LMFDB - Embedded newform 1764.2.l.h.961.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(949,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1764.949");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.l (of order $3$, degree $2$, not 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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} + 16x^{8} - 39x^{6} + 144x^{4} - 162x^{2} + 729 $ x^12 - 2x^10 + 16x^8 - 39x^6 + 144x^4 - 162*x^2 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.4
Root			$0.965975 - 1.43767i$ of defining polynomial
Character	$\chi$	$=$	1764.961
Dual form			1764.2.l.h.949.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965975 + 1.43767i) q^{3} -3.90027 q^{5} +(-1.13378 + 2.77751i) q^{9} +O(q^{10})$	\(q+(0.965975 + 1.43767i) q^{3} -3.90027 q^{5} +(-1.13378 + 2.77751i) q^{9} -4.26757 q^{11} +(-2.71221 - 4.69768i) q^{13} +(-3.76757 - 5.60730i) q^{15} +(2.49012 + 4.31301i) q^{17} +(-0.222091 + 0.384673i) q^{19} +8.21213 q^{23} +10.2121 q^{25} +(-5.08834 + 1.05300i) q^{27} +(1.33850 - 2.31835i) q^{29} +(0.425996 - 0.737847i) q^{31} +(-4.12236 - 6.13535i) q^{33} +(4.90135 - 8.48939i) q^{37} +(4.13378 - 8.43710i) q^{39} +(-2.69402 - 4.66618i) q^{41} +(4.31078 - 7.46649i) q^{43} +(4.42207 - 10.8330i) q^{45} +(1.74623 + 3.02456i) q^{47} +(-3.79529 + 7.74622i) q^{51} +(2.83850 + 4.91642i) q^{53} +16.6447 q^{55} +(-0.767567 + 0.0522912i) q^{57} +(-0.947789 + 1.64162i) q^{59} +(-5.62832 - 9.74853i) q^{61} +(10.5783 + 18.3222i) q^{65} +(-1.29529 + 2.24350i) q^{67} +(7.93272 + 11.8063i) q^{69} +0.141862 q^{71} +(-5.16595 - 8.94769i) q^{73} +(9.86467 + 14.6817i) q^{75} +(0.204714 + 0.354576i) q^{79} +(-6.42907 - 6.29818i) q^{81} +(-2.08231 + 3.60666i) q^{83} +(-9.71213 - 16.8219i) q^{85} +(4.62597 - 0.315148i) q^{87} +(1.20625 - 2.08929i) q^{89} +(1.47228 - 0.100301i) q^{93} +(0.866216 - 1.50033i) q^{95} +(-3.80448 + 6.58955i) q^{97} +(4.83850 - 11.8532i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{9}+O(q^{10}) $ 12 * q + 4 * q^9	$ 12 q + 4 q^{9} - 16 q^{11} - 10 q^{15} + 24 q^{25} + 2 q^{29} + 6 q^{37} + 32 q^{39} + 6 q^{43} - 42 q^{51} + 20 q^{53} + 26 q^{57} + 46 q^{65} - 12 q^{67} + 44 q^{71} + 6 q^{79} - 56 q^{81} - 18 q^{85} - 14 q^{93} + 28 q^{95} + 44 q^{99}+O(q^{100}) $ 12 * q + 4 * q^9 - 16 * q^11 - 10 * q^15 + 24 * q^25 + 2 * q^29 + 6 * q^37 + 32 * q^39 + 6 * q^43 - 42 * q^51 + 20 * q^53 + 26 * q^57 + 46 * q^65 - 12 * q^67 + 44 * q^71 + 6 * q^79 - 56 * q^81 - 18 * q^85 - 14 * q^93 + 28 * q^95 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.965975	+	1.43767i	0.557706	+	0.830039i
$3$	0.965975	+	1.43767i	0.557706	+	0.830039i
$4$		0			0
$5$	−3.90027			−1.74426			−0.872128	−	0.489279i	$-0.837260\pi$
$5$	−3.90027			−1.74426			−0.872128	+	0.489279i	$0.837260\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−1.13378	+	2.77751i	−0.377928	+	0.925835i
$10$		0			0
$11$	−4.26757			−1.28672			−0.643360	−	0.765564i	$-0.722460\pi$
$11$	−4.26757			−1.28672			−0.643360	+	0.765564i	$0.722460\pi$
$12$		0			0
$13$	−2.71221	−	4.69768i	−0.752231	−	1.30290i	−0.946739	−	0.322001i	$-0.895645\pi$
$13$	−2.71221	−	4.69768i	−0.752231	−	1.30290i	0.194508	−	0.980901i	$-0.437689\pi$
$14$		0			0
$15$	−3.76757	−	5.60730i	−0.972782	−	1.44780i
$16$		0			0
$17$	2.49012	+	4.31301i	0.603942	+	1.04606i	0.992218	+	0.124515i	$0.0397374\pi$
$17$	2.49012	+	4.31301i	0.603942	+	1.04606i	−0.388276	+	0.921543i	$0.626929\pi$
$18$		0			0
$19$	−0.222091	+	0.384673i	−0.0509512	+	0.0882501i	−0.890376	−	0.455226i	$-0.849559\pi$
$19$	−0.222091	+	0.384673i	−0.0509512	+	0.0882501i	0.839425	+	0.543476i	$0.182892\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	8.21213			1.71235			0.856174	−	0.516688i	$-0.172835\pi$
$23$	8.21213			1.71235			0.856174	+	0.516688i	$0.172835\pi$
$24$		0			0
$25$	10.2121			2.04243
$26$		0			0
$27$	−5.08834	+	1.05300i	−0.979251	+	0.202649i
$28$		0			0
$29$	1.33850	−	2.31835i	0.248553	−	0.430506i	−0.714572	−	0.699562i	$-0.753378\pi$
$29$	1.33850	−	2.31835i	0.248553	−	0.430506i	0.963125	+	0.269056i	$0.0867117\pi$
$30$		0			0
$31$	0.425996	−	0.737847i	0.0765112	−	0.132521i	−0.825231	−	0.564795i	$-0.808955\pi$
$31$	0.425996	−	0.737847i	0.0765112	−	0.132521i	0.901742	+	0.432274i	$0.142289\pi$
$32$		0			0
$33$	−4.12236	−	6.13535i	−0.717612	−	1.06803i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.90135	−	8.48939i	0.805777	−	1.39565i	−0.109988	−	0.993933i	$-0.535081\pi$
$37$	4.90135	−	8.48939i	0.805777	−	1.39565i	0.915765	−	0.401714i	$-0.131585\pi$
$38$		0			0
$39$	4.13378	−	8.43710i	0.661935	−	1.35102i
$40$		0			0
$41$	−2.69402	−	4.66618i	−0.420735	−	0.728735i	0.575276	−	0.817959i	$-0.304895\pi$
$41$	−2.69402	−	4.66618i	−0.420735	−	0.728735i	−0.996012	+	0.0892242i	$0.971561\pi$
$42$		0			0
$43$	4.31078	−	7.46649i	0.657388	−	1.13863i	−0.323902	−	0.946091i	$-0.604995\pi$
$43$	4.31078	−	7.46649i	0.657388	−	1.13863i	0.981289	−	0.192538i	$-0.0616720\pi$
$44$		0			0
$45$	4.42207	−	10.8330i	0.659203	−	1.61489i
$46$		0			0
$47$	1.74623	+	3.02456i	0.254714	+	0.441178i	0.964818	−	0.262919i	$-0.0846853\pi$
$47$	1.74623	+	3.02456i	0.254714	+	0.441178i	−0.710104	+	0.704097i	$0.751352\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−3.79529	+	7.74622i	−0.531446	+	1.08469i
$52$		0			0
$53$	2.83850	+	4.91642i	0.389898	+	0.675323i	0.992435	−	0.122768i	$-0.0391770\pi$
$53$	2.83850	+	4.91642i	0.389898	+	0.675323i	−0.602538	+	0.798090i	$0.705844\pi$
$54$		0			0
$55$	16.6447			2.24437
$56$		0			0
$57$	−0.767567	+	0.0522912i	−0.101667	+	0.00692614i
$58$		0			0
$59$	−0.947789	+	1.64162i	−0.123392	+	0.213721i	−0.921103	−	0.389319i	$-0.872710\pi$
$59$	−0.947789	+	1.64162i	−0.123392	+	0.213721i	0.797711	+	0.603039i	$0.206044\pi$
$60$		0			0
$61$	−5.62832	−	9.74853i	−0.720632	−	1.24817i	−0.960747	−	0.277427i	$-0.910518\pi$
$61$	−5.62832	−	9.74853i	−0.720632	−	1.24817i	0.240114	−	0.970745i	$-0.422815\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	10.5783	+	18.3222i	1.31208	+	2.27259i
$66$		0			0
$67$	−1.29529	+	2.24350i	−0.158244	+	0.274087i	−0.934236	−	0.356656i	$-0.883917\pi$
$67$	−1.29529	+	2.24350i	−0.158244	+	0.274087i	0.775991	+	0.630744i	$0.217250\pi$
$68$		0			0
$69$	7.93272	+	11.8063i	0.954987	+	1.42131i
$70$		0			0
$71$	0.141862			0.0168359			0.00841794	−	0.999965i	$-0.497320\pi$
$71$	0.141862			0.0168359			0.00841794	+	0.999965i	$0.497320\pi$
$72$		0			0
$73$	−5.16595	−	8.94769i	−0.604629	−	1.04725i	−0.992110	−	0.125370i	$-0.959988\pi$
$73$	−5.16595	−	8.94769i	−0.604629	−	1.04725i	0.387481	−	0.921878i	$-0.373345\pi$
$74$		0			0
$75$	9.86467	+	14.6817i	1.13907	+	1.69529i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	0.204714	+	0.354576i	0.0230322	+	0.0398929i	0.877312	−	0.479921i	$-0.159335\pi$
$79$	0.204714	+	0.354576i	0.0230322	+	0.0398929i	−0.854280	+	0.519814i	$0.826001\pi$
$80$		0			0
$81$	−6.42907	−	6.29818i	−0.714341	−	0.699798i
$82$		0			0
$83$	−2.08231	+	3.60666i	−0.228563	+	0.395882i	−0.957382	−	0.288823i	$-0.906736\pi$
$83$	−2.08231	+	3.60666i	−0.228563	+	0.395882i	0.728820	+	0.684706i	$0.240069\pi$
$84$		0			0
$85$	−9.71213	−	16.8219i	−1.05343	−	1.82459i
$86$		0			0
$87$	4.62597	−	0.315148i	0.495956	−	0.0337875i
$88$		0			0
$89$	1.20625	−	2.08929i	0.127863	−	0.221464i	−0.794986	−	0.606628i	$-0.792522\pi$
$89$	1.20625	−	2.08929i	0.127863	−	0.221464i	0.922848	+	0.385164i	$0.125855\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.47228	−	0.100301i	0.152669	−	0.0104007i
$94$		0			0
$95$	0.866216	−	1.50033i	0.0888719	−	0.153931i
$96$		0			0
$97$	−3.80448	+	6.58955i	−0.386286	+	0.669067i	−0.991947	−	0.126656i	$-0.959576\pi$
$97$	−3.80448	+	6.58955i	−0.386286	+	0.669067i	0.605661	+	0.795723i	$0.292909\pi$
$98$		0			0
$99$	4.83850	−	11.8532i	0.486287	−	1.19129i
$100$		0			0
$101$	−5.12370			−0.509828			−0.254914	−	0.966964i	$-0.582047\pi$
$101$	−5.12370			−0.509828			−0.254914	+	0.966964i	$0.582047\pi$
$102$		0			0
$103$	12.9606			1.27705			0.638524	−	0.769602i	$-0.279545\pi$
$103$	12.9606			1.27705			0.638524	+	0.769602i	$0.279545\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.76757	−	9.98972i	0.557572	−	0.965743i	−0.440127	−	0.897936i	$-0.645066\pi$
$107$	5.76757	−	9.98972i	0.557572	−	0.965743i	0.997698	−	0.0678070i	$-0.0216002\pi$
$108$		0			0
$109$	0.204714	+	0.354576i	0.0196081	+	0.0339622i	0.875663	−	0.482923i	$-0.160425\pi$
$109$	0.204714	+	0.354576i	0.0196081	+	0.0339622i	−0.856055	+	0.516885i	$0.827091\pi$
$110$		0			0
$111$	16.9395	−	1.15402i	1.60783	−	0.109535i
$112$		0			0
$113$	−6.94456	−	12.0283i	−0.653290	−	1.13153i	−0.982320	−	0.187211i	$-0.940055\pi$
$113$	−6.94456	−	12.0283i	−0.653290	−	1.13153i	0.329030	−	0.944319i	$-0.393278\pi$
$114$		0			0
$115$	−32.0296			−2.98677
$116$		0			0
$117$	16.1229	−	2.20702i	1.49056	−	0.204039i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	7.21213			0.655648
$122$		0			0
$123$	4.10607	−	8.38052i	0.370231	−	0.755646i
$124$		0			0
$125$	−20.3287			−1.81826
$126$		0			0
$127$	11.6216			1.03125			0.515623	−	0.856815i	$-0.327560\pi$
$127$	11.6216			1.03125			0.515623	+	0.856815i	$0.327560\pi$
$128$		0			0
$129$	14.8984	−	1.01497i	1.31174	−	0.0893631i
$130$		0			0
$131$	−4.05549			−0.354330			−0.177165	−	0.984181i	$-0.556693\pi$
$131$	−4.05549			−0.354330			−0.177165	+	0.984181i	$0.556693\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	19.8459	−	4.10697i	1.70806	−	0.353472i
$136$		0			0
$137$	9.15669			0.782309			0.391155	−	0.920325i	$-0.372076\pi$
$137$	9.15669			0.782309			0.391155	+	0.920325i	$0.372076\pi$
$138$		0			0
$139$	−5.23869	−	9.07369i	−0.444340	−	0.769620i	0.553666	−	0.832739i	$-0.313229\pi$
$139$	−5.23869	−	9.07369i	−0.444340	−	0.769620i	−0.998006	+	0.0631191i	$0.979895\pi$
$140$		0			0
$141$	−2.66150	+	5.43215i	−0.224139	+	0.457470i
$142$		0			0
$143$	11.5745	+	20.0477i	0.967910	+	1.67647i
$144$		0			0
$145$	−5.22051	+	9.04219i	−0.433540	+	0.750913i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−16.2676			−1.33269			−0.666346	−	0.745643i	$-0.732142\pi$
$149$	−16.2676			−1.33269			−0.666346	+	0.745643i	$0.732142\pi$
$150$		0			0
$151$	−7.21213			−0.586915			−0.293457	−	0.955972i	$-0.594806\pi$
$151$	−7.21213			−0.586915			−0.293457	+	0.955972i	$0.594806\pi$
$152$		0			0
$153$	−14.8027	+	2.02629i	−1.19672	+	0.163816i
$154$		0			0
$155$	−1.66150	+	2.87781i	−0.133455	+	0.231151i
$156$		0			0
$157$	0.593529	−	1.02802i	0.0473688	−	0.0820451i	−0.841369	−	0.540461i	$-0.818250\pi$
$157$	0.593529	−	1.02802i	0.0473688	−	0.0820451i	0.888738	+	0.458416i	$0.151583\pi$
$158$		0			0
$159$	−4.32627	+	8.82996i	−0.343095	+	0.700262i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−10.5074	+	18.1994i	−0.823004	+	1.42549i	0.0804306	+	0.996760i	$0.474370\pi$
$163$	−10.5074	+	18.1994i	−0.823004	+	1.42549i	−0.903435	+	0.428725i	$0.858963\pi$
$164$		0			0
$165$	16.0783	+	23.9295i	1.25170	+	1.86291i
$166$		0			0
$167$	−10.0322	−	17.3763i	−0.776315	−	1.34462i	−0.934053	−	0.357136i	$-0.883753\pi$
$167$	−10.0322	−	17.3763i	−0.776315	−	1.34462i	0.157738	−	0.987481i	$-0.449580\pi$
$168$		0			0
$169$	−8.21213	+	14.2238i	−0.631702	+	1.09414i
$170$		0			0
$171$	−0.816628	−	1.05300i	−0.0624491	−	0.0805246i
$172$		0			0
$173$	3.03009	+	5.24828i	0.230374	+	0.399019i	0.957918	−	0.287042i	$-0.0926718\pi$
$173$	3.03009	+	5.24828i	0.230374	+	0.399019i	−0.727544	+	0.686061i	$0.759338\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.27565	+	0.223156i	−0.246213	+	0.0167735i
$178$		0			0
$179$	−4.41685	−	7.65020i	−0.330131	−	0.571803i	0.652407	−	0.757869i	$-0.273759\pi$
$179$	−4.41685	−	7.65020i	−0.330131	−	0.571803i	−0.982537	+	0.186066i	$0.940426\pi$
$180$		0			0
$181$	24.1809			1.79735			0.898676	−	0.438614i	$-0.144530\pi$
$181$	24.1809			1.79735			0.898676	+	0.438614i	$0.144530\pi$
$182$		0			0
$183$	8.57835	−	17.5085i	0.634130	−	1.29427i
$184$		0			0
$185$	−19.1166	+	33.1109i	−1.40548	+	2.43436i
$186$		0			0
$187$	−10.6267	−	18.4060i	−0.777104	−	1.34598i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−10.1135	−	17.5171i	−0.731786	−	1.26749i	−0.956119	−	0.292978i	$-0.905354\pi$
$191$	−10.1135	−	17.5171i	−0.731786	−	1.26749i	0.224333	−	0.974512i	$-0.427980\pi$
$192$		0			0
$193$	6.19664	−	10.7329i	0.446044	−	0.772570i	−0.552081	−	0.833791i	$-0.686166\pi$
$193$	6.19664	−	10.7329i	0.446044	−	0.772570i	0.998124	+	0.0612205i	$0.0194993\pi$
$194$		0			0
$195$	−16.1229	+	32.9070i	−1.15458	+	2.35652i
$196$		0			0
$197$	14.3933			1.02548			0.512739	−	0.858544i	$-0.328631\pi$
$197$	14.3933			1.02548			0.512739	+	0.858544i	$0.328631\pi$
$198$		0			0
$199$	5.25688	+	9.10518i	0.372650	+	0.645449i	0.989972	−	0.141261i	$-0.0451157\pi$
$199$	5.25688	+	9.10518i	0.372650	+	0.645449i	−0.617322	+	0.786711i	$0.711782\pi$
$200$		0			0
$201$	−4.47662	+	0.304974i	−0.315757	+	0.0215112i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	10.5074	+	18.1994i	0.733870	+	1.27110i
$206$		0			0
$207$	−9.31078	+	22.8092i	−0.647144	+	1.58535i
$208$		0			0
$209$	0.947789	−	1.64162i	0.0655599	−	0.113553i
$210$		0			0
$211$	11.7121	+	20.2860i	0.806296	+	1.39655i	0.915412	+	0.402517i	$0.131865\pi$
$211$	11.7121	+	20.2860i	0.806296	+	1.39655i	−0.109116	+	0.994029i	$0.534802\pi$
$212$		0			0
$213$	0.137035	+	0.203950i	0.00938947	+	0.0139744i
$214$		0			0
$215$	−16.8132	+	29.1214i	−1.14665	+	1.98606i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	7.87363	−	16.0702i	0.532051	−	1.08592i
$220$		0			0
$221$	13.5074	−	23.3955i	0.908607	−	1.57375i
$222$		0			0
$223$	12.6727	−	21.9497i	0.848625	−	1.46986i	−0.0338111	−	0.999428i	$-0.510764\pi$
$223$	12.6727	−	21.9497i	0.848625	−	1.46986i	0.882436	−	0.470433i	$-0.155902\pi$
$224$		0			0
$225$	−11.5783	+	28.3642i	−0.771890	+	1.89095i
$226$		0			0
$227$	18.0253			1.19638			0.598192	−	0.801353i	$-0.295886\pi$
$227$	18.0253			1.19638			0.598192	+	0.801353i	$0.295886\pi$
$228$		0			0
$229$	5.42441			0.358455			0.179228	−	0.983808i	$-0.442640\pi$
$229$	5.42441			0.358455			0.179228	+	0.983808i	$0.442640\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.42165	−	2.46237i	0.0931356	−	0.161316i	−0.815693	−	0.578484i	$-0.803644\pi$
$233$	1.42165	−	2.46237i	0.0931356	−	0.161316i	0.908829	+	0.417169i	$0.136978\pi$
$234$		0			0
$235$	−6.81078	−	11.7966i	−0.444286	−	0.769526i
$236$		0			0
$237$	−0.312014	+	0.636823i	−0.0202675	+	0.0413661i
$238$		0			0
$239$	−6.09057	−	10.5492i	−0.393966	−	0.682370i	0.599002	−	0.800747i	$-0.295564\pi$
$239$	−6.09057	−	10.5492i	−0.393966	−	0.682370i	−0.992969	+	0.118378i	$0.962231\pi$
$240$		0			0
$241$	−18.6247			−1.19973			−0.599863	−	0.800103i	$-0.704778\pi$
$241$	−18.6247			−1.19973			−0.599863	+	0.800103i	$0.704778\pi$
$242$		0			0
$243$	2.84438	−	15.3268i	0.182467	−	0.983212i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.40943			0.153308
$248$		0			0
$249$	−7.19664	+	0.490277i	−0.456068	+	0.0310701i
$250$		0			0
$251$	−7.14015			−0.450682			−0.225341	−	0.974280i	$-0.572350\pi$
$251$	−7.14015			−0.450682			−0.225341	+	0.974280i	$0.572350\pi$
$252$		0			0
$253$	−35.0458			−2.20331
$254$		0			0
$255$	14.8027	−	30.2124i	0.926978	−	1.89197i
$256$		0			0
$257$	1.34430			0.0838549			0.0419274	−	0.999121i	$-0.486650\pi$
$257$	1.34430			0.0838549			0.0419274	+	0.999121i	$0.486650\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	4.92165	+	6.34619i	0.304643	+	0.392819i
$262$		0			0
$263$	−24.2986			−1.49831			−0.749157	−	0.662393i	$-0.769541\pi$
$263$	−24.2986			−1.49831			−0.749157	+	0.662393i	$0.769541\pi$
$264$		0			0
$265$	−11.0709	−	19.1754i	−0.680081	−	1.17794i
$266$		0			0
$267$	4.16892	−	0.284011i	0.255134	−	0.0173812i
$268$		0			0
$269$	2.69989	+	4.67636i	0.164615	+	0.285122i	0.936519	−	0.350618i	$-0.114028\pi$
$269$	2.69989	+	4.67636i	0.164615	+	0.285122i	−0.771903	+	0.635740i	$0.780695\pi$
$270$		0			0
$271$	6.78589	−	11.7535i	0.412213	−	0.713974i	−0.582918	−	0.812531i	$-0.698089\pi$
$271$	6.78589	−	11.7535i	0.412213	−	0.713974i	0.995131	+	0.0985565i	$0.0314225\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−43.5810			−2.62803
$276$		0			0
$277$	−29.0148			−1.74333			−0.871666	−	0.490100i	$-0.836960\pi$
$277$	−29.0148			−1.74333			−0.871666	+	0.490100i	$0.836960\pi$
$278$		0			0
$279$	1.56639	+	2.01977i	0.0937771	+	0.120920i
$280$		0			0
$281$	0.885857	−	1.53435i	0.0528458	−	0.0915316i	−0.838392	−	0.545067i	$-0.816504\pi$
$281$	0.885857	−	1.53435i	0.0528458	−	0.0915316i	0.891238	+	0.453536i	$0.149837\pi$
$282$		0			0
$283$	12.1268	−	21.0043i	0.720864	−	1.24857i	−0.239789	−	0.970825i	$-0.577078\pi$
$283$	12.1268	−	21.0043i	0.720864	−	1.24857i	0.960654	−	0.277749i	$-0.0895883\pi$
$284$		0			0
$285$	2.99372	−	0.203950i	0.177333	−	0.0120810i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−3.90135	+	6.75734i	−0.229491	+	0.397490i
$290$		0			0
$291$	−13.1486	+	0.895761i	−0.770786	+	0.0525105i
$292$		0			0
$293$	7.52491	+	13.0335i	0.439610	+	0.761426i	0.997659	−	0.0683813i	$-0.0217835\pi$
$293$	7.52491	+	13.0335i	0.439610	+	0.761426i	−0.558050	+	0.829808i	$0.688450\pi$
$294$		0			0
$295$	3.69664	−	6.40276i	0.215226	−	0.372783i
$296$		0			0
$297$	21.7148	−	4.49373i	1.26002	−	0.260753i
$298$		0			0
$299$	−22.2730	−	38.5780i	−1.28808	−	2.23102i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−4.94937	−	7.36619i	−0.284334	−	0.423177i
$304$		0			0
$305$	21.9520	+	38.0219i	1.25697	+	2.17713i
$306$		0			0
$307$	4.01912			0.229383			0.114692	−	0.993401i	$-0.463412\pi$
$307$	4.01912			0.229383			0.114692	+	0.993401i	$0.463412\pi$
$308$		0			0
$309$	12.5196	+	18.6331i	0.712217	+	1.06000i
$310$		0			0
$311$	0.798442	−	1.38294i	0.0452755	−	0.0784195i	−0.842500	−	0.538697i	$-0.818917\pi$
$311$	0.798442	−	1.38294i	0.0452755	−	0.0784195i	0.887775	+	0.460278i	$0.152250\pi$
$312$		0			0
$313$	−2.43556	−	4.21851i	−0.137666	−	0.238444i	0.788947	−	0.614461i	$-0.210627\pi$
$313$	−2.43556	−	4.21851i	−0.137666	−	0.238444i	−0.926613	+	0.376017i	$0.877293\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.18922	+	7.25594i	0.235290	+	0.407534i	0.959357	−	0.282195i	$-0.0910627\pi$
$317$	4.18922	+	7.25594i	0.235290	+	0.407534i	−0.724067	+	0.689730i	$0.757729\pi$
$318$		0			0
$319$	−5.71213	+	9.89370i	−0.319818	+	0.553941i
$320$		0			0
$321$	19.9332	−	1.35797i	1.11256	−	0.0757945i
$322$		0			0
$323$	−2.21213			−0.123086
$324$		0			0
$325$	−27.6974	−	47.9733i	−1.53638	−	2.66108i
$326$		0			0
$327$	−0.312014	+	0.636823i	−0.0172544	+	0.0352164i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−12.9168	−	22.3726i	−0.709974	−	1.22971i	−0.964866	−	0.262742i	$-0.915373\pi$
$331$	−12.9168	−	22.3726i	−0.709974	−	1.22971i	0.254892	−	0.966969i	$-0.417960\pi$
$332$		0			0
$333$	18.0222	+	23.2387i	0.987613	+	1.27347i
$334$		0			0
$335$	5.05197	−	8.75026i	0.276018	−	0.478078i
$336$		0			0
$337$	9.81820	+	17.0056i	0.534831	+	0.926355i	0.999171	+	0.0406980i	$0.0129582\pi$
$337$	9.81820	+	17.0056i	0.534831	+	0.926355i	−0.464340	+	0.885657i	$0.653709\pi$
$338$		0			0
$339$	10.5845	−	21.6031i	0.574871	−	1.17332i
$340$		0			0
$341$	−1.81797	+	3.14881i	−0.0984485	+	0.170518i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−30.9398	−	46.0479i	−1.66574	−	2.47914i
$346$		0			0
$347$	11.2047	−	19.4071i	0.601501	−	1.04183i	−0.391093	−	0.920351i	$-0.627903\pi$
$347$	11.2047	−	19.4071i	0.601501	−	1.04183i	0.992594	−	0.121479i	$-0.0387636\pi$
$348$		0			0
$349$	5.38804	−	9.33236i	0.288415	−	0.499550i	−0.685016	−	0.728528i	$-0.740205\pi$
$349$	5.38804	−	9.33236i	0.288415	−	0.499550i	0.973432	+	0.228978i	$0.0735383\pi$
$350$		0			0
$351$	18.7473	+	21.0474i	1.00066	+	1.12343i
$352$		0			0
$353$	11.4021			0.606874			0.303437	−	0.952852i	$-0.401866\pi$
$353$	11.4021			0.606874			0.303437	+	0.952852i	$0.401866\pi$
$354$		0			0
$355$	−0.553299			−0.0293661
$356$		0			0
$357$		0			0
$358$		0			0
$359$	9.38171	−	16.2496i	0.495148	−	0.857621i	−0.504837	−	0.863215i	$-0.668447\pi$
$359$	9.38171	−	16.2496i	0.495148	−	0.857621i	0.999984	+	0.00559386i	$0.00178059\pi$
$360$		0			0
$361$	9.40135	+	16.2836i	0.494808	+	0.857033i
$362$		0			0
$363$	6.96674	+	10.3687i	0.365659	+	0.544213i
$364$		0			0
$365$	20.1486	+	34.8984i	1.05463	+	1.82667i
$366$		0			0
$367$	−1.66761			−0.0870487			−0.0435243	−	0.999052i	$-0.513859\pi$
$367$	−1.66761			−0.0870487			−0.0435243	+	0.999052i	$0.513859\pi$
$368$		0			0
$369$	16.0148	−	2.19222i	0.833696	−	0.114122i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−25.0458			−1.29682			−0.648412	−	0.761290i	$-0.724566\pi$
$373$	−25.0458			−1.29682			−0.648412	+	0.761290i	$0.724566\pi$
$374$		0			0
$375$	−19.6371	−	29.2260i	−1.01405	−	1.50922i
$376$		0			0
$377$	−14.5211			−0.747876
$378$		0			0
$379$	5.21213			0.267729			0.133865	−	0.991000i	$-0.457261\pi$
$379$	5.21213			0.267729			0.133865	+	0.991000i	$0.457261\pi$
$380$		0			0
$381$	11.2261	+	16.7080i	0.575133	+	0.855974i
$382$		0			0
$383$	−22.4769			−1.14852			−0.574258	−	0.818674i	$-0.694709\pi$
$383$	−22.4769			−1.14852			−0.574258	+	0.818674i	$0.694709\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	15.8507	+	20.4386i	0.805737	+	1.03895i
$388$		0			0
$389$	−10.4094			−0.527779			−0.263889	−	0.964553i	$-0.585005\pi$
$389$	−10.4094			−0.527779			−0.263889	+	0.964553i	$0.585005\pi$
$390$		0			0
$391$	20.4492	+	35.4190i	1.03416	+	1.79121i
$392$		0			0
$393$	−3.91751	−	5.83046i	−0.197612	−	0.294108i
$394$		0			0
$395$	−0.798442	−	1.38294i	−0.0401740	−	0.0695834i
$396$		0			0
$397$	1.31436	−	2.27654i	0.0659659	−	0.114256i	−0.831156	−	0.556039i	$-0.812320\pi$
$397$	1.31436	−	2.27654i	0.0659659	−	0.114256i	0.897122	+	0.441783i	$0.145654\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−11.1973			−0.559166			−0.279583	−	0.960121i	$-0.590196\pi$
$401$	−11.1973			−0.559166			−0.279583	+	0.960121i	$0.590196\pi$
$402$		0			0
$403$	−4.62156			−0.230216
$404$		0			0
$405$	25.0751	+	24.5646i	1.24599	+	1.22063i
$406$		0			0
$407$	−20.9168	+	36.2290i	−1.03681	+	1.79581i
$408$		0			0
$409$	−15.8654	+	27.4797i	−0.784495	+	1.35879i	0.144805	+	0.989460i	$0.453744\pi$
$409$	−15.8654	+	27.4797i	−0.784495	+	1.35879i	−0.929300	+	0.369325i	$0.879589\pi$
$410$		0			0
$411$	8.84514	+	13.1643i	0.436299	+	0.649347i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	8.12156	−	14.0670i	0.398672	−	0.690520i
$416$		0			0
$417$	7.98451	−	16.2965i	0.391003	−	0.798041i
$418$		0			0
$419$	−19.0449	−	32.9867i	−0.930403	−	1.61151i	−0.782633	−	0.622483i	$-0.786124\pi$
$419$	−19.0449	−	32.9867i	−0.930403	−	1.61151i	−0.147770	−	0.989022i	$-0.547209\pi$
$420$		0			0
$421$	−0.614143	+	1.06373i	−0.0299315	+	0.0518429i	−0.880603	−	0.473855i	$-0.842862\pi$
$421$	−0.614143	+	1.06373i	−0.0299315	+	0.0518429i	0.850672	+	0.525697i	$0.176196\pi$
$422$		0			0
$423$	−10.3806	+	1.42097i	−0.504721	+	0.0690898i
$424$		0			0
$425$	25.4294	+	44.0450i	1.23351	+	2.13650i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−17.6412	+	36.0059i	−0.851725	+	1.73838i
$430$		0			0
$431$	4.66150	+	8.07396i	0.224537	+	0.388909i	0.956180	−	0.292778i	$-0.0945798\pi$
$431$	4.66150	+	8.07396i	0.224537	+	0.388909i	−0.731644	+	0.681687i	$0.761246\pi$
$432$		0			0
$433$	15.3849			0.739350			0.369675	−	0.929161i	$-0.379469\pi$
$433$	15.3849			0.739350			0.369675	+	0.929161i	$0.379469\pi$
$434$		0			0
$435$	−18.0426	+	1.22917i	−0.865074	+	0.0589340i
$436$		0			0
$437$	−1.82384	+	3.15899i	−0.0872462	+	0.151115i
$438$		0			0
$439$	−2.54467	−	4.40750i	−0.121451	−	0.210359i	0.798889	−	0.601478i	$-0.205421\pi$
$439$	−2.54467	−	4.40750i	−0.121451	−	0.210359i	−0.920340	+	0.391119i	$0.872088\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	17.3933	+	30.1260i	0.826379	+	1.43133i	0.900861	+	0.434109i	$0.142937\pi$
$443$	17.3933	+	30.1260i	0.826379	+	1.43133i	−0.0744812	+	0.997222i	$0.523730\pi$
$444$		0			0
$445$	−4.70471	+	8.14880i	−0.223025	+	0.386290i
$446$		0			0
$447$	−15.7141	−	23.3874i	−0.743250	−	1.10618i
$448$		0			0
$449$	−23.8337			−1.12478			−0.562391	−	0.826872i	$-0.690118\pi$
$449$	−23.8337			−1.12478			−0.562391	+	0.826872i	$0.690118\pi$
$450$		0			0
$451$	11.4969	+	19.9132i	0.541369	+	0.937678i
$452$		0			0
$453$	−6.96674	−	10.3687i	−0.327326	−	0.487162i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−8.41685	−	14.5784i	−0.393723	−	0.681949i	0.599214	−	0.800589i	$-0.295480\pi$
$457$	−8.41685	−	14.5784i	−0.393723	−	0.681949i	−0.992937	+	0.118640i	$0.962147\pi$
$458$		0			0
$459$	−17.2121	−	19.3240i	−0.803393	−	0.901965i
$460$		0			0
$461$	−6.13780	+	10.6310i	−0.285866	+	0.495134i	−0.972819	−	0.231568i	$-0.925614\pi$
$461$	−6.13780	+	10.6310i	−0.285866	+	0.495134i	0.686953	+	0.726702i	$0.258948\pi$
$462$		0			0
$463$	6.10607	+	10.5760i	0.283773	+	0.491509i	0.972311	−	0.233691i	$-0.0750805\pi$
$463$	6.10607	+	10.5760i	0.283773	+	0.491509i	−0.688538	+	0.725200i	$0.741747\pi$
$464$		0			0
$465$	−5.74230	+	0.391199i	−0.266293	+	0.0181414i
$466$		0			0
$467$	16.8791	−	29.2354i	0.781071	−	1.35285i	−0.150248	−	0.988648i	$-0.548007\pi$
$467$	16.8791	−	29.2354i	0.781071	−	1.35285i	0.931318	−	0.364206i	$-0.118660\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	2.05129	−	0.139746i	0.0945185	−	0.00643916i
$472$		0			0
$473$	−18.3965	+	31.8637i	−0.845874	+	1.46510i
$474$		0			0
$475$	−2.26802	+	3.92833i	−0.104064	+	0.180244i
$476$		0			0
$477$	−16.8736	+	2.30978i	−0.772591	+	0.105758i
$478$		0			0
$479$	−23.9186			−1.09287			−0.546434	−	0.837502i	$-0.684015\pi$
$479$	−23.9186			−1.09287			−0.546434	+	0.837502i	$0.684015\pi$
$480$		0			0
$481$	−53.1739			−2.42452
$482$		0			0
$483$		0			0
$484$		0			0
$485$	14.8385	−	25.7010i	0.673781	−	1.16702i
$486$		0			0
$487$	5.19664	+	9.00084i	0.235482	+	0.407867i	0.959413	−	0.282006i	$-0.0909998\pi$
$487$	5.19664	+	9.00084i	0.235482	+	0.407867i	−0.723931	+	0.689873i	$0.757666\pi$
$488$		0			0
$489$	−36.3146	+	2.47396i	−1.64220	+	0.111877i
$490$		0			0
$491$	−2.68922	−	4.65787i	−0.121363	−	0.210207i	0.798943	−	0.601407i	$-0.205393\pi$
$491$	−2.68922	−	4.65787i	−0.121363	−	0.210207i	−0.920305	+	0.391201i	$0.872060\pi$
$492$		0			0
$493$	13.3321			0.600446
$494$		0			0
$495$	−18.8715	+	46.2307i	−0.848209	+	2.07791i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−19.2431			−0.861440			−0.430720	−	0.902486i	$-0.641740\pi$
$499$	−19.2431			−0.861440			−0.430720	+	0.902486i	$0.641740\pi$
$500$		0			0
$501$	15.2905	−	31.2080i	0.683128	−	1.39427i
$502$		0			0
$503$	−22.3334			−0.995798			−0.497899	−	0.867235i	$-0.665895\pi$
$503$	−22.3334			−0.995798			−0.497899	+	0.867235i	$0.665895\pi$
$504$		0			0
$505$	19.9838			0.889269
$506$		0			0
$507$	−28.3819	+	1.93354i	−1.26048	+	0.0858716i
$508$		0			0
$509$	40.2262			1.78299			0.891497	−	0.453027i	$-0.149656\pi$
$509$	40.2262			1.78299			0.891497	+	0.453027i	$0.149656\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	0.725016	−	2.19121i	0.0320102	−	0.0967442i
$514$		0			0
$515$	−50.5500			−2.22750
$516$		0			0
$517$	−7.45216	−	12.9075i	−0.327746	−	0.567672i
$518$		0			0
$519$	−4.61829	+	9.42598i	−0.202720	+	0.413755i
$520$		0			0
$521$	18.3497	+	31.7826i	0.803914	+	1.39242i	0.917022	+	0.398837i	$0.130586\pi$
$521$	18.3497	+	31.7826i	0.803914	+	1.39242i	−0.113108	+	0.993583i	$0.536081\pi$
$522$		0			0
$523$	14.1727	−	24.5479i	0.619731	−	1.07341i	−0.369804	−	0.929110i	$-0.620575\pi$
$523$	14.1727	−	24.5479i	0.619731	−	1.07341i	0.989535	−	0.144296i	$-0.0460916\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.24312			0.184833
$528$		0			0
$529$	44.4391			1.93213
$530$		0			0
$531$	−3.48502	−	4.49373i	−0.151237	−	0.195011i
$532$		0			0
$533$	−14.6135	+	25.3113i	−0.632980	+	1.09635i
$534$		0			0
$535$	−22.4951	+	38.9626i	−0.972547	+	1.68450i
$536$		0			0
$537$	6.73189	−	13.7399i	0.290503	−	0.592919i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	12.3027	−	21.3089i	0.528934	−	0.916141i	−0.470496	−	0.882402i	$-0.655925\pi$
$541$	12.3027	−	21.3089i	0.528934	−	0.916141i	0.999431	−	0.0337394i	$-0.0107416\pi$
$542$		0			0
$543$	23.3581	+	34.7641i	1.00239	+	1.49187i
$544$		0			0
$545$	−0.798442	−	1.38294i	−0.0342015	−	0.0592388i
$546$		0			0
$547$	−0.106065	+	0.183711i	−0.00453503	+	0.00785491i	−0.868284	−	0.496067i	$-0.834777\pi$
$547$	−0.106065	+	0.183711i	−0.00453503	+	0.00785491i	0.863749	+	0.503922i	$0.168110\pi$
$548$		0			0
$549$	33.4579	−	4.57996i	1.42795	−	0.195468i
$550$		0			0
$551$	0.594537	+	1.02977i	0.0253281	+	0.0438696i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−66.0687	+	4.50099i	−2.80446	+	0.191056i
$556$		0			0
$557$	−9.40877	−	16.2965i	−0.398662	−	0.690503i	0.594899	−	0.803801i	$-0.297192\pi$
$557$	−9.40877	−	16.2965i	−0.398662	−	0.690503i	−0.993561	+	0.113297i	$0.963859\pi$
$558$		0			0
$559$	−46.7669			−1.97803
$560$		0			0
$561$	16.1966	−	33.0575i	0.683823	−	1.39569i
$562$		0			0
$563$	−6.43907	+	11.1528i	−0.271375	+	0.470035i	−0.969214	−	0.246220i	$-0.920812\pi$
$563$	−6.43907	+	11.1528i	−0.271375	+	0.470035i	0.697839	+	0.716254i	$0.254145\pi$
$564$		0			0
$565$	27.0857	+	46.9138i	1.13950	+	1.97368i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	13.5000	+	23.3827i	0.565949	+	0.980253i	0.996961	+	0.0779066i	$0.0248236\pi$
$569$	13.5000	+	23.3827i	0.565949	+	0.980253i	−0.431011	+	0.902347i	$0.641843\pi$
$570$		0			0
$571$	5.42492	−	9.39624i	0.227026	−	0.393221i	−0.729899	−	0.683555i	$-0.760433\pi$
$571$	5.42492	−	9.39624i	0.227026	−	0.393221i	0.956925	+	0.290334i	$0.0937664\pi$
$572$		0			0
$573$	15.4144	−	31.4609i	0.643944	−	1.31430i
$574$		0			0
$575$	83.8634			3.49734
$576$		0			0
$577$	−10.6085	−	18.3745i	−0.441640	−	0.764942i	0.556172	−	0.831067i	$-0.312270\pi$
$577$	−10.6085	−	18.3745i	−0.441640	−	0.764942i	−0.997811	+	0.0661250i	$0.978936\pi$
$578$		0			0
$579$	21.4161	−	1.45899i	0.890024	−	0.0606337i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−12.1135	−	20.9812i	−0.501689	−	0.868951i
$584$		0			0
$585$	−62.8837	+	8.60796i	−2.59992	+	0.355895i
$586$		0			0
$587$	−7.92684	+	13.7297i	−0.327176	+	0.566685i	−0.981950	−	0.189139i	$-0.939430\pi$
$587$	−7.92684	+	13.7297i	−0.327176	+	0.566685i	0.654775	+	0.755824i	$0.272764\pi$
$588$		0			0
$589$	0.189220	+	0.327739i	0.00779668	+	0.0135042i
$590$		0			0
$591$	13.9035	+	20.6928i	0.571915	+	0.851186i
$592$		0			0
$593$	−12.2580	+	21.2314i	−0.503375	+	0.871871i	0.496618	+	0.867969i	$0.334575\pi$
$593$	−12.2580	+	21.2314i	−0.503375	+	0.871871i	−0.999992	+	0.00390123i	$0.998758\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−8.01222	+	16.3530i	−0.327918	+	0.669285i
$598$		0			0
$599$	−2.21213	+	3.83152i	−0.0903852	+	0.156552i	−0.907673	−	0.419678i	$-0.862143\pi$
$599$	−2.21213	+	3.83152i	−0.0903852	+	0.156552i	0.817288	+	0.576229i	$0.195476\pi$
$600$		0			0
$601$	4.47075	−	7.74357i	0.182366	−	0.315867i	−0.760320	−	0.649549i	$-0.774958\pi$
$601$	4.47075	−	7.74357i	0.182366	−	0.315867i	0.942686	+	0.333682i	$0.108291\pi$
$602$		0			0
$603$	−4.76276	−	6.14131i	−0.193955	−	0.250093i
$604$		0			0
$605$	−28.1293			−1.14362
$606$		0			0
$607$	37.8254			1.53529			0.767643	−	0.640878i	$-0.221429\pi$
$607$	37.8254			1.53529			0.767643	+	0.640878i	$0.221429\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	9.47228	−	16.4065i	0.383208	−	0.663735i
$612$		0			0
$613$	9.33369	+	16.1664i	0.376984	+	0.652956i	0.990622	−	0.136632i	$-0.0436278\pi$
$613$	9.33369	+	16.1664i	0.376984	+	0.652956i	−0.613638	+	0.789588i	$0.710294\pi$
$614$		0			0
$615$	−16.0148	+	32.6863i	−0.645778	+	1.31804i
$616$		0			0
$617$	−14.9365	−	25.8708i	−0.601320	−	1.04152i	−0.992621	−	0.121255i	$-0.961308\pi$
$617$	−14.9365	−	25.8708i	−0.601320	−	1.04152i	0.391301	−	0.920263i	$-0.372025\pi$
$618$		0			0
$619$	−3.81578			−0.153369			−0.0766846	−	0.997055i	$-0.524433\pi$
$619$	−3.81578			−0.153369			−0.0766846	+	0.997055i	$0.524433\pi$
$620$		0			0
$621$	−41.7861	+	8.64734i	−1.67682	+	0.347006i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	28.2270			1.12908
$626$		0			0
$627$	3.27565	−	0.223156i	0.130817	−	0.00891200i
$628$		0			0
$629$	48.8197			1.94657
$630$		0			0
$631$	20.0458			0.798012			0.399006	−	0.916948i	$-0.369355\pi$
$631$	20.0458			0.798012			0.399006	+	0.916948i	$0.369355\pi$
$632$		0			0
$633$	−17.8509	+	36.4339i	−0.709511	+	1.44812i
$634$		0			0
$635$	−45.3273			−1.79876
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−0.160840	+	0.394021i	−0.00636275	+	0.0155872i
$640$		0			0
$641$	−9.50415			−0.375391			−0.187696	−	0.982227i	$-0.560102\pi$
$641$	−9.50415			−0.375391			−0.187696	+	0.982227i	$0.560102\pi$
$642$		0			0
$643$	15.0611	+	26.0866i	0.593952	+	1.02876i	0.993694	+	0.112128i	$0.0357666\pi$
$643$	15.0611	+	26.0866i	0.593952	+	1.02876i	−0.399741	+	0.916628i	$0.630900\pi$
$644$		0			0
$645$	−58.1080	+	3.95866i	−2.28800	+	0.155872i
$646$		0			0
$647$	−10.6267	−	18.4060i	−0.417780	−	0.723616i	0.577936	−	0.816082i	$-0.303858\pi$
$647$	−10.6267	−	18.4060i	−0.417780	−	0.723616i	−0.995716	+	0.0924659i	$0.970525\pi$
$648$		0			0
$649$	4.04475	−	7.00572i	0.158770	−	0.274999i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.450032			−0.0176111			−0.00880556	−	0.999961i	$-0.502803\pi$
$653$	−0.450032			−0.0176111			−0.00880556	+	0.999961i	$0.502803\pi$
$654$		0			0
$655$	15.8175			0.618042
$656$		0			0
$657$	30.7093	−	4.20371i	1.19808	−	0.164002i
$658$		0			0
$659$	8.68441	−	15.0418i	0.338297	−	0.585947i	−0.645816	−	0.763493i	$-0.723483\pi$
$659$	8.68441	−	15.0418i	0.338297	−	0.585947i	0.984112	+	0.177546i	$0.0568159\pi$
$660$		0			0
$661$	17.0048	−	29.4532i	0.661411	−	1.14560i	−0.318835	−	0.947810i	$-0.603291\pi$
$661$	17.0048	−	29.4532i	0.661411	−	1.14560i	0.980245	−	0.197786i	$-0.0633752\pi$
$662$		0			0
$663$	46.6829	−	3.18031i	1.81301	−	0.123513i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	10.9919	−	19.0386i	0.425609	−	0.737176i
$668$		0			0
$669$	43.7979	−	2.98377i	1.69332	−	0.115359i
$670$		0			0
$671$	24.0192	+	41.6025i	0.927252	+	1.60605i
$672$		0			0
$673$	−10.5825	+	18.3294i	−0.407925	+	0.706547i	−0.994657	−	0.103234i	$-0.967081\pi$
$673$	−10.5825	+	18.3294i	−0.407925	+	0.706547i	0.586732	+	0.809781i	$0.300414\pi$
$674$		0			0
$675$	−51.9628	+	10.7533i	−2.00005	+	0.413896i
$676$		0			0
$677$	−8.85745	−	15.3416i	−0.340420	−	0.589624i	0.644091	−	0.764949i	$-0.277236\pi$
$677$	−8.85745	−	15.3416i	−0.340420	−	0.589624i	−0.984511	+	0.175325i	$0.943902\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	17.4120	+	25.9145i	0.667231	+	0.993045i
$682$		0			0
$683$	16.2676	+	28.1763i	0.622461	+	1.07813i	0.989026	+	0.147742i	$0.0472005\pi$
$683$	16.2676	+	28.1763i	0.622461	+	1.07813i	−0.366565	+	0.930393i	$0.619466\pi$
$684$		0			0
$685$	−35.7136			−1.36455
$686$		0			0
$687$	5.23985	+	7.79851i	0.199913	+	0.297532i
$688$		0			0
$689$	15.3972	−	26.6687i	0.586586	−	1.01600i
$690$		0			0
$691$	15.6910	+	27.1776i	0.596914	+	1.03389i	0.993274	+	0.115791i	$0.0369401\pi$
$691$	15.6910	+	27.1776i	0.596914	+	1.03389i	−0.396359	+	0.918095i	$0.629727\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	20.4323	+	35.3899i	0.775043	+	1.34241i
$696$		0			0
$697$	13.4168	−	23.2387i	0.508199	−	0.880227i
$698$		0			0
$699$	4.91336	−	0.334727i	0.185840	−	0.0126605i
$700$		0			0
$701$	−11.7163			−0.442518			−0.221259	−	0.975215i	$-0.571017\pi$
$701$	−11.7163			−0.442518			−0.221259	+	0.975215i	$0.571017\pi$
$702$		0			0
$703$	2.17709	+	3.77084i	0.0821106	+	0.142220i
$704$		0			0
$705$	10.3806	−	21.1869i	0.390955	−	0.797944i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−3.59057	−	6.21905i	−0.134847	−	0.233561i	0.790692	−	0.612214i	$-0.209721\pi$
$709$	−3.59057	−	6.21905i	−0.134847	−	0.233561i	−0.925539	+	0.378653i	$0.876388\pi$
$710$		0			0
$711$	−1.21694	+	0.166583i	−0.0456387	+	0.00624736i
$712$		0			0
$713$	3.49834	−	6.05930i	0.131014	−	0.226922i
$714$		0			0
$715$	−45.1438	−	78.1914i	−1.68828	−	2.92419i
$716$		0			0
$717$	9.28288	−	18.9465i	0.346676	−	0.707569i
$718$		0			0
$719$	7.82360	−	13.5509i	0.291771	−	0.505362i	−0.682458	−	0.730925i	$-0.739089\pi$
$719$	7.82360	−	13.5509i	0.291771	−	0.505362i	0.974229	+	0.225563i	$0.0724222\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−17.9910	−	26.7762i	−0.669094	−	0.995818i
$724$		0			0
$725$	13.6689	−	23.6753i	0.507651	−	0.879277i
$726$		0			0
$727$	22.5678	−	39.0886i	0.836995	−	1.44972i	−0.0554015	−	0.998464i	$-0.517644\pi$
$727$	22.5678	−	39.0886i	0.836995	−	1.44972i	0.892396	−	0.451253i	$-0.149023\pi$
$728$		0			0
$729$	24.7824	−	10.7160i	0.917867	−	0.396889i
$730$		0			0
$731$	42.9374			1.58810
$732$		0			0
$733$	−41.2334			−1.52299			−0.761495	−	0.648171i	$-0.775534\pi$
$733$	−41.2334			−1.52299			−0.761495	+	0.648171i	$0.775534\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.52772	−	9.57429i	0.203616	−	0.352673i
$738$		0			0
$739$	−16.6209	−	28.7882i	−0.611410	−	1.05899i	−0.991003	−	0.133839i	$-0.957269\pi$
$739$	−16.6209	−	28.7882i	−0.611410	−	1.05899i	0.379593	−	0.925153i	$-0.376064\pi$
$740$		0			0
$741$	2.32745	+	3.46396i	0.0855010	+	0.127252i
$742$		0			0
$743$	−16.3263	−	28.2779i	−0.598953	−	1.03742i	−0.992976	−	0.118316i	$-0.962250\pi$
$743$	−16.3263	−	28.2779i	−0.598953	−	1.03742i	0.394023	−	0.919101i	$-0.371083\pi$
$744$		0			0
$745$	63.4480			2.32455
$746$		0			0
$747$	−7.65663	−	9.87278i	−0.280141	−	0.361226i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	40.0768			1.46242			0.731212	−	0.682151i	$-0.238955\pi$
$751$	40.0768			1.46242			0.731212	+	0.682151i	$0.238955\pi$
$752$		0			0
$753$	−6.89721	−	10.2652i	−0.251348	−	0.374083i
$754$		0			0
$755$	28.1293			1.02373
$756$		0			0
$757$	21.8337			0.793559			0.396779	−	0.917914i	$-0.370128\pi$
$757$	21.8337			0.793559			0.396779	+	0.917914i	$0.370128\pi$
$758$		0			0
$759$	−33.8534	−	50.3843i	−1.22880	−	1.82883i
$760$		0			0
$761$	−9.12135			−0.330649			−0.165324	−	0.986239i	$-0.552867\pi$
$761$	−9.12135			−0.330649			−0.165324	+	0.986239i	$0.552867\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	57.7344	−	7.90309i	2.08739	−	0.285737i
$766$		0			0
$767$	10.2824			0.371276
$768$		0			0
$769$	14.3654	+	24.8815i	0.518028	+	0.897250i	0.999781	+	0.0209433i	$0.00666695\pi$
$769$	14.3654	+	24.8815i	0.518028	+	0.897250i	−0.481753	+	0.876307i	$0.660000\pi$
$770$		0			0
$771$	1.29856	+	1.93265i	0.0467664	+	0.0696028i
$772$		0			0
$773$	−19.7283	−	34.1705i	−0.709578	−	1.22903i	−0.965014	−	0.262200i	$-0.915552\pi$
$773$	−19.7283	−	34.1705i	−0.709578	−	1.22903i	0.255435	−	0.966826i	$-0.417781\pi$
$774$		0			0
$775$	4.35033	−	7.53499i	0.156268	−	0.270665i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.39327			0.0857479
$780$		0			0
$781$	−0.605404			−0.0216631
$782$		0			0
$783$	−4.36952	+	13.2060i	−0.156154	+	0.471943i
$784$		0			0
$785$	−2.31493	+	4.00957i	−0.0826232	+	0.143108i
$786$		0			0
$787$	5.51534	−	9.55286i	0.196601	−	0.340523i	−0.750823	−	0.660503i	$-0.770343\pi$
$787$	5.51534	−	9.55286i	0.196601	−	0.340523i	0.947424	+	0.319981i	$0.103676\pi$
$788$		0			0
$789$	−23.4718	−	34.9333i	−0.835618	−	1.24366i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−30.5303	+	52.8801i	−1.08416	+	1.87783i
$794$		0			0
$795$	16.8736	−	34.4393i	0.598446	−	1.22144i
$796$		0			0
$797$	1.15757	+	2.00497i	0.0410032	+	0.0710196i	0.885799	−	0.464070i	$-0.153611\pi$
$797$	1.15757	+	2.00497i	0.0410032	+	0.0710196i	−0.844796	+	0.535089i	$0.820278\pi$
$798$		0			0
$799$	−8.69664	+	15.0630i	−0.307665	+	0.532891i
$800$		0			0
$801$	4.43539	+	5.71918i	0.156717	+	0.202077i
$802$		0			0
$803$	22.0460	+	38.1849i	0.777988	+	1.34751i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−4.11502	+	8.39880i	−0.144856	+	0.295652i
$808$		0			0
$809$	3.70471	+	6.41675i	0.130251	+	0.225601i	0.923773	−	0.382940i	$-0.125088\pi$
$809$	3.70471	+	6.41675i	0.130251	+	0.225601i	−0.793522	+	0.608541i	$0.791755\pi$
$810$		0			0
$811$	−12.8879			−0.452555			−0.226277	−	0.974063i	$-0.572656\pi$
$811$	−12.8879			−0.452555			−0.226277	+	0.974063i	$0.572656\pi$
$812$		0			0
$813$	23.4526	−	1.59773i	0.822520	−	0.0560349i
$814$		0			0
$815$	40.9818	−	70.9826i	1.43553	−	2.48641i
$816$		0			0
$817$	1.91477	+	3.31648i	0.0669894	+	0.116029i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	12.9371	+	22.4078i	0.451510	+	0.782037i	0.998480	−	0.0551144i	$-0.0175524\pi$
$821$	12.9371	+	22.4078i	0.451510	+	0.782037i	−0.546970	+	0.837152i	$0.684219\pi$
$822$		0			0
$823$	−22.0310	+	38.1588i	−0.767952	+	1.33013i	0.170720	+	0.985320i	$0.445391\pi$
$823$	−22.0310	+	38.1588i	−0.767952	+	1.33013i	−0.938672	+	0.344812i	$0.887943\pi$
$824$		0			0
$825$	−42.0981	−	62.6550i	−1.46567	−	2.18137i
$826$		0			0
$827$	−6.81753			−0.237069			−0.118534	−	0.992950i	$-0.537820\pi$
$827$	−6.81753			−0.237069			−0.118534	+	0.992950i	$0.537820\pi$
$828$		0			0
$829$	4.27759	+	7.40900i	0.148567	+	0.257325i	0.930698	−	0.365789i	$-0.119201\pi$
$829$	4.27759	+	7.40900i	0.148567	+	0.257325i	−0.782131	+	0.623114i	$0.785867\pi$
$830$		0			0
$831$	−28.0276	−	41.7137i	−0.972267	−	1.44703i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	39.1283	+	67.7722i	1.35409	+	2.34535i
$836$		0			0
$837$	−1.39066	+	4.20299i	−0.0480684	+	0.145277i
$838$		0			0
$839$	18.0971	−	31.3451i	0.624781	−	1.08215i	−0.363803	−	0.931476i	$-0.618522\pi$
$839$	18.0971	−	31.3451i	0.624781	−	1.08215i	0.988583	−	0.150676i	$-0.0481450\pi$
$840$		0			0
$841$	10.9168	+	18.9085i	0.376443	+	0.652018i
$842$		0			0
$843$	3.06160	−	0.208574i	0.105447	−	0.00718368i
$844$		0			0
$845$	32.0296	−	55.4768i	1.10185	−	1.90846i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	41.9114	−	2.85525i	1.43839	−	0.0979919i
$850$		0			0
$851$	40.2505	−	69.7160i	1.37977	−	2.38983i
$852$		0			0
$853$	−3.97889	+	6.89164i	−0.136235	+	0.235965i	−0.926068	−	0.377356i	$-0.876833\pi$
$853$	−3.97889	+	6.89164i	−0.136235	+	0.235965i	0.789834	+	0.613321i	$0.210167\pi$
$854$		0			0
$855$	3.18507	+	4.10697i	0.108927	+	0.140455i
$856$		0			0
$857$	−45.5798			−1.55698			−0.778489	−	0.627658i	$-0.784014\pi$
$857$	−45.5798			−1.55698			−0.778489	+	0.627658i	$0.784014\pi$
$858$		0			0
$859$	20.9035			0.713219			0.356609	−	0.934254i	$-0.383933\pi$
$859$	20.9035			0.713219			0.356609	+	0.934254i	$0.383933\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	3.88586	−	6.73050i	0.132276	−	0.229109i	−0.792278	−	0.610161i	$-0.791105\pi$
$863$	3.88586	−	6.73050i	0.132276	−	0.229109i	0.924554	+	0.381052i	$0.124438\pi$
$864$		0			0
$865$	−11.8182	−	20.4697i	−0.401831	−	0.695991i
$866$		0			0
$867$	−13.4834	+	0.918570i	−0.457921	+	0.0311963i
$868$		0			0
$869$	−0.873633	−	1.51318i	−0.0296360	−	0.0513310i
$870$		0			0
$871$	14.0523			0.476145
$872$		0			0
$873$	−13.9890	−	18.0381i	−0.473457	−	0.610496i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−39.3771			−1.32967			−0.664835	−	0.746990i	$-0.731498\pi$
$877$	−39.3771			−1.32967			−0.664835	+	0.746990i	$0.731498\pi$
$878$		0			0
$879$	−11.4690	+	23.4084i	−0.386840	+	0.789545i
$880$		0			0
$881$	26.7967			0.902805			0.451402	−	0.892320i	$-0.350924\pi$
$881$	26.7967			0.902805			0.451402	+	0.892320i	$0.350924\pi$
$882$		0			0
$883$	−43.0755			−1.44961			−0.724803	−	0.688956i	$-0.758069\pi$
$883$	−43.0755			−1.44961			−0.724803	+	0.688956i	$0.758069\pi$
$884$		0			0
$885$	12.7759	−	0.870371i	0.429458	−	0.0292572i
$886$		0			0
$887$	37.2506			1.25075			0.625377	−	0.780323i	$-0.284945\pi$
$887$	37.2506			1.25075			0.625377	+	0.780323i	$0.284945\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	27.4365	+	26.8779i	0.919157	+	0.900444i
$892$		0			0
$893$	−1.55129			−0.0519120
$894$		0			0
$895$	17.2269	+	29.8379i	0.575832	+	0.997370i
$896$		0			0
$897$	33.9472	−	69.2866i	1.13346	−	2.31341i
$898$		0			0
$899$	−1.14039	−	1.97521i	−0.0380342	−	0.0658771i
$900$		0			0
$901$	−14.1364	+	24.4849i	−0.470951	+	0.815711i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−94.3121			−3.13504
$906$		0			0
$907$	−9.78655			−0.324957			−0.162478	−	0.986712i	$-0.551949\pi$
$907$	−9.78655			−0.324957			−0.162478	+	0.986712i	$0.551949\pi$
$908$		0			0
$909$	5.80917	−	14.2311i	0.192678	−	0.472016i
$910$		0			0
$911$	14.2979	−	24.7647i	0.473710	−	0.820490i	−0.525837	−	0.850586i	$-0.676248\pi$
$911$	14.2979	−	24.7647i	0.473710	−	0.820490i	0.999547	+	0.0300951i	$0.00958102\pi$
$912$		0			0
$913$	8.88638	−	15.3917i	0.294096	−	0.509390i
$914$		0			0
$915$	−33.4579	+	68.2879i	−1.10608	+	2.25753i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	8.61348	−	14.9190i	0.284133	−	0.492132i	−0.688266	−	0.725459i	$-0.741628\pi$
$919$	8.61348	−	14.9190i	0.284133	−	0.492132i	0.972398	+	0.233326i	$0.0749611\pi$
$920$		0			0
$921$	3.88237	+	5.77817i	0.127929	+	0.190397i
$922$		0			0
$923$	−0.384758	−	0.666420i	−0.0126645	−	0.0219355i
$924$		0			0
$925$	50.0532	−	86.6948i	1.64574	−	2.85051i
$926$		0			0
$927$	−14.6945	+	35.9982i	−0.482632	+	1.18234i
$928$		0			0
$929$	−13.4299	−	23.2612i	−0.440620	−	0.763176i	0.557116	−	0.830435i	$-0.311908\pi$
$929$	−13.4299	−	23.2612i	−0.440620	−	0.763176i	−0.997736	+	0.0672589i	$0.978575\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	2.75949	−	0.187993i	0.0903416	−	0.00615460i
$934$		0			0
$935$	41.4472	+	71.7886i	1.35547	+	2.34774i
$936$		0			0
$937$	−51.5653			−1.68456			−0.842282	−	0.539037i	$-0.818788\pi$
$937$	−51.5653			−1.68456			−0.842282	+	0.539037i	$0.818788\pi$
$938$		0			0
$939$	3.71213	−	7.57650i	0.121141	−	0.247250i
$940$		0			0
$941$	−20.9002	+	36.2002i	−0.681328	+	1.18009i	0.293248	+	0.956036i	$0.405264\pi$
$941$	−20.9002	+	36.2002i	−0.681328	+	1.18009i	−0.974576	+	0.224058i	$0.928070\pi$
$942$		0			0
$943$	−22.1237	−	38.3193i	−0.720445	−	1.24785i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.75207	−	8.23083i	−0.154422	−	0.267466i	0.778427	−	0.627736i	$-0.216018\pi$
$947$	−4.75207	−	8.23083i	−0.154422	−	0.267466i	−0.932848	+	0.360269i	$0.882685\pi$
$948$		0			0
$949$	−28.0222	+	48.5360i	−0.909641	+	1.57554i
$950$		0			0
$951$	−6.38496	+	13.0318i	−0.207046	+	0.422584i
$952$		0			0
$953$	−58.4539			−1.89351			−0.946754	−	0.321957i	$-0.895659\pi$
$953$	−58.4539			−1.89351			−0.946754	+	0.321957i	$0.895659\pi$
$954$		0			0
$955$	39.4453	+	68.3213i	1.27642	+	2.21083i
$956$		0			0
$957$	−19.7416	+	1.34492i	−0.638157	+	0.0434750i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	15.1371	+	26.2181i	0.488292	+	0.845747i
$962$		0			0
$963$	21.2073	+	27.3456i	0.683396	+	0.881201i
$964$		0			0
$965$	−24.1686	+	41.8612i	−0.778014	+	1.34756i
$966$		0			0
$967$	−5.09799	−	8.82997i	−0.163940	−	0.283953i	0.772338	−	0.635212i	$-0.219087\pi$
$967$	−5.09799	−	8.82997i	−0.163940	−	0.283953i	−0.936278	+	0.351259i	$0.885754\pi$
$968$		0			0
$969$	−2.13686	−	3.18031i	−0.0686460	−	0.102166i
$970$		0			0
$971$	−19.4238	+	33.6429i	−0.623338	+	1.07965i	0.365522	+	0.930803i	$0.380891\pi$
$971$	−19.4238	+	33.6429i	−0.623338	+	1.07965i	−0.988860	+	0.148850i	$0.952443\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	42.2147	−	86.1607i	1.35195	−	2.75935i
$976$		0			0
$977$	21.0661	−	36.4876i	0.673965	−	1.16734i	−0.302805	−	0.953052i	$-0.597923\pi$
$977$	21.0661	−	36.4876i	0.673965	−	1.16734i	0.976770	−	0.214289i	$-0.0687435\pi$
$978$		0			0
$979$	−5.14776	+	8.91619i	−0.164523	+	0.284963i
$980$		0			0
$981$	−1.21694	+	0.166583i	−0.0388538	+	0.00531859i
$982$		0			0
$983$	34.0569			1.08625			0.543123	−	0.839653i	$-0.317242\pi$
$983$	34.0569			1.08625			0.543123	+	0.839653i	$0.317242\pi$
$984$		0			0
$985$	−56.1377			−1.78870
$986$		0			0
$987$		0			0
$988$		0			0
$989$	35.4007	−	61.3158i	1.12568	−	1.94973i
$990$		0			0
$991$	−20.5980	−	35.6768i	−0.654317	−	1.13331i	−0.982065	−	0.188544i	$-0.939623\pi$
$991$	−20.5980	−	35.6768i	−0.654317	−	1.13331i	0.327748	−	0.944765i	$-0.393710\pi$
$992$		0			0
$993$	19.6871	−	40.1816i	0.624751	−	1.27512i
$994$		0			0
$995$	−20.5033	−	35.5127i	−0.649997	−	1.12583i
$996$		0			0
$997$	31.4399			0.995711			0.497856	−	0.867260i	$-0.334121\pi$
$997$	31.4399			0.995711			0.497856	+	0.867260i	$0.334121\pi$
$998$		0			0
$999$	−16.0004	+	48.3580i	−0.506232	+	1.52998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.l.h.961.4		12
3.2	odd	2		5292.2.l.h.3313.6		12
7.2	even	3		1764.2.j.f.1177.1	yes	12
7.3	odd	6		1764.2.i.h.1537.2		12
7.4	even	3		1764.2.i.h.1537.5		12
7.5	odd	6		1764.2.j.f.1177.6	yes	12
7.6	odd	2	inner	1764.2.l.h.961.3		12
9.4	even	3		1764.2.i.h.373.5		12
9.5	odd	6		5292.2.i.h.1549.1		12
21.2	odd	6		5292.2.j.f.3529.1		12
21.5	even	6		5292.2.j.f.3529.6		12
21.11	odd	6		5292.2.i.h.2125.1		12
21.17	even	6		5292.2.i.h.2125.6		12
21.20	even	2		5292.2.l.h.3313.1		12
63.4	even	3	inner	1764.2.l.h.949.4		12
63.5	even	6		5292.2.j.f.1765.6		12
63.13	odd	6		1764.2.i.h.373.2		12
63.23	odd	6		5292.2.j.f.1765.1		12
63.31	odd	6	inner	1764.2.l.h.949.3		12
63.32	odd	6		5292.2.l.h.361.6		12
63.40	odd	6		1764.2.j.f.589.6	yes	12
63.41	even	6		5292.2.i.h.1549.6		12
63.58	even	3		1764.2.j.f.589.1	✓	12
63.59	even	6		5292.2.l.h.361.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1764.2.i.h.373.2		12	63.13	odd	6
1764.2.i.h.373.5		12	9.4	even	3
1764.2.i.h.1537.2		12	7.3	odd	6
1764.2.i.h.1537.5		12	7.4	even	3
1764.2.j.f.589.1	✓	12	63.58	even	3
1764.2.j.f.589.6	yes	12	63.40	odd	6
1764.2.j.f.1177.1	yes	12	7.2	even	3
1764.2.j.f.1177.6	yes	12	7.5	odd	6
1764.2.l.h.949.3		12	63.31	odd	6	inner
1764.2.l.h.949.4		12	63.4	even	3	inner
1764.2.l.h.961.3		12	7.6	odd	2	inner
1764.2.l.h.961.4		12	1.1	even	1	trivial
5292.2.i.h.1549.1		12	9.5	odd	6
5292.2.i.h.1549.6		12	63.41	even	6
5292.2.i.h.2125.1		12	21.11	odd	6
5292.2.i.h.2125.6		12	21.17	even	6
5292.2.j.f.1765.1		12	63.23	odd	6
5292.2.j.f.1765.6		12	63.5	even	6
5292.2.j.f.3529.1		12	21.2	odd	6
5292.2.j.f.3529.6		12	21.5	even	6
5292.2.l.h.361.1		12	63.59	even	6
5292.2.l.h.361.6		12	63.32	odd	6
5292.2.l.h.3313.1		12	21.20	even	2
5292.2.l.h.3313.6		12	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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.965975 + 1.43767i) q^{3} -3.90027 q^{5} +(-1.13378 + 2.77751i) q^{9} +O(q^{10})\)	\(q+(0.965975 + 1.43767i) q^{3} -3.90027 q^{5} +(-1.13378 + 2.77751i) q^{9} -4.26757 q^{11} +(-2.71221 - 4.69768i) q^{13} +(-3.76757 - 5.60730i) q^{15} +(2.49012 + 4.31301i) q^{17} +(-0.222091 + 0.384673i) q^{19} +8.21213 q^{23} +10.2121 q^{25} +(-5.08834 + 1.05300i) q^{27} +(1.33850 - 2.31835i) q^{29} +(0.425996 - 0.737847i) q^{31} +(-4.12236 - 6.13535i) q^{33} +(4.90135 - 8.48939i) q^{37} +(4.13378 - 8.43710i) q^{39} +(-2.69402 - 4.66618i) q^{41} +(4.31078 - 7.46649i) q^{43} +(4.42207 - 10.8330i) q^{45} +(1.74623 + 3.02456i) q^{47} +(-3.79529 + 7.74622i) q^{51} +(2.83850 + 4.91642i) q^{53} +16.6447 q^{55} +(-0.767567 + 0.0522912i) q^{57} +(-0.947789 + 1.64162i) q^{59} +(-5.62832 - 9.74853i) q^{61} +(10.5783 + 18.3222i) q^{65} +(-1.29529 + 2.24350i) q^{67} +(7.93272 + 11.8063i) q^{69} +0.141862 q^{71} +(-5.16595 - 8.94769i) q^{73} +(9.86467 + 14.6817i) q^{75} +(0.204714 + 0.354576i) q^{79} +(-6.42907 - 6.29818i) q^{81} +(-2.08231 + 3.60666i) q^{83} +(-9.71213 - 16.8219i) q^{85} +(4.62597 - 0.315148i) q^{87} +(1.20625 - 2.08929i) q^{89} +(1.47228 - 0.100301i) q^{93} +(0.866216 - 1.50033i) q^{95} +(-3.80448 + 6.58955i) q^{97} +(4.83850 - 11.8532i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{9}+O(q^{10}) \) 12 * q + 4 * q^9	\( 12 q + 4 q^{9} - 16 q^{11} - 10 q^{15} + 24 q^{25} + 2 q^{29} + 6 q^{37} + 32 q^{39} + 6 q^{43} - 42 q^{51} + 20 q^{53} + 26 q^{57} + 46 q^{65} - 12 q^{67} + 44 q^{71} + 6 q^{79} - 56 q^{81} - 18 q^{85} - 14 q^{93} + 28 q^{95} + 44 q^{99}+O(q^{100}) \) 12 * q + 4 * q^9 - 16 * q^11 - 10 * q^15 + 24 * q^25 + 2 * q^29 + 6 * q^37 + 32 * q^39 + 6 * q^43 - 42 * q^51 + 20 * q^53 + 26 * q^57 + 46 * q^65 - 12 * q^67 + 44 * q^71 + 6 * q^79 - 56 * q^81 - 18 * q^85 - 14 * q^93 + 28 * q^95 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more