LMFDB - Embedded newform 198.6.l.b.35.7

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			35.7
Character	$\chi$	$=$	198.35
Dual form			198.6.l.b.17.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23607 + 3.80423i) q^{2} +(-12.9443 - 9.40456i) q^{4} +(28.7854 - 9.35295i) q^{5} +(56.7383 - 78.0936i) q^{7} +(51.7771 - 37.6183i) q^{8} +O(q^{10})$	\(q+(-1.23607 + 3.80423i) q^{2} +(-12.9443 - 9.40456i) q^{4} +(28.7854 - 9.35295i) q^{5} +(56.7383 - 78.0936i) q^{7} +(51.7771 - 37.6183i) q^{8} +121.067i q^{10} +(-339.095 + 214.630i) q^{11} +(804.378 + 261.358i) q^{13} +(226.953 + 312.374i) q^{14} +(79.1084 + 243.470i) q^{16} +(-171.905 - 529.070i) q^{17} +(-1648.13 - 2268.46i) q^{19} +(-460.567 - 149.647i) q^{20} +(-397.356 - 1555.29i) q^{22} -937.766i q^{23} +(-1787.05 + 1298.37i) q^{25} +(-1988.53 + 2736.98i) q^{26} +(-1468.87 + 477.266i) q^{28} +(3234.01 + 2349.65i) q^{29} +(2393.38 - 7366.08i) q^{31} -1024.00 q^{32} +2225.19 q^{34} +(902.831 - 2778.63i) q^{35} +(-7158.19 - 5200.73i) q^{37} +(10666.9 - 3465.89i) q^{38} +(1138.58 - 1567.13i) q^{40} +(3913.40 - 2843.25i) q^{41} -23731.3i q^{43} +(6407.83 + 410.811i) q^{44} +(3567.47 + 1159.14i) q^{46} +(13436.8 + 18494.2i) q^{47} +(2314.28 + 7122.61i) q^{49} +(-2730.38 - 8403.24i) q^{50} +(-7954.13 - 10947.9i) q^{52} +(-12144.8 - 3946.09i) q^{53} +(-7753.56 + 9349.74i) q^{55} -6177.86i q^{56} +(-12936.0 + 9398.59i) q^{58} +(23384.7 - 32186.3i) q^{59} +(29293.7 - 9518.09i) q^{61} +(25063.9 + 18210.0i) q^{62} +(1265.73 - 3895.53i) q^{64} +25598.8 q^{65} +15054.2 q^{67} +(-2750.49 + 8465.13i) q^{68} +(9454.57 + 6869.15i) q^{70} +(35536.2 - 11546.4i) q^{71} +(41533.6 - 57166.2i) q^{73} +(28632.8 - 20802.9i) q^{74} +44863.4i q^{76} +(-2478.45 + 38658.8i) q^{77} +(-85693.3 - 27843.4i) q^{79} +(4554.34 + 6268.51i) q^{80} +(5979.14 + 18401.9i) q^{82} +(20387.5 + 62746.2i) q^{83} +(-9896.74 - 13621.7i) q^{85} +(90279.1 + 29333.5i) q^{86} +(-9483.33 + 23869.0i) q^{88} -116584. i q^{89} +(66049.5 - 47987.8i) q^{91} +(-8819.28 + 12138.7i) q^{92} +(-86965.1 + 28256.7i) q^{94} +(-68658.9 - 49883.6i) q^{95} +(2790.03 - 8586.84i) q^{97} -29956.6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

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

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
$5$	28.7854	−	9.35295i	0.514929	−	0.167311i	−0.0400135	−	0.999199i	$-0.512740\pi$
$5$	28.7854	−	9.35295i	0.514929	−	0.167311i	0.554943	+	0.831888i	$0.312740\pi$
$6$		0			0
$7$	56.7383	−	78.0936i	0.437654	−	0.602380i	−0.532034	−	0.846723i	$-0.678572\pi$
$7$	56.7383	−	78.0936i	0.437654	−	0.602380i	0.969689	+	0.244343i	$0.0785723\pi$
$8$	51.7771	−	37.6183i	0.286031	−	0.207813i
$9$		0			0
$10$			121.067i			0.382848i
$11$	−339.095	+	214.630i	−0.844966	+	0.534821i
$11$	−339.095	+	214.630i	−0.844966	+	0.534821i
$12$		0			0
$13$	804.378	+	261.358i	1.32009	+	0.428922i	0.882524	−	0.470267i	$-0.155842\pi$
$13$	804.378	+	261.358i	1.32009	+	0.428922i	0.437561	+	0.899189i	$0.355842\pi$
$14$	226.953	+	312.374i	0.309468	+	0.425947i
$15$		0			0
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	−171.905	−	529.070i	−0.144267	−	0.444008i	0.852649	−	0.522484i	$-0.174995\pi$
$17$	−171.905	−	529.070i	−0.144267	−	0.444008i	−0.996916	+	0.0784758i	$0.974995\pi$
$18$		0			0
$19$	−1648.13	−	2268.46i	−1.04739	−	1.44160i	−0.891052	−	0.453901i	$-0.850032\pi$
$19$	−1648.13	−	2268.46i	−1.04739	−	1.44160i	−0.156335	−	0.987704i	$-0.549968\pi$
$20$	−460.567	−	149.647i	−0.257465	−	0.0836554i
$21$		0			0
$22$	−397.356	−	1555.29i	−0.175034	−	0.685101i
$23$		−	937.766i		−	0.369637i	−0.982773	−	0.184818i	$-0.940830\pi$
$23$		−	937.766i		−	0.369637i	0.982773	−	0.184818i	$-0.0591697\pi$
$24$		0			0
$25$	−1787.05	+	1298.37i	−0.571857	+	0.415479i
$26$	−1988.53	+	2736.98i	−0.576898	+	0.794032i
$27$		0			0
$28$	−1468.87	+	477.266i	−0.354070	+	0.115044i
$29$	3234.01	+	2349.65i	0.714080	+	0.518809i	0.884487	−	0.466564i	$-0.154508\pi$
$29$	3234.01	+	2349.65i	0.714080	+	0.518809i	−0.170408	+	0.985374i	$0.554508\pi$
$30$		0			0
$31$	2393.38	−	7366.08i	0.447310	−	1.37668i	−0.432621	−	0.901576i	$-0.642411\pi$
$31$	2393.38	−	7366.08i	0.447310	−	1.37668i	0.879931	−	0.475102i	$-0.157589\pi$
$32$	−1024.00			−0.176777
$33$		0			0
$34$	2225.19			0.330119
$35$	902.831	−	2778.63i	0.124577	−	0.383407i
$36$		0			0
$37$	−7158.19	−	5200.73i	−0.859605	−	0.624539i	0.0681727	−	0.997674i	$-0.478283\pi$
$37$	−7158.19	−	5200.73i	−0.859605	−	0.624539i	−0.927777	+	0.373134i	$0.878283\pi$
$38$	10666.9	−	3465.89i	1.19834	−	0.389364i
$39$		0			0
$40$	1138.58	−	1567.13i	0.112516	−	0.154865i
$41$	3913.40	−	2843.25i	0.363575	−	0.264153i	−0.390967	−	0.920405i	$-0.627859\pi$
$41$	3913.40	−	2843.25i	0.363575	−	0.264153i	0.754542	+	0.656252i	$0.227859\pi$
$42$		0			0
$43$		−	23731.3i		−	1.95727i	−0.205613	−	0.978633i	$-0.565919\pi$
$43$		−	23731.3i		−	1.95727i	0.205613	−	0.978633i	$-0.434081\pi$
$44$	6407.83	+	410.811i	0.498976	+	0.0319897i
$45$		0			0
$46$	3567.47	+	1159.14i	0.248580	+	0.0807686i
$47$	13436.8	+	18494.2i	0.887264	+	1.22121i	0.974356	+	0.225013i	$0.0722426\pi$
$47$	13436.8	+	18494.2i	0.887264	+	1.22121i	−0.0870919	+	0.996200i	$0.527757\pi$
$48$		0			0
$49$	2314.28	+	7122.61i	0.137697	+	0.423788i
$50$	−2730.38	−	8403.24i	−0.154453	−	0.475359i
$51$		0			0
$52$	−7954.13	−	10947.9i	−0.407929	−	0.561466i
$53$	−12144.8	−	3946.09i	−0.593883	−	0.192964i	−0.00337251	−	0.999994i	$-0.501074\pi$
$53$	−12144.8	−	3946.09i	−0.593883	−	0.192964i	−0.590510	+	0.807030i	$0.701074\pi$
$54$		0			0
$55$	−7753.56	+	9349.74i	−0.345617	+	0.416767i
$56$		−	6177.86i		−	0.263250i
$57$		0			0
$58$	−12936.0	+	9398.59i	−0.504930	+	0.366853i
$59$	23384.7	−	32186.3i	0.874584	−	1.20376i	−0.103308	−	0.994649i	$-0.532943\pi$
$59$	23384.7	−	32186.3i	0.874584	−	1.20376i	0.977892	−	0.209112i	$-0.0670574\pi$
$60$		0			0
$61$	29293.7	−	9518.09i	1.00797	−	0.327510i	0.241926	−	0.970295i	$-0.422221\pi$
$61$	29293.7	−	9518.09i	1.00797	−	0.327510i	0.766047	+	0.642784i	$0.222221\pi$
$62$	25063.9	+	18210.0i	0.828073	+	0.601630i
$63$		0			0
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	25598.8			0.751514
$66$		0			0
$67$	15054.2			0.409704			0.204852	−	0.978793i	$-0.434329\pi$
$67$	15054.2			0.409704			0.204852	+	0.978793i	$0.434329\pi$
$68$	−2750.49	+	8465.13i	−0.0721335	+	0.222004i
$69$		0			0
$70$	9454.57	+	6869.15i	0.230620	+	0.167555i
$71$	35536.2	−	11546.4i	0.836615	−	0.271833i	0.140786	−	0.990040i	$-0.455037\pi$
$71$	35536.2	−	11546.4i	0.836615	−	0.271833i	0.695829	+	0.718207i	$0.255037\pi$
$72$		0			0
$73$	41533.6	−	57166.2i	0.912206	−	1.25554i	−0.0542017	−	0.998530i	$-0.517261\pi$
$73$	41533.6	−	57166.2i	0.912206	−	1.25554i	0.966408	−	0.257014i	$-0.0827386\pi$
$74$	28632.8	−	20802.9i	0.607832	−	0.441616i
$75$		0			0
$76$			44863.4i			0.890961i
$77$	−2478.45	+	38658.8i	−0.0476379	+	0.743057i
$78$		0			0
$79$	−85693.3	−	27843.4i	−1.54482	−	0.501944i	−0.592122	−	0.805849i	$-0.701710\pi$
$79$	−85693.3	−	27843.4i	−1.54482	−	0.501944i	−0.952702	+	0.303905i	$0.901710\pi$
$80$	4554.34	+	6268.51i	0.0795610	+	0.109506i
$81$		0			0
$82$	5979.14	+	18401.9i	0.0981983	+	0.302223i
$83$	20387.5	+	62746.2i	0.324839	+	0.999752i	0.971513	+	0.236986i	$0.0761594\pi$
$83$	20387.5	+	62746.2i	0.324839	+	0.999752i	−0.646674	+	0.762766i	$0.723841\pi$
$84$		0			0
$85$	−9896.74	−	13621.7i	−0.148575	−	0.204496i
$86$	90279.1	+	29333.5i	1.31626	+	0.427678i
$87$		0			0
$88$	−9483.33	+	23869.0i	−0.130543	+	0.328570i
$89$		−	116584.i		−	1.56015i	−0.625689	−	0.780073i	$-0.715182\pi$
$89$		−	116584.i		−	1.56015i	0.625689	−	0.780073i	$-0.284818\pi$
$90$		0			0
$91$	66049.5	−	47987.8i	0.836115	−	0.607473i
$92$	−8819.28	+	12138.7i	−0.108633	+	0.149521i
$93$		0			0
$94$	−86965.1	+	28256.7i	−1.01514	+	0.329839i
$95$	−68658.9	−	49883.6i	−0.780527	−	0.567086i
$96$		0			0
$97$	2790.03	−	8586.84i	0.0301079	−	0.0926625i	−0.934873	−	0.354981i	$-0.884487\pi$
$97$	2790.03	−	8586.84i	0.0301079	−	0.0926625i	0.964981	+	0.262319i	$0.0844872\pi$
$98$	−29956.6			−0.315085
$99$		0			0
$100$	35342.7			0.353427
$101$	−2364.75	+	7277.96i	−0.0230665	+	0.0709915i	−0.961927	−	0.273306i	$-0.911883\pi$
$101$	−2364.75	+	7277.96i	−0.0230665	+	0.0709915i	0.938861	+	0.344297i	$0.111883\pi$
$102$		0			0
$103$	−24418.4	−	17741.0i	−0.226790	−	0.164773i	0.468588	−	0.883417i	$-0.344763\pi$
$103$	−24418.4	−	17741.0i	−0.226790	−	0.164773i	−0.695378	+	0.718644i	$0.744763\pi$
$104$	51480.2	−	16726.9i	0.466721	−	0.151647i
$105$		0			0
$106$	30023.6	−	41323.9i	0.259536	−	0.357221i
$107$	−7446.32	+	5410.07i	−0.0628756	+	0.0456818i	−0.618779	−	0.785565i	$-0.712372\pi$
$107$	−7446.32	+	5410.07i	−0.0628756	+	0.0456818i	0.555904	+	0.831247i	$0.312372\pi$
$108$		0			0
$109$			59482.8i			0.479540i	0.970830	+	0.239770i	$0.0770721\pi$
$109$			59482.8i			0.479540i	−0.970830	+	0.239770i	$0.922928\pi$
$110$	−25984.6	−	41053.2i	−0.204755	−	0.323493i
$111$		0			0
$112$	23502.0	+	7636.25i	0.177035	+	0.0575221i
$113$	−25221.6	−	34714.5i	−0.185813	−	0.255750i	0.705940	−	0.708271i	$-0.250525\pi$
$113$	−25221.6	−	34714.5i	−0.185813	−	0.255750i	−0.891754	+	0.452521i	$0.850525\pi$
$114$		0			0
$115$	−8770.89	−	26994.0i	−0.0618442	−	0.190337i
$116$	−19764.5	−	60828.9i	−0.136377	−	0.419725i
$117$		0			0
$118$	93538.8	+	128745.i	0.618424	+	0.851188i
$119$	−51070.6	−	16593.9i	−0.330601	−	0.107419i
$120$		0			0
$121$	68919.2	−	145560.i	0.427934	−	0.903810i
$122$			123205.i			0.749424i
$123$		0			0
$124$	−100255.	+	72839.8i	−0.585536	+	0.425417i
$125$	−94892.5	+	130608.i	−0.543196	+	0.747645i
$126$		0			0
$127$	−10624.8	+	3452.20i	−0.0584535	+	0.0189927i	−0.338098	−	0.941111i	$-0.609783\pi$
$127$	−10624.8	+	3452.20i	−0.0584535	+	0.0189927i	0.279644	+	0.960104i	$0.409783\pi$
$128$	13254.9	+	9630.27i	0.0715077	+	0.0519534i
$129$		0			0
$130$	−31641.9	+	97383.8i	−0.164212	+	0.505392i
$131$	−243595.			−1.24020			−0.620098	−	0.784524i	$-0.712907\pi$
$131$	−243595.			−1.24020			−0.620098	+	0.784524i	$0.712907\pi$
$132$		0			0
$133$	−270664.			−1.32679
$134$	−18608.0	+	57269.5i	−0.0895236	+	0.275525i
$135$		0			0
$136$	−28803.5	−	20926.9i	−0.133536	−	0.0970194i
$137$	−348516.	+	113240.i	−1.58643	+	0.515463i	−0.963703	−	0.266976i	$-0.913976\pi$
$137$	−348516.	+	113240.i	−1.58643	+	0.515463i	−0.622728	+	0.782438i	$0.713976\pi$
$138$		0			0
$139$	184904.	−	254499.i	0.811727	−	1.11725i	−0.179327	−	0.983790i	$-0.557392\pi$
$139$	184904.	−	254499.i	0.811727	−	1.11725i	0.991055	−	0.133457i	$-0.0426080\pi$
$140$	−37818.3	+	27476.6i	−0.163073	+	0.118479i
$141$		0			0
$142$			149460.i			0.622020i
$143$	−328856.	+	84018.3i	−1.34482	+	0.343585i
$144$		0			0
$145$	115069.	+	37388.0i	0.454503	+	0.147677i
$146$	166135.	+	228665.i	0.645027	+	0.887804i
$147$		0			0
$148$	43747.0	+	134639.i	0.164170	+	0.505263i
$149$	4171.51	+	12838.6i	0.0153931	+	0.0473752i	0.958458	−	0.285234i	$-0.0920712\pi$
$149$	4171.51	+	12838.6i	0.0153931	+	0.0473752i	−0.943065	+	0.332609i	$0.892071\pi$
$150$		0			0
$151$	120936.	+	166454.i	0.431632	+	0.594090i	0.968327	−	0.249686i	$-0.0803274\pi$
$151$	120936.	+	166454.i	0.431632	+	0.594090i	−0.536695	+	0.843776i	$0.680327\pi$
$152$	−170671.	−	55454.3i	−0.599170	−	0.194682i
$153$		0			0
$154$	−144003.	−	57213.5i	−0.489295	−	0.194400i
$155$		−	234421.i		−	0.783732i
$156$		0			0
$157$	−210769.	+	153133.i	−0.682430	+	0.495814i	−0.874163	−	0.485633i	$-0.838589\pi$
$157$	−210769.	+	153133.i	−0.682430	+	0.495814i	0.191733	+	0.981447i	$0.438589\pi$
$158$	211845.	−	291580.i	0.675113	−	0.929213i
$159$		0			0
$160$	−29476.3	+	9577.43i	−0.0910275	+	0.0295766i
$161$	−73233.5	−	53207.3i	−0.222662	−	0.161773i
$162$		0			0
$163$	62983.3	−	193843.i	0.185676	−	0.571452i	−0.814283	−	0.580468i	$-0.802870\pi$
$163$	62983.3	−	193843.i	0.185676	−	0.571452i	0.999959	+	0.00901535i	$0.00286971\pi$
$164$	−77395.6			−0.224702
$165$		0			0
$166$	−263901.			−0.743312
$167$	−5873.66	+	18077.3i	−0.0162974	+	0.0501581i	−0.958874	−	0.283830i	$-0.908395\pi$
$167$	−5873.66	+	18077.3i	−0.0162974	+	0.0501581i	0.942577	+	0.333989i	$0.108395\pi$
$168$		0			0
$169$	278334.	+	202221.i	0.749634	+	0.544641i
$170$	64053.1	−	20812.1i	0.169988	−	0.0552324i
$171$		0			0
$172$	−223182.	+	307184.i	−0.575226	+	0.791731i
$173$	−349493.	+	253922.i	−0.887817	+	0.645036i	−0.935308	−	0.353835i	$-0.884877\pi$
$173$	−349493.	+	253922.i	−0.887817	+	0.645036i	0.0474913	+	0.998872i	$0.484877\pi$
$174$		0			0
$175$			213225.i			0.526312i
$176$	−79081.2	−	65580.5i	−0.192438	−	0.159585i
$177$		0			0
$178$	443513.	+	144106.i	1.04920	+	0.340904i
$179$	−68657.8	−	94499.4i	−0.160161	−	0.220443i	0.721393	−	0.692526i	$-0.243502\pi$
$179$	−68657.8	−	94499.4i	−0.160161	−	0.220443i	−0.881554	+	0.472083i	$0.843502\pi$
$180$		0			0
$181$	30314.1	+	93297.1i	0.0687777	+	0.211676i	0.979538	−	0.201260i	$-0.0645035\pi$
$181$	30314.1	+	93297.1i	0.0687777	+	0.211676i	−0.910760	+	0.412936i	$0.864503\pi$
$182$	100915.	+	310583.i	0.225827	+	0.695024i
$183$		0			0
$184$	−35277.1	−	48554.8i	−0.0768155	−	0.105727i
$185$	−254694.	−	82755.0i	−0.547128	−	0.177773i
$186$		0			0
$187$	171846.	+	142509.i	0.359366	+	0.298015i
$188$		−	365762.i		−	0.754752i
$189$		0			0
$190$	274636.	−	199534.i	0.551916	−	0.400990i
$191$	188271.	−	259133.i	0.373422	−	0.513972i	−0.580405	−	0.814328i	$-0.697106\pi$
$191$	188271.	−	259133.i	0.373422	−	0.513972i	0.953827	+	0.300356i	$0.0971056\pi$
$192$		0			0
$193$	−456190.	+	148225.i	−0.881562	+	0.286437i	−0.714606	−	0.699527i	$-0.753394\pi$
$193$	−456190.	+	148225.i	−0.881562	+	0.286437i	−0.166956	+	0.985964i	$0.553394\pi$
$194$	29217.6	+	21227.8i	0.0557366	+	0.0404950i
$195$		0			0
$196$	37028.4	−	113962.i	0.0688486	−	0.211894i
$197$	520551.			0.955648			0.477824	−	0.878456i	$-0.341426\pi$
$197$	520551.			0.955648			0.477824	+	0.878456i	$0.341426\pi$
$198$		0			0
$199$	434589.			0.777939			0.388970	−	0.921251i	$-0.372831\pi$
$199$	434589.			0.777939			0.388970	+	0.921251i	$0.372831\pi$
$200$	−43686.0	+	134452.i	−0.0772267	+	0.237679i
$201$		0			0
$202$	−24764.0	−	17992.1i	−0.0427014	−	0.0310244i
$203$	366985.	−	119241.i	0.625040	−	0.203088i
$204$		0			0
$205$	86056.0	−	118446.i	0.143020	−	0.196850i
$206$	97673.7	−	70964.1i	0.160365	−	0.116512i
$207$		0			0
$208$			216518.i			0.347005i
$209$	1.04575e6	+	415483.i	1.65601	+	0.657942i
$210$		0			0
$211$	−133572.	−	43400.1i	−0.206542	−	0.0671096i	0.203919	−	0.978988i	$-0.434632\pi$
$211$	−133572.	−	43400.1i	−0.206542	−	0.0671096i	−0.410461	+	0.911878i	$0.634632\pi$
$212$	120094.	+	165296.i	0.183520	+	0.252593i
$213$		0			0
$214$	−11377.0	−	35014.7i	−0.0169821	−	0.0522656i
$215$	−221958.	−	683115.i	−0.327472	−	1.00785i
$216$		0			0
$217$	−439447.	−	604847.i	−0.633516	−	0.871959i
$218$	−226286.	−	73524.8i	−0.322490	−	0.104783i
$219$		0			0
$220$	188294.	−	48106.8i	0.262289	−	0.0670115i
$221$		−	470502.i		−	0.648008i
$222$		0			0
$223$	−203452.	+	147816.i	−0.273968	+	0.199049i	−0.716282	−	0.697811i	$-0.754158\pi$
$223$	−203452.	+	147816.i	−0.273968	+	0.199049i	0.442314	+	0.896860i	$0.354158\pi$
$224$	−58100.0	+	79967.8i	−0.0773671	+	0.106487i
$225$		0			0
$226$	163238.	−	53039.1i	0.212593	−	0.0690757i
$227$	805193.	+	585007.i	1.03714	+	0.753523i	0.969724	−	0.244203i	$-0.0785262\pi$
$227$	805193.	+	585007.i	1.03714	+	0.753523i	0.0674109	+	0.997725i	$0.478526\pi$
$228$		0			0
$229$	−147950.	+	455343.i	−0.186434	+	0.573786i	−0.999970	−	0.00772896i	$-0.997540\pi$
$229$	−147950.	+	455343.i	−0.186434	+	0.573786i	0.813536	+	0.581515i	$0.197540\pi$
$230$	113533.			0.141515
$231$		0			0
$232$	255837.			0.312064
$233$	−93107.5	+	286555.i	−0.112356	+	0.345795i	−0.991386	−	0.130970i	$-0.958191\pi$
$233$	−93107.5	+	286555.i	−0.112356	+	0.345795i	0.879031	+	0.476765i	$0.158191\pi$
$234$		0			0
$235$	559761.	+	406690.i	0.661200	+	0.480390i
$236$	−605396.	+	196705.i	−0.707553	+	0.229898i
$237$		0			0
$238$	126254.	−	173773.i	0.144478	−	0.198857i
$239$	−1.26860e6	+	921695.i	−1.43659	+	1.04374i	−0.447843	+	0.894112i	$0.647808\pi$
$239$	−1.26860e6	+	921695.i	−1.43659	+	1.04374i	−0.988742	+	0.149628i	$0.952192\pi$
$240$		0			0
$241$			142133.i			0.157635i	0.996889	+	0.0788173i	$0.0251144\pi$
$241$			142133.i			0.157635i	−0.996889	+	0.0788173i	$0.974886\pi$
$242$	468553.	+	442106.i	0.514304	+	0.485275i
$243$		0			0
$244$	−468698.	−	152289.i	−0.503987	−	0.163755i
$245$	133235.	+	183382.i	0.141809	+	0.195183i
$246$		0			0
$247$	−732840.	−	2.25545e6i	−0.764305	−	2.35229i
$248$	−153177.	−	471429.i	−0.158148	−	0.486729i
$249$		0			0
$250$	−379570.	−	522433.i	−0.384098	−	0.528665i
$251$	1.03885e6	+	337542.i	1.04080	+	0.338177i	0.779052	−	0.626959i	$-0.215701\pi$
$251$	1.03885e6	+	337542.i	1.04080	+	0.338177i	0.261749	+	0.965136i	$0.415701\pi$
$252$		0			0
$253$	201273.	+	317991.i	0.197689	+	0.312330i
$254$		−	44686.2i		−	0.0434599i
$255$		0			0
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	1.08477e6	−	1.49306e6i	1.02449	−	1.41008i	0.115477	−	0.993310i	$-0.463160\pi$
$257$	1.08477e6	−	1.49306e6i	1.02449	−	1.41008i	0.909010	−	0.416775i	$-0.136840\pi$
$258$		0			0
$259$	−812287.	+	263928.i	−0.752420	+	0.244476i
$260$	−331358.	−	240746.i	−0.303994	−	0.220864i
$261$		0			0
$262$	301100.	−	926691.i	0.270993	−	0.834030i
$263$	−430277.			−0.383583			−0.191791	−	0.981436i	$-0.561430\pi$
$263$	−430277.			−0.383583			−0.191791	+	0.981436i	$0.561430\pi$
$264$		0			0
$265$	−386501.			−0.338093
$266$	334559.	−	1.02967e6i	0.289914	−	0.892262i
$267$		0			0
$268$	−194865.	−	141578.i	−0.165729	−	0.120409i
$269$	1.33674e6	−	434334.i	1.12633	−	0.365968i	0.314152	−	0.949373i	$-0.398280\pi$
$269$	1.33674e6	−	434334.i	1.12633	−	0.365968i	0.812181	+	0.583405i	$0.198280\pi$
$270$		0			0
$271$	403619.	−	555535.i	0.333848	−	0.459502i	−0.608784	−	0.793336i	$-0.708342\pi$
$271$	403619.	−	555535.i	0.333848	−	0.459502i	0.942632	+	0.333834i	$0.108342\pi$
$272$	115214.	−	83707.8i	0.0944240	−	0.0686031i
$273$		0			0
$274$		−	1.46581e6i		−	1.17951i
$275$	327311.	−	823826.i	0.260993	−	0.656906i
$276$		0			0
$277$	202406.	+	65765.8i	0.158498	+	0.0514993i	0.387192	−	0.921999i	$-0.373445\pi$
$277$	202406.	+	65765.8i	0.158498	+	0.0514993i	−0.228693	+	0.973499i	$0.573445\pi$
$278$	739618.	+	1.01800e6i	0.573978	+	0.790013i
$279$		0			0
$280$	−57781.2	−	177832.i	−0.0440445	−	0.135555i
$281$	785101.	+	2.41629e6i	0.593143	+	1.82551i	0.563759	+	0.825940i	$0.309355\pi$
$281$	785101.	+	2.41629e6i	0.593143	+	1.82551i	0.0293849	+	0.999568i	$0.490645\pi$
$282$		0			0
$283$	1.36690e6	+	1.88138e6i	1.01454	+	1.39640i	0.915959	+	0.401272i	$0.131432\pi$
$283$	1.36690e6	+	1.88138e6i	1.01454	+	1.39640i	0.0985854	+	0.995129i	$0.468568\pi$
$284$	−568580.	−	184743.i	−0.418307	−	0.135916i
$285$		0			0
$286$	86863.2	−	1.35489e6i	0.0627944	−	0.979467i
$287$		−	466932.i		−	0.334618i
$288$		0			0
$289$	898324.	−	652671.i	0.632686	−	0.459674i
$290$	−284465.	+	391533.i	−0.198625	+	0.273384i
$291$		0			0
$292$	−1.07525e6	+	349368.i	−0.737990	+	0.239788i
$293$	450832.	+	327548.i	0.306793	+	0.222898i	0.730519	−	0.682892i	$-0.239278\pi$
$293$	450832.	+	327548.i	0.306793	+	0.222898i	−0.423726	+	0.905790i	$0.639278\pi$
$294$		0			0
$295$	372102.	−	1.14521e6i	0.248947	−	0.766180i
$296$	−566272.			−0.375661
$297$		0			0
$298$	−53997.1			−0.0352233
$299$	245093.	−	754319.i	0.158545	−	0.487952i
$300$		0			0
$301$	−1.85326e6	−	1.34647e6i	−1.17902	−	0.856607i
$302$	−782715.	+	254319.i	−0.493840	+	0.160458i
$303$		0			0
$304$	421921.	−	580725.i	0.261847	−	0.360401i
$305$	754208.	−	547964.i	0.464239	−	0.337289i
$306$		0			0
$307$			1.17501e6i			0.711534i	0.934575	+	0.355767i	$0.115780\pi$
$307$			1.17501e6i			0.711534i	−0.934575	+	0.355767i	$0.884220\pi$
$308$	395651.	−	477102.i	0.237649	−	0.286572i
$309$		0			0
$310$	891791.	+	289760.i	0.527058	+	0.171252i
$311$	844827.	+	1.16280e6i	0.495298	+	0.681719i	0.981354	−	0.192208i	$-0.0615649\pi$
$311$	844827.	+	1.16280e6i	0.495298	+	0.681719i	−0.486056	+	0.873928i	$0.661565\pi$
$312$		0			0
$313$	−176701.	−	543831.i	−0.101948	−	0.313764i	0.887054	−	0.461666i	$-0.152748\pi$
$313$	−176701.	−	543831.i	−0.101948	−	0.313764i	−0.989002	+	0.147902i	$0.952748\pi$
$314$	−322027.	−	991096.i	−0.184318	−	0.567273i
$315$		0			0
$316$	847382.	+	1.16632e6i	0.477377	+	0.657053i
$317$	−2.80712e6	−	912088.i	−1.56896	−	0.509787i	−0.609779	−	0.792571i	$-0.708742\pi$
$317$	−2.80712e6	−	912088.i	−1.56896	−	0.509787i	−0.959184	+	0.282784i	$0.908742\pi$
$318$		0			0
$319$	−1.60094e6	−	102637.i	−0.880843	−	0.0564715i
$320$		−	123973.i		−	0.0676786i
$321$		0			0
$322$	292934.	−	212829.i	0.157446	−	0.114391i
$323$	−916850.	+	1.26194e6i	−0.488981	+	0.673025i
$324$		0			0
$325$	−1.77681e6	+	577320.i	−0.933108	+	0.303185i
$326$	659569.	+	479205.i	0.343729	+	0.249734i
$327$		0			0
$328$	95666.2	−	294430.i	0.0490991	−	0.151112i
$329$	2.20667e6			1.12395
$330$		0			0
$331$	98596.1			0.0494640			0.0247320	−	0.999694i	$-0.492127\pi$
$331$	98596.1			0.0494640			0.0247320	+	0.999694i	$0.492127\pi$
$332$	326200.	−	1.00394e6i	0.162420	−	0.499876i
$333$		0			0
$334$	−61509.7	−	44689.4i	−0.0301702	−	0.0219199i
$335$	433341.	−	140801.i	0.210969	−	0.0685479i
$336$		0			0
$337$	−1.59877e6	+	2.20051e6i	−0.766850	+	1.05548i	0.229763	+	0.973247i	$0.426205\pi$
$337$	−1.59877e6	+	2.20051e6i	−0.766850	+	1.05548i	−0.996613	+	0.0822319i	$0.973795\pi$
$338$	−1.11334e6	+	808885.i	−0.530071	+	0.385119i
$339$		0			0
$340$			269398.i			0.126385i
$341$	769396.	+	3.01149e6i	0.358314	+	1.40248i
$342$		0			0
$343$	2.23050e6	+	724732.i	1.02368	+	0.332615i
$344$	−892729.	−	1.22874e6i	−0.406746	−	0.559838i
$345$		0			0
$346$	−533978.	−	1.64341e6i	−0.239791	−	0.738001i
$347$	−776470.	−	2.38973e6i	−0.346179	−	1.06543i	−0.960949	−	0.276724i	$-0.910751\pi$
$347$	−776470.	−	2.38973e6i	−0.346179	−	1.06543i	0.614770	−	0.788706i	$-0.289249\pi$
$348$		0			0
$349$	2.48309e6	+	3.41768e6i	1.09126	+	1.50199i	0.846485	+	0.532413i	$0.178715\pi$
$349$	2.48309e6	+	3.41768e6i	1.09126	+	1.50199i	0.244777	+	0.969580i	$0.421285\pi$
$350$	−811156.	−	263561.i	−0.353944	−	0.115003i
$351$		0			0
$352$	347233.	−	219781.i	0.149370	−	0.0945438i
$353$			655682.i			0.280063i	0.990147	+	0.140032i	$0.0447204\pi$
$353$			655682.i			0.280063i	−0.990147	+	0.140032i	$0.955280\pi$
$354$		0			0
$355$	914933.	−	664738.i	0.385317	−	0.279949i
$356$	−1.09642e6	+	1.50910e6i	−0.458515	+	0.631092i
$357$		0			0
$358$	444363.	−	144382.i	0.183244	−	0.0595396i
$359$	−3.32146e6	−	2.41318e6i	−1.36017	−	0.988221i	−0.998434	−	0.0559395i	$-0.982185\pi$
$359$	−3.32146e6	−	2.41318e6i	−1.36017	−	0.988221i	−0.361735	−	0.932281i	$-0.617815\pi$
$360$		0			0
$361$	−1.66440e6	+	5.12251e6i	−0.672188	+	2.06878i
$362$	−392393.			−0.157380
$363$		0			0
$364$	−1.30627e6			−0.516747
$365$	660892.	−	2.03402e6i	0.259656	−	0.799138i
$366$		0			0
$367$	654091.	+	475225.i	0.253497	+	0.184176i	0.707275	−	0.706938i	$-0.249924\pi$
$367$	654091.	+	475225.i	0.253497	+	0.184176i	−0.453778	+	0.891115i	$0.649924\pi$
$368$	228318.	−	74185.1i	0.0878863	−	0.0285560i
$369$		0			0
$370$	629638.	−	866622.i	0.239104	−	0.329098i
$371$	−997240.	+	724537.i	−0.376153	+	0.273291i
$372$		0			0
$373$			3.58916e6i			1.33573i	0.744280	+	0.667867i	$0.232793\pi$
$373$			3.58916e6i			1.33573i	−0.744280	+	0.667867i	$0.767207\pi$
$374$	−754550.	+	477592.i	−0.278939	+	0.176554i
$375$		0			0
$376$	1.39144e6	+	452107.i	0.507569	+	0.164919i
$377$	1.98727e6	+	2.73524e6i	0.720117	+	0.991156i
$378$		0			0
$379$	−550375.	−	1.69388e6i	−0.196816	−	0.605738i	−0.999951	−	0.00993998i	$-0.996836\pi$
$379$	−550375.	−	1.69388e6i	−0.196816	−	0.605738i	0.803134	−	0.595798i	$-0.203164\pi$
$380$	419606.	+	1.29141e6i	0.149067	+	0.458782i
$381$		0			0
$382$	753085.	+	1.03653e6i	0.264050	+	0.363433i
$383$	468664.	+	152278.i	0.163254	+	0.0530445i	0.389504	−	0.921025i	$-0.372647\pi$
$383$	468664.	+	152278.i	0.163254	+	0.0530445i	−0.226250	+	0.974069i	$0.572647\pi$
$384$		0			0
$385$	290231.	+	1.13599e6i	0.0997912	+	0.390592i
$386$		−	1.91867e6i		−	0.655438i
$387$		0			0
$388$	−116870.	+	84911.3i	−0.0394117	+	0.0286343i
$389$	−1.13452e6	+	1.56153e6i	−0.380135	+	0.523211i	−0.955620	−	0.294601i	$-0.904813\pi$
$389$	−1.13452e6	+	1.56153e6i	−0.380135	+	0.523211i	0.575485	+	0.817812i	$0.304813\pi$
$390$		0			0
$391$	−496144.	+	161207.i	−0.164122	+	0.0533264i
$392$	387766.	+	281729.i	0.127454	+	0.0926011i
$393$		0			0
$394$	−643437.	+	1.98029e6i	−0.208817	+	0.642672i
$395$	−2.72714e6			−0.879456
$396$		0			0
$397$	3.05179e6			0.971802			0.485901	−	0.874014i	$-0.338492\pi$
$397$	3.05179e6			0.971802			0.485901	+	0.874014i	$0.338492\pi$
$398$	−537181.	+	1.65327e6i	−0.169986	+	0.523163i
$399$		0			0
$400$	−457486.	−	332383.i	−0.142964	−	0.103870i
$401$	−5.77484e6	+	1.87636e6i	−1.79341	+	0.582714i	−0.999674	−	0.0255496i	$-0.991866\pi$
$401$	−5.77484e6	+	1.87636e6i	−1.79341	+	0.582714i	−0.793735	+	0.608263i	$0.791866\pi$
$402$		0			0
$403$	3.85037e6	−	5.29958e6i	1.18097	−	1.62547i
$404$	99056.0	−	71968.4i	0.0301945	−	0.0219376i
$405$		0			0
$406$			1.54348e6i			0.464715i
$407$	3.54353e6	+	227179.i	1.06035	+	0.0679800i
$408$		0			0
$409$	−3.30170e6	−	1.07279e6i	−0.975953	−	0.317106i	−0.222736	−	0.974879i	$-0.571499\pi$
$409$	−3.30170e6	−	1.07279e6i	−0.975953	−	0.317106i	−0.753217	+	0.657772i	$0.771499\pi$
$410$	344224.	+	473784.i	0.101130	+	0.139194i
$411$		0			0
$412$	149232.	+	459289.i	0.0433131	+	0.133304i
$413$	−1.18673e6	−	3.65239e6i	−0.342356	−	1.05366i
$414$		0			0
$415$	1.17372e6	+	1.61549e6i	0.334538	+	0.460453i
$416$	−823683.	−	267631.i	−0.233360	−	0.0758234i
$417$		0			0
$418$	−2.87321e6	+	3.46470e6i	−0.804316	+	0.969896i
$419$		−	5.61235e6i		−	1.56174i	−0.624691	−	0.780872i	$-0.714775\pi$
$419$		−	5.61235e6i		−	1.56174i	0.624691	−	0.780872i	$-0.285225\pi$
$420$		0			0
$421$	−3.40493e6	+	2.47383e6i	−0.936274	+	0.680243i	−0.947521	−	0.319694i	$-0.896420\pi$
$421$	−3.40493e6	+	2.47383e6i	−0.936274	+	0.680243i	0.0112471	+	0.999937i	$0.496420\pi$
$422$	330208.	−	454492.i	0.0902622	−	0.124235i
$423$		0			0
$424$	−777267.	+	252549.i	−0.209969	+	0.0682232i
$425$	994134.	+	722281.i	0.266976	+	0.193970i
$426$		0			0
$427$	918771.	−	2.82769e6i	0.243858	−	0.750519i
$428$	147266.			0.0388593
$429$		0			0
$430$	2.87308e6			0.749336
$431$	1960.69	−	6034.39i	0.000508412	−	0.00156473i	−0.950802	−	0.309799i	$-0.899738\pi$
$431$	1960.69	−	6034.39i	0.000508412	−	0.00156473i	0.951310	+	0.308235i	$0.0997381\pi$
$432$		0			0
$433$	−473466.	−	343993.i	−0.121358	−	0.0881718i	0.525451	−	0.850824i	$-0.323897\pi$
$433$	−473466.	−	343993.i	−0.121358	−	0.0881718i	−0.646809	+	0.762652i	$0.723897\pi$
$434$	2.84416e6	−	924124.i	0.724820	−	0.235508i
$435$		0			0
$436$	559410.	−	769961.i	0.140933	−	0.193978i
$437$	−2.12728e6	+	1.54556e6i	−0.532870	+	0.387153i
$438$		0			0
$439$			476880.i			0.118099i	0.998255	+	0.0590497i	$0.0188071\pi$
$439$			476880.i			0.118099i	−0.998255	+	0.0590497i	$0.981193\pi$
$440$	−49735.7	+	775778.i	−0.0122472	+	0.191032i
$441$		0			0
$442$	1.78989e6	+	581572.i	0.435785	+	0.141595i
$443$	−1.22763e6	−	1.68969e6i	−0.297207	−	0.409070i	0.634131	−	0.773225i	$-0.281358\pi$
$443$	−1.22763e6	−	1.68969e6i	−0.297207	−	0.409070i	−0.931338	+	0.364155i	$0.881358\pi$
$444$		0			0
$445$	−1.09041e6	−	3.35593e6i	−0.261029	−	0.803365i
$446$	−310847.	−	956687.i	−0.0739961	−	0.227737i
$447$		0			0
$448$	−232400.	−	319871.i	−0.0547068	−	0.0752975i
$449$	−3.17147e6	−	1.03047e6i	−0.742413	−	0.241224i	−0.0866994	−	0.996235i	$-0.527632\pi$
$449$	−3.17147e6	−	1.03047e6i	−0.742413	−	0.241224i	−0.655713	+	0.755010i	$0.727632\pi$
$450$		0			0
$451$	−716766.	+	1.80406e6i	−0.165934	+	0.417648i
$452$			686552.i			0.158062i
$453$		0			0
$454$	−3.22077e6	+	2.34003e6i	−0.733365	+	0.532821i
$455$	1.45244e6	−	1.99911e6i	0.328903	−	0.452697i
$456$		0			0
$457$	−2.57272e6	+	835928.i	−0.576239	+	0.187231i	−0.582615	−	0.812748i	$-0.697970\pi$
$457$	−2.57272e6	+	835928.i	−0.576239	+	0.187231i	0.00637624	+	0.999980i	$0.497970\pi$
$458$	−1.54935e6	−	1.12567e6i	−0.345133	−	0.250754i
$459$		0			0
$460$	−140334.	+	431904.i	−0.0309221	+	0.0951684i
$461$	−4.07303e6			−0.892617			−0.446308	−	0.894879i	$-0.647262\pi$
$461$	−4.07303e6			−0.892617			−0.446308	+	0.894879i	$0.647262\pi$
$462$		0			0
$463$	1.45481e6			0.315394			0.157697	−	0.987488i	$-0.449593\pi$
$463$	1.45481e6			0.315394			0.157697	+	0.987488i	$0.449593\pi$
$464$	−316232.	+	973263.i	−0.0681885	+	0.209863i
$465$		0			0
$466$	−975034.	−	708404.i	−0.207996	−	0.151118i
$467$	−7.46634e6	+	2.42596e6i	−1.58422	+	0.514745i	−0.963140	−	0.269001i	$-0.913306\pi$
$467$	−7.46634e6	+	2.42596e6i	−1.58422	+	0.514745i	−0.621081	+	0.783746i	$0.713306\pi$
$468$		0			0
$469$	854149.	−	1.17564e6i	0.179309	−	0.246797i
$470$	−2.23904e6	+	1.62676e6i	−0.467539	+	0.339687i
$471$		0			0
$472$		−	2.54620e6i		−	0.526063i
$473$	5.09344e6	+	8.04715e6i	1.04679	+	1.65382i
$474$		0			0
$475$	5.89059e6	+	1.91397e6i	1.19791	+	0.389225i
$476$	505014.	+	695093.i	0.102161	+	0.140613i
$477$		0			0
$478$	−1.93826e6	−	5.96534e6i	−0.388008	−	1.19417i
$479$	1.80136e6	+	5.54403e6i	0.358726	+	1.10404i	0.953817	+	0.300387i	$0.0971158\pi$
$479$	1.80136e6	+	5.54403e6i	0.358726	+	1.10404i	−0.595092	+	0.803658i	$0.702884\pi$
$480$		0			0
$481$	−4.39864e6	−	6.05420e6i	−0.866873	−	1.19315i
$482$	−540705.	−	175686.i	−0.106009	−	0.0344444i
$483$		0			0
$484$	−2.26103e6	+	1.23601e6i	−0.438726	+	0.239832i
$485$		−	273271.i		−	0.0527520i
$486$		0			0
$487$	3.76253e6	−	2.73364e6i	0.718882	−	0.522299i	−0.167145	−	0.985932i	$-0.553455\pi$
$487$	3.76253e6	−	2.73364e6i	0.718882	−	0.522299i	0.886027	+	0.463634i	$0.153455\pi$
$488$	1.15869e6	−	1.59479e6i	0.220250	−	0.303148i
$489$		0			0
$490$	−862314.	+	280183.i	−0.162246	+	0.0527171i
$491$	−889829.	−	646499.i	−0.166572	−	0.121022i	0.501376	−	0.865229i	$-0.332827\pi$
$491$	−889829.	−	646499.i	−0.166572	−	0.121022i	−0.667948	+	0.744208i	$0.732827\pi$
$492$		0			0
$493$	687185.	−	2.11494e6i	0.127337	−	0.391904i
$494$	9.48608e6			1.74892
$495$		0			0
$496$	1.98276e6			0.361881
$497$	1.11456e6	−	3.43028e6i	0.202402	−	0.622929i
$498$		0			0
$499$	−7.30132e6	−	5.30472e6i	−1.31265	−	0.953699i	−0.999993	−	0.00383432i	$-0.998779\pi$
$499$	−7.30132e6	−	5.30472e6i	−1.31265	−	0.953699i	−0.312661	−	0.949865i	$-0.601221\pi$
$500$	2.45663e6	−	798207.i	0.439455	−	0.142788i
$501$		0			0
$502$	−2.56818e6	+	3.53479e6i	−0.454847	+	0.626043i
$503$	1.70411e6	−	1.23811e6i	0.300315	−	0.218191i	−0.427415	−	0.904056i	$-0.640576\pi$
$503$	1.70411e6	−	1.23811e6i	0.300315	−	0.218191i	0.727730	+	0.685864i	$0.240576\pi$
$504$		0			0
$505$			231617.i			0.0404149i
$506$	−1.45850e6	+	372627.i	−0.253238	+	0.0646991i
$507$		0			0
$508$	169996.	+	55235.2i	0.0292267	+	0.00949634i
$509$	4.19353e6	+	5.77190e6i	0.717440	+	0.987471i	0.999605	+	0.0281054i	$0.00894739\pi$
$509$	4.19353e6	+	5.77190e6i	0.717440	+	0.987471i	−0.282165	+	0.959366i	$0.591053\pi$
$510$		0			0
$511$	−2.10776e6	−	6.48702e6i	−0.357083	−	1.09899i
$512$	−81007.0	−	249314.i	−0.0136568	−	0.0420312i
$513$		0			0
$514$	4.33909e6	+	5.97225e6i	0.724421	+	0.997081i
$515$	−868826.	−	282299.i	−0.144349	−	0.0469020i
$516$		0			0
$517$	−8.52577e6	−	3.38735e6i	−1.40284	−	0.557357i
$518$		−	3.41636e6i		−	0.559421i
$519$		0			0
$520$	1.32543e6	−	962984.i	0.214956	−	0.156175i
$521$	424156.	−	583801.i	0.0684592	−	0.0942260i	−0.773414	−	0.633901i	$-0.781453\pi$
$521$	424156.	−	583801.i	0.0684592	−	0.0942260i	0.841874	+	0.539675i	$0.181453\pi$
$522$		0			0
$523$	6.72183e6	−	2.18405e6i	1.07457	−	0.349148i	0.282302	−	0.959326i	$-0.408902\pi$
$523$	6.72183e6	−	2.18405e6i	1.07457	−	0.349148i	0.792264	+	0.610178i	$0.208902\pi$
$524$	3.15316e6	+	2.29091e6i	0.501670	+	0.364484i
$525$		0			0
$526$	531852.	−	1.63687e6i	0.0838159	−	0.257959i
$527$	−4.30861e6			−0.675789
$528$		0			0
$529$	5.55694e6			0.863369
$530$	477741.	−	1.47034e6i	0.0738760	−	0.227367i
$531$		0			0
$532$	3.50355e6	+	2.54548e6i	0.536697	+	0.389933i
$533$	3.89096e6	−	1.26425e6i	0.593251	−	0.192759i
$534$		0			0
$535$	−163745.	+	225376.i	−0.0247334	+	0.0340427i
$536$	779462.	−	566312.i	0.117188	−	0.0851420i
$537$		0			0
$538$			5.62213e6i			0.837424i
$539$	−2.31348e6	−	1.91852e6i	−0.343000	−	0.284443i
$540$		0			0
$541$	1.23382e7	+	4.00894e6i	1.81243	+	0.588893i	0.999983	+	0.00585163i	$0.00186264\pi$
$541$	1.23382e7	+	4.00894e6i	1.81243	+	0.588893i	0.812443	+	0.583041i	$0.198137\pi$
$542$	1.61448e6	+	2.22214e6i	0.236066	+	0.324917i
$543$		0			0
$544$	176031.	+	541768.i	0.0255031	+	0.0784903i
$545$	556340.	+	1.71224e6i	0.0802322	+	0.246929i
$546$		0			0
$547$	1.80202e6	+	2.48027e6i	0.257508	+	0.354430i	0.918123	−	0.396295i	$-0.129704\pi$
$547$	1.80202e6	+	2.48027e6i	0.257508	+	0.354430i	−0.660615	+	0.750725i	$0.729704\pi$
$548$	5.57626e6	+	1.81184e6i	0.793216	+	0.257731i
$549$		0			0
$550$	2.72944e6	+	2.26347e6i	0.384739	+	0.319057i
$551$		−	1.12087e7i		−	1.57281i
$552$		0			0
$553$	−7.03649e6	+	5.11231e6i	−0.978460	+	0.710893i
$554$	−500376.	+	688709.i	−0.0692663	+	0.0953369i
$555$		0			0
$556$	−4.78691e6	+	1.55536e6i	−0.656701	+	0.213375i
$557$	2.73382e6	+	1.98624e6i	0.373364	+	0.271264i	0.758604	−	0.651552i	$-0.225882\pi$
$557$	2.73382e6	+	1.98624e6i	0.373364	+	0.271264i	−0.385241	+	0.922816i	$0.625882\pi$
$558$		0			0
$559$	6.20237e6	−	1.90889e7i	0.839514	−	2.58376i
$560$	747936.			0.100785
$561$		0			0
$562$	−1.01626e7			−1.35726
$563$	4.10083e6	−	1.26210e7i	0.545256	−	1.67813i	−0.175125	−	0.984546i	$-0.556033\pi$
$563$	4.10083e6	−	1.26210e7i	0.545256	−	1.67813i	0.720381	−	0.693579i	$-0.243967\pi$
$564$		0			0
$565$	−1.05070e6	−	763377.i	−0.138470	−	0.100605i
$566$	−8.84677e6	+	2.87449e6i	−1.16076	+	0.377155i
$567$		0			0
$568$	1.40561e6	−	1.93465e6i	0.182807	−	0.251612i
$569$	1.05288e7	−	7.64965e6i	1.36333	−	0.990515i	0.365101	−	0.930968i	$-0.381034\pi$
$569$	1.05288e7	−	7.64965e6i	1.36333	−	0.990515i	0.998226	−	0.0595470i	$-0.0189656\pi$
$570$		0			0
$571$			2.62192e6i			0.336534i	0.985741	+	0.168267i	$0.0538171\pi$
$571$			2.62192e6i			0.336534i	−0.985741	+	0.168267i	$0.946183\pi$
$572$	5.04695e6	+	2.00519e6i	0.644969	+	0.256251i
$573$		0			0
$574$	1.77632e6	+	577160.i	0.225030	+	0.0731167i
$575$	1.21757e6	+	1.67584e6i	0.153576	+	0.211379i
$576$		0			0
$577$	−3.18179e6	−	9.79253e6i	−0.397861	−	1.22449i	−0.926711	−	0.375775i	$-0.877377\pi$
$577$	−3.18179e6	−	9.79253e6i	−0.397861	−	1.22449i	0.528850	−	0.848715i	$-0.322623\pi$
$578$	1.37252e6	+	4.22417e6i	0.170883	+	0.525923i
$579$		0			0
$580$	−1.13786e6	−	1.56613e6i	−0.140449	−	0.193312i
$581$	6.05683e6	+	1.96798e6i	0.744398	+	0.241869i
$582$		0			0
$583$	4.96518e6	−	1.26854e6i	0.605012	−	0.154573i
$584$		−	4.52232e6i		−	0.548693i
$585$		0			0
$586$	−1.80333e6	+	1.31019e6i	−0.216935	+	0.157613i
$587$	2.02152e6	−	2.78238e6i	0.242149	−	0.333289i	−0.670594	−	0.741825i	$-0.733961\pi$
$587$	2.02152e6	−	2.78238e6i	0.242149	−	0.333289i	0.912742	+	0.408536i	$0.133961\pi$
$588$		0			0
$589$	−2.06542e7	+	6.71097e6i	−2.45313	+	0.797071i
$590$	3.89670e6	+	2.83112e6i	0.460858	+	0.334833i
$591$		0			0
$592$	699951.	−	2.15423e6i	0.0820849	−	0.252631i
$593$	1.21369e7			1.41733			0.708667	−	0.705543i	$-0.249297\pi$
$593$	1.21369e7			1.41733			0.708667	+	0.705543i	$0.249297\pi$
$594$		0			0
$595$	−1.62529e6			−0.188208
$596$	66744.1	−	205417.i	0.00769657	−	0.0236876i
$597$		0			0
$598$	2.56665e6	+	1.86478e6i	0.293503	+	0.213243i
$599$	−8.62672e6	+	2.80299e6i	−0.982378	+	0.319194i	−0.755803	−	0.654799i	$-0.772753\pi$
$599$	−8.62672e6	+	2.80299e6i	−0.982378	+	0.319194i	−0.226576	+	0.973994i	$0.572753\pi$
$600$		0			0
$601$	3.59261e6	−	4.94480e6i	0.405717	−	0.558422i	−0.556450	−	0.830881i	$-0.687837\pi$
$601$	3.59261e6	−	4.94480e6i	0.405717	−	0.558422i	0.962167	+	0.272459i	$0.0878369\pi$
$602$	7.41304e6	−	5.38589e6i	0.833691	−	0.605712i
$603$		0			0
$604$		−	3.29198e6i		−	0.367168i
$605$	622457.	−	4.83459e6i	0.0691386	−	0.536996i
$606$		0			0
$607$	4.23157e6	+	1.37492e6i	0.466154	+	0.151463i	0.532671	−	0.846323i	$-0.321188\pi$
$607$	4.23157e6	+	1.37492e6i	0.466154	+	0.151463i	−0.0665163	+	0.997785i	$0.521188\pi$
$608$	1.68768e6	+	2.32290e6i	0.185154	+	0.254842i
$609$		0			0
$610$	1.15233e6	+	3.54650e6i	0.125387	+	0.385901i
$611$	5.97469e6	+	1.83882e7i	0.647459	+	1.99267i
$612$		0			0
$613$	5.33568e6	+	7.34394e6i	0.573507	+	0.789365i	0.992965	−	0.118410i	$-0.0377797\pi$
$613$	5.33568e6	+	7.34394e6i	0.573507	+	0.789365i	−0.419458	+	0.907775i	$0.637780\pi$
$614$	−4.47000e6	−	1.45239e6i	−0.478505	−	0.155476i
$615$		0			0
$616$	1.32595e6	+	2.09488e6i	0.140791	+	0.222437i
$617$			1.01553e7i			1.07394i	0.843601	+	0.536971i	$0.180431\pi$
$617$			1.01553e7i			1.07394i	−0.843601	+	0.536971i	$0.819569\pi$
$618$		0			0
$619$	169422.	−	123093.i	0.0177723	−	0.0129123i	−0.578864	−	0.815424i	$-0.696504\pi$
$619$	169422.	−	123093.i	0.0177723	−	0.0129123i	0.596636	+	0.802512i	$0.296504\pi$
$620$	−2.20463e6	+	3.03441e6i	−0.230333	+	0.317026i
$621$		0			0
$622$	−5.46783e6	+	1.77661e6i	−0.566682	+	0.184126i
$623$	−9.10449e6	−	6.61480e6i	−0.939800	−	0.682805i
$624$		0			0
$625$	623159.	−	1.91789e6i	0.0638115	−	0.196392i
$626$	2.28727e6			0.233282
$627$		0			0
$628$	4.16840e6			0.421765
$629$	−1.52102e6	+	4.68122e6i	−0.153288	+	0.471772i
$630$		0			0
$631$	5.23316e6	+	3.80211e6i	0.523228	+	0.380147i	0.817818	−	0.575476i	$-0.195183\pi$
$631$	5.23316e6	+	3.80211e6i	0.523228	+	0.380147i	−0.294591	+	0.955623i	$0.595183\pi$
$632$	−5.48437e6	+	1.78198e6i	−0.546178	+	0.177464i
$633$		0			0
$634$	6.93958e6	−	9.55151e6i	0.685662	−	0.943733i
$635$	−273550.	+	198746.i	−0.0269217	+	0.0195598i
$636$		0			0
$637$			6.33413e6i			0.618498i
$638$	2.36933e6	−	5.96347e6i	0.230448	−	0.580026i
$639$		0			0
$640$	471621.	+	153239.i	0.0455138	+	0.0147883i
$641$	−5.10801e6	−	7.03058e6i	−0.491029	−	0.675843i	0.489548	−	0.871976i	$-0.337162\pi$
$641$	−5.10801e6	−	7.03058e6i	−0.491029	−	0.675843i	−0.980577	+	0.196133i	$0.937162\pi$
$642$		0			0
$643$	−5.82221e6	−	1.79189e7i	−0.555342	−	1.70917i	−0.695040	−	0.718971i	$-0.744613\pi$
$643$	−5.82221e6	−	1.79189e7i	−0.555342	−	1.70917i	0.139698	−	0.990194i	$-0.455387\pi$
$644$	447564.	+	1.37746e6i	0.0425246	+	0.130877i
$645$		0			0
$646$	−3.66740e6	−	5.04775e6i	−0.345762	−	0.475900i
$647$	−3.16957e6	−	1.02985e6i	−0.297673	−	0.0967198i	0.156373	−	0.987698i	$-0.450020\pi$
$647$	−3.16957e6	−	1.02985e6i	−0.297673	−	0.0967198i	−0.454046	+	0.890978i	$0.650020\pi$
$648$		0			0
$649$	−1.02149e6	+	1.59332e7i	−0.0951969	+	1.48488i
$650$		−	7.47299e6i		−	0.693762i
$651$		0			0
$652$	−2.63828e6	+	1.91682e6i	−0.243053	+	0.176589i
$653$	5.55237e6	−	7.64218e6i	0.509560	−	0.701349i	−0.474285	−	0.880371i	$-0.657293\pi$
$653$	5.55237e6	−	7.64218e6i	0.509560	−	0.701349i	0.983845	+	0.179022i	$0.0572934\pi$
$654$		0			0
$655$	−7.01199e6	+	2.27833e6i	−0.638613	+	0.207498i
$656$	1.00183e6	+	727872.i	0.0908938	+	0.0660382i
$657$		0			0
$658$	−2.72759e6	+	8.39465e6i	−0.245592	+	0.755854i
$659$	100923.			0.00905267			0.00452634	−	0.999990i	$-0.498559\pi$
$659$	100923.			0.00905267			0.00452634	+	0.999990i	$0.498559\pi$
$660$		0			0
$661$	9.35583e6			0.832873			0.416436	−	0.909165i	$-0.363279\pi$
$661$	9.35583e6			0.832873			0.416436	+	0.909165i	$0.363279\pi$
$662$	−121871.	+	375082.i	−0.0108083	+	0.0332645i
$663$		0			0
$664$	3.41601e6	+	2.48187e6i	0.300676	+	0.218454i
$665$	−7.79118e6	+	2.53151e6i	−0.683202	+	0.221986i
$666$		0			0
$667$	2.20342e6	−	3.03275e6i	0.191771	−	0.263950i
$668$	246039.	−	178758.i	0.0213335	−	0.0154997i
$669$		0			0
$670$			1.82257e6i			0.156854i
$671$	−7.89045e6	+	9.51482e6i	−0.676543	+	0.815820i
$672$		0			0
$673$	9.20805e6	+	2.99188e6i	0.783664	+	0.254628i	0.673404	−	0.739275i	$-0.264832\pi$
$673$	9.20805e6	+	2.99188e6i	0.783664	+	0.254628i	0.110260	+	0.993903i	$0.464832\pi$
$674$	−6.39507e6	−	8.80206e6i	−0.542245	−	0.746336i
$675$		0			0
$676$	−1.70102e6	−	5.23522e6i	−0.143167	−	0.440624i
$677$	1.98537e6	+	6.11033e6i	0.166483	+	0.512381i	0.999142	−	0.0414037i	$-0.0131830\pi$
$677$	1.98537e6	+	6.11033e6i	0.166483	+	0.512381i	−0.832660	+	0.553785i	$0.813183\pi$
$678$		0			0
$679$	−512275.	−	705087.i	−0.0426412	−	0.0586905i
$680$	−1.02485e6	−	332994.i	−0.0849939	−	0.0276162i
$681$		0			0
$682$	−1.24074e7	−	795448.i	−1.02146	−	0.0654864i
$683$			7.48207e6i			0.613720i	0.951755	+	0.306860i	$0.0992783\pi$
$683$			7.48207e6i			0.613720i	−0.951755	+	0.306860i	$0.900722\pi$
$684$		0			0
$685$	−8.97306e6	+	6.51931e6i	−0.730658	+	0.530854i
$686$	−5.51409e6	+	7.58950e6i	−0.447367	+	0.615747i
$687$		0			0
$688$	5.77787e6	−	1.87734e6i	0.465368	−	0.151207i
$689$	−8.73767e6	−	6.34829e6i	−0.701209	−	0.509458i
$690$		0			0
$691$	−1.39601e6	+	4.29648e6i	−0.111223	+	0.342308i	−0.991140	−	0.132818i	$-0.957598\pi$
$691$	−1.39601e6	+	4.29648e6i	−0.111223	+	0.342308i	0.879918	+	0.475126i	$0.157598\pi$
$692$	6.91195e6			0.548701
$693$		0			0
$694$	1.00508e7			0.792143
$695$	2.94223e6	−	9.05527e6i	0.231055	−	0.711114i
$696$		0			0
$697$	−2.17701e6	−	1.58169e6i	−0.169738	−	0.123322i
$698$	−1.60709e7	+	5.22175e6i	−1.24854	+	0.405674i
$699$		0			0
$700$	2.00529e6	−	2.76004e6i	0.154679	−	0.212897i
$701$	−1.35811e7	+	9.86725e6i	−1.04385	+	0.758405i	−0.971034	−	0.238940i	$-0.923200\pi$
$701$	−1.35811e7	+	9.86725e6i	−1.04385	+	0.758405i	−0.0728202	+	0.997345i	$0.523200\pi$
$702$		0			0
$703$			2.48095e7i			1.89334i
$704$	406893.	+	1.59262e6i	0.0309420	+	0.121110i
$705$		0			0
$706$	−2.49436e6	−	810467.i	−0.188342	−	0.0611961i
$707$	434190.	+	597611.i	0.0326687	+	0.0449645i
$708$		0			0
$709$	−4.69005e6	−	1.44345e7i	−0.350398	−	1.07842i	−0.958630	−	0.284656i	$-0.908121\pi$
$709$	−4.69005e6	−	1.44345e7i	−0.350398	−	1.07842i	0.608231	−	0.793760i	$-0.291879\pi$
$710$	1.39789e6	+	4.30227e6i	0.104071	+	0.320296i
$711$		0			0
$712$	−4.38570e6	−	6.03640e6i	−0.324219	−	0.446250i
$713$	−6.90766e6	−	2.24444e6i	−0.508871	−	0.165342i
$714$		0			0
$715$	−8.68043e6	+	5.49427e6i	−0.635003	+	0.401925i
$716$			1.86892e6i			0.136241i
$717$		0			0
$718$	1.32858e7	−	9.65273e6i	0.961785	−	0.698777i
$719$	1.87306e6	−	2.57804e6i	0.135123	−	0.185981i	−0.736093	−	0.676880i	$-0.763332\pi$
$719$	1.87306e6	−	2.57804e6i	0.135123	−	0.185981i	0.871216	+	0.490899i	$0.163332\pi$
$720$		0			0
$721$	−2.77092e6	+	900327.i	−0.198512	+	0.0645004i
$722$	−1.74299e7	−	1.26635e7i	−1.24437	−	0.904090i
$723$		0			0
$724$	485025.	−	1.49275e6i	0.0343889	−	0.105838i
$725$	−8.83007e6			−0.623906
$726$		0			0
$727$	1.58255e7			1.11051			0.555253	−	0.831682i	$-0.312622\pi$
$727$	1.58255e7			1.11051			0.555253	+	0.831682i	$0.312622\pi$
$728$	1.61463e6	−	4.96933e6i	0.112913	−	0.347512i
$729$		0			0
$730$	6.92095e6	+	5.02836e6i	0.480683	+	0.349236i
$731$	−1.25555e7	+	4.07954e6i	−0.869043	+	0.282369i
$732$		0			0
$733$	−8.78309e6	+	1.20889e7i	−0.603792	+	0.831048i	−0.996049	−	0.0888075i	$-0.971694\pi$
$733$	−8.78309e6	+	1.20889e7i	−0.603792	+	0.831048i	0.392257	+	0.919856i	$0.371694\pi$
$734$	−2.61636e6	+	1.90090e6i	−0.179249	+	0.130232i
$735$		0			0
$736$			960273.i			0.0653431i
$737$	−5.10479e6	+	3.23107e6i	−0.346186	+	0.219118i
$738$		0			0
$739$	3.17093e6	+	1.03030e6i	0.213588	+	0.0693988i	0.413856	−	0.910342i	$-0.364182\pi$
$739$	3.17093e6	+	1.03030e6i	0.213588	+	0.0693988i	−0.200269	+	0.979741i	$0.564182\pi$
$740$	2.51855e6	+	3.46649e6i	0.169072	+	0.232707i
$741$		0			0
$742$	−1.52365e6	−	4.68930e6i	−0.101596	−	0.312679i
$743$	386981.	+	1.19100e6i	0.0257168	+	0.0791482i	0.963091	−	0.269175i	$-0.0867511\pi$
$743$	386981.	+	1.19100e6i	0.0257168	+	0.0791482i	−0.937374	+	0.348323i	$0.886751\pi$
$744$		0			0
$745$	240157.	+	330548.i	0.0158528	+	0.0218195i
$746$	−1.36540e7	−	4.43644e6i	−0.898280	−	0.291869i
$747$		0			0
$748$	−884193.	−	3.46081e6i	−0.0577821	−	0.226164i
$749$			888468.i			0.0578678i
$750$		0			0
$751$	−1.57194e7	+	1.14208e7i	−1.01703	+	0.738918i	−0.965673	−	0.259762i	$-0.916356\pi$
$751$	−1.57194e7	+	1.14208e7i	−1.01703	+	0.738918i	−0.0513606	+	0.998680i	$0.516356\pi$
$752$	−3.43983e6	+	4.73452e6i	−0.221816	+	0.305303i
$753$		0			0
$754$	−1.28619e7	+	4.17908e6i	−0.823903	+	0.267702i
$755$	5.03803e6	+	3.66035e6i	0.321658	+	0.233698i
$756$		0			0
$757$	7.94908e6	−	2.44648e7i	0.504170	−	1.55168i	−0.297991	−	0.954569i	$-0.596317\pi$
$757$	7.94908e6	−	2.44648e7i	0.504170	−	1.55168i	0.802161	−	0.597108i	$-0.203683\pi$
$758$	7.12420e6			0.450364
$759$		0			0
$760$	−5.43149e6			−0.341103
$761$	−552708.	+	1.70106e6i	−0.0345967	+	0.106478i	−0.966864	−	0.255294i	$-0.917828\pi$
$761$	−552708.	+	1.70106e6i	−0.0345967	+	0.106478i	0.932267	+	0.361771i	$0.117828\pi$
$762$		0			0
$763$	4.64522e6	+	3.37495e6i	0.288865	+	0.209873i
$764$	−4.87407e6	+	1.58368e6i	−0.302105	+	0.0981599i
$765$		0			0
$766$	−1.15860e6	+	1.59468e6i	−0.0713447	+	0.0981975i
$767$	2.72223e7	−	1.97781e7i	1.67084	−	1.21394i
$768$		0			0
$769$			5.67507e6i			0.346063i	0.984916	+	0.173032i	$0.0553563\pi$
$769$			5.67507e6i			0.346063i	−0.984916	+	0.173032i	$0.944644\pi$
$770$	−4.68032e6	−	300059.i	−0.284478	−	0.0182381i
$771$		0			0
$772$	7.29905e6	+	2.37160e6i	0.440781	+	0.143218i
$773$	2.79684e6	+	3.84952e6i	0.168352	+	0.231717i	0.884854	−	0.465868i	$-0.154258\pi$
$773$	2.79684e6	+	3.84952e6i	0.168352	+	0.231717i	−0.716502	+	0.697585i	$0.754258\pi$
$774$		0			0
$775$	5.28680e6	+	1.62711e7i	0.316183	+	0.973111i
$776$	−178562.	−	549558.i	−0.0106447	−	0.0327611i
$777$		0			0
$778$	−4.53808e6	−	6.24613e6i	−0.268796	−	0.369966i
$779$	−1.28996e7	−	4.19132e6i	−0.761608	−	0.247461i
$780$		0			0
$781$	−9.57194e6	+	1.15425e7i	−0.561529	+	0.677128i
$782$		−	2.08671e6i		−	0.122024i
$783$		0			0
$784$	−1.55107e6	+	1.12692e6i	−0.0901239	+	0.0654789i
$785$	−4.63484e6	+	6.37931e6i	−0.268448	+	0.369487i
$786$		0			0
$787$	−3.34242e6	+	1.08602e6i	−0.192364	+	0.0625029i	−0.403615	−	0.914929i	$-0.632246\pi$
$787$	−3.34242e6	+	1.08602e6i	−0.192364	+	0.0625029i	0.211251	+	0.977432i	$0.432246\pi$
$788$	−6.73816e6	−	4.89556e6i	−0.386568	−	0.280858i
$789$		0			0
$790$	3.37093e6	−	1.03746e7i	0.192168	−	0.591433i
$791$	−4.14201e6			−0.235380
$792$		0			0
$793$	2.60508e7			1.47109
$794$	−3.77221e6	+	1.16097e7i	−0.212346	+	0.653535i
$795$		0			0
$796$	−5.62543e6	−	4.08712e6i	−0.314683	−	0.228631i
$797$	2.04576e7	−	6.64708e6i	1.14080	−	0.370668i	0.323129	−	0.946355i	$-0.395265\pi$
$797$	2.04576e7	−	6.64708e6i	1.14080	−	0.370668i	0.817670	+	0.575687i	$0.195265\pi$
$798$		0			0
$799$	7.47489e6	−	1.02883e7i	0.414226	−	0.570134i
$800$	1.82994e6	−	1.32953e6i	0.101091	−	0.0734470i
$801$		0			0
$802$		−	2.42881e7i		−	1.33339i
$803$	−1.81428e6	+	2.82991e7i	−0.0992920	+	1.54876i
$804$		0			0
$805$	−2.60570e6	−	846645.i	−0.141721	−	0.0460481i
$806$	1.54015e7	+	2.11983e7i	0.835075	+	1.14938i
$807$		0			0
$808$	151344.	+	465789.i	0.00815525	+	0.0250993i
$809$	6.44781e6	+	1.98443e7i	0.346371	+	1.06602i	0.960846	+	0.277083i	$0.0893677\pi$
$809$	6.44781e6	+	1.98443e7i	0.346371	+	1.06602i	−0.614475	+	0.788936i	$0.710632\pi$
$810$		0			0
$811$	−3.36112e6	−	4.62618e6i	−0.179445	−	0.246985i	0.709814	−	0.704390i	$-0.248779\pi$
$811$	−3.36112e6	−	4.62618e6i	−0.179445	−	0.246985i	−0.889259	+	0.457405i	$0.848779\pi$
$812$	−5.87176e6	−	1.90785e6i	−0.312520	−	0.101544i
$813$		0			0
$814$	−5.24429e6	+	1.31996e7i	−0.277412	+	0.698232i
$815$		−	6.16892e6i		−	0.325323i
$816$		0			0
$817$	−5.38333e7	+	3.91122e7i	−2.82160	+	2.05002i
$818$	8.16224e6	−	1.12344e7i	0.426507	−	0.587037i
$819$		0			0
$820$	−2.22787e6	+	723877.i	−0.115706	+	0.0375950i
$821$	−2.02412e7	−	1.47061e7i	−1.04804	−	0.761448i	−0.0762034	−	0.997092i	$-0.524280\pi$
$821$	−2.02412e7	−	1.47061e7i	−1.04804	−	0.761448i	−0.971839	+	0.235645i	$0.924280\pi$
$822$		0			0
$823$	−3.16202e6	+	9.73171e6i	−0.162729	+	0.500829i	−0.998862	−	0.0476984i	$-0.984811\pi$
$823$	−3.16202e6	+	9.73171e6i	−0.162729	+	0.500829i	0.836133	+	0.548527i	$0.184811\pi$
$824$	−1.93170e6			−0.0991111
$825$		0			0
$826$	1.53614e7			0.783395
$827$	1.17318e7	−	3.61068e7i	0.596487	−	1.83580i	0.0493072	−	0.998784i	$-0.484299\pi$
$827$	1.17318e7	−	3.61068e7i	0.596487	−	1.83580i	0.547180	−	0.837015i	$-0.315701\pi$
$828$		0			0
$829$	1.34430e7	+	9.76690e6i	0.679375	+	0.493595i	0.873150	−	0.487451i	$-0.162073\pi$
$829$	1.34430e7	+	9.76690e6i	0.679375	+	0.493595i	−0.193775	+	0.981046i	$0.562073\pi$
$830$	−7.59651e6	+	2.46825e6i	−0.382753	+	0.124364i
$831$		0			0
$832$	2.03626e6	−	2.80267e6i	0.101982	−	0.140366i
$833$	3.37052e6	−	2.44883e6i	0.168300	−	0.122277i
$834$		0			0
$835$			575298.i			0.0285546i
$836$	−9.62903e6	−	1.52129e7i	−0.476504	−	0.752831i
$837$		0			0
$838$	2.13507e7	+	6.93725e6i	1.05027	+	0.341254i
$839$	−5.21460e6	−	7.17728e6i	−0.255750	−	0.352010i	0.661764	−	0.749712i	$-0.269808\pi$
$839$	−5.21460e6	−	7.17728e6i	−0.255750	−	0.352010i	−0.917515	+	0.397702i	$0.869808\pi$
$840$		0			0
$841$	−1.40030e6	−	4.30969e6i	−0.0682703	−	0.210114i
$842$	−5.20227e6	−	1.60109e7i	−0.252879	−	0.778281i
$843$		0			0
$844$	1.32083e6	+	1.81797e6i	0.0638250	+	0.0878476i
$845$	9.90333e6	+	3.21779e6i	0.477133	+	0.155030i
$846$		0			0
$847$	−7.45691e6	−	1.36409e7i	−0.357150	−	0.653335i
$848$		−	3.26907e6i		−	0.156111i
$849$		0			0
$850$	−3.97654e6	+	2.88912e6i	−0.188781	+	0.137157i
$851$	−4.87707e6	+	6.71271e6i	−0.230853	+	0.317741i
$852$		0			0
$853$	2.52173e7	−	8.19359e6i	1.18666	−	0.385568i	0.351822	−	0.936067i	$-0.385562\pi$
$853$	2.52173e7	−	8.19359e6i	1.18666	−	0.385568i	0.834836	+	0.550499i	$0.185562\pi$
$854$	9.62150e6	+	6.99043e6i	0.451438	+	0.327989i
$855$		0			0
$856$	−182031.	+	560235.i	−0.00849106	+	0.0261328i
$857$	1.96228e7			0.912659			0.456330	−	0.889811i	$-0.349164\pi$
$857$	1.96228e7			0.912659			0.456330	+	0.889811i	$0.349164\pi$
$858$		0			0
$859$	2.18177e7			1.00885			0.504425	−	0.863456i	$-0.331705\pi$
$859$	2.18177e7			1.00885			0.504425	+	0.863456i	$0.331705\pi$
$860$	−3.55132e6	+	1.09298e7i	−0.163736	+	0.503927i
$861$		0			0
$862$	20532.6	+	14917.8i	0.000941188	+	0.000683813i
$863$	−3.26010e7	+	1.05927e7i	−1.49006	+	0.484149i	−0.937100	−	0.349060i	$-0.886501\pi$
$863$	−3.26010e7	+	1.05927e7i	−1.49006	+	0.484149i	−0.552958	+	0.833209i	$0.686501\pi$
$864$		0			0
$865$	−7.68539e6	+	1.05780e7i	−0.349241	+	0.480690i
$866$	1.89386e6	−	1.37597e6i	0.0858131	−	0.0623469i
$867$		0			0
$868$			1.19621e7i			0.538901i
$869$	3.50341e7	−	8.95077e6i	1.57377	−	0.402078i
$870$		0			0
$871$	1.21093e7	+	3.93454e6i	0.540844	+	0.175731i
$872$	2.23764e6	+	3.07985e6i	0.0996549	+	0.137163i
$873$		0			0
$874$	−3.25020e6	−	1.00031e7i	−0.143923	−	0.442950i
$875$	4.81563e6	+	1.48210e7i	0.212634	+	0.654421i
$876$		0			0
$877$	7.65870e6	+	1.05413e7i	0.336245	+	0.462802i	0.943340	−	0.331827i	$-0.107665\pi$
$877$	7.65870e6	+	1.05413e7i	0.336245	+	0.462802i	−0.607095	+	0.794629i	$0.707665\pi$
$878$	−1.81416e6	−	589456.i	−0.0794217	−	0.0258057i
$879$		0			0
$880$	−2.88976e6	−	1.14812e6i	−0.125793	−	0.0499782i
$881$			3.75131e7i			1.62833i	0.580632	+	0.814166i	$0.302806\pi$
$881$			3.75131e7i			1.62833i	−0.580632	+	0.814166i	$0.697194\pi$
$882$		0			0
$883$	−7.54574e6	+	5.48230e6i	−0.325687	+	0.236625i	−0.738598	−	0.674146i	$-0.764512\pi$
$883$	−7.54574e6	+	5.48230e6i	−0.325687	+	0.236625i	0.412911	+	0.910771i	$0.364512\pi$
$884$	−4.42486e6	+	6.09030e6i	−0.190445	+	0.262125i
$885$		0			0
$886$	7.94540e6	−	2.58162e6i	0.340041	−	0.110486i
$887$	3.40041e6	+	2.47054e6i	0.145118	+	0.105435i	0.657976	−	0.753039i	$-0.271413\pi$
$887$	3.40041e6	+	2.47054e6i	0.145118	+	0.105435i	−0.512857	+	0.858474i	$0.671413\pi$
$888$		0			0
$889$	−333237.	+	1.02560e6i	−0.0141416	+	0.0435234i
$890$	1.41145e7			0.597299
$891$		0			0
$892$	4.02368e6			0.169321
$893$	1.98077e7	−	6.09618e7i	0.831199	−	2.55817i
$894$		0			0
$895$	−2.86019e6	−	2.07805e6i	−0.119354	−	0.0867159i
$896$	1.50413e6	−	488720.i	0.0625913	−	0.0203371i
$897$		0			0
$898$	7.84032e6	−	1.07913e7i	0.324446	−	0.446562i
$899$	2.50479e7	−	1.81984e7i	1.03365	−	0.750989i
$900$		0			0
$901$			7.10381e6i			0.291527i
$902$	−5.97709e6	−	4.95668e6i	−0.244609	−	0.202850i
$903$		0			0
$904$	−2.61180e6	−	848625.i	−0.106296	−	0.0345378i
$905$	1.74521e6	+	2.40207e6i	0.0708313	+	0.0974910i
$906$		0			0
$907$	−4.68836e6	−	1.44293e7i	−0.189236	−	0.582408i	0.810760	−	0.585379i	$-0.199054\pi$
$907$	−4.68836e6	−	1.44293e7i	−0.189236	−	0.582408i	−0.999996	+	0.00297117i	$0.999054\pi$
$908$	−4.92090e6	−	1.51450e7i	−0.198075	−	0.609613i
$909$		0			0
$910$	5.80974e6	+	7.99643e6i	0.232570	+	0.320105i
$911$	4.47079e7	+	1.45265e7i	1.78480	+	0.579915i	0.999244	−	0.0388806i	$-0.0123792\pi$
$911$	4.47079e7	+	1.45265e7i	1.78480	+	0.579915i	0.785552	+	0.618796i	$0.212379\pi$
$912$		0			0
$913$	−2.03805e7	−	1.69011e7i	−0.809166	−	0.671025i
$914$		−	1.08205e7i		−	0.428431i
$915$		0			0
$916$	6.19740e6	−	4.50268e6i	0.244046	−	0.177310i
$917$	−1.38212e7	+	1.90232e7i	−0.542777	+	0.747069i
$918$		0			0
$919$	−3.24916e7	+	1.05572e7i	−1.26906	+	0.412342i	−0.864714	−	0.502264i	$-0.832501\pi$
$919$	−3.24916e7	+	1.05572e7i	−1.26906	+	0.412342i	−0.404345	+	0.914606i	$0.632501\pi$
$920$	−1.46960e6	−	1.06773e6i	−0.0572439	−	0.0415901i
$921$		0			0
$922$	5.03454e6	−	1.54947e7i	0.195044	−	0.600283i
$923$	3.16023e7			1.22100
$924$		0			0
$925$	1.95445e7			0.751054
$926$	−1.79825e6	+	5.53443e6i	−0.0689162	+	0.212102i
$927$		0			0
$928$	−3.31163e6	−	2.40604e6i	−0.126233	−	0.0917134i
$929$	6.81349e6	−	2.21384e6i	0.259018	−	0.0841602i	−0.176629	−	0.984277i	$-0.556519\pi$
$929$	6.81349e6	−	2.21384e6i	0.259018	−	0.0841602i	0.435648	+	0.900117i	$0.356519\pi$
$930$		0			0
$931$	1.23431e7	−	1.69888e7i	0.466713	−	0.642375i
$932$	3.90014e6	−	2.83362e6i	0.147075	−	0.106857i
$933$		0			0
$934$		−	3.14023e7i		−	1.17786i
$935$	6.27955e6	+	2.49491e6i	0.234909	+	0.0933309i
$936$		0			0
$937$	−9.54430e6	−	3.10113e6i	−0.355136	−	0.115391i	0.126015	−	0.992028i	$-0.459781\pi$
$937$	−9.54430e6	−	3.10113e6i	−0.355136	−	0.115391i	−0.481151	+	0.876638i	$0.659781\pi$
$938$	3.41660e6	+	4.70254e6i	0.126790	+	0.174512i
$939$		0			0
$940$	−3.42096e6	−	1.05286e7i	−0.126278	−	0.388644i
$941$	6.82529e6	+	2.10061e7i	0.251274	+	0.773341i	0.994541	+	0.104346i	$0.0332750\pi$
$941$	6.82529e6	+	2.10061e7i	0.251274	+	0.773341i	−0.743267	+	0.668995i	$0.766725\pi$
$942$		0			0
$943$	−2.66630e6	−	3.66985e6i	−0.0976406	−	0.134391i
$944$	9.68633e6	+	3.14728e6i	0.353777	+	0.114949i
$945$		0			0
$946$	−3.69090e7	+	9.42977e6i	−1.34092	+	0.342589i
$947$			4.68339e6i			0.169701i	0.996394	+	0.0848506i	$0.0270413\pi$
$947$			4.68339e6i			0.169701i	−0.996394	+	0.0848506i	$0.972959\pi$
$948$		0			0
$949$	4.83496e7	−	3.51281e7i	1.74272	−	1.26616i
$950$	−1.45623e7	+	2.00434e7i	−0.523507	+	0.720545i
$951$		0			0
$952$	−3.26852e6	+	1.06201e6i	−0.116885	+	0.0379783i
$953$	−3.10454e7	−	2.25558e7i	−1.10730	−	0.804501i	−0.125064	−	0.992149i	$-0.539914\pi$
$953$	−3.10454e7	−	2.25558e7i	−1.10730	−	0.804501i	−0.982236	+	0.187648i	$0.939914\pi$
$954$		0			0
$955$	2.99581e6	−	9.22015e6i	0.106293	−	0.327137i
$956$	2.50893e7			0.887859
$957$		0			0
$958$	−2.33173e7			−0.820853
$959$	−1.09309e7	+	3.36419e7i	−0.383804	+	1.18123i
$960$		0			0
$961$	−2.53694e7	−	1.84319e7i	−0.886139	−	0.643817i
$962$	2.84686e7	−	9.25000e6i	0.991809	−	0.322258i
$963$		0			0
$964$	1.33670e6	−	1.83980e6i	0.0463276	−	0.0637645i
$965$	−1.17453e7	+	8.53346e6i	−0.406018	+	0.294990i
$966$		0			0
$967$		−	4.86478e6i		−	0.167301i	−0.996495	−	0.0836503i	$-0.973342\pi$
$967$		−	4.86478e6i		−	0.167301i	0.996495	−	0.0836503i	$-0.0266579\pi$
$968$	−1.90726e6	−	1.01293e7i	−0.0654217	−	0.347448i
$969$		0			0
$970$	1.03958e6	+	337782.i	0.0354757	+	0.0115267i
$971$	−1.90540e7	−	2.62256e7i	−0.648542	−	0.892642i	0.350493	−	0.936566i	$-0.386014\pi$
$971$	−1.90540e7	−	2.62256e7i	−0.648542	−	0.892642i	−0.999035	+	0.0439236i	$0.986014\pi$
$972$		0			0
$973$	−9.38358e6	−	2.88797e7i	−0.317751	−	0.977936i
$974$	5.74864e6	+	1.76925e7i	0.194163	+	0.597574i
$975$		0			0
$976$	4.63475e6	+	6.37918e6i	0.155740	+	0.214358i
$977$	−7.24065e6	−	2.35263e6i	−0.242684	−	0.0788528i	0.185150	−	0.982710i	$-0.440723\pi$
$977$	−7.24065e6	−	2.35263e6i	−0.242684	−	0.0788528i	−0.427834	+	0.903858i	$0.640723\pi$
$978$		0			0
$979$	2.50225e7	+	3.95331e7i	0.834398	+	1.31827i
$980$		−	3.62676e6i		−	0.120630i
$981$		0			0
$982$	3.55932e6	−	2.58599e6i	0.117784	−	0.0855754i
$983$	2.07421e7	−	2.85490e7i	0.684650	−	0.942340i	−0.315328	−	0.948983i	$-0.602115\pi$
$983$	2.07421e7	−	2.85490e7i	0.684650	−	0.942340i	0.999978	+	0.00664299i	$0.00211455\pi$
$984$		0			0
$985$	1.49843e7	−	4.86869e6i	0.492091	−	0.159890i
$986$	7.19629e6	+	5.22841e6i	0.235731	+	0.171269i
$987$		0			0
$988$	−1.17254e7	+	3.60872e7i	−0.382152	+	1.17614i
$989$	−2.22544e7			−0.723477
$990$		0			0
$991$	−2.37257e7			−0.767424			−0.383712	−	0.923453i	$-0.625355\pi$
$991$	−2.37257e7			−0.767424			−0.383712	+	0.923453i	$0.625355\pi$
$992$	−2.45083e6	+	7.54287e6i	−0.0790739	+	0.243365i
$993$		0			0
$994$	1.16719e7	+	8.48011e6i	0.374692	+	0.272230i
$995$	1.25098e7	−	4.06469e6i	0.400584	−	0.130158i
$996$		0			0
$997$	1.15042e7	−	1.58342e7i	0.366537	−	0.504495i	−0.585418	−	0.810731i	$-0.699070\pi$
$997$	1.15042e7	−	1.58342e7i	0.366537	−	0.504495i	0.951956	+	0.306236i	$0.0990697\pi$
$998$	2.92053e7	−	2.12189e7i	0.928187	−	0.674367i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.6.l.a.17.4	✓	40	11.6	odd	10
198.6.l.a.35.4	yes	40	3.2	odd	2
198.6.l.b.17.7	yes	40	33.17	even	10	inner
198.6.l.b.35.7	yes	40	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-1.23607 + 3.80423i) q^{2} +(-12.9443 - 9.40456i) q^{4} +(28.7854 - 9.35295i) q^{5} +(56.7383 - 78.0936i) q^{7} +(51.7771 - 37.6183i) q^{8} +O(q^{10})\)	\(q+(-1.23607 + 3.80423i) q^{2} +(-12.9443 - 9.40456i) q^{4} +(28.7854 - 9.35295i) q^{5} +(56.7383 - 78.0936i) q^{7} +(51.7771 - 37.6183i) q^{8} +121.067i q^{10} +(-339.095 + 214.630i) q^{11} +(804.378 + 261.358i) q^{13} +(226.953 + 312.374i) q^{14} +(79.1084 + 243.470i) q^{16} +(-171.905 - 529.070i) q^{17} +(-1648.13 - 2268.46i) q^{19} +(-460.567 - 149.647i) q^{20} +(-397.356 - 1555.29i) q^{22} -937.766i q^{23} +(-1787.05 + 1298.37i) q^{25} +(-1988.53 + 2736.98i) q^{26} +(-1468.87 + 477.266i) q^{28} +(3234.01 + 2349.65i) q^{29} +(2393.38 - 7366.08i) q^{31} -1024.00 q^{32} +2225.19 q^{34} +(902.831 - 2778.63i) q^{35} +(-7158.19 - 5200.73i) q^{37} +(10666.9 - 3465.89i) q^{38} +(1138.58 - 1567.13i) q^{40} +(3913.40 - 2843.25i) q^{41} -23731.3i q^{43} +(6407.83 + 410.811i) q^{44} +(3567.47 + 1159.14i) q^{46} +(13436.8 + 18494.2i) q^{47} +(2314.28 + 7122.61i) q^{49} +(-2730.38 - 8403.24i) q^{50} +(-7954.13 - 10947.9i) q^{52} +(-12144.8 - 3946.09i) q^{53} +(-7753.56 + 9349.74i) q^{55} -6177.86i q^{56} +(-12936.0 + 9398.59i) q^{58} +(23384.7 - 32186.3i) q^{59} +(29293.7 - 9518.09i) q^{61} +(25063.9 + 18210.0i) q^{62} +(1265.73 - 3895.53i) q^{64} +25598.8 q^{65} +15054.2 q^{67} +(-2750.49 + 8465.13i) q^{68} +(9454.57 + 6869.15i) q^{70} +(35536.2 - 11546.4i) q^{71} +(41533.6 - 57166.2i) q^{73} +(28632.8 - 20802.9i) q^{74} +44863.4i q^{76} +(-2478.45 + 38658.8i) q^{77} +(-85693.3 - 27843.4i) q^{79} +(4554.34 + 6268.51i) q^{80} +(5979.14 + 18401.9i) q^{82} +(20387.5 + 62746.2i) q^{83} +(-9896.74 - 13621.7i) q^{85} +(90279.1 + 29333.5i) q^{86} +(-9483.33 + 23869.0i) q^{88} -116584. i q^{89} +(66049.5 - 47987.8i) q^{91} +(-8819.28 + 12138.7i) q^{92} +(-86965.1 + 28256.7i) q^{94} +(-68658.9 - 49883.6i) q^{95} +(2790.03 - 8586.84i) q^{97} -29956.6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 160 q^{4} + 640 q^{8}+O(q^{10}) \) 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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