LMFDB - Embedded newform 198.6.l.b.17.4

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			17.4
Character	$\chi$	$=$	198.17
Dual form			198.6.l.b.35.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23607 - 3.80423i) q^{2} +(-12.9443 + 9.40456i) q^{4} +(-27.5399 - 8.94827i) q^{5} +(-22.3921 - 30.8201i) q^{7} +(51.7771 + 37.6183i) q^{8} +O(q^{10})$	\(q+(-1.23607 - 3.80423i) q^{2} +(-12.9443 + 9.40456i) q^{4} +(-27.5399 - 8.94827i) q^{5} +(-22.3921 - 30.8201i) q^{7} +(51.7771 + 37.6183i) q^{8} +115.829i q^{10} +(357.943 + 181.459i) q^{11} +(515.345 - 167.446i) q^{13} +(-89.5686 + 123.281i) q^{14} +(79.1084 - 243.470i) q^{16} +(-200.704 + 617.704i) q^{17} +(187.428 - 257.972i) q^{19} +(440.639 - 143.172i) q^{20} +(247.870 - 1585.99i) q^{22} +761.182i q^{23} +(-1849.80 - 1343.96i) q^{25} +(-1274.00 - 1753.52i) q^{26} +(579.700 + 188.356i) q^{28} +(176.294 - 128.085i) q^{29} +(-1329.51 - 4091.81i) q^{31} -1024.00 q^{32} +2597.97 q^{34} +(340.891 + 1049.16i) q^{35} +(10082.9 - 7325.63i) q^{37} +(-1213.06 - 394.146i) q^{38} +(-1089.32 - 1499.32i) q^{40} +(-11834.0 - 8597.92i) q^{41} -9797.77i q^{43} +(-6339.86 + 1017.44i) q^{44} +(2895.71 - 940.873i) q^{46} +(3271.99 - 4503.51i) q^{47} +(4745.18 - 14604.1i) q^{49} +(-2826.25 + 8698.29i) q^{50} +(-5096.01 + 7014.06i) q^{52} +(-26580.3 + 8636.47i) q^{53} +(-8233.99 - 8200.35i) q^{55} -2438.13i q^{56} +(-705.176 - 512.340i) q^{58} +(-4223.11 - 5812.61i) q^{59} +(7300.93 + 2372.21i) q^{61} +(-13922.8 + 10115.5i) q^{62} +(1265.73 + 3895.53i) q^{64} -15690.9 q^{65} +1017.77 q^{67} +(-3211.27 - 9883.26i) q^{68} +(3569.86 - 2593.65i) q^{70} +(-35287.2 - 11465.5i) q^{71} +(-29313.9 - 40347.1i) q^{73} +(-40331.5 - 29302.5i) q^{74} +5101.94i q^{76} +(-2422.52 - 15095.1i) q^{77} +(-14761.7 + 4796.35i) q^{79} +(-4357.28 + 5997.28i) q^{80} +(-18080.8 + 55646.9i) q^{82} +(1938.56 - 5966.29i) q^{83} +(11054.8 - 15215.6i) q^{85} +(-37272.9 + 12110.7i) q^{86} +(11707.1 + 22860.6i) q^{88} -61182.9i q^{89} +(-16700.4 - 12133.5i) q^{91} +(-7158.59 - 9852.95i) q^{92} +(-21176.8 - 6880.76i) q^{94} +(-7470.15 + 5427.38i) q^{95} +(-20507.6 - 63115.9i) q^{97} -61422.8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−27.5399	−	8.94827i	−0.492649	−	0.160071i	0.0521478	−	0.998639i	$-0.483393\pi$
$5$	−27.5399	−	8.94827i	−0.492649	−	0.160071i	−0.544797	+	0.838568i	$0.683393\pi$
$6$		0			0
$7$	−22.3921	−	30.8201i	−0.172723	−	0.237733i	0.713875	−	0.700273i	$-0.246938\pi$
$7$	−22.3921	−	30.8201i	−0.172723	−	0.237733i	−0.886599	+	0.462540i	$0.846938\pi$
$8$	51.7771	+	37.6183i	0.286031	+	0.207813i
$9$		0			0
$10$			115.829i			0.366283i
$11$	357.943	+	181.459i	0.891934	+	0.452166i
$11$	357.943	+	181.459i	0.891934	+	0.452166i
$12$		0			0
$13$	515.345	−	167.446i	0.845746	−	0.274799i	0.146083	−	0.989272i	$-0.453333\pi$
$13$	515.345	−	167.446i	0.845746	−	0.274799i	0.699663	+	0.714473i	$0.253333\pi$
$14$	−89.5686	+	123.281i	−0.122134	+	0.168103i
$15$		0			0
$16$	79.1084	−	243.470i	0.0772542	−	0.237764i
$17$	−200.704	+	617.704i	−0.168436	+	0.518391i	−0.999273	−	0.0381237i	$-0.987862\pi$
$17$	−200.704	+	617.704i	−0.168436	+	0.518391i	0.830837	+	0.556515i	$0.187862\pi$
$18$		0			0
$19$	187.428	−	257.972i	0.119110	−	0.163941i	−0.745298	−	0.666731i	$-0.767693\pi$
$19$	187.428	−	257.972i	0.119110	−	0.163941i	0.864409	+	0.502790i	$0.167693\pi$
$20$	440.639	−	143.172i	0.246325	−	0.0800357i
$21$		0			0
$22$	247.870	−	1585.99i	0.109186	−	0.698626i
$23$			761.182i			0.300033i	0.988683	+	0.150017i	$0.0479327\pi$
$23$			761.182i			0.300033i	−0.988683	+	0.150017i	$0.952067\pi$
$24$		0			0
$25$	−1849.80	−	1343.96i	−0.591937	−	0.430067i
$26$	−1274.00	−	1753.52i	−0.369604	−	0.508717i
$27$		0			0
$28$	579.700	+	188.356i	0.139736	+	0.0454030i
$29$	176.294	−	128.085i	0.0389263	−	0.0282816i	−0.568152	−	0.822924i	$-0.692341\pi$
$29$	176.294	−	128.085i	0.0389263	−	0.0282816i	0.607078	+	0.794642i	$0.292341\pi$
$30$		0			0
$31$	−1329.51	−	4091.81i	−0.248478	−	0.764736i	−0.995045	−	0.0994258i	$-0.968299\pi$
$31$	−1329.51	−	4091.81i	−0.248478	−	0.764736i	0.746567	−	0.665310i	$-0.231701\pi$
$32$	−1024.00			−0.176777
$33$		0			0
$34$	2597.97			0.385422
$35$	340.891	+	1049.16i	0.0470377	+	0.144767i
$36$		0			0
$37$	10082.9	−	7325.63i	1.21082	−	0.879712i	0.215515	−	0.976500i	$-0.430857\pi$
$37$	10082.9	−	7325.63i	1.21082	−	0.879712i	0.995305	+	0.0967880i	$0.0308569\pi$
$38$	−1213.06	−	394.146i	−0.136277	−	0.0442791i
$39$		0			0
$40$	−1089.32	−	1499.32i	−0.107648	−	0.148165i
$41$	−11834.0	−	8597.92i	−1.09944	−	0.798792i	−0.118474	−	0.992957i	$-0.537800\pi$
$41$	−11834.0	−	8597.92i	−1.09944	−	0.798792i	−0.980969	+	0.194166i	$0.937800\pi$
$42$		0			0
$43$		−	9797.77i		−	0.808083i	−0.914741	−	0.404041i	$-0.867605\pi$
$43$		−	9797.77i		−	0.808083i	0.914741	−	0.404041i	$-0.132395\pi$
$44$	−6339.86	+	1017.44i	−0.493683	+	0.0792280i
$45$		0			0
$46$	2895.71	−	940.873i	0.201772	−	0.0655596i
$47$	3271.99	−	4503.51i	0.216057	−	0.297377i	−0.687208	−	0.726461i	$-0.741164\pi$
$47$	3271.99	−	4503.51i	0.216057	−	0.297377i	0.903264	+	0.429084i	$0.141164\pi$
$48$		0			0
$49$	4745.18	−	14604.1i	0.282333	−	0.868933i
$50$	−2826.25	+	8698.29i	−0.159877	+	0.492050i
$51$		0			0
$52$	−5096.01	+	7014.06i	−0.261350	+	0.359717i
$53$	−26580.3	+	8636.47i	−1.29978	+	0.422325i	−0.875505	−	0.483208i	$-0.839471\pi$
$53$	−26580.3	+	8636.47i	−1.29978	+	0.422325i	−0.424276	+	0.905533i	$0.639471\pi$
$54$		0			0
$55$	−8233.99	−	8200.35i	−0.367032	−	0.365532i
$56$		−	2438.13i		−	0.103893i
$57$		0			0
$58$	−705.176	−	512.340i	−0.0275250	−	0.0199981i
$59$	−4223.11	−	5812.61i	−0.157944	−	0.217391i	0.722710	−	0.691151i	$-0.242896\pi$
$59$	−4223.11	−	5812.61i	−0.157944	−	0.217391i	−0.880654	+	0.473761i	$0.842896\pi$
$60$		0			0
$61$	7300.93	+	2372.21i	0.251220	+	0.0816262i	0.431920	−	0.901912i	$-0.357836\pi$
$61$	7300.93	+	2372.21i	0.251220	+	0.0816262i	−0.180700	+	0.983538i	$0.557836\pi$
$62$	−13922.8	+	10115.5i	−0.459989	+	0.334202i
$63$		0			0
$64$	1265.73	+	3895.53i	0.0386271	+	0.118882i
$65$	−15690.9			−0.460644
$66$		0			0
$67$	1017.77			0.0276990			0.0138495	−	0.999904i	$-0.495591\pi$
$67$	1017.77			0.0276990			0.0138495	+	0.999904i	$0.495591\pi$
$68$	−3211.27	−	9883.26i	−0.0842178	−	0.259196i
$69$		0			0
$70$	3569.86	−	2593.65i	0.0870775	−	0.0632655i
$71$	−35287.2	−	11465.5i	−0.830752	−	0.269928i	−0.137390	−	0.990517i	$-0.543871\pi$
$71$	−35287.2	−	11465.5i	−0.830752	−	0.269928i	−0.693362	+	0.720589i	$0.743871\pi$
$72$		0			0
$73$	−29313.9	−	40347.1i	−0.643823	−	0.886146i	0.354989	−	0.934870i	$-0.384485\pi$
$73$	−29313.9	−	40347.1i	−0.643823	−	0.886146i	−0.998812	+	0.0487240i	$0.984485\pi$
$74$	−40331.5	−	29302.5i	−0.856179	−	0.622051i
$75$		0			0
$76$			5101.94i			0.101321i
$77$	−2422.52	−	15095.1i	−0.0465629	−	0.290142i
$78$		0			0
$79$	−14761.7	+	4796.35i	−0.266114	+	0.0864656i	−0.439035	−	0.898470i	$-0.644679\pi$
$79$	−14761.7	+	4796.35i	−0.266114	+	0.0864656i	0.172921	+	0.984936i	$0.444679\pi$
$80$	−4357.28	+	5997.28i	−0.0761185	+	0.104768i
$81$		0			0
$82$	−18080.8	+	55646.9i	−0.296949	+	0.913916i
$83$	1938.56	−	5966.29i	0.0308877	−	0.0950624i	−0.934424	−	0.356162i	$-0.884085\pi$
$83$	1938.56	−	5966.29i	0.0308877	−	0.0950624i	0.965312	+	0.261100i	$0.0840851\pi$
$84$		0			0
$85$	11054.8	−	15215.6i	0.165959	−	0.228423i
$86$	−37272.9	+	12110.7i	−0.543435	+	0.176573i
$87$		0			0
$88$	11707.1	+	22860.6i	0.161154	+	0.314689i
$89$		−	61182.9i		−	0.818758i	−0.912365	−	0.409379i	$-0.865745\pi$
$89$		−	61182.9i		−	0.818758i	0.912365	−	0.409379i	$-0.134255\pi$
$90$		0			0
$91$	−16700.4	−	12133.5i	−0.211409	−	0.153597i
$92$	−7158.59	−	9852.95i	−0.0881775	−	0.121366i
$93$		0			0
$94$	−21176.8	−	6880.76i	−0.247195	−	0.0803187i
$95$	−7470.15	+	5427.38i	−0.0849220	+	0.0616995i
$96$		0			0
$97$	−20507.6	−	63115.9i	−0.221302	−	0.681098i	−0.998646	−	0.0520217i	$-0.983433\pi$
$97$	−20507.6	−	63115.9i	−0.221302	−	0.681098i	0.777344	−	0.629076i	$-0.216567\pi$
$98$	−61422.8			−0.646048
$99$		0			0
$100$	36583.7			0.365837
$101$	30255.0	+	93115.3i	0.295117	+	0.908275i	0.983182	+	0.182627i	$0.0584601\pi$
$101$	30255.0	+	93115.3i	0.295117	+	0.908275i	−0.688066	+	0.725648i	$0.741540\pi$
$102$		0			0
$103$	84900.8	−	61684.1i	0.788531	−	0.572901i	−0.118996	−	0.992895i	$-0.537968\pi$
$103$	84900.8	−	61684.1i	0.788531	−	0.572901i	0.907527	+	0.419993i	$0.137968\pi$
$104$	32982.1	+	10716.5i	0.299016	+	0.0971563i
$105$		0			0
$106$	65710.1	+	90442.2i	0.568025	+	0.781820i
$107$	46748.0	+	33964.4i	0.394733	+	0.286790i	0.767392	−	0.641178i	$-0.221554\pi$
$107$	46748.0	+	33964.4i	0.394733	+	0.286790i	−0.372659	+	0.927968i	$0.621554\pi$
$108$		0			0
$109$		−	89712.4i		−	0.723246i	−0.932324	−	0.361623i	$-0.882223\pi$
$109$		−	89712.4i		−	0.723246i	0.932324	−	0.361623i	$-0.117777\pi$
$110$	−21018.2	+	41460.2i	−0.165620	+	0.326700i
$111$		0			0
$112$	−9275.20	+	3013.69i	−0.0698680	+	0.0227015i
$113$	71012.8	−	97740.7i	0.523167	−	0.720078i	−0.462903	−	0.886409i	$-0.653192\pi$
$113$	71012.8	−	97740.7i	0.523167	−	0.720078i	0.986070	+	0.166331i	$0.0531922\pi$
$114$		0			0
$115$	6811.26	−	20962.9i	0.0480267	−	0.147811i
$116$	−1077.41	+	3315.94i	−0.00743425	+	0.0228803i
$117$		0			0
$118$	−16892.4	+	23250.4i	−0.111683	+	0.153719i
$119$	23531.9	−	7645.98i	0.152331	−	0.0494955i
$120$		0			0
$121$	95196.0	+	129904.i	0.591093	+	0.806604i
$122$		−	30706.6i		−	0.186781i
$123$		0			0
$124$	55691.2	+	40462.1i	0.325262	+	0.236316i
$125$	92106.7	+	126774.i	0.527250	+	0.725697i
$126$		0			0
$127$	−262018.	−	85134.9i	−1.44153	−	0.468380i	−0.519153	−	0.854681i	$-0.673753\pi$
$127$	−262018.	−	85134.9i	−1.44153	−	0.468380i	−0.922373	+	0.386301i	$0.873753\pi$
$128$	13254.9	−	9630.27i	0.0715077	−	0.0519534i
$129$		0			0
$130$	19395.0	+	59691.8i	0.100654	+	0.309782i
$131$	347488.			1.76914			0.884569	−	0.466409i	$-0.154452\pi$
$131$	347488.			1.76914			0.884569	+	0.466409i	$0.154452\pi$
$132$		0			0
$133$	−12147.6			−0.0595474
$134$	−1258.04	−	3871.84i	−0.00605245	−	0.0186275i
$135$		0			0
$136$	−33628.8	+	24432.8i	−0.155906	+	0.113273i
$137$	312554.	+	101555.i	1.42273	+	0.462274i	0.916469	−	0.400105i	$-0.131026\pi$
$137$	312554.	+	101555.i	1.42273	+	0.462274i	0.506263	+	0.862379i	$0.331026\pi$
$138$		0			0
$139$	−5975.14	−	8224.07i	−0.0262308	−	0.0361036i	0.795700	−	0.605691i	$-0.207103\pi$
$139$	−5975.14	−	8224.07i	−0.0262308	−	0.0361036i	−0.821931	+	0.569587i	$0.807103\pi$
$140$	−14279.4	−	10374.6i	−0.0615731	−	0.0447355i
$141$		0			0
$142$			148413.i			0.617661i
$143$	214849.	+	33578.1i	0.878604	+	0.137314i
$144$		0			0
$145$	−6001.27	+	1949.93i	−0.0237041	+	0.00770192i
$146$	−117256.	+	161389.i	−0.455252	+	0.626600i
$147$		0			0
$148$	−61621.0	+	189650.i	−0.231246	+	0.711702i
$149$	42695.1	−	131402.i	0.157548	−	0.484882i	−0.840862	−	0.541249i	$-0.817952\pi$
$149$	42695.1	−	131402.i	0.157548	−	0.484882i	0.998410	+	0.0563669i	$0.0179517\pi$
$150$		0			0
$151$	114878.	−	158116.i	0.410011	−	0.564332i	−0.553210	−	0.833042i	$-0.686597\pi$
$151$	114878.	−	158116.i	0.410011	−	0.564332i	0.963221	+	0.268710i	$0.0865974\pi$
$152$	19408.9	−	6306.34i	0.0681385	−	0.0221395i
$153$		0			0
$154$	−54430.9	+	27874.4i	−0.184945	+	0.0947118i
$155$			124585.i			0.416521i
$156$		0			0
$157$	48991.0	+	35594.1i	0.158623	+	0.115247i	0.664266	−	0.747497i	$-0.268744\pi$
$157$	48991.0	+	35594.1i	0.158623	+	0.115247i	−0.505642	+	0.862743i	$0.668744\pi$
$158$	36492.8	+	50228.0i	0.116296	+	0.160068i
$159$		0			0
$160$	28200.9	+	9163.02i	0.0870889	+	0.0282969i
$161$	23459.7	−	17044.5i	0.0713278	−	0.0518227i
$162$		0			0
$163$	37638.2	+	115838.i	0.110958	+	0.341494i	0.991083	−	0.133249i	$-0.0425410\pi$
$163$	37638.2	+	115838.i	0.110958	+	0.341494i	−0.880124	+	0.474743i	$0.842541\pi$
$164$	234042.			0.679493
$165$		0			0
$166$	−25093.3			−0.0706786
$167$	5703.13	+	17552.4i	0.0158242	+	0.0487019i	0.958657	−	0.284565i	$-0.0918491\pi$
$167$	5703.13	+	17552.4i	0.0158242	+	0.0487019i	−0.942833	+	0.333267i	$0.891849\pi$
$168$		0			0
$169$	−62839.7	+	45655.7i	−0.169246	+	0.122964i
$170$	−71547.9	−	23247.3i	−0.189878	−	0.0616951i
$171$		0			0
$172$	92143.7	+	126825.i	0.237490	+	0.326876i
$173$	−80043.6	−	58155.1i	−0.203335	−	0.147731i	0.481458	−	0.876469i	$-0.340107\pi$
$173$	−80043.6	−	58155.1i	−0.203335	−	0.147731i	−0.684793	+	0.728738i	$0.740107\pi$
$174$		0			0
$175$			87105.3i			0.215005i
$176$	72496.3	−	72793.7i	0.176414	−	0.177138i
$177$		0			0
$178$	−232754.	+	75626.3i	−0.550613	+	0.178905i
$179$	371259.	−	510995.i	0.866054	−	1.19202i	−0.114038	−	0.993476i	$-0.536379\pi$
$179$	371259.	−	510995.i	0.866054	−	1.19202i	0.980092	−	0.198545i	$-0.0636215\pi$
$180$		0			0
$181$	−39937.0	+	122913.i	−0.0906106	+	0.278871i	−0.986085	−	0.166242i	$-0.946837\pi$
$181$	−39937.0	+	122913.i	−0.0906106	+	0.278871i	0.895474	+	0.445113i	$0.146837\pi$
$182$	−25515.9	+	78529.9i	−0.0570996	+	0.175734i
$183$		0			0
$184$	−28634.4	+	39411.8i	−0.0623509	+	0.0858187i
$185$	−343233.	+	111523.i	−0.737327	+	0.239572i
$186$		0			0
$187$	−183929.	+	184683.i	−0.384632	+	0.386210i
$188$			89066.4i			0.183789i
$189$		0			0
$190$	29880.6	+	21709.5i	0.0600489	+	0.0436281i
$191$	64524.5	+	88810.3i	0.127980	+	0.176149i	0.868198	−	0.496217i	$-0.165278\pi$
$191$	64524.5	+	88810.3i	0.127980	+	0.176149i	−0.740219	+	0.672366i	$0.765278\pi$
$192$		0			0
$193$	−175823.	−	57128.4i	−0.339768	−	0.110397i	0.134163	−	0.990959i	$-0.457165\pi$
$193$	−175823.	−	57128.4i	−0.339768	−	0.110397i	−0.473931	+	0.880562i	$0.657165\pi$
$194$	−214758.	+	156031.i	−0.409681	+	0.297651i
$195$		0			0
$196$	75922.8	+	233666.i	0.141167	+	0.434466i
$197$	−403404.			−0.740584			−0.370292	−	0.928915i	$-0.620742\pi$
$197$	−403404.			−0.740584			−0.370292	+	0.928915i	$0.620742\pi$
$198$		0			0
$199$	−7512.05			−0.0134470			−0.00672351	−	0.999977i	$-0.502140\pi$
$199$	−7512.05			−0.0134470			−0.00672351	+	0.999977i	$0.502140\pi$
$200$	−45219.9	−	139173.i	−0.0799383	−	0.246025i
$201$		0			0
$202$	316834.	−	230194.i	0.546328	−	0.396931i
$203$	−7895.20	−	2565.31i	−0.0134469	−	0.00436917i
$204$		0			0
$205$	248972.	+	342680.i	0.413776	+	0.569513i
$206$	−339603.	−	246736.i	−0.557576	−	0.405102i
$207$		0			0
$208$		−	138718.i		−	0.222317i
$209$	113900.	−	58328.9i	0.180367	−	0.0923673i
$210$		0			0
$211$	363535.	−	118120.i	0.562134	−	0.182648i	−0.0141472	−	0.999900i	$-0.504503\pi$
$211$	363535.	−	118120.i	0.562134	−	0.182648i	0.576281	+	0.817252i	$0.304503\pi$
$212$	262841.	−	361769.i	0.401655	−	0.552830i
$213$		0			0
$214$	71424.6	−	219822.i	0.106614	−	0.328124i
$215$	−87673.0	+	269830.i	−0.129351	+	0.398101i
$216$		0			0
$217$	−96339.6	+	132600.i	−0.138885	+	0.191159i
$218$	−341286.	+	110891.i	−0.486382	+	0.158035i
$219$		0			0
$220$	183704.	+	28710.5i	0.255895	+	0.0399929i
$221$			351938.i			0.484713i
$222$		0			0
$223$	−741125.	−	538459.i	−0.997998	−	0.725088i	−0.0363397	−	0.999339i	$-0.511570\pi$
$223$	−741125.	−	538459.i	−0.997998	−	0.725088i	−0.961658	+	0.274252i	$0.911570\pi$
$224$	22929.6	+	31559.8i	0.0305334	+	0.0420257i
$225$		0			0
$226$	−459604.	−	149334.i	−0.598567	−	0.194486i
$227$	−205905.	+	149598.i	−0.265217	+	0.192691i	−0.712444	−	0.701729i	$-0.752412\pi$
$227$	−205905.	+	149598.i	−0.265217	+	0.192691i	0.447227	+	0.894421i	$0.352412\pi$
$228$		0			0
$229$	77297.9	+	237898.i	0.0974045	+	0.299780i	0.987873	−	0.155265i	$-0.0496231\pi$
$229$	77297.9	+	237898.i	0.0974045	+	0.299780i	−0.890468	+	0.455045i	$0.849623\pi$
$230$	−88166.8			−0.109897
$231$		0			0
$232$	13946.3			0.0170114
$233$	−45940.7	−	141391.i	−0.0554380	−	0.170621i	0.919504	−	0.393082i	$-0.128591\pi$
$233$	−45940.7	−	141391.i	−0.0554380	−	0.170621i	−0.974942	+	0.222461i	$0.928591\pi$
$234$		0			0
$235$	−130409.	+	94747.8i	−0.154042	+	0.111918i
$236$	109330.	+	35523.5i	0.127779	+	0.0415180i
$237$		0			0
$238$	−58174.1	−	80069.7i	−0.0665713	−	0.0916275i
$239$	−1.23883e6	−	900065.i	−1.40287	−	1.01925i	−0.994311	−	0.106516i	$-0.966031\pi$
$239$	−1.23883e6	−	900065.i	−1.40287	−	1.01925i	−0.408561	−	0.912731i	$-0.633969\pi$
$240$		0			0
$241$		−	562395.i		−	0.623734i	−0.950126	−	0.311867i	$-0.899046\pi$
$241$		−	562395.i		−	0.623734i	0.950126	−	0.311867i	$-0.100954\pi$
$242$	376517.	−	522718.i	0.413281	−	0.573758i
$243$		0			0
$244$	−116815.	+	37955.4i	−0.125610	+	0.0408131i
$245$	−261364.	+	359736.i	−0.278183	+	0.382885i
$246$		0			0
$247$	53393.6	−	164329.i	0.0556861	−	0.171384i
$248$	85088.6	−	261876.i	0.0878501	−	0.270375i
$249$		0			0
$250$	368427.	−	507096.i	0.372822	−	0.513145i
$251$	−18317.9	+	5951.84i	−0.0183523	+	0.00596303i	−0.318179	−	0.948031i	$-0.603071\pi$
$251$	−18317.9	+	5951.84i	−0.0183523	+	0.00596303i	0.299826	+	0.953994i	$0.403071\pi$
$252$		0			0
$253$	−138124.	+	272460.i	−0.135665	+	0.267610i
$254$			1.10201e6i			1.07177i
$255$		0			0
$256$	−53019.7	−	38521.1i	−0.0505636	−	0.0367366i
$257$	68097.2	+	93727.8i	0.0643127	+	0.0885188i	0.839962	−	0.542646i	$-0.182577\pi$
$257$	68097.2	+	93727.8i	0.0643127	+	0.0885188i	−0.775649	+	0.631164i	$0.782577\pi$
$258$		0			0
$259$	−451554.	−	146719.i	−0.418273	−	0.135905i
$260$	203108.	−	147566.i	0.186334	−	0.135380i
$261$		0			0
$262$	−429519.	−	1.32192e6i	−0.386571	−	1.18974i
$263$	−1.58134e6			−1.40973			−0.704866	−	0.709341i	$-0.748993\pi$
$263$	−1.58134e6			−1.40973			−0.704866	+	0.709341i	$0.748993\pi$
$264$		0			0
$265$	809301.			0.707938
$266$	15015.3	+	46212.4i	0.0130116	+	0.0400456i
$267$		0			0
$268$	−13174.3	+	9571.71i	−0.0112045	+	0.00814053i
$269$	−793803.	−	257922.i	−0.668855	−	0.217324i	−0.0451457	−	0.998980i	$-0.514375\pi$
$269$	−793803.	−	257922.i	−0.668855	−	0.217324i	−0.623710	+	0.781656i	$0.714375\pi$
$270$		0			0
$271$	63823.5	+	87845.6i	0.0527907	+	0.0726602i	0.834596	−	0.550862i	$-0.185701\pi$
$271$	63823.5	+	87845.6i	0.0527907	+	0.0726602i	−0.781805	+	0.623522i	$0.785701\pi$
$272$	134515.	+	97731.0i	0.110243	+	0.0800959i
$273$		0			0
$274$		−	1.31455e6i		−	1.05780i
$275$	−418250.	−	816725.i	−0.333507	−	0.651245i
$276$		0			0
$277$	1.71985e6	−	558812.i	1.34676	−	0.437589i	0.455159	−	0.890410i	$-0.349582\pi$
$277$	1.71985e6	−	558812.i	1.34676	−	0.437589i	0.891601	+	0.452821i	$0.149582\pi$
$278$	−23900.6	+	32896.3i	−0.0185480	+	0.0255291i
$279$		0			0
$280$	−21817.0	+	67145.9i	−0.0166303	+	0.0511829i
$281$	−310763.	+	956430.i	−0.234781	+	0.722582i	0.762369	+	0.647142i	$0.224036\pi$
$281$	−310763.	+	956430.i	−0.234781	+	0.722582i	−0.997150	+	0.0754398i	$0.975964\pi$
$282$		0			0
$283$	1.32995e6	−	1.83053e6i	0.987122	−	1.35866i	0.0542184	−	0.998529i	$-0.482733\pi$
$283$	1.32995e6	−	1.83053e6i	0.987122	−	1.35866i	0.932903	−	0.360127i	$-0.117267\pi$
$284$	564595.	−	183448.i	0.415376	−	0.134964i
$285$		0			0
$286$	−137830.	−	858839.i	−0.0996385	−	0.620864i
$287$			557252.i			0.399344i
$288$		0			0
$289$	807413.	+	586620.i	0.568658	+	0.413154i
$290$	14835.9	+	20419.9i	0.0103591	+	0.0142580i
$291$		0			0
$292$	758894.	+	246580.i	0.520864	+	0.169239i
$293$	180262.	−	130968.i	0.122669	−	0.0891244i	−0.524759	−	0.851251i	$-0.675845\pi$
$293$	180262.	−	130968.i	0.122669	−	0.0891244i	0.647428	+	0.762126i	$0.275845\pi$
$294$		0			0
$295$	64291.4	+	197868.i	0.0430128	+	0.132380i
$296$	797639.			0.529148
$297$		0			0
$298$	−552657.			−0.360508
$299$	127457.	+	392272.i	0.0824489	+	0.253752i
$300$		0			0
$301$	−301968.	+	219393.i	−0.192108	+	0.139575i
$302$	−743508.	−	241580.i	−0.469103	−	0.152421i
$303$		0			0
$304$	−47981.5	−	66040.9i	−0.0297776	−	0.0409854i
$305$	−179840.	−	130661.i	−0.110697	−	0.0804262i
$306$		0			0
$307$		−	1.37330e6i		−	0.831608i	−0.909454	−	0.415804i	$-0.863500\pi$
$307$		−	1.37330e6i		−	0.831608i	0.909454	−	0.415804i	$-0.136500\pi$
$308$	173321.	+	172613.i	0.104106	+	0.103680i
$309$		0			0
$310$	473950.	−	153996.i	0.280110	−	0.0910131i
$311$	1.25894e6	−	1.73278e6i	0.738080	−	1.01588i	−0.260647	−	0.965434i	$-0.583936\pi$
$311$	1.25894e6	−	1.73278e6i	0.738080	−	1.01588i	0.998727	−	0.0504460i	$-0.0160643\pi$
$312$		0			0
$313$	−1.00285e6	+	3.08646e6i	−0.578596	+	1.78074i	0.0449981	+	0.998987i	$0.485672\pi$
$313$	−1.00285e6	+	3.08646e6i	−0.578596	+	1.78074i	−0.623594	+	0.781748i	$0.714328\pi$
$314$	74851.6	−	230370.i	0.0428427	−	0.131856i
$315$		0			0
$316$	145971.	−	200912.i	0.0822337	−	0.113185i
$317$	−2.78600e6	+	905225.i	−1.55716	+	0.505951i	−0.956047	−	0.293215i	$-0.905275\pi$
$317$	−2.78600e6	+	905225.i	−1.55716	+	0.505951i	−0.601111	+	0.799166i	$0.705275\pi$
$318$		0			0
$319$	86345.5	−	13857.0i	0.0475076	−	0.00762419i
$320$		−	118609.i		−	0.0647503i
$321$		0			0
$322$	−93839.0	−	68178.0i	−0.0504364	−	0.0366442i
$323$	121733.	+	167551.i	0.0649234	+	0.0893594i
$324$		0			0
$325$	−1.17833e6	−	382862.i	−0.618810	−	0.201064i
$326$	394152.	−	286368.i	0.205409	−	0.149238i
$327$		0			0
$328$	−289292.	−	890350.i	−0.148475	−	0.456958i
$329$	−212066.			−0.108014
$330$		0			0
$331$	−2.89145e6			−1.45059			−0.725296	−	0.688437i	$-0.758297\pi$
$331$	−2.89145e6			−1.45059			−0.725296	+	0.688437i	$0.758297\pi$
$332$	31017.0	+	95460.6i	0.0154438	+	0.0475312i
$333$		0			0
$334$	59723.9	−	43392.0i	0.0292942	−	0.0212835i
$335$	−28029.4	−	9107.31i	−0.0136459	−	0.00443382i
$336$		0			0
$337$	2.11984e6	+	2.91771e6i	1.01678	+	1.39948i	0.914435	+	0.404732i	$0.132635\pi$
$337$	2.11984e6	+	2.91771e6i	1.01678	+	1.39948i	0.102347	+	0.994749i	$0.467365\pi$
$338$	251359.	+	182623.i	0.119675	+	0.0869488i
$339$		0			0
$340$			300920.i			0.141173i
$341$	266608.	−	1.70589e6i	0.124161	−	0.794447i
$342$		0			0
$343$	−1.16530e6	+	378627.i	−0.534811	+	0.173771i
$344$	368575.	−	507300.i	0.167930	−	0.231137i
$345$		0			0
$346$	−122296.	+	376387.i	−0.0549188	+	0.169023i
$347$	238250.	−	733257.i	0.106221	−	0.326913i	−0.883794	−	0.467875i	$-0.845020\pi$
$347$	238250.	−	733257.i	0.106221	−	0.326913i	0.990015	+	0.140962i	$0.0450196\pi$
$348$		0			0
$349$	317698.	−	437273.i	0.139621	−	0.192172i	−0.733480	−	0.679711i	$-0.762105\pi$
$349$	317698.	−	437273.i	0.139621	−	0.192172i	0.873101	+	0.487539i	$0.162105\pi$
$350$	331368.	−	107668.i	0.144591	−	0.0469804i
$351$		0			0
$352$	−366534.	−	185814.i	−0.157673	−	0.0799323i
$353$			3.71456e6i			1.58661i	0.608823	+	0.793306i	$0.291642\pi$
$353$			3.71456e6i			1.58661i	−0.608823	+	0.793306i	$0.708358\pi$
$354$		0			0
$355$	869211.	+	631518.i	0.366062	+	0.265959i
$356$	575399.	+	791969.i	0.240627	+	0.331194i
$357$		0			0
$358$	−2.40284e6	−	780731.i	−0.990872	−	0.321954i
$359$	1.68438e6	−	1.22377e6i	0.689769	−	0.501146i	−0.186815	−	0.982395i	$-0.559817\pi$
$359$	1.68438e6	−	1.22377e6i	0.689769	−	0.501146i	0.876584	+	0.481249i	$0.159817\pi$
$360$		0			0
$361$	733736.	+	2.25821e6i	0.296327	+	0.912002i
$362$	516955.			0.207339
$363$		0			0
$364$	330285.			0.130658
$365$	446266.	+	1.37347e6i	0.175332	+	0.539617i
$366$		0			0
$367$	−2.34400e6	+	1.70302e6i	−0.908432	+	0.660014i	−0.940618	−	0.339468i	$-0.889753\pi$
$367$	−2.34400e6	+	1.70302e6i	−0.908432	+	0.660014i	0.0321860	+	0.999482i	$0.489753\pi$
$368$	185325.	+	60215.9i	0.0713371	+	0.0231788i
$369$		0			0
$370$	848519.	+	1.16789e6i	0.322224	+	0.443503i
$371$	861367.	+	625820.i	0.324903	+	0.236056i
$372$		0			0
$373$			1.30158e6i			0.484395i	0.970227	+	0.242197i	$0.0778682\pi$
$373$			1.30158e6i			0.484395i	−0.970227	+	0.242197i	$0.922132\pi$
$374$	929926.	+	471426.i	0.343771	+	0.174275i
$375$		0			0
$376$	338829.	−	110092.i	0.123598	−	0.0401593i
$377$	69405.0	−	95527.8i	0.0251500	−	0.0346159i
$378$		0			0
$379$	−1.46074e6	+	4.49570e6i	−0.522367	+	1.60768i	0.247098	+	0.968991i	$0.420523\pi$
$379$	−1.46074e6	+	4.49570e6i	−0.522367	+	1.60768i	−0.769465	+	0.638689i	$0.779477\pi$
$380$	45653.5	−	140507.i	0.0162187	−	0.0499159i
$381$		0			0
$382$	258098.	−	355241.i	0.0904953	−	0.124556i
$383$	2.37539e6	−	771811.i	0.827442	−	0.268852i	0.135475	−	0.990781i	$-0.456744\pi$
$383$	2.37539e6	−	771811.i	0.827442	−	0.268852i	0.691968	+	0.721928i	$0.256744\pi$
$384$		0			0
$385$	−68359.2	+	437396.i	−0.0235042	+	0.150391i
$386$			739486.i			0.252616i
$387$		0			0
$388$	859033.	+	624124.i	0.289688	+	0.210471i
$389$	−168265.	−	231597.i	−0.0563794	−	0.0775996i	0.779896	−	0.625909i	$-0.215272\pi$
$389$	−168265.	−	231597.i	−0.0563794	−	0.0775996i	−0.836276	+	0.548309i	$0.815272\pi$
$390$		0			0
$391$	−470185.	−	152772.i	−0.155535	−	0.0505363i
$392$	795074.	−	577655.i	0.261332	−	0.189869i
$393$		0			0
$394$	498635.	+	1.53464e6i	0.161824	+	0.498042i
$395$	449454.			0.144941
$396$		0			0
$397$	248283.			0.0790627			0.0395313	−	0.999218i	$-0.487414\pi$
$397$	248283.			0.0790627			0.0395313	+	0.999218i	$0.487414\pi$
$398$	9285.41	+	28577.6i	0.00293828	+	0.00904310i
$399$		0			0
$400$	−473549.	+	344054.i	−0.147984	+	0.107517i
$401$	−1.87904e6	−	610538.i	−0.583546	−	0.189606i	0.00234226	−	0.999997i	$-0.499254\pi$
$401$	−1.87904e6	−	610538.i	−0.583546	−	0.189606i	−0.585889	+	0.810392i	$0.699254\pi$
$402$		0			0
$403$	−1.37031e6	−	1.88607e6i	−0.420298	−	0.578490i
$404$	−1.26734e6	−	920775.i	−0.386313	−	0.280673i
$405$		0			0
$406$			33206.0i			0.00999774i
$407$	4.93840e6	−	792532.i	1.47775	−	0.237154i
$408$		0			0
$409$	5.58039e6	−	1.81318e6i	1.64952	−	0.535960i	0.670881	−	0.741565i	$-0.265916\pi$
$409$	5.58039e6	−	1.81318e6i	1.64952	−	0.535960i	0.978635	+	0.205605i	$0.0659163\pi$
$410$	995886.	−	1.37072e6i	0.292584	−	0.402707i
$411$		0			0
$412$	−518868.	+	1.59691e6i	−0.150596	+	0.463487i
$413$	−84581.0	+	260314.i	−0.0244005	+	0.0750969i
$414$		0			0
$415$	−106776.	+	146964.i	−0.0304336	+	0.0418882i
$416$	−527714.	+	171465.i	−0.149508	+	0.0485781i
$417$		0			0
$418$	−362685.	−	361203.i	−0.101529	−	0.101114i
$419$			1.63562e6i			0.455144i	0.973761	+	0.227572i	$0.0730786\pi$
$419$			1.63562e6i			0.455144i	−0.973761	+	0.227572i	$0.926921\pi$
$420$		0			0
$421$	917961.	+	666938.i	0.252417	+	0.183392i	0.706797	−	0.707416i	$-0.250139\pi$
$421$	917961.	+	666938.i	0.252417	+	0.183392i	−0.454380	+	0.890808i	$0.650139\pi$
$422$	−898707.	−	1.23696e6i	−0.245662	−	0.338124i
$423$		0			0
$424$	−1.70114e6	−	552734.i	−0.459542	−	0.149314i
$425$	1.20143e6	−	872891.i	0.322646	−	0.234416i
$426$		0			0
$427$	−90371.4	−	278135.i	−0.0239862	−	0.0738219i
$428$	−924539.			−0.243959
$429$		0			0
$430$	1.13486e6			0.295987
$431$	1.97990e6	+	6.09350e6i	0.513393	+	1.58006i	0.786188	+	0.617988i	$0.212052\pi$
$431$	1.97990e6	+	6.09350e6i	0.513393	+	1.58006i	−0.272795	+	0.962072i	$0.587948\pi$
$432$		0			0
$433$	−2.85872e6	+	2.07698e6i	−0.732744	+	0.532370i	−0.890430	−	0.455119i	$-0.849597\pi$
$433$	−2.85872e6	+	2.07698e6i	−0.732744	+	0.532370i	0.157686	+	0.987489i	$0.449597\pi$
$434$	623523.	+	202595.i	0.158902	+	0.0516303i
$435$		0			0
$436$	843706.	+	1.16126e6i	0.212557	+	0.292559i
$437$	196364.	+	142667.i	0.0491879	+	0.0357371i
$438$		0			0
$439$		−	3.40380e6i		−	0.842951i	−0.906840	−	0.421476i	$-0.861512\pi$
$439$		−	3.40380e6i		−	0.842951i	0.906840	−	0.421476i	$-0.138488\pi$
$440$	−117849.	−	734339.i	−0.0290199	−	0.180828i
$441$		0			0
$442$	1.33885e6	−	435019.i	0.325969	−	0.105914i
$443$	2.52118e6	−	3.47010e6i	0.610371	−	0.840103i	−0.386237	−	0.922400i	$-0.626225\pi$
$443$	2.52118e6	−	3.47010e6i	0.610371	−	0.840103i	0.996608	+	0.0822961i	$0.0262253\pi$
$444$		0			0
$445$	−547481.	+	1.68497e6i	−0.131060	+	0.403360i
$446$	−1.13234e6	+	3.48498e6i	−0.269550	+	0.829589i
$447$		0			0
$448$	91718.2	−	126239.i	0.0215904	−	0.0297166i
$449$	−1.91470e6	+	622122.i	−0.448212	+	0.145633i	−0.524421	−	0.851459i	$-0.675718\pi$
$449$	−1.91470e6	+	622122.i	−0.448212	+	0.145633i	0.0762091	+	0.997092i	$0.475718\pi$
$450$		0			0
$451$	−2.67574e6	−	5.22496e6i	−0.619444	−	1.20960i
$452$			1.93303e6i			0.445032i
$453$		0			0
$454$	823618.	+	598394.i	0.187537	+	0.136253i
$455$	351353.	+	483596.i	0.0795638	+	0.109510i
$456$		0			0
$457$	−791337.	−	257121.i	−0.177244	−	0.0575900i	0.219051	−	0.975714i	$-0.429704\pi$
$457$	−791337.	−	257121.i	−0.177244	−	0.0575900i	−0.396294	+	0.918123i	$0.629704\pi$
$458$	809474.	−	588117.i	0.180318	−	0.131009i
$459$		0			0
$460$	108980.	+	335407.i	0.0240134	+	0.0739055i
$461$	700423.			0.153500			0.0767499	−	0.997050i	$-0.475546\pi$
$461$	700423.			0.153500			0.0767499	+	0.997050i	$0.475546\pi$
$462$		0			0
$463$	6.85068e6			1.48519			0.742593	−	0.669743i	$-0.233596\pi$
$463$	6.85068e6			1.48519			0.742593	+	0.669743i	$0.233596\pi$
$464$	−17238.6	−	53055.0i	−0.00371713	−	0.0114401i
$465$		0			0
$466$	−481097.	+	349538.i	−0.102629	+	0.0745640i
$467$	541181.	+	175840.i	0.114829	+	0.0373101i	0.365868	−	0.930667i	$-0.380772\pi$
$467$	541181.	+	175840.i	0.114829	+	0.0373101i	−0.251039	+	0.967977i	$0.580772\pi$
$468$		0			0
$469$	−22790.1	−	31367.9i	−0.00478426	−	0.00658497i
$470$	521637.	+	378991.i	0.108924	+	0.0791379i
$471$		0			0
$472$		−	459826.i		−	0.0950033i
$473$	1.77790e6	−	3.50705e6i	0.365387	−	0.720757i
$474$		0			0
$475$	−693408.	+	225302.i	−0.141012	+	0.0458175i
$476$	−232696.	+	320279.i	−0.0470730	+	0.0647905i
$477$		0			0
$478$	−1.89277e6	+	5.82534e6i	−0.378903	+	1.16614i
$479$	2.46207e6	−	7.57746e6i	0.490299	−	1.50898i	−0.333858	−	0.942623i	$-0.608351\pi$
$479$	2.46207e6	−	7.57746e6i	0.490299	−	1.50898i	0.824157	−	0.566361i	$-0.191649\pi$
$480$		0			0
$481$	3.96951e6	−	5.46356e6i	0.782302	−	1.07675i
$482$	−2.13948e6	+	695159.i	−0.419460	+	0.136291i
$483$		0			0
$484$	−2.45394e6	−	786240.i	−0.476157	−	0.152560i
$485$			1.92171e6i			0.370966i
$486$		0			0
$487$	−8.30348e6	−	6.03283e6i	−1.58649	−	1.15265i	−0.908740	−	0.417362i	$-0.862955\pi$
$487$	−8.30348e6	−	6.03283e6i	−1.58649	−	1.15265i	−0.677751	−	0.735291i	$-0.737045\pi$
$488$	288782.	+	397475.i	0.0548935	+	0.0755544i
$489$		0			0
$490$	1.69158e6	+	549628.i	0.318275	+	0.103414i
$491$	−1.84248e6	+	1.33864e6i	−0.344904	+	0.250587i	−0.746728	−	0.665130i	$-0.768376\pi$
$491$	−1.84248e6	+	1.33864e6i	−0.344904	+	0.250587i	0.401824	+	0.915717i	$0.368376\pi$
$492$		0			0
$493$	43735.7	+	134605.i	0.00810436	+	0.0249427i
$494$	−691142.			−0.127424
$495$		0			0
$496$	−1.10141e6			−0.201023
$497$	436787.	+	1.34429e6i	0.0793194	+	0.244120i
$498$		0			0
$499$	5.60507e6	−	4.07232e6i	1.00770	−	0.732134i	0.0439719	−	0.999033i	$-0.485999\pi$
$499$	5.60507e6	−	4.07232e6i	1.00770	−	0.732134i	0.963725	+	0.266898i	$0.0859988\pi$
$500$	−2.38451e6	−	774774.i	−0.426554	−	0.138596i
$501$		0			0
$502$	45284.3	+	62328.5i	0.00802026	+	0.0110389i
$503$	−4.09139e6	−	2.97257e6i	−0.721027	−	0.523856i	0.165685	−	0.986179i	$-0.447016\pi$
$503$	−4.09139e6	−	2.97257e6i	−0.721027	−	0.523856i	−0.886712	+	0.462322i	$0.847016\pi$
$504$		0			0
$505$		−	2.83512e6i		−	0.494701i
$506$	1.20723e6	+	188674.i	0.209611	+	0.0327594i
$507$		0			0
$508$	4.19229e6	−	1.36216e6i	0.720763	−	0.234190i
$509$	−1.08504e6	+	1.49343e6i	−0.185631	+	0.255500i	−0.891683	−	0.452661i	$-0.850475\pi$
$509$	−1.08504e6	+	1.49343e6i	−0.185631	+	0.255500i	0.706051	+	0.708161i	$0.250475\pi$
$510$		0			0
$511$	−587103.	+	1.80692e6i	−0.0994631	+	0.306116i
$512$	−81007.0	+	249314.i	−0.0136568	+	0.0420312i
$513$		0			0
$514$	272389.	−	374911.i	0.0454759	−	0.0625923i
$515$	−2.89013e6	+	939060.i	−0.480174	+	0.156018i
$516$		0			0
$517$	1.98839e6	−	1.01827e6i	0.327172	−	0.167547i
$518$			1.89917e6i			0.310985i
$519$		0			0
$520$	−812430.	−	590265.i	−0.131758	−	0.0957280i
$521$	4.12656e6	+	5.67973e6i	0.666031	+	0.916712i	0.999662	−	0.0259911i	$-0.00827415\pi$
$521$	4.12656e6	+	5.67973e6i	0.666031	+	0.916712i	−0.333632	+	0.942704i	$0.608274\pi$
$522$		0			0
$523$	−9.73193e6	−	3.16209e6i	−1.55577	−	0.505499i	−0.600094	−	0.799929i	$-0.704870\pi$
$523$	−9.73193e6	−	3.16209e6i	−1.55577	−	0.505499i	−0.955673	+	0.294430i	$0.904870\pi$
$524$	−4.49798e6	+	3.26798e6i	−0.715632	+	0.519937i
$525$		0			0
$526$	1.95465e6	+	6.01578e6i	0.308038	+	0.948043i
$527$	2.79436e6			0.438285
$528$		0			0
$529$	5.85694e6			0.909980
$530$	−1.00035e6	−	3.07876e6i	−0.154690	−	0.476088i
$531$		0			0
$532$	157242.	−	114243.i	0.0240874	−	0.0175006i
$533$	−7.53829e6	−	2.44934e6i	−1.14936	−	0.373449i
$534$		0			0
$535$	−983514.	−	1.35369e6i	−0.148558	−	0.204473i
$536$	52697.3	+	38286.9i	0.00792276	+	0.00575622i
$537$		0			0
$538$			3.33862e6i			0.497291i
$539$	4.34856e6	−	4.36640e6i	0.644724	−	0.647369i
$540$		0			0
$541$	3.02536e6	−	982998.i	0.444410	−	0.144397i	−0.0782595	−	0.996933i	$-0.524936\pi$
$541$	3.02536e6	−	982998.i	0.444410	−	0.144397i	0.522669	+	0.852536i	$0.324936\pi$
$542$	255294.	−	351382.i	0.0373287	−	0.0513785i
$543$		0			0
$544$	205521.	−	632529.i	0.0297755	−	0.0916395i
$545$	−802770.	+	2.47067e6i	−0.115771	+	0.356307i
$546$		0			0
$547$	4.56068e6	−	6.27723e6i	0.651720	−	0.897015i	−0.347452	−	0.937698i	$-0.612953\pi$
$547$	4.56068e6	−	6.27723e6i	0.651720	−	0.897015i	0.999172	+	0.0406823i	$0.0129531\pi$
$548$	−5.00086e6	+	1.62488e6i	−0.711366	+	0.231137i
$549$		0			0
$550$	−2.59002e6	+	2.60065e6i	−0.365087	+	0.366585i
$551$		−	69485.7i		−	0.00975026i
$552$		0			0
$553$	478369.	+	347556.i	0.0665197	+	0.0483294i
$554$	−4.25170e6	−	5.85196e6i	−0.588556	−	0.810078i
$555$		0			0
$556$	154688.	+	50261.1i	0.0212211	+	0.00689517i
$557$	−9.52783e6	+	6.92238e6i	−1.30124	+	0.945404i	−0.999967	−	0.00813540i	$-0.997410\pi$
$557$	−9.52783e6	+	6.92238e6i	−1.30124	+	0.945404i	−0.301270	+	0.953539i	$0.597410\pi$
$558$		0			0
$559$	−1.64059e6	−	5.04923e6i	−0.222061	−	0.683433i
$560$	282406.			0.0380543
$561$		0			0
$562$	4.02260e6			0.537237
$563$	193108.	+	594327.i	0.0256762	+	0.0790231i	0.963073	−	0.269239i	$-0.0867720\pi$
$563$	193108.	+	594327.i	0.0256762	+	0.0790231i	−0.937397	+	0.348262i	$0.886772\pi$
$564$		0			0
$565$	−2.83030e6	+	2.05633e6i	−0.373002	+	0.271002i
$566$	−8.60765e6	−	2.79679e6i	−1.12939	−	0.366961i
$567$		0			0
$568$	−1.39576e6	−	1.92109e6i	−0.181526	−	0.249849i
$569$	−1.22962e6	−	893375.i	−0.159218	−	0.115679i	0.505324	−	0.862930i	$-0.331373\pi$
$569$	−1.22962e6	−	893375.i	−0.159218	−	0.115679i	−0.664542	+	0.747251i	$0.731373\pi$
$570$		0			0
$571$		−	1.04259e7i		−	1.33821i	−0.743169	−	0.669104i	$-0.766678\pi$
$571$		−	1.04259e7i		−	1.33821i	0.743169	−	0.669104i	$-0.233322\pi$
$572$	−3.09685e6	+	1.58592e6i	−0.395759	+	0.202671i
$573$		0			0
$574$	2.11991e6	−	688801.i	0.268558	−	0.0872598i
$575$	1.02300e6	−	1.40804e6i	0.129034	−	0.177601i
$576$		0			0
$577$	−3.55225e6	+	1.09327e7i	−0.444186	+	1.36706i	0.439189	+	0.898395i	$0.355266\pi$
$577$	−3.55225e6	+	1.09327e7i	−0.444186	+	1.36706i	−0.883374	+	0.468668i	$0.844734\pi$
$578$	1.23362e6	−	3.79668e6i	0.153589	−	0.472699i
$579$		0			0
$580$	59343.8	−	81679.7i	0.00732496	−	0.0100819i
$581$	−227290.	+	73851.1i	−0.0279345	+	0.00907647i
$582$		0			0
$583$	−1.10814e7	−	1.73188e6i	−1.35028	−	0.211031i
$584$		−	3.19179e6i		−	0.387260i
$585$		0			0
$586$	−721049.	−	523873.i	−0.0867403	−	0.0630205i
$587$	−7.59331e6	−	1.04513e7i	−0.909569	−	1.25191i	−0.967313	−	0.253584i	$-0.918391\pi$
$587$	−7.59331e6	−	1.04513e7i	−0.909569	−	1.25191i	0.0577440	−	0.998331i	$-0.481609\pi$
$588$		0			0
$589$	−1.30476e6	−	423942.i	−0.154968	−	0.0503522i
$590$	673268.	−	489158.i	0.0796265	−	0.0578521i
$591$		0			0
$592$	−985936.	−	3.03440e6i	−0.115623	−	0.355851i
$593$	−1.69012e6			−0.197370			−0.0986850	−	0.995119i	$-0.531464\pi$
$593$	−1.69012e6			−0.197370			−0.0986850	+	0.995119i	$0.531464\pi$
$594$		0			0
$595$	−716485.			−0.0829688
$596$	683121.	+	2.10243e6i	0.0787739	+	0.242441i
$597$		0			0
$598$	1.33475e6	−	969749.i	0.152632	−	0.110894i
$599$	−9.81396e6	−	3.18875e6i	−1.11758	−	0.363122i	−0.308734	−	0.951148i	$-0.599905\pi$
$599$	−9.81396e6	−	3.18875e6i	−1.11758	−	0.363122i	−0.808842	+	0.588026i	$0.799905\pi$
$600$		0			0
$601$	6.81688e6	+	9.38262e6i	0.769838	+	1.05959i	0.996331	+	0.0855782i	$0.0272737\pi$
$601$	6.81688e6	+	9.38262e6i	0.769838	+	1.05959i	−0.226494	+	0.974013i	$0.572726\pi$
$602$	1.20787e6	+	877572.i	0.135841	+	0.0986942i
$603$		0			0
$604$			3.12708e6i			0.348776i
$605$	−1.45927e6	−	4.42940e6i	−0.162087	−	0.491990i
$606$		0			0
$607$	1.32350e7	−	4.30032e6i	1.45798	−	0.473727i	0.530530	−	0.847666i	$-0.321993\pi$
$607$	1.32350e7	−	4.30032e6i	1.45798	−	0.473727i	0.927453	+	0.373939i	$0.121993\pi$
$608$	−191926.	+	264164.i	−0.0210560	+	0.0289810i
$609$		0			0
$610$	−274771.	+	845658.i	−0.0298983	+	0.0920174i
$611$	932112.	−	2.86875e6i	0.101010	−	0.310877i
$612$		0			0
$613$	−1.90088e6	+	2.61634e6i	−0.204317	+	0.281218i	−0.898863	−	0.438231i	$-0.855605\pi$
$613$	−1.90088e6	+	2.61634e6i	−0.204317	+	0.281218i	0.694546	+	0.719448i	$0.255605\pi$
$614$	−5.22433e6	+	1.69749e6i	−0.559255	+	0.181713i
$615$		0			0
$616$	442421.	−	872713.i	0.0469769	−	0.0926658i
$617$		−	4.91228e6i		−	0.519482i	−0.965678	−	0.259741i	$-0.916363\pi$
$617$		−	4.91228e6i		−	0.519482i	0.965678	−	0.259741i	$-0.0836372\pi$
$618$		0			0
$619$	−6.48153e6	−	4.70910e6i	−0.679909	−	0.493983i	0.193419	−	0.981116i	$-0.438042\pi$
$619$	−6.48153e6	−	4.70910e6i	−0.679909	−	0.493983i	−0.873327	+	0.487134i	$0.838042\pi$
$620$	−1.17167e6	−	1.61266e6i	−0.122412	−	0.168486i
$621$		0			0
$622$	−8.14802e6	−	2.64745e6i	−0.844454	−	0.274380i
$623$	−1.88567e6	+	1.37002e6i	−0.194646	+	0.141418i
$624$		0			0
$625$	805799.	+	2.47999e6i	0.0825138	+	0.253951i
$626$	1.29812e7			1.32397
$627$		0			0
$628$	−968900.			−0.0980347
$629$	2.50140e6	+	7.69851e6i	0.252090	+	0.775854i
$630$		0			0
$631$	−1.45235e6	+	1.05519e6i	−0.145210	+	0.105501i	−0.658018	−	0.753002i	$-0.728605\pi$
$631$	−1.45235e6	+	1.05519e6i	−0.145210	+	0.105501i	0.512808	+	0.858503i	$0.328605\pi$
$632$	−944746.	−	306967.i	−0.0940854	−	0.0305702i
$633$		0			0
$634$	6.88736e6	+	9.47964e6i	0.680503	+	0.936632i
$635$	6.45416e6	+	4.68922e6i	0.635192	+	0.461494i
$636$		0			0
$637$		−	8.32074e6i		−	0.812481i
$638$	−159444.	−	311350.i	−0.0155080	−	0.0302828i
$639$		0			0
$640$	−451214.	+	146608.i	−0.0435445	+	0.0141485i
$641$	−2.88100e6	+	3.96536e6i	−0.276948	+	0.381186i	−0.924720	−	0.380648i	$-0.875701\pi$
$641$	−2.88100e6	+	3.96536e6i	−0.276948	+	0.381186i	0.647772	+	0.761834i	$0.275701\pi$
$642$		0			0
$643$	−4.45514e6	+	1.37115e7i	−0.424946	+	1.30785i	0.478099	+	0.878306i	$0.341326\pi$
$643$	−4.45514e6	+	1.37115e7i	−0.424946	+	1.30785i	−0.903046	+	0.429545i	$0.858674\pi$
$644$	−143373.	+	441257.i	−0.0136224	+	0.0419254i
$645$		0			0
$646$	486931.	−	670203.i	0.0459078	−	0.0631867i
$647$	2.82491e6	−	917868.i	0.265304	−	0.0862024i	−0.173345	−	0.984861i	$-0.555457\pi$
$647$	2.82491e6	−	917868.i	0.265304	−	0.0862024i	0.438648	+	0.898659i	$0.355457\pi$
$648$		0			0
$649$	−456882.	−	2.84691e6i	−0.0425787	−	0.265315i
$650$			4.95586e6i			0.460083i
$651$		0			0
$652$	−1.57661e6	−	1.14547e6i	−0.145246	−	0.105528i
$653$	1.47594e6	+	2.03146e6i	0.135452	+	0.186434i	0.871355	−	0.490653i	$-0.163242\pi$
$653$	1.47594e6	+	2.03146e6i	0.135452	+	0.186434i	−0.735902	+	0.677088i	$0.763242\pi$
$654$		0			0
$655$	−9.56980e6	−	3.10942e6i	−0.871565	−	0.283189i
$656$	−3.02951e6	+	2.20107e6i	−0.274861	+	0.199698i
$657$		0			0
$658$	262128.	+	806747.i	0.0236020	+	0.0726394i
$659$	1.07088e7			0.960568			0.480284	−	0.877113i	$-0.340534\pi$
$659$	1.07088e7			0.960568			0.480284	+	0.877113i	$0.340534\pi$
$660$		0			0
$661$	1.96405e7			1.74843			0.874215	−	0.485539i	$-0.161377\pi$
$661$	1.96405e7			1.74843			0.874215	+	0.485539i	$0.161377\pi$
$662$	3.57402e6	+	1.09997e7i	0.316966	+	0.975521i
$663$		0			0
$664$	324815.	−	235992.i	0.0285901	−	0.0207719i
$665$	334545.	+	108700.i	0.0293360	+	0.00953184i
$666$		0			0
$667$	97496.1	+	134192.i	0.00848541	+	0.0116792i
$668$	−238896.	−	173568.i	−0.0207141	−	0.0150497i
$669$		0			0
$670$			117887.i			0.0101457i
$671$	2.18286e6	+	2.17394e6i	0.187163	+	0.186398i
$672$		0			0
$673$	−3.93158e6	+	1.27745e6i	−0.334603	+	0.108719i	−0.471500	−	0.881866i	$-0.656287\pi$
$673$	−3.93158e6	+	1.27745e6i	−0.334603	+	0.108719i	0.136897	+	0.990585i	$0.456287\pi$
$674$	8.47936e6	−	1.16708e7i	0.718974	−	0.989583i
$675$		0			0
$676$	384042.	−	1.18196e6i	0.0323230	−	0.0994801i
$677$	5.64478e6	−	1.73729e7i	0.473343	−	1.45680i	−0.374837	−	0.927091i	$-0.622301\pi$
$677$	5.64478e6	−	1.73729e7i	0.473343	−	1.45680i	0.848180	−	0.529708i	$-0.177699\pi$
$678$		0			0
$679$	−1.48603e6	+	2.04535e6i	−0.123695	+	0.170252i
$680$	1.14477e6	−	371957.i	0.0949389	−	0.0308475i
$681$		0			0
$682$	−6.81913e6	+	1.09436e6i	−0.561395	+	0.0900946i
$683$		−	1.44451e6i		−	0.118487i	−0.998244	−	0.0592434i	$-0.981131\pi$
$683$		−	1.44451e6i		−	0.118487i	0.998244	−	0.0592434i	$-0.0188688\pi$
$684$		0			0
$685$	−7.69897e6	−	5.59363e6i	−0.626911	−	0.455478i
$686$	2.88077e6	+	3.96504e6i	0.233721	+	0.321690i
$687$		0			0
$688$	−2.38547e6	−	775085.i	−0.192133	−	0.0624278i
$689$	−1.22519e7	+	8.90152e6i	−0.983230	+	0.714359i
$690$		0			0
$691$	6.50298e6	+	2.00141e7i	0.518104	+	1.59456i	0.777562	+	0.628806i	$0.216456\pi$
$691$	6.50298e6	+	2.00141e7i	0.518104	+	1.59456i	−0.259458	+	0.965755i	$0.583544\pi$
$692$	1.58303e6			0.125668
$693$		0			0
$694$	−3.08397e6			−0.243059
$695$	90963.7	+	279958.i	0.00714342	+	0.0219852i
$696$		0			0
$697$	7.68610e6	−	5.58428e6i	0.599272	−	0.435397i
$698$	−2.05618e6	−	668094.i	−0.159743	−	0.0519038i
$699$		0			0
$700$	−819187.	−	1.12751e6i	−0.0631885	−	0.0869715i
$701$	2.02307e7	+	1.46985e7i	1.55495	+	1.12974i	0.940000	+	0.341173i	$0.110824\pi$
$701$	2.02307e7	+	1.46985e7i	1.55495	+	1.12974i	0.614951	+	0.788565i	$0.289176\pi$
$702$		0			0
$703$		−	3.97413e6i		−	0.303287i
$704$	−253819.	+	1.62406e6i	−0.0193015	+	0.123501i
$705$		0			0
$706$	1.41310e7	−	4.59145e6i	1.06699	−	0.346687i
$707$	2.19235e6	−	3.01751e6i	0.164954	−	0.227039i
$708$		0			0
$709$	−5.53522e6	+	1.70357e7i	−0.413542	+	1.27275i	0.500007	+	0.866021i	$0.333331\pi$
$709$	−5.53522e6	+	1.70357e7i	−0.413542	+	1.27275i	−0.913549	+	0.406729i	$0.866669\pi$
$710$	1.32804e6	−	4.08727e6i	0.0988698	−	0.304290i
$711$		0			0
$712$	2.30160e6	−	3.16787e6i	0.170149	−	0.234190i
$713$	3.11461e6	−	1.01200e6i	0.229446	−	0.0745515i
$714$		0			0
$715$	−5.61646e6	−	2.84726e6i	−0.410864	−	0.208287i
$716$			1.01060e7i			0.736709i
$717$		0			0
$718$	−6.73751e6	−	4.89509e6i	−0.487740	−	0.354364i
$719$	1.44041e7	+	1.98256e7i	1.03912	+	1.43022i	0.897876	+	0.440247i	$0.145109\pi$
$719$	1.44041e7	+	1.98256e7i	1.03912	+	1.43022i	0.141241	+	0.989975i	$0.454891\pi$
$720$		0			0
$721$	−3.80222e6	−	1.23542e6i	−0.272395	−	0.0885065i
$722$	7.68379e6	−	5.58260e6i	0.548570	−	0.398560i
$723$		0			0
$724$	−638992.	−	1.96662e6i	−0.0453053	−	0.139435i
$725$	−498250.			−0.0352048
$726$		0			0
$727$	1.89699e7			1.33115			0.665577	−	0.746329i	$-0.268186\pi$
$727$	1.89699e7			1.33115			0.665577	+	0.746329i	$0.268186\pi$
$728$	−408255.	−	1.25648e6i	−0.0285498	−	0.0878672i
$729$		0			0
$730$	4.67336e6	−	3.39539e6i	0.324580	−	0.235821i
$731$	6.05212e6	+	1.96645e6i	0.418903	+	0.136110i
$732$		0			0
$733$	9.56734e6	+	1.31683e7i	0.657705	+	0.905253i	0.999403	−	0.0345565i	$-0.0110019\pi$
$733$	9.56734e6	+	1.31683e7i	0.657705	+	0.905253i	−0.341698	+	0.939810i	$0.611002\pi$
$734$	9.37600e6	+	6.81206e6i	0.642358	+	0.466701i
$735$		0			0
$736$		−	779451.i		−	0.0530389i
$737$	364305.	+	184684.i	0.0247057	+	0.0125245i
$738$		0			0
$739$	−2.16885e6	+	704701.i	−0.146089	+	0.0474672i	−0.381149	−	0.924514i	$-0.624471\pi$
$739$	−2.16885e6	+	704701.i	−0.146089	+	0.0474672i	0.235060	+	0.971981i	$0.424471\pi$
$740$	3.39408e6	−	4.67154e6i	0.227846	−	0.313604i
$741$		0			0
$742$	1.31605e6	−	4.05039e6i	0.0877532	−	0.270077i
$743$	4.17195e6	−	1.28399e7i	0.277247	−	0.853279i	−0.711369	−	0.702819i	$-0.751925\pi$
$743$	4.17195e6	−	1.28399e7i	0.277247	−	0.853279i	0.988616	−	0.150460i	$-0.0480755\pi$
$744$		0			0
$745$	−2.35164e6	+	3.23675e6i	−0.155232	+	0.213658i
$746$	4.95151e6	−	1.60884e6i	0.325755	−	0.105844i
$747$		0			0
$748$	643958.	−	4.12036e6i	0.0420827	−	0.269266i
$749$		−	2.20132e6i		−	0.143376i
$750$		0			0
$751$	−5.05654e6	−	3.67379e6i	−0.327155	−	0.237692i	0.412067	−	0.911153i	$-0.364807\pi$
$751$	−5.05654e6	−	3.67379e6i	−0.327155	−	0.237692i	−0.739223	+	0.673461i	$0.764807\pi$
$752$	−837631.	−	1.15290e6i	−0.0540142	−	0.0743442i
$753$		0			0
$754$	−449198.	−	145953.i	−0.0287746	−	0.00934945i
$755$	−4.57861e6	+	3.32655e6i	−0.292325	+	0.212387i
$756$		0			0
$757$	8.86586e6	+	2.72863e7i	0.562317	+	1.73063i	0.675791	+	0.737093i	$0.263802\pi$
$757$	8.86586e6	+	2.72863e7i	0.562317	+	1.73063i	−0.113474	+	0.993541i	$0.536198\pi$
$758$	1.89082e7			1.19530
$759$		0			0
$760$	−590951.			−0.0371123
$761$	4.98723e6	+	1.53491e7i	0.312175	+	0.960775i	0.976902	+	0.213689i	$0.0685478\pi$
$761$	4.98723e6	+	1.53491e7i	0.312175	+	0.960775i	−0.664727	+	0.747086i	$0.731452\pi$
$762$		0			0
$763$	−2.76495e6	+	2.00885e6i	−0.171940	+	0.124921i
$764$	−1.67044e6	−	542760.i	−0.103538	−	0.0336415i
$765$		0			0
$766$	−5.87228e6	−	8.08251e6i	−0.361606	−	0.497707i
$767$	−3.14966e6	−	2.28836e6i	−0.193319	−	0.140455i
$768$		0			0
$769$		−	5.58667e6i		−	0.340673i	−0.985386	−	0.170336i	$-0.945515\pi$
$769$		−	5.58667e6i		−	0.340673i	0.985386	−	0.170336i	$-0.0544854\pi$
$770$	1.74845e6	−	280598.i	0.106274	−	0.0170552i
$771$		0			0
$772$	2.81317e6	−	914055.i	0.169884	−	0.0551987i
$773$	1.35197e6	−	1.86083e6i	0.0813803	−	0.112010i	−0.766386	−	0.642380i	$-0.777947\pi$
$773$	1.35197e6	−	1.86083e6i	0.0813803	−	0.112010i	0.847766	+	0.530370i	$0.177947\pi$
$774$		0			0
$775$	−3.03990e6	+	9.35585e6i	−0.181805	+	0.559537i
$776$	1.31249e6	−	4.03942e6i	0.0782421	−	0.240804i
$777$		0			0
$778$	−673061.	+	926390.i	−0.0398663	+	0.0548712i
$779$	−4.43605e6	+	1.44136e6i	−0.261910	+	0.0850998i
$780$		0			0
$781$	−1.05503e7	−	1.05072e7i	−0.618924	−	0.616395i
$782$			1.97753e6i			0.115639i
$783$		0			0
$784$	−3.18030e6	−	2.31062e6i	−0.184790	−	0.134257i
$785$	−1.03070e6	−	1.41864e6i	−0.0596980	−	0.0821673i
$786$		0			0
$787$	7.71319e6	+	2.50617e6i	0.443912	+	0.144236i	0.522440	−	0.852676i	$-0.325022\pi$
$787$	7.71319e6	+	2.50617e6i	0.443912	+	0.144236i	−0.0785278	+	0.996912i	$0.525022\pi$
$788$	5.22177e6	−	3.79384e6i	0.299573	−	0.217652i
$789$		0			0
$790$	−555556.	−	1.70982e6i	−0.0316709	−	0.0974729i
$791$	−4.60251e6			−0.261549
$792$		0			0
$793$	4.15972e6			0.234899
$794$	−306895.	−	944526.i	−0.0172758	−	0.0531695i
$795$		0			0
$796$	97238.1	−	70647.6i	0.00543943	−	0.00395198i
$797$	−2.50558e7	−	8.14112e6i	−1.39721	−	0.453982i	−0.488924	−	0.872326i	$-0.662610\pi$
$797$	−2.50558e7	−	8.14112e6i	−1.39721	−	0.453982i	−0.908288	+	0.418345i	$0.862610\pi$
$798$		0			0
$799$	2.12513e6	+	2.92500e6i	0.117766	+	0.162091i
$800$	1.89420e6	+	1.37621e6i	0.104641	+	0.0760258i
$801$		0			0
$802$			7.90296e6i			0.433864i
$803$	−3.17136e6	−	1.97613e7i	−0.173563	−	1.08150i
$804$		0			0
$805$	−798599.	+	259480.i	−0.0434349	+	0.0141129i
$806$	−5.48125e6	+	7.54430e6i	−0.297196	+	0.409055i
$807$		0			0
$808$	−1.93632e6	+	5.95938e6i	−0.104339	+	0.321124i
$809$	4.33467e6	−	1.33408e7i	0.232855	−	0.716653i	−0.764544	−	0.644572i	$-0.777036\pi$
$809$	4.33467e6	−	1.33408e7i	0.232855	−	0.716653i	0.997399	−	0.0720816i	$-0.0229642\pi$
$810$		0			0
$811$	−1.93591e7	+	2.66456e7i	−1.03356	+	1.42257i	−0.131313	+	0.991341i	$0.541919\pi$
$811$	−1.93591e7	+	2.66456e7i	−1.03356	+	1.42257i	−0.902243	+	0.431227i	$0.858081\pi$
$812$	126323.	−	41044.9i	0.00672346	−	0.00218459i
$813$		0			0
$814$	−9.11917e6	−	1.78072e7i	−0.482385	−	0.941963i
$815$		−	3.52698e6i		−	0.185998i
$816$		0			0
$817$	−2.52755e6	−	1.83637e6i	−0.132478	−	0.0962511i
$818$	−1.37955e7	−	1.89879e7i	−0.720865	−	0.992185i
$819$		0			0
$820$	−6.44551e6	−	2.09427e6i	−0.334752	−	0.108767i
$821$	4.97588e6	−	3.61519e6i	0.257639	−	0.187186i	−0.451466	−	0.892288i	$-0.649099\pi$
$821$	4.97588e6	−	3.61519e6i	0.257639	−	0.187186i	0.709106	+	0.705102i	$0.249099\pi$
$822$		0			0
$823$	1.84510e6	+	5.67862e6i	0.0949553	+	0.292242i	0.987242	−	0.159227i	$-0.0509001\pi$
$823$	1.84510e6	+	5.67862e6i	0.0949553	+	0.292242i	−0.892287	+	0.451469i	$0.850900\pi$
$824$	6.71636e6			0.344601
$825$		0			0
$826$	1.09484e6			0.0558342
$827$	7.03766e6	+	2.16597e7i	0.357820	+	1.10126i	0.954356	+	0.298671i	$0.0965432\pi$
$827$	7.03766e6	+	2.16597e7i	0.357820	+	1.10126i	−0.596536	+	0.802586i	$0.703457\pi$
$828$		0			0
$829$	−6.90347e6	+	5.01566e6i	−0.348884	+	0.253479i	−0.748401	−	0.663247i	$-0.769178\pi$
$829$	−6.90347e6	+	5.01566e6i	−0.348884	+	0.253479i	0.399517	+	0.916726i	$0.369178\pi$
$830$	691068.	+	224542.i	0.0348197	+	0.0113136i
$831$		0			0
$832$	1.30458e6	+	1.79560e6i	0.0653375	+	0.0899293i
$833$	8.06866e6	+	5.86222e6i	0.402892	+	0.292718i
$834$		0			0
$835$		−	534425.i		−	0.0265259i
$836$	−925794.	+	1.82621e6i	−0.0458141	+	0.0903720i
$837$		0			0
$838$	6.22228e6	−	2.02174e6i	0.306083	−	0.0994525i
$839$	−7.83718e6	+	1.07870e7i	−0.384375	+	0.529047i	−0.956737	−	0.290954i	$-0.906027\pi$
$839$	−7.83718e6	+	1.07870e7i	−0.384375	+	0.529047i	0.572362	+	0.820001i	$0.306027\pi$
$840$		0			0
$841$	−6.32362e6	+	1.94621e7i	−0.308302	+	0.948855i
$842$	1.40252e6	−	4.31651e6i	0.0681756	−	0.209823i
$843$		0			0
$844$	−3.59483e6	+	4.94786e6i	−0.173709	+	0.239090i
$845$	2.13914e6	−	695049.i	0.103062	−	0.0334868i
$846$		0			0
$847$	1.87203e6	−	5.84279e6i	0.0896610	−	0.279841i
$848$			7.15474e6i			0.341668i
$849$		0			0
$850$	−4.80573e6	−	3.49156e6i	−0.228145	−	0.165757i
$851$	5.57614e6	+	7.67490e6i	0.263943	+	0.363286i
$852$		0			0
$853$	−1.42591e7	−	4.63305e6i	−0.670993	−	0.218019i	−0.0463454	−	0.998925i	$-0.514757\pi$
$853$	−1.42591e7	−	4.63305e6i	−0.670993	−	0.218019i	−0.624648	+	0.780907i	$0.714757\pi$
$854$	−946382.	+	687586.i	−0.0444039	+	0.0322614i
$855$		0			0
$856$	1.14279e6	+	3.51716e6i	0.0533069	+	0.164062i
$857$	−1.97374e7			−0.917990			−0.458995	−	0.888439i	$-0.651790\pi$
$857$	−1.97374e7			−0.917990			−0.458995	+	0.888439i	$0.651790\pi$
$858$		0			0
$859$	3.64184e7			1.68398			0.841992	−	0.539490i	$-0.181383\pi$
$859$	3.64184e7			1.68398			0.841992	+	0.539490i	$0.181383\pi$
$860$	−1.40277e6	−	4.31728e6i	−0.0646755	−	0.199051i
$861$		0			0
$862$	2.07338e7	−	1.50640e7i	0.950407	−	0.690511i
$863$	−2.64993e7	−	8.61015e6i	−1.21118	−	0.393535i	−0.367316	−	0.930096i	$-0.619723\pi$
$863$	−2.64993e7	−	8.61015e6i	−1.21118	−	0.393535i	−0.843862	+	0.536561i	$0.819723\pi$
$864$		0			0
$865$	1.68401e6	+	2.31784e6i	0.0765251	+	0.105328i
$866$	1.14349e7	+	8.30794e6i	0.518129	+	0.376442i
$867$		0			0
$868$		−	2.62244e6i		−	0.118143i
$869$	−6.15418e6	−	961817.i	−0.276453	−	0.0432059i
$870$		0			0
$871$	524505.	−	170422.i	0.0234263	−	0.00761167i
$872$	3.37482e6	−	4.64505e6i	0.150300	−	0.206871i
$873$		0			0
$874$	300017.	−	923358.i	0.0132852	−	0.0408876i
$875$	1.84473e6	−	5.67748e6i	0.0814539	−	0.250689i
$876$		0			0
$877$	2.35160e6	−	3.23670e6i	0.103244	−	0.142103i	−0.754269	−	0.656565i	$-0.772009\pi$
$877$	2.35160e6	−	3.23670e6i	0.103244	−	0.142103i	0.857513	+	0.514463i	$0.172009\pi$
$878$	−1.29488e7	+	4.20733e6i	−0.566883	+	0.184192i
$879$		0			0
$880$	−2.64792e6	+	1.35602e6i	−0.115265	+	0.0590281i
$881$			2.19282e7i			0.951840i	0.879489	+	0.475920i	$0.157885\pi$
$881$			2.19282e7i			0.951840i	−0.879489	+	0.475920i	$0.842115\pi$
$882$		0			0
$883$	−7.44535e6	−	5.40936e6i	−0.321354	−	0.233477i	0.415399	−	0.909639i	$-0.363642\pi$
$883$	−7.44535e6	−	5.40936e6i	−0.321354	−	0.233477i	−0.736753	+	0.676162i	$0.763642\pi$
$884$	−3.30982e6	−	4.55558e6i	−0.142454	−	0.196071i
$885$		0			0
$886$	−1.63174e7	−	5.30184e6i	−0.698339	−	0.226904i
$887$	−1.89111e7	+	1.37397e7i	−0.807063	+	0.586365i	−0.912978	−	0.408010i	$-0.866223\pi$
$887$	−1.89111e7	+	1.37397e7i	−0.807063	+	0.586365i	0.105915	+	0.994375i	$0.466223\pi$
$888$		0			0
$889$	3.24328e6	+	9.98180e6i	0.137635	+	0.423598i
$890$	7.08675e6			0.299897
$891$		0			0
$892$	1.46573e7			0.616796
$893$	−548519.	−	1.68817e6i	−0.0230177	−	0.0708413i
$894$		0			0
$895$	−1.47970e7	+	1.07506e7i	−0.617469	+	0.448618i
$896$	−593613.	−	192876.i	−0.0247021	−	0.00802619i
$897$		0			0
$898$	4.73339e6	+	6.51495e6i	0.195876	+	0.269600i
$899$	−758485.	−	551071.i	−0.0313002	−	0.0227410i
$900$		0			0
$901$		−	1.81521e7i		−	0.744930i
$902$	−1.65695e7	+	1.66375e7i	−0.678100	+	0.680882i
$903$		0			0
$904$	7.35367e6	−	2.38935e6i	0.299284	−	0.0972431i
$905$	2.19972e6	−	3.02766e6i	0.0892785	−	0.122881i
$906$		0			0
$907$	3.39082e6	−	1.04359e7i	0.136863	−	0.421221i	−0.859012	−	0.511955i	$-0.828921\pi$
$907$	3.39082e6	−	1.04359e7i	0.136863	−	0.421221i	0.995875	+	0.0907340i	$0.0289213\pi$
$908$	1.25838e6	−	3.87288e6i	0.0506519	−	0.155891i
$909$		0			0
$910$	1.40541e6	−	1.93439e6i	0.0562601	−	0.0774354i
$911$	719200.	−	233682.i	0.0287113	−	0.00932888i	−0.294626	−	0.955613i	$-0.595195\pi$
$911$	719200.	−	233682.i	0.0287113	−	0.00932888i	0.323337	+	0.946284i	$0.395195\pi$
$912$		0			0
$913$	1.77653e6	−	1.78382e6i	0.0705337	−	0.0708231i
$914$			3.32825e6i			0.131780i
$915$		0			0
$916$	−3.23790e6	−	2.35247e6i	−0.127504	−	0.0926372i
$917$	−7.78101e6	−	1.07096e7i	−0.305571	−	0.420583i
$918$		0			0
$919$	−2.52500e6	−	820423.i	−0.0986218	−	0.0320442i	0.259290	−	0.965799i	$-0.416511\pi$
$919$	−2.52500e6	−	820423.i	−0.0986218	−	0.0320442i	−0.357912	+	0.933755i	$0.616511\pi$
$920$	1.14126e6	−	829171.i	0.0444543	−	0.0322979i
$921$		0			0
$922$	−865770.	−	2.66457e6i	−0.0335410	−	0.103228i
$923$	−2.01049e7			−0.776781
$924$		0			0
$925$	−2.84967e7			−1.09506
$926$	−8.46790e6	−	2.60615e7i	−0.324525	−	0.998786i
$927$		0			0
$928$	−180525.	+	131159.i	−0.00688125	+	0.00499952i
$929$	−4.04954e7	−	1.31577e7i	−1.53945	−	0.500198i	−0.588227	−	0.808696i	$-0.700174\pi$
$929$	−4.04954e7	−	1.31577e7i	−1.53945	−	0.500198i	−0.951225	+	0.308498i	$0.900174\pi$
$930$		0			0
$931$	−2.87809e6	−	3.96135e6i	−0.108825	−	0.149785i
$932$	1.92439e6	+	1.39815e6i	0.0725693	+	0.0527247i
$933$		0			0
$934$		−	2.27612e6i		−	0.0853746i
$935$	6.71798e6	−	3.44032e6i	0.251310	−	0.128698i
$936$		0			0
$937$	5.09646e7	−	1.65594e7i	1.89636	−	0.616163i	0.924153	−	0.382023i	$-0.124772\pi$
$937$	5.09646e7	−	1.65594e7i	1.89636	−	0.616163i	0.972203	−	0.234140i	$-0.0752275\pi$
$938$	−91160.5	+	125472.i	−0.00338298	+	0.00465627i
$939$		0			0
$940$	796990.	−	2.45288e6i	0.0294194	−	0.0905435i
$941$	1.34703e7	−	4.14573e7i	0.495911	−	1.52626i	−0.319622	−	0.947545i	$-0.603556\pi$
$941$	1.34703e7	−	4.14573e7i	0.495911	−	1.52626i	0.815533	−	0.578711i	$-0.196444\pi$
$942$		0			0
$943$	6.54458e6	−	9.00784e6i	0.239664	−	0.329869i
$944$	−1.74928e6	+	568376.i	−0.0638896	+	0.0207590i
$945$		0			0
$946$	−1.55392e7	−	2.42857e6i	−0.564548	−	0.0882313i
$947$		−	2.41869e7i		−	0.876406i	−0.898876	−	0.438203i	$-0.855615\pi$
$947$		−	2.41869e7i		−	0.876406i	0.898876	−	0.438203i	$-0.144385\pi$
$948$		0			0
$949$	−2.18627e7	−	1.58842e7i	−0.788023	−	0.572532i
$950$	1.71420e6	+	2.35939e6i	0.0616244	+	0.0848187i
$951$		0			0
$952$	1.50604e6	+	489343.i	0.0538573	+	0.0174993i
$953$	−1.62219e7	+	1.17859e7i	−0.578587	+	0.420368i	−0.838215	−	0.545341i	$-0.816400\pi$
$953$	−1.62219e7	+	1.17859e7i	−0.578587	+	0.420368i	0.259627	+	0.965709i	$0.416400\pi$
$954$		0			0
$955$	−982301.	−	3.02321e6i	−0.0348527	−	0.107266i
$956$	2.45005e7			0.867023
$957$		0			0
$958$	−3.18697e7			−1.12192
$959$	−3.86881e6	−	1.19070e7i	−0.135841	−	0.418076i
$960$		0			0
$961$	8.18615e6	−	5.94758e6i	0.285938	−	0.207746i
$962$	−2.56912e7	−	8.34758e6i	−0.895049	−	0.290819i
$963$		0			0
$964$	5.28908e6	+	7.27980e6i	0.183311	+	0.252306i
$965$	4.33096e6	+	3.14663e6i	0.149715	+	0.108774i
$966$		0			0
$967$		−	8.71335e6i		−	0.299653i	−0.988712	−	0.149827i	$-0.952128\pi$
$967$		−	8.71335e6i		−	0.299653i	0.988712	−	0.149827i	$-0.0478715\pi$
$968$	42198.8	+	1.03072e7i	0.00144748	+	0.353550i
$969$		0			0
$970$	7.31064e6	−	2.37537e6i	0.249474	−	0.0810591i
$971$	−1.85058e7	+	2.54711e7i	−0.629884	+	0.866961i	−0.998026	−	0.0628085i	$-0.979994\pi$
$971$	−1.85058e7	+	2.54711e7i	−0.629884	+	0.866961i	0.368141	+	0.929770i	$0.379994\pi$
$972$		0			0
$973$	−119671.	+	368309.i	−0.00405235	+	0.0124718i
$974$	−1.26866e7	+	3.90453e7i	−0.428497	+	1.31878i
$975$		0			0
$976$	1.15513e6	−	1.58990e6i	0.0388156	−	0.0534250i
$977$	1.05884e7	−	3.44038e6i	0.354891	−	0.115311i	−0.126145	−	0.992012i	$-0.540261\pi$
$977$	1.05884e7	−	3.44038e6i	0.354891	−	0.115311i	0.481036	+	0.876701i	$0.340261\pi$
$978$		0			0
$979$	1.11022e7	−	2.19000e7i	0.370214	−	0.730278i
$980$		−	7.11453e6i		−	0.236636i
$981$		0			0
$982$	7.36990e6	+	5.35455e6i	0.243884	+	0.177192i
$983$	1.18596e6	+	1.63233e6i	0.0391459	+	0.0538797i	0.828141	−	0.560519i	$-0.189398\pi$
$983$	1.18596e6	+	1.63233e6i	0.0391459	+	0.0538797i	−0.788995	+	0.614399i	$0.789398\pi$
$984$		0			0
$985$	1.11097e7	+	3.60977e6i	0.364848	+	0.118546i
$986$	458006.	−	332761.i	0.0150030	−	0.0109003i
$987$		0			0
$988$	854298.	+	2.62926e6i	0.0278431	+	0.0856922i
$989$	7.45789e6			0.242452
$990$		0			0
$991$	2.55874e7			0.827640			0.413820	−	0.910359i	$-0.364194\pi$
$991$	2.55874e7			0.827640			0.413820	+	0.910359i	$0.364194\pi$
$992$	1.36142e6	+	4.19001e6i	0.0439251	+	0.135187i
$993$		0			0
$994$	4.57410e6	−	3.32328e6i	0.146838	−	0.106684i
$995$	206881.	+	67219.9i	0.00662466	+	0.00215248i
$996$		0			0
$997$	−2.66959e7	−	3.67437e7i	−0.850562	−	1.17070i	−0.983739	−	0.179606i	$-0.942518\pi$
$997$	−2.66959e7	−	3.67437e7i	−0.850562	−	1.17070i	0.133176	−	0.991092i	$-0.457482\pi$
$998$	−2.24203e7	−	1.62893e7i	−0.712549	−	0.517697i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.6.l.b.17.4	yes	40
3.2	odd	2		198.6.l.a.17.7	✓	40
11.2	odd	10		198.6.l.a.35.7	yes	40
33.2	even	10	inner	198.6.l.b.35.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.6.l.a.17.7	✓	40	3.2	odd	2
198.6.l.a.35.7	yes	40	11.2	odd	10
198.6.l.b.17.4	yes	40	1.1	even	1	trivial
198.6.l.b.35.4	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)

\(f(q)\)	\(=\)	\(q+(-1.23607 - 3.80423i) q^{2} +(-12.9443 + 9.40456i) q^{4} +(-27.5399 - 8.94827i) q^{5} +(-22.3921 - 30.8201i) q^{7} +(51.7771 + 37.6183i) q^{8} +O(q^{10})\)	\(q+(-1.23607 - 3.80423i) q^{2} +(-12.9443 + 9.40456i) q^{4} +(-27.5399 - 8.94827i) q^{5} +(-22.3921 - 30.8201i) q^{7} +(51.7771 + 37.6183i) q^{8} +115.829i q^{10} +(357.943 + 181.459i) q^{11} +(515.345 - 167.446i) q^{13} +(-89.5686 + 123.281i) q^{14} +(79.1084 - 243.470i) q^{16} +(-200.704 + 617.704i) q^{17} +(187.428 - 257.972i) q^{19} +(440.639 - 143.172i) q^{20} +(247.870 - 1585.99i) q^{22} +761.182i q^{23} +(-1849.80 - 1343.96i) q^{25} +(-1274.00 - 1753.52i) q^{26} +(579.700 + 188.356i) q^{28} +(176.294 - 128.085i) q^{29} +(-1329.51 - 4091.81i) q^{31} -1024.00 q^{32} +2597.97 q^{34} +(340.891 + 1049.16i) q^{35} +(10082.9 - 7325.63i) q^{37} +(-1213.06 - 394.146i) q^{38} +(-1089.32 - 1499.32i) q^{40} +(-11834.0 - 8597.92i) q^{41} -9797.77i q^{43} +(-6339.86 + 1017.44i) q^{44} +(2895.71 - 940.873i) q^{46} +(3271.99 - 4503.51i) q^{47} +(4745.18 - 14604.1i) q^{49} +(-2826.25 + 8698.29i) q^{50} +(-5096.01 + 7014.06i) q^{52} +(-26580.3 + 8636.47i) q^{53} +(-8233.99 - 8200.35i) q^{55} -2438.13i q^{56} +(-705.176 - 512.340i) q^{58} +(-4223.11 - 5812.61i) q^{59} +(7300.93 + 2372.21i) q^{61} +(-13922.8 + 10115.5i) q^{62} +(1265.73 + 3895.53i) q^{64} -15690.9 q^{65} +1017.77 q^{67} +(-3211.27 - 9883.26i) q^{68} +(3569.86 - 2593.65i) q^{70} +(-35287.2 - 11465.5i) q^{71} +(-29313.9 - 40347.1i) q^{73} +(-40331.5 - 29302.5i) q^{74} +5101.94i q^{76} +(-2422.52 - 15095.1i) q^{77} +(-14761.7 + 4796.35i) q^{79} +(-4357.28 + 5997.28i) q^{80} +(-18080.8 + 55646.9i) q^{82} +(1938.56 - 5966.29i) q^{83} +(11054.8 - 15215.6i) q^{85} +(-37272.9 + 12110.7i) q^{86} +(11707.1 + 22860.6i) q^{88} -61182.9i q^{89} +(-16700.4 - 12133.5i) q^{91} +(-7158.59 - 9852.95i) q^{92} +(-21176.8 - 6880.76i) q^{94} +(-7470.15 + 5427.38i) q^{95} +(-20507.6 - 63115.9i) q^{97} -61422.8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 160 q^{4} + 640 q^{8}+O(q^{10}) \) 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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