LMFDB - Embedded newform 63.6.e.a.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,6,Mod(37,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("63.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	63.e (of order $3$, degree $2$, 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:	$10.1041806482$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	63.46
Dual form			63.6.e.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(14.0000 - 24.2487i) q^{4} +(5.50000 + 9.52628i) q^{5} +(129.500 - 6.06218i) q^{7} -120.000 q^{8} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(14.0000 - 24.2487i) q^{4} +(5.50000 + 9.52628i) q^{5} +(129.500 - 6.06218i) q^{7} -120.000 q^{8} +(11.0000 - 19.0526i) q^{10} +(134.500 - 232.961i) q^{11} -308.000 q^{13} +(-140.000 - 218.238i) q^{14} +(-328.000 - 568.113i) q^{16} +(948.000 - 1641.98i) q^{17} +(82.0000 + 142.028i) q^{19} +308.000 q^{20} -538.000 q^{22} +(-1632.00 - 2826.71i) q^{23} +(1502.00 - 2601.54i) q^{25} +(308.000 + 533.472i) q^{26} +(1666.00 - 3225.08i) q^{28} -2417.00 q^{29} +(-1420.50 + 2460.38i) q^{31} +(-2576.00 + 4461.76i) q^{32} -3792.00 q^{34} +(770.000 + 1200.31i) q^{35} +(5664.00 + 9810.34i) q^{37} +(164.000 - 284.056i) q^{38} +(-660.000 - 1143.15i) q^{40} +16856.0 q^{41} -7894.00 q^{43} +(-3766.00 - 6522.90i) q^{44} +(-3264.00 + 5653.41i) q^{46} +(10551.0 + 18274.9i) q^{47} +(16733.5 - 1570.10i) q^{49} -6008.00 q^{50} +(-4312.00 + 7468.60i) q^{52} +(-14845.5 + 25713.2i) q^{53} +2959.00 q^{55} +(-15540.0 + 727.461i) q^{56} +(2417.00 + 4186.37i) q^{58} +(-4081.50 + 7069.37i) q^{59} +(-7583.00 - 13134.1i) q^{61} +5682.00 q^{62} -10688.0 q^{64} +(-1694.00 - 2934.09i) q^{65} +(16039.0 - 27780.4i) q^{67} +(-26544.0 - 45975.6i) q^{68} +(1309.00 - 2533.99i) q^{70} +38274.0 q^{71} +(-17433.0 + 30194.8i) q^{73} +(11328.0 - 19620.7i) q^{74} +4592.00 q^{76} +(16005.5 - 30983.8i) q^{77} +(-6764.50 - 11716.5i) q^{79} +(3608.00 - 6249.24i) q^{80} +(-16856.0 - 29195.4i) q^{82} +68103.0 q^{83} +20856.0 q^{85} +(7894.00 + 13672.8i) q^{86} +(-16140.0 + 27955.3i) q^{88} +(-57461.0 - 99525.4i) q^{89} +(-39886.0 + 1867.15i) q^{91} -91392.0 q^{92} +(21102.0 - 36549.7i) q^{94} +(-902.000 + 1562.31i) q^{95} +154959. q^{97} +(-19453.0 - 27413.2i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 28 q^{4} + 11 q^{5} + 259 q^{7} - 240 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 + 28 * q^4 + 11 * q^5 + 259 * q^7 - 240 * q^8	$ 2 q - 2 q^{2} + 28 q^{4} + 11 q^{5} + 259 q^{7} - 240 q^{8} + 22 q^{10} + 269 q^{11} - 616 q^{13} - 280 q^{14} - 656 q^{16} + 1896 q^{17} + 164 q^{19} + 616 q^{20} - 1076 q^{22} - 3264 q^{23} + 3004 q^{25} + 616 q^{26} + 3332 q^{28} - 4834 q^{29} - 2841 q^{31} - 5152 q^{32} - 7584 q^{34} + 1540 q^{35} + 11328 q^{37} + 328 q^{38} - 1320 q^{40} + 33712 q^{41} - 15788 q^{43} - 7532 q^{44} - 6528 q^{46} + 21102 q^{47} + 33467 q^{49} - 12016 q^{50} - 8624 q^{52} - 29691 q^{53} + 5918 q^{55} - 31080 q^{56} + 4834 q^{58} - 8163 q^{59} - 15166 q^{61} + 11364 q^{62} - 21376 q^{64} - 3388 q^{65} + 32078 q^{67} - 53088 q^{68} + 2618 q^{70} + 76548 q^{71} - 34866 q^{73} + 22656 q^{74} + 9184 q^{76} + 32011 q^{77} - 13529 q^{79} + 7216 q^{80} - 33712 q^{82} + 136206 q^{83} + 41712 q^{85} + 15788 q^{86} - 32280 q^{88} - 114922 q^{89} - 79772 q^{91} - 182784 q^{92} + 42204 q^{94} - 1804 q^{95} + 309918 q^{97} - 38906 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 28 * q^4 + 11 * q^5 + 259 * q^7 - 240 * q^8 + 22 * q^10 + 269 * q^11 - 616 * q^13 - 280 * q^14 - 656 * q^16 + 1896 * q^17 + 164 * q^19 + 616 * q^20 - 1076 * q^22 - 3264 * q^23 + 3004 * q^25 + 616 * q^26 + 3332 * q^28 - 4834 * q^29 - 2841 * q^31 - 5152 * q^32 - 7584 * q^34 + 1540 * q^35 + 11328 * q^37 + 328 * q^38 - 1320 * q^40 + 33712 * q^41 - 15788 * q^43 - 7532 * q^44 - 6528 * q^46 + 21102 * q^47 + 33467 * q^49 - 12016 * q^50 - 8624 * q^52 - 29691 * q^53 + 5918 * q^55 - 31080 * q^56 + 4834 * q^58 - 8163 * q^59 - 15166 * q^61 + 11364 * q^62 - 21376 * q^64 - 3388 * q^65 + 32078 * q^67 - 53088 * q^68 + 2618 * q^70 + 76548 * q^71 - 34866 * q^73 + 22656 * q^74 + 9184 * q^76 + 32011 * q^77 - 13529 * q^79 + 7216 * q^80 - 33712 * q^82 + 136206 * q^83 + 41712 * q^85 + 15788 * q^86 - 32280 * q^88 - 114922 * q^89 - 79772 * q^91 - 182784 * q^92 + 42204 * q^94 - 1804 * q^95 + 309918 * q^97 - 38906 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.00000	−	1.73205i	−0.176777	−	0.306186i	0.763998	−	0.645219i	$-0.223234\pi$
$2$	−1.00000	−	1.73205i	−0.176777	−	0.306186i	−0.940775	+	0.339032i	$0.889900\pi$
$3$		0			0
$3$		0			0
$4$	14.0000	−	24.2487i	0.437500	−	0.757772i
$5$	5.50000	+	9.52628i	0.0983870	+	0.170411i	0.911017	−	0.412368i	$-0.135298\pi$
$5$	5.50000	+	9.52628i	0.0983870	+	0.170411i	−0.812630	+	0.582780i	$0.801965\pi$
$6$		0			0
$7$	129.500	−	6.06218i	0.998906	−	0.0467610i
$7$	129.500	−	6.06218i	0.998906	−	0.0467610i
$8$	−120.000			−0.662913
$9$		0			0
$10$	11.0000	−	19.0526i	0.0347851	−	0.0602495i
$11$	134.500	−	232.961i	0.335151	−	0.580499i	−0.648363	−	0.761332i	$-0.724546\pi$
$11$	134.500	−	232.961i	0.335151	−	0.580499i	0.983514	+	0.180833i	$0.0578793\pi$
$12$		0			0
$13$	−308.000			−0.505466			−0.252733	−	0.967536i	$-0.581329\pi$
$13$	−308.000			−0.505466			−0.252733	+	0.967536i	$0.581329\pi$
$14$	−140.000	−	218.238i	−0.190901	−	0.297585i
$15$		0			0
$16$	−328.000	−	568.113i	−0.320312	−	0.554798i
$17$	948.000	−	1641.98i	0.795584	−	1.37799i	−0.126884	−	0.991918i	$-0.540498\pi$
$17$	948.000	−	1641.98i	0.795584	−	1.37799i	0.922468	−	0.386074i	$-0.126169\pi$
$18$		0			0
$19$	82.0000	+	142.028i	0.0521111	+	0.0902590i	0.890904	−	0.454191i	$-0.150072\pi$
$19$	82.0000	+	142.028i	0.0521111	+	0.0902590i	−0.838793	+	0.544450i	$0.816738\pi$
$20$	308.000			0.172177
$21$		0			0
$22$	−538.000			−0.236988
$23$	−1632.00	−	2826.71i	−0.643281	−	1.11419i	−0.984696	−	0.174282i	$-0.944239\pi$
$23$	−1632.00	−	2826.71i	−0.643281	−	1.11419i	0.341415	−	0.939913i	$-0.389094\pi$
$24$		0			0
$25$	1502.00	−	2601.54i	0.480640	−	0.832493i
$26$	308.000	+	533.472i	0.0893547	+	0.154767i
$27$		0			0
$28$	1666.00	−	3225.08i	0.401587	−	0.777401i
$29$	−2417.00			−0.533681			−0.266840	−	0.963741i	$-0.585980\pi$
$29$	−2417.00			−0.533681			−0.266840	+	0.963741i	$0.585980\pi$
$30$		0			0
$31$	−1420.50	+	2460.38i	−0.265483	+	0.459830i	−0.967690	−	0.252143i	$-0.918865\pi$
$31$	−1420.50	+	2460.38i	−0.265483	+	0.459830i	0.702207	+	0.711973i	$0.252198\pi$
$32$	−2576.00	+	4461.76i	−0.444704	+	0.770250i
$33$		0			0
$34$	−3792.00			−0.562563
$35$	770.000	+	1200.31i	0.106248	+	0.165624i
$36$		0			0
$37$	5664.00	+	9810.34i	0.680172	+	1.17809i	0.974928	+	0.222520i	$0.0714284\pi$
$37$	5664.00	+	9810.34i	0.680172	+	1.17809i	−0.294756	+	0.955573i	$0.595238\pi$
$38$	164.000	−	284.056i	0.0184240	−	0.0319114i
$39$		0			0
$40$	−660.000	−	1143.15i	−0.0652220	−	0.112968i
$41$	16856.0			1.56601			0.783006	−	0.622015i	$-0.213686\pi$
$41$	16856.0			1.56601			0.783006	+	0.622015i	$0.213686\pi$
$42$		0			0
$43$	−7894.00			−0.651067			−0.325534	−	0.945530i	$-0.605544\pi$
$43$	−7894.00			−0.651067			−0.325534	+	0.945530i	$0.605544\pi$
$44$	−3766.00	−	6522.90i	−0.293257	−	0.507936i
$45$		0			0
$46$	−3264.00	+	5653.41i	−0.227434	+	0.393927i
$47$	10551.0	+	18274.9i	0.696705	+	1.20673i	0.969603	+	0.244685i	$0.0786847\pi$
$47$	10551.0	+	18274.9i	0.696705	+	1.20673i	−0.272897	+	0.962043i	$0.587982\pi$
$48$		0			0
$49$	16733.5	−	1570.10i	0.995627	−	0.0934196i
$50$	−6008.00			−0.339864
$51$		0			0
$52$	−4312.00	+	7468.60i	−0.221142	+	0.383028i
$53$	−14845.5	+	25713.2i	−0.725947	+	1.25738i	0.232635	+	0.972564i	$0.425265\pi$
$53$	−14845.5	+	25713.2i	−0.725947	+	1.25738i	−0.958583	+	0.284814i	$0.908068\pi$
$54$		0			0
$55$	2959.00			0.131898
$56$	−15540.0	+	727.461i	−0.662187	+	0.0309984i
$57$		0			0
$58$	2417.00	+	4186.37i	0.0943423	+	0.163406i
$59$	−4081.50	+	7069.37i	−0.152648	+	0.264393i	−0.932200	−	0.361944i	$-0.882113\pi$
$59$	−4081.50	+	7069.37i	−0.152648	+	0.264393i	0.779552	+	0.626337i	$0.215447\pi$
$60$		0			0
$61$	−7583.00	−	13134.1i	−0.260925	−	0.451936i	0.705563	−	0.708648i	$-0.250694\pi$
$61$	−7583.00	−	13134.1i	−0.260925	−	0.451936i	−0.966488	+	0.256711i	$0.917361\pi$
$62$	5682.00			0.187725
$63$		0			0
$64$	−10688.0			−0.326172
$65$	−1694.00	−	2934.09i	−0.0497313	−	0.0861372i
$66$		0			0
$67$	16039.0	−	27780.4i	0.436506	−	0.756051i	−0.560911	−	0.827876i	$-0.689549\pi$
$67$	16039.0	−	27780.4i	0.436506	−	0.756051i	0.997417	+	0.0718253i	$0.0228824\pi$
$68$	−26544.0	−	45975.6i	−0.696136	−	1.20574i
$69$		0			0
$70$	1309.00	−	2533.99i	0.0319297	−	0.0618102i
$71$	38274.0			0.901069			0.450534	−	0.892759i	$-0.351233\pi$
$71$	38274.0			0.901069			0.450534	+	0.892759i	$0.351233\pi$
$72$		0			0
$73$	−17433.0	+	30194.8i	−0.382882	+	0.663171i	−0.991473	−	0.130313i	$-0.958402\pi$
$73$	−17433.0	+	30194.8i	−0.382882	+	0.663171i	0.608591	+	0.793484i	$0.291735\pi$
$74$	11328.0	−	19620.7i	0.240477	−	0.416519i
$75$		0			0
$76$	4592.00			0.0911943
$77$	16005.5	−	30983.8i	0.307640	−	0.595536i
$78$		0			0
$79$	−6764.50	−	11716.5i	−0.121946	−	0.211217i	0.798589	−	0.601877i	$-0.205580\pi$
$79$	−6764.50	−	11716.5i	−0.121946	−	0.211217i	−0.920535	+	0.390660i	$0.872247\pi$
$80$	3608.00	−	6249.24i	0.0630292	−	0.109170i
$81$		0			0
$82$	−16856.0	−	29195.4i	−0.276834	−	0.479491i
$83$	68103.0			1.08510			0.542552	−	0.840023i	$-0.317458\pi$
$83$	68103.0			1.08510			0.542552	+	0.840023i	$0.317458\pi$
$84$		0			0
$85$	20856.0			0.313100
$86$	7894.00	+	13672.8i	0.115094	+	0.199348i
$87$		0			0
$88$	−16140.0	+	27955.3i	−0.222176	+	0.384820i
$89$	−57461.0	−	99525.4i	−0.768950	−	1.33186i	−0.938133	−	0.346276i	$-0.887446\pi$
$89$	−57461.0	−	99525.4i	−0.768950	−	1.33186i	0.169183	−	0.985585i	$-0.445887\pi$
$90$		0			0
$91$	−39886.0	+	1867.15i	−0.504914	+	0.0236361i
$92$	−91392.0			−1.12574
$93$		0			0
$94$	21102.0	−	36549.7i	0.246322	−	0.426643i
$95$	−902.000	+	1562.31i	−0.0102541	+	0.0177606i
$96$		0			0
$97$	154959.			1.67220			0.836099	−	0.548579i	$-0.184831\pi$
$97$	154959.			1.67220			0.836099	+	0.548579i	$0.184831\pi$
$98$	−19453.0	−	27413.2i	−0.204607	−	0.288333i
$99$		0			0
$100$	−42056.0	−	72843.1i	−0.420560	−	0.728431i
$101$	−53785.0	+	93158.4i	−0.524636	+	0.908695i	0.474953	+	0.880011i	$0.342465\pi$
$101$	−53785.0	+	93158.4i	−0.524636	+	0.908695i	−0.999589	+	0.0286843i	$0.990868\pi$
$102$		0			0
$103$	−4468.00	−	7738.80i	−0.0414973	−	0.0718755i	0.844531	−	0.535507i	$-0.179879\pi$
$103$	−4468.00	−	7738.80i	−0.0414973	−	0.0718755i	−0.886028	+	0.463632i	$0.846546\pi$
$104$	36960.0			0.335080
$105$		0			0
$106$	59382.0			0.513322
$107$	96833.5	+	167721.i	0.817648	+	1.41621i	0.907411	+	0.420244i	$0.138056\pi$
$107$	96833.5	+	167721.i	0.817648	+	1.41621i	−0.0897634	+	0.995963i	$0.528611\pi$
$108$		0			0
$109$	−102555.	+	177630.i	−0.826781	+	1.43203i	0.0737692	+	0.997275i	$0.476497\pi$
$109$	−102555.	+	177630.i	−0.826781	+	1.43203i	−0.900550	+	0.434752i	$0.856836\pi$
$110$	−2959.00	−	5125.14i	−0.0233165	−	0.0403854i
$111$		0			0
$112$	−45920.0	−	71582.2i	−0.345905	−	0.539213i
$113$	−46664.0			−0.343784			−0.171892	−	0.985116i	$-0.554988\pi$
$113$	−46664.0			−0.343784			−0.171892	+	0.985116i	$0.554988\pi$
$114$		0			0
$115$	17952.0	−	31093.8i	0.126581	−	0.219245i
$116$	−33838.0	+	58609.1i	−0.233485	+	0.404409i
$117$		0			0
$118$	16326.0			0.107938
$119$	112812.	−	218384.i	0.730277	−	1.41369i
$120$		0			0
$121$	44345.0	+	76807.8i	0.275348	+	0.476916i
$122$	−15166.0	+	26268.3i	−0.0922511	+	0.159784i
$123$		0			0
$124$	39774.0	+	68890.6i	0.232298	+	0.402352i
$125$	67419.0			0.385929
$126$		0			0
$127$	−304365.			−1.67450			−0.837250	−	0.546820i	$-0.815838\pi$
$127$	−304365.			−1.67450			−0.837250	+	0.546820i	$0.815838\pi$
$128$	93120.0	+	161289.i	0.502363	+	0.870119i
$129$		0			0
$130$	−3388.00	+	5868.19i	−0.0175827	+	0.0304541i
$131$	−6651.50	−	11520.7i	−0.0338642	−	0.0586546i	0.848597	−	0.529041i	$-0.177448\pi$
$131$	−6651.50	−	11520.7i	−0.0338642	−	0.0586546i	−0.882461	+	0.470386i	$0.844115\pi$
$132$		0			0
$133$	11480.0	+	17895.5i	0.0562746	+	0.0877235i
$134$	−64156.0			−0.308656
$135$		0			0
$136$	−113760.	+	197038.i	−0.527403	+	0.913488i
$137$	−199131.	+	344905.i	−0.906437	+	1.56999i	−0.0874596	+	0.996168i	$0.527875\pi$
$137$	−199131.	+	344905.i	−0.906437	+	1.56999i	−0.818977	+	0.573826i	$0.805458\pi$
$138$		0			0
$139$	230286.			1.01095			0.505476	−	0.862841i	$-0.331317\pi$
$139$	230286.			1.01095			0.505476	+	0.862841i	$0.331317\pi$
$140$	39886.0	−	1867.15i	0.171989	−	0.00805118i
$141$		0			0
$142$	−38274.0	−	66292.5i	−0.159288	−	0.275895i
$143$	−41426.0	+	71751.9i	−0.169408	+	0.293423i
$144$		0			0
$145$	−13293.5	−	23025.0i	−0.0525073	−	0.0909452i
$146$	69732.0			0.270738
$147$		0			0
$148$	317184.			1.19030
$149$	−48567.0	−	84120.5i	−0.179216	−	0.310410i	0.762397	−	0.647110i	$-0.224023\pi$
$149$	−48567.0	−	84120.5i	−0.179216	−	0.310410i	−0.941612	+	0.336700i	$0.890689\pi$
$150$		0			0
$151$	14523.5	−	25155.4i	0.0518357	−	0.0897821i	−0.838943	−	0.544219i	$-0.816826\pi$
$151$	14523.5	−	25155.4i	0.0518357	−	0.0897821i	0.890779	+	0.454437i	$0.150159\pi$
$152$	−9840.00	−	17043.4i	−0.0345451	−	0.0598338i
$153$		0			0
$154$	−69671.0	+	3261.45i	−0.236728	+	0.0110818i
$155$	−31251.0			−0.104480
$156$		0			0
$157$	288250.	−	499264.i	0.933298	−	1.61652i	0.155656	−	0.987811i	$-0.450251\pi$
$157$	288250.	−	499264.i	0.933298	−	1.61652i	0.777642	−	0.628708i	$-0.216416\pi$
$158$	−13529.0	+	23432.9i	−0.0431145	+	0.0746764i
$159$		0			0
$160$	−56672.0			−0.175012
$161$	−228480.	−	356165.i	−0.694678	−	1.08290i
$162$		0			0
$163$	132616.	+	229698.i	0.390955	+	0.677154i	0.992576	−	0.121628i	$-0.0388114\pi$
$163$	132616.	+	229698.i	0.390955	+	0.677154i	−0.601621	+	0.798782i	$0.705478\pi$
$164$	235984.	−	408736.i	0.685130	−	1.18668i
$165$		0			0
$166$	−68103.0	−	117958.i	−0.191821	−	0.332244i
$167$	363790.			1.00939			0.504696	−	0.863297i	$-0.331605\pi$
$167$	363790.			1.00939			0.504696	+	0.863297i	$0.331605\pi$
$168$		0			0
$169$	−276429.			−0.744504
$170$	−20856.0	−	36123.7i	−0.0553489	−	0.0958670i
$171$		0			0
$172$	−110516.	+	191419.i	−0.284842	+	0.493361i
$173$	−82423.0	−	142761.i	−0.209379	−	0.362655i	0.742140	−	0.670245i	$-0.233811\pi$
$173$	−82423.0	−	142761.i	−0.209379	−	0.362655i	−0.951519	+	0.307590i	$0.900478\pi$
$174$		0			0
$175$	178738.	−	346005.i	0.441186	−	0.854057i
$176$	−176464.			−0.429412
$177$		0			0
$178$	−114922.	+	199051.i	−0.271865	+	0.470884i
$179$	15314.0	−	26524.6i	0.0357237	−	0.0618752i	−0.847611	−	0.530618i	$-0.821960\pi$
$179$	15314.0	−	26524.6i	0.0357237	−	0.0618752i	0.883334	+	0.468743i	$0.155293\pi$
$180$		0			0
$181$	−651392.			−1.47790			−0.738952	−	0.673759i	$-0.764679\pi$
$181$	−651392.			−1.47790			−0.738952	+	0.673759i	$0.764679\pi$
$182$	43120.0	+	67217.4i	0.0964940	+	0.150419i
$183$		0			0
$184$	195840.	+	339205.i	0.426439	+	0.738614i
$185$	−62304.0	+	107914.i	−0.133840	+	0.231818i
$186$		0			0
$187$	−255012.	−	441694.i	−0.533282	−	0.923671i
$188$	590856.			1.21923
$189$		0			0
$190$	3608.00			0.00725074
$191$	−378680.	−	655893.i	−0.751085	−	1.30092i	−0.947297	−	0.320356i	$-0.896198\pi$
$191$	−378680.	−	655893.i	−0.751085	−	1.30092i	0.196213	−	0.980561i	$-0.437136\pi$
$192$		0			0
$193$	80169.5	−	138858.i	0.154923	−	0.268335i	−0.778108	−	0.628131i	$-0.783820\pi$
$193$	80169.5	−	138858.i	0.154923	−	0.268335i	0.933031	+	0.359796i	$0.117154\pi$
$194$	−154959.	−	268397.i	−0.295605	−	0.512004i
$195$		0			0
$196$	196196.	−	427747.i	0.364796	−	0.795329i
$197$	61738.0			0.113341			0.0566705	−	0.998393i	$-0.481952\pi$
$197$	61738.0			0.113341			0.0566705	+	0.998393i	$0.481952\pi$
$198$		0			0
$199$	−185454.	+	321216.i	−0.331974	+	0.574995i	−0.982899	−	0.184147i	$-0.941048\pi$
$199$	−185454.	+	321216.i	−0.331974	+	0.574995i	0.650925	+	0.759142i	$0.274381\pi$
$200$	−180240.	+	312185.i	−0.318622	+	0.551870i
$201$		0			0
$202$	215140.			0.370973
$203$	−313001.	+	14652.3i	−0.533097	+	0.0249554i
$204$		0			0
$205$	92708.0	+	160575.i	0.154075	+	0.266866i
$206$	−8936.00	+	15477.6i	−0.0146715	+	0.0254118i
$207$		0			0
$208$	101024.	+	174979.i	0.161907	+	0.280432i
$209$	44116.0			0.0698603
$210$		0			0
$211$	217450.			0.336243			0.168122	−	0.985766i	$-0.446230\pi$
$211$	217450.			0.336243			0.168122	+	0.985766i	$0.446230\pi$
$212$	415674.	+	719968.i	0.635204	+	1.10021i
$213$		0			0
$214$	193667.	−	335441.i	0.289082	−	0.500705i
$215$	−43417.0	−	75200.4i	−0.0640566	−	0.110949i
$216$		0			0
$217$	−169040.	+	327230.i	−0.243691	+	0.471742i
$218$	410220.			0.584623
$219$		0			0
$220$	41426.0	−	71751.9i	0.0577054	−	0.0999486i
$221$	−291984.	+	505731.i	−0.402141	+	0.696529i
$222$		0			0
$223$	589771.			0.794184			0.397092	−	0.917779i	$-0.370019\pi$
$223$	589771.			0.794184			0.397092	+	0.917779i	$0.370019\pi$
$224$	−306544.	+	593414.i	−0.408200	+	0.790202i
$225$		0			0
$226$	46664.0	+	80824.4i	0.0607730	+	0.105262i
$227$	−193522.	+	335191.i	−0.249268	+	0.431745i	−0.963323	−	0.268345i	$-0.913523\pi$
$227$	−193522.	+	335191.i	−0.249268	+	0.431745i	0.714055	+	0.700090i	$0.246857\pi$
$228$		0			0
$229$	116366.	+	201552.i	0.146635	+	0.253979i	0.929982	−	0.367606i	$-0.119822\pi$
$229$	116366.	+	201552.i	0.146635	+	0.253979i	−0.783347	+	0.621585i	$0.786489\pi$
$230$	−71808.0			−0.0895062
$231$		0			0
$232$	290040.			0.353784
$233$	21048.0	+	36456.2i	0.0253993	+	0.0439928i	0.878446	−	0.477842i	$-0.158581\pi$
$233$	21048.0	+	36456.2i	0.0253993	+	0.0439928i	−0.853046	+	0.521835i	$0.825248\pi$
$234$		0			0
$235$	−116061.	+	201024.i	−0.137093	+	0.237453i
$236$	114282.	+	197942.i	0.133567	+	0.231344i
$237$		0			0
$238$	−491064.	+	22987.8i	−0.561947	+	0.0263060i
$239$	313416.			0.354917			0.177458	−	0.984128i	$-0.443212\pi$
$239$	313416.			0.354917			0.177458	+	0.984128i	$0.443212\pi$
$240$		0			0
$241$	−428904.	+	742883.i	−0.475682	+	0.823906i	−0.999612	−	0.0278556i	$-0.991132\pi$
$241$	−428904.	+	742883.i	−0.475682	+	0.823906i	0.523930	+	0.851762i	$0.324465\pi$
$242$	88690.0	−	153616.i	0.0973501	−	0.168615i
$243$		0			0
$244$	−424648.			−0.456620
$245$	106992.	+	150772.i	0.113876	+	0.160475i
$246$		0			0
$247$	−25256.0	−	43744.7i	−0.0263404	−	0.0456229i
$248$	170460.	−	295245.i	0.175992	−	0.304827i
$249$		0			0
$250$	−67419.0	−	116773.i	−0.0682232	−	0.118166i
$251$	−454517.			−0.455371			−0.227686	−	0.973735i	$-0.573116\pi$
$251$	−454517.			−0.455371			−0.227686	+	0.973735i	$0.573116\pi$
$252$		0			0
$253$	−878016.			−0.862385
$254$	304365.	+	527176.i	0.296013	+	0.512709i
$255$		0			0
$256$	15232.0	−	26382.6i	0.0145264	−	0.0251604i
$257$	439091.	+	760528.i	0.414688	+	0.718261i	0.995396	−	0.0958512i	$-0.0305573\pi$
$257$	439091.	+	760528.i	0.414688	+	0.718261i	−0.580707	+	0.814112i	$0.697224\pi$
$258$		0			0
$259$	792960.	+	1.23610e6i	0.734517	+	1.14500i
$260$	−94864.0			−0.0870298
$261$		0			0
$262$	−13303.0	+	23041.5i	−0.0119728	+	0.0207375i
$263$	980467.	−	1.69822e6i	0.874065	−	1.51392i	0.0163091	−	0.999867i	$-0.494808\pi$
$263$	980467.	−	1.69822e6i	0.874065	−	1.51392i	0.857756	−	0.514058i	$-0.171858\pi$
$264$		0			0
$265$	−326601.			−0.285695
$266$	19516.0	−	37779.5i	0.0169117	−	0.0327380i
$267$		0			0
$268$	−449092.	−	777850.i	−0.381943	−	0.661544i
$269$	−526898.	+	912613.i	−0.443962	+	0.768964i	−0.997979	−	0.0635408i	$-0.979761\pi$
$269$	−526898.	+	912613.i	−0.443962	+	0.768964i	0.554018	+	0.832505i	$0.313094\pi$
$270$		0			0
$271$	52529.5	+	90983.8i	0.0434490	+	0.0752559i	0.886932	−	0.461900i	$-0.152832\pi$
$271$	52529.5	+	90983.8i	0.0434490	+	0.0752559i	−0.843483	+	0.537156i	$0.819499\pi$
$272$	−1.24378e6			−1.01934
$273$		0			0
$274$	796524.			0.640948
$275$	−404038.	−	699814.i	−0.322174	−	0.558022i
$276$		0			0
$277$	213796.	−	370306.i	0.167417	−	0.289975i	−0.770094	−	0.637931i	$-0.779791\pi$
$277$	213796.	−	370306.i	0.167417	−	0.289975i	0.937511	+	0.347955i	$0.113124\pi$
$278$	−230286.	−	398867.i	−0.178713	−	0.309540i
$279$		0			0
$280$	−92400.0	−	144037.i	−0.0704331	−	0.109794i
$281$	−638878.			−0.482672			−0.241336	−	0.970442i	$-0.577586\pi$
$281$	−638878.			−0.482672			−0.241336	+	0.970442i	$0.577586\pi$
$282$		0			0
$283$	1.22571e6	−	2.12299e6i	0.909750	−	1.57573i	0.0953386	−	0.995445i	$-0.469607\pi$
$283$	1.22571e6	−	2.12299e6i	0.909750	−	1.57573i	0.814411	−	0.580288i	$-0.197060\pi$
$284$	535836.	−	928095.i	0.394218	−	0.682805i
$285$		0			0
$286$	165704.			0.119789
$287$	2.18285e6	−	102184.i	1.56430	−	0.0732282i
$288$		0			0
$289$	−1.08748e6	−	1.88357e6i	−0.765908	−	1.32659i
$290$	−26587.0	+	46050.0i	−0.0185641	+	0.0321540i
$291$		0			0
$292$	488124.	+	845456.i	0.335022	+	0.580275i
$293$	−1.71617e6			−1.16786			−0.583930	−	0.811804i	$-0.698486\pi$
$293$	−1.71617e6			−1.16786			−0.583930	+	0.811804i	$0.698486\pi$
$294$		0			0
$295$	−89793.0			−0.0600741
$296$	−679680.	−	1.17724e6i	−0.450895	−	0.780973i
$297$		0			0
$298$	−97134.0	+	168241.i	−0.0633623	+	0.109747i
$299$	502656.	+	870626.i	0.325157	+	0.563188i
$300$		0			0
$301$	−1.02227e6	+	47854.8i	−0.650355	+	0.0304445i
$302$	−58094.0			−0.0366534
$303$		0			0
$304$	53792.0	−	93170.5i	0.0333836	−	0.0578222i
$305$	83413.0	−	144476.i	0.0513433	−	0.0889293i
$306$		0			0
$307$	1.80897e6			1.09543			0.547715	−	0.836665i	$-0.315498\pi$
$307$	1.80897e6			1.09543			0.547715	+	0.836665i	$0.315498\pi$
$308$	−527240.	−	821886.i	−0.316688	−	0.493668i
$309$		0			0
$310$	31251.0	+	54128.3i	0.0184697	+	0.0319904i
$311$	760728.	−	1.31762e6i	0.445993	−	0.772483i	−0.552127	−	0.833760i	$-0.686184\pi$
$311$	760728.	−	1.31762e6i	0.445993	−	0.772483i	0.998121	+	0.0612765i	$0.0195171\pi$
$312$		0			0
$313$	674200.	+	1.16775e6i	0.388980	+	0.673734i	0.992313	−	0.123756i	$-0.0394941\pi$
$313$	674200.	+	1.16775e6i	0.388980	+	0.673734i	−0.603332	+	0.797490i	$0.706161\pi$
$314$	−1.15300e6			−0.659941
$315$		0			0
$316$	−378812.			−0.213406
$317$	−24847.5	−	43037.1i	−0.0138878	−	0.0240544i	0.858998	−	0.511979i	$-0.171087\pi$
$317$	−24847.5	−	43037.1i	−0.0138878	−	0.0240544i	−0.872886	+	0.487925i	$0.837754\pi$
$318$		0			0
$319$	−325086.	+	563066.i	−0.178864	+	0.309801i
$320$	−58784.0	−	101817.i	−0.0320911	−	0.0555834i
$321$		0			0
$322$	−388416.	+	751904.i	−0.208765	+	0.404132i
$323$	310944.			0.165835
$324$		0			0
$325$	−462616.	+	801274.i	−0.242947	+	0.420797i
$326$	265232.	−	459395.i	0.138224	−	0.239410i
$327$		0			0
$328$	−2.02272e6			−1.03813
$329$	1.47714e6	+	2.30263e6i	0.752371	+	1.17283i
$330$		0			0
$331$	−793918.	−	1.37511e6i	−0.398296	−	0.689868i	0.595220	−	0.803563i	$-0.297065\pi$
$331$	−793918.	−	1.37511e6i	−0.398296	−	0.689868i	−0.993516	+	0.113694i	$0.963732\pi$
$332$	953442.	−	1.65141e6i	0.474733	−	0.822261i
$333$		0			0
$334$	−363790.	−	630103.i	−0.178437	−	0.309062i
$335$	352858.			0.171786
$336$		0			0
$337$	214825.			0.103041			0.0515205	−	0.998672i	$-0.483593\pi$
$337$	214825.			0.103041			0.0515205	+	0.998672i	$0.483593\pi$
$338$	276429.	+	478789.i	0.131611	+	0.227957i
$339$		0			0
$340$	291984.	−	505731.i	0.136981	−	0.237259i
$341$	382114.	+	661842.i	0.177954	+	0.308225i
$342$		0			0
$343$	2.15747e6	−	304770.i	0.990169	−	0.139874i
$344$	947280.			0.431601
$345$		0			0
$346$	−164846.	+	285522.i	−0.0740267	+	0.128218i
$347$	1.29430e6	−	2.24179e6i	0.577046	−	0.999473i	−0.418770	−	0.908092i	$-0.637539\pi$
$347$	1.29430e6	−	2.24179e6i	0.577046	−	0.999473i	0.995816	−	0.0913809i	$-0.0291281\pi$
$348$		0			0
$349$	−24878.0			−0.0109333			−0.00546666	−	0.999985i	$-0.501740\pi$
$349$	−24878.0			−0.0109333			−0.00546666	+	0.999985i	$0.501740\pi$
$350$	−778036.	+	36421.6i	−0.339492	+	0.0158924i
$351$		0			0
$352$	692944.	+	1.20021e6i	0.298086	+	0.516300i
$353$	−868004.	+	1.50343e6i	−0.370753	+	0.642163i	−0.989682	−	0.143284i	$-0.954234\pi$
$353$	−868004.	+	1.50343e6i	−0.370753	+	0.642163i	0.618928	+	0.785447i	$0.287567\pi$
$354$		0			0
$355$	210507.	+	364609.i	0.0886535	+	0.153552i
$356$	−3.21782e6			−1.34566
$357$		0			0
$358$	−61256.0			−0.0252604
$359$	431213.	+	746883.i	0.176586	+	0.305856i	0.940709	−	0.339215i	$-0.110161\pi$
$359$	431213.	+	746883.i	0.176586	+	0.305856i	−0.764123	+	0.645070i	$0.776828\pi$
$360$		0			0
$361$	1.22460e6	−	2.12107e6i	0.494569	−	0.856618i
$362$	651392.	+	1.12824e6i	0.261259	+	0.452514i
$363$		0			0
$364$	−513128.	+	993324.i	−0.202989	+	0.392950i
$365$	−383526.			−0.150682
$366$		0			0
$367$	−1.55771e6	+	2.69803e6i	−0.603700	+	1.04564i	0.388555	+	0.921425i	$0.372974\pi$
$367$	−1.55771e6	+	2.69803e6i	−0.603700	+	1.04564i	−0.992255	+	0.124214i	$0.960359\pi$
$368$	−1.07059e6	+	1.85432e6i	−0.412102	+	0.713781i
$369$		0			0
$370$	249216.			0.0946393
$371$	−1.76661e6	+	3.41985e6i	−0.666357	+	1.28995i
$372$		0			0
$373$	898472.	+	1.55620e6i	0.334374	+	0.579153i	0.983364	−	0.181644i	$-0.0581418\pi$
$373$	898472.	+	1.55620e6i	0.334374	+	0.579153i	−0.648990	+	0.760797i	$0.724808\pi$
$374$	−510024.	+	883387.i	−0.188544	+	0.326567i
$375$		0			0
$376$	−1.26612e6	−	2.19298e6i	−0.461855	−	0.799956i
$377$	744436.			0.269758
$378$		0			0
$379$	3.45466e6			1.23540			0.617699	−	0.786415i	$-0.288065\pi$
$379$	3.45466e6			1.23540			0.617699	+	0.786415i	$0.288065\pi$
$380$	25256.0	+	43744.7i	0.00897234	+	0.0155405i
$381$		0			0
$382$	−757360.	+	1.31179e6i	−0.265549	+	0.459944i
$383$	1.07752e6	+	1.86632e6i	0.375343	+	0.650113i	0.990378	−	0.138387i	$-0.0441917\pi$
$383$	1.07752e6	+	1.86632e6i	0.375343	+	0.650113i	−0.615036	+	0.788499i	$0.710858\pi$
$384$		0			0
$385$	383191.	−	17938.0i	0.131754	−	0.00616768i
$386$	−320678.			−0.109547
$387$		0			0
$388$	2.16943e6	−	3.75756e6i	0.731586	−	1.26714i
$389$	−231387.	+	400774.i	−0.0775291	+	0.134284i	−0.902183	−	0.431353i	$-0.858036\pi$
$389$	−231387.	+	400774.i	−0.0775291	+	0.134284i	0.824654	+	0.565637i	$0.191370\pi$
$390$		0			0
$391$	−6.18854e6			−2.04714
$392$	−2.00802e6	+	188412.i	−0.660014	+	0.0619291i
$393$		0			0
$394$	−61738.0	−	106933.i	−0.0200360	−	0.0347034i
$395$	74409.5	−	128881.i	0.0239958	−	0.0415620i
$396$		0			0
$397$	2.03311e6	+	3.52144e6i	0.647416	+	1.12136i	0.983738	+	0.179611i	$0.0574839\pi$
$397$	2.03311e6	+	3.52144e6i	0.647416	+	1.12136i	−0.336321	+	0.941747i	$0.609183\pi$
$398$	741816.			0.234741
$399$		0			0
$400$	−1.97062e6			−0.615820
$401$	−2.53432e6	−	4.38956e6i	−0.787045	−	1.36320i	−0.927769	−	0.373154i	$-0.878276\pi$
$401$	−2.53432e6	−	4.38956e6i	−0.787045	−	1.36320i	0.140724	−	0.990049i	$-0.455057\pi$
$402$		0			0
$403$	437514.	−	757796.i	0.134193	−	0.232429i
$404$	1.50598e6	+	2.60843e6i	0.459056	+	0.795109i
$405$		0			0
$406$	338380.	+	527482.i	0.101880	+	0.158815i
$407$	3.04723e6			0.911842
$408$		0			0
$409$	−1.43867e6	+	2.49185e6i	−0.425258	+	0.736568i	−0.996444	−	0.0842522i	$-0.973150\pi$
$409$	−1.43867e6	+	2.49185e6i	−0.425258	+	0.736568i	0.571187	+	0.820820i	$0.306483\pi$
$410$	185416.	−	321150.i	0.0544738	−	0.0943514i
$411$		0			0
$412$	−250208.			−0.0726203
$413$	−485698.	+	940226.i	−0.140117	+	0.271242i
$414$		0			0
$415$	374567.	+	648768.i	0.106760	+	0.184914i
$416$	793408.	−	1.37422e6i	0.224783	−	0.389335i
$417$		0			0
$418$	−44116.0	−	76411.2i	−0.0123497	−	0.0213903i
$419$	3.41342e6			0.949850			0.474925	−	0.880026i	$-0.342475\pi$
$419$	3.41342e6			0.949850			0.474925	+	0.880026i	$0.342475\pi$
$420$		0			0
$421$	−1.30737e6			−0.359496			−0.179748	−	0.983713i	$-0.557528\pi$
$421$	−1.30737e6			−0.359496			−0.179748	+	0.983713i	$0.557528\pi$
$422$	−217450.	−	376634.i	−0.0594399	−	0.102953i
$423$		0			0
$424$	1.78146e6	−	3.08558e6i	0.481240	−	0.833532i
$425$	−2.84779e6	−	4.93252e6i	−0.764779	−	1.32464i
$426$		0			0
$427$	−1.06162e6	−	1.65490e6i	−0.281773	−	0.439241i
$428$	5.42268e6			1.43088
$429$		0			0
$430$	−86834.0	+	150401.i	−0.0226474	+	0.0392265i
$431$	967734.	−	1.67616e6i	0.250936	−	0.434634i	−0.712848	−	0.701319i	$-0.752595\pi$
$431$	967734.	−	1.67616e6i	0.250936	−	0.434634i	0.963784	+	0.266685i	$0.0859283\pi$
$432$		0			0
$433$	516670.			0.132432			0.0662161	−	0.997805i	$-0.478907\pi$
$433$	516670.			0.132432			0.0662161	+	0.997805i	$0.478907\pi$
$434$	735819.	−	34445.3i	0.187520	−	0.00877820i
$435$		0			0
$436$	2.87154e6	+	4.97365e6i	0.723434	+	1.25302i
$437$	267648.	−	463580.i	0.0670441	−	0.116124i
$438$		0			0
$439$	−1.45765e6	−	2.52472e6i	−0.360987	−	0.625249i	0.627136	−	0.778910i	$-0.284227\pi$
$439$	−1.45765e6	−	2.52472e6i	−0.360987	−	0.625249i	−0.988124	+	0.153661i	$0.950894\pi$
$440$	−355080.			−0.0874369
$441$		0			0
$442$	1.16794e6			0.284357
$443$	−891896.	−	1.54481e6i	−0.215926	−	0.373995i	0.737633	−	0.675202i	$-0.235944\pi$
$443$	−891896.	−	1.54481e6i	−0.215926	−	0.373995i	−0.953559	+	0.301208i	$0.902610\pi$
$444$		0			0
$445$	632071.	−	1.09478e6i	0.151309	−	0.262076i
$446$	−589771.	−	1.02151e6i	−0.140393	−	0.243168i
$447$		0			0
$448$	−1.38410e6	+	64792.6i	−0.325815	+	0.0152521i
$449$	−4.00158e6			−0.936733			−0.468366	−	0.883534i	$-0.655157\pi$
$449$	−4.00158e6			−0.936733			−0.468366	+	0.883534i	$0.655157\pi$
$450$		0			0
$451$	2.26713e6	−	3.92679e6i	0.524850	−	0.909067i
$452$	−653296.	+	1.13154e6i	−0.150406	+	0.260510i
$453$		0			0
$454$	774090.			0.176259
$455$	−237160.	−	369696.i	−0.0537048	−	0.0837175i
$456$		0			0
$457$	583832.	+	1.01123e6i	0.130767	+	0.226495i	0.923972	−	0.382459i	$-0.124923\pi$
$457$	583832.	+	1.01123e6i	0.130767	+	0.226495i	−0.793206	+	0.608954i	$0.791589\pi$
$458$	232732.	−	403104.i	0.0518433	−	0.0897952i
$459$		0			0
$460$	−502656.	−	870626.i	−0.110758	−	0.191839i
$461$	−3.61358e6			−0.791928			−0.395964	−	0.918266i	$-0.629589\pi$
$461$	−3.61358e6			−0.791928			−0.395964	+	0.918266i	$0.629589\pi$
$462$		0			0
$463$	−1.80111e6			−0.390471			−0.195235	−	0.980756i	$-0.562547\pi$
$463$	−1.80111e6			−0.390471			−0.195235	+	0.980756i	$0.562547\pi$
$464$	792776.	+	1.37313e6i	0.170945	+	0.296085i
$465$		0			0
$466$	42096.0	−	72912.4i	0.00897999	−	0.0155538i
$467$	−1.18487e6	−	2.05226e6i	−0.251409	−	0.435452i	0.712505	−	0.701667i	$-0.247560\pi$
$467$	−1.18487e6	−	2.05226e6i	−0.251409	−	0.435452i	−0.963914	+	0.266214i	$0.914227\pi$
$468$		0			0
$469$	1.90864e6	−	3.69479e6i	0.400675	−	0.775635i
$470$	464244.			0.0969397
$471$		0			0
$472$	489780.	−	848324.i	0.101192	−	0.175270i
$473$	−1.06174e6	+	1.83899e6i	−0.218206	+	0.377944i
$474$		0			0
$475$	492656.			0.100187
$476$	−3.71616e6	−	5.79292e6i	−0.751756	−	1.17187i
$477$		0			0
$478$	−313416.	−	542852.i	−0.0627410	−	0.108671i
$479$	259073.	−	448728.i	0.0515921	−	0.0893602i	−0.839076	−	0.544014i	$-0.816904\pi$
$479$	259073.	−	448728.i	0.0515921	−	0.0893602i	0.890668	+	0.454654i	$0.150237\pi$
$480$		0			0
$481$	−1.74451e6	−	3.02158e6i	−0.343804	−	0.595486i
$482$	1.71561e6			0.336358
$483$		0			0
$484$	2.48332e6			0.481858
$485$	852274.	+	1.47618e6i	0.164522	+	0.284961i
$486$		0			0
$487$	−1.41306e6	+	2.44750e6i	−0.269985	+	0.467627i	−0.968858	−	0.247619i	$-0.920352\pi$
$487$	−1.41306e6	+	2.44750e6i	−0.269985	+	0.467627i	0.698873	+	0.715246i	$0.253685\pi$
$488$	909960.	+	1.57610e6i	0.172971	+	0.299594i
$489$		0			0
$490$	154154.	−	336087.i	0.0290044	−	0.0632356i
$491$	−9.34747e6			−1.74981			−0.874904	−	0.484296i	$-0.839076\pi$
$491$	−9.34747e6			−1.74981			−0.874904	+	0.484296i	$0.839076\pi$
$492$		0			0
$493$	−2.29132e6	+	3.96868e6i	−0.424588	+	0.735408i
$494$	−50512.0	+	87489.4i	−0.00931273	+	0.0161301i
$495$		0			0
$496$	1.86370e6			0.340150
$497$	4.95648e6	−	232024.i	0.900083	−	0.0421349i
$498$		0			0
$499$	−4.08593e6	−	7.07703e6i	−0.734580	−	1.27233i	−0.954907	−	0.296904i	$-0.904046\pi$
$499$	−4.08593e6	−	7.07703e6i	−0.734580	−	1.27233i	0.220327	−	0.975426i	$-0.429288\pi$
$500$	943866.	−	1.63482e6i	0.168844	−	0.292446i
$501$		0			0
$502$	454517.	+	787247.i	0.0804991	+	0.139428i
$503$	7.37713e6			1.30007			0.650036	−	0.759903i	$-0.274754\pi$
$503$	7.37713e6			1.30007			0.650036	+	0.759903i	$0.274754\pi$
$504$		0			0
$505$	−1.18327e6			−0.206469
$506$	878016.	+	1.52077e6i	0.152450	+	0.264050i
$507$		0			0
$508$	−4.26111e6	+	7.38046e6i	−0.732594	+	1.26889i
$509$	−163158.	−	282597.i	−0.0279134	−	0.0483474i	0.851731	−	0.523979i	$-0.175553\pi$
$509$	−163158.	−	282597.i	−0.0279134	−	0.0483474i	−0.879645	+	0.475631i	$0.842220\pi$
$510$		0			0
$511$	−2.07453e6	+	4.01591e6i	−0.351453	+	0.680350i
$512$	5.89875e6			0.994455
$513$		0			0
$514$	878182.	−	1.52106e6i	0.146614	−	0.253944i
$515$	49148.0	−	85126.8i	0.00816559	−	0.0141432i
$516$		0			0
$517$	5.67644e6			0.934006
$518$	1.34803e6	−	2.60955e6i	0.220737	−	0.427308i
$519$		0			0
$520$	203280.	+	352091.i	0.0329675	+	0.0571014i
$521$	−1.08351e6	+	1.87670e6i	−0.174880	+	0.302901i	−0.940120	−	0.340844i	$-0.889287\pi$
$521$	−1.08351e6	+	1.87670e6i	−0.174880	+	0.302901i	0.765240	+	0.643745i	$0.222620\pi$
$522$		0			0
$523$	361702.	+	626486.i	0.0578225	+	0.100151i	0.893488	−	0.449088i	$-0.148251\pi$
$523$	361702.	+	626486.i	0.0578225	+	0.100151i	−0.835665	+	0.549239i	$0.814918\pi$
$524$	−372484.			−0.0592624
$525$		0			0
$526$	−3.92187e6			−0.618057
$527$	2.69327e6	+	4.66488e6i	0.422428	+	0.731667i
$528$		0			0
$529$	−2.10868e6	+	3.65233e6i	−0.327620	+	0.567455i
$530$	326601.	+	565690.i	0.0505042	+	0.0874759i
$531$		0			0
$532$	594664.	−	27837.5i	0.0910946	−	0.00426434i
$533$	−5.19165e6			−0.791566
$534$		0			0
$535$	−1.06517e6	+	1.84493e6i	−0.160892	+	0.278673i
$536$	−1.92468e6	+	3.33364e6i	−0.289365	+	0.501196i
$537$		0			0
$538$	2.10759e6			0.313928
$539$	1.88488e6	−	4.10943e6i	0.279455	−	0.609270i
$540$		0			0
$541$	−2.99982e6	−	5.19584e6i	−0.440659	−	0.763243i	0.557080	−	0.830459i	$-0.311922\pi$
$541$	−2.99982e6	−	5.19584e6i	−0.440659	−	0.763243i	−0.997738	+	0.0672159i	$0.978588\pi$
$542$	105059.	−	181968.i	0.0153616	−	0.0266070i
$543$		0			0
$544$	4.88410e6	+	8.45950e6i	0.707599	+	1.22560i
$545$	−2.25621e6			−0.325378
$546$		0			0
$547$	7.01570e6			1.00254			0.501271	−	0.865290i	$-0.332866\pi$
$547$	7.01570e6			1.00254			0.501271	+	0.865290i	$0.332866\pi$
$548$	5.57567e6	+	9.65734e6i	0.793132	+	1.37375i
$549$		0			0
$550$	−808076.	+	1.39963e6i	−0.113906	+	0.197290i
$551$	−198194.	−	343282.i	−0.0278107	−	0.0481695i
$552$		0			0
$553$	−947030.	−	1.47627e6i	−0.131689	−	0.205284i
$554$	−855184.			−0.118382
$555$		0			0
$556$	3.22400e6	−	5.58414e6i	0.442291	−	0.766071i
$557$	−4.45936e6	+	7.72384e6i	−0.609025	+	1.05486i	0.382377	+	0.924006i	$0.375106\pi$
$557$	−4.45936e6	+	7.72384e6i	−0.609025	+	1.05486i	−0.991402	+	0.130855i	$0.958228\pi$
$558$		0			0
$559$	2.43135e6			0.329093
$560$	429352.	−	831149.i	0.0578553	−	0.111998i
$561$		0			0
$562$	638878.	+	1.10657e6i	0.0853252	+	0.147788i
$563$	−6.67412e6	+	1.15599e7i	−0.887407	+	1.53703i	−0.0444767	+	0.999010i	$0.514162\pi$
$563$	−6.67412e6	+	1.15599e7i	−0.887407	+	1.53703i	−0.842930	+	0.538023i	$0.819171\pi$
$564$		0			0
$565$	−256652.	−	444534.i	−0.0338239	−	0.0585847i
$566$	−4.90284e6			−0.643290
$567$		0			0
$568$	−4.59288e6			−0.597330
$569$	551074.	+	954488.i	0.0713558	+	0.123592i	0.899496	−	0.436930i	$-0.143934\pi$
$569$	551074.	+	954488.i	0.0713558	+	0.123592i	−0.828140	+	0.560521i	$0.810601\pi$
$570$		0			0
$571$	−946741.	+	1.63980e6i	−0.121518	+	0.210475i	−0.920367	−	0.391057i	$-0.872110\pi$
$571$	−946741.	+	1.63980e6i	−0.121518	+	0.210475i	0.798848	+	0.601532i	$0.205443\pi$
$572$	1.15993e6	+	2.00905e6i	0.148232	+	0.256745i
$573$		0			0
$574$	−2.35984e6	−	3.67863e6i	−0.298953	−	0.466022i
$575$	−9.80506e6			−1.23675
$576$		0			0
$577$	−1.41476e6	+	2.45043e6i	−0.176906	+	0.306410i	−0.940819	−	0.338909i	$-0.889942\pi$
$577$	−1.41476e6	+	2.45043e6i	−0.176906	+	0.306410i	0.763913	+	0.645319i	$0.223275\pi$
$578$	−2.17496e6	+	3.76714e6i	−0.270789	+	0.469021i
$579$		0			0
$580$	−744436.			−0.0918877
$581$	8.81934e6	−	412852.i	1.08392	−	0.0507405i
$582$		0			0
$583$	3.99344e6	+	6.91684e6i	0.486604	+	0.842823i
$584$	2.09196e6	−	3.62338e6i	0.253817	−	0.439624i
$585$		0			0
$586$	1.71617e6	+	2.97249e6i	0.206451	+	0.357583i
$587$	1.06799e7			1.27930			0.639649	−	0.768667i	$-0.279080\pi$
$587$	1.06799e7			1.27930			0.639649	+	0.768667i	$0.279080\pi$
$588$		0			0
$589$	−465924.			−0.0553384
$590$	89793.0	+	155526.i	0.0106197	+	0.0183939i
$591$		0			0
$592$	3.71558e6	−	6.43558e6i	0.435735	−	0.754716i
$593$	−7.34984e6	−	1.27303e7i	−0.858304	−	1.48663i	−0.873545	−	0.486743i	$-0.838185\pi$
$593$	−7.34984e6	−	1.27303e7i	−0.858304	−	1.48663i	0.0152406	−	0.999884i	$-0.495149\pi$
$594$		0			0
$595$	2.70085e6	−	126433.i	0.312758	−	0.0146409i
$596$	−2.71975e6			−0.313627
$597$		0			0
$598$	1.00531e6	−	1.74125e6i	0.114960	−	0.199117i
$599$	4.24581e6	−	7.35396e6i	0.483497	−	0.837441i	−0.516323	−	0.856394i	$-0.672700\pi$
$599$	4.24581e6	−	7.35396e6i	0.483497	−	0.837441i	0.999820	+	0.0189523i	$0.00603306\pi$
$600$		0			0
$601$	8.62947e6			0.974536			0.487268	−	0.873253i	$-0.337994\pi$
$601$	8.62947e6			0.974536			0.487268	+	0.873253i	$0.337994\pi$
$602$	1.10516e6	+	1.72277e6i	0.124289	+	0.193748i
$603$		0			0
$604$	−406658.	−	704352.i	−0.0453562	−	0.0785593i
$605$	−487795.	+	844886.i	−0.0541812	+	0.0938447i
$606$		0			0
$607$	−5.29037e6	−	9.16319e6i	−0.582793	−	1.00943i	−0.995147	−	0.0984029i	$-0.968627\pi$
$607$	−5.29037e6	−	9.16319e6i	−0.582793	−	1.00943i	0.412354	−	0.911024i	$-0.364707\pi$
$608$	−844928.			−0.0926959
$609$		0			0
$610$	−333652.			−0.0363052
$611$	−3.24971e6	−	5.62866e6i	−0.352161	−	0.609961i
$612$		0			0
$613$	−1.92392e6	+	3.33233e6i	−0.206793	+	0.358176i	−0.950703	−	0.310104i	$-0.899636\pi$
$613$	−1.92392e6	+	3.33233e6i	−0.206793	+	0.358176i	0.743910	+	0.668280i	$0.232969\pi$
$614$	−1.80897e6	−	3.13322e6i	−0.193647	−	0.335406i
$615$		0			0
$616$	−1.92066e6	+	3.71805e6i	−0.203938	+	0.394788i
$617$	1.51001e7			1.59686			0.798428	−	0.602090i	$-0.205665\pi$
$617$	1.51001e7			1.59686			0.798428	+	0.602090i	$0.205665\pi$
$618$		0			0
$619$	−4.96551e6	+	8.60051e6i	−0.520879	+	0.902190i	0.478826	+	0.877910i	$0.341063\pi$
$619$	−4.96551e6	+	8.60051e6i	−0.520879	+	0.902190i	−0.999705	+	0.0242796i	$0.992271\pi$
$620$	−437514.	+	757796.i	−0.0457102	+	0.0791723i
$621$		0			0
$622$	−3.04291e6			−0.315365
$623$	−8.04454e6	−	1.25402e7i	−0.830388	−	1.29445i
$624$		0			0
$625$	−4.32295e6	−	7.48756e6i	−0.442670	−	0.766726i
$626$	1.34840e6	−	2.33550e6i	0.137525	−	0.238201i
$627$		0			0
$628$	−8.07100e6	−	1.39794e7i	−0.816635	−	1.41445i
$629$	2.14779e7			2.16454
$630$		0			0
$631$	−9.25224e6			−0.925068			−0.462534	−	0.886602i	$-0.653060\pi$
$631$	−9.25224e6			−0.925068			−0.462534	+	0.886602i	$0.653060\pi$
$632$	811740.	+	1.40597e6i	0.0808396	+	0.140018i
$633$		0			0
$634$	−49695.0	+	86074.3i	−0.00491009	+	0.00850453i
$635$	−1.67401e6	−	2.89947e6i	−0.164749	−	0.285354i
$636$		0			0
$637$	−5.15392e6	+	483592.i	−0.503256	+	0.0472205i
$638$	1.30035e6			0.126476
$639$		0			0
$640$	−1.02432e6	+	1.77417e6i	−0.0988521	+	0.171217i
$641$	2.50214e6	−	4.33384e6i	0.240529	−	0.416608i	−0.720336	−	0.693625i	$-0.756013\pi$
$641$	2.50214e6	−	4.33384e6i	0.240529	−	0.416608i	0.960865	+	0.277017i	$0.0893459\pi$
$642$		0			0
$643$	1.26137e7			1.20314			0.601569	−	0.798821i	$-0.294543\pi$
$643$	1.26137e7			1.20314			0.601569	+	0.798821i	$0.294543\pi$
$644$	−1.18353e7	+	554035.i	−1.12451	+	0.0526408i
$645$		0			0
$646$	−310944.	−	538571.i	−0.0293157	−	0.0507764i
$647$	−6.26916e6	+	1.08585e7i	−0.588774	+	1.01979i	0.405620	+	0.914042i	$0.367056\pi$
$647$	−6.26916e6	+	1.08585e7i	−0.588774	+	1.01979i	−0.994393	+	0.105744i	$0.966278\pi$
$648$		0			0
$649$	1.09792e6	+	1.90166e6i	0.102320	+	0.177223i
$650$	1.85046e6			0.171790
$651$		0			0
$652$	7.42650e6			0.684171
$653$	−4.33033e6	−	7.50035e6i	−0.397409	−	0.688333i	0.595996	−	0.802987i	$-0.296757\pi$
$653$	−4.33033e6	−	7.50035e6i	−0.397409	−	0.688333i	−0.993405	+	0.114654i	$0.963424\pi$
$654$		0			0
$655$	73166.5	−	126728.i	0.00666360	−	0.0115417i
$656$	−5.52877e6	−	9.57611e6i	−0.501613	−	0.868819i
$657$		0			0
$658$	2.51114e6	−	4.86111e6i	0.226103	−	0.437695i
$659$	−7.94177e6			−0.712367			−0.356183	−	0.934416i	$-0.615922\pi$
$659$	−7.94177e6			−0.712367			−0.356183	+	0.934416i	$0.615922\pi$
$660$		0			0
$661$	1.05708e6	−	1.83092e6i	0.0941032	−	0.162992i	−0.815131	−	0.579277i	$-0.803335\pi$
$661$	1.05708e6	−	1.83092e6i	0.0941032	−	0.162992i	0.909234	+	0.416285i	$0.136668\pi$
$662$	−1.58784e6	+	2.75021e6i	−0.140819	+	0.243905i
$663$		0			0
$664$	−8.17236e6			−0.719329
$665$	−107338.	+	207787.i	−0.00941238	+	0.0182207i
$666$		0			0
$667$	3.94454e6	+	6.83215e6i	0.343307	+	0.594625i
$668$	5.09306e6	−	8.82144e6i	0.441609	−	0.764889i
$669$		0			0
$670$	−352858.	−	611168.i	−0.0303678	−	0.0525985i
$671$	−4.07965e6			−0.349798
$672$		0			0
$673$	−442307.			−0.0376432			−0.0188216	−	0.999823i	$-0.505991\pi$
$673$	−442307.			−0.0376432			−0.0188216	+	0.999823i	$0.505991\pi$
$674$	−214825.	−	372088.i	−0.0182152	−	0.0315497i
$675$		0			0
$676$	−3.87001e6	+	6.70305e6i	−0.325720	+	0.564164i
$677$	5.37804e6	+	9.31503e6i	0.450975	+	0.781111i	0.998447	−	0.0557130i	$-0.0177432\pi$
$677$	5.37804e6	+	9.31503e6i	0.450975	+	0.781111i	−0.547472	+	0.836824i	$0.684410\pi$
$678$		0			0
$679$	2.00672e7	−	939389.i	1.67037	−	0.0781936i
$680$	−2.50272e6			−0.207558
$681$		0			0
$682$	764229.	−	1.32368e6i	0.0629162	−	0.108974i
$683$	−5.74430e6	+	9.94941e6i	−0.471178	+	0.816104i	−0.999456	−	0.0329669i	$-0.989504\pi$
$683$	−5.74430e6	+	9.94941e6i	−0.471178	+	0.816104i	0.528278	+	0.849071i	$0.322838\pi$
$684$		0			0
$685$	−4.38088e6			−0.356726
$686$	−2.68535e6	−	3.43208e6i	−0.217866	−	0.278450i
$687$		0			0
$688$	2.58923e6	+	4.48468e6i	0.208545	+	0.361211i
$689$	4.57241e6	−	7.91965e6i	0.366942	−	0.635562i
$690$		0			0
$691$	−5.06942e6	−	8.78049e6i	−0.403890	−	0.699558i	0.590302	−	0.807183i	$-0.299009\pi$
$691$	−5.06942e6	−	8.78049e6i	−0.403890	−	0.699558i	−0.994192	+	0.107625i	$0.965675\pi$
$692$	−4.61569e6			−0.366413
$693$		0			0
$694$	−5.17719e6			−0.408033
$695$	1.26657e6	+	2.19377e6i	0.0994645	+	0.172278i
$696$		0			0
$697$	1.59795e7	−	2.76773e7i	1.24589	−	2.15795i
$698$	24878.0	+	43090.0i	0.00193276	+	0.00334763i
$699$		0			0
$700$	−5.88784e6	−	9.17823e6i	−0.454162	−	0.707969i
$701$	1.96839e7			1.51292			0.756459	−	0.654041i	$-0.226927\pi$
$701$	1.96839e7			1.51292			0.756459	+	0.654041i	$0.226927\pi$
$702$		0			0
$703$	−928896.	+	1.60890e6i	−0.0708890	+	0.122783i
$704$	−1.43754e6	+	2.48989e6i	−0.109317	+	0.189342i
$705$		0			0
$706$	3.47202e6			0.262162
$707$	−6.40042e6	+	1.23901e7i	−0.481570	+	0.932234i
$708$		0			0
$709$	1.00859e7	+	1.74692e7i	0.753524	+	1.30514i	0.946105	+	0.323861i	$0.104981\pi$
$709$	1.00859e7	+	1.74692e7i	0.753524	+	1.30514i	−0.192581	+	0.981281i	$0.561686\pi$
$710$	421014.	−	729218.i	0.0313437	−	0.0542889i
$711$		0			0
$712$	6.89532e6	+	1.19430e7i	0.509747	+	0.882907i
$713$	9.27302e6			0.683121
$714$		0			0
$715$	−911372.			−0.0666700
$716$	−428792.	−	742690.i	−0.0312582	−	0.0541408i
$717$		0			0
$718$	862426.	−	1.49377e6i	0.0624325	−	0.108136i
$719$	2.07867e6	+	3.60037e6i	0.149956	+	0.259731i	0.931211	−	0.364481i	$-0.118753\pi$
$719$	2.07867e6	+	3.60037e6i	0.149956	+	0.259731i	−0.781255	+	0.624212i	$0.785420\pi$
$720$		0			0
$721$	−625520.	−	975089.i	−0.0448129	−	0.0698564i
$722$	−4.89841e6			−0.349713
$723$		0			0
$724$	−9.11949e6	+	1.57954e7i	−0.646583	+	1.11991i
$725$	−3.63033e6	+	6.28792e6i	−0.256508	+	0.444286i
$726$		0			0
$727$	−1.54433e7			−1.08369			−0.541845	−	0.840479i	$-0.682274\pi$
$727$	−1.54433e7			−1.08369			−0.541845	+	0.840479i	$0.682274\pi$
$728$	4.78632e6	−	224058.i	0.334714	−	0.0156687i
$729$		0			0
$730$	383526.	+	664287.i	0.0266371	+	0.0461369i
$731$	−7.48351e6	+	1.29618e7i	−0.517979	+	0.897166i
$732$		0			0
$733$	3.10207e6	+	5.37294e6i	0.213251	+	0.369362i	0.952730	−	0.303818i	$-0.0982614\pi$
$733$	3.10207e6	+	5.37294e6i	0.213251	+	0.369362i	−0.739479	+	0.673180i	$0.764928\pi$
$734$	6.23084e6			0.426880
$735$		0			0
$736$	1.68161e7			1.14428
$737$	−4.31449e6	−	7.47292e6i	−0.292591	−	0.506782i
$738$		0			0
$739$	−1.09492e7	+	1.89646e7i	−0.737517	+	1.27742i	0.216093	+	0.976373i	$0.430669\pi$
$739$	−1.09492e7	+	1.89646e7i	−0.737517	+	1.27742i	−0.953610	+	0.301045i	$0.902665\pi$
$740$	1.74451e6	+	3.02158e6i	0.117110	+	0.202841i
$741$		0			0
$742$	7.68997e6	−	359984.i	0.512761	−	0.0240035i
$743$	2.75483e6			0.183073			0.0915363	−	0.995802i	$-0.470822\pi$
$743$	2.75483e6			0.183073			0.0915363	+	0.995802i	$0.470822\pi$
$744$		0			0
$745$	534237.	−	925326.i	0.0352650	−	0.0610807i
$746$	1.79694e6	−	3.11240e6i	0.118219	−	0.204761i
$747$		0			0
$748$	−1.42807e7			−0.933243
$749$	1.35567e7	+	2.11328e7i	0.882976	+	1.37642i
$750$		0			0
$751$	−6.45604e6	−	1.11822e7i	−0.417702	−	0.723481i	0.578006	−	0.816032i	$-0.303831\pi$
$751$	−6.45604e6	−	1.11822e7i	−0.417702	−	0.723481i	−0.995708	+	0.0925517i	$0.970498\pi$
$752$	6.92146e6	−	1.19883e7i	0.446327	−	0.773061i
$753$		0			0
$754$	−744436.	−	1.28940e6i	−0.0476869	−	0.0825961i
$755$	319517.			0.0203998
$756$		0			0
$757$	−2.64315e7			−1.67642			−0.838209	−	0.545349i	$-0.816397\pi$
$757$	−2.64315e7			−1.67642			−0.838209	+	0.545349i	$0.816397\pi$
$758$	−3.45466e6	−	5.98364e6i	−0.218390	−	0.378262i
$759$		0			0
$760$	108240.	−	187477.i	0.00679757	−	0.0117737i
$761$	6.11069e6	+	1.05840e7i	0.382498	+	0.662506i	0.991419	−	0.130725i	$-0.0417306\pi$
$761$	6.11069e6	+	1.05840e7i	0.382498	+	0.662506i	−0.608921	+	0.793231i	$0.708397\pi$
$762$		0			0
$763$	−1.22040e7	+	2.36249e7i	−0.758914	+	1.46912i
$764$	−2.12061e7			−1.31440
$765$		0			0
$766$	2.15504e6	−	3.73264e6i	0.132704	−	0.229850i
$767$	1.25710e6	−	2.17736e6i	0.0771582	−	0.133642i
$768$		0			0
$769$	6.10654e6			0.372374			0.186187	−	0.982514i	$-0.440387\pi$
$769$	6.10654e6			0.372374			0.186187	+	0.982514i	$0.440387\pi$
$770$	−414260.	−	645767.i	−0.0251794	−	0.0392509i
$771$		0			0
$772$	−2.24475e6	−	3.88801e6i	−0.135558	−	0.234793i
$773$	−1.51110e6	+	2.61730e6i	−0.0909588	+	0.157545i	−0.907915	−	0.419155i	$-0.862326\pi$
$773$	−1.51110e6	+	2.61730e6i	−0.0909588	+	0.157545i	0.816956	+	0.576700i	$0.195660\pi$
$774$		0			0
$775$	4.26718e6	+	7.39098e6i	0.255204	+	0.442026i
$776$	−

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(14.0000 - 24.2487i) q^{4} +(5.50000 + 9.52628i) q^{5} +(129.500 - 6.06218i) q^{7} -120.000 q^{8} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(14.0000 - 24.2487i) q^{4} +(5.50000 + 9.52628i) q^{5} +(129.500 - 6.06218i) q^{7} -120.000 q^{8} +(11.0000 - 19.0526i) q^{10} +(134.500 - 232.961i) q^{11} -308.000 q^{13} +(-140.000 - 218.238i) q^{14} +(-328.000 - 568.113i) q^{16} +(948.000 - 1641.98i) q^{17} +(82.0000 + 142.028i) q^{19} +308.000 q^{20} -538.000 q^{22} +(-1632.00 - 2826.71i) q^{23} +(1502.00 - 2601.54i) q^{25} +(308.000 + 533.472i) q^{26} +(1666.00 - 3225.08i) q^{28} -2417.00 q^{29} +(-1420.50 + 2460.38i) q^{31} +(-2576.00 + 4461.76i) q^{32} -3792.00 q^{34} +(770.000 + 1200.31i) q^{35} +(5664.00 + 9810.34i) q^{37} +(164.000 - 284.056i) q^{38} +(-660.000 - 1143.15i) q^{40} +16856.0 q^{41} -7894.00 q^{43} +(-3766.00 - 6522.90i) q^{44} +(-3264.00 + 5653.41i) q^{46} +(10551.0 + 18274.9i) q^{47} +(16733.5 - 1570.10i) q^{49} -6008.00 q^{50} +(-4312.00 + 7468.60i) q^{52} +(-14845.5 + 25713.2i) q^{53} +2959.00 q^{55} +(-15540.0 + 727.461i) q^{56} +(2417.00 + 4186.37i) q^{58} +(-4081.50 + 7069.37i) q^{59} +(-7583.00 - 13134.1i) q^{61} +5682.00 q^{62} -10688.0 q^{64} +(-1694.00 - 2934.09i) q^{65} +(16039.0 - 27780.4i) q^{67} +(-26544.0 - 45975.6i) q^{68} +(1309.00 - 2533.99i) q^{70} +38274.0 q^{71} +(-17433.0 + 30194.8i) q^{73} +(11328.0 - 19620.7i) q^{74} +4592.00 q^{76} +(16005.5 - 30983.8i) q^{77} +(-6764.50 - 11716.5i) q^{79} +(3608.00 - 6249.24i) q^{80} +(-16856.0 - 29195.4i) q^{82} +68103.0 q^{83} +20856.0 q^{85} +(7894.00 + 13672.8i) q^{86} +(-16140.0 + 27955.3i) q^{88} +(-57461.0 - 99525.4i) q^{89} +(-39886.0 + 1867.15i) q^{91} -91392.0 q^{92} +(21102.0 - 36549.7i) q^{94} +(-902.000 + 1562.31i) q^{95} +154959. q^{97} +(-19453.0 - 27413.2i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 28 q^{4} + 11 q^{5} + 259 q^{7} - 240 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 + 28 * q^4 + 11 * q^5 + 259 * q^7 - 240 * q^8	\( 2 q - 2 q^{2} + 28 q^{4} + 11 q^{5} + 259 q^{7} - 240 q^{8} + 22 q^{10} + 269 q^{11} - 616 q^{13} - 280 q^{14} - 656 q^{16} + 1896 q^{17} + 164 q^{19} + 616 q^{20} - 1076 q^{22} - 3264 q^{23} + 3004 q^{25} + 616 q^{26} + 3332 q^{28} - 4834 q^{29} - 2841 q^{31} - 5152 q^{32} - 7584 q^{34} + 1540 q^{35} + 11328 q^{37} + 328 q^{38} - 1320 q^{40} + 33712 q^{41} - 15788 q^{43} - 7532 q^{44} - 6528 q^{46} + 21102 q^{47} + 33467 q^{49} - 12016 q^{50} - 8624 q^{52} - 29691 q^{53} + 5918 q^{55} - 31080 q^{56} + 4834 q^{58} - 8163 q^{59} - 15166 q^{61} + 11364 q^{62} - 21376 q^{64} - 3388 q^{65} + 32078 q^{67} - 53088 q^{68} + 2618 q^{70} + 76548 q^{71} - 34866 q^{73} + 22656 q^{74} + 9184 q^{76} + 32011 q^{77} - 13529 q^{79} + 7216 q^{80} - 33712 q^{82} + 136206 q^{83} + 41712 q^{85} + 15788 q^{86} - 32280 q^{88} - 114922 q^{89} - 79772 q^{91} - 182784 q^{92} + 42204 q^{94} - 1804 q^{95} + 309918 q^{97} - 38906 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 28 * q^4 + 11 * q^5 + 259 * q^7 - 240 * q^8 + 22 * q^10 + 269 * q^11 - 616 * q^13 - 280 * q^14 - 656 * q^16 + 1896 * q^17 + 164 * q^19 + 616 * q^20 - 1076 * q^22 - 3264 * q^23 + 3004 * q^25 + 616 * q^26 + 3332 * q^28 - 4834 * q^29 - 2841 * q^31 - 5152 * q^32 - 7584 * q^34 + 1540 * q^35 + 11328 * q^37 + 328 * q^38 - 1320 * q^40 + 33712 * q^41 - 15788 * q^43 - 7532 * q^44 - 6528 * q^46 + 21102 * q^47 + 33467 * q^49 - 12016 * q^50 - 8624 * q^52 - 29691 * q^53 + 5918 * q^55 - 31080 * q^56 + 4834 * q^58 - 8163 * q^59 - 15166 * q^61 + 11364 * q^62 - 21376 * q^64 - 3388 * q^65 + 32078 * q^67 - 53088 * q^68 + 2618 * q^70 + 76548 * q^71 - 34866 * q^73 + 22656 * q^74 + 9184 * q^76 + 32011 * q^77 - 13529 * q^79 + 7216 * q^80 - 33712 * q^82 + 136206 * q^83 + 41712 * q^85 + 15788 * q^86 - 32280 * q^88 - 114922 * q^89 - 79772 * q^91 - 182784 * q^92 + 42204 * q^94 - 1804 * q^95 + 309918 * q^97 - 38906 * q^98

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