LMFDB - Embedded newform 198.6.l.b.35.5

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			35.5
Character	$\chi$	$=$	198.35
Dual form			198.6.l.b.17.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23607 + 3.80423i) q^{2} +(-12.9443 - 9.40456i) q^{4} +(-11.5390 + 3.74924i) q^{5} +(-64.3821 + 88.6144i) q^{7} +(51.7771 - 37.6183i) q^{8} +O(q^{10})$	\(q+(-1.23607 + 3.80423i) q^{2} +(-12.9443 - 9.40456i) q^{4} +(-11.5390 + 3.74924i) q^{5} +(-64.3821 + 88.6144i) q^{7} +(51.7771 - 37.6183i) q^{8} -48.5312i q^{10} +(27.8454 + 400.344i) q^{11} +(-158.649 - 51.5482i) q^{13} +(-257.528 - 354.457i) q^{14} +(79.1084 + 243.470i) q^{16} +(-106.424 - 327.538i) q^{17} +(1272.65 + 1751.65i) q^{19} +(184.624 + 59.9879i) q^{20} +(-1557.42 - 388.923i) q^{22} -2372.55i q^{23} +(-2409.09 + 1750.30i) q^{25} +(392.202 - 539.819i) q^{26} +(1666.76 - 541.563i) q^{28} +(-6170.11 - 4482.85i) q^{29} +(1367.21 - 4207.83i) q^{31} -1024.00 q^{32} +1377.58 q^{34} +(410.667 - 1263.90i) q^{35} +(-473.366 - 343.921i) q^{37} +(-8236.75 + 2676.28i) q^{38} +(-456.415 + 628.202i) q^{40} +(-377.484 + 274.258i) q^{41} -5420.66i q^{43} +(3404.63 - 5444.04i) q^{44} +(9025.71 + 2932.63i) q^{46} +(-14952.3 - 20580.1i) q^{47} +(1486.20 + 4574.05i) q^{49} +(-3680.76 - 11328.2i) q^{50} +(1568.81 + 2159.28i) q^{52} +(-21780.0 - 7076.74i) q^{53} +(-1822.30 - 4515.17i) q^{55} +7010.14i q^{56} +(24680.4 - 17931.4i) q^{58} +(24681.1 - 33970.6i) q^{59} +(13735.2 - 4462.85i) q^{61} +(14317.6 + 10402.3i) q^{62} +(1265.73 - 3895.53i) q^{64} +2023.91 q^{65} +36674.1 q^{67} +(-1702.78 + 5240.61i) q^{68} +(4300.56 + 3124.54i) q^{70} +(-9569.10 + 3109.19i) q^{71} +(36204.6 - 49831.3i) q^{73} +(1893.46 - 1375.68i) q^{74} -34642.5i q^{76} +(-37269.0 - 23307.5i) q^{77} +(-59921.9 - 19469.8i) q^{79} +(-1825.66 - 2512.81i) q^{80} +(-576.744 - 1775.04i) q^{82} +(611.792 + 1882.90i) q^{83} +(2456.04 + 3380.45i) q^{85} +(20621.4 + 6700.30i) q^{86} +(16502.0 + 19681.2i) q^{88} -52615.8i q^{89} +(14782.1 - 10739.8i) q^{91} +(-22312.8 + 30710.9i) q^{92} +(96773.4 - 31443.6i) q^{94} +(-21252.4 - 15440.8i) q^{95} +(-29779.3 + 91651.3i) q^{97} -19237.8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

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

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
$5$	−11.5390	+	3.74924i	−0.206416	+	0.0670685i	−0.410400	−	0.911906i	$-0.634611\pi$
$5$	−11.5390	+	3.74924i	−0.206416	+	0.0670685i	0.203984	+	0.978974i	$0.434611\pi$
$6$		0			0
$7$	−64.3821	+	88.6144i	−0.496615	+	0.683532i	−0.981591	−	0.190995i	$-0.938828\pi$
$7$	−64.3821	+	88.6144i	−0.496615	+	0.683532i	0.484976	+	0.874528i	$0.338828\pi$
$8$	51.7771	−	37.6183i	0.286031	−	0.207813i
$9$		0			0
$10$		−	48.5312i		−	0.153469i
$11$	27.8454	+	400.344i	0.0693860	+	0.997590i
$11$	27.8454	+	400.344i	0.0693860	+	0.997590i
$12$		0			0
$13$	−158.649	−	51.5482i	−0.260363	−	0.0845970i	0.175927	−	0.984403i	$-0.443708\pi$
$13$	−158.649	−	51.5482i	−0.260363	−	0.0845970i	−0.436290	+	0.899806i	$0.643708\pi$
$14$	−257.528	−	354.457i	−0.351160	−	0.483330i
$15$		0			0
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	−106.424	−	327.538i	−0.0893133	−	0.274878i	0.896417	−	0.443212i	$-0.146161\pi$
$17$	−106.424	−	327.538i	−0.0893133	−	0.274878i	−0.985730	+	0.168334i	$0.946161\pi$
$18$		0			0
$19$	1272.65	+	1751.65i	0.808768	+	1.11317i	0.991512	+	0.130014i	$0.0415021\pi$
$19$	1272.65	+	1751.65i	0.808768	+	1.11317i	−0.182744	+	0.983161i	$0.558498\pi$
$20$	184.624	+	59.9879i	0.103208	+	0.0335343i
$21$		0			0
$22$	−1557.42	−	388.923i	−0.686039	−	0.171319i
$23$		−	2372.55i		−	0.935180i	−0.883945	−	0.467590i	$-0.845122\pi$
$23$		−	2372.55i		−	0.935180i	0.883945	−	0.467590i	$-0.154878\pi$
$24$		0			0
$25$	−2409.09	+	1750.30i	−0.770908	+	0.560097i
$26$	392.202	−	539.819i	0.113783	−	0.156608i
$27$		0			0
$28$	1666.76	−	541.563i	0.401770	−	0.130543i
$29$	−6170.11	−	4482.85i	−1.36238	−	0.989826i	−0.998290	−	0.0584621i	$-0.981380\pi$
$29$	−6170.11	−	4482.85i	−1.36238	−	0.989826i	−0.364089	−	0.931364i	$-0.618620\pi$
$30$		0			0
$31$	1367.21	−	4207.83i	0.255523	−	0.786418i	−0.738203	−	0.674578i	$-0.764326\pi$
$31$	1367.21	−	4207.83i	0.255523	−	0.786418i	0.993726	−	0.111840i	$-0.0356745\pi$
$32$	−1024.00			−0.176777
$33$		0			0
$34$	1377.58			0.204371
$35$	410.667	−	1263.90i	0.0566657	−	0.174399i
$36$		0			0
$37$	−473.366	−	343.921i	−0.0568451	−	0.0413004i	0.559000	−	0.829168i	$-0.311185\pi$
$37$	−473.366	−	343.921i	−0.0568451	−	0.0413004i	−0.615845	+	0.787867i	$0.711185\pi$
$38$	−8236.75	+	2676.28i	−0.925330	+	0.300658i
$39$		0			0
$40$	−456.415	+	628.202i	−0.0451035	+	0.0620796i
$41$	−377.484	+	274.258i	−0.0350703	+	0.0254800i	−0.605182	−	0.796087i	$-0.706900\pi$
$41$	−377.484	+	274.258i	−0.0350703	+	0.0254800i	0.570112	+	0.821567i	$0.306900\pi$
$42$		0			0
$43$		−	5420.66i		−	0.447076i	−0.974695	−	0.223538i	$-0.928239\pi$
$43$		−	5420.66i		−	0.447076i	0.974695	−	0.223538i	$-0.0717606\pi$
$44$	3404.63	−	5444.04i	0.265117	−	0.423926i
$45$		0			0
$46$	9025.71	+	2932.63i	0.628907	+	0.204344i
$47$	−14952.3	−	20580.1i	−0.987333	−	1.35895i	−0.932784	−	0.360436i	$-0.882628\pi$
$47$	−14952.3	−	20580.1i	−0.987333	−	1.35895i	−0.0545488	−	0.998511i	$-0.517372\pi$
$48$		0			0
$49$	1486.20	+	4574.05i	0.0884274	+	0.272151i
$50$	−3680.76	−	11328.2i	−0.208215	−	0.640820i
$51$		0			0
$52$	1568.81	+	2159.28i	0.0804565	+	0.110739i
$53$	−21780.0	−	7076.74i	−1.06504	−	0.346054i	−0.276488	−	0.961017i	$-0.589171\pi$
$53$	−21780.0	−	7076.74i	−1.06504	−	0.346054i	−0.788555	+	0.614964i	$0.789171\pi$
$54$		0			0
$55$	−1822.30	−	4515.17i	−0.0812292	−	0.201265i
$56$			7010.14i			0.298715i
$57$		0			0
$58$	24680.4	−	17931.4i	0.963347	−	0.699913i
$59$	24681.1	−	33970.6i	0.923070	−	1.27050i	−0.0394319	−	0.999222i	$-0.512555\pi$
$59$	24681.1	−	33970.6i	0.923070	−	1.27050i	0.962502	−	0.271275i	$-0.0874452\pi$
$60$		0			0
$61$	13735.2	−	4462.85i	0.472620	−	0.153563i	−0.0630161	−	0.998013i	$-0.520072\pi$
$61$	13735.2	−	4462.85i	0.472620	−	0.153563i	0.535636	+	0.844449i	$0.320072\pi$
$62$	14317.6	+	10402.3i	0.473031	+	0.343677i
$63$		0			0
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	2023.91			0.0594167
$66$		0			0
$67$	36674.1			0.998095			0.499048	−	0.866574i	$-0.333683\pi$
$67$	36674.1			0.998095			0.499048	+	0.866574i	$0.333683\pi$
$68$	−1702.78	+	5240.61i	−0.0446566	+	0.137439i
$69$		0			0
$70$	4300.56	+	3124.54i	0.104901	+	0.0762152i
$71$	−9569.10	+	3109.19i	−0.225281	+	0.0731983i	−0.419483	−	0.907763i	$-0.637788\pi$
$71$	−9569.10	+	3109.19i	−0.225281	+	0.0731983i	0.194201	+	0.980962i	$0.437788\pi$
$72$		0			0
$73$	36204.6	−	49831.3i	0.795163	−	1.09445i	−0.198283	−	0.980145i	$-0.563536\pi$
$73$	36204.6	−	49831.3i	0.795163	−	1.09445i	0.993446	−	0.114303i	$-0.0364636\pi$
$74$	1893.46	−	1375.68i	0.0401955	−	0.0292038i
$75$		0			0
$76$		−	34642.5i		−	0.687979i
$77$	−37269.0	−	23307.5i	−0.716343	−	0.447991i
$78$		0			0
$79$	−59921.9	−	19469.8i	−1.08023	−	0.350990i	−0.285769	−	0.958299i	$-0.592249\pi$
$79$	−59921.9	−	19469.8i	−1.08023	−	0.350990i	−0.794466	+	0.607309i	$0.792249\pi$
$80$	−1825.66	−	2512.81i	−0.0318930	−	0.0438969i
$81$		0			0
$82$	−576.744	−	1775.04i	−0.00947215	−	0.0291523i
$83$	611.792	+	1882.90i	0.00974784	+	0.0300008i	0.955812	−	0.293978i	$-0.0949793\pi$
$83$	611.792	+	1882.90i	0.00974784	+	0.0300008i	−0.946064	+	0.323979i	$0.894979\pi$
$84$		0			0
$85$	2456.04	+	3380.45i	0.0368713	+	0.0507490i
$86$	20621.4	+	6700.30i	0.300658	+	0.0976896i
$87$		0			0
$88$	16502.0	+	19681.2i	0.227159	+	0.270922i
$89$		−	52615.8i		−	0.704112i	−0.935979	−	0.352056i	$-0.885483\pi$
$89$		−	52615.8i		−	0.704112i	0.935979	−	0.352056i	$-0.114517\pi$
$90$		0			0
$91$	14782.1	−	10739.8i	0.187125	−	0.135954i
$92$	−22312.8	+	30710.9i	−0.274843	+	0.378288i
$93$		0			0
$94$	96773.4	−	31443.6i	1.12963	−	0.367039i
$95$	−21252.4	−	15440.8i	−0.241601	−	0.175534i
$96$		0			0
$97$	−29779.3	+	91651.3i	−0.321355	+	0.989030i	0.651704	+	0.758474i	$0.274055\pi$
$97$	−29779.3	+	91651.3i	−0.321355	+	0.989030i	−0.973059	+	0.230556i	$0.925945\pi$
$98$	−19237.8			−0.202344
$99$		0			0
$100$	47644.7			0.476447
$101$	20721.6	−	63774.5i	0.202125	−	0.622076i	−0.797694	−	0.603062i	$-0.793947\pi$
$101$	20721.6	−	63774.5i	0.202125	−	0.622076i	0.999819	−	0.0190142i	$-0.00605278\pi$
$102$		0			0
$103$	−112374.	−	81644.4i	−1.04369	−	0.758287i	−0.0726891	−	0.997355i	$-0.523158\pi$
$103$	−112374.	−	81644.4i	−1.04369	−	0.758287i	−0.971003	+	0.239068i	$0.923158\pi$
$104$	−10153.5	+	3299.08i	−0.0920521	+	0.0299095i
$105$		0			0
$106$	53843.0	−	74108.5i	0.465441	−	0.640625i
$107$	−35478.0	+	25776.3i	−0.299571	+	0.217651i	−0.727409	−	0.686205i	$-0.759275\pi$
$107$	−35478.0	+	25776.3i	−0.299571	+	0.217651i	0.427838	+	0.903856i	$0.359275\pi$
$108$		0			0
$109$			94949.0i			0.765463i	0.923860	+	0.382732i	$0.125017\pi$
$109$			94949.0i			0.765463i	−0.923860	+	0.382732i	$0.874983\pi$
$110$	19429.2	−	1351.37i	0.153099	−	0.0106486i
$111$		0			0
$112$	−26668.1	−	8665.00i	−0.200885	−	0.0652715i
$113$	−6812.13	−	9376.10i	−0.0501865	−	0.0690758i	0.783186	−	0.621787i	$-0.213593\pi$
$113$	−6812.13	−	9376.10i	−0.0501865	−	0.0690758i	−0.833373	+	0.552711i	$0.813593\pi$
$114$		0			0
$115$	8895.26	+	27376.8i	0.0627212	+	0.193036i
$116$	37708.4	+	116054.i	0.260191	+	0.800786i
$117$		0			0
$118$	98724.4	+	135883.i	0.652709	+	0.898377i
$119$	35876.4	+	11656.9i	0.232242	+	0.0754601i
$120$		0			0
$121$	−159500.	+	22295.5i	−0.990371	+	0.138438i
$122$			57768.4i			0.351391i
$123$		0			0
$124$	−57270.3	+	41609.3i	−0.334484	+	0.243017i
$125$	43522.0	−	59902.9i	0.249134	−	0.342904i
$126$		0			0
$127$	−200346.	+	65096.2i	−1.10223	+	0.358135i	−0.802959	−	0.596035i	$-0.796742\pi$
$127$	−200346.	+	65096.2i	−1.10223	+	0.358135i	−0.299267	+	0.954170i	$0.596742\pi$
$128$	13254.9	+	9630.27i	0.0715077	+	0.0519534i
$129$		0			0
$130$	−2501.70	+	7699.43i	−0.0129830	+	0.0399577i
$131$	128040.			0.651881			0.325941	−	0.945390i	$-0.394319\pi$
$131$	128040.			0.651881			0.325941	+	0.945390i	$0.394319\pi$
$132$		0			0
$133$	−237157.			−1.16254
$134$	−45331.6	+	139516.i	−0.218092	+	0.671218i
$135$		0			0
$136$	−17831.7	−	12955.5i	−0.0826697	−	0.0600630i
$137$	−175240.	+	56938.8i	−0.797685	+	0.259183i	−0.679373	−	0.733793i	$-0.737748\pi$
$137$	−175240.	+	56938.8i	−0.797685	+	0.259183i	−0.118312	+	0.992977i	$0.537748\pi$
$138$		0			0
$139$	−228652.	+	314713.i	−1.00378	+	1.38159i	−0.0808042	+	0.996730i	$0.525749\pi$
$139$	−228652.	+	314713.i	−1.00378	+	1.38159i	−0.922977	+	0.384856i	$0.874251\pi$
$140$	−17202.3	+	12498.2i	−0.0741763	+	0.0538923i
$141$		0			0
$142$		−	40246.2i		−	0.167496i
$143$	16219.4	−	64949.6i	0.0663275	−	0.265605i
$144$		0			0
$145$	88004.1	+	28594.3i	0.347603	+	0.112943i
$146$	144818.	+	199325.i	0.562265	+	0.773892i
$147$		0			0
$148$	2892.96	+	8903.61i	0.0108564	+	0.0334127i
$149$	107338.	+	330353.i	0.396085	+	1.21902i	0.928113	+	0.372298i	$0.121430\pi$
$149$	107338.	+	330353.i	0.396085	+	1.21902i	−0.532028	+	0.846727i	$0.678570\pi$
$150$		0			0
$151$	42530.2	+	58537.7i	0.151794	+	0.208927i	0.878141	−	0.478401i	$-0.158784\pi$
$151$	42530.2	+	58537.7i	0.151794	+	0.208927i	−0.726347	+	0.687328i	$0.758784\pi$
$152$	131788.	+	42820.5i	0.462665	+	0.150329i
$153$		0			0
$154$	134734.	−	112970.i	0.457800	−	0.383850i
$155$			53680.1i			0.179467i
$156$		0			0
$157$	−11487.6	+	8346.23i	−0.0371946	+	0.0270235i	−0.606227	−	0.795291i	$-0.707318\pi$
$157$	−11487.6	+	8346.23i	−0.0371946	+	0.0270235i	0.569033	+	0.822315i	$0.307318\pi$
$158$	148135.	−	203891.i	0.472080	−	0.649762i
$159$		0			0
$160$	11815.9	−	3839.23i	0.0364895	−	0.0118562i
$161$	210242.	+	152750.i	0.639226	+	0.464425i
$162$		0			0
$163$	−124400.	+	382863.i	−0.366733	+	1.12869i	0.582155	+	0.813078i	$0.302210\pi$
$163$	−124400.	+	382863.i	−0.366733	+	1.12869i	−0.948889	+	0.315611i	$0.897790\pi$
$164$	7465.54			0.0216746
$165$		0			0
$166$	−7919.20			−0.0223055
$167$	−28520.3	+	87776.5i	−0.0791340	+	0.243549i	−0.982795	−	0.184699i	$-0.940869\pi$
$167$	−28520.3	+	87776.5i	−0.0791340	+	0.243549i	0.903661	+	0.428248i	$0.140869\pi$
$168$		0			0
$169$	−277870.	−	201884.i	−0.748385	−	0.543733i
$170$	−15895.8	+	5164.87i	−0.0421853	+	0.0137068i
$171$		0			0
$172$	−50978.9	+	70166.5i	−0.131392	+	0.180846i
$173$	175628.	−	127601.i	0.446148	−	0.324145i	−0.341925	−	0.939727i	$-0.611079\pi$
$173$	175628.	−	127601.i	0.446148	−	0.324145i	0.788073	+	0.615582i	$0.211079\pi$
$174$		0			0
$175$		−	326168.i		−	0.805093i
$176$	−95269.2	+	38450.1i	−0.231831	+	0.0935656i
$177$		0			0
$178$	200163.	+	65036.8i	0.473514	+	0.153854i
$179$	−187751.	−	258418.i	−0.437976	−	0.602823i	0.531784	−	0.846880i	$-0.321522\pi$
$179$	−187751.	−	258418.i	−0.437976	−	0.602823i	−0.969761	+	0.244057i	$0.921522\pi$
$180$		0			0
$181$	−21717.5	−	66839.7i	−0.0492736	−	0.151649i	0.923392	−	0.383858i	$-0.125405\pi$
$181$	−21717.5	−	66839.7i	−0.0492736	−	0.151649i	−0.972666	+	0.232209i	$0.925405\pi$
$182$	22585.0	+	69509.4i	0.0505407	+	0.155548i
$183$		0			0
$184$	−89251.1	−	122844.i	−0.194343	−	0.267490i
$185$	6751.61	+	2193.73i	0.0145037	+	0.00471253i
$186$		0			0
$187$	128165.	−	51726.6i	0.268018	−	0.108171i
$188$			407014.i			0.839875i
$189$		0			0
$190$	85009.7	−	61763.2i	0.170838	−	0.124121i
$191$	−293087.	+	403400.i	−0.581318	+	0.800116i	−0.993839	−	0.110832i	$-0.964648\pi$
$191$	−293087.	+	403400.i	−0.581318	+	0.800116i	0.412521	+	0.910948i	$0.364648\pi$
$192$		0			0
$193$	433561.	−	140873.i	0.837833	−	0.272228i	0.141492	−	0.989939i	$-0.454810\pi$
$193$	433561.	−	140873.i	0.837833	−	0.272228i	0.696341	+	0.717711i	$0.254810\pi$
$194$	−311853.	−	226575.i	−0.594902	−	0.432222i
$195$		0			0
$196$	23779.2	−	73184.8i	0.0442137	−	0.136076i
$197$	340274.			0.624687			0.312344	−	0.949969i	$-0.398886\pi$
$197$	340274.			0.624687			0.312344	+	0.949969i	$0.398886\pi$
$198$		0			0
$199$	−195141.			−0.349313			−0.174657	−	0.984629i	$-0.555882\pi$
$199$	−195141.			−0.349313			−0.174657	+	0.984629i	$0.555882\pi$
$200$	−58892.1	+	181251.i	−0.104108	+	0.320410i
$201$		0			0
$202$	216999.	+	157659.i	0.374179	+	0.271857i
$203$	794489.	−	258145.i	1.35316	−	0.439667i
$204$		0			0
$205$	3327.52	−	4579.94i	0.00553014	−	0.00761159i
$206$	449496.	−	326578.i	0.738002	−	0.536190i
$207$		0			0
$208$		−	42704.2i		−	0.0684404i
$209$	−665825.	+	558273.i	−1.05437	+	0.884058i
$210$		0			0
$211$	−533996.	−	173506.i	−0.825718	−	0.268292i	−0.134477	−	0.990917i	$-0.542936\pi$
$211$	−533996.	−	173506.i	−0.825718	−	0.268292i	−0.691241	+	0.722625i	$0.742936\pi$
$212$	215372.	+	296434.i	0.329116	+	0.452990i
$213$		0			0
$214$	−54205.5	−	166827.i	−0.0809113	−	0.249019i
$215$	20323.4	+	62548.9i	0.0299847	+	0.0922834i
$216$		0			0
$217$	284850.	+	392063.i	0.410646	+	0.565205i
$218$	−361208.	−	117363.i	−0.514773	−	0.167260i
$219$		0			0
$220$	−18874.9	+	75583.5i	−0.0262923	+	0.105286i
$221$			57449.5i			0.0791236i
$222$		0			0
$223$	1.17384e6	−	852847.i	1.58070	−	1.14844i	0.664803	−	0.747019i	$-0.268516\pi$
$223$	1.17384e6	−	852847.i	1.58070	−	1.14844i	0.915893	−	0.401423i	$-0.131484\pi$
$224$	65927.3	−	90741.1i	0.0877900	−	0.120833i
$225$		0			0
$226$	44089.0	−	14325.4i	0.0574195	−	0.0186567i
$227$	−857615.	−	623094.i	−1.10466	−	0.802581i	−0.122844	−	0.992426i	$-0.539201\pi$
$227$	−857615.	−	623094.i	−1.10466	−	0.802581i	−0.981814	+	0.189845i	$0.939201\pi$
$228$		0			0
$229$	187194.	−	576125.i	0.235887	−	0.725985i	−0.761116	−	0.648616i	$-0.775348\pi$
$229$	187194.	−	576125.i	0.235887	−	0.725985i	0.997003	−	0.0773690i	$-0.0246520\pi$
$230$	−115143.			−0.143521
$231$		0			0
$232$	−488107.			−0.595381
$233$	280631.	−	863692.i	0.338645	−	1.04224i	−0.626253	−	0.779620i	$-0.715412\pi$
$233$	280631.	−	863692.i	0.338645	−	1.04224i	0.964898	−	0.262624i	$-0.0845877\pi$
$234$		0			0
$235$	249694.	+	181413.i	0.294944	+	0.214289i
$236$	−638958.	+	207610.i	−0.746779	+	0.242643i
$237$		0			0
$238$	−88691.3	+	122073.i	−0.101494	+	0.139694i
$239$	906990.	−	658967.i	1.02709	−	0.746223i	0.0593645	−	0.998236i	$-0.481093\pi$
$239$	906990.	−	658967.i	1.02709	−	0.746223i	0.967724	+	0.252013i	$0.0810926\pi$
$240$		0			0
$241$			793911.i			0.880500i	0.897875	+	0.440250i	$0.145110\pi$
$241$			793911.i			0.880500i	−0.897875	+	0.440250i	$0.854890\pi$
$242$	112336.	−	634334.i	0.123305	−	0.696273i
$243$		0			0
$244$	−219764.	−	71405.6i	−0.236310	−	0.0767817i
$245$	−34298.5	−	47207.8i	−0.0365056	−	0.0502456i
$246$		0			0
$247$	−111610.	−	343500.i	−0.116402	−	0.358248i
$248$	−87501.2	−	269301.i	−0.0903410	−	0.278041i
$249$		0			0
$250$	174088.	+	239612.i	0.176165	+	0.242470i
$251$	−183277.	−	59550.2i	−0.183621	−	0.0596622i	0.215763	−	0.976446i	$-0.430776\pi$
$251$	−183277.	−	59550.2i	−0.183621	−	0.0596622i	−0.399384	+	0.916784i	$0.630776\pi$
$252$		0			0
$253$	949836.	−	66064.6i	0.932926	−	0.0648884i
$254$		−	842623.i		−	0.819500i
$255$		0			0
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	−208387.	+	286820.i	−0.196806	+	0.270880i	−0.896002	−	0.444050i	$-0.853541\pi$
$257$	−208387.	+	286820.i	−0.196806	+	0.270880i	0.699196	+	0.714930i	$0.253541\pi$
$258$		0			0
$259$	60952.6	−	19804.7i	0.0564603	−	0.0183451i
$260$	−26198.1	−	19034.0i	−0.0240346	−	0.0174621i
$261$		0			0
$262$	−158267.	+	487094.i	−0.142441	+	0.438389i
$263$	−11186.2			−0.00997227			−0.00498614	−	0.999988i	$-0.501587\pi$
$263$	−11186.2			−0.00997227			−0.00498614	+	0.999988i	$0.501587\pi$
$264$		0			0
$265$	277851.			0.243051
$266$	293142.	−	902199.i	0.254024	−	0.781804i
$267$		0			0
$268$	−474719.	−	344904.i	−0.403738	−	0.293333i
$269$	−1.92738e6	+	626243.i	−1.62400	+	0.527670i	−0.972881	−	0.231305i	$-0.925700\pi$
$269$	−1.92738e6	+	626243.i	−1.62400	+	0.527670i	−0.651119	+	0.758975i	$0.725700\pi$
$270$		0			0
$271$	−240151.	+	330539.i	−0.198637	+	0.273401i	−0.896703	−	0.442633i	$-0.854044\pi$
$271$	−240151.	+	330539.i	−0.198637	+	0.273401i	0.698066	+	0.716034i	$0.254044\pi$
$272$	71326.9	−	51822.0i	0.0584563	−	0.0424710i
$273$		0			0
$274$		−	737032.i		−	0.593075i
$275$	−767806.	−	915726.i	−0.612238	−	0.730187i
$276$		0			0
$277$	1.40649e6	+	456995.i	1.10138	+	0.357859i	0.802633	−	0.596474i	$-0.203432\pi$
$277$	1.40649e6	+	456995.i	1.10138	+	0.357859i	0.298745	+	0.954333i	$0.403432\pi$
$278$	−914610.	−	1.25885e6i	−0.709780	−	0.976929i
$279$		0			0
$280$	−26282.7	−	80889.9i	−0.0200343	−	0.0616594i
$281$	240749.	+	740950.i	0.181886	+	0.559788i	0.999881	−	0.0154380i	$-0.00491425\pi$
$281$	240749.	+	740950.i	0.181886	+	0.559788i	−0.817995	+	0.575226i	$0.804914\pi$
$282$		0			0
$283$	−704312.	−	969403.i	−0.522756	−	0.719512i	0.463249	−	0.886228i	$-0.346684\pi$
$283$	−704312.	−	969403.i	−0.522756	−	0.719512i	−0.986005	+	0.166716i	$0.946684\pi$
$284$	153106.	+	49747.0i	0.112641	+	0.0365992i
$285$		0			0
$286$	227035.	+	141984.i	0.164126	+	0.102642i
$287$		−	51107.8i		−	0.0366254i
$288$		0			0
$289$	1.05273e6	−	764855.i	0.741436	−	0.538685i
$290$	−217558.	+	299443.i	−0.151908	+	0.209083i
$291$		0			0
$292$	−937284.	+	304542.i	−0.643300	+	0.209021i
$293$	−1.36783e6	−	993783.i	−0.930811	−	0.676274i	0.0153801	−	0.999882i	$-0.495104\pi$
$293$	−1.36783e6	−	993783.i	−0.930811	−	0.676274i	−0.946191	+	0.323608i	$0.895104\pi$
$294$		0			0
$295$	−157431.	+	484522.i	−0.105326	+	0.324159i
$296$	−37447.2			−0.0248422
$297$		0			0
$298$	−1.38941e6			−0.906340
$299$	−122300.	+	376402.i	−0.0791134	+	0.243486i
$300$		0			0
$301$	480348.	+	348994.i	0.305591	+	0.222025i
$302$	−275261.	+	89437.7i	−0.173671	+	0.0564291i
$303$		0			0
$304$	−325798.	+	448422.i	−0.202192	+	0.278294i
$305$	−141759.	+	102994.i	−0.0872569	+	0.0633958i
$306$		0			0
$307$		−	170560.i		−	0.103283i	−0.998666	−	0.0516417i	$-0.983555\pi$
$307$		−	170560.i		−	0.103283i	0.998666	−	0.0516417i	$-0.0164454\pi$
$308$	263223.	+	652198.i	0.158106	+	0.391744i
$309$		0			0
$310$	−204211.	−	66352.2i	−0.120691	−	0.0392149i
$311$	−269135.	−	370432.i	−0.157786	−	0.217174i	0.722803	−	0.691054i	$-0.242853\pi$
$311$	−269135.	−	370432.i	−0.157786	−	0.217174i	−0.880590	+	0.473880i	$0.842853\pi$
$312$		0			0
$313$	617004.	+	1.89894e6i	0.355981	+	1.09560i	0.955438	+	0.295191i	$0.0953833\pi$
$313$	617004.	+	1.89894e6i	0.355981	+	1.09560i	−0.599457	+	0.800407i	$0.704617\pi$
$314$	−17551.5	−	54018.0i	−0.0100459	−	0.0309182i
$315$		0			0
$316$	592541.	+	815562.i	0.333811	+	0.459451i
$317$	172149.	+	55934.4i	0.0962177	+	0.0312630i	0.356730	−	0.934207i	$-0.383892\pi$
$317$	172149.	+	55934.4i	0.0962177	+	0.0312630i	−0.260513	+	0.965470i	$0.583892\pi$
$318$		0			0
$319$	1.62287e6	−	2.59500e6i	0.892911	−	1.42778i
$320$			49696.0i			0.0271298i
$321$		0			0
$322$	−840967.	+	610998.i	−0.452001	+	0.328398i
$323$	438293.	−	603258.i	0.233753	−	0.321734i
$324$		0			0
$325$	472424.	−	153500.i	0.248098	−	0.0806120i
$326$	−1.30273e6	−	946489.i	−0.678908	−	0.493255i
$327$		0			0
$328$	−9227.91	+	28400.6i	−0.00473608	+	0.0145761i
$329$	2.78635e6			1.41921
$330$		0			0
$331$	−2.32090e6			−1.16436			−0.582180	−	0.813060i	$-0.697800\pi$
$331$	−2.32090e6			−1.16436			−0.582180	+	0.813060i	$0.697800\pi$
$332$	9788.67	−	30126.4i	0.00487392	−	0.0150004i
$333$		0			0
$334$	−298668.	−	216995.i	−0.146495	−	0.106435i
$335$	−423182.	+	137500.i	−0.206023	+	0.0669408i
$336$		0			0
$337$	1.90817e6	−	2.62637e6i	0.915255	−	1.25974i	−0.0500852	−	0.998745i	$-0.515949\pi$
$337$	1.90817e6	−	2.62637e6i	0.915255	−	1.25974i	0.965340	−	0.260995i	$-0.0840507\pi$
$338$	1.11148e6	−	807538.i	0.529188	−	0.384478i
$339$		0			0
$340$		−	66855.5i		−	0.0313646i
$341$	1.72265e6	+	430185.i	0.802253	+	0.200341i
$342$		0			0
$343$	−2.25184e6	−	731666.i	−1.03348	−	0.335798i
$344$	−203916.	−	280666.i	−0.0929084	−	0.127877i
$345$		0			0
$346$	268336.	+	825852.i	0.120500	+	0.370862i
$347$	678758.	+	2.08900e6i	0.302616	+	0.931355i	0.980556	+	0.196238i	$0.0628727\pi$
$347$	678758.	+	2.08900e6i	0.302616	+	0.931355i	−0.677941	+	0.735117i	$0.737127\pi$
$348$		0			0
$349$	1.55870e6	+	2.14537e6i	0.685014	+	0.942841i	0.999980	−	0.00626201i	$-0.00199327\pi$
$349$	1.55870e6	+	2.14537e6i	0.685014	+	0.942841i	−0.314966	+	0.949103i	$0.601993\pi$
$350$	1.24082e6	+	403166.i	0.541424	+	0.175919i
$351$		0			0
$352$	−28513.7	−	409953.i	−0.0122658	−	0.176351i
$353$			3.42738e6i			1.46395i	0.681333	+	0.731974i	$0.261401\pi$
$353$			3.42738e6i			1.46395i	−0.681333	+	0.731974i	$0.738599\pi$
$354$		0			0
$355$	98760.6	−	71753.8i	0.0415923	−	0.0302186i
$356$	−494829.	+	681074.i	−0.206933	+	0.284819i
$357$		0			0
$358$	1.21515e6	−	394827.i	0.501099	−	0.162817i
$359$	1.97547e6	+	1.43527e6i	0.808975	+	0.587755i	0.913533	−	0.406764i	$-0.133343\pi$
$359$	1.97547e6	+	1.43527e6i	0.808975	+	0.587755i	−0.104558	+	0.994519i	$0.533343\pi$
$360$		0			0
$361$	−683486.	+	2.10355e6i	−0.276033	+	0.849543i
$362$	281118.			0.112750
$363$		0			0
$364$	−292346.			−0.115649
$365$	−230934.	+	710743.i	−0.0907311	+	0.279242i
$366$		0			0
$367$	−1.26946e6	−	922316.i	−0.491987	−	0.357449i	0.313961	−	0.949436i	$-0.398344\pi$
$367$	−1.26946e6	−	922316.i	−0.491987	−	0.357449i	−0.805948	+	0.591986i	$0.798344\pi$
$368$	577645.	−	187688.i	0.222352	−	0.0722466i
$369$		0			0
$370$	−16690.9	+	22973.0i	−0.00633834	+	0.00872397i
$371$	2.02934e6	−	1.47440e6i	0.765456	−	0.556136i
$372$		0			0
$373$		−	897025.i		−	0.333835i	−0.985971	−	0.166918i	$-0.946619\pi$
$373$		−	897025.i		−	0.333835i	0.985971	−	0.166918i	$-0.0533814\pi$
$374$	38359.2	+	551505.i	0.0141805	+	0.203878i
$375$		0			0
$376$	−1.54837e6	−	503097.i	−0.564815	−	0.183520i
$377$	747799.	+	1.02926e6i	0.270976	+	0.372967i
$378$		0			0
$379$	868492.	+	2.67294e6i	0.310576	+	0.955855i	0.977537	+	0.210762i	$0.0675946\pi$
$379$	868492.	+	2.67294e6i	0.310576	+	0.955855i	−0.666961	+	0.745092i	$0.732405\pi$
$380$	129883.	+	399740.i	0.0461418	+	0.142010i
$381$		0			0
$382$	−1.17235e6	−	1.61360e6i	−0.411054	−	0.565767i
$383$	2.74817e6	+	892936.i	0.957299	+	0.311045i	0.745678	−	0.666307i	$-0.232126\pi$
$383$	2.74817e6	+	892936.i	0.957299	+	0.311045i	0.211621	+	0.977352i	$0.432126\pi$
$384$		0			0
$385$	517432.	+	129214.i	0.177911	+	0.0444283i
$386$			1.82349e6i			0.622925i
$387$		0			0
$388$	1.24741e6	−	906298.i	0.420660	−	0.305627i
$389$	−2.47805e6	+	3.41074e6i	−0.830302	+	1.14281i	0.157565	+	0.987509i	$0.449636\pi$
$389$	−2.47805e6	+	3.41074e6i	−0.830302	+	1.14281i	−0.987867	+	0.155304i	$0.950364\pi$
$390$		0			0
$391$	−777100.	+	252495.i	−0.257060	+	0.0835240i
$392$	249019.	+	180923.i	0.0818497	+	0.0594673i
$393$		0			0
$394$	−420601.	+	1.29448e6i	−0.136499	+	0.420101i
$395$	764436.			0.246518
$396$		0			0
$397$	−567291.			−0.180647			−0.0903233	−	0.995912i	$-0.528790\pi$
$397$	−567291.			−0.180647			−0.0903233	+	0.995912i	$0.528790\pi$
$398$	241207.	−	742359.i	0.0763277	−	0.234913i
$399$		0			0
$400$	−616726.	−	448078.i	−0.192727	−	0.140024i
$401$	−4.56292e6	+	1.48258e6i	−1.41704	+	0.460424i	−0.914660	−	0.404224i	$-0.867542\pi$
$401$	−4.56292e6	+	1.48258e6i	−1.41704	+	0.460424i	−0.502379	+	0.864648i	$0.667542\pi$
$402$		0			0
$403$	−433811.	+	597090.i	−0.133057	+	0.183138i
$404$	−867997.	+	630637.i	−0.264585	+	0.192232i
$405$		0			0
$406$			3.34150e6i			1.00607i
$407$	124506.	−	199086.i	0.0372566	−	0.0595738i
$408$		0			0
$409$	−5.65102e6	−	1.83613e6i	−1.67039	−	0.542744i	−0.687383	−	0.726295i	$-0.741240\pi$
$409$	−5.65102e6	−	1.83613e6i	−1.67039	−	0.542744i	−0.983010	+	0.183552i	$0.941240\pi$
$410$	13310.1	+	18319.8i	0.00391040	+	0.00538221i
$411$		0			0
$412$	686768.	+	2.11365e6i	0.199327	+	0.613467i
$413$	1.42126e6	+	4.37420e6i	0.410015	+	1.26190i
$414$		0			0
$415$	−14118.9	−	19433.0i	−0.00402421	−	0.00553886i
$416$	162456.	+	52785.3i	0.0460260	+	0.0149548i
$417$		0			0
$418$	−1.30079e6	−	3.22301e6i	−0.364138	−	0.902239i
$419$		−	1.41133e6i		−	0.392728i	−0.980531	−	0.196364i	$-0.937087\pi$
$419$		−	1.41133e6i		−	0.392728i	0.980531	−	0.196364i	$-0.0629135\pi$
$420$		0			0
$421$	750462.	−	545243.i	0.206359	−	0.149929i	−0.479806	−	0.877375i	$-0.659293\pi$
$421$	750462.	−	545243.i	0.206359	−	0.149929i	0.686165	+	0.727446i	$0.259293\pi$
$422$	1.32011e6	−	1.81698e6i	0.360852	−	0.496670i
$423$		0			0
$424$	−1.39392e6	+	452911.i	−0.376550	+	0.122348i
$425$	829676.	+	602795.i	0.222811	+	0.161881i
$426$		0			0
$427$	−488831.	+	1.50447e6i	−0.129745	+	0.399313i
$428$	701651.			0.185145
$429$		0			0
$430$	−263071.			−0.0686124
$431$	1.68118e6	−	5.17413e6i	0.435934	−	1.34167i	−0.456193	−	0.889881i	$-0.650787\pi$
$431$	1.68118e6	−	5.17413e6i	0.435934	−	1.34167i	0.892127	−	0.451785i	$-0.149213\pi$
$432$		0			0
$433$	4.25571e6	+	3.09195e6i	1.09082	+	0.792525i	0.979537	−	0.201264i	$-0.0645048\pi$
$433$	4.25571e6	+	3.09195e6i	1.09082	+	0.792525i	0.111280	+	0.993789i	$0.464505\pi$
$434$	−1.84359e6	+	599019.i	−0.469829	+	0.152657i
$435$		0			0
$436$	892954.	−	1.22905e6i	0.224964	−	0.309636i
$437$	4.15587e6	−	3.01942e6i	1.04102	−	0.756344i
$438$		0			0
$439$			450552.i			0.111579i	0.998443	+	0.0557896i	$0.0177676\pi$
$439$			450552.i			0.111579i	−0.998443	+	0.0557896i	$0.982232\pi$
$440$	−264206.	−	165231.i	−0.0650595	−	0.0406873i
$441$		0			0
$442$	−218551.	−	71011.5i	−0.0532105	−	0.0172891i
$443$	−79778.4	−	109806.i	−0.0193142	−	0.0265837i	0.799251	−	0.600998i	$-0.205230\pi$
$443$	−79778.4	−	109806.i	−0.0193142	−	0.0265837i	−0.818565	+	0.574414i	$0.805230\pi$
$444$		0			0
$445$	197270.	+	607134.i	0.0472237	+	0.145340i
$446$	1.79347e6	+	5.51974e6i	0.426931	+	1.31396i
$447$		0			0
$448$	263709.	+	362964.i	0.0620769	+	0.0854415i
$449$	−6.38291e6	−	2.07393e6i	−1.49418	−	0.485488i	−0.555865	−	0.831273i	$-0.687613\pi$
$449$	−6.38291e6	−	2.07393e6i	−1.49418	−	0.485488i	−0.938314	+	0.345785i	$0.887613\pi$
$450$		0			0
$451$	−120309.	−	143487.i	−0.0278520	−	0.0332178i
$452$			185432.i			0.0426912i
$453$		0			0
$454$	3.43046e6	−	2.49238e6i	0.781111	−	0.567511i
$455$	−130304.	+	179348.i	−0.0295073	+	0.0406132i
$456$		0			0
$457$	3.95344e6	−	1.28455e6i	0.885491	−	0.287713i	0.169256	−	0.985572i	$-0.445864\pi$
$457$	3.95344e6	−	1.28455e6i	0.885491	−	0.287713i	0.716235	+	0.697859i	$0.245864\pi$
$458$	1.96032e6	+	1.42426e6i	0.436681	+	0.317267i
$459$		0			0
$460$	142324.	−	438029.i	0.0313606	−	0.0965179i
$461$	2.32088e6			0.508629			0.254315	−	0.967122i	$-0.418150\pi$
$461$	2.32088e6			0.508629			0.254315	+	0.967122i	$0.418150\pi$
$462$		0			0
$463$	−8.16191e6			−1.76945			−0.884727	−	0.466110i	$-0.845655\pi$
$463$	−8.16191e6			−1.76945			−0.884727	+	0.466110i	$0.845655\pi$
$464$	603334.	−	1.85687e6i	0.130096	−	0.400393i
$465$		0			0
$466$	2.93880e6	+	2.13516e6i	0.626910	+	0.455477i
$467$	−8.20226e6	+	2.66508e6i	−1.74037	+	0.565480i	−0.994882	−	0.101041i	$-0.967783\pi$
$467$	−8.20226e6	+	2.66508e6i	−1.74037	+	0.565480i	−0.745486	+	0.666521i	$0.767783\pi$
$468$		0			0
$469$	−2.36115e6	+	3.24985e6i	−0.495669	+	0.682230i
$470$	−998777.	+	725654.i	−0.208557	+	0.151525i
$471$		0			0
$472$		−	2.68736e6i		−	0.555228i
$473$	2.17013e6	−	150941.i	0.445998	−	0.0310208i
$474$		0			0
$475$	−6.13184e6	−	1.99235e6i	−1.24697	−	0.405166i
$476$	−354765.	−	488292.i	−0.0717668	−	0.0987785i
$477$		0			0
$478$	1.38576e6	+	4.26492e6i	0.277407	+	0.853771i
$479$	−1.76200e6	−	5.42288e6i	−0.350887	−	1.07992i	−0.958356	−	0.285576i	$-0.907815\pi$
$479$	−1.76200e6	−	5.42288e6i	−0.350887	−	1.07992i	0.607469	−	0.794344i	$-0.292185\pi$
$480$		0			0
$481$	57370.6	+	78963.8i	0.0113065	+	0.0155620i
$482$	−3.02022e6	−	981328.i	−0.592135	−	0.192396i
$483$		0			0
$484$	2.27429e6	+	1.21143e6i	0.441299	+	0.235064i
$485$		−	1.16921e6i		−	0.225704i
$486$		0			0
$487$	−4.84185e6	+	3.51781e6i	−0.925101	+	0.672125i	−0.944789	−	0.327681i	$-0.893733\pi$
$487$	−4.84185e6	+	3.51781e6i	−0.925101	+	0.672125i	0.0196872	+	0.999806i	$0.493733\pi$
$488$	543286.	−	747770.i	0.103271	−	0.142141i
$489$		0			0
$490$	221984.	−	72127.1i	0.0417669	−	0.0135709i
$491$	−3.52358e6	−	2.56003e6i	−0.659600	−	0.479228i	0.206928	−	0.978356i	$-0.433654\pi$
$491$	−3.52358e6	−	2.56003e6i	−0.659600	−	0.479228i	−0.866528	+	0.499129i	$0.833654\pi$
$492$		0			0
$493$	−811659.	+	2.49803e6i	−0.150403	+	0.462893i
$494$	1.44471e6			0.266356
$495$		0			0
$496$	1.13264e6			0.206722
$497$	340560.	−	1.04814e6i	0.0618447	−	0.190338i
$498$		0			0
$499$	−7.81490e6	−	5.67786e6i	−1.40499	−	1.02078i	−0.994028	−	0.109128i	$-0.965194\pi$
$499$	−7.81490e6	−	5.67786e6i	−1.40499	−	1.02078i	−0.410958	−	0.911654i	$-0.634806\pi$
$500$	−1.12672e6	+	366094.i	−0.201554	+	0.0654889i
$501$		0			0
$502$	453085.	−	623618.i	0.0802454	−	0.110448i
$503$	4.46944e6	−	3.24723e6i	0.787649	−	0.572260i	−0.119616	−	0.992820i	$-0.538166\pi$
$503$	4.46944e6	−	3.24723e6i	0.787649	−	0.572260i	0.907265	+	0.420560i	$0.138166\pi$
$504$		0			0
$505$			813583.i			0.141962i
$506$	−922737.	+	3.69505e6i	−0.160214	+	0.641570i
$507$		0			0
$508$	3.20553e6	+	1.04154e6i	0.551113	+	0.179067i
$509$	−1.01534e6	−	1.39749e6i	−0.173706	−	0.239086i	0.713283	−	0.700876i	$-0.247207\pi$
$509$	−1.01534e6	−	1.39749e6i	−0.173706	−	0.239086i	−0.886989	+	0.461790i	$0.847207\pi$
$510$		0			0
$511$	2.08484e6	+	6.41649e6i	0.353200	+	1.08704i
$512$	−81007.0	−	249314.i	−0.0136568	−	0.0420312i
$513$		0			0
$514$	−833547.	−	1.14728e6i	−0.139163	−	0.191541i
$515$	1.60279e6	+	520777.i	0.266292	+	0.0865234i
$516$		0			0
$517$	7.82277e6	−	6.55913e6i	1.28716	−	1.07925i
$518$			256358.i			0.0419780i
$519$		0			0
$520$	104792.	−	76136.1i	0.0169950	−	0.0123476i
$521$	−1.21241e6	+	1.66874e6i	−0.195684	+	0.269336i	−0.895572	−	0.444917i	$-0.853233\pi$
$521$	−1.21241e6	+	1.66874e6i	−0.195684	+	0.269336i	0.699888	+	0.714253i	$0.253233\pi$
$522$		0			0
$523$	3.23554e6	−	1.05129e6i	0.517241	−	0.168062i	−0.0387521	−	0.999249i	$-0.512338\pi$
$523$	3.23554e6	−	1.05129e6i	0.517241	−	0.168062i	0.555993	+	0.831187i	$0.312338\pi$
$524$	−1.65739e6	−	1.20416e6i	−0.263692	−	0.191583i
$525$		0			0
$526$	13826.9	−	42554.9i	0.00217902	−	0.00670634i
$527$	−1.52373e6			−0.238991
$528$		0			0
$529$	807362.			0.125438
$530$	−343443.	+	1.05701e6i	−0.0531086	+	0.163451i
$531$		0			0
$532$	3.06982e6	+	2.23036e6i	0.470256	+	0.341661i
$533$	74024.9	−	24052.2i	0.0112865	−	0.00366721i
$534$		0			0
$535$	312738.	−	430447.i	0.0472386	−	0.0650183i
$536$	1.89888e6	−	1.37961e6i	0.285486	−	0.207418i
$537$		0			0
$538$		−	8.10626e6i		−	1.20744i
$539$	−1.78981e6	+	722358.i	−0.265360	+	0.107098i
$540$		0			0
$541$	3.16591e6	+	1.02867e6i	0.465056	+	0.151106i	0.532166	−	0.846640i	$-0.321378\pi$
$541$	3.16591e6	+	1.02867e6i	0.465056	+	0.151106i	−0.0671108	+	0.997746i	$0.521378\pi$
$542$	−960603.	−	1.32216e6i	−0.140458	−	0.193323i
$543$		0			0
$544$	108978.	+	335399.i	0.0157885	+	0.0485920i
$545$	−355987.	−	1.09562e6i	−0.0513385	−	0.158004i
$546$		0			0
$547$	−1.49852e6	−	2.06253e6i	−0.214138	−	0.294736i	0.688413	−	0.725319i	$-0.258308\pi$
$547$	−1.49852e6	−	2.06253e6i	−0.214138	−	0.294736i	−0.902551	+	0.430583i	$0.858308\pi$
$548$	2.80384e6	+	911022.i	0.398842	+	0.129592i
$549$		0			0
$550$	4.43269e6	−	1.78901e6i	0.624828	−	0.252177i
$551$		−	1.65130e7i		−	2.31710i
$552$		0			0
$553$	5.58321e6	−	4.05644e6i	0.776374	−	0.564068i
$554$	−3.47703e6	+	4.78572e6i	−0.481320	+	0.662480i
$555$		0			0
$556$	5.91948e6	−	1.92336e6i	0.812076	−	0.263859i
$557$	−1.09672e7	−	7.96816e6i	−1.49782	−	1.08823i	−0.971240	−	0.238101i	$-0.923475\pi$
$557$	−1.09672e7	−	7.96816e6i	−1.49782	−	1.08823i	−0.526577	−	0.850127i	$-0.676525\pi$
$558$		0			0
$559$	−279425.	+	859982.i	−0.0378212	+	0.116402i
$560$	340211.			0.0458435
$561$		0			0
$562$	−3.11633e6			−0.416200
$563$	1.55113e6	−	4.77389e6i	0.206242	−	0.634748i	−0.793418	−	0.608677i	$-0.791700\pi$
$563$	1.55113e6	−	4.77389e6i	0.206242	−	0.634748i	0.999660	−	0.0260707i	$-0.00829951\pi$
$564$		0			0
$565$	113758.	+	82650.3i	0.0149921	+	0.0108924i
$566$	4.55840e6	−	1.48112e6i	0.598097	−	0.194334i
$567$		0			0
$568$	−378498.	+	520957.i	−0.0492258	+	0.0677534i
$569$	−2.60575e6	+	1.89319e6i	−0.337406	+	0.245140i	−0.743566	−	0.668662i	$-0.766867\pi$
$569$	−2.60575e6	+	1.89319e6i	−0.337406	+	0.245140i	0.406161	+	0.913802i	$0.366867\pi$
$570$		0			0
$571$		−	1.05835e7i		−	1.35843i	−0.733939	−	0.679216i	$-0.762320\pi$
$571$		−	1.05835e7i		−	1.35843i	0.733939	−	0.679216i	$-0.237680\pi$
$572$	−820770.	+	688189.i	−0.104889	+	0.0879463i
$573$		0			0
$574$	194426.	+	63172.8i	0.0246305	+	0.00800295i
$575$	4.15268e6	+	5.71567e6i	0.523792	+	0.720938i
$576$		0			0
$577$	4.51416e6	+	1.38932e7i	0.564466	+	1.73725i	0.669533	+	0.742782i	$0.266494\pi$
$577$	4.51416e6	+	1.38932e7i	0.564466	+	1.73725i	−0.105068	+	0.994465i	$0.533506\pi$
$578$	1.60843e6	+	4.95025e6i	0.200255	+	0.616322i
$579$		0			0
$580$	−870232.	−	1.19777e6i	−0.107415	−	0.147844i
$581$	−206241.	−	67011.6i	−0.0253474	−	0.00823588i
$582$		0			0
$583$	2.22666e6	−	8.91654e6i	0.271320	−	1.08649i
$584$		−	3.94207e6i		−	0.478291i
$585$		0			0
$586$	5.47130e6	−	3.97513e6i	0.658183	−	0.478198i
$587$	5.99289e6	−	8.24850e6i	0.717862	−	0.988052i	−0.281730	−	0.959494i	$-0.590908\pi$
$587$	5.99289e6	−	8.24850e6i	0.717862	−	0.988052i	0.999592	−	0.0285585i	$-0.00909168\pi$
$588$		0			0
$589$	9.11061e6	−	2.96022e6i	1.08208	−	0.351589i
$590$	−1.64864e6	−	1.19780e6i	−0.194982	−	0.141663i
$591$		0			0
$592$	46287.3	−	142458.i	0.00542822	−	0.0167064i
$593$	−3.76549e6			−0.439729			−0.219864	−	0.975530i	$-0.570561\pi$
$593$	−3.76549e6			−0.439729			−0.219864	+	0.975530i	$0.570561\pi$
$594$		0			0
$595$	−457682.			−0.0529994
$596$	1.71741e6	−	5.28565e6i	0.198043	−	0.609512i
$597$		0			0
$598$	−1.28075e6	−	930517.i	−0.146457	−	0.106407i
$599$	−1.11240e7	+	3.61440e6i	−1.26676	+	0.411595i	−0.863898	−	0.503667i	$-0.831984\pi$
$599$	−1.11240e7	+	3.61440e6i	−1.26676	+	0.411595i	−0.402860	+	0.915262i	$0.631984\pi$
$600$		0			0
$601$	−9.30728e6	+	1.28104e7i	−1.05108	+	1.44669i	−0.163214	+	0.986591i	$0.552186\pi$
$601$	−9.30728e6	+	1.28104e7i	−1.05108	+	1.44669i	−0.887868	+	0.460099i	$0.847814\pi$
$602$	−1.92139e6	+	1.39597e6i	−0.216085	+	0.156995i
$603$		0			0
$604$		−	1.15771e6i		−	0.129124i
$605$	1.75688e6	−	855273.i	0.195143	−	0.0949984i
$606$		0			0
$607$	−1.08498e7	−	3.52530e6i	−1.19522	−	0.388351i	−0.357222	−	0.934020i	$-0.616276\pi$
$607$	−1.08498e7	−	3.52530e6i	−1.19522	−	0.388351i	−0.838001	+	0.545668i	$0.816276\pi$
$608$	−1.30319e6	−	1.79369e6i	−0.142971	−	0.196783i
$609$		0			0
$610$	−216588.	−	666589.i	−0.0235673	−	0.0725326i
$611$	1.31130e6	+	4.03577e6i	0.142102	+	0.437344i
$612$		0			0
$613$	−4.41737e6	−	6.07999e6i	−0.474802	−	0.653509i	0.502694	−	0.864465i	$-0.332342\pi$
$613$	−4.41737e6	−	6.07999e6i	−0.474802	−	0.653509i	−0.977496	+	0.210956i	$0.932342\pi$
$614$	648848.	+	210823.i	0.0694579	+	0.0225682i
$615$		0			0
$616$	−2.80647e6	+	195200.i	−0.297995	+	0.0207266i
$617$			2.51482e6i			0.265946i	0.991120	+	0.132973i	$0.0424523\pi$
$617$			2.51482e6i			0.265946i	−0.991120	+	0.132973i	$0.957548\pi$
$618$		0			0
$619$	9.24615e6	−	6.71772e6i	0.969916	−	0.704685i	0.0144837	−	0.999895i	$-0.495390\pi$
$619$	9.24615e6	−	6.71772e6i	0.969916	−	0.704685i	0.955432	+	0.295210i	$0.0953895\pi$
$620$	504837.	−	694849.i	0.0527439	−	0.0725958i
$621$		0			0
$622$	1.74188e6	−	565970.i	0.180527	−	0.0586567i
$623$	4.66252e6	+	3.38752e6i	0.481283	+	0.349673i
$624$		0			0
$625$	2.59798e6	−	7.99577e6i	0.266033	−	0.818767i
$626$	−7.98667e6			−0.814573
$627$		0			0
$628$	227191.			0.0229875
$629$	−62269.9	+	191647.i	−0.00627554	+	0.0193141i
$630$		0			0
$631$	7.76534e6	+	5.64185e6i	0.776403	+	0.564090i	0.903897	−	0.427749i	$-0.140693\pi$
$631$	7.76534e6	+	5.64185e6i	0.776403	+	0.564090i	−0.127494	+	0.991839i	$0.540693\pi$
$632$	−3.83500e6	+	1.24607e6i	−0.381921	+	0.124094i
$633$		0			0
$634$	−425575.	+	585753.i	−0.0420487	+	0.0578751i
$635$	2.06772e6	−	1.50229e6i	0.203497	−	0.147849i
$636$		0			0
$637$		−	802279.i		−	0.0783388i
$638$	7.86597e6	+	9.38137e6i	0.765069	+	0.912461i
$639$		0			0
$640$	−189055.	−	61427.6i	−0.0182447	−	0.00592808i
$641$	8.02825e6	+	1.10499e7i	0.771748	+	1.06222i	0.996145	+	0.0877225i	$0.0279589\pi$
$641$	8.02825e6	+	1.10499e7i	0.771748	+	1.06222i	−0.224397	+	0.974498i	$0.572041\pi$
$642$		0			0
$643$	−2.99686e6	−	9.22338e6i	−0.285850	−	0.879756i	−0.986143	−	0.165900i	$-0.946947\pi$
$643$	−2.99686e6	−	9.22338e6i	−0.285850	−	0.879756i	0.700292	−	0.713856i	$-0.253053\pi$
$644$	−1.28488e6	−	3.95446e6i	−0.122081	−	0.375728i
$645$		0			0
$646$	1.75317e6	+	2.41303e6i	0.165289	+	0.227500i
$647$	−1.36261e7	−	4.42737e6i	−1.27970	−	0.415801i	−0.411228	−	0.911533i	$-0.634900\pi$
$647$	−1.36261e7	−	4.42737e6i	−1.27970	−	0.415801i	−0.868476	+	0.495732i	$0.834900\pi$
$648$		0			0
$649$	1.42872e7	+	8.93502e6i	1.33148	+	0.832691i
$650$			1.98694e6i			0.184460i
$651$		0			0
$652$	5.21092e6	−	3.78596e6i	0.480060	−	0.348784i
$653$	−4.24746e6	+	5.84613e6i	−0.389804	+	0.536519i	−0.958149	−	0.286272i	$-0.907584\pi$
$653$	−4.24746e6	+	5.84613e6i	−0.389804	+	0.536519i	0.568345	+	0.822791i	$0.307584\pi$
$654$		0			0
$655$	−1.47746e6	+	480055.i	−0.134559	+	0.0437207i
$656$	−96635.9	−	70210.1i	−0.00876757	−	0.00637001i
$657$		0			0
$658$	−3.44412e6	+	1.05999e7i	−0.310108	+	0.954416i
$659$	1.96922e7			1.76636			0.883182	−	0.469031i	$-0.155397\pi$
$659$	1.96922e7			1.76636			0.883182	+	0.469031i	$0.155397\pi$
$660$		0			0
$661$	−1.54589e7			−1.37618			−0.688088	−	0.725627i	$-0.741550\pi$
$661$	−1.54589e7			−1.37618			−0.688088	+	0.725627i	$0.741550\pi$
$662$	2.86880e6	−	8.82924e6i	0.254422	−	0.783030i
$663$		0			0
$664$	102508.	+	74476.6i	0.00902275	+	0.00655541i
$665$	2.73655e6	−	889159.i	0.239966	−	0.0779696i
$666$		0			0
$667$	−1.06358e7	+	1.46389e7i	−0.925666	+	1.27407i
$668$	1.19467e6	−	867981.i	0.103588	−	0.0752609i
$669$		0			0
$670$		−	1.77984e6i		−	0.153177i
$671$	2.16914e6	+	5.37456e6i	0.185987	+	0.460826i
$672$		0			0
$673$	−7.45504e6	−	2.42229e6i	−0.634472	−	0.206152i	−0.0259170	−	0.999664i	$-0.508251\pi$
$673$	−7.45504e6	−	2.42229e6i	−0.634472	−	0.206152i	−0.608555	+	0.793512i	$0.708251\pi$
$674$	7.63268e6	+	1.05055e7i	0.647183	+	0.890771i
$675$		0			0
$676$	1.69819e6	+	5.22649e6i	0.142929	+	0.439890i
$677$	2.82010e6	+	8.67937e6i	0.236479	+	0.727807i	0.996922	+	0.0784025i	$0.0249819\pi$
$677$	2.82010e6	+	8.67937e6i	0.236479	+	0.727807i	−0.760443	+	0.649405i	$0.775018\pi$
$678$		0			0
$679$	−6.20437e6	−	8.53958e6i	−0.516444	−	0.710824i
$680$	254333.	+	82638.0i	0.0210927	+	0.00685342i
$681$		0			0
$682$	−3.76583e6	+	6.02161e6i	−0.310027	+	0.495738i
$683$		−	2.01120e7i		−	1.64970i	−0.565354	−	0.824848i	$-0.691261\pi$
$683$		−	2.01120e7i		−	1.64970i	0.565354	−	0.824848i	$-0.308739\pi$
$684$		0			0
$685$	1.80861e6	−	1.31403e6i	0.147272	−	0.106999i
$686$	5.56685e6	−	7.66211e6i	0.451647	−	0.621639i
$687$		0			0
$688$	1.31977e6	−	428820.i	0.106299	−	0.0345385i
$689$	3.09057e6	+	2.24543e6i	0.248022	+	0.180199i
$690$		0			0
$691$	−6.15365e6	+	1.89390e7i	−0.490272	+	1.50890i	0.333925	+	0.942600i	$0.391627\pi$
$691$	−6.15365e6	+	1.89390e7i	−0.490272	+	1.50890i	−0.824197	+	0.566303i	$0.808373\pi$
$692$	−3.47341e6			−0.275734
$693$		0			0
$694$	−8.78603e6			−0.692459
$695$	1.45848e6	−	4.48875e6i	0.114535	−	0.352503i
$696$		0			0
$697$	130003.	+	94453.0i	0.0101361	+	0.00736434i
$698$	−1.00881e7	+	3.27783e6i	−0.783740	+	0.254653i
$699$		0			0
$700$	−3.06747e6	+	4.22201e6i	−0.236611	+	0.325667i
$701$	−1.20020e7	+	8.71999e6i	−0.922486	+	0.670225i	−0.944142	−	0.329540i	$-0.893106\pi$
$701$	−1.20020e7	+	8.71999e6i	−0.922486	+	0.670225i	0.0216555	+	0.999765i	$0.493106\pi$
$702$		0			0
$703$		−	1.26686e6i		−	0.0966809i
$704$	1.59480e6	+	398257.i	0.121276	+	0.0302853i
$705$		0			0
$706$	−1.30385e7	−	4.23647e6i	−0.984502	−	0.319884i
$707$	4.31724e6	+	5.94216e6i	0.324831	+	0.447091i
$708$		0			0
$709$	8.05300e6	+	2.47846e7i	0.601647	+	1.85168i	0.518375	+	0.855154i	$0.326537\pi$
$709$	8.05300e6	+	2.47846e7i	0.601647	+	1.85168i	0.0832729	+	0.996527i	$0.473463\pi$
$710$	150893.	+	464400.i	0.0112337	+	0.0345737i
$711$		0			0
$712$	−1.97932e6	−	2.72430e6i	−0.146324	−	0.201398i
$713$	−9.98327e6	−	3.24376e6i	−0.735443	−	0.238960i
$714$		0			0
$715$	56356.7	+	810263.i	0.00412269	+	0.0592735i
$716$			5.11075e6i			0.372565i
$717$		0			0
$718$	−7.90189e6	+	5.74106e6i	−0.572032	+	0.415605i
$719$	−4.54131e6	+	6.25058e6i	−0.327611	+	0.450918i	−0.940772	−	0.339040i	$-0.889898\pi$
$719$	−4.54131e6	+	6.25058e6i	−0.327611	+	0.450918i	0.613161	+	0.789958i	$0.289898\pi$
$720$		0			0
$721$	1.44697e7	−	4.70150e6i	1.03663	−	0.336820i
$722$	−7.15756e6	−	5.20027e6i	−0.511001	−	0.371264i
$723$		0			0
$724$	−347481.	+	1.06944e6i	−0.0246368	+	0.0758243i
$725$	2.27107e7			1.60467
$726$		0			0
$727$	7.39622e6			0.519008			0.259504	−	0.965742i	$-0.416441\pi$
$727$	7.39622e6			0.519008			0.259504	+	0.965742i	$0.416441\pi$
$728$	361360.	−	1.11215e6i	0.0252703	−	0.0777741i
$729$		0			0
$730$	−2.41838e6	−	1.75705e6i	−0.167964	−	0.122033i
$731$	−1.77547e6	+	576887.i	−0.122891	+	0.0399298i
$732$		0			0
$733$	2.83465e6	−	3.90156e6i	0.194867	−	0.268212i	−0.700391	−	0.713759i	$-0.746991\pi$
$733$	2.83465e6	−	3.90156e6i	0.194867	−	0.268212i	0.895258	+	0.445548i	$0.146991\pi$
$734$	5.07784e6	−	3.68926e6i	0.347887	−	0.252755i
$735$		0			0
$736$			2.42949e6i			0.165318i
$737$	1.02120e6	+	1.46823e7i	0.0692539	+	0.995690i
$738$		0			0
$739$	−1.37501e7	−	4.46769e6i	−0.926182	−	0.300935i	−0.193181	−	0.981163i	$-0.561881\pi$
$739$	−1.37501e7	−	4.46769e6i	−0.926182	−	0.300935i	−0.733000	+	0.680228i	$0.761881\pi$
$740$	−66763.6	−	91892.2i	−0.00448188	−	0.00616878i
$741$		0			0
$742$	3.10056e6	+	9.54253e6i	0.206742	+	0.636288i
$743$	6.40838e6	+	1.97230e7i	0.425869	+	1.31069i	0.902159	+	0.431403i	$0.141981\pi$
$743$	6.40838e6	+	1.97230e7i	0.425869	+	1.31069i	−0.476290	+	0.879288i	$0.658019\pi$
$744$		0			0
$745$	−2.47715e6	−	3.40950e6i	−0.163516	−	0.225061i
$746$	3.41248e6	+	1.10878e6i	0.224504	+	0.0729457i
$747$		0			0
$748$	−2.14547e6	−	535771.i	−0.140206	−	0.0350127i
$749$		−	4.80339e6i		−	0.312855i
$750$		0			0
$751$	−9.01240e6	+	6.54789e6i	−0.583097	+	0.423645i	−0.839839	−	0.542835i	$-0.817351\pi$
$751$	−9.01240e6	+	6.54789e6i	−0.583097	+	0.423645i	0.256742	+	0.966480i	$0.417351\pi$
$752$	3.82779e6	−	5.26850e6i	0.246833	−	0.339737i
$753$		0			0
$754$	−4.83985e6	+	1.57256e6i	−0.310030	+	0.100735i
$755$	−710227.	−	516010.i	−0.0453451	−	0.0329451i
$756$		0			0
$757$	−1.66618e6	+	5.12797e6i	−0.105677	+	0.325242i	−0.989889	−	0.141845i	$-0.954696\pi$
$757$	−1.66618e6	+	5.12797e6i	−0.105677	+	0.325242i	0.884211	+	0.467087i	$0.154696\pi$
$758$	−1.12420e7			−0.710674
$759$		0			0
$760$	−1.68124e6			−0.105584
$761$	−5.49204e6	+	1.69028e7i	−0.343773	+	1.05803i	0.618464	+	0.785813i	$0.287755\pi$
$761$	−5.49204e6	+	1.69028e7i	−0.343773	+	1.05803i	−0.962237	+	0.272212i	$0.912245\pi$
$762$		0			0
$763$	−8.41385e6	−	6.11302e6i	−0.523219	−	0.380141i
$764$	7.58761e6	−	2.46536e6i	0.470296	−	0.152808i
$765$		0			0
$766$	−6.79386e6	+	9.35095e6i	−0.418355	+	0.575816i
$767$	−5.66675e6	+	4.11714e6i	−0.347813	+	0.252701i
$768$		0			0
$769$		−	6.47772e6i		−	0.395008i	−0.980302	−	0.197504i	$-0.936716\pi$
$769$		−	6.47772e6i		−	0.395008i	0.980302	−	0.197504i	$-0.0632836\pi$
$770$	−1.13114e6	+	1.80871e6i	−0.0687528	+	0.109937i
$771$		0			0
$772$	−6.93698e6	−	2.25396e6i	−0.418916	−	0.136114i
$773$	7.89588e6	+	1.08677e7i	0.475283	+	0.654170i	0.977590	−	0.210519i	$-0.0675154\pi$
$773$	7.89588e6	+	1.08677e7i	0.475283	+	0.654170i	−0.502307	+	0.864689i	$0.667515\pi$
$774$		0			0
$775$	4.07126e6	+	1.25300e7i	0.243486	+	0.749374i
$776$	1.90588e6	+	5.86568e6i	0.113616	+	0.349675i
$777$		0			0
$778$	−9.91220e6	−	1.36430e7i	−0.587112	−	0.808090i
$779$	−960809.	−	312186.i	−0.0567274	−	0.0184319i
$780$		0			0
$781$	−1.51120e6	−	3.74436e6i	−0.0886533	−	0.219659i
$782$		−	3.26837e6i		−	0.191123i
$783$		0			0
$784$	−996075.	+	723691.i	−0.0578765	+	0.0420497i
$785$	101263.	−	139377.i	0.00586513	−	0.00807266i
$786$		0			0
$787$	3.06126e7	−	9.94665e6i	1.76183	−	0.572453i	0.764442	−	0.644693i	$-0.223015\pi$
$787$	3.06126e7	−	9.94665e6i	1.76183	−	0.572453i	0.997387	+	0.0722398i	$0.0230147\pi$
$788$	−4.40459e6	−	3.20012e6i	−0.252691	−	0.183591i
$789$		0			0
$790$	−944894.	+	2.90809e6i	−0.0538661	+	0.165783i
$791$	1.26944e6			0.0721389
$792$		0			0
$793$	−2.40913e6			−0.136044
$794$	701210.	−	2.15810e6i	0.0394727	−	0.121485i
$795$		0			0
$796$	2.52595e6	+	1.83521e6i	0.141300	+	0.102661i
$797$	−1.23621e7	+	4.01668e6i	−0.689358	+	0.223986i	−0.632688	−	0.774407i	$-0.718048\pi$
$797$	−1.23621e7	+	4.01668e6i	−0.689358	+	0.223986i	−0.0566703	+	0.998393i	$0.518048\pi$
$798$		0			0
$799$	−5.14949e6	+	7.08766e6i	−0.285363	+	0.392768i
$800$	2.46690e6	−	1.79231e6i	0.136279	−	0.0990121i
$801$		0			0
$802$		−	1.91909e7i		−	1.05356i
$803$	2.09578e7	+	1.31067e7i	1.14698	+	0.717307i
$804$		0			0
$805$	−2.99867e6	−	974328.i	−0.163095	−	0.0529926i
$806$	−1.73525e6	−	2.38836e6i	−0.0940856	−	0.129498i
$807$		0			0
$808$	−1.32618e6	−	4.08157e6i	−0.0714619	−	0.219937i
$809$	−7.90922e6	−	2.43421e7i	−0.424876	−	1.30763i	−0.903113	−	0.429403i	$-0.858724\pi$
$809$	−7.90922e6	−	2.43421e7i	−0.424876	−	1.30763i	0.478237	−	0.878231i	$-0.341276\pi$
$810$		0			0
$811$	6.46714e6	+	8.90125e6i	0.345271	+	0.475225i	0.945972	−	0.324249i	$-0.105112\pi$
$811$	6.46714e6	+	8.90125e6i	0.345271	+	0.475225i	−0.600701	+	0.799474i	$0.705112\pi$
$812$	−1.27118e7	−	4.13032e6i	−0.676578	−	0.219834i
$813$		0			0
$814$	603471.	+	719732.i	0.0319224	+	0.0380723i
$815$		−	4.88426e6i		−	0.257575i
$816$		0			0
$817$	9.49510e6	−	6.89859e6i	0.497673	−	0.361581i
$818$	1.39701e7	−	1.92282e7i	0.729988	−	1.00474i
$819$		0			0
$820$	−86144.7	+	27990.1i	−0.00447398	+	0.00145368i
$821$	2.16737e7	+	1.57469e7i	1.12221	+	0.815337i	0.984543	−	0.175141i	$-0.0560383\pi$
$821$	2.16737e7	+	1.57469e7i	1.12221	+	0.815337i	0.137671	+	0.990478i	$0.456038\pi$
$822$		0			0
$823$	2.29515e6	−	7.06374e6i	0.118117	−	0.363526i	−0.874468	−	0.485084i	$-0.838789\pi$
$823$	2.29515e6	−	7.06374e6i	0.118117	−	0.363526i	0.992584	+	0.121558i	$0.0387891\pi$
$824$	−8.88971e6			−0.456110
$825$		0			0
$826$	−1.83972e7			−0.938215
$827$	−5.09123e6	+	1.56692e7i	−0.258856	+	0.796677i	0.734189	+	0.678945i	$0.237563\pi$
$827$	−5.09123e6	+	1.56692e7i	−0.258856	+	0.796677i	−0.993045	+	0.117732i	$0.962437\pi$
$828$		0			0
$829$	−2.35270e7	−	1.70934e7i	−1.18899	−	0.863855i	−0.195837	−	0.980636i	$-0.562742\pi$
$829$	−2.35270e7	−	1.70934e7i	−1.18899	−	0.863855i	−0.993158	+	0.116781i	$0.962742\pi$
$830$	91379.5	−	29691.0i	0.00460420	−	0.00149599i
$831$		0			0
$832$	−401614.	+	552775.i	−0.0201141	+	0.0276847i
$833$	1.34001e6	−	973574.i	0.0669107	−	0.0486135i
$834$		0			0
$835$		−	1.11978e6i		−	0.0555798i
$836$	1.38689e7	−	964635.i	0.686321	−	0.0477362i
$837$		0			0
$838$	5.36900e6	+	1.74449e6i	0.264109	+	0.0858143i
$839$	2.75189e6	+	3.78765e6i	0.134966	+	0.185765i	0.871151	−	0.491016i	$-0.163374\pi$
$839$	2.75189e6	+	3.78765e6i	0.134966	+	0.185765i	−0.736184	+	0.676781i	$0.763374\pi$
$840$		0			0
$841$	1.16360e7	+	3.58121e7i	0.567303	+	1.74598i
$842$	1.14660e6	+	3.52889e6i	0.0557357	+	0.171537i
$843$		0			0
$844$	5.28044e6	+	7.26790e6i	0.255161	+	0.351199i
$845$	3.96325e6	+	1.28774e6i	0.190946	+	0.0620420i
$846$		0			0
$847$	8.29326e6	−	1.55694e7i	0.397207	−	0.745701i
$848$		−	5.86260e6i		−	0.279963i
$849$		0			0
$850$	−3.31870e6	+	2.41118e6i	−0.157551	+	0.114467i
$851$	−815968.	+	1.12308e6i	−0.0386233	+	0.0531604i
$852$		0			0
$853$	4.03488e7	−	1.31101e7i	1.89871	−	0.616928i	0.930872	−	0.365344i	$-0.119049\pi$
$853$	4.03488e7	−	1.31101e7i	1.89871	−	0.616928i	0.967836	−	0.251583i	$-0.0809512\pi$
$854$	−5.11911e6	−	3.71925e6i	−0.240187	−	0.174506i
$855$		0			0
$856$	−867288.	+	2.66924e6i	−0.0404556	+	0.124510i
$857$	1.76910e7			0.822810			0.411405	−	0.911453i	$-0.365038\pi$
$857$	1.76910e7			0.822810			0.411405	+	0.911453i	$0.365038\pi$
$858$		0			0
$859$	2.75895e7			1.27574			0.637868	−	0.770146i	$-0.279817\pi$
$859$	2.75895e7			1.27574			0.637868	+	0.770146i	$0.279817\pi$
$860$	325174.	−	1.00078e6i	0.0149924	−	0.0461417i
$861$		0			0
$862$	1.76055e7	+	1.27912e7i	0.807013	+	0.586330i
$863$	−1.37622e7	+	4.47160e6i	−0.629013	+	0.204379i	−0.606138	−	0.795360i	$-0.707282\pi$
$863$	−1.37622e7	+	4.47160e6i	−0.629013	+	0.204379i	−0.0228751	+	0.999738i	$0.507282\pi$
$864$		0			0
$865$	−1.54816e6	+	2.13086e6i	−0.0703519	+	0.0968311i
$866$	−1.70228e7	+	1.23678e7i	−0.771324	+	0.560400i
$867$		0			0
$868$		−	7.75386e6i		−	0.349316i
$869$	6.12608e6	−	2.45316e7i	0.275190	−	1.10198i
$870$		0			0
$871$	−5.81830e6	−	1.89048e6i	−0.259867	−	0.0844358i
$872$	3.57182e6	+	4.91618e6i	0.159074	+	0.218946i
$873$		0			0
$874$	6.34961e6	+	1.95421e7i	0.281169	+	0.865351i
$875$	2.50622e6	+	7.71335e6i	0.110662	+	0.340583i
$876$		0			0
$877$	−2.34151e7	−	3.22281e7i	−1.02801	−	1.41493i	−0.906434	−	0.422348i	$-0.861206\pi$
$877$	−2.34151e7	−	3.22281e7i	−1.02801	−	1.41493i	−0.121574	−	0.992582i	$-0.538794\pi$
$878$	−1.71400e6	−	556913.i	−0.0750369	−	0.0243810i
$879$		0			0
$880$	955152.	−	800863.i	0.0415782	−	0.0348619i
$881$		−	1.46960e7i		−	0.637912i	−0.947770	−	0.318956i	$-0.896668\pi$
$881$		−	1.46960e7i		−	0.637912i	0.947770	−	0.318956i	$-0.103332\pi$
$882$		0			0
$883$	1.84948e7	−	1.34373e7i	0.798267	−	0.579975i	−0.112138	−	0.993693i	$-0.535770\pi$
$883$	1.84948e7	−	1.34373e7i	0.798267	−	0.579975i	0.910405	+	0.413718i	$0.135770\pi$
$884$	540288.	−	743643.i	0.0232538	−	0.0320062i
$885$		0			0
$886$	516337.	−	167768.i	0.0220978	−	0.00718000i
$887$	−2.00110e6	−	1.45388e6i	−0.0854004	−	0.0620470i	0.544266	−	0.838913i	$-0.316808\pi$
$887$	−2.00110e6	−	1.45388e6i	−0.0854004	−	0.0620470i	−0.629666	+	0.776866i	$0.716808\pi$
$888$		0			0
$889$	7.13021e6	−	2.19445e7i	0.302585	−	0.931262i
$890$	−2.55351e6			−0.108059
$891$		0			0
$892$	−2.32152e7			−0.976923
$893$	1.70201e7	−	5.23824e7i	0.714221	−	2.19815i
$894$		0			0
$895$	3.13533e6	+	2.27795e6i	0.130836	+	0.0950577i
$896$	−1.70676e6	+	554560.i	−0.0710236	+	0.0230770i
$897$		0			0
$898$	1.57794e7	−	2.17185e7i	0.652980	−	0.898750i
$899$	−2.72989e7	+	1.98338e7i	−1.12654	+	0.818477i
$900$		0			0
$901$			7.88690e6i			0.323664i
$902$	694566.	−	280323.i	0.0284248	−	0.0114721i
$903$		0			0
$904$	−705425.	−	229206.i	−0.0287098	−	0.00932837i
$905$	501197.	+	689838.i	0.0203417	+	0.0279979i
$906$		0			0
$907$	5.64640e6	+	1.73778e7i	0.227905	+	0.701419i	0.997984	+	0.0634702i	$0.0202168\pi$
$907$	5.64640e6	+	1.73778e7i	0.227905	+	0.701419i	−0.770079	+	0.637949i	$0.779783\pi$
$908$	5.24128e6	+	1.61310e7i	0.210971	+	0.649302i
$909$		0			0
$910$	−521215.	−	717391.i	−0.0208648	−	0.0287179i
$911$	−1.35171e7	−	4.39197e6i	−0.539619	−	0.175333i	0.0265116	−	0.999649i	$-0.491560\pi$
$911$	−1.35171e7	−	4.39197e6i	−0.539619	−	0.175333i	−0.566130	+	0.824316i	$0.691560\pi$
$912$		0			0
$913$	−736774.	+	297358.i	−0.0292521	+	0.0118060i
$914$			1.66276e7i			0.658359i
$915$		0			0
$916$	−7.84130e6	+	5.69703e6i	−0.308780	+	0.224342i
$917$	−8.24351e6	+	1.13462e7i	−0.323734	+	0.445582i
$918$		0			0
$919$	−2.81462e6	+	914525.i	−0.109934	+	0.0357196i	−0.363467	−	0.931607i	$-0.618407\pi$
$919$	−2.81462e6	+	914525.i	−0.109934	+	0.0357196i	0.253534	+	0.967327i	$0.418407\pi$
$920$	1.49044e6	+	1.08287e6i	0.0580556	+	0.0421799i
$921$		0			0
$922$	−2.86877e6	+	8.82917e6i	−0.111140	+	0.342052i
$923$	1.67840e6			0.0648472
$924$		0			0
$925$	1.74235e6			0.0669545
$926$	1.00887e7	−	3.10497e7i	0.386640	−	1.18995i
$927$		0			0
$928$	6.31819e6	+	4.59044e6i	0.240837	+	0.174978i
$929$	−1.90118e7	+	6.17729e6i	−0.722741	+	0.234833i	−0.647211	−	0.762311i	$-0.724065\pi$
$929$	−1.90118e7	+	6.17729e6i	−0.722741	+	0.234833i	−0.0755300	+	0.997144i	$0.524065\pi$
$930$		0			0
$931$	−6.12072e6	+	8.42445e6i	−0.231435	+	0.318543i
$932$	−1.17552e7	+	8.54066e6i	−0.443293	+	0.322071i
$933$		0			0
$934$		−	3.44975e7i		−	1.29396i
$935$	−1.28496e6	+	1.07739e6i	−0.0480683	+	0.0403037i
$936$		0			0
$937$	−7.10464e6	−	2.30844e6i	−0.264358	−	0.0858952i	0.173839	−	0.984774i	$-0.444383\pi$
$937$	−7.10464e6	−	2.30844e6i	−0.264358	−	0.0858952i	−0.438197	+	0.898879i	$0.644383\pi$
$938$	−9.44461e6	−	1.29994e7i	−0.350491	−	0.482410i
$939$		0			0
$940$	−1.52600e6	−	4.69653e6i	−0.0563292	−	0.173363i
$941$	12133.5	+	37343.0i	0.000446696	+	0.00137479i	0.951280	−	0.308330i	$-0.0997699\pi$
$941$	12133.5	+	37343.0i	0.000446696	+	0.00137479i	−0.950833	+	0.309704i	$0.899770\pi$
$942$		0			0
$943$	650691.	+	895599.i	0.0238284	+	0.0327970i
$944$	1.02233e7	+	3.32176e6i	0.373390	+	0.121322i
$945$		0			0
$946$	−2.10822e6	+	8.44224e6i	−0.0765927	+	0.306711i
$947$		−	4.85984e7i		−	1.76095i	−0.474093	−	0.880475i	$-0.657224\pi$
$947$		−	4.85984e7i		−	1.76095i	0.474093	−	0.880475i	$-0.342776\pi$
$948$		0			0
$949$	−8.31253e6	+	6.03940e6i	−0.299618	+	0.217685i
$950$	1.51587e7	−	2.08642e7i	0.544947	−	0.750055i
$951$		0			0
$952$	2.29609e6	−	746044.i	0.0821100	−	0.0266792i
$953$	−1.78462e7	−	1.29660e7i	−0.636523	−	0.462461i	0.222131	−	0.975017i	$-0.428699\pi$
$953$	−1.78462e7	−	1.29660e7i	−0.636523	−	0.462461i	−0.858654	+	0.512556i	$0.828699\pi$
$954$		0			0
$955$	1.86949e6	−	5.75369e6i	0.0663306	−	0.204145i
$956$	−1.79376e7			−0.634776
$957$		0			0
$958$	2.28078e7			0.802916
$959$	6.23670e6	−	1.91946e7i	0.218982	−	0.673958i
$960$		0			0
$961$	7.32491e6	+	5.32186e6i	0.255855	+	0.185890i
$962$	−371310.	+	120646.i	−0.0129360	+	0.00420315i
$963$		0			0
$964$	7.46639e6	−	1.02766e7i	0.258772	−	0.356170i
$965$	−4.47469e6	+	3.25106e6i	−0.154684	+	0.112384i
$966$		0			0
$967$			1.14017e6i			0.0392106i	0.999808	+	0.0196053i	$0.00624096\pi$
$967$			1.14017e6i			0.0392106i	−0.999808	+	0.0196053i	$0.993759\pi$
$968$	−7.41974e6	+	7.15452e6i	−0.254507	+	0.245410i
$969$		0			0
$970$	4.44795e6	+	1.44523e6i	0.151786	+	0.0493182i
$971$	7.34183e6	+	1.01052e7i	0.249894	+	0.343950i	0.915474	−	0.402377i	$-0.131816\pi$
$971$	7.34183e6	+	1.01052e7i	0.249894	+	0.343950i	−0.665580	+	0.746326i	$0.731816\pi$
$972$		0			0
$973$	−1.31670e7	−	4.05238e7i	−0.445866	−	1.37223i
$974$	−7.39770e6	−	2.27678e7i	−0.249861	−	0.768994i
$975$		0			0
$976$	2.17315e6	+	2.99108e6i	0.0730238	+	0.100509i
$977$	−4.50168e7	−	1.46268e7i	−1.50882	−	0.490246i	−0.566246	−	0.824236i	$-0.691605\pi$
$977$	−4.50168e7	−	1.46268e7i	−1.50882	−	0.490246i	−0.942577	+	0.333990i	$0.891605\pi$
$978$		0			0
$979$	2.10645e7	−	1.46511e6i	0.702415	−	0.0488555i
$980$			933632.i			0.0310535i
$981$		0			0
$982$	1.40943e7	−	1.02401e7i	0.466408	−	0.338865i
$983$	−1.63944e7	+	2.25650e7i	−0.541144	+	0.744821i	−0.988777	−	0.149396i	$-0.952267\pi$
$983$	−1.63944e7	+	2.25650e7i	−0.541144	+	0.744821i	0.447633	+	0.894217i	$0.352267\pi$
$984$		0			0
$985$	−3.92641e6	+	1.27577e6i	−0.128945	+	0.0418969i
$986$	−8.49980e6	−	6.17547e6i	−0.278430	−	0.202291i
$987$		0			0
$988$	−1.78576e6	+	5.49600e6i	−0.0582010	+	0.179124i
$989$	−1.28608e7			−0.418096
$990$		0			0
$991$	9.07402e6			0.293505			0.146752	−	0.989173i	$-0.453118\pi$
$991$	9.07402e6			0.293505			0.146752	+	0.989173i	$0.453118\pi$
$992$	−1.40002e6	+	4.30881e6i	−0.0451705	+	0.139020i
$993$		0			0
$994$	3.56639e6	+	2.59113e6i	0.114489	+	0.0831809i
$995$	2.25172e6	−	731630.i	0.0721037	−	0.0234279i
$996$		0			0
$997$	1.39824e7	−	1.92452e7i	0.445497	−	0.613174i	−0.525925	−	0.850531i	$-0.676281\pi$
$997$	1.39824e7	−	1.92452e7i	0.445497	−	0.613174i	0.971423	+	0.237356i	$0.0762809\pi$
$998$	3.12596e7	−	2.27114e7i	0.993475	−	0.721802i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.6.l.b.35.5	yes	40
3.2	odd	2		198.6.l.a.35.6	yes	40
11.6	odd	10		198.6.l.a.17.6	✓	40
33.17	even	10	inner	198.6.l.b.17.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.6.l.a.17.6	✓	40	11.6	odd	10
198.6.l.a.35.6	yes	40	3.2	odd	2
198.6.l.b.17.5	yes	40	33.17	even	10	inner
198.6.l.b.35.5	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)

\(f(q)\)	\(=\)	\(q+(-1.23607 + 3.80423i) q^{2} +(-12.9443 - 9.40456i) q^{4} +(-11.5390 + 3.74924i) q^{5} +(-64.3821 + 88.6144i) q^{7} +(51.7771 - 37.6183i) q^{8} +O(q^{10})\)	\(q+(-1.23607 + 3.80423i) q^{2} +(-12.9443 - 9.40456i) q^{4} +(-11.5390 + 3.74924i) q^{5} +(-64.3821 + 88.6144i) q^{7} +(51.7771 - 37.6183i) q^{8} -48.5312i q^{10} +(27.8454 + 400.344i) q^{11} +(-158.649 - 51.5482i) q^{13} +(-257.528 - 354.457i) q^{14} +(79.1084 + 243.470i) q^{16} +(-106.424 - 327.538i) q^{17} +(1272.65 + 1751.65i) q^{19} +(184.624 + 59.9879i) q^{20} +(-1557.42 - 388.923i) q^{22} -2372.55i q^{23} +(-2409.09 + 1750.30i) q^{25} +(392.202 - 539.819i) q^{26} +(1666.76 - 541.563i) q^{28} +(-6170.11 - 4482.85i) q^{29} +(1367.21 - 4207.83i) q^{31} -1024.00 q^{32} +1377.58 q^{34} +(410.667 - 1263.90i) q^{35} +(-473.366 - 343.921i) q^{37} +(-8236.75 + 2676.28i) q^{38} +(-456.415 + 628.202i) q^{40} +(-377.484 + 274.258i) q^{41} -5420.66i q^{43} +(3404.63 - 5444.04i) q^{44} +(9025.71 + 2932.63i) q^{46} +(-14952.3 - 20580.1i) q^{47} +(1486.20 + 4574.05i) q^{49} +(-3680.76 - 11328.2i) q^{50} +(1568.81 + 2159.28i) q^{52} +(-21780.0 - 7076.74i) q^{53} +(-1822.30 - 4515.17i) q^{55} +7010.14i q^{56} +(24680.4 - 17931.4i) q^{58} +(24681.1 - 33970.6i) q^{59} +(13735.2 - 4462.85i) q^{61} +(14317.6 + 10402.3i) q^{62} +(1265.73 - 3895.53i) q^{64} +2023.91 q^{65} +36674.1 q^{67} +(-1702.78 + 5240.61i) q^{68} +(4300.56 + 3124.54i) q^{70} +(-9569.10 + 3109.19i) q^{71} +(36204.6 - 49831.3i) q^{73} +(1893.46 - 1375.68i) q^{74} -34642.5i q^{76} +(-37269.0 - 23307.5i) q^{77} +(-59921.9 - 19469.8i) q^{79} +(-1825.66 - 2512.81i) q^{80} +(-576.744 - 1775.04i) q^{82} +(611.792 + 1882.90i) q^{83} +(2456.04 + 3380.45i) q^{85} +(20621.4 + 6700.30i) q^{86} +(16502.0 + 19681.2i) q^{88} -52615.8i q^{89} +(14782.1 - 10739.8i) q^{91} +(-22312.8 + 30710.9i) q^{92} +(96773.4 - 31443.6i) q^{94} +(-21252.4 - 15440.8i) q^{95} +(-29779.3 + 91651.3i) q^{97} -19237.8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 160 q^{4} + 640 q^{8}+O(q^{10}) \) 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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