LMFDB - Embedded newform 108.6.h.a.71.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,6,Mod(35,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("108.35");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	108.h (of order $6$, degree $2$, not 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:	$17.3214525398$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.3
Character	$\chi$	$=$	108.71
Dual form			108.6.h.a.35.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.48009 + 1.40307i) q^{2} +(28.0628 - 15.3779i) q^{4} +(77.8058 + 44.9212i) q^{5} +(-124.034 + 71.6112i) q^{7} +(-132.210 + 123.647i) q^{8} +O(q^{10})$	\(q+(-5.48009 + 1.40307i) q^{2} +(28.0628 - 15.3779i) q^{4} +(77.8058 + 44.9212i) q^{5} +(-124.034 + 71.6112i) q^{7} +(-132.210 + 123.647i) q^{8} +(-489.410 - 137.005i) q^{10} +(278.231 + 481.910i) q^{11} +(179.796 - 311.416i) q^{13} +(579.243 - 566.465i) q^{14} +(551.037 - 863.095i) q^{16} -1076.42i q^{17} +348.135i q^{19} +(2874.24 + 64.1196i) q^{20} +(-2200.88 - 2250.53i) q^{22} +(-1469.06 + 2544.48i) q^{23} +(2473.33 + 4283.93i) q^{25} +(-548.358 + 1958.85i) q^{26} +(-2379.51 + 3917.00i) q^{28} +(-3331.19 + 1923.26i) q^{29} +(-2346.41 - 1354.70i) q^{31} +(-1808.75 + 5502.99i) q^{32} +(1510.30 + 5898.87i) q^{34} -12867.4 q^{35} -1992.90 q^{37} +(-488.460 - 1907.81i) q^{38} +(-15841.1 + 3681.39i) q^{40} +(13432.0 + 7754.99i) q^{41} +(-12474.1 + 7201.91i) q^{43} +(15218.7 + 9245.10i) q^{44} +(4480.46 - 16005.2i) q^{46} +(1232.97 + 2135.56i) q^{47} +(1852.82 - 3209.17i) q^{49} +(-19564.7 - 20006.0i) q^{50} +(256.637 - 11504.1i) q^{52} +13364.2i q^{53} +49993.8i q^{55} +(7544.08 - 24804.1i) q^{56} +(15556.7 - 15213.6i) q^{58} +(-19878.8 + 34431.1i) q^{59} +(-211.489 - 366.310i) q^{61} +(14759.3 + 4131.70i) q^{62} +(2191.00 - 32694.7i) q^{64} +(27978.3 - 16153.3i) q^{65} +(14018.6 + 8093.63i) q^{67} +(-16553.1 - 30207.3i) q^{68} +(70514.7 - 18054.0i) q^{70} +6902.73 q^{71} -11089.5 q^{73} +(10921.3 - 2796.19i) q^{74} +(5353.60 + 9769.63i) q^{76} +(-69020.2 - 39848.8i) q^{77} +(64310.3 - 37129.6i) q^{79} +(81645.2 - 42400.5i) q^{80} +(-84489.6 - 23651.9i) q^{82} +(-48564.9 - 84116.9i) q^{83} +(48354.0 - 83751.6i) q^{85} +(58254.2 - 56969.2i) q^{86} +(-96371.4 - 29311.0i) q^{88} +74459.8i q^{89} +51501.6i q^{91} +(-2096.90 + 93996.2i) q^{92} +(-9753.11 - 9973.11i) q^{94} +(-15638.6 + 27086.9i) q^{95} +(47958.5 + 83066.5i) q^{97} +(-5650.89 + 20186.2i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) $ 56 * q + 3 * q^2 - q^4 + 6 * q^5	$ 56 q + 3 q^{2} - q^{4} + 6 q^{5} - 68 q^{10} - 2 q^{13} + 1518 q^{14} - q^{16} + 1242 q^{20} + 63 q^{22} + 12498 q^{25} - 2052 q^{28} + 11946 q^{29} + 7233 q^{32} + 6361 q^{34} - 8 q^{37} + 14877 q^{38} - 1526 q^{40} + 43536 q^{41} - 26880 q^{46} + 38414 q^{49} - 38631 q^{50} + 24988 q^{52} - 21186 q^{56} - 3314 q^{58} - 2 q^{61} - 106342 q^{64} - 35970 q^{65} - 31413 q^{68} + 10524 q^{70} + 53620 q^{73} + 20406 q^{74} + 26193 q^{76} - 26178 q^{77} - 151286 q^{82} + 6248 q^{85} - 279237 q^{86} - 122541 q^{88} - 435804 q^{92} + 63480 q^{94} - 58148 q^{97}+O(q^{100}) $ 56 * q + 3 * q^2 - q^4 + 6 * q^5 - 68 * q^10 - 2 * q^13 + 1518 * q^14 - q^16 + 1242 * q^20 + 63 * q^22 + 12498 * q^25 - 2052 * q^28 + 11946 * q^29 + 7233 * q^32 + 6361 * q^34 - 8 * q^37 + 14877 * q^38 - 1526 * q^40 + 43536 * q^41 - 26880 * q^46 + 38414 * q^49 - 38631 * q^50 + 24988 * q^52 - 21186 * q^56 - 3314 * q^58 - 2 * q^61 - 106342 * q^64 - 35970 * q^65 - 31413 * q^68 + 10524 * q^70 + 53620 * q^73 + 20406 * q^74 + 26193 * q^76 - 26178 * q^77 - 151286 * q^82 + 6248 * q^85 - 279237 * q^86 - 122541 * q^88 - 435804 * q^92 + 63480 * q^94 - 58148 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−5.48009	+	1.40307i	−0.968752	+	0.248031i
$2$	−5.48009	+	1.40307i	−0.968752	+	0.248031i
$3$		0			0
$3$		0			0
$4$	28.0628	−	15.3779i	0.876961	−	0.480561i
$5$	77.8058	+	44.9212i	1.39183	+	0.803575i	0.993518	−	0.113675i	$-0.0362621\pi$
$5$	77.8058	+	44.9212i	1.39183	+	0.803575i	0.398314	+	0.917249i	$0.369595\pi$
$6$		0			0
$7$	−124.034	+	71.6112i	−0.956745	+	0.552377i	−0.895170	−	0.445725i	$-0.852946\pi$
$7$	−124.034	+	71.6112i	−0.956745	+	0.552377i	−0.0615753	+	0.998102i	$0.519612\pi$
$8$	−132.210	+	123.647i	−0.730364	+	0.683058i
$9$		0			0
$10$	−489.410	−	137.005i	−1.54765	−	0.433247i
$11$	278.231	+	481.910i	0.693303	+	1.20084i	0.970749	+	0.240095i	$0.0771787\pi$
$11$	278.231	+	481.910i	0.693303	+	1.20084i	−0.277446	+	0.960741i	$0.589488\pi$
$12$		0			0
$13$	179.796	−	311.416i	0.295068	−	0.511072i	−0.679933	−	0.733274i	$-0.737991\pi$
$13$	179.796	−	311.416i	0.295068	−	0.511072i	0.975001	+	0.222202i	$0.0713245\pi$
$14$	579.243	−	566.465i	0.789842	−	0.772419i
$15$		0			0
$16$	551.037	−	863.095i	0.538123	−	0.842867i
$17$		−	1076.42i		−	0.903356i	−0.892181	−	0.451678i	$-0.850826\pi$
$17$		−	1076.42i		−	0.903356i	0.892181	−	0.451678i	$-0.149174\pi$
$18$		0			0
$19$			348.135i			0.221240i	0.993863	+	0.110620i	$0.0352837\pi$
$19$			348.135i			0.221240i	−0.993863	+	0.110620i	$0.964716\pi$
$20$	2874.24	+	64.1196i	1.60675	+	0.0358439i
$21$		0			0
$22$	−2200.88	−	2250.53i	−0.969484	−	0.991352i
$23$	−1469.06	+	2544.48i	−0.579054	+	1.00295i	0.416535	+	0.909120i	$0.363244\pi$
$23$	−1469.06	+	2544.48i	−0.579054	+	1.00295i	−0.995588	+	0.0938304i	$0.970089\pi$
$24$		0			0
$25$	2473.33	+	4283.93i	0.791464	+	1.37086i
$26$	−548.358	+	1958.85i	−0.159086	+	0.568288i
$27$		0			0
$28$	−2379.51	+	3917.00i	−0.573578	+	0.944188i
$29$	−3331.19	+	1923.26i	−0.735536	+	0.424662i	−0.820444	−	0.571727i	$-0.806274\pi$
$29$	−3331.19	+	1923.26i	−0.735536	+	0.424662i	0.0849079	+	0.996389i	$0.472940\pi$
$30$		0			0
$31$	−2346.41	−	1354.70i	−0.438531	−	0.253186i	0.264443	−	0.964401i	$-0.414812\pi$
$31$	−2346.41	−	1354.70i	−0.438531	−	0.253186i	−0.702974	+	0.711215i	$0.748145\pi$
$32$	−1808.75	+	5502.99i	−0.312250	+	0.950000i
$33$		0			0
$34$	1510.30	+	5898.87i	0.224060	+	0.875128i
$35$	−12867.4			−1.77550
$36$		0			0
$37$	−1992.90			−0.239321			−0.119661	−	0.992815i	$-0.538181\pi$
$37$	−1992.90			−0.239321			−0.119661	+	0.992815i	$0.538181\pi$
$38$	−488.460	−	1907.81i	−0.0548744	−	0.214327i
$39$		0			0
$40$	−15841.1	+	3681.39i	−1.56543	+	0.363800i
$41$	13432.0	+	7754.99i	1.24791	+	0.720479i	0.970692	−	0.240329i	$-0.0772552\pi$
$41$	13432.0	+	7754.99i	1.24791	+	0.720479i	0.277215	+	0.960808i	$0.410589\pi$
$42$		0			0
$43$	−12474.1	+	7201.91i	−1.02882	+	0.593987i	−0.916645	−	0.399702i	$-0.869113\pi$
$43$	−12474.1	+	7201.91i	−1.02882	+	0.593987i	−0.112170	+	0.993689i	$0.535780\pi$
$44$	15218.7	+	9245.10i	1.18508	+	0.719913i
$45$		0			0
$46$	4480.46	−	16005.2i	0.312197	−	1.11523i
$47$	1232.97	+	2135.56i	0.0814153	+	0.141015i	0.903858	−	0.427832i	$-0.140723\pi$
$47$	1232.97	+	2135.56i	0.0814153	+	0.141015i	−0.822443	+	0.568848i	$0.807389\pi$
$48$		0			0
$49$	1852.82	−	3209.17i	0.110241	−	0.190943i
$50$	−19564.7	−	20006.0i	−1.10675	−	1.13171i
$51$		0			0
$52$	256.637	−	11504.1i	0.0131617	−	0.589988i
$53$			13364.2i			0.653514i	0.945108	+	0.326757i	$0.105956\pi$
$53$			13364.2i			0.653514i	−0.945108	+	0.326757i	$0.894044\pi$
$54$		0			0
$55$			49993.8i			2.22848i
$56$	7544.08	−	24804.1i	0.321467	−	1.05695i
$57$		0			0
$58$	15556.7	−	15213.6i	0.607223	−	0.593828i
$59$	−19878.8	+	34431.1i	−0.743464	+	1.28772i	0.207445	+	0.978247i	$0.433485\pi$
$59$	−19878.8	+	34431.1i	−0.743464	+	1.28772i	−0.950909	+	0.309470i	$0.899848\pi$
$60$		0			0
$61$	−211.489	−	366.310i	−0.00727718	−	0.0126044i	0.862364	−	0.506289i	$-0.168983\pi$
$61$	−211.489	−	366.310i	−0.00727718	−	0.0126044i	−0.869641	+	0.493685i	$0.835650\pi$
$62$	14759.3	+	4131.70i	0.487626	+	0.136505i
$63$		0			0
$64$	2191.00	−	32694.7i	0.0668640	−	0.997762i
$65$	27978.3	−	16153.3i	0.821369	−	0.474218i
$66$		0			0
$67$	14018.6	+	8093.63i	0.381520	+	0.220271i	0.678479	−	0.734620i	$-0.262639\pi$
$67$	14018.6	+	8093.63i	0.381520	+	0.220271i	−0.296960	+	0.954890i	$0.595973\pi$
$68$	−16553.1	−	30207.3i	−0.434118	−	0.792209i
$69$		0			0
$70$	70514.7	−	18054.0i	1.72002	−	0.440380i
$71$	6902.73			0.162508			0.0812541	−	0.996693i	$-0.474107\pi$
$71$	6902.73			0.162508			0.0812541	+	0.996693i	$0.474107\pi$
$72$		0			0
$73$	−11089.5			−0.243558			−0.121779	−	0.992557i	$-0.538860\pi$
$73$	−11089.5			−0.243558			−0.121779	+	0.992557i	$0.538860\pi$
$74$	10921.3	−	2796.19i	0.231843	−	0.0593590i
$75$		0			0
$76$	5353.60	+	9769.63i	0.106319	+	0.194019i
$77$	−69020.2	−	39848.8i	−1.32663	−	0.765930i
$78$		0			0
$79$	64310.3	−	37129.6i	1.15935	−	0.669349i	0.208199	−	0.978086i	$-0.433240\pi$
$79$	64310.3	−	37129.6i	1.15935	−	0.669349i	0.951147	+	0.308738i	$0.0999065\pi$
$80$	81645.2	−	42400.5i	1.42628	−	0.740707i
$81$		0			0
$82$	−84489.6	−	23651.9i	−1.38761	−	0.388446i
$83$	−48564.9	−	84116.9i	−0.773798	−	1.34026i	−0.935468	−	0.353412i	$-0.885021\pi$
$83$	−48564.9	−	84116.9i	−0.773798	−	1.34026i	0.161670	−	0.986845i	$-0.448312\pi$
$84$		0			0
$85$	48354.0	−	83751.6i	0.725914	−	1.25732i
$86$	58254.2	−	56969.2i	0.849340	−	0.830604i
$87$		0			0
$88$	−96371.4	−	29311.0i	−1.32660	−	0.403482i
$89$			74459.8i			0.996430i	0.867054	+	0.498215i	$0.166011\pi$
$89$			74459.8i			0.996430i	−0.867054	+	0.498215i	$0.833989\pi$
$90$		0			0
$91$			51501.6i			0.651954i
$92$	−2096.90	+	93996.2i	−0.0258290	+	1.15782i
$93$		0			0
$94$	−9753.11	−	9973.11i	−0.113847	−	0.116416i
$95$	−15638.6	+	27086.9i	−0.177783	+	0.307929i
$96$		0			0
$97$	47958.5	+	83066.5i	0.517530	+	0.896389i	0.999793	+	0.0203622i	$0.00648193\pi$
$97$	47958.5	+	83066.5i	0.517530	+	0.896389i	−0.482262	+	0.876027i	$0.660185\pi$
$98$	−5650.89	+	20186.2i	−0.0594363	+	0.212319i
$99$		0			0
$100$	135286.	+	82184.1i	1.35286	+	0.821841i
$101$	34890.0	−	20143.7i	0.340328	−	0.196488i	−0.320089	−	0.947387i	$-0.603713\pi$
$101$	34890.0	−	20143.7i	0.340328	−	0.196488i	0.660417	+	0.750899i	$0.270380\pi$
$102$		0			0
$103$	42984.3	+	24817.0i	0.399225	+	0.230492i	0.686149	−	0.727461i	$-0.259300\pi$
$103$	42984.3	+	24817.0i	0.399225	+	0.230492i	−0.286925	+	0.957953i	$0.592633\pi$
$104$	14734.7	+	63403.5i	0.133585	+	0.574817i
$105$		0			0
$106$	−18751.0	−	73237.2i	−0.162092	−	0.633093i
$107$	−14176.4			−0.119703			−0.0598517	−	0.998207i	$-0.519063\pi$
$107$	−14176.4			−0.119703			−0.0598517	+	0.998207i	$0.519063\pi$
$108$		0			0
$109$	21788.2			0.175653			0.0878264	−	0.996136i	$-0.472008\pi$
$109$	21788.2			0.175653			0.0878264	+	0.996136i	$0.472008\pi$
$110$	−70145.0	−	273971.i	−0.552733	−	2.15885i
$111$		0			0
$112$	−6540.21	+	146514.i	−0.0492659	+	1.10365i
$113$	−129459.	−	74743.4i	−0.953756	−	0.550651i	−0.0595101	−	0.998228i	$-0.518954\pi$
$113$	−129459.	−	74743.4i	−0.953756	−	0.550651i	−0.894246	+	0.447577i	$0.852287\pi$
$114$		0			0
$115$	−228602.	+	131983.i	−1.61189	+	0.930625i
$116$	−63906.5	+	105199.i	−0.440961	+	0.725882i
$117$		0			0
$118$	60628.2	−	216577.i	0.400839	−	1.43188i
$119$	77083.6	+	133513.i	0.498993	+	0.864282i
$120$		0			0
$121$	−74299.1	+	128690.i	−0.461339	+	0.799062i
$122$	1672.94	+	1710.68i	0.0101761	+	0.0104056i
$123$		0			0
$124$	−86679.4	−	1933.67i	−0.506246	−	0.0112935i
$125$			163661.i			0.936853i
$126$		0			0
$127$		−	257349.i		−	1.41584i	−0.706293	−	0.707919i	$-0.749634\pi$
$127$		−	257349.i		−	1.41584i	0.706293	−	0.707919i	$-0.250366\pi$
$128$	33866.2	+	182244.i	0.182701	+	0.983168i
$129$		0			0
$130$	−130659.	+	127777.i	−0.678082	+	0.663124i
$131$	−3161.94	+	5476.65i	−0.0160982	+	0.0278828i	−0.873962	−	0.485994i	$-0.838458\pi$
$131$	−3161.94	+	5476.65i	−0.0160982	+	0.0278828i	0.857864	+	0.513877i	$0.171791\pi$
$132$		0			0
$133$	−24930.4	−	43180.7i	−0.122208	−	0.211670i
$134$	−88179.0	−	24684.7i	−0.424232	−	0.118759i
$135$		0			0
$136$	133096.	+	142313.i	0.617045	+	0.659779i
$137$	250464.	−	144606.i	1.14010	−	0.658239i	0.193647	−	0.981071i	$-0.437968\pi$
$137$	250464.	−	144606.i	1.14010	−	0.658239i	0.946456	+	0.322832i	$0.104635\pi$
$138$		0			0
$139$	−86135.1	−	49730.1i	−0.378132	−	0.218315i	0.298873	−	0.954293i	$-0.403389\pi$
$139$	−86135.1	−	49730.1i	−0.378132	−	0.218315i	−0.677005	+	0.735978i	$0.736723\pi$
$140$	−361096.	+	197875.i	−1.55705	+	0.853238i
$141$		0			0
$142$	−37827.6	+	9685.05i	−0.157430	+	0.0403070i
$143$	200099.			0.818285
$144$		0			0
$145$	−345581.			−1.36499
$146$	60771.2	−	15559.3i	0.235948	−	0.0604100i
$147$		0			0
$148$	−55926.3	+	30646.7i	−0.209875	+	0.115008i
$149$	323359.	+	186691.i	1.19322	+	0.688904i	0.959035	−	0.283289i	$-0.0914255\pi$
$149$	323359.	+	186691.i	1.19322	+	0.688904i	0.234182	+	0.972193i	$0.424759\pi$
$150$		0			0
$151$	320356.	−	184958.i	1.14338	−	0.660131i	0.196115	−	0.980581i	$-0.437167\pi$
$151$	320356.	−	184958.i	1.14338	−	0.660131i	0.947266	+	0.320450i	$0.103834\pi$
$152$	−43045.8	−	46027.0i	−0.151120	−	0.161586i
$153$		0			0
$154$	434148.	+	121535.i	1.47515	+	0.412951i
$155$	−121710.	−	210807.i	−0.406908	−	0.704785i
$156$		0			0
$157$	196653.	−	340613.i	0.636724	−	1.10284i	−0.349423	−	0.936965i	$-0.613622\pi$
$157$	196653.	−	340613.i	0.636724	−	1.10284i	0.986147	−	0.165873i	$-0.0530442\pi$
$158$	−300331.	+	293706.i	−0.957100	+	0.935987i
$159$		0			0
$160$	−387932.	+	346913.i	−1.19800	+	1.07132i
$161$		−	420803.i		−	1.27942i
$162$		0			0
$163$		−	154747.i		−	0.456198i	−0.973638	−	0.228099i	$-0.926749\pi$
$163$		−	154747.i		−	0.456198i	0.973638	−	0.228099i	$-0.0732509\pi$
$164$	496196.	+	11069.3i	1.44060	+	0.0321374i
$165$		0			0
$166$	384163.	+	392828.i	1.08204	+	1.10645i
$167$	98410.6	−	170452.i	0.273055	−	0.472946i	−0.696587	−	0.717472i	$-0.745299\pi$
$167$	98410.6	−	170452.i	0.273055	−	0.472946i	0.969643	+	0.244526i	$0.0786325\pi$
$168$		0			0
$169$	120993.	+	209567.i	0.325870	+	0.564424i
$170$	−147475.	+	526811.i	−0.391377	+	1.39808i
$171$		0			0
$172$	−239306.	+	393931.i	−0.616784	+	1.01531i
$173$	−583484.	+	336874.i	−1.48222	+	0.855762i	−0.999796	−	0.0201751i	$-0.993578\pi$
$173$	−583484.	+	336874.i	−1.48222	+	0.855762i	−0.482426	+	0.875937i	$0.660244\pi$
$174$		0			0
$175$	−613554.	−	354235.i	−1.51446	−	0.874373i
$176$	569249.	+	25410.7i	1.38523	+	0.0618350i
$177$		0			0
$178$	−104473.	−	408046.i	−0.247145	−	0.965293i
$179$	583842.			1.36196			0.680978	−	0.732304i	$-0.261555\pi$
$179$	583842.			1.36196			0.680978	+	0.732304i	$0.261555\pi$
$180$		0			0
$181$	−623067.			−1.41364			−0.706819	−	0.707395i	$-0.749870\pi$
$181$	−623067.			−1.41364			−0.706819	+	0.707395i	$0.749870\pi$
$182$	−72260.5	−	282233.i	−0.161705	−	0.631582i
$183$		0			0
$184$	−120392.	−	518050.i	−0.262153	−	1.12805i
$185$	−155059.	−	89523.4i	−0.333095	−	0.192312i
$186$		0			0
$187$	518737.	−	299493.i	1.08478	−	0.626300i
$188$	67440.9	+	40969.2i	0.139165	+	0.0845401i
$189$		0			0
$190$	47696.2	−	170381.i	0.0958517	−	0.342403i
$191$	92566.8	+	160330.i	0.183600	+	0.318004i	0.943104	−	0.332499i	$-0.107892\pi$
$191$	92566.8	+	160330.i	0.183600	+	0.318004i	−0.759504	+	0.650502i	$0.774558\pi$
$192$		0			0
$193$	145169.	−	251439.i	0.280530	−	0.485892i	−0.690985	−	0.722869i	$-0.742823\pi$
$193$	145169.	−	251439.i	0.280530	−	0.485892i	0.971515	+	0.236977i	$0.0761565\pi$
$194$	−379365.	−	387923.i	−0.723691	−	0.740015i
$195$		0			0
$196$	2644.67	−	118551.i	0.00491735	−	0.220427i
$197$		−	232595.i		−	0.427007i	−0.976942	−	0.213504i	$-0.931512\pi$
$197$		−	232595.i		−	0.427007i	0.976942	−	0.213504i	$-0.0684875\pi$
$198$		0			0
$199$			524007.i			0.938004i	0.883197	+	0.469002i	$0.155386\pi$
$199$			524007.i			0.938004i	−0.883197	+	0.469002i	$0.844614\pi$
$200$	−856692.	−	260560.i	−1.51443	−	0.460609i
$201$		0			0
$202$	−162937.	+	159343.i	−0.280958	+	0.274760i
$203$	275454.	−	477100.i	0.469147	−	0.812587i
$204$		0			0
$205$	696727.	+	1.20677e6i	1.15792	+	2.00557i
$206$	−270378.	−	75689.3i	−0.443919	−	0.124270i
$207$		0			0
$208$	−169707.	−	326783.i	−0.271983	−	0.523722i
$209$	−167770.	+	96861.9i	−0.265673	+	0.153386i
$210$		0			0
$211$	389705.	+	224996.i	0.602601	+	0.347912i	0.770064	−	0.637967i	$-0.220224\pi$
$211$	389705.	+	224996.i	0.602601	+	0.347912i	−0.167463	+	0.985878i	$0.553558\pi$
$212$	205515.	+	375038.i	0.314053	+	0.573106i
$213$		0			0
$214$	77688.0	−	19890.5i	0.115963	−	0.0296901i
$215$	−1.29407e6			−1.90925
$216$		0			0
$217$	388047.			0.559416
$218$	−119401.	+	30570.4i	−0.170164	+	0.0435673i
$219$		0			0
$220$	768802.	+	1.40296e6i	1.07092	+	1.95429i
$221$	−335214.	−	193536.i	−0.461680	−	0.266551i
$222$		0			0
$223$	−33442.0	+	19307.7i	−0.0450329	+	0.0259998i	−0.522347	−	0.852733i	$-0.674944\pi$
$223$	−33442.0	+	19307.7i	−0.0450329	+	0.0259998i	0.477315	+	0.878733i	$0.341610\pi$
$224$	−169729.	−	812085.i	−0.226014	−	1.08139i
$225$		0			0
$226$	814319.	+	227959.i	1.06053	+	0.296884i
$227$	447303.	+	774752.i	0.576152	+	0.997925i	0.995915	+	0.0902911i	$0.0287798\pi$
$227$	447303.	+	774752.i	0.576152	+	0.997925i	−0.419763	+	0.907634i	$0.637887\pi$
$228$		0			0
$229$	714088.	−	1.23684e6i	0.899836	−	1.55856i	0.0721321	−	0.997395i	$-0.477020\pi$
$229$	714088.	−	1.23684e6i	0.899836	−	1.55856i	0.827703	−	0.561166i	$-0.189647\pi$
$230$	1.06758e6	−	1.04403e6i	1.33070	−	1.30134i
$231$		0			0
$232$	202612.	−	666165.i	0.247141	−	0.812572i
$233$		−	379913.i		−	0.458453i	−0.973373	−	0.229226i	$-0.926380\pi$
$233$		−	379913.i		−	0.458453i	0.973373	−	0.229226i	$-0.0736196\pi$
$234$		0			0
$235$			221545.i			0.261693i
$236$	−28374.6	+	1.27193e6i	−0.0331626	+	1.48656i
$237$		0			0
$238$	−609753.	−	623508.i	−0.697769	−	0.713509i
$239$	379157.	−	656720.i	0.429363	−	0.743679i	−0.567454	−	0.823405i	$-0.692071\pi$
$239$	379157.	−	656720.i	0.429363	−	0.743679i	0.996817	+	0.0797266i	$0.0254047\pi$
$240$		0			0
$241$	−595565.	−	1.03155e6i	−0.660520	−	1.14405i	−0.980479	−	0.196623i	$-0.937002\pi$
$241$	−595565.	−	1.03155e6i	−0.660520	−	1.14405i	0.319959	−	0.947432i	$-0.396331\pi$
$242$	226604.	−	809479.i	0.248731	−	0.888520i
$243$		0			0
$244$	−11568.1	−	7027.40i	−0.0124390	−	0.00755649i
$245$	288320.	−	166461.i	0.306873	−	0.177173i
$246$		0			0
$247$	108415.	+	62593.3i	0.113070	+	0.0652808i
$248$	477724.	−	111021.i	0.493228	−	0.114624i
$249$		0			0
$250$	−229629.	−	896880.i	−0.232368	−	0.907578i
$251$	705353.			0.706679			0.353340	−	0.935495i	$-0.385046\pi$
$251$	705353.			0.706679			0.353340	+	0.935495i	$0.385046\pi$
$252$		0			0
$253$	−1.63495e6			−1.60584
$254$	361080.	+	1.41030e6i	0.351172	+	1.37160i
$255$		0			0
$256$	−441291.	−	951196.i	−0.420848	−	0.907131i
$257$	1.11396e6	+	643145.i	1.05205	+	0.607402i	0.923223	−	0.384265i	$-0.125545\pi$
$257$	1.11396e6	+	643145.i	1.05205	+	0.607402i	0.128828	+	0.991667i	$0.458878\pi$
$258$		0			0
$259$	247188.	−	142714.i	0.228969	−	0.132196i
$260$	536745.	−	883555.i	0.492418	−	0.810588i
$261$		0			0
$262$	9643.59	−	34449.0i	0.00867932	−	0.0310044i
$263$	−812371.	−	1.40707e6i	−0.724211	−	1.25437i	−0.959298	−	0.282396i	$-0.908871\pi$
$263$	−812371.	−	1.40707e6i	−0.724211	−	1.25437i	0.235087	−	0.971974i	$-0.424463\pi$
$264$		0			0
$265$	−600338.	+	1.03982e6i	−0.525147	+	0.909581i
$266$	197206.	+	201655.i	0.170890	+	0.174745i
$267$		0			0
$268$	517863.	+	11552.7i	0.440431	+	0.00982530i
$269$			1.30693e6i			1.10121i	0.834766	+	0.550605i	$0.185603\pi$
$269$			1.30693e6i			1.10121i	−0.834766	+	0.550605i	$0.814397\pi$
$270$		0			0
$271$			109448.i			0.0905280i	0.998975	+	0.0452640i	$0.0144129\pi$
$271$			109448.i			0.0905280i	−0.998975	+	0.0452640i	$0.985587\pi$
$272$	−929052.	−	593147.i	−0.761409	−	0.486116i
$273$		0			0
$274$	−1.16967e6	+	1.14387e6i	−0.941214	+	0.920451i
$275$	−1.37631e6	+	2.38384e6i	−1.09745	+	1.90084i
$276$		0			0
$277$	377853.	+	654461.i	0.295885	+	0.512488i	0.975190	−	0.221368i	$-0.0710520\pi$
$277$	377853.	+	654461.i	0.295885	+	0.512488i	−0.679305	+	0.733856i	$0.737719\pi$
$278$	541803.	+	151672.i	0.420465	+	0.117704i
$279$		0			0
$280$	1.70120e6	−	1.59102e6i	1.29677	−	1.21277i
$281$	133655.	−	77165.9i	0.100977	−	0.0582988i	−0.448661	−	0.893702i	$-0.648099\pi$
$281$	133655.	−	77165.9i	0.100977	−	0.0582988i	0.549638	+	0.835403i	$0.314766\pi$
$282$		0			0
$283$	921332.	+	531931.i	0.683833	+	0.394811i	0.801298	−	0.598266i	$-0.204143\pi$
$283$	921332.	+	531931.i	0.683833	+	0.394811i	−0.117465	+	0.993077i	$0.537477\pi$
$284$	193710.	−	106150.i	0.142513	−	0.0780951i
$285$		0			0
$286$	−1.09656e6	+	280754.i	−0.792716	+	0.202960i
$287$	−2.22137e6			−1.59190
$288$		0			0
$289$	261179.			0.183947
$290$	1.89381e6	−	484876.i	1.32234	−	0.338560i
$291$		0			0
$292$	−311201.	+	170533.i	−0.213591	+	0.117045i
$293$	519996.	+	300220.i	0.353860	+	0.204301i	0.666384	−	0.745609i	$-0.267841\pi$
$293$	519996.	+	300220.i	0.353860	+	0.204301i	−0.312524	+	0.949910i	$0.601175\pi$
$294$		0			0
$295$	−3.09337e6	+	1.78596e6i	−2.06955	+	1.19486i
$296$	263481.	−	246415.i	0.174792	−	0.163470i
$297$		0			0
$298$	−2.03398e6	−	569389.i	−1.32680	−	0.371423i
$299$	528261.	+	914974.i	0.341720	+	0.591876i
$300$		0			0
$301$	1.03147e6	−	1.78657e6i	0.656209	−	1.13659i
$302$	−1.49607e6	+	1.46307e6i	−0.943920	+	0.923097i
$303$		0			0
$304$	300474.	+	191836.i	0.186476	+	0.119054i
$305$		−	38001.3i		−	0.0233910i
$306$		0			0
$307$			2.78186e6i			1.68457i	0.539031	+	0.842286i	$0.318791\pi$
$307$			2.78186e6i			1.68457i	−0.539031	+	0.842286i	$0.681209\pi$
$308$	−2.54969e6	−	56879.4i	−1.53148	−	0.0341647i
$309$		0			0
$310$	962758.	+	984475.i	0.569001	+	0.581836i
$311$	−1.14667e6	+	1.98609e6i	−0.672262	+	1.16439i	0.304999	+	0.952353i	$0.401344\pi$
$311$	−1.14667e6	+	1.98609e6i	−0.672262	+	1.16439i	−0.977261	+	0.212039i	$0.931990\pi$
$312$		0			0
$313$	1.41302e6	+	2.44742e6i	0.815244	+	1.41204i	0.909153	+	0.416463i	$0.136730\pi$
$313$	1.41302e6	+	2.44742e6i	0.815244	+	1.41204i	−0.0939092	+	0.995581i	$0.529936\pi$
$314$	−599770.	+	2.14251e6i	−0.343290	+	1.22630i
$315$		0			0
$316$	1.23375e6	−	2.03092e6i	0.695039	−	1.14413i
$317$	185665.	−	107194.i	0.103773	−	0.0599132i	−0.447215	−	0.894426i	$-0.647584\pi$
$317$	185665.	−	107194.i	0.103773	−	0.0599132i	0.550988	+	0.834513i	$0.314251\pi$
$318$		0			0
$319$	−1.85368e6	−	1.07022e6i	−1.01990	−	0.588839i
$320$	1.63916e6	−	2.44541e6i	0.894840	−	1.33499i
$321$		0			0
$322$	590418.	+	2.30604e6i	0.317337	+	1.23944i
$323$	374739.			0.199859
$324$		0			0
$325$	1.77878e6			0.934142
$326$	217121.	+	848027.i	0.113151	+	0.441943i
$327$		0			0
$328$	−2.73473e6	+	635539.i	−1.40356	+	0.326180i
$329$	−305860.	−	176588.i	−0.155787	−	0.0899439i
$330$		0			0
$331$	352745.	−	203658.i	0.176967	−	0.102172i	−0.408900	−	0.912579i	$-0.634088\pi$
$331$	352745.	−	203658.i	0.176967	−	0.102172i	0.585867	+	0.810407i	$0.300754\pi$
$332$	−2.65641e6	−	1.61372e6i	−1.32267	−	0.803497i
$333$		0			0
$334$	−300142.	+	1.07217e6i	−0.147218	+	0.525893i
$335$	727151.	+	1.25946e6i	0.354008	+	0.613159i
$336$		0			0
$337$	−1.44822e6	+	2.50838e6i	−0.694638	+	1.20315i	0.275664	+	0.961254i	$0.411102\pi$
$337$	−1.44822e6	+	2.50838e6i	−0.694638	+	1.20315i	−0.970302	+	0.241895i	$0.922231\pi$
$338$	−957092.	−	978681.i	−0.455682	−	0.465961i
$339$		0			0
$340$	69019.5	−	3.09389e6i	0.0323798	−	1.45147i
$341$		−	1.50768e6i		−	0.702139i
$342$		0			0
$343$		−	1.87641e6i		−	0.861176i
$344$	758706.	−	2.49454e6i	0.345683	−	1.13657i
$345$		0			0
$346$	2.72488e6	−	2.66477e6i	1.22365	−	1.19666i
$347$	1.79724e6	−	3.11291e6i	0.801275	−	1.38785i	−0.117502	−	0.993073i	$-0.537488\pi$
$347$	1.79724e6	−	3.11291e6i	0.801275	−	1.38785i	0.918777	−	0.394777i	$-0.129178\pi$
$348$		0			0
$349$	−956981.	−	1.65754e6i	−0.420571	−	0.728451i	0.575424	−	0.817855i	$-0.304837\pi$
$349$	−956981.	−	1.65754e6i	−0.420571	−	0.728451i	−0.995995	+	0.0894044i	$0.971504\pi$
$350$	3.85935e6	+	1.08038e6i	1.68401	+	0.471418i
$351$		0			0
$352$	−3.15519e6	+	659447.i	−1.35728	+	0.283676i
$353$	−2.21063e6	+	1.27631e6i	−0.944232	+	0.545152i	−0.891284	−	0.453445i	$-0.850195\pi$
$353$	−2.21063e6	+	1.27631e6i	−0.944232	+	0.545152i	−0.0529474	+	0.998597i	$0.516862\pi$
$354$		0			0
$355$	537073.	+	310079.i	0.226184	+	0.130587i
$356$	1.14504e6	+	2.08955e6i	0.478845	+	0.873830i
$357$		0			0
$358$	−3.19951e6	+	819174.i	−1.31940	+	0.337807i
$359$	−2.70497e6			−1.10771			−0.553856	−	0.832612i	$-0.686844\pi$
$359$	−2.70497e6			−1.10771			−0.553856	+	0.832612i	$0.686844\pi$
$360$		0			0
$361$	2.35490e6			0.951053
$362$	3.41446e6	−	874209.i	1.36946	−	0.350626i
$363$		0			0
$364$	791989.	+	1.44528e6i	0.313304	+	0.571739i
$365$	−862824.	−	498151.i	−0.338992	−	0.195717i
$366$		0			0
$367$	3.78493e6	−	2.18523e6i	1.46687	−	0.846900i	0.467561	−	0.883961i	$-0.345133\pi$
$367$	3.78493e6	−	2.18523e6i	1.46687	−	0.846900i	0.999313	+	0.0370602i	$0.0117993\pi$
$368$	1.38662e6	+	2.67004e6i	0.533751	+	1.02778i
$369$		0			0
$370$	975346.	+	273037.i	0.370386	+	0.103685i
$371$	−957029.	−	1.65762e6i	−0.360986	−	0.625246i
$372$		0			0
$373$	−1.08643e6	+	1.88176e6i	−0.404325	+	0.700312i	−0.994243	−	0.107152i	$-0.965827\pi$
$373$	−1.08643e6	+	1.88176e6i	−0.404325	+	0.700312i	0.589917	+	0.807464i	$0.299160\pi$
$374$	−2.42251e6	+	2.36907e6i	−0.895544	+	0.875789i
$375$		0			0
$376$	−427065.	−	129890.i	−0.155785	−	0.0473813i
$377$			1.38318e6i			0.501216i
$378$		0			0
$379$		−	872712.i		−	0.312085i	−0.987750	−	0.156043i	$-0.950126\pi$
$379$		−	872712.i		−	0.312085i	0.987750	−	0.156043i	$-0.0498737\pi$
$380$	−22322.3	+	1.00062e6i	−0.00793011	+	0.355477i
$381$		0			0
$382$	−732230.	−	748747.i	−0.256737	−	0.262529i
$383$	817267.	−	1.41555e6i	0.284687	−	0.493092i	−0.687846	−	0.725856i	$-0.741444\pi$
$383$	817267.	−	1.41555e6i	0.284687	−	0.493092i	0.972533	+	0.232764i	$0.0747771\pi$
$384$		0			0
$385$	−3.58011e6	−	6.20094e6i	−1.23096	−	2.13209i
$386$	−442748.	+	1.58159e6i	−0.151248	+	0.540289i
$387$		0			0
$388$	2.62324e6	+	1.59357e6i	0.884624	+	0.537394i
$389$	89924.7	−	51918.0i	0.0301304	−	0.0173958i	−0.484859	−	0.874592i	$-0.661129\pi$
$389$	89924.7	−	51918.0i	0.0301304	−	0.0173958i	0.514990	+	0.857196i	$0.327796\pi$
$390$		0			0
$391$	2.73893e6	+	1.58132e6i	0.906021	+	0.523092i
$392$	151842.	+	653379.i	0.0499089	+	0.214758i
$393$		0			0
$394$	326348.	+	1.27464e6i	0.105911	+	0.413664i
$395$	6.67162e6			2.15149
$396$		0			0
$397$	−3.33523e6			−1.06206			−0.531031	−	0.847352i	$-0.678195\pi$
$397$	−3.33523e6			−1.06206			−0.531031	+	0.847352i	$0.678195\pi$
$398$	−735221.	−	2.87161e6i	−0.232654	−	0.908693i
$399$		0			0
$400$	5.06033e6	+	225888.i	1.58135	+	0.0705899i
$401$	−144161.	−	83231.6i	−0.0447701	−	0.0258480i	0.477448	−	0.878660i	$-0.341562\pi$
$401$	−144161.	−	83231.6i	−0.0447701	−	0.0258480i	−0.522218	+	0.852812i	$0.674895\pi$
$402$		0			0
$403$	−843751.	+	487140.i	−0.258793	+	0.149414i
$404$	669340.	−	1.10183e6i	0.204030	−	0.335861i
$405$		0			0
$406$	−840105.	+	3.00104e6i	−0.252941	+	0.903558i
$407$	−554486.	−	960398.i	−0.165922	−	0.287386i
$408$		0			0
$409$	2.56963e6	−	4.45073e6i	0.759560	−	1.31560i	−0.183515	−	0.983017i	$-0.558748\pi$
$409$	2.56963e6	−	4.45073e6i	0.759560	−	1.31560i	0.943075	−	0.332580i	$-0.107919\pi$
$410$	−5.51131e6	−	5.63563e6i	−1.61918	−	1.65570i
$411$		0			0
$412$	1.58789e6	+	35423.3i	0.460870	+	0.0102812i
$413$		−	5.69417e6i		−	1.64269i
$414$		0			0
$415$		−	8.72638e6i		−	2.48722i
$416$	1.38851e6	+	1.55269e6i	0.393383	+	0.439897i
$417$		0			0
$418$	783488.	−	766205.i	0.219327	−	0.214489i
$419$	1.65720e6	−	2.87035e6i	0.461146	−	0.798729i	−0.537872	−	0.843027i	$-0.680772\pi$
$419$	1.65720e6	−	2.87035e6i	0.461146	−	0.798729i	0.999018	+	0.0442975i	$0.0141050\pi$
$420$		0			0
$421$	1.80550e6	+	3.12721e6i	0.496468	+	0.859908i	0.999992	−	0.00407351i	$-0.00129664\pi$
$421$	1.80550e6	+	3.12721e6i	0.496468	+	0.859908i	−0.503524	+	0.863981i	$0.667963\pi$
$422$	−2.45130e6	−	686214.i	−0.670064	−	0.187577i
$423$		0			0
$424$	−1.65244e6	−	1.76689e6i	−0.446388	−	0.477303i
$425$	4.61130e6	−	2.66234e6i	1.23837	−	0.714974i
$426$		0			0
$427$	52463.7	+	30289.9i	0.0139248	+	0.00803950i
$428$	−397829.	+	218004.i	−0.104975	+	0.0575248i
$429$		0			0
$430$	7.09164e6	−	1.81568e6i	1.84959	−	0.473553i
$431$	7.53077e6			1.95275			0.976374	−	0.216090i	$-0.0693303\pi$
$431$	7.53077e6			1.95275			0.976374	+	0.216090i	$0.0693303\pi$
$432$		0			0
$433$	2.24585e6			0.575653			0.287827	−	0.957683i	$-0.407067\pi$
$433$	2.24585e6			0.575653			0.287827	+	0.957683i	$0.407067\pi$
$434$	−2.12653e6	+	544459.i	−0.541936	+	0.138753i
$435$		0			0
$436$	611437.	−	335058.i	0.154041	−	0.0844118i
$437$	−885823.	−	511430.i	−0.221893	−	0.128110i
$438$		0			0
$439$	925006.	−	534052.i	0.229078	−	0.132258i	−0.381069	−	0.924547i	$-0.624444\pi$
$439$	925006.	−	534052.i	0.229078	−	0.132258i	0.610147	+	0.792289i	$0.291111\pi$
$440$	−6.18157e6	−	6.60968e6i	−1.52218	−	1.62760i
$441$		0			0
$442$	2.10855e6	+	590263.i	0.513367	+	0.143711i
$443$	149436.	+	258831.i	0.0361781	+	0.0626623i	0.883548	−	0.468342i	$-0.155148\pi$
$443$	149436.	+	258831.i	0.0361781	+	0.0626623i	−0.847369	+	0.531004i	$0.821815\pi$
$444$		0			0
$445$	−3.34482e6	+	5.79340e6i	−0.800705	+	1.38686i
$446$	156175.	−	152730.i	0.0371770	−	0.0363569i
$447$		0			0
$448$	2.06954e6	+	4.21216e6i	0.487169	+	0.991538i
$449$			8.39456e6i			1.96509i	0.186028	+	0.982544i	$0.440439\pi$
$449$			8.39456e6i			1.96509i	−0.186028	+	0.982544i	$0.559561\pi$
$450$		0			0
$451$			8.63070e6i			1.99804i
$452$	−4.78239e6	−	106687.i	−1.10103	−	0.0245621i
$453$		0			0
$454$	−3.53829e6	−	3.61811e6i	−0.805665	−	0.823838i
$455$	−2.31351e6	+	4.00712e6i	−0.523894	+	0.907411i
$456$		0			0
$457$	−1.98648e6	−	3.44069e6i	−0.444933	−	0.770646i	0.553115	−	0.833105i	$-0.313439\pi$
$457$	−1.98648e6	−	3.44069e6i	−0.444933	−	0.770646i	−0.998048	+	0.0624588i	$0.980106\pi$
$458$	−2.17789e6	+	7.77990e6i	−0.485146	+	1.73305i
$459$		0			0
$460$	−4.38557e6	+	7.21925e6i	−0.966344	+	1.59073i
$461$	2.12064e6	−	1.22435e6i	0.464744	−	0.268320i	−0.249293	−	0.968428i	$-0.580198\pi$
$461$	2.12064e6	−	1.22435e6i	0.464744	−	0.268320i	0.714037	+	0.700108i	$0.246865\pi$
$462$		0			0
$463$	−5.77486e6	−	3.33412e6i	−1.25196	−	0.722817i	−0.280459	−	0.959866i	$-0.590487\pi$
$463$	−5.77486e6	−	3.33412e6i	−1.25196	−	0.722817i	−0.971498	+	0.237049i	$0.923820\pi$
$464$	−175651.	+	3.93492e6i	−0.0378752	+	0.848479i
$465$		0			0
$466$	533047.	+	2.08196e6i	0.113710	+	0.444127i
$467$	−3.34371e6			−0.709474			−0.354737	−	0.934966i	$-0.615430\pi$
$467$	−3.34371e6			−0.709474			−0.354737	+	0.934966i	$0.615430\pi$
$468$		0			0
$469$	−2.31838e6			−0.486689
$470$	−310844.	−	1.21409e6i	−0.0649080	−	0.253516i
$471$		0			0
$472$	−1.62911e6	−	7.01008e6i	−0.336586	−	1.44833i
$473$	−6.94134e6	−	4.00759e6i	−1.42656	−	0.823626i
$474$		0			0
$475$	−1.49139e6	+	861052.i	−0.303288	+	0.175104i
$476$	4.21633e6	+	2.56135e6i	0.852938	+	0.518145i
$477$		0			0
$478$	−1.15639e6	+	4.13087e6i	−0.231491	+	0.826936i
$479$	−2.32045e6	−	4.01914e6i	−0.462097	−	0.800376i	0.536968	−	0.843603i	$-0.319570\pi$
$479$	−2.32045e6	−	4.01914e6i	−0.462097	−	0.800376i	−0.999065	+	0.0432268i	$0.986236\pi$
$480$		0			0
$481$	−358315.	+	620620.i	−0.0706159	+	0.122310i
$482$	4.71109e6	+	4.81735e6i	0.923642	+	0.944476i
$483$		0			0
$484$	−106053.	+	4.75396e6i	−0.0205783	+	0.922448i
$485$			8.61740e6i			1.66350i
$486$		0			0
$487$		−	4.91616e6i		−	0.939299i	−0.882853	−	0.469650i	$-0.844380\pi$
$487$		−	4.91616e6i		−	0.939299i	0.882853	−	0.469650i	$-0.155620\pi$
$488$	73253.9	+	22279.9i	0.0139246	+	0.00423510i
$489$		0			0
$490$	−1.34646e6	+	1.31676e6i	−0.253340	+	0.247751i
$491$	346602.	−	600332.i	0.0648824	−	0.112380i	−0.831759	−	0.555136i	$-0.812666\pi$
$491$	346602.	−	600332.i	0.0648824	−	0.112380i	0.896642	+	0.442757i	$0.145999\pi$
$492$		0			0
$493$	2.07024e6	+	3.58575e6i	0.383621	+	0.664451i
$494$	−681946.	−	190903.i	−0.125728	−	0.0351961i
$495$		0			0
$496$	−2.46220e6	+	1.27869e6i	−0.449385	+	0.233378i
$497$	−856175.	+	494313.i	−0.155479	+	0.0897658i
$498$		0			0
$499$	400079.	+	230986.i	0.0719274	+	0.0415273i	0.535532	−	0.844515i	$-0.320111\pi$
$499$	400079.	+	230986.i	0.0719274	+	0.0415273i	−0.463605	+	0.886042i	$0.653444\pi$
$500$	2.51678e6	+	4.59279e6i	0.450215	+	0.821584i
$501$		0			0
$502$	−3.86540e6	+	989663.i	−0.684597	+	0.175278i
$503$	−3.22518e6			−0.568373			−0.284187	−	0.958769i	$-0.591724\pi$
$503$	−3.22518e6			−0.568373			−0.284187	+	0.958769i	$0.591724\pi$
$504$		0			0
$505$	3.61952e6			0.631572
$506$	8.95965e6	−	2.29395e6i	1.55566	−	0.398298i
$507$		0			0
$508$	−3.95750e6	−	7.22193e6i	−0.680396	−	1.24164i
$509$	213328.	+	123165.i	0.0364967	+	0.0210714i	0.518137	−	0.855297i	$-0.326626\pi$
$509$	213328.	+	123165.i	0.0364967	+	0.0210714i	−0.481641	+	0.876369i	$0.659959\pi$
$510$		0			0
$511$	1.37547e6	−	794129.i	0.233023	−	0.134536i
$512$	3.75291e6	+	4.59347e6i	0.632694	+	0.774402i
$513$		0			0
$514$	−7.00698e6	−	1.96152e6i	−1.16983	−	0.327481i
$515$	2.22962e6	+	3.86181e6i	0.370436	+	0.641613i
$516$		0			0
$517$	−686097.	+	1.18836e6i	−0.112891	+	0.195533i
$518$	−1.15437e6	+	1.12891e6i	−0.189026	+	0.184856i
$519$		0			0
$520$	−1.70171e6	+	5.59505e6i	−0.275981	+	0.907394i
$521$		−	5.09612e6i		−	0.822519i	−0.911518	−	0.411259i	$-0.865089\pi$
$521$		−	5.09612e6i		−	0.822519i	0.911518	−	0.411259i	$-0.134911\pi$
$522$		0			0
$523$		−	5.13482e6i		−	0.820863i	−0.911891	−	0.410432i	$-0.865378\pi$
$523$		−	5.13482e6i		−	0.820863i	0.911891	−	0.410432i	$-0.134622\pi$
$524$	−4513.29	+	202314.i	−0.000718068	+	0.0321883i
$525$		0			0
$526$	6.42609e6	+	6.57104e6i	1.01270	+	1.03555i
$527$	−1.45823e6	+	2.52572e6i	−0.228717	+	0.396150i
$528$		0			0
$529$	−1.09808e6	−	1.90193e6i	−0.170606	−	0.295498i
$530$	1.83097e6	−	6.54060e6i	0.283133	−	1.01141i
$531$		0			0
$532$	−1.36364e6	−	828391.i	−0.208892	−	0.126898i
$533$	4.83005e6	−	2.78863e6i	0.736434	−	0.425180i
$534$		0			0
$535$	−1.10301e6	−	636821.i	−0.166607	−	0.0961906i
$536$	−2.85415e6	+	663291.i	−0.429106	+	0.0997223i
$537$		0			0
$538$	−1.83372e6	−	7.16207e6i	−0.273134	−	1.06680i
$539$	2.06204e6			0.305721
$540$		0			0
$541$	1.10092e7			1.61720			0.808601	−	0.588357i	$-0.200225\pi$
$541$	1.10092e7			1.61720			0.808601	+	0.588357i	$0.200225\pi$
$542$	−153563.	−	599783.i	−0.0224537	−	0.0876992i
$543$		0			0
$544$	5.92352e6	+	1.94697e6i	0.858188	+	0.282073i
$545$	1.69525e6	+	978751.i	0.244479	+	0.141150i
$546$		0			0
$547$	−3.43955e6	+	1.98583e6i	−0.491511	+	0.283774i	−0.725201	−	0.688537i	$-0.758253\pi$
$547$	−3.43955e6	+	1.98583e6i	−0.491511	+	0.283774i	0.233690	+	0.972311i	$0.424920\pi$
$548$	4.80498e6	−	7.90966e6i	0.683503	−	1.12514i
$549$		0			0
$550$	4.19760e6	−	1.49947e7i	0.591690	−	2.11364i
$551$	−669555.	−	1.15970e6i	−0.0939523	−	0.162730i
$552$		0			0
$553$	−5.31779e6	+	9.21068e6i	−0.739466	+	1.28079i
$554$	−2.98893e6	−	3.05635e6i	−0.413752	−	0.423086i
$555$		0			0
$556$	−3.18194e6	−	70983.8i	−0.436521	−	0.00973805i
$557$		−	9.38422e6i		−	1.28162i	−0.767698	−	0.640812i	$-0.778598\pi$
$557$		−	9.38422e6i		−	1.28162i	0.767698	−	0.640812i	$-0.221402\pi$
$558$		0			0
$559$			5.17950e6i			0.701065i
$560$	−7.09044e6	+	1.11058e7i	−0.955439	+	1.49651i
$561$		0			0
$562$	−624174.	+	610405.i	−0.0833613	+	0.0815224i
$563$	−2.54261e6	+	4.40393e6i	−0.338072	+	0.585558i	−0.984070	−	0.177781i	$-0.943108\pi$
$563$	−2.54261e6	+	4.40393e6i	−0.338072	+	0.585558i	0.645998	+	0.763339i	$0.276441\pi$
$564$		0			0
$565$	−6.71512e6	−	1.16309e7i	−0.884978	−	1.53283i
$566$	−5.79532e6	−	1.62233e6i	−0.760390	−	0.212863i
$567$		0			0
$568$	−912611.	+	853500.i	−0.118690	+	0.111002i
$569$	−7.59213e6	+	4.38332e6i	−0.983067	+	0.567574i	−0.903195	−	0.429231i	$-0.858785\pi$
$569$	−7.59213e6	+	4.38332e6i	−0.983067	+	0.567574i	−0.0798721	+	0.996805i	$0.525451\pi$
$570$		0			0
$571$	1.07595e7	+	6.21203e6i	1.38103	+	0.797339i	0.992282	−	0.124004i	$-0.0395735\pi$
$571$	1.07595e7	+	6.21203e6i	1.38103	+	0.797339i	0.388750	+	0.921343i	$0.372907\pi$
$572$	5.61533e6	−	3.07711e6i	0.717605	−	0.393236i
$573$		0			0
$574$	1.21733e7	−	3.11675e6i	1.54216	−	0.394842i
$575$	−1.45338e7			−1.83320
$576$		0			0
$577$	9.43597e6			1.17990			0.589952	−	0.807438i	$-0.299146\pi$
$577$	9.43597e6			1.17990			0.589952	+	0.807438i	$0.299146\pi$
$578$	−1.43128e6	+	366453.i	−0.178199	+	0.0456246i
$579$		0			0
$580$	−9.69795e6	+	5.31432e6i	−1.19704	+	0.655961i
$581$	1.20474e7	+	6.95558e6i	1.48065	+	0.854856i
$582$		0			0
$583$	−6.44036e6	+	3.71834e6i	−0.784763	+	0.453083i
$584$	1.46614e6	−	1.37117e6i	0.177886	−	0.166364i
$585$		0			0
$586$	−3.27086e6	−	915639.i	−0.393475	−	0.110149i
$587$	6.76932e6	+	1.17248e7i	0.810868	+	1.40446i	0.912258	+	0.409617i	$0.134338\pi$
$587$	6.76932e6	+	1.17248e7i	0.810868	+	1.40446i	−0.101390	+	0.994847i	$0.532329\pi$
$588$		0			0
$589$	471619.	−	816869.i	0.0560149	−	0.0970206i
$590$	1.44461e7	−	1.41274e7i	1.70852	−	1.67083i
$591$		0			0
$592$	−1.09816e6	+	1.72006e6i	−0.128784	+	0.201716i
$593$		−	1.76321e6i		−	0.205905i	−0.994686	−	0.102952i	$-0.967171\pi$
$593$		−	1.76321e6i		−	0.205905i	0.994686	−	0.102952i	$-0.0328289\pi$
$594$		0			0
$595$			1.38508e7i			1.60391i
$596$	1.19453e7	+	266479.i	1.37746	+	0.0307290i
$597$		0			0
$598$	−4.17869e6	−	4.27295e6i	−0.477845	−	0.488624i
$599$	−3.59905e6	+	6.23374e6i	−0.409846	+	0.709875i	−0.994872	−	0.101140i	$-0.967751\pi$
$599$	−3.59905e6	+	6.23374e6i	−0.409846	+	0.709875i	0.585026	+	0.811015i	$0.301084\pi$
$600$		0			0
$601$	1.35517e6	+	2.34722e6i	0.153041	+	0.265075i	0.932344	−	0.361573i	$-0.117760\pi$
$601$	1.35517e6	+	2.34722e6i	0.153041	+	0.265075i	−0.779303	+	0.626647i	$0.784427\pi$
$602$	−3.14589e6	+	1.12378e7i	−0.353795	+	1.26383i
$603$		0			0
$604$	6.14581e6	−	1.01168e7i	0.685467	−	1.12837i
$605$	−1.15618e7	+	6.67521e6i	−1.28421	+	0.741440i
$606$		0			0
$607$	−1.91340e6	−	1.10470e6i	−0.210782	−	0.121695i	0.390893	−	0.920436i	$-0.372166\pi$
$607$	−1.91340e6	−	1.10470e6i	−0.210782	−	0.121695i	−0.601675	+	0.798741i	$0.705500\pi$
$608$	−1.91578e6	−	629689.i	−0.210178	−	0.0690823i
$609$		0			0
$610$	53318.7	+	208251.i	0.00580170	+	0.0226601i
$611$	886728.			0.0960921
$612$		0			0
$613$	−4.95842e6			−0.532957			−0.266478	−	0.963841i	$-0.585860\pi$
$613$	−4.95842e6			−0.532957			−0.266478	+	0.963841i	$0.585860\pi$
$614$	−3.90316e6	−	1.52449e7i	−0.417826	−	1.63193i
$615$		0			0
$616$	1.40523e7	−	3.26570e6i	1.49210	−	0.346757i
$617$	6.51356e6	+	3.76060e6i	0.688819	+	0.397690i	0.803170	−	0.595750i	$-0.203145\pi$
$617$	6.51356e6	+	3.76060e6i	0.688819	+	0.397690i	−0.114350	+	0.993440i	$0.536479\pi$
$618$		0			0
$619$	−3.79004e6	+	2.18818e6i	−0.397573	+	0.229539i	−0.685436	−	0.728133i	$-0.740388\pi$
$619$	−3.79004e6	+	2.18818e6i	−0.397573	+	0.229539i	0.287863	+	0.957671i	$0.407055\pi$
$620$	−6.65729e6	−	4.04419e6i	−0.695534	−	0.422525i
$621$		0			0
$622$	3.49723e6	−	1.24928e7i	0.362450	−	1.29475i
$623$	−5.33215e6	−	9.23555e6i	−0.550405	−	0.953329i
$624$		0			0
$625$	377275.	−	653459.i	0.0386329	−	0.0669142i
$626$	−1.11774e7	−	1.14295e7i	−1.14000	−	1.16571i
$627$		0			0
$628$	280698.	−	1.25827e7i	0.0284014	−	1.27313i
$629$			2.14520e6i			0.216192i
$630$		0			0
$631$			2.79597e6i			0.279549i	0.990183	+	0.139775i	$0.0446378\pi$
$631$			2.79597e6i			0.279549i	−0.990183	+	0.139775i	$0.955362\pi$
$632$	−3.91152e6	+	1.28607e7i	−0.389541	+	1.28077i
$633$		0			0
$634$	−867062.	+	847935.i	−0.0856697	+	0.0837798i
$635$	1.15604e7	−	2.00233e7i	1.13773	−	1.97061i
$636$		0			0
$637$	−666257.	−	1.15399e6i	−0.0650569	−	0.112682i
$638$	1.16599e7	+	3.26406e6i	1.13408	+	0.317473i
$639$		0			0
$640$	−5.55163e6	+	1.57009e7i	−0.535760	+	1.51522i
$641$	4.59173e6	−	2.65104e6i	0.441399	−	0.254842i	−0.262792	−	0.964853i	$-0.584643\pi$
$641$	4.59173e6	−	2.65104e6i	0.441399	−	0.254842i	0.704191	+	0.710011i	$0.251310\pi$
$642$		0			0
$643$	1.45248e7	+	8.38588e6i	1.38542	+	0.799873i	0.992795	−	0.119825i	$-0.0382334\pi$
$643$	1.45248e7	+	8.38588e6i	1.38542	+	0.799873i	0.392626	+	0.919698i	$0.371567\pi$
$644$	−6.47109e6	−	1.18089e7i	−0.614841	−	1.12201i
$645$		0			0
$646$	−2.05361e6	+	525787.i	−0.193614	+	0.0495711i
$647$	−8.06422e6			−0.757359			−0.378679	−	0.925528i	$-0.623622\pi$
$647$	−8.06422e6			−0.757359			−0.378679	+	0.925528i	$0.623622\pi$
$648$		0			0
$649$	−2.21235e7			−2.06178
$650$	−9.74785e6	+	2.49575e6i	−0.904952	+	0.231696i
$651$		0			0
$652$	−2.37969e6	−	4.34263e6i	−0.219231	−	0.400068i
$653$	620058.	+	357991.i	0.0569049	+	0.0328540i	0.528183	−	0.849131i	$-0.322874\pi$
$653$	620058.	+	357991.i	0.0569049	+	0.0328540i	−0.471278	+	0.881985i	$0.656207\pi$
$654$		0			0
$655$	−492035.	+	284077.i	−0.0448118	+	0.0258721i
$656$	1.40948e7	−	7.31984e6i	1.27879	−	0.664113i
$657$		0			0
$658$	1.92390e6	+	538575.i	0.173228	+	0.0484933i
$659$	−15687.4	−	27171.4i	−0.00140714	−	0.00243724i	0.865321	−	0.501218i	$-0.167115\pi$
$659$	−15687.4	−	27171.4i	−0.00140714	−	0.00243724i	−0.866728	+	0.498781i	$0.833781\pi$
$660$		0			0
$661$	4.41600e6	−	7.64875e6i	0.393121	−	0.680905i	−0.599739	−	0.800196i	$-0.704729\pi$
$661$	4.41600e6	−	7.64875e6i	0.393121	−	0.680905i	0.992859	+	0.119291i	$0.0380621\pi$
$662$	−1.64733e6	+	1.61099e6i	−0.146095	+	0.142872i
$663$		0			0
$664$	1.68216e7	+	5.11621e6i	1.48063	+	0.450327i
$665$		−	4.47961e6i		−	0.392813i
$666$		0			0
$667$		−	1.13015e7i		−	0.983608i
$668$	140469.	−	6.29671e6i	0.0121798	−	0.545975i
$669$		0			0
$670$	−5.75197e6	−	5.88172e6i	−0.495028	−	0.506194i
$671$	117685.	−	203837.i	0.0100906	−	0.0174774i
$672$		0			0
$673$	3.33892e6	+	5.78318e6i	0.284163	+	0.492186i	0.972406	−	0.233295i	$-0.0749508\pi$
$673$	3.33892e6	+	5.78318e6i	0.284163	+	0.492186i	−0.688242	+	0.725481i	$0.741617\pi$
$674$	4.41691e6	−	1.57781e7i	0.374514	−	1.33784i
$675$		0			0
$676$	6.61811e6	+	4.02039e6i	0.557016	+	0.338377i
$677$	−1.26099e7	+	7.28033e6i	−1.05740	+	0.610491i	−0.924712	−	0.380667i	$-0.875694\pi$
$677$	−1.26099e7	+	7.28033e6i	−1.05740	+	0.610491i	−0.132689	+	0.991158i	$0.542361\pi$
$678$		0			0
$679$	−1.18970e7	−	6.86872e6i	−0.990289	−	0.571744i
$680$	3.96272e6	+	1.70516e7i	0.328641	+	1.41414i
$681$		0			0
$682$	2.11539e6	+	8.26221e6i	0.174152	+	0.680198i
$683$	5.63380e6			0.462114			0.231057	−	0.972940i	$-0.425782\pi$
$683$	5.63380e6			0.462114			0.231057	+	0.972940i	$0.425782\pi$
$684$		0			0
$685$	2.59834e7			2.11578
$686$	2.63274e6	+	1.02829e7i	0.213598	+	0.834266i
$687$		0			0
$688$	−657747.	+	1.47348e7i	−0.0529771	+	1.18679i
$689$	4.16183e6	+	2.40284e6i	0.333993	+	0.192831i
$690$		0			0
$691$	9.00873e6	−	5.20119e6i	0.717742	−	0.414389i	−0.0961788	−	0.995364i	$-0.530662\pi$
$691$	9.00873e6	−	5.20119e6i	0.717742	−	0.414389i	0.813921	+	0.580975i	$0.197329\pi$
$692$	−1.11937e7	+	1.84264e7i	−0.888606	+	1.46277i
$693$		0			0
$694$	−5.48138e6	+	1.95807e7i	−0.432008	+	1.54322i
$695$	−4.46787e6	−	7.73858e6i	−0.350864	−	0.607714i
$696$		0			0
$697$	8.34762e6	−	1.44585e7i	0.650850	−	1.12730i
$698$	7.56999e6	+	7.74075e6i	0.588108	+	0.601374i
$699$		0			0
$700$	−2.26654e7	−	505628.i	−1.74831	−	0.0390019i
$701$		−	1.19679e7i		−	0.919862i	−0.887955	−	0.459931i	$-0.847874\pi$
$701$		−	1.19679e7i		−	0.919862i	0.887955	−	0.459931i	$-0.152126\pi$
$702$		0			0
$703$		−	693798.i		−	0.0529474i
$704$	1.63655e7	−	8.04079e6i	1.24451	−	0.611459i
$705$		0			0
$706$	1.03237e7	−	1.00959e7i	0.779512	−	0.762316i
$707$	−2.88503e6	+	4.99702e6i	−0.217071	+	0.375978i
$708$		0			0
$709$	−3.72698e6	−	6.45531e6i	−0.278446	−	0.482283i	0.692553	−	0.721367i	$-0.256486\pi$
$709$	−3.72698e6	−	6.45531e6i	−0.278446	−	0.482283i	−0.970999	+	0.239084i	$0.923153\pi$
$710$	−3.37827e6	−	945708.i	−0.251506	−	0.0704062i
$711$		0			0
$712$	−9.20670e6	−	9.84433e6i	−0.680619	−	0.727757i
$713$	6.89402e6	−	3.98027e6i	0.507866	−	0.293216i
$714$		0			0
$715$	1.55689e7	+	8.98868e6i	1.13892	+	0.657553i
$716$	1.63842e7	−	8.97830e6i	1.19438	−	0.654503i
$717$		0			0
$718$	1.48235e7	−	3.79528e6i	1.07310	−	0.274747i
$719$	−1.53936e7			−1.11050			−0.555248	−	0.831685i	$-0.687377\pi$
$719$	−1.53936e7			−1.11050			−0.555248	+	0.831685i	$0.687377\pi$
$720$		0			0
$721$	−7.10870e6			−0.509275
$722$	−1.29051e7	+	3.30410e6i	−0.921334	+	0.235890i
$723$		0			0
$724$	−1.74850e7	+	9.58149e6i	−1.23971	+	0.679339i
$725$	−1.64782e7	−	9.51371e6i	−1.16430	−	0.672210i
$726$		0			0
$727$	7.42385e6	−	4.28616e6i	0.520946	−	0.300768i	−0.216375	−	0.976310i	$-0.569424\pi$
$727$	7.42385e6	−	4.28616e6i	0.520946	−	0.300768i	0.737322	+	0.675542i	$0.236090\pi$
$728$	−6.36800e6	−	6.80903e6i	−0.445322	−	0.476164i
$729$		0			0
$730$	5.42729e6	+	1.51931e6i	0.376943	+	0.105521i
$731$	7.75228e6	+	1.34273e7i	0.536582	+	0.929387i
$732$		0			0
$733$	−8.79172e6	+	1.52277e7i	−0.604386	+	1.04683i	0.387763	+	0.921759i	$0.373248\pi$
$733$	−8.79172e6	+	1.52277e7i	−0.604386	+	1.04683i	−0.992148	+	0.125067i	$0.960085\pi$
$734$	−1.76757e7	+	1.72858e7i	−1.21098	+	1.18427i
$735$		0			0
$736$	−1.13451e7	−	1.26865e7i	−0.771993	−	0.863272i
$737$			9.00758e6i			0.610857i
$738$		0			0
$739$			186950.i			0.0125926i	0.999980	+	0.00629629i	$0.00200418\pi$
$739$			186950.i			0.0125926i	−0.999980	+	0.00629629i	$0.997996\pi$
$740$	−5.72807e6	−	127784.i	−0.384529	−	0.00857821i
$741$		0			0
$742$	7.57037e6	+	7.74114e6i	0.504786	+	0.516173i
$743$	−3.19316e6	+	5.53072e6i	−0.212202	+	0.367544i	−0.952403	−	0.304841i	$-0.901397\pi$
$743$	−3.19316e6	+	5.53072e6i	−0.212202	+	0.367544i	0.740202	+	0.672385i	$0.234730\pi$
$744$		0			0
$745$	1.67728e7	+	2.90513e7i	1.10717	+	1.91768i
$746$	3.31351e6	−	1.18365e7i	0.217992	−	0.778714i
$747$		0			0
$748$	9.95160e6	−	1.63817e7i	0.650338	−	1.07055i
$749$	1.75836e6	−	1.01519e6i	0.114526	−	0.0661214i
$750$		0			0
$751$	−2.55553e7	−	1.47544e7i	−1.65341	−	0.954598i	−0.975655	−	0.219312i	$-0.929619\pi$
$751$	−2.55553e7	−	1.47544e7i	−1.65341	−	0.954598i	−0.677757	−	0.735286i	$-0.737048\pi$
$752$	2.52260e6	+	112606.i	0.162669	+	0.00726135i
$753$		0			0
$754$	−1.94070e6	−	7.57994e6i	−0.124317	−	0.485554i
$755$	3.32341e7			2.12186
$756$		0			0
$757$	−2.98899e7			−1.89576			−0.947882	−	0.318621i	$-0.896780\pi$
$757$	−2.98899e7			−1.89576			−0.947882	+	0.318621i	$0.896780\pi$
$758$	1.22448e6	+	4.78254e6i	0.0774067	+	0.302333i
$759$		0			0
$760$	−1.28162e6	−	5.51483e6i	−0.0804871	−	0.346336i
$761$	−1.12672e7	−	6.50513e6i	−0.705269	−	0.407187i	0.104038	−	0.994573i	$-0.466824\pi$
$761$	−1.12672e7	−	6.50513e6i	−0.705269	−	0.407187i	−0.809307	+	0.587386i	$0.800157\pi$
$762$		0			0
$763$	−2.70248e6	+	1.56028e6i	−0.168055	+	0.0970265i
$764$	5.06323e6	+	3.07583e6i	0.313830	+	0.190646i
$765$		0			0
$766$	−2.49258e6	+	8.90402e6i	−0.153489	+	0.548295i
$767$	7.14825e6	+	1.23811e7i	0.438744	+	0.759927i
$768$		0			0
$769$	−1.45635e6	+	2.52248e6i	−0.0888077	+	0.153819i	−0.907007	−	0.421115i	$-0.861639\pi$
$769$	−1.45635e6	+	2.52248e6i	−0.0888077	+	0.153819i	0.818200	+	0.574934i	$0.194972\pi$
$770$	2.83197e7	+	2.89585e7i	1.72132	+	1.76015i
$771$		0			0
$772$	207210.	−	9.28847e6i	0.0125132	−	0.560920i
$773$			6.84734e6i			0.412167i	0.978534	+	0.206084i	$0.0660719\pi$
$773$			6.84734e6i			0.412167i	−0.978534	+	0.206084i	$0.933928\pi$
$774$		0			0
$775$		−	1.34025e7i		−	0.801551i
$776$	−1.66115e7	−	5.05232e6i	−0.990271	−	0.301187i
$777$		0			0
$778$	−419950.	+	410686.i	−0.0248742	+	0.0243255i
$779$	−2.69978e6	+	4.67616e6i	−0.159399	+	0.276087i
$780$		0			0
$781$	1.92055e6	+	3.32649e6i	0.112667	+	0.195146i
$782$	−1.72283e7	−	4.82286e6i	−1.00745	−	0.282025i
$783$		0			0
$784$	−1.74885e6	−	3.36753e6i	−0.101616	−	0.195669i
$785$	3.06015e7	−	1.76678e7i	1.77243	−	1.02331i
$786$		0			0
$787$	−2.80432e7	−	1.61907e7i	−1.61395	−	0.931814i	−0.988443	−	0.151596i	$-0.951559\pi$
$787$	−2.80432e7	−	1.61907e7i	−1.61395	−	0.931814i	−0.625507	−	0.780218i	$-0.715108\pi$
$788$	−3.57684e6	−	6.52727e6i	−0.205203	−	0.374469i
$789$		0			0
$790$	−3.65611e7	+	9.36078e6i	−2.08426	+	0.533635i
$791$	2.14098e7			1.21667
$792$		0			0
$793$	−152099.			−0.00858904
$794$	1.82774e7	−	4.67958e6i	1.02888	−	0.263424i
$795$		0			0
$796$	8.05816e6	+	1.47051e7i	0.450768	+	0.822593i
$797$	4.17052e6	+	2.40785e6i	0.232565	+	0.134271i	0.611755	−	0.791047i	$-0.290464\pi$
$797$	4.17052e6	+	2.40785e6i	0.232565	+	0.134271i	−0.379190	+	0.925319i	$0.623797\pi$
$798$		0			0
$799$	2.29876e6	−	1.32719e6i	0.127387	−	0.0735471i
$800$	−2.80480e7	+	5.86214e6i	−1.54945	+	0.323840i
$801$		0			0
$802$	906797.	+	253847.i	0.0497822	+	0.0139360i
$803$	−3.08543e6	−	5.34411e6i	−0.168860	−	0.292474i
$804$		0			0
$805$	1.89030e7	−	3.27409e7i	1.02811	−	1.78074i
$806$	3.94034e6	−	3.85342e6i	0.213647	−	0.208934i
$807$		0			0
$808$	−2.12210e6	+	6.97724e6i	−0.114350	+	0.375972i
$809$			7.74333e6i			0.415965i	0.978133	+	0.207982i	$0.0666897\pi$
$809$			7.74333e6i			0.415965i	−0.978133	+	0.207982i	$0.933310\pi$
$810$		0			0
$811$			2.68630e7i			1.43417i	0.696984	+	0.717087i	$0.254525\pi$
$811$			2.68630e7i			1.43417i	−0.696984	+	0.717087i	$0.745475\pi$
$812$	393177.	−	1.76247e7i	0.0209266	−	0.938061i
$813$		0			0
$814$	4.38614e6	+	4.48508e6i	0.232018	+	0.237252i
$815$	6.95142e6	−	1.20402e7i	0.366589	−	0.634951i
$816$		0			0
$817$	−2.50724e6	−	4.34267e6i	−0.131414	−	0.227615i
$818$	−7.83709e6	+	2.79958e7i	−0.409517	+	1.46288i
$819$		0			0
$820$	3.81097e7	+	2.31510e7i	1.97925	+	1.20236i
$821$	−1.13361e7	+	6.54492e6i	−0.586958	+	0.338881i	−0.763894	−	0.645342i	$-0.776715\pi$
$821$	−1.13361e7	+	6.54492e6i	−0.586958	+	0.338881i	0.176936	+	0.984222i	$0.443382\pi$
$822$		0			0
$823$	5.45404e6	+	3.14889e6i	0.280684	+	0.162053i	0.633733	−	0.773552i	$-0.281522\pi$
$823$	5.45404e6	+	3.14889e6i	0.280684	+	0.162053i	−0.353049	+	0.935605i	$0.614855\pi$
$824$	−8.75150e6	+	2.03381e6i	−0.449019	+	0.104350i
$825$		0			0
$826$	7.98935e6	+	3.12046e7i	0.407438	+	1.59136i
$827$	−1.03982e7			−0.528680			−0.264340	−	0.964430i	$-0.585154\pi$
$827$	−1.03982e7			−0.528680			−0.264340	+	0.964430i	$0.585154\pi$
$828$		0			0
$829$	7.24354e6			0.366070			0.183035	−	0.983106i	$-0.441408\pi$
$829$	7.24354e6			0.366070			0.183035	+	0.983106i	$0.441408\pi$
$830$	1.22438e7	+	4.78213e7i	0.616907	+	2.40950i
$831$		0			0
$832$	−9.78770e6	−	6.56068e6i	−0.490199	−	0.328580i
$833$	−3.45441e6	−	1.99441e6i	−0.172489	−	0.0995867i
$834$		0			0
$835$	1.53138e7	−	8.84144e6i	0.760094	−	0.438841i
$836$	−3.21854e6	+	5.29816e6i	−0.159274	+	0.262186i
$837$		0			0
$838$	−5.05427e6	+	1.80549e7i	−0.248627	+	0.888149i
$839$	−1.22662e7	−	2.12456e7i	−0.601595	−	1.04199i	−0.992580	−	0.121596i	$-0.961199\pi$
$839$	−1.22662e7	−	2.12456e7i	−0.601595	−	1.04199i	0.390985	−	0.920397i	$-0.372134\pi$
$840$		0			0
$841$	−2.85770e6	+	4.94968e6i	−0.139324	+	0.241317i
$842$	−1.42820e7	−	1.46042e7i	−0.694238	−	0.709898i
$843$		0			0
$844$	1.43962e7	+	321155.i	0.695650	+	0.0155188i
$845$			2.17407e7i			1.04744i
$846$		0			0
$847$		−	2.12826e7i		−	1.01933i
$848$	1.15346e7	+	7.36420e6i	0.550825	+	0.351670i
$849$		0			0
$850$	−2.15349e7	+	2.10598e7i	−1.02234	+	0.999787i
$851$	2.92768e6	−	5.07089e6i	0.138580	−	0.240027i
$852$		0			0
$853$	−2.26783e6	−	3.92799e6i	−0.106718	−	0.184841i	0.807721	−	0.589565i	$-0.200701\pi$
$853$	−2.26783e6	−	3.92799e6i	−0.106718	−	0.184841i	−0.914439	+	0.404724i	$0.867368\pi$
$854$	−330005.	−	92381.1i	−0.0154837	−	0.00433449i
$855$		0			0
$856$	1.87426e6	−	1.75287e6i	0.0874271	−	0.0817644i
$857$	−4.32468e6	+	2.49686e6i	−0.201142	+	0.116129i	−0.597188	−	0.802101i	$-0.703715\pi$
$857$	−4.32468e6	+	2.49686e6i	−0.201142	+	0.116129i	0.396046	+	0.918231i	$0.370382\pi$
$858$		0			0
$859$	−2.79301e7	−	1.61254e7i	−1.29149	−	0.745640i	−0.312568	−	0.949895i	$-0.601189\pi$
$859$	−2.79301e7	−	1.61254e7i	−1.29149	−	0.745640i	−0.978918	+	0.204256i	$0.934523\pi$
$860$	−3.63153e7	+	1.99002e7i	−1.67434	+	0.917511i
$861$		0			0
$862$	−4.12693e7	+	1.05662e7i	−1.89173	+	0.484342i
$863$	−2.09873e7			−0.959247			−0.479624	−	0.877474i	$-0.659227\pi$
$863$	−2.09873e7			−0.959247			−0.479624	+	0.877474i	$0.659227\pi$
$864$		0			0
$865$	−6.05312e7			−2.75067
$866$	−1.23075e7	+	3.15109e6i	−0.557665	+	0.142780i
$867$		0			0
$868$	1.08897e7	−	5.96737e6i	0.490587	−	0.268834i
$869$	3.57862e7	+	2.06612e7i	1.60756	+	0.928123i
$870$		0			0
$871$	5.04097e6	−	2.91040e6i	0.225148	−	0.129989i
$872$	−2.88062e6	+	2.69404e6i	−0.128290	+	0.119981i
$873$		0			0
$874$	5.57196e6	+	1.55981e6i	0.246734	+	0.0690705i
$875$	−1.17200e7	−	2.02996e7i	−0.517496	−	0.896330i
$876$		0			0
$877$	−1.12204e7	+	1.94343e7i	−0.492616	+	0.853236i	−0.999964	−	0.00850516i	$-0.997293\pi$
$877$	−1.12204e7	+	1.94343e7i	−0.492616	+	0.853236i	0.507348	+	0.861742i	$0.330626\pi$
$878$	−4.31980e6	+	4.22451e6i	−0.189116	+	0.184944i
$879$		0			0
$880$	4.31494e7	+	2.75485e7i	1.87831	+	1.19920i
$881$		−	2.46288e7i		−	1.06906i	−0.845149	−	0.534531i	$-0.820488\pi$
$881$		−	2.46288e7i		−	1.06906i	0.845149	−	0.534531i	$-0.179512\pi$
$882$		0			0
$883$		−	1.33073e7i		−	0.574365i	−0.957876	−	0.287183i	$-0.907281\pi$
$883$		−	1.33073e7i		−	0.574365i	0.957876	−	0.287183i	$-0.0927187\pi$
$884$	−1.23832e7	−	276249.i	−0.532970	−	0.0118897i
$885$		0			0
$886$	−1.18208e6	−	1.20875e6i	−0.0505898	−	0.0517310i
$887$	1.14459e7	−	1.98249e7i	0.488474	−	0.846062i	−0.511438	−	0.859320i	$-0.670887\pi$
$887$	1.14459e7	−	1.98249e7i	0.488474	−	0.846062i	0.999912	+	0.0132580i	$0.00422028\pi$
$888$		0			0
$889$	1.84291e7	+	3.19201e7i	0.782077	+	1.35460i
$890$	1.02013e7	−	3.64414e7i	0.431700	−	1.54213i
$891$		0			0
$892$	−641561.	+	1.05610e6i	−0.0269977	+	0.0444418i
$893$	−743463.	+	429239.i	−0.0311983	+	0.0180123i
$894$		0			0
$895$	4.54263e7	+	2.62269e7i	1.89561	+	1.09443i
$896$	−1.72513e7	−	2.01793e7i	−0.717878	−	0.839722i
$897$		0			0
$898$	−1.17782e7	−	4.60030e7i	−0.487403	−	1.90368i
$899$	1.04218e7			0.430074
$900$		0			0
$901$	1.43855e7			0.590356
$902$	−1.21095e7	−	4.72970e7i	−0.495576	−	1.93561i
$903$		0			0
$904$	2.63576e7	−	6.12539e6i	1.07272	−	0.249294i
$905$	−4.84782e7	−	2.79889e7i	−1.96755	−	1.13596i
$906$		0			0
$907$	2.40173e7	−	1.38664e7i	0.969407	−	0.559688i	0.0703518	−	0.997522i	$-0.477588\pi$
$907$	2.40173e7	−	1.38664e7i	0.969407	−	0.559688i	0.899055	+	0.437835i	$0.144254\pi$
$908$	2.44666e7	+	1.48631e7i	0.984827	+	0.598265i
$909$		0			0
$910$	7.05596e6	−	2.52054e7i	0.282457	−	1.00900i
$911$	1.93415e7	+	3.35005e7i	0.772138	+	1.33738i	0.936389	+	0.350964i	$0.114146\pi$
$911$	1.93415e7	+	3.35005e7i	0.772138	+	1.33738i	−0.164250	+	0.986419i	$0.552521\pi$
$912$		0			0
$913$	2.70245e7	−	4.68078e7i	1.07295	−	1.85841i
$914$	1.57137e7	+	1.60681e7i	0.622174	+	0.636208i
$915$		0			0
$916$	1.01927e6	−	4.56903e7i	0.0401377	−	1.79922i
$917$		−	905722.i		−	0.0355690i
$918$		0			0
$919$			1.70205e6i			0.0664790i	0.999447	+	0.0332395i	$0.0105824\pi$
$919$			1.70205e6i			0.0664790i	−0.999447	+	0.0332395i	$0.989418\pi$
$920$	1.39042e7	−	4.57154e7i	0.541596	−	1.78071i
$921$		0			0
$922$	−9.90342e6	+	9.68495e6i	−0.383670	+	0.375206i
$923$	1.24108e6	−	2.14962e6i	0.0479509	−	0.0830534i
$924$		0			0
$925$	−4.92909e6	−	8.53743e6i	−0.189414	−	0.328075i
$926$	3.63248e7	+	1.01687e7i	1.39212	+	0.389707i
$927$		0			0
$928$	−4.55841e6	−	2.18102e7i	−0.173757	−	0.831360i
$929$	−2.05945e6	+	1.18902e6i	−0.0782908	+	0.0452012i	−0.538634	−	0.842540i	$-0.681060\pi$
$929$	−2.05945e6	+	1.18902e6i	−0.0782908	+	0.0452012i	0.460344	+	0.887741i	$0.347726\pi$
$930$		0			0
$931$	1.11723e6	+	645030.i	0.0422441	+	0.0243897i
$932$	−5.84229e6	−	1.06614e7i	−0.220314	−	0.402045i
$933$		0			0
$934$	1.83238e7	−	4.69147e6i	0.687304	−	0.175971i
$935$	5.38143e7			2.01311
$936$		0			0
$937$	−1.36658e6			−0.0508495			−0.0254248	−	0.999677i	$-0.508094\pi$
$937$	−1.36658e6			−0.0508495			−0.0254248	+	0.999677i	$0.508094\pi$
$938$	1.27049e7	−	3.25286e6i	0.471481	−	0.120714i
$939$		0			0
$940$	3.40691e6	+	6.21717e6i	0.125759	+	0.229495i
$941$	−1.57768e7	−	9.10873e6i	−0.580824	−	0.335339i	0.180637	−	0.983550i	$-0.442184\pi$
$941$	−1.57768e7	−	9.10873e6i	−0.580824	−	0.335339i	−0.761461	+	0.648211i	$0.775517\pi$
$942$		0			0
$943$	−3.94648e7	+	2.27850e7i	−1.44521	+	0.834392i
$944$	1.87633e7	+	3.61301e7i	0.685299	+	1.31959i
$945$		0			0
$946$	4.36621e7	+	1.22227e7i	1.58627	+	0.444058i
$947$	−1.49933e6	−	2.59692e6i	−0.0543279	−	0.0940987i	0.837582	−	0.546311i	$-0.183968\pi$
$947$	−1.49933e6	−	2.59692e6i	−0.0543279	−	0.0940987i	−0.891910	+	0.452212i	$0.850635\pi$
$948$		0			0
$949$	−1.99384e6	+	3.45343e6i	−0.0718662	+	0.124476i
$950$	6.96481e6	−	6.81116e6i	0.250380	−	0.244857i
$951$		0			0
$952$	−2.66996e7	−	8.12059e6i	−0.954801	−	0.290399i
$953$			5.86700e6i			0.209259i	0.994511	+	0.104629i	$0.0333656\pi$
$953$			5.86700e6i			0.209259i	−0.994511	+	0.104629i	$0.966634\pi$
$954$		0			0
$955$			1.66328e7i			0.590144i
$956$	541201.	−	2.42600e7i	0.0191520	−	0.858513i
$957$		0			0
$958$	1.83554e7	+	1.87695e7i	0.646175	+	0.660751i
$959$	−2.07107e7	+	3.58721e7i	−0.727192	+	1.25953i
$960$		0			0
$961$	−1.06441e7	−	1.84362e7i	−0.371794	−	0.643966i
$962$	1.09282e6	−	3.90380e6i	0.0380726	−	0.136003i
$963$		0			0
$964$	−3.25763e7	−	1.97895e7i	−1.12904	−	0.685872i
$965$	2.25899e7	−	1.30423e7i	0.780901	−	0.450853i
$966$		0			0
$967$	2.39133e7	+	1.38063e7i	0.822381	+	0.474802i	0.851237	−	0.524782i	$-0.175853\pi$
$967$	2.39133e7	+	1.38063e7i	0.822381	+	0.474802i	−0.0288561	+	0.999584i	$0.509186\pi$
$968$	−6.08898e6	−	2.62009e7i	−0.208860	−	0.898728i
$969$		0			0
$970$	−1.20909e7	−	4.72241e7i	−0.412599	−	1.61152i
$971$	−3.42357e7			−1.16528			−0.582642	−	0.812729i	$-0.697981\pi$
$971$	−3.42357e7			−1.16528			−0.582642	+	0.812729i	$0.697981\pi$
$972$		0			0
$973$	1.42449e7			0.482368
$974$	6.89774e6	+	2.69410e7i	0.232975	+	0.909948i
$975$		0			0
$976$	−432699.	−	19315.2i	−0.0145399	−	0.000649044i
$977$	2.71573e7	+	1.56793e7i	0.910229	+	0.525521i	0.880505	−	0.474037i	$-0.157204\pi$
$977$	2.71573e7	+	1.56793e7i	0.910229	+	0.525521i	0.0297244	+	0.999558i	$0.490537\pi$
$978$		0			0
$979$	−3.58829e7	+	2.07170e7i	−1.19655	+	0.690828i
$980$	5.53121e6	−	9.10513e6i	0.183973	−	0.302845i
$981$		0			0
$982$	−1.05710e6	+	3.77618e6i	−0.0349814	+	0.124961i
$983$	3.01652e6	+	5.22477e6i	0.0995686	+	0.172458i	0.911506	−	0.411286i	$-0.134920\pi$
$983$	3.01652e6	+	5.22477e6i	0.0995686	+	0.172458i	−0.811938	+	0.583744i	$0.801587\pi$
$984$		0			0
$985$	1.04485e7	−	1.80973e7i	0.343132	−	0.594322i
$986$	−1.63762e7	−	1.67456e7i	−0.536438	−	0.548539i
$987$		0			0
$988$	4.00497e6	+	89344.3i	0.130529	+	0.00291189i
$989$		−	4.23200e7i		−	1.37580i
$990$		0			0
$991$			3.95516e7i			1.27932i	0.768657	+	0.639661i	$0.220925\pi$
$991$			3.95516e7i			1.27932i	−0.768657	+	0.639661i	$0.779075\pi$
$992$	1.16990e7	−	1.04620e7i	0.377458	−	0.337547i
$993$		0			0
$994$	3.99836e6	−	3.91016e6i	0.128356	−	0.125524i
$995$	−2.35390e7	+	4.07708e7i	−0.753756	+	1.30554i
$996$		0			0
$997$	8.17737e6	+	1.41636e7i	0.260541	+	0.451270i	0.966386	−	0.257096i	$-0.0827658\pi$
$997$	8.17737e6	+	1.41636e7i	0.260541	+	0.451270i	−0.705845	+	0.708366i	$0.749432\pi$
$998$	−2.51656e6	−	704482.i	−0.0799799	−	0.0223894i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.h.a.71.3		56
3.2	odd	2		36.6.h.a.23.26	yes	56
4.3	odd	2	inner	108.6.h.a.71.7		56
9.2	odd	6	inner	108.6.h.a.35.7		56
9.7	even	3		36.6.h.a.11.22	✓	56
12.11	even	2		36.6.h.a.23.22	yes	56
36.7	odd	6		36.6.h.a.11.26	yes	56
36.11	even	6	inner	108.6.h.a.35.3		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.6.h.a.11.22	✓	56	9.7	even	3
36.6.h.a.11.26	yes	56	36.7	odd	6
36.6.h.a.23.22	yes	56	12.11	even	2
36.6.h.a.23.26	yes	56	3.2	odd	2
108.6.h.a.35.3		56	36.11	even	6	inner
108.6.h.a.35.7		56	9.2	odd	6	inner
108.6.h.a.71.3		56	1.1	even	1	trivial
108.6.h.a.71.7		56	4.3	odd	2	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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	108.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-5.48009 + 1.40307i) q^{2} +(28.0628 - 15.3779i) q^{4} +(77.8058 + 44.9212i) q^{5} +(-124.034 + 71.6112i) q^{7} +(-132.210 + 123.647i) q^{8} +O(q^{10})\)	\(q+(-5.48009 + 1.40307i) q^{2} +(28.0628 - 15.3779i) q^{4} +(77.8058 + 44.9212i) q^{5} +(-124.034 + 71.6112i) q^{7} +(-132.210 + 123.647i) q^{8} +(-489.410 - 137.005i) q^{10} +(278.231 + 481.910i) q^{11} +(179.796 - 311.416i) q^{13} +(579.243 - 566.465i) q^{14} +(551.037 - 863.095i) q^{16} -1076.42i q^{17} +348.135i q^{19} +(2874.24 + 64.1196i) q^{20} +(-2200.88 - 2250.53i) q^{22} +(-1469.06 + 2544.48i) q^{23} +(2473.33 + 4283.93i) q^{25} +(-548.358 + 1958.85i) q^{26} +(-2379.51 + 3917.00i) q^{28} +(-3331.19 + 1923.26i) q^{29} +(-2346.41 - 1354.70i) q^{31} +(-1808.75 + 5502.99i) q^{32} +(1510.30 + 5898.87i) q^{34} -12867.4 q^{35} -1992.90 q^{37} +(-488.460 - 1907.81i) q^{38} +(-15841.1 + 3681.39i) q^{40} +(13432.0 + 7754.99i) q^{41} +(-12474.1 + 7201.91i) q^{43} +(15218.7 + 9245.10i) q^{44} +(4480.46 - 16005.2i) q^{46} +(1232.97 + 2135.56i) q^{47} +(1852.82 - 3209.17i) q^{49} +(-19564.7 - 20006.0i) q^{50} +(256.637 - 11504.1i) q^{52} +13364.2i q^{53} +49993.8i q^{55} +(7544.08 - 24804.1i) q^{56} +(15556.7 - 15213.6i) q^{58} +(-19878.8 + 34431.1i) q^{59} +(-211.489 - 366.310i) q^{61} +(14759.3 + 4131.70i) q^{62} +(2191.00 - 32694.7i) q^{64} +(27978.3 - 16153.3i) q^{65} +(14018.6 + 8093.63i) q^{67} +(-16553.1 - 30207.3i) q^{68} +(70514.7 - 18054.0i) q^{70} +6902.73 q^{71} -11089.5 q^{73} +(10921.3 - 2796.19i) q^{74} +(5353.60 + 9769.63i) q^{76} +(-69020.2 - 39848.8i) q^{77} +(64310.3 - 37129.6i) q^{79} +(81645.2 - 42400.5i) q^{80} +(-84489.6 - 23651.9i) q^{82} +(-48564.9 - 84116.9i) q^{83} +(48354.0 - 83751.6i) q^{85} +(58254.2 - 56969.2i) q^{86} +(-96371.4 - 29311.0i) q^{88} +74459.8i q^{89} +51501.6i q^{91} +(-2096.90 + 93996.2i) q^{92} +(-9753.11 - 9973.11i) q^{94} +(-15638.6 + 27086.9i) q^{95} +(47958.5 + 83066.5i) q^{97} +(-5650.89 + 20186.2i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) \) 56 * q + 3 * q^2 - q^4 + 6 * q^5	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5} - 68 q^{10} - 2 q^{13} + 1518 q^{14} - q^{16} + 1242 q^{20} + 63 q^{22} + 12498 q^{25} - 2052 q^{28} + 11946 q^{29} + 7233 q^{32} + 6361 q^{34} - 8 q^{37} + 14877 q^{38} - 1526 q^{40} + 43536 q^{41} - 26880 q^{46} + 38414 q^{49} - 38631 q^{50} + 24988 q^{52} - 21186 q^{56} - 3314 q^{58} - 2 q^{61} - 106342 q^{64} - 35970 q^{65} - 31413 q^{68} + 10524 q^{70} + 53620 q^{73} + 20406 q^{74} + 26193 q^{76} - 26178 q^{77} - 151286 q^{82} + 6248 q^{85} - 279237 q^{86} - 122541 q^{88} - 435804 q^{92} + 63480 q^{94} - 58148 q^{97}+O(q^{100}) \) 56 * q + 3 * q^2 - q^4 + 6 * q^5 - 68 * q^10 - 2 * q^13 + 1518 * q^14 - q^16 + 1242 * q^20 + 63 * q^22 + 12498 * q^25 - 2052 * q^28 + 11946 * q^29 + 7233 * q^32 + 6361 * q^34 - 8 * q^37 + 14877 * q^38 - 1526 * q^40 + 43536 * q^41 - 26880 * q^46 + 38414 * q^49 - 38631 * q^50 + 24988 * q^52 - 21186 * q^56 - 3314 * q^58 - 2 * q^61 - 106342 * q^64 - 35970 * q^65 - 31413 * q^68 + 10524 * q^70 + 53620 * q^73 + 20406 * q^74 + 26193 * q^76 - 26178 * q^77 - 151286 * q^82 + 6248 * q^85 - 279237 * q^86 - 122541 * q^88 - 435804 * q^92 + 63480 * q^94 - 58148 * q^97

Introduction

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