LMFDB - Embedded newform 198.6.l.b.17.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("198.17");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	198.l (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$31.7559963230$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			17.9
Character	$\chi$	$=$	198.17
Dual form			198.6.l.b.35.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23607 - 3.80423i) q^{2} +(-12.9443 + 9.40456i) q^{4} +(74.1025 + 24.0774i) q^{5} +(-84.1988 - 115.890i) q^{7} +(51.7771 + 37.6183i) q^{8} +O(q^{10})$	\(q+(-1.23607 - 3.80423i) q^{2} +(-12.9443 + 9.40456i) q^{4} +(74.1025 + 24.0774i) q^{5} +(-84.1988 - 115.890i) q^{7} +(51.7771 + 37.6183i) q^{8} -311.664i q^{10} +(-369.261 + 157.155i) q^{11} +(160.738 - 52.2269i) q^{13} +(-336.795 + 463.559i) q^{14} +(79.1084 - 243.470i) q^{16} +(77.0799 - 237.227i) q^{17} +(-448.565 + 617.397i) q^{19} +(-1185.64 + 385.238i) q^{20} +(1054.28 + 1210.50i) q^{22} -4445.10i q^{23} +(2383.28 + 1731.55i) q^{25} +(-397.366 - 546.927i) q^{26} +(2179.78 + 708.255i) q^{28} +(3971.67 - 2885.58i) q^{29} +(-1130.03 - 3477.86i) q^{31} -1024.00 q^{32} -997.743 q^{34} +(-3449.02 - 10615.0i) q^{35} +(-1271.49 + 923.788i) q^{37} +(2903.18 + 943.299i) q^{38} +(2931.06 + 4034.26i) q^{40} +(-11553.3 - 8393.95i) q^{41} -5116.91i q^{43} +(3301.84 - 5506.99i) q^{44} +(-16910.2 + 5494.45i) q^{46} +(-2015.59 + 2774.22i) q^{47} +(-1147.34 + 3531.14i) q^{49} +(3641.33 - 11206.9i) q^{50} +(-1589.46 + 2187.71i) q^{52} +(-28729.8 + 9334.87i) q^{53} +(-31147.0 + 2754.73i) q^{55} -9167.84i q^{56} +(-15886.7 - 11542.3i) q^{58} +(-16640.1 - 22903.1i) q^{59} +(23713.9 + 7705.12i) q^{61} +(-11833.8 + 8597.75i) q^{62} +(1265.73 + 3895.53i) q^{64} +13168.6 q^{65} -53227.5 q^{67} +(1233.28 + 3795.64i) q^{68} +(-36118.6 + 26241.7i) q^{70} +(-43503.1 - 14135.0i) q^{71} +(30255.5 + 41643.1i) q^{73} +(5085.94 + 3695.15i) q^{74} -12210.3i q^{76} +(49303.9 + 29561.3i) q^{77} +(15425.0 - 5011.90i) q^{79} +(11724.2 - 16137.0i) q^{80} +(-17651.8 + 54326.8i) q^{82} +(22823.0 - 70242.0i) q^{83} +(11423.6 - 15723.3i) q^{85} +(-19465.9 + 6324.85i) q^{86} +(-25031.1 - 5753.93i) q^{88} -122742. i q^{89} +(-19586.5 - 14230.4i) q^{91} +(41804.2 + 57538.6i) q^{92} +(13045.2 + 4238.63i) q^{94} +(-48105.1 + 34950.4i) q^{95} +(-16932.5 - 52113.0i) q^{97} +14851.4 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} - 160 q^{4} + 640 q^{8}+O(q^{10}) $ 40 * q + 40 * q^2 - 160 * q^4 + 640 * q^8	$ 40 q + 40 q^{2} - 160 q^{4} + 640 q^{8} - 476 q^{11} - 2560 q^{16} - 1424 q^{17} - 1656 q^{22} + 11574 q^{25} + 10480 q^{26} + 3040 q^{28} - 10658 q^{29} - 5302 q^{31} - 40960 q^{32} - 13984 q^{34} - 50 q^{35} - 4344 q^{37} + 35120 q^{38} + 19840 q^{40} - 16856 q^{41} + 6624 q^{44} - 52400 q^{46} - 10900 q^{47} - 40698 q^{49} - 6256 q^{50} + 41920 q^{52} + 10290 q^{53} + 158396 q^{55} + 42632 q^{58} + 62620 q^{59} - 134780 q^{61} - 30272 q^{62} - 40960 q^{64} - 137296 q^{65} - 36856 q^{67} - 22784 q^{68} + 79400 q^{70} + 62180 q^{71} + 100030 q^{73} + 17376 q^{74} - 162888 q^{77} + 35900 q^{79} + 79360 q^{80} - 90096 q^{82} - 12276 q^{83} + 270600 q^{85} - 137680 q^{86} - 26496 q^{88} + 406656 q^{91} + 134720 q^{92} - 91600 q^{94} - 75128 q^{95} - 364164 q^{97} + 358192 q^{98}+O(q^{100}) $ 40 * q + 40 * q^2 - 160 * q^4 + 640 * q^8 - 476 * q^11 - 2560 * q^16 - 1424 * q^17 - 1656 * q^22 + 11574 * q^25 + 10480 * q^26 + 3040 * q^28 - 10658 * q^29 - 5302 * q^31 - 40960 * q^32 - 13984 * q^34 - 50 * q^35 - 4344 * q^37 + 35120 * q^38 + 19840 * q^40 - 16856 * q^41 + 6624 * q^44 - 52400 * q^46 - 10900 * q^47 - 40698 * q^49 - 6256 * q^50 + 41920 * q^52 + 10290 * q^53 + 158396 * q^55 + 42632 * q^58 + 62620 * q^59 - 134780 * q^61 - 30272 * q^62 - 40960 * q^64 - 137296 * q^65 - 36856 * q^67 - 22784 * q^68 + 79400 * q^70 + 62180 * q^71 + 100030 * q^73 + 17376 * q^74 - 162888 * q^77 + 35900 * q^79 + 79360 * q^80 - 90096 * q^82 - 12276 * q^83 + 270600 * q^85 - 137680 * q^86 - 26496 * q^88 + 406656 * q^91 + 134720 * q^92 - 91600 * q^94 - 75128 * q^95 - 364164 * q^97 + 358192 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.23607	−	3.80423i	−0.218508	−	0.672499i
$2$	−1.23607	−	3.80423i	−0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−12.9443	+	9.40456i	−0.404508	+	0.293893i
$5$	74.1025	+	24.0774i	1.32559	+	0.430709i	0.884409	−	0.466712i	$-0.154561\pi$
$5$	74.1025	+	24.0774i	1.32559	+	0.430709i	0.441176	+	0.897421i	$0.354561\pi$
$6$		0			0
$7$	−84.1988	−	115.890i	−0.649473	−	0.893922i	0.349604	−	0.936898i	$-0.386316\pi$
$7$	−84.1988	−	115.890i	−0.649473	−	0.893922i	−0.999076	+	0.0429755i	$0.986316\pi$
$8$	51.7771	+	37.6183i	0.286031	+	0.207813i
$9$		0			0
$10$		−	311.664i		−	0.985567i
$11$	−369.261	+	157.155i	−0.920135	+	0.391602i
$11$	−369.261	+	157.155i	−0.920135	+	0.391602i
$12$		0			0
$13$	160.738	−	52.2269i	0.263791	−	0.0857108i	−0.174135	−	0.984722i	$-0.555713\pi$
$13$	160.738	−	52.2269i	0.263791	−	0.0857108i	0.437926	+	0.899011i	$0.355713\pi$
$14$	−336.795	+	463.559i	−0.459246	+	0.632098i
$15$		0			0
$16$	79.1084	−	243.470i	0.0772542	−	0.237764i
$17$	77.0799	−	237.227i	0.0646872	−	0.199087i	−0.913489	−	0.406863i	$-0.866623\pi$
$17$	77.0799	−	237.227i	0.0646872	−	0.199087i	0.978176	+	0.207776i	$0.0666226\pi$
$18$		0			0
$19$	−448.565	+	617.397i	−0.285064	+	0.392356i	−0.927403	−	0.374064i	$-0.877964\pi$
$19$	−448.565	+	617.397i	−0.285064	+	0.392356i	0.642339	+	0.766420i	$0.277964\pi$
$20$	−1185.64	+	385.238i	−0.662793	+	0.215354i
$21$		0			0
$22$	1054.28	+	1210.50i	0.464409	+	0.533221i
$23$		−	4445.10i		−	1.75211i	−0.482209	−	0.876056i	$-0.660165\pi$
$23$		−	4445.10i		−	1.75211i	0.482209	−	0.876056i	$-0.339835\pi$
$24$		0			0
$25$	2383.28	+	1731.55i	0.762649	+	0.554097i
$26$	−397.366	−	546.927i	−0.115281	−	0.158670i
$27$		0			0
$28$	2179.78	+	708.255i	0.525434	+	0.170724i
$29$	3971.67	−	2885.58i	0.876956	−	0.637146i	−0.0554884	−	0.998459i	$-0.517672\pi$
$29$	3971.67	−	2885.58i	0.876956	−	0.637146i	0.932444	+	0.361313i	$0.117672\pi$
$30$		0			0
$31$	−1130.03	−	3477.86i	−0.211195	−	0.649992i	−0.999402	−	0.0345815i	$-0.988990\pi$
$31$	−1130.03	−	3477.86i	−0.211195	−	0.649992i	0.788207	−	0.615411i	$-0.211010\pi$
$32$	−1024.00			−0.176777
$33$		0			0
$34$	−997.743			−0.148020
$35$	−3449.02	−	10615.0i	−0.475911	−	1.46470i
$36$		0			0
$37$	−1271.49	+	923.788i	−0.152689	+	0.110935i	−0.661507	−	0.749939i	$-0.730083\pi$
$37$	−1271.49	+	923.788i	−0.152689	+	0.110935i	0.508818	+	0.860874i	$0.330083\pi$
$38$	2903.18	+	943.299i	0.326148	+	0.105972i
$39$		0			0
$40$	2931.06	+	4034.26i	0.289651	+	0.398670i
$41$	−11553.3	−	8393.95i	−1.07336	−	0.779843i	−0.0968478	−	0.995299i	$-0.530876\pi$
$41$	−11553.3	−	8393.95i	−1.07336	−	0.779843i	−0.976513	+	0.215457i	$0.930876\pi$
$42$		0			0
$43$		−	5116.91i		−	0.422024i	−0.977483	−	0.211012i	$-0.932324\pi$
$43$		−	5116.91i		−	0.422024i	0.977483	−	0.211012i	$-0.0676759\pi$
$44$	3301.84	−	5506.99i	0.257113	−	0.428827i
$45$		0			0
$46$	−16910.2	+	5494.45i	−1.17829	+	0.382851i
$47$	−2015.59	+	2774.22i	−0.133093	+	0.183187i	−0.870362	−	0.492412i	$-0.836115\pi$
$47$	−2015.59	+	2774.22i	−0.133093	+	0.183187i	0.737269	+	0.675600i	$0.236115\pi$
$48$		0			0
$49$	−1147.34	+	3531.14i	−0.0682654	+	0.210099i
$50$	3641.33	−	11206.9i	0.205985	−	0.633955i
$51$		0			0
$52$	−1589.46	+	2187.71i	−0.0815159	+	0.112197i
$53$	−28729.8	+	9334.87i	−1.40489	+	0.456477i	−0.910769	−	0.412916i	$-0.864510\pi$
$53$	−28729.8	+	9334.87i	−1.40489	+	0.456477i	−0.494122	+	0.869393i	$0.664510\pi$
$54$		0			0
$55$	−31147.0	+	2754.73i	−1.38838	+	0.122792i
$56$		−	9167.84i		−	0.390658i
$57$		0			0
$58$	−15886.7	−	11542.3i	−0.620102	−	0.450530i
$59$	−16640.1	−	22903.1i	−0.622337	−	0.856573i	0.375184	−	0.926950i	$-0.377580\pi$
$59$	−16640.1	−	22903.1i	−0.622337	−	0.856573i	−0.997520	+	0.0703776i	$0.977580\pi$
$60$		0			0
$61$	23713.9	+	7705.12i	0.815979	+	0.265128i	0.687128	−	0.726536i	$-0.258871\pi$
$61$	23713.9	+	7705.12i	0.815979	+	0.265128i	0.128851	+	0.991664i	$0.458871\pi$
$62$	−11833.8	+	8597.75i	−0.390971	+	0.284057i
$63$		0			0
$64$	1265.73	+	3895.53i	0.0386271	+	0.118882i
$65$	13168.6			0.386594
$66$		0			0
$67$	−53227.5			−1.44860			−0.724301	−	0.689484i	$-0.757837\pi$
$67$	−53227.5			−1.44860			−0.724301	+	0.689484i	$0.757837\pi$
$68$	1233.28	+	3795.64i	0.0323436	+	0.0995434i
$69$		0			0
$70$	−36118.6	+	26241.7i	−0.881021	+	0.640099i
$71$	−43503.1	−	14135.0i	−1.02417	−	0.332774i	−0.251690	−	0.967808i	$-0.580986\pi$
$71$	−43503.1	−	14135.0i	−1.02417	−	0.332774i	−0.772485	+	0.635034i	$0.780986\pi$
$72$		0			0
$73$	30255.5	+	41643.1i	0.664503	+	0.914609i	0.999620	−	0.0275671i	$-0.00877598\pi$
$73$	30255.5	+	41643.1i	0.664503	+	0.914609i	−0.335117	+	0.942176i	$0.608776\pi$
$74$	5085.94	+	3695.15i	0.107967	+	0.0784428i
$75$		0			0
$76$		−	12210.3i		−	0.242490i
$77$	49303.9	+	29561.3i	0.947664	+	0.568194i
$78$		0			0
$79$	15425.0	−	5011.90i	0.278073	−	0.0903514i	−0.166661	−	0.986014i	$-0.553298\pi$
$79$	15425.0	−	5011.90i	0.278073	−	0.0903514i	0.444733	+	0.895663i	$0.353298\pi$
$80$	11724.2	−	16137.0i	0.204814	−	0.281903i
$81$		0			0
$82$	−17651.8	+	54326.8i	−0.289905	+	0.892236i
$83$	22823.0	−	70242.0i	0.363645	−	1.11918i	−0.587180	−	0.809456i	$-0.699762\pi$
$83$	22823.0	−	70242.0i	0.363645	−	1.11918i	0.950825	−	0.309728i	$-0.100238\pi$
$84$		0			0
$85$	11423.6	−	15723.3i	0.171497	−	0.236045i
$86$	−19465.9	+	6324.85i	−0.283810	+	0.0922156i
$87$		0			0
$88$	−25031.1	−	5753.93i	−0.344567	−	0.0792060i
$89$		−	122742.i		−	1.64254i	−0.570537	−	0.821272i	$-0.693265\pi$
$89$		−	122742.i		−	1.64254i	0.570537	−	0.821272i	$-0.306735\pi$
$90$		0			0
$91$	−19586.5	−	14230.4i	−0.247944	−	0.180142i
$92$	41804.2	+	57538.6i	0.514933	+	0.708744i
$93$		0			0
$94$	13045.2	+	4238.63i	0.152275	+	0.0494772i
$95$	−48105.1	+	34950.4i	−0.546867	+	0.397322i
$96$		0			0
$97$	−16932.5	−	52113.0i	−0.182723	−	0.562363i	0.817179	−	0.576384i	$-0.195537\pi$
$97$	−16932.5	−	52113.0i	−0.182723	−	0.562363i	−0.999902	+	0.0140211i	$0.995537\pi$
$98$	14851.4			0.156208
$99$		0			0
$100$	−47134.3			−0.471343
$101$	2727.50	+	8394.39i	0.0266049	+	0.0818815i	0.963477	−	0.267790i	$-0.0862933\pi$
$101$	2727.50	+	8394.39i	0.0266049	+	0.0818815i	−0.936872	+	0.349671i	$0.886293\pi$
$102$		0			0
$103$	−107329.	+	77979.4i	−0.996840	+	0.724247i	−0.961408	−	0.275125i	$-0.911281\pi$
$103$	−107329.	+	77979.4i	−0.996840	+	0.724247i	−0.0354320	+	0.999372i	$0.511281\pi$
$104$	10287.2	+	3342.52i	0.0932642	+	0.0303034i
$105$		0			0
$106$	71023.9	+	97756.1i	0.613960	+	0.845043i
$107$	−166052.	−	120644.i	−1.40212	−	1.01870i	−0.994410	−	0.105588i	$-0.966328\pi$
$107$	−166052.	−	120644.i	−1.40212	−	1.01870i	−0.407710	−	0.913112i	$-0.633672\pi$
$108$		0			0
$109$		−	95099.2i		−	0.766673i	−0.923609	−	0.383337i	$-0.874775\pi$
$109$		−	95099.2i		−	0.766673i	0.923609	−	0.383337i	$-0.125225\pi$
$110$	48979.4	+	115085.i	0.385951	+	0.906855i
$111$		0			0
$112$	−34876.5	+	11332.1i	−0.262717	+	0.0853620i
$113$	−94230.6	+	129697.i	−0.694218	+	0.955509i	0.305776	+	0.952103i	$0.401084\pi$
$113$	−94230.6	+	129697.i	−0.694218	+	0.955509i	−0.999994	+	0.00340592i	$0.998916\pi$
$114$		0			0
$115$	107026.	−	329393.i	0.754650	−	2.32257i
$116$	−24272.7	+	74703.6i	−0.167484	+	0.515462i
$117$		0			0
$118$	−66560.3	+	91612.4i	−0.440058	+	0.605688i
$119$	−33982.2	+	11041.5i	−0.219981	+	0.0714761i
$120$		0			0
$121$	111656.	−	116062.i	0.693295	−	0.720654i
$122$		−	99737.2i		−	0.606677i
$123$		0			0
$124$	47335.1	+	34391.0i	0.276458	+	0.200859i
$125$	−8202.63	−	11289.9i	−0.0469546	−	0.0646274i
$126$		0			0
$127$	268672.	+	87296.7i	1.47813	+	0.480273i	0.933553	−	0.358438i	$-0.116691\pi$
$127$	268672.	+	87296.7i	1.47813	+	0.480273i	0.544576	+	0.838712i	$0.316691\pi$
$128$	13254.9	−	9630.27i	0.0715077	−	0.0519534i
$129$		0			0
$130$	−16277.2	−	50096.2i	−0.0844738	−	0.259984i
$131$	313327.			1.59522			0.797608	−	0.603176i	$-0.206098\pi$
$131$	313327.			1.59522			0.797608	+	0.603176i	$0.206098\pi$
$132$		0			0
$133$	109319.			0.535877
$134$	65792.8	+	202489.i	0.316531	+	0.974183i
$135$		0			0
$136$	12915.1	−	9383.33i	0.0598755	−	0.0435021i
$137$	308617.	+	100276.i	1.40481	+	0.456452i	0.910745	−	0.412970i	$-0.135509\pi$
$137$	308617.	+	100276.i	1.40481	+	0.456452i	0.494070	+	0.869422i	$0.335509\pi$
$138$		0			0
$139$	67093.9	+	92346.9i	0.294541	+	0.405401i	0.930483	−	0.366336i	$-0.119388\pi$
$139$	67093.9	+	92346.9i	0.294541	+	0.405401i	−0.635941	+	0.771737i	$0.719388\pi$
$140$	144474.	+	104967.i	0.622976	+	0.452618i
$141$		0			0
$142$			182967.i			0.761470i
$143$	−51146.5	+	44546.0i	−0.209158	+	0.182167i
$144$		0			0
$145$	363788.	−	118202.i	1.43690	−	0.466879i
$146$	121022.	−	166572.i	0.469874	−	0.646726i
$147$		0			0
$148$	7770.63	−	23915.5i	0.0291610	−	0.0897482i
$149$	−20111.8	+	61897.6i	−0.0742137	+	0.228406i	−0.981282	−	0.192578i	$-0.938315\pi$
$149$	−20111.8	+	61897.6i	−0.0742137	+	0.228406i	0.907068	+	0.420984i	$0.138315\pi$
$150$		0			0
$151$	249160.	−	342939.i	0.889275	−	1.22398i	−0.0844898	−	0.996424i	$-0.526926\pi$
$151$	249160.	−	342939.i	0.889275	−	1.22398i	0.973765	−	0.227557i	$-0.0730740\pi$
$152$	−46450.8	+	15092.8i	−0.163074	+	0.0529859i
$153$		0			0
$154$	51514.8	−	224103.i	0.175037	−	0.761458i
$155$		−	284926.i		−	0.952584i
$156$		0			0
$157$	247774.	+	180019.i	0.802245	+	0.582865i	0.911572	−	0.411140i	$-0.134869\pi$
$157$	247774.	+	180019.i	0.802245	+	0.582865i	−0.109327	+	0.994006i	$0.534869\pi$
$158$	−38132.8	−	52485.3i	−0.121522	−	0.167261i
$159$		0			0
$160$	−75880.9	−	24655.2i	−0.234333	−	0.0761393i
$161$	−515141.	+	374272.i	−1.56625	+	1.13795i
$162$		0			0
$163$	97574.4	+	300303.i	0.287652	+	0.885301i	0.985591	+	0.169144i	$0.0541004\pi$
$163$	97574.4	+	300303.i	0.287652	+	0.885301i	−0.697940	+	0.716157i	$0.745900\pi$
$164$	228490.			0.663374
$165$		0			0
$166$	−295427.			−0.832109
$167$	140551.	+	432572.i	0.389981	+	1.20024i	0.932802	+	0.360389i	$0.117356\pi$
$167$	140551.	+	432572.i	0.389981	+	1.20024i	−0.542821	+	0.839848i	$0.682644\pi$
$168$		0			0
$169$	−277273.	+	201451.i	−0.746778	+	0.542566i
$170$	−73935.2	−	24023.0i	−0.196214	−	0.0637536i
$171$		0			0
$172$	48122.3	+	66234.7i	0.124030	+	0.170712i
$173$	65346.3	+	47476.9i	0.165999	+	0.120605i	0.667683	−	0.744445i	$-0.267286\pi$
$173$	65346.3	+	47476.9i	0.165999	+	0.120605i	−0.501684	+	0.865051i	$0.667286\pi$
$174$		0			0
$175$		−	421992.i		−	1.04162i
$176$	9050.91	+	102336.i	0.0220247	+	0.249028i
$177$		0			0
$178$	−466937.	+	151717.i	−1.10461	+	0.358909i
$179$	−114019.	+	156934.i	−0.265977	+	0.366086i	−0.921027	−	0.389500i	$-0.872648\pi$
$179$	−114019.	+	156934.i	−0.265977	+	0.366086i	0.655049	+	0.755586i	$0.272648\pi$
$180$		0			0
$181$	13734.1	−	42269.3i	0.0311606	−	0.0959023i	−0.934267	−	0.356575i	$-0.883944\pi$
$181$	13734.1	−	42269.3i	0.0311606	−	0.0959023i	0.965427	+	0.260673i	$0.0839444\pi$
$182$	−29925.5	+	92101.2i	−0.0669673	+	0.206104i
$183$		0			0
$184$	167217.	−	230154.i	0.364113	−	0.501158i
$185$	−116463.	+	37841.0i	−0.250183	+	0.0812893i
$186$		0			0
$187$	8818.82	+	99712.2i	0.0184419	+	0.208518i
$188$		−	54865.9i		−	0.113216i
$189$		0			0
$190$	192420.	+	139802.i	0.386694	+	0.280949i
$191$	117751.	+	162070.i	0.233550	+	0.321454i	0.909666	−	0.415342i	$-0.136338\pi$
$191$	117751.	+	162070.i	0.233550	+	0.321454i	−0.676115	+	0.736796i	$0.736338\pi$
$192$		0			0
$193$	−599942.	−	194933.i	−1.15935	−	0.376697i	−0.334695	−	0.942327i	$-0.608633\pi$
$193$	−599942.	−	194933.i	−1.15935	−	0.376697i	−0.824659	+	0.565630i	$0.808633\pi$
$194$	−177320.	+	128830.i	−0.338262	+	0.245762i
$195$		0			0
$196$	−18357.4	−	56498.2i	−0.0341327	−	0.105050i
$197$	884523.			1.62384			0.811921	−	0.583767i	$-0.198422\pi$
$197$	884523.			1.62384			0.811921	+	0.583767i	$0.198422\pi$
$198$		0			0
$199$	−727235.			−1.30179			−0.650897	−	0.759166i	$-0.725607\pi$
$199$	−727235.			−1.30179			−0.650897	+	0.759166i	$0.725607\pi$
$200$	58261.2	+	179310.i	0.102992	+	0.316978i
$201$		0			0
$202$	28562.8	−	20752.1i	0.0492518	−	0.0357835i
$203$	−668819.	−	217313.i	−1.13912	−	0.370122i
$204$		0			0
$205$	−654023.	−	900185.i	−1.08695	−	1.49605i
$206$	429318.	+	311918.i	0.704873	+	0.512120i
$207$		0			0
$208$		−	43266.5i		−	0.0693415i
$209$	68610.7	−	298475.i	0.108649	−	0.472652i
$210$		0			0
$211$	605906.	−	196871.i	0.936912	−	0.304421i	0.199526	−	0.979893i	$-0.436060\pi$
$211$	605906.	−	196871.i	0.936912	−	0.304421i	0.737386	+	0.675471i	$0.236060\pi$
$212$	284096.	−	391024.i	0.434135	−	0.597536i
$213$		0			0
$214$	−253705.	+	780824.i	−0.378700	+	1.16552i
$215$	123202.	−	379176.i	0.181769	−	0.559429i
$216$		0			0
$217$	−307902.	+	423790.i	−0.443877	+	0.610944i
$218$	−361779.	+	117549.i	−0.515587	+	0.167524i
$219$		0			0
$220$	377268.	−	328582.i	0.525525	−	0.457706i
$221$		−	42157.1i		−	0.0580617i
$222$		0			0
$223$	99111.5	+	72008.7i	0.133463	+	0.0969668i	0.652514	−	0.757777i	$-0.273714\pi$
$223$	99111.5	+	72008.7i	0.133463	+	0.0969668i	−0.519051	+	0.854744i	$0.673714\pi$
$224$	86219.6	+	118671.i	0.114812	+	0.158025i
$225$		0			0
$226$	609873.	+	198160.i	0.794271	+	0.258074i
$227$	−60268.3	+	43787.5i	−0.0776290	+	0.0564008i	−0.625923	−	0.779885i	$-0.715278\pi$
$227$	−60268.3	+	43787.5i	−0.0776290	+	0.0564008i	0.548294	+	0.836286i	$0.315278\pi$
$228$		0			0
$229$	103531.	+	318634.i	0.130461	+	0.401517i	0.994856	−	0.101295i	$-0.0322987\pi$
$229$	103531.	+	318634.i	0.130461	+	0.401517i	−0.864396	+	0.502812i	$0.832299\pi$
$230$	−1.38538e6			−1.72683
$231$		0			0
$232$	314192.			0.383244
$233$	−398121.	−	1.22529e6i	−0.480424	−	1.47859i	−0.838500	−	0.544902i	$-0.816567\pi$
$233$	−398121.	−	1.22529e6i	−0.480424	−	1.47859i	0.358076	−	0.933693i	$-0.383433\pi$
$234$		0			0
$235$	−216156.	+	157046.i	−0.255327	+	0.185506i
$236$	430787.	+	139971.i	0.503481	+	0.163591i
$237$		0			0
$238$	84008.7	+	115628.i	0.0961351	+	0.132319i
$239$	424558.	+	308459.i	0.480775	+	0.349304i	0.801626	−	0.597826i	$-0.203969\pi$
$239$	424558.	+	308459.i	0.480775	+	0.349304i	−0.320851	+	0.947130i	$0.603969\pi$
$240$		0			0
$241$			1.56745e6i			1.73840i	0.494460	+	0.869200i	$0.335366\pi$
$241$			1.56745e6i			1.73840i	−0.494460	+	0.869200i	$0.664634\pi$
$242$	−579540.	−	281304.i	−0.636129	−	0.308771i
$243$		0			0
$244$	−379423.	+	123282.i	−0.407989	+	0.132564i
$245$	−170041.	+	234041.i	−0.180983	+	0.249102i
$246$		0			0
$247$	−39856.7	+	122666.i	−0.0415680	+	0.127933i
$248$	72321.7	−	222583.i	0.0746688	−	0.229807i
$249$		0			0
$250$	−32810.5	+	45159.8i	−0.0332019	+	0.0456985i
$251$	305709.	−	99330.9i	0.306284	−	0.0995177i	−0.151843	−	0.988405i	$-0.548521\pi$
$251$	305709.	−	99330.9i	0.306284	−	0.0995177i	0.458126	+	0.888887i	$0.348521\pi$
$252$		0			0
$253$	698568.	+	1.64140e6i	0.686132	+	1.61218i
$254$		−	1.12999e6i		−	1.09898i
$255$		0			0
$256$	−53019.7	−	38521.1i	−0.0505636	−	0.0367366i
$257$	−771047.	−	1.06125e6i	−0.728195	−	1.00227i	−0.999212	−	0.0397002i	$-0.987360\pi$
$257$	−771047.	−	1.06125e6i	−0.728195	−	1.00227i	0.271016	−	0.962575i	$-0.412640\pi$
$258$		0			0
$259$	214115.	+	69570.2i	0.198334	+	0.0644427i
$260$	−170457.	+	123845.i	−0.156380	+	0.113617i
$261$		0			0
$262$	−387293.	−	1.19197e6i	−0.348568	−	1.07278i
$263$	−139963.			−0.124774			−0.0623868	−	0.998052i	$-0.519871\pi$
$263$	−139963.			−0.124774			−0.0623868	+	0.998052i	$0.519871\pi$
$264$		0			0
$265$	−2.35371e6			−2.05891
$266$	−135125.	−	415873.i	−0.117093	−	0.360377i
$267$		0			0
$268$	688991.	−	500581.i	0.585972	−	0.425733i
$269$	86170.4	+	27998.5i	0.0726068	+	0.0235914i	0.345095	−	0.938568i	$-0.387847\pi$
$269$	86170.4	+	27998.5i	0.0726068	+	0.0235914i	−0.272488	+	0.962159i	$0.587847\pi$
$270$		0			0
$271$	−534009.	−	735000.i	−0.441698	−	0.607945i	0.528890	−	0.848690i	$-0.322608\pi$
$271$	−534009.	−	735000.i	−0.441698	−	0.607945i	−0.970588	+	0.240745i	$0.922608\pi$
$272$	−51660.2	−	37533.3i	−0.0423383	−	0.0307606i
$273$		0			0
$274$		−	1.29800e6i		−	1.04447i
$275$	−1.15217e6	−	264851.i	−0.918726	−	0.211189i
$276$		0			0
$277$	−225290.	+	73201.1i	−0.176418	+	0.0573216i	−0.395894	−	0.918296i	$-0.629565\pi$
$277$	−225290.	+	73201.1i	−0.176418	+	0.0573216i	0.219476	+	0.975618i	$0.429565\pi$
$278$	268376.	−	369388.i	0.208272	−	0.286662i
$279$		0			0
$280$	220737.	−	679360.i	0.168260	−	0.517851i
$281$	755537.	−	2.32530e6i	0.570808	−	1.75677i	−0.0792230	−	0.996857i	$-0.525244\pi$
$281$	755537.	−	2.32530e6i	0.570808	−	1.75677i	0.650031	−	0.759908i	$-0.274756\pi$
$282$		0			0
$283$	257183.	−	353982.i	0.190887	−	0.262733i	−0.702837	−	0.711351i	$-0.748084\pi$
$283$	257183.	−	353982.i	0.190887	−	0.262733i	0.893724	+	0.448618i	$0.148084\pi$
$284$	696049.	−	226160.i	0.512087	−	0.166387i
$285$		0			0
$286$	232684.	+	139511.i	0.168210	+	0.100854i
$287$			2.04567e6i			1.46599i
$288$		0			0
$289$	1.09835e6	+	798000.i	0.773566	+	0.562028i
$290$	−899332.	−	1.23782e6i	−0.627950	−	0.864299i
$291$		0			0
$292$	−783270.	−	254500.i	−0.537594	−	0.174675i
$293$	−389715.	+	283144.i	−0.265203	+	0.192681i	−0.712437	−	0.701736i	$-0.752409\pi$
$293$	−389715.	+	283144.i	−0.265203	+	0.192681i	0.447235	+	0.894417i	$0.352409\pi$
$294$		0			0
$295$	−681625.	−	2.09783e6i	−0.456027	−	1.40351i
$296$	−100585.			−0.0667274
$297$		0			0
$298$	260332.			0.169819
$299$	−232154.	−	714496.i	−0.150175	−	0.462191i
$300$		0			0
$301$	−592998.	+	430838.i	−0.377256	+	0.274093i
$302$	−1.61260e6	−	523965.i	−1.01744	−	0.330586i
$303$		0			0
$304$	114833.	+	158054.i	0.0712659	+	0.0980891i
$305$	1.57174e6	+	1.14194e6i	0.967457	+	0.702898i
$306$		0			0
$307$			590723.i			0.357715i	0.983875	+	0.178858i	$0.0572402\pi$
$307$			590723.i			0.357715i	−0.983875	+	0.178858i	$0.942760\pi$
$308$	−916214.	+	81032.5i	−0.550326	+	0.0486724i
$309$		0			0
$310$	−1.08392e6	+	352188.i	−0.640611	+	0.208147i
$311$	−1.47782e6	+	2.03405e6i	−0.866407	+	1.19251i	0.113597	+	0.993527i	$0.463763\pi$
$311$	−1.47782e6	+	2.03405e6i	−0.866407	+	1.19251i	−0.980004	+	0.198980i	$0.936237\pi$
$312$		0			0
$313$	−438668.	+	1.35008e6i	−0.253090	+	0.778932i	0.741110	+	0.671384i	$0.234300\pi$
$313$	−438668.	+	1.35008e6i	−0.253090	+	0.778932i	−0.994200	+	0.107548i	$0.965700\pi$
$314$	378566.	−	1.16511e6i	0.216679	−	0.666870i
$315$		0			0
$316$	−152531.	+	209941.i	−0.0859293	+	0.118271i
$317$	3.02700e6	−	983531.i	1.69186	−	0.549718i	0.704706	−	0.709500i	$-0.251079\pi$
$317$	3.02700e6	−	983531.i	1.69186	−	0.549718i	0.987152	+	0.159782i	$0.0510791\pi$
$318$		0			0
$319$	−1.01310e6	+	1.68970e6i	−0.557410	+	0.929678i
$320$			319144.i			0.174225i
$321$		0			0
$322$	2.06057e6	+	1.49709e6i	1.10751	+	0.804651i
$323$	111888.	+	154001.i	0.0596730	+	0.0821329i
$324$		0			0
$325$	473517.	+	153855.i	0.248672	+	0.0807984i
$326$	1.02181e6	−	742390.i	0.532509	−	0.386891i
$327$		0			0
$328$	−282430.	−	869229.i	−0.144952	−	0.446118i
$329$	491213.			0.250196
$330$		0			0
$331$	2.63000e6			1.31943			0.659714	−	0.751516i	$-0.270677\pi$
$331$	2.63000e6			1.31943			0.659714	+	0.751516i	$0.270677\pi$
$332$	365168.	+	1.12387e6i	0.181822	+	0.559592i
$333$		0			0
$334$	1.47187e6	−	1.06938e6i	0.721944	−	0.524523i
$335$	−3.94429e6	−	1.28158e6i	−1.92025	−	0.623925i
$336$		0			0
$337$	88758.2	+	122165.i	0.0425729	+	0.0585966i	0.829773	−	0.558101i	$-0.188470\pi$
$337$	88758.2	+	122165.i	0.0425729	+	0.0585966i	−0.787200	+	0.616698i	$0.788470\pi$
$338$	1.10909e6	+	805803.i	0.528052	+	0.383652i
$339$		0			0
$340$			310960.i			0.145884i
$341$	963836.	+	1.10665e6i	0.448867	+	0.515376i
$342$		0			0
$343$	−1.78390e6	+	579624.i	−0.818720	+	0.266018i
$344$	192489.	−	264939.i	0.0877022	−	0.120712i
$345$		0			0
$346$	99840.3	−	307277.i	0.0448348	−	0.137987i
$347$	453034.	−	1.39430e6i	0.201980	−	0.621629i	−0.797844	−	0.602864i	$-0.794026\pi$
$347$	453034.	−	1.39430e6i	0.201980	−	0.621629i	0.999824	−	0.0187657i	$-0.00597366\pi$
$348$		0			0
$349$	496765.	−	683739.i	0.218317	−	0.300488i	−0.685785	−	0.727804i	$-0.740541\pi$
$349$	496765.	−	683739.i	0.218317	−	0.300488i	0.904102	+	0.427316i	$0.140541\pi$
$350$	−1.60535e6	+	521611.i	−0.700488	+	0.227602i
$351$		0			0
$352$	378123.	−	160926.i	0.162658	−	0.0692262i
$353$			2.57165e6i			1.09844i	0.835679	+	0.549219i	$0.185075\pi$
$353$			2.57165e6i			1.09844i	−0.835679	+	0.549219i	$0.814925\pi$
$354$		0			0
$355$	−2.88335e6	−	2.09488e6i	−1.21430	−	0.882242i
$356$	1.15433e6	+	1.58880e6i	0.482732	+	0.664423i
$357$		0			0
$358$	737946.	+	239773.i	0.304311	+	0.0988766i
$359$	153655.	−	111637.i	0.0629232	−	0.0457164i	−0.555879	−	0.831263i	$-0.687618\pi$
$359$	153655.	−	111637.i	0.0629232	−	0.0457164i	0.618802	+	0.785547i	$0.287618\pi$
$360$		0			0
$361$	585188.	+	1.80102e6i	0.236335	+	0.727363i
$362$	−177778.			−0.0713030
$363$		0			0
$364$	387364.			0.153238
$365$	1.23935e6	+	3.81433e6i	0.486925	+	1.49860i
$366$		0			0
$367$	55720.6	−	40483.4i	0.0215949	−	0.0156896i	−0.576935	−	0.816790i	$-0.695752\pi$
$367$	55720.6	−	40483.4i	0.0215949	−	0.0156896i	0.598530	+	0.801100i	$0.295752\pi$
$368$	−1.08225e6	−	351645.i	−0.416590	−	0.135358i
$369$		0			0
$370$	287911.	+	396276.i	0.109334	+	0.150485i
$371$	3.50083e6	+	2.54350e6i	1.32049	+	0.959394i
$372$		0			0
$373$		−	792692.i		−	0.295007i	−0.989062	−	0.147503i	$-0.952876\pi$
$373$		−	792692.i		−	0.295007i	0.989062	−	0.147503i	$-0.0471238\pi$
$374$	368427.	−	156800.i	0.136199	−	0.0579651i
$375$		0			0
$376$	−208722.	+	67818.0i	−0.0761377	+	0.0247386i
$377$	487692.	−	671250.i	0.176723	−	0.243238i
$378$		0			0
$379$	1.33856e6	−	4.11965e6i	0.478673	−	1.47320i	−0.362267	−	0.932074i	$-0.617997\pi$
$379$	1.33856e6	−	4.11965e6i	0.478673	−	1.47320i	0.840940	−	0.541129i	$-0.182003\pi$
$380$	293992.	−	904815.i	0.104442	−	0.321441i
$381$		0			0
$382$	471003.	−	648280.i	0.165145	−	0.227302i
$383$	1.05102e6	−	341497.i	0.366112	−	0.118957i	−0.120183	−	0.992752i	$-0.538348\pi$
$383$	1.05102e6	−	341497.i	0.366112	−	0.118957i	0.486295	+	0.873795i	$0.338348\pi$
$384$		0			0
$385$	2.94178e6	+	3.37767e6i	1.01148	+	1.16136i
$386$			2.52327e6i			0.861975i
$387$		0			0
$388$	709280.	+	515322.i	0.239187	+	0.173780i
$389$	2.99712e6	+	4.12519e6i	1.00422	+	1.38220i	0.922697	+	0.385525i	$0.125980\pi$
$389$	2.99712e6	+	4.12519e6i	1.00422	+	1.38220i	0.0815269	+	0.996671i	$0.474020\pi$
$390$		0			0
$391$	−1.05450e6	−	342628.i	−0.348823	−	0.113339i
$392$	−192241.	+	139671.i	−0.0631875	+	0.0459084i
$393$		0			0
$394$	−1.09333e6	−	3.36493e6i	−0.354822	−	1.09203i
$395$	1.26371e6			0.407524
$396$		0			0
$397$	−1.17716e6			−0.374852			−0.187426	−	0.982279i	$-0.560014\pi$
$397$	−1.17716e6			−0.374852			−0.187426	+	0.982279i	$0.560014\pi$
$398$	898912.	+	2.76657e6i	0.284452	+	0.875454i
$399$		0			0
$400$	610119.	−	443278.i	0.190662	−	0.138524i
$401$	−3.17842e6	−	1.03273e6i	−0.987074	−	0.320720i	−0.229385	−	0.973336i	$-0.573672\pi$
$401$	−3.17842e6	−	1.03273e6i	−0.987074	−	0.320720i	−0.757689	+	0.652616i	$0.773672\pi$
$402$		0			0
$403$	−363276.	−	500006.i	−0.111423	−	0.153360i
$404$	−114251.	−	83008.3i	−0.0348263	−	0.0253028i
$405$		0			0
$406$			2.81295e6i			0.846930i
$407$	324332.	−	540938.i	0.0970518	−	0.161868i
$408$		0			0
$409$	−5.04711e6	+	1.63991e6i	−1.49188	+	0.484742i	−0.937639	−	0.347612i	$-0.886993\pi$
$409$	−5.04711e6	+	1.63991e6i	−1.49188	+	0.484742i	−0.554245	+	0.832354i	$0.686993\pi$
$410$	−2.61609e6	+	3.60074e6i	−0.768587	+	1.05787i
$411$		0			0
$412$	655939.	−	2.01877e6i	0.190380	−	0.585928i
$413$	−1.25316e6	+	3.85683e6i	−0.361519	+	1.11264i
$414$		0			0
$415$	3.38248e6	−	4.65559e6i	0.964085	−	1.32695i
$416$	−164596.	+	53480.3i	−0.0466321	+	0.0151517i
$417$		0			0
$418$	−1.22027e6	+	107924.i	−0.341599	+	0.0302119i
$419$		−	3.18835e6i		−	0.887220i	−0.896220	−	0.443610i	$-0.853698\pi$
$419$		−	3.18835e6i		−	0.887220i	0.896220	−	0.443610i	$-0.146302\pi$
$420$		0			0
$421$	2.54067e6	+	1.84590e6i	0.698623	+	0.507579i	0.879483	−	0.475930i	$-0.157888\pi$
$421$	2.54067e6	+	1.84590e6i	0.698623	+	0.507579i	−0.180861	+	0.983509i	$0.557888\pi$
$422$	−1.49788e6	−	2.06166e6i	−0.409446	−	0.563553i
$423$		0			0
$424$	−1.83871e6	−	597432.i	−0.496704	−	0.161389i
$425$	594475.	−	431911.i	0.159647	−	0.115990i
$426$		0			0
$427$	−1.10374e6	−	3.39696e6i	−0.292952	−	0.901615i
$428$	3.28403e6			0.866558
$429$		0			0
$430$	−1.59476e6			−0.415933
$431$	−1.23312e6	−	3.79514e6i	−0.319750	−	0.984090i	−0.973755	−	0.227599i	$-0.926912\pi$
$431$	−1.23312e6	−	3.79514e6i	−0.319750	−	0.984090i	0.654005	−	0.756490i	$-0.273088\pi$
$432$		0			0
$433$	−440578.	+	320098.i	−0.112928	+	0.0820472i	−0.642816	−	0.766021i	$-0.722234\pi$
$433$	−440578.	+	320098.i	−0.112928	+	0.0820472i	0.529888	+	0.848068i	$0.322234\pi$
$434$	1.99278e6	+	647494.i	0.507850	+	0.165010i
$435$		0			0
$436$	894366.	+	1.23099e6i	0.225320	+	0.310126i
$437$	2.74439e6	+	1.99392e6i	0.687453	+	0.499464i
$438$		0			0
$439$			2.45261e6i			0.607390i	0.952769	+	0.303695i	$0.0982204\pi$
$439$			2.45261e6i			0.607390i	−0.952769	+	0.303695i	$0.901780\pi$
$440$	−1.71633e6	−	1.02906e6i	−0.422638	−	0.253402i
$441$		0			0
$442$	−160375.	+	52109.0i	−0.0390464	+	0.0126869i
$443$	−927776.	+	1.27697e6i	−0.224612	+	0.309152i	−0.906419	−	0.422380i	$-0.861195\pi$
$443$	−927776.	+	1.27697e6i	−0.224612	+	0.309152i	0.681806	+	0.731533i	$0.261195\pi$
$444$		0			0
$445$	2.95530e6	−	9.09546e6i	0.707458	−	2.17733i
$446$	151429.	−	466050.i	0.0360472	−	0.110942i
$447$		0			0
$448$	344878.	−	474684.i	0.0811841	−	0.111740i
$449$	−1.50570e6	+	489230.i	−0.352469	+	0.114524i	−0.479900	−	0.877323i	$-0.659327\pi$
$449$	−1.50570e6	+	489230.i	−0.352469	+	0.114524i	0.127430	+	0.991848i	$0.459327\pi$
$450$		0			0
$451$	5.58532e6	+	1.28390e6i	1.29302	+	0.297229i
$452$		−	2.56504e6i		−	0.590537i
$453$		0			0
$454$	241073.	+	175150.i	0.0548920	+	0.0398814i
$455$	−1.10878e6	−	1.52610e6i	−0.251082	−	0.345585i
$456$		0			0
$457$	5.96936e6	+	1.93956e6i	1.33702	+	0.434423i	0.888305	−	0.459253i	$-0.151883\pi$
$457$	5.96936e6	+	1.93956e6i	1.33702	+	0.434423i	0.448712	+	0.893677i	$0.351883\pi$
$458$	1.08419e6	−	787707.i	0.241513	−	0.175469i
$459$		0			0
$460$	1.71242e6	+	5.27029e6i	0.377325	+	1.16129i
$461$	2.55733e6			0.560446			0.280223	−	0.959935i	$-0.409592\pi$
$461$	2.55733e6			0.560446			0.280223	+	0.959935i	$0.409592\pi$
$462$		0			0
$463$	−2.91465e6			−0.631878			−0.315939	−	0.948779i	$-0.602320\pi$
$463$	−2.91465e6			−0.631878			−0.315939	+	0.948779i	$0.602320\pi$
$464$	−388363.	−	1.19526e6i	−0.0837418	−	0.257731i
$465$		0			0
$466$	−4.16918e6	+	3.02908e6i	−0.889376	+	0.646169i
$467$	−7.65949e6	−	2.48872e6i	−1.62520	−	0.528060i	−0.652041	−	0.758184i	$-0.726087\pi$
$467$	−7.65949e6	−	2.48872e6i	−1.62520	−	0.528060i	−0.973161	+	0.230123i	$0.926087\pi$
$468$		0			0
$469$	4.48169e6	+	6.16852e6i	0.940827	+	1.29494i
$470$	864623.	+	628185.i	0.180544	+	0.131173i
$471$		0			0
$472$		−	1.81183e6i		−	0.374336i
$473$	804147.	+	1.88948e6i	0.165266	+	0.388319i
$474$		0			0
$475$	−2.13811e6	+	694715.i	−0.434807	+	0.141277i
$476$	336035.	−	462512.i	0.0679778	−	0.0935634i
$477$		0			0
$478$	648667.	−	1.99639e6i	0.129853	−	0.399646i
$479$	1.40448e6	−	4.32256e6i	0.279691	−	0.860800i	−0.708249	−	0.705963i	$-0.750515\pi$
$479$	1.40448e6	−	4.32256e6i	0.279691	−	0.860800i	0.987940	−	0.154837i	$-0.0494853\pi$
$480$		0			0
$481$	−156129.	+	214893.i	−0.0307696	+	0.0423507i
$482$	5.96292e6	−	1.93747e6i	1.16907	−	0.379855i
$483$		0			0
$484$	−353791.	+	2.55241e6i	−0.0686489	+	0.495265i
$485$		−	4.26939e6i		−	0.824161i
$486$		0			0
$487$	4.79775e6	+	3.48577e6i	0.916675	+	0.666004i	0.942694	−	0.333658i	$-0.108283\pi$
$487$	4.79775e6	+	3.48577e6i	0.916675	+	0.666004i	−0.0260190	+	0.999661i	$0.508283\pi$
$488$	937985.	+	1.29103e6i	0.178298	+	0.245406i
$489$		0			0
$490$	1.10053e6	+	357583.i	0.207067	+	0.0672802i
$491$	−3.93196e6	+	2.85674e6i	−0.736047	+	0.534770i	−0.891471	−	0.453078i	$-0.850326\pi$
$491$	−3.93196e6	+	2.85674e6i	−0.736047	+	0.534770i	0.155423	+	0.987848i	$0.450326\pi$
$492$		0			0
$493$	−378404.	−	1.16461e6i	−0.0701195	−	0.215806i
$494$	515916.			0.0951177
$495$		0			0
$496$	−936151.			−0.170861
$497$	2.02480e6	+	6.23171e6i	0.367699	+	1.13166i
$498$		0			0
$499$	7.40136e6	−	5.37740e6i	1.33064	−	0.966766i	0.330906	−	0.943664i	$-0.392646\pi$
$499$	7.40136e6	−	5.37740e6i	1.33064	−	0.966766i	0.999733	−	0.0231018i	$-0.00735418\pi$
$500$	212354.	+	68998.0i	0.0379871	+	0.0123427i
$501$		0			0
$502$	−755755.	−	1.04021e6i	−0.133851	−	0.184230i
$503$	−2.50314e6	−	1.81864e6i	−0.441129	−	0.320499i	0.344954	−	0.938619i	$-0.387894\pi$
$503$	−2.50314e6	−	1.81864e6i	−0.441129	−	0.320499i	−0.786083	+	0.618120i	$0.787894\pi$
$504$		0			0
$505$			687716.i			0.120000i
$506$	5.38078e6	−	4.68639e6i	0.934263	−	0.813697i
$507$		0			0
$508$	−4.29874e6	+	1.39675e6i	−0.739065	+	0.240137i
$509$	5.44927e6	−	7.50027e6i	0.932274	−	1.28317i	−0.0266914	−	0.999644i	$-0.508497\pi$
$509$	5.44927e6	−	7.50027e6i	0.932274	−	1.28317i	0.958966	−	0.283522i	$-0.0915028\pi$
$510$		0			0
$511$	2.27853e6	−	7.01259e6i	0.386013	−	1.18803i
$512$	−81007.0	+	249314.i	−0.0136568	+	0.0420312i
$513$		0			0
$514$	−3.08419e6	+	4.24502e6i	−0.514912	+	0.708715i
$515$	−9.83091e6	+	3.19426e6i	−1.63334	+	0.530703i
$516$		0			0
$517$	308296.	−	1.34117e6i	0.0507272	−	0.220677i
$518$		−	900536.i		−	0.147461i
$519$		0			0
$520$	681829.	+	495378.i	0.110578	+	0.0803394i
$521$	−6.74725e6	−	9.28680e6i	−1.08901	−	1.49890i	−0.849195	−	0.528079i	$-0.822913\pi$
$521$	−6.74725e6	−	9.28680e6i	−1.08901	−	1.49890i	−0.239817	−	0.970818i	$-0.577087\pi$
$522$		0			0
$523$	2.47349e6	+	803686.i	0.395417	+	0.128479i	0.499975	−	0.866040i	$-0.333343\pi$
$523$	2.47349e6	+	803686.i	0.395417	+	0.128479i	−0.104557	+	0.994519i	$0.533343\pi$
$524$	−4.05579e6	+	2.94670e6i	−0.645278	+	0.468822i
$525$		0			0
$526$	173003.	+	532450.i	0.0272640	+	0.0839101i
$527$	−912146.			−0.143067
$528$		0			0
$529$	−1.33226e7			−2.06990
$530$	2.90934e6	+	8.95403e6i	0.449889	+	1.38462i
$531$		0			0
$532$	−1.41505e6	+	1.02809e6i	−0.216767	+	0.157490i
$533$	−2.29544e6	−	745834.i	−0.349984	−	0.113717i
$534$		0			0
$535$	−9.40009e6	−	1.29381e7i	−1.41987	−	1.95428i
$536$	−2.75596e6	−	2.00233e6i	−0.414345	−	0.301039i
$537$		0			0
$538$		−	362420.i		−	0.0539829i
$539$	−131269.	−	1.48422e6i	−0.0194621	−	0.220053i
$540$		0			0
$541$	−628219.	+	204121.i	−0.0922822	+	0.0299843i	−0.354794	−	0.934944i	$-0.615449\pi$
$541$	−628219.	+	204121.i	−0.0922822	+	0.0299843i	0.262512	+	0.964929i	$0.415449\pi$
$542$	−2.13604e6	+	2.94000e6i	−0.312328	+	0.429882i
$543$		0			0
$544$	−78929.8	+	242921.i	−0.0114352	+	0.0351939i
$545$	2.28974e6	−	7.04708e6i	0.330213	−	1.01629i
$546$		0			0
$547$	−7.03662e6	+	9.68508e6i	−1.00553	+	1.38400i	−0.0836634	+	0.996494i	$0.526662\pi$
$547$	−7.03662e6	+	9.68508e6i	−1.00553	+	1.38400i	−0.921869	+	0.387502i	$0.873338\pi$
$548$	−4.93788e6	+	1.60441e6i	−0.702407	+	0.228226i
$549$		0			0
$550$	416610.	+	4.71050e6i	0.0587249	+	0.663988i
$551$			3.74647e6i			0.525706i
$552$		0			0
$553$	−1.87960e6	−	1.36561e6i	−0.261368	−	0.189895i
$554$	556947.	+	766572.i	0.0770974	+	0.106115i
$555$		0			0
$556$	−1.73696e6	−	564374.i	−0.238289	−	0.0774248i
$557$	330965.	−	240460.i	0.0452006	−	0.0328402i	−0.564956	−	0.825121i	$-0.691107\pi$
$557$	330965.	−	240460.i	0.0452006	−	0.0328402i	0.610156	+	0.792281i	$0.291107\pi$
$558$		0			0
$559$	−267241.	−	822482.i	−0.0361720	−	0.111326i
$560$	−2.85728e6			−0.385020
$561$		0			0
$562$	−9.77987e6			−1.30615
$563$	1.88582e6	+	5.80396e6i	0.250743	+	0.771709i	0.994639	+	0.103413i	$0.0329762\pi$
$563$	1.88582e6	+	5.80396e6i	0.250743	+	0.771709i	−0.743895	+	0.668296i	$0.767024\pi$
$564$		0			0
$565$	−1.01055e7	+	7.34207e6i	−1.33179	+	0.967603i
$566$	−1.66452e6	−	540836.i	−0.218398	−	0.0709618i
$567$		0			0
$568$	−1.72073e6	−	2.36838e6i	−0.223790	−	0.308021i
$569$	−7.17564e6	−	5.21341e6i	−0.929137	−	0.675058i	0.0166442	−	0.999861i	$-0.494702\pi$
$569$	−7.17564e6	−	5.21341e6i	−0.929137	−	0.675058i	−0.945781	+	0.324804i	$0.894702\pi$
$570$		0			0
$571$		−	4.47409e6i		−	0.574268i	−0.957890	−	0.287134i	$-0.907297\pi$
$571$		−	4.47409e6i		−	0.574268i	0.957890	−	0.287134i	$-0.0927025\pi$
$572$	243118.	−	1.05763e6i	0.0310690	−	0.135158i
$573$		0			0
$574$	7.78218e6	−	2.52858e6i	0.985875	−	0.320330i
$575$	7.69693e6	−	1.05939e7i	0.970841	−	1.33625i
$576$		0			0
$577$	−3.20942e6	+	9.87759e6i	−0.401317	+	1.23513i	0.522615	+	0.852569i	$0.324957\pi$
$577$	−3.20942e6	+	9.87759e6i	−0.401317	+	1.23513i	−0.923932	+	0.382558i	$0.875043\pi$
$578$	1.67813e6	−	5.16477e6i	0.208933	−	0.643030i
$579$		0			0
$580$	−3.59733e6	+	4.95130e6i	−0.444028	+	0.611152i
$581$	−1.00620e7	+	3.26934e6i	−1.23664	+	0.401809i
$582$		0			0
$583$	9.14176e6	−	7.96202e6i	1.11393	−	0.970179i
$584$			3.29431e6i			0.399699i
$585$		0			0
$586$	1.55886e6	+	1.13258e6i	0.187527	+	0.136246i
$587$	−9.16552e6	−	1.26153e7i	−1.09790	−	1.51113i	−0.838143	−	0.545451i	$-0.816358\pi$
$587$	−9.16552e6	−	1.26153e7i	−1.09790	−	1.51113i	−0.259755	−	0.965675i	$-0.583642\pi$
$588$		0			0
$589$	2.65411e6	+	862374.i	0.315233	+	0.102425i
$590$	−7.13807e6	+	5.18611e6i	−0.844210	+	0.613355i
$591$		0			0
$592$	124330.	+	382648.i	0.0145805	+	0.0448741i
$593$	1.54683e7			1.80637			0.903184	−	0.429254i	$-0.141224\pi$
$593$	1.54683e7			1.80637			0.903184	+	0.429254i	$0.141224\pi$
$594$		0			0
$595$	−2.78402e6			−0.322389
$596$	−321788.	−	990362.i	−0.0371069	−	0.114203i
$597$		0			0
$598$	−2.43115e6	+	1.76633e6i	−0.278009	+	0.201985i
$599$	−2.72540e6	−	885537.i	−0.310359	−	0.100842i	0.149696	−	0.988732i	$-0.452170\pi$
$599$	−2.72540e6	−	885537.i	−0.310359	−	0.100842i	−0.460055	+	0.887890i	$0.652170\pi$
$600$		0			0
$601$	8.89316e6	+	1.22404e7i	1.00432	+	1.38232i	0.922640	+	0.385662i	$0.126027\pi$
$601$	8.89316e6	+	1.22404e7i	1.00432	+	1.38232i	0.0816753	+	0.996659i	$0.473973\pi$
$602$	2.37199e6	+	1.72335e6i	0.266761	+	0.193813i
$603$		0			0
$604$			6.78234e6i			0.756462i
$605$	1.10684e7	−	5.91211e6i	1.22941	−	0.656680i
$606$		0			0
$607$	−1.44446e7	+	4.69334e6i	−1.59123	+	0.517023i	−0.964919	−	0.262546i	$-0.915438\pi$
$607$	−1.44446e7	+	4.69334e6i	−1.59123	+	0.517023i	−0.626315	+	0.779570i	$0.715438\pi$
$608$	459331.	−	632215.i	0.0503926	−	0.0693595i
$609$		0			0
$610$	2.40141e6	−	7.39077e6i	0.261301	−	0.804202i
$611$	−179092.	+	551189.i	−0.0194077	+	0.0597307i
$612$		0			0
$613$	−5.37214e6	+	7.39412e6i	−0.577426	+	0.794759i	−0.993410	−	0.114613i	$-0.963437\pi$
$613$	−5.37214e6	+	7.39412e6i	−0.577426	+	0.794759i	0.415984	+	0.909372i	$0.363437\pi$
$614$	2.24724e6	−	730173.i	0.240563	−	0.0781637i
$615$		0			0
$616$	1.44077e6	+	3.38532e6i	0.152983	+	0.359458i
$617$		−	8.54921e6i		−	0.904093i	−0.891994	−	0.452046i	$-0.850694\pi$
$617$		−	8.54921e6i		−	0.904093i	0.891994	−	0.452046i	$-0.149306\pi$
$618$		0			0
$619$	−963657.	−	700138.i	−0.101087	−	0.0734441i	0.536093	−	0.844159i	$-0.319899\pi$
$619$	−963657.	−	700138.i	−0.101087	−	0.0734441i	−0.637181	+	0.770715i	$0.719899\pi$
$620$	2.67961e6	+	3.68816e6i	0.279957	+	0.385328i
$621$		0			0
$622$	9.56468e6	+	3.10775e6i	0.991276	+	0.322085i
$623$	−1.42245e7	+	1.03347e7i	−1.46831	+	1.06679i
$624$		0			0
$625$	−3.18079e6	−	9.78946e6i	−0.325713	−	1.00244i
$626$	5.67824e6			0.579133
$627$		0			0
$628$	−4.90026e6			−0.495815
$629$	121142.	+	372837.i	0.0122087	+	0.0375744i
$630$		0			0
$631$	9.87153e6	−	7.17209e6i	0.986986	−	0.717088i	0.0277273	−	0.999616i	$-0.491173\pi$
$631$	9.87153e6	−	7.17209e6i	0.986986	−	0.717088i	0.959259	+	0.282528i	$0.0911730\pi$
$632$	987203.	+	320762.i	0.0983136	+	0.0319440i
$633$		0			0
$634$	−7.48315e6	−	1.02997e7i	−0.739369	−	1.01765i
$635$	1.78074e7	+	1.29378e7i	1.75253	+	1.27329i
$636$		0			0
$637$			627510.i			0.0612734i
$638$	7.68025e6	+	1.76547e6i	0.747006	+	0.171715i
$639$		0			0
$640$	1.21409e6	−	394483.i	0.117166	−	0.0380696i
$641$	2.85742e6	−	3.93290e6i	0.274681	−	0.378066i	−0.649282	−	0.760548i	$-0.724931\pi$
$641$	2.85742e6	−	3.93290e6i	0.274681	−	0.378066i	0.923963	+	0.382482i	$0.124931\pi$
$642$		0			0
$643$	4.22942e6	−	1.30168e7i	0.403416	−	1.24159i	−0.518794	−	0.854899i	$-0.673619\pi$
$643$	4.22942e6	−	1.30168e7i	0.403416	−	1.24159i	0.922210	−	0.386689i	$-0.126381\pi$
$644$	3.14826e6	−	9.68936e6i	0.299128	−	0.920620i
$645$		0			0
$646$	447553.	−	616004.i	0.0421952	−	0.0580767i
$647$	−1.17512e6	+	381818.i	−0.110362	+	0.0358588i	−0.363677	−	0.931525i	$-0.618479\pi$
$647$	−1.17512e6	+	381818.i	−0.110362	+	0.0358588i	0.253315	+	0.967384i	$0.418479\pi$
$648$		0			0
$649$	9.74385e6	+	5.84215e6i	0.908069	+	0.544454i
$650$		−	1.99154e6i		−	0.184887i
$651$		0			0
$652$	−4.08725e6	−	2.96956e6i	−0.376541	−	0.273573i
$653$	2.33724e6	+	3.21694e6i	0.214497	+	0.295230i	0.902684	−	0.430303i	$-0.141593\pi$
$653$	2.33724e6	+	3.21694e6i	0.214497	+	0.295230i	−0.688187	+	0.725533i	$0.741593\pi$
$654$		0			0
$655$	2.32183e7	+	7.54408e6i	2.11460	+	0.687074i
$656$	−2.95764e6	+	2.14885e6i	−0.268340	+	0.194961i
$657$		0			0
$658$	−607173.	−	1.86869e6i	−0.0546698	−	0.168256i
$659$	−7.86347e6			−0.705343			−0.352672	−	0.935747i	$-0.614727\pi$
$659$	−7.86347e6			−0.705343			−0.352672	+	0.935747i	$0.614727\pi$
$660$		0			0
$661$	−9.34347e6			−0.831773			−0.415886	−	0.909417i	$-0.636529\pi$
$661$	−9.34347e6			−0.831773			−0.415886	+	0.909417i	$0.636529\pi$
$662$	−3.25086e6	−	1.00051e7i	−0.288306	−	0.887314i
$663$		0			0
$664$	3.82409e6	−	2.77836e6i	0.336595	−	0.244551i
$665$	8.10078e6	+	2.63210e6i	0.710351	+	0.230807i
$666$		0			0
$667$	−1.28267e7	−	1.76545e7i	−1.11635	−	1.53653i
$668$	−5.88748e6	−	4.27751e6i	−0.510491	−	0.370894i
$669$		0			0
$670$			1.65891e7i			1.42769i
$671$	−9.96751e6	+	881554.i	−0.854635	+	0.0755863i
$672$		0			0
$673$	−4.30488e6	+	1.39874e6i	−0.366373	+	0.119042i	−0.486417	−	0.873727i	$-0.661696\pi$
$673$	−4.30488e6	+	1.39874e6i	−0.366373	+	0.119042i	0.120044	+	0.992769i	$0.461696\pi$
$674$	355033.	−	488661.i	0.0301036	−	0.0414341i
$675$		0			0
$676$	1.69454e6	−	5.21527e6i	0.142622	−	0.438945i
$677$	−4.28320e6	+	1.31823e7i	−0.359168	+	1.10540i	0.594386	+	0.804180i	$0.297395\pi$
$677$	−4.28320e6	+	1.31823e7i	−0.359168	+	1.10540i	−0.953553	+	0.301224i	$0.902605\pi$
$678$		0			0
$679$	−4.61366e6	+	6.35016e6i	−0.384035	+	0.528579i
$680$	1.18296e6	−	384368.i	0.0981068	−	0.0318768i
$681$		0			0
$682$	3.01858e6	−	5.03454e6i	0.248508	−	0.414476i
$683$			2.42934e7i			1.99267i	0.0855189	+	0.996337i	$0.472745\pi$
$683$			2.42934e7i			1.99267i	−0.0855189	+	0.996337i	$0.527255\pi$
$684$		0			0
$685$	2.04549e7	+	1.48614e7i	1.66560	+	1.21013i
$686$	4.41004e6	+	6.06990e6i	0.357794	+	0.492461i
$687$		0			0
$688$	−1.24582e6	−	404791.i	−0.100342	−	0.0326031i
$689$	−4.13043e6	+	3.00093e6i	−0.331472	+	0.240829i
$690$		0			0
$691$	−2.16550e6	−	6.66474e6i	−0.172530	−	0.530992i	0.826982	−	0.562228i	$-0.190056\pi$
$691$	−2.16550e6	−	6.66474e6i	−0.172530	−	0.530992i	−0.999512	+	0.0312361i	$0.990056\pi$
$692$	−1.29236e6			−0.102593
$693$		0			0
$694$	−5.86420e6			−0.462179
$695$	2.74836e6	+	8.45858e6i	0.215830	+	0.664256i
$696$		0			0
$697$	−2.88180e6	+	2.09375e6i	−0.224689	+	0.163246i
$698$	−3.21513e6	−	1.04466e6i	−0.249782	−	0.0811590i
$699$		0			0
$700$	3.96865e6	+	5.46238e6i	0.306124	+	0.421344i
$701$	−9.86422e6	−	7.16678e6i	−0.758172	−	0.550844i	0.140177	−	0.990126i	$-0.455233\pi$
$701$	−9.86422e6	−	7.16678e6i	−0.758172	−	0.550844i	−0.898349	+	0.439282i	$0.855233\pi$
$702$		0			0
$703$		−	1.19939e6i		−	0.0915319i
$704$	−1.07959e6	−	1.23955e6i	−0.0820967	−	0.0942610i
$705$		0			0
$706$	9.78314e6	−	3.17874e6i	0.738698	−	0.240017i
$707$	743171.	−	1.02289e6i	0.0559165	−	0.0769625i
$708$		0			0
$709$	5.80458e6	−	1.78647e7i	0.433666	−	1.33469i	−0.460782	−	0.887513i	$-0.652431\pi$
$709$	5.80458e6	−	1.78647e7i	0.433666	−	1.33469i	0.894448	−	0.447173i	$-0.147569\pi$
$710$	−4.40537e6	+	1.35583e7i	−0.327972	+	1.00939i
$711$		0			0
$712$	4.61733e6	−	6.35521e6i	0.341343	−	0.469818i
$713$	−1.54594e7	+	5.02308e6i	−1.13886	+	0.370038i
$714$		0			0
$715$	−4.86263e6	+	2.06950e6i	−0.355718	+	0.151391i
$716$		−	3.10369e6i		−	0.226254i
$717$		0			0
$718$	−614621.	−	446548.i	−0.0444935	−	0.0323264i
$719$	6.09363e6	+	8.38716e6i	0.439596	+	0.605052i	0.970122	−	0.242617i	$-0.0780057\pi$
$719$	6.09363e6	+	8.38716e6i	0.439596	+	0.605052i	−0.530526	+	0.847668i	$0.678006\pi$
$720$		0			0
$721$	1.80740e7	+	5.87260e6i	1.29484	+	0.420719i
$722$	6.12817e6	−	4.45238e6i	0.437510	−	0.317869i
$723$		0			0
$724$	219746.	+	676310.i	0.0155803	+	0.0479512i
$725$	1.44621e7			1.02185
$726$		0			0
$727$	2.18638e7			1.53422			0.767112	−	0.641513i	$-0.221693\pi$
$727$	2.18638e7			1.53422			0.767112	+	0.641513i	$0.221693\pi$
$728$	−478808.	−	1.47362e6i	−0.0334837	−	0.103052i
$729$		0			0
$730$	1.29786e7	−	9.42953e6i	0.901409	−	0.654912i
$731$	−1.21387e6	−	394411.i	−0.0840194	−	0.0272996i
$732$		0			0
$733$	−1.28910e7	−	1.77430e7i	−0.886192	−	1.21974i	−0.974667	−	0.223660i	$-0.928199\pi$
$733$	−1.28910e7	−	1.77430e7i	−0.886192	−	1.21974i	0.0884754	−	0.996078i	$-0.471801\pi$
$734$	−222882.	−	161933.i	−0.0152699	−	0.0110942i
$735$		0			0
$736$			4.55178e6i			0.309733i
$737$	1.96548e7	−	8.36495e6i	1.33291	−	0.567276i
$738$		0			0
$739$	−1.66583e7	+	5.41260e6i	−1.12207	+	0.364582i	−0.810556	−	0.585661i	$-0.800835\pi$
$739$	−1.66583e7	+	5.41260e6i	−1.12207	+	0.364582i	−0.311511	+	0.950243i	$0.600835\pi$
$740$	1.15165e6	−	1.58510e6i	0.0773107	−	0.106409i
$741$		0			0
$742$	5.34879e6	−	1.64619e7i	0.356653	−	1.09767i
$743$	3.80974e6	−	1.17252e7i	0.253177	−	0.779197i	−0.741007	−	0.671497i	$-0.765651\pi$
$743$	3.80974e6	−	1.17252e7i	0.253177	−	0.779197i	0.994183	−	0.107700i	$-0.0343485\pi$
$744$		0			0
$745$	−2.98066e6	+	4.10253e6i	−0.196753	+	0.270808i
$746$	−3.01558e6	+	979821.i	−0.198392	+	0.0644614i
$747$		0			0
$748$	−1.05190e6	−	1.20776e6i	−0.0687419	−	0.0789275i
$749$			2.94018e7i			1.91500i
$750$		0			0
$751$	1.38218e7	+	1.00421e7i	0.894261	+	0.649719i	0.936985	−	0.349368i	$-0.113604\pi$
$751$	1.38218e7	+	1.00421e7i	0.894261	+	0.649719i	−0.0427245	+	0.999087i	$0.513604\pi$
$752$	515990.	+	710200.i	0.0332734	+	0.0457969i
$753$		0			0
$754$	−3.15641e6	−	1.02558e6i	−0.202192	−	0.0656963i
$755$	2.67204e7	−	1.94135e7i	1.70599	−	1.23947i
$756$		0			0
$757$	3.44796e6	+	1.06117e7i	0.218687	+	0.673049i	0.998871	+	0.0474993i	$0.0151252\pi$
$757$	3.44796e6	+	1.06117e7i	0.218687	+	0.673049i	−0.780184	+	0.625550i	$0.784875\pi$
$758$	−1.73266e7			−1.09532
$759$		0			0
$760$	−3.80552e6			−0.238990
$761$	7.95645e6	+	2.44874e7i	0.498032	+	1.53279i	0.812177	+	0.583411i	$0.198282\pi$
$761$	7.95645e6	+	2.44874e7i	0.498032	+	1.53279i	−0.314145	+	0.949375i	$0.601718\pi$
$762$		0			0
$763$	−1.10210e7	+	8.00723e6i	−0.685346	+	0.497933i
$764$	−3.04839e6	−	990483.i	−0.188946	−	0.0613923i
$765$		0			0
$766$	−2.59826e6	−	3.57620e6i	−0.159997	−	0.220217i
$767$	−3.87085e6	−	2.81234e6i	−0.237584	−	0.172615i
$768$		0			0
$769$		−	5.95995e6i		−	0.363435i	−0.983351	−	0.181717i	$-0.941834\pi$
$769$		−	5.95995e6i		−	0.363435i	0.983351	−	0.181717i	$-0.0581656\pi$
$770$	9.21318e6	−	1.53662e7i	0.559993	−	0.933987i
$771$		0			0
$772$	9.59908e6	−	3.11893e6i	0.579677	−	0.188349i
$773$	1.37574e7	−	1.89355e7i	0.828110	−	1.13980i	−0.160162	−	0.987091i	$-0.551202\pi$
$773$	1.37574e7	−	1.89355e7i	0.828110	−	1.13980i	0.988272	−	0.152705i	$-0.0487984\pi$
$774$		0			0
$775$	3.32894e6	−	1.02454e7i	0.199091	−	0.612739i
$776$	1.08368e6	−	3.33523e6i	0.0646023	−	0.198825i
$777$		0			0
$778$	1.19885e7	−	1.65007e7i	0.710094	−	0.977360i
$779$	1.03648e7	−	3.36773e6i	0.611952	−	0.198835i
$780$		0			0
$781$	1.82853e7	−	1.61721e6i	1.07269	−	0.0948720i
$782$			4.43507e6i			0.259348i
$783$		0			0
$784$	768964.	+	558685.i	0.0446803	+	0.0324621i
$785$	1.40263e7	+	1.93056e7i	0.812400	+	1.11817i
$786$		0			0
$787$	1.01961e7	+	3.31293e6i	0.586812	+	0.190667i	0.587350	−	0.809333i	$-0.300171\pi$
$787$	1.01961e7	+	3.31293e6i	0.586812	+	0.190667i	−0.000537801		1.00000i	$0.500171\pi$
$788$	−1.14495e7	+	8.31856e6i	−0.656858	+	0.477235i
$789$		0			0
$790$	−1.56203e6	−	4.80743e6i	−0.0890474	−	0.274060i
$791$	2.29647e7			1.30503
$792$		0			0
$793$	4.21414e6			0.237972
$794$	1.45505e6	+	4.47819e6i	0.0819082	+	0.252087i
$795$		0			0
$796$	9.41353e6	−	6.83933e6i	0.526586	−	0.382587i
$797$	−2.31207e7	−	7.51238e6i	−1.28930	−	0.418920i	−0.417456	−	0.908697i	$-0.637078\pi$
$797$	−2.31207e7	−	7.51238e6i	−1.28930	−	0.418920i	−0.871848	+	0.489777i	$0.837078\pi$
$798$		0			0
$799$	502759.	+	691989.i	0.0278608	+	0.0383471i
$800$	−2.44048e6	−	1.77311e6i	−0.134819	−	0.0979515i
$801$		0			0
$802$			1.33679e7i			0.733886i
$803$	−1.77166e7	−	1.06224e7i	−0.969595	−	0.581343i
$804$		0			0
$805$	−4.71847e7	+	1.53312e7i	−2.56633	+	0.833850i
$806$	−1.45310e6	+	2.00003e6i	−0.0787878	+	0.108442i
$807$		0			0
$808$	−174560.	+	537241.i	−0.00940625	+	0.0289495i
$809$	4.04010e6	−	1.24342e7i	0.217031	−	0.667952i	−0.781973	−	0.623313i	$-0.785786\pi$
$809$	4.04010e6	−	1.24342e7i	0.217031	−	0.667952i	0.999003	−	0.0446388i	$-0.0142137\pi$
$810$		0			0
$811$	−8.39440e6	+	1.15539e7i	−0.448165	+	0.616846i	−0.972002	−	0.234973i	$-0.924500\pi$
$811$	−8.39440e6	+	1.15539e7i	−0.448165	+	0.616846i	0.523837	+	0.851818i	$0.324500\pi$
$812$	1.07011e7	−	3.47700e6i	0.569559	−	0.185061i
$813$		0			0
$814$	−2.45875e6	−	565195.i	−0.130063	−	0.0298977i
$815$			2.46025e7i			1.29744i
$816$		0			0
$817$	3.15917e6	+	2.29527e6i	0.165584	+	0.120304i
$818$	1.24772e7	+	1.71733e7i	0.651977	+	0.897369i
$819$		0			0
$820$	1.69317e7	+	5.50144e6i	0.879358	+	0.285721i
$821$	5.27920e6	−	3.83556e6i	0.273344	−	0.198596i	−0.442665	−	0.896687i	$-0.645967\pi$
$821$	5.27920e6	−	3.83556e6i	0.273344	−	0.198596i	0.716009	+	0.698091i	$0.245967\pi$
$822$		0			0
$823$	−97565.3	−	300275.i	−0.00502107	−	0.0154533i	0.948515	−	0.316733i	$-0.102586\pi$
$823$	−97565.3	−	300275.i	−0.00502107	−	0.0154533i	−0.953536	+	0.301280i	$0.902586\pi$
$824$	−8.49065e6			−0.435635
$825$		0			0
$826$	1.62212e7			0.827244
$827$	−1.36476e6	−	4.20030e6i	−0.0693893	−	0.213558i	0.910349	−	0.413842i	$-0.135814\pi$
$827$	−1.36476e6	−	4.20030e6i	−0.0693893	−	0.213558i	−0.979738	+	0.200284i	$0.935814\pi$
$828$		0			0
$829$	−6.98168e6	+	5.07249e6i	−0.352837	+	0.256351i	−0.750058	−	0.661372i	$-0.769974\pi$
$829$	−6.98168e6	+	5.07249e6i	−0.352837	+	0.256351i	0.397221	+	0.917723i	$0.369974\pi$
$830$	−2.18919e7	−	7.11310e6i	−1.10303	−	0.358397i
$831$		0			0
$832$	406903.	+	560053.i	0.0203790	+	0.0280492i
$833$	749247.	+	544360.i	0.0374121	+	0.0271815i
$834$		0			0
$835$			3.54387e7i			1.75899i
$836$	1.91891e6	+	4.50879e6i	0.0949595	+	0.223123i
$837$		0			0
$838$	−1.21292e7	+	3.94102e6i	−0.596654	+	0.193865i
$839$	−6.86083e6	+	9.44313e6i	−0.336490	+	0.463139i	−0.943412	−	0.331623i	$-0.892404\pi$
$839$	−6.86083e6	+	9.44313e6i	−0.336490	+	0.463139i	0.606922	+	0.794761i	$0.292404\pi$
$840$		0			0
$841$	1.10924e6	−	3.41390e6i	0.0540800	−	0.166441i
$842$	3.88180e6	−	1.19469e7i	0.188692	−	0.580733i
$843$		0			0
$844$	−5.99152e6	+	8.24662e6i	−0.289522	+	0.398492i
$845$	−2.53970e7	+	8.25200e6i	−1.22361	+	0.397573i
$846$		0			0
$847$	−2.28517e7	−	3.16748e6i	−1.09448	−	0.151707i
$848$			7.73332e6i			0.369298i
$849$		0			0
$850$	−2.37790e6	−	1.72764e6i	−0.112888	−	0.0820176i
$851$	4.10633e6	+	5.65188e6i	0.194370	+	0.267528i
$852$		0			0
$853$	−3.62996e7	−	1.17945e7i	−1.70816	−	0.555016i	−0.718138	−	0.695900i	$-0.755005\pi$
$853$	−3.62996e7	−	1.17945e7i	−1.70816	−	0.555016i	−0.990026	+	0.140884i	$0.955005\pi$
$854$	−1.15585e7	+	8.39775e6i	−0.542322	+	0.394020i
$855$		0			0
$856$	−4.05928e6	−	1.24932e7i	−0.189350	−	0.582759i
$857$	9.56994e6			0.445099			0.222550	−	0.974921i	$-0.428562\pi$
$857$	9.56994e6			0.445099			0.222550	+	0.974921i	$0.428562\pi$
$858$		0			0
$859$	1.32274e7			0.611635			0.305817	−	0.952090i	$-0.401070\pi$
$859$	1.32274e7			0.611635			0.305817	+	0.952090i	$0.401070\pi$
$860$	1.97123e6	+	6.06682e6i	0.0908847	+	0.279714i
$861$		0			0
$862$	−1.29134e7	+	9.38210e6i	−0.591931	+	0.430063i
$863$	−3.00689e7	−	9.76999e6i	−1.37433	−	0.446547i	−0.473529	−	0.880778i	$-0.657020\pi$
$863$	−3.00689e7	−	9.76999e6i	−1.37433	−	0.446547i	−0.900801	+	0.434232i	$0.857020\pi$
$864$		0			0
$865$	3.69920e6	+	5.09152e6i	0.168100	+	0.231370i
$866$	1.76231e6	+	1.28039e6i	0.0798523	+	0.0580161i
$867$		0			0
$868$		−	8.38133e6i		−	0.377584i
$869$	−4.90822e6	+	4.27481e6i	−0.220483	+	0.192029i
$870$		0			0
$871$	−8.55567e6	+	2.77991e6i	−0.382128	+	0.124161i
$872$	3.57746e6	−	4.92396e6i	0.159325	−	0.219292i
$873$		0			0
$874$	4.19306e6	−	1.29049e7i	0.185675	−	0.571448i
$875$	−617737.	+	1.90120e6i	−0.0272762	+	0.0839475i
$876$		0			0
$877$	1.29795e7	−	1.78648e7i	0.569849	−	0.784330i	−0.422688	−	0.906275i	$-0.638913\pi$
$877$	1.29795e7	−	1.78648e7i	0.569849	−	0.784330i	0.992537	+	0.121946i	$0.0389133\pi$
$878$	9.33030e6	−	3.03160e6i	0.408469	−	0.132720i
$879$		0			0
$880$	−1.79329e6	+	7.80129e6i	−0.0780629	+	0.339594i
$881$			4.48636e7i			1.94740i	0.227839	+	0.973699i	$0.426834\pi$
$881$			4.48636e7i			1.94740i	−0.227839	+	0.973699i	$0.573166\pi$
$882$		0			0
$883$	−2.92942e7	−	2.12835e7i	−1.26439	−	0.918630i	−0.265422	−	0.964132i	$-0.585511\pi$
$883$	−2.92942e7	−	2.12835e7i	−1.26439	−	0.918630i	−0.998964	+	0.0455020i	$0.985511\pi$
$884$	396469.	+	545692.i	0.0170639	+	0.0234864i
$885$		0			0
$886$	6.00469e6	+	1.95104e6i	0.256984	+	0.0834992i
$887$	2.85267e7	−	2.07258e7i	1.21742	−	0.884511i	0.221541	−	0.975151i	$-0.428891\pi$
$887$	2.85267e7	−	2.07258e7i	1.21742	−	0.884511i	0.995884	+	0.0906401i	$0.0288913\pi$
$888$		0			0
$889$	−1.25050e7	−	3.84865e7i	−0.530677	−	1.63326i
$890$	−3.82541e7			−1.61884
$891$		0			0
$892$	−1.96014e6			−0.0824849
$893$	−808672.	−	2.48884e6i	−0.0339347	−	0.104440i
$894$		0			0
$895$	−1.22276e7	+	8.88390e6i	−0.510252	+	0.370720i
$896$	−2.23210e6	−	725253.i	−0.0928845	−	0.0301800i
$897$		0			0
$898$	3.72229e6	+	5.12329e6i	0.154035	+	0.212011i
$899$	−1.45238e7	−	1.05521e7i	−0.599349	−	0.435452i
$900$		0			0
$901$			7.53502e6i			0.309224i
$902$	−2.01957e6	−	2.28348e7i	−0.0826501	−	0.934504i
$903$		0			0
$904$	−9.75798e6	+	3.17056e6i	−0.397135	+	0.129037i
$905$	2.03547e6	−	2.80158e6i	0.0826119	−	0.113706i
$906$		0			0
$907$	7.92785e6	−	2.43994e7i	0.319991	−	0.984830i	−0.653661	−	0.756788i	$-0.726768\pi$
$907$	7.92785e6	−	2.43994e7i	0.319991	−	0.984830i	0.973651	−	0.228042i	$-0.0732323\pi$
$908$	368327.	−	1.13359e6i	0.0148258	−	0.0456292i
$909$		0			0
$910$	−4.43511e6	+	6.10440e6i	−0.177542	+	0.244365i
$911$	1.02531e7	−	3.33143e6i	0.409316	−	0.132995i	−0.0971196	−	0.995273i	$-0.530963\pi$
$911$	1.02531e7	−	3.33143e6i	0.409316	−	0.132995i	0.506435	+	0.862278i	$0.330963\pi$
$912$		0			0
$913$	2.61121e6	+	2.95243e7i	0.103673	+	1.17220i
$914$		−	2.51062e7i		−	0.994067i
$915$		0			0
$916$	−4.33674e6	−	3.15083e6i	−0.170775	−	0.124075i
$917$	−2.63818e7	−	3.63114e7i	−1.03605	−	1.42600i
$918$		0			0
$919$	1.23113e7	+	4.00020e6i	0.480858	+	0.156240i	0.539408	−	0.842044i	$-0.318648\pi$
$919$	1.23113e7	+	4.00020e6i	0.480858	+	0.156240i	−0.0585506	+	0.998284i	$0.518648\pi$
$920$	1.79327e7	−	1.30289e7i	0.698515	−	0.507501i
$921$		0			0
$922$	−3.16103e6	−	9.72864e6i	−0.122462	−	0.376899i
$923$	−7.73081e6			−0.298690
$924$		0			0
$925$	−4.62989e6			−0.177917
$926$	3.60270e6	+	1.10880e7i	0.138071	+	0.424937i
$927$		0			0
$928$	−4.06699e6	+	2.95484e6i	−0.155025	+	0.112633i
$929$	2.76086e7	+	8.97058e6i	1.04956	+	0.341021i	0.782494	−	0.622658i	$-0.213947\pi$
$929$	2.76086e7	+	8.97058e6i	1.04956	+	0.341021i	0.267061	+	0.963680i	$0.413947\pi$
$930$		0			0
$931$	−1.66546e6	−	2.29231e6i	−0.0629738	−	0.0866761i
$932$	1.66767e7	+	1.21163e7i	0.628884	+	0.456911i
$933$		0			0
$934$			3.22146e7i			1.20833i
$935$	−1.74731e6	+	7.60125e6i	−0.0653643	+	0.284352i
$936$		0			0
$937$	3.14946e6	−	1.02332e6i	0.117189	−	0.0380770i	−0.249835	−	0.968288i	$-0.580377\pi$
$937$	3.14946e6	−	1.02332e6i	0.117189	−	0.0380770i	0.367024	+	0.930211i	$0.380377\pi$
$938$	1.79268e7	−	2.46741e7i	0.665265	−	0.915659i
$939$		0			0
$940$	1.32103e6	−	4.06570e6i	0.0487632	−	0.150078i
$941$	−6.90414e6	+	2.12488e7i	−0.254177	+	0.782275i	0.739814	+	0.672811i	$0.234913\pi$
$941$	−6.90414e6	+	2.12488e7i	−0.254177	+	0.782275i	−0.993991	+	0.109464i	$0.965087\pi$
$942$		0			0
$943$	−3.73120e7	+	5.13555e7i	−1.36637	+	1.88065i
$944$	−6.89260e6	+	2.23954e6i	−0.251740	+	0.0817954i
$945$		0			0
$946$	6.19401e6	−	5.39468e6i	0.225032	−	0.195992i
$947$			9.14834e6i			0.331488i	0.986169	+	0.165744i	$0.0530025\pi$
$947$			9.14834e6i			0.331488i	−0.986169	+	0.165744i	$0.946997\pi$
$948$		0			0
$949$	7.03809e6	+	5.11347e6i	0.253682	+	0.184311i
$950$	5.28571e6	+	7.27515e6i	0.190018	+	0.261537i
$951$		0			0
$952$	−2.17486e6	−	706656.i	−0.0777749	−	0.0252706i
$953$	1.05385e7	−	7.65663e6i	0.375876	−	0.273090i	−0.383767	−	0.923430i	$-0.625374\pi$
$953$	1.05385e7	−	7.65663e6i	0.375876	−	0.273090i	0.759643	+	0.650340i	$0.225374\pi$
$954$		0			0
$955$	4.82340e6	+	1.48449e7i	0.171137	+	0.526707i
$956$	−8.39652e6			−0.297135
$957$		0			0
$958$	−1.81800e7			−0.640001
$959$	−1.43643e7	−	4.42087e7i	−0.504356	−	1.55225i
$960$		0			0
$961$	1.23429e7	−	8.96764e6i	0.431131	−	0.313235i
$962$	1.01049e6	+	328328.i	0.0352042	+	0.0114385i
$963$		0			0
$964$	−1.47411e7	−	2.02894e7i	−0.510903	−	0.703198i
$965$	−3.97637e7	−	2.88900e7i	−1.37458	−	0.998688i
$966$		0			0
$967$			2.23241e7i			0.767730i	0.923389	+	0.383865i	$0.125407\pi$
$967$			2.23241e7i			0.767730i	−0.923389	+	0.383865i	$0.874593\pi$
$968$	1.01473e7	−	1.80906e6i	0.348065	−	0.0620531i
$969$		0			0
$970$	−1.62417e7	+	5.27726e6i	−0.554247	+	0.180086i
$971$	2.13107e7	−	2.93316e7i	0.725353	−	0.998363i	−0.273976	−	0.961736i	$-0.588339\pi$
$971$	2.13107e7	−	2.93316e7i	0.725353	−	0.998363i	0.999329	−	0.0366260i	$-0.0116610\pi$
$972$		0			0
$973$	5.05282e6	−	1.55510e7i	0.171101	−	0.526594i
$974$	7.33031e6	−	2.25604e7i	0.247585	−	0.761990i
$975$		0			0
$976$	3.75194e6	−	5.16410e6i	0.126076	−	0.173528i
$977$	−8.46733e6	+	2.75120e6i	−0.283799	+	0.0922118i	−0.447457	−	0.894305i	$-0.647670\pi$
$977$	−8.46733e6	+	2.75120e6i	−0.283799	+	0.0922118i	0.163659	+	0.986517i	$0.447670\pi$
$978$		0			0
$979$	1.92894e7	+	4.53237e7i	0.643224	+	1.51136i
$980$		−	4.62866e6i		−	0.153954i
$981$		0			0
$982$	1.57279e7	+	1.14270e7i	0.520464	+	0.378139i
$983$	−9.67069e6	−	1.33106e7i	−0.319208	−	0.439352i	0.619017	−	0.785377i	$-0.287531\pi$
$983$	−9.67069e6	−	1.33106e7i	−0.319208	−	0.439352i	−0.938225	+	0.346025i	$0.887531\pi$
$984$		0			0
$985$	6.55454e7	+	2.12970e7i	2.15254	+	0.699403i
$986$	−3.96270e6	+	2.87907e6i	−0.129807	+	0.0943105i
$987$		0			0
$988$	−637707.	−	1.96266e6i	−0.0207840	−	0.0639665i
$989$	−2.27452e7			−0.739433
$990$		0			0
$991$	3.27272e7			1.05858			0.529291	−	0.848440i	$-0.322458\pi$
$991$	3.27272e7			1.05858			0.529291	+	0.848440i	$0.322458\pi$
$992$	1.15715e6	+	3.56133e6i	0.0373344	+	0.114903i
$993$		0			0
$994$	2.12040e7	−	1.54056e7i	0.680695	−	0.494554i
$995$	−5.38899e7	−	1.75099e7i	−1.72564	−	0.560694i
$996$		0			0
$997$	−2.32239e7	−	3.19650e7i	−0.739942	−	1.01844i	−0.998622	−	0.0524797i	$-0.983288\pi$
$997$	−2.32239e7	−	3.19650e7i	−0.739942	−	1.01844i	0.258680	−	0.965963i	$-0.416712\pi$
$998$	−2.96054e7	−	2.15096e7i	−0.940904	−	0.683607i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.6.l.b.17.9	yes	40
3.2	odd	2		198.6.l.a.17.2	✓	40
11.2	odd	10		198.6.l.a.35.2	yes	40
33.2	even	10	inner	198.6.l.b.35.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.6.l.a.17.2	✓	40	3.2	odd	2
198.6.l.a.35.2	yes	40	11.2	odd	10
198.6.l.b.17.9	yes	40	1.1	even	1	trivial
198.6.l.b.35.9	yes	40	33.2	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	198.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23607 - 3.80423i) q^{2} +(-12.9443 + 9.40456i) q^{4} +(74.1025 + 24.0774i) q^{5} +(-84.1988 - 115.890i) q^{7} +(51.7771 + 37.6183i) q^{8} +O(q^{10})\)	\(q+(-1.23607 - 3.80423i) q^{2} +(-12.9443 + 9.40456i) q^{4} +(74.1025 + 24.0774i) q^{5} +(-84.1988 - 115.890i) q^{7} +(51.7771 + 37.6183i) q^{8} -311.664i q^{10} +(-369.261 + 157.155i) q^{11} +(160.738 - 52.2269i) q^{13} +(-336.795 + 463.559i) q^{14} +(79.1084 - 243.470i) q^{16} +(77.0799 - 237.227i) q^{17} +(-448.565 + 617.397i) q^{19} +(-1185.64 + 385.238i) q^{20} +(1054.28 + 1210.50i) q^{22} -4445.10i q^{23} +(2383.28 + 1731.55i) q^{25} +(-397.366 - 546.927i) q^{26} +(2179.78 + 708.255i) q^{28} +(3971.67 - 2885.58i) q^{29} +(-1130.03 - 3477.86i) q^{31} -1024.00 q^{32} -997.743 q^{34} +(-3449.02 - 10615.0i) q^{35} +(-1271.49 + 923.788i) q^{37} +(2903.18 + 943.299i) q^{38} +(2931.06 + 4034.26i) q^{40} +(-11553.3 - 8393.95i) q^{41} -5116.91i q^{43} +(3301.84 - 5506.99i) q^{44} +(-16910.2 + 5494.45i) q^{46} +(-2015.59 + 2774.22i) q^{47} +(-1147.34 + 3531.14i) q^{49} +(3641.33 - 11206.9i) q^{50} +(-1589.46 + 2187.71i) q^{52} +(-28729.8 + 9334.87i) q^{53} +(-31147.0 + 2754.73i) q^{55} -9167.84i q^{56} +(-15886.7 - 11542.3i) q^{58} +(-16640.1 - 22903.1i) q^{59} +(23713.9 + 7705.12i) q^{61} +(-11833.8 + 8597.75i) q^{62} +(1265.73 + 3895.53i) q^{64} +13168.6 q^{65} -53227.5 q^{67} +(1233.28 + 3795.64i) q^{68} +(-36118.6 + 26241.7i) q^{70} +(-43503.1 - 14135.0i) q^{71} +(30255.5 + 41643.1i) q^{73} +(5085.94 + 3695.15i) q^{74} -12210.3i q^{76} +(49303.9 + 29561.3i) q^{77} +(15425.0 - 5011.90i) q^{79} +(11724.2 - 16137.0i) q^{80} +(-17651.8 + 54326.8i) q^{82} +(22823.0 - 70242.0i) q^{83} +(11423.6 - 15723.3i) q^{85} +(-19465.9 + 6324.85i) q^{86} +(-25031.1 - 5753.93i) q^{88} -122742. i q^{89} +(-19586.5 - 14230.4i) q^{91} +(41804.2 + 57538.6i) q^{92} +(13045.2 + 4238.63i) q^{94} +(-48105.1 + 34950.4i) q^{95} +(-16932.5 - 52113.0i) q^{97} +14851.4 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 160 q^{4} + 640 q^{8}+O(q^{10}) \) 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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