LMFDB - Embedded newform 120.4.f.d.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(49,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("120.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	120.f (of order $2$, degree $1$, 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:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{129})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 65x^{2} + 1024 $ x^4 + 65*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.4
Root			$6.17891i$ of defining polynomial
Character	$\chi$	$=$	120.49
Dual form			120.4.f.d.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.00000i q^{3} +(11.1789 + 0.178908i) q^{5} -33.0735i q^{7} -9.00000 q^{9} +O(q^{10})$	$q+3.00000i q^{3} +(11.1789 + 0.178908i) q^{5} -33.0735i q^{7} -9.00000 q^{9} +48.3578 q^{11} +60.3578i q^{13} +(-0.536725 + 33.5367i) q^{15} -17.7891i q^{17} +130.863 q^{19} +99.2204 q^{21} -70.8625i q^{23} +(124.936 + 4.00000i) q^{25} -27.0000i q^{27} -104.505 q^{29} -210.441 q^{31} +145.073i q^{33} +(5.91712 - 369.725i) q^{35} +300.945i q^{37} -181.073 q^{39} +240.147 q^{41} +108.000i q^{43} +(-100.610 - 1.61018i) q^{45} -278.991i q^{47} -750.853 q^{49} +53.3673 q^{51} -328.358i q^{53} +(540.588 + 8.65162i) q^{55} +392.588i q^{57} -889.533 q^{59} -241.450 q^{61} +297.661i q^{63} +(-10.7985 + 674.735i) q^{65} +103.834i q^{67} +212.588 q^{69} -277.597 q^{71} -274.403i q^{73} +(-12.0000 + 374.808i) q^{75} -1599.36i q^{77} -366.991 q^{79} +81.0000 q^{81} -57.7251i q^{83} +(3.18262 - 198.863i) q^{85} -313.514i q^{87} +203.175 q^{89} +1996.24 q^{91} -631.322i q^{93} +(1462.90 + 23.4124i) q^{95} +1283.45i q^{97} -435.220 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 22 q^{5} - 36 q^{9}+O(q^{10}) $ 4 * q + 22 * q^5 - 36 * q^9	$ 4 q + 22 q^{5} - 36 q^{9} + 148 q^{11} + 66 q^{15} + 160 q^{19} - 12 q^{21} - 100 q^{29} - 24 q^{31} + 796 q^{35} - 588 q^{39} + 688 q^{41} - 198 q^{45} - 3276 q^{49} - 468 q^{51} + 1072 q^{55} - 1332 q^{59} + 488 q^{61} + 820 q^{65} - 240 q^{69} + 616 q^{71} - 48 q^{75} - 2104 q^{79} + 324 q^{81} + 2148 q^{85} - 1368 q^{89} + 1352 q^{91} + 2944 q^{95} - 1332 q^{99}+O(q^{100}) $ 4 * q + 22 * q^5 - 36 * q^9 + 148 * q^11 + 66 * q^15 + 160 * q^19 - 12 * q^21 - 100 * q^29 - 24 * q^31 + 796 * q^35 - 588 * q^39 + 688 * q^41 - 198 * q^45 - 3276 * q^49 - 468 * q^51 + 1072 * q^55 - 1332 * q^59 + 488 * q^61 + 820 * q^65 - 240 * q^69 + 616 * q^71 - 48 * q^75 - 2104 * q^79 + 324 * q^81 + 2148 * q^85 - 1368 * q^89 + 1352 * q^91 + 2944 * q^95 - 1332 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$		0			0
$5$	11.1789	+	0.178908i	0.999872	+	0.0160020i
$5$	11.1789	+	0.178908i	0.999872	+	0.0160020i
$6$		0			0
$7$		−	33.0735i		−	1.78580i	−0.450257	−	0.892899i	$-0.648667\pi$
$7$		−	33.0735i		−	1.78580i	0.450257	−	0.892899i	$-0.351333\pi$
$8$		0			0
$9$	−9.00000			−0.333333
$10$		0			0
$11$	48.3578			1.32549			0.662747	−	0.748844i	$-0.269391\pi$
$11$	48.3578			1.32549			0.662747	+	0.748844i	$0.269391\pi$
$12$		0			0
$13$			60.3578i			1.28771i	0.765147	+	0.643856i	$0.222666\pi$
$13$			60.3578i			1.28771i	−0.765147	+	0.643856i	$0.777334\pi$
$14$		0			0
$15$	−0.536725	+	33.5367i	−0.00923879	+	0.577276i
$16$		0			0
$17$		−	17.7891i		−	0.253793i	−0.991916	−	0.126897i	$-0.959498\pi$
$17$		−	17.7891i		−	0.253793i	0.991916	−	0.126897i	$-0.0405017\pi$
$18$		0			0
$19$	130.863			1.58010			0.790051	−	0.613042i	$-0.210054\pi$
$19$	130.863			1.58010			0.790051	+	0.613042i	$0.210054\pi$
$20$		0			0
$21$	99.2204			1.03103
$22$		0			0
$23$		−	70.8625i		−	0.642429i	−0.947007	−	0.321214i	$-0.895909\pi$
$23$		−	70.8625i		−	0.642429i	0.947007	−	0.321214i	$-0.104091\pi$
$24$		0			0
$25$	124.936	+	4.00000i	0.999488	+	0.0320000i
$26$		0			0
$27$		−	27.0000i		−	0.192450i
$28$		0			0
$29$	−104.505			−0.669174			−0.334587	−	0.942365i	$-0.608597\pi$
$29$	−104.505			−0.669174			−0.334587	+	0.942365i	$0.608597\pi$
$30$		0			0
$31$	−210.441			−1.21923			−0.609617	−	0.792696i	$-0.708677\pi$
$31$	−210.441			−1.21923			−0.609617	+	0.792696i	$0.708677\pi$
$32$		0			0
$33$			145.073i			0.765274i
$34$		0			0
$35$	5.91712	−	369.725i	0.0285764	−	1.78557i
$36$		0			0
$37$			300.945i			1.33717i	0.743638	+	0.668583i	$0.233099\pi$
$37$			300.945i			1.33717i	−0.743638	+	0.668583i	$0.766901\pi$
$38$		0			0
$39$	−181.073			−0.743460
$40$		0			0
$41$	240.147			0.914747			0.457374	−	0.889275i	$-0.348790\pi$
$41$	240.147			0.914747			0.457374	+	0.889275i	$0.348790\pi$
$42$		0			0
$43$			108.000i			0.383020i	0.981491	+	0.191510i	$0.0613384\pi$
$43$			108.000i			0.383020i	−0.981491	+	0.191510i	$0.938662\pi$
$44$		0			0
$45$	−100.610	−	1.61018i	−0.333291	−	0.00533402i
$46$		0			0
$47$		−	278.991i		−	0.865850i	−0.901430	−	0.432925i	$-0.857481\pi$
$47$		−	278.991i		−	0.865850i	0.901430	−	0.432925i	$-0.142519\pi$
$48$		0			0
$49$	−750.853			−2.18908
$50$		0			0
$51$	53.3673			0.146528
$52$		0			0
$53$		−	328.358i		−	0.851008i	−0.904957	−	0.425504i	$-0.860097\pi$
$53$		−	328.358i		−	0.851008i	0.904957	−	0.425504i	$-0.139903\pi$
$54$		0			0
$55$	540.588	+	8.65162i	1.32532	+	0.0212106i
$56$		0			0
$57$			392.588i			0.912272i
$58$		0			0
$59$	−889.533			−1.96284			−0.981418	−	0.191882i	$-0.938541\pi$
$59$	−889.533			−1.96284			−0.981418	+	0.191882i	$0.938541\pi$
$60$		0			0
$61$	−241.450			−0.506795			−0.253398	−	0.967362i	$-0.581548\pi$
$61$	−241.450			−0.506795			−0.253398	+	0.967362i	$0.581548\pi$
$62$		0			0
$63$			297.661i			0.595266i
$64$		0			0
$65$	−10.7985	+	674.735i	−0.0206060	+	1.28755i
$66$		0			0
$67$			103.834i			0.189334i	0.995509	+	0.0946669i	$0.0301786\pi$
$67$			103.834i			0.189334i	−0.995509	+	0.0946669i	$0.969821\pi$
$68$		0			0
$69$	212.588			0.370906
$70$		0			0
$71$	−277.597			−0.464010			−0.232005	−	0.972715i	$-0.574529\pi$
$71$	−277.597			−0.464010			−0.232005	+	0.972715i	$0.574529\pi$
$72$		0			0
$73$		−	274.403i		−	0.439951i	−0.975505	−	0.219976i	$-0.929402\pi$
$73$		−	274.403i		−	0.439951i	0.975505	−	0.219976i	$-0.0705978\pi$
$74$		0			0
$75$	−12.0000	+	374.808i	−0.0184752	+	0.577055i
$76$		0			0
$77$		−	1599.36i		−	2.36706i
$78$		0			0
$79$	−366.991			−0.522654			−0.261327	−	0.965250i	$-0.584160\pi$
$79$	−366.991			−0.522654			−0.261327	+	0.965250i	$0.584160\pi$
$80$		0			0
$81$	81.0000			0.111111
$82$		0			0
$83$		−	57.7251i		−	0.0763391i	−0.999271	−	0.0381696i	$-0.987847\pi$
$83$		−	57.7251i		−	0.0763391i	0.999271	−	0.0381696i	$-0.0121527\pi$
$84$		0			0
$85$	3.18262	−	198.863i	0.00406121	−	0.253761i
$86$		0			0
$87$		−	313.514i		−	0.386348i
$88$		0			0
$89$	203.175			0.241983			0.120992	−	0.992654i	$-0.461393\pi$
$89$	203.175			0.241983			0.120992	+	0.992654i	$0.461393\pi$
$90$		0			0
$91$	1996.24			2.29959
$92$		0			0
$93$		−	631.322i		−	0.703925i
$94$		0			0
$95$	1462.90	+	23.4124i	1.57990	+	0.0252849i
$96$		0			0
$97$			1283.45i			1.34345i	0.740801	+	0.671725i	$0.234446\pi$
$97$			1283.45i			1.34345i	−0.740801	+	0.671725i	$0.765554\pi$
$98$		0			0
$99$	−435.220			−0.441831
$100$		0			0
$101$	886.908			0.873768			0.436884	−	0.899518i	$-0.356082\pi$
$101$	886.908			0.873768			0.436884	+	0.899518i	$0.356082\pi$
$102$		0			0
$103$			783.055i			0.749094i	0.927208	+	0.374547i	$0.122202\pi$
$103$			783.055i			0.749094i	−0.927208	+	0.374547i	$0.877798\pi$
$104$		0			0
$105$	1109.18	+	17.7513i	1.03090	+	0.0164986i
$106$		0			0
$107$			1301.51i			1.17590i	0.808897	+	0.587950i	$0.200065\pi$
$107$			1301.51i			1.17590i	−0.808897	+	0.587950i	$0.799935\pi$
$108$		0			0
$109$	−1161.91			−1.02102			−0.510508	−	0.859873i	$-0.670543\pi$
$109$	−1161.91			−1.02102			−0.510508	+	0.859873i	$0.670543\pi$
$110$		0			0
$111$	−902.836			−0.772013
$112$		0			0
$113$		−	507.808i		−	0.422748i	−0.977405	−	0.211374i	$-0.932206\pi$
$113$		−	507.808i		−	0.422748i	0.977405	−	0.211374i	$-0.0677938\pi$
$114$		0			0
$115$	12.6779	−	792.166i	0.0102802	−	0.642346i
$116$		0			0
$117$		−	543.220i		−	0.429237i
$118$		0			0
$119$	−588.346			−0.453224
$120$		0			0
$121$	1007.48			0.756933
$122$		0			0
$123$			720.441i			0.528130i
$124$		0			0
$125$	1395.93	+	67.0677i	0.998848	+	0.0479898i
$126$		0			0
$127$			796.064i			0.556215i	0.960550	+	0.278107i	$0.0897071\pi$
$127$			796.064i			0.556215i	−0.960550	+	0.278107i	$0.910293\pi$
$128$		0			0
$129$	−324.000			−0.221137
$130$		0			0
$131$	−91.4764			−0.0610102			−0.0305051	−	0.999535i	$-0.509712\pi$
$131$	−91.4764			−0.0610102			−0.0305051	+	0.999535i	$0.509712\pi$
$132$		0			0
$133$		−	4328.08i		−	2.82174i
$134$		0			0
$135$	4.83053	−	301.831i	0.00307960	−	0.192425i
$136$		0			0
$137$			2273.28i			1.41766i	0.705380	+	0.708829i	$0.250776\pi$
$137$			2273.28i			1.41766i	−0.705380	+	0.708829i	$0.749224\pi$
$138$		0			0
$139$	738.735			0.450782			0.225391	−	0.974268i	$-0.427634\pi$
$139$	738.735			0.450782			0.225391	+	0.974268i	$0.427634\pi$
$140$		0			0
$141$	836.972			0.499899
$142$		0			0
$143$			2918.77i			1.70685i
$144$		0			0
$145$	−1168.25	−	18.6968i	−0.669088	−	0.0107082i
$146$		0			0
$147$		−	2252.56i		−	1.26386i
$148$		0			0
$149$	−1507.15			−0.828661			−0.414330	−	0.910127i	$-0.635984\pi$
$149$	−1507.15			−0.828661			−0.414330	+	0.910127i	$0.635984\pi$
$150$		0			0
$151$	154.365			0.0831925			0.0415962	−	0.999135i	$-0.486756\pi$
$151$	154.365			0.0831925			0.0415962	+	0.999135i	$0.486756\pi$
$152$		0			0
$153$			160.102i			0.0845978i
$154$		0			0
$155$	−2352.50	−	37.6496i	−1.21908	−	0.0195102i
$156$		0			0
$157$		−	315.514i		−	0.160387i	−0.996779	−	0.0801935i	$-0.974446\pi$
$157$		−	315.514i		−	0.160387i	0.996779	−	0.0801935i	$-0.0255538\pi$
$158$		0			0
$159$	985.073			0.491330
$160$		0			0
$161$	−2343.67			−1.14725
$162$		0			0
$163$			1457.85i			0.700539i	0.936649	+	0.350270i	$0.113910\pi$
$163$			1457.85i			0.700539i	−0.936649	+	0.350270i	$0.886090\pi$
$164$		0			0
$165$	−25.9549	+	1621.76i	−0.0122460	+	0.765176i
$166$		0			0
$167$		−	2198.61i		−	1.01876i	−0.860541	−	0.509381i	$-0.829874\pi$
$167$		−	2198.61i		−	1.01876i	0.860541	−	0.509381i	$-0.170126\pi$
$168$		0			0
$169$	−1446.07			−0.658200
$170$		0			0
$171$	−1177.76			−0.526700
$172$		0			0
$173$			2030.49i			0.892343i	0.894948	+	0.446171i	$0.147213\pi$
$173$			2030.49i			0.892343i	−0.894948	+	0.446171i	$0.852787\pi$
$174$		0			0
$175$	132.294	−	4132.06i	0.0571456	−	1.78488i
$176$		0			0
$177$		−	2668.60i		−	1.13324i
$178$		0			0
$179$	−427.220			−0.178391			−0.0891954	−	0.996014i	$-0.528430\pi$
$179$	−427.220			−0.178391			−0.0891954	+	0.996014i	$0.528430\pi$
$180$		0			0
$181$	−3779.97			−1.55228			−0.776140	−	0.630561i	$-0.782825\pi$
$181$	−3779.97			−1.55228			−0.776140	+	0.630561i	$0.782825\pi$
$182$		0			0
$183$		−	724.350i		−	0.292598i
$184$		0			0
$185$	−53.8416	+	3364.24i	−0.0213974	+	1.33699i
$186$		0			0
$187$		−	860.241i		−	0.336401i
$188$		0			0
$189$	−892.983			−0.343677
$190$		0			0
$191$	1565.60			0.593103			0.296551	−	0.955017i	$-0.404163\pi$
$191$	1565.60			0.593103			0.296551	+	0.955017i	$0.404163\pi$
$192$		0			0
$193$			2642.63i			0.985599i	0.870143	+	0.492800i	$0.164026\pi$
$193$			2642.63i			0.985599i	−0.870143	+	0.492800i	$0.835974\pi$
$194$		0			0
$195$	−2024.20	−	32.3956i	−0.743365	−	0.0118969i
$196$		0			0
$197$			98.4522i			0.0356062i	0.999842	+	0.0178031i	$0.00566721\pi$
$197$			98.4522i			0.0356062i	−0.999842	+	0.0178031i	$0.994333\pi$
$198$		0			0
$199$	−1131.62			−0.403106			−0.201553	−	0.979478i	$-0.564599\pi$
$199$	−1131.62			−0.403106			−0.201553	+	0.979478i	$0.564599\pi$
$200$		0			0
$201$	−311.503			−0.109312
$202$		0			0
$203$			3456.33i			1.19501i
$204$		0			0
$205$	2684.58	+	42.9643i	0.914630	+	0.0146378i
$206$		0			0
$207$			637.763i			0.214143i
$208$		0			0
$209$	6328.23			2.09441
$210$		0			0
$211$	−1902.85			−0.620841			−0.310420	−	0.950599i	$-0.600470\pi$
$211$	−1902.85			−0.620841			−0.310420	+	0.950599i	$0.600470\pi$
$212$		0			0
$213$		−	832.791i		−	0.267896i
$214$		0			0
$215$	−19.3221	+	1207.32i	−0.00612910	+	0.382971i
$216$		0			0
$217$			6960.00i			2.17731i
$218$		0			0
$219$	823.209			0.254006
$220$		0			0
$221$	1073.71			0.326813
$222$		0			0
$223$		−	4855.59i		−	1.45809i	−0.684465	−	0.729046i	$-0.739964\pi$
$223$		−	4855.59i		−	1.45809i	0.684465	−	0.729046i	$-0.260036\pi$
$224$		0			0
$225$	−1124.42	−	36.0000i	−0.333163	−	0.0106667i
$226$		0			0
$227$		−	6536.19i		−	1.91111i	−0.294812	−	0.955555i	$-0.595257\pi$
$227$		−	6536.19i		−	1.91111i	0.294812	−	0.955555i	$-0.404743\pi$
$228$		0			0
$229$	5510.35			1.59011			0.795053	−	0.606539i	$-0.207443\pi$
$229$	5510.35			1.59011			0.795053	+	0.606539i	$0.207443\pi$
$230$		0			0
$231$	4798.08			1.36663
$232$		0			0
$233$		−	5915.65i		−	1.66329i	−0.555306	−	0.831646i	$-0.687399\pi$
$233$		−	5915.65i		−	1.66329i	0.555306	−	0.831646i	$-0.312601\pi$
$234$		0			0
$235$	49.9137	−	3118.81i	0.0138554	−	0.865739i
$236$		0			0
$237$		−	1100.97i		−	0.301754i
$238$		0			0
$239$	−2263.25			−0.612543			−0.306272	−	0.951944i	$-0.599082\pi$
$239$	−2263.25			−0.612543			−0.306272	+	0.951944i	$0.599082\pi$
$240$		0			0
$241$	772.493			0.206476			0.103238	−	0.994657i	$-0.467080\pi$
$241$	772.493			0.206476			0.103238	+	0.994657i	$0.467080\pi$
$242$		0			0
$243$			243.000i			0.0641500i
$244$		0			0
$245$	−8393.72	−	134.334i	−2.18880	−	0.0350297i
$246$		0			0
$247$			7898.58i			2.03471i
$248$		0			0
$249$	173.175			0.0440744
$250$		0			0
$251$	596.192			0.149926			0.0749628	−	0.997186i	$-0.476116\pi$
$251$	596.192			0.149926			0.0749628	+	0.997186i	$0.476116\pi$
$252$		0			0
$253$		−	3426.76i		−	0.851535i
$254$		0			0
$255$	596.588	+	9.54785i	0.146509	+	0.00234474i
$256$		0			0
$257$			4139.19i			1.00465i	0.864678	+	0.502326i	$0.167522\pi$
$257$			4139.19i			1.00465i	−0.864678	+	0.502326i	$0.832478\pi$
$258$		0			0
$259$	9953.30			2.38791
$260$		0			0
$261$	940.542			0.223058
$262$		0			0
$263$			1611.34i			0.377792i	0.981997	+	0.188896i	$0.0604909\pi$
$263$			1611.34i			0.377792i	−0.981997	+	0.188896i	$0.939509\pi$
$264$		0			0
$265$	58.7460	−	3670.68i	0.0136179	−	0.850899i
$266$		0			0
$267$			609.526i			0.139709i
$268$		0			0
$269$	7031.33			1.59371			0.796855	−	0.604171i	$-0.206496\pi$
$269$	7031.33			1.59371			0.796855	+	0.604171i	$0.206496\pi$
$270$		0			0
$271$	−5441.27			−1.21968			−0.609840	−	0.792524i	$-0.708766\pi$
$271$	−5441.27			−1.21968			−0.609840	+	0.792524i	$0.708766\pi$
$272$		0			0
$273$			5988.72i			1.32767i
$274$		0			0
$275$	6041.63	+	193.431i	1.32481	+	0.0424158i
$276$		0			0
$277$			1080.43i			0.234355i	0.993111	+	0.117178i	$0.0373847\pi$
$277$			1080.43i			0.234355i	−0.993111	+	0.117178i	$0.962615\pi$
$278$		0			0
$279$	1893.97			0.406411
$280$		0			0
$281$	−1602.99			−0.340308			−0.170154	−	0.985417i	$-0.554427\pi$
$281$	−1602.99			−0.340308			−0.170154	+	0.985417i	$0.554427\pi$
$282$		0			0
$283$		−	334.810i		−	0.0703265i	−0.999382	−	0.0351632i	$-0.988805\pi$
$283$		−	334.810i		−	0.0703265i	0.999382	−	0.0351632i	$-0.0111951\pi$
$284$		0			0
$285$	−70.2372	+	4388.70i	−0.0145982	+	0.912155i
$286$		0			0
$287$		−	7942.49i		−	1.63355i
$288$		0			0
$289$	4596.55			0.935589
$290$		0			0
$291$	−3850.35			−0.775641
$292$		0			0
$293$		−	539.250i		−	0.107520i	−0.998554	−	0.0537599i	$-0.982879\pi$
$293$		−	539.250i		−	0.107520i	0.998554	−	0.0537599i	$-0.0171206\pi$
$294$		0			0
$295$	−9944.01	−	159.145i	−1.96258	−	0.0314094i
$296$		0			0
$297$		−	1305.66i		−	0.255091i
$298$		0			0
$299$	4277.11			0.827263
$300$		0			0
$301$	3571.93			0.683996
$302$		0			0
$303$			2660.72i			0.504470i
$304$		0			0
$305$	−2699.15	−	43.1974i	−0.506731	−	0.00810977i
$306$		0			0
$307$			8477.58i			1.57603i	0.615656	+	0.788015i	$0.288891\pi$
$307$			8477.58i			1.57603i	−0.615656	+	0.788015i	$0.711109\pi$
$308$		0			0
$309$	−2349.16			−0.432490
$310$		0			0
$311$	3646.92			0.664945			0.332473	−	0.943113i	$-0.392117\pi$
$311$	3646.92			0.664945			0.332473	+	0.943113i	$0.392117\pi$
$312$		0			0
$313$		−	7537.05i		−	1.36108i	−0.732709	−	0.680542i	$-0.761745\pi$
$313$		−	7537.05i		−	1.36108i	0.732709	−	0.680542i	$-0.238255\pi$
$314$		0			0
$315$	−53.2540	+	3327.53i	−0.00952548	+	0.595190i
$316$		0			0
$317$		−	10721.2i		−	1.89956i	−0.312916	−	0.949781i	$-0.601306\pi$
$317$		−	10721.2i		−	1.89956i	0.312916	−	0.949781i	$-0.398694\pi$
$318$		0			0
$319$	−5053.62			−0.886986
$320$		0			0
$321$	−3904.52			−0.678907
$322$		0			0
$323$		−	2327.92i		−	0.401019i
$324$		0			0
$325$	−241.431	+	7540.86i	−0.0412068	+	1.28705i
$326$		0			0
$327$		−	3485.73i		−	0.589484i
$328$		0			0
$329$	−9227.18			−1.54623
$330$		0			0
$331$	−4405.14			−0.731505			−0.365753	−	0.930712i	$-0.619188\pi$
$331$	−4405.14			−0.731505			−0.365753	+	0.930712i	$0.619188\pi$
$332$		0			0
$333$		−	2708.51i		−	0.445722i
$334$		0			0
$335$	−18.5768	+	1160.75i	−0.00302973	+	0.189310i
$336$		0			0
$337$		−	186.117i		−	0.0300844i	−0.999887	−	0.0150422i	$-0.995212\pi$
$337$		−	186.117i		−	0.0300844i	0.999887	−	0.0150422i	$-0.00478827\pi$
$338$		0			0
$339$	1523.42			0.244074
$340$		0			0
$341$	−10176.5			−1.61609
$342$		0			0
$343$			13489.1i			2.12345i
$344$		0			0
$345$	2376.50	+	38.0337i	0.370859	+	0.00593526i
$346$		0			0
$347$			5547.38i			0.858211i	0.903254	+	0.429105i	$0.141171\pi$
$347$			5547.38i			0.858211i	−0.903254	+	0.429105i	$0.858829\pi$
$348$		0			0
$349$	−9078.82			−1.39249			−0.696244	−	0.717805i	$-0.745147\pi$
$349$	−9078.82			−1.39249			−0.696244	+	0.717805i	$0.745147\pi$
$350$		0			0
$351$	1629.66			0.247820
$352$		0			0
$353$		−	10678.1i		−	1.61002i	−0.593262	−	0.805009i	$-0.702160\pi$
$353$		−	10678.1i		−	1.61002i	0.593262	−	0.805009i	$-0.297840\pi$
$354$		0			0
$355$	−3103.23	−	49.6644i	−0.463951	−	0.00742511i
$356$		0			0
$357$		−	1765.04i		−	0.261669i
$358$		0			0
$359$	265.733			0.0390665			0.0195332	−	0.999809i	$-0.493782\pi$
$359$	265.733			0.0390665			0.0195332	+	0.999809i	$0.493782\pi$
$360$		0			0
$361$	10266.0			1.49672
$362$		0			0
$363$			3022.44i			0.437016i
$364$		0			0
$365$	49.0930	−	3067.53i	0.00704012	−	0.439895i
$366$		0			0
$367$		−	5854.21i		−	0.832663i	−0.909213	−	0.416332i	$-0.863316\pi$
$367$		−	5854.21i		−	0.832663i	0.909213	−	0.416332i	$-0.136684\pi$
$368$		0			0
$369$	−2161.32			−0.304916
$370$		0			0
$371$	−10859.9			−1.51973
$372$		0			0
$373$			10134.5i			1.40682i	0.710787	+	0.703408i	$0.248339\pi$
$373$			10134.5i			1.40682i	−0.710787	+	0.703408i	$0.751661\pi$
$374$		0			0
$375$	−201.203	+	4187.80i	−0.0277069	+	0.576685i
$376$		0			0
$377$		−	6307.68i		−	0.861703i
$378$		0			0
$379$	4235.70			0.574072			0.287036	−	0.957920i	$-0.407330\pi$
$379$	4235.70			0.574072			0.287036	+	0.957920i	$0.407330\pi$
$380$		0			0
$381$	−2388.19			−0.321131
$382$		0			0
$383$		−	8100.84i		−	1.08077i	−0.841419	−	0.540383i	$-0.818279\pi$
$383$		−	8100.84i		−	1.08077i	0.841419	−	0.540383i	$-0.181721\pi$
$384$		0			0
$385$	286.139	−	17879.1i	0.0378779	−	2.36676i
$386$		0			0
$387$		−	972.000i		−	0.127673i
$388$		0			0
$389$	13820.2			1.80131			0.900656	−	0.434532i	$-0.143086\pi$
$389$	13820.2			1.80131			0.900656	+	0.434532i	$0.143086\pi$
$390$		0			0
$391$	−1260.58			−0.163044
$392$		0			0
$393$		−	274.429i		−	0.0352242i
$394$		0			0
$395$	−4102.55	−	65.6577i	−0.522587	−	0.00836353i
$396$		0			0
$397$			11523.9i			1.45685i	0.685125	+	0.728425i	$0.259748\pi$
$397$			11523.9i			1.45685i	−0.685125	+	0.728425i	$0.740252\pi$
$398$		0			0
$399$	12984.2			1.62913
$400$		0			0
$401$	700.915			0.0872869			0.0436434	−	0.999047i	$-0.486103\pi$
$401$	700.915			0.0872869			0.0436434	+	0.999047i	$0.486103\pi$
$402$		0			0
$403$		−	12701.7i		−	1.57002i
$404$		0			0
$405$	905.492	+	14.4916i	0.111097	+	0.00177801i
$406$		0			0
$407$			14553.1i			1.77240i
$408$		0			0
$409$	−6650.69			−0.804047			−0.402024	−	0.915629i	$-0.631693\pi$
$409$	−6650.69			−0.804047			−0.402024	+	0.915629i	$0.631693\pi$
$410$		0			0
$411$	−6819.83			−0.818485
$412$		0			0
$413$			29419.9i			3.50523i
$414$		0			0
$415$	10.3275	−	645.303i	0.00122158	−	0.0763294i
$416$		0			0
$417$			2216.20i			0.260259i
$418$		0			0
$419$	−13844.4			−1.61418			−0.807091	−	0.590426i	$-0.798960\pi$
$419$	−13844.4			−1.61418			−0.807091	+	0.590426i	$0.798960\pi$
$420$		0			0
$421$	12576.3			1.45590			0.727949	−	0.685631i	$-0.240474\pi$
$421$	12576.3			1.45590			0.727949	+	0.685631i	$0.240474\pi$
$422$		0			0
$423$			2510.92i			0.288617i
$424$		0			0
$425$	71.1563	−	2222.50i	0.00812139	−	0.253663i
$426$		0			0
$427$			7985.59i			0.905035i
$428$		0			0
$429$	−8756.32			−0.985452
$430$		0			0
$431$	13440.6			1.50212			0.751059	−	0.660236i	$-0.229544\pi$
$431$	13440.6			1.50212			0.751059	+	0.660236i	$0.229544\pi$
$432$		0			0
$433$		−	3012.87i		−	0.334387i	−0.985924	−	0.167193i	$-0.946530\pi$
$433$		−	3012.87i		−	0.334387i	0.985924	−	0.167193i	$-0.0534704\pi$
$434$		0			0
$435$	56.0903	−	3504.75i	0.00618235	−	0.386298i
$436$		0			0
$437$		−	9273.25i		−	1.01510i
$438$		0			0
$439$	−10675.0			−1.16057			−0.580283	−	0.814415i	$-0.697058\pi$
$439$	−10675.0			−1.16057			−0.580283	+	0.814415i	$0.697058\pi$
$440$		0			0
$441$	6757.68			0.729692
$442$		0			0
$443$		−	125.868i		−	0.0134992i	−0.999977	−	0.00674962i	$-0.997852\pi$
$443$		−	125.868i		−	0.0134992i	0.999977	−	0.00674962i	$-0.00214849\pi$
$444$		0			0
$445$	2271.28	+	36.3497i	0.241952	+	0.00387223i
$446$		0			0
$447$		−	4521.45i		−	0.478428i
$448$		0			0
$449$	9707.21			1.02029			0.510146	−	0.860088i	$-0.329591\pi$
$449$	9707.21			1.02029			0.510146	+	0.860088i	$0.329591\pi$
$450$		0			0
$451$	11613.0			1.21249
$452$		0			0
$453$			463.096i			0.0480312i
$454$		0			0
$455$	22315.8	+	357.144i	2.29930	+	0.0367982i
$456$		0			0
$457$		−	1279.97i		−	0.131016i	−0.997852	−	0.0655082i	$-0.979133\pi$
$457$		−	1279.97i		−	0.131016i	0.997852	−	0.0655082i	$-0.0208668\pi$
$458$		0			0
$459$	−480.305			−0.0488425
$460$		0			0
$461$	3080.48			0.311220			0.155610	−	0.987819i	$-0.450266\pi$
$461$	3080.48			0.311220			0.155610	+	0.987819i	$0.450266\pi$
$462$		0			0
$463$		−	18017.3i		−	1.80850i	−0.427008	−	0.904248i	$-0.640432\pi$
$463$		−	18017.3i		−	1.80850i	0.427008	−	0.904248i	$-0.359568\pi$
$464$		0			0
$465$	112.949	−	7057.49i	0.0112642	−	0.703835i
$466$		0			0
$467$		−	7236.77i		−	0.717083i	−0.933514	−	0.358541i	$-0.883274\pi$
$467$		−	7236.77i		−	0.717083i	0.933514	−	0.358541i	$-0.116726\pi$
$468$		0			0
$469$	3434.16			0.338112
$470$		0			0
$471$	946.542			0.0925995
$472$		0			0
$473$			5222.64i			0.507690i
$474$		0			0
$475$	16349.4	+	523.450i	1.57929	+	0.0505632i
$476$		0			0
$477$			2955.22i			0.283669i
$478$		0			0
$479$	−4932.78			−0.470532			−0.235266	−	0.971931i	$-0.575596\pi$
$479$	−4932.78			−0.470532			−0.235266	+	0.971931i	$0.575596\pi$
$480$		0			0
$481$	−18164.4			−1.72188
$482$		0			0
$483$		−	7031.01i		−	0.662364i
$484$		0			0
$485$	−229.620	+	14347.6i	−0.0214979	+	1.34328i
$486$		0			0
$487$		−	5937.91i		−	0.552510i	−0.961084	−	0.276255i	$-0.910907\pi$
$487$		−	5937.91i		−	0.552510i	0.961084	−	0.276255i	$-0.0890934\pi$
$488$		0			0
$489$	−4373.56			−0.404456
$490$		0			0
$491$	15703.5			1.44336			0.721678	−	0.692229i	$-0.243371\pi$
$491$	15703.5			1.44336			0.721678	+	0.692229i	$0.243371\pi$
$492$		0			0
$493$			1859.04i			0.169832i
$494$		0			0
$495$	−4865.29	−	77.8646i	−0.441775	−	0.00707020i
$496$		0			0
$497$			9181.09i			0.828628i
$498$		0			0
$499$	5656.77			0.507478			0.253739	−	0.967273i	$-0.418340\pi$
$499$	5656.77			0.507478			0.253739	+	0.967273i	$0.418340\pi$
$500$		0			0
$501$	6595.82			0.588183
$502$		0			0
$503$		−	290.441i		−	0.0257457i	−0.999917	−	0.0128729i	$-0.995902\pi$
$503$		−	290.441i		−	0.0257457i	0.999917	−	0.0128729i	$-0.00409768\pi$
$504$		0			0
$505$	9914.66	+	158.675i	0.873657	+	0.0139821i
$506$		0			0
$507$		−	4338.20i		−	0.380012i
$508$		0			0
$509$	−17330.6			−1.50916			−0.754582	−	0.656206i	$-0.772160\pi$
$509$	−17330.6			−1.50916			−0.754582	+	0.656206i	$0.772160\pi$
$510$		0			0
$511$	−9075.45			−0.785664
$512$		0			0
$513$		−	3533.29i		−	0.304091i
$514$		0			0
$515$	−140.095	+	8753.70i	−0.0119870	+	0.748998i
$516$		0			0
$517$		−	13491.4i		−	1.14768i
$518$		0			0
$519$	−6091.47			−0.515194
$520$		0			0
$521$	6174.36			0.519201			0.259601	−	0.965716i	$-0.416409\pi$
$521$	6174.36			0.519201			0.259601	+	0.965716i	$0.416409\pi$
$522$		0			0
$523$			13389.4i			1.11946i	0.828675	+	0.559730i	$0.189095\pi$
$523$			13389.4i			1.11946i	−0.828675	+	0.559730i	$0.810905\pi$
$524$		0			0
$525$	12396.2	+	396.881i	1.03050	+	0.0329930i
$526$		0			0
$527$			3743.55i			0.309434i
$528$		0			0
$529$	7145.50			0.587285
$530$		0			0
$531$	8005.80			0.654279
$532$		0			0
$533$			14494.7i			1.17793i
$534$		0			0
$535$	−232.850	+	14549.4i	−0.0188168	+	1.17575i
$536$		0			0
$537$		−	1281.66i		−	0.102994i
$538$		0			0
$539$	−36309.6			−2.90161
$540$		0			0
$541$	−14355.5			−1.14084			−0.570418	−	0.821354i	$-0.693219\pi$
$541$	−14355.5			−1.14084			−0.570418	+	0.821354i	$0.693219\pi$
$542$		0			0
$543$		−	11339.9i		−	0.896209i
$544$		0			0
$545$	−12988.9	−	207.875i	−1.02089	−	0.0163384i
$546$		0			0
$547$		−	21133.9i		−	1.65195i	−0.563704	−	0.825977i	$-0.690624\pi$
$547$		−	21133.9i		−	1.65195i	0.563704	−	0.825977i	$-0.309376\pi$
$548$		0			0
$549$	2173.05			0.168932
$550$		0			0
$551$	−13675.8			−1.05736
$552$		0			0
$553$			12137.6i			0.933355i
$554$		0			0
$555$	−10092.7	−	161.525i	−0.771914	−	0.0123538i
$556$		0			0
$557$			3098.60i			0.235713i	0.993031	+	0.117856i	$0.0376023\pi$
$557$			3098.60i			0.235713i	−0.993031	+	0.117856i	$0.962398\pi$
$558$		0			0
$559$	−6518.64			−0.493219
$560$		0			0
$561$	2580.72			0.194221
$562$		0			0
$563$		−	7908.77i		−	0.592033i	−0.955183	−	0.296017i	$-0.904342\pi$
$563$		−	7908.77i		−	0.592033i	0.955183	−	0.296017i	$-0.0956584\pi$
$564$		0			0
$565$	90.8511	−	5676.74i	0.00676484	−	0.422694i
$566$		0			0
$567$		−	2678.95i		−	0.198422i
$568$		0			0
$569$	10740.7			0.791345			0.395673	−	0.918392i	$-0.370512\pi$
$569$	10740.7			0.791345			0.395673	+	0.918392i	$0.370512\pi$
$570$		0			0
$571$	14701.2			1.07745			0.538725	−	0.842482i	$-0.318906\pi$
$571$	14701.2			1.07745			0.538725	+	0.842482i	$0.318906\pi$
$572$		0			0
$573$			4696.79i			0.342428i
$574$		0			0
$575$	283.450	−	8853.28i	0.0205577	−	0.642100i
$576$		0			0
$577$			15788.1i			1.13911i	0.821954	+	0.569554i	$0.192884\pi$
$577$			15788.1i			1.13911i	−0.821954	+	0.569554i	$0.807116\pi$
$578$		0			0
$579$	−7927.89			−0.569036
$580$		0			0
$581$	−1909.17			−0.136326
$582$		0			0
$583$		−	15878.7i		−	1.12801i
$584$		0			0
$585$	97.1867	−	6072.61i	0.00686867	−	0.429182i
$586$		0			0
$587$			14778.5i			1.03913i	0.854430	+	0.519567i	$0.173907\pi$
$587$			14778.5i			1.03913i	−0.854430	+	0.519567i	$0.826093\pi$
$588$		0			0
$589$	−27538.8			−1.92651
$590$		0			0
$591$	−295.356			−0.0205573
$592$		0			0
$593$		−	11143.9i		−	0.771713i	−0.922559	−	0.385857i	$-0.873906\pi$
$593$		−	11143.9i		−	0.771713i	0.922559	−	0.385857i	$-0.126094\pi$
$594$		0			0
$595$	−6577.07	−	105.260i	−0.453166	−	0.00725251i
$596$		0			0
$597$		−	3394.85i		−	0.232733i
$598$		0			0
$599$	7707.87			0.525768			0.262884	−	0.964827i	$-0.415326\pi$
$599$	7707.87			0.525768			0.262884	+	0.964827i	$0.415326\pi$
$600$		0			0
$601$	−13681.4			−0.928580			−0.464290	−	0.885683i	$-0.653691\pi$
$601$	−13681.4			−0.928580			−0.464290	+	0.885683i	$0.653691\pi$
$602$		0			0
$603$		−	934.508i		−	0.0631113i
$604$		0			0
$605$	11262.5	+	180.246i	0.756837	+	0.0121125i
$606$		0			0
$607$			11552.4i			0.772481i	0.922398	+	0.386241i	$0.126227\pi$
$607$			11552.4i			0.772481i	−0.922398	+	0.386241i	$0.873773\pi$
$608$		0			0
$609$	−10369.0			−0.689939
$610$		0			0
$611$	16839.3			1.11496
$612$		0			0
$613$			9904.66i			0.652603i	0.945266	+	0.326301i	$0.105802\pi$
$613$			9904.66i			0.652603i	−0.945266	+	0.326301i	$0.894198\pi$
$614$		0			0
$615$	−128.893	+	8053.74i	−0.00845116	+	0.528062i
$616$		0			0
$617$			20323.5i			1.32608i	0.748582	+	0.663042i	$0.230735\pi$
$617$			20323.5i			1.32608i	−0.748582	+	0.663042i	$0.769265\pi$
$618$		0			0
$619$	9223.99			0.598940			0.299470	−	0.954106i	$-0.403190\pi$
$619$	9223.99			0.598940			0.299470	+	0.954106i	$0.403190\pi$
$620$		0			0
$621$	−1913.29			−0.123635
$622$		0			0
$623$		−	6719.70i		−	0.432134i
$624$		0			0
$625$	15593.0	+	999.488i	0.997952	+	0.0639672i
$626$		0			0
$627$			18984.7i			1.20921i
$628$		0			0
$629$	5353.54			0.339364
$630$		0			0
$631$	−16916.0			−1.06722			−0.533610	−	0.845730i	$-0.679165\pi$
$631$	−16916.0			−1.06722			−0.533610	+	0.845730i	$0.679165\pi$
$632$		0			0
$633$		−	5708.54i		−	0.358443i
$634$		0			0
$635$	−142.422	+	8899.13i	−0.00890057	+	0.556143i
$636$		0			0
$637$		−	45319.9i		−	2.81890i
$638$		0			0
$639$	2498.37			0.154670
$640$		0			0
$641$	−5811.35			−0.358088			−0.179044	−	0.983841i	$-0.557300\pi$
$641$	−5811.35			−0.358088			−0.179044	+	0.983841i	$0.557300\pi$
$642$		0			0
$643$		−	27931.7i		−	1.71309i	−0.516069	−	0.856547i	$-0.672605\pi$
$643$		−	27931.7i		−	1.71309i	0.516069	−	0.856547i	$-0.327395\pi$
$644$		0			0
$645$	−3621.97	−	57.9663i	−0.221108	−	0.00353864i
$646$		0			0
$647$			25437.8i			1.54569i	0.634595	+	0.772845i	$0.281167\pi$
$647$			25437.8i			1.54569i	−0.634595	+	0.772845i	$0.718833\pi$
$648$		0			0
$649$	−43015.9			−2.60173
$650$		0			0
$651$	−20880.0			−1.25707
$652$		0			0
$653$		−	22647.7i		−	1.35723i	−0.734493	−	0.678617i	$-0.762580\pi$
$653$		−	22647.7i		−	1.35723i	0.734493	−	0.678617i	$-0.237420\pi$
$654$		0			0
$655$	−1022.61	−	16.3659i	−0.0610024	−	0.000976288i
$656$		0			0
$657$			2469.63i			0.146650i
$658$		0			0
$659$	−25158.5			−1.48716			−0.743579	−	0.668649i	$-0.766873\pi$
$659$	−25158.5			−1.48716			−0.743579	+	0.668649i	$0.766873\pi$
$660$		0			0
$661$	23441.0			1.37935			0.689675	−	0.724119i	$-0.257753\pi$
$661$	23441.0			1.37935			0.689675	+	0.724119i	$0.257753\pi$
$662$		0			0
$663$			3221.13i			0.188685i
$664$		0			0
$665$	774.329	−	48383.2i	0.0451537	−	2.82138i
$666$		0			0
$667$			7405.47i			0.429896i
$668$		0			0
$669$	14566.8			0.841829
$670$		0			0
$671$	−11676.0			−0.671754
$672$		0			0
$673$			3145.33i			0.180154i	0.995935	+	0.0900770i	$0.0287113\pi$
$673$			3145.33i			0.180154i	−0.995935	+	0.0900770i	$0.971289\pi$
$674$		0			0
$675$	108.000	−	3373.27i	0.00615840	−	0.192352i
$676$		0			0
$677$		−	10606.2i		−	0.602109i	−0.953607	−	0.301054i	$-0.902661\pi$
$677$		−	10606.2i		−	0.602109i	0.953607	−	0.301054i	$-0.0973386\pi$
$678$		0			0
$679$	42448.1			2.39913
$680$		0			0
$681$	19608.6			1.10338
$682$		0			0
$683$			7825.06i			0.438386i	0.975682	+	0.219193i	$0.0703424\pi$
$683$			7825.06i			0.438386i	−0.975682	+	0.219193i	$0.929658\pi$
$684$		0			0
$685$	−406.708	+	25412.8i	−0.0226854	+	1.41748i
$686$		0			0
$687$			16531.1i			0.918049i
$688$		0			0
$689$	19819.0			1.09585
$690$		0			0
$691$	22750.9			1.25251			0.626256	−	0.779618i	$-0.284587\pi$
$691$	22750.9			1.25251			0.626256	+	0.779618i	$0.284587\pi$
$692$		0			0
$693$			14394.2i			0.789022i
$694$		0			0
$695$	8258.25	+	132.166i	0.450724	+	0.00721343i
$696$		0			0
$697$		−	4271.99i		−	0.232157i
$698$		0			0
$699$	17747.0			0.960302
$700$		0			0
$701$	−133.598			−0.00719817			−0.00359908	−	0.999994i	$-0.501146\pi$
$701$	−133.598			−0.00719817			−0.00359908	+	0.999994i	$0.501146\pi$
$702$		0			0
$703$			39382.5i			2.11286i
$704$		0			0
$705$	9356.43	+	149.741i	0.499835	+	0.00799941i
$706$		0			0
$707$		−	29333.1i		−	1.56037i
$708$		0			0
$709$	−6886.26			−0.364766			−0.182383	−	0.983228i	$-0.558381\pi$
$709$	−6886.26			−0.364766			−0.182383	+	0.983228i	$0.558381\pi$
$710$		0			0
$711$	3302.92			0.174218
$712$		0			0
$713$			14912.4i			0.783271i
$714$		0			0
$715$	−522.193	+	32628.7i	−0.0273131	+	1.70663i
$716$		0			0
$717$		−	6789.76i		−	0.353652i
$718$		0			0
$719$	1570.18			0.0814436			0.0407218	−	0.999171i	$-0.487034\pi$
$719$	1570.18			0.0814436			0.0407218	+	0.999171i	$0.487034\pi$
$720$		0			0
$721$	25898.3			1.33773
$722$		0			0
$723$			2317.48i			0.119209i
$724$		0			0
$725$	−13056.4	−	418.019i	−0.668831	−	0.0214136i
$726$		0			0
$727$		−	3399.18i		−	0.173409i	−0.996234	−	0.0867047i	$-0.972366\pi$
$727$		−	3399.18i		−	0.173409i	0.996234	−	0.0867047i	$-0.0276337\pi$
$728$		0			0
$729$	−729.000			−0.0370370
$730$		0			0
$731$	1921.22			0.0972078
$732$		0			0
$733$			14152.1i			0.713125i	0.934272	+	0.356562i	$0.116051\pi$
$733$			14152.1i			0.713125i	−0.934272	+	0.356562i	$0.883949\pi$
$734$		0			0
$735$	403.002	−	25181.2i	0.0202244	−	1.26370i
$736$		0			0
$737$			5021.20i			0.250961i
$738$		0			0
$739$	14919.5			0.742655			0.371328	−	0.928502i	$-0.378903\pi$
$739$	14919.5			0.742655			0.371328	+	0.928502i	$0.378903\pi$
$740$		0			0
$741$	−23695.7			−1.17474
$742$		0			0
$743$		−	7287.29i		−	0.359818i	−0.983683	−	0.179909i	$-0.942420\pi$
$743$		−	7287.29i		−	0.359818i	0.983683	−	0.179909i	$-0.0575803\pi$
$744$		0			0
$745$	−16848.3	−	269.642i	−0.828555	−	0.0132603i
$746$		0			0
$747$			519.526i			0.0254464i
$748$		0			0
$749$	43045.3			2.09992
$750$		0			0
$751$	18783.4			0.912670			0.456335	−	0.889808i	$-0.349162\pi$
$751$	18783.4			0.912670			0.456335	+	0.889808i	$0.349162\pi$
$752$		0			0
$753$			1788.58i			0.0865595i
$754$		0			0
$755$	1725.63	+	27.6172i	0.0831818	+	0.00133125i
$756$		0			0
$757$		−	30614.3i		−	1.46988i	−0.678134	−	0.734939i	$-0.737211\pi$
$757$		−	30614.3i		−	1.46988i	0.678134	−	0.734939i	$-0.262789\pi$
$758$		0			0
$759$	10280.3			0.491634
$760$		0			0
$761$	−15277.2			−0.727723			−0.363861	−	0.931453i	$-0.618542\pi$
$761$	−15277.2			−0.727723			−0.363861	+	0.931453i	$0.618542\pi$
$762$		0			0
$763$			38428.4i			1.82333i
$764$		0			0
$765$	−28.6435	+	1789.76i	−0.00135374	+	0.0845869i
$766$		0			0
$767$		−	53690.3i		−	2.52757i
$768$		0			0
$769$	17700.1			0.830016			0.415008	−	0.909818i	$-0.363779\pi$
$769$	17700.1			0.830016			0.415008	+	0.909818i	$0.363779\pi$
$770$		0			0
$771$	−12417.6			−0.580036
$772$		0			0
$773$		−	29362.5i		−	1.36623i	−0.730310	−	0.683116i	$-0.760625\pi$
$773$		−	29362.5i		−	1.36623i	0.730310	−	0.683116i	$-0.239375\pi$
$774$		0			0
$775$	−26291.6	−	841.763i	−1.21861	−	0.0390155i
$776$		0			0
$777$			29859.9i			1.37866i
$778$		0			0
$779$	31426.2			1.44539
$780$		0			0
$781$	−13424.0			−0.615042
$782$		0			0
$783$			2821.63i			0.128783i
$784$		0			0
$785$	56.4481	−	3527.10i	0.00256652	−	0.160367i
$786$		0			0
$787$		−	2816.92i		−	0.127589i	−0.997963	−	0.0637943i	$-0.979680\pi$
$787$		−	2816.92i		−	0.127589i	0.997963	−	0.0637943i	$-0.0203202\pi$
$788$		0			0
$789$	−4834.01			−0.218118
$790$		0			0
$791$	−16795.0			−0.754943

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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.00000i q^{3} +(11.1789 + 0.178908i) q^{5} -33.0735i q^{7} -9.00000 q^{9} +O(q^{10})\)	\(q+3.00000i q^{3} +(11.1789 + 0.178908i) q^{5} -33.0735i q^{7} -9.00000 q^{9} +48.3578 q^{11} +60.3578i q^{13} +(-0.536725 + 33.5367i) q^{15} -17.7891i q^{17} +130.863 q^{19} +99.2204 q^{21} -70.8625i q^{23} +(124.936 + 4.00000i) q^{25} -27.0000i q^{27} -104.505 q^{29} -210.441 q^{31} +145.073i q^{33} +(5.91712 - 369.725i) q^{35} +300.945i q^{37} -181.073 q^{39} +240.147 q^{41} +108.000i q^{43} +(-100.610 - 1.61018i) q^{45} -278.991i q^{47} -750.853 q^{49} +53.3673 q^{51} -328.358i q^{53} +(540.588 + 8.65162i) q^{55} +392.588i q^{57} -889.533 q^{59} -241.450 q^{61} +297.661i q^{63} +(-10.7985 + 674.735i) q^{65} +103.834i q^{67} +212.588 q^{69} -277.597 q^{71} -274.403i q^{73} +(-12.0000 + 374.808i) q^{75} -1599.36i q^{77} -366.991 q^{79} +81.0000 q^{81} -57.7251i q^{83} +(3.18262 - 198.863i) q^{85} -313.514i q^{87} +203.175 q^{89} +1996.24 q^{91} -631.322i q^{93} +(1462.90 + 23.4124i) q^{95} +1283.45i q^{97} -435.220 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 22 q^{5} - 36 q^{9}+O(q^{10}) \) 4 * q + 22 * q^5 - 36 * q^9	\( 4 q + 22 q^{5} - 36 q^{9} + 148 q^{11} + 66 q^{15} + 160 q^{19} - 12 q^{21} - 100 q^{29} - 24 q^{31} + 796 q^{35} - 588 q^{39} + 688 q^{41} - 198 q^{45} - 3276 q^{49} - 468 q^{51} + 1072 q^{55} - 1332 q^{59} + 488 q^{61} + 820 q^{65} - 240 q^{69} + 616 q^{71} - 48 q^{75} - 2104 q^{79} + 324 q^{81} + 2148 q^{85} - 1368 q^{89} + 1352 q^{91} + 2944 q^{95} - 1332 q^{99}+O(q^{100}) \) 4 * q + 22 * q^5 - 36 * q^9 + 148 * q^11 + 66 * q^15 + 160 * q^19 - 12 * q^21 - 100 * q^29 - 24 * q^31 + 796 * q^35 - 588 * q^39 + 688 * q^41 - 198 * q^45 - 3276 * q^49 - 468 * q^51 + 1072 * q^55 - 1332 * q^59 + 488 * q^61 + 820 * q^65 - 240 * q^69 + 616 * q^71 - 48 * q^75 - 2104 * q^79 + 324 * q^81 + 2148 * q^85 - 1368 * q^89 + 1352 * q^91 + 2944 * q^95 - 1332 * q^99

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