LMFDB - Embedded newform 198.6.l.b.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,6,Mod(17,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("198.17");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	198.l (of order $10$, degree $4$, 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:	$31.7559963230$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	198.17
Dual form			198.6.l.b.35.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23607 - 3.80423i) q^{2} +(-12.9443 + 9.40456i) q^{4} +(-55.4865 - 18.0286i) q^{5} +(111.028 + 152.817i) q^{7} +(51.7771 + 37.6183i) q^{8} +O(q^{10})$	\(q+(-1.23607 - 3.80423i) q^{2} +(-12.9443 + 9.40456i) q^{4} +(-55.4865 - 18.0286i) q^{5} +(111.028 + 152.817i) q^{7} +(51.7771 + 37.6183i) q^{8} +233.368i q^{10} +(-373.403 + 147.042i) q^{11} +(538.953 - 175.116i) q^{13} +(444.114 - 611.270i) q^{14} +(79.1084 - 243.470i) q^{16} +(78.2115 - 240.710i) q^{17} +(675.162 - 929.281i) q^{19} +(887.784 - 288.458i) q^{20} +(1020.93 + 1238.76i) q^{22} -516.449i q^{23} +(225.539 + 163.863i) q^{25} +(-1332.36 - 1833.84i) q^{26} +(-2874.36 - 933.937i) q^{28} +(-2508.18 + 1822.30i) q^{29} +(-433.171 - 1333.16i) q^{31} -1024.00 q^{32} -1012.39 q^{34} +(-3405.48 - 10481.0i) q^{35} +(-1261.05 + 916.206i) q^{37} +(-4369.74 - 1419.81i) q^{38} +(-2194.72 - 3020.78i) q^{40} +(-16182.7 - 11757.4i) q^{41} +7770.64i q^{43} +(3450.57 - 5415.04i) q^{44} +(-1964.69 + 638.366i) q^{46} +(10311.3 - 14192.3i) q^{47} +(-5832.23 + 17949.8i) q^{49} +(344.593 - 1060.55i) q^{50} +(-5329.46 + 7335.37i) q^{52} +(19423.3 - 6311.00i) q^{53} +(23369.8 - 1426.86i) q^{55} +12089.1i q^{56} +(10032.7 + 7289.21i) q^{58} +(-13162.0 - 18115.9i) q^{59} +(-45868.3 - 14903.5i) q^{61} +(-4536.23 + 3295.76i) q^{62} +(1265.73 + 3895.53i) q^{64} -33061.7 q^{65} -18877.8 q^{67} +(1251.38 + 3851.36i) q^{68} +(-35662.7 + 25910.4i) q^{70} +(-15687.4 - 5097.13i) q^{71} +(-42570.9 - 58593.8i) q^{73} +(5044.20 + 3664.83i) q^{74} +18378.5i q^{76} +(-63928.9 - 40736.7i) q^{77} +(-43389.7 + 14098.2i) q^{79} +(-8778.89 + 12083.1i) q^{80} +(-24724.9 + 76095.5i) q^{82} +(663.433 - 2041.84i) q^{83} +(-8679.36 + 11946.1i) q^{85} +(29561.3 - 9605.04i) q^{86} +(-24865.2 - 6433.39i) q^{88} +30448.3i q^{89} +(86599.9 + 62918.5i) q^{91} +(4856.97 + 6685.05i) q^{92} +(-66736.0 - 21683.9i) q^{94} +(-54216.0 + 39390.3i) q^{95} +(-11667.3 - 35908.1i) q^{97} +75494.0 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} - 160 q^{4} + 640 q^{8}+O(q^{10}) $ 40 * q + 40 * q^2 - 160 * q^4 + 640 * q^8	$ 40 q + 40 q^{2} - 160 q^{4} + 640 q^{8} - 476 q^{11} - 2560 q^{16} - 1424 q^{17} - 1656 q^{22} + 11574 q^{25} + 10480 q^{26} + 3040 q^{28} - 10658 q^{29} - 5302 q^{31} - 40960 q^{32} - 13984 q^{34} - 50 q^{35} - 4344 q^{37} + 35120 q^{38} + 19840 q^{40} - 16856 q^{41} + 6624 q^{44} - 52400 q^{46} - 10900 q^{47} - 40698 q^{49} - 6256 q^{50} + 41920 q^{52} + 10290 q^{53} + 158396 q^{55} + 42632 q^{58} + 62620 q^{59} - 134780 q^{61} - 30272 q^{62} - 40960 q^{64} - 137296 q^{65} - 36856 q^{67} - 22784 q^{68} + 79400 q^{70} + 62180 q^{71} + 100030 q^{73} + 17376 q^{74} - 162888 q^{77} + 35900 q^{79} + 79360 q^{80} - 90096 q^{82} - 12276 q^{83} + 270600 q^{85} - 137680 q^{86} - 26496 q^{88} + 406656 q^{91} + 134720 q^{92} - 91600 q^{94} - 75128 q^{95} - 364164 q^{97} + 358192 q^{98}+O(q^{100}) $ 40 * q + 40 * q^2 - 160 * q^4 + 640 * q^8 - 476 * q^11 - 2560 * q^16 - 1424 * q^17 - 1656 * q^22 + 11574 * q^25 + 10480 * q^26 + 3040 * q^28 - 10658 * q^29 - 5302 * q^31 - 40960 * q^32 - 13984 * q^34 - 50 * q^35 - 4344 * q^37 + 35120 * q^38 + 19840 * q^40 - 16856 * q^41 + 6624 * q^44 - 52400 * q^46 - 10900 * q^47 - 40698 * q^49 - 6256 * q^50 + 41920 * q^52 + 10290 * q^53 + 158396 * q^55 + 42632 * q^58 + 62620 * q^59 - 134780 * q^61 - 30272 * q^62 - 40960 * q^64 - 137296 * q^65 - 36856 * q^67 - 22784 * q^68 + 79400 * q^70 + 62180 * q^71 + 100030 * q^73 + 17376 * q^74 - 162888 * q^77 + 35900 * q^79 + 79360 * q^80 - 90096 * q^82 - 12276 * q^83 + 270600 * q^85 - 137680 * q^86 - 26496 * q^88 + 406656 * q^91 + 134720 * q^92 - 91600 * q^94 - 75128 * q^95 - 364164 * q^97 + 358192 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$

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 $

$2$	−1.23607	−	3.80423i	−0.218508	−	0.672499i
$2$	−1.23607	−	3.80423i	−0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−12.9443	+	9.40456i	−0.404508	+	0.293893i
$5$	−55.4865	−	18.0286i	−0.992572	−	0.322506i	−0.232679	−	0.972554i	$-0.574749\pi$
$5$	−55.4865	−	18.0286i	−0.992572	−	0.322506i	−0.759894	+	0.650047i	$0.774749\pi$
$6$		0			0
$7$	111.028	+	152.817i	0.856424	+	1.17877i	0.982410	+	0.186735i	$0.0597906\pi$
$7$	111.028	+	152.817i	0.856424	+	1.17877i	−0.125986	+	0.992032i	$0.540209\pi$
$8$	51.7771	+	37.6183i	0.286031	+	0.207813i
$9$		0			0
$10$			233.368i			0.737974i
$11$	−373.403	+	147.042i	−0.930457	+	0.366402i
$11$	−373.403	+	147.042i	−0.930457	+	0.366402i
$12$		0			0
$13$	538.953	−	175.116i	0.884489	−	0.287388i	0.168669	−	0.985673i	$-0.446053\pi$
$13$	538.953	−	175.116i	0.884489	−	0.287388i	0.715820	+	0.698285i	$0.246053\pi$
$14$	444.114	−	611.270i	0.605583	−	0.833514i
$15$		0			0
$16$	79.1084	−	243.470i	0.0772542	−	0.237764i
$17$	78.2115	−	240.710i	0.0656369	−	0.202010i	−0.912859	−	0.408274i	$-0.866131\pi$
$17$	78.2115	−	240.710i	0.0656369	−	0.202010i	0.978496	+	0.206264i	$0.0661307\pi$
$18$		0			0
$19$	675.162	−	929.281i	0.429066	−	0.590558i	−0.538673	−	0.842515i	$-0.681074\pi$
$19$	675.162	−	929.281i	0.429066	−	0.590558i	0.967739	+	0.251957i	$0.0810740\pi$
$20$	887.784	−	288.458i	0.496286	−	0.161253i
$21$		0			0
$22$	1020.93	+	1238.76i	0.449717	+	0.545669i
$23$		−	516.449i		−	0.203567i	−0.994807	−	0.101784i	$-0.967545\pi$
$23$		−	516.449i		−	0.203567i	0.994807	−	0.101784i	$-0.0324549\pi$
$24$		0			0
$25$	225.539	+	163.863i	0.0721724	+	0.0524363i
$26$	−1332.36	−	1833.84i	−0.386536	−	0.532021i
$27$		0			0
$28$	−2874.36	−	933.937i	−0.692862	−	0.225124i
$29$	−2508.18	+	1822.30i	−0.553814	+	0.402370i	−0.829190	−	0.558967i	$-0.811198\pi$
$29$	−2508.18	+	1822.30i	−0.553814	+	0.402370i	0.275376	+	0.961337i	$0.411198\pi$
$30$		0			0
$31$	−433.171	−	1333.16i	−0.0809572	−	0.249161i	0.902383	−	0.430935i	$-0.141816\pi$
$31$	−433.171	−	1333.16i	−0.0809572	−	0.249161i	−0.983340	+	0.181774i	$0.941816\pi$
$32$	−1024.00			−0.176777
$33$		0			0
$34$	−1012.39			−0.150193
$35$	−3405.48	−	10481.0i	−0.469903	−	1.44621i
$36$		0			0
$37$	−1261.05	+	916.206i	−0.151436	+	0.110024i	−0.660923	−	0.750454i	$-0.729835\pi$
$37$	−1261.05	+	916.206i	−0.151436	+	0.110024i	0.509487	+	0.860478i	$0.329835\pi$
$38$	−4369.74	−	1419.81i	−0.490904	−	0.159504i
$39$		0			0
$40$	−2194.72	−	3020.78i	−0.216885	−	0.298517i
$41$	−16182.7	−	11757.4i	−1.50346	−	1.09232i	−0.968980	−	0.247141i	$-0.920509\pi$
$41$	−16182.7	−	11757.4i	−1.50346	−	1.09232i	−0.534476	−	0.845183i	$-0.679491\pi$
$42$		0			0
$43$			7770.64i			0.640893i	0.947267	+	0.320447i	$0.103833\pi$
$43$			7770.64i			0.640893i	−0.947267	+	0.320447i	$0.896167\pi$
$44$	3450.57	−	5415.04i	0.268695	−	0.421667i
$45$		0			0
$46$	−1964.69	+	638.366i	−0.136899	+	0.0444810i
$47$	10311.3	−	14192.3i	0.680876	−	0.937146i	−0.319068	−	0.947732i	$-0.603370\pi$
$47$	10311.3	−	14192.3i	0.680876	−	0.937146i	0.999944	+	0.0105861i	$0.00336974\pi$
$48$		0			0
$49$	−5832.23	+	17949.8i	−0.347012	+	1.06799i
$50$	344.593	−	1060.55i	0.0194931	−	0.0599936i
$51$		0			0
$52$	−5329.46	+	7335.37i	−0.273322	+	0.376196i
$53$	19423.3	−	6311.00i	0.949801	−	0.308609i	0.207166	−	0.978306i	$-0.433576\pi$
$53$	19423.3	−	6311.00i	0.949801	−	0.308609i	0.742635	+	0.669697i	$0.233576\pi$
$54$		0			0
$55$	23369.8	−	1426.86i	1.04171	−	0.0636027i
$56$			12089.1i			0.515140i
$57$		0			0
$58$	10032.7	+	7289.21i	0.391606	+	0.284518i
$59$	−13162.0	−	18115.9i	−0.492257	−	0.677533i	0.488545	−	0.872538i	$-0.337528\pi$
$59$	−13162.0	−	18115.9i	−0.492257	−	0.677533i	−0.980802	+	0.195005i	$0.937528\pi$
$60$		0			0
$61$	−45868.3	−	14903.5i	−1.57829	−	0.512819i	−0.616677	−	0.787216i	$-0.711522\pi$
$61$	−45868.3	−	14903.5i	−1.57829	−	0.512819i	−0.961616	+	0.274397i	$0.911522\pi$
$62$	−4536.23	+	3295.76i	−0.149870	+	0.108887i
$63$		0			0
$64$	1265.73	+	3895.53i	0.0386271	+	0.118882i
$65$	−33061.7			−0.970603
$66$		0			0
$67$	−18877.8			−0.513764			−0.256882	−	0.966443i	$-0.582695\pi$
$67$	−18877.8			−0.513764			−0.256882	+	0.966443i	$0.582695\pi$
$68$	1251.38	+	3851.36i	0.0328185	+	0.101005i
$69$		0			0
$70$	−35662.7	+	25910.4i	−0.869899	+	0.632019i
$71$	−15687.4	−	5097.13i	−0.369321	−	0.120000i	0.118476	−	0.992957i	$-0.462199\pi$
$71$	−15687.4	−	5097.13i	−0.369321	−	0.120000i	−0.487797	+	0.872957i	$0.662199\pi$
$72$		0			0
$73$	−42570.9	−	58593.8i	−0.934987	−	1.28690i	−0.957882	−	0.287161i	$-0.907289\pi$
$73$	−42570.9	−	58593.8i	−0.934987	−	1.28690i	0.0228956	−	0.999738i	$-0.492711\pi$
$74$	5044.20	+	3664.83i	0.107081	+	0.0777990i
$75$		0			0
$76$			18378.5i			0.364985i
$77$	−63928.9	−	40736.7i	−1.22877	−	0.782996i
$78$		0			0
$79$	−43389.7	+	14098.2i	−0.782202	+	0.254153i	−0.672780	−	0.739843i	$-0.734900\pi$
$79$	−43389.7	+	14098.2i	−0.782202	+	0.254153i	−0.109422	+	0.993995i	$0.534900\pi$
$80$	−8778.89	+	12083.1i	−0.153361	+	0.211083i
$81$		0			0
$82$	−24724.9	+	76095.5i	−0.406070	+	1.24975i
$83$	663.433	−	2041.84i	0.0105707	−	0.0325331i	−0.945632	−	0.325238i	$-0.894555\pi$
$83$	663.433	−	2041.84i	0.0105707	−	0.0325331i	0.956203	+	0.292705i	$0.0945555\pi$
$84$		0			0
$85$	−8679.36	+	11946.1i	−0.130299	+	0.179341i
$86$	29561.3	−	9605.04i	0.431000	−	0.140040i
$87$		0			0
$88$	−24865.2	−	6433.39i	−0.342282	−	0.0885591i
$89$			30448.3i			0.407463i	0.979027	+	0.203731i	$0.0653069\pi$
$89$			30448.3i			0.407463i	−0.979027	+	0.203731i	$0.934693\pi$
$90$		0			0
$91$	86599.9	+	62918.5i	1.09626	+	0.796480i
$92$	4856.97	+	6685.05i	0.0598269	+	0.0823446i
$93$		0			0
$94$	−66736.0	−	21683.9i	−0.779006	−	0.253114i
$95$	−54216.0	+	39390.3i	−0.616338	+	0.447796i
$96$		0			0
$97$	−11667.3	−	35908.1i	−0.125904	−	0.387493i	0.868161	−	0.496283i	$-0.165302\pi$
$97$	−11667.3	−	35908.1i	−0.125904	−	0.387493i	−0.994065	+	0.108790i	$0.965302\pi$
$98$	75494.0			0.794049
$99$		0			0
$100$	−4460.50			−0.0446050
$101$	−62850.9	−	193435.i	−0.613067	−	1.88683i	−0.426870	−	0.904313i	$-0.640384\pi$
$101$	−62850.9	−	193435.i	−0.613067	−	1.88683i	−0.186197	−	0.982512i	$-0.559616\pi$
$102$		0			0
$103$	169553.	−	123188.i	1.57476	−	1.14413i	0.652342	−	0.757925i	$-0.273787\pi$
$103$	169553.	−	123188.i	1.57476	−	1.14413i	0.922414	−	0.386203i	$-0.126213\pi$
$104$	34493.0	+	11207.4i	0.312714	+	0.101607i
$105$		0			0
$106$	−48016.9	−	66089.7i	−0.415078	−	0.571306i
$107$	145332.	+	105590.i	1.22716	+	0.891583i	0.996674	−	0.0814930i	$-0.0259688\pi$
$107$	145332.	+	105590.i	1.22716	+	0.891583i	0.230485	+	0.973076i	$0.425969\pi$
$108$		0			0
$109$			36243.5i			0.292189i	0.989271	+	0.146094i	$0.0466703\pi$
$109$			36243.5i			0.292189i	−0.989271	+	0.146094i	$0.953330\pi$
$110$	−34314.7	−	87140.2i	−0.270395	−	0.686652i
$111$		0			0
$112$	45989.8	−	14943.0i	0.346431	−	0.112562i
$113$	41565.7	−	57210.3i	0.306224	−	0.421481i	−0.627975	−	0.778234i	$-0.716116\pi$
$113$	41565.7	−	57210.3i	0.306224	−	0.421481i	0.934199	+	0.356752i	$0.116116\pi$
$114$		0			0
$115$	−9310.87	+	28655.9i	−0.0656517	+	0.202055i
$116$	15328.6	−	47176.7i	0.105769	−	0.325524i
$117$		0			0
$118$	−52648.0	+	72463.7i	−0.348078	+	0.479088i
$119$	45468.4	−	14773.6i	0.294336	−	0.0956354i
$120$		0			0
$121$	117809.	−	109811.i	0.731499	−	0.681843i
$122$			192915.i			1.17346i
$123$		0			0
$124$	18144.9	+	13183.0i	0.105974	+	0.0769948i
$125$	97604.0	+	134340.i	0.558718	+	0.769010i
$126$		0			0
$127$	273479.	+	88858.6i	1.50458	+	0.488867i	0.941349	−	0.337435i	$-0.109559\pi$
$127$	273479.	+	88858.6i	1.50458	+	0.488867i	0.563228	+	0.826302i	$0.309559\pi$
$128$	13254.9	−	9630.27i	0.0715077	−	0.0519534i
$129$		0			0
$130$	40866.5	+	125774.i	0.212085	+	0.652729i
$131$	−202835.			−1.03268			−0.516339	−	0.856384i	$-0.672706\pi$
$131$	−202835.			−1.03268			−0.516339	+	0.856384i	$0.672706\pi$
$132$		0			0
$133$	216972.			1.06359
$134$	23334.2	+	71815.3i	0.112262	+	0.345506i
$135$		0			0
$136$	13104.7	−	9521.10i	0.0607545	−	0.0441407i
$137$	−43749.9	−	14215.2i	−0.199148	−	0.0647071i	0.207745	−	0.978183i	$-0.433388\pi$
$137$	−43749.9	−	14215.2i	−0.199148	−	0.0647071i	−0.406893	+	0.913476i	$0.633388\pi$
$138$		0			0
$139$	−222219.	−	305858.i	−0.975537	−	1.34271i	−0.939200	−	0.343371i	$-0.888431\pi$
$139$	−222219.	−	305858.i	−0.975537	−	1.34271i	−0.0363368	−	0.999340i	$-0.511569\pi$
$140$	142651.	+	103642.i	0.615111	+	0.446905i
$141$		0			0
$142$			65978.7i			0.274589i
$143$	−175497.	+	144637.i	−0.717679	+	0.591481i
$144$		0			0
$145$	172024.	−	55893.9i	0.679467	−	0.220772i
$146$	−170284.	+	234375.i	−0.661135	+	0.909975i
$147$		0			0
$148$	7706.85	−	23719.2i	0.0289216	−	0.0890116i
$149$	25864.5	−	79602.6i	0.0954416	−	0.293739i	−0.891927	−	0.452180i	$-0.850647\pi$
$149$	25864.5	−	79602.6i	0.0954416	−	0.293739i	0.987369	+	0.158441i	$0.0506466\pi$
$150$		0			0
$151$	301263.	−	414653.i	1.07523	−	1.47993i	0.210573	−	0.977578i	$-0.432467\pi$
$151$	301263.	−	414653.i	1.07523	−	1.47993i	0.864662	−	0.502355i	$-0.167533\pi$
$152$	69915.8	−	22717.0i	0.245452	−	0.0797522i
$153$		0			0
$154$	−75951.3	+	293553.i	−0.258068	+	0.997436i
$155$			81782.0i			0.273419i
$156$		0			0
$157$	−876.256	−	636.637i	−0.00283715	−	0.00206131i	0.586366	−	0.810046i	$-0.300558\pi$
$157$	−876.256	−	636.637i	−0.00283715	−	0.00206131i	−0.589203	+	0.807985i	$0.700558\pi$
$158$	107265.	+	147638.i	0.341835	+	0.470495i
$159$		0			0
$160$	56818.2	+	18461.3i	0.175464	+	0.0570116i
$161$	78922.4	−	57340.5i	0.239958	−	0.174340i
$162$		0			0
$163$	−173173.	−	532970.i	−0.510517	−	1.57121i	−0.791294	−	0.611436i	$-0.790592\pi$
$163$	−173173.	−	532970.i	−0.510517	−	1.57121i	0.280777	−	0.959773i	$-0.409408\pi$
$164$	320046.			0.929187
$165$		0			0
$166$	−8587.66			−0.0241882
$167$	41984.4	+	129215.i	0.116492	+	0.358526i	0.992255	−	0.124215i	$-0.0396412\pi$
$167$	41984.4	+	129215.i	0.116492	+	0.358526i	−0.875763	+	0.482741i	$0.839641\pi$
$168$		0			0
$169$	−40578.1	+	29481.7i	−0.109289	+	0.0794028i
$170$	56174.0	+	18252.0i	0.149078	+	0.0484383i
$171$		0			0
$172$	−73079.5	−	100585.i	−0.188354	−	0.259247i
$173$	530956.	+	385762.i	1.34879	+	0.979951i	0.999071	+	0.0430957i	$0.0137220\pi$
$173$	530956.	+	385762.i	1.34879	+	0.979951i	0.349716	+	0.936856i	$0.386278\pi$
$174$		0			0
$175$			52659.8i			0.129982i
$176$	6260.97	+	102545.i	0.0152356	+	0.249535i
$177$		0			0
$178$	115832.	−	37636.2i	0.274018	−	0.0890339i
$179$	117587.	−	161845.i	0.274302	−	0.377544i	−0.649534	−	0.760332i	$-0.725036\pi$
$179$	117587.	−	161845.i	0.274302	−	0.377544i	0.923836	+	0.382788i	$0.125036\pi$
$180$		0			0
$181$	−134581.	+	414199.i	−0.305344	+	0.939751i	0.674205	+	0.738544i	$0.264486\pi$
$181$	−134581.	+	414199.i	−0.305344	+	0.939751i	−0.979549	+	0.201207i	$0.935514\pi$
$182$	132313.	−	407217.i	0.296090	−	0.911271i
$183$		0			0
$184$	19427.9	−	26740.2i	0.0423040	−	0.0582264i
$185$	86489.2	−	28102.0i	0.185794	−	0.0603682i
$186$		0			0
$187$	6189.99	+	101382.i	0.0129445	+	0.212011i
$188$			280682.i			0.579188i
$189$		0			0
$190$	216864.	+	157561.i	0.435817	+	0.316639i
$191$	12671.1	+	17440.3i	0.0251322	+	0.0345915i	0.821398	−	0.570355i	$-0.193194\pi$
$191$	12671.1	+	17440.3i	0.0251322	+	0.0345915i	−0.796266	+	0.604947i	$0.793194\pi$
$192$		0			0
$193$	121739.	+	39555.5i	0.235254	+	0.0764387i	0.424271	−	0.905535i	$-0.360530\pi$
$193$	121739.	+	39555.5i	0.235254	+	0.0764387i	−0.189017	+	0.981974i	$0.560530\pi$
$194$	−122181.	+	88769.8i	−0.233077	+	0.169341i
$195$		0			0
$196$	−93315.7	−	287196.i	−0.173506	−	0.533996i
$197$	−282934.			−0.519421			−0.259710	−	0.965687i	$-0.583627\pi$
$197$	−282934.			−0.519421			−0.259710	+	0.965687i	$0.583627\pi$
$198$		0			0
$199$	−240937.			−0.431291			−0.215646	−	0.976472i	$-0.569186\pi$
$199$	−240937.			−0.431291			−0.215646	+	0.976472i	$0.569186\pi$
$200$	5513.48	+	16968.7i	0.00974655	+	0.0299968i
$201$		0			0
$202$	−658183.	+	478198.i	−1.13493	+	0.824573i
$203$	−556959.	−	180967.i	−0.948600	−	0.308219i
$204$		0			0
$205$	685950.	+	944129.i	1.14001	+	1.56908i
$206$	−678213.	−	492751.i	−1.11352	−	0.809020i
$207$		0			0
$208$		−	145072.i		−	0.232502i
$209$	−115465.	+	446273.i	−0.182845	+	0.706700i
$210$		0			0
$211$	−976788.	+	317378.i	−1.51041	+	0.490761i	−0.943033	−	0.332699i	$-0.892041\pi$
$211$	−976788.	+	317378.i	−1.51041	+	0.490761i	−0.567374	+	0.823460i	$0.692041\pi$
$212$	−192068.	+	264359.i	−0.293505	+	0.403974i
$213$		0			0
$214$	222047.	−	683390.i	0.331444	−	1.02008i
$215$	140094.	−	431165.i	0.206692	−	0.636133i
$216$		0			0
$217$	155636.	−	214215.i	0.224368	−	0.308817i
$218$	137878.	−	44799.4i	0.196496	−	0.0638456i
$219$		0			0
$220$	−289086.	+	238252.i	−0.402689	+	0.331879i
$221$		−	143428.i		−	0.197539i
$222$		0			0
$223$	39541.2	+	28728.3i	0.0532461	+	0.0386855i	0.614090	−	0.789236i	$-0.289523\pi$
$223$	39541.2	+	28728.3i	0.0532461	+	0.0386855i	−0.560844	+	0.827922i	$0.689523\pi$
$224$	−113693.	−	156485.i	−0.151396	−	0.208379i
$225$		0			0
$226$	−269019.	−	87409.6i	−0.350358	−	0.113838i
$227$	183811.	−	133546.i	0.236759	−	0.172015i	−0.463079	−	0.886317i	$-0.653255\pi$
$227$	183811.	−	133546.i	0.236759	−	0.172015i	0.699838	+	0.714301i	$0.253255\pi$
$228$		0			0
$229$	−290053.	−	892692.i	−0.365501	−	1.12490i	−0.949667	−	0.313262i	$-0.898578\pi$
$229$	−290053.	−	892692.i	−0.365501	−	1.12490i	0.584165	−	0.811635i	$-0.301422\pi$
$230$	120522.			0.150227
$231$		0			0
$232$	−198418.			−0.242026
$233$	370625.	+	1.14067e6i	0.447244	+	1.37648i	0.880004	+	0.474967i	$0.157540\pi$
$233$	370625.	+	1.14067e6i	0.447244	+	1.37648i	−0.432759	+	0.901510i	$0.642460\pi$
$234$		0			0
$235$	−828004.	+	601580.i	−0.978054	+	0.710598i
$236$	340745.	+	110715.i	0.398244	+	0.129397i
$237$		0			0
$238$	−112404.	−	154711.i	−0.128629	−	0.177043i
$239$	−341192.	−	247891.i	−0.386371	−	0.280715i	0.377596	−	0.925970i	$-0.376751\pi$
$239$	−341192.	−	247891.i	−0.386371	−	0.280715i	−0.763967	+	0.645256i	$0.776751\pi$
$240$		0			0
$241$			541841.i			0.600938i	0.953792	+	0.300469i	$0.0971431\pi$
$241$			541841.i			0.600938i	−0.953792	+	0.300469i	$0.902857\pi$
$242$	−563367.	−	312436.i	−0.618377	−	0.342944i
$243$		0			0
$244$	733892.	−	238456.i	0.789147	−	0.256409i
$245$	647220.	−	890822.i	0.688869	−	0.948147i
$246$		0			0
$247$	201148.	−	619070.i	0.209785	−	0.645651i
$248$	27723.0	−	85322.5i	0.0286227	−	0.0880915i
$249$		0			0
$250$	390416.	−	537362.i	0.395073	−	0.543772i
$251$	−1.22984e6	+	399598.i	−1.23215	+	0.400349i	−0.851492	−	0.524367i	$-0.824302\pi$
$251$	−1.22984e6	+	399598.i	−1.23215	+	0.400349i	−0.380656	+	0.924717i	$0.624302\pi$
$252$		0			0
$253$	75939.4	+	192843.i	0.0745874	+	0.189410i
$254$		−	1.15021e6i		−	1.11865i
$255$		0			0
$256$	−53019.7	−	38521.1i	−0.0505636	−	0.0367366i
$257$	−59958.0	−	82525.2i	−0.0566258	−	0.0779388i	0.779765	−	0.626072i	$-0.215339\pi$
$257$	−59958.0	−	82525.2i	−0.0566258	−	0.0779388i	−0.836391	+	0.548134i	$0.815339\pi$
$258$		0			0
$259$	−280025.	−	90985.5i	−0.259386	−	0.0842797i
$260$	427960.	−	310931.i	0.392617	−	0.285253i
$261$		0			0
$262$	250718.	+	771631.i	0.225649	+	0.694475i
$263$	770186.			0.686603			0.343302	−	0.939225i	$-0.388455\pi$
$263$	770186.			0.686603			0.343302	+	0.939225i	$0.388455\pi$
$264$		0			0
$265$	−1.19151e6			−1.04227
$266$	−268193.	−	825412.i	−0.232404	−	0.715265i
$267$		0			0
$268$	244359.	−	177537.i	0.207822	−	0.150992i
$269$	−2.07807e6	−	675207.i	−1.75098	−	0.568927i	−0.754773	−	0.655986i	$-0.772253\pi$
$269$	−2.07807e6	−	675207.i	−1.75098	−	0.568927i	−0.996203	+	0.0870589i	$0.972253\pi$
$270$		0			0
$271$	857133.	+	1.17974e6i	0.708965	+	0.975807i	0.999819	+	0.0190392i	$0.00606074\pi$
$271$	857133.	+	1.17974e6i	0.708965	+	0.975807i	−0.290854	+	0.956768i	$0.593939\pi$
$272$	−52418.7	−	38084.4i	−0.0429599	−	0.0312122i
$273$		0			0
$274$			184005.i			0.148066i
$275$	−108312.	−	28023.6i	−0.0863661	−	0.0223456i
$276$		0			0
$277$	−2.11502e6	+	687211.i	−1.65621	+	0.538134i	−0.980072	−	0.198643i	$-0.936347\pi$
$277$	−2.11502e6	+	687211.i	−1.65621	+	0.538134i	−0.676135	+	0.736777i	$0.736347\pi$
$278$	−888875.	+	1.22343e6i	−0.689809	+	0.949440i
$279$		0			0
$280$	217951.	−	670784.i	0.166136	−	0.511314i
$281$	567917.	−	1.74787e6i	0.429061	−	1.32051i	−0.469990	−	0.882672i	$-0.655743\pi$
$281$	567917.	−	1.74787e6i	0.429061	−	1.32051i	0.899051	−	0.437843i	$-0.144257\pi$
$282$		0			0
$283$	352515.	−	485196.i	0.261645	−	0.360123i	−0.657902	−	0.753103i	$-0.728556\pi$
$283$	352515.	−	485196.i	0.261645	−	0.360123i	0.919547	+	0.392980i	$0.128556\pi$
$284$	250998.	−	81554.1i	0.184660	−	0.0599998i
$285$		0			0
$286$	767160.	+	488849.i	0.554588	+	0.353395i
$287$		−	3.77840e6i		−	2.70772i
$288$		0			0
$289$	1.09686e6	+	796918.i	0.772517	+	0.561267i
$290$	−425266.	−	585329.i	−0.296938	−	0.408700i
$291$		0			0
$292$	1.10210e6	+	358093.i	0.756420	+	0.245776i
$293$	−946891.	+	687957.i	−0.644364	+	0.468158i	−0.861347	−	0.508018i	$-0.830378\pi$
$293$	−946891.	+	687957.i	−0.644364	+	0.468158i	0.216983	+	0.976175i	$0.430378\pi$
$294$		0			0
$295$	403707.	+	1.24248e6i	0.270092	+	0.831257i
$296$	−99759.6			−0.0661798
$297$		0			0
$298$	−334797.			−0.218394
$299$	−90438.6	−	278341.i	−0.0585027	−	0.180053i
$300$		0			0
$301$	−1.18749e6	+	862762.i	−0.755464	+	0.548876i
$302$	−1.94981e6	−	633533.i	−1.23020	−	0.399716i
$303$		0			0
$304$	−172841.	−	237896.i	−0.107266	−	0.147640i
$305$	2.27638e6	+	1.65389e6i	1.40118	+	1.01802i
$306$		0			0
$307$		−	1.09919e6i		−	0.665622i	−0.942994	−	0.332811i	$-0.892003\pi$
$307$		−	1.09919e6i		−	0.665622i	0.942994	−	0.332811i	$-0.107997\pi$
$308$	1.21062e6	−	73915.8i	0.727164	−	0.0443977i
$309$		0			0
$310$	311117.	−	101088.i	0.183874	−	0.0597442i
$311$	−508841.	+	700360.i	−0.298319	+	0.410601i	−0.931694	−	0.363244i	$-0.881669\pi$
$311$	−508841.	+	700360.i	−0.298319	+	0.410601i	0.633375	+	0.773845i	$0.281669\pi$
$312$		0			0
$313$	−84692.7	+	260657.i	−0.0488636	+	0.150387i	−0.972511	−	0.232856i	$-0.925193\pi$
$313$	−84692.7	+	260657.i	−0.0488636	+	0.150387i	0.923648	+	0.383243i	$0.125193\pi$
$314$	−1338.80	+	4120.40i	−0.000766287	+	0.00235839i
$315$		0			0
$316$	429061.	−	590552.i	0.241714	−	0.332690i
$317$	966118.	−	313911.i	0.539985	−	0.175452i	−0.0263107	−	0.999654i	$-0.508376\pi$
$317$	966118.	−	313911.i	0.539985	−	0.175452i	0.566296	+	0.824202i	$0.308376\pi$
$318$		0			0
$319$	668609.	−	1.04926e6i	0.367871	−	0.577306i
$320$		−	238969.i		−	0.130457i
$321$		0			0
$322$	−315690.	−	229362.i	−0.169676	−	0.123277i
$323$	−170882.	−	235199.i	−0.0911360	−	0.125438i
$324$		0			0
$325$	150250.	+	48819.1i	0.0789052	+	0.0256379i
$326$	−1.81349e6	+	1.31758e6i	−0.945084	+	0.686644i
$327$		0			0
$328$	−395599.	−	1.21753e6i	−0.203035	−	0.624877i
$329$	3.31367e6			1.68780
$330$		0			0
$331$	−2.58179e6			−1.29524			−0.647622	−	0.761962i	$-0.724236\pi$
$331$	−2.58179e6			−1.29524			−0.647622	+	0.761962i	$0.724236\pi$
$332$	10614.9	+	32669.4i	0.00528533	+	0.0162666i
$333$		0			0
$334$	439666.	−	319436.i	0.215654	−	0.156682i
$335$	1.04746e6	+	340341.i	0.509948	+	0.165692i
$336$		0			0
$337$	−650722.	−	895642.i	−0.312119	−	0.429595i	0.623921	−	0.781487i	$-0.285539\pi$
$337$	−650722.	−	895642.i	−0.312119	−	0.429595i	−0.936041	+	0.351892i	$0.885539\pi$
$338$	162312.	+	117927.i	0.0772787	+	0.0561462i
$339$		0			0
$340$		−	236259.i		−	0.110839i
$341$	357778.	+	434113.i	0.166620	+	0.202170i
$342$		0			0
$343$	−371240.	+	120623.i	−0.170381	+	0.0553600i
$344$	−292318.	+	402341.i	−0.133186	+	0.183315i
$345$		0			0
$346$	811229.	−	2.49671e6i	0.364295	−	1.12118i
$347$	−969210.	+	2.98292e6i	−0.432110	+	1.32990i	0.463909	+	0.885883i	$0.346446\pi$
$347$	−969210.	+	2.98292e6i	−0.432110	+	1.32990i	−0.896019	+	0.444015i	$0.853554\pi$
$348$		0			0
$349$	−2.18158e6	+	3.00268e6i	−0.958754	+	1.31961i	−0.0112267	+	0.999937i	$0.503574\pi$
$349$	−2.18158e6	+	3.00268e6i	−0.958754	+	1.31961i	−0.947527	+	0.319675i	$0.896426\pi$
$350$	200330.	−	65091.1i	0.0874128	−	0.0284021i
$351$		0			0
$352$	382365.	−	150571.i	0.164483	−	0.0647714i
$353$			2.17924e6i			0.930826i	0.885094	+	0.465413i	$0.154094\pi$
$353$			2.17924e6i			0.930826i	−0.885094	+	0.465413i	$0.845906\pi$
$354$		0			0
$355$	778542.	+	565644.i	0.327877	+	0.238217i
$356$	−286353.	−	394131.i	−0.119750	−	0.164822i
$357$		0			0
$358$	−761042.	−	247277.i	−0.313835	−	0.101971i
$359$	−3.01659e6	+	2.19168e6i	−1.23532	+	0.897514i	−0.997278	−	0.0737399i	$-0.976507\pi$
$359$	−3.01659e6	+	2.19168e6i	−1.23532	+	0.897514i	−0.238045	+	0.971254i	$0.576507\pi$
$360$		0			0
$361$	357438.	+	1.10008e6i	0.144355	+	0.444280i
$362$	1.74206e6			0.698701
$363$		0			0
$364$	−1.71269e6			−0.677526
$365$	1.30574e6	+	4.01866e6i	0.513009	+	1.57888i
$366$		0			0
$367$	3.74019e6	−	2.71741e6i	1.44954	−	1.05315i	0.463596	−	0.886047i	$-0.346559\pi$
$367$	3.74019e6	−	2.71741e6i	1.44954	−	1.05315i	0.985940	−	0.167102i	$-0.0534410\pi$
$368$	−125740.	−	40855.4i	−0.0484009	−	0.0157264i
$369$		0			0
$370$	−213813.	−	294288.i	−0.0811951	−	0.111755i
$371$	3.12097e6	+	2.26751e6i	1.17721	+	0.855294i
$372$		0			0
$373$		−	206140.i		−	0.0767167i	−0.999264	−	0.0383584i	$-0.987787\pi$
$373$		−	206140.i		−	0.0767167i	0.999264	−	0.0383584i	$-0.0122128\pi$
$374$	378030.	−	148864.i	0.139748	−	0.0550312i
$375$		0			0
$376$	1.06778e6	−	346942.i	0.389503	−	0.126557i
$377$	−1.03268e6	+	1.42136e6i	−0.374206	+	0.515051i
$378$		0			0
$379$	740397.	−	2.27871e6i	0.264769	−	0.814875i	−0.726978	−	0.686661i	$-0.759076\pi$
$379$	740397.	−	2.27871e6i	0.264769	−	0.814875i	0.991747	−	0.128214i	$-0.0409243\pi$
$380$	331339.	−	1.01976e6i	0.117710	−	0.362274i
$381$		0			0
$382$	50684.3	−	69761.0i	0.0177711	−	0.0244599i
$383$	−2.13590e6	+	693995.i	−0.744017	+	0.241746i	−0.656405	−	0.754409i	$-0.727924\pi$
$383$	−2.13590e6	+	693995.i	−0.744017	+	0.241746i	−0.0876124	+	0.996155i	$0.527924\pi$
$384$		0			0
$385$	2.81276e6	+	3.41289e6i	0.967121	+	1.17347i
$386$		−	512017.i		−	0.174910i
$387$		0			0
$388$	488725.	+	355079.i	0.164811	+	0.119742i
$389$	−2.31995e6	−	3.19314e6i	−0.777328	−	1.06990i	−0.995572	−	0.0940063i	$-0.970033\pi$
$389$	−2.31995e6	−	3.19314e6i	−0.777328	−	1.06990i	0.218243	−	0.975894i	$-0.429967\pi$
$390$		0			0
$391$	−124314.	−	40392.2i	−0.0411225	−	0.0133615i
$392$	−977214.	+	709988.i	−0.321199	+	0.233365i
$393$		0			0
$394$	349725.	+	1.07634e6i	0.113498	+	0.349310i
$395$	2.66171e6			0.858358
$396$		0			0
$397$	−2153.12			−0.000685635			−0.000342817	−	1.00000i	$-0.500109\pi$
$397$	−2153.12			−0.000685635			−0.000342817		1.00000i	$0.500109\pi$
$398$	297814.	+	916579.i	0.0942406	+	0.290043i
$399$		0			0
$400$	57737.9	−	41949.1i	0.0180431	−	0.0131091i
$401$	2.30183e6	+	747910.i	0.714846	+	0.232267i	0.643787	−	0.765205i	$-0.277362\pi$
$401$	2.30183e6	+	747910.i	0.714846	+	0.232267i	0.0710587	+	0.997472i	$0.477362\pi$
$402$		0			0
$403$	−466917.	−	642657.i	−0.143211	−	0.197114i
$404$	2.63273e6	+	1.91279e6i	0.802515	+	0.583061i
$405$		0			0
$406$			2.34249e6i			0.705280i
$407$	336159.	−	527541.i	0.100591	−	0.157859i
$408$		0			0
$409$	−1.51774e6	+	493144.i	−0.448631	+	0.145769i	−0.524614	−	0.851340i	$-0.675790\pi$
$409$	−1.51774e6	+	493144.i	−0.448631	+	0.145769i	0.0759831	+	0.997109i	$0.475790\pi$
$410$	2.74380e6	−	3.77651e6i	0.806107	−	1.10951i
$411$		0			0
$412$	−1.03622e6	+	3.18915e6i	−0.300752	+	0.925618i
$413$	1.30708e6	−	4.02277e6i	0.377073	−	1.16051i
$414$		0			0
$415$	−73623.1	+	101334.i	−0.0209843	+	0.0288824i
$416$	−551888.	+	179319.i	−0.156357	+	0.0508035i
$417$		0			0
$418$	1.84045e6	−	112370.i	0.515208	−	0.0314565i
$419$			2.54567e6i			0.708380i	0.935173	+	0.354190i	$0.115243\pi$
$419$			2.54567e6i			0.708380i	−0.935173	+	0.354190i	$0.884757\pi$
$420$		0			0
$421$	4.76812e6	+	3.46424e6i	1.31112	+	0.952583i	0.999998	+	0.00221240i	$0.000704230\pi$
$421$	4.76812e6	+	3.46424e6i	1.31112	+	0.952583i	0.311120	+	0.950371i	$0.399296\pi$
$422$	2.41475e6	+	3.32362e6i	0.660072	+	0.908511i
$423$		0			0
$424$	1.24309e6	+	403904.i	0.335805	+	0.109110i
$425$	57083.4	−	41473.5i	0.0153298	−	0.0111378i
$426$		0			0
$427$	−2.81516e6	−	8.66419e6i	−0.747195	−	2.29963i
$428$	−2.87424e6			−0.758426
$429$		0			0
$430$	−1.81342e6			−0.472962
$431$	718274.	+	2.21062e6i	0.186250	+	0.573220i	0.999968	−	0.00804113i	$-0.00255960\pi$
$431$	718274.	+	2.21062e6i	0.186250	+	0.573220i	−0.813717	+	0.581261i	$0.802560\pi$
$432$		0			0
$433$	1.71187e6	−	1.24375e6i	0.438785	−	0.318796i	−0.346367	−	0.938099i	$-0.612585\pi$
$433$	1.71187e6	−	1.24375e6i	0.438785	−	0.318796i	0.785152	+	0.619303i	$0.212585\pi$
$434$	−1.00730e6	−	327292.i	−0.256705	−	0.0834085i
$435$		0			0
$436$	−340854.	−	469145.i	−0.0858721	−	0.118193i
$437$	−479926.	−	348686.i	−0.120218	−	0.0873437i
$438$		0			0
$439$		−	7.50383e6i		−	1.85832i	−0.369672	−	0.929162i	$-0.620530\pi$
$439$		−	7.50383e6i		−	1.85832i	0.369672	−	0.929162i	$-0.379470\pi$
$440$	1.26370e6	+	805251.i	0.311179	+	0.198290i
$441$		0			0
$442$	−545631.	+	177286.i	−0.132844	+	0.0431638i
$443$	−2.45763e6	+	3.38263e6i	−0.594985	+	0.818927i	−0.995238	−	0.0974778i	$-0.968922\pi$
$443$	−2.45763e6	+	3.38263e6i	−0.594985	+	0.818927i	0.400252	+	0.916405i	$0.368922\pi$
$444$		0			0
$445$	548942.	−	1.68947e6i	0.131409	−	0.404436i
$446$	60413.5	−	185934.i	0.0143813	−	0.0442610i
$447$		0			0
$448$	−454772.	+	625940.i	−0.107053	+	0.147346i
$449$	7.19958e6	−	2.33929e6i	1.68536	−	0.547605i	0.699417	−	0.714714i	$-0.253443\pi$
$449$	7.19958e6	−	2.33929e6i	1.68536	−	0.547605i	0.985938	+	0.167109i	$0.0534432\pi$
$450$		0			0
$451$	7.77149e6	+	2.01072e6i	1.79913	+	0.465491i
$452$			1.13145e6i			0.260490i
$453$		0			0
$454$	−735243.	−	534186.i	−0.167414	−	0.121633i
$455$	−3.67079e6	−	5.05241e6i	−0.831248	−	1.14412i
$456$		0			0
$457$	2.45041e6	+	796186.i	0.548843	+	0.178330i	0.570295	−	0.821440i	$-0.306829\pi$
$457$	2.45041e6	+	796186.i	0.548843	+	0.178330i	−0.0214519	+	0.999770i	$0.506829\pi$
$458$	−3.03748e6	+	2.20686e6i	−0.676627	+	0.491598i
$459$		0			0
$460$	−148974.	−	458495.i	−0.0328258	−	0.101028i
$461$	−67882.5			−0.0148767			−0.00743833	−	0.999972i	$-0.502368\pi$
$461$	−67882.5			−0.0148767			−0.00743833	+	0.999972i	$0.502368\pi$
$462$		0			0
$463$	−8.38848e6			−1.81857			−0.909287	−	0.416170i	$-0.863372\pi$
$463$	−8.38848e6			−1.81857			−0.909287	+	0.416170i	$0.863372\pi$
$464$	245258.	+	754828.i	0.0528846	+	0.162762i
$465$		0			0
$466$	3.88123e6	−	2.81988e6i	0.827952	−	0.601542i
$467$	−5.43283e6	−	1.76523e6i	−1.15275	−	0.374550i	−0.330569	−	0.943782i	$-0.607241\pi$
$467$	−5.43283e6	−	1.76523e6i	−1.15275	−	0.374550i	−0.822177	+	0.569232i	$0.807241\pi$
$468$		0			0
$469$	−2.09597e6	−	2.88485e6i	−0.440000	−	0.605608i
$470$	3.31202e6	+	2.40632e6i	0.691589	+	0.502469i
$471$		0			0
$472$		−	1.43312e6i		−	0.296093i
$473$	−1.14261e6	−	2.90158e6i	−0.234825	−	0.596323i
$474$		0			0
$475$	304550.	−	98954.4i	0.0619334	−	0.0201234i
$476$	−449617.	+	618844.i	−0.0909547	+	0.125188i
$477$		0			0
$478$	−521295.	+	1.60438e6i	−0.104355	+	0.321172i
$479$	1.34790e6	−	4.14840e6i	0.268422	−	0.826117i	−0.722464	−	0.691409i	$-0.756990\pi$
$479$	1.34790e6	−	4.14840e6i	0.268422	−	0.826117i	0.990885	−	0.134708i	$-0.0430097\pi$
$480$		0			0
$481$	−519204.	+	714622.i	−0.102323	+	0.140836i
$482$	2.06129e6	−	669752.i	0.404130	−	0.131310i
$483$		0			0
$484$	−492217.	+	2.52937e6i	−0.0955088	+	0.490793i
$485$			2.20276e6i			0.425219i
$486$		0			0
$487$	5.53017e6	+	4.01790e6i	1.05661	+	0.767674i	0.973459	−	0.228862i	$-0.0735005\pi$
$487$	5.53017e6	+	4.01790e6i	1.05661	+	0.767674i	0.0831544	+	0.996537i	$0.473501\pi$
$488$	−1.81428e6	−	2.49714e6i	−0.344870	−	0.474673i
$489$		0			0
$490$	−4.18889e6	−	1.36105e6i	−0.788151	−	0.256086i
$491$	620372.	−	450727.i	0.116131	−	0.0843742i	−0.528204	−	0.849118i	$-0.677134\pi$
$491$	620372.	−	450727.i	0.116131	−	0.0843742i	0.644335	+	0.764743i	$0.277134\pi$
$492$		0			0
$493$	242478.	+	746270.i	0.0449319	+	0.138286i
$494$	−2.60372e6			−0.480039
$495$		0			0
$496$	−358853.			−0.0654957
$497$	−962812.	−	2.96323e6i	−0.174844	−	0.538114i
$498$		0			0
$499$	−3.31398e6	+	2.40775e6i	−0.595797	+	0.432872i	−0.844385	−	0.535738i	$-0.820034\pi$
$499$	−3.31398e6	+	2.40775e6i	−0.595797	+	0.432872i	0.248587	+	0.968609i	$0.420034\pi$
$500$	−2.52683e6	−	821016.i	−0.452012	−	0.146868i
$501$		0			0
$502$	3.04032e6	+	4.18464e6i	0.538469	+	0.741138i
$503$	−2.14161e6	−	1.55597e6i	−0.377416	−	0.274209i	0.382863	−	0.923805i	$-0.374938\pi$
$503$	−2.14161e6	−	1.55597e6i	−0.377416	−	0.274209i	−0.760279	+	0.649596i	$0.774938\pi$
$504$		0			0
$505$			1.18661e7i			2.07053i
$506$	639754.	−	527258.i	0.111080	−	0.0915476i
$507$		0			0
$508$	−4.37566e6	+	1.42174e6i	−0.752288	+	0.244433i
$509$	3.87733e6	−	5.33669e6i	0.663344	−	0.913015i	−0.336242	−	0.941775i	$-0.609156\pi$
$509$	3.87733e6	−	5.33669e6i	0.663344	−	0.913015i	0.999586	+	0.0287609i	$0.00915614\pi$
$510$		0			0
$511$	4.22758e6	−	1.30111e7i	0.716208	−	2.20426i
$512$	−81007.0	+	249314.i	−0.0136568	+	0.0420312i
$513$		0			0
$514$	−239832.	+	330101.i	−0.0400405	+	0.0551110i
$515$	−1.16288e7	+	3.77843e6i	−1.93205	+	0.627760i
$516$		0			0
$517$	−1.76341e6	+	6.81562e6i	−0.290153	+	1.12145i
$518$			1.17774e6i			0.192853i
$519$		0			0
$520$	−1.71184e6	−	1.24372e6i	−0.277622	−	0.201704i
$521$	459391.	+	632298.i	0.0741461	+	0.102053i	0.844479	−	0.535588i	$-0.179910\pi$
$521$	459391.	+	632298.i	0.0741461	+	0.102053i	−0.770333	+	0.637642i	$0.779910\pi$
$522$		0			0
$523$	5.92221e6	+	1.92424e6i	0.946738	+	0.307614i	0.741389	−	0.671075i	$-0.234167\pi$
$523$	5.92221e6	+	1.92424e6i	0.946738	+	0.307614i	0.205348	+	0.978689i	$0.434167\pi$
$524$	2.62555e6	−	1.90758e6i	0.417727	−	0.303497i
$525$		0			0
$526$	−952002.	−	2.92996e6i	−0.150028	−	0.461740i
$527$	−354785.			−0.0556466
$528$		0			0
$529$	6.16962e6			0.958560
$530$	1.47278e6	+	4.53276e6i	0.227745	+	0.700928i
$531$		0			0
$532$	−2.80855e6	+	2.04053e6i	−0.430232	+	0.312582i
$533$	−1.07806e7	−	3.50283e6i	−1.64371	−	0.534074i
$534$		0			0
$535$	−6.16030e6	−	8.47893e6i	−0.930503	−	1.28073i
$536$	−977436.	−	710149.i	−0.146952	−	0.106767i
$537$		0			0
$538$			8.74007e6i			1.30184i
$539$	−461587.	−	7.56007e6i	−0.0684356	−	1.12087i
$540$		0			0
$541$	−4.58684e6	+	1.49035e6i	−0.673783	+	0.218925i	−0.625872	−	0.779926i	$-0.715257\pi$
$541$	−4.58684e6	+	1.49035e6i	−0.673783	+	0.218925i	−0.0479117	+	0.998852i	$0.515257\pi$
$542$	3.42853e6	−	4.71897e6i	0.501314	−	0.690000i
$543$		0			0
$544$	−80088.6	+	246487.i	−0.0116031	+	0.0357106i
$545$	653421.	−	2.01102e6i	0.0942327	−	0.290018i
$546$		0			0
$547$	4.42586e6	−	6.09167e6i	0.632454	−	0.870498i	−0.365731	−	0.930721i	$-0.619181\pi$
$547$	4.42586e6	−	6.09167e6i	0.632454	−	0.870498i	0.998185	+	0.0602224i	$0.0191810\pi$
$548$	699998.	−	227443.i	0.0995739	−	0.0323535i
$549$		0			0
$550$	27272.5	+	446681.i	0.00384431	+	0.0629637i
$551$			3.56115e6i			0.499703i
$552$		0			0
$553$	−6.97193e6	−	5.06541e6i	−0.969483	−	0.704371i
$554$	5.22861e6	+	7.19657e6i	0.723789	+	0.996210i
$555$		0			0
$556$	5.75292e6	+	1.86924e6i	0.789226	+	0.256435i
$557$	6.35081e6	−	4.61413e6i	0.867344	−	0.630162i	−0.0625291	−	0.998043i	$-0.519917\pi$
$557$	6.35081e6	−	4.61413e6i	0.867344	−	0.630162i	0.929873	+	0.367881i	$0.119917\pi$
$558$		0			0
$559$	1.36077e6	+	4.18801e6i	0.184185	+	0.566863i
$560$	−2.82122e6			−0.380160
$561$		0			0
$562$	−7.35128e6			−0.981798
$563$	−1.16535e6	−	3.58658e6i	−0.154948	−	0.476880i	0.843208	−	0.537588i	$-0.180664\pi$
$563$	−1.16535e6	−	3.58658e6i	−0.154948	−	0.476880i	−0.998156	+	0.0607076i	$0.980664\pi$
$564$		0			0
$565$	−3.33776e6	+	2.42502e6i	−0.439880	+	0.319591i
$566$	−2.28153e6	−	741313.i	−0.299354	−	0.0972659i
$567$		0			0
$568$	−620501.	−	854046.i	−0.0806996	−	0.111073i
$569$	4.91058e6	+	3.56774e6i	0.635846	+	0.461969i	0.858421	−	0.512946i	$-0.171446\pi$
$569$	4.91058e6	+	3.56774e6i	0.635846	+	0.461969i	−0.222575	+	0.974916i	$0.571446\pi$
$570$		0			0
$571$		−	588638.i		−	0.0755541i	−0.999286	−	0.0377771i	$-0.987972\pi$
$571$		−	588638.i		−	0.0755541i	0.999286	−	0.0377771i	$-0.0120277\pi$
$572$	911432.	−	3.52270e6i	0.116475	−	0.450179i
$573$		0			0
$574$	−1.43739e7	+	4.67036e6i	−1.82094	+	0.591658i
$575$	84627.1	−	116479.i	0.0106743	−	0.0146919i
$576$		0			0
$577$	2.10273e6	−	6.47154e6i	0.262933	−	0.809223i	−0.729230	−	0.684269i	$-0.760121\pi$
$577$	2.10273e6	−	6.47154e6i	0.262933	−	0.809223i	0.992162	−	0.124955i	$-0.0398785\pi$
$578$	1.67586e6	−	5.15776e6i	0.208650	−	0.642158i
$579$		0			0
$580$	−1.70107e6	+	2.34132e6i	−0.209967	+	0.288995i
$581$	385688.	−	125318.i	0.0474019	−	0.0154018i
$582$		0			0
$583$	−6.32473e6	+	5.21257e6i	−0.770673	+	0.635156i
$584$		−	4.63526e6i		−	0.562395i
$585$		0			0
$586$	3.78757e6	+	2.75183e6i	0.455634	+	0.331038i
$587$	−689901.	−	949568.i	−0.0826403	−	0.113745i	0.765695	−	0.643203i	$-0.222395\pi$
$587$	−689901.	−	949568.i	−0.0826403	−	0.113745i	−0.848336	+	0.529459i	$0.822395\pi$
$588$		0			0
$589$	−1.53134e6	−	497564.i	−0.181880	−	0.0590963i
$590$	4.22767e6	−	3.07159e6i	0.500002	−	0.363272i
$591$		0			0
$592$	123310.	+	379508.i	0.0144608	+	0.0445058i
$593$	5.48179e6			0.640156			0.320078	−	0.947391i	$-0.396291\pi$
$593$	5.48179e6			0.640156			0.320078	+	0.947391i	$0.396291\pi$
$594$		0			0
$595$	−2.78923e6			−0.322992
$596$	413831.	+	1.27364e6i	0.0477208	+	0.146869i
$597$		0			0
$598$	−947085.	+	688098.i	−0.108302	+	0.0786859i
$599$	−1.56358e7	−	5.08037e6i	−1.78054	−	0.578533i	−0.781568	−	0.623820i	$-0.785580\pi$
$599$	−1.56358e7	−	5.08037e6i	−1.78054	−	0.578533i	−0.998974	+	0.0452862i	$0.985580\pi$
$600$		0			0
$601$	−411630.	−	566560.i	−0.0464859	−	0.0639823i	0.785141	−	0.619317i	$-0.212590\pi$
$601$	−411630.	−	566560.i	−0.0464859	−	0.0639823i	−0.831627	+	0.555334i	$0.812590\pi$
$602$	4.74996e6	+	3.45105e6i	0.534193	+	0.388114i
$603$		0			0
$604$			8.20062e6i			0.914649i
$605$	−8.51654e6	+	3.96912e6i	−0.945964	+	0.440865i
$606$		0			0
$607$	−1.10827e7	+	3.60098e6i	−1.22088	+	0.396687i	−0.847402	−	0.530952i	$-0.821834\pi$
$607$	−1.10827e7	+	3.60098e6i	−1.22088	+	0.396687i	−0.373477	+	0.927640i	$0.621834\pi$
$608$	−691366.	+	951583.i	−0.0758488	+	0.104397i
$609$		0			0
$610$	3.47800e6	−	1.07042e7i	0.378447	−	1.16474i
$611$	3.07200e6	−	9.45464e6i	0.332903	−	1.02457i
$612$		0			0
$613$	−5.71868e6	+	7.87109e6i	−0.614674	+	0.846026i	−0.996952	−	0.0780214i	$-0.975140\pi$
$613$	−5.71868e6	+	7.87109e6i	−0.614674	+	0.846026i	0.382278	+	0.924047i	$0.375140\pi$
$614$	−4.18157e6	+	1.35868e6i	−0.447629	+	0.145444i
$615$		0			0
$616$	−1.77761e6	−	4.51412e6i	−0.188749	−	0.479315i
$617$			1.66441e7i			1.76014i	0.474840	+	0.880072i	$0.342506\pi$
$617$			1.66441e7i			1.76014i	−0.474840	+	0.880072i	$0.657494\pi$
$618$		0			0
$619$	−981939.	−	713420.i	−0.103005	−	0.0748374i	0.535091	−	0.844795i	$-0.320277\pi$
$619$	−981939.	−	713420.i	−0.103005	−	0.0748374i	−0.638095	+	0.769957i	$0.720277\pi$
$620$	−769124.	−	1.05861e6i	−0.0803558	−	0.110600i
$621$		0			0
$622$	3.29329e6	+	1.07005e6i	0.341314	+	0.110900i
$623$	−4.65303e6	+	3.38063e6i	−0.480304	+	0.348961i
$624$		0			0
$625$	−3.26294e6	−	1.00423e7i	−0.334125	−	1.02833i
$626$	1.09629e6			0.111812
$627$		0			0
$628$	17329.8			0.00175345
$629$	121912.	+	375206.i	0.0122862	+	0.0378131i
$630$		0			0
$631$	−3.01882e6	+	2.19330e6i	−0.301831	+	0.219293i	−0.728383	−	0.685170i	$-0.759728\pi$
$631$	−3.01882e6	+	2.19330e6i	−0.301831	+	0.219293i	0.426552	+	0.904463i	$0.359728\pi$
$632$	−2.77694e6	−	902282.i	−0.276550	−	0.0898566i
$633$		0			0
$634$	−2.38837e6	−	3.28732e6i	−0.235982	−	0.324802i
$635$	−1.35724e7	−	9.86091e6i	−1.33574	−	0.970471i
$636$		0			0
$637$			1.06954e7i			1.04435i
$638$	−4.81807e6	−	1.24658e6i	−0.468620	−	0.121247i
$639$		0			0
$640$	−909090.	+	295381.i	−0.0877318	+	0.0285058i
$641$	−5.51918e6	+	7.59650e6i	−0.530554	+	0.730245i	−0.987215	−	0.159396i	$-0.949045\pi$
$641$	−5.51918e6	+	7.59650e6i	−0.530554	+	0.730245i	0.456661	+	0.889641i	$0.349045\pi$
$642$		0			0
$643$	5.28509e6	−	1.62658e7i	0.504109	−	1.55149i	−0.298153	−	0.954518i	$-0.596371\pi$
$643$	5.28509e6	−	1.62658e7i	0.504109	−	1.55149i	0.802263	−	0.596971i	$-0.203629\pi$
$644$	−482331.	+	1.48446e6i	−0.0458279	+	0.141044i
$645$		0			0
$646$	−683528.	+	940795.i	−0.0644429	+	0.0886980i
$647$	−1.67935e6	+	545655.i	−0.157718	+	0.0512457i	−0.386812	−	0.922159i	$-0.626424\pi$
$647$	−1.67935e6	+	545655.i	−0.157718	+	0.0512457i	0.229094	+	0.973404i	$0.426424\pi$
$648$		0			0
$649$	7.57852e6	+	4.82918e6i	0.706273	+	0.450051i
$650$		−	631928.i		−	0.0586657i
$651$		0			0
$652$	7.25395e6	+	5.27030e6i	0.668275	+	0.485530i
$653$	1.11034e7	+	1.52825e7i	1.01899	+	1.40253i	0.912906	+	0.408169i	$0.133833\pi$
$653$	1.11034e7	+	1.52825e7i	1.01899	+	1.40253i	0.106089	+	0.994357i	$0.466167\pi$
$654$		0			0
$655$	1.12546e7	+	3.65685e6i	1.02501	+	0.333045i
$656$	−4.14276e6	+	3.00989e6i	−0.375864	+	0.273081i
$657$		0			0
$658$	−4.09592e6	−	1.26060e7i	−0.368797	−	1.13504i
$659$	1.72599e7			1.54820			0.774098	−	0.633066i	$-0.218204\pi$
$659$	1.72599e7			1.54820			0.774098	+	0.633066i	$0.218204\pi$
$660$		0			0
$661$	1.66702e7			1.48402			0.742008	−	0.670391i	$-0.233874\pi$
$661$	1.66702e7			1.48402			0.742008	+	0.670391i	$0.233874\pi$
$662$	3.19127e6	+	9.82173e6i	0.283021	+	0.871050i
$663$		0			0
$664$	111161.	−	80763.2i	0.00978435	−	0.00710875i
$665$	−1.20390e7	−	3.91172e6i	−1.05569	−	0.343015i
$666$		0			0
$667$	941125.	+	1.29535e6i	0.0819092	+	0.112738i
$668$	−1.75867e6	−	1.27775e6i	−0.152490	−	0.110791i
$669$		0			0
$670$		−	4.40546e6i		−	0.379144i
$671$	1.93188e7	−	1.17953e6i	1.65643	−	0.101135i
$672$		0			0
$673$	−1.47284e7	+	4.78555e6i	−1.25348	+	0.407281i	−0.859167	−	0.511695i	$-0.829018\pi$
$673$	−1.47284e7	+	4.78555e6i	−1.25348	+	0.407281i	−0.394314	+	0.918976i	$0.629018\pi$
$674$	−2.60289e6	+	3.58257e6i	−0.220702	+	0.303770i
$675$		0			0
$676$	247991.	−	763238.i	0.0208723	−	0.0642382i
$677$	2.92375e6	−	8.99838e6i	0.245171	−	0.754558i	−0.750438	−	0.660941i	$-0.770157\pi$
$677$	2.92375e6	−	8.99838e6i	0.245171	−	0.754558i	0.995608	−	0.0936167i	$-0.0298428\pi$
$678$		0			0
$679$	4.19199e6	−	5.76979e6i	0.348936	−	0.480270i
$680$	−898784.	+	292033.i	−0.0745389	+	0.0242192i
$681$		0			0
$682$	1.20923e6	−	1.89766e6i	0.0995513	−	0.156228i
$683$		−	1.91424e6i		−	0.157016i	−0.996913	−	0.0785080i	$-0.974984\pi$
$683$		−	1.91424e6i		−	0.157016i	0.996913	−	0.0785080i	$-0.0250156\pi$
$684$		0			0
$685$	2.17125e6	+	1.57750e6i	0.176800	+	0.128453i
$686$	917757.	+	1.26318e6i	0.0744590	+	0.102484i
$687$		0			0
$688$	1.89192e6	+	614722.i	0.152381	+	0.0495117i
$689$	9.36306e6	−	6.80266e6i	0.751398	−	0.545922i
$690$		0			0
$691$	2.64900e6	+	8.15279e6i	0.211051	+	0.649548i	0.999410	+	0.0343332i	$0.0109307\pi$
$691$	2.64900e6	+	8.15279e6i	0.211051	+	0.649548i	−0.788359	+	0.615215i	$0.789069\pi$
$692$	−1.05008e7			−0.833596
$693$		0			0
$694$	1.25457e7			0.988774
$695$	6.81593e6	+	2.09773e7i	0.535258	+	1.64735i
$696$		0			0
$697$	−4.09580e6	+	2.97577e6i	−0.319342	+	0.232016i
$698$	1.41195e7	+	4.58769e6i	1.09693	+	0.356415i
$699$		0			0
$700$	−495242.	−	681642.i	−0.0382008	−	0.0525789i
$701$	1.38189e7	+	1.00400e7i	1.06213	+	0.771684i	0.974482	−	0.224467i	$-0.0720642\pi$
$701$	1.38189e7	+	1.00400e7i	1.06213	+	0.771684i	0.0876502	+	0.996151i	$0.472064\pi$
$702$		0			0
$703$			1.79046e6i			0.136639i
$704$	−1.04543e6	−	1.26849e6i	−0.0794995	−	0.0964615i
$705$		0			0
$706$	8.29033e6	−	2.69369e6i	0.625979	−	0.203393i
$707$	2.25820e7	−	3.10815e7i	1.69908	−	2.33859i
$708$		0			0
$709$	4.59771e6	−	1.41503e7i	0.343499	−	1.05718i	−0.618883	−	0.785483i	$-0.712414\pi$
$709$	4.59771e6	−	1.41503e7i	0.343499	−	1.05718i	0.962382	−	0.271699i	$-0.0875855\pi$
$710$	1.18951e6	−	3.66092e6i	0.0885566	−	0.272549i
$711$		0			0
$712$	−1.14541e6	+	1.57652e6i	−0.0846763	+	0.116547i
$713$	−688510.	+	223711.i	−0.0507209	+	0.0164802i
$714$		0			0
$715$	1.23453e7	−	4.86144e6i	0.903104	−	0.355631i
$716$			3.20083e6i			0.233335i
$717$		0			0
$718$	1.20664e7	+	8.76673e6i	0.873505	+	0.634638i
$719$	−98679.2	−	135820.i	−0.00711874	−	0.00979811i	0.805443	−	0.592674i	$-0.201928\pi$
$719$	−98679.2	−	135820.i	−0.00711874	−	0.00979811i	−0.812562	+	0.582875i	$0.801928\pi$
$720$		0			0
$721$	3.76505e7	+	1.22334e7i	2.69732	+	0.876412i
$722$	3.74314e6	−	2.71955e6i	0.267235	−	0.194157i
$723$		0			0
$724$	−2.15330e6	−	6.62719e6i	−0.152672	−	0.469875i
$725$	−864301.			−0.0610689
$726$		0			0
$727$	−1.61449e7			−1.13292			−0.566460	−	0.824090i	$-0.691687\pi$
$727$	−1.61449e7			−1.13292			−0.566460	+	0.824090i	$0.691687\pi$
$728$	2.11701e6	+	6.51547e6i	0.148045	+	0.455636i
$729$		0			0
$730$	1.36739e7	−	9.93467e6i	0.949697	−	0.689995i
$731$	1.87047e6	+	607753.i	0.129467	+	0.0420663i
$732$		0			0
$733$	−1.19223e7	−	1.64096e7i	−0.819596	−	1.12808i	−0.989771	−	0.142664i	$-0.954433\pi$
$733$	−1.19223e7	−	1.64096e7i	−0.819596	−	1.12808i	0.170175	−	0.985414i	$-0.445567\pi$
$734$	−1.49608e7	−	1.08696e7i	−1.02498	−	0.744689i
$735$		0			0
$736$			528843.i			0.0359859i
$737$	7.04902e6	−	2.77582e6i	0.478035	−	0.188244i
$738$		0			0
$739$	7.63455e6	−	2.48062e6i	0.514248	−	0.167089i	−0.0403854	−	0.999184i	$-0.512859\pi$
$739$	7.63455e6	−	2.48062e6i	0.514248	−	0.167089i	0.554633	+	0.832095i	$0.312859\pi$
$740$	−855252.	+	1.17715e6i	−0.0574136	+	0.0790230i
$741$		0			0
$742$	4.76841e6	−	1.46757e7i	0.317954	−	0.978561i
$743$	−7.78217e6	+	2.39511e7i	−0.517165	+	1.59167i	0.262144	+	0.965029i	$0.415570\pi$
$743$	−7.78217e6	+	2.39511e7i	−0.517165	+	1.59167i	−0.779309	+	0.626640i	$0.784430\pi$
$744$		0			0
$745$	−2.87025e6	+	3.95057e6i	−0.189465	+	0.260777i
$746$	−784203.	+	254803.i	−0.0515919	+	0.0167632i
$747$		0			0
$748$	−1.03358e6	−	1.25411e6i	−0.0675446	−	0.0819559i
$749$			3.39327e7i			2.21011i
$750$		0			0
$751$	−6.45895e6	−	4.69270e6i	−0.417890	−	0.303615i	0.358898	−	0.933377i	$-0.383152\pi$
$751$	−6.45895e6	−	4.69270e6i	−0.417890	−	0.303615i	−0.776788	+	0.629762i	$0.783152\pi$
$752$	−2.63969e6	−	3.63322e6i	−0.170219	−	0.234286i
$753$		0			0
$754$	6.68363e6	+	2.17164e6i	0.428138	+	0.139110i
$755$	−2.41916e7	+	1.75763e7i	−1.54454	+	1.12217i
$756$		0			0
$757$	−3.17328e6	−	9.76634e6i	−0.201265	−	0.619430i	−0.999846	−	0.0175429i	$-0.994416\pi$
$757$	−3.17328e6	−	9.76634e6i	−0.201265	−	0.619430i	0.798581	−	0.601887i	$-0.205584\pi$
$758$	−9.58390e6			−0.605856
$759$		0			0
$760$	−4.28894e6			−0.269349
$761$	−1.61270e6	−	4.96338e6i	−0.100947	−	0.310682i	0.887811	−	0.460208i	$-0.152225\pi$
$761$	−1.61270e6	−	4.96338e6i	−0.100947	−	0.310682i	−0.988758	+	0.149526i	$0.952225\pi$
$762$		0			0
$763$	−5.53863e6	+	4.02405e6i	−0.344422	+	0.250238i
$764$	−328036.	−	106585.i	−0.0203324	−	0.00660639i
$765$		0			0
$766$	5.28022e6	+	7.26761e6i	0.325148	+	0.447527i
$767$	−1.02661e7	−	7.45875e6i	−0.630110	−	0.457802i
$768$		0			0
$769$			1.93201e7i			1.17813i	0.808084	+	0.589067i	$0.200504\pi$
$769$			1.93201e7i			1.17813i	−0.808084	+	0.589067i	$0.799496\pi$
$770$	9.50664e6	−	1.49189e7i	0.577830	−	0.906799i
$771$		0			0
$772$	−1.94783e6	+	632887.i	−0.117627	+	0.0382193i
$773$	7.69397e6	−	1.05898e7i	0.463129	−	0.637442i	−0.512025	−	0.858971i	$-0.671104\pi$
$773$	7.69397e6	−	1.05898e7i	0.463129	−	0.637442i	0.975154	+	0.221528i	$0.0711045\pi$
$774$		0			0
$775$	120760.	−	371661.i	0.00722219	−	0.0222276i
$776$	746705.	−	2.29812e6i	0.0445138	−	0.136999i
$777$		0			0
$778$	−9.27980e6	+	1.27725e7i	−0.549654	+	0.756534i
$779$	−2.18519e7	+	7.10010e6i	−1.29016	+	0.419199i
$780$		0			0
$781$	6.60720e6	−	403409.i	0.387605	−	0.0236656i
$782$			522848.i			0.0305744i
$783$		0			0
$784$	3.90886e6	+	2.83995e6i	0.227122	+	0.165014i
$785$	37142.7	+	51122.5i	0.00215129	+	0.00296100i
$786$		0			0
$787$	3.92301e6	+	1.27466e6i	0.225778	+	0.0733598i	0.419721	−	0.907653i	$-0.362128\pi$
$787$	3.92301e6	+	1.27466e6i	0.225778	+	0.0733598i	−0.193943	+	0.981013i	$0.562128\pi$
$788$	3.66237e6	−	2.66087e6i	0.210110	−	0.152654i
$789$		0			0
$790$	−3.29006e6	−	1.01258e7i	−0.187558	−	0.577244i
$791$	1.33577e7			0.759086
$792$		0			0
$793$	−2.73307e7			−1.54336
$794$	2661.41	+	8190.97i	0.000149817	+	0.000461088i
$795$		0			0
$796$	3.11875e6	−	2.26591e6i	0.174461	−	0.126753i
$797$	1.61686e6	+	525350.i	0.0901628	+	0.0292957i	0.353751	−	0.935340i	$-0.384906\pi$
$797$	1.61686e6	+	525350.i	0.0901628	+	0.0292957i	−0.263588	+	0.964635i	$0.584906\pi$
$798$		0			0
$799$	−2.60976e6	−	3.59203e6i	−0.144622	−	0.199055i
$800$	−230952.	−	167796.i	−0.0127584	−	0.00926952i
$801$		0			0
$802$		−	9.68115e6i		−	0.531485i
$803$	2.45118e7	+	1.56194e7i	1.34149	+	0.854822i
$804$		0			0
$805$	−5.41290e6	+	1.75876e6i	−0.294401	+	0.0956568i
$806$	−1.86767e6	+	2.57063e6i	−0.101266	+	0.139380i
$807$		0			0
$808$	4.02246e6	−	1.23798e7i	0.216752	−	0.667094i
$809$	4.00196e6	−	1.23168e7i	0.214982	−	0.661646i	−0.784173	−	0.620542i	$-0.786913\pi$
$809$	4.00196e6	−	1.23168e7i	0.214982	−	0.661646i	0.999155	−	0.0411038i	$-0.0130874\pi$
$810$		0			0
$811$	−1.11470e7	+	1.53425e7i	−0.595120	+	0.819113i	−0.995251	−	0.0973453i	$-0.968965\pi$
$811$	−1.11470e7	+	1.53425e7i	−0.595120	+	0.819113i	0.400130	+	0.916458i	$0.368965\pi$
$812$	8.91134e6	−	2.89547e6i	0.474300	−	0.154109i
$813$		0			0
$814$	−2.42240e6	−	626750.i	−0.128140	−	0.0331538i
$815$			3.26947e7i			1.72418i
$816$		0			0
$817$	7.22110e6	+	5.24644e6i	0.378485	+	0.274985i
$818$	3.75206e6	+	5.16427e6i	0.196059	+	0.269852i
$819$		0			0
$820$	−1.77582e7	−	5.77000e6i	−0.922285	−	0.299669i
$821$	−1.54271e7	+	1.12084e7i	−0.798777	+	0.580345i	−0.910555	−	0.413388i	$-0.864345\pi$
$821$	−1.54271e7	+	1.12084e7i	−0.798777	+	0.580345i	0.111778	+	0.993733i	$0.464345\pi$
$822$		0			0
$823$	−3.90658e6	−	1.20232e7i	−0.201047	−	0.618758i	−0.999853	−	0.0171693i	$-0.994535\pi$
$823$	−3.90658e6	−	1.20232e7i	−0.201047	−	0.618758i	0.798806	−	0.601589i	$-0.205465\pi$
$824$	1.34131e7			0.688194
$825$		0			0
$826$	−1.69191e7			−0.862836
$827$	−1.50970e6	−	4.64637e6i	−0.0767584	−	0.236238i	0.905314	−	0.424743i	$-0.139636\pi$
$827$	−1.50970e6	−	4.64637e6i	−0.0767584	−	0.236238i	−0.982072	+	0.188505i	$0.939636\pi$
$828$		0			0
$829$	4.17488e6	−	3.03323e6i	0.210988	−	0.153292i	−0.477273	−	0.878755i	$-0.658375\pi$
$829$	4.17488e6	−	3.03323e6i	0.210988	−	0.153292i	0.688261	+	0.725464i	$0.258375\pi$
$830$	476499.	+	154824.i	0.0240086	+	0.00780086i
$831$		0			0
$832$	1.36434e6	+	1.87785e6i	0.0683305	+	0.0940489i
$833$	3.86454e6	+	2.80776e6i	0.192968	+	0.140200i
$834$		0			0
$835$		−	7.92659e6i		−	0.393432i
$836$	−2.70240e6	−	6.86257e6i	−0.133731	−	0.339603i
$837$		0			0
$838$	9.68429e6	−	3.14662e6i	0.476384	−	0.154787i
$839$	6.23850e6	−	8.58656e6i	0.305968	−	0.421128i	−0.628151	−	0.778092i	$-0.716188\pi$
$839$	6.23850e6	−	8.58656e6i	0.305968	−	0.421128i	0.934118	+	0.356963i	$0.116188\pi$
$840$		0			0
$841$	−3.36810e6	+	1.03659e7i	−0.164208	+	0.505380i
$842$	7.28504e6	−	2.24210e7i	0.354121	−	1.08987i
$843$		0			0
$844$	9.65901e6	−	1.32945e7i	0.466742	−	0.642415i
$845$	2.78305e6	−	904267.i	0.134085	−	0.0435667i
$846$		0			0
$847$	2.98612e7	+	5.81102e6i	1.43021	+	0.278320i
$848$		−	5.22824e6i		−	0.249670i
$849$		0			0
$850$	−228333.	−	165894.i	−0.0108398	−	0.00787559i
$851$	473173.	+	651267.i	0.0223973	+	0.0308273i
$852$		0			0
$853$	1.83550e7	+	5.96392e6i	0.863740	+	0.280646i	0.707190	−	0.707024i	$-0.249963\pi$
$853$	1.83550e7	+	5.96392e6i	0.863740	+	0.280646i	0.156550	+	0.987670i	$0.449963\pi$
$854$	−2.94808e7	+	2.14190e7i	−1.38323	+	1.00498i
$855$		0			0
$856$	3.55275e6	+	1.09342e7i	0.165722	+	0.510040i
$857$	1.48801e7			0.692074			0.346037	−	0.938221i	$-0.387527\pi$
$857$	1.48801e7			0.692074			0.346037	+	0.938221i	$0.387527\pi$
$858$		0			0
$859$	−2.59749e7			−1.20108			−0.600538	−	0.799596i	$-0.705047\pi$
$859$	−2.59749e7			−1.20108			−0.600538	+	0.799596i	$0.705047\pi$
$860$	2.24151e6	+	6.89865e6i	0.103346	+	0.318066i
$861$		0			0
$862$	7.52187e6	−	5.46496e6i	0.344792	−	0.250506i
$863$	1.80833e7	+	5.87561e6i	0.826514	+	0.268551i	0.691576	−	0.722304i	$-0.256917\pi$
$863$	1.80833e7	+	5.87561e6i	0.826514	+	0.268551i	0.134938	+	0.990854i	$0.456917\pi$
$864$		0			0
$865$	−2.25061e7	−	3.09770e7i	−1.02273	−	1.40766i
$866$	−6.84749e6	−	4.97499e6i	−0.310268	−	0.225423i
$867$		0			0
$868$			4.23655e6i			0.190859i
$869$	1.41288e7	−	1.16444e7i	0.634683	−	0.523079i
$870$		0			0
$871$	−1.01742e7	+	3.30581e6i	−0.454419	+	0.147650i
$872$	−1.36342e6	+	1.87658e6i	−0.0607207	+	0.0835749i
$873$		0			0
$874$	−733261.	+	2.25675e6i	−0.0324698	+	0.0999319i
$875$	−9.69275e6	+	2.98312e7i	−0.427983	+	1.31720i
$876$		0			0
$877$	−2.41157e7	+	3.31924e7i	−1.05877	+	1.45727i	−0.177816	+	0.984064i	$0.556903\pi$
$877$	−2.41157e7	+	3.31924e7i	−1.05877	+	1.45727i	−0.880952	+	0.473206i	$0.843097\pi$
$878$	−2.85463e7	+	9.27524e6i	−1.24972	+	0.406059i
$879$		0			0
$880$	1.50135e6	−	5.80273e6i	0.0653543	−	0.252595i
$881$		−	2.64642e7i		−	1.14873i	−0.818599	−	0.574365i	$-0.805249\pi$
$881$		−	2.64642e7i		−	1.14873i	0.818599	−	0.574365i	$-0.194751\pi$
$882$		0			0
$883$	5.21978e6	+	3.79239e6i	0.225295	+	0.163686i	0.694707	−	0.719293i	$-0.255534\pi$
$883$	5.21978e6	+	3.79239e6i	0.225295	+	0.163686i	−0.469412	+	0.882979i	$0.655534\pi$
$884$	1.34887e6	+	1.85657e6i	0.0580551	+	0.0799060i
$885$		0			0
$886$	1.59061e7	+	5.16820e6i	0.680736	+	0.221185i
$887$	4.70117e6	−	3.41560e6i	0.200631	−	0.145767i	−0.482934	−	0.875657i	$-0.660429\pi$
$887$	4.70117e6	−	3.41560e6i	0.200631	−	0.145767i	0.683564	+	0.729890i	$0.260429\pi$
$888$		0			0
$889$	1.67848e7	+	5.16582e7i	0.712296	+	2.19222i
$890$	−7.10565e6			−0.300697
$891$		0			0
$892$	−782009.			−0.0329079
$893$	−6.22681e6	−	1.91642e7i	−0.261299	−	0.804194i
$894$		0			0
$895$	−9.44236e6	+	6.86028e6i	−0.394024	+	0.286275i
$896$	2.94335e6	+	956352.i	0.122482	+	0.0397968i
$897$		0			0
$898$	−1.77983e7	−	2.44973e7i	−0.736527	−	1.01374i
$899$	3.51590e6	+	2.55445e6i	0.145090	+	0.105414i
$900$		0			0
$901$		−	5.16897e6i		−	0.212125i
$902$	−1.95684e6	−	3.20499e7i	−0.0800826	−	1.31163i
$903$		0			0
$904$	4.30430e6	−	1.39855e6i	0.175179	−	0.0569191i
$905$	1.49349e7	−	2.05561e7i	0.606151	−	0.834295i
$906$		0			0
$907$	−5.17657e6	+	1.59318e7i	−0.208941	+	0.643055i	0.790587	+	0.612349i	$0.209775\pi$
$907$	−5.17657e6	+	1.59318e7i	−0.208941	+	0.643055i	−0.999528	+	0.0307054i	$0.990225\pi$
$908$	−1.12335e6	+	3.45732e6i	−0.0452169	+	0.139163i
$909$		0			0
$910$	−1.46831e7	+	2.02096e7i	−0.587781	+	0.809012i
$911$	−2.60012e7	+	8.44829e6i	−1.03800	+	0.337266i	−0.777948	−	0.628329i	$-0.783739\pi$
$911$	−2.60012e7	+	8.44829e6i	−1.03800	+	0.337266i	−0.260050	+	0.965595i	$0.583739\pi$
$912$		0			0
$913$	52506.9	+	859980.i	0.00208468	+	0.0341438i
$914$		−	1.03061e7i		−	0.408063i
$915$		0			0
$916$	1.21499e7	+	8.82742e6i	0.478447	+	0.347612i
$917$	−2.25205e7	−	3.09968e7i	−0.884411	−	1.21729i
$918$		0			0
$919$	−1.22800e7	−	3.99001e6i	−0.479633	−	0.155842i	0.0592147	−	0.998245i	$-0.481140\pi$
$919$	−1.22800e7	−	3.99001e6i	−0.479633	−	0.155842i	−0.538848	+	0.842403i	$0.681140\pi$
$920$	−1.56008e6	+	1.13346e6i	−0.0607681	+	0.0441506i
$921$		0			0
$922$	83907.3	+	258240.i	0.00325067	+	0.0100045i
$923$	−9.34734e6			−0.361147
$924$		0			0
$925$	−434548.			−0.0166987
$926$	1.03687e7	+	3.19117e7i	0.397373	+	1.22299i
$927$		0			0
$928$	2.56838e6	−	1.86604e6i	0.0979015	−	0.0711296i
$929$	−3.63192e7	−	1.18008e7i	−1.38069	−	0.448614i	−0.477796	−	0.878471i	$-0.658564\pi$
$929$	−3.63192e7	−	1.18008e7i	−1.38069	−	0.448614i	−0.902897	+	0.429856i	$0.858564\pi$
$930$		0			0
$931$	1.27427e7	+	1.75388e7i	0.481821	+	0.663170i
$932$	−1.55249e7	−	1.12795e7i	−0.585450	−	0.425355i
$933$		0			0
$934$			2.28497e7i			0.857063i
$935$	1.48432e6	−	5.73694e6i	0.0555265	−	0.214611i
$936$		0			0
$937$	−4.81317e7	+	1.56389e7i	−1.79094	+	0.581913i	−0.999567	−	0.0294146i	$-0.990636\pi$
$937$	−4.81317e7	+	1.56389e7i	−1.79094	+	0.581913i	−0.791377	+	0.611328i	$0.790636\pi$
$938$	−8.38388e6	+	1.15394e7i	−0.311127	+	0.428230i
$939$		0			0
$940$	5.06031e6	−	1.55740e7i	0.186792	−	0.574886i
$941$	−1.03874e7	+	3.19691e7i	−0.382413	+	1.17695i	0.555927	+	0.831231i	$0.312363\pi$
$941$	−1.03874e7	+	3.19691e7i	−0.382413	+	1.17695i	−0.938340	+	0.345715i	$0.887637\pi$
$942$		0			0
$943$	−6.07209e6	+	8.35752e6i	−0.222361	+	0.306054i
$944$	−5.45192e6	+	1.77144e6i	−0.199122	+	0.0646987i
$945$		0			0
$946$	−9.62593e6	+	7.93328e6i	−0.349715	+	0.288221i
$947$		−	3.65340e7i		−	1.32380i	−0.749593	−	0.661899i	$-0.769751\pi$
$947$		−	3.65340e7i		−	1.32380i	0.749593	−	0.661899i	$-0.230249\pi$
$948$		0			0
$949$	−3.32044e7	−	2.41244e7i	−1.19682	−	0.869544i
$950$	−752890.	−	1.03626e6i	−0.0270659	−	0.0372530i
$951$		0			0
$952$	2.90998e6	+	945510.i	0.104063	+	0.0338122i
$953$	2.61597e7	−	1.90061e7i	0.933041	−	0.677894i	−0.0136944	−	0.999906i	$-0.504359\pi$
$953$	2.61597e7	−	1.90061e7i	0.933041	−	0.677894i	0.946736	+	0.322012i	$0.104359\pi$
$954$		0			0
$955$	−388650.	−	1.19614e6i	−0.0137895	−	0.0424399i
$956$	6.74779e6			0.238790
$957$		0			0
$958$	−1.74475e7			−0.614215
$959$	−2.68515e6	−	8.26404e6i	−0.0942805	−	0.290166i
$960$		0			0
$961$	2.15718e7	−	1.56728e7i	0.753490	−	0.547443i
$962$	3.36036e6	+	1.09185e6i	0.117071	+	0.0380385i
$963$		0			0
$964$	−5.09578e6	−	7.01374e6i	−0.176611	−	0.243084i
$965$	−6.04175e6	−	4.38959e6i	−0.208855	−	0.151742i
$966$		0			0
$967$		−	1.12957e7i		−	0.388462i	−0.980956	−	0.194231i	$-0.937779\pi$
$967$		−	1.12957e7i		−	0.388462i	0.980956	−	0.194231i	$-0.0622212\pi$
$968$	1.02307e7	−	1.25396e6i	0.350927	−	0.0430127i
$969$		0			0
$970$	8.37980e6	−	2.72276e6i	0.285959	−	0.0929138i
$971$	1.63135e7	−	2.24536e7i	0.555264	−	0.764255i	−0.435451	−	0.900212i	$-0.643411\pi$
$971$	1.63135e7	−	2.24536e7i	0.555264	−	0.764255i	0.990715	+	0.135958i	$0.0434111\pi$
$972$		0			0
$973$	2.20678e7	−	6.79178e7i	0.747270	−	2.29986i
$974$	8.44935e6	−	2.60044e7i	0.285381	−	0.878314i
$975$		0			0
$976$	−7.25713e6	+	9.98858e6i	−0.243860	+	0.335644i
$977$	−3.73267e7	+	1.21282e7i	−1.25107	+	0.406499i	−0.858306	−	0.513138i	$-0.828483\pi$
$977$	−3.73267e7	+	1.21282e7i	−1.25107	+	0.406499i	−0.392769	+	0.919637i	$0.628483\pi$
$978$		0			0
$979$	−4.47716e6	−	1.13695e7i	−0.149295	−	0.379126i
$980$			1.76179e7i			0.585987i
$981$		0			0
$982$	−2.48149e6	−	1.80291e6i	−0.0821171	−	0.0596616i
$983$	−2.41892e7	−	3.32936e7i	−0.798433	−	1.09895i	−0.993006	−	0.118061i	$-0.962332\pi$
$983$	−2.41892e7	−	3.32936e7i	−0.798433	−	1.09895i	0.194573	−	0.980888i	$-0.437668\pi$
$984$		0			0
$985$	1.56990e7	+	5.10091e6i	0.515563	+	0.167516i
$986$	2.53926e6	−	1.84488e6i	0.0831793	−	0.0604333i
$987$		0			0
$988$	3.21837e6	+	9.90512e6i	0.104892	+	0.322825i
$989$	4.01314e6			0.130465
$990$		0			0
$991$	1.06389e7			0.344122			0.172061	−	0.985086i	$-0.444957\pi$
$991$	1.06389e7			0.344122			0.172061	+	0.985086i	$0.444957\pi$
$992$	443567.	+	1.36516e6i	0.0143113	+	0.0440458i
$993$		0			0
$994$	−1.00827e7	+	7.32551e6i	−0.323676	+	0.235164i
$995$	1.33687e7	+	4.34377e6i	0.428088	+	0.139094i
$996$		0			0
$997$	−2.86643e7	−	3.94530e7i	−0.913278	−	1.25702i	−0.966035	−	0.258411i	$-0.916801\pi$
$997$	−2.86643e7	−	3.94530e7i	−0.913278	−	1.25702i	0.0527575	−	0.998607i	$-0.483199\pi$
$998$	1.32559e7	+	9.63099e6i	0.421292	+	0.306087i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.6.l.b.17.3	yes	40
3.2	odd	2		198.6.l.a.17.8	✓	40
11.2	odd	10		198.6.l.a.35.8	yes	40
33.2	even	10	inner	198.6.l.b.35.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.6.l.a.17.8	✓	40	3.2	odd	2
198.6.l.a.35.8	yes	40	11.2	odd	10
198.6.l.b.17.3	yes	40	1.1	even	1	trivial
198.6.l.b.35.3	yes	40	33.2	even	10	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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	198.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23607 - 3.80423i) q^{2} +(-12.9443 + 9.40456i) q^{4} +(-55.4865 - 18.0286i) q^{5} +(111.028 + 152.817i) q^{7} +(51.7771 + 37.6183i) q^{8} +O(q^{10})\)	\(q+(-1.23607 - 3.80423i) q^{2} +(-12.9443 + 9.40456i) q^{4} +(-55.4865 - 18.0286i) q^{5} +(111.028 + 152.817i) q^{7} +(51.7771 + 37.6183i) q^{8} +233.368i q^{10} +(-373.403 + 147.042i) q^{11} +(538.953 - 175.116i) q^{13} +(444.114 - 611.270i) q^{14} +(79.1084 - 243.470i) q^{16} +(78.2115 - 240.710i) q^{17} +(675.162 - 929.281i) q^{19} +(887.784 - 288.458i) q^{20} +(1020.93 + 1238.76i) q^{22} -516.449i q^{23} +(225.539 + 163.863i) q^{25} +(-1332.36 - 1833.84i) q^{26} +(-2874.36 - 933.937i) q^{28} +(-2508.18 + 1822.30i) q^{29} +(-433.171 - 1333.16i) q^{31} -1024.00 q^{32} -1012.39 q^{34} +(-3405.48 - 10481.0i) q^{35} +(-1261.05 + 916.206i) q^{37} +(-4369.74 - 1419.81i) q^{38} +(-2194.72 - 3020.78i) q^{40} +(-16182.7 - 11757.4i) q^{41} +7770.64i q^{43} +(3450.57 - 5415.04i) q^{44} +(-1964.69 + 638.366i) q^{46} +(10311.3 - 14192.3i) q^{47} +(-5832.23 + 17949.8i) q^{49} +(344.593 - 1060.55i) q^{50} +(-5329.46 + 7335.37i) q^{52} +(19423.3 - 6311.00i) q^{53} +(23369.8 - 1426.86i) q^{55} +12089.1i q^{56} +(10032.7 + 7289.21i) q^{58} +(-13162.0 - 18115.9i) q^{59} +(-45868.3 - 14903.5i) q^{61} +(-4536.23 + 3295.76i) q^{62} +(1265.73 + 3895.53i) q^{64} -33061.7 q^{65} -18877.8 q^{67} +(1251.38 + 3851.36i) q^{68} +(-35662.7 + 25910.4i) q^{70} +(-15687.4 - 5097.13i) q^{71} +(-42570.9 - 58593.8i) q^{73} +(5044.20 + 3664.83i) q^{74} +18378.5i q^{76} +(-63928.9 - 40736.7i) q^{77} +(-43389.7 + 14098.2i) q^{79} +(-8778.89 + 12083.1i) q^{80} +(-24724.9 + 76095.5i) q^{82} +(663.433 - 2041.84i) q^{83} +(-8679.36 + 11946.1i) q^{85} +(29561.3 - 9605.04i) q^{86} +(-24865.2 - 6433.39i) q^{88} +30448.3i q^{89} +(86599.9 + 62918.5i) q^{91} +(4856.97 + 6685.05i) q^{92} +(-66736.0 - 21683.9i) q^{94} +(-54216.0 + 39390.3i) q^{95} +(-11667.3 - 35908.1i) q^{97} +75494.0 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 160 q^{4} + 640 q^{8}+O(q^{10}) \) 40 * q + 40 * q^2 - 160 * q^4 + 640 * q^8	\( 40 q + 40 q^{2} - 160 q^{4} + 640 q^{8} - 476 q^{11} - 2560 q^{16} - 1424 q^{17} - 1656 q^{22} + 11574 q^{25} + 10480 q^{26} + 3040 q^{28} - 10658 q^{29} - 5302 q^{31} - 40960 q^{32} - 13984 q^{34} - 50 q^{35} - 4344 q^{37} + 35120 q^{38} + 19840 q^{40} - 16856 q^{41} + 6624 q^{44} - 52400 q^{46} - 10900 q^{47} - 40698 q^{49} - 6256 q^{50} + 41920 q^{52} + 10290 q^{53} + 158396 q^{55} + 42632 q^{58} + 62620 q^{59} - 134780 q^{61} - 30272 q^{62} - 40960 q^{64} - 137296 q^{65} - 36856 q^{67} - 22784 q^{68} + 79400 q^{70} + 62180 q^{71} + 100030 q^{73} + 17376 q^{74} - 162888 q^{77} + 35900 q^{79} + 79360 q^{80} - 90096 q^{82} - 12276 q^{83} + 270600 q^{85} - 137680 q^{86} - 26496 q^{88} + 406656 q^{91} + 134720 q^{92} - 91600 q^{94} - 75128 q^{95} - 364164 q^{97} + 358192 q^{98}+O(q^{100}) \) 40 * q + 40 * q^2 - 160 * q^4 + 640 * q^8 - 476 * q^11 - 2560 * q^16 - 1424 * q^17 - 1656 * q^22 + 11574 * q^25 + 10480 * q^26 + 3040 * q^28 - 10658 * q^29 - 5302 * q^31 - 40960 * q^32 - 13984 * q^34 - 50 * q^35 - 4344 * q^37 + 35120 * q^38 + 19840 * q^40 - 16856 * q^41 + 6624 * q^44 - 52400 * q^46 - 10900 * q^47 - 40698 * q^49 - 6256 * q^50 + 41920 * q^52 + 10290 * q^53 + 158396 * q^55 + 42632 * q^58 + 62620 * q^59 - 134780 * q^61 - 30272 * q^62 - 40960 * q^64 - 137296 * q^65 - 36856 * q^67 - 22784 * q^68 + 79400 * q^70 + 62180 * q^71 + 100030 * q^73 + 17376 * q^74 - 162888 * q^77 + 35900 * q^79 + 79360 * q^80 - 90096 * q^82 - 12276 * q^83 + 270600 * q^85 - 137680 * q^86 - 26496 * q^88 + 406656 * q^91 + 134720 * q^92 - 91600 * q^94 - 75128 * q^95 - 364164 * q^97 + 358192 * q^98

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