
$318$		0			0
$319$	−12325.2	−	21347.8i	−0.121119	−	0.209784i
$320$		0			0
$321$			105018.i			1.01918i
$322$		0			0
$323$	−66072.7			−0.633311
$324$		0			0
$325$	2620.86	−	1513.15i	0.0248129	−	0.0143257i
$326$		0			0
$327$	62537.7	+	36106.1i	0.584852	+	0.337665i
$328$		0			0
$329$	−107929.	−	130883.i	−0.997117	−	1.20918i
$330$		0			0
$331$	70786.1	−	122605.i	0.646088	−	1.11906i	−0.337961	−	0.941160i	$-0.609737\pi$
$331$	70786.1	−	122605.i	0.646088	−	1.11906i	0.984049	−	0.177897i	$-0.0569295\pi$
$332$		0			0
$333$	24924.9	+	43171.2i	0.224773	+	0.389319i
$334$		0			0
$335$			68694.0i			0.612109i
$336$		0			0
$337$	17493.4			0.154033			0.0770165	−	0.997030i	$-0.475461\pi$
$337$	17493.4			0.154033			0.0770165	+	0.997030i	$0.475461\pi$
$338$		0			0
$339$	58783.6	−	33938.7i	0.511513	−	0.295322i
$340$		0			0
$341$	1378.77	+	796.033i	0.0118572	+	0.00684577i
$342$		0			0
$343$	56190.2	+	103363.i	0.477609	+	0.878573i
$344$		0			0
$345$	67130.9	−	116274.i	0.564007	−	0.976889i
$346$		0			0
$347$	−44994.5	−	77932.8i	−0.373681	−	0.647234i	0.616448	−	0.787396i	$-0.288571\pi$
$347$	−44994.5	−	77932.8i	−0.373681	−	0.647234i	−0.990129	+	0.140162i	$0.955238\pi$
$348$		0			0
$349$		−	175555.i		−	1.44133i	−0.693283	−	0.720665i	$-0.743837\pi$
$349$		−	175555.i		−	1.44133i	0.693283	−	0.720665i	$-0.256163\pi$
$350$		0			0
$351$	379.435			0.00307981
$352$		0			0
$353$	−195496.	+	112869.i	−1.56887	+	0.905789i	−0.572571	+	0.819855i	$0.694054\pi$
$353$	−195496.	+	112869.i	−1.56887	+	0.905789i	−0.996301	+	0.0859335i	$0.972613\pi$
$354$		0			0
$355$	−197080.	−	113784.i	−1.56382	−	0.902872i
$356$		0			0
$357$	−65809.3	+	54267.9i	−0.516358	+	0.425801i
$358$		0			0
$359$	1447.85	−	2507.75i	0.0112340	−	0.0194579i	−0.860354	−	0.509697i	$-0.829757\pi$
$359$	1447.85	−	2507.75i	0.0112340	−	0.0194579i	0.871588	+	0.490240i	$0.163091\pi$
$360$		0			0
$361$	−45712.0	−	79175.5i	−0.350765	−	0.607542i
$362$		0			0
$363$			74643.3i			0.566471i
$364$		0			0
$365$	328842.			2.46832
$366$		0			0
$367$	−145975.	+	84278.7i	−1.08379	+	0.625728i	−0.931917	−	0.362671i	$-0.881865\pi$
$367$	−145975.	+	84278.7i	−1.08379	+	0.625728i	−0.151876	+	0.988400i	$0.548531\pi$
$368$		0			0
$369$	51913.9	+	29972.5i	0.381269	+	0.220126i
$370$		0			0
$371$	−32837.2	−	196022.i	−0.238572	−	1.42415i
$372$		0			0
$373$	−72127.8	+	124929.i	−0.518424	+	0.897936i	0.481347	+	0.876530i	$0.340148\pi$
$373$	−72127.8	+	124929.i	−0.518424	+	0.897936i	−0.999771	+	0.0214063i	$0.993186\pi$
$374$		0			0
$375$	−53595.6	−	92830.3i	−0.381124	−	0.660127i
$376$		0			0
$377$		−	4013.75i		−	0.0282402i
$378$		0			0
$379$	−2876.66			−0.0200267			−0.0100134	−	0.999950i	$-0.503187\pi$
$379$	−2876.66			−0.0200267			−0.0100134	+	0.999950i	$0.503187\pi$
$380$		0			0
$381$	−75678.3	+	43692.9i	−0.521341	+	0.300996i
$382$		0			0
$383$	240541.	+	138877.i	1.63981	+	0.946742i	0.980899	+	0.194517i	$0.0623138\pi$
$383$	240541.	+	138877.i	1.63981	+	0.946742i	0.658906	+	0.752225i	$0.271019\pi$
$384$		0			0
$385$	11897.6	−	31838.1i	0.0802670	−	0.214796i
$386$		0			0
$387$	31688.1	−	54885.4i	0.211580	−	0.366467i
$388$		0			0
$389$	95683.8	+	165729.i	0.632323	+	1.09522i	0.987076	+	0.160256i	$0.0512319\pi$
$389$	95683.8	+	165729.i	0.632323	+	1.09522i	−0.354752	+	0.934960i	$0.615435\pi$
$390$		0			0
$391$			207283.i			1.35585i
$392$		0			0
$393$	42087.2			0.272499
$394$		0			0
$395$	−192994.	+	111425.i	−1.23694	+	0.714149i
$396$		0			0
$397$	2321.69	+	1340.43i	0.0147307	+	0.00850478i	0.507347	−	0.861742i	$-0.330626\pi$
$397$	2321.69	+	1340.43i	0.0147307	+	0.00850478i	−0.492617	+	0.870246i	$0.663959\pi$
$398$		0			0
$399$	47038.3	+	17577.7i	0.295465	+	0.110412i
$400$		0			0
$401$	80466.3	−	139372.i	0.500409	−	0.866734i	−0.499591	−	0.866262i	$-0.666516\pi$
$401$	80466.3	−	139372.i	0.500409	−	0.866734i	1.00000		0.000472765i	$-0.000150486\pi$
$402$		0			0
$403$	129.616	+	224.501i	0.000798083	+	0.00138232i
$404$		0			0
$405$		−	30443.7i		−	0.185604i
$406$		0			0
$407$	30666.5			0.185130
$408$		0			0
$409$	9206.94	−	5315.63i	0.0550388	−	0.0317767i	−0.472228	−	0.881476i	$-0.656550\pi$
$409$	9206.94	−	5315.63i	0.0550388	−	0.0317767i	0.527267	+	0.849700i	$0.323217\pi$
$410$		0			0
$411$	85784.6	+	49527.8i	0.507839	+	0.293201i
$412$		0			0
$413$	−105397.	+	17655.9i	−0.617914	+	0.103512i
$414$		0			0
$415$	66930.8	−	115928.i	0.388624	−	0.673117i
$416$		0			0
$417$	29740.8	+	51512.5i	0.171033	+	0.296238i
$418$		0			0
$419$			243459.i			1.38675i	0.720579	+	0.693373i	$0.243876\pi$
$419$			243459.i			1.38675i	−0.720579	+	0.693373i	$0.756124\pi$
$420$		0			0
$421$	215529.			1.21602			0.608010	−	0.793929i	$-0.291968\pi$
$421$	215529.			1.21602			0.608010	+	0.793929i	$0.291968\pi$
$422$		0			0
$423$	−80953.5	+	46738.5i	−0.452434	+	0.261213i
$424$		0			0
$425$	324651.	+	187437.i	1.79737	+	1.03771i
$426$		0			0
$427$	48542.2	+	58865.9i	0.266234	+	0.322855i
$428$		0			0
$429$	116.710	−	202.148i	0.000634154	−	0.00109839i
$430$		0			0
$431$	73267.6	+	126903.i	0.394418	+	0.683153i	0.993027	−	0.117889i	$-0.0376128\pi$
$431$	73267.6	+	126903.i	0.394418	+	0.683153i	−0.598608	+	0.801042i	$0.704279\pi$
$432$		0			0
$433$			359910.i			1.91963i	0.280627	+	0.959817i	$0.409458\pi$
$433$			359910.i			1.91963i	−0.280627	+	0.959817i	$0.590542\pi$
$434$		0			0
$435$	−322040.			−1.70189
$436$		0			0
$437$	105679.	−	61013.8i	0.553383	−	0.319496i
$438$		0			0
$439$	158304.	+	91396.9i	0.821416	+	0.474245i	0.850905	−	0.525320i	$-0.176055\pi$
$439$	158304.	+	91396.9i	0.821416	+	0.474245i	−0.0294885	+	0.999565i	$0.509388\pi$
$440$		0			0
$441$	61287.9	−	21126.5i	0.315136	−	0.108630i
$442$		0			0
$443$	63410.0	−	109829.i	0.323110	−	0.559643i	−0.658018	−	0.753002i	$-0.728605\pi$
$443$	63410.0	−	109829.i	0.323110	−	0.559643i	0.981128	+	0.193359i	$0.0619382\pi$
$444$		0			0
$445$	−33281.1	−	57644.6i	−0.168065	−	0.291098i
$446$		0			0
$447$			111348.i			0.557271i
$448$		0			0
$449$	146291.			0.725645			0.362822	−	0.931858i	$-0.381813\pi$
$449$	146291.			0.725645			0.362822	+	0.931858i	$0.381813\pi$
$450$		0			0
$451$	31936.3	−	18438.5i	0.157012	−	0.0906508i
$452$		0			0
$453$	−195361.	−	112792.i	−0.952008	−	0.549642i
$454$		0			0
$455$	4269.76	−	3520.94i	0.0206244	−	0.0170073i
$456$		0			0
$457$	−161868.	+	280364.i	−0.775048	+	1.34242i	0.159719	+	0.987163i	$0.448941\pi$
$457$	−161868.	+	280364.i	−0.775048	+	1.34242i	−0.934767	+	0.355261i	$0.884392\pi$
$458$		0			0
$459$	23500.7	+	40704.3i	0.111546	+	0.193204i
$460$		0			0
$461$		−	343678.i		−	1.61715i	−0.588395	−	0.808573i	$-0.700240\pi$
$461$		−	343678.i		−	1.61715i	0.588395	−	0.808573i	$-0.299760\pi$
$462$		0			0
$463$	−94441.9			−0.440558			−0.220279	−	0.975437i	$-0.570697\pi$
$463$	−94441.9			−0.440558			−0.220279	+	0.975437i	$0.570697\pi$
$464$		0			0
$465$	18012.7	−	10399.6i	0.0833053	−	0.0480964i
$466$		0			0
$467$	−198437.	−	114568.i	−0.909891	−	0.525326i	−0.0294946	−	0.999565i	$-0.509390\pi$
$467$	−198437.	−	114568.i	−0.909891	−	0.525326i	−0.880396	+	0.474239i	$0.842723\pi$
$468$		0			0
$469$	13316.7	+	79494.1i	0.0605412	+	0.361401i
$470$		0			0
$471$	71149.0	−	123234.i	0.320721	−	0.555504i
$472$		0			0
$473$	−19493.9	−	33764.4i	−0.0871316	−	0.150916i
$474$		0			0
$475$		−	220688.i		−	0.978120i
$476$		0			0
$477$	−109517.			−0.481333
$478$		0			0
$479$	−221555.	+	127915.i	−0.965631	+	0.557508i	−0.897902	−	0.440196i	$-0.854909\pi$
$479$	−221555.	+	127915.i	−0.965631	+	0.557508i	−0.0677297	+	0.997704i	$0.521576\pi$
$480$		0			0
$481$	4324.37	+	2496.67i	0.0186910	+	0.0107913i
$482$		0			0
$483$	55144.9	−	147569.i	0.236380	−	0.632557i
$484$		0			0
$485$	−167079.	+	289389.i	−0.710295	+	1.23027i
$486$		0			0
$487$	105835.	+	183311.i	0.446241	+	0.772913i	0.998138	−	0.0609998i	$-0.0194289\pi$
$487$	105835.	+	183311.i	0.446241	+	0.772913i	−0.551896	+	0.833913i	$0.686096\pi$
$488$		0			0
$489$			100679.i			0.421038i
$490$		0			0
$491$	−53830.1			−0.223286			−0.111643	−	0.993748i	$-0.535611\pi$
$491$	−53830.1			−0.223286			−0.111643	+	0.993748i	$0.535611\pi$
$492$		0			0
$493$	430579.	−	248595.i	1.77157	−	1.02282i
$494$		0			0
$495$	−16219.2	−	9364.17i	−0.0661941	−	0.0382172i
$496$		0			0
$497$	−250123.	−	93468.5i	−1.01261	−	0.378401i
$498$		0			0
$499$	−7483.83	+	12962.4i	−0.0300554	+	0.0520575i	−0.880662	−	0.473745i	$-0.842902\pi$
$499$	−7483.83	+	12962.4i	−0.0300554	+	0.0520575i	0.850606	+	0.525803i	$0.176235\pi$
$500$		0			0
$501$	−120702.	−	209061.i	−0.480881	−	0.832910i
$502$		0			0
$503$		−	203381.i		−	0.803850i	−0.915673	−	0.401925i	$-0.868341\pi$
$503$		−	203381.i		−	0.803850i	0.915673	−	0.401925i	$-0.131659\pi$
$504$		0			0
$505$	−52244.4			−0.204860
$506$		0			0
$507$	−128492.	+	74184.7i	−0.499872	+	0.288601i
$508$		0			0
$509$	−247167.	−	142702.i	−0.954013	−	0.550800i	−0.0596876	−	0.998217i	$-0.519010\pi$
$509$	−247167.	−	142702.i	−0.954013	−	0.550800i	−0.894325	+	0.447418i	$0.852344\pi$
$510$		0			0
$511$	380543.	−	63747.8i	1.45734	−	0.244131i
$512$		0			0
$513$	13834.8	−	23962.6i	0.0525701	−	0.0910541i
$514$		0			0
$515$	−79540.7	−	137769.i	−0.299899	−	0.519440i
$516$		0			0
$517$			57505.1i			0.215142i
$518$		0			0
$519$	−2772.63			−0.0102934
$520$		0			0
$521$	−121232.	+	69993.1i	−0.446622	+	0.257857i	−0.706403	−	0.707810i	$-0.749683\pi$
$521$	−121232.	+	69993.1i	−0.446622	+	0.257857i	0.259780	+	0.965668i	$0.416350\pi$
$522$		0			0
$523$	−284484.	−	164247.i	−1.04005	−	0.600474i	−0.120203	−	0.992749i	$-0.538355\pi$
$523$	−284484.	−	164247.i	−1.04005	−	0.600474i	−0.919848	+	0.392276i	$0.871688\pi$
$524$		0			0
$525$	−181259.	−	219808.i	−0.657629	−	0.797490i
$526$		0			0
$527$	−16055.7	+	27809.4i	−0.0578108	+	0.100131i
$528$		0			0
$529$	−51492.2	−	89187.1i	−0.184005	−	0.318706i
$530$		0			0
$531$			58885.1i			0.208841i
$532$		0			0
$533$	6004.57			0.0211362
$534$		0			0
$535$	730941.	−	422009.i	2.55373	−	1.47440i
$536$		0			0
$537$	140851.	+	81320.6i	0.488441	+	0.282002i
$538$		0			0
$539$	7596.13	−	39150.1i	0.0261466	−	0.134758i
$540$		0			0
$541$	−237359.	+	411117.i	−0.810981	+	1.40466i	0.101197	+	0.994866i	$0.467733\pi$
$541$	−237359.	+	411117.i	−0.810981	+	1.40466i	−0.912178	+	0.409794i	$0.865601\pi$
$542$		0			0
$543$	77123.2	+	133581.i	0.261568	+	0.453050i
$544$		0			0
$545$		−	580363.i		−	1.95392i
$546$		0			0
$547$	368007.			1.22993			0.614967	−	0.788553i	$-0.289169\pi$
$547$	368007.			1.22993			0.614967	+	0.788553i	$0.289169\pi$
$548$		0			0
$549$	36409.7	−	21021.1i	0.120802	−	0.0697448i
$550$		0			0
$551$	−253482.	−	146348.i	−0.834917	−	0.482039i
$552$		0			0
$553$	−201736.	+	166356.i	−0.659680	+	0.543988i
$554$		0			0
$555$	200319.	−	346963.i	0.650333	−	1.12641i
$556$		0			0
$557$	−48968.3	−	84815.5i	−0.157835	−	0.273379i	0.776252	−	0.630422i	$-0.217118\pi$
$557$	−48968.3	−	84815.5i	−0.157835	−	0.273379i	−0.934088	+	0.357043i	$0.883785\pi$
$558$		0			0
$559$		−	6348.26i		−	0.0203157i
$560$		0			0
$561$	28914.2			0.0918725
$562$		0			0
$563$	196254.	−	113308.i	0.619160	−	0.357472i	−0.157382	−	0.987538i	$-0.550305\pi$
$563$	196254.	−	113308.i	0.619160	−	0.357472i	0.776542	+	0.630066i	$0.216972\pi$
$564$		0			0
$565$	−472438.	−	272762.i	−1.47995	−	0.854451i
$566$		0			0
$567$	−5901.68	−	35230.1i	−0.0183573	−	0.109584i
$568$		0			0
$569$	9569.61	−	16575.1i	0.0295577	−	0.0511954i	−0.850868	−	0.525379i	$-0.823923\pi$
$569$	9569.61	−	16575.1i	0.0295577	−	0.0511954i	0.880426	+	0.474184i	$0.157257\pi$
$570$		0			0
$571$	179555.	+	310999.i	0.550713	+	0.953863i	0.998223	+	0.0595843i	$0.0189775\pi$
$571$	179555.	+	310999.i	0.550713	+	0.953863i	−0.447510	+	0.894279i	$0.647689\pi$
$572$		0			0
$573$			142813.i			0.434970i
$574$		0			0
$575$	−692343.			−2.09404
$576$		0			0
$577$	−112190.	+	64772.6i	−0.336977	+	0.194554i	−0.658935	−	0.752200i	$-0.728993\pi$
$577$	−112190.	+	64772.6i	−0.336977	+	0.194554i	0.321957	+	0.946754i	$0.395659\pi$
$578$		0			0
$579$	27542.6	+	15901.7i	0.0821576	+	0.0474337i
$580$		0			0
$581$	54980.5	−	147129.i	0.162876	−	0.435858i
$582$		0			0
$583$	−33686.3	+	58346.4i	−0.0991097	+	0.171663i
$584$		0			0
$585$	−1524.74	−	2640.93i	−0.00445538	−	0.00771694i
$586$		0			0
$587$			528603.i			1.53410i	0.641588	+	0.767049i	$0.278276\pi$
$587$			528603.i			1.53410i	−0.641588	+	0.767049i	$0.721724\pi$
$588$		0			0
$589$	18904.0			0.0544908
$590$		0			0
$591$	168955.	−	97546.3i	0.483723	−	0.279278i
$592$		0			0
$593$	−319323.	−	184361.i	−0.908073	−	0.524276i	−0.0282627	−	0.999601i	$-0.508997\pi$
$593$	−319323.	−	184361.i	−0.908073	−	0.524276i	−0.879811	+	0.475324i	$0.842331\pi$
$594$		0			0
$595$	642164.	+	239970.i	1.81390	+	0.677835i
$596$		0			0
$597$	−121658.	+	210718.i	−0.341345	+	0.591226i
$598$		0			0
$599$	10588.1	+	18339.2i	0.0295097	+	0.0511123i	0.880403	−	0.474226i	$-0.157272\pi$
$599$	10588.1	+	18339.2i	0.0295097	+	0.0511123i	−0.850893	+	0.525338i	$0.823939\pi$
$600$		0			0
$601$		−	545501.i		−	1.51024i	−0.655585	−	0.755121i	$-0.727578\pi$
$601$		−	545501.i		−	1.51024i	0.655585	−	0.755121i	$-0.272422\pi$
$602$		0			0
$603$	44413.2			0.122145
$604$		0			0
$605$	519529.	−	299950.i	1.41938	−	0.819481i
$606$		0			0
$607$	−298483.	−	172329.i	−0.810107	−	0.467716i	0.0368859	−	0.999319i	$-0.488256\pi$
$607$	−298483.	−	172329.i	−0.810107	−	0.467716i	−0.846993	+	0.531604i	$0.821590\pi$
$608$		0			0
$609$	−372671.	+	62429.2i	−1.00483	+	0.168327i
$610$		0			0
$611$	−4681.70	+	8108.94i	−0.0125407	+	0.0217211i
$612$		0			0
$613$	222703.	+	385733.i	0.592659	+	1.02652i	0.993873	+	0.110532i	$0.0352553\pi$
$613$	222703.	+	385733.i	0.592659	+	1.02652i	−0.401213	+	0.915985i	$0.631411\pi$
$614$		0			0
$615$		−	481772.i		−	1.27377i
$616$		0			0
$617$	−242700.			−0.637529			−0.318765	−	0.947834i	$-0.603268\pi$
$617$	−242700.			−0.637529			−0.318765	+	0.947834i	$0.603268\pi$
$618$		0			0
$619$	214130.	−	123628.i	0.558850	−	0.322652i	−0.193834	−	0.981034i	$-0.562092\pi$
$619$	214130.	−	123628.i	0.558850	−	0.322652i	0.752684	+	0.658382i	$0.228759\pi$
$620$		0			0
$621$	−75175.6	−	43402.6i	−0.194937	−	0.112547i
$622$		0			0
$623$	−49688.3	−	60255.8i	−0.128020	−	0.155247i
$624$		0			0
$625$	−81062.1	+	140404.i	−0.207519	+	0.359434i
$626$		0			0
$627$	−8510.89	−	14741.3i	−0.0216491	−	0.0374973i
$628$		0			0
$629$			618535.i			1.56337i
$630$		0			0
$631$	−533577.			−1.34010			−0.670051	−	0.742315i	$-0.733728\pi$
$631$	−533577.			−1.34010			−0.670051	+	0.742315i	$0.733728\pi$
$632$		0			0
$633$	−160961.	+	92931.1i	−0.401712	+	0.231928i
$634$		0			0
$635$	608219.	+	351155.i	1.50839	+	0.870867i
$636$		0			0
$637$	4258.50	−	4902.22i	0.0104949	−	0.0120813i
$638$		0			0
$639$	−73565.9	+	127420.i	−0.180167	+	0.312058i
$640$		0			0
$641$	76313.2	+	132178.i	0.185731	+	0.321695i	0.943823	−	0.330453i	$-0.107201\pi$
$641$	76313.2	+	132178.i	0.185731	+	0.321695i	−0.758092	+	0.652148i	$0.773868\pi$
$642$		0			0
$643$			129442.i			0.313079i	0.987672	+	0.156540i	$0.0500339\pi$
$643$			129442.i			0.313079i	−0.987672	+	0.156540i	$0.949966\pi$
$644$		0			0
$645$	−509349.			−1.22432
$646$		0			0
$647$	32661.0	−	18856.8i	0.0780227	−	0.0450464i	−0.460481	−	0.887670i	$-0.652323\pi$
$647$	32661.0	−	18856.8i	0.0780227	−	0.0450464i	0.538504	+	0.842623i	$0.318990\pi$
$648$		0			0
$649$	31371.6	+	18112.4i	0.0744814	+	0.0430019i
$650$		0			0
$651$	18828.6	−	15526.5i	0.0444280	−	0.0366364i
$652$		0			0
$653$	188157.	−	325898.i	0.441261	−	0.764286i	−0.556523	−	0.830832i	$-0.687865\pi$
$653$	188157.	−	325898.i	0.441261	−	0.764286i	0.997783	+	0.0665467i	$0.0211981\pi$
$654$		0			0
$655$	−169125.	−	292934.i	−0.394209	−	0.682790i
$656$		0			0
$657$		−	212609.i		−	0.492550i
$658$		0			0
$659$	−332703.			−0.766100			−0.383050	−	0.923728i	$-0.625126\pi$
$659$	−332703.			−0.766100			−0.383050	+	0.923728i	$0.625126\pi$
$660$		0			0
$661$	302337.	−	174555.i	0.691973	−	0.399511i	−0.112378	−	0.993666i	$-0.535847\pi$
$661$	302337.	−	174555.i	0.691973	−	0.399511i	0.804351	+	0.594155i	$0.202513\pi$
$662$		0			0
$663$	4077.27	+	2354.01i	0.00927560	+	0.00535527i
$664$		0			0
$665$	−66677.1	−	398029.i	−0.150776	−	0.900060i
$666$		0			0
$667$	−459122.	+	795223.i	−1.03199	+	1.78746i
$668$		0			0
$669$	−31461.4	−	54492.8i	−0.0702953	−	0.121755i
$670$		0			0
$671$		−	25863.5i		−	0.0574437i
$672$		0			0
$673$	402571.			0.888817			0.444408	−	0.895824i	$-0.353414\pi$
$673$	402571.			0.888817			0.444408	+	0.895824i	$0.353414\pi$
$674$		0			0
$675$	−135956.	+	78494.1i	−0.298394	+	0.172278i
$676$		0			0
$677$	625649.	+	361219.i	1.36507	+	0.788121i	0.990293	−	0.138995i	$-0.0443873\pi$
$677$	625649.	+	361219.i	1.36507	+	0.788121i	0.374773	+	0.927117i	$0.377721\pi$
$678$		0			0
$679$	−137248.	+	367276.i	−0.297690	+	0.796624i
$680$		0			0
$681$	−90346.3	+	156484.i	−0.194812	+	0.337425i
$682$		0			0
$683$	145964.	+	252817.i	0.312898	+	0.541956i	0.978989	−	0.203915i	$-0.0653667\pi$
$683$	145964.	+	252817.i	0.312898	+	0.541956i	−0.666090	+	0.745871i	$0.732033\pi$
$684$		0			0
$685$		−	796099.i		−	1.69663i
$686$		0			0
$687$	281375.			0.596173
$688$		0			0
$689$	−9500.38	+	5485.05i	−0.0200126	+	0.0115543i
$690$		0			0
$691$	434793.	+	251028.i	0.910597	+	0.525734i	0.880623	−	0.473817i	$-0.157124\pi$
$691$	434793.	+	251028.i	0.910597	+	0.525734i	0.0299740	+	0.999551i	$0.490458\pi$
$692$		0			0
$693$	−20584.5	−	7692.22i	−0.0428621	−	0.0160172i
$694$		0			0
$695$	239024.	−	414001.i	0.494847	−	0.857100i
$696$		0			0
$697$	371898.	+	644146.i	0.765523	+	1.32593i
$698$		0			0
$699$			236565.i			0.484168i
$700$		0			0
$701$	76801.7			0.156291			0.0781456	−	0.996942i	$-0.475100\pi$
$701$	76801.7			0.156291			0.0781456	+	0.996942i	$0.475100\pi$
$702$		0			0
$703$	315347.	−	182066.i	0.638084	−	0.368398i
$704$		0			0
$705$	650615.	+	375633.i	1.30902	+	0.755763i
$706$		0			0
$707$	−60458.3	+	10127.9i	−0.120953	+	0.0202618i
$708$		0			0
$709$	−456190.	+	790143.i	−0.907513	+	1.57186i	−0.0900049	+	0.995941i	$0.528688\pi$
$709$	−456190.	+	790143.i	−0.907513	+	1.57186i	−0.817508	+	0.575917i	$0.804645\pi$
$710$		0			0
$711$	72040.5	+	124778.i	0.142507	+	0.246830i
$712$		0			0
$713$		−	59305.7i		−	0.116659i
$714$		0			0
$715$	−1875.98			−0.00366957
$716$		0			0
$717$	−345090.	+	199238.i	−0.671265	+	0.387555i
$718$		0			0
$719$	−323430.	−	186733.i	−0.625638	−	0.361212i	0.153423	−	0.988161i	$-0.450970\pi$
$719$	−323430.	−	186733.i	−0.625638	−	0.361212i	−0.779061	+	0.626948i	$0.784304\pi$
$720$		0			0
$721$	−118753.	−	144009.i	−0.228441	−	0.277025i
$722$		0			0
$723$	183325.	−	317528.i	0.350707	−	0.607443i
$724$		0			0
$725$	830327.	+	1.43817e6i	1.57969	+	2.73611i
$726$		0			0
$727$			343752.i			0.650394i	0.945646	+	0.325197i	$0.105431\pi$
$727$			343752.i			0.650394i	−0.945646	+	0.325197i	$0.894569\pi$
$728$		0			0
$729$	−19683.0			−0.0370370
$730$		0			0
$731$	681017.	−	393185.i	1.27445	−	0.735804i
$732$		0			0
$733$	−511360.	−	295234.i	−0.951742	−	0.549488i	−0.0581203	−	0.998310i	$-0.518511\pi$
$733$	−511360.	−	295234.i	−0.951742	−	0.549488i	−0.893622	+	0.448821i	$0.851844\pi$
$734$		0			0
$735$	−393327.	−	341678.i	−0.728079	−	0.632473i
$736$		0			0
$737$	13661.0	−	23661.6i	0.0251506	−	0.0435621i
$738$		0			0
$739$	−10809.0	−	18721.8i	−0.0197924	−	0.0342814i	0.855960	−	0.517043i	$-0.172967\pi$
$739$	−10809.0	−	18721.8i	−0.0197924	−	0.0342814i	−0.875752	+	0.482761i	$0.839634\pi$
$740$		0			0
$741$		−	2771.61i		−	0.00504772i
$742$		0			0
$743$	−767926.			−1.39105			−0.695524	−	0.718503i	$-0.744828\pi$
$743$	−767926.			−1.39105			−0.695524	+	0.718503i	$0.744828\pi$
$744$		0			0
$745$	774999.	−	447446.i	1.39633	−	0.806172i
$746$		0			0
$747$	−74951.4	−	43273.2i	−0.134319	−	0.0775493i
$748$		0			0
$749$	764051.	−	630054.i	1.36194	−	1.12309i
$750$		0			0
$751$	274726.	−	475840.i	0.487102	−	0.843686i	−0.512788	−	0.858515i	$-0.671387\pi$
$751$	274726.	−	475840.i	0.487102	−	0.843686i	0.999890	+	0.0148295i	$0.00472056\pi$
$752$		0			0
$753$	223052.	+	386337.i	0.393384	+	0.681360i
$754$		0			0
$755$			1.81299e6i			3.18054i
$756$		0			0
$757$	−138901.			−0.242390			−0.121195	−	0.992629i	$-0.538673\pi$
$757$	−138901.			−0.242390			−0.121195	+	0.992629i	$0.538673\pi$
$758$		0			0
$759$	−46246.4	+	26700.4i	−0.0802776	+	0.0463483i
$760$		0			0
$761$	265183.	+	153103.i	0.457906	+	0.264372i	0.711163	−	0.703027i	$-0.248169\pi$
$761$	265183.	+	153103.i	0.457906	+	0.264372i	−0.253257	+	0.967399i	$0.581502\pi$
$762$		0			0
$763$	−112506.	−	671608.i	−0.193254	−	1.15363i
$764$		0			0
$765$	188872.	−	327137.i	0.322735	−	0.558993i
$766$		0			0
$767$	2949.20	+	5108.16i	0.00501318	+	0.00868308i
$768$		0			0
$769$			465964.i			0.787952i	0.919121	+	0.393976i	$0.128901\pi$
$769$			465964.i			0.787952i	−0.919121	+	0.393976i	$0.871099\pi$
$770$		0			0
$771$	290197.			0.488185
$772$		0			0
$773$	−928679.	+	536173.i	−1.55420	+	0.897318i	−0.556407	+	0.830910i	$0.687820\pi$
$773$	−928679.	+	536173.i	−1.55420	+	0.897318i	−0.997793	+	0.0664077i	$0.978846\pi$
$774$		0			0
$775$	−92885.5	−	53627.4i	−0.154648	−	0.0892861i
$776$		0			0
$777$	164553.	−	440345.i	0.272560	−	0.729375i
$778$		0			0
$779$	218936.	−	379209.i	0.360780	−	0.624889i
$780$		0			0
$781$	45256.2	+	78386.0i	0.0741952	+	0.128510i
$782$		0			0
$783$			208211.i			0.339610i
$784$		0			0
$785$	−1.14363e6			−1.85587
$786$		0			0
$787$	−232575.	+	134277.i	−0.375502	+	0.216796i	−0.675860	−	0.737030i	$-0.736227\pi$
$787$	−232575.	+	134277.i	−0.375502	+	0.216796i	0.300357	+	0.953827i	$0.402894\pi$
$788$		0			0
$789$	484366.	+	279649.i	0.778072	+	0.449220i
$790$		0			0
$791$	−599591.	−	224061.i	−0.958301	−	0.358108i
$792$		0			0
$793$	2105.64	−	3647.08i	0.00334841	−	0.00579961i
$794$		0			0
$795$	440089.	+	762257.i	0.696316	+	1.20605i
$796$		0			0
$797$			148887.i			0.234390i	0.993109	+	0.117195i	$0.0373902\pi$
$797$			148887.i			0.234390i	−0.993109	+	0.117195i	$0.962610\pi$
$798$		0			0
$799$	−1.15986e6			−1.81682
$800$		0			0
$801$	−37269.4	+	21517.5i	−0.0580881	+	0.0335372i
$802$		0			0
$803$	−113269.	−	65396.2i	−0.175664	−	0.101419i
$804$		0			0
$805$	−1.24870e6	+	209179.i	−1.92693	+	0.322795i
$806$		0			0
$807$	95791.4	−	165915.i	0.147089	−	0.254765i
$808$		0			0
$809$	−322930.	−	559331.i	−0.493414	−	0.854618i	0.506558	−	0.862206i	$-0.330918\pi$
$809$	−322930.	−	559331.i	−0.493414	−	0.854618i	−0.999971	+	0.00758857i	$0.997584\pi$
$810$		0			0
$811$		−	999048.i		−	1.51895i	−0.650534	−	0.759477i	$-0.725455\pi$
$811$		−	999048.i		−	1.51895i	0.650534	−	0.759477i	$-0.274545\pi$
$812$		0			0
$813$	731134.			1.10616
$814$		0			0
$815$	700741.	−	404573.i	1.05498	−	0.609091i
$816$		0			0
$817$	−400914.	−	231468.i	−0.600630	−	0.346774i
$818$		0			0
$819$	−2276.42	−	2760.56i	−0.00339379	−	0.00411556i
$820$		0			0
$821$	451840.	−	782609.i	0.670345	−	1.16107i	−0.307462	−	0.951560i	$-0.599480\pi$
$821$	451840.	−	782609.i	0.670345	−	1.16107i	0.977806	−	0.209510i	$-0.0671870\pi$
$822$		0			0
$823$	−295286.	−	511451.i	−0.435957	−	0.755100i	0.561416	−	0.827534i	$-0.310257\pi$
$823$	−295286.	−	511451.i	−0.435957	−	0.755100i	−0.997373	+	0.0724337i	$0.976923\pi$
$824$		0			0
$825$			96575.8i			0.141893i
$826$		0			0
$827$	−756375.			−1.10593			−0.552963	−	0.833206i	$-0.686503\pi$
$827$	−756375.			−1.10593			−0.552963	+	0.833206i	$0.686503\pi$
$828$		0			0
$829$	−121118.	+	69927.6i	−0.176238	+	0.101751i	−0.585524	−	0.810655i	$-0.699111\pi$
$829$	−121118.	+	69927.6i	−0.176238	+	0.101751i	0.409286	+	0.912406i	$0.365778\pi$
$830$		0			0
$831$	476997.	+	275394.i	0.690739	+	0.398798i
$832$		0			0
$833$	789645.	+	153212.i	1.13800	+	0.220801i
$834$		0			0
$835$	−970066.	+	1.68020e6i	−1.39132	+	2.40984i
$836$		0			0
$837$	−6723.75	−	11645.9i	−0.00959755	−	0.0166235i
$838$		0			0
$839$			319067.i			0.453271i	0.973980	+	0.226636i	$0.0727726\pi$
$839$			319067.i			0.453271i	−0.973980	+	0.226636i	$0.927227\pi$
$840$		0			0
$841$	1.49522e6			2.11404
$842$		0			0
$843$	−307883.	+	177756.i	−0.433242	+	0.250132i
$844$		0			0
$845$	1.03267e6	+	596215.i	1.44627	+	0.835005i
$846$		0			0
$847$	543063.	−	447822.i	0.756978	−	0.624222i
$848$		0			0
$849$	29537.4	−	51160.2i	0.0409785	−	0.0709769i
$850$		0			0
$851$	−571176.	−	989306.i	−0.788699	−	1.36607i
$852$		0			0
$853$		−	174276.i		−	0.239518i	−0.992803	−	0.119759i	$-0.961788\pi$
$853$		−	174276.i		−	0.239518i	0.992803	−	0.119759i	$-0.0382122\pi$
$854$		0			0
$855$	−222378.			−0.304200
$856$		0			0
$857$	−520689.	+	300620.i	−0.708951	+	0.409313i	−0.810673	−	0.585500i	$-0.800898\pi$
$857$	−520689.	+	300620.i	−0.708951	+	0.409313i	0.101721	+	0.994813i	$0.467565\pi$
$858$		0			0
$859$	−884544.	−	510692.i	−1.19876	−	0.692106i	−0.238483	−	0.971147i	$-0.576650\pi$
$859$	−884544.	−	510692.i	−1.19876	−	0.692106i	−0.960279	+	0.279041i	$0.909983\pi$
$860$		0			0
$861$	−93394.2	−	557517.i	−0.125983	−	0.752058i
$862$		0			0
$863$	−240339.	+	416279.i	−0.322702	+	0.558937i	−0.981045	−	0.193782i	$-0.937925\pi$
$863$	−240339.	+	416279.i	−0.322702	+	0.558937i	0.658342	+	0.752719i	$0.271258\pi$
$864$		0			0
$865$	11141.7	+	19297.9i	0.0148908	+	0.0257916i
$866$		0			0
$867$			149203.i			0.198490i
$868$		0			0
$869$	88635.5			0.117373
$870$		0			0
$871$	3852.75	−	2224.39i	0.00507849	−	0.00293207i
$872$		0			0
$873$	187101.	+	108023.i	0.245498	+	0.141738i
$874$		0			0
$875$	−353835.	+	946867.i	−0.462151	+	1.23672i
$876$		0			0
$877$	592995.	−	1.02710e6i	0.770996	−	1.33540i	−0.166021	−	0.986122i	$-0.553092\pi$
$877$	592995.	−	1.02710e6i	0.770996	−	1.33540i	0.937018	−	0.349282i	$-0.113575\pi$
$878$		0			0
$879$	190704.	+	330308.i	0.246820	+	0.427506i
$880$		0			0
$881$		−	425722.i		−	0.548498i	−0.961659	−	0.274249i	$-0.911571\pi$
$881$		−	425722.i		−	0.548498i	0.961659	−	0.274249i	$-0.0884292\pi$
$882$		0			0
$883$	704717.			0.903844			0.451922	−	0.892058i	$-0.350739\pi$
$883$	704717.			0.903844			0.451922	+	0.892058i	$0.350739\pi$
$884$		0			0
$885$	409850.	−	236627.i	0.523285	−	0.302119i
$886$		0			0
$887$	355103.	+	205019.i	0.451343	+	0.260583i	0.708397	−	0.705814i	$-0.249419\pi$
$887$	355103.	+	205019.i	0.451343	+	0.260583i	−0.257054	+	0.966397i	$0.582752\pi$
$888$		0			0
$889$	771917.	+	288458.i	0.976713	+	0.364988i
$890$		0			0
$891$	−6054.28	+	10486.3i	−0.00762618	+	0.0132089i
$892$		0			0
$893$	341404.	+	591330.i	0.428121	+	0.741527i
$894$		0			0
$895$		−	1.30713e6i		−	1.63182i
$896$		0			0
$897$	−8695.10			−0.0108066
$898$		0			0
$899$	−123193.	+	71125.2i	−0.152428	+	0.0880044i
$900$		0			0
$901$	−1.17683e6	−	679442.i	−1.44965	−	0.836957i
$902$		0			0
$903$	−589428.	+	98740.0i	−0.722862	+	0.121093i
$904$		0			0
$905$	619831.	−	1.07358e6i	0.756792	−	1.31080i
$906$		0			0
$907$	−45535.5	−	78869.7i	−0.0553522	−	0.0958729i	0.837022	−	0.547170i	$-0.184295\pi$
$907$	−45535.5	−	78869.7i	−0.0553522	−	0.0958729i	−0.892374	+	0.451297i	$0.850962\pi$
$908$		0			0
$909$			33777.9i			0.0408795i
$910$		0			0
$911$	1.61216e6			1.94255			0.971273	−	0.237966i	$-0.0764807\pi$
$911$	1.61216e6			1.94255			0.971273	+	0.237966i	$0.0764807\pi$
$912$		0			0
$913$	−46108.5	+	26620.8i	−0.0553146	+	0.0319359i
$914$		0			0
$915$	−292621.	−	168945.i	−0.349513	−	0.201791i
$916$		0			0
$917$	−252502.	−	306203.i	−0.300280	−	0.364142i
$918$		0			0
$919$	−356265.	+	617069.i	−0.421834	+	0.730638i	−0.996119	−	0.0880173i	$-0.971947\pi$
$919$	−356265.	+	617069.i	−0.421834	+	0.730638i	0.574285	+	0.818656i	$0.305280\pi$
$920$		0			0
$921$	−211497.	−	366323.i	−0.249336	−	0.431862i
$922$		0			0
$923$			14737.9i			0.0172994i
$924$		0			0
$925$	−2.06596e6			−2.41456
$926$		0			0
$927$	−89072.4	+	51426.0i	−0.103653	+	0.0598444i
$928$		0			0
$929$	−1.12944e6	−	652085.i	−1.30868	−	0.755566i	−0.326804	−	0.945092i	$-0.605972\pi$
$929$	−1.12944e6	−	652085.i	−1.30868	−	0.755566i	−0.981876	+	0.189526i	$0.939305\pi$
$930$		0			0
$931$	−154320.	−	447681.i	−0.178042	−	0.516499i
$932$		0			0
$933$	−140588.	+	243506.i	−0.161505	+	0.279735i
$934$		0			0
$935$	−116190.	−	201247.i	−0.132907	−	0.230201i
$936$		0			0
$937$		−	51494.5i		−	0.0586518i	−0.999570	−	0.0293259i	$-0.990664\pi$
$937$		−	51494.5i		−	0.0586518i	0.999570	−	0.0293259i	$-0.00933606\pi$
$938$		0			0
$939$	−464867.			−0.527227
$940$		0			0
$941$	853741.	−	492908.i	0.964155	−	0.556655i	0.0667058	−	0.997773i	$-0.478751\pi$
$941$	853741.	−	492908.i	0.964155	−	0.556655i	0.897449	+	0.441117i	$0.145418\pi$
$942$		0			0
$943$	−1.18965e6	−	686847.i	−1.33782	−	0.772390i
$944$		0			0
$945$	−221491.	+	182647.i	−0.248024	+	0.204526i
$946$		0			0
$947$	210727.	−	364990.i	0.234975	−	0.406988i	−0.724291	−	0.689495i	$-0.757833\pi$
$947$	210727.	−	364990.i	0.234975	−	0.406988i	0.959265	+	0.282507i	$0.0911660\pi$
$948$		0			0
$949$	−10648.3	−	18443.4i	−0.0118235	−	0.0204789i
$950$		0			0
$951$		−	598118.i		−	0.661342i
$952$		0			0
$953$	−507816.			−0.559140			−0.279570	−	0.960125i	$-0.590192\pi$
$953$	−507816.			−0.559140			−0.279570	+	0.960125i	$0.590192\pi$
$954$		0			0
$955$	994002.	−	573888.i	1.08989	−	0.629245i
$956$		0			0
$957$	110927.	+	64043.5i	0.121119	+	0.0699280i
$958$		0			0
$959$	−154328.	−	921262.i	−0.167806	−	1.00172i
$960$		0			0
$961$	−457167.	+	791836.i	−0.495026	+	0.857410i
$962$		0			0
$963$	−272844.	−	472580.i	−0.294213	−	0.509592i
$964$		0			0
$965$		−	255601.i		−	0.274478i
$966$		0			0
$967$	−415363.			−0.444196			−0.222098	−	0.975024i	$-0.571290\pi$
$967$	−415363.			−0.444196			−0.222098	+	0.975024i	$0.571290\pi$
$968$		0			0
$969$	297327.	−	171662.i	0.316656	−	0.182821i
$970$		0			0
$971$	−671707.	−	387810.i	−0.712428	−	0.411321i	0.0995311	−	0.995034i	$-0.468266\pi$
$971$	−671707.	−	387810.i	−0.712428	−	0.411321i	−0.811960	+	0.583714i	$0.801599\pi$
$972$		0			0
$973$	196347.	−	525426.i	0.207395	−	0.554991i
$974$		0			0
$975$	−7862.58	+	13618.4i	−0.00827096	+	0.0143257i
$976$		0			0
$977$	−68977.7	−	119473.i	−0.0722636	−	0.125164i	0.827629	−	0.561275i	$-0.189689\pi$
$977$	−68977.7	−	119473.i	−0.0722636	−	0.125164i	−0.899893	+	0.436111i	$0.856356\pi$
$978$		0			0
$979$			26474.2i			0.0276221i
$980$		0			0
$981$	−375226.			−0.389902
$982$		0			0
$983$	356603.	−	205885.i	0.369044	−	0.213067i	−0.303997	−	0.952673i	$-0.598321\pi$
$983$	356603.	−	205885.i	0.369044	−	0.213067i	0.673041	+	0.739606i	$0.264988\pi$
$984$		0			0
$985$	−1.35788e6	−	783970.i	−1.39955	−	0.808029i
$986$		0			0
$987$	825723.	+	308565.i	0.847618	+	0.316747i
$988$		0			0
$989$	−726161.	+	1.25775e6i	−0.742404	+	1.28588i
$990$		0			0
$991$	−764949.	−	1.32493e6i	−0.778906	−	1.34910i	−0.932573	−	0.360982i	$-0.882442\pi$
$991$	−764949.	−	1.32493e6i	−0.778906	−	1.34910i	0.153667	−	0.988123i	$-0.450892\pi$
$992$		0			0
$993$			735630.i			0.746038i
$994$		0			0
$995$	1.95551e6			1.97521
$996$		0			0
$997$	94470.0	−	54542.3i	0.0950393	−	0.0548710i	−0.451727	−	0.892156i	$-0.649192\pi$
$997$	94470.0	−	54542.3i	0.0950393	−	0.0548710i	0.546766	+	0.837285i	$0.315859\pi$
$998$		0			0
$999$	−224324.	−	129514.i	−0.224773	−	0.129773i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.5.z.a.145.8	yes	16
3.2	odd	2		504.5.by.a.145.1		16
4.3	odd	2		336.5.bh.i.145.8		16
7.2	even	3		1176.5.f.b.97.1		16
7.3	odd	6	inner	168.5.z.a.73.8	✓	16
7.5	odd	6		1176.5.f.b.97.16		16
21.17	even	6		504.5.by.a.73.1		16
28.3	even	6		336.5.bh.i.241.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.5.z.a.73.8	✓	16	7.3	odd	6	inner
168.5.z.a.145.8	yes	16	1.1	even	1	trivial
336.5.bh.i.145.8		16	4.3	odd	2
336.5.bh.i.241.8		16	28.3	even	6
504.5.by.a.73.1		16	21.17	even	6
504.5.by.a.145.1		16	3.2	odd	2
1176.5.f.b.97.1		16	7.2	even	3
1176.5.f.b.97.16		16	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	168.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.50000 + 2.59808i) q^{3} +(36.1660 + 20.8805i) q^{5} +(45.8999 + 17.1523i) q^{7} +(13.5000 - 23.3827i) q^{9} +O(q^{10})\)	\(q+(-4.50000 + 2.59808i) q^{3} +(36.1660 + 20.8805i) q^{5} +(45.8999 + 17.1523i) q^{7} +(13.5000 - 23.3827i) q^{9} +(-8.30491 - 14.3845i) q^{11} -2.70453i q^{13} -216.996 q^{15} +(290.132 - 167.508i) q^{17} +(-170.800 - 98.6116i) q^{19} +(-251.112 + 42.0659i) q^{21} +(-309.364 + 535.835i) q^{23} +(559.489 + 969.063i) q^{25} +140.296i q^{27} +1484.08 q^{29} +(-83.0093 + 47.9254i) q^{31} +(74.7442 + 43.1536i) q^{33} +(1301.87 + 1578.74i) q^{35} +(-923.145 + 1598.93i) q^{37} +(7.02658 + 12.1704i) q^{39} +2220.19i q^{41} +2347.27 q^{43} +(976.483 - 563.773i) q^{45} +(-2998.28 - 1731.06i) q^{47} +(1812.60 + 1574.58i) q^{49} +(-870.395 + 1507.57i) q^{51} +(-2028.09 - 3512.76i) q^{53} -693.642i q^{55} +1024.80 q^{57} +(-1888.74 + 1090.46i) q^{59} +(1348.51 + 778.561i) q^{61} +(1020.72 - 841.706i) q^{63} +(56.4719 - 97.8122i) q^{65} +(822.467 + 1424.55i) q^{67} -3215.01i q^{69} -5449.32 q^{71} +(6819.43 - 3937.20i) q^{73} +(-5035.40 - 2907.19i) q^{75} +(-134.466 - 802.697i) q^{77} +(-2668.17 + 4621.40i) q^{79} +(-364.500 - 631.333i) q^{81} -3205.42i q^{83} +13990.5 q^{85} +(-6678.37 + 3855.76i) q^{87} +(-1380.35 - 796.944i) q^{89} +(46.3890 - 124.138i) q^{91} +(249.028 - 431.329i) q^{93} +(-4118.11 - 7132.78i) q^{95} +8001.69i q^{97} -448.465 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 72 q^{3} + 12 q^{5} + 40 q^{7} + 216 q^{9}+O(q^{10}) \) 16 * q - 72 * q^3 + 12 * q^5 + 40 * q^7 + 216 * q^9	\( 16 q - 72 q^{3} + 12 q^{5} + 40 q^{7} + 216 q^{9} - 108 q^{11} - 72 q^{15} - 168 q^{17} + 948 q^{19} - 252 q^{21} - 768 q^{23} + 1908 q^{25} - 1608 q^{29} - 3216 q^{31} + 972 q^{33} + 696 q^{35} - 1820 q^{37} - 1188 q^{39} + 2888 q^{43} + 324 q^{45} + 744 q^{47} - 3784 q^{49} + 504 q^{51} + 4476 q^{53} - 5688 q^{57} - 4668 q^{59} + 17760 q^{61} + 1188 q^{63} + 8760 q^{65} + 1580 q^{67} + 48 q^{71} + 588 q^{73} - 17172 q^{75} - 17508 q^{77} - 3824 q^{79} - 5832 q^{81} + 11440 q^{85} + 7236 q^{87} - 360 q^{89} + 25860 q^{91} + 9648 q^{93} - 21792 q^{95} - 5832 q^{99}+O(q^{100}) \) 16 * q - 72 * q^3 + 12 * q^5 + 40 * q^7 + 216 * q^9 - 108 * q^11 - 72 * q^15 - 168 * q^17 + 948 * q^19 - 252 * q^21 - 768 * q^23 + 1908 * q^25 - 1608 * q^29 - 3216 * q^31 + 972 * q^33 + 696 * q^35 - 1820 * q^37 - 1188 * q^39 + 2888 * q^43 + 324 * q^45 + 744 * q^47 - 3784 * q^49 + 504 * q^51 + 4476 * q^53 - 5688 * q^57 - 4668 * q^59 + 17760 * q^61 + 1188 * q^63 + 8760 * q^65 + 1580 * q^67 + 48 * q^71 + 588 * q^73 - 17172 * q^75 - 17508 * q^77 - 3824 * q^79 - 5832 * q^81 + 11440 * q^85 + 7236 * q^87 - 360 * q^89 + 25860 * q^91 + 9648 * q^93 - 21792 * q^95 - 5832 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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