LMFDB - Embedded newform 63.6.p.b.17.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,6,Mod(17,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("63.17");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	63.p (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:	$10.1041806482$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.11
Character	$\chi$	$=$	63.17
Dual form			63.6.p.b.26.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.14327 - 4.70152i) q^{2} +(28.2086 - 48.8587i) q^{4} +(-33.1882 - 57.4837i) q^{5} +(-116.271 - 57.3420i) q^{7} -229.595i q^{8} +O(q^{10})$	\(q+(8.14327 - 4.70152i) q^{2} +(28.2086 - 48.8587i) q^{4} +(-33.1882 - 57.4837i) q^{5} +(-116.271 - 57.3420i) q^{7} -229.595i q^{8} +(-540.521 - 312.070i) q^{10} +(383.606 + 221.475i) q^{11} -437.107i q^{13} +(-1216.42 + 79.6982i) q^{14} +(-176.771 - 306.177i) q^{16} +(476.524 - 825.364i) q^{17} +(1934.59 - 1116.94i) q^{19} -3744.77 q^{20} +4165.07 q^{22} +(-2096.62 + 1210.49i) q^{23} +(-640.416 + 1109.23i) q^{25} +(-2055.06 - 3559.48i) q^{26} +(-6081.48 + 4063.30i) q^{28} +6381.19i q^{29} +(5912.80 + 3413.76i) q^{31} +(3483.73 + 2011.33i) q^{32} -8961.54i q^{34} +(562.593 + 8586.75i) q^{35} +(-7604.18 - 13170.8i) q^{37} +(10502.6 - 18191.0i) q^{38} +(-13198.0 + 7619.85i) q^{40} +1729.95 q^{41} +13717.1 q^{43} +(21641.9 - 12495.0i) q^{44} +(-11382.2 + 19714.6i) q^{46} +(-9079.05 - 15725.4i) q^{47} +(10230.8 + 13334.4i) q^{49} +12043.7i q^{50} +(-21356.4 - 12330.1i) q^{52} +(20788.0 + 12002.0i) q^{53} -29401.4i q^{55} +(-13165.4 + 26695.2i) q^{56} +(30001.3 + 51963.8i) q^{58} +(-21226.0 + 36764.5i) q^{59} +(-17731.8 + 10237.5i) q^{61} +64199.4 q^{62} +49138.6 q^{64} +(-25126.5 + 14506.8i) q^{65} +(-290.744 + 503.584i) q^{67} +(-26884.1 - 46564.6i) q^{68} +(44952.1 + 67279.2i) q^{70} +32681.9i q^{71} +(-47409.2 - 27371.7i) q^{73} +(-123846. - 71502.4i) q^{74} -126029. i q^{76} +(-31902.3 - 47747.7i) q^{77} +(-18594.6 - 32206.7i) q^{79} +(-11733.5 + 20322.9i) q^{80} +(14087.5 - 8133.41i) q^{82} +44677.3 q^{83} -63259.9 q^{85} +(111702. - 64491.0i) q^{86} +(50849.5 - 88073.9i) q^{88} +(-12075.8 - 20915.9i) q^{89} +(-25064.6 + 50822.7i) q^{91} +136584. i q^{92} +(-147866. - 85370.6i) q^{94} +(-128411. - 74138.2i) q^{95} -28906.5i q^{97} +(146004. + 60485.3i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 304 q^{4} - 436 q^{7}+O(q^{10}) $ 24 * q + 304 * q^4 - 436 * q^7	$ 24 q + 304 q^{4} - 436 q^{7} + 1992 q^{10} - 3644 q^{16} + 3804 q^{19} - 5648 q^{22} - 18852 q^{25} - 39172 q^{28} + 38652 q^{31} + 20548 q^{37} + 132060 q^{40} + 2200 q^{43} - 25712 q^{46} - 125676 q^{49} - 2940 q^{52} + 154300 q^{58} + 48504 q^{61} - 327880 q^{64} + 156324 q^{67} - 9468 q^{70} - 703236 q^{73} + 165756 q^{79} + 1081020 q^{82} - 284448 q^{85} + 582308 q^{88} - 19812 q^{91} - 1481724 q^{94}+O(q^{100}) $ 24 * q + 304 * q^4 - 436 * q^7 + 1992 * q^10 - 3644 * q^16 + 3804 * q^19 - 5648 * q^22 - 18852 * q^25 - 39172 * q^28 + 38652 * q^31 + 20548 * q^37 + 132060 * q^40 + 2200 * q^43 - 25712 * q^46 - 125676 * q^49 - 2940 * q^52 + 154300 * q^58 + 48504 * q^61 - 327880 * q^64 + 156324 * q^67 - 9468 * q^70 - 703236 * q^73 + 165756 * q^79 + 1081020 * q^82 - 284448 * q^85 + 582308 * q^88 - 19812 * q^91 - 1481724 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	8.14327	−	4.70152i	1.43954	−	0.831119i	0.441723	−	0.897152i	$-0.354367\pi$
$2$	8.14327	−	4.70152i	1.43954	−	0.831119i	0.997817	+	0.0660327i	$0.0210342\pi$
$3$		0			0
$3$		0			0
$4$	28.2086	−	48.8587i	0.881517	−	1.52683i
$5$	−33.1882	−	57.4837i	−0.593689	−	1.02830i	−0.993730	−	0.111802i	$-0.964338\pi$
$5$	−33.1882	−	57.4837i	−0.593689	−	1.02830i	0.400042	−	0.916497i	$-0.368996\pi$
$6$		0			0
$7$	−116.271	−	57.3420i	−0.896862	−	0.442311i
$7$	−116.271	−	57.3420i	−0.896862	−	0.442311i
$8$		−	229.595i		−	1.26835i
$9$		0			0
$10$	−540.521	−	312.070i	−1.70928	−	0.986852i
$11$	383.606	+	221.475i	0.955880	+	0.551877i	0.894902	−	0.446262i	$-0.147245\pi$
$11$	383.606	+	221.475i	0.955880	+	0.551877i	0.0609771	+	0.998139i	$0.480578\pi$
$12$		0			0
$13$		−	437.107i		−	0.717347i	−0.933463	−	0.358673i	$-0.883229\pi$
$13$		−	437.107i		−	0.717347i	0.933463	−	0.358673i	$-0.116771\pi$
$14$	−1216.42	+	79.6982i	−1.65868	+	0.108675i
$15$		0			0
$16$	−176.771	−	306.177i	−0.172628	−	0.299001i
$17$	476.524	−	825.364i	0.399910	−	0.692665i	−0.593804	−	0.804609i	$-0.702375\pi$
$17$	476.524	−	825.364i	0.399910	−	0.692665i	0.993714	+	0.111945i	$0.0357080\pi$
$18$		0			0
$19$	1934.59	−	1116.94i	1.22943	−	0.709813i	0.262522	−	0.964926i	$-0.415446\pi$
$19$	1934.59	−	1116.94i	1.22943	−	0.709813i	0.966911	+	0.255113i	$0.0821126\pi$
$20$	−3744.77			−2.09339
$21$		0			0
$22$	4165.07			1.83470
$23$	−2096.62	+	1210.49i	−0.826420	+	0.477134i	−0.852625	−	0.522523i	$-0.824991\pi$
$23$	−2096.62	+	1210.49i	−0.826420	+	0.477134i	0.0262052	+	0.999657i	$0.491658\pi$
$24$		0			0
$25$	−640.416	+	1109.23i	−0.204933	+	0.354954i
$26$	−2055.06	−	3559.48i	−0.596200	−	1.03265i
$27$		0			0
$28$	−6081.48	+	4063.30i	−1.46593	+	0.979454i
$29$			6381.19i			1.40899i	0.709711	+	0.704493i	$0.248826\pi$
$29$			6381.19i			1.40899i	−0.709711	+	0.704493i	$0.751174\pi$
$30$		0			0
$31$	5912.80	+	3413.76i	1.10507	+	0.638012i	0.937548	−	0.347857i	$-0.113091\pi$
$31$	5912.80	+	3413.76i	1.10507	+	0.638012i	0.167521	+	0.985869i	$0.446424\pi$
$32$	3483.73	+	2011.33i	0.601408	+	0.347223i
$33$		0			0
$34$		−	8961.54i		−	1.32949i
$35$	562.593	+	8586.75i	0.0776291	+	1.18484i
$36$		0			0
$37$	−7604.18	−	13170.8i	−0.913163	−	1.58164i	−0.809569	−	0.587025i	$-0.800299\pi$
$37$	−7604.18	−	13170.8i	−0.913163	−	1.58164i	−0.103594	−	0.994620i	$-0.533034\pi$
$38$	10502.6	−	18191.0i	1.17988	−	2.04361i
$39$		0			0
$40$	−13198.0	+	7619.85i	−1.30424	+	0.753002i
$41$	1729.95			0.160722			0.0803609	−	0.996766i	$-0.474393\pi$
$41$	1729.95			0.160722			0.0803609	+	0.996766i	$0.474393\pi$
$42$		0			0
$43$	13717.1			1.13133			0.565666	−	0.824634i	$-0.308619\pi$
$43$	13717.1			1.13133			0.565666	+	0.824634i	$0.308619\pi$
$44$	21641.9	−	12495.0i	1.68525	−	0.972979i
$45$		0			0
$46$	−11382.2	+	19714.6i	−0.793110	+	1.37371i
$47$	−9079.05	−	15725.4i	−0.599509	−	1.03838i	−0.992894	−	0.119006i	$-0.962029\pi$
$47$	−9079.05	−	15725.4i	−0.599509	−	1.03838i	0.393384	−	0.919374i	$-0.371304\pi$
$48$		0			0
$49$	10230.8	+	13334.4i	0.608722	+	0.793383i
$50$			12043.7i			0.681295i
$51$		0			0
$52$	−21356.4	−	12330.1i	−1.09527	−	0.632353i
$53$	20788.0	+	12002.0i	1.01654	+	0.586898i	0.913099	−	0.407738i	$-0.133682\pi$
$53$	20788.0	+	12002.0i	1.01654	+	0.586898i	0.103439	+	0.994636i	$0.467015\pi$
$54$		0			0
$55$		−	29401.4i		−	1.31057i
$56$	−13165.4	+	26695.2i	−0.561003	+	1.13753i
$57$		0			0
$58$	30001.3	+	51963.8i	1.17104	+	2.02829i
$59$	−21226.0	+	36764.5i	−0.793850	+	1.37499i	0.129718	+	0.991551i	$0.458593\pi$
$59$	−21226.0	+	36764.5i	−0.793850	+	1.37499i	−0.923567	+	0.383437i	$0.874740\pi$
$60$		0			0
$61$	−17731.8	+	10237.5i	−0.610139	+	0.352264i	−0.773020	−	0.634382i	$-0.781255\pi$
$61$	−17731.8	+	10237.5i	−0.610139	+	0.352264i	0.162881	+	0.986646i	$0.447921\pi$
$62$	64199.4			2.12105
$63$		0			0
$64$	49138.6			1.49959
$65$	−25126.5	+	14506.8i	−0.737647	+	0.425881i
$66$		0			0
$67$	−290.744	+	503.584i	−0.00791269	+	0.0137052i	−0.869955	−	0.493132i	$-0.835852\pi$
$67$	−290.744	+	503.584i	−0.00791269	+	0.0137052i	0.862042	+	0.506837i	$0.169185\pi$
$68$	−26884.1	−	46564.6i	−0.705055	−	1.22119i
$69$		0			0
$70$	44952.1	+	67279.2i	1.09649	+	1.64110i
$71$			32681.9i			0.769416i	0.923038	+	0.384708i	$0.125698\pi$
$71$			32681.9i			0.769416i	−0.923038	+	0.384708i	$0.874302\pi$
$72$		0			0
$73$	−47409.2	−	27371.7i	−1.04125	−	0.601167i	−0.121064	−	0.992645i	$-0.538631\pi$
$73$	−47409.2	−	27371.7i	−1.04125	−	0.601167i	−0.920187	+	0.391478i	$0.871964\pi$
$74$	−123846.	−	71502.4i	−2.62907	−	1.51789i
$75$		0			0
$76$		−	126029.i		−	2.50285i
$77$	−31902.3	−	47747.7i	−0.613191	−	0.917753i
$78$		0			0
$79$	−18594.6	−	32206.7i	−0.335211	−	0.580603i	0.648314	−	0.761373i	$-0.275474\pi$
$79$	−18594.6	−	32206.7i	−0.335211	−	0.580603i	−0.983525	+	0.180770i	$0.942141\pi$
$80$	−11733.5	+	20322.9i	−0.204975	+	0.355027i
$81$		0			0
$82$	14087.5	−	8133.41i	0.231365	−	0.133579i
$83$	44677.3			0.711855			0.355928	−	0.934514i	$-0.384165\pi$
$83$	44677.3			0.711855			0.355928	+	0.934514i	$0.384165\pi$
$84$		0			0
$85$	−63259.9			−0.949689
$86$	111702.	−	64491.0i	1.62860	−	0.940271i
$87$		0			0
$88$	50849.5	−	88073.9i	0.699971	−	1.21239i
$89$	−12075.8	−	20915.9i	−0.161600	−	0.279899i	0.773843	−	0.633378i	$-0.218332\pi$
$89$	−12075.8	−	20915.9i	−0.161600	−	0.279899i	−0.935443	+	0.353479i	$0.884999\pi$
$90$		0			0
$91$	−25064.6	+	50822.7i	−0.317290	+	0.643361i
$92$			136584.i			1.68241i
$93$		0			0
$94$	−147866.	−	85370.6i	−1.72603	−	0.996527i
$95$	−128411.	−	74138.2i	−1.45980	−	0.842817i
$96$		0			0
$97$		−	28906.5i		−	0.311937i	−0.987762	−	0.155968i	$-0.950150\pi$
$97$		−	28906.5i		−	0.311937i	0.987762	−	0.155968i	$-0.0498498\pi$
$98$	146004.	+	60485.3i	1.53568	+	0.636186i
$99$		0			0
$100$	36130.4	+	62579.7i	0.361304	+	0.625797i
$101$	−49025.4	+	84914.5i	−0.478209	+	0.828283i	−0.999688	−	0.0249816i	$-0.992047\pi$
$101$	−49025.4	+	84914.5i	−0.478209	+	0.828283i	0.521479	+	0.853264i	$0.325381\pi$
$102$		0			0
$103$	−101433.	+	58562.5i	−0.942078	+	0.543909i	−0.890611	−	0.454766i	$-0.849723\pi$
$103$	−101433.	+	58562.5i	−0.942078	+	0.543909i	−0.0514670	+	0.998675i	$0.516390\pi$
$104$	−100357.			−0.909843
$105$		0			0
$106$	225710.			1.95113
$107$	93124.6	−	53765.5i	0.786330	−	0.453988i	−0.0523390	−	0.998629i	$-0.516668\pi$
$107$	93124.6	−	53765.5i	0.786330	−	0.453988i	0.838669	+	0.544642i	$0.183334\pi$
$108$		0			0
$109$	6225.96	−	10783.7i	0.0501927	−	0.0869362i	−0.839837	−	0.542838i	$-0.817350\pi$
$109$	6225.96	−	10783.7i	0.0501927	−	0.0869362i	0.890030	+	0.455902i	$0.150683\pi$
$110$	−138231.	−	239424.i	−1.08924	−	1.88662i
$111$		0			0
$112$	2996.56	+	45735.9i	0.0225724	+	0.344518i
$113$		−	11586.2i		−	0.0853583i	−0.999089	−	0.0426792i	$-0.986411\pi$
$113$		−	11586.2i		−	0.0853583i	0.999089	−	0.0426792i	$-0.0135893\pi$
$114$		0			0
$115$	139166.	+	80347.8i	0.981273	+	0.566538i
$116$	311777.	+	180004.i	2.15129	+	1.24205i
$117$		0			0
$118$			399178.i			2.63913i
$119$	−102734.	+	68640.9i	−0.665037	+	0.444340i
$120$		0			0
$121$	17576.6	+	30443.6i	0.109137	+	0.189031i
$122$	−96263.4	+	166733.i	−0.585547	+	1.01420i
$123$		0			0
$124$	333583.	−	192594.i	1.94827	−	1.12484i
$125$	−122409.			−0.700712
$126$		0			0
$127$	−79605.0			−0.437957			−0.218978	−	0.975730i	$-0.570272\pi$
$127$	−79605.0			−0.437957			−0.218978	+	0.975730i	$0.570272\pi$
$128$	288670.	−	166664.i	1.55731	−	0.899116i
$129$		0			0
$130$	−136408.	+	236265.i	−0.707915	+	1.22614i
$131$	94339.7	+	163401.i	0.480304	+	0.831911i	0.999745	−	0.0225953i	$-0.00719291\pi$
$131$	94339.7	+	163401.i	0.480304	+	0.831911i	−0.519440	+	0.854507i	$0.673860\pi$
$132$		0			0
$133$	−288984.	+	18933.8i	−1.41659	+	0.0928132i
$134$			5467.76i			0.0263055i
$135$		0			0
$136$	−189499.	−	109407.i	−0.878538	−	0.507224i
$137$	242004.	+	139721.i	1.10159	+	0.636006i	0.936639	−	0.350295i	$-0.113919\pi$
$137$	242004.	+	139721.i	1.10159	+	0.636006i	0.164955	+	0.986301i	$0.447252\pi$
$138$		0			0
$139$		−	297273.i		−	1.30502i	−0.757778	−	0.652512i	$-0.773715\pi$
$139$		−	297273.i		−	1.30502i	0.757778	−	0.652512i	$-0.226285\pi$
$140$	435407.	+	214732.i	1.87748	+	0.925928i
$141$		0			0
$142$	153654.	+	266137.i	0.639476	+	1.10760i
$143$	96808.1	−	167677.i	0.395887	−	0.685697i
$144$		0			0
$145$	366815.	−	211780.i	1.44886	−	0.836500i
$146$	−514755.			−1.99856
$147$		0			0
$148$	−858012.			−3.21988
$149$	35158.2	−	20298.6i	0.129736	−	0.0749033i	−0.433727	−	0.901044i	$-0.642802\pi$
$149$	35158.2	−	20298.6i	0.129736	−	0.0749033i	0.563464	+	0.826141i	$0.309469\pi$
$150$		0			0
$151$	29119.5	−	50436.5i	0.103930	−	0.180012i	−0.809370	−	0.587298i	$-0.800191\pi$
$151$	29119.5	−	50436.5i	0.103930	−	0.180012i	0.913301	+	0.407286i	$0.133525\pi$
$152$	−256443.	−	444172.i	−0.900288	−	1.55935i
$153$		0			0
$154$	−484276.	−	238833.i	−1.64547	−	0.811509i
$155$		−	453186.i		−	1.51512i
$156$		0			0
$157$	423501.	+	244508.i	1.37121	+	0.791671i	0.991081	−	0.133261i	$-0.0425447\pi$
$157$	423501.	+	244508.i	1.37121	+	0.791671i	0.380133	+	0.924932i	$0.375878\pi$
$158$	−302841.	−	174845.i	−0.965100	−	0.557201i
$159$		0			0
$160$		−	267010.i		−	0.824570i
$161$	313188.	−	20519.7i	0.952226	−	0.0623887i
$162$		0			0
$163$	54486.7	+	94373.8i	0.160628	+	0.278216i	0.935094	−	0.354399i	$-0.115315\pi$
$163$	54486.7	+	94373.8i	0.160628	+	0.278216i	−0.774466	+	0.632616i	$0.781981\pi$
$164$	48799.5	−	84523.2i	0.141679	−	0.245395i
$165$		0			0
$166$	363819.	−	210051.i	1.02474	−	0.591636i
$167$	−78858.6			−0.218805			−0.109403	−	0.993998i	$-0.534894\pi$
$167$	−78858.6			−0.218805			−0.109403	+	0.993998i	$0.534894\pi$
$168$		0			0
$169$	180231.			0.485414
$170$	−515142.	+	297418.i	−1.36712	+	0.789304i
$171$		0			0
$172$	386939.	−	670197.i	0.997289	−	1.72735i
$173$	211590.	+	366485.i	0.537502	+	0.930980i	0.999038	+	0.0438588i	$0.0139652\pi$
$173$	211590.	+	366485.i	0.537502	+	0.930980i	−0.461536	+	0.887121i	$0.652701\pi$
$174$		0			0
$175$	138067.	−	92248.6i	0.340797	−	0.227701i
$176$		−	156602.i		−	0.381079i
$177$		0			0
$178$	−196673.	−	113549.i	−0.465259	−	0.268617i
$179$	−287231.	−	165833.i	−0.670036	−	0.386846i	0.126054	−	0.992023i	$-0.459769\pi$
$179$	−287231.	−	165833.i	−0.670036	−	0.386846i	−0.796090	+	0.605178i	$0.793102\pi$
$180$		0			0
$181$			469062.i			1.06423i	0.846673	+	0.532113i	$0.178602\pi$
$181$			469062.i			1.06423i	−0.846673	+	0.532113i	$0.821398\pi$
$182$	34836.6	+	531705.i	0.0779575	+	1.18985i
$183$		0			0
$184$	277922.	+	481374.i	0.605170	+	1.04819i
$185$	−504738.	+	874233.i	−1.08427	+	1.87801i
$186$		0			0
$187$	365594.	−	211076.i	0.764532	−	0.441403i
$188$	−1.02443e6			−2.11391
$189$		0			0
$190$	−1.39425e6			−2.80192
$191$	243913.	−	140823.i	0.483784	−	0.279313i	−0.238208	−	0.971214i	$-0.576560\pi$
$191$	243913.	−	140823.i	0.483784	−	0.279313i	0.721992	+	0.691901i	$0.243227\pi$
$192$		0			0
$193$	−301997.	+	523075.i	−0.583593	+	1.01081i	0.411456	+	0.911429i	$0.365020\pi$
$193$	−301997.	+	523075.i	−0.583593	+	1.01081i	−0.995049	+	0.0993830i	$0.968313\pi$
$194$	−135905.	−	235394.i	−0.259256	−	0.449045i
$195$		0			0
$196$	940096.	−	123719.i	1.74796	−	0.230036i
$197$		−	14019.1i		−	0.0257369i	−0.999917	−	0.0128684i	$-0.995904\pi$
$197$		−	14019.1i		−	0.0257369i	0.999917	−	0.0128684i	$-0.00409626\pi$
$198$		0			0
$199$	357535.	+	206423.i	0.640008	+	0.369509i	0.784618	−	0.619980i	$-0.212859\pi$
$199$	357535.	+	206423.i	0.640008	+	0.369509i	−0.144610	+	0.989489i	$0.546193\pi$
$200$	254674.	+	147036.i	0.450205	+	0.259926i
$201$		0			0
$202$			921976.i			1.58979i
$203$	365910.	−	741947.i	0.623210	−	1.26367i
$204$		0			0
$205$	−57414.1	−	99444.1i	−0.0954187	−	0.165270i
$206$	−550665.	+	953780.i	−0.904106	+	1.56596i
$207$		0			0
$208$	−133832.	+	77267.9i	−0.214487	+	0.123834i
$209$	989492.			1.56692
$210$		0			0
$211$	729963.			1.12874			0.564371	−	0.825521i	$-0.309119\pi$
$211$	729963.			1.12874			0.564371	+	0.825521i	$0.309119\pi$
$212$	1.17280e6	−	677116.i	1.79219	−	1.03472i
$213$		0			0
$214$	505559.	−	875654.i	0.754636	−	1.30707i
$215$	−455245.	−	788507.i	−0.671659	−	1.16335i
$216$		0			0
$217$	−491735.	−	735972.i	−0.708894	−	1.06099i
$218$		−	117086.i		−	0.166864i
$219$		0			0
$220$	−1.43651e6	−	829371.i	−2.00103	−	1.15529i
$221$	−360772.	−	208292.i	−0.496881	−	0.286874i
$222$		0			0
$223$		−	494953.i		−	0.666503i	−0.942838	−	0.333251i	$-0.891854\pi$
$223$		−	494953.i		−	0.666503i	0.942838	−	0.333251i	$-0.108146\pi$
$224$	−289722.	−	433623.i	−0.385800	−	0.577421i
$225$		0			0
$226$	−54472.8	−	94349.7i	−0.0709429	−	0.122877i
$227$	141019.	−	244252.i	0.181641	−	0.314611i	−0.760799	−	0.648988i	$-0.775192\pi$
$227$	141019.	−	244252.i	0.181641	−	0.314611i	0.942439	+	0.334377i	$0.108526\pi$
$228$		0			0
$229$	−971368.	+	560820.i	−1.22404	+	0.706699i	−0.965777	−	0.259376i	$-0.916483\pi$
$229$	−971368.	+	560820.i	−1.22404	+	0.706699i	−0.258262	+	0.966075i	$0.583150\pi$
$230$	1.51103e6			1.88344
$231$		0			0
$232$	1.46509e6			1.78708
$233$	81173.9	−	46865.8i	0.0979550	−	0.0565544i	−0.450222	−	0.892917i	$-0.648655\pi$
$233$	81173.9	−	46865.8i	0.0979550	−	0.0565544i	0.548177	+	0.836362i	$0.315322\pi$
$234$		0			0
$235$	−602635.	+	1.04379e6i	−0.711844	+	1.23295i
$236$	1.19751e6	+	2.07415e6i	1.39958	+	2.42415i
$237$		0			0
$238$	−513873.	+	1.04197e6i	−0.588048	+	1.19237i
$239$			666306.i			0.754534i	0.926104	+	0.377267i	$0.123136\pi$
$239$			666306.i			0.754534i	−0.926104	+	0.377267i	$0.876864\pi$
$240$		0			0
$241$	−154322.	−	89097.9i	−0.171153	−	0.0988155i	0.411976	−	0.911195i	$-0.364839\pi$
$241$	−154322.	−	89097.9i	−0.171153	−	0.0988155i	−0.583130	+	0.812379i	$0.698172\pi$
$242$	286263.	+	165274.i	0.314214	+	0.181412i
$243$		0			0
$244$			1.15514e6i			1.24211i
$245$	426968.	−	1.03065e6i	0.454444	−	1.09697i
$246$		0			0
$247$	−488220.	−	845622.i	−0.509182	−	0.881929i
$248$	783782.	−	1.35755e6i	0.809219	−	1.40161i
$249$		0			0
$250$	−996812.	+	575510.i	−1.00870	+	0.582375i
$251$	265419.			0.265918			0.132959	−	0.991122i	$-0.457552\pi$
$251$	265419.			0.265918			0.132959	+	0.991122i	$0.457552\pi$
$252$		0			0
$253$	−1.07237e6			−1.05328
$254$	−648245.	+	374264.i	−0.630456	+	0.363994i
$255$		0			0
$256$	780926.	−	1.35260e6i	0.744749	−	1.28994i
$257$	349659.	+	605628.i	0.330227	+	0.571969i	0.982556	−	0.185966i	$-0.0595415\pi$
$257$	349659.	+	605628.i	0.330227	+	0.571969i	−0.652329	+	0.757936i	$0.726208\pi$
$258$		0			0
$259$	128903.	+	1.96742e6i	0.119403	+	1.82242i
$260$			1.63686e6i			1.50168i
$261$		0			0
$262$	1.53647e6	+	887080.i	1.38283	+	0.798380i
$263$	−1.51168e6	−	872769.i	−1.34763	−	0.778054i	−0.359716	−	0.933062i	$-0.617127\pi$
$263$	−1.51168e6	−	872769.i	−1.34763	−	0.778054i	−0.987913	+	0.155007i	$0.950460\pi$
$264$		0			0
$265$		−	1.59330e6i		−	1.39374i
$266$	−2.26425e6	+	1.51284e6i	−1.96210	+	1.31096i
$267$		0			0
$268$	16402.9	+	28410.7i	0.0139503	+	0.0241627i
$269$	83991.2	−	145477.i	0.0707707	−	0.122578i	−0.828469	−	0.560036i	$-0.810787\pi$
$269$	83991.2	−	145477.i	0.0707707	−	0.122578i	0.899239	+	0.437457i	$0.144121\pi$
$270$		0			0
$271$	1.69618e6	−	979291.i	1.40297	−	0.810006i	0.408275	−	0.912859i	$-0.366130\pi$
$271$	1.69618e6	−	979291.i	1.40297	−	0.810006i	0.994697	+	0.102853i	$0.0327970\pi$
$272$	−336943.			−0.276143
$273$		0			0
$274$	2.62761e6			2.11439
$275$	−491334.	+	283672.i	−0.391783	+	0.226196i
$276$		0			0
$277$	−924728.	+	1.60168e6i	−0.724126	+	1.25422i	0.235206	+	0.971946i	$0.424423\pi$
$277$	−924728.	+	1.60168e6i	−0.724126	+	1.25422i	−0.959333	+	0.282278i	$0.908910\pi$
$278$	−1.39764e6	−	2.42078e6i	−1.08463	−	1.87864i
$279$		0			0
$280$	1.97148e6	−	129169.i	1.50278	−	0.0984605i
$281$			431966.i			0.326350i	0.986597	+	0.163175i	$0.0521735\pi$
$281$			431966.i			0.326350i	−0.986597	+	0.163175i	$0.947826\pi$
$282$		0			0
$283$	−288875.	−	166782.i	−0.214409	−	0.123789i	0.388950	−	0.921259i	$-0.372838\pi$
$283$	−288875.	−	166782.i	−0.214409	−	0.123789i	−0.603359	+	0.797470i	$0.706171\pi$
$284$	1.59679e6	+	921908.i	1.17477	+	0.678253i
$285$		0			0
$286$		−	1.82058e6i		−	1.31612i
$287$	−201143.	−	99198.9i	−0.144145	−	0.0710890i
$288$		0			0
$289$	255779.	+	443021.i	0.180144	+	0.312018i
$290$	1.99138e6	−	3.44917e6i	1.39046	−	2.40835i
$291$		0			0
$292$	−2.67469e6	+	1.54423e6i	−1.83576	+	1.05988i
$293$	−1.89373e6			−1.28869			−0.644347	−	0.764733i	$-0.722871\pi$
$293$	−1.89373e6			−1.28869			−0.644347	+	0.764733i	$0.722871\pi$
$294$		0			0
$295$	2.81781e6			1.88520
$296$	−3.02396e6	+	1.74588e6i	−2.00607	+	1.15821i
$297$		0			0
$298$	190869.	−	330594.i	0.124507	−	0.215653i
$299$	529112.	+	916448.i	0.342270	+	0.592830i
$300$		0			0
$301$	−1.59489e6	−	786564.i	−1.01465	−	0.500400i
$302$		−	547624.i		−	0.345513i
$303$		0			0
$304$	−683960.	−	394885.i	−0.424470	−	0.245068i
$305$	1.17698e6	+	679527.i	0.724466	+	0.418271i
$306$		0			0
$307$		−	2.37284e6i		−	1.43689i	−0.695585	−	0.718443i	$-0.744855\pi$
$307$		−	2.37284e6i		−	1.43689i	0.695585	−	0.718443i	$-0.255145\pi$
$308$	−3.23281e6	+	211810.i	−1.94179	+	0.127224i
$309$		0			0
$310$	−2.13066e6	−	3.69042e6i	−1.25925	−	2.18108i
$311$	−430680.	+	745960.i	−0.252496	+	0.437335i	−0.964212	−	0.265131i	$-0.914585\pi$
$311$	−430680.	+	745960.i	−0.252496	+	0.437335i	0.711717	+	0.702467i	$0.247918\pi$
$312$		0			0
$313$	−2.49997e6	+	1.44336e6i	−1.44236	+	0.832747i	−0.998007	−	0.0631051i	$-0.979900\pi$
$313$	−2.49997e6	+	1.44336e6i	−1.44236	+	0.832747i	−0.444353	+	0.895852i	$0.646566\pi$
$314$	4.59824e6			2.63189
$315$		0			0
$316$	−2.09810e6			−1.18198
$317$	−1.38969e6	+	802336.i	−0.776727	+	0.448444i	−0.835269	−	0.549841i	$-0.814688\pi$
$317$	−1.38969e6	+	802336.i	−0.776727	+	0.448444i	0.0585418	+	0.998285i	$0.481355\pi$
$318$		0			0
$319$	−1.41327e6	+	2.44786e6i	−0.777588	+	1.34682i
$320$	−1.63082e6	−	2.82467e6i	−0.890291	−	1.54203i
$321$		0			0
$322$	2.45390e6	−	1.63956e6i	1.31892	−	0.881224i
$323$		−	2.12899e6i		−	1.13545i
$324$		0			0
$325$	484853.	+	279930.i	0.254625	+	0.147008i
$326$	887400.	+	512341.i	0.462461	+	0.267002i
$327$		0			0
$328$		−	397189.i		−	0.203851i
$329$	153904.	+	2.34901e6i	0.0783901	+	1.19645i
$330$		0			0
$331$	−1.05295e6	−	1.82376e6i	−0.528248	−	0.914952i	−0.999458	−	0.0329309i	$-0.989516\pi$
$331$	−1.05295e6	−	1.82376e6i	−0.528248	−	0.914952i	0.471210	−	0.882021i	$-0.343817\pi$
$332$	1.26028e6	−	2.18287e6i	0.627513	−	1.08688i
$333$		0			0
$334$	−642167.	+	370755.i	−0.314979	+	0.181853i
$335$	38597.1			0.0187907
$336$		0			0
$337$	3.17015e6			1.52056			0.760282	−	0.649593i	$-0.225061\pi$
$337$	3.17015e6			1.52056			0.760282	+	0.649593i	$0.225061\pi$
$338$	1.46767e6	−	847358.i	0.698773	−	0.403437i
$339$		0			0
$340$	−1.78447e6	+	3.09079e6i	−0.837167	+	1.45002i
$341$	1.51212e6	+	2.61907e6i	0.704208	+	1.21972i
$342$		0			0
$343$	−424923.	−	2.13705e6i	−0.195018	−	0.980800i
$344$		−	3.14937e6i		−	1.43492i
$345$		0			0
$346$	3.44607e6	+	1.98959e6i	1.54751	+	0.893456i
$347$	−1.65067e6	−	953013.i	−0.735928	−	0.424888i	0.0846587	−	0.996410i	$-0.473020\pi$
$347$	−1.65067e6	−	953013.i	−0.735928	−	0.424888i	−0.820587	+	0.571522i	$0.806353\pi$
$348$		0			0
$349$		−	3.96883e6i		−	1.74421i	−0.489317	−	0.872106i	$-0.662754\pi$
$349$		−	3.96883e6i		−	1.74421i	0.489317	−	0.872106i	$-0.337246\pi$
$350$	690610.	−	1.40033e6i	0.301344	−	0.611027i
$351$		0			0
$352$	890919.	+	1.54312e6i	0.383249	+	0.663807i
$353$	−1.18997e6	+	2.06109e6i	−0.508275	+	0.880359i	0.491679	+	0.870777i	$0.336383\pi$
$353$	−1.18997e6	+	2.06109e6i	−0.508275	+	0.880359i	−0.999954	+	0.00958205i	$0.996950\pi$
$354$		0			0
$355$	1.87867e6	−	1.08465e6i	0.791190	−	0.456794i
$356$	−1.36256e6			−0.569812
$357$		0			0
$358$	−3.11866e6			−1.28606
$359$	2.27068e6	−	1.31098e6i	0.929865	−	0.536858i	0.0430964	−	0.999071i	$-0.486278\pi$
$359$	2.27068e6	−	1.31098e6i	0.929865	−	0.536858i	0.886769	+	0.462213i	$0.152944\pi$
$360$		0			0
$361$	1.25704e6	−	2.17726e6i	0.507670	−	0.879310i
$362$	2.20530e6	+	3.81970e6i	0.884498	+	1.53200i
$363$		0			0
$364$	1.77610e6	+	2.65826e6i	0.702608	+	1.05158i
$365$			3.63367e6i			1.42762i
$366$		0			0
$367$	2.12630e6	+	1.22762e6i	0.824060	+	0.475771i	0.851815	−	0.523844i	$-0.175502\pi$
$367$	2.12630e6	+	1.22762e6i	0.824060	+	0.475771i	−0.0277546	+	0.999615i	$0.508836\pi$
$368$	741246.	+	427959.i	0.285327	+	0.164734i
$369$		0			0
$370$			9.49215e6i			3.60463i
$371$	−1.72882e6	−	2.58750e6i	−0.652102	−	0.975992i
$372$		0			0
$373$	1.60705e6	+	2.78349e6i	0.598077	+	1.03590i	0.993105	+	0.117231i	$0.0374018\pi$
$373$	1.60705e6	+	2.78349e6i	0.598077	+	1.03590i	−0.395027	+	0.918669i	$0.629265\pi$
$374$	1.98476e6	−	3.43770e6i	0.733716	−	1.27083i
$375$		0			0
$376$	−3.61047e6	+	2.08450e6i	−1.31702	+	0.760384i
$377$	2.78926e6			1.01073
$378$		0			0
$379$	−1.46777e6			−0.524879			−0.262440	−	0.964948i	$-0.584527\pi$
$379$	−1.46777e6			−0.524879			−0.262440	+	0.964948i	$0.584527\pi$
$380$	−7.24459e6	+	4.18266e6i	−2.57368	+	1.48591i
$381$		0			0
$382$	1.32417e6	−	2.29352e6i	0.464284	−	0.804164i
$383$	1.22044e6	+	2.11387e6i	0.425129	+	0.736345i	0.996432	−	0.0843939i	$-0.0268954\pi$
$383$	1.22044e6	+	2.11387e6i	0.425129	+	0.736345i	−0.571304	+	0.820739i	$0.693562\pi$
$384$		0			0
$385$	−1.68593e6	+	3.41853e6i	−0.579681	+	1.17540i
$386$			5.67939e6i			1.94014i
$387$		0			0
$388$	−1.41233e6	−	815411.i	−0.476275	−	0.274978i
$389$	−295356.	−	170524.i	−0.0989629	−	0.0571362i	0.449702	−	0.893179i	$-0.351530\pi$
$389$	−295356.	−	170524.i	−0.0989629	−	0.0571362i	−0.548665	+	0.836043i	$0.684864\pi$
$390$		0			0
$391$			2.30730e6i			0.763243i
$392$	3.06151e6	−	2.34894e6i	1.00628	−	0.772070i
$393$		0			0
$394$	−65911.2	−	114162.i	−0.0213904	−	0.0370492i
$395$	−1.23424e6	+	2.13777e6i	−0.398022	+	0.689395i
$396$		0			0
$397$	−185747.	+	107241.i	−0.0591488	+	0.0341496i	−0.529283	−	0.848445i	$-0.677539\pi$
$397$	−185747.	+	107241.i	−0.0591488	+	0.0341496i	0.470134	+	0.882595i	$0.344206\pi$
$398$	3.88200e6			1.22842
$399$		0			0
$400$	452829.			0.141509
$401$	−1.94476e6	+	1.12281e6i	−0.603957	+	0.348695i	−0.770597	−	0.637323i	$-0.780042\pi$
$401$	−1.94476e6	+	1.12281e6i	−0.603957	+	0.348695i	0.166640	+	0.986018i	$0.446708\pi$
$402$		0			0
$403$	1.49218e6	−	2.58453e6i	0.457675	−	0.792717i
$404$	2.76587e6	+	4.79063e6i	0.843099	+	1.46029i
$405$		0			0
$406$	−508570.	−	7.76220e6i	−0.153121	−	2.33706i
$407$		−	6.73654e6i		−	2.01582i
$408$		0			0
$409$	−938943.	−	542099.i	−0.277543	−	0.160240i	0.354767	−	0.934955i	$-0.384560\pi$
$409$	−938943.	−	542099.i	−0.277543	−	0.160240i	−0.632311	+	0.774715i	$0.717893\pi$
$410$	−935076.	−	539866.i	−0.274718	−	0.158609i
$411$		0			0
$412$			6.60785e6i			1.91786i
$413$	4.57611e6	−	3.05750e6i	1.32015	−	0.882046i
$414$		0			0
$415$	−1.48276e6	−	2.56822e6i	−0.422621	−	0.732000i
$416$	879167.	−	1.52276e6i	0.249079	−	0.431418i
$417$		0			0
$418$	8.05770e6	−	4.65212e6i	2.25564	−	1.30230i
$419$	−5.00675e6			−1.39322			−0.696612	−	0.717448i	$-0.745310\pi$
$419$	−5.00675e6			−1.39322			−0.696612	+	0.717448i	$0.745310\pi$
$420$		0			0
$421$	−3.58647e6			−0.986192			−0.493096	−	0.869975i	$-0.664135\pi$
$421$	−3.58647e6			−0.986192			−0.493096	+	0.869975i	$0.664135\pi$
$422$	5.94429e6	−	3.43194e6i	1.62487	−	0.938119i
$423$		0			0
$424$	2.75559e6	−	4.77283e6i	0.744390	−	1.28932i
$425$	610347.	+	1.05715e6i	0.163910	+	0.283900i
$426$		0			0
$427$	2.64873e6	−	173542.i	0.703021	−	0.0460611i
$428$		−	6.06659e6i		−	1.60079i
$429$		0			0
$430$	−7.41436e6	−	4.28069e6i	−1.93376	−	1.11646i
$431$	−1.00224e6	−	578644.i	−0.259884	−	0.150044i	0.364398	−	0.931243i	$-0.381275\pi$
$431$	−1.00224e6	−	578644.i	−0.259884	−	0.150044i	−0.624281	+	0.781200i	$0.714608\pi$
$432$		0			0
$433$			3.11440e6i			0.798279i	0.916890	+	0.399140i	$0.130691\pi$
$433$			3.11440e6i			0.798279i	−0.916890	+	0.399140i	$0.869309\pi$
$434$	−7.46452e6	−	3.68132e6i	−1.90229	−	0.938165i
$435$		0			0
$436$	−351251.	−	608384.i	−0.0884914	−	0.153272i
$437$	−2.70407e6	+	4.68359e6i	−0.677352	+	1.17321i
$438$		0			0
$439$	−1.95943e6	+	1.13128e6i	−0.485254	+	0.280162i	−0.722603	−	0.691263i	$-0.757055\pi$
$439$	−1.95943e6	+	1.13128e6i	−0.485254	+	0.280162i	0.237349	+	0.971424i	$0.423721\pi$
$440$	−6.75042e6			−1.66226
$441$		0			0
$442$	−3.91715e6			−0.953706
$443$	1.62039e6	−	935535.i	0.392294	−	0.226491i	−0.290860	−	0.956766i	$-0.593941\pi$
$443$	1.62039e6	−	935535.i	0.392294	−	0.226491i	0.683154	+	0.730275i	$0.260608\pi$
$444$		0			0
$445$	−801548.	+	1.38832e6i	−0.191880	+	0.332346i
$446$	−2.32703e6	−	4.03054e6i	−0.553943	−	0.959457i
$447$		0			0
$448$	−5.71339e6	−	2.81771e6i	−1.34493	−	0.663286i
$449$		−	5.11523e6i		−	1.19743i	−0.800963	−	0.598714i	$-0.795679\pi$
$449$		−	5.11523e6i		−	1.19743i	0.800963	−	0.598714i	$-0.204321\pi$
$450$		0			0
$451$	663619.	+	383141.i	0.153631	+	0.0886987i
$452$	−566087.	−	326831.i	−0.130328	−	0.0752448i
$453$		0			0
$454$		−	2.65202e6i		−	0.603861i
$455$	3.75333e6	−	245913.i	0.849939	−	0.0556869i
$456$		0			0
$457$	−1.56673e6	−	2.71366e6i	−0.350916	−	0.607805i	0.635494	−	0.772106i	$-0.280796\pi$
$457$	−1.56673e6	−	2.71366e6i	−0.350916	−	0.607805i	−0.986410	+	0.164301i	$0.947463\pi$
$458$	−5.27341e6	+	9.13381e6i	−1.17470	+	2.03464i
$459$		0			0
$460$	7.85137e6	−	4.53299e6i	1.73002	−	0.998826i
$461$	−1.57943e6			−0.346137			−0.173068	−	0.984910i	$-0.555368\pi$
$461$	−1.57943e6			−0.346137			−0.173068	+	0.984910i	$0.555368\pi$
$462$		0			0
$463$	−1.73622e6			−0.376402			−0.188201	−	0.982131i	$-0.560266\pi$
$463$	−1.73622e6			−0.376402			−0.188201	+	0.982131i	$0.560266\pi$
$464$	1.95377e6	−	1.12801e6i	0.421288	−	0.243231i
$465$		0			0
$466$	440681.	−	763281.i	0.0940068	−	0.162825i
$467$	−920630.	−	1.59458e6i	−0.195341	−	0.338340i	0.751671	−	0.659538i	$-0.229248\pi$
$467$	−920630.	−	1.59458e6i	−0.195341	−	0.338340i	−0.947012	+	0.321198i	$0.895915\pi$
$468$		0			0
$469$	62681.5	−	41880.2i	0.0131585	−	0.00879178i
$470$			1.13332e7i			2.36651i
$471$		0			0
$472$	8.44095e6	+	4.87338e6i	1.74396	+	1.00688i
$473$	5.26194e6	+	3.03798e6i	1.08142	+	0.624356i
$474$		0			0
$475$			2.86121e6i			0.581857i
$476$	455728.	+	6.95569e6i	0.0921910	+	1.40709i
$477$		0			0
$478$	3.13265e6	+	5.42591e6i	0.627108	+	1.08618i
$479$	2.47327e6	−	4.28383e6i	0.492530	−	0.853088i	−0.507433	−	0.861691i	$-0.669405\pi$
$479$	2.47327e6	−	4.28383e6i	0.492530	−	0.853088i	0.999963	+	0.00860373i	$0.00273869\pi$
$480$		0			0
$481$	−5.75706e6	+	3.32384e6i	−1.13459	+	0.655054i
$482$	−1.67558e6			−0.328510
$483$		0			0
$484$	1.98325e6			0.384825
$485$	−1.66165e6	+	959356.i	−0.320764	+	0.185193i
$486$		0			0
$487$	−1.49950e6	+	2.59722e6i	−0.286500	+	0.496233i	−0.972972	−	0.230924i	$-0.925825\pi$
$487$	−1.49950e6	+	2.59722e6i	−0.286500	+	0.496233i	0.686472	+	0.727157i	$0.259159\pi$
$488$	2.35047e6	+	4.07114e6i	0.446792	+	0.773867i
$489$		0			0
$490$	−1.36870e6	−	1.04002e7i	−0.257524	−	1.95683i
$491$		−	5.51530e6i		−	1.03244i	−0.856455	−	0.516221i	$-0.827338\pi$
$491$		−	5.51530e6i		−	1.03244i	0.856455	−	0.516221i	$-0.172662\pi$
$492$		0			0
$493$	5.26680e6	+	3.04079e6i	0.975955	+	0.563468i
$494$	−7.95141e6	−	4.59075e6i	−1.46598	−	0.846382i
$495$		0			0
$496$		−	2.41382e6i		−	0.440555i
$497$	1.87404e6	−	3.79995e6i	0.340321	−	0.690060i
$498$		0			0
$499$	987310.	+	1.71007e6i	0.177502	+	0.307442i	0.941024	−	0.338339i	$-0.109865\pi$
$499$	987310.	+	1.71007e6i	0.177502	+	0.307442i	−0.763523	+	0.645781i	$0.776532\pi$
$500$	−3.45299e6	+	5.98076e6i	−0.617690	+	1.06987i
$501$		0			0
$502$	2.16138e6	−	1.24787e6i	0.382799	−	0.221009i
$503$	−9.81653e6			−1.72997			−0.864984	−	0.501800i	$-0.832671\pi$
$503$	−9.81653e6			−1.72997			−0.864984	+	0.501800i	$0.832671\pi$
$504$		0			0
$505$	6.50827e6			1.13563
$506$	−8.73259e6	+	5.04176e6i	−1.51624	+	0.875399i
$507$		0			0
$508$	−2.24554e6	+	3.88939e6i	−0.386066	+	0.668686i
$509$	−4.74859e6	−	8.22480e6i	−0.812401	−	1.40712i	−0.911179	−	0.412010i	$-0.864827\pi$
$509$	−4.74859e6	−	8.22480e6i	−0.812401	−	1.40712i	0.0987782	−	0.995109i	$-0.468507\pi$
$510$		0			0
$511$	3.94276e6	+	5.90107e6i	0.667956	+	0.999720i
$512$		−	4.01968e6i		−	0.677667i
$513$		0			0
$514$	5.69474e6	+	3.28786e6i	0.950749	+	0.548915i
$515$	6.73277e6	+	3.88717e6i	1.11860	+	0.645826i
$516$		0			0
$517$		−	8.04312e6i		−	1.32342i
$518$	1.02996e7	+	1.54152e7i	1.68653	+	2.52421i
$519$		0			0
$520$	3.33069e6	+	5.76892e6i	0.540164	+	0.935591i
$521$	4.99494e6	−	8.65149e6i	0.806188	−	1.39636i	−0.109298	−	0.994009i	$-0.534860\pi$
$521$	4.99494e6	−	8.65149e6i	0.806188	−	1.39636i	0.915486	−	0.402349i	$-0.131806\pi$
$522$		0			0
$523$	5.77282e6	−	3.33294e6i	0.922856	−	0.532811i	0.0383108	−	0.999266i	$-0.487802\pi$
$523$	5.77282e6	−	3.33294e6i	0.922856	−	0.532811i	0.884545	+	0.466455i	$0.154469\pi$
$524$	1.06448e7			1.69359
$525$		0			0
$526$	−1.64134e7			−2.58662
$527$	5.63518e6	−	3.25347e6i	0.883856	−	0.510295i
$528$		0			0
$529$	−287618.	+	498168.i	−0.0446865	+	0.0773993i
$530$	−7.49091e6	−	1.29746e7i	−1.15836	−	2.00634i
$531$		0			0
$532$	−7.22673e6	+	1.46534e7i	−1.10704	+	2.24471i
$533$		−	756174.i		−	0.115293i
$534$		0			0
$535$	−6.18128e6	−	3.56876e6i	−0.933671	−	0.539055i
$536$	115620.	+	66753.4i	0.0173829	+	0.0100360i
$537$		0			0
$538$		−	1.57955e6i		−	0.235275i
$539$	971359.	+	7.38101e6i	0.144015	+	1.09432i
$540$		0			0
$541$	−1.73070e6	−	2.99766e6i	−0.254231	−	0.440341i	0.710456	−	0.703742i	$-0.248489\pi$
$541$	−1.73070e6	−	2.99766e6i	−0.254231	−	0.440341i	−0.964686	+	0.263401i	$0.915156\pi$
$542$	9.20831e6	−	1.59493e7i	1.34642	−	2.33207i
$543$		0			0
$544$	3.32016e6	−	1.91690e6i	0.481018	−	0.277716i
$545$	−826514.			−0.119195
$546$		0			0
$547$	−6.12419e6			−0.875146			−0.437573	−	0.899183i	$-0.644162\pi$
$547$	−6.12419e6			−0.875146			−0.437573	+	0.899183i	$0.644162\pi$
$548$	1.36532e7	−	7.88267e6i	1.94215	−	1.12130i
$549$		0			0
$550$	−2.66738e6	+	4.62003e6i	−0.375991	+	0.651236i
$551$	7.12738e6	+	1.23450e7i	1.00012	+	1.73225i
$552$		0			0
$553$	315208.	+	4.81095e6i	0.0438313	+	0.668988i
$554$			1.73905e7i			2.40734i
$555$		0			0
$556$	−1.45244e7	−	8.38565e6i	−1.99255	−	1.15040i
$557$	7.46159e6	+	4.30795e6i	1.01905	+	0.588346i	0.913827	−	0.406103i	$-0.133113\pi$
$557$	7.46159e6	+	4.30795e6i	1.01905	+	0.588346i	0.105218	+	0.994449i	$0.466446\pi$
$558$		0			0
$559$		−	5.99582e6i		−	0.811557i
$560$	2.52962e6	−	1.69015e6i	0.340867	−	0.227748i
$561$		0			0
$562$	2.03090e6	+	3.51762e6i	0.271236	+	0.469794i
$563$	−3.67238e6	+	6.36075e6i	−0.488288	+	0.845740i	−0.999909	−	0.0134710i	$-0.995712\pi$
$563$	−3.67238e6	+	6.36075e6i	−0.488288	+	0.845740i	0.511621	+	0.859211i	$0.329045\pi$
$564$		0			0
$565$	−666019.	+	384526.i	−0.0877739	+	0.0506763i
$566$	−3.13651e6			−0.411534
$567$		0			0
$568$	7.50359e6			0.975885
$569$	−7.23229e6	+	4.17556e6i	−0.936472	+	0.540672i	−0.888853	−	0.458193i	$-0.848497\pi$
$569$	−7.23229e6	+	4.17556e6i	−0.936472	+	0.540672i	−0.0476195	+	0.998866i	$0.515164\pi$
$570$		0			0
$571$	503910.	−	872798.i	0.0646789	−	0.112027i	−0.831873	−	0.554967i	$-0.812731\pi$
$571$	503910.	−	872798.i	0.0646789	−	0.112027i	0.896552	+	0.442939i	$0.146064\pi$
$572$	−5.46163e6	−	9.45982e6i	−0.697963	−	1.20891i
$573$		0			0
$574$	−2.10435e6	+	137874.i	−0.266586	+	0.0174664i
$575$		−	3.10086e6i		−	0.391122i
$576$		0			0
$577$	−8.77180e6	−	5.06440e6i	−1.09685	−	0.633269i	−0.161462	−	0.986879i	$-0.551621\pi$
$577$	−8.77180e6	−	5.06440e6i	−1.09685	−	0.633269i	−0.935393	+	0.353610i	$0.884954\pi$
$578$	4.16575e6	+	2.40510e6i	0.518649	+	0.299442i
$579$		0			0
$580$		−	2.38961e7i		−	2.94956i
$581$	−5.19466e6	−	2.56188e6i	−0.638436	−	0.314861i
$582$		0			0
$583$	5.31627e6	+	9.20804e6i	0.647792	+	1.12201i
$584$	−6.28441e6	+	1.08849e7i	−0.762487	+	1.32067i
$585$		0			0
$586$	−1.54212e7	+	8.90342e6i	−1.85513	+	1.07106i
$587$	1.07648e7			1.28947			0.644733	−	0.764408i	$-0.276969\pi$
$587$	1.07648e7			1.28947			0.644733	+	0.764408i	$0.276969\pi$
$588$		0			0
$589$	1.52518e7			1.81148
$590$	2.29462e7	−	1.32480e7i	2.71382	−	1.56682i
$591$		0			0
$592$	−2.68840e6	+	4.65645e6i	−0.315275	+	0.546073i
$593$	−3.25915e6	−	5.64502e6i	−0.380600	−	0.659218i	0.610549	−	0.791979i	$-0.290949\pi$
$593$	−3.25915e6	−	5.64502e6i	−0.380600	−	0.659218i	−0.991148	+	0.132761i	$0.957616\pi$
$594$		0			0
$595$	7.35528e6	+	3.62745e6i	0.851740	+	0.420058i
$596$		−	2.29038e6i		−	0.264114i
$597$		0			0
$598$	8.61740e6	+	4.97526e6i	0.985424	+	0.568935i
$599$	−2.97856e6	−	1.71967e6i	−0.339187	−	0.195830i	0.320725	−	0.947172i	$-0.396073\pi$
$599$	−2.97856e6	−	1.71967e6i	−0.339187	−	0.195830i	−0.659913	+	0.751342i	$0.729407\pi$
$600$		0			0
$601$			6.52015e6i			0.736329i	0.929761	+	0.368164i	$0.120014\pi$
$601$			6.52015e6i			0.736329i	−0.929761	+	0.368164i	$0.879986\pi$
$602$	−1.66857e7	+	1.09323e6i	−1.87652	+	0.122947i
$603$		0			0
$604$	−1.64284e6	−	2.84548e6i	−0.183233	−	0.317368i
$605$	1.16667e6	−	2.02074e6i	0.129587	−	0.224451i
$606$		0			0
$607$	−1.26515e6	+	730432.i	−0.139370	+	0.0804652i	−0.568064	−	0.822985i	$-0.692307\pi$
$607$	−1.26515e6	+	730432.i	−0.139370	+	0.0804652i	0.428694	+	0.903450i	$0.358974\pi$
$608$	8.98611e6			0.985855
$609$		0			0
$610$	1.27792e7			1.39053
$611$	−6.87367e6	+	3.96851e6i	−0.744878	+	0.430056i
$612$		0			0
$613$	8.22442e6	−	1.42451e7i	0.884004	−	1.53114i	0.0371523	−	0.999310i	$-0.488171\pi$
$613$	8.22442e6	−	1.42451e7i	0.884004	−	1.53114i	0.846851	−	0.531830i	$-0.178495\pi$
$614$	−1.11560e7	−	1.93227e7i	−1.19422	−	2.06846i
$615$		0			0
$616$	−1.09626e7	+	7.32461e6i	−1.16403	+	0.777737i
$617$			3.81821e6i			0.403782i	0.979408	+	0.201891i	$0.0647087\pi$
$617$			3.81821e6i			0.403782i	−0.979408	+	0.201891i	$0.935291\pi$
$618$		0			0
$619$	−2.61645e6	−	1.51061e6i	−0.274464	−	0.158462i	0.356450	−	0.934314i	$-0.383987\pi$
$619$	−2.61645e6	−	1.51061e6i	−0.274464	−	0.158462i	−0.630915	+	0.775852i	$0.717320\pi$
$620$	−2.21421e7	−	1.27837e7i	−2.31334	−	1.33561i
$621$		0			0
$622$			8.09940e6i			0.839416i
$623$	204704.	+	3.12436e6i	0.0211303	+	0.322508i
$624$		0			0
$625$	6.06385e6	+	1.05029e7i	0.620938	+	1.07550i
$626$	−1.35719e7	+	2.35073e7i	−1.38422	+	2.39754i
$627$		0			0
$628$	2.38927e7	−	1.37945e7i	2.41750	−	1.39574i
$629$	−1.44943e7			−1.46073
$630$		0			0
$631$	1.62315e7			1.62288			0.811438	−	0.584439i	$-0.198685\pi$
$631$	1.62315e7			1.62288			0.811438	+	0.584439i	$0.198685\pi$
$632$	−7.39451e6	+	4.26922e6i	−0.736405	+	0.425163i
$633$		0			0
$634$	−7.54439e6	+	1.30673e7i	−0.745420	+	1.29111i
$635$	2.64195e6	+	4.57599e6i	0.260010	+	0.450350i
$636$		0			0
$637$	5.82855e6	−	4.47195e6i	0.569131	−	0.436665i
$638$			2.65781e7i			2.58507i
$639$		0			0
$640$	−1.91609e7	−	1.10625e7i	−1.84912	−	1.06759i
$641$	−3.11331e6	−	1.79747e6i	−0.299280	−	0.172789i	0.342840	−	0.939394i	$-0.388611\pi$
$641$	−3.11331e6	−	1.79747e6i	−0.299280	−	0.172789i	−0.642119	+	0.766605i	$0.721945\pi$
$642$		0			0
$643$			5.61426e6i			0.535507i	0.963487	+	0.267754i	$0.0862813\pi$
$643$			5.61426e6i			0.535507i	−0.963487	+	0.267754i	$0.913719\pi$
$644$	7.83201e6	−	1.58808e7i	0.744147	−	1.50889i
$645$		0			0
$646$	−1.00095e7	−	1.73369e7i	−0.943691	−	1.63452i
$647$	−2.93988e6	+	5.09203e6i	−0.276102	+	0.478222i	−0.970413	−	0.241453i	$-0.922376\pi$
$647$	−2.93988e6	+	5.09203e6i	−0.276102	+	0.478222i	0.694311	+	0.719675i	$0.255709\pi$
$648$		0			0
$649$	−1.62848e7	+	9.40205e6i	−1.51765	+	0.876215i
$650$	5.26438e6			0.488724
$651$		0			0
$652$	6.14797e6			0.566386
$653$	1.50765e7	−	8.70444e6i	1.38363	−	0.798837i	0.391039	−	0.920374i	$-0.372116\pi$
$653$	1.50765e7	−	8.70444e6i	1.38363	−	0.798837i	0.992587	+	0.121537i	$0.0387824\pi$
$654$		0			0
$655$	6.26194e6	−	1.08460e7i	0.570303	−	0.987793i
$656$	−305806.	−	529672.i	−0.0277451	−	0.0480560i
$657$		0			0
$658$	1.22972e7	+	1.84051e7i	1.10724	+	1.65719i
$659$			5.65316e6i			0.507081i	0.967325	+	0.253541i	$0.0815952\pi$
$659$			5.65316e6i			0.507081i	−0.967325	+	0.253541i	$0.918405\pi$
$660$		0			0
$661$	−1.17378e7	−	6.77682e6i	−1.04492	−	0.603285i	−0.123697	−	0.992320i	$-0.539475\pi$
$661$	−1.17378e7	−	6.77682e6i	−1.04492	−	0.603285i	−0.921223	+	0.389035i	$0.872809\pi$
$662$	−1.71489e7	−	9.90093e6i	−1.52087	−	0.878073i
$663$		0			0
$664$		−	1.02577e7i		−	0.902878i
$665$	1.06792e7	+	1.59835e7i	0.936453	+	1.40158i
$666$		0			0
$667$	−7.72435e6	−	1.33790e7i	−0.672275	−	1.16442i
$668$	−2.22449e6	+	3.85293e6i	−0.192881	+	0.334079i
$669$		0			0
$670$	314307.	−	181465.i	0.0270500	−	0.0156173i
$671$	−9.06937e6			−0.777626
$672$		0			0
$673$	−3.85676e6			−0.328235			−0.164118	−	0.986441i	$-0.552478\pi$
$673$	−3.85676e6			−0.328235			−0.164118	+	0.986441i	$0.552478\pi$
$674$	2.58154e7	−	1.49045e7i	2.18891	−	1.26377i
$675$		0			0
$676$	5.08405e6	−	8.80583e6i	0.427901	−	0.741146i
$677$	5.93780e6	+	1.02846e7i	0.497913	+	0.862411i	0.999997	−	0.00240761i	$-0.000766368\pi$
$677$	5.93780e6	+	1.02846e7i	0.497913	+	0.862411i	−0.502084	+	0.864819i	$0.667433\pi$
$678$		0			0
$679$	−1.65756e6	+	3.36098e6i	−0.137973	+	0.279764i
$680$			1.45242e7i			1.20453i
$681$		0			0
$682$	2.46272e7	+	1.42185e7i	2.02747	+	1.17056i
$683$	−6.89816e6	−	3.98266e6i	−0.565824	−	0.326679i	0.189656	−	0.981851i	$-0.439263\pi$
$683$	−6.89816e6	−	3.98266e6i	−0.565824	−	0.326679i	−0.755480	+	0.655172i	$0.772596\pi$
$684$		0			0
$685$		−	1.85484e7i		−	1.51036i
$686$	−1.35077e7	−	1.54048e7i	−1.09590	−	1.24982i
$687$		0			0
$688$	−2.42478e6	−	4.19985e6i	−0.195300	−	0.338269i
$689$	5.24614e6	−	9.08658e6i	0.421009	−	0.729210i
$690$		0			0
$691$	−2.04326e7	+	1.17968e7i	−1.62790	+	0.939870i	−0.643186	+	0.765710i	$0.722388\pi$
$691$	−2.04326e7	+	1.17968e7i	−1.62790	+	0.939870i	−0.984717	+	0.174160i	$0.944279\pi$
$692$	2.38746e7			1.89527
$693$		0			0
$694$	−1.79224e7			−1.41253
$695$	−1.70884e7	+	9.86597e6i	−1.34196	+	0.774779i
$696$		0			0
$697$	824364.	−	1.42784e6i	0.0642742	−	0.111326i
$698$	−1.86595e7	−	3.23193e7i	−1.44965	−	2.51086i
$699$		0			0
$700$	−612468.	−	9.34798e6i	−0.0472431	−	0.721062i
$701$		−	1.79714e7i		−	1.38129i	−0.723192	−	0.690647i	$-0.757326\pi$
$701$		−	1.79714e7i		−	1.38129i	0.723192	−	0.690647i	$-0.242674\pi$
$702$		0			0
$703$	−2.94219e7	−	1.69868e7i	−2.24534	−	1.29635i
$704$	1.88498e7	+	1.08830e7i	1.43343	+	0.827591i
$705$		0			0
$706$			2.23787e7i			1.68975i
$707$	1.05694e7	−	7.06187e6i	0.795246	−	0.531338i
$708$		0			0
$709$	3.36632e6	+	5.83064e6i	0.251501	+	0.435613i	0.963939	−	0.266122i	$-0.0857424\pi$
$709$	3.36632e6	+	5.83064e6i	0.251501	+	0.435613i	−0.712438	+	0.701735i	$0.752409\pi$
$710$	1.01990e7	−	1.76652e7i	0.759300	−	1.31515i
$711$		0			0
$712$	−4.80218e6	+	2.77254e6i	−0.355009	+	0.204964i
$713$	−1.65292e7			−1.21767
$714$		0			0
$715$	−1.28516e7			−0.940136
$716$	−1.62047e7	+	9.35581e6i	−1.18130	+	0.682022i
$717$		0			0
$718$	1.23272e7	−	2.13513e7i	0.892386	−	1.54566i
$719$	5.08775e6	+	8.81225e6i	0.367032	+	0.635718i	0.989100	−	0.147245i	$-0.0470406\pi$
$719$	5.08775e6	+	8.81225e6i	0.367032	+	0.635718i	−0.622068	+	0.782963i	$0.713707\pi$
$720$		0			0
$721$	1.51518e7	−	992727.i	1.08549	−	0.0711200i
$722$		−	2.36400e7i		−	1.68774i
$723$		0			0
$724$	2.29177e7	+	1.32316e7i	1.62490	+	0.938134i
$725$	−7.07823e6	−	4.08662e6i	−0.500126	−	0.288748i
$726$		0			0
$727$			9.35279e6i			0.656304i	0.944625	+	0.328152i	$0.106426\pi$
$727$			9.35279e6i			0.656304i	−0.944625	+	0.328152i	$0.893574\pi$
$728$	1.16686e7	+	5.75470e6i	0.816004	+	0.402433i
$729$		0			0
$730$	1.70838e7	+	2.95900e7i	1.18653	+	2.05512i
$731$	6.53651e6	−	1.13216e7i	0.452431	−	0.783634i
$732$		0			0
$733$	1.30765e7	−	7.54971e6i	0.898940	−	0.519003i	0.0220841	−	0.999756i	$-0.492970\pi$
$733$	1.30765e7	−	7.54971e6i	0.898940	−	0.519003i	0.876856	+	0.480753i	$0.159636\pi$
$734$	2.30867e7			1.58169
$735$		0			0
$736$	−9.73876e6			−0.662688
$737$	−223062.	+	128785.i	−0.0151271	+	0.00873366i
$738$		0			0
$739$	−9.46139e6	+	1.63876e7i	−0.637300	+	1.10384i	0.348723	+	0.937226i	$0.386615\pi$
$739$	−9.46139e6	+	1.63876e7i	−0.637300	+	1.10384i	−0.986023	+	0.166610i	$0.946718\pi$
$740$	2.84759e7	+	4.93217e7i	1.91160	+	3.31100i
$741$		0			0
$742$	−2.62435e7	−	1.29427e7i	−1.74989	−	0.863005i
$743$			1.40170e7i			0.931501i	0.884916	+	0.465750i	$0.154216\pi$
$743$			1.40170e7i			0.931501i	−0.884916	+	0.465750i	$0.845784\pi$
$744$		0			0
$745$	−2.33368e6	−	1.34735e6i	−0.154046	−	0.0889385i
$746$	2.61733e7	+	1.51112e7i	1.72191	+	0.994147i
$747$		0			0
$748$		−	2.38166e7i		−	1.55642i
$749$	−1.39107e7	+	911411.i	−0.906033	+	0.0593622i
$750$		0			0
$751$	−6.33649e6	−	1.09751e7i	−0.409967	−	0.710084i	0.584919	−	0.811092i	$-0.301126\pi$
$751$	−6.33649e6	−	1.09751e7i	−0.409967	−	0.710084i	−0.994886	+	0.101008i	$0.967793\pi$
$752$	−3.20983e6	+	5.55959e6i	−0.206984	+	0.358508i
$753$		0			0
$754$	2.27137e7	−	1.31138e7i	1.45499	−	0.840038i
$755$	−3.86570e6			−0.246809
$756$		0			0
$757$	8.38368e6			0.531735			0.265867	−	0.964010i	$-0.414342\pi$
$757$	8.38368e6			0.531735			0.265867	+	0.964010i	$0.414342\pi$
$758$	−1.19524e7	+	6.90074e6i	−0.755585	+	0.436237i
$759$		0			0
$760$	−1.70218e7	+	2.94826e7i	−1.06898	+	1.85153i
$761$	−3.94333e6	−	6.83004e6i	−0.246832	−	0.427525i	0.715813	−	0.698292i	$-0.246056\pi$
$761$	−3.94333e6	−	6.83004e6i	−0.246832	−	0.427525i	−0.962645	+	0.270767i	$0.912723\pi$
$762$		0			0
$763$	−1.34226e6	+	896818.i	−0.0834687	+	0.0557690i
$764$		−	1.58897e7i		−	0.984877i
$765$		0			0
$766$	1.98768e7	+	1.14759e7i	1.22398	+	0.706665i
$767$	1.60700e7	+	9.27803e6i	0.986343	+	0.569465i
$768$		0			0
$769$			2.85431e7i			1.74055i	0.492568	+	0.870274i	$0.336058\pi$
$769$			2.85431e7i			1.74055i	−0.492568	+	0.870274i	$0.663942\pi$
$770$	2.34324e6	+	3.57644e7i	0.142426	+	2.17382i
$771$		0			0
$772$	1.70378e7	+	2.95104e7i	1.02889	+	1.78210i
$773$	−9.06870e6	+	1.57075e7i	−0.545879	+	0.945490i	0.452672	+	0.891677i	$0.350471\pi$
$773$	−9.06870e6	+	1.57075e7i	−0.545879	+	0.945490i	−0.998551	+	0.0538132i	$0.982862\pi$
$774$		0			0
$775$	−7.57330e6	+	4.37245e6i	−0.452930	+	0.261499i
$776$	−6.63679e6			−0.395643
$777$		0			0
$778$	−3.20689e6			−0.189948
$779$	3.34675e6	−	1.93225e6i	0.197597	−	0.114082i
$780$		0			0
$781$	−7.23821e6	+	1.25369e7i	−0.424623	+	0.735469i
$782$	1.08478e7	+	1.87890e7i	0.634345	+	1.09872i
$783$		0			0
$784$	2.27417e6	−	5.48957e6i	0.132140	−	0.318969i
$785$		−	3.24592e7i		−	1.88003i
$786$		0			0
$787$	9.29400e6	+	5.36589e6i	0.534892	+	0.308820i	0.743006	−	0.669285i	$-0.233399\pi$
$787$	9.29400e6	+	5.36589e6i	0.534892	+	0.308820i	−0.208115	+	0.978104i	$0.566733\pi$
$788$	−684956.	−	395459.i	−0.0392959	−	0.0226875i
$789$		0			0
$790$			2.32112e7i			1.32322i
$791$	−664377.	+	1.34714e6i	−0.0377549	+	0.0765546i
$792$		0			0
$793$	4.47487e6	+	7.75070e6i	0.252695	+	0.437681i
$794$	−1.00839e6	+	1.74659e6i	−0.0567647	+	0.0983194i
$795$		0			0
$796$	2.01711e7	−	1.16458e7i	1.12836	−	0.651457i
$797$	−2.16530e7			−1.20746			−0.603729	−	0.797189i	$-0.706319\pi$
$797$	−2.16530e7			−1.20746			−0.603729	+	0.797189i	$0.706319\pi$
$798$		0			0
$799$	−1.73055e7			−0.958999
$800$	−4.46207e6	+	2.57618e6i	−0.246497	+	0.142315i
$801$		0			0
$802$	−1.05578e7	+	1.82867e7i	−0.579613	+	1.00392i
$803$	−1.21243e7	−	2.09999e7i	−0.663540	−	1.14929i
$804$		0			0
$805$	−1.15737e7	−	1.73222e7i	−0.629480	−	0.942134i
$806$		−	2.80620e7i		−	1.52153i
$807$		0			0
$808$	1.94960e7	+	1.12560e7i	1.05055	+	0.606534i
$809$	2.51511e7	+	1.45210e7i	1.35109	+	0.780054i	0.988403	−	0.151855i	$-0.0485247\pi$
$809$	2.51511e7	+	1.45210e7i	1.35109	+	0.780054i	0.362691	+	0.931909i	$0.381858\pi$
$810$		0			0
$811$		−	1.01783e7i		−	0.543405i	−0.962381	−	0.271703i	$-0.912413\pi$
$811$		−	1.01783e7i		−	0.543405i	0.962381	−	0.271703i	$-0.0875867\pi$
$812$	−2.59287e7	−	3.88071e7i	−1.38004	−	2.06548i
$813$		0			0
$814$	−3.16720e7	−	5.48574e7i	−1.67538	−	2.90185i
$815$	3.61664e6	−	6.26420e6i	0.190726	−	0.330348i
$816$		0			0
$817$	2.65369e7	−	1.53211e7i	1.39090	−	0.803035i
$818$	−1.01948e7			−0.532713
$819$		0			0
$820$	−6.47827e6			−0.336453
$821$	−2.93963e7	+	1.69719e7i	−1.52207	+	0.878766i	−0.522408	+	0.852696i	$0.674966\pi$
$821$	−2.93963e7	+	1.69719e7i	−1.52207	+	0.878766i	−0.999660	+	0.0260706i	$0.991701\pi$
$822$		0			0
$823$	383232.	−	663777.i	0.0197225	−	0.0341604i	−0.855996	−	0.516983i	$-0.827055\pi$
$823$	383232.	−	663777.i	0.0197225	−	0.0341604i	0.875718	+	0.482823i	$0.160388\pi$
$824$	1.34456e7	+	2.32885e7i	0.689864	+	1.19488i
$825$		0			0
$826$	2.28896e7	−	4.64127e7i	1.16732	−	2.36694i
$827$			1.50733e7i			0.766381i	0.923669	+	0.383191i	$0.125175\pi$
$827$			1.50733e7i			0.766381i	−0.923669	+	0.383191i	$0.874825\pi$
$828$		0			0
$829$	2.15108e7	+	1.24192e7i	1.08710	+	0.627638i	0.932803	−	0.360387i	$-0.117355\pi$
$829$	2.15108e7	+	1.24192e7i	1.08710	+	0.627638i	0.154297	+	0.988024i	$0.450689\pi$
$830$	−2.41490e7	−	1.39424e7i	−1.21676	−	0.702496i
$831$		0			0
$832$		−	2.14788e7i		−	1.07573i
$833$	1.58809e7	−	2.08997e6i	0.792983	−	0.104358i
$834$		0			0
$835$	2.61718e6	+	4.53308e6i	0.129902	+	0.224997i
$836$	2.79121e7	−	4.83453e7i	1.38127	−	2.39242i
$837$		0			0
$838$	−4.07713e7	+	2.35393e7i	−2.00560	+	1.15793i
$839$	1.88795e6			0.0925947			0.0462974	−	0.998928i	$-0.485258\pi$
$839$	1.88795e6			0.0925947			0.0462974	+	0.998928i	$0.485258\pi$
$840$		0			0
$841$	−2.02085e7			−0.985244
$842$	−2.92055e7	+	1.68618e7i	−1.41966	+	0.819643i
$843$		0			0
$844$	2.05912e7	−	3.56650e7i	0.995006	−	1.72340i
$845$	−5.98154e6	−	1.03603e7i	−0.288185	−	0.499151i
$846$		0			0
$847$	−297952.	−	4.54758e6i	−0.0142705	−	0.217807i
$848$		−	8.48642e6i		−	0.405261i
$849$		0			0
$850$	9.94043e6	+	5.73911e6i	0.471909	+	0.272457i
$851$	3.18862e7	+	1.84095e7i	1.50931	+	0.871402i
$852$		0			0
$853$			2.82848e6i			0.133101i	0.997783	+	0.0665504i	$0.0211993\pi$
$853$			2.82848e6i			0.133101i	−0.997783	+	0.0665504i	$0.978801\pi$
$854$	2.07534e7	−	1.38663e7i	0.973745	−	0.650601i
$855$		0			0
$856$	−1.23443e7	−	2.13809e7i	−0.575813	−	0.997338i
$857$	1.19125e7	−	2.06331e7i	0.554054	−	0.959650i	−0.443922	−	0.896065i	$-0.646413\pi$
$857$	1.19125e7	−	2.06331e7i	0.554054	−	0.959650i	0.997976	−	0.0635847i	$-0.0202533\pi$
$858$		0			0
$859$	−9.92340e6	+	5.72927e6i	−0.458857	+	0.264921i	−0.711564	−	0.702622i	$-0.752013\pi$
$859$	−9.92340e6	+	5.72927e6i	−0.458857	+	0.264921i	0.252707	+	0.967543i	$0.418679\pi$
$860$	−5.13672e7			−2.36832
$861$		0			0
$862$	−1.08820e7			−0.498817
$863$	1.23304e7	−	7.11898e6i	0.563575	−	0.325380i	−0.191004	−	0.981589i	$-0.561174\pi$
$863$	1.23304e7	−	7.11898e6i	0.563575	−	0.325380i	0.754579	+	0.656209i	$0.227841\pi$
$864$		0			0
$865$	1.40446e7	−	2.43259e7i	0.638218	−	1.10543i
$866$	1.46424e7	+	2.53614e7i	0.663465	+	1.14916i
$867$		0			0
$868$	−4.98297e7	+	3.26478e6i	−2.24486	+	0.147080i
$869$		−	1.64729e7i		−	0.739982i
$870$		0			0
$871$	220120.	+	127086.i	0.00983136	+	0.00567614i
$872$	−2.47588e6	−	1.42945e6i	−0.110265	−	0.0636616i
$873$		0			0
$874$			5.08530e7i			2.25184i
$875$	1.42326e7	+	7.01919e6i	0.628442	+	0.309932i
$876$		0			0
$877$	−1.73898e7	−	3.01200e7i	−0.763477	−	1.32238i	−0.941048	−	0.338273i	$-0.890157\pi$
$877$	−1.73898e7	−	3.01200e7i	−0.763477	−	1.32238i	0.177571	−	0.984108i	$-0.443176\pi$
$878$	−1.06375e7	+	1.84246e7i	−0.465695	+	0.806608i
$879$		0			0
$880$	−9.00204e6	+	5.19733e6i	−0.391863	+	0.226242i
$881$	9.40367e6			0.408186			0.204093	−	0.978952i	$-0.434576\pi$
$881$	9.40367e6			0.408186			0.204093	+	0.978952i	$0.434576\pi$
$882$		0			0
$883$	1.30301e7			0.562399			0.281199	−	0.959649i	$-0.409268\pi$
$883$	1.30301e7			0.562399			0.281199	+	0.959649i	$0.409268\pi$
$884$	−2.03537e7	+	1.17512e7i	−0.876018	+	0.505769i
$885$		0			0
$886$	8.79687e6	−	1.52366e7i	0.376482	−	0.652086i
$887$	6.51276e6	+	1.12804e7i	0.277943	+	0.481411i	0.970873	−	0.239593i	$-0.0770140\pi$
$887$	6.51276e6	+	1.12804e7i	0.277943	+	0.481411i	−0.692930	+	0.721004i	$0.743681\pi$
$888$		0			0
$889$	9.25574e6	+	4.56471e6i	0.392787	+	0.193713i
$890$			1.50740e7i			0.637900i
$891$		0			0
$892$	−2.41827e7	−	1.39619e7i	−1.01764	−	0.587534i
$893$	−3.51285e7	−	2.02814e7i	−1.47411	−	0.851079i
$894$		0			0
$895$			2.20148e7i			0.918664i
$896$	−4.31207e7	+	2.82521e6i	−1.79438	+	0.117566i
$897$		0			0
$898$	−2.40493e7	−	4.16547e7i	−0.995205	−	1.72374i
$899$	−2.17839e7	+	3.77307e7i	−0.898950	+	1.55703i
$900$		0			0
$901$	1.98120e7	−	1.14384e7i	0.813047	−	0.469413i
$902$	7.20538e6			0.294877
$903$		0			0
$904$	−2.66014e6			−0.108264
$905$	2.69634e7	−	1.55673e7i	1.09434	−	0.631819i
$906$		0			0
$907$	9.82796e6	−	1.70225e7i	0.396685	−	0.687078i	−0.596630	−	0.802516i	$-0.703494\pi$
$907$	9.82796e6	−	1.70225e7i	0.396685	−	0.687078i	0.993315	+	0.115439i	$0.0368273\pi$
$908$	−7.95590e6	−	1.37800e7i	−0.320239	−	0.554671i
$909$		0			0
$910$	2.94082e7	−	1.96489e7i	1.17724	−	0.786564i
$911$			2.66058e7i			1.06214i	0.847329	+	0.531069i	$0.178209\pi$
$911$			2.66058e7i			1.06214i	−0.847329	+	0.531069i	$0.821791\pi$
$912$		0			0
$913$	1.71385e7	+	9.89489e6i	0.680448	+	0.392857i
$914$	−2.55166e7	−	1.47320e7i	−1.01032	−	0.583306i
$915$		0			0
$916$			6.32797e7i			2.49187i
$917$	−1.59921e6	−	2.44084e7i	−0.0628032	−	0.958553i
$918$		0			0
$919$	1.42661e7	+	2.47096e7i	0.557206	+	0.965109i	0.997728	+	0.0673674i	$0.0214600\pi$
$919$	1.42661e7	+	2.47096e7i	0.557206	+	0.965109i	−0.440522	+	0.897742i	$0.645207\pi$
$920$	1.84474e7	−	3.19519e7i	0.718566	−	1.24459i
$921$		0			0
$922$	−1.28617e7	+	7.42571e6i	−0.498278	+	0.287681i
$923$	1.42855e7			0.551938
$924$		0			0
$925$	1.94793e7			0.748549
$926$	−1.41385e7	+	8.16286e6i	−0.541846	+	0.312835i
$927$		0			0
$928$	−1.28347e7	+	2.22304e7i	−0.489233	+	0.847376i
$929$	2.01679e7	+	3.49319e7i	0.766694	+	1.32795i	0.939347	+	0.342969i	$0.111433\pi$
$929$	2.01679e7	+	3.49319e7i	0.766694	+	1.32795i	−0.172653	+	0.984983i	$0.555234\pi$
$930$		0			0
$931$	3.46861e7	+	1.43694e7i	1.31154	+	0.543332i
$932$		−	5.28806e6i		−	0.199415i
$933$		0			0
$934$	−1.49939e7	−	8.65672e6i	−0.562402	−	0.324703i
$935$	−2.42669e7	−	1.40105e7i	−0.907788	−	0.524112i
$936$		0			0
$937$		−	2.03556e7i		−	0.757417i	−0.925516	−	0.378708i	$-0.876368\pi$
$937$		−	2.03556e7i		−	0.757417i	0.925516	−	0.378708i	$-0.123632\pi$
$938$	313532.	−	635740.i	0.0116352	−	0.0235924i
$939$		0			0
$940$	3.39989e7	+	5.88879e7i	1.25501	+	2.17373i
$941$	1.74195e7	−	3.01714e7i	0.641299	−	1.11076i	−0.343844	−	0.939027i	$-0.611729\pi$
$941$	1.74195e7	−	3.01714e7i	0.641299	−	1.11076i	0.985143	−	0.171736i	$-0.0549376\pi$
$942$		0			0
$943$	−3.62706e6	+	2.09408e6i	−0.132824	+	0.0766858i
$944$	1.50086e7			0.548164
$945$		0			0
$946$	5.71326e7			2.07566
$947$	−6.18612e6	+	3.57156e6i	−0.224153	+	0.129415i	−0.607872	−	0.794035i	$-0.707976\pi$
$947$	−6.18612e6	+	3.57156e6i	−0.224153	+	0.129415i	0.383719	+	0.923450i	$0.374643\pi$
$948$		0			0
$949$	−1.19644e7	+	2.07229e7i	−0.431245	+	0.746938i
$950$	1.34520e7	+	2.32996e7i	0.483592	+	0.837606i
$951$		0			0
$952$	1.57596e7	+	2.35872e7i	0.563576	+	0.843497i
$953$		−	6.28996e6i		−	0.224344i	−0.993689	−	0.112172i	$-0.964219\pi$
$953$		−	6.28996e6i		−	0.224344i	0.993689	−	0.112172i	$-0.0357808\pi$
$954$		0			0
$955$	−1.61901e7	−	9.34735e6i	−0.574435	−	0.331650i
$956$	3.25548e7	+	1.87955e7i	1.15205	+	0.665135i
$957$		0			0
$958$		−	4.65125e7i		−	1.63741i
$959$	−2.01261e7	−	3.01225e7i	−0.706666	−	1.05766i
$960$		0			0
$961$	8.99292e6	+	1.55762e7i	0.314118	+	0.544068i
$962$	−3.12542e7	+	5.41338e7i	−1.08886	+	1.88595i
$963$		0			0
$964$	−8.70641e6	+	5.02665e6i	−0.301749	+	0.174215i
$965$	4.00910e7			1.38589
$966$		0			0
$967$	3.55035e7			1.22097			0.610485	−	0.792028i	$-0.290975\pi$
$967$	3.55035e7			1.22097			0.610485	+	0.792028i	$0.290975\pi$
$968$	6.98970e6	−	4.03551e6i	0.239757	−	0.138423i
$969$		0			0
$970$	−9.02086e6	+	1.56246e7i	−0.307835	+	0.533187i
$971$	1.32813e7	+	2.30038e7i	0.452055	+	0.782982i	0.998514	−	0.0545043i	$-0.0173578\pi$
$971$	1.32813e7	+	2.30038e7i	0.452055	+	0.782982i	−0.546459	+	0.837486i	$0.684025\pi$
$972$		0			0
$973$	−1.70462e7	+	3.45642e7i	−0.577226	+	1.17043i
$974$			2.81998e7i			0.952463i
$975$		0			0
$976$	6.26896e6	+	3.61939e6i	0.210655	+	0.121622i
$977$	3.05413e7	+	1.76330e7i	1.02365	+	0.591004i	0.915159	−	0.403093i	$-0.132065\pi$
$977$	3.05413e7	+	1.76330e7i	1.02365	+	0.591004i	0.108490	+	0.994098i	$0.465398\pi$
$978$		0			0
$979$		−	1.06979e7i		−	0.356733i
$980$	−3.83119e7	−	4.99342e7i	−1.27429	−	1.66086i
$981$		0			0
$982$	−2.59303e7	−	4.49126e7i	−0.858082	−	1.48624i
$983$	−1.59341e7	+	2.75987e7i	−0.525951	+	0.910973i	0.473592	+	0.880744i	$0.342957\pi$
$983$	−1.59341e7	+	2.75987e7i	−0.525951	+	0.910973i	−0.999543	+	0.0302290i	$0.990376\pi$
$984$		0			0
$985$	−805871.	+	465270.i	−0.0264652	+	0.0152797i
$986$	5.71853e7			1.87324
$987$		0			0
$988$	−5.50879e7			−1.79541
$989$	−2.87595e7	+	1.66043e7i	−0.934956	+	0.539797i
$990$		0			0
$991$	2.80173e7	−	4.85275e7i	0.906239	−	1.56965i	0.0869941	−	0.996209i	$-0.472274\pi$
$991$	2.80173e7	−	4.85275e7i	0.906239	−	1.56965i	0.819245	−	0.573444i	$-0.194393\pi$
$992$	1.37324e7	+	2.37852e7i	0.443065	+	0.767411i
$993$		0			0
$994$	−2.60469e6	−	3.97548e7i	−0.0836161	−	1.27622i
$995$		−	2.74032e7i		−	0.877493i
$996$		0			0
$997$	5.15391e6	+	2.97561e6i	0.164210	+	0.0948065i	0.579853	−	0.814721i	$-0.303110\pi$
$997$	5.15391e6	+	2.97561e6i	0.164210	+	0.0948065i	−0.415643	+	0.909528i	$0.636443\pi$
$998$	1.60799e7	+	9.28372e6i	0.511041	+	0.295050i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.p.b.17.11	yes	24
3.2	odd	2	inner	63.6.p.b.17.2	✓	24
7.3	odd	6		441.6.c.b.440.8		24
7.4	even	3		441.6.c.b.440.18		24
7.5	odd	6	inner	63.6.p.b.26.2	yes	24
21.5	even	6	inner	63.6.p.b.26.11	yes	24
21.11	odd	6		441.6.c.b.440.7		24
21.17	even	6		441.6.c.b.440.17		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.p.b.17.2	✓	24	3.2	odd	2	inner
63.6.p.b.17.11	yes	24	1.1	even	1	trivial
63.6.p.b.26.2	yes	24	7.5	odd	6	inner
63.6.p.b.26.11	yes	24	21.5	even	6	inner
441.6.c.b.440.7		24	21.11	odd	6
441.6.c.b.440.8		24	7.3	odd	6
441.6.c.b.440.17		24	21.17	even	6
441.6.c.b.440.18		24	7.4	even	3

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(8.14327 - 4.70152i) q^{2} +(28.2086 - 48.8587i) q^{4} +(-33.1882 - 57.4837i) q^{5} +(-116.271 - 57.3420i) q^{7} -229.595i q^{8} +O(q^{10})\)	\(q+(8.14327 - 4.70152i) q^{2} +(28.2086 - 48.8587i) q^{4} +(-33.1882 - 57.4837i) q^{5} +(-116.271 - 57.3420i) q^{7} -229.595i q^{8} +(-540.521 - 312.070i) q^{10} +(383.606 + 221.475i) q^{11} -437.107i q^{13} +(-1216.42 + 79.6982i) q^{14} +(-176.771 - 306.177i) q^{16} +(476.524 - 825.364i) q^{17} +(1934.59 - 1116.94i) q^{19} -3744.77 q^{20} +4165.07 q^{22} +(-2096.62 + 1210.49i) q^{23} +(-640.416 + 1109.23i) q^{25} +(-2055.06 - 3559.48i) q^{26} +(-6081.48 + 4063.30i) q^{28} +6381.19i q^{29} +(5912.80 + 3413.76i) q^{31} +(3483.73 + 2011.33i) q^{32} -8961.54i q^{34} +(562.593 + 8586.75i) q^{35} +(-7604.18 - 13170.8i) q^{37} +(10502.6 - 18191.0i) q^{38} +(-13198.0 + 7619.85i) q^{40} +1729.95 q^{41} +13717.1 q^{43} +(21641.9 - 12495.0i) q^{44} +(-11382.2 + 19714.6i) q^{46} +(-9079.05 - 15725.4i) q^{47} +(10230.8 + 13334.4i) q^{49} +12043.7i q^{50} +(-21356.4 - 12330.1i) q^{52} +(20788.0 + 12002.0i) q^{53} -29401.4i q^{55} +(-13165.4 + 26695.2i) q^{56} +(30001.3 + 51963.8i) q^{58} +(-21226.0 + 36764.5i) q^{59} +(-17731.8 + 10237.5i) q^{61} +64199.4 q^{62} +49138.6 q^{64} +(-25126.5 + 14506.8i) q^{65} +(-290.744 + 503.584i) q^{67} +(-26884.1 - 46564.6i) q^{68} +(44952.1 + 67279.2i) q^{70} +32681.9i q^{71} +(-47409.2 - 27371.7i) q^{73} +(-123846. - 71502.4i) q^{74} -126029. i q^{76} +(-31902.3 - 47747.7i) q^{77} +(-18594.6 - 32206.7i) q^{79} +(-11733.5 + 20322.9i) q^{80} +(14087.5 - 8133.41i) q^{82} +44677.3 q^{83} -63259.9 q^{85} +(111702. - 64491.0i) q^{86} +(50849.5 - 88073.9i) q^{88} +(-12075.8 - 20915.9i) q^{89} +(-25064.6 + 50822.7i) q^{91} +136584. i q^{92} +(-147866. - 85370.6i) q^{94} +(-128411. - 74138.2i) q^{95} -28906.5i q^{97} +(146004. + 60485.3i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 304 q^{4} - 436 q^{7}+O(q^{10}) \) 24 * q + 304 * q^4 - 436 * q^7	\( 24 q + 304 q^{4} - 436 q^{7} + 1992 q^{10} - 3644 q^{16} + 3804 q^{19} - 5648 q^{22} - 18852 q^{25} - 39172 q^{28} + 38652 q^{31} + 20548 q^{37} + 132060 q^{40} + 2200 q^{43} - 25712 q^{46} - 125676 q^{49} - 2940 q^{52} + 154300 q^{58} + 48504 q^{61} - 327880 q^{64} + 156324 q^{67} - 9468 q^{70} - 703236 q^{73} + 165756 q^{79} + 1081020 q^{82} - 284448 q^{85} + 582308 q^{88} - 19812 q^{91} - 1481724 q^{94}+O(q^{100}) \) 24 * q + 304 * q^4 - 436 * q^7 + 1992 * q^10 - 3644 * q^16 + 3804 * q^19 - 5648 * q^22 - 18852 * q^25 - 39172 * q^28 + 38652 * q^31 + 20548 * q^37 + 132060 * q^40 + 2200 * q^43 - 25712 * q^46 - 125676 * q^49 - 2940 * q^52 + 154300 * q^58 + 48504 * q^61 - 327880 * q^64 + 156324 * q^67 - 9468 * q^70 - 703236 * q^73 + 165756 * q^79 + 1081020 * q^82 - 284448 * q^85 + 582308 * q^88 - 19812 * q^91 - 1481724 * q^94

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