LMFDB - Embedded newform 108.5.d.a.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,5,Mod(55,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("108.55");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	108.d (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:	$11.1639560131$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 6 x^{14} - 22 x^{13} + 19 x^{12} + 18 x^{11} + 1423 x^{10} + 660 x^{9} + \cdots + 2924100 $ x^16 - 2x^15 + 6x^14 - 22x^13 + 19x^12 + 18x^11 + 1423x^10 + 660x^9 - 7353x^8 - 22934x^7 - 36353x^6 - 16248x^5 + 360646x^4 + 1077384x^3 + 2005641x^2 + 2990790*x + 2924100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{26} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.1
Root			$-1.64756 - 0.974628i$ of defining polynomial
Character	$\chi$	$=$	108.55
Dual form			108.5.d.a.55.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.81409 - 1.20528i) q^{2} +(13.0946 + 9.19411i) q^{4} -13.3855 q^{5} +25.4062i q^{7} +(-38.8625 - 50.8499i) q^{8} +O(q^{10})$	\(q+(-3.81409 - 1.20528i) q^{2} +(13.0946 + 9.19411i) q^{4} -13.3855 q^{5} +25.4062i q^{7} +(-38.8625 - 50.8499i) q^{8} +(51.0536 + 16.1333i) q^{10} -34.7583i q^{11} +116.909 q^{13} +(30.6216 - 96.9015i) q^{14} +(86.9367 + 240.786i) q^{16} -109.608 q^{17} -264.951i q^{19} +(-175.278 - 123.068i) q^{20} +(-41.8936 + 132.571i) q^{22} -890.392i q^{23} -445.828 q^{25} +(-445.900 - 140.908i) q^{26} +(-233.587 + 332.683i) q^{28} -1116.85 q^{29} -1661.48i q^{31} +(-41.3691 - 1023.16i) q^{32} +(418.055 + 132.108i) q^{34} -340.075i q^{35} -1989.22 q^{37} +(-319.341 + 1010.55i) q^{38} +(520.194 + 680.652i) q^{40} +1229.27 q^{41} -3144.02i q^{43} +(319.572 - 455.146i) q^{44} +(-1073.17 + 3396.04i) q^{46} +2361.16i q^{47} +1755.53 q^{49} +(1700.43 + 537.348i) q^{50} +(1530.87 + 1074.87i) q^{52} +2187.65 q^{53} +465.258i q^{55} +(1291.90 - 987.347i) q^{56} +(4259.76 + 1346.12i) q^{58} +1808.52i q^{59} +1510.52 q^{61} +(-2002.56 + 6337.06i) q^{62} +(-1075.42 + 3952.30i) q^{64} -1564.88 q^{65} -5254.33i q^{67} +(-1435.27 - 1007.75i) q^{68} +(-409.886 + 1297.08i) q^{70} +1129.85i q^{71} -6351.81 q^{73} +(7587.07 + 2397.57i) q^{74} +(2435.99 - 3469.43i) q^{76} +883.075 q^{77} +445.921i q^{79} +(-1163.69 - 3223.05i) q^{80} +(-4688.55 - 1481.62i) q^{82} -1116.30i q^{83} +1467.16 q^{85} +(-3789.43 + 11991.6i) q^{86} +(-1767.45 + 1350.79i) q^{88} +10384.7 q^{89} +2970.20i q^{91} +(8186.36 - 11659.3i) q^{92} +(2845.86 - 9005.67i) q^{94} +3546.51i q^{95} +474.819 q^{97} +(-6695.74 - 2115.90i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 14 q^{4}+O(q^{10}) $ 16 * q - 14 * q^4	$ 16 q - 14 q^{4} - 202 q^{10} - 352 q^{13} - 206 q^{16} + 738 q^{22} + 1632 q^{25} + 342 q^{28} - 2536 q^{34} + 3200 q^{37} - 2854 q^{40} + 36 q^{46} - 896 q^{49} + 2288 q^{52} + 2492 q^{58} - 2752 q^{61} + 682 q^{64} - 14166 q^{70} + 8240 q^{73} - 33084 q^{76} + 68 q^{82} + 8800 q^{85} + 48294 q^{88} + 52596 q^{94} - 6928 q^{97}+O(q^{100}) $ 16 * q - 14 * q^4 - 202 * q^10 - 352 * q^13 - 206 * q^16 + 738 * q^22 + 1632 * q^25 + 342 * q^28 - 2536 * q^34 + 3200 * q^37 - 2854 * q^40 + 36 * q^46 - 896 * q^49 + 2288 * q^52 + 2492 * q^58 - 2752 * q^61 + 682 * q^64 - 14166 * q^70 + 8240 * q^73 - 33084 * q^76 + 68 * q^82 + 8800 * q^85 + 48294 * q^88 + 52596 * q^94 - 6928 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$1$	$-1$

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 $

$2$	−3.81409	−	1.20528i	−0.953523	−	0.301320i
$2$	−3.81409	−	1.20528i	−0.953523	−	0.301320i
$3$		0			0
$3$		0			0
$4$	13.0946	+	9.19411i	0.818412	+	0.574632i
$5$	−13.3855			−0.535421			−0.267710	−	0.963499i	$-0.586267\pi$
$5$	−13.3855			−0.535421			−0.267710	+	0.963499i	$0.586267\pi$
$6$		0			0
$7$			25.4062i			0.518493i	0.965811	+	0.259247i	$0.0834742\pi$
$7$			25.4062i			0.518493i	−0.965811	+	0.259247i	$0.916526\pi$
$8$	−38.8625	−	50.8499i	−0.607226	−	0.794529i
$9$		0			0
$10$	51.0536	+	16.1333i	0.510536	+	0.161333i
$11$		−	34.7583i		−	0.287259i	−0.989632	−	0.143629i	$-0.954123\pi$
$11$		−	34.7583i		−	0.287259i	0.989632	−	0.143629i	$-0.0458773\pi$
$12$		0			0
$13$	116.909			0.691767			0.345883	−	0.938278i	$-0.387579\pi$
$13$	116.909			0.691767			0.345883	+	0.938278i	$0.387579\pi$
$14$	30.6216	−	96.9015i	0.156233	−	0.494395i
$15$		0			0
$16$	86.9367	+	240.786i	0.339596	+	0.940571i
$17$	−109.608			−0.379266			−0.189633	−	0.981855i	$-0.560730\pi$
$17$	−109.608			−0.379266			−0.189633	+	0.981855i	$0.560730\pi$
$18$		0			0
$19$		−	264.951i		−	0.733937i	−0.930233	−	0.366968i	$-0.880396\pi$
$19$		−	264.951i		−	0.733937i	0.930233	−	0.366968i	$-0.119604\pi$
$20$	−175.278	−	123.068i	−0.438195	−	0.307670i
$21$		0			0
$22$	−41.8936	+	132.571i	−0.0865569	+	0.273908i
$23$		−	890.392i		−	1.68316i	−0.540132	−	0.841580i	$-0.681626\pi$
$23$		−	890.392i		−	1.68316i	0.540132	−	0.841580i	$-0.318374\pi$
$24$		0			0
$25$	−445.828			−0.713325
$26$	−445.900	−	140.908i	−0.659615	−	0.208443i
$27$		0			0
$28$	−233.587	+	332.683i	−0.297943	+	0.424341i
$29$	−1116.85			−1.32800			−0.664000	−	0.747733i	$-0.731143\pi$
$29$	−1116.85			−1.32800			−0.664000	+	0.747733i	$0.731143\pi$
$30$		0			0
$31$		−	1661.48i		−	1.72891i	−0.502708	−	0.864456i	$-0.667663\pi$
$31$		−	1661.48i		−	1.72891i	0.502708	−	0.864456i	$-0.332337\pi$
$32$	−41.3691	−	1023.16i	−0.0403995	−	0.999184i
$33$		0			0
$34$	418.055	+	132.108i	0.361639	+	0.114281i
$35$		−	340.075i		−	0.277612i
$36$		0			0
$37$	−1989.22			−1.45305			−0.726523	−	0.687142i	$-0.758865\pi$
$37$	−1989.22			−1.45305			−0.726523	+	0.687142i	$0.758865\pi$
$38$	−319.341	+	1010.55i	−0.221150	+	0.699826i
$39$		0			0
$40$	520.194	+	680.652i	0.325121	+	0.425407i
$41$	1229.27			0.731274			0.365637	−	0.930758i	$-0.380851\pi$
$41$	1229.27			0.731274			0.365637	+	0.930758i	$0.380851\pi$
$42$		0			0
$43$		−	3144.02i		−	1.70039i	−0.526469	−	0.850194i	$-0.676484\pi$
$43$		−	3144.02i		−	1.70039i	0.526469	−	0.850194i	$-0.323516\pi$
$44$	319.572	−	455.146i	0.165068	−	0.235096i
$45$		0			0
$46$	−1073.17	+	3396.04i	−0.507171	+	1.60493i
$47$			2361.16i			1.06888i	0.845206	+	0.534440i	$0.179478\pi$
$47$			2361.16i			1.06888i	−0.845206	+	0.534440i	$0.820522\pi$
$48$		0			0
$49$	1755.53			0.731165
$50$	1700.43	+	537.348i	0.680172	+	0.214939i
$51$		0			0
$52$	1530.87	+	1074.87i	0.566150	+	0.397511i
$53$	2187.65			0.778800			0.389400	−	0.921069i	$-0.372682\pi$
$53$	2187.65			0.778800			0.389400	+	0.921069i	$0.372682\pi$
$54$		0			0
$55$			465.258i			0.153804i
$56$	1291.90	−	987.347i	0.411958	−	0.314843i
$57$		0			0
$58$	4259.76	+	1346.12i	1.26628	+	0.400154i
$59$			1808.52i			0.519540i	0.965671	+	0.259770i	$0.0836467\pi$
$59$			1808.52i			0.519540i	−0.965671	+	0.259770i	$0.916353\pi$
$60$		0			0
$61$	1510.52			0.405943			0.202972	−	0.979185i	$-0.434940\pi$
$61$	1510.52			0.405943			0.202972	+	0.979185i	$0.434940\pi$
$62$	−2002.56	+	6337.06i	−0.520957	+	1.64856i
$63$		0			0
$64$	−1075.42	+	3952.30i	−0.262553	+	0.964918i
$65$	−1564.88			−0.370386
$66$		0			0
$67$		−	5254.33i		−	1.17049i	−0.810856	−	0.585245i	$-0.800998\pi$
$67$		−	5254.33i		−	1.17049i	0.810856	−	0.585245i	$-0.199002\pi$
$68$	−1435.27	−	1007.75i	−0.310396	−	0.217938i
$69$		0			0
$70$	−409.886	+	1297.08i	−0.0836502	+	0.264709i
$71$			1129.85i			0.224133i	0.993701	+	0.112067i	$0.0357470\pi$
$71$			1129.85i			0.224133i	−0.993701	+	0.112067i	$0.964253\pi$
$72$		0			0
$73$	−6351.81			−1.19193			−0.595966	−	0.803010i	$-0.703231\pi$
$73$	−6351.81			−1.19193			−0.595966	+	0.803010i	$0.703231\pi$
$74$	7587.07	+	2397.57i	1.38551	+	0.437833i
$75$		0			0
$76$	2435.99	−	3469.43i	0.421744	−	0.600663i
$77$	883.075			0.148942
$78$		0			0
$79$			445.921i			0.0714502i	0.999362	+	0.0357251i	$0.0113741\pi$
$79$			445.921i			0.0714502i	−0.999362	+	0.0357251i	$0.988626\pi$
$80$	−1163.69	−	3223.05i	−0.181827	−	0.503601i
$81$		0			0
$82$	−4688.55	−	1481.62i	−0.697286	−	0.220348i
$83$		−	1116.30i		−	0.162040i	−0.996712	−	0.0810202i	$-0.974182\pi$
$83$		−	1116.30i		−	0.162040i	0.996712	−	0.0810202i	$-0.0258178\pi$
$84$		0			0
$85$	1467.16			0.203067
$86$	−3789.43	+	11991.6i	−0.512362	+	1.62136i
$87$		0			0
$88$	−1767.45	+	1350.79i	−0.228235	+	0.174431i
$89$	10384.7			1.31104			0.655520	−	0.755178i	$-0.272450\pi$
$89$	10384.7			1.31104			0.655520	+	0.755178i	$0.272450\pi$
$90$		0			0
$91$			2970.20i			0.358676i
$92$	8186.36	−	11659.3i	0.967198	−	1.37752i
$93$		0			0
$94$	2845.86	−	9005.67i	0.322075	−	1.01920i
$95$			3546.51i			0.392965i
$96$		0			0
$97$	474.819			0.0504643			0.0252321	−	0.999682i	$-0.491968\pi$
$97$	474.819			0.0504643			0.0252321	+	0.999682i	$0.491968\pi$
$98$	−6695.74	−	2115.90i	−0.697182	−	0.220315i
$99$		0			0
$100$	−5837.94	−	4098.99i	−0.583794	−	0.409899i
$101$	−15785.2			−1.54742			−0.773709	−	0.633542i	$-0.781601\pi$
$101$	−15785.2			−1.54742			−0.773709	+	0.633542i	$0.781601\pi$
$102$		0			0
$103$			3784.74i			0.356748i	0.983963	+	0.178374i	$0.0570837\pi$
$103$			3784.74i			0.356748i	−0.983963	+	0.178374i	$0.942916\pi$
$104$	−4543.36	−	5944.78i	−0.420059	−	0.549629i
$105$		0			0
$106$	−8343.89	−	2636.73i	−0.742603	−	0.234668i
$107$		−	12301.5i		−	1.07446i	−0.843435	−	0.537231i	$-0.819470\pi$
$107$		−	12301.5i		−	1.07446i	0.843435	−	0.537231i	$-0.180530\pi$
$108$		0			0
$109$	530.931			0.0446874			0.0223437	−	0.999750i	$-0.492887\pi$
$109$	530.931			0.0446874			0.0223437	+	0.999750i	$0.492887\pi$
$110$	560.767	−	1774.54i	0.0463444	−	0.146656i
$111$		0			0
$112$	−6117.46	+	2208.73i	−0.487680	+	0.176078i
$113$	−11047.5			−0.865183			−0.432591	−	0.901590i	$-0.642401\pi$
$113$	−11047.5			−0.865183			−0.432591	+	0.901590i	$0.642401\pi$
$114$		0			0
$115$			11918.4i			0.901199i
$116$	−14624.7	−	10268.4i	−1.08685	−	0.763111i
$117$		0			0
$118$	2179.77	−	6897.85i	0.156548	−	0.495393i
$119$		−	2784.72i		−	0.196647i
$120$		0			0
$121$	13432.9			0.917482
$122$	−5761.24	−	1820.60i	−0.387076	−	0.122319i
$123$		0			0
$124$	15275.9	−	21756.5i	0.993488	−	1.41496i
$125$	14333.6			0.917349
$126$		0			0
$127$			25919.1i			1.60699i	0.595314	+	0.803493i	$0.297028\pi$
$127$			25919.1i			1.60699i	−0.595314	+	0.803493i	$0.702972\pi$
$128$	8865.37	−	13778.3i	0.541099	−	0.840959i
$129$		0			0
$130$	5968.60	+	1886.12i	0.353172	+	0.111605i
$131$		−	15334.4i		−	0.893559i	−0.894644	−	0.446779i	$-0.852571\pi$
$131$		−	15334.4i		−	0.893559i	0.894644	−	0.446779i	$-0.147429\pi$
$132$		0			0
$133$	6731.40			0.380541
$134$	−6332.95	+	20040.5i	−0.352693	+	1.11609i
$135$		0			0
$136$	4259.63	+	5573.54i	0.230300	+	0.301338i
$137$	−29216.9			−1.55666			−0.778329	−	0.627856i	$-0.783933\pi$
$137$	−29216.9			−1.55666			−0.778329	+	0.627856i	$0.783933\pi$
$138$		0			0
$139$			27071.9i			1.40116i	0.713571	+	0.700582i	$0.247076\pi$
$139$			27071.9i			1.40116i	−0.713571	+	0.700582i	$0.752924\pi$
$140$	3126.68	−	4453.14i	0.159525	−	0.227201i
$141$		0			0
$142$	1361.79	−	4309.37i	0.0675359	−	0.213716i
$143$		−	4063.54i		−	0.198716i
$144$		0			0
$145$	14949.6			0.711039
$146$	24226.4	+	7655.72i	1.13653	+	0.359154i
$147$		0			0
$148$	−26048.0	−	18289.1i	−1.18919	−	0.834967i
$149$	27443.5			1.23614			0.618068	−	0.786125i	$-0.287916\pi$
$149$	27443.5			1.23614			0.618068	+	0.786125i	$0.287916\pi$
$150$		0			0
$151$			5044.14i			0.221225i	0.993864	+	0.110612i	$0.0352812\pi$
$151$			5044.14i			0.221225i	−0.993864	+	0.110612i	$0.964719\pi$
$152$	−13472.7	+	10296.7i	−0.583134	+	0.445666i
$153$		0			0
$154$	−3368.13	−	1064.35i	−0.142019	−	0.0448792i
$155$			22239.8i			0.925695i
$156$		0			0
$157$	−11939.3			−0.484374			−0.242187	−	0.970230i	$-0.577865\pi$
$157$	−11939.3			−0.484374			−0.242187	+	0.970230i	$0.577865\pi$
$158$	537.460	−	1700.78i	0.0215294	−	0.0681294i
$159$		0			0
$160$	553.747	+	13695.6i	0.0216307	+	0.534984i
$161$	22621.4			0.872707
$162$		0			0
$163$		−	24289.6i		−	0.914207i	−0.889414	−	0.457103i	$-0.848887\pi$
$163$		−	24289.6i		−	0.914207i	0.889414	−	0.457103i	$-0.151113\pi$
$164$	16096.8	+	11302.1i	0.598483	+	0.420213i
$165$		0			0
$166$	−1345.45	+	4257.66i	−0.0488261	+	0.154509i
$167$			14400.8i			0.516363i	0.966096	+	0.258181i	$0.0831232\pi$
$167$			14400.8i			0.516363i	−0.966096	+	0.258181i	$0.916877\pi$
$168$		0			0
$169$	−14893.4			−0.521459
$170$	−5595.88	−	1768.34i	−0.193629	−	0.0611882i
$171$		0			0
$172$	28906.5	−	41169.6i	0.977098	−	1.39162i
$173$	−35985.6			−1.20237			−0.601183	−	0.799111i	$-0.705304\pi$
$173$	−35985.6			−1.20237			−0.601183	+	0.799111i	$0.705304\pi$
$174$		0			0
$175$		−	11326.8i		−	0.369854i
$176$	8369.32	−	3021.77i	0.270187	−	0.0975520i
$177$		0			0
$178$	−39608.4	−	12516.5i	−1.25011	−	0.395043i
$179$		−	4221.93i		−	0.131766i	−0.997827	−	0.0658832i	$-0.979014\pi$
$179$		−	4221.93i		−	0.131766i	0.997827	−	0.0658832i	$-0.0209865\pi$
$180$		0			0
$181$	18881.9			0.576353			0.288176	−	0.957577i	$-0.406951\pi$
$181$	18881.9			0.576353			0.288176	+	0.957577i	$0.406951\pi$
$182$	3579.93	−	11328.6i	0.108077	−	0.342006i
$183$		0			0
$184$	−45276.3	+	34602.8i	−1.33732	+	1.02206i
$185$	26626.7			0.777991
$186$		0			0
$187$			3809.78i			0.108947i
$188$	−21708.7	+	30918.4i	−0.614213	+	0.874784i
$189$		0			0
$190$	4274.54	−	13526.7i	0.118408	−	0.374701i
$191$			67734.8i			1.85671i	0.371689	+	0.928357i	$0.378779\pi$
$191$			67734.8i			1.85671i	−0.371689	+	0.928357i	$0.621221\pi$
$192$		0			0
$193$	−52984.0			−1.42243			−0.711213	−	0.702976i	$-0.751854\pi$
$193$	−52984.0			−1.42243			−0.711213	+	0.702976i	$0.751854\pi$
$194$	−1811.00	−	572.290i	−0.0481189	−	0.0152059i
$195$		0			0
$196$	22987.9	+	16140.5i	0.598394	+	0.420151i
$197$	39007.1			1.00511			0.502553	−	0.864547i	$-0.332394\pi$
$197$	39007.1			1.00511			0.502553	+	0.864547i	$0.332394\pi$
$198$		0			0
$199$		−	58823.4i		−	1.48540i	−0.669623	−	0.742701i	$-0.733544\pi$
$199$		−	58823.4i		−	1.48540i	0.669623	−	0.742701i	$-0.266456\pi$
$200$	17326.0	+	22670.3i	0.433150	+	0.566757i
$201$		0			0
$202$	60206.2	+	19025.6i	1.47550	+	0.466268i
$203$		−	28374.8i		−	0.688559i
$204$		0			0
$205$	−16454.4			−0.391539
$206$	4561.68	−	14435.3i	0.107495	−	0.340167i
$207$		0			0
$208$	10163.6	+	28150.0i	0.234921	+	0.650656i
$209$	−9209.25			−0.210830
$210$		0			0
$211$			8214.89i			0.184517i	0.995735	+	0.0922586i	$0.0294087\pi$
$211$			8214.89i			0.184517i	−0.995735	+	0.0922586i	$0.970591\pi$
$212$	28646.4	+	20113.5i	0.637379	+	0.447523i
$213$		0			0
$214$	−14826.8	+	46919.1i	−0.323758	+	1.02452i
$215$			42084.3i			0.910423i
$216$		0			0
$217$	42212.0			0.896429
$218$	−2025.02	−	639.921i	−0.0426105	−	0.0134652i
$219$		0			0
$220$	−4277.63	+	6092.36i	−0.0883808	+	0.125875i
$221$	−12814.1			−0.262364
$222$		0			0
$223$		−	36518.9i		−	0.734357i	−0.930150	−	0.367179i	$-0.880324\pi$
$223$		−	36518.9i		−	0.734357i	0.930150	−	0.367179i	$-0.119676\pi$
$224$	25994.7	−	1051.03i	0.518070	−	0.0209469i
$225$		0			0
$226$	42136.2	+	13315.4i	0.824972	+	0.260697i
$227$		−	83547.6i		−	1.62137i	−0.585483	−	0.810685i	$-0.699095\pi$
$227$		−	83547.6i		−	1.62137i	0.585483	−	0.810685i	$-0.300905\pi$
$228$		0			0
$229$	−8882.43			−0.169379			−0.0846897	−	0.996407i	$-0.526990\pi$
$229$	−8882.43			−0.169379			−0.0846897	+	0.996407i	$0.526990\pi$
$230$	14365.0	−	45457.7i	0.271550	−	0.859314i
$231$		0			0
$232$	43403.5	+	56791.6i	0.806396	+	1.05513i
$233$	5239.47			0.0965108			0.0482554	−	0.998835i	$-0.484634\pi$
$233$	5239.47			0.0965108			0.0482554	+	0.998835i	$0.484634\pi$
$234$		0			0
$235$		−	31605.3i		−	0.572301i
$236$	−16627.7	+	23681.8i	−0.298544	+	0.425197i
$237$		0			0
$238$	−3356.37	+	10621.2i	−0.0592537	+	0.187507i
$239$			5031.54i			0.0880856i	0.999030	+	0.0440428i	$0.0140238\pi$
$239$			5031.54i			0.0880856i	−0.999030	+	0.0440428i	$0.985976\pi$
$240$		0			0
$241$	37868.6			0.651996			0.325998	−	0.945370i	$-0.394300\pi$
$241$	37868.6			0.651996			0.325998	+	0.945370i	$0.394300\pi$
$242$	−51234.2	−	16190.4i	−0.874841	−	0.276456i
$243$		0			0
$244$	19779.6	+	13887.8i	0.332229	+	0.233268i
$245$	−23498.6			−0.391481
$246$		0			0
$247$		−	30975.1i		−	0.507713i
$248$	−84486.3	+	64569.4i	−1.37367	+	1.04984i
$249$		0			0
$250$	−54669.6	−	17276.0i	−0.874714	−	0.276416i
$251$		−	91242.6i		−	1.44827i	−0.689657	−	0.724136i	$-0.742239\pi$
$251$		−	91242.6i		−	1.44827i	0.689657	−	0.724136i	$-0.257761\pi$
$252$		0			0
$253$	−30948.5			−0.483502
$254$	31239.8	−	98857.8i	0.484218	−	1.53230i
$255$		0			0
$256$	−50420.0	+	41866.3i	−0.769349	+	0.638829i
$257$	−73598.9			−1.11431			−0.557154	−	0.830409i	$-0.688107\pi$
$257$	−73598.9			−1.11431			−0.557154	+	0.830409i	$0.688107\pi$
$258$		0			0
$259$		−	50538.5i		−	0.753395i
$260$	−20491.5	−	14387.7i	−0.303128	−	0.212836i
$261$		0			0
$262$	−18482.2	+	58486.7i	−0.269247	+	0.852029i
$263$		−	5368.69i		−	0.0776170i	−0.999247	−	0.0388085i	$-0.987644\pi$
$263$		−	5368.69i		−	0.0776170i	0.999247	−	0.0388085i	$-0.0123562\pi$
$264$		0			0
$265$	−29282.8			−0.416985
$266$	−25674.2	−	8113.23i	−0.362855	−	0.114665i
$267$		0			0
$268$	48308.9	−	68803.3i	0.672601	−	0.957943i
$269$	−90206.5			−1.24662			−0.623308	−	0.781976i	$-0.714212\pi$
$269$	−90206.5			−1.24662			−0.623308	+	0.781976i	$0.714212\pi$
$270$		0			0
$271$			13029.5i			0.177415i	0.996058	+	0.0887073i	$0.0282736\pi$
$271$			13029.5i			0.177415i	−0.996058	+	0.0887073i	$0.971726\pi$
$272$	−9528.94	−	26392.1i	−0.128797	−	0.356727i
$273$		0			0
$274$	111436.	+	35214.6i	1.48431	+	0.469053i
$275$			15496.2i			0.204909i
$276$		0			0
$277$	−21241.5			−0.276837			−0.138419	−	0.990374i	$-0.544202\pi$
$277$	−21241.5			−0.276837			−0.138419	+	0.990374i	$0.544202\pi$
$278$	32629.3	−	103255.i	0.422200	−	1.33604i
$279$		0			0
$280$	−17292.7	+	13216.1i	−0.220571	+	0.168573i
$281$	110158.			1.39510			0.697549	−	0.716537i	$-0.254274\pi$
$281$	110158.			1.39510			0.697549	+	0.716537i	$0.254274\pi$
$282$		0			0
$283$		−	51723.9i		−	0.645830i	−0.946428	−	0.322915i	$-0.895337\pi$
$283$		−	51723.9i		−	0.645830i	0.946428	−	0.322915i	$-0.104663\pi$
$284$	−10388.0	+	14795.0i	−0.128794	+	0.183433i
$285$		0			0
$286$	−4897.72	+	15498.7i	−0.0598772	+	0.189480i
$287$			31231.1i			0.379161i
$288$		0			0
$289$	−71507.1			−0.856157
$290$	−57019.1	−	18018.5i	−0.677992	−	0.214250i
$291$		0			0
$292$	−83174.3	−	58399.2i	−0.975492	−	0.684922i
$293$	20425.2			0.237920			0.118960	−	0.992899i	$-0.462044\pi$
$293$	20425.2			0.237920			0.118960	+	0.992899i	$0.462044\pi$
$294$		0			0
$295$		−	24207.9i		−	0.278172i
$296$	77306.1	+	101152.i	0.882328	+	1.15449i
$297$		0			0
$298$	−104672.	−	33077.1i	−1.17868	−	0.372473i
$299$		−	104094.i		−	1.16435i
$300$		0			0
$301$	79877.5			0.881640
$302$	6079.61	−	19238.8i	0.0666595	−	0.210943i
$303$		0			0
$304$	63796.6	−	23034.0i	0.690320	−	0.249242i
$305$	−20219.0			−0.217350
$306$		0			0
$307$			70255.6i			0.745426i	0.927947	+	0.372713i	$0.121572\pi$
$307$			70255.6i			0.745426i	−0.927947	+	0.372713i	$0.878428\pi$
$308$	11563.5	+	8119.09i	0.121896	+	0.0855867i
$309$		0			0
$310$	26805.3	−	84824.8i	0.278931	−	0.882672i
$311$			132510.i			1.37002i	0.728532	+	0.685012i	$0.240203\pi$
$311$			132510.i			1.37002i	−0.728532	+	0.685012i	$0.759797\pi$
$312$		0			0
$313$	−95836.7			−0.978234			−0.489117	−	0.872218i	$-0.662681\pi$
$313$	−95836.7			−0.978234			−0.489117	+	0.872218i	$0.662681\pi$
$314$	45537.7	+	14390.3i	0.461861	+	0.145952i
$315$		0			0
$316$	−4099.84	+	5839.15i	−0.0410576	+	0.0584757i
$317$	91986.8			0.915392			0.457696	−	0.889109i	$-0.348675\pi$
$317$	91986.8			0.915392			0.457696	+	0.889109i	$0.348675\pi$
$318$		0			0
$319$			38819.7i			0.381480i
$320$	14395.0	−	52903.6i	0.140576	−	0.516637i
$321$		0			0
$322$	−86280.3	−	27265.2i	−0.832146	−	0.262965i
$323$			29040.7i			0.278357i
$324$		0			0
$325$	−52121.1			−0.493454
$326$	−29275.8	+	92642.6i	−0.275469	+	0.871717i
$327$		0			0
$328$	−47772.5	−	62508.3i	−0.444049	−	0.581018i
$329$	−59987.9			−0.554207
$330$		0			0
$331$			109298.i			0.997602i	0.866717	+	0.498801i	$0.166226\pi$
$331$			109298.i			0.997602i	−0.866717	+	0.498801i	$0.833774\pi$
$332$	10263.4	−	14617.5i	0.0931136	−	0.132616i
$333$		0			0
$334$	17357.1	−	54926.1i	0.155591	−	0.492364i
$335$			70331.9i			0.626705i
$336$		0			0
$337$	198743.			1.74998			0.874989	−	0.484144i	$-0.160869\pi$
$337$	198743.			1.74998			0.874989	+	0.484144i	$0.160869\pi$
$338$	56804.7	+	17950.7i	0.497223	+	0.157126i
$339$		0			0
$340$	19211.8	+	13489.2i	0.166192	+	0.116689i
$341$	−57750.4			−0.496645
$342$		0			0
$343$			105601.i			0.897597i
$344$	−159873.	+	122184.i	−1.35101	+	1.03252i
$345$		0			0
$346$	137252.	+	43372.8i	1.14648	+	0.362297i
$347$		−	167328.i		−	1.38966i	−0.719174	−	0.694830i	$-0.755480\pi$
$347$		−	167328.i		−	1.38966i	0.719174	−	0.694830i	$-0.244520\pi$
$348$		0			0
$349$	188371.			1.54655			0.773274	−	0.634072i	$-0.218618\pi$
$349$	188371.			1.54655			0.773274	+	0.634072i	$0.218618\pi$
$350$	−13652.0	+	43201.4i	−0.111445	+	0.352664i
$351$		0			0
$352$	−35563.4	+	1437.92i	−0.287024	+	0.0116051i
$353$	115038.			0.923189			0.461594	−	0.887091i	$-0.347278\pi$
$353$	115038.			0.923189			0.461594	+	0.887091i	$0.347278\pi$
$354$		0			0
$355$		−	15123.7i		−	0.120005i
$356$	135984.	+	95478.5i	1.07297	+	0.753365i
$357$		0			0
$358$	−5088.61	+	16102.8i	−0.0397039	+	0.125642i
$359$			117266.i			0.909882i	0.890522	+	0.454941i	$0.150340\pi$
$359$			117266.i			0.909882i	−0.890522	+	0.454941i	$0.849660\pi$
$360$		0			0
$361$	60121.9			0.461337
$362$	−72017.3	−	22758.0i	−0.549566	−	0.173667i
$363$		0			0
$364$	−27308.3	+	38893.5i	−0.206107	+	0.293545i
$365$	85022.2			0.638185
$366$		0			0
$367$			263083.i			1.95326i	0.214929	+	0.976630i	$0.431048\pi$
$367$			263083.i			1.95326i	−0.214929	+	0.976630i	$0.568952\pi$
$368$	214394.	−	77407.7i	1.58313	−	0.571595i
$369$		0			0
$370$	−101557.	−	32092.7i	−0.741832	−	0.234425i
$371$			55579.8i			0.403802i
$372$		0			0
$373$	−34514.3			−0.248074			−0.124037	−	0.992278i	$-0.539584\pi$
$373$	−34514.3			−0.248074			−0.124037	+	0.992278i	$0.539584\pi$
$374$	4591.86	−	14530.9i	0.0328281	−	0.103884i
$375$		0			0
$376$	120064.	−	91760.4i	0.849256	−	0.649052i
$377$	−130569.			−0.918666
$378$		0			0
$379$			152446.i			1.06130i	0.847591	+	0.530650i	$0.178052\pi$
$379$			152446.i			1.06130i	−0.847591	+	0.530650i	$0.821948\pi$
$380$	−32607.0	+	46440.1i	−0.225810	+	0.321607i
$381$		0			0
$382$	81639.5	−	258347.i	0.559466	−	1.77042i
$383$			154427.i			1.05275i	0.850253	+	0.526375i	$0.176449\pi$
$383$			154427.i			1.05275i	−0.850253	+	0.526375i	$0.823551\pi$
$384$		0			0
$385$	−11820.4			−0.0797465
$386$	202086.	+	63860.6i	1.35632	+	0.428606i
$387$		0			0
$388$	6217.56	+	4365.53i	0.0413006	+	0.0289984i
$389$	109925.			0.726435			0.363217	−	0.931704i	$-0.381678\pi$
$389$	109925.			0.726435			0.363217	+	0.931704i	$0.381678\pi$
$390$		0			0
$391$			97593.9i			0.638365i
$392$	−68224.1	−	89268.3i	−0.443982	−	0.580932i
$393$		0			0
$394$	−148777.	−	47014.6i	−0.958391	−	0.302859i
$395$		−	5968.88i		−	0.0382559i
$396$		0			0
$397$	−148277.			−0.940789			−0.470394	−	0.882456i	$-0.655888\pi$
$397$	−148277.			−0.940789			−0.470394	+	0.882456i	$0.655888\pi$
$398$	−70898.8	+	224358.i	−0.447582	+	1.41636i
$399$		0			0
$400$	−38758.8	−	107349.i	−0.242242	−	0.670933i
$401$	144225.			0.896913			0.448457	−	0.893805i	$-0.351974\pi$
$401$	144225.			0.896913			0.448457	+	0.893805i	$0.351974\pi$
$402$		0			0
$403$		−	194242.i		−	1.19600i
$404$	−206701.	−	145131.i	−1.26642	−	0.889195i
$405$		0			0
$406$	−34199.7	+	108224.i	−0.207477	+	0.656557i
$407$			69141.9i			0.417400i
$408$		0			0
$409$	54102.7			0.323424			0.161712	−	0.986838i	$-0.448298\pi$
$409$	54102.7			0.323424			0.161712	+	0.986838i	$0.448298\pi$
$410$	62758.7	+	19832.2i	0.373342	+	0.117979i
$411$		0			0
$412$	−34797.3	+	49559.6i	−0.204999	+	0.291967i
$413$	−45947.5			−0.269378
$414$		0			0
$415$			14942.2i			0.0867598i
$416$	−4836.40	−	119617.i	−0.0279470	−	0.691202i
$417$		0			0
$418$	35124.9	+	11099.7i	0.201031	+	0.0635273i
$419$		−	283173.i		−	1.61296i	−0.591261	−	0.806480i	$-0.701370\pi$
$419$		−	283173.i		−	1.61296i	0.591261	−	0.806480i	$-0.298630\pi$
$420$		0			0
$421$	2339.30			0.0131984			0.00659920	−	0.999978i	$-0.497899\pi$
$421$	2339.30			0.0131984			0.00659920	+	0.999978i	$0.497899\pi$
$422$	9901.26	−	31332.4i	0.0555988	−	0.175941i
$423$		0			0
$424$	−85017.4	−	111242.i	−0.472908	−	0.618779i
$425$	48866.3			0.270540
$426$		0			0
$427$			38376.4i			0.210479i
$428$	113102.	−	161083.i	0.617420	−	0.879353i
$429$		0			0
$430$	50723.5	−	160513.i	0.274329	−	0.868109i
$431$			250884.i			1.35057i	0.737555	+	0.675287i	$0.235980\pi$
$431$			250884.i			1.35057i	−0.737555	+	0.675287i	$0.764020\pi$
$432$		0			0
$433$	−28542.2			−0.152234			−0.0761169	−	0.997099i	$-0.524252\pi$
$433$	−28542.2			−0.152234			−0.0761169	+	0.997099i	$0.524252\pi$
$434$	−161000.	−	50877.3i	−0.854766	−	0.270112i
$435$		0			0
$436$	6952.32	+	4881.44i	0.0365727	+	0.0256788i
$437$	−235910.			−1.23533
$438$		0			0
$439$		−	204222.i		−	1.05968i	−0.848099	−	0.529838i	$-0.822253\pi$
$439$		−	204222.i		−	1.05968i	0.848099	−	0.529838i	$-0.177747\pi$
$440$	23658.3	−	18081.1i	0.122202	−	0.0933940i
$441$		0			0
$442$	48874.2	+	15444.6i	0.250170	+	0.0790555i
$443$		−	319736.i		−	1.62924i	−0.579997	−	0.814619i	$-0.696946\pi$
$443$		−	319736.i		−	1.62924i	0.579997	−	0.814619i	$-0.303054\pi$
$444$		0			0
$445$	−139005.			−0.701958
$446$	−44015.5	+	139286.i	−0.221277	+	0.700227i
$447$		0			0
$448$	−100413.	−	27322.2i	−0.500303	−	0.136132i
$449$	−325480.			−1.61448			−0.807239	−	0.590225i	$-0.799039\pi$
$449$	−325480.			−1.61448			−0.807239	+	0.590225i	$0.799039\pi$
$450$		0			0
$451$		−	42727.4i		−	0.210065i
$452$	−144663.	−	101572.i	−0.708076	−	0.497162i
$453$		0			0
$454$	−100698.	+	318658.i	−0.488552	+	1.54601i
$455$		−	39757.6i		−	0.192043i
$456$		0			0
$457$	1088.11			0.00521003			0.00260501	−	0.999997i	$-0.499171\pi$
$457$	1088.11			0.00521003			0.00260501	+	0.999997i	$0.499171\pi$
$458$	33878.4	+	10705.8i	0.161507	+	0.0510375i
$459$		0			0
$460$	−109579.	+	156066.i	−0.517858	+	0.737552i
$461$	127607.			0.600445			0.300222	−	0.953869i	$-0.402939\pi$
$461$	127607.			0.600445			0.300222	+	0.953869i	$0.402939\pi$
$462$		0			0
$463$		−	119526.i		−	0.557572i	−0.960353	−	0.278786i	$-0.910068\pi$
$463$		−	119526.i		−	0.557572i	0.960353	−	0.278786i	$-0.0899320\pi$
$464$	−97095.0	−	268922.i	−0.450984	−	1.24908i
$465$		0			0
$466$	−19983.8	−	6315.04i	−0.0920252	−	0.0290807i
$467$		−	351752.i		−	1.61288i	−0.591314	−	0.806442i	$-0.701391\pi$
$467$		−	351752.i		−	1.61288i	0.591314	−	0.806442i	$-0.298609\pi$
$468$		0			0
$469$	133492.			0.606891
$470$	−38093.3	+	120546.i	−0.172446	+	0.545702i
$471$		0			0
$472$	91962.8	−	70283.5i	0.412789	−	0.315478i
$473$	−109281.			−0.488451
$474$		0			0
$475$			118123.i			0.523535i
$476$	25603.0	−	36464.7i	0.113000	−	0.160938i
$477$		0			0
$478$	6064.42	−	19190.8i	0.0265420	−	0.0839917i
$479$		−	44703.0i		−	0.194835i	−0.995244	−	0.0974173i	$-0.968942\pi$
$479$		−	44703.0i		−	0.194835i	0.995244	−	0.0974173i	$-0.0310581\pi$
$480$		0			0
$481$	−232557.			−1.00517
$482$	−144434.	−	45642.3i	−0.621693	−	0.196460i
$483$		0			0
$484$	175898.	+	123503.i	0.750879	+	0.527215i
$485$	−6355.69			−0.0270196
$486$		0			0
$487$		−	171347.i		−	0.722469i	−0.932475	−	0.361235i	$-0.882355\pi$
$487$		−	171347.i		−	0.722469i	0.932475	−	0.361235i	$-0.117645\pi$
$488$	−58702.4	−	76809.5i	−0.246499	−	0.322534i
$489$		0			0
$490$	89625.9	+	28322.5i	0.373286	+	0.117961i
$491$			198915.i			0.825095i	0.910936	+	0.412548i	$0.135361\pi$
$491$			198915.i			0.825095i	−0.910936	+	0.412548i	$0.864639\pi$
$492$		0			0
$493$	122415.			0.503665
$494$	−37333.7	+	118142.i	−0.152984	+	0.484116i
$495$		0			0
$496$	400063.	−	144444.i	1.62617	−	0.587132i
$497$	−28705.3			−0.116211
$498$		0			0
$499$		−	114935.i		−	0.461585i	−0.973003	−	0.230793i	$-0.925868\pi$
$499$		−	114935.i		−	0.461585i	0.973003	−	0.230793i	$-0.0741319\pi$
$500$	187692.	+	131785.i	0.750770	+	0.527138i
$501$		0			0
$502$	−109973.	+	348008.i	−0.436394	+	1.38096i
$503$		−	95086.4i		−	0.375822i	−0.982186	−	0.187911i	$-0.939828\pi$
$503$		−	95086.4i		−	0.375822i	0.982186	−	0.187911i	$-0.0601717\pi$
$504$		0			0
$505$	211293.			0.828519
$506$	118040.	+	37301.7i	0.461031	+	0.145689i
$507$		0			0
$508$	−238303.	+	339400.i	−0.923426	+	1.31518i
$509$	23238.2			0.0896947			0.0448474	−	0.998994i	$-0.485720\pi$
$509$	23238.2			0.0896947			0.0448474	+	0.998994i	$0.485720\pi$
$510$		0			0
$511$		−	161375.i		−	0.618009i
$512$	242767.	−	98911.6i	0.926084	−	0.377318i
$513$		0			0
$514$	280713.	+	88707.4i	1.06252	+	0.335764i
$515$		−	50660.7i		−	0.191010i
$516$		0			0
$517$	82069.8			0.307045
$518$	−60913.1	+	192758.i	−0.227013	+	0.718379i
$519$		0			0
$520$	60815.2	+	79574.0i	0.224908	+	0.294283i
$521$	292204.			1.07649			0.538245	−	0.842788i	$-0.319087\pi$
$521$	292204.			1.07649			0.538245	+	0.842788i	$0.319087\pi$
$522$		0			0
$523$		−	415479.i		−	1.51896i	−0.650532	−	0.759479i	$-0.725454\pi$
$523$		−	415479.i		−	1.51896i	0.650532	−	0.759479i	$-0.274546\pi$
$524$	140986.	−	200797.i	0.513467	−	0.731299i
$525$		0			0
$526$	−6470.79	+	20476.7i	−0.0233876	+	0.0740096i
$527$			182112.i			0.655718i
$528$		0			0
$529$	−512956.			−1.83303
$530$	111687.	+	35294.0i	0.397605	+	0.125646i
$531$		0			0
$532$	88144.9	+	61889.2i	0.311440	+	0.218671i
$533$	143712.			0.505871
$534$		0			0
$535$			164662.i			0.575289i
$536$	−267182.	+	204196.i	−0.929989	+	0.710753i
$537$		0			0
$538$	344056.	+	108724.i	1.18868	+	0.375631i
$539$		−	61019.1i		−	0.210033i
$540$		0			0
$541$	−90006.8			−0.307525			−0.153763	−	0.988108i	$-0.549139\pi$
$541$	−90006.8			−0.307525			−0.153763	+	0.988108i	$0.549139\pi$
$542$	15704.2	−	49695.7i	0.0534587	−	0.169169i
$543$		0			0
$544$	4534.38	+	112147.i	0.0153222	+	0.378956i
$545$	−7106.78			−0.0239266
$546$		0			0
$547$			159823.i			0.534153i	0.963675	+	0.267077i	$0.0860577\pi$
$547$			159823.i			0.534153i	−0.963675	+	0.267077i	$0.913942\pi$
$548$	−382584.	−	268624.i	−1.27399	−	0.894506i
$549$		0			0
$550$	18677.3	−	59104.0i	0.0617432	−	0.195385i
$551$			295910.i			0.974668i
$552$		0			0
$553$	−11329.1			−0.0370464
$554$	81016.9	+	25601.9i	0.263971	+	0.0834168i
$555$		0			0
$556$	−248902.	+	354496.i	−0.805154	+	1.14673i
$557$	−91192.2			−0.293932			−0.146966	−	0.989142i	$-0.546951\pi$
$557$	−91192.2			−0.293932			−0.146966	+	0.989142i	$0.546951\pi$
$558$		0			0
$559$		−	367563.i		−	1.17627i
$560$	81885.3	−	29565.0i	0.261114	−	0.0942760i
$561$		0			0
$562$	−420154.	−	132772.i	−1.33026	−	0.420371i
$563$			287297.i			0.906390i	0.891412	+	0.453195i	$0.149716\pi$
$563$			287297.i			0.906390i	−0.891412	+	0.453195i	$0.850284\pi$
$564$		0			0
$565$	147877.			0.463237
$566$	−62341.8	+	197280.i	−0.194602	+	0.615814i
$567$		0			0
$568$	57453.0	−	43909.0i	0.178080	−	0.136099i
$569$	−248591.			−0.767824			−0.383912	−	0.923370i	$-0.625423\pi$
$569$	−248591.			−0.767824			−0.383912	+	0.923370i	$0.625423\pi$
$570$		0			0
$571$		−	237006.i		−	0.726921i	−0.931610	−	0.363461i	$-0.881595\pi$
$571$		−	237006.i		−	0.726921i	0.931610	−	0.363461i	$-0.118405\pi$
$572$	37360.7	−	53210.4i	0.114189	−	0.162632i
$573$		0			0
$574$	37642.2	−	119118.i	0.114249	−	0.361538i
$575$			396962.i			1.20064i
$576$		0			0
$577$	567965.			1.70596			0.852982	−	0.521940i	$-0.174792\pi$
$577$	567965.			1.70596			0.852982	+	0.521940i	$0.174792\pi$
$578$	272735.	+	86186.2i	0.816366	+	0.257978i
$579$		0			0
$580$	195759.	+	137448.i	0.581922	+	0.408585i
$581$	28360.8			0.0840169
$582$		0			0
$583$		−	76038.9i		−	0.223717i
$584$	246847.	+	322988.i	0.723773	+	0.947025i
$585$		0			0
$586$	−77903.4	−	24618.1i	−0.226862	−	0.0716900i
$587$		−	254380.i		−	0.738256i	−0.929379	−	0.369128i	$-0.879656\pi$
$587$		−	254380.i		−	0.738256i	0.929379	−	0.369128i	$-0.120344\pi$
$588$		0			0
$589$	−440212.			−1.26891
$590$	−29177.4	+	92331.3i	−0.0838190	+	0.265244i
$591$		0			0
$592$	−172936.	−	478977.i	−0.493449	−	1.36669i
$593$	522460.			1.48574			0.742871	−	0.669434i	$-0.233463\pi$
$593$	522460.			1.48574			0.742871	+	0.669434i	$0.233463\pi$
$594$		0			0
$595$			37274.9i			0.105289i
$596$	359361.	+	252318.i	1.01167	+	0.710323i
$597$		0			0
$598$	−125463.	+	397026.i	−0.350844	+	1.11024i
$599$		−	160888.i		−	0.448406i	−0.974543	−	0.224203i	$-0.928022\pi$
$599$		−	160888.i		−	0.448406i	0.974543	−	0.224203i	$-0.0719778\pi$
$600$		0			0
$601$	−305068.			−0.844594			−0.422297	−	0.906458i	$-0.638776\pi$
$601$	−305068.			−0.844594			−0.422297	+	0.906458i	$0.638776\pi$
$602$	−304660.	−	96274.9i	−0.840664	−	0.265656i
$603$		0			0
$604$	−46376.4	+	66051.0i	−0.127123	+	0.181053i
$605$	−179806.			−0.491239
$606$		0			0
$607$		−	68932.7i		−	0.187089i	−0.995615	−	0.0935444i	$-0.970180\pi$
$607$		−	68932.7i		−	0.187089i	0.995615	−	0.0935444i	$-0.0298197\pi$
$608$	−271089.	+	10960.8i	−0.733338	+	0.0296507i
$609$		0			0
$610$	77117.2	+	24369.6i	0.207249	+	0.0654921i
$611$			276039.i			0.739416i
$612$		0			0
$613$	−504419.			−1.34237			−0.671183	−	0.741292i	$-0.734213\pi$
$613$	−504419.			−1.34237			−0.671183	+	0.741292i	$0.734213\pi$
$614$	84677.8	−	267961.i	0.224612	−	0.710780i
$615$		0			0
$616$	−34318.5	−	44904.3i	−0.0904413	−	0.118338i
$617$	348479.			0.915391			0.457696	−	0.889109i	$-0.348675\pi$
$617$	348479.			0.915391			0.457696	+	0.889109i	$0.348675\pi$
$618$		0			0
$619$		−	311340.i		−	0.812557i	−0.913749	−	0.406278i	$-0.866826\pi$
$619$		−	311340.i		−	0.812557i	0.913749	−	0.406278i	$-0.133174\pi$
$620$	−204475.	+	291221.i	−0.531934	+	0.757600i
$621$		0			0
$622$	159712.	−	505406.i	0.412816	−	1.30635i
$623$			263837.i			0.679765i
$624$		0			0
$625$	86780.1			0.222157
$626$	365530.	+	115510.i	0.932769	+	0.294762i
$627$		0			0
$628$	−156341.	−	109771.i	−0.396417	−	0.278337i
$629$	218034.			0.551091
$630$		0			0
$631$		−	58353.5i		−	0.146558i	−0.997311	−	0.0732788i	$-0.976654\pi$
$631$		−	58353.5i		−	0.146558i	0.997311	−	0.0732788i	$-0.0233463\pi$
$632$	22675.0	−	17329.6i	0.0567692	−	0.0433864i
$633$		0			0
$634$	−350846.	−	110870.i	−0.872847	−	0.275826i
$635$		−	346940.i		−	0.860414i
$636$		0			0
$637$	205236.			0.505795
$638$	46788.7	−	148062.i	0.114948	−	0.363750i
$639$		0			0
$640$	−118668.	+	184429.i	−0.289716	+	0.450267i
$641$	42450.2			0.103315			0.0516575	−	0.998665i	$-0.483550\pi$
$641$	42450.2			0.103315			0.0516575	+	0.998665i	$0.483550\pi$
$642$		0			0
$643$			670263.i			1.62115i	0.585634	+	0.810575i	$0.300846\pi$
$643$			670263.i			1.62115i	−0.585634	+	0.810575i	$0.699154\pi$
$644$	296219.	+	207984.i	0.714234	+	0.501485i
$645$		0			0
$646$	35002.3	−	110764.i	0.0838748	−	0.265420i
$647$		−	524487.i		−	1.25293i	−0.779450	−	0.626465i	$-0.784501\pi$
$647$		−	524487.i		−	1.25293i	0.779450	−	0.626465i	$-0.215499\pi$
$648$		0			0
$649$	62861.0			0.149242
$650$	198795.	+	62820.6i	0.470520	+	0.148688i
$651$		0			0
$652$	223321.	−	318062.i	0.525332	−	0.748198i
$653$	−308366.			−0.723169			−0.361584	−	0.932339i	$-0.617764\pi$
$653$	−308366.			−0.723169			−0.361584	+	0.932339i	$0.617764\pi$
$654$		0			0
$655$			205258.i			0.478430i
$656$	106869.	+	295992.i	0.248338	+	0.687815i
$657$		0			0
$658$	228800.	+	72302.4i	0.528449	+	0.166994i
$659$			569201.i			1.31068i	0.755336	+	0.655338i	$0.227474\pi$
$659$			569201.i			1.31068i	−0.755336	+	0.655338i	$0.772526\pi$
$660$		0			0
$661$	218315.			0.499667			0.249833	−	0.968289i	$-0.419624\pi$
$661$	218315.			0.499667			0.249833	+	0.968289i	$0.419624\pi$
$662$	131735.	−	416874.i	0.300598	−	0.951236i
$663$		0			0
$664$	−56763.5	+	43382.1i	−0.128746	+	0.0983952i
$665$	−90103.2			−0.203750
$666$		0			0
$667$			994432.i			2.23524i
$668$	−132403.	+	188573.i	−0.296719	+	0.422598i
$669$		0			0
$670$	84769.8	−	268252.i	0.188839	−	0.597577i
$671$		−	52503.0i		−	0.116611i
$672$		0			0
$673$	417495.			0.921768			0.460884	−	0.887460i	$-0.347532\pi$
$673$	417495.			0.921768			0.460884	+	0.887460i	$0.347532\pi$
$674$	−758025.	−	239541.i	−1.66864	−	0.527304i
$675$		0			0
$676$	−195023.	−	136931.i	−0.426768	−	0.299647i
$677$	−904642.			−1.97378			−0.986891	−	0.161385i	$-0.948404\pi$
$677$	−904642.			−1.97378			−0.986891	+	0.161385i	$0.948404\pi$
$678$		0			0
$679$			12063.3i			0.0261654i
$680$	−57017.4	−	74604.8i	−0.123308	−	0.161342i
$681$		0			0
$682$	220265.	+	69605.5i	0.473563	+	0.149649i
$683$		−	382473.i		−	0.819897i	−0.912109	−	0.409948i	$-0.865547\pi$
$683$		−	382473.i		−	0.819897i	0.912109	−	0.409948i	$-0.134453\pi$
$684$		0			0
$685$	391084.			0.833467
$686$	127279.	−	402773.i	0.270464	−	0.855880i
$687$		0			0
$688$	757036.	−	273330.i	1.59934	−	0.577446i
$689$	255755.			0.538748
$690$		0			0
$691$			248456.i			0.520348i	0.965562	+	0.260174i	$0.0837799\pi$
$691$			248456.i			0.520348i	−0.965562	+	0.260174i	$0.916220\pi$
$692$	−471217.	−	330856.i	−0.984031	−	0.690918i
$693$		0			0
$694$	−201677.	+	638202.i	−0.418733	+	1.32507i
$695$		−	362371.i		−	0.750213i
$696$		0			0
$697$	−134738.			−0.277347
$698$	−718465.	−	227040.i	−1.47467	−	0.466007i
$699$		0			0
$700$	104140.	−	148320.i	0.212530	−	0.302693i
$701$	689676.			1.40349			0.701744	−	0.712429i	$-0.252405\pi$
$701$	689676.			1.40349			0.701744	+	0.712429i	$0.252405\pi$
$702$		0			0
$703$			527046.i			1.06644i
$704$	137375.	+	37379.6i	0.277181	+	0.0754205i
$705$		0			0
$706$	−438764.	−	138653.i	−0.880281	−	0.278176i
$707$		−	401041.i		−	0.802325i
$708$		0			0
$709$	511438.			1.01742			0.508711	−	0.860938i	$-0.330122\pi$
$709$	511438.			1.01742			0.508711	+	0.860938i	$0.330122\pi$
$710$	−18228.3	+	57683.1i	−0.0361601	+	0.114428i
$711$		0			0
$712$	−403577.	−	528063.i	−0.796098	−	1.04166i
$713$	−1.47937e6			−2.91004
$714$		0			0
$715$			54392.6i			0.106397i
$716$	38816.9	−	55284.4i	0.0757172	−	0.107839i
$717$		0			0
$718$	141339.	−	447265.i	0.274166	−	0.867593i
$719$		−	84661.7i		−	0.163768i	−0.996642	−	0.0818841i	$-0.973906\pi$
$719$		−	84661.7i		−	0.163768i	0.996642	−	0.0818841i	$-0.0260937\pi$
$720$		0			0
$721$	−96155.7			−0.184971
$722$	−229310.	−	72463.8i	−0.439895	−	0.139010i
$723$		0			0
$724$	247251.	+	173602.i	0.471694	+	0.331191i
$725$	497922.			0.947295
$726$		0			0
$727$			677593.i			1.28203i	0.767526	+	0.641017i	$0.221487\pi$
$727$			677593.i			1.28203i	−0.767526	+	0.641017i	$0.778513\pi$
$728$	151034.	−	115429.i	0.284979	−	0.217798i
$729$		0			0
$730$	−324283.	−	102476.i	−0.608524	−	0.192298i
$731$			344609.i			0.644900i
$732$		0			0
$733$	523901.			0.975083			0.487542	−	0.873100i	$-0.337894\pi$
$733$	523901.			0.975083			0.487542	+	0.873100i	$0.337894\pi$
$734$	317089.	−	1.00342e6i	0.588557	−	1.86248i
$735$		0			0
$736$	−911017.	+	36834.7i	−1.68179	+	0.0679989i
$737$	−182632.			−0.336234
$738$		0			0
$739$		−	603562.i		−	1.10518i	−0.833453	−	0.552590i	$-0.813640\pi$
$739$		−	603562.i		−	1.10518i	0.833453	−	0.552590i	$-0.186360\pi$
$740$	348666.	+	244809.i	0.636717	+	0.447059i
$741$		0			0
$742$	66989.3	−	211986.i	0.121674	−	0.385035i
$743$		−	55911.8i		−	0.101280i	−0.998717	−	0.0506402i	$-0.983874\pi$
$743$		−	55911.8i		−	0.101280i	0.998717	−	0.0506402i	$-0.0161262\pi$
$744$		0			0
$745$	−367345.			−0.661853
$746$	131641.	+	41599.4i	0.236544	+	0.0747498i
$747$		0			0
$748$	−35027.6	+	49887.6i	−0.0626047	+	0.0891639i
$749$	312535.			0.557102
$750$		0			0
$751$		−	55305.5i		−	0.0980593i	−0.998797	−	0.0490297i	$-0.984387\pi$
$751$		−	55305.5i		−	0.0980593i	0.998797	−	0.0490297i	$-0.0156129\pi$
$752$	−568534.	+	205271.i	−1.00536	+	0.362988i
$753$		0			0
$754$	498003.	+	157373.i	0.875969	+	0.276813i
$755$		−	67518.4i		−	0.118448i
$756$		0			0
$757$	−813185.			−1.41905			−0.709525	−	0.704680i	$-0.751090\pi$
$757$	−813185.			−1.41905			−0.709525	+	0.704680i	$0.751090\pi$
$758$	183741.	−	581444.i	0.319791	−	1.01197i
$759$		0			0
$760$	180339.	−	137826.i	0.312222	−	0.238619i
$761$	84610.9			0.146102			0.0730512	−	0.997328i	$-0.476726\pi$
$761$	84610.9			0.146102			0.0730512	+	0.997328i	$0.476726\pi$
$762$		0			0
$763$			13488.9i			0.0231701i
$764$	−622761.	+	886959.i	−1.06693	+	1.51956i
$765$		0			0
$766$	186128.	−	588998.i	0.317215	−	1.00382i
$767$			211431.i			0.359400i
$768$		0			0
$769$	499058.			0.843914			0.421957	−	0.906616i	$-0.361343\pi$
$769$	499058.			0.843914			0.421957	+	0.906616i	$0.361343\pi$
$770$	45084.2	+	14246.9i	0.0760401	+	0.0240292i
$771$		0			0
$772$	−693803.	−	487140.i	−1.16413	−	0.817372i
$773$	149060.			0.249460			0.124730	−	0.992191i	$-0.460194\pi$
$773$	149060.			0.249460			0.124730	+	0.992191i	$0.460194\pi$
$774$		0			0
$775$			740736.i			1.23328i
$776$	−18452.6	−	24144.5i	−0.0306432	−	0.0400953i
$777$		0			0
$778$	−419263.	−	132490.i	−0.692672	−	0.218890i
$779$		−	325697.i		−	0.536709i
$780$		0			0
$781$	39271.8			0.0643842
$782$	117628.	−	372232.i	0.192353	−	0.608696i
$783$		0			0
$784$	152620.	+	422707.i	0.248301	+	0.687713i
$785$	159814.			0.259344
$786$		0			0
$787$			217138.i			0.350579i	0.984517	+	0.175289i	$0.0560861\pi$
$787$			217138.i			0.350579i	−0.984517	+	0.175289i	$0.943914\pi$
$788$	510782.	+	358636.i	0.822590	+	0.577565i
$789$		0			0
$790$	−7194.18	+	22765.8i	−0.0115273	+	0.0364779i
$791$		−	280675.i		−	0.448591i
$792$		0			0
$793$	176592.			0.280818
$794$	565541.	+	178715.i	0.897064	+	0.283479i
$795$		0			0
$796$	540829.	−	770268.i	0.853559	−	1.21567i
$797$	−459700.			−0.723699			−0.361849	−	0.932237i	$-0.617855\pi$
$797$	−459700.			−0.723699			−0.361849	+	0.932237i	$0.617855\pi$
$798$		0			0
$799$		−	258801.i		−	0.405390i
$800$	18443.5	+	456155.i	0.0288180	+	0.712742i
$801$		0			0
$802$	−550086.	−	173831.i	−0.855227	−	0.270258i
$803$			220778.i			0.342393i
$804$		0			0
$805$	−302800.			−0.467265
$806$	−234116.	+	740856.i	−0.360380	+	1.14042i
$807$		0			0
$808$	613452.	+	802675.i	0.939632	+	1.22947i
$809$	578149.			0.883371			0.441685	−	0.897170i	$-0.354381\pi$
$809$	578149.			0.883371			0.441685	+	0.897170i	$0.354381\pi$
$810$		0			0
$811$		−	433798.i		−	0.659547i	−0.944060	−	0.329774i	$-0.893028\pi$
$811$		−	433798.i		−	0.659547i	0.944060	−	0.329774i	$-0.106972\pi$
$812$	260881.	−	371557.i	0.395668	−	0.563525i
$813$		0			0
$814$	83335.5	−	263714.i	0.125771	−	0.398001i
$815$			325128.i			0.489485i
$816$		0			0
$817$	−833012.			−1.24798
$818$	−206353.	−	65209.0i	−0.308392	−	0.0974542i
$819$		0			0
$820$	−215464.	−	151284.i	−0.320440	−	0.224991i
$821$	−545456.			−0.809233			−0.404616	−	0.914487i	$-0.632595\pi$
$821$	−545456.			−0.809233			−0.404616	+	0.914487i	$0.632595\pi$
$822$		0			0
$823$		−	706175.i		−	1.04259i	−0.853377	−	0.521294i	$-0.825450\pi$
$823$		−	706175.i		−	1.04259i	0.853377	−	0.521294i	$-0.174550\pi$
$824$	192453.	−	147084.i	0.283446	−	0.216627i
$825$		0			0
$826$	175248.	+	55379.7i	0.256858	+	0.0811690i
$827$			485600.i			0.710015i	0.934863	+	0.355008i	$0.115522\pi$
$827$			485600.i			0.710015i	−0.934863	+	0.355008i	$0.884478\pi$
$828$		0			0
$829$	−1.22839e6			−1.78743			−0.893714	−	0.448636i	$-0.851910\pi$
$829$	−1.22839e6			−1.78743			−0.893714	+	0.448636i	$0.851910\pi$
$830$	18009.6	−	56991.0i	0.0261425	−	0.0827275i
$831$		0			0
$832$	−125725.	+	462058.i	−0.181625	+	0.667498i
$833$	−192420.			−0.277306
$834$		0			0
$835$		−	192763.i		−	0.276471i
$836$	−120591.	−	84670.9i	−0.172546	−	0.121150i
$837$		0			0
$838$	−341303.	+	1.08005e6i	−0.486018	+	1.53799i
$839$		−	1.04043e6i		−	1.47805i	−0.673678	−	0.739025i	$-0.735287\pi$
$839$		−	1.04043e6i		−	1.47805i	0.673678	−	0.739025i	$-0.264713\pi$
$840$		0			0
$841$	540068.			0.763584
$842$	−8922.30	−	2819.51i	−0.0125850	−	0.00397695i
$843$		0			0
$844$	−75528.6	+	107571.i	−0.106030	+	0.151011i
$845$	199356.			0.279200
$846$		0			0
$847$			341278.i			0.475708i
$848$	190187.	+	526756.i	0.264478	+	0.732517i
$849$		0			0
$850$	−186380.	−	58897.6i	−0.257966	−	0.0815192i
$851$			1.77119e6i			2.44571i
$852$		0			0
$853$	979792.			1.34659			0.673295	−	0.739374i	$-0.264878\pi$
$853$	979792.			1.34659			0.673295	+	0.739374i	$0.264878\pi$
$854$	46254.4	−	146371.i	0.0634216	−	0.200696i
$855$		0			0
$856$	−625531.	+	478068.i	−0.853692	+	0.652442i
$857$	1.20931e6			1.64656			0.823279	−	0.567637i	$-0.192142\pi$
$857$	1.20931e6			1.64656			0.823279	+	0.567637i	$0.192142\pi$
$858$		0			0
$859$		−	989256.i		−	1.34067i	−0.742058	−	0.670336i	$-0.766150\pi$
$859$		−	989256.i		−	1.34067i	0.742058	−	0.670336i	$-0.233850\pi$
$860$	−386928.	+	551077.i	−0.523158	+	0.745101i
$861$		0			0
$862$	302386.	−	956894.i	0.406955	−	1.28780i
$863$		−	617696.i		−	0.829379i	−0.909963	−	0.414690i	$-0.863890\pi$
$863$		−	617696.i		−	0.829379i	0.909963	−	0.414690i	$-0.136110\pi$
$864$		0			0
$865$	481686.			0.643772
$866$	108862.	+	34401.3i	0.145158	+	0.0458711i
$867$		0			0
$868$	552748.	+	388101.i	0.733648	+	0.515117i
$869$	15499.4			0.0205247
$870$		0			0
$871$		−	614276.i		−	0.809706i
$872$	−20633.3	−	26997.8i	−0.0271354	−	0.0355054i
$873$		0			0
$874$	899784.	+	284338.i	1.17792	+	0.372231i
$875$			364161.i			0.475639i
$876$		0			0
$877$	339273.			0.441114			0.220557	−	0.975374i	$-0.429213\pi$
$877$	339273.			0.441114			0.220557	+	0.975374i	$0.429213\pi$
$878$	−246145.	+	778921.i	−0.319302	+	1.01043i
$879$		0			0
$880$	−112028.	+	40448.0i	−0.144664	+	0.0522314i
$881$	−504812.			−0.650396			−0.325198	−	0.945646i	$-0.605431\pi$
$881$	−504812.			−0.650396			−0.325198	+	0.945646i	$0.605431\pi$
$882$		0			0
$883$			230755.i			0.295957i	0.988991	+	0.147979i	$0.0472767\pi$
$883$			230755.i			0.295957i	−0.988991	+	0.147979i	$0.952723\pi$
$884$	−167795.	−	117814.i	−0.214722	−	0.150762i
$885$		0			0
$886$	−385372.	+	1.21950e6i	−0.490923	+	1.55352i
$887$		−	558777.i		−	0.710218i	−0.934825	−	0.355109i	$-0.884444\pi$
$887$		−	558777.i		−	0.710218i	0.934825	−	0.355109i	$-0.115556\pi$
$888$		0			0
$889$	−658505.			−0.833211
$890$	530178.	+	167540.i	0.669333	+	0.211514i
$891$		0			0
$892$	335758.	−	478200.i	0.421985	−	0.601007i
$893$	625591.			0.784491
$894$		0			0
$895$			56512.7i			0.0705504i
$896$	350053.	+	225235.i	0.436031	+	0.280556i
$897$		0			0
$898$	1.24141e6	+	392296.i	1.53944	+	0.486475i
$899$			1.85563e6i			2.29600i
$900$		0			0
$901$	−239783.			−0.295372
$902$	−51498.5	+	162966.i	−0.0632968	+	0.200302i
$903$		0			0
$904$	429334.	+	561765.i	0.525362	+	0.687413i
$905$	−252744.			−0.308591
$906$		0			0
$907$			89214.6i			0.108448i	0.998529	+	0.0542240i	$0.0172685\pi$
$907$			89214.6i			0.108448i	−0.998529	+	0.0542240i	$0.982732\pi$
$908$	768146.	−	1.09402e6i	0.931691	−	1.32695i
$909$		0			0
$910$	−47919.2	+	151639.i	−0.0578664	+	0.183117i
$911$			228071.i			0.274810i	0.990515	+	0.137405i	$0.0438762\pi$
$911$			228071.i			0.274810i	−0.990515	+	0.137405i	$0.956124\pi$
$912$		0			0
$913$	−38800.6			−0.0465475
$914$	−4150.15	−	1311.48i	−0.00496788	−	0.00156989i
$915$		0			0
$916$	−116312.	−	81666.0i	−0.138622	−	0.0973309i
$917$	389587.			0.463304
$918$		0			0
$919$		−	309892.i		−	0.366926i	−0.983027	−	0.183463i	$-0.941269\pi$
$919$		−	309892.i		−	0.366926i	0.983027	−	0.183463i	$-0.0587308\pi$
$920$	606046.	−	463177.i	0.716028	−	0.547231i
$921$		0			0
$922$	−486705.	−	153802.i	−0.572538	−	0.180926i
$923$			132090.i			0.155048i
$924$		0			0
$925$	886850.			1.03649
$926$	−144063.	+	455884.i	−0.168008	+	0.531658i
$927$		0			0
$928$	46203.0	+	1.14272e6i	0.0536506	+	1.32692i
$929$	−499855.			−0.579178			−0.289589	−	0.957151i	$-0.593519\pi$
$929$	−499855.			−0.579178			−0.289589	+	0.957151i	$0.593519\pi$
$930$		0			0
$931$		−	465129.i		−	0.536629i
$932$	68608.8	+	48172.3i	0.0789856	+	0.0554582i
$933$		0			0
$934$	−423960.	+	1.34161e6i	−0.485995	+	1.53792i
$935$		−	50995.9i		−	0.0583327i
$936$		0			0
$937$	714133.			0.813392			0.406696	−	0.913564i	$-0.366681\pi$
$937$	714133.			0.813392			0.406696	+	0.913564i	$0.366681\pi$
$938$	−509152.	−	160896.i	−0.578685	−	0.182869i
$939$		0			0
$940$	290583.	−	413858.i	0.328862	−	0.468378i
$941$	816785.			0.922420			0.461210	−	0.887291i	$-0.347416\pi$
$941$	816785.			0.922420			0.461210	+	0.887291i	$0.347416\pi$
$942$		0			0
$943$		−	1.09453e6i		−	1.23085i
$944$	−435466.	+	157226.i	−0.488664	+	0.176434i
$945$		0			0
$946$	416807.	+	131714.i	0.465750	+	0.147180i
$947$		−	44436.8i		−	0.0495499i	−0.999693	−	0.0247750i	$-0.992113\pi$
$947$		−	44436.8i		−	0.0495499i	0.999693	−	0.0247750i	$-0.00788692\pi$
$948$		0			0
$949$	−742581.			−0.824539
$950$	142371.	−	450531.i	0.157752	−	0.499203i
$951$		0			0
$952$	−141602.	+	108221.i	−0.156242	+	0.119409i
$953$	517187.			0.569458			0.284729	−	0.958608i	$-0.408096\pi$
$953$	517187.			0.569458			0.284729	+	0.958608i	$0.408096\pi$
$954$		0			0
$955$		−	906665.i		−	0.994123i
$956$	−46260.5	+	65886.0i	−0.0506168	+	0.0720903i
$957$		0			0
$958$	−53879.8	+	170502.i	−0.0587076	+	0.185779i
$959$		−	742290.i		−	0.807117i
$960$		0			0
$961$	−1.83701e6			−1.98914
$962$	886994.	+	280297.i	0.958452	+	0.302878i
$963$		0			0
$964$	495874.	+	348168.i	0.533602	+	0.374658i
$965$	709218.			0.761597
$966$		0			0
$967$			1.15608e6i			1.23633i	0.786048	+	0.618166i	$0.212124\pi$
$967$			1.15608e6i			1.23633i	−0.786048	+	0.618166i	$0.787876\pi$
$968$	−522034.	−	683059.i	−0.557119	−	0.728966i
$969$		0			0
$970$	24241.2	+	7660.40i	0.0257638	+	0.00814157i
$971$		−	1.31116e6i		−	1.39064i	−0.718699	−	0.695322i	$-0.755262\pi$
$971$		−	1.31116e6i		−	1.39064i	0.718699	−	0.695322i	$-0.244738\pi$
$972$		0			0
$973$	−687793.			−0.726494
$974$	−206522.	+	653534.i	−0.217695	+	0.688891i
$975$		0			0
$976$	131319.	+	363711.i	0.137857	+	0.381819i
$977$	−1.03691e6			−1.08631			−0.543154	−	0.839633i	$-0.682770\pi$
$977$	−1.03691e6			−1.08631			−0.543154	+	0.839633i	$0.682770\pi$
$978$		0			0
$979$		−	360956.i		−	0.376608i
$980$	−307705.	−	216049.i	−0.320392	−	0.224957i
$981$		0			0
$982$	239748.	−	758679.i	0.248618	−	0.786747i
$983$		−	614380.i		−	0.635814i	−0.948122	−	0.317907i	$-0.897020\pi$
$983$		−	614380.i		−	0.635814i	0.948122	−	0.317907i	$-0.102980\pi$
$984$		0			0
$985$	−522130.			−0.538154
$986$	−466903.	−	147545.i	−0.480256	−	0.151765i
$987$		0			0
$988$	284788.	−	405606.i	0.291748	−	0.415518i
$989$	−2.79941e6			−2.86203
$990$		0			0
$991$		−	1.50218e6i		−	1.52959i	−0.644273	−	0.764795i	$-0.722840\pi$
$991$		−	1.50218e6i		−	1.52959i	0.644273	−	0.764795i	$-0.277160\pi$
$992$	−1.69997e6	+	68734.2i	−1.72750	+	0.0698472i
$993$		0			0
$994$	109485.	+	34598.0i	0.110810	+	0.0350169i
$995$			787382.i			0.795315i
$996$		0			0
$997$	1.10845e6			1.11513			0.557567	−	0.830132i	$-0.311735\pi$
$997$	1.10845e6			1.11513			0.557567	+	0.830132i	$0.311735\pi$
$998$	−138529.	+	438373.i	−0.139085	+	0.440132i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.d.a.55.1	✓	16
3.2	odd	2	inner	108.5.d.a.55.16	yes	16
4.3	odd	2	inner	108.5.d.a.55.2	yes	16
12.11	even	2	inner	108.5.d.a.55.15	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.5.d.a.55.1	✓	16	1.1	even	1	trivial
108.5.d.a.55.2	yes	16	4.3	odd	2	inner
108.5.d.a.55.15	yes	16	12.11	even	2	inner
108.5.d.a.55.16	yes	16	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.81409 - 1.20528i) q^{2} +(13.0946 + 9.19411i) q^{4} -13.3855 q^{5} +25.4062i q^{7} +(-38.8625 - 50.8499i) q^{8} +O(q^{10})\)	\(q+(-3.81409 - 1.20528i) q^{2} +(13.0946 + 9.19411i) q^{4} -13.3855 q^{5} +25.4062i q^{7} +(-38.8625 - 50.8499i) q^{8} +(51.0536 + 16.1333i) q^{10} -34.7583i q^{11} +116.909 q^{13} +(30.6216 - 96.9015i) q^{14} +(86.9367 + 240.786i) q^{16} -109.608 q^{17} -264.951i q^{19} +(-175.278 - 123.068i) q^{20} +(-41.8936 + 132.571i) q^{22} -890.392i q^{23} -445.828 q^{25} +(-445.900 - 140.908i) q^{26} +(-233.587 + 332.683i) q^{28} -1116.85 q^{29} -1661.48i q^{31} +(-41.3691 - 1023.16i) q^{32} +(418.055 + 132.108i) q^{34} -340.075i q^{35} -1989.22 q^{37} +(-319.341 + 1010.55i) q^{38} +(520.194 + 680.652i) q^{40} +1229.27 q^{41} -3144.02i q^{43} +(319.572 - 455.146i) q^{44} +(-1073.17 + 3396.04i) q^{46} +2361.16i q^{47} +1755.53 q^{49} +(1700.43 + 537.348i) q^{50} +(1530.87 + 1074.87i) q^{52} +2187.65 q^{53} +465.258i q^{55} +(1291.90 - 987.347i) q^{56} +(4259.76 + 1346.12i) q^{58} +1808.52i q^{59} +1510.52 q^{61} +(-2002.56 + 6337.06i) q^{62} +(-1075.42 + 3952.30i) q^{64} -1564.88 q^{65} -5254.33i q^{67} +(-1435.27 - 1007.75i) q^{68} +(-409.886 + 1297.08i) q^{70} +1129.85i q^{71} -6351.81 q^{73} +(7587.07 + 2397.57i) q^{74} +(2435.99 - 3469.43i) q^{76} +883.075 q^{77} +445.921i q^{79} +(-1163.69 - 3223.05i) q^{80} +(-4688.55 - 1481.62i) q^{82} -1116.30i q^{83} +1467.16 q^{85} +(-3789.43 + 11991.6i) q^{86} +(-1767.45 + 1350.79i) q^{88} +10384.7 q^{89} +2970.20i q^{91} +(8186.36 - 11659.3i) q^{92} +(2845.86 - 9005.67i) q^{94} +3546.51i q^{95} +474.819 q^{97} +(-6695.74 - 2115.90i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 14 q^{4}+O(q^{10}) \) 16 * q - 14 * q^4	\( 16 q - 14 q^{4} - 202 q^{10} - 352 q^{13} - 206 q^{16} + 738 q^{22} + 1632 q^{25} + 342 q^{28} - 2536 q^{34} + 3200 q^{37} - 2854 q^{40} + 36 q^{46} - 896 q^{49} + 2288 q^{52} + 2492 q^{58} - 2752 q^{61} + 682 q^{64} - 14166 q^{70} + 8240 q^{73} - 33084 q^{76} + 68 q^{82} + 8800 q^{85} + 48294 q^{88} + 52596 q^{94} - 6928 q^{97}+O(q^{100}) \) 16 * q - 14 * q^4 - 202 * q^10 - 352 * q^13 - 206 * q^16 + 738 * q^22 + 1632 * q^25 + 342 * q^28 - 2536 * q^34 + 3200 * q^37 - 2854 * q^40 + 36 * q^46 - 896 * q^49 + 2288 * q^52 + 2492 * q^58 - 2752 * q^61 + 682 * q^64 - 14166 * q^70 + 8240 * q^73 - 33084 * q^76 + 68 * q^82 + 8800 * q^85 + 48294 * q^88 + 52596 * q^94 - 6928 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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