LMFDB - Embedded newform 108.6.b.b.107.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,6,Mod(107,108)]

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, 1]))

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

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

chi := DirichletCharacter("108.107");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	108.b (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:	$17.3214525398$
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} + 30x^{14} + 619x^{12} + 5604x^{10} + 40971x^{8} - 4866x^{6} + 568069x^{4} - 7909632x^{2} + 20340100 $ x^16 + 30x^14 + 619x^12 + 5604x^10 + 40971x^8 - 4866x^6 + 568069x^4 - 7909632*x^2 + 20340100
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{30}\cdot 3^{32}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			107.9
Root			$-1.73205 - 1.98106i$ of defining polynomial
Character	$\chi$	$=$	108.107
Dual form			108.6.b.b.107.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.79734 - 5.36373i) q^{2} +(-25.5392 - 19.2809i) q^{4} +44.9719i q^{5} +28.5094i q^{7} +(-149.320 + 102.331i) q^{8} +O(q^{10})$	\(q+(1.79734 - 5.36373i) q^{2} +(-25.5392 - 19.2809i) q^{4} +44.9719i q^{5} +28.5094i q^{7} +(-149.320 + 102.331i) q^{8} +(241.217 + 80.8297i) q^{10} +411.905 q^{11} +684.385 q^{13} +(152.917 + 51.2411i) q^{14} +(280.497 + 984.834i) q^{16} -1516.97i q^{17} +2045.09i q^{19} +(867.098 - 1148.55i) q^{20} +(740.332 - 2209.34i) q^{22} +3070.67 q^{23} +1102.53 q^{25} +(1230.07 - 3670.85i) q^{26} +(549.686 - 728.107i) q^{28} -643.596i q^{29} -731.030i q^{31} +(5786.53 + 265.570i) q^{32} +(-8136.61 - 2726.51i) q^{34} -1282.12 q^{35} -5461.90 q^{37} +(10969.3 + 3675.71i) q^{38} +(-4602.02 - 6715.20i) q^{40} -6382.62i q^{41} +17907.2i q^{43} +(-10519.7 - 7941.88i) q^{44} +(5519.03 - 16470.2i) q^{46} +19287.6 q^{47} +15994.2 q^{49} +(1981.61 - 5913.65i) q^{50} +(-17478.6 - 13195.5i) q^{52} -11400.4i q^{53} +18524.2i q^{55} +(-2917.39 - 4257.02i) q^{56} +(-3452.07 - 1156.76i) q^{58} -424.395 q^{59} -6907.86 q^{61} +(-3921.05 - 1313.91i) q^{62} +(11824.8 - 30560.0i) q^{64} +30778.1i q^{65} +58593.9i q^{67} +(-29248.5 + 38742.1i) q^{68} +(-2304.41 + 6876.97i) q^{70} -49133.0 q^{71} +70200.7 q^{73} +(-9816.87 + 29296.1i) q^{74} +(39431.1 - 52229.8i) q^{76} +11743.2i q^{77} +95223.5i q^{79} +(-44289.9 + 12614.5i) q^{80} +(-34234.6 - 11471.7i) q^{82} -55856.8 q^{83} +68221.1 q^{85} +(96049.4 + 32185.3i) q^{86} +(-61505.5 + 42150.6i) q^{88} +93780.9i q^{89} +19511.4i q^{91} +(-78422.3 - 59205.1i) q^{92} +(34666.3 - 103453. i) q^{94} -91971.6 q^{95} -182666. q^{97} +(28747.0 - 85788.6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 94 q^{4}+O(q^{10}) $ 16 * q + 94 * q^4	$ 16 q + 94 q^{4} + 1454 q^{10} + 896 q^{13} + 178 q^{16} + 30 q^{22} + 9888 q^{25} + 11454 q^{28} - 6172 q^{34} - 71008 q^{37} - 16618 q^{40} + 35304 q^{46} - 49376 q^{49} + 14876 q^{52} - 10492 q^{58} + 77888 q^{61} + 89206 q^{64} + 229398 q^{70} - 38032 q^{73} + 48960 q^{76} - 224488 q^{82} - 371264 q^{85} + 249102 q^{88} + 68772 q^{94} - 976 q^{97}+O(q^{100}) $ 16 * q + 94 * q^4 + 1454 * q^10 + 896 * q^13 + 178 * q^16 + 30 * q^22 + 9888 * q^25 + 11454 * q^28 - 6172 * q^34 - 71008 * q^37 - 16618 * q^40 + 35304 * q^46 - 49376 * q^49 + 14876 * q^52 - 10492 * q^58 + 77888 * q^61 + 89206 * q^64 + 229398 * q^70 - 38032 * q^73 + 48960 * q^76 - 224488 * q^82 - 371264 * q^85 + 249102 * q^88 + 68772 * q^94 - 976 * 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 $

$2$	1.79734	−	5.36373i	0.317727	−	0.948182i
$2$	1.79734	−	5.36373i	0.317727	−	0.948182i
$3$		0			0
$3$		0			0
$4$	−25.5392	−	19.2809i	−0.798099	−	0.602527i
$5$			44.9719i			0.804482i	0.915534	+	0.402241i	$0.131769\pi$
$5$			44.9719i			0.804482i	−0.915534	+	0.402241i	$0.868231\pi$
$6$		0			0
$7$			28.5094i			0.219909i	0.993937	+	0.109955i	$0.0350706\pi$
$7$			28.5094i			0.219909i	−0.993937	+	0.109955i	$0.964929\pi$
$8$	−149.320	+	102.331i	−0.824883	+	0.565303i
$9$		0			0
$10$	241.217	+	80.8297i	0.762796	+	0.255606i
$11$	411.905			1.02640			0.513198	−	0.858270i	$-0.328461\pi$
$11$	411.905			1.02640			0.513198	+	0.858270i	$0.328461\pi$
$12$		0			0
$13$	684.385			1.12316			0.561580	−	0.827422i	$-0.310194\pi$
$13$	684.385			1.12316			0.561580	+	0.827422i	$0.310194\pi$
$14$	152.917	+	51.2411i	0.208514	+	0.0698712i
$15$		0			0
$16$	280.497	+	984.834i	0.273923	+	0.961752i
$17$		−	1516.97i		−	1.27308i	−0.771245	−	0.636538i	$-0.780366\pi$
$17$		−	1516.97i		−	1.27308i	0.771245	−	0.636538i	$-0.219634\pi$
$18$		0			0
$19$			2045.09i			1.29966i	0.760082	+	0.649828i	$0.225159\pi$
$19$			2045.09i			1.29966i	−0.760082	+	0.649828i	$0.774841\pi$
$20$	867.098	−	1148.55i	0.484722	−	0.642056i
$21$		0			0
$22$	740.332	−	2209.34i	0.326114	−	0.973211i
$23$	3070.67			1.21036			0.605178	−	0.796090i	$-0.293102\pi$
$23$	3070.67			1.21036			0.605178	+	0.796090i	$0.293102\pi$
$24$		0			0
$25$	1102.53			0.352808
$26$	1230.07	−	3670.85i	0.356859	−	1.06496i
$27$		0			0
$28$	549.686	−	728.107i	0.132501	−	0.175509i
$29$		−	643.596i		−	0.142108i	−0.997472	−	0.0710539i	$-0.977364\pi$
$29$		−	643.596i		−	0.142108i	0.997472	−	0.0710539i	$-0.0226362\pi$
$30$		0			0
$31$		−	731.030i		−	0.136625i	−0.997664	−	0.0683126i	$-0.978238\pi$
$31$		−	731.030i		−	0.136625i	0.997664	−	0.0683126i	$-0.0217615\pi$
$32$	5786.53	+	265.570i	0.998949	+	0.0458464i
$33$		0			0
$34$	−8136.61	−	2726.51i	−1.20711	−	0.404491i
$35$	−1282.12			−0.176913
$36$		0			0
$37$	−5461.90			−0.655902			−0.327951	−	0.944695i	$-0.606358\pi$
$37$	−5461.90			−0.655902			−0.327951	+	0.944695i	$0.606358\pi$
$38$	10969.3	+	3675.71i	1.23231	+	0.412936i
$39$		0			0
$40$	−4602.02	−	6715.20i	−0.454777	−	0.663604i
$41$		−	6382.62i		−	0.592979i	−0.955036	−	0.296490i	$-0.904184\pi$
$41$		−	6382.62i		−	0.592979i	0.955036	−	0.296490i	$-0.0958160\pi$
$42$		0			0
$43$			17907.2i			1.47692i	0.674297	+	0.738460i	$0.264447\pi$
$43$			17907.2i			1.47692i	−0.674297	+	0.738460i	$0.735553\pi$
$44$	−10519.7	−	7941.88i	−0.819165	−	0.618431i
$45$		0			0
$46$	5519.03	−	16470.2i	0.384564	−	1.14764i
$47$	19287.6			1.27360			0.636801	−	0.771029i	$-0.280257\pi$
$47$	19287.6			1.27360			0.636801	+	0.771029i	$0.280257\pi$
$48$		0			0
$49$	15994.2			0.951640
$50$	1981.61	−	5913.65i	0.112097	−	0.334526i
$51$		0			0
$52$	−17478.6	−	13195.5i	−0.896393	−	0.676734i
$53$		−	11400.4i		−	0.557483i	−0.960366	−	0.278741i	$-0.910083\pi$
$53$		−	11400.4i		−	0.557483i	0.960366	−	0.278741i	$-0.0899172\pi$
$54$		0			0
$55$			18524.2i			0.825718i
$56$	−2917.39	−	4257.02i	−0.124315	−	0.181399i
$57$		0			0
$58$	−3452.07	−	1156.76i	−0.134744	−	0.0451516i
$59$	−424.395			−0.0158723			−0.00793616	−	0.999969i	$-0.502526\pi$
$59$	−424.395			−0.0158723			−0.00793616	+	0.999969i	$0.502526\pi$
$60$		0			0
$61$	−6907.86			−0.237695			−0.118847	−	0.992913i	$-0.537920\pi$
$61$	−6907.86			−0.237695			−0.118847	+	0.992913i	$0.537920\pi$
$62$	−3921.05	−	1313.91i	−0.129546	−	0.0434096i
$63$		0			0
$64$	11824.8	−	30560.0i	0.360864	−	0.932618i
$65$			30778.1i			0.903563i
$66$		0			0
$67$			58593.9i			1.59465i	0.603549	+	0.797326i	$0.293753\pi$
$67$			58593.9i			1.59465i	−0.603549	+	0.797326i	$0.706247\pi$
$68$	−29248.5	+	38742.1i	−0.767063	+	1.01604i
$69$		0			0
$70$	−2304.41	+	6876.97i	−0.0562101	+	0.167746i
$71$	−49133.0			−1.15672			−0.578359	−	0.815782i	$-0.696307\pi$
$71$	−49133.0			−1.15672			−0.578359	+	0.815782i	$0.696307\pi$
$72$		0			0
$73$	70200.7			1.54182			0.770911	−	0.636943i	$-0.219801\pi$
$73$	70200.7			1.54182			0.770911	+	0.636943i	$0.219801\pi$
$74$	−9816.87	+	29296.1i	−0.208398	+	0.621915i
$75$		0			0
$76$	39431.1	−	52229.8i	0.783077	−	1.03725i
$77$			11743.2i			0.225714i
$78$		0			0
$79$			95223.5i			1.71663i	0.513124	+	0.858315i	$0.328488\pi$
$79$			95223.5i			1.71663i	−0.513124	+	0.858315i	$0.671512\pi$
$80$	−44289.9	+	12614.5i	−0.773712	+	0.220366i
$81$		0			0
$82$	−34234.6	−	11471.7i	−0.562252	−	0.188406i
$83$	−55856.8			−0.889981			−0.444990	−	0.895535i	$-0.646793\pi$
$83$	−55856.8			−0.889981			−0.444990	+	0.895535i	$0.646793\pi$
$84$		0			0
$85$	68221.1			1.02417
$86$	96049.4	+	32185.3i	1.40039	+	0.469258i
$87$		0			0
$88$	−61505.5	+	42150.6i	−0.846657	+	0.580225i
$89$			93780.9i			1.25499i	0.778622	+	0.627493i	$0.215919\pi$
$89$			93780.9i			1.25499i	−0.778622	+	0.627493i	$0.784081\pi$
$90$		0			0
$91$			19511.4i			0.246993i
$92$	−78422.3	−	59205.1i	−0.965984	−	0.729273i
$93$		0			0
$94$	34666.3	−	103453.i	0.404658	−	1.20761i
$95$	−91971.6			−1.04555
$96$		0			0
$97$	−182666.			−1.97119			−0.985594	−	0.169129i	$-0.945905\pi$
$97$	−182666.			−1.97119			−0.985594	+	0.169129i	$0.945905\pi$
$98$	28747.0	−	85788.6i	0.302362	−	0.902328i
$99$		0			0
$100$	−28157.6	−	21257.6i	−0.281576	−	0.212576i
$101$		−	13318.9i		−	0.129916i	−0.997888	−	0.0649582i	$-0.979309\pi$
$101$		−	13318.9i		−	0.129916i	0.997888	−	0.0649582i	$-0.0206914\pi$
$102$		0			0
$103$		−	173353.i		−	1.61005i	−0.593242	−	0.805024i	$-0.702152\pi$
$103$		−	173353.i		−	1.61005i	0.593242	−	0.805024i	$-0.297848\pi$
$104$	−102192.	+	70033.7i	−0.926476	+	0.634927i
$105$		0			0
$106$	−61148.8	−	20490.4i	−0.528595	−	0.177128i
$107$	167439.			1.41383			0.706916	−	0.707298i	$-0.250086\pi$
$107$	167439.			1.41383			0.706916	+	0.707298i	$0.250086\pi$
$108$		0			0
$109$	23854.1			0.192308			0.0961539	−	0.995366i	$-0.469346\pi$
$109$	23854.1			0.192308			0.0961539	+	0.995366i	$0.469346\pi$
$110$	99358.5	+	33294.2i	0.782931	+	0.262353i
$111$		0			0
$112$	−28077.1	+	7996.80i	−0.211498	+	0.0602381i
$113$		−	257760.i		−	1.89897i	−0.313807	−	0.949487i	$-0.601605\pi$
$113$		−	257760.i		−	1.89897i	0.313807	−	0.949487i	$-0.398395\pi$
$114$		0			0
$115$			138094.i			0.973711i
$116$	−12409.1	+	16436.9i	−0.0856238	+	0.113416i
$117$		0			0
$118$	−762.781	+	2276.34i	−0.00504307	+	0.0150498i
$119$	43247.9			0.279961
$120$		0			0
$121$	8614.52			0.0534894
$122$	−12415.8	+	37051.9i	−0.0755221	+	0.225378i
$123$		0			0
$124$	−14094.9	+	18669.9i	−0.0823204	+	0.109040i
$125$			190120.i			1.08831i
$126$		0			0
$127$		−	172491.i		−	0.948978i	−0.880261	−	0.474489i	$-0.842633\pi$
$127$		−	172491.i		−	0.948978i	0.880261	−	0.474489i	$-0.157367\pi$
$128$	−142663.	−	118352.i	−0.769636	−	0.638483i
$129$		0			0
$130$	165085.	+	55318.6i	0.856742	+	0.287087i
$131$	50777.3			0.258518			0.129259	−	0.991611i	$-0.458740\pi$
$131$	50777.3			0.258518			0.129259	+	0.991611i	$0.458740\pi$
$132$		0			0
$133$	−58304.3			−0.285806
$134$	314282.	+	105313.i	1.51202	+	0.506664i
$135$		0			0
$136$	155233.	+	226514.i	0.719675	+	1.05014i
$137$			57768.8i			0.262961i	0.991319	+	0.131481i	$0.0419731\pi$
$137$			57768.8i			0.262961i	−0.991319	+	0.131481i	$0.958027\pi$
$138$		0			0
$139$		−	84989.7i		−	0.373103i	−0.982445	−	0.186552i	$-0.940269\pi$
$139$		−	84989.7i		−	0.373103i	0.982445	−	0.186552i	$-0.0597312\pi$
$140$	32744.4	+	24720.5i	0.141194	+	0.106595i
$141$		0			0
$142$	−88308.6	+	263536.i	−0.367521	+	1.09678i
$143$	281901.			1.15281
$144$		0			0
$145$	28943.7			0.114323
$146$	126174.	−	376538.i	0.489879	−	1.46193i
$147$		0			0
$148$	139492.	+	105310.i	0.523475	+	0.395199i
$149$		−	492003.i		−	1.81552i	−0.419487	−	0.907761i	$-0.637790\pi$
$149$		−	492003.i		−	1.81552i	0.419487	−	0.907761i	$-0.362210\pi$
$150$		0			0
$151$		−	368120.i		−	1.31385i	−0.753954	−	0.656927i	$-0.771856\pi$
$151$		−	368120.i		−	1.31385i	0.753954	−	0.656927i	$-0.228144\pi$
$152$	−209276.	−	305372.i	−0.734699	−	1.07206i
$153$		0			0
$154$	62987.2	+	21106.4i	0.214018	+	0.0717155i
$155$	32875.8			0.109913
$156$		0			0
$157$	82795.9			0.268077			0.134039	−	0.990976i	$-0.457205\pi$
$157$	82795.9			0.268077			0.134039	+	0.990976i	$0.457205\pi$
$158$	510753.	+	171149.i	1.62768	+	0.545420i
$159$		0			0
$160$	−11943.2	+	260231.i	−0.0368826	+	0.803636i
$161$			87543.0i			0.266169i
$162$		0			0
$163$		−	191541.i		−	0.564668i	−0.959316	−	0.282334i	$-0.908891\pi$
$163$		−	191541.i		−	0.564668i	0.959316	−	0.282334i	$-0.0911086\pi$
$164$	−123062.	+	163007.i	−0.357286	+	0.473256i
$165$		0			0
$166$	−100394.	+	299601.i	−0.282771	+	0.843864i
$167$	−318616.			−0.884048			−0.442024	−	0.897003i	$-0.645739\pi$
$167$	−318616.			−0.884048			−0.442024	+	0.897003i	$0.645739\pi$
$168$		0			0
$169$	97089.3			0.261490
$170$	122616.	−	365919.i	0.325406	−	0.971098i
$171$		0			0
$172$	345267.	−	457335.i	0.889884	−	1.17873i
$173$			87741.7i			0.222890i	0.993771	+	0.111445i	$0.0355479\pi$
$173$			87741.7i			0.222890i	−0.993771	+	0.111445i	$0.964452\pi$
$174$		0			0
$175$			31432.4i			0.0775858i
$176$	115538.	+	405658.i	0.281153	+	0.987138i
$177$		0			0
$178$	503015.	+	168556.i	1.18996	+	0.398744i
$179$	−197646.			−0.461057			−0.230528	−	0.973066i	$-0.574045\pi$
$179$	−197646.			−0.461057			−0.230528	+	0.973066i	$0.574045\pi$
$180$		0			0
$181$	−638617.			−1.44892			−0.724459	−	0.689318i	$-0.757910\pi$
$181$	−638617.			−1.44892			−0.724459	+	0.689318i	$0.757910\pi$
$182$	104654.	+	35068.6i	0.234195	+	0.0784766i
$183$		0			0
$184$	−458512.	+	314224.i	−0.998403	+	0.684219i
$185$		−	245632.i		−	0.527662i
$186$		0			0
$187$		−	624847.i		−	1.30668i
$188$	−492589.	−	371881.i	−1.01646	−	0.767379i
$189$		0			0
$190$	−165304.	+	493311.i	−0.332200	+	0.991371i
$191$	280543.			0.556438			0.278219	−	0.960518i	$-0.410256\pi$
$191$	280543.			0.556438			0.278219	+	0.960518i	$0.410256\pi$
$192$		0			0
$193$	−366016.			−0.707305			−0.353652	−	0.935377i	$-0.615060\pi$
$193$	−366016.			−0.707305			−0.353652	+	0.935377i	$0.615060\pi$
$194$	−328312.	+	979770.i	−0.626300	+	1.86905i
$195$		0			0
$196$	−408479.	−	308382.i	−0.759502	−	0.573389i
$197$			876478.i			1.60907i	0.593904	+	0.804536i	$0.297586\pi$
$197$			876478.i			1.60907i	−0.593904	+	0.804536i	$0.702414\pi$
$198$		0			0
$199$		−	146658.i		−	0.262527i	−0.991348	−	0.131263i	$-0.958097\pi$
$199$		−	146658.i		−	0.262527i	0.991348	−	0.131263i	$-0.0419034\pi$
$200$	−164629.	+	112822.i	−0.291025	+	0.199444i
$201$		0			0
$202$	−71438.8	−	23938.5i	−0.123184	−	0.0412780i
$203$	18348.5			0.0312508
$204$		0			0
$205$	287039.			0.477041
$206$	−929820.	−	311574.i	−1.52662	−	0.511556i
$207$		0			0
$208$	191968.	+	674005.i	0.307659	+	1.08020i
$209$			842382.i			1.33396i
$210$		0			0
$211$		−	616213.i		−	0.952850i	−0.879215	−	0.476425i	$-0.841932\pi$
$211$		−	616213.i		−	0.952850i	0.879215	−	0.476425i	$-0.158068\pi$
$212$	−219810.	+	291157.i	−0.335898	+	0.444926i
$213$		0			0
$214$	300945.	−	898099.i	0.449213	−	1.34057i
$215$	−805322.			−1.18816
$216$		0			0
$217$	20841.3			0.0300452
$218$	42873.9	−	127947.i	0.0611014	−	0.182343i
$219$		0			0
$220$	357162.	−	473091.i	0.497517	−	0.659004i
$221$		−	1.03819e6i		−	1.42987i
$222$		0			0
$223$			541567.i			0.729273i	0.931150	+	0.364636i	$0.118807\pi$
$223$			541567.i			0.729273i	−0.931150	+	0.364636i	$0.881193\pi$
$224$	−7571.26	+	164971.i	−0.0100820	+	0.219678i
$225$		0			0
$226$	−1.38255e6	−	463281.i	−1.80057	−	0.603356i
$227$	164616.			0.212035			0.106017	−	0.994364i	$-0.466190\pi$
$227$	164616.			0.212035			0.106017	+	0.994364i	$0.466190\pi$
$228$		0			0
$229$	−624301.			−0.786693			−0.393346	−	0.919390i	$-0.628683\pi$
$229$	−624301.			−0.786693			−0.393346	+	0.919390i	$0.628683\pi$
$230$	740698.	+	248201.i	0.923255	+	0.309375i
$231$		0			0
$232$	65859.7	+	96101.6i	0.0803341	+	0.117222i
$233$		−	400393.i		−	0.483166i	−0.970380	−	0.241583i	$-0.922333\pi$
$233$		−	400393.i		−	0.483166i	0.970380	−	0.241583i	$-0.0776666\pi$
$234$		0			0
$235$			867400.i			1.02459i
$236$	10838.7	+	8182.70i	0.0126677	+	0.00956350i
$237$		0			0
$238$	77731.2	−	231970.i	0.0889514	−	0.265454i
$239$	−1.04899e6			−1.18789			−0.593945	−	0.804505i	$-0.702430\pi$
$239$	−1.04899e6			−1.18789			−0.593945	+	0.804505i	$0.702430\pi$
$240$		0			0
$241$	937726.			1.04000			0.520000	−	0.854166i	$-0.325932\pi$
$241$	937726.			1.04000			0.520000	+	0.854166i	$0.325932\pi$
$242$	15483.2	−	46206.0i	0.0169951	−	0.0507177i
$243$		0			0
$244$	176421.	+	133190.i	0.189704	+	0.143217i
$245$			719291.i			0.765578i
$246$		0			0
$247$			1.39963e6i			1.45972i
$248$	74806.9	+	109157.i	0.0772347	+	0.112700i
$249$		0			0
$250$	1.01975e6	+	341710.i	1.03192	+	0.345786i
$251$	998062.			0.999938			0.499969	−	0.866043i	$-0.333345\pi$
$251$	998062.			0.999938			0.499969	+	0.866043i	$0.333345\pi$
$252$		0			0
$253$	1.26482e6			1.24231
$254$	−925193.	−	310024.i	−0.899804	−	0.301516i
$255$		0			0
$256$	−891219.	+	552485.i	−0.849933	+	0.526891i
$257$		−	428916.i		−	0.405079i	−0.979274	−	0.202539i	$-0.935081\pi$
$257$		−	428916.i		−	0.405079i	0.979274	−	0.202539i	$-0.0649194\pi$
$258$		0			0
$259$		−	155716.i		−	0.144239i
$260$	593428.	−	786047.i	0.544421	−	0.721132i
$261$		0			0
$262$	91264.0	−	272356.i	0.0821384	−	0.245122i
$263$	−769512.			−0.686003			−0.343001	−	0.939335i	$-0.611444\pi$
$263$	−769512.			−0.686003			−0.343001	+	0.939335i	$0.611444\pi$
$264$		0			0
$265$	512699.			0.448485
$266$	−104793.	+	312728.i	−0.0908084	+	0.270996i
$267$		0			0
$268$	1.12974e6	−	1.49644e6i	0.960820	−	1.27269i
$269$			1.64167e6i			1.38326i	0.722251	+	0.691631i	$0.243108\pi$
$269$			1.64167e6i			1.38326i	−0.722251	+	0.691631i	$0.756892\pi$
$270$		0			0
$271$			1.16025e6i			0.959680i	0.877356	+	0.479840i	$0.159305\pi$
$271$			1.16025e6i			0.959680i	−0.877356	+	0.479840i	$0.840695\pi$
$272$	1.49396e6	−	425505.i	1.22438	−	0.348725i
$273$		0			0
$274$	309856.	+	103830.i	0.249335	+	0.0835500i
$275$	454135.			0.362121
$276$		0			0
$277$	422037.			0.330484			0.165242	−	0.986253i	$-0.447159\pi$
$277$	422037.			0.330484			0.165242	+	0.986253i	$0.447159\pi$
$278$	−455862.	−	152755.i	−0.353770	−	0.118545i
$279$		0			0
$280$	191447.	−	131201.i	0.145933	−	0.100010i
$281$		−	545437.i		−	0.412077i	−0.978544	−	0.206039i	$-0.933943\pi$
$281$		−	545437.i		−	0.412077i	0.978544	−	0.206039i	$-0.0660573\pi$
$282$		0			0
$283$			2.52288e6i			1.87253i	0.351289	+	0.936267i	$0.385744\pi$
$283$			2.52288e6i			1.87253i	−0.351289	+	0.936267i	$0.614256\pi$
$284$	1.25482e6	+	947327.i	0.923175	+	0.696954i
$285$		0			0
$286$	506672.	−	1.51204e6i	0.366279	−	1.09307i
$287$	181965.			0.130402
$288$		0			0
$289$	−881340.			−0.620725
$290$	52021.7	−	155246.i	0.0363236	−	0.108399i
$291$		0			0
$292$	−1.79287e6	−	1.35353e6i	−1.23053	−	0.928990i
$293$		−	1.91422e6i		−	1.30263i	−0.758806	−	0.651317i	$-0.774217\pi$
$293$		−	1.91422e6i		−	1.30263i	0.758806	−	0.651317i	$-0.225783\pi$
$294$		0			0
$295$		−	19085.9i		−	0.0127690i
$296$	815569.	−	558921.i	0.541043	−	0.370784i
$297$		0			0
$298$	−2.63897e6	−	884295.i	−1.72145	−	0.576841i
$299$	2.10152e6			1.35942
$300$		0			0
$301$	−510525.			−0.324788
$302$	−1.97449e6	−	661636.i	−1.24577	−	0.417447i
$303$		0			0
$304$	−2.01407e6	+	573641.i	−1.24995	+	0.356005i
$305$		−	310660.i		−	0.191221i
$306$		0			0
$307$		−	759821.i		−	0.460114i	−0.973177	−	0.230057i	$-0.926109\pi$
$307$		−	759821.i		−	0.460114i	0.973177	−	0.230057i	$-0.0738913\pi$
$308$	226418.	−	299911.i	0.135999	−	0.180142i
$309$		0			0
$310$	59089.0	−	176337.i	0.0349223	−	0.104217i
$311$	1.14702e6			0.672464			0.336232	−	0.941779i	$-0.390847\pi$
$311$	1.14702e6			0.672464			0.336232	+	0.941779i	$0.390847\pi$
$312$		0			0
$313$	358045.			0.206575			0.103287	−	0.994652i	$-0.467064\pi$
$313$	358045.			0.206575			0.103287	+	0.994652i	$0.467064\pi$
$314$	148812.	−	444095.i	0.0851754	−	0.254186i
$315$		0			0
$316$	1.83599e6	−	2.43193e6i	1.03432	−	1.37004i
$317$		−	2.80135e6i		−	1.56574i	−0.622186	−	0.782870i	$-0.713755\pi$
$317$		−	2.80135e6i		−	1.56574i	0.622186	−	0.782870i	$-0.286245\pi$
$318$		0			0
$319$		−	265100.i		−	0.145859i
$320$	1.37434e6	+	531784.i	0.750275	+	0.290309i
$321$		0			0
$322$	469557.	+	157344.i	0.252376	+	0.0845691i
$323$	3.10234e6			1.65456
$324$		0			0
$325$	754551.			0.396260
$326$	−1.02737e6	−	344264.i	−0.535408	−	0.179410i
$327$		0			0
$328$	653139.	+	953051.i	0.335213	+	0.489138i
$329$			549878.i			0.280077i
$330$		0			0
$331$			465048.i			0.233307i	0.993173	+	0.116654i	$0.0372167\pi$
$331$			465048.i			0.233307i	−0.993173	+	0.116654i	$0.962783\pi$
$332$	1.42653e6	+	1.07697e6i	0.710292	+	0.536237i
$333$		0			0
$334$	−572660.	+	1.70897e6i	−0.280886	+	0.838239i
$335$	−2.63508e6			−1.28287
$336$		0			0
$337$	−1.16600e6			−0.559274			−0.279637	−	0.960106i	$-0.590214\pi$
$337$	−1.16600e6			−0.559274			−0.279637	+	0.960106i	$0.590214\pi$
$338$	174502.	−	520761.i	0.0830825	−	0.247940i
$339$		0			0
$340$	−1.74231e6	−	1.31536e6i	−0.817387	−	0.617089i
$341$		−	301115.i		−	0.140232i
$342$		0			0
$343$			935144.i			0.429184i
$344$	−1.83246e6	−	2.67390e6i	−0.834908	−	1.21829i
$345$		0			0
$346$	470623.	+	157702.i	0.211341	+	0.0708183i
$347$	−1.11960e6			−0.499160			−0.249580	−	0.968354i	$-0.580293\pi$
$347$	−1.11960e6			−0.499160			−0.249580	+	0.968354i	$0.580293\pi$
$348$		0			0
$349$	−514671.			−0.226186			−0.113093	−	0.993584i	$-0.536076\pi$
$349$	−514671.			−0.226186			−0.113093	+	0.993584i	$0.536076\pi$
$350$	168595.	+	56494.6i	0.0735654	+	0.0246511i
$351$		0			0
$352$	2.38350e6	+	109390.i	1.02532	+	0.0470565i
$353$			2.78955e6i			1.19151i	0.803167	+	0.595754i	$0.203147\pi$
$353$			2.78955e6i			1.19151i	−0.803167	+	0.595754i	$0.796853\pi$
$354$		0			0
$355$		−	2.20961e6i		−	0.930559i
$356$	1.80818e6	−	2.39508e6i	0.756163	−	1.00160i
$357$		0			0
$358$	−355236.	+	1.06012e6i	−0.146490	+	0.437166i
$359$	−1.28814e6			−0.527504			−0.263752	−	0.964590i	$-0.584960\pi$
$359$	−1.28814e6			−0.527504			−0.263752	+	0.964590i	$0.584960\pi$
$360$		0			0
$361$	−1.70629e6			−0.689103
$362$	−1.14781e6	+	3.42537e6i	−0.460361	+	1.37384i
$363$		0			0
$364$	376197.	−	498305.i	0.148820	−	0.197125i
$365$			3.15706e6i			1.24037i
$366$		0			0
$367$			1.88011e6i			0.728648i	0.931272	+	0.364324i	$0.118700\pi$
$367$			1.88011e6i			0.728648i	−0.931272	+	0.364324i	$0.881300\pi$
$368$	861313.	+	3.02410e6i	0.331544	+	1.16406i
$369$		0			0
$370$	−1.31750e6	−	441484.i	−0.500320	−	0.167653i
$371$	325020.			0.122596
$372$		0			0
$373$	4.22175e6			1.57116			0.785580	−	0.618761i	$-0.212365\pi$
$373$	4.22175e6			1.57116			0.785580	+	0.618761i	$0.212365\pi$
$374$	−3.35151e6	−	1.12306e6i	−1.23897	−	0.415169i
$375$		0			0
$376$	−2.88002e6	+	1.97372e6i	−1.05057	+	0.719971i
$377$		−	440467.i		−	0.159610i
$378$		0			0
$379$		−	770147.i		−	0.275407i	−0.990473	−	0.137704i	$-0.956028\pi$
$379$		−	770147.i		−	0.275407i	0.990473	−	0.137704i	$-0.0439722\pi$
$380$	2.34888e6	+	1.77329e6i	0.834452	+	0.629972i
$381$		0			0
$382$	504231.	−	1.50476e6i	0.176796	−	0.527604i
$383$	−2.69430e6			−0.938532			−0.469266	−	0.883057i	$-0.655482\pi$
$383$	−2.69430e6			−0.938532			−0.469266	+	0.883057i	$0.655482\pi$
$384$		0			0
$385$	−528113.			−0.181583
$386$	−657854.	+	1.96321e6i	−0.224730	+	0.670654i
$387$		0			0
$388$	4.66513e6	+	3.52195e6i	1.57320	+	1.18769i
$389$		−	220210.i		−	0.0737843i	−0.999319	−	0.0368922i	$-0.988254\pi$
$389$		−	220210.i		−	0.0737843i	0.999319	−	0.0368922i	$-0.0117458\pi$
$390$		0			0
$391$		−	4.65811e6i		−	1.54088i
$392$	−2.38825e6	+	1.63670e6i	−0.784992	+	0.537965i
$393$		0			0
$394$	4.70119e6	+	1.57533e6i	1.52569	+	0.511246i
$395$	−4.28239e6			−1.38100
$396$		0			0
$397$	−2.28702e6			−0.728271			−0.364135	−	0.931346i	$-0.618635\pi$
$397$	−2.28702e6			−0.728271			−0.364135	+	0.931346i	$0.618635\pi$
$398$	−786635.	−	263594.i	−0.248923	−	0.0834120i
$399$		0			0
$400$	309255.	+	1.08580e6i	0.0966421	+	0.339314i
$401$			640352.i			0.198865i	0.995044	+	0.0994324i	$0.0317027\pi$
$401$			640352.i			0.198865i	−0.995044	+	0.0994324i	$0.968297\pi$
$402$		0			0
$403$		−	500306.i		−	0.153452i
$404$	−256799.	+	340153.i	−0.0782781	+	0.103686i
$405$		0			0
$406$	32978.5	−	98416.6i	0.00992925	−	0.0296315i
$407$	−2.24978e6			−0.673216
$408$		0			0
$409$	2.58655e6			0.764562			0.382281	−	0.924046i	$-0.375139\pi$
$409$	2.58655e6			0.764562			0.382281	+	0.924046i	$0.375139\pi$
$410$	515906.	−	1.53960e6i	0.151569	−	0.452322i
$411$		0			0
$412$	−3.34240e6	+	4.42730e6i	−0.970097	+	1.28498i
$413$		−	12099.3i		−	0.00349047i
$414$		0			0
$415$		−	2.51199e6i		−	0.715974i
$416$	3.96021e6	+	181752.i	1.12198	+	0.0514928i
$417$		0			0
$418$	4.51831e6	+	1.51404e6i	1.26484	+	0.423836i
$419$	5.31201e6			1.47817			0.739084	−	0.673614i	$-0.235259\pi$
$419$	5.31201e6			1.47817			0.739084	+	0.673614i	$0.235259\pi$
$420$		0			0
$421$	−5.16990e6			−1.42160			−0.710799	−	0.703395i	$-0.751666\pi$
$421$	−5.16990e6			−1.42160			−0.710799	+	0.703395i	$0.751666\pi$
$422$	−3.30520e6	−	1.10754e6i	−0.903476	−	0.302747i
$423$		0			0
$424$	1.16662e6	+	1.70231e6i	0.315147	+	0.459858i
$425$		−	1.67250e6i		−	0.449152i
$426$		0			0
$427$		−	196939.i		−	0.0522712i
$428$	−4.27626e6	−	3.22837e6i	−1.12838	−	0.851872i
$429$		0			0
$430$	−1.44744e6	+	4.31953e6i	−0.377510	+	1.12659i
$431$	−2.70546e6			−0.701534			−0.350767	−	0.936463i	$-0.614079\pi$
$431$	−2.70546e6			−0.701534			−0.350767	+	0.936463i	$0.614079\pi$
$432$		0			0
$433$	6.62153e6			1.69722			0.848611	−	0.529018i	$-0.177439\pi$
$433$	6.62153e6			1.69722			0.848611	+	0.529018i	$0.177439\pi$
$434$	37458.8	−	111787.i	0.00954617	−	0.0284883i
$435$		0			0
$436$	−609213.	−	459927.i	−0.153481	−	0.115871i
$437$			6.27979e6i			1.57305i
$438$		0			0
$439$		−	4.18212e6i		−	1.03570i	−0.855470	−	0.517852i	$-0.826732\pi$
$439$		−	4.18212e6i		−	1.03570i	0.855470	−	0.517852i	$-0.173268\pi$
$440$	−1.89559e6	−	2.76602e6i	−0.466781	−	0.681121i
$441$		0			0
$442$	−5.56857e6	−	1.86598e6i	−1.35578	−	0.454309i
$443$	5.45464e6			1.32056			0.660278	−	0.751021i	$-0.270438\pi$
$443$	5.45464e6			1.32056			0.660278	+	0.751021i	$0.270438\pi$
$444$		0			0
$445$	−4.21751e6			−1.00961
$446$	2.90482e6	+	973379.i	0.691484	+	0.231710i
$447$		0			0
$448$	871249.	+	337118.i	0.205091	+	0.0793573i
$449$		−	6.49269e6i		−	1.51988i	−0.649994	−	0.759939i	$-0.725229\pi$
$449$		−	6.49269e6i		−	1.51988i	0.649994	−	0.759939i	$-0.274771\pi$
$450$		0			0
$451$		−	2.62903e6i		−	0.608631i
$452$	−4.96983e6	+	6.58296e6i	−1.14418	+	1.51557i
$453$		0			0
$454$	295870.	−	882955.i	0.0673693	−	0.201048i
$455$	−877466.			−0.198702
$456$		0			0
$457$	−5.42147e6			−1.21430			−0.607151	−	0.794586i	$-0.707688\pi$
$457$	−5.42147e6			−1.21430			−0.607151	+	0.794586i	$0.707688\pi$
$458$	−1.12208e6	+	3.34858e6i	−0.249954	+	0.745928i
$459$		0			0
$460$	2.66257e6	−	3.52680e6i	0.586687	−	0.777117i
$461$		−	585086.i		−	0.128223i	−0.997943	−	0.0641117i	$-0.979579\pi$
$461$		−	585086.i		−	0.128223i	0.997943	−	0.0641117i	$-0.0204214\pi$
$462$		0			0
$463$		−	2.73814e6i		−	0.593613i	−0.954938	−	0.296806i	$-0.904078\pi$
$463$		−	2.73814e6i		−	0.593613i	0.954938	−	0.296806i	$-0.0959216\pi$
$464$	633835.	−	180527.i	0.136673	−	0.0389266i
$465$		0			0
$466$	−2.14760e6	−	719641.i	−0.458129	−	0.153515i
$467$	3.07143e6			0.651701			0.325850	−	0.945421i	$-0.394349\pi$
$467$	3.07143e6			0.651701			0.325850	+	0.945421i	$0.394349\pi$
$468$		0			0
$469$	−1.67048e6			−0.350679
$470$	4.65250e6	+	1.55901e6i	0.971498	+	0.325540i
$471$		0			0
$472$	63370.6	−	43428.7i	0.0130928	−	0.00897267i
$473$			7.37607e6i			1.51591i
$474$		0			0
$475$			2.25476e6i			0.458529i
$476$	−1.10452e6	−	833858.i	−0.223437	−	0.168684i
$477$		0			0
$478$	−1.88539e6	+	5.62649e6i	−0.377425	+	1.12634i
$479$	−6.67442e6			−1.32915			−0.664576	−	0.747221i	$-0.731388\pi$
$479$	−6.67442e6			−1.32915			−0.664576	+	0.747221i	$0.731388\pi$
$480$		0			0
$481$	−3.73804e6			−0.736684
$482$	1.68541e6	−	5.02971e6i	0.330437	−	0.986110i
$483$		0			0
$484$	−220008.	−	166095.i	−0.0426898	−	0.0322288i
$485$		−	8.21484e6i		−	1.58579i
$486$		0			0
$487$		−	9.75720e6i		−	1.86425i	−0.362143	−	0.932123i	$-0.617955\pi$
$487$		−	9.75720e6i		−	1.86425i	0.362143	−	0.932123i	$-0.382045\pi$
$488$	1.03148e6	−	706888.i	0.196070	−	0.134370i
$489$		0			0
$490$	3.85808e6	+	1.29281e6i	0.725907	+	0.243245i
$491$	9.36580e6			1.75324			0.876619	−	0.481185i	$-0.159793\pi$
$491$	9.36580e6			1.75324			0.876619	+	0.481185i	$0.159793\pi$
$492$		0			0
$493$	−976315.			−0.180914
$494$	7.50722e6	+	2.51560e6i	1.38408	+	0.463793i
$495$		0			0
$496$	719943.	−	205052.i	0.131400	−	0.0374248i
$497$		−	1.40075e6i		−	0.254373i
$498$		0			0
$499$			3930.38i			0.000706615i	1.00000		0.000353307i	$0.000112461\pi$
$499$			3930.38i			0.000706615i	−1.00000		0.000353307i	$0.999888\pi$
$500$	3.66568e6	−	4.85550e6i	0.655736	−	0.868579i
$501$		0			0
$502$	1.79385e6	−	5.35333e6i	0.317708	−	0.948123i
$503$	−8.81634e6			−1.55371			−0.776853	−	0.629683i	$-0.783185\pi$
$503$	−8.81634e6			−1.55371			−0.776853	+	0.629683i	$0.783185\pi$
$504$		0			0
$505$	598975.			0.104515
$506$	2.27331e6	−	6.78417e6i	0.394715	−	1.17793i
$507$		0			0
$508$	−3.32577e6	+	4.40527e6i	−0.571785	+	0.757378i
$509$			1.95674e6i			0.334764i	0.985892	+	0.167382i	$0.0535313\pi$
$509$			1.95674e6i			0.334764i	−0.985892	+	0.167382i	$0.946469\pi$
$510$		0			0
$511$			2.00138e6i			0.339061i
$512$	1.36156e6	+	5.77326e6i	0.229542	+	0.973299i
$513$		0			0
$514$	−2.30059e6	−	770907.i	−0.384089	−	0.128705i
$515$	7.79603e6			1.29526
$516$		0			0
$517$	7.94465e6			1.30722
$518$	−835216.	−	279873.i	−0.136765	−	0.0458287i
$519$		0			0
$520$	−3.14955e6	−	4.59578e6i	−0.510787	−	0.745334i
$521$		−	3.57120e6i		−	0.576394i	−0.957571	−	0.288197i	$-0.906944\pi$
$521$		−	3.57120e6i		−	0.576394i	0.957571	−	0.288197i	$-0.0930558\pi$
$522$		0			0
$523$			7.38907e6i			1.18123i	0.806953	+	0.590616i	$0.201115\pi$
$523$			7.38907e6i			1.18123i	−0.806953	+	0.590616i	$0.798885\pi$
$524$	−1.29681e6	−	979030.i	−0.206323	−	0.155764i
$525$		0			0
$526$	−1.38307e6	+	4.12745e6i	−0.217962	+	0.650456i
$527$	−1.10895e6			−0.173934
$528$		0			0
$529$	2.99266e6			0.464963
$530$	921494.	−	2.74998e6i	0.142496	−	0.425246i
$531$		0			0
$532$	1.48904e6	+	1.12416e6i	0.228101	+	0.172206i
$533$		−	4.36817e6i		−	0.666011i
$534$		0			0
$535$			7.53007e6i			1.13740i
$536$	−5.99597e6	−	8.74923e6i	−0.901462	−	1.31540i
$537$		0			0
$538$	8.80546e6	+	2.95063e6i	1.31158	+	0.439500i
$539$	6.58809e6			0.976760
$540$		0			0
$541$	2.71204e6			0.398385			0.199192	−	0.979960i	$-0.436168\pi$
$541$	2.71204e6			0.398385			0.199192	+	0.979960i	$0.436168\pi$
$542$	6.22324e6	+	2.08535e6i	0.909952	+	0.304917i
$543$		0			0
$544$	402862.	−	8.77799e6i	0.0583659	−	1.27174i
$545$			1.07276e6i			0.154708i
$546$		0			0
$547$			6.90947e6i			0.987362i	0.869643	+	0.493681i	$0.164349\pi$
$547$			6.90947e6i			0.987362i	−0.869643	+	0.493681i	$0.835651\pi$
$548$	1.11383e6	−	1.47537e6i	0.158441	−	0.209869i
$549$		0			0
$550$	816235.	−	2.43586e6i	0.115056	−	0.343357i
$551$	1.31621e6			0.184691
$552$		0			0
$553$	−2.71477e6			−0.377503
$554$	758542.	−	2.26369e6i	0.105004	−	0.313359i
$555$		0			0
$556$	−1.63867e6	+	2.17057e6i	−0.224805	+	0.297773i
$557$			2.31133e6i			0.315664i	0.987466	+	0.157832i	$0.0504504\pi$
$557$			2.31133e6i			0.315664i	−0.987466	+	0.157832i	$0.949550\pi$
$558$		0			0
$559$			1.22554e7i			1.65882i
$560$	−359632.	−	1.26268e6i	−0.0484605	−	0.170146i
$561$		0			0
$562$	−2.92558e6	−	980335.i	−0.390724	−	0.130928i
$563$	579007.			0.0769862			0.0384931	−	0.999259i	$-0.487744\pi$
$563$	579007.			0.0769862			0.0384931	+	0.999259i	$0.487744\pi$
$564$		0			0
$565$	1.15920e7			1.52769
$566$	1.35320e7	+	4.53446e6i	1.77550	+	0.594955i
$567$		0			0
$568$	7.33653e6	−	5.02782e6i	0.954157	−	0.653897i
$569$		−	4.15072e6i		−	0.537456i	−0.963216	−	0.268728i	$-0.913397\pi$
$569$		−	4.15072e6i		−	0.537456i	0.963216	−	0.268728i	$-0.0866033\pi$
$570$		0			0
$571$		−	4.30846e6i		−	0.553009i	−0.961013	−	0.276504i	$-0.910824\pi$
$571$		−	4.30846e6i		−	0.553009i	0.961013	−	0.276504i	$-0.0891760\pi$
$572$	−7.19952e6	−	5.43530e6i	−0.920054	−	0.694598i
$573$		0			0
$574$	327052.	−	976010.i	0.0414322	−	0.123644i
$575$	3.38549e6			0.427024
$576$		0			0
$577$	1.61480e6			0.201921			0.100960	−	0.994890i	$-0.467809\pi$
$577$	1.61480e6			0.201921			0.100960	+	0.994890i	$0.467809\pi$
$578$	−1.58407e6	+	4.72727e6i	−0.197221	+	0.588560i
$579$		0			0
$580$	−739199.	−	558060.i	−0.0912413	−	0.0688829i
$581$		−	1.59245e6i		−	0.195715i
$582$		0			0
$583$		−	4.69589e6i		−	0.572198i
$584$	−1.04824e7	+	7.18370e6i	−1.27182	+	0.871598i
$585$		0			0
$586$	−1.02673e7	−	3.44050e6i	−1.23513	−	0.413882i
$587$	−9.37987e6			−1.12357			−0.561787	−	0.827282i	$-0.689886\pi$
$587$	−9.37987e6			−1.12357			−0.561787	+	0.827282i	$0.689886\pi$
$588$		0			0
$589$	1.49502e6			0.177566
$590$	−102371.	−	34303.7i	−0.0121073	−	0.00405706i
$591$		0			0
$592$	−1.53204e6	−	5.37906e6i	−0.179667	−	0.630815i
$593$			4.50800e6i			0.526438i	0.964736	+	0.263219i	$0.0847842\pi$
$593$			4.50800e6i			0.526438i	−0.964736	+	0.263219i	$0.915216\pi$
$594$		0			0
$595$			1.94494e6i			0.225224i
$596$	−9.48623e6	+	1.25653e7i	−1.09390	+	1.44897i
$597$		0			0
$598$	3.77714e6	−	1.12720e7i	0.431927	−	1.28898i
$599$	−1.18281e7			−1.34694			−0.673469	−	0.739215i	$-0.735197\pi$
$599$	−1.18281e7			−1.34694			−0.673469	+	0.739215i	$0.735197\pi$
$600$		0			0
$601$	501339.			0.0566168			0.0283084	−	0.999599i	$-0.490988\pi$
$601$	501339.			0.0566168			0.0283084	+	0.999599i	$0.490988\pi$
$602$	−917585.	+	2.73832e6i	−0.103194	+	0.307958i
$603$		0			0
$604$	−7.09767e6	+	9.40147e6i	−0.791632	+	1.04858i
$605$			387412.i			0.0430313i
$606$		0			0
$607$			1.52223e7i			1.67691i	0.544972	+	0.838454i	$0.316540\pi$
$607$			1.52223e7i			1.67691i	−0.544972	+	0.838454i	$0.683460\pi$
$608$	−543115.	+	1.18340e7i	−0.0595844	+	1.29829i
$609$		0			0
$610$	−1.66630e6	−	558361.i	−0.181312	−	0.0607562i
$611$	1.32001e7			1.43046
$612$		0			0
$613$	−1.50361e7			−1.61616			−0.808080	−	0.589073i	$-0.799493\pi$
$613$	−1.50361e7			−1.61616			−0.808080	+	0.589073i	$0.799493\pi$
$614$	−4.07547e6	−	1.36566e6i	−0.436272	−	0.146191i
$615$		0			0
$616$	−1.20169e6	−	1.75349e6i	−0.127597	−	0.186188i
$617$			1.04780e7i			1.10807i	0.832495	+	0.554033i	$0.186912\pi$
$617$			1.04780e7i			1.10807i	−0.832495	+	0.554033i	$0.813088\pi$
$618$		0			0
$619$		−	5.04678e6i		−	0.529404i	−0.964330	−	0.264702i	$-0.914726\pi$
$619$		−	5.04678e6i		−	0.529404i	0.964330	−	0.264702i	$-0.0852737\pi$
$620$	−839621.	−	633875.i	−0.0877211	−	0.0662253i
$621$		0			0
$622$	2.06158e6	−	6.15229e6i	0.213660	−	0.637618i
$623$	−2.67364e6			−0.275983
$624$		0			0
$625$	−5.10467e6			−0.522718
$626$	643528.	−	1.92046e6i	0.0656344	−	0.195870i
$627$		0			0
$628$	−2.11454e6	−	1.59638e6i	−0.213952	−	0.161524i
$629$			8.28553e6i			0.835014i
$630$		0			0
$631$			1.24449e7i			1.24428i	0.782907	+	0.622139i	$0.213736\pi$
$631$			1.24449e7i			1.24428i	−0.782907	+	0.622139i	$0.786264\pi$
$632$	−9.74431e6	−	1.42188e7i	−0.970417	−	1.41602i
$633$		0			0
$634$	−1.50257e7	−	5.03497e6i	−1.48461	−	0.497478i
$635$	7.75724e6			0.763436
$636$		0			0
$637$	1.09462e7			1.06884
$638$	−1.42193e6	−	476474.i	−0.138301	−	0.0463434i
$639$		0			0
$640$	5.32250e6	−	6.41581e6i	0.513649	−	0.619158i
$641$		−	2.36665e6i		−	0.227504i	−0.993509	−	0.113752i	$-0.963713\pi$
$641$		−	2.36665e6i		−	0.227504i	0.993509	−	0.113752i	$-0.0362870\pi$
$642$		0			0
$643$			4.58591e6i			0.437419i	0.975790	+	0.218710i	$0.0701847\pi$
$643$			4.58591e6i			0.437419i	−0.975790	+	0.218710i	$0.929815\pi$
$644$	1.68790e6	−	2.23577e6i	0.160374	−	0.212429i
$645$		0			0
$646$	5.57595e6	−	1.66401e7i	0.525699	−	1.56882i
$647$	−1.96170e7			−1.84235			−0.921175	−	0.389149i	$-0.872769\pi$
$647$	−1.96170e7			−1.84235			−0.921175	+	0.389149i	$0.872769\pi$
$648$		0			0
$649$	−174810.			−0.0162913
$650$	1.35618e6	−	4.04721e6i	0.125903	−	0.375727i
$651$		0			0
$652$	−3.69308e6	+	4.89180e6i	−0.340227	+	0.450660i
$653$		−	1.11892e6i		−	0.102687i	−0.998681	−	0.0513435i	$-0.983650\pi$
$653$		−	1.11892e6i		−	0.102687i	0.998681	−	0.0513435i	$-0.0163503\pi$
$654$		0			0
$655$			2.28355e6i			0.207973i
$656$	6.28582e6	−	1.79030e6i	0.570299	−	0.162430i
$657$		0			0
$658$	2.94940e6	+	988317.i	0.265564	+	0.0889880i
$659$	−1.42425e7			−1.27753			−0.638766	−	0.769401i	$-0.720555\pi$
$659$	−1.42425e7			−1.27753			−0.638766	+	0.769401i	$0.720555\pi$
$660$		0			0
$661$	−1.50585e6			−0.134053			−0.0670267	−	0.997751i	$-0.521351\pi$
$661$	−1.50585e6			−0.134053			−0.0670267	+	0.997751i	$0.521351\pi$
$662$	2.49439e6	+	835849.i	0.221218	+	0.0741281i
$663$		0			0
$664$	8.34052e6	−	5.71587e6i	0.734130	−	0.503109i
$665$		−	2.62206e6i		−	0.229926i
$666$		0			0
$667$		−	1.97627e6i		−	0.172001i
$668$	8.13717e6	+	6.14318e6i	0.705558	+	0.532663i
$669$		0			0
$670$	−4.73613e6	+	1.41339e7i	−0.407603	+	1.21639i
$671$	−2.84538e6			−0.243969
$672$		0			0
$673$	1.34440e7			1.14417			0.572084	−	0.820195i	$-0.306135\pi$
$673$	1.34440e7			1.14417			0.572084	+	0.820195i	$0.306135\pi$
$674$	−2.09570e6	+	6.25412e6i	−0.177697	+	0.530294i
$675$		0			0
$676$	−2.47958e6	−	1.87197e6i	−0.208695	−	0.157555i
$677$			1.49438e7i			1.25311i	0.779378	+	0.626554i	$0.215535\pi$
$677$			1.49438e7i			1.25311i	−0.779378	+	0.626554i	$0.784465\pi$
$678$		0			0
$679$		−	5.20770e6i		−	0.433482i
$680$	−1.01868e7	+	6.98112e6i	−0.844819	+	0.578966i
$681$		0			0
$682$	−1.61510e6	−	541205.i	−0.132965	−	0.0445555i
$683$	−3.84256e6			−0.315187			−0.157594	−	0.987504i	$-0.550374\pi$
$683$	−3.84256e6			−0.315187			−0.157594	+	0.987504i	$0.550374\pi$
$684$		0			0
$685$	−2.59797e6			−0.211548
$686$	5.01586e6	+	1.68077e6i	0.406944	+	0.136363i
$687$		0			0
$688$	−1.76356e7	+	5.02292e6i	−1.42043	+	0.404562i
$689$		−	7.80228e6i		−	0.626143i
$690$		0			0
$691$		−	1.36756e7i		−	1.08956i	−0.838578	−	0.544781i	$-0.816613\pi$
$691$		−	1.36756e7i		−	1.08956i	0.838578	−	0.544781i	$-0.183387\pi$
$692$	1.69174e6	−	2.24085e6i	0.134297	−	0.177888i
$693$		0			0
$694$	−2.01230e6	+	6.00523e6i	−0.158597	+	0.473294i
$695$	3.82215e6			0.300155
$696$		0			0
$697$	−9.68224e6			−0.754908
$698$	−925038.	+	2.76056e6i	−0.0718656	+	0.214466i
$699$		0			0
$700$	606043.	−	802756.i	0.0467475	−	0.0619211i
$701$		−	1.32451e7i		−	1.01803i	−0.860758	−	0.509015i	$-0.830010\pi$
$701$		−	1.32451e7i		−	1.01803i	0.860758	−	0.509015i	$-0.169990\pi$
$702$		0			0
$703$		−	1.11701e7i		−	0.852447i
$704$	4.87069e6	−	1.25878e7i	0.370390	−	0.957236i
$705$		0			0
$706$	1.49624e7	+	5.01376e6i	1.12977	+	0.378575i
$707$	379713.			0.0285698
$708$		0			0
$709$	−1.82356e7			−1.36240			−0.681200	−	0.732098i	$-0.738541\pi$
$709$	−1.82356e7			−1.36240			−0.681200	+	0.732098i	$0.738541\pi$
$710$	−1.18517e7	−	3.97141e6i	−0.882340	−	0.295664i
$711$		0			0
$712$	−9.59668e6	−	1.40033e7i	−0.709448	−	1.03522i
$713$		−	2.24475e6i		−	0.165365i
$714$		0			0
$715$			1.26776e7i			0.927414i
$716$	5.04770e6	+	3.81078e6i	0.367969	+	0.277799i
$717$		0			0
$718$	−2.31522e6	+	6.90922e6i	−0.167603	+	0.500170i
$719$	555013.			0.0400388			0.0200194	−	0.999800i	$-0.493627\pi$
$719$	555013.			0.0400388			0.0200194	+	0.999800i	$0.493627\pi$
$720$		0			0
$721$	4.94220e6			0.354064
$722$	−3.06678e6	+	9.15206e6i	−0.218947	+	0.653395i
$723$		0			0
$724$	1.63097e7	+	1.23131e7i	1.15638	+	0.873012i
$725$		−	709581.i		−	0.0501368i
$726$		0			0
$727$			1.12242e7i			0.787625i	0.919191	+	0.393813i	$0.128844\pi$
$727$			1.12242e7i			0.787625i	−0.919191	+	0.393813i	$0.871156\pi$
$728$	−1.99662e6	−	2.91344e6i	−0.139626	−	0.203741i
$729$		0			0
$730$	1.69336e7	+	5.67431e6i	1.17610	+	0.394099i
$731$	2.71647e7			1.88023
$732$		0			0
$733$	7.30346e6			0.502075			0.251038	−	0.967977i	$-0.419228\pi$
$733$	7.30346e6			0.502075			0.251038	+	0.967977i	$0.419228\pi$
$734$	1.00844e7	+	3.37919e6i	0.690891	+	0.231511i
$735$		0			0
$736$	1.77685e7	+	815479.i	1.20908	+	0.0554904i
$737$			2.41351e7i			1.63674i
$738$		0			0
$739$		−	1.03409e7i		−	0.696543i	−0.937394	−	0.348271i	$-0.886769\pi$
$739$		−	1.03409e7i		−	0.696543i	0.937394	−	0.348271i	$-0.113231\pi$
$740$	−4.73600e6	+	6.27324e6i	−0.317930	+	0.421126i
$741$		0			0
$742$	584170.	−	1.74332e6i	0.0389520	−	0.116243i
$743$	−1.25176e7			−0.831858			−0.415929	−	0.909397i	$-0.636543\pi$
$743$	−1.25176e7			−0.831858			−0.415929	+	0.909397i	$0.636543\pi$
$744$		0			0
$745$	2.21263e7			1.46056
$746$	7.58791e6	−	2.26443e7i	0.499200	−	1.48975i
$747$		0			0
$748$	−1.20476e7	+	1.59581e7i	−0.787311	+	1.04286i
$749$			4.77360e6i			0.310915i
$750$		0			0
$751$		−	1.04022e7i		−	0.673015i	−0.941681	−	0.336508i	$-0.890754\pi$
$751$		−	1.04022e7i		−	0.673015i	0.941681	−	0.336508i	$-0.109246\pi$
$752$	5.41011e6	+	1.89951e7i	0.348868	+	1.22489i
$753$		0			0
$754$	−2.36255e6	−	791668.i	−0.151339	−	0.0507125i
$755$	1.65551e7			1.05697
$756$		0			0
$757$	1.77986e7			1.12888			0.564438	−	0.825475i	$-0.309093\pi$
$757$	1.77986e7			1.12888			0.564438	+	0.825475i	$0.309093\pi$
$758$	−4.13086e6	−	1.38421e6i	−0.261136	−	0.0875045i
$759$		0			0
$760$	1.37332e7	−	9.41153e6i	0.862456	−	0.591053i
$761$		−	2.42339e7i		−	1.51691i	−0.651723	−	0.758457i	$-0.725953\pi$
$761$		−	2.42339e7i		−	1.51691i	0.651723	−	0.758457i	$-0.274047\pi$
$762$		0			0
$763$			680067.i			0.0422902i
$764$	−7.16484e6	−	5.40912e6i	−0.444092	−	0.335269i
$765$		0			0
$766$	−4.84257e6	+	1.44515e7i	−0.298197	+	0.889900i
$767$	−290449.			−0.0178272
$768$		0			0
$769$	−1.26552e7			−0.771708			−0.385854	−	0.922560i	$-0.626093\pi$
$769$	−1.26552e7			−0.771708			−0.385854	+	0.922560i	$0.626093\pi$
$770$	−949198.	+	2.83265e6i	−0.0576939	+	0.172174i
$771$		0			0
$772$	9.34774e6	+	7.05710e6i	0.564499	+	0.426170i
$773$		−	9.16670e6i		−	0.551778i	−0.961190	−	0.275889i	$-0.911028\pi$
$773$		−	9.16670e6i		−	0.551778i	0.961190	−	0.275889i	$-0.0889722\pi$
$774$		0			0
$775$		−	805979.i		−	0.0482025i
$776$	2.72756e7	−	1.86924e7i	1.62600	−	1.11432i
$777$		0			0
$778$	−1.18115e6	−	395793.i	−0.0699610	−	0.0234433i
$779$	1.30530e7			0.770668
$780$		0			0
$781$	−2.02381e7			−1.18725
$782$	−2.49848e7	−	8.37220e6i	−1.46103	−	0.489579i
$783$		0			0
$784$	4.48633e6	+	1.57516e7i	0.260676	+	0.915241i
$785$			3.72349e6i			0.215663i
$786$		0			0
$787$		−	8.49494e6i		−	0.488904i	−0.969661	−	0.244452i	$-0.921392\pi$
$787$		−	8.49494e6i		−	0.488904i	0.969661	−	0.244452i	$-0.0786080\pi$
$788$	1.68992e7	−	2.23845e7i	0.969509	−	1.28420i
$789$		0			0
$790$	−7.69689e6	+	2.29696e7i	−0.438781	+	1.30944i
$791$	7.34858e6			0.417602
$792$		0			0
$793$	−4.72764e6			−0.266969
$794$	−4.11054e6	+	1.22669e7i	−0.231392	+	0.690533i
$795$		0			0
$796$	−2.82770e6	+	3.74553e6i	−0.158179	+	0.209522i
$797$		−	3.28175e7i		−	1.83004i	−0.403410	−	0.915019i	$-0.632175\pi$
$797$		−	3.28175e7i		−	1.83004i	0.403410	−	0.915019i	$-0.367825\pi$
$798$		0			0
$799$		−	2.92587e7i		−	1.62139i
$800$	6.37979e6	+	292798.i	0.352437	+	0.0161750i
$801$		0			0
$802$	3.43467e6	+	1.15093e6i	0.188560	+	0.0631848i
$803$	2.89160e7			1.58252
$804$		0			0
$805$	−3.93698e6			−0.214128
$806$	−2.68350e6	−	899219.i	−0.145501	−	0.0487560i
$807$		0			0
$808$	1.36293e6	+	1.98877e6i	0.0734421	+	0.107166i
$809$			1.20827e7i			0.649073i	0.945873	+	0.324536i	$0.105208\pi$
$809$			1.20827e7i			0.649073i	−0.945873	+	0.324536i	$0.894792\pi$
$810$		0			0
$811$		−	1.34126e7i		−	0.716080i	−0.933706	−	0.358040i	$-0.883445\pi$
$811$		−	1.34126e7i		−	0.716080i	0.933706	−	0.358040i	$-0.116555\pi$
$812$	−468606.	−	353776.i	−0.0249412	−	0.0188295i
$813$		0			0
$814$	−4.04362e6	+	1.20672e7i	−0.213899	+	0.638331i
$815$	8.61397e6			0.454265
$816$		0			0
$817$	−3.66218e7			−1.91949
$818$	4.64890e6	−	1.38735e7i	0.242922	−	0.724944i
$819$		0			0
$820$	−7.33073e6	−	5.53435e6i	−0.380726	−	0.287430i
$821$		−	1.22879e7i		−	0.636238i	−0.948051	−	0.318119i	$-0.896949\pi$
$821$		−	1.22879e7i		−	0.636238i	0.948051	−	0.318119i	$-0.103051\pi$
$822$		0			0
$823$		−	2.19120e7i		−	1.12767i	−0.825887	−	0.563836i	$-0.809325\pi$
$823$		−	2.19120e7i		−	1.12767i	0.825887	−	0.563836i	$-0.190675\pi$
$824$	1.77394e7	+	2.58851e7i	0.910166	+	1.32810i
$825$		0			0
$826$	−64897.1	−	21746.5i	−0.00330960	−	0.00110902i
$827$	−2.06837e7			−1.05163			−0.525816	−	0.850598i	$-0.676240\pi$
$827$	−2.06837e7			−1.05163			−0.525816	+	0.850598i	$0.676240\pi$
$828$		0			0
$829$	−7.09815e6			−0.358723			−0.179361	−	0.983783i	$-0.557403\pi$
$829$	−7.09815e6			−0.358723			−0.179361	+	0.983783i	$0.557403\pi$
$830$	−1.34736e7	−	4.51489e6i	−0.678874	−	0.227485i
$831$		0			0
$832$	8.09271e6	−	2.09148e7i	0.405308	−	1.04748i
$833$		−	2.42627e7i		−	1.21151i
$834$		0			0
$835$		−	1.43288e7i		−	0.711201i
$836$	1.62418e7	−	2.15137e7i	0.803747	−	1.06463i
$837$		0			0
$838$	9.54747e6	−	2.84922e7i	0.469654	−	1.40157i
$839$	−2.57457e7			−1.26270			−0.631350	−	0.775498i	$-0.717499\pi$
$839$	−2.57457e7			−1.26270			−0.631350	+	0.775498i	$0.717499\pi$
$840$		0			0
$841$	2.00969e7			0.979805
$842$	−9.29205e6	+	2.77299e7i	−0.451681	+	1.34793i
$843$		0			0
$844$	−1.18811e7	+	1.57376e7i	−0.574118	+	0.760469i
$845$			4.36629e6i			0.210364i
$846$		0			0
$847$			245595.i			0.0117628i
$848$	1.12275e7	−	3.19778e6i	0.536160	−	0.152707i
$849$		0			0
$850$	−8.97082e6	−	3.00604e6i	−0.425878	−	0.142708i
$851$	−1.67717e7			−0.793876
$852$		0			0
$853$	−1.11214e7			−0.523342			−0.261671	−	0.965157i	$-0.584274\pi$
$853$	−1.11214e7			−0.523342			−0.261671	+	0.965157i	$0.584274\pi$
$854$	−1.05633e6	−	353966.i	−0.0495626	−	0.0166080i
$855$		0			0
$856$	−2.50020e7	+	1.71342e7i	−1.16625	+	0.799244i
$857$			2.05795e7i			0.957158i	0.878044	+	0.478579i	$0.158848\pi$
$857$			2.05795e7i			0.957158i	−0.878044	+	0.478579i	$0.841152\pi$
$858$		0			0
$859$		−	3.38288e7i		−	1.56424i	−0.623126	−	0.782121i	$-0.714138\pi$
$859$		−	3.38288e7i		−	1.56424i	0.623126	−	0.782121i	$-0.285862\pi$
$860$	2.05672e7	+	1.55273e7i	0.948266	+	0.715896i
$861$		0			0
$862$	−4.86263e6	+	1.45114e7i	−0.222897	+	0.665182i
$863$	3.87801e6			0.177248			0.0886241	−	0.996065i	$-0.471753\pi$
$863$	3.87801e6			0.177248			0.0886241	+	0.996065i	$0.471753\pi$
$864$		0			0
$865$	−3.94592e6			−0.179311
$866$	1.19011e7	−	3.55161e7i	0.539254	−	1.60928i
$867$		0			0
$868$	−532268.	−	401837.i	−0.0239790	−	0.0181030i
$869$			3.92230e7i			1.76194i
$870$		0			0
$871$			4.01008e7i			1.79105i
$872$	−3.56189e6	+	2.44101e6i	−0.158631	+	0.108712i
$873$		0			0
$874$	3.36831e7	+	1.12869e7i	1.49153	+	0.499800i
$875$	−5.42021e6			−0.239329
$876$		0			0
$877$	2.05430e7			0.901914			0.450957	−	0.892546i	$-0.351083\pi$
$877$	2.05430e7			0.901914			0.450957	+	0.892546i	$0.351083\pi$
$878$	−2.24318e7	−	7.51669e6i	−0.982036	−	0.329072i
$879$		0			0
$880$	−1.82432e7	+	5.19597e6i	−0.794135	+	0.226183i
$881$			1.83153e7i			0.795012i	0.917600	+	0.397506i	$0.130124\pi$
$881$			1.83153e7i			0.795012i	−0.917600	+	0.397506i	$0.869876\pi$
$882$		0			0
$883$			484318.i			0.0209040i	0.999945	+	0.0104520i	$0.00332703\pi$
$883$			484318.i			0.0209040i	−0.999945	+	0.0104520i	$0.996673\pi$
$884$	−2.00172e7	+	2.65145e7i	−0.861535	+	1.14118i
$885$		0			0
$886$	9.80383e6	−	2.92572e7i	0.419577	−	1.25213i
$887$	−1.01816e7			−0.434519			−0.217259	−	0.976114i	$-0.569712\pi$
$887$	−1.01816e7			−0.434519			−0.217259	+	0.976114i	$0.569712\pi$
$888$		0			0
$889$	4.91761e6			0.208689
$890$	−7.58028e6	+	2.26216e7i	−0.320782	+	0.957299i
$891$		0			0
$892$	1.04419e7	−	1.38312e7i	0.439407	−	0.582032i
$893$			3.94448e7i			1.65524i
$894$		0			0
$895$		−	8.88850e6i		−	0.370912i
$896$	3.37414e6	−	4.06723e6i	0.140408	−	0.169250i
$897$		0			0
$898$	−3.48250e7	−	1.16696e7i	−1.44112	−	0.482907i
$899$	−470488.			−0.0194155
$900$		0			0
$901$	−1.72941e7			−0.709719
$902$	−1.41014e7	−	4.72526e6i	−0.577093	−	0.193379i
$903$		0			0
$904$	2.63768e7	+	3.84886e7i	1.07350	+	1.56643i
$905$		−	2.87198e7i		−	1.16563i
$906$		0			0
$907$			3.22924e7i			1.30341i	0.758471	+	0.651707i	$0.225947\pi$
$907$			3.22924e7i			1.30341i	−0.758471	+	0.651707i	$0.774053\pi$
$908$	−4.20415e6	−	3.17394e6i	−0.169225	−	0.127757i
$909$		0			0
$910$	−1.57710e6	+	4.70649e6i	−0.0631330	+	0.188406i
$911$	6.89661e6			0.275321			0.137661	−	0.990479i	$-0.456042\pi$
$911$	6.89661e6			0.275321			0.137661	+	0.990479i	$0.456042\pi$
$912$		0			0
$913$	−2.30077e7			−0.913473
$914$	−9.74422e6	+	2.90793e7i	−0.385817	+	1.15138i
$915$		0			0
$916$	1.59441e7	+	1.20371e7i	0.627858	+	0.474003i
$917$			1.44763e6i			0.0568506i
$918$		0			0
$919$		−	1.92298e7i		−	0.751078i	−0.926807	−	0.375539i	$-0.877458\pi$
$919$		−	1.92298e7i		−	0.751078i	0.926807	−	0.375539i	$-0.122542\pi$
$920$	−1.41313e7	−	2.06202e7i	−0.550442	−	0.803197i
$921$		0			0
$922$	−3.13824e6	−	1.05160e6i	−0.121579	−	0.0407401i
$923$	−3.36259e7			−1.29918
$924$		0			0
$925$	−6.02188e6			−0.231408
$926$	−1.46866e7	−	4.92136e6i	−0.562853	−	0.188607i
$927$		0			0
$928$	170920.	−	3.72418e6i	0.00651513	−	0.141958i
$929$		−	2.70174e7i		−	1.02708i	−0.858066	−	0.513540i	$-0.828334\pi$
$929$		−	2.70174e7i		−	1.02708i	0.858066	−	0.513540i	$-0.171666\pi$
$930$		0			0
$931$			3.27096e7i			1.23680i
$932$	−7.71991e6	+	1.02257e7i	−0.291120	+	0.385614i
$933$		0			0
$934$	5.52040e6	−	1.64743e7i	0.207063	−	0.617931i
$935$	2.81006e7			1.05120
$936$		0			0
$937$	3.17247e7			1.18045			0.590227	−	0.807238i	$-0.299038\pi$
$937$	3.17247e7			1.18045			0.590227	+	0.807238i	$0.299038\pi$
$938$	−3.00242e6	+	8.96000e6i	−0.111420	+	0.332507i
$939$		0			0
$940$	1.67242e7	−	2.21527e7i	0.617343	−	0.817724i
$941$		−	2.17844e7i		−	0.801994i	−0.916079	−	0.400997i	$-0.868664\pi$
$941$		−	2.17844e7i		−	0.801994i	0.916079	−	0.400997i	$-0.131336\pi$
$942$		0			0
$943$		−	1.95989e7i		−	0.717716i
$944$	−119041.	−	417959.i	−0.00434779	−	0.0152652i
$945$		0			0
$946$	3.95632e7	+	1.32573e7i	1.43735	+	0.481645i
$947$	−1.96765e7			−0.712974			−0.356487	−	0.934300i	$-0.616026\pi$
$947$	−1.96765e7			−0.712974			−0.356487	+	0.934300i	$0.616026\pi$
$948$		0			0
$949$	4.80443e7			1.73171
$950$	1.20939e7	+	4.05257e6i	0.434769	+	0.145687i
$951$		0			0
$952$	−6.45777e6	+	4.42560e6i	−0.230935	+	0.158263i
$953$			2.78664e7i			0.993912i	0.867776	+	0.496956i	$0.165549\pi$
$953$			2.78664e7i			0.993912i	−0.867776	+	0.496956i	$0.834451\pi$
$954$		0			0
$955$			1.26166e7i			0.447644i
$956$	2.67903e7	+	2.02254e7i	0.948054	+	0.715736i
$957$		0			0
$958$	−1.19962e7	+	3.57998e7i	−0.422308	+	1.26028i
$959$	−1.64696e6			−0.0578276
$960$		0			0
$961$	2.80947e7			0.981334
$962$	−6.71852e6	+	2.00498e7i	−0.234065	+	0.698510i
$963$		0			0
$964$	−2.39487e7	−	1.80802e7i	−0.830023	−	0.626628i
$965$		−	1.64604e7i		−	0.569014i
$966$		0			0
$967$			3.89285e7i			1.33876i	0.742922	+	0.669378i	$0.233439\pi$
$967$			3.89285e7i			1.33876i	−0.742922	+	0.669378i	$0.766561\pi$
$968$	−1.28632e6	+	881531.i	−0.0441225	+	0.0302377i
$969$		0			0
$970$	−4.40621e7	−	1.47648e7i	−1.50361	−	0.503848i
$971$	468345.			0.0159411			0.00797054	−	0.999968i	$-0.497463\pi$
$971$	468345.			0.0159411			0.00797054	+	0.999968i	$0.497463\pi$
$972$		0			0
$973$	2.42301e6			0.0820489
$974$	−5.23350e7	−	1.75370e7i	−1.76764	−	0.592322i
$975$		0			0
$976$	−1.93763e6	−	6.80310e6i	−0.0651099	−	0.228603i
$977$		−	8.75275e6i		−	0.293365i	−0.989184	−	0.146682i	$-0.953140\pi$
$977$		−	8.75275e6i		−	0.293365i	0.989184	−	0.146682i	$-0.0468595\pi$
$978$		0			0
$979$			3.86288e7i			1.28811i
$980$	1.38685e7	−	1.83701e7i	0.461281	−	0.611006i
$981$		0			0
$982$	1.68335e7	−	5.02356e7i	0.557052	−	1.66239i
$983$	−9.57574e6			−0.316074			−0.158037	−	0.987433i	$-0.550517\pi$
$983$	−9.57574e6			−0.316074			−0.158037	+	0.987433i	$0.550517\pi$
$984$		0			0
$985$	−3.94169e7			−1.29447
$986$	−1.75477e6	+	5.23669e6i	−0.0574814	+	0.171540i
$987$		0			0
$988$	2.69860e7	−	3.57453e7i	0.879521	−	1.16500i
$989$			5.49871e7i			1.78760i
$990$		0			0
$991$			1.16300e7i			0.376179i	0.982152	+	0.188090i	$0.0602296\pi$
$991$			1.16300e7i			0.376179i	−0.982152	+	0.188090i	$0.939770\pi$
$992$	194140.	−	4.23013e6i	0.00626377	−	0.136482i
$993$		0			0
$994$	−7.51326e6	−	2.51763e6i	−0.241192	−	0.0808213i
$995$	6.59550e6			0.211198
$996$		0			0
$997$	1.59698e7			0.508817			0.254409	−	0.967097i	$-0.418119\pi$
$997$	1.59698e7			0.508817			0.254409	+	0.967097i	$0.418119\pi$
$998$	21081.5	+	7064.21i	0.000669999	+	0.000224511i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.b.b.107.9	yes	16
3.2	odd	2	inner	108.6.b.b.107.8	yes	16
4.3	odd	2	inner	108.6.b.b.107.7	✓	16
12.11	even	2	inner	108.6.b.b.107.10	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.6.b.b.107.7	✓	16	4.3	odd	2	inner
108.6.b.b.107.8	yes	16	3.2	odd	2	inner
108.6.b.b.107.9	yes	16	1.1	even	1	trivial
108.6.b.b.107.10	yes	16	12.11	even	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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	108.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.79734 - 5.36373i) q^{2} +(-25.5392 - 19.2809i) q^{4} +44.9719i q^{5} +28.5094i q^{7} +(-149.320 + 102.331i) q^{8} +O(q^{10})\)	\(q+(1.79734 - 5.36373i) q^{2} +(-25.5392 - 19.2809i) q^{4} +44.9719i q^{5} +28.5094i q^{7} +(-149.320 + 102.331i) q^{8} +(241.217 + 80.8297i) q^{10} +411.905 q^{11} +684.385 q^{13} +(152.917 + 51.2411i) q^{14} +(280.497 + 984.834i) q^{16} -1516.97i q^{17} +2045.09i q^{19} +(867.098 - 1148.55i) q^{20} +(740.332 - 2209.34i) q^{22} +3070.67 q^{23} +1102.53 q^{25} +(1230.07 - 3670.85i) q^{26} +(549.686 - 728.107i) q^{28} -643.596i q^{29} -731.030i q^{31} +(5786.53 + 265.570i) q^{32} +(-8136.61 - 2726.51i) q^{34} -1282.12 q^{35} -5461.90 q^{37} +(10969.3 + 3675.71i) q^{38} +(-4602.02 - 6715.20i) q^{40} -6382.62i q^{41} +17907.2i q^{43} +(-10519.7 - 7941.88i) q^{44} +(5519.03 - 16470.2i) q^{46} +19287.6 q^{47} +15994.2 q^{49} +(1981.61 - 5913.65i) q^{50} +(-17478.6 - 13195.5i) q^{52} -11400.4i q^{53} +18524.2i q^{55} +(-2917.39 - 4257.02i) q^{56} +(-3452.07 - 1156.76i) q^{58} -424.395 q^{59} -6907.86 q^{61} +(-3921.05 - 1313.91i) q^{62} +(11824.8 - 30560.0i) q^{64} +30778.1i q^{65} +58593.9i q^{67} +(-29248.5 + 38742.1i) q^{68} +(-2304.41 + 6876.97i) q^{70} -49133.0 q^{71} +70200.7 q^{73} +(-9816.87 + 29296.1i) q^{74} +(39431.1 - 52229.8i) q^{76} +11743.2i q^{77} +95223.5i q^{79} +(-44289.9 + 12614.5i) q^{80} +(-34234.6 - 11471.7i) q^{82} -55856.8 q^{83} +68221.1 q^{85} +(96049.4 + 32185.3i) q^{86} +(-61505.5 + 42150.6i) q^{88} +93780.9i q^{89} +19511.4i q^{91} +(-78422.3 - 59205.1i) q^{92} +(34666.3 - 103453. i) q^{94} -91971.6 q^{95} -182666. q^{97} +(28747.0 - 85788.6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 94 q^{4}+O(q^{10}) \) 16 * q + 94 * q^4	\( 16 q + 94 q^{4} + 1454 q^{10} + 896 q^{13} + 178 q^{16} + 30 q^{22} + 9888 q^{25} + 11454 q^{28} - 6172 q^{34} - 71008 q^{37} - 16618 q^{40} + 35304 q^{46} - 49376 q^{49} + 14876 q^{52} - 10492 q^{58} + 77888 q^{61} + 89206 q^{64} + 229398 q^{70} - 38032 q^{73} + 48960 q^{76} - 224488 q^{82} - 371264 q^{85} + 249102 q^{88} + 68772 q^{94} - 976 q^{97}+O(q^{100}) \) 16 * q + 94 * q^4 + 1454 * q^10 + 896 * q^13 + 178 * q^16 + 30 * q^22 + 9888 * q^25 + 11454 * q^28 - 6172 * q^34 - 71008 * q^37 - 16618 * q^40 + 35304 * q^46 - 49376 * q^49 + 14876 * q^52 - 10492 * q^58 + 77888 * q^61 + 89206 * q^64 + 229398 * q^70 - 38032 * q^73 + 48960 * q^76 - 224488 * q^82 - 371264 * q^85 + 249102 * q^88 + 68772 * q^94 - 976 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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