LMFDB - Embedded newform 684.3.be.a.425.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(425,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("684.425");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.be (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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			425.13
Character	$\chi$	$=$	684.425
Dual form			684.3.be.a.581.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61894 + 2.52567i) q^{3} +(6.09418 + 3.51848i) q^{5} +(2.95479 - 5.11784i) q^{7} +(-3.75805 - 8.17784i) q^{9} +O(q^{10})$	\(q+(-1.61894 + 2.52567i) q^{3} +(6.09418 + 3.51848i) q^{5} +(2.95479 - 5.11784i) q^{7} +(-3.75805 - 8.17784i) q^{9} +(14.8621 + 8.58065i) q^{11} -1.69095 q^{13} +(-18.7527 + 9.69569i) q^{15} +(22.0157 - 12.7108i) q^{17} +(9.01588 - 16.7247i) q^{19} +(8.14236 + 15.7483i) q^{21} -24.5609i q^{23} +(12.2594 + 21.2339i) q^{25} +(26.7386 + 3.74787i) q^{27} +(4.33936 - 2.50533i) q^{29} +(-25.4929 - 44.1550i) q^{31} +(-45.7328 + 23.6453i) q^{33} +(36.0140 - 20.7927i) q^{35} -30.6535 q^{37} +(2.73756 - 4.27080i) q^{39} +(61.7782 + 35.6677i) q^{41} +5.36109 q^{43} +(5.87134 - 63.0599i) q^{45} +(-33.2249 + 19.1824i) q^{47} +(7.03844 + 12.1909i) q^{49} +(-3.53892 + 76.1824i) q^{51} +(-12.6088 - 7.27967i) q^{53} +(60.3817 + 104.584i) q^{55} +(27.6448 + 49.8474i) q^{57} +(-40.9541 - 23.6449i) q^{59} +(47.3668 + 82.0417i) q^{61} +(-52.9572 - 4.93070i) q^{63} +(-10.3050 - 5.94958i) q^{65} +80.5590 q^{67} +(62.0329 + 39.7628i) q^{69} +(-116.450 + 67.2326i) q^{71} +(-0.432590 - 0.749268i) q^{73} +(-73.4770 - 3.41325i) q^{75} +(87.8289 - 50.7080i) q^{77} -67.3609 q^{79} +(-52.7542 + 61.4654i) q^{81} +(85.0365 + 49.0958i) q^{83} +178.890 q^{85} +(-0.697532 + 15.0158i) q^{87} +(28.9575 + 16.7186i) q^{89} +(-4.99641 + 8.65404i) q^{91} +(152.793 + 7.09772i) q^{93} +(113.790 - 70.2009i) q^{95} +7.99364 q^{97} +(14.3187 - 153.787i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 4 * q^3 + q^7 + 4 * q^9	$ 80 q + 4 q^{3} + q^{7} + 4 q^{9} + 18 q^{11} + 10 q^{13} - 11 q^{15} + 9 q^{17} + 20 q^{19} - 30 q^{21} + 200 q^{25} + 25 q^{27} - 27 q^{29} - 8 q^{31} + 23 q^{33} + 22 q^{37} + 39 q^{39} - 54 q^{41} + 88 q^{43} - 196 q^{45} + 198 q^{47} - 267 q^{49} - 56 q^{51} + 36 q^{53} + 78 q^{57} + 171 q^{59} + 7 q^{61} + 82 q^{63} - 144 q^{65} + 154 q^{67} + 44 q^{69} + 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} + 34 q^{79} - 44 q^{81} - 171 q^{83} - 244 q^{87} - 216 q^{89} + 122 q^{91} - 104 q^{93} - 216 q^{95} + 16 q^{97} - 305 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 + q^7 + 4 * q^9 + 18 * q^11 + 10 * q^13 - 11 * q^15 + 9 * q^17 + 20 * q^19 - 30 * q^21 + 200 * q^25 + 25 * q^27 - 27 * q^29 - 8 * q^31 + 23 * q^33 + 22 * q^37 + 39 * q^39 - 54 * q^41 + 88 * q^43 - 196 * q^45 + 198 * q^47 - 267 * q^49 - 56 * q^51 + 36 * q^53 + 78 * q^57 + 171 * q^59 + 7 * q^61 + 82 * q^63 - 144 * q^65 + 154 * q^67 + 44 * q^69 + 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 + 34 * q^79 - 44 * q^81 - 171 * q^83 - 244 * q^87 - 216 * q^89 + 122 * q^91 - 104 * q^93 - 216 * q^95 + 16 * q^97 - 305 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.61894	+	2.52567i	−0.539648	+	0.841891i
$3$	−1.61894	+	2.52567i	−0.539648	+	0.841891i
$4$		0			0
$5$	6.09418	+	3.51848i	1.21884	+	0.703696i	0.964669	−	0.263465i	$-0.0848653\pi$
$5$	6.09418	+	3.51848i	1.21884	+	0.703696i	0.254167	+	0.967160i	$0.418199\pi$
$6$		0			0
$7$	2.95479	−	5.11784i	0.422113	−	0.731121i	−0.574033	−	0.818832i	$-0.694622\pi$
$7$	2.95479	−	5.11784i	0.422113	−	0.731121i	0.996146	+	0.0877114i	$0.0279553\pi$
$8$		0			0
$9$	−3.75805	−	8.17784i	−0.417561	−	0.908649i
$10$		0			0
$11$	14.8621	+	8.58065i	1.35110	+	0.780059i	0.988404	−	0.151848i	$-0.0485223\pi$
$11$	14.8621	+	8.58065i	1.35110	+	0.780059i	0.362698	+	0.931907i	$0.381856\pi$
$12$		0			0
$13$	−1.69095			−0.130073			−0.0650367	−	0.997883i	$-0.520716\pi$
$13$	−1.69095			−0.130073			−0.0650367	+	0.997883i	$0.520716\pi$
$14$		0			0
$15$	−18.7527	+	9.69569i	−1.25018	+	0.646380i
$16$		0			0
$17$	22.0157	−	12.7108i	1.29504	−	0.747692i	0.315497	−	0.948927i	$-0.397829\pi$
$17$	22.0157	−	12.7108i	1.29504	−	0.747692i	0.979543	+	0.201235i	$0.0644955\pi$
$18$		0			0
$19$	9.01588	−	16.7247i	0.474520	−	0.880245i
$19$	9.01588	−	16.7247i	0.474520	−	0.880245i
$20$		0			0
$21$	8.14236	+	15.7483i	0.387732	+	0.749920i
$22$		0			0
$23$		−	24.5609i		−	1.06787i	−0.845526	−	0.533934i	$-0.820713\pi$
$23$		−	24.5609i		−	1.06787i	0.845526	−	0.533934i	$-0.179287\pi$
$24$		0			0
$25$	12.2594	+	21.2339i	0.490375	+	0.849354i
$26$		0			0
$27$	26.7386	+	3.74787i	0.990319	+	0.138810i
$28$		0			0
$29$	4.33936	−	2.50533i	0.149633	−	0.0863907i	−0.423314	−	0.905983i	$-0.639133\pi$
$29$	4.33936	−	2.50533i	0.149633	−	0.0863907i	0.572947	+	0.819592i	$0.305800\pi$
$30$		0			0
$31$	−25.4929	−	44.1550i	−0.822352	−	1.42436i	−0.903926	−	0.427689i	$-0.859328\pi$
$31$	−25.4929	−	44.1550i	−0.822352	−	1.42436i	0.0815735	−	0.996667i	$-0.474005\pi$
$32$		0			0
$33$	−45.7328	+	23.6453i	−1.38584	+	0.716523i
$34$		0			0
$35$	36.0140	−	20.7927i	1.02897	−	0.594078i
$36$		0			0
$37$	−30.6535			−0.828473			−0.414237	−	0.910169i	$-0.635951\pi$
$37$	−30.6535			−0.828473			−0.414237	+	0.910169i	$0.635951\pi$
$38$		0			0
$39$	2.73756	−	4.27080i	0.0701938	−	0.109508i
$40$		0			0
$41$	61.7782	+	35.6677i	1.50679	+	0.869943i	0.999969	+	0.00788886i	$0.00251113\pi$
$41$	61.7782	+	35.6677i	1.50679	+	0.869943i	0.506816	+	0.862054i	$0.330822\pi$
$42$		0			0
$43$	5.36109			0.124677			0.0623383	−	0.998055i	$-0.480144\pi$
$43$	5.36109			0.124677			0.0623383	+	0.998055i	$0.480144\pi$
$44$		0			0
$45$	5.87134	−	63.0599i	0.130474	−	1.40133i
$46$		0			0
$47$	−33.2249	+	19.1824i	−0.706912	+	0.408136i	−0.809917	−	0.586545i	$-0.800488\pi$
$47$	−33.2249	+	19.1824i	−0.706912	+	0.408136i	0.103005	+	0.994681i	$0.467154\pi$
$48$		0			0
$49$	7.03844	+	12.1909i	0.143642	+	0.248795i
$50$		0			0
$51$	−3.53892	+	76.1824i	−0.0693906	+	1.49377i
$52$		0			0
$53$	−12.6088	−	7.27967i	−0.237901	−	0.137352i	0.376311	−	0.926494i	$-0.377193\pi$
$53$	−12.6088	−	7.27967i	−0.237901	−	0.137352i	−0.614212	+	0.789141i	$0.710526\pi$
$54$		0			0
$55$	60.3817	+	104.584i	1.09785	+	1.90153i
$56$		0			0
$57$	27.6448	+	49.8474i	0.484997	+	0.874516i
$58$		0			0
$59$	−40.9541	−	23.6449i	−0.694137	−	0.400760i	0.111023	−	0.993818i	$-0.464587\pi$
$59$	−40.9541	−	23.6449i	−0.694137	−	0.400760i	−0.805160	+	0.593057i	$0.797921\pi$
$60$		0			0
$61$	47.3668	+	82.0417i	0.776505	+	1.34495i	0.933945	+	0.357417i	$0.116343\pi$
$61$	47.3668	+	82.0417i	0.776505	+	1.34495i	−0.157440	+	0.987529i	$0.550324\pi$
$62$		0			0
$63$	−52.9572	−	4.93070i	−0.840590	−	0.0782652i
$64$		0			0
$65$	−10.3050	−	5.94958i	−0.158538	−	0.0915321i
$66$		0			0
$67$	80.5590			1.20237			0.601186	−	0.799109i	$-0.294695\pi$
$67$	80.5590			1.20237			0.601186	+	0.799109i	$0.294695\pi$
$68$		0			0
$69$	62.0329	+	39.7628i	0.899028	+	0.576272i
$70$		0			0
$71$	−116.450	+	67.2326i	−1.64014	+	0.946938i	−0.659364	+	0.751824i	$0.729175\pi$
$71$	−116.450	+	67.2326i	−1.64014	+	0.946938i	−0.980780	+	0.195114i	$0.937492\pi$
$72$		0			0
$73$	−0.432590	−	0.749268i	−0.00592589	−	0.0102639i	0.863047	−	0.505123i	$-0.168553\pi$
$73$	−0.432590	−	0.749268i	−0.00592589	−	0.0102639i	−0.868973	+	0.494859i	$0.835220\pi$
$74$		0			0
$75$	−73.4770	−	3.41325i	−0.979693	−	0.0455099i
$76$		0			0
$77$	87.8289	−	50.7080i	1.14063	−	0.658546i
$78$		0			0
$79$	−67.3609			−0.852669			−0.426335	−	0.904566i	$-0.640195\pi$
$79$	−67.3609			−0.852669			−0.426335	+	0.904566i	$0.640195\pi$
$80$		0			0
$81$	−52.7542	+	61.4654i	−0.651286	+	0.758832i
$82$		0			0
$83$	85.0365	+	49.0958i	1.02454	+	0.591516i	0.915414	−	0.402512i	$-0.131863\pi$
$83$	85.0365	+	49.0958i	1.02454	+	0.591516i	0.109121	+	0.994028i	$0.465196\pi$
$84$		0			0
$85$	178.890			2.10459
$86$		0			0
$87$	−0.697532	+	15.0158i	−0.00801761	+	0.172595i
$88$		0			0
$89$	28.9575	+	16.7186i	0.325365	+	0.187849i	0.653781	−	0.756684i	$-0.273182\pi$
$89$	28.9575	+	16.7186i	0.325365	+	0.187849i	−0.328417	+	0.944533i	$0.606515\pi$
$90$		0			0
$91$	−4.99641	+	8.65404i	−0.0549056	+	0.0950994i
$92$		0			0
$93$	152.793	+	7.09772i	1.64293	+	0.0763196i
$94$		0			0
$95$	113.790	−	70.2009i	1.19779	−	0.738957i
$96$		0			0
$97$	7.99364			0.0824086			0.0412043	−	0.999151i	$-0.486881\pi$
$97$	7.99364			0.0824086			0.0412043	+	0.999151i	$0.486881\pi$
$98$		0			0
$99$	14.3187	−	153.787i	0.144633	−	1.55340i
$100$		0			0
$101$	28.8327	−	16.6466i	0.285473	−	0.164818i	−0.350426	−	0.936591i	$-0.613963\pi$
$101$	28.8327	−	16.6466i	0.285473	−	0.164818i	0.635898	+	0.771773i	$0.280630\pi$
$102$		0			0
$103$	−67.4528	−	116.832i	−0.654882	−	1.13429i	−0.981923	−	0.189278i	$-0.939385\pi$
$103$	−67.4528	−	116.832i	−0.654882	−	1.13429i	0.327042	−	0.945010i	$-0.393948\pi$
$104$		0			0
$105$	−5.78909	+	124.622i	−0.0551342	+	1.18688i
$106$		0			0
$107$			19.5810i			0.183000i	0.995805	+	0.0915002i	$0.0291662\pi$
$107$			19.5810i			0.183000i	−0.995805	+	0.0915002i	$0.970834\pi$
$108$		0			0
$109$	86.2205	+	149.338i	0.791014	+	1.37008i	0.925340	+	0.379139i	$0.123780\pi$
$109$	86.2205	+	149.338i	0.791014	+	1.37008i	−0.134326	+	0.990937i	$0.542887\pi$
$110$		0			0
$111$	49.6263	−	77.4207i	0.447084	−	0.697484i
$112$		0			0
$113$	−116.759	+	67.4111i	−1.03327	+	0.596559i	−0.917920	−	0.396766i	$-0.870132\pi$
$113$	−116.759	+	67.4111i	−1.03327	+	0.596559i	−0.115350	+	0.993325i	$0.536799\pi$
$114$		0			0
$115$	86.4171	−	149.679i	0.751453	−	1.30156i
$116$		0			0
$117$	6.35468	+	13.8284i	0.0543135	+	0.118191i
$118$		0			0
$119$		−	150.230i		−	1.26244i
$120$		0			0
$121$	86.7551	+	150.264i	0.716985	+	1.24185i
$122$		0			0
$123$	−190.100	+	98.2876i	−1.54553	+	0.799086i
$124$		0			0
$125$		−	3.38662i		−	0.0270929i
$126$		0			0
$127$	−73.3589	+	127.061i	−0.577629	+	1.00048i	0.418122	+	0.908391i	$0.362689\pi$
$127$	−73.3589	+	127.061i	−0.577629	+	1.00048i	−0.995751	+	0.0920915i	$0.970645\pi$
$128$		0			0
$129$	−8.67930	+	13.5404i	−0.0672814	+	0.104964i
$130$		0			0
$131$	−161.973	−	93.5151i	−1.23643	−	0.713855i	−0.268070	−	0.963399i	$-0.586386\pi$
$131$	−161.973	−	93.5151i	−1.23643	−	0.713855i	−0.968363	+	0.249544i	$0.919719\pi$
$132$		0			0
$133$	−58.9542	−	95.5597i	−0.443264	−	0.718494i
$134$		0			0
$135$	149.763	+	116.919i	1.10936	+	0.866070i
$136$		0			0
$137$	41.2192	−	23.7979i	0.300870	−	0.173707i	−0.341964	−	0.939713i	$-0.611092\pi$
$137$	41.2192	−	23.7979i	0.300870	−	0.173707i	0.642834	+	0.766006i	$0.277759\pi$
$138$		0			0
$139$	129.892			0.934476			0.467238	−	0.884132i	$-0.345249\pi$
$139$	129.892			0.934476			0.467238	+	0.884132i	$0.345249\pi$
$140$		0			0
$141$	5.34075	−	114.970i	0.0378776	−	0.815392i
$142$		0			0
$143$	−25.1312	−	14.5095i	−0.175742	−	0.101465i
$144$		0			0
$145$	35.2598			0.243171
$146$		0			0
$147$	−42.1852	−	1.95964i	−0.286974	−	0.0133309i
$148$		0			0
$149$	−222.082	−	128.219i	−1.49048	−	0.860530i	−0.490541	−	0.871418i	$-0.663201\pi$
$149$	−222.082	−	128.219i	−1.49048	−	0.860530i	−0.999941	+	0.0108886i	$0.996534\pi$
$150$		0			0
$151$	−37.8395	+	65.5400i	−0.250593	+	0.434040i	−0.963689	−	0.267026i	$-0.913959\pi$
$151$	−37.8395	+	65.5400i	−0.250593	+	0.434040i	0.713096	+	0.701066i	$0.247292\pi$
$152$		0			0
$153$	−186.682	−	132.273i	−1.22015	−	0.864530i
$154$		0			0
$155$		−	358.785i		−	2.31474i
$156$		0			0
$157$	−68.6526	+	118.910i	−0.437278	+	0.757387i	−0.997478	−	0.0709695i	$-0.977391\pi$
$157$	−68.6526	+	118.910i	−0.437278	+	0.757387i	0.560201	+	0.828357i	$0.310724\pi$
$158$		0			0
$159$	38.7989	−	20.0602i	0.244018	−	0.126165i
$160$		0			0
$161$	−125.699	−	72.5724i	−0.780740	−	0.450760i
$162$		0			0
$163$	−204.632			−1.25541			−0.627707	−	0.778450i	$-0.716006\pi$
$163$	−204.632			−1.25541			−0.627707	+	0.778450i	$0.716006\pi$
$164$		0			0
$165$	−361.900	−	16.8114i	−2.19333	−	0.101887i
$166$		0			0
$167$		−	48.9598i		−	0.293172i	−0.989198	−	0.146586i	$-0.953171\pi$
$167$		−	48.9598i		−	0.293172i	0.989198	−	0.146586i	$-0.0468286\pi$
$168$		0			0
$169$	−166.141			−0.983081
$170$		0			0
$171$	−170.654	−	10.8784i	−0.997974	−	0.0636165i
$172$		0			0
$173$			235.500i			1.36127i	0.732622	+	0.680635i	$0.238296\pi$
$173$			235.500i			1.36127i	−0.732622	+	0.680635i	$0.761704\pi$
$174$		0			0
$175$	144.895			0.827974
$176$		0			0
$177$	126.022	−	65.1570i	0.711986	−	0.368119i
$178$		0			0
$179$		−	295.150i		−	1.64888i	−0.565949	−	0.824440i	$-0.691490\pi$
$179$		−	295.150i		−	1.64888i	0.565949	−	0.824440i	$-0.308510\pi$
$180$		0			0
$181$	17.0737	−	29.5724i	0.0943296	−	0.163384i	−0.814999	−	0.579462i	$-0.803263\pi$
$181$	17.0737	−	29.5724i	0.0943296	−	0.163384i	0.909329	+	0.416079i	$0.136596\pi$
$182$		0			0
$183$	−283.895	−	13.1878i	−1.55134	−	0.0720646i
$184$		0			0
$185$	−186.808	−	107.854i	−1.00977	−	0.582993i
$186$		0			0
$187$	436.266			2.33297
$188$		0			0
$189$	98.1880	−	125.770i	0.519513	−	0.665449i
$190$		0			0
$191$	282.384	+	163.034i	1.47845	+	0.853584i	0.999703	−	0.0243694i	$-0.00775778\pi$
$191$	282.384	+	163.034i	1.47845	+	0.853584i	0.478747	+	0.877953i	$0.341091\pi$
$192$		0			0
$193$	54.2566	−	93.9752i	0.281122	−	0.486918i	−0.690539	−	0.723295i	$-0.742627\pi$
$193$	54.2566	−	93.9752i	0.281122	−	0.486918i	0.971661	+	0.236377i	$0.0759600\pi$
$194$		0			0
$195$	31.7099	−	16.3950i	0.162615	−	0.0840768i
$196$		0			0
$197$			62.3757i			0.316628i	0.987389	+	0.158314i	$0.0506058\pi$
$197$			62.3757i			0.316628i	−0.987389	+	0.158314i	$0.949394\pi$
$198$		0			0
$199$	−66.6982	+	115.525i	−0.335167	+	0.580526i	−0.983517	−	0.180817i	$-0.942126\pi$
$199$	−66.6982	+	115.525i	−0.335167	+	0.580526i	0.648350	+	0.761342i	$0.275459\pi$
$200$		0			0
$201$	−130.420	+	203.466i	−0.648858	+	1.01227i
$202$		0			0
$203$		−	29.6109i		−	0.145866i
$204$		0			0
$205$	250.992	+	434.730i	1.22435	+	2.12064i
$206$		0			0
$207$	−200.856	+	92.3012i	−0.970317	+	0.445899i
$208$		0			0
$209$	277.503	−	171.202i	1.32777	−	0.819147i
$210$		0			0
$211$	79.6230	−	137.911i	0.377360	−	0.653607i	−0.613317	−	0.789837i	$-0.710165\pi$
$211$	79.6230	−	137.911i	0.377360	−	0.653607i	0.990677	+	0.136230i	$0.0434985\pi$
$212$		0			0
$213$	18.7189	−	402.961i	0.0878819	−	1.89184i
$214$		0			0
$215$	32.6715	+	18.8629i	0.151960	+	0.0877343i
$216$		0			0
$217$	−301.305			−1.38850
$218$		0			0
$219$	2.59274	+	0.120441i	0.0118390	+	0.000549961i
$220$		0			0
$221$	−37.2275	+	21.4933i	−0.168450	+	0.0972548i
$222$		0			0
$223$	−42.1356			−0.188949			−0.0944744	−	0.995527i	$-0.530117\pi$
$223$	−42.1356			−0.188949			−0.0944744	+	0.995527i	$0.530117\pi$
$224$		0			0
$225$	127.576	−	180.053i	0.567004	−	0.800235i
$226$		0			0
$227$	121.312	+	70.0396i	0.534415	+	0.308545i	0.742812	−	0.669500i	$-0.233491\pi$
$227$	121.312	+	70.0396i	0.534415	+	0.308545i	−0.208398	+	0.978044i	$0.566825\pi$
$228$		0			0
$229$	95.4470	+	165.319i	0.416799	+	0.721917i	0.995615	−	0.0935406i	$-0.0298185\pi$
$229$	95.4470	+	165.319i	0.416799	+	0.721917i	−0.578816	+	0.815458i	$0.696485\pi$
$230$		0			0
$231$	−14.1181	+	303.920i	−0.0611173	+	1.31567i
$232$		0			0
$233$	84.4012	−	48.7290i	0.362237	−	0.209138i	−0.307825	−	0.951443i	$-0.599601\pi$
$233$	84.4012	−	48.7290i	0.362237	−	0.209138i	0.670062	+	0.742306i	$0.266268\pi$
$234$		0			0
$235$	−269.971			−1.14881
$236$		0			0
$237$	109.053	−	170.132i	0.460141	−	0.717855i
$238$		0			0
$239$	−11.7618	+	6.79066i	−0.0492124	+	0.0284128i	−0.524404	−	0.851469i	$-0.675712\pi$
$239$	−11.7618	+	6.79066i	−0.0492124	+	0.0284128i	0.475192	+	0.879882i	$0.342379\pi$
$240$		0			0
$241$	12.5763	+	21.7829i	0.0521840	+	0.0903853i	0.890937	−	0.454126i	$-0.150048\pi$
$241$	12.5763	+	21.7829i	0.0521840	+	0.0903853i	−0.838753	+	0.544511i	$0.816715\pi$
$242$		0			0
$243$	−69.8354	−	232.749i	−0.287389	−	0.957814i
$244$		0			0
$245$			99.0584i			0.404320i
$246$		0			0
$247$	−15.2454	+	28.2806i	−0.0617224	+	0.114496i
$248$		0			0
$249$	−261.669	+	135.291i	−1.05088	+	0.543337i
$250$		0			0
$251$	−284.518	−	164.266i	−1.13354	−	0.654447i	−0.188714	−	0.982032i	$-0.560432\pi$
$251$	−284.518	−	164.266i	−1.13354	−	0.654447i	−0.944822	+	0.327585i	$0.893765\pi$
$252$		0			0
$253$	210.749	−	365.028i	0.833000	−	1.44280i
$254$		0			0
$255$	−289.613	+	451.818i	−1.13574	+	1.77183i
$256$		0			0
$257$		−	497.762i		−	1.93682i	−0.249371	−	0.968408i	$-0.580224\pi$
$257$		−	497.762i		−	1.93682i	0.249371	−	0.968408i	$-0.419776\pi$
$258$		0			0
$259$	−90.5747	+	156.880i	−0.349709	+	0.605714i
$260$		0			0
$261$	−36.7957	−	26.0714i	−0.140980	−	0.0998906i
$262$		0			0
$263$		−	443.885i		−	1.68777i	−0.536521	−	0.843887i	$-0.680262\pi$
$263$		−	443.885i		−	1.68777i	0.536521	−	0.843887i	$-0.319738\pi$
$264$		0			0
$265$	−51.2267	−	88.7272i	−0.193308	−	0.334820i
$266$		0			0
$267$	−89.1062	+	46.0706i	−0.333731	+	0.172549i
$268$		0			0
$269$	−67.1951	+	38.7951i	−0.249796	+	0.144220i	−0.619671	−	0.784862i	$-0.712734\pi$
$269$	−67.1951	+	38.7951i	−0.249796	+	0.144220i	0.369875	+	0.929082i	$0.379401\pi$
$270$		0			0
$271$	−14.1771	−	24.5554i	−0.0523140	−	0.0906105i	0.838683	−	0.544621i	$-0.183326\pi$
$271$	−14.1771	−	24.5554i	−0.0523140	−	0.0906105i	−0.890997	+	0.454010i	$0.849993\pi$
$272$		0			0
$273$	−13.7684	−	26.6297i	−0.0504336	−	0.0975447i
$274$		0			0
$275$			420.773i			1.53009i
$276$		0			0
$277$	−80.2383	+	138.977i	−0.289669	+	0.501721i	−0.973731	−	0.227703i	$-0.926878\pi$
$277$	−80.2383	+	138.977i	−0.289669	+	0.501721i	0.684062	+	0.729424i	$0.260212\pi$
$278$		0			0
$279$	−265.289	+	374.414i	−0.950858	+	1.34198i
$280$		0			0
$281$	−166.952	+	96.3898i	−0.594135	+	0.343024i	−0.766731	−	0.641969i	$-0.778118\pi$
$281$	−166.952	+	96.3898i	−0.594135	+	0.343024i	0.172596	+	0.984993i	$0.444785\pi$
$282$		0			0
$283$	140.393	−	243.168i	0.496088	−	0.859250i	−0.503902	−	0.863761i	$-0.668103\pi$
$283$	140.393	−	243.168i	0.496088	−	0.859250i	0.999990	+	0.00451135i	$0.00143601\pi$
$284$		0			0
$285$	−6.91455	+	401.047i	−0.0242616	+	1.40718i
$286$		0			0
$287$	365.083	−	210.781i	1.27207	−	0.734428i
$288$		0			0
$289$	178.627	−	309.391i	0.618086	−	1.07056i
$290$		0			0
$291$	−12.9412	+	20.1893i	−0.0444716	+	0.0693791i
$292$		0			0
$293$	−17.7905	+	10.2714i	−0.0607185	+	0.0350559i	−0.530052	−	0.847965i	$-0.677828\pi$
$293$	−17.7905	+	10.2714i	−0.0607185	+	0.0350559i	0.469333	+	0.883021i	$0.344494\pi$
$294$		0			0
$295$	−166.388	−	288.192i	−0.564027	−	0.976923i
$296$		0			0
$297$	365.233	+	285.136i	1.22974	+	0.960054i
$298$		0			0
$299$			41.5314i			0.138901i
$300$		0			0
$301$	15.8409	−	27.4372i	0.0526275	−	0.0911536i
$302$		0			0
$303$	−4.63473	+	99.7719i	−0.0152961	+	0.329280i
$304$		0			0
$305$			666.636i			2.18569i
$306$		0			0
$307$	−43.0811	−	74.6187i	−0.140329	−	0.243058i	0.787291	−	0.616581i	$-0.211483\pi$
$307$	−43.0811	−	74.6187i	−0.140329	−	0.243058i	−0.927621	+	0.373524i	$0.878149\pi$
$308$		0			0
$309$	404.281	+	18.7802i	1.30835	+	0.0607772i
$310$		0			0
$311$	−519.182	+	299.750i	−1.66940	+	0.963826i	−0.701433	+	0.712736i	$0.747456\pi$
$311$	−519.182	+	299.750i	−1.66940	+	0.963826i	−0.967964	+	0.251090i	$0.919211\pi$
$312$		0			0
$313$	81.4152	+	141.015i	0.260112	+	0.450528i	0.966272	−	0.257525i	$-0.0829071\pi$
$313$	81.4152	+	141.015i	0.260112	+	0.450528i	−0.706159	+	0.708053i	$0.749574\pi$
$314$		0			0
$315$	−305.382	−	216.377i	−0.969467	−	0.686912i
$316$		0			0
$317$	185.646	−	107.183i	0.585634	−	0.338116i	−0.177735	−	0.984078i	$-0.556877\pi$
$317$	185.646	−	107.183i	0.585634	−	0.338116i	0.763369	+	0.645962i	$0.223544\pi$
$318$		0			0
$319$	85.9894			0.269559
$320$		0			0
$321$	−49.4553	−	31.7006i	−0.154066	−	0.0987558i
$322$		0			0
$323$	−14.0924	−	482.803i	−0.0436296	−	1.49475i
$324$		0			0
$325$	−20.7300	−	35.9055i	−0.0637847	−	0.110478i
$326$		0			0
$327$	−516.766	−	24.0055i	−1.58032	−	0.0734112i
$328$		0			0
$329$			226.720i			0.689117i
$330$		0			0
$331$	−233.185	+	403.888i	−0.704487	+	1.22021i	0.262390	+	0.964962i	$0.415489\pi$
$331$	−233.185	+	403.888i	−0.704487	+	1.22021i	−0.966877	+	0.255245i	$0.917844\pi$
$332$		0			0
$333$	115.197	+	250.680i	0.345938	+	0.752791i
$334$		0			0
$335$	490.941	+	283.445i	1.46550	+	0.846104i
$336$		0			0
$337$	5.52445	−	9.56863i	0.0163930	−	0.0283936i	−0.857713	−	0.514130i	$-0.828115\pi$
$337$	5.52445	−	9.56863i	0.0163930	−	0.0283936i	0.874106	+	0.485736i	$0.161448\pi$
$338$		0			0
$339$	18.7686	−	404.031i	0.0553645	−	1.19183i
$340$		0			0
$341$		−	874.984i		−	2.56593i
$342$		0			0
$343$	372.758			1.08676
$344$		0			0
$345$	238.135	+	460.583i	0.690248	+	1.33502i
$346$		0			0
$347$	57.5958	+	33.2529i	0.165982	+	0.0958298i	0.580690	−	0.814125i	$-0.302783\pi$
$347$	57.5958	+	33.2529i	0.165982	+	0.0958298i	−0.414708	+	0.909955i	$0.636116\pi$
$348$		0			0
$349$	−74.8996	+	129.730i	−0.214612	+	0.371719i	−0.953152	−	0.302490i	$-0.902182\pi$
$349$	−74.8996	+	129.730i	−0.214612	+	0.371719i	0.738540	+	0.674209i	$0.235515\pi$
$350$		0			0
$351$	−45.2138	−	6.33748i	−0.128814	−	0.0180555i
$352$		0			0
$353$	402.700	+	232.499i	1.14079	+	0.658638i	0.946627	−	0.322331i	$-0.104466\pi$
$353$	402.700	+	232.499i	1.14079	+	0.658638i	0.194167	+	0.980968i	$0.437800\pi$
$354$		0			0
$355$	−946.226			−2.66542
$356$		0			0
$357$	379.433	+	243.215i	1.06284	+	0.681273i
$358$		0			0
$359$	62.8015	−	36.2585i	0.174935	−	0.100999i	−0.409976	−	0.912096i	$-0.634463\pi$
$359$	62.8015	−	36.2585i	0.174935	−	0.100999i	0.584911	+	0.811098i	$0.301130\pi$
$360$		0			0
$361$	−198.428	−	301.575i	−0.549662	−	0.835387i
$362$		0			0
$363$	−519.970	−	24.1543i	−1.43242	−	0.0665408i
$364$		0			0
$365$		−	6.08823i		−	0.0166801i
$366$		0			0
$367$	−43.6168	−	75.5466i	−0.118847	−	0.205849i	0.800464	−	0.599381i	$-0.204586\pi$
$367$	−43.6168	−	75.5466i	−0.118847	−	0.205849i	−0.919311	+	0.393532i	$0.871253\pi$
$368$		0			0
$369$	59.5192	−	639.253i	0.161299	−	1.73239i
$370$		0			0
$371$	−74.5124	+	43.0198i	−0.200842	+	0.115956i
$372$		0			0
$373$	22.9854	+	39.8119i	0.0616231	+	0.106734i	0.895191	−	0.445683i	$-0.147039\pi$
$373$	22.9854	+	39.8119i	0.0616231	+	0.106734i	−0.833568	+	0.552417i	$0.813706\pi$
$374$		0			0
$375$	8.55349	+	5.48274i	0.0228093	+	0.0146206i
$376$		0			0
$377$	−7.33766	+	4.23640i	−0.0194633	+	0.0112371i
$378$		0			0
$379$	619.505			1.63458			0.817288	−	0.576229i	$-0.195476\pi$
$379$	619.505			1.63458			0.817288	+	0.576229i	$0.195476\pi$
$380$		0			0
$381$	−202.151	−	390.986i	−0.530581	−	1.02621i
$382$		0			0
$383$	478.580	+	276.308i	1.24956	+	0.721432i	0.971021	−	0.238994i	$-0.0768177\pi$
$383$	478.580	+	276.308i	1.24956	+	0.721432i	0.278535	+	0.960426i	$0.410151\pi$
$384$		0			0
$385$	713.660			1.85366
$386$		0			0
$387$	−20.1472	−	43.8422i	−0.0520600	−	0.113287i
$388$		0			0
$389$	57.9442	−	33.4541i	0.148957	−	0.0860003i	−0.423669	−	0.905817i	$-0.639258\pi$
$389$	57.9442	−	33.4541i	0.148957	−	0.0860003i	0.572626	+	0.819817i	$0.305925\pi$
$390$		0			0
$391$	−312.188	−	540.726i	−0.798435	−	1.38293i
$392$		0			0
$393$	498.413	−	257.695i	1.26823	−	0.655712i
$394$		0			0
$395$	−410.509	−	237.008i	−1.03926	−	0.600020i
$396$		0			0
$397$	−380.194	−	658.515i	−0.957667	−	1.65873i	−0.728144	−	0.685424i	$-0.759617\pi$
$397$	−380.194	−	658.515i	−0.957667	−	1.65873i	−0.229523	−	0.973303i	$-0.573717\pi$
$398$		0			0
$399$	336.796	+	5.80678i	0.844100	+	0.0145533i
$400$		0			0
$401$	229.471	+	132.485i	0.572247	+	0.330387i	0.758046	−	0.652201i	$-0.226154\pi$
$401$	229.471	+	132.485i	0.572247	+	0.330387i	−0.185799	+	0.982588i	$0.559487\pi$
$402$		0			0
$403$	43.1074	+	74.6642i	0.106966	+	0.185271i
$404$		0			0
$405$	−537.758	+	188.967i	−1.32780	+	0.466585i
$406$		0			0
$407$	−455.576	−	263.027i	−1.11935	−	0.646258i
$408$		0			0
$409$	−446.236			−1.09104			−0.545521	−	0.838097i	$-0.683668\pi$
$409$	−446.236			−1.09104			−0.545521	+	0.838097i	$0.683668\pi$
$410$		0			0
$411$	−6.62579	+	142.634i	−0.0161212	+	0.347040i
$412$		0			0
$413$	−242.022	+	139.731i	−0.586008	+	0.338332i
$414$		0			0
$415$	345.485	+	598.398i	0.832494	+	1.44192i
$416$		0			0
$417$	−210.288	+	328.065i	−0.504288	+	0.786727i
$418$		0			0
$419$	−314.327	+	181.477i	−0.750183	+	0.433119i	−0.825760	−	0.564021i	$-0.809254\pi$
$419$	−314.327	+	181.477i	−0.750183	+	0.433119i	0.0755768	+	0.997140i	$0.475920\pi$
$420$		0			0
$421$	−170.301			−0.404515			−0.202257	−	0.979332i	$-0.564828\pi$
$421$	−170.301			−0.404515			−0.202257	+	0.979332i	$0.564828\pi$
$422$		0			0
$423$	281.731	+	199.619i	0.666031	+	0.471914i
$424$		0			0
$425$	539.797	+	311.652i	1.27011	+	0.733298i
$426$		0			0
$427$	559.835			1.31109
$428$		0			0
$429$	77.3322	−	39.9831i	0.180261	−	0.0932006i
$430$		0			0
$431$	−183.959	−	106.209i	−0.426818	−	0.246424i	0.271172	−	0.962531i	$-0.412589\pi$
$431$	−183.959	−	106.209i	−0.426818	−	0.246424i	−0.697990	+	0.716107i	$0.745922\pi$
$432$		0			0
$433$	−178.510	+	309.188i	−0.412263	+	0.714061i	−0.995137	−	0.0985019i	$-0.968595\pi$
$433$	−178.510	+	309.188i	−0.412263	+	0.714061i	0.582874	+	0.812563i	$0.301928\pi$
$434$		0			0
$435$	−57.0836	+	89.0547i	−0.131227	+	0.204723i
$436$		0			0
$437$	−410.773	−	221.438i	−0.939985	−	0.506724i
$438$		0			0
$439$	−129.965			−0.296048			−0.148024	−	0.988984i	$-0.547291\pi$
$439$	−129.965			−0.296048			−0.148024	+	0.988984i	$0.547291\pi$
$440$		0			0
$441$	73.2448	−	103.373i	0.166088	−	0.234407i
$442$		0			0
$443$	−310.039	+	179.001i	−0.699863	+	0.404066i	−0.807296	−	0.590146i	$-0.799070\pi$
$443$	−310.039	+	179.001i	−0.699863	+	0.404066i	0.107434	+	0.994212i	$0.465737\pi$
$444$		0			0
$445$	117.648	+	203.772i	0.264378	+	0.457915i
$446$		0			0
$447$	683.377	−	353.327i	1.52881	−	0.790440i
$448$		0			0
$449$		−	146.426i		−	0.326116i	−0.986616	−	0.163058i	$-0.947864\pi$
$449$		−	146.426i		−	0.326116i	0.986616	−	0.163058i	$-0.0521358\pi$
$450$		0			0
$451$	612.103	+	1060.19i	1.35721	+	2.35076i
$452$		0			0
$453$	−104.273	−	201.676i	−0.230182	−	0.445200i
$454$		0			0
$455$	−60.8981	+	35.1595i	−0.133842	+	0.0772737i
$456$		0			0
$457$	424.977	−	736.082i	0.929928	−	1.61068i	0.146491	−	0.989212i	$-0.453202\pi$
$457$	424.977	−	736.082i	0.929928	−	1.61068i	0.783437	−	0.621471i	$-0.213465\pi$
$458$		0			0
$459$	636.307	−	257.356i	1.38629	−	0.560689i
$460$		0			0
$461$			611.058i			1.32551i	0.748838	+	0.662753i	$0.230612\pi$
$461$			611.058i			1.32551i	−0.748838	+	0.662753i	$0.769388\pi$
$462$		0			0
$463$	295.664	+	512.105i	0.638583	+	1.10606i	0.985744	+	0.168252i	$0.0538124\pi$
$463$	295.664	+	512.105i	0.638583	+	1.10606i	−0.347161	+	0.937806i	$0.612854\pi$
$464$		0			0
$465$	906.174	+	580.853i	1.94876	+	1.24915i
$466$		0			0
$467$		−	288.535i		−	0.617848i	−0.951087	−	0.308924i	$-0.900031\pi$
$467$		−	288.535i		−	0.617848i	0.951087	−	0.308924i	$-0.0999688\pi$
$468$		0			0
$469$	238.035	−	412.288i	0.507537	−	0.879080i
$470$		0			0
$471$	−189.183	−	365.902i	−0.401662	−	0.776863i
$472$		0			0
$473$	79.6772	+	46.0016i	0.168451	+	0.0972551i
$474$		0			0
$475$	465.658	−	13.5919i	0.980332	−	0.0286145i
$476$		0			0
$477$	−12.1477	+	130.470i	−0.0254669	+	0.273521i
$478$		0			0
$479$	−9.66681	+	5.58113i	−0.0201812	+	0.0116516i	−0.510057	−	0.860141i	$-0.670376\pi$
$479$	−9.66681	+	5.58113i	−0.0201812	+	0.0116516i	0.489875	+	0.871792i	$0.337042\pi$
$480$		0			0
$481$	51.8337			0.107762
$482$		0			0
$483$	386.794	−	199.984i	0.800816	−	0.414046i
$484$		0			0
$485$	48.7147	+	28.1254i	0.100443	+	0.0579906i
$486$		0			0
$487$	372.703			0.765304			0.382652	−	0.923892i	$-0.375011\pi$
$487$	372.703			0.765304			0.382652	+	0.923892i	$0.375011\pi$
$488$		0			0
$489$	331.288	−	516.834i	0.677481	−	1.05692i
$490$		0			0
$491$	219.366	+	126.651i	0.446774	+	0.257945i	0.706467	−	0.707746i	$-0.250288\pi$
$491$	219.366	+	126.651i	0.446774	+	0.257945i	−0.259693	+	0.965691i	$0.583621\pi$
$492$		0			0
$493$	63.6893	−	110.313i	0.129187	−	0.223759i
$494$		0			0
$495$	628.355	−	886.823i	1.26940	−	1.79156i
$496$		0			0
$497$			794.633i			1.59886i
$498$		0			0
$499$	−426.697	+	739.062i	−0.855105	+	1.48109i	0.0214423	+	0.999770i	$0.493174\pi$
$499$	−426.697	+	739.062i	−0.855105	+	1.48109i	−0.876547	+	0.481315i	$0.840159\pi$
$500$		0			0
$501$	123.656	+	79.2631i	0.246819	+	0.158210i
$502$		0			0
$503$	362.114	+	209.067i	0.719908	+	0.415639i	0.814719	−	0.579856i	$-0.196891\pi$
$503$	362.114	+	209.067i	0.719908	+	0.415639i	−0.0948105	+	0.995495i	$0.530225\pi$
$504$		0			0
$505$	234.283			0.463926
$506$		0			0
$507$	268.972	−	419.617i	0.530517	−	0.827647i
$508$		0			0
$509$			183.285i			0.360088i	0.983659	+	0.180044i	$0.0576240\pi$
$509$			183.285i			0.360088i	−0.983659	+	0.180044i	$0.942376\pi$
$510$		0			0
$511$	−5.11285			−0.0100056
$512$		0			0
$513$	303.754	−	413.404i	0.592113	−	0.805855i
$514$		0			0
$515$		−	949.325i		−	1.84335i
$516$		0			0
$517$	−658.389			−1.27348
$518$		0			0
$519$	−594.796	−	381.261i	−1.14604	−	0.734607i
$520$		0			0
$521$			434.260i			0.833513i	0.909018	+	0.416757i	$0.136833\pi$
$521$			434.260i			0.833513i	−0.909018	+	0.416757i	$0.863167\pi$
$522$		0			0
$523$	−389.570	+	674.755i	−0.744875	+	1.29016i	0.205378	+	0.978683i	$0.434158\pi$
$523$	−389.570	+	674.755i	−0.744875	+	1.29016i	−0.950253	+	0.311479i	$0.899176\pi$
$524$		0			0
$525$	−234.577	+	365.958i	−0.446814	+	0.697063i
$526$		0			0
$527$	−1122.49	−	648.069i	−2.12996	−	1.22973i
$528$		0			0
$529$	−74.2401			−0.140340
$530$		0			0
$531$	−39.4566	+	423.775i	−0.0743062	+	0.798069i
$532$		0			0
$533$	−104.464	−	60.3124i	−0.195993	−	0.113156i
$534$		0			0
$535$	−68.8955	+	119.330i	−0.128777	+	0.223048i
$536$		0			0
$537$	745.451	+	477.830i	1.38818	+	0.889815i
$538$		0			0
$539$			241.578i			0.448196i
$540$		0			0
$541$	−191.863	+	332.316i	−0.354644	+	0.614262i	−0.987057	−	0.160370i	$-0.948731\pi$
$541$	−191.863	+	332.316i	−0.354644	+	0.614262i	0.632413	+	0.774632i	$0.282065\pi$
$542$		0			0
$543$	47.0490	+	90.9986i	0.0866465	+	0.167585i
$544$		0			0
$545$			1213.46i			2.22653i
$546$		0			0
$547$	262.281	+	454.284i	0.479489	+	0.830500i	0.999723	−	0.0235238i	$-0.00748855\pi$
$547$	262.281	+	454.284i	0.479489	+	0.830500i	−0.520234	+	0.854024i	$0.674155\pi$
$548$		0			0
$549$	492.917	−	695.675i	0.897846	−	1.26717i
$550$		0			0
$551$	−2.77765	−	95.1620i	−0.00504110	−	0.172708i
$552$		0			0
$553$	−199.037	+	344.742i	−0.359923	+	0.623404i
$554$		0			0
$555$	574.835	−	297.207i	1.03574	−	0.535508i
$556$		0			0
$557$	648.964	+	374.680i	1.16511	+	0.672674i	0.952522	−	0.304469i	$-0.0984789\pi$
$557$	648.964	+	374.680i	1.16511	+	0.672674i	0.212583	+	0.977143i	$0.431812\pi$
$558$		0			0
$559$	−9.06536			−0.0162171
$560$		0			0
$561$	−706.290	+	1101.87i	−1.25898	+	1.96411i
$562$		0			0
$563$	384.547	−	222.018i	0.683032	−	0.394348i	−0.117965	−	0.993018i	$-0.537637\pi$
$563$	384.547	−	222.018i	0.683032	−	0.394348i	0.800996	+	0.598669i	$0.204304\pi$
$564$		0			0
$565$	−948.738			−1.67918
$566$		0			0
$567$	158.693	+	451.605i	0.279882	+	0.796482i
$568$		0			0
$569$	142.613	+	82.3379i	0.250639	+	0.144706i	0.620057	−	0.784557i	$-0.287110\pi$
$569$	142.613	+	82.3379i	0.250639	+	0.144706i	−0.369418	+	0.929263i	$0.620443\pi$
$570$		0			0
$571$	264.801	+	458.649i	0.463750	+	0.803238i	0.999144	−	0.0413641i	$-0.0131703\pi$
$571$	264.801	+	458.649i	0.463750	+	0.803238i	−0.535394	+	0.844602i	$0.679837\pi$
$572$		0			0
$573$	−868.935	+	449.266i	−1.51647	+	0.784059i
$574$		0			0
$575$	521.523	−	301.102i	0.906997	−	0.523655i
$576$		0			0
$577$	−907.310			−1.57246			−0.786230	−	0.617933i	$-0.787970\pi$
$577$	−907.310			−1.57246			−0.786230	+	0.617933i	$0.787970\pi$
$578$		0			0
$579$	149.512	+	289.175i	0.258225	+	0.499439i
$580$		0			0
$581$	502.530	−	290.136i	0.864939	−	0.499373i
$582$		0			0
$583$	−124.929	−	216.383i	−0.214286	−	0.371154i
$584$		0			0
$585$	−9.92817	+	106.631i	−0.0169712	+	0.182276i
$586$		0			0
$587$		−	60.8421i		−	0.103649i	−0.998656	−	0.0518246i	$-0.983496\pi$
$587$		−	60.8421i		−	0.103649i	0.998656	−	0.0518246i	$-0.0165037\pi$
$588$		0			0
$589$	−968.319	+	28.2639i	−1.64400	+	0.0479862i
$590$		0			0
$591$	−157.541	−	100.983i	−0.266566	−	0.170868i
$592$		0			0
$593$	−431.969	−	249.397i	−0.728447	−	0.420569i	0.0894067	−	0.995995i	$-0.471503\pi$
$593$	−431.969	−	249.397i	−0.728447	−	0.420569i	−0.817854	+	0.575426i	$0.804836\pi$
$594$		0			0
$595$	528.582	−	915.532i	0.888374	−	1.53871i
$596$		0			0
$597$	−183.797	−	355.486i	−0.307867	−	0.595453i
$598$		0			0
$599$			903.010i			1.50753i	0.657145	+	0.753764i	$0.271764\pi$
$599$			903.010i			1.50753i	−0.657145	+	0.753764i	$0.728236\pi$
$600$		0			0
$601$	98.9079	−	171.314i	0.164572	−	0.285047i	−0.771931	−	0.635706i	$-0.780709\pi$
$601$	98.9079	−	171.314i	0.164572	−	0.285047i	0.936503	+	0.350659i	$0.114042\pi$
$602$		0			0
$603$	−302.744	−	658.799i	−0.502063	−	1.09253i
$604$		0			0
$605$			1220.98i			2.01816i
$606$		0			0
$607$	−262.991	−	455.514i	−0.433264	−	0.750435i	0.563888	−	0.825851i	$-0.309305\pi$
$607$	−262.991	−	455.514i	−0.433264	−	0.750435i	−0.997152	+	0.0754162i	$0.975971\pi$
$608$		0			0
$609$	74.7874	+	47.9383i	0.122804	+	0.0787165i
$610$		0			0
$611$	56.1817	−	32.4365i	0.0919505	−	0.0530876i
$612$		0			0
$613$	−246.020	−	426.118i	−0.401337	−	0.695136i	0.592551	−	0.805533i	$-0.298121\pi$
$613$	−246.020	−	426.118i	−0.401337	−	0.695136i	−0.993888	+	0.110397i	$0.964788\pi$
$614$		0			0
$615$	−1504.33	−	69.8809i	−2.44606	−	0.113628i
$616$		0			0
$617$			656.509i			1.06403i	0.846734	+	0.532017i	$0.178566\pi$
$617$			656.509i			1.06403i	−0.846734	+	0.532017i	$0.821434\pi$
$618$		0			0
$619$	−483.420	+	837.308i	−0.780969	+	1.35268i	0.150409	+	0.988624i	$0.451941\pi$
$619$	−483.420	+	837.308i	−0.780969	+	1.35268i	−0.931378	+	0.364054i	$0.881392\pi$
$620$		0			0
$621$	92.0512	−	656.726i	0.148231	−	1.05753i
$622$		0			0
$623$	171.126	−	98.7999i	0.274681	−	0.158587i
$624$		0			0
$625$	318.400	−	551.485i	0.509440	−	0.882376i
$626$		0			0
$627$	−16.8628	+	978.049i	−0.0268944	+	1.55989i
$628$		0			0
$629$	−674.858	+	389.629i	−1.07291	+	0.619443i
$630$		0			0
$631$	340.653	−	590.028i	0.539862	−	0.935068i	−0.459049	−	0.888411i	$-0.651810\pi$
$631$	340.653	−	590.028i	0.539862	−	0.935068i	0.998911	−	0.0466568i	$-0.0148567\pi$
$632$		0			0
$633$	219.413	+	424.372i	0.346624	+	0.670414i
$634$		0			0
$635$	−894.125	+	516.223i	−1.40807	+	0.812950i
$636$		0			0
$637$	−11.9017	−	20.6143i	−0.0186840	−	0.0323616i
$638$		0			0
$639$	987.443	+	699.649i	1.54529	+	1.09491i
$640$		0			0
$641$		−	514.323i		−	0.802377i	−0.915996	−	0.401188i	$-0.868597\pi$
$641$		−	514.323i		−	0.802377i	0.915996	−	0.401188i	$-0.131403\pi$
$642$		0			0
$643$	105.365	−	182.498i	0.163865	−	0.283823i	−0.772387	−	0.635153i	$-0.780937\pi$
$643$	105.365	−	182.498i	0.163865	−	0.283823i	0.936252	+	0.351330i	$0.114270\pi$
$644$		0			0
$645$	−100.535	+	51.9795i	−0.155868	+	0.0805884i
$646$		0			0
$647$		−	547.085i		−	0.845572i	−0.906230	−	0.422786i	$-0.861052\pi$
$647$		−	547.085i		−	0.845572i	0.906230	−	0.422786i	$-0.138948\pi$
$648$		0			0
$649$	−405.777	−	702.826i	−0.625234	−	1.08294i
$650$		0			0
$651$	487.795	−	760.997i	0.749302	−	1.16897i
$652$		0			0
$653$	713.415	−	411.890i	1.09252	−	0.630766i	0.158273	−	0.987395i	$-0.449407\pi$
$653$	713.415	−	411.890i	1.09252	−	0.630766i	0.934246	+	0.356629i	$0.116074\pi$
$654$		0			0
$655$	−658.061	−	1139.80i	−1.00467	−	1.74015i
$656$		0			0
$657$	−4.50170	+	6.35344i	−0.00685191	+	0.00967038i
$658$		0			0
$659$	34.8216	−	20.1043i	0.0528401	−	0.0305073i	−0.473347	−	0.880876i	$-0.656954\pi$
$659$	34.8216	−	20.1043i	0.0528401	−	0.0305073i	0.526187	+	0.850369i	$0.323621\pi$
$660$		0			0
$661$	−786.041			−1.18917			−0.594585	−	0.804033i	$-0.702684\pi$
$661$	−786.041			−1.18917			−0.594585	+	0.804033i	$0.702684\pi$
$662$		0			0
$663$	5.98415	−	128.821i	0.00902587	−	0.194300i
$664$		0			0
$665$	−23.0528	−	789.787i	−0.0346659	−	1.18765i
$666$		0			0
$667$	−61.5333	−	106.579i	−0.0922538	−	0.159788i
$668$		0			0
$669$	68.2151	−	106.421i	0.101966	−	0.159074i
$670$		0			0
$671$			1625.75i			2.42288i
$672$		0			0
$673$	512.431	−	887.556i	0.761413	−	1.31881i	−0.180710	−	0.983536i	$-0.557840\pi$
$673$	512.431	−	887.556i	0.761413	−	1.31881i	0.942122	−	0.335269i	$-0.108827\pi$
$674$		0			0
$675$	248.217	+	613.710i	0.367729	+	0.909200i
$676$		0			0
$677$	−202.004	−	116.627i	−0.298380	−	0.172270i	0.343335	−	0.939213i	$-0.388444\pi$
$677$	−202.004	−	116.627i	−0.298380	−	0.172270i	−0.641715	+	0.766943i	$0.721777\pi$
$678$		0			0
$679$	23.6195	−	40.9102i	0.0347857	−	0.0602507i
$680$		0			0
$681$	−373.295	+	193.005i	−0.548157	+	0.283414i
$682$		0			0
$683$		−	669.562i		−	0.980326i	−0.871631	−	0.490163i	$-0.836937\pi$
$683$		−	669.562i		−	0.980326i	0.871631	−	0.490163i	$-0.163063\pi$
$684$		0			0
$685$	334.929			0.488948
$686$		0			0
$687$	−572.065	−	26.5743i	−0.832700	−	0.0386816i
$688$		0			0
$689$	21.3208	+	12.3096i	0.0309446	+	0.0178659i
$690$		0			0
$691$	495.592	−	858.390i	0.717210	−	1.24224i	−0.244891	−	0.969551i	$-0.578752\pi$
$691$	495.592	−	858.390i	0.717210	−	1.24224i	0.962101	−	0.272693i	$-0.0879143\pi$
$692$		0			0
$693$	−744.747	−	527.688i	−1.07467	−	0.761454i
$694$		0			0
$695$	791.586	+	457.023i	1.13897	+	0.657586i
$696$		0			0
$697$	1813.45			2.60180
$698$		0			0
$699$	−13.5671	+	292.059i	−0.0194093	+	0.417824i
$700$		0			0
$701$	225.129	−	129.978i	0.321154	−	0.185418i	−0.330753	−	0.943717i	$-0.607303\pi$
$701$	225.129	−	129.978i	0.321154	−	0.185418i	0.651907	+	0.758299i	$0.273969\pi$
$702$		0			0
$703$	−276.368	+	512.669i	−0.393127	+	0.729259i
$704$		0			0
$705$	437.068	−	681.859i	0.619955	−	0.967176i
$706$		0			0
$707$		−	196.749i		−	0.278287i
$708$		0			0
$709$	−119.700	−	207.326i	−0.168829	−	0.292420i	0.769180	−	0.639033i	$-0.220665\pi$
$709$	−119.700	−	207.326i	−0.168829	−	0.292420i	−0.938008	+	0.346613i	$0.887332\pi$
$710$		0			0
$711$	253.145	+	550.867i	0.356041	+	0.774777i
$712$		0			0
$713$	−1084.49	+	626.130i	−1.52102	+	0.878163i
$714$		0			0
$715$	−102.103	−	176.847i	−0.142801	−	0.247338i
$716$		0			0
$717$	1.89065	−	40.7001i	0.00263689	−	0.0567644i
$718$		0			0
$719$	369.672	−	213.430i	0.514147	−	0.296843i	−0.220390	−	0.975412i	$-0.570733\pi$
$719$	369.672	−	213.430i	0.514147	−	0.296843i	0.734537	+	0.678569i	$0.237400\pi$
$720$		0			0
$721$	−797.235			−1.10574
$722$		0			0
$723$	−75.3768	−	3.50150i	−0.104256	−	0.00484301i
$724$		0			0
$725$	106.396	+	61.4275i	0.146753	+	0.0847276i
$726$		0			0
$727$	−1034.99			−1.42365			−0.711824	−	0.702358i	$-0.752131\pi$
$727$	−1034.99			−1.42365			−0.711824	+	0.702358i	$0.752131\pi$
$728$		0			0
$729$	700.907	+	200.426i	0.961464	+	0.274932i
$730$		0			0
$731$	118.028	−	68.1435i	0.161461	−	0.0932196i
$732$		0			0
$733$	−327.088	−	566.533i	−0.446232	−	0.772896i	0.551905	−	0.833907i	$-0.313901\pi$
$733$	−327.088	−	566.533i	−0.446232	−	0.772896i	−0.998137	+	0.0610108i	$0.980568\pi$
$734$		0			0
$735$	−250.189	−	160.370i	−0.340393	−	0.218190i
$736$		0			0
$737$	1197.28	+	691.248i	1.62453	+	0.937922i
$738$		0			0
$739$	−683.303	−	1183.51i	−0.924631	−	1.60151i	−0.792153	−	0.610322i	$-0.791040\pi$
$739$	−683.303	−	1183.51i	−0.924631	−	1.60151i	−0.132478	−	0.991186i	$-0.542293\pi$
$740$		0			0
$741$	−46.7461	−	84.2897i	−0.0630852	−	0.113751i
$742$		0			0
$743$	280.625	+	162.019i	0.377692	+	0.218061i	0.676814	−	0.736154i	$-0.263360\pi$
$743$	280.625	+	162.019i	0.377692	+	0.218061i	−0.299122	+	0.954215i	$0.596694\pi$
$744$		0			0
$745$	−902.271	−	1562.78i	−1.21110	−	2.09769i
$746$		0			0
$747$	81.9270	−	879.919i	0.109675	−	1.17794i
$748$		0			0
$749$	100.213	+	57.8579i	0.133795	+	0.0772468i
$750$		0			0
$751$	363.697			0.484284			0.242142	−	0.970241i	$-0.422150\pi$
$751$	363.697			0.484284			0.242142	+	0.970241i	$0.422150\pi$
$752$		0			0
$753$	875.501	−	452.660i	1.16268	−	0.601143i
$754$		0			0
$755$	−461.202	+	266.275i	−0.610864	+	0.352682i
$756$		0			0
$757$	538.057	+	931.942i	0.710775	+	1.23110i	0.964566	+	0.263840i	$0.0849891\pi$
$757$	538.057	+	931.942i	0.710775	+	1.23110i	−0.253791	+	0.967259i	$0.581678\pi$
$758$		0			0
$759$	580.750	+	1123.24i	0.765152	+	1.47990i
$760$		0			0
$761$	−659.022	+	380.487i	−0.865995	+	0.499983i	−0.866015	−	0.500017i	$-0.833327\pi$
$761$	−659.022	+	380.487i	−0.865995	+	0.499983i	2.00331e−5		1.00000i	$0.499994\pi$
$762$		0			0
$763$	1019.05			1.33559
$764$		0			0
$765$	−672.277	−	1462.93i	−0.878793	−	1.91233i
$766$		0			0
$767$	69.2515	+	39.9824i	0.0902888	+	0.0521283i
$768$		0			0
$769$	665.877			0.865900			0.432950	−	0.901418i	$-0.357473\pi$
$769$	665.877			0.865900			0.432950	+	0.901418i	$0.357473\pi$
$770$		0			0
$771$	1257.18	+	805.848i	1.63059	+	1.04520i
$772$		0			0
$773$	−182.002	−	105.079i	−0.235449	−	0.135936i	0.377634	−	0.925955i	$-0.376738\pi$
$773$	−182.002	−	105.079i	−0.235449	−	0.135936i	−0.613083	+	0.790018i	$0.710071\pi$
$774$		0			0
$775$	625.054	−	1082.63i	0.806522	−	1.39694i
$776$		0			0
$777$	−249.592	−	482.742i	−0.321225	−	0.621289i
$778$		0			0
$779$	1153.51	−	711.644i	1.48076	−	0.913535i
$780$		0			0
$781$	−2307.60			−2.95467
$782$		0			0
$783$	125.418	−	50.7257i	0.160176	−	0.0647838i
$784$		0			0
$785$	−836.763	+	483.105i	−1.06594	+	0.615421i
$786$		0			0
$787$	643.922	+	1115.30i	0.818198	+	1.41716i	0.907009	+	0.421111i	$0.138360\pi$
$787$	643.922	+	1115.30i	0.818198	+	1.41716i	−0.0888113	+	0.996048i	$0.528307\pi$
$788$		0			0
$789$	1121.11	+	718.624i	1.42092	+	0.910804i
$790$		0			0
$791$			796.743i			1.00726i
$792$		0			0
$793$	−80.0951	−	138.729i	−0.101003	−	0.174942i
$794$		0			0
$795$	307.029	+	14.2625i	0.386200	+	0.0179403i
$796$		0			0
$797$	−353.437	+	204.057i	−0.443459	+	0.256031i	−0.705064	−	0.709144i	$-0.749082\pi$
$797$	−353.437	+	204.057i	−0.443459	+	0.256031i	0.261605	+	0.965175i	$0.415748\pi$
$798$		0			0
$799$	−487.645	+	844.626i	−0.610320	+	1.05710i
$800$		0			0
$801$	27.8986	−	299.639i	0.0348297	−	0.374081i
$802$		0			0
$803$		−	14.8476i		−	0.0184902i
$804$		0			0
$805$	−510.689	−	884.539i	−0.634396	−	1.09881i
$806$		0			0
$807$	10.8013	−	232.520i	0.0133845	−	0.288129i
$808$		0			0
$809$		−	1173.72i		−	1.45082i	−0.688315	−	0.725412i	$-0.741649\pi$
$809$		−	1173.72i		−	1.45082i	0.688315	−	0.725412i	$-0.258351\pi$
$810$		0			0
$811$	−695.637	+	1204.88i	−0.857752	+	1.48567i	0.0163156	+	0.999867i	$0.494806\pi$
$811$	−695.637	+	1204.88i	−0.857752	+	1.48567i	−0.874068	+	0.485804i	$0.838527\pi$
$812$		0			0
$813$	84.9709	+	3.94718i	0.104515	+	0.00485508i
$814$		0			0
$815$	−1247.07	−	719.994i	−1.53014	−	0.883429i
$816$		0			0
$817$	48.3349	−	89.6624i	0.0591615	−	0.109746i
$818$		0			0
$819$	89.5481	+	8.33760i	0.109338	+	0.0101802i
$820$		0			0
$821$	−125.681	+	72.5620i	−0.153083	+	0.0883824i	−0.574585	−	0.818445i	$-0.694836\pi$
$821$	−125.681	+	72.5620i	−0.153083	+	0.0883824i	0.421502	+	0.906828i	$0.361503\pi$
$822$		0			0
$823$	−1165.56			−1.41623			−0.708117	−	0.706096i	$-0.750455\pi$
$823$	−1165.56			−1.41623			−0.708117	+	0.706096i	$0.750455\pi$
$824$		0			0
$825$	−1062.74	−	681.208i	−1.28816	−	0.825707i
$826$		0			0
$827$	−1350.34	−	779.619i	−1.63282	−	0.942707i	−0.983219	−	0.182429i	$-0.941604\pi$
$827$	−1350.34	−	779.619i	−1.63282	−	0.942707i	−0.649597	−	0.760278i	$-0.725063\pi$
$828$		0			0
$829$	−1328.51			−1.60255			−0.801275	−	0.598297i	$-0.795844\pi$
$829$	−1328.51			−1.60255			−0.801275	+	0.598297i	$0.795844\pi$
$830$		0			0
$831$	−221.109	−	427.651i	−0.266075	−	0.514622i
$832$		0			0
$833$	309.912	+	178.928i	0.372044	+	0.214799i
$834$		0			0
$835$	172.264	−	298.370i	0.206304	−	0.357329i
$836$		0			0
$837$	−516.158	−	1276.19i	−0.616676	−	1.52472i
$838$		0			0
$839$			140.127i			0.167017i	0.996507	+	0.0835084i	$0.0266125\pi$
$839$			140.127i			0.167017i	−0.996507	+	0.0835084i	$0.973387\pi$
$840$		0			0
$841$	−407.947	+	706.584i	−0.485073	+	0.840172i
$842$		0			0
$843$	26.8368	−	577.716i	0.0318348	−	0.685309i
$844$		0			0
$845$	−1012.49	−	584.562i	−1.19821	−	0.691790i
$846$		0			0
$847$	1025.37			1.21059
$848$		0			0
$849$	386.874	+	748.261i	0.455682	+	0.881344i
$850$		0			0
$851$			752.879i			0.884699i
$852$		0			0
$853$	−372.208			−0.436351			−0.218176	−	0.975910i	$-0.570011\pi$
$853$	−372.208			−0.436351			−0.218176	+	0.975910i	$0.570011\pi$
$854$		0			0
$855$	−1001.72	−	666.736i	−1.17160	−	0.779808i
$856$		0			0
$857$		−	1289.23i		−	1.50435i	−0.658964	−	0.752175i	$-0.729005\pi$
$857$		−	1289.23i		−	1.50435i	0.658964	−	0.752175i	$-0.270995\pi$
$858$		0			0
$859$	−346.837			−0.403769			−0.201884	−	0.979409i	$-0.564707\pi$
$859$	−346.837			−0.403769			−0.201884	+	0.979409i	$0.564707\pi$
$860$		0			0
$861$	−58.6854	+	1263.32i	−0.0681596	+	1.46727i
$862$		0			0
$863$		−	450.329i		−	0.521818i	−0.965363	−	0.260909i	$-0.915978\pi$
$863$		−	450.329i		−	0.521818i	0.965363	−	0.260909i	$-0.0840222\pi$
$864$		0			0
$865$	−828.601	+	1435.18i	−0.957920	+	1.65917i
$866$		0			0
$867$	492.233	+	952.038i	0.567742	+	1.09808i
$868$		0			0
$869$	−1001.13	−	578.000i	−1.15204	−	0.665132i
$870$		0			0
$871$	−136.222			−0.156397
$872$		0			0
$873$	−30.0405	−	65.3707i	−0.0344106	−	0.0748805i
$874$		0			0
$875$	−17.3322	−	10.0067i	−0.0198082	−	0.0114363i
$876$		0			0
$877$	752.685	−	1303.69i	0.858250	−	1.48653i	−0.0153476	−	0.999882i	$-0.504885\pi$
$877$	752.685	−	1303.69i	0.858250	−	1.48653i	0.873597	−	0.486650i	$-0.161781\pi$
$878$		0			0
$879$	2.85975	−	61.5618i	0.00325341	−	0.0700362i
$880$		0			0
$881$		−	42.9592i		−	0.0487619i	−0.999703	−	0.0243809i	$-0.992239\pi$
$881$		−	42.9592i		−	0.0487619i	0.999703	−	0.0243809i	$-0.00776147\pi$
$882$		0			0
$883$	603.628	−	1045.51i	0.683610	−	1.18405i	−0.290262	−	0.956947i	$-0.593742\pi$
$883$	603.628	−	1045.51i	0.683610	−	1.18405i	0.973871	−	0.227100i	$-0.0729243\pi$
$884$		0			0
$885$	997.252	+	46.3256i	1.12684	+	0.0523453i
$886$		0			0
$887$			970.655i			1.09431i	0.837031	+	0.547156i	$0.184290\pi$
$887$			970.655i			1.09431i	−0.837031	+	0.547156i	$0.815710\pi$
$888$		0			0
$889$	433.520	+	750.879i	0.487649	+	0.844633i
$890$		0			0
$891$	−1311.45	+	460.841i	−1.47189	+	0.517218i
$892$		0			0
$893$	21.2674	+	728.620i	0.0238157	+	0.815924i
$894$		0			0
$895$	1038.48	−	1798.70i	1.16031	−	2.00972i
$896$		0			0
$897$	−104.895	−	67.2370i	−0.116940	−	0.0749577i
$898$		0			0
$899$	−221.246	−	127.736i	−0.246102	−	0.142087i
$900$		0			0
$901$	−370.120			−0.410788
$902$		0			0
$903$	43.6520	+	84.4282i	0.0483410	+	0.0934975i
$904$		0			0
$905$	208.100	−	120.147i	0.229945	−	0.132759i
$906$		0			0
$907$	67.9690			0.0749383			0.0374692	−	0.999298i	$-0.488070\pi$
$907$	67.9690			0.0749383			0.0374692	+	0.999298i	$0.488070\pi$
$908$		0			0
$909$	−244.488	−	173.231i	−0.268964	−	0.190573i
$910$		0			0
$911$	583.794	+	337.054i	0.640828	+	0.369982i	0.784933	−	0.619580i	$-0.212697\pi$
$911$	583.794	+	337.054i	0.640828	+	0.369982i	−0.144106	+	0.989562i	$0.546031\pi$
$912$		0			0
$913$	842.548	+	1459.34i	0.922835	+	1.59840i
$914$		0			0
$915$	−1683.70	−	1079.25i	−1.84011	−	1.17950i
$916$		0			0
$917$	−957.191	+	552.635i	−1.04383	+	0.602655i
$918$		0			0
$919$	−1229.42			−1.33778			−0.668892	−	0.743360i	$-0.733231\pi$
$919$	−1229.42			−1.33778			−0.668892	+	0.743360i	$0.733231\pi$
$920$		0			0
$921$	258.208	+	11.9946i	0.280356	+	0.0130235i
$922$		0			0
$923$	196.912	−	113.687i	0.213339	−	0.123171i
$924$		0			0
$925$	−375.793	−	650.892i	−0.406262	−	0.703667i
$926$		0			0
$927$	−701.940	+	990.677i	−0.757217	+	1.06869i
$928$		0			0
$929$		−	230.413i		−	0.248023i	−0.992281	−	0.124012i	$-0.960424\pi$
$929$		−	230.413i		−	0.248023i	0.992281	−	0.124012i	$-0.0395760\pi$
$930$		0			0
$931$	267.347	−	7.80349i	0.287161	−	0.00838184i
$932$		0			0
$933$	83.4562	−	1796.56i	0.0894493	−	1.92558i
$934$		0			0
$935$	2658.69	+	1534.99i	2.84351	+	1.64170i
$936$		0			0
$937$	−78.2109	+	135.465i	−0.0834695	+	0.144573i	−0.904738	−	0.425968i	$-0.859933\pi$
$937$	−78.2109	+	135.465i	−0.0834695	+	0.144573i	0.821269	+	0.570542i	$0.193267\pi$
$938$		0			0
$939$	−487.965	−	22.6676i	−0.519664	−	0.0241401i
$940$		0			0
$941$		−	105.417i		−	0.112027i	−0.998430	−	0.0560133i	$-0.982161\pi$
$941$		−	105.417i		−	0.112027i	0.998430	−	0.0560133i	$-0.0178389\pi$
$942$		0			0
$943$	876.031	−	1517.33i	0.928984	−	1.60905i
$944$		0			0
$945$	1040.89	−	420.992i	1.10148	−	0.445495i
$946$		0			0
$947$		−	428.358i		−	0.452331i	−0.974089	−	0.226166i	$-0.927381\pi$
$947$		−	428.358i		−	0.452331i	0.974089	−	0.226166i	$-0.0726190\pi$
$948$		0			0
$949$	0.731490	+	1.26698i	0.000770801	+	0.00133507i
$950$		0			0
$951$	−29.8418	+	642.404i	−0.0313793	+	0.675504i
$952$		0			0
$953$	1015.22	−	586.140i	1.06529	−	0.615047i	0.138401	−	0.990376i	$-0.455804\pi$
$953$	1015.22	−	586.140i	1.06529	−	0.615047i	0.926891	+	0.375330i	$0.122470\pi$
$954$		0			0
$955$	1147.27	+	1987.12i	1.20133	+	2.08076i
$956$		0			0
$957$	−139.212	+	217.181i	−0.145467	+	0.226940i
$958$		0			0
$959$		−	281.271i		−	0.293296i
$960$		0			0
$961$	−819.279	+	1419.03i	−0.852527	+	1.47662i
$962$		0			0
$963$	160.131	−	73.5865i	0.166283	−	0.0764138i
$964$		0			0
$965$	661.300	−	381.801i	0.685285	−	0.395649i
$966$		0			0
$967$	−322.838	+	559.172i	−0.333856	+	0.578255i	−0.983264	−	0.182185i	$-0.941683\pi$
$967$	−322.838	+	559.172i	−0.333856	+	0.578255i	0.649409	+	0.760440i	$0.275016\pi$
$968$		0			0
$969$	1242.22	+	746.038i	1.28196	+	0.769905i
$970$		0			0
$971$	213.035	−	122.996i	0.219398	−	0.126669i	−0.386274	−	0.922384i	$-0.626238\pi$
$971$	213.035	−	122.996i	0.219398	−	0.126669i	0.605671	+	0.795715i	$0.292905\pi$
$972$		0			0
$973$	383.804	−	664.768i	0.394454	−	0.683215i
$974$		0			0
$975$	124.246	+	5.77164i	0.127432	+	0.00591963i
$976$		0			0
$977$	−1330.58	+	768.213i	−1.36191	+	0.786297i	−0.989878	−	0.141923i	$-0.954671\pi$
$977$	−1330.58	+	768.213i	−1.36191	+	0.786297i	−0.372030	+	0.928221i	$0.621338\pi$
$978$		0			0
$979$	286.913	+	496.948i	0.293067	+	0.507608i
$980$		0			0
$981$	897.244	−	1266.32i	0.914622	−	1.29084i
$982$		0			0
$983$		−	1091.10i		−	1.10997i	−0.831860	−	0.554985i	$-0.812724\pi$
$983$		−	1091.10i		−	1.10997i	0.831860	−	0.554985i	$-0.187276\pi$
$984$		0			0
$985$	−219.468	+	380.129i	−0.222810	+	0.385918i
$986$		0			0
$987$	−572.620	−	367.046i	−0.580162	−	0.371881i
$988$		0			0
$989$		−	131.673i		−	0.133138i
$990$		0			0
$991$	56.2143	+	97.3661i	0.0567248	+	0.0982503i	0.892993	−	0.450070i	$-0.148601\pi$
$991$	56.2143	+	97.3661i	0.0567248	+	0.0982503i	−0.836269	+	0.548320i	$0.815268\pi$
$992$		0			0
$993$	−642.576	−	1242.82i	−0.647106	−	1.25158i
$994$		0			0
$995$	−812.942	+	469.352i	−0.817027	+	0.471711i
$996$		0			0
$997$	−144.320	−	249.970i	−0.144754	−	0.250722i	0.784527	−	0.620095i	$-0.212906\pi$
$997$	−144.320	−	249.970i	−0.144754	−	0.250722i	−0.929281	+	0.369373i	$0.879573\pi$
$998$		0			0
$999$	−819.632	−	114.885i	−0.820453	−	0.115000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.be.a.425.13	yes	80
3.2	odd	2		2052.3.be.a.197.4		80
9.4	even	3		2052.3.m.a.881.4		80
9.5	odd	6		684.3.m.a.653.40	yes	80
19.11	even	3		684.3.m.a.353.40	✓	80
57.11	odd	6		2052.3.m.a.1493.37		80
171.49	even	3		2052.3.be.a.125.4		80
171.68	odd	6	inner	684.3.be.a.581.13	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.40	✓	80	19.11	even	3
684.3.m.a.653.40	yes	80	9.5	odd	6
684.3.be.a.425.13	yes	80	1.1	even	1	trivial
684.3.be.a.581.13	yes	80	171.68	odd	6	inner
2052.3.m.a.881.4		80	9.4	even	3
2052.3.m.a.1493.37		80	57.11	odd	6
2052.3.be.a.125.4		80	171.49	even	3
2052.3.be.a.197.4		80	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61894 + 2.52567i) q^{3} +(6.09418 + 3.51848i) q^{5} +(2.95479 - 5.11784i) q^{7} +(-3.75805 - 8.17784i) q^{9} +O(q^{10})\)	\(q+(-1.61894 + 2.52567i) q^{3} +(6.09418 + 3.51848i) q^{5} +(2.95479 - 5.11784i) q^{7} +(-3.75805 - 8.17784i) q^{9} +(14.8621 + 8.58065i) q^{11} -1.69095 q^{13} +(-18.7527 + 9.69569i) q^{15} +(22.0157 - 12.7108i) q^{17} +(9.01588 - 16.7247i) q^{19} +(8.14236 + 15.7483i) q^{21} -24.5609i q^{23} +(12.2594 + 21.2339i) q^{25} +(26.7386 + 3.74787i) q^{27} +(4.33936 - 2.50533i) q^{29} +(-25.4929 - 44.1550i) q^{31} +(-45.7328 + 23.6453i) q^{33} +(36.0140 - 20.7927i) q^{35} -30.6535 q^{37} +(2.73756 - 4.27080i) q^{39} +(61.7782 + 35.6677i) q^{41} +5.36109 q^{43} +(5.87134 - 63.0599i) q^{45} +(-33.2249 + 19.1824i) q^{47} +(7.03844 + 12.1909i) q^{49} +(-3.53892 + 76.1824i) q^{51} +(-12.6088 - 7.27967i) q^{53} +(60.3817 + 104.584i) q^{55} +(27.6448 + 49.8474i) q^{57} +(-40.9541 - 23.6449i) q^{59} +(47.3668 + 82.0417i) q^{61} +(-52.9572 - 4.93070i) q^{63} +(-10.3050 - 5.94958i) q^{65} +80.5590 q^{67} +(62.0329 + 39.7628i) q^{69} +(-116.450 + 67.2326i) q^{71} +(-0.432590 - 0.749268i) q^{73} +(-73.4770 - 3.41325i) q^{75} +(87.8289 - 50.7080i) q^{77} -67.3609 q^{79} +(-52.7542 + 61.4654i) q^{81} +(85.0365 + 49.0958i) q^{83} +178.890 q^{85} +(-0.697532 + 15.0158i) q^{87} +(28.9575 + 16.7186i) q^{89} +(-4.99641 + 8.65404i) q^{91} +(152.793 + 7.09772i) q^{93} +(113.790 - 70.2009i) q^{95} +7.99364 q^{97} +(14.3187 - 153.787i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 4 * q^3 + q^7 + 4 * q^9	\( 80 q + 4 q^{3} + q^{7} + 4 q^{9} + 18 q^{11} + 10 q^{13} - 11 q^{15} + 9 q^{17} + 20 q^{19} - 30 q^{21} + 200 q^{25} + 25 q^{27} - 27 q^{29} - 8 q^{31} + 23 q^{33} + 22 q^{37} + 39 q^{39} - 54 q^{41} + 88 q^{43} - 196 q^{45} + 198 q^{47} - 267 q^{49} - 56 q^{51} + 36 q^{53} + 78 q^{57} + 171 q^{59} + 7 q^{61} + 82 q^{63} - 144 q^{65} + 154 q^{67} + 44 q^{69} + 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} + 34 q^{79} - 44 q^{81} - 171 q^{83} - 244 q^{87} - 216 q^{89} + 122 q^{91} - 104 q^{93} - 216 q^{95} + 16 q^{97} - 305 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + q^7 + 4 * q^9 + 18 * q^11 + 10 * q^13 - 11 * q^15 + 9 * q^17 + 20 * q^19 - 30 * q^21 + 200 * q^25 + 25 * q^27 - 27 * q^29 - 8 * q^31 + 23 * q^33 + 22 * q^37 + 39 * q^39 - 54 * q^41 + 88 * q^43 - 196 * q^45 + 198 * q^47 - 267 * q^49 - 56 * q^51 + 36 * q^53 + 78 * q^57 + 171 * q^59 + 7 * q^61 + 82 * q^63 - 144 * q^65 + 154 * q^67 + 44 * q^69 + 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 + 34 * q^79 - 44 * q^81 - 171 * q^83 - 244 * q^87 - 216 * q^89 + 122 * q^91 - 104 * q^93 - 216 * q^95 + 16 * q^97 - 305 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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