LMFDB - Embedded newform 384.6.c.c.383.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,6,Mod(383,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("384.383");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	384.c (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:	$61.5873868082$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 306 x^{18} + 37827 x^{16} + 2442168 x^{14} + 88368509 x^{12} + 1774000974 x^{10} + \cdots + 2870280625 $ x^20 + 306x^18 + 37827x^16 + 2442168x^14 + 88368509x^12 + 1774000974x^10 + 18093172325x^8 + 74958811500x^6 + 79355888475x^4 + 28497132750*x^2 + 2870280625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{88}\cdot 3^{14}\cdot 41^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			383.8
Root			$7.32004i$ of defining polynomial
Character	$\chi$	$=$	384.383
Dual form			384.6.c.c.383.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.3565 + 11.6509i) q^{3} -68.3281i q^{5} -220.652i q^{7} +(-28.4850 - 241.325i) q^{9} +O(q^{10})$	\(q+(-10.3565 + 11.6509i) q^{3} -68.3281i q^{5} -220.652i q^{7} +(-28.4850 - 241.325i) q^{9} +127.204 q^{11} +822.495 q^{13} +(796.081 + 707.641i) q^{15} -1614.81i q^{17} -1811.98i q^{19} +(2570.79 + 2285.19i) q^{21} +1271.87 q^{23} -1543.73 q^{25} +(3106.65 + 2167.41i) q^{27} -7510.51i q^{29} +8582.98i q^{31} +(-1317.39 + 1482.04i) q^{33} -15076.8 q^{35} +5301.04 q^{37} +(-8518.19 + 9582.78i) q^{39} -2358.09i q^{41} +10770.8i q^{43} +(-16489.3 + 1946.33i) q^{45} -4892.49 q^{47} -31880.4 q^{49} +(18813.9 + 16723.8i) q^{51} -3955.35i q^{53} -8691.62i q^{55} +(21111.2 + 18765.8i) q^{57} +41587.0 q^{59} +20088.6 q^{61} +(-53248.8 + 6285.28i) q^{63} -56199.5i q^{65} -44682.4i q^{67} +(-13172.1 + 14818.4i) q^{69} +25092.1 q^{71} -61375.3 q^{73} +(15987.7 - 17985.8i) q^{75} -28067.9i q^{77} -44086.5i q^{79} +(-57426.2 + 13748.3i) q^{81} +1956.05 q^{83} -110337. q^{85} +(87503.9 + 77782.8i) q^{87} -89705.2i q^{89} -181485. i q^{91} +(-99999.1 - 88889.8i) q^{93} -123809. q^{95} +132194. q^{97} +(-3623.41 - 30697.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3}+O(q^{10}) $ 20 * q + 2 * q^3	$ 20 q + 2 q^{3} + 948 q^{11} - 852 q^{15} + 1640 q^{21} - 328 q^{23} - 12500 q^{25} + 2030 q^{27} + 2836 q^{33} - 7184 q^{35} + 15056 q^{37} + 12980 q^{39} + 11800 q^{45} - 36640 q^{47} - 33388 q^{49} + 1936 q^{51} + 15404 q^{57} + 62908 q^{59} + 73264 q^{61} - 23608 q^{63} - 84024 q^{69} - 34888 q^{71} + 52568 q^{73} + 115698 q^{75} + 55444 q^{81} - 225172 q^{83} - 30112 q^{85} + 225700 q^{87} - 148016 q^{93} - 418616 q^{95} + 7600 q^{97} + 378260 q^{99}+O(q^{100}) $ 20 * q + 2 * q^3 + 948 * q^11 - 852 * q^15 + 1640 * q^21 - 328 * q^23 - 12500 * q^25 + 2030 * q^27 + 2836 * q^33 - 7184 * q^35 + 15056 * q^37 + 12980 * q^39 + 11800 * q^45 - 36640 * q^47 - 33388 * q^49 + 1936 * q^51 + 15404 * q^57 + 62908 * q^59 + 73264 * q^61 - 23608 * q^63 - 84024 * q^69 - 34888 * q^71 + 52568 * q^73 + 115698 * q^75 + 55444 * q^81 - 225172 * q^83 - 30112 * q^85 + 225700 * q^87 - 148016 * q^93 - 418616 * q^95 + 7600 * q^97 + 378260 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−10.3565	+	11.6509i	−0.664371	+	0.747403i
$3$	−10.3565	+	11.6509i	−0.664371	+	0.747403i
$4$		0			0
$5$		−	68.3281i		−	1.22229i	−0.791519	−	0.611145i	$-0.790709\pi$
$5$		−	68.3281i		−	1.22229i	0.791519	−	0.611145i	$-0.209291\pi$
$6$		0			0
$7$		−	220.652i		−	1.70201i	−0.525154	−	0.851007i	$-0.675992\pi$
$7$		−	220.652i		−	1.70201i	0.525154	−	0.851007i	$-0.324008\pi$
$8$		0			0
$9$	−28.4850	−	241.325i	−0.117222	−	0.993106i
$10$		0			0
$11$	127.204			0.316971			0.158485	−	0.987361i	$-0.449339\pi$
$11$	127.204			0.316971			0.158485	+	0.987361i	$0.449339\pi$
$12$		0			0
$13$	822.495			1.34982			0.674909	−	0.737901i	$-0.264183\pi$
$13$	822.495			1.34982			0.674909	+	0.737901i	$0.264183\pi$
$14$		0			0
$15$	796.081	+	707.641i	0.913543	+	0.812054i
$16$		0			0
$17$		−	1614.81i		−	1.35518i	−0.735438	−	0.677592i	$-0.763023\pi$
$17$		−	1614.81i		−	1.35518i	0.735438	−	0.677592i	$-0.236977\pi$
$18$		0			0
$19$		−	1811.98i		−	1.15152i	−0.817620	−	0.575758i	$-0.804707\pi$
$19$		−	1811.98i		−	1.15152i	0.817620	−	0.575758i	$-0.195293\pi$
$20$		0			0
$21$	2570.79	+	2285.19i	1.27209	+	1.13077i
$22$		0			0
$23$	1271.87			0.501329			0.250664	−	0.968074i	$-0.419351\pi$
$23$	1271.87			0.501329			0.250664	+	0.968074i	$0.419351\pi$
$24$		0			0
$25$	−1543.73			−0.493994
$26$		0			0
$27$	3106.65	+	2167.41i	0.820129	+	0.572178i
$28$		0			0
$29$		−	7510.51i		−	1.65834i	−0.558993	−	0.829172i	$-0.688812\pi$
$29$		−	7510.51i		−	1.65834i	0.558993	−	0.829172i	$-0.311188\pi$
$30$		0			0
$31$			8582.98i			1.60411i	0.597250	+	0.802055i	$0.296260\pi$
$31$			8582.98i			1.60411i	−0.597250	+	0.802055i	$0.703740\pi$
$32$		0			0
$33$	−1317.39	+	1482.04i	−0.210586	+	0.236905i
$34$		0			0
$35$	−15076.8			−2.08036
$36$		0			0
$37$	5301.04			0.636585			0.318293	−	0.947993i	$-0.396891\pi$
$37$	5301.04			0.636585			0.318293	+	0.947993i	$0.396891\pi$
$38$		0			0
$39$	−8518.19	+	9582.78i	−0.896780	+	1.00886i
$40$		0			0
$41$		−	2358.09i		−	0.219079i	−0.993982	−	0.109540i	$-0.965062\pi$
$41$		−	2358.09i		−	0.219079i	0.993982	−	0.109540i	$-0.0349376\pi$
$42$		0			0
$43$			10770.8i			0.888339i	0.895943	+	0.444169i	$0.146501\pi$
$43$			10770.8i			0.888339i	−0.895943	+	0.444169i	$0.853499\pi$
$44$		0			0
$45$	−16489.3	+	1946.33i	−1.21386	+	0.143280i
$46$		0			0
$47$	−4892.49			−0.323062			−0.161531	−	0.986868i	$-0.551643\pi$
$47$	−4892.49			−0.323062			−0.161531	+	0.986868i	$0.551643\pi$
$48$		0			0
$49$	−31880.4			−1.89685
$50$		0			0
$51$	18813.9	+	16723.8i	1.01287	+	0.900345i
$52$		0			0
$53$		−	3955.35i		−	0.193417i	−0.995313	−	0.0967087i	$-0.969168\pi$
$53$		−	3955.35i		−	0.193417i	0.995313	−	0.0967087i	$-0.0308315\pi$
$54$		0			0
$55$		−	8691.62i		−	0.387431i
$56$		0			0
$57$	21111.2	+	18765.8i	0.860647	+	0.765034i
$58$		0			0
$59$	41587.0			1.55535			0.777673	−	0.628669i	$-0.216400\pi$
$59$	41587.0			1.55535			0.777673	+	0.628669i	$0.216400\pi$
$60$		0			0
$61$	20088.6			0.691234			0.345617	−	0.938376i	$-0.387670\pi$
$61$	20088.6			0.691234			0.345617	+	0.938376i	$0.387670\pi$
$62$		0			0
$63$	−53248.8	+	6285.28i	−1.69028	+	0.199514i
$64$		0			0
$65$		−	56199.5i		−	1.64987i
$66$		0			0
$67$		−	44682.4i		−	1.21604i	−0.793920	−	0.608022i	$-0.791963\pi$
$67$		−	44682.4i		−	1.21604i	0.793920	−	0.608022i	$-0.208037\pi$
$68$		0			0
$69$	−13172.1	+	14818.4i	−0.333068	+	0.374695i
$70$		0			0
$71$	25092.1			0.590732			0.295366	−	0.955384i	$-0.404558\pi$
$71$	25092.1			0.590732			0.295366	+	0.955384i	$0.404558\pi$
$72$		0			0
$73$	−61375.3			−1.34799			−0.673995	−	0.738736i	$-0.735423\pi$
$73$	−61375.3			−1.34799			−0.673995	+	0.738736i	$0.735423\pi$
$74$		0			0
$75$	15987.7	−	17985.8i	0.328195	−	0.369212i
$76$		0			0
$77$		−	28067.9i		−	0.539489i
$78$		0			0
$79$		−	44086.5i		−	0.794763i	−0.917654	−	0.397381i	$-0.869919\pi$
$79$		−	44086.5i		−	0.794763i	0.917654	−	0.397381i	$-0.130081\pi$
$80$		0			0
$81$	−57426.2	+	13748.3i	−0.972518	+	0.232828i
$82$		0			0
$83$	1956.05			0.0311663			0.0155831	−	0.999879i	$-0.495040\pi$
$83$	1956.05			0.0311663			0.0155831	+	0.999879i	$0.495040\pi$
$84$		0			0
$85$	−110337.			−1.65643
$86$		0			0
$87$	87503.9	+	77782.8i	1.23945	+	1.10176i
$88$		0			0
$89$		−	89705.2i		−	1.20045i	−0.799833	−	0.600223i	$-0.795079\pi$
$89$		−	89705.2i		−	1.20045i	0.799833	−	0.600223i	$-0.204921\pi$
$90$		0			0
$91$		−	181485.i		−	2.29741i
$92$		0			0
$93$	−99999.1	−	88889.8i	−1.19892	−	1.06572i
$94$		0			0
$95$	−123809.			−1.40749
$96$		0			0
$97$	132194.			1.42653			0.713266	−	0.700893i	$-0.247215\pi$
$97$	132194.			1.42653			0.713266	+	0.700893i	$0.247215\pi$
$98$		0			0
$99$	−3623.41	−	30697.5i	−0.0371561	−	0.314786i
$100$		0			0
$101$		−	87841.5i		−	0.856833i	−0.903581	−	0.428417i	$-0.859072\pi$
$101$		−	87841.5i		−	0.856833i	0.903581	−	0.428417i	$-0.140928\pi$
$102$		0			0
$103$			73320.5i			0.680977i	0.940249	+	0.340488i	$0.110592\pi$
$103$			73320.5i			0.680977i	−0.940249	+	0.340488i	$0.889408\pi$
$104$		0			0
$105$	156143.	−	175657.i	1.38213	−	1.55486i
$106$		0			0
$107$	102567.			0.866059			0.433030	−	0.901380i	$-0.357445\pi$
$107$	102567.			0.866059			0.433030	+	0.901380i	$0.357445\pi$
$108$		0			0
$109$	54319.7			0.437917			0.218958	−	0.975734i	$-0.429734\pi$
$109$	54319.7			0.437917			0.218958	+	0.975734i	$0.429734\pi$
$110$		0			0
$111$	−54900.3	+	61761.6i	−0.422929	+	0.475786i
$112$		0			0
$113$			183565.i			1.35237i	0.736734	+	0.676183i	$0.236367\pi$
$113$			183565.i			1.35237i	−0.736734	+	0.676183i	$0.763633\pi$
$114$		0			0
$115$		−	86904.4i		−	0.612769i
$116$		0			0
$117$	−23428.8	−	198488.i	−0.158229	−	1.34051i
$118$		0			0
$119$	−356311.			−2.30654
$120$		0			0
$121$	−144870.			−0.899529
$122$		0			0
$123$	27473.8	+	24421.6i	0.163740	+	0.145550i
$124$		0			0
$125$		−	108045.i		−	0.618487i
$126$		0			0
$127$			188684.i			1.03807i	0.854753	+	0.519035i	$0.173709\pi$
$127$			188684.i			1.03807i	−0.854753	+	0.519035i	$0.826291\pi$
$128$		0			0
$129$	−125490.	−	111548.i	−0.663947	−	0.590186i
$130$		0			0
$131$	−16695.8			−0.0850018			−0.0425009	−	0.999096i	$-0.513533\pi$
$131$	−16695.8			−0.0850018			−0.0425009	+	0.999096i	$0.513533\pi$
$132$		0			0
$133$	−399818.			−1.95990
$134$		0			0
$135$	148095.	−	212271.i	0.699368	−	1.00244i
$136$		0			0
$137$		−	266279.i		−	1.21209i	−0.795430	−	0.606045i	$-0.792755\pi$
$137$		−	266279.i		−	1.21209i	0.795430	−	0.606045i	$-0.207245\pi$
$138$		0			0
$139$			184340.i			0.809251i	0.914483	+	0.404625i	$0.132598\pi$
$139$			184340.i			0.809251i	−0.914483	+	0.404625i	$0.867402\pi$
$140$		0			0
$141$	50669.2	−	57001.7i	0.214633	−	0.241457i
$142$		0			0
$143$	104625.			0.427853
$144$		0			0
$145$	−513179.			−2.02698
$146$		0			0
$147$	330170.	−	371434.i	1.26021	−	1.41771i
$148$		0			0
$149$			423693.i			1.56346i	0.623619	+	0.781728i	$0.285662\pi$
$149$			423693.i			1.56346i	−0.623619	+	0.781728i	$0.714338\pi$
$150$		0			0
$151$			144922.i			0.517238i	0.965979	+	0.258619i	$0.0832675\pi$
$151$			144922.i			0.517238i	−0.965979	+	0.258619i	$0.916733\pi$
$152$		0			0
$153$	−389693.	+	45997.8i	−1.34584	+	0.158858i
$154$		0			0
$155$	586459.			1.96069
$156$		0			0
$157$	212694.			0.688661			0.344330	−	0.938849i	$-0.388106\pi$
$157$	212694.			0.688661			0.344330	+	0.938849i	$0.388106\pi$
$158$		0			0
$159$	46083.3	+	40963.7i	0.144561	+	0.128501i
$160$		0			0
$161$		−	280641.i		−	0.853269i
$162$		0			0
$163$			221937.i			0.654276i	0.944977	+	0.327138i	$0.106084\pi$
$163$			221937.i			0.654276i	−0.944977	+	0.327138i	$0.893916\pi$
$164$		0			0
$165$	101265.	+	90014.9i	0.289567	+	0.257398i
$166$		0			0
$167$	−591426.			−1.64100			−0.820501	−	0.571645i	$-0.806305\pi$
$167$	−591426.			−1.64100			−0.820501	+	0.571645i	$0.806305\pi$
$168$		0			0
$169$	305205.			0.822007
$170$		0			0
$171$	−437276.	+	51614.4i	−1.14358	+	0.134983i
$172$		0			0
$173$		−	5002.26i		−	0.0127072i	−0.999980	−	0.00635361i	$-0.997978\pi$
$173$		−	5002.26i		−	0.0127072i	0.999980	−	0.00635361i	$-0.00202243\pi$
$174$		0			0
$175$			340627.i			0.840784i
$176$		0			0
$177$	−430696.	+	484524.i	−1.03333	+	1.16247i
$178$		0			0
$179$	−107536.			−0.250854			−0.125427	−	0.992103i	$-0.540030\pi$
$179$	−107536.			−0.250854			−0.125427	+	0.992103i	$0.540030\pi$
$180$		0			0
$181$	−243918.			−0.553410			−0.276705	−	0.960955i	$-0.589243\pi$
$181$	−243918.			−0.553410			−0.276705	+	0.960955i	$0.589243\pi$
$182$		0			0
$183$	−208048.	+	234049.i	−0.459236	+	0.516630i
$184$		0			0
$185$		−	362210.i		−	0.778092i
$186$		0			0
$187$		−	205410.i		−	0.429554i
$188$		0			0
$189$	478244.	−	685488.i	0.973856	−	1.39587i
$190$		0			0
$191$	160053.			0.317455			0.158727	−	0.987322i	$-0.449261\pi$
$191$	160053.			0.317455			0.158727	+	0.987322i	$0.449261\pi$
$192$		0			0
$193$	−204379.			−0.394951			−0.197475	−	0.980308i	$-0.563274\pi$
$193$	−204379.			−0.394951			−0.197475	+	0.980308i	$0.563274\pi$
$194$		0			0
$195$	654773.	+	582032.i	1.23312	+	1.09612i
$196$		0			0
$197$		−	30745.1i		−	0.0564431i	−0.999602	−	0.0282215i	$-0.991016\pi$
$197$		−	30745.1i		−	0.0564431i	0.999602	−	0.0282215i	$-0.00898439\pi$
$198$		0			0
$199$			311400.i			0.557424i	0.960375	+	0.278712i	$0.0899075\pi$
$199$			311400.i			0.557424i	−0.960375	+	0.278712i	$0.910093\pi$
$200$		0			0
$201$	520588.	+	462754.i	0.908875	+	0.807905i
$202$		0			0
$203$	−1.65721e6			−2.82253
$204$		0			0
$205$	−161124.			−0.267778
$206$		0			0
$207$	−36229.2	−	306933.i	−0.0587669	−	0.497873i
$208$		0			0
$209$		−	230492.i		−	0.364997i
$210$		0			0
$211$			494519.i			0.764675i	0.924023	+	0.382337i	$0.124881\pi$
$211$			494519.i			0.764675i	−0.924023	+	0.382337i	$0.875119\pi$
$212$		0			0
$213$	−259866.	+	292344.i	−0.392465	+	0.441515i
$214$		0			0
$215$	735951.			1.08581
$216$		0			0
$217$	1.89385e6			2.73022
$218$		0			0
$219$	635635.	−	715075.i	0.895566	−	1.00749i
$220$		0			0
$221$		−	1.32817e6i		−	1.82925i
$222$		0			0
$223$		−	234819.i		−	0.316206i	−0.987423	−	0.158103i	$-0.949462\pi$
$223$		−	234819.i		−	0.316206i	0.987423	−	0.158103i	$-0.0505379\pi$
$224$		0			0
$225$	43973.2	+	372540.i	0.0579071	+	0.490588i
$226$		0			0
$227$	−578888.			−0.745641			−0.372820	−	0.927904i	$-0.621609\pi$
$227$	−578888.			−0.745641			−0.372820	+	0.927904i	$0.621609\pi$
$228$		0			0
$229$	680645.			0.857693			0.428846	−	0.903377i	$-0.358920\pi$
$229$	680645.			0.857693			0.428846	+	0.903377i	$0.358920\pi$
$230$		0			0
$231$	327015.	+	290686.i	0.403216	+	0.358421i
$232$		0			0
$233$		−	1.00982e6i		−	1.21858i	−0.792946	−	0.609292i	$-0.791454\pi$
$233$		−	1.00982e6i		−	1.21858i	0.792946	−	0.609292i	$-0.208546\pi$
$234$		0			0
$235$			334295.i			0.394875i
$236$		0			0
$237$	513645.	+	456582.i	0.594008	+	0.528017i
$238$		0			0
$239$	174729.			0.197866			0.0989330	−	0.995094i	$-0.468457\pi$
$239$	174729.			0.197866			0.0989330	+	0.995094i	$0.468457\pi$
$240$		0			0
$241$	−542258.			−0.601400			−0.300700	−	0.953719i	$-0.597220\pi$
$241$	−542258.			−0.601400			−0.300700	+	0.953719i	$0.597220\pi$
$242$		0			0
$243$	434556.	−	811449.i	0.472096	−	0.881547i
$244$		0			0
$245$			2.17833e6i			2.31851i
$246$		0			0
$247$		−	1.49035e6i		−	1.55434i
$248$		0			0
$249$	−20257.9	+	22789.7i	−0.0207060	+	0.0232938i
$250$		0			0
$251$	−1.22026e6			−1.22255			−0.611275	−	0.791418i	$-0.709343\pi$
$251$	−1.22026e6			−1.22255			−0.611275	+	0.791418i	$0.709343\pi$
$252$		0			0
$253$	161787.			0.158907
$254$		0			0
$255$	1.14270e6	−	1.28552e6i	1.10048	−	1.23802i
$256$		0			0
$257$			1.94731e6i			1.83909i	0.392985	+	0.919545i	$0.371443\pi$
$257$			1.94731e6i			1.83909i	−0.392985	+	0.919545i	$0.628557\pi$
$258$		0			0
$259$		−	1.16969e6i		−	1.08348i
$260$		0			0
$261$	−1.81247e6	+	213937.i	−1.64691	+	0.194395i
$262$		0			0
$263$	−756097.			−0.674044			−0.337022	−	0.941497i	$-0.609420\pi$
$263$	−756097.			−0.674044			−0.337022	+	0.941497i	$0.609420\pi$
$264$		0			0
$265$	−270262.			−0.236412
$266$		0			0
$267$	1.04514e6	+	929033.i	0.897217	+	0.797541i
$268$		0			0
$269$			2.16001e6i			1.82002i	0.414589	+	0.910009i	$0.363926\pi$
$269$			2.16001e6i			1.82002i	−0.414589	+	0.910009i	$0.636074\pi$
$270$		0			0
$271$		−	552826.i		−	0.457262i	−0.973513	−	0.228631i	$-0.926575\pi$
$271$		−	552826.i		−	0.457262i	0.973513	−	0.228631i	$-0.0734249\pi$
$272$		0			0
$273$	2.11446e6	+	1.87956e6i	1.71709	+	1.52633i
$274$		0			0
$275$	−196369.			−0.156582
$276$		0			0
$277$	−156564.			−0.122600			−0.0613001	−	0.998119i	$-0.519525\pi$
$277$	−156564.			−0.122600			−0.0613001	+	0.998119i	$0.519525\pi$
$278$		0			0
$279$	2.07129e6	−	244486.i	1.59305	−	0.188037i
$280$		0			0
$281$		−	250121.i		−	0.188967i	−0.995526	−	0.0944833i	$-0.969880\pi$
$281$		−	250121.i		−	0.188967i	0.995526	−	0.0944833i	$-0.0301199\pi$
$282$		0			0
$283$		−	901607.i		−	0.669193i	−0.942362	−	0.334596i	$-0.891400\pi$
$283$		−	901607.i		−	0.669193i	0.942362	−	0.334596i	$-0.108600\pi$
$284$		0			0
$285$	1.28223e6	−	1.44249e6i	0.935094	−	1.05196i
$286$		0			0
$287$	−520318.			−0.372876
$288$		0			0
$289$	−1.18775e6			−0.836525
$290$		0			0
$291$	−1.36907e6	+	1.54017e6i	−0.947747	+	1.06619i
$292$		0			0
$293$			1.05731e6i			0.719502i	0.933048	+	0.359751i	$0.117138\pi$
$293$			1.05731e6i			0.719502i	−0.933048	+	0.359751i	$0.882862\pi$
$294$		0			0
$295$		−	2.84156e6i		−	1.90109i
$296$		0			0
$297$	395178.	+	275703.i	0.259957	+	0.181364i
$298$		0			0
$299$	1.04611e6			0.676702
$300$		0			0
$301$	2.37661e6			1.51197
$302$		0			0
$303$	1.02343e6	+	909732.i	0.640400	+	0.569255i
$304$		0			0
$305$		−	1.37262e6i		−	0.844888i
$306$		0			0
$307$			2.73925e6i			1.65877i	0.558680	+	0.829383i	$0.311308\pi$
$307$			2.73925e6i			1.65877i	−0.558680	+	0.829383i	$0.688692\pi$
$308$		0			0
$309$	−854247.	−	759345.i	−0.508964	−	0.452421i
$310$		0			0
$311$	−690547.			−0.404848			−0.202424	−	0.979298i	$-0.564882\pi$
$311$	−690547.			−0.404848			−0.202424	+	0.979298i	$0.564882\pi$
$312$		0			0
$313$	2.15682e6			1.24438			0.622190	−	0.782866i	$-0.286243\pi$
$313$	2.15682e6			1.24438			0.622190	+	0.782866i	$0.286243\pi$
$314$		0			0
$315$	429462.	+	3.63839e6i	0.243864	+	2.06601i
$316$		0			0
$317$			1.54663e6i			0.864444i	0.901767	+	0.432222i	$0.142270\pi$
$317$			1.54663e6i			0.864444i	−0.901767	+	0.432222i	$0.857730\pi$
$318$		0			0
$319$		−	955368.i		−	0.525647i
$320$		0			0
$321$	−1.06224e6	+	1.19499e6i	−0.575385	+	0.647295i
$322$		0			0
$323$	−2.92600e6			−1.56052
$324$		0			0
$325$	−1.26971e6			−0.666801
$326$		0			0
$327$	−562563.	+	632871.i	−0.290939	+	0.327300i
$328$		0			0
$329$			1.07954e6i			0.549856i
$330$		0			0
$331$			1.83481e6i			0.920492i	0.887791	+	0.460246i	$0.152239\pi$
$331$			1.83481e6i			0.920492i	−0.887791	+	0.460246i	$0.847761\pi$
$332$		0			0
$333$	−151000.	−	1.27927e6i	−0.0746220	−	0.632196i
$334$		0			0
$335$	−3.05306e6			−1.48636
$336$		0			0
$337$	967875.			0.464242			0.232121	−	0.972687i	$-0.425433\pi$
$337$	967875.			0.464242			0.232121	+	0.972687i	$0.425433\pi$
$338$		0			0
$339$	−2.13869e6	−	1.90110e6i	−1.01076	−	0.898473i
$340$		0			0
$341$			1.09179e6i			0.508456i
$342$		0			0
$343$			3.32599e6i			1.52646i
$344$		0			0
$345$	1.01251e6	+	900027.i	0.457986	+	0.407106i
$346$		0			0
$347$	−1.57684e6			−0.703014			−0.351507	−	0.936185i	$-0.614331\pi$
$347$	−1.57684e6			−0.703014			−0.351507	+	0.936185i	$0.614331\pi$
$348$		0			0
$349$	3.26606e6			1.43536			0.717680	−	0.696373i	$-0.245204\pi$
$349$	3.26606e6			1.43536			0.717680	+	0.696373i	$0.245204\pi$
$350$		0			0
$351$	2.55520e6	+	1.78268e6i	1.10702	+	0.772336i
$352$		0			0
$353$			3.52395e6i			1.50520i	0.658480	+	0.752598i	$0.271200\pi$
$353$			3.52395e6i			1.50520i	−0.658480	+	0.752598i	$0.728800\pi$
$354$		0			0
$355$		−	1.71449e6i		−	0.722046i
$356$		0			0
$357$	3.69014e6	−	4.15133e6i	1.53240	−	1.72392i
$358$		0			0
$359$	4.54119e6			1.85966			0.929831	−	0.367987i	$-0.119953\pi$
$359$	4.54119e6			1.85966			0.929831	+	0.367987i	$0.119953\pi$
$360$		0			0
$361$	−807182.			−0.325989
$362$		0			0
$363$	1.50035e6	−	1.68786e6i	0.597621	−	0.672311i
$364$		0			0
$365$			4.19366e6i			1.64764i
$366$		0			0
$367$			2.65740e6i			1.02989i	0.857222	+	0.514947i	$0.172188\pi$
$367$			2.65740e6i			1.02989i	−0.857222	+	0.514947i	$0.827812\pi$
$368$		0			0
$369$	−569066.	+	67170.3i	−0.217569	+	0.0256810i
$370$		0			0
$371$	−872758.			−0.329199
$372$		0			0
$373$	1.64352e6			0.611650			0.305825	−	0.952088i	$-0.401068\pi$
$373$	1.64352e6			0.611650			0.305825	+	0.952088i	$0.401068\pi$
$374$		0			0
$375$	1.25882e6	+	1.11897e6i	0.462259	+	0.410905i
$376$		0			0
$377$		−	6.17736e6i		−	2.23846i
$378$		0			0
$379$		−	2.95754e6i		−	1.05763i	−0.848738	−	0.528813i	$-0.822637\pi$
$379$		−	2.95754e6i		−	1.05763i	0.848738	−	0.528813i	$-0.177363\pi$
$380$		0			0
$381$	−2.19833e6	−	1.95411e6i	−0.775856	−	0.689663i
$382$		0			0
$383$	−5.01058e6			−1.74538			−0.872691	−	0.488272i	$-0.837627\pi$
$383$	−5.01058e6			−1.74538			−0.872691	+	0.488272i	$0.837627\pi$
$384$		0			0
$385$	−1.91783e6			−0.659413
$386$		0			0
$387$	2.59927e6	−	306808.i	0.882214	−	0.104133i
$388$		0			0
$389$			4.58862e6i			1.53748i	0.639564	+	0.768738i	$0.279115\pi$
$389$			4.58862e6i			1.53748i	−0.639564	+	0.768738i	$0.720885\pi$
$390$		0			0
$391$		−	2.05382e6i		−	0.679393i
$392$		0			0
$393$	172910.	−	194520.i	0.0564727	−	0.0635306i
$394$		0			0
$395$	−3.01234e6			−0.971431
$396$		0			0
$397$	−607181.			−0.193349			−0.0966745	−	0.995316i	$-0.530821\pi$
$397$	−607181.			−0.193349			−0.0966745	+	0.995316i	$0.530821\pi$
$398$		0			0
$399$	4.14072e6	−	4.65822e6i	1.30210	−	1.46483i
$400$		0			0
$401$		−	5.86565e6i		−	1.82161i	−0.412839	−	0.910804i	$-0.635463\pi$
$401$		−	5.86565e6i		−	1.82161i	0.412839	−	0.910804i	$-0.364537\pi$
$402$		0			0
$403$			7.05946e6i			2.16525i
$404$		0			0
$405$	939394.	+	3.92382e6i	0.284584	+	1.18870i
$406$		0			0
$407$	674314.			0.201779
$408$		0			0
$409$	−5.60951e6			−1.65812			−0.829062	−	0.559157i	$-0.811125\pi$
$409$	−5.60951e6			−1.65812			−0.829062	+	0.559157i	$0.811125\pi$
$410$		0			0
$411$	3.10238e6	+	2.75772e6i	0.905920	+	0.805278i
$412$		0			0
$413$		−	9.17626e6i		−	2.64722i
$414$		0			0
$415$		−	133653.i		−	0.0380942i
$416$		0			0
$417$	−2.14772e6	−	1.90912e6i	−0.604836	−	0.537643i
$418$		0			0
$419$	4.07630e6			1.13431			0.567154	−	0.823612i	$-0.308044\pi$
$419$	4.07630e6			1.13431			0.567154	+	0.823612i	$0.308044\pi$
$420$		0			0
$421$	833004.			0.229056			0.114528	−	0.993420i	$-0.463464\pi$
$421$	833004.			0.229056			0.114528	+	0.993420i	$0.463464\pi$
$422$		0			0
$423$	139363.	+	1.18068e6i	0.0378700	+	0.320834i
$424$		0			0
$425$			2.49283e6i			0.669452i
$426$		0			0
$427$		−	4.43259e6i		−	1.17649i
$428$		0			0
$429$	−1.08355e6	+	1.21897e6i	−0.284253	+	0.319779i
$430$		0			0
$431$	150608.			0.0390529			0.0195265	−	0.999809i	$-0.493784\pi$
$431$	150608.			0.0390529			0.0195265	+	0.999809i	$0.493784\pi$
$432$		0			0
$433$	5.74052e6			1.47140			0.735702	−	0.677306i	$-0.236853\pi$
$433$	5.74052e6			1.47140			0.735702	+	0.677306i	$0.236853\pi$
$434$		0			0
$435$	5.31475e6	−	5.97898e6i	1.34667	−	1.51497i
$436$		0			0
$437$		−	2.30460e6i		−	0.577288i
$438$		0			0
$439$			2.36366e6i			0.585360i	0.956210	+	0.292680i	$0.0945470\pi$
$439$			2.36366e6i			0.585360i	−0.956210	+	0.292680i	$0.905453\pi$
$440$		0			0
$441$	908115.	+	7.69353e6i	0.222354	+	1.88378i
$442$		0			0
$443$	−3.59887e6			−0.871279			−0.435639	−	0.900121i	$-0.643478\pi$
$443$	−3.59887e6			−0.871279			−0.435639	+	0.900121i	$0.643478\pi$
$444$		0			0
$445$	−6.12939e6			−1.46729
$446$		0			0
$447$	−4.93639e6	−	4.38799e6i	−1.16853	−	1.03872i
$448$		0			0
$449$		−	5.82578e6i		−	1.36376i	−0.731464	−	0.681880i	$-0.761163\pi$
$449$		−	5.82578e6i		−	1.36376i	0.731464	−	0.681880i	$-0.238837\pi$
$450$		0			0
$451$		−	299959.i		−	0.0694417i
$452$		0			0
$453$	−1.68846e6	−	1.50088e6i	−0.386585	−	0.343638i
$454$		0			0
$455$	−1.24006e7			−2.80810
$456$		0			0
$457$	4.36862e6			0.978485			0.489243	−	0.872148i	$-0.337273\pi$
$457$	4.36862e6			0.978485			0.489243	+	0.872148i	$0.337273\pi$
$458$		0			0
$459$	3.49995e6	−	5.01663e6i	0.775407	−	1.11143i
$460$		0			0
$461$			2.49466e6i			0.546713i	0.961913	+	0.273356i	$0.0881338\pi$
$461$			2.49466e6i			0.546713i	−0.961913	+	0.273356i	$0.911866\pi$
$462$		0			0
$463$			2.72945e6i			0.591728i	0.955230	+	0.295864i	$0.0956075\pi$
$463$			2.72945e6i			0.591728i	−0.955230	+	0.295864i	$0.904392\pi$
$464$		0			0
$465$	−6.07367e6	+	6.83275e6i	−1.30262	+	1.46542i
$466$		0			0
$467$	−4.70534e6			−0.998387			−0.499194	−	0.866491i	$-0.666370\pi$
$467$	−4.70534e6			−0.998387			−0.499194	+	0.866491i	$0.666370\pi$
$468$		0			0
$469$	−9.85927e6			−2.06973
$470$		0			0
$471$	−2.20277e6	+	2.47806e6i	−0.457526	+	0.514707i
$472$		0			0
$473$			1.37010e6i			0.281578i
$474$		0			0
$475$			2.79721e6i			0.568842i
$476$		0			0
$477$	−954524.	+	112668.i	−0.192084	+	0.0226728i
$478$		0			0
$479$	−647214.			−0.128887			−0.0644435	−	0.997921i	$-0.520527\pi$
$479$	−647214.			−0.128887			−0.0644435	+	0.997921i	$0.520527\pi$
$480$		0			0
$481$	4.36008e6			0.859274
$482$		0			0
$483$	3.26971e6	+	2.90646e6i	0.637736	+	0.566887i
$484$		0			0
$485$		−	9.03255e6i		−	1.74364i
$486$		0			0
$487$		−	5.76449e6i		−	1.10138i	−0.834709	−	0.550692i	$-0.814364\pi$
$487$		−	5.76449e6i		−	1.10138i	0.834709	−	0.550692i	$-0.185636\pi$
$488$		0			0
$489$	−2.58576e6	−	2.29850e6i	−0.489008	−	0.434682i
$490$		0			0
$491$	4.99013e6			0.934132			0.467066	−	0.884222i	$-0.345311\pi$
$491$	4.99013e6			0.934132			0.467066	+	0.884222i	$0.345311\pi$
$492$		0			0
$493$	−1.21280e7			−2.24736
$494$		0			0
$495$	−2.09750e6	+	247581.i	−0.384759	+	0.0454155i
$496$		0			0
$497$		−	5.53662e6i		−	1.00543i
$498$		0			0
$499$		−	5.44565e6i		−	0.979036i	−0.871993	−	0.489518i	$-0.837173\pi$
$499$		−	5.44565e6i		−	0.979036i	0.871993	−	0.489518i	$-0.162827\pi$
$500$		0			0
$501$	6.12511e6	−	6.89062e6i	1.09023	−	1.22649i
$502$		0			0
$503$	526428.			0.0927724			0.0463862	−	0.998924i	$-0.485230\pi$
$503$	526428.			0.0927724			0.0463862	+	0.998924i	$0.485230\pi$
$504$		0			0
$505$	−6.00204e6			−1.04730
$506$		0			0
$507$	−3.16087e6	+	3.55590e6i	−0.546117	+	0.614370i
$508$		0			0
$509$			9.15695e6i			1.56659i	0.621648	+	0.783297i	$0.286464\pi$
$509$			9.15695e6i			1.56659i	−0.621648	+	0.783297i	$0.713536\pi$
$510$		0			0
$511$			1.35426e7i			2.29430i
$512$		0			0
$513$	3.92731e6	−	5.62919e6i	0.658873	−	0.944392i
$514$		0			0
$515$	5.00985e6			0.832351
$516$		0			0
$517$	−622345.			−0.102401
$518$		0			0
$519$	58280.6	+	51806.0i	0.00949741	+	0.00844231i
$520$		0			0
$521$		−	5.56653e6i		−	0.898443i	−0.893421	−	0.449221i	$-0.851701\pi$
$521$		−	5.56653e6i		−	0.898443i	0.893421	−	0.449221i	$-0.148299\pi$
$522$		0			0
$523$		−	6.05676e6i		−	0.968246i	−0.875000	−	0.484123i	$-0.839139\pi$
$523$		−	6.05676e6i		−	0.968246i	0.875000	−	0.484123i	$-0.160861\pi$
$524$		0			0
$525$	−3.96860e6	−	3.52772e6i	−0.628405	−	0.558593i
$526$		0			0
$527$	1.38599e7			2.17386
$528$		0			0
$529$	−4.81869e6			−0.748669
$530$		0			0
$531$	−1.18461e6	−	1.00360e7i	−0.182321	−	1.54462i
$532$		0			0
$533$		−	1.93952e6i		−	0.295717i
$534$		0			0
$535$		−	7.00820e6i		−	1.05858i
$536$		0			0
$537$	1.11370e6	−	1.25289e6i	0.166660	−	0.187489i
$538$		0			0
$539$	−4.05532e6			−0.601248
$540$		0			0
$541$	5.29133e6			0.777270			0.388635	−	0.921392i	$-0.372947\pi$
$541$	5.29133e6			0.777270			0.388635	+	0.921392i	$0.372947\pi$
$542$		0			0
$543$	2.52614e6	−	2.84185e6i	0.367670	−	0.413621i
$544$		0			0
$545$		−	3.71156e6i		−	0.535261i
$546$		0			0
$547$		−	8.21711e6i		−	1.17422i	−0.809506	−	0.587112i	$-0.800265\pi$
$547$		−	8.21711e6i		−	1.17422i	0.809506	−	0.587112i	$-0.199735\pi$
$548$		0			0
$549$	−572224.	−	4.84787e6i	−0.0810280	−	0.686468i
$550$		0			0
$551$	−1.36089e7			−1.90961
$552$		0			0
$553$	−9.72778e6			−1.35270
$554$		0			0
$555$	4.22005e6	+	3.75123e6i	0.581548	+	0.516942i
$556$		0			0
$557$		−	2.41544e6i		−	0.329882i	−0.986303	−	0.164941i	$-0.947257\pi$
$557$		−	2.41544e6i		−	0.329882i	0.986303	−	0.164941i	$-0.0527434\pi$
$558$		0			0
$559$			8.85897e6i			1.19909i
$560$		0			0
$561$	2.39320e6	+	2.12733e6i	0.321050	+	0.285383i
$562$		0			0
$563$	4.33439e6			0.576311			0.288155	−	0.957584i	$-0.406958\pi$
$563$	4.33439e6			0.576311			0.288155	+	0.957584i	$0.406958\pi$
$564$		0			0
$565$	1.25427e7			1.65298
$566$		0			0
$567$	3.03359e6	+	1.26712e7i	0.396277	+	1.65524i
$568$		0			0
$569$		−	2.65391e6i		−	0.343642i	−0.985128	−	0.171821i	$-0.945035\pi$
$569$		−	2.65391e6i		−	0.343642i	0.985128	−	0.171821i	$-0.0549650\pi$
$570$		0			0
$571$		−	6.15066e6i		−	0.789463i	−0.918797	−	0.394731i	$-0.870838\pi$
$571$		−	6.15066e6i		−	0.789463i	0.918797	−	0.394731i	$-0.129162\pi$
$572$		0			0
$573$	−1.65760e6	+	1.86476e6i	−0.210908	+	0.237266i
$574$		0			0
$575$	−1.96342e6			−0.247653
$576$		0			0
$577$	9.44669e6			1.18125			0.590623	−	0.806948i	$-0.298882\pi$
$577$	9.44669e6			1.18125			0.590623	+	0.806948i	$0.298882\pi$
$578$		0			0
$579$	2.11665e6	−	2.38119e6i	0.262394	−	0.295187i
$580$		0			0
$581$		−	431607.i		−	0.0530454i
$582$		0			0
$583$		−	503137.i		−	0.0613077i
$584$		0			0
$585$	−1.35623e7	+	1.60084e6i	−1.63849	+	0.193401i
$586$		0			0
$587$	8.38191e6			1.00403			0.502016	−	0.864858i	$-0.332592\pi$
$587$	8.38191e6			1.00403			0.502016	+	0.864858i	$0.332592\pi$
$588$		0			0
$589$	1.55522e7			1.84716
$590$		0			0
$591$	358207.	+	318412.i	0.0421857	+	0.0374991i
$592$		0			0
$593$		−	2.37462e6i		−	0.277304i	−0.990341	−	0.138652i	$-0.955723\pi$
$593$		−	2.37462e6i		−	0.277304i	0.990341	−	0.138652i	$-0.0442770\pi$
$594$		0			0
$595$			2.43460e7i			2.81927i
$596$		0			0
$597$	−3.62807e6	−	3.22502e6i	−0.416620	−	0.370336i
$598$		0			0
$599$	4.94883e6			0.563554			0.281777	−	0.959480i	$-0.409076\pi$
$599$	4.94883e6			0.563554			0.281777	+	0.959480i	$0.409076\pi$
$600$		0			0
$601$	−5.67466e6			−0.640846			−0.320423	−	0.947275i	$-0.603825\pi$
$601$	−5.67466e6			−0.640846			−0.320423	+	0.947275i	$0.603825\pi$
$602$		0			0
$603$	−1.07830e7	+	1.27278e6i	−1.20766	+	0.142547i
$604$		0			0
$605$			9.89870e6i			1.09949i
$606$		0			0
$607$		−	1.07623e7i		−	1.18558i	−0.805356	−	0.592792i	$-0.798026\pi$
$607$		−	1.07623e7i		−	1.18558i	0.805356	−	0.592792i	$-0.201974\pi$
$608$		0			0
$609$	1.71629e7	−	1.93079e7i	1.87520	−	2.10956i
$610$		0			0
$611$	−4.02405e6			−0.436074
$612$		0			0
$613$	7.22959e6			0.777075			0.388537	−	0.921433i	$-0.372980\pi$
$613$	7.22959e6			0.777075			0.388537	+	0.921433i	$0.372980\pi$
$614$		0			0
$615$	1.66868e6	−	1.87723e6i	0.177904	−	0.200138i
$616$		0			0
$617$			7.18290e6i			0.759603i	0.925068	+	0.379802i	$0.124008\pi$
$617$			7.18290e6i			0.759603i	−0.925068	+	0.379802i	$0.875992\pi$
$618$		0			0
$619$		−	3.97240e6i		−	0.416703i	−0.978054	−	0.208352i	$-0.933190\pi$
$619$		−	3.97240e6i		−	0.416703i	0.978054	−	0.208352i	$-0.0668098\pi$
$620$		0			0
$621$	3.95125e6	+	2.75666e6i	0.411154	+	0.286850i
$622$		0			0
$623$	−1.97937e7			−2.04318
$624$		0			0
$625$	−1.22067e7			−1.24996
$626$		0			0
$627$	2.68543e6	+	2.38709e6i	0.272800	+	0.242494i
$628$		0			0
$629$		−	8.56015e6i		−	0.862690i
$630$		0			0
$631$			1.86816e7i			1.86784i	0.357483	+	0.933920i	$0.383635\pi$
$631$			1.86816e7i			1.86784i	−0.357483	+	0.933920i	$0.616365\pi$
$632$		0			0
$633$	−5.76157e6	−	5.12149e6i	−0.571520	−	0.508028i
$634$		0			0
$635$	1.28924e7			1.26882
$636$		0			0
$637$	−2.62215e7			−2.56041
$638$		0			0
$639$	−714748.	−	6.05533e6i	−0.0692469	−	0.586659i
$640$		0			0
$641$			1.64916e7i			1.58533i	0.609660	+	0.792663i	$0.291306\pi$
$641$			1.64916e7i			1.58533i	−0.609660	+	0.792663i	$0.708694\pi$
$642$		0			0
$643$			7.36471e6i			0.702471i	0.936287	+	0.351235i	$0.114238\pi$
$643$			7.36471e6i			0.702471i	−0.936287	+	0.351235i	$0.885762\pi$
$644$		0			0
$645$	−7.62189e6	+	8.57446e6i	−0.721379	+	0.811536i
$646$		0			0
$647$	−928916.			−0.0872400			−0.0436200	−	0.999048i	$-0.513889\pi$
$647$	−928916.			−0.0872400			−0.0436200	+	0.999048i	$0.513889\pi$
$648$		0			0
$649$	5.29003e6			0.493000
$650$		0			0
$651$	−1.96137e7	+	2.20650e7i	−1.81388	+	2.04057i
$652$		0			0
$653$		−	3.32193e6i		−	0.304865i	−0.988314	−	0.152432i	$-0.951289\pi$
$653$		−	3.32193e6i		−	0.304865i	0.988314	−	0.152432i	$-0.0487106\pi$
$654$		0			0
$655$			1.14079e6i			0.103897i
$656$		0			0
$657$	1.74828e6	+	1.48114e7i	0.158014	+	1.33870i
$658$		0			0
$659$	−4.68098e6			−0.419878			−0.209939	−	0.977714i	$-0.567327\pi$
$659$	−4.68098e6			−0.419878			−0.209939	+	0.977714i	$0.567327\pi$
$660$		0			0
$661$	1.17187e7			1.04322			0.521609	−	0.853185i	$-0.325332\pi$
$661$	1.17187e7			1.04322			0.521609	+	0.853185i	$0.325332\pi$
$662$		0			0
$663$	1.54743e7	+	1.37552e7i	1.36719	+	1.21530i
$664$		0			0
$665$			2.73188e7i			2.39556i
$666$		0			0
$667$		−	9.55239e6i		−	0.831376i
$668$		0			0
$669$	2.73584e6	+	2.43190e6i	0.236334	+	0.210078i
$670$		0			0
$671$	2.55535e6			0.219101
$672$		0			0
$673$	−6.90423e6			−0.587594			−0.293797	−	0.955868i	$-0.594919\pi$
$673$	−6.90423e6			−0.587594			−0.293797	+	0.955868i	$0.594919\pi$
$674$		0			0
$675$	−4.79582e6	−	3.34589e6i	−0.405139	−	0.282652i
$676$		0			0
$677$		−	988176.i		−	0.0828634i	−0.999141	−	0.0414317i	$-0.986808\pi$
$677$		−	988176.i		−	0.0828634i	0.999141	−	0.0414317i	$-0.0131919\pi$
$678$		0			0
$679$		−	2.91688e7i		−	2.42798i
$680$		0			0
$681$	5.99526e6	−	6.74454e6i	0.495382	−	0.557294i
$682$		0			0
$683$	−8.25770e6			−0.677341			−0.338671	−	0.940905i	$-0.609977\pi$
$683$	−8.25770e6			−0.677341			−0.338671	+	0.940905i	$0.609977\pi$
$684$		0			0
$685$	−1.81943e7			−1.48153
$686$		0			0
$687$	−7.04911e6	+	7.93009e6i	−0.569826	+	0.641042i
$688$		0			0
$689$		−	3.25326e6i		−	0.261078i
$690$		0			0
$691$			4.01124e6i			0.319583i	0.987151	+	0.159792i	$0.0510822\pi$
$691$			4.01124e6i			0.319583i	−0.987151	+	0.159792i	$0.948918\pi$
$692$		0			0
$693$	−6.77347e6	+	799514.i	−0.535770	+	0.0632402i
$694$		0			0
$695$	1.25956e7			0.989139
$696$		0			0
$697$	−3.80786e6			−0.296893
$698$		0			0
$699$	1.17653e7	+	1.04582e7i	0.910773	+	0.809591i
$700$		0			0
$701$			1.50880e7i			1.15968i	0.814732	+	0.579838i	$0.196884\pi$
$701$			1.50880e7i			1.15968i	−0.814732	+	0.579838i	$0.803116\pi$
$702$		0			0
$703$		−	9.60539e6i		−	0.733038i
$704$		0			0
$705$	−3.89482e6	−	3.46213e6i	−0.295131	−	0.262344i
$706$		0			0
$707$	−1.93824e7			−1.45834
$708$		0			0
$709$	1.97543e7			1.47587			0.737933	−	0.674874i	$-0.235802\pi$
$709$	1.97543e7			1.47587			0.737933	+	0.674874i	$0.235802\pi$
$710$		0			0
$711$	−1.06392e7	+	1.25580e6i	−0.789283	+	0.0931639i
$712$		0			0
$713$			1.09164e7i			0.804187i
$714$		0			0
$715$		−	7.14881e6i		−	0.522960i
$716$		0			0
$717$	−1.80959e6	+	2.03575e6i	−0.131456	+	0.147886i
$718$		0			0
$719$	1.41299e7			1.01933			0.509666	−	0.860372i	$-0.329769\pi$
$719$	1.41299e7			1.01933			0.509666	+	0.860372i	$0.329769\pi$
$720$		0			0
$721$	1.61783e7			1.15903
$722$		0			0
$723$	5.61591e6	−	6.31777e6i	0.399553	−	0.449488i
$724$		0			0
$725$			1.15942e7i			0.819211i
$726$		0			0
$727$		−	2.30159e7i		−	1.61507i	−0.589819	−	0.807535i	$-0.700801\pi$
$727$		−	2.30159e7i		−	1.61507i	0.589819	−	0.807535i	$-0.299199\pi$
$728$		0			0
$729$	4.95358e6	+	1.34667e7i	0.345224	+	0.938520i
$730$		0			0
$731$	1.73928e7			1.20386
$732$		0			0
$733$	2.21014e7			1.51936			0.759680	−	0.650297i	$-0.225356\pi$
$733$	2.21014e7			1.51936			0.759680	+	0.650297i	$0.225356\pi$
$734$		0			0
$735$	−2.53794e7	−	2.25599e7i	−1.73286	−	1.54035i
$736$		0			0
$737$		−	5.68378e6i		−	0.385451i
$738$		0			0
$739$			1.47260e7i			0.991915i	0.868347	+	0.495957i	$0.165183\pi$
$739$			1.47260e7i			0.991915i	−0.868347	+	0.495957i	$0.834817\pi$
$740$		0			0
$741$	1.73638e7	+	1.54348e7i	1.16172	+	1.03266i
$742$		0			0
$743$	2.30141e7			1.52940			0.764702	−	0.644384i	$-0.222886\pi$
$743$	2.30141e7			1.52940			0.764702	+	0.644384i	$0.222886\pi$
$744$		0			0
$745$	2.89502e7			1.91100
$746$		0			0
$747$	−55718.1	−	472043.i	−0.00365338	−	0.0309514i
$748$		0			0
$749$		−	2.26316e7i		−	1.47405i
$750$		0			0
$751$			1.17181e7i			0.758152i	0.925366	+	0.379076i	$0.123758\pi$
$751$			1.17181e7i			0.758152i	−0.925366	+	0.379076i	$0.876242\pi$
$752$		0			0
$753$	1.26376e7	−	1.42170e7i	0.812226	−	0.913737i
$754$		0			0
$755$	9.90222e6			0.632215
$756$		0			0
$757$	−3.44069e6			−0.218225			−0.109113	−	0.994029i	$-0.534801\pi$
$757$	−3.44069e6			−0.218225			−0.109113	+	0.994029i	$0.534801\pi$
$758$		0			0
$759$	−1.67555e6	+	1.88496e6i	−0.105573	+	0.118767i
$760$		0			0
$761$		−	1.85414e7i		−	1.16060i	−0.814404	−	0.580298i	$-0.802936\pi$
$761$		−	1.85414e7i		−	1.16060i	0.814404	−	0.580298i	$-0.197064\pi$
$762$		0			0
$763$		−	1.19858e7i		−	0.745340i
$764$		0			0
$765$	3.14294e6	+	2.66270e7i	0.194170	+	1.64501i
$766$		0			0
$767$	3.42051e7			2.09943
$768$		0			0
$769$	2.66322e6			0.162402			0.0812009	−	0.996698i	$-0.474124\pi$
$769$	2.66322e6			0.162402			0.0812009	+	0.996698i	$0.474124\pi$
$770$		0			0
$771$	−2.26879e7	−	2.01674e7i	−1.37454	−	1.22184i
$772$		0			0
$773$			2.35235e6i			0.141597i	0.997491	+	0.0707983i	$0.0225547\pi$
$773$			2.35235e6i			0.141597i	−0.997491	+	0.0707983i	$0.977445\pi$
$774$		0			0
$775$		−	1.32498e7i		−	0.792420i
$776$		0			0
$777$	1.36278e7	+	1.21139e7i	0.809794	+	0.719831i
$778$		0			0
$779$	−4.27282e6			−0.252273
$780$		0			0
$781$	3.19181e6			0.187245
$782$		0			0
$783$	1.62784e7	−	2.33325e7i	0.948869	−	1.36006i
$784$		0			0
$785$		−	1.45330e7i		−	0.841743i
$786$		0			0
$787$		−	3.11139e7i		−	1.79068i	−0.445383	−	0.895340i	$-0.646932\pi$
$787$		−	3.11139e7i		−	1.79068i	0.445383	−	0.895340i	$-0.353068\pi$
$788$		0			0
$789$	7.83053e6	−	8.80918e6i	0.447815	−	0.503782i
$790$		0			0
$791$	4.05041e7			2.30175
$792$		0			0
$793$	1.65228e7			0.933039
$794$		0			0
$795$	2.79897e6	−	3.14878e6i	0.157065	−	0.176695i
$796$		0			0
$797$		−	7.70228e6i		−	0.429510i	−0.976668	−	0.214755i	$-0.931105\pi$
$797$		−	7.70228e6i		−	0.429510i	0.976668	−	0.214755i	$-0.0688954\pi$
$798$		0			0
$799$			7.90043e6i			0.437808i
$800$		0			0
$801$	−2.16481e7	+	2.55525e6i	−1.19217	+	0.140719i
$802$		0			0
$803$	−7.80720e6			−0.427274
$804$		0			0
$805$	−1.91757e7			−1.04294
$806$		0			0
$807$	−2.51660e7	−	2.23702e7i	−1.36029	−	1.20917i
$808$		0			0
$809$			1.60228e7i			0.860729i	0.902655	+	0.430365i	$0.141615\pi$
$809$			1.60228e7i			0.860729i	−0.902655	+	0.430365i	$0.858385\pi$
$810$		0			0
$811$			3.53749e7i			1.88861i	0.329070	+	0.944305i	$0.393265\pi$
$811$			3.53749e7i			1.88861i	−0.329070	+	0.944305i	$0.606735\pi$
$812$		0			0
$813$	6.44089e6	+	5.72535e6i	0.341759	+	0.303792i
$814$		0			0
$815$	1.51645e7			0.799715
$816$		0			0
$817$	1.95166e7			1.02294
$818$		0			0
$819$	−4.37969e7	+	5.16962e6i	−2.28157	+	0.269308i
$820$		0			0
$821$		−	1.50635e7i		−	0.779951i	−0.920825	−	0.389975i	$-0.872484\pi$
$821$		−	1.50635e7i		−	0.779951i	0.920825	−	0.389975i	$-0.127516\pi$
$822$		0			0
$823$			2.45822e7i			1.26509i	0.774524	+	0.632544i	$0.217989\pi$
$823$			2.45822e7i			1.26509i	−0.774524	+	0.632544i	$0.782011\pi$
$824$		0			0
$825$	2.03370e6	−	2.28787e6i	0.104028	−	0.117030i
$826$		0			0
$827$	−1.92939e7			−0.980969			−0.490484	−	0.871450i	$-0.663180\pi$
$827$	−1.92939e7			−0.980969			−0.490484	+	0.871450i	$0.663180\pi$
$828$		0			0
$829$	−3.05144e6			−0.154212			−0.0771060	−	0.997023i	$-0.524568\pi$
$829$	−3.05144e6			−0.154212			−0.0771060	+	0.997023i	$0.524568\pi$
$830$		0			0
$831$	1.62145e6	−	1.82410e6i	0.0814521	−	0.0916318i
$832$		0			0
$833$			5.14808e7i			2.57059i
$834$		0			0
$835$			4.04110e7i			2.00578i
$836$		0			0
$837$	−1.86028e7	+	2.66643e7i	−0.917837	+	1.31558i
$838$		0			0
$839$	−3.63919e7			−1.78484			−0.892422	−	0.451202i	$-0.850995\pi$
$839$	−3.63919e7			−1.78484			−0.892422	+	0.451202i	$0.850995\pi$
$840$		0			0
$841$	−3.58967e7			−1.75011
$842$		0			0
$843$	2.91413e6	+	2.59039e6i	0.141234	+	0.125544i
$844$		0			0
$845$		−	2.08541e7i		−	1.00473i
$846$		0			0
$847$			3.19659e7i			1.53101i
$848$		0			0
$849$	1.05045e7	+	9.33751e6i	0.500157	+	0.444592i
$850$		0			0
$851$	6.74222e6			0.319139
$852$		0			0
$853$	−1.71323e7			−0.806200			−0.403100	−	0.915156i	$-0.632067\pi$
$853$	−1.71323e7			−0.806200			−0.403100	+	0.915156i	$0.632067\pi$
$854$		0			0
$855$	3.52671e6	+	2.98782e7i	0.164989	+	1.39778i
$856$		0			0
$857$		−	8.01969e6i		−	0.372997i	−0.982455	−	0.186499i	$-0.940286\pi$
$857$		−	8.01969e6i		−	0.372997i	0.982455	−	0.186499i	$-0.0597140\pi$
$858$		0			0
$859$			2.37490e6i			0.109815i	0.998491	+	0.0549076i	$0.0174864\pi$
$859$			2.37490e6i			0.109815i	−0.998491	+	0.0549076i	$0.982514\pi$
$860$		0			0
$861$	5.38869e6	−	6.06216e6i	0.247728	−	0.278689i
$862$		0			0
$863$	−3.70210e7			−1.69208			−0.846041	−	0.533117i	$-0.821021\pi$
$863$	−3.70210e7			−1.69208			−0.846041	+	0.533117i	$0.821021\pi$
$864$		0			0
$865$	−341795.			−0.0155319
$866$		0			0
$867$	1.23009e7	−	1.38383e7i	0.555763	−	0.625221i
$868$		0			0
$869$		−	5.60798e6i		−	0.251917i
$870$		0			0
$871$		−	3.67511e7i		−	1.64144i
$872$		0			0
$873$	−3.76554e6	−	3.19016e7i	−0.167221	−	1.41670i
$874$		0			0
$875$	−2.38404e7			−1.05267
$876$		0			0
$877$	3.91978e7			1.72093			0.860465	−	0.509510i	$-0.170173\pi$
$877$	3.91978e7			1.72093			0.860465	+	0.509510i	$0.170173\pi$
$878$		0			0
$879$	−1.23185e7	−	1.09500e7i	−0.537758	−	0.478016i
$880$		0			0
$881$			2.86822e7i			1.24501i	0.782616	+	0.622505i	$0.213885\pi$
$881$			2.86822e7i			1.24501i	−0.782616	+	0.622505i	$0.786115\pi$
$882$		0			0
$883$			1.08775e6i			0.0469493i	0.999724	+	0.0234747i	$0.00747290\pi$
$883$			1.08775e6i			0.0469493i	−0.999724	+	0.0234747i	$0.992527\pi$
$884$		0			0
$885$	3.31066e7	+	2.94287e7i	1.42088	+	1.26303i
$886$		0			0
$887$	2.02518e7			0.864280			0.432140	−	0.901806i	$-0.357759\pi$
$887$	2.02518e7			0.864280			0.432140	+	0.901806i	$0.357759\pi$
$888$		0			0
$889$	4.16336e7			1.76681
$890$		0			0
$891$	−7.30485e6	+	1.74884e6i	−0.308260	+	0.0737998i
$892$		0			0
$893$			8.86511e6i			0.372011i
$894$		0			0
$895$			7.34774e6i			0.306617i
$896$		0			0
$897$	−1.08340e7	+	1.21880e7i	−0.449581	+	0.505769i
$898$		0			0
$899$	6.44626e7			2.66017
$900$		0			0
$901$	−6.38713e6			−0.262116
$902$		0			0
$903$	−2.46134e7	+	2.76896e7i	−1.00451	+	1.13005i
$904$		0			0
$905$			1.66665e7i			0.676428i
$906$		0			0
$907$		−	1.16401e7i		−	0.469826i	−0.972016	−	0.234913i	$-0.924520\pi$
$907$		−	1.16401e7i		−	0.469826i	0.972016	−	0.234913i	$-0.0754805\pi$
$908$		0			0
$909$	−2.11983e7	+	2.50217e6i	−0.850926	+	0.100440i
$910$		0			0
$911$	4.42143e7			1.76509			0.882546	−	0.470227i	$-0.155828\pi$
$911$	4.42143e7			1.76509			0.882546	+	0.470227i	$0.155828\pi$
$912$		0			0
$913$	248818.			0.00987880
$914$		0			0
$915$	1.59921e7	+	1.42155e7i	0.631472	+	0.561319i
$916$		0			0
$917$			3.68396e6i			0.144674i
$918$		0			0
$919$			5.62228e6i			0.219596i	0.993954	+	0.109798i	$0.0350203\pi$
$919$			5.62228e6i			0.219596i	−0.993954	+	0.109798i	$0.964980\pi$
$920$		0			0
$921$	−3.19146e7	−	2.83691e7i	−1.23977	−	1.10204i
$922$		0			0
$923$	2.06381e7			0.797380
$924$		0			0
$925$	−8.18337e6			−0.314469
$926$		0			0
$927$	1.76940e7	−	2.08854e6i	0.676282	−	0.0798257i
$928$		0			0
$929$			1.57038e7i			0.596988i	0.954411	+	0.298494i	$0.0964844\pi$
$929$			1.57038e7i			0.596988i	−0.954411	+	0.298494i	$0.903516\pi$
$930$		0			0
$931$			5.77668e7i			2.18426i
$932$		0			0
$933$	7.15167e6	−	8.04547e6i	0.268970	−	0.302585i
$934$		0			0
$935$	−1.40353e7			−0.525040
$936$		0			0
$937$	−3.89002e7			−1.44745			−0.723724	−	0.690090i	$-0.757571\pi$
$937$	−3.89002e7			−1.44745			−0.723724	+	0.690090i	$0.757571\pi$
$938$		0			0
$939$	−2.23371e7	+	2.51288e7i	−0.826730	+	0.930053i
$940$		0			0
$941$		−	9.47173e6i		−	0.348703i	−0.984684	−	0.174351i	$-0.944217\pi$
$941$		−	9.47173e6i		−	0.348703i	0.984684	−	0.174351i	$-0.0557828\pi$
$942$		0			0
$943$		−	2.99918e6i		−	0.109831i
$944$		0			0
$945$	−4.68381e7	−	3.26775e7i	−1.70616	−	1.19033i
$946$		0			0
$947$	2.70747e6			0.0981046			0.0490523	−	0.998796i	$-0.484380\pi$
$947$	2.70747e6			0.0981046			0.0490523	+	0.998796i	$0.484380\pi$
$948$		0			0
$949$	−5.04809e7			−1.81954
$950$		0			0
$951$	−1.80195e7	−	1.60177e7i	−0.646088	−	0.574312i
$952$		0			0
$953$		−	2.73874e7i		−	0.976829i	−0.872612	−	0.488415i	$-0.837575\pi$
$953$		−	2.73874e7i		−	0.976829i	0.872612	−	0.488415i	$-0.162425\pi$
$954$		0			0
$955$		−	1.09361e7i		−	0.388022i
$956$		0			0
$957$	1.11309e7	+	9.89429e6i	0.392870	+	0.349225i
$958$		0			0
$959$	−5.87550e7			−2.06300
$960$		0			0
$961$	−4.50385e7			−1.57317
$962$		0			0
$963$	−2.92162e6	−	2.47519e7i	−0.101521	−	0.860088i
$964$		0			0
$965$			1.39648e7i			0.482744i
$966$		0			0
$967$		−	2.76304e7i		−	0.950213i	−0.879928	−	0.475106i	$-0.842410\pi$
$967$		−	2.76304e7i		−	0.950213i	0.879928	−	0.475106i	$-0.157590\pi$
$968$		0			0
$969$	3.03032e7	−	3.40904e7i	1.03676	−	1.16633i
$970$		0			0
$971$	1.38859e7			0.472637			0.236318	−	0.971676i	$-0.424059\pi$
$971$	1.38859e7			0.472637			0.236318	+	0.971676i	$0.424059\pi$
$972$		0			0
$973$	4.06751e7			1.37736
$974$		0			0
$975$	1.31498e7	−	1.47932e7i	0.443003	−	0.498369i
$976$		0			0
$977$			1.19296e7i			0.399843i	0.979812	+	0.199922i	$0.0640688\pi$
$977$			1.19296e7i			0.399843i	−0.979812	+	0.199922i	$0.935931\pi$
$978$		0			0
$979$		−	1.14109e7i		−	0.380506i
$980$		0			0
$981$	−1.54730e6	−	1.31087e7i	−0.0513336	−	0.434897i
$982$		0			0
$983$	2.64907e7			0.874398			0.437199	−	0.899365i	$-0.355971\pi$
$983$	2.64907e7			0.874398			0.437199	+	0.899365i	$0.355971\pi$
$984$		0			0
$985$	−2.10076e6			−0.0689898
$986$		0			0
$987$	−1.25776e7	−	1.11803e7i	−0.410964	−	0.365308i
$988$		0			0
$989$			1.36991e7i			0.445350i
$990$		0			0
$991$			1.31128e6i			0.0424142i	0.999775	+	0.0212071i	$0.00675094\pi$
$991$			1.31128e6i			0.0424142i	−0.999775	+	0.0212071i	$0.993249\pi$
$992$		0			0
$993$	−2.13771e7	−	1.90022e7i	−0.687978	−	0.611548i
$994$		0			0
$995$	2.12774e7			0.681334
$996$		0			0
$997$	−8.74925e6			−0.278762			−0.139381	−	0.990239i	$-0.544511\pi$
$997$	−8.74925e6			−0.278762			−0.139381	+	0.990239i	$0.544511\pi$
$998$		0			0
$999$	1.64684e7	+	1.14895e7i	0.522082	+	0.364240i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.6.c.c.383.8	yes	20
3.2	odd	2		384.6.c.b.383.14	yes	20
4.3	odd	2		384.6.c.b.383.13	yes	20
8.3	odd	2		384.6.c.d.383.8	yes	20
8.5	even	2		384.6.c.a.383.13	✓	20
12.11	even	2	inner	384.6.c.c.383.7	yes	20
24.5	odd	2		384.6.c.d.383.7	yes	20
24.11	even	2		384.6.c.a.383.14	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.6.c.a.383.13	✓	20	8.5	even	2
384.6.c.a.383.14	yes	20	24.11	even	2
384.6.c.b.383.13	yes	20	4.3	odd	2
384.6.c.b.383.14	yes	20	3.2	odd	2
384.6.c.c.383.7	yes	20	12.11	even	2	inner
384.6.c.c.383.8	yes	20	1.1	even	1	trivial
384.6.c.d.383.7	yes	20	24.5	odd	2
384.6.c.d.383.8	yes	20	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	384.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-10.3565 + 11.6509i) q^{3} -68.3281i q^{5} -220.652i q^{7} +(-28.4850 - 241.325i) q^{9} +O(q^{10})\)	\(q+(-10.3565 + 11.6509i) q^{3} -68.3281i q^{5} -220.652i q^{7} +(-28.4850 - 241.325i) q^{9} +127.204 q^{11} +822.495 q^{13} +(796.081 + 707.641i) q^{15} -1614.81i q^{17} -1811.98i q^{19} +(2570.79 + 2285.19i) q^{21} +1271.87 q^{23} -1543.73 q^{25} +(3106.65 + 2167.41i) q^{27} -7510.51i q^{29} +8582.98i q^{31} +(-1317.39 + 1482.04i) q^{33} -15076.8 q^{35} +5301.04 q^{37} +(-8518.19 + 9582.78i) q^{39} -2358.09i q^{41} +10770.8i q^{43} +(-16489.3 + 1946.33i) q^{45} -4892.49 q^{47} -31880.4 q^{49} +(18813.9 + 16723.8i) q^{51} -3955.35i q^{53} -8691.62i q^{55} +(21111.2 + 18765.8i) q^{57} +41587.0 q^{59} +20088.6 q^{61} +(-53248.8 + 6285.28i) q^{63} -56199.5i q^{65} -44682.4i q^{67} +(-13172.1 + 14818.4i) q^{69} +25092.1 q^{71} -61375.3 q^{73} +(15987.7 - 17985.8i) q^{75} -28067.9i q^{77} -44086.5i q^{79} +(-57426.2 + 13748.3i) q^{81} +1956.05 q^{83} -110337. q^{85} +(87503.9 + 77782.8i) q^{87} -89705.2i q^{89} -181485. i q^{91} +(-99999.1 - 88889.8i) q^{93} -123809. q^{95} +132194. q^{97} +(-3623.41 - 30697.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3}+O(q^{10}) \) 20 * q + 2 * q^3	\( 20 q + 2 q^{3} + 948 q^{11} - 852 q^{15} + 1640 q^{21} - 328 q^{23} - 12500 q^{25} + 2030 q^{27} + 2836 q^{33} - 7184 q^{35} + 15056 q^{37} + 12980 q^{39} + 11800 q^{45} - 36640 q^{47} - 33388 q^{49} + 1936 q^{51} + 15404 q^{57} + 62908 q^{59} + 73264 q^{61} - 23608 q^{63} - 84024 q^{69} - 34888 q^{71} + 52568 q^{73} + 115698 q^{75} + 55444 q^{81} - 225172 q^{83} - 30112 q^{85} + 225700 q^{87} - 148016 q^{93} - 418616 q^{95} + 7600 q^{97} + 378260 q^{99}+O(q^{100}) \) 20 * q + 2 * q^3 + 948 * q^11 - 852 * q^15 + 1640 * q^21 - 328 * q^23 - 12500 * q^25 + 2030 * q^27 + 2836 * q^33 - 7184 * q^35 + 15056 * q^37 + 12980 * q^39 + 11800 * q^45 - 36640 * q^47 - 33388 * q^49 + 1936 * q^51 + 15404 * q^57 + 62908 * q^59 + 73264 * q^61 - 23608 * q^63 - 84024 * q^69 - 34888 * q^71 + 52568 * q^73 + 115698 * q^75 + 55444 * q^81 - 225172 * q^83 - 30112 * q^85 + 225700 * q^87 - 148016 * q^93 - 418616 * q^95 + 7600 * q^97 + 378260 * q^99

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