LMFDB - Embedded newform 245.6.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,6,Mod(1,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("245.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	245.a (trivial)

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:	yes
Analytic conductor:	$39.2940358542$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 128x^{3} + 288x^{2} + 3551x - 6510 $ x^5 - 2x^4 - 128x^3 + 288x^2 + 3551x - 6510
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-9.65317$ of defining polynomial
Character	$\chi$	$=$	245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.6532 q^{2} -22.7173 q^{3} +81.4900 q^{4} -25.0000 q^{5} +242.012 q^{6} -527.226 q^{8} +273.078 q^{9} +O(q^{10})$	\(q-10.6532 q^{2} -22.7173 q^{3} +81.4900 q^{4} -25.0000 q^{5} +242.012 q^{6} -527.226 q^{8} +273.078 q^{9} +266.329 q^{10} +521.603 q^{11} -1851.24 q^{12} +530.380 q^{13} +567.933 q^{15} +3008.94 q^{16} +1993.70 q^{17} -2909.14 q^{18} +2493.88 q^{19} -2037.25 q^{20} -5556.73 q^{22} -3557.19 q^{23} +11977.2 q^{24} +625.000 q^{25} -5650.23 q^{26} -683.281 q^{27} -4286.15 q^{29} -6050.29 q^{30} +5037.75 q^{31} -15183.6 q^{32} -11849.4 q^{33} -21239.2 q^{34} +22253.1 q^{36} -2620.52 q^{37} -26567.8 q^{38} -12048.8 q^{39} +13180.6 q^{40} +1829.50 q^{41} -5081.96 q^{43} +42505.5 q^{44} -6826.94 q^{45} +37895.4 q^{46} -4980.47 q^{47} -68355.2 q^{48} -6658.23 q^{50} -45291.5 q^{51} +43220.7 q^{52} +19053.8 q^{53} +7279.11 q^{54} -13040.1 q^{55} -56654.4 q^{57} +45661.1 q^{58} -8937.52 q^{59} +46280.9 q^{60} +13599.0 q^{61} -53668.0 q^{62} +65466.8 q^{64} -13259.5 q^{65} +126234. q^{66} -3376.76 q^{67} +162466. q^{68} +80810.0 q^{69} +46940.4 q^{71} -143973. q^{72} +9799.09 q^{73} +27916.9 q^{74} -14198.3 q^{75} +203227. q^{76} +128358. q^{78} +68534.8 q^{79} -75223.6 q^{80} -50835.5 q^{81} -19490.0 q^{82} -25551.0 q^{83} -49842.4 q^{85} +54139.0 q^{86} +97370.0 q^{87} -275003. q^{88} -112201. q^{89} +72728.5 q^{90} -289876. q^{92} -114444. q^{93} +53057.7 q^{94} -62347.1 q^{95} +344930. q^{96} +156847. q^{97} +142438. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 3 q^{2} + 7 q^{3} + 101 q^{4} - 125 q^{5} + 304 q^{6} - 675 q^{8} + 284 q^{9}+O(q^{10}) $ 5 * q - 3 * q^2 + 7 * q^3 + 101 * q^4 - 125 * q^5 + 304 * q^6 - 675 * q^8 + 284 * q^9	\( 5 q - 3 q^{2} + 7 q^{3} + 101 q^{4} - 125 q^{5} + 304 q^{6} - 675 q^{8} + 284 q^{9} + 75 q^{10} + 1033 q^{11} - 1226 q^{12} + 1117 q^{13} - 175 q^{15} + 297 q^{16} + 3403 q^{17} + 887 q^{18} + 2846 q^{19} - 2525 q^{20} - 1858 q^{22} - 2756 q^{23} + 13290 q^{24} + 3125 q^{25} + 2544 q^{26} + 3661 q^{27} + 485 q^{29} - 7600 q^{30} + 10726 q^{31} - 17383 q^{32} + 12597 q^{33} - 16414 q^{34} + 38165 q^{36} - 2660 q^{37} - 14378 q^{38} - 13171 q^{39} + 16875 q^{40} - 8334 q^{41} - 17294 q^{43} + 42876 q^{44} - 7100 q^{45} + 45724 q^{46} + 59799 q^{47} - 94218 q^{48} - 1875 q^{50} - 12049 q^{51} + 87974 q^{52} - 9250 q^{53} + 106342 q^{54} - 25825 q^{55} - 121778 q^{57} + 35868 q^{58} + 52994 q^{59} + 30650 q^{60} + 81540 q^{61} - 74048 q^{62} + 39745 q^{64} - 27925 q^{65} + 311614 q^{66} - 726 q^{67} + 276216 q^{68} + 21388 q^{69} + 3760 q^{71} - 154815 q^{72} + 90634 q^{73} - 57342 q^{74} + 4375 q^{75} + 43902 q^{76} + 152598 q^{78} + 68243 q^{79} - 7425 q^{80} + 17645 q^{81} + 191552 q^{82} - 133292 q^{83} - 85075 q^{85} - 88352 q^{86} + 216813 q^{87} - 273040 q^{88} + 102852 q^{89} - 22175 q^{90} - 140852 q^{92} + 184862 q^{93} + 332618 q^{94} - 71150 q^{95} + 245574 q^{96} + 186175 q^{97} + 454710 q^{99}+O(q^{100}) \) 5 * q - 3 * q^2 + 7 * q^3 + 101 * q^4 - 125 * q^5 + 304 * q^6 - 675 * q^8 + 284 * q^9 + 75 * q^10 + 1033 * q^11 - 1226 * q^12 + 1117 * q^13 - 175 * q^15 + 297 * q^16 + 3403 * q^17 + 887 * q^18 + 2846 * q^19 - 2525 * q^20 - 1858 * q^22 - 2756 * q^23 + 13290 * q^24 + 3125 * q^25 + 2544 * q^26 + 3661 * q^27 + 485 * q^29 - 7600 * q^30 + 10726 * q^31 - 17383 * q^32 + 12597 * q^33 - 16414 * q^34 + 38165 * q^36 - 2660 * q^37 - 14378 * q^38 - 13171 * q^39 + 16875 * q^40 - 8334 * q^41 - 17294 * q^43 + 42876 * q^44 - 7100 * q^45 + 45724 * q^46 + 59799 * q^47 - 94218 * q^48 - 1875 * q^50 - 12049 * q^51 + 87974 * q^52 - 9250 * q^53 + 106342 * q^54 - 25825 * q^55 - 121778 * q^57 + 35868 * q^58 + 52994 * q^59 + 30650 * q^60 + 81540 * q^61 - 74048 * q^62 + 39745 * q^64 - 27925 * q^65 + 311614 * q^66 - 726 * q^67 + 276216 * q^68 + 21388 * q^69 + 3760 * q^71 - 154815 * q^72 + 90634 * q^73 - 57342 * q^74 + 4375 * q^75 + 43902 * q^76 + 152598 * q^78 + 68243 * q^79 - 7425 * q^80 + 17645 * q^81 + 191552 * q^82 - 133292 * q^83 - 85075 * q^85 - 88352 * q^86 + 216813 * q^87 - 273040 * q^88 + 102852 * q^89 - 22175 * q^90 - 140852 * q^92 + 184862 * q^93 + 332618 * q^94 - 71150 * q^95 + 245574 * q^96 + 186175 * q^97 + 454710 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−10.6532	−1.88323	−0.941616	−	0.336689i	$-0.890693\pi$
$2$	−10.6532	−1.88323	−0.941616	+	0.336689i	$0.890693\pi$
$3$	−22.7173	−1.45732	−0.728659	−	0.684877i	$-0.759856\pi$
$3$	−22.7173	−1.45732	−0.728659	+	0.684877i	$0.759856\pi$
$4$	81.4900	2.54656
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	242.012	2.74447
$7$	0	0
$7$	0	0
$8$	−527.226	−2.91254
$9$	273.078	1.12378
$10$	266.329	0.842207
$11$	521.603	1.29975	0.649873	−	0.760043i	$-0.274822\pi$
$11$	521.603	1.29975	0.649873	+	0.760043i	$0.274822\pi$
$12$	−1851.24	−3.71115
$13$	530.380	0.870419	0.435210	−	0.900329i	$-0.356674\pi$
$13$	530.380	0.870419	0.435210	+	0.900329i	$0.356674\pi$
$14$	0	0
$15$	567.933	0.651732
$16$	3008.94	2.93842
$17$	1993.70	1.67316	0.836579	−	0.547846i	$-0.184552\pi$
$17$	1993.70	1.67316	0.836579	+	0.547846i	$0.184552\pi$
$18$	−2909.14	−2.11633
$19$	2493.88	1.58487	0.792433	−	0.609959i	$-0.208814\pi$
$19$	2493.88	1.58487	0.792433	+	0.609959i	$0.208814\pi$
$20$	−2037.25	−1.13886
$21$	0	0
$22$	−5556.73	−2.44772
$23$	−3557.19	−1.40213	−0.701065	−	0.713098i	$-0.747292\pi$
$23$	−3557.19	−1.40213	−0.701065	+	0.713098i	$0.747292\pi$
$24$	11977.2	4.24449
$25$	625.000	0.200000
$26$	−5650.23	−1.63920
$27$	−683.281	−0.180381
$28$	0	0
$29$	−4286.15	−0.946395	−0.473198	−	0.880956i	$-0.656900\pi$
$29$	−4286.15	−0.946395	−0.473198	+	0.880956i	$0.656900\pi$
$30$	−6050.29	−1.22736
$31$	5037.75	0.941526	0.470763	−	0.882260i	$-0.343979\pi$
$31$	5037.75	0.941526	0.470763	+	0.882260i	$0.343979\pi$
$32$	−15183.6	−2.62119
$33$	−11849.4	−1.89414
$34$	−21239.2	−3.15094
$35$	0	0
$36$	22253.1	2.86177
$37$	−2620.52	−0.314691	−0.157345	−	0.987544i	$-0.550294\pi$
$37$	−2620.52	−0.314691	−0.157345	+	0.987544i	$0.550294\pi$
$38$	−26567.8	−2.98467
$39$	−12048.8	−1.26848
$40$	13180.6	1.30253
$41$	1829.50	0.169970	0.0849851	−	0.996382i	$-0.472916\pi$
$41$	1829.50	0.169970	0.0849851	+	0.996382i	$0.472916\pi$
$42$	0	0
$43$	−5081.96	−0.419141	−0.209570	−	0.977794i	$-0.567207\pi$
$43$	−5081.96	−0.419141	−0.209570	+	0.977794i	$0.567207\pi$
$44$	42505.5	3.30989
$45$	−6826.94	−0.502568
$46$	37895.4	2.64053
$47$	−4980.47	−0.328871	−0.164435	−	0.986388i	$-0.552580\pi$
$47$	−4980.47	−0.328871	−0.164435	+	0.986388i	$0.552580\pi$
$48$	−68355.2	−4.28221
$49$	0	0
$50$	−6658.23	−0.376646
$51$	−45291.5	−2.43832
$52$	43220.7	2.21658
$53$	19053.8	0.931732	0.465866	−	0.884855i	$-0.345743\pi$
$53$	19053.8	0.931732	0.465866	+	0.884855i	$0.345743\pi$
$54$	7279.11	0.339699
$55$	−13040.1	−0.581264
$56$	0	0
$57$	−56654.4	−2.30965
$58$	45661.1	1.78228
$59$	−8937.52	−0.334262	−0.167131	−	0.985935i	$-0.553450\pi$
$59$	−8937.52	−0.334262	−0.167131	+	0.985935i	$0.553450\pi$
$60$	46280.9	1.65968
$61$	13599.0	0.467930	0.233965	−	0.972245i	$-0.424830\pi$
$61$	13599.0	0.467930	0.233965	+	0.972245i	$0.424830\pi$
$62$	−53668.0	−1.77311
$63$	0	0
$64$	65466.8	1.99789
$65$	−13259.5	−0.389263
$66$	126234.	3.56711
$67$	−3376.76	−0.0918994	−0.0459497	−	0.998944i	$-0.514631\pi$
$67$	−3376.76	−0.0918994	−0.0459497	+	0.998944i	$0.514631\pi$
$68$	162466.	4.26080
$69$	80810.0	2.04335
$70$	0	0
$71$	46940.4	1.10510	0.552549	−	0.833480i	$-0.313655\pi$
$71$	46940.4	1.10510	0.552549	+	0.833480i	$0.313655\pi$
$72$	−143973.	−3.27304
$73$	9799.09	0.215218	0.107609	−	0.994193i	$-0.465681\pi$
$73$	9799.09	0.215218	0.107609	+	0.994193i	$0.465681\pi$
$74$	27916.9	0.592635
$75$	−14198.3	−0.291464
$76$	203227.	4.03596
$77$	0	0
$78$	128358.	2.38884
$79$	68534.8	1.23550	0.617751	−	0.786374i	$-0.288044\pi$
$79$	68534.8	1.23550	0.617751	+	0.786374i	$0.288044\pi$
$80$	−75223.6	−1.31410
$81$	−50835.5	−0.860904
$82$	−19490.0	−0.320093
$83$	−25551.0	−0.407110	−0.203555	−	0.979063i	$-0.565250\pi$
$83$	−25551.0	−0.407110	−0.203555	+	0.979063i	$0.565250\pi$
$84$	0	0
$85$	−49842.4	−0.748259
$86$	54139.0	0.789339
$87$	97370.0	1.37920
$88$	−275003.	−3.78556
$89$	−112201.	−1.50149	−0.750743	−	0.660594i	$-0.770304\pi$
$89$	−112201.	−1.50149	−0.750743	+	0.660594i	$0.770304\pi$
$90$	72728.5	0.946452
$91$	0	0
$92$	−289876.	−3.57061
$93$	−114444.	−1.37210
$94$	53057.7	0.619340
$95$	−62347.1	−0.708773
$96$	344930.	3.81991
$97$	156847.	1.69257	0.846287	−	0.532727i	$-0.178833\pi$
$97$	156847.	1.69257	0.846287	+	0.532727i	$0.178833\pi$
$98$	0	0
$99$	142438.	1.46062
$100$	50931.3	0.509313
$101$	−75158.7	−0.733121	−0.366561	−	0.930394i	$-0.619465\pi$
$101$	−75158.7	−0.733121	−0.366561	+	0.930394i	$0.619465\pi$
$102$	482498.	4.59193
$103$	57981.5	0.538513	0.269257	−	0.963068i	$-0.413222\pi$
$103$	57981.5	0.538513	0.269257	+	0.963068i	$0.413222\pi$
$104$	−279630.	−2.53513
$105$	0	0
$106$	−202983.	−1.75467
$107$	−75351.7	−0.636259	−0.318129	−	0.948047i	$-0.603055\pi$
$107$	−75351.7	−0.636259	−0.318129	+	0.948047i	$0.603055\pi$
$108$	−55680.6	−0.459351
$109$	−69501.5	−0.560309	−0.280155	−	0.959955i	$-0.590386\pi$
$109$	−69501.5	−0.560309	−0.280155	+	0.959955i	$0.590386\pi$
$110$	138918.	1.09466
$111$	59531.3	0.458604
$112$	0	0
$113$	191120.	1.40802	0.704010	−	0.710190i	$-0.251391\pi$
$113$	191120.	1.40802	0.704010	+	0.710190i	$0.251391\pi$
$114$	603549.	4.34961
$115$	88929.9	0.627051
$116$	−349279.	−2.41006
$117$	144835.	0.978156
$118$	95212.9	0.629493
$119$	0	0
$120$	−299429.	−1.89819
$121$	111019.	0.689340
$122$	−144872.	−0.881222
$123$	−41561.4	−0.247701
$124$	410526.	2.39765
$125$	−15625.0	−0.0894427
$126$	0	0
$127$	183545.	1.00980	0.504899	−	0.863179i	$-0.331530\pi$
$127$	183545.	1.00980	0.504899	+	0.863179i	$0.331530\pi$
$128$	−211556.	−1.14130
$129$	115449.	0.610821
$130$	141256.	0.733073
$131$	−129380.	−0.658701	−0.329350	−	0.944208i	$-0.606830\pi$
$131$	−129380.	−0.658701	−0.329350	+	0.944208i	$0.606830\pi$
$132$	−965611.	−4.82356
$133$	0	0
$134$	35973.2	0.173068
$135$	17082.0	0.0806687
$136$	−1.05113e6	−4.87313
$137$	−193279.	−0.879798	−0.439899	−	0.898047i	$-0.644986\pi$
$137$	−193279.	−0.879798	−0.439899	+	0.898047i	$0.644986\pi$
$138$	−860883.	−3.84810
$139$	200701.	0.881072	0.440536	−	0.897735i	$-0.354788\pi$
$139$	200701.	0.881072	0.440536	+	0.897735i	$0.354788\pi$
$140$	0	0
$141$	113143.	0.479269
$142$	−500064.	−2.08116
$143$	276648.	1.13132
$144$	821675.	3.30213
$145$	107154.	0.423241
$146$	−104391.	−0.405306
$147$	0	0
$148$	−213546.	−0.801379
$149$	−81934.7	−0.302345	−0.151172	−	0.988507i	$-0.548305\pi$
$149$	−81934.7	−0.302345	−0.151172	+	0.988507i	$0.548305\pi$
$150$	151257.	0.548894
$151$	−173292.	−0.618496	−0.309248	−	0.950981i	$-0.600077\pi$
$151$	−173292.	−0.618496	−0.309248	+	0.950981i	$0.600077\pi$
$152$	−1.31484e6	−4.61598
$153$	544434.	1.88025
$154$	0	0
$155$	−125944.	−0.421063
$156$	−981858.	−3.23026
$157$	436373.	1.41289	0.706446	−	0.707767i	$-0.250297\pi$
$157$	436373.	1.41289	0.706446	+	0.707767i	$0.250297\pi$
$158$	−730113.	−2.32674
$159$	−432851.	−1.35783
$160$	379589.	1.17223
$161$	0	0
$162$	541559.	1.62128
$163$	−188828.	−0.556670	−0.278335	−	0.960484i	$-0.589783\pi$
$163$	−188828.	−0.556670	−0.278335	+	0.960484i	$0.589783\pi$
$164$	149086.	0.432840
$165$	296236.	0.847087
$166$	272199.	0.766683
$167$	76400.4	0.211985	0.105992	−	0.994367i	$-0.466198\pi$
$167$	76400.4	0.211985	0.105992	+	0.994367i	$0.466198\pi$
$168$	0	0
$169$	−89990.3	−0.242370
$170$	530980.	1.40915
$171$	681024.	1.78103
$172$	−414129.	−1.06737
$173$	−522030.	−1.32611	−0.663056	−	0.748570i	$-0.730741\pi$
$173$	−522030.	−1.32611	−0.663056	+	0.748570i	$0.730741\pi$
$174$	−1.03730e6	−2.59735
$175$	0	0
$176$	1.56947e6	3.81920
$177$	203037.	0.487126
$178$	1.19530e6	2.82765
$179$	776384.	1.81111	0.905553	−	0.424232i	$-0.139456\pi$
$179$	776384.	1.81111	0.905553	+	0.424232i	$0.139456\pi$
$180$	−556327.	−1.27982
$181$	11307.3	0.0256545	0.0128273	−	0.999918i	$-0.495917\pi$
$181$	11307.3	0.0256545	0.0128273	+	0.999918i	$0.495917\pi$
$182$	0	0
$183$	−308932.	−0.681924
$184$	1.87544e6	4.08375
$185$	65513.1	0.140734
$186$	1.21919e6	2.58399
$187$	1.03992e6	2.17468
$188$	−405858.	−0.837490
$189$	0	0
$190$	664194.	1.33478
$191$	281505.	0.558346	0.279173	−	0.960241i	$-0.409940\pi$
$191$	281505.	0.558346	0.279173	+	0.960241i	$0.409940\pi$
$192$	−1.48723e6	−2.91156
$193$	56411.2	0.109011	0.0545057	−	0.998513i	$-0.482642\pi$
$193$	56411.2	0.109011	0.0545057	+	0.998513i	$0.482642\pi$
$194$	−1.67092e6	−3.18751
$195$	301220.	0.567281
$196$	0	0
$197$	−591591.	−1.08607	−0.543033	−	0.839711i	$-0.682724\pi$
$197$	−591591.	−1.08607	−0.543033	+	0.839711i	$0.682724\pi$
$198$	−1.51742e6	−2.75069
$199$	−876529.	−1.56904	−0.784519	−	0.620105i	$-0.787090\pi$
$199$	−876529.	−1.56904	−0.784519	+	0.620105i	$0.787090\pi$
$200$	−329516.	−0.582507
$201$	76710.9	0.133927
$202$	800678.	1.38064
$203$	0	0
$204$	−3.69080e6	−6.20934
$205$	−45737.5	−0.0760130
$206$	−617687.	−1.01415
$207$	−971390.	−1.57568
$208$	1.59588e6	2.55766
$209$	1.30082e6	2.05992
$210$	0	0
$211$	−325243.	−0.502924	−0.251462	−	0.967867i	$-0.580911\pi$
$211$	−325243.	−0.502924	−0.251462	+	0.967867i	$0.580911\pi$
$212$	1.55269e6	2.37272
$213$	−1.06636e6	−1.61048
$214$	802735.	1.19822
$215$	127049.	0.187445
$216$	360243.	0.525366
$217$	0	0
$218$	740411.	1.05519
$219$	−222609.	−0.313641
$220$	−1.06264e6	−1.48023
$221$	1.05742e6	1.45635
$222$	−634197.	−0.863658
$223$	274917.	0.370202	0.185101	−	0.982720i	$-0.440739\pi$
$223$	274917.	0.370202	0.185101	+	0.982720i	$0.440739\pi$
$224$	0	0
$225$	170673.	0.224755
$226$	−2.03603e6	−2.65163
$227$	797132.	1.02675	0.513376	−	0.858164i	$-0.328395\pi$
$227$	797132.	1.02675	0.513376	+	0.858164i	$0.328395\pi$
$228$	−4.61677e6	−5.88168
$229$	−248992.	−0.313759	−0.156879	−	0.987618i	$-0.550143\pi$
$229$	−248992.	−0.313759	−0.156879	+	0.987618i	$0.550143\pi$
$230$	−947385.	−1.18088
$231$	0	0
$232$	2.25977e6	2.75641
$233$	−589865.	−0.711808	−0.355904	−	0.934523i	$-0.615827\pi$
$233$	−589865.	−0.711808	−0.355904	+	0.934523i	$0.615827\pi$
$234$	−1.54295e6	−1.84210
$235$	124512.	0.147075
$236$	−728319.	−0.851219
$237$	−1.55693e6	−1.80052
$238$	0	0
$239$	−303701.	−0.343915	−0.171958	−	0.985104i	$-0.555009\pi$
$239$	−303701.	−0.343915	−0.171958	+	0.985104i	$0.555009\pi$
$240$	1.70888e6	1.91506
$241$	−557910.	−0.618759	−0.309380	−	0.950939i	$-0.600121\pi$
$241$	−557910.	−0.618759	−0.309380	+	0.950939i	$0.600121\pi$
$242$	−1.18270e6	−1.29819
$243$	1.32088e6	1.43499
$244$	1.10818e6	1.19161
$245$	0	0
$246$	442761.	0.466478
$247$	1.32271e6	1.37950
$248$	−2.65603e6	−2.74223
$249$	580450.	0.593289
$250$	166456.	0.168441
$251$	1.26644e6	1.26882	0.634411	−	0.772996i	$-0.281243\pi$
$251$	1.26644e6	1.26882	0.634411	+	0.772996i	$0.281243\pi$
$252$	0	0
$253$	−1.85544e6	−1.82241
$254$	−1.95534e6	−1.90168
$255$	1.13229e6	1.09045
$256$	158798.	0.151442
$257$	1.33548e6	1.26126	0.630630	−	0.776084i	$-0.282797\pi$
$257$	1.33548e6	1.26126	0.630630	+	0.776084i	$0.282797\pi$
$258$	−1.22989e6	−1.15032
$259$	0	0
$260$	−1.08052e6	−0.991284
$261$	−1.17045e6	−1.06354
$262$	1.37830e6	1.24049
$263$	853053.	0.760478	0.380239	−	0.924888i	$-0.375842\pi$
$263$	853053.	0.760478	0.380239	+	0.924888i	$0.375842\pi$
$264$	6.24733e6	5.51676
$265$	−476344.	−0.416683
$266$	0	0
$267$	2.54891e6	2.18814
$268$	−275172.	−0.234028
$269$	1.45318e6	1.22444	0.612221	−	0.790686i	$-0.290276\pi$
$269$	1.45318e6	1.22444	0.612221	+	0.790686i	$0.290276\pi$
$270$	−181978.	−0.151918
$271$	−121179.	−0.100232	−0.0501158	−	0.998743i	$-0.515959\pi$
$271$	−121179.	−0.100232	−0.0501158	+	0.998743i	$0.515959\pi$
$272$	5.99892e6	4.91644
$273$	0	0
$274$	2.05903e6	1.65686
$275$	326002.	0.259949
$276$	6.58521e6	5.20352
$277$	1.95114e6	1.52788	0.763938	−	0.645290i	$-0.223263\pi$
$277$	1.95114e6	1.52788	0.763938	+	0.645290i	$0.223263\pi$
$278$	−2.13810e6	−1.65926
$279$	1.37570e6	1.05806
$280$	0	0
$281$	−1.57688e6	−1.19133	−0.595667	−	0.803231i	$-0.703112\pi$
$281$	−1.57688e6	−1.19133	−0.595667	+	0.803231i	$0.703112\pi$
$282$	−1.20533e6	−0.902575
$283$	−2.46307e6	−1.82815	−0.914073	−	0.405549i	$-0.867080\pi$
$283$	−2.46307e6	−1.82815	−0.914073	+	0.405549i	$0.867080\pi$
$284$	3.82517e6	2.81420
$285$	1.41636e6	1.03291
$286$	−2.94718e6	−2.13055
$287$	0	0
$288$	−4.14629e6	−2.94563
$289$	2.55497e6	1.79946
$290$	−1.14153e6	−0.797061
$291$	−3.56315e6	−2.46662
$292$	798528.	0.548066
$293$	−335444.	−0.228271	−0.114136	−	0.993465i	$-0.536410\pi$
$293$	−335444.	−0.228271	−0.114136	+	0.993465i	$0.536410\pi$
$294$	0	0
$295$	223438.	0.149487
$296$	1.38161e6	0.916548
$297$	−356402.	−0.234449
$298$	872864.	0.569385
$299$	−1.88666e6	−1.22044
$300$	−1.15702e6	−0.742230
$301$	0	0
$302$	1.84611e6	1.16477
$303$	1.70741e6	1.06839
$304$	7.50396e6	4.65700
$305$	−339974.	−0.209265
$306$	−5.79995e6	−3.54096
$307$	1.76328e6	1.06777	0.533883	−	0.845558i	$-0.320732\pi$
$307$	1.76328e6	1.06777	0.533883	+	0.845558i	$0.320732\pi$
$308$	0	0
$309$	−1.31719e6	−0.784785
$310$	1.34170e6	0.792960
$311$	−3.26685e6	−1.91526	−0.957630	−	0.288000i	$-0.907010\pi$
$311$	−3.26685e6	−1.91526	−0.957630	+	0.288000i	$0.907010\pi$
$312$	6.35244e6	3.69449
$313$	−1.44329e6	−0.832707	−0.416354	−	0.909203i	$-0.636692\pi$
$313$	−1.44329e6	−0.832707	−0.416354	+	0.909203i	$0.636692\pi$
$314$	−4.64876e6	−2.66080
$315$	0	0
$316$	5.58490e6	3.14628
$317$	233126.	0.130299	0.0651497	−	0.997876i	$-0.479248\pi$
$317$	233126.	0.130299	0.0651497	+	0.997876i	$0.479248\pi$
$318$	4.61123e6	2.55711
$319$	−2.23567e6	−1.23007
$320$	−1.63667e6	−0.893483
$321$	1.71179e6	0.927231
$322$	0	0
$323$	4.97205e6	2.65173
$324$	−4.14259e6	−2.19235
$325$	331487.	0.174084
$326$	2.01162e6	1.04834
$327$	1.57889e6	0.816549
$328$	−964560.	−0.495045
$329$	0	0
$330$	−3.15585e6	−1.59526
$331$	209816.	0.105261	0.0526306	−	0.998614i	$-0.483239\pi$
$331$	209816.	0.105261	0.0526306	+	0.998614i	$0.483239\pi$
$332$	−2.08215e6	−1.03673
$333$	−715606.	−0.353642
$334$	−813906.	−0.399216
$335$	84418.9	0.0410987
$336$	0	0
$337$	−40475.5	−0.0194141	−0.00970706	−	0.999953i	$-0.503090\pi$
$337$	−40475.5	−0.0194141	−0.00970706	+	0.999953i	$0.503090\pi$
$338$	958682.	0.456439
$339$	−4.34173e6	−2.05193
$340$	−4.06166e6	−1.90549
$341$	2.62771e6	1.22374
$342$	−7.25506e6	−3.35410
$343$	0	0
$344$	2.67934e6	1.22076
$345$	−2.02025e6	−0.913813
$346$	5.56127e6	2.49738
$347$	639325.	0.285035	0.142517	−	0.989792i	$-0.454480\pi$
$347$	639325.	0.285035	0.142517	+	0.989792i	$0.454480\pi$
$348$	7.93468e6	3.51222
$349$	−1.08171e6	−0.475388	−0.237694	−	0.971340i	$-0.576391\pi$
$349$	−1.08171e6	−0.475388	−0.237694	+	0.971340i	$0.576391\pi$
$350$	0	0
$351$	−362399.	−0.157007
$352$	−7.91979e6	−3.40688
$353$	−2.10988e6	−0.901198	−0.450599	−	0.892727i	$-0.648790\pi$
$353$	−2.10988e6	−0.901198	−0.450599	+	0.892727i	$0.648790\pi$
$354$	−2.16298e6	−0.917371
$355$	−1.17351e6	−0.494215
$356$	−9.14326e6	−3.82363
$357$	0	0
$358$	−8.27095e6	−3.41073
$359$	1.83822e6	0.752767	0.376383	−	0.926464i	$-0.377168\pi$
$359$	1.83822e6	0.752767	0.376383	+	0.926464i	$0.377168\pi$
$360$	3.59934e6	1.46375
$361$	3.74336e6	1.51180
$362$	−120459.	−0.0483134
$363$	−2.52205e6	−1.00459
$364$	0	0
$365$	−244977.	−0.0962484
$366$	3.29111e6	1.28422
$367$	2.28999e6	0.887502	0.443751	−	0.896150i	$-0.353648\pi$
$367$	2.28999e6	0.887502	0.443751	+	0.896150i	$0.353648\pi$
$368$	−1.07034e7	−4.12005
$369$	499596.	0.191008
$370$	−697922.	−0.265035
$371$	0	0
$372$	−9.32606e6	−3.49415
$373$	−1.85793e6	−0.691443	−0.345722	−	0.938337i	$-0.612366\pi$
$373$	−1.85793e6	−0.691443	−0.345722	+	0.938337i	$0.612366\pi$
$374$	−1.10784e7	−4.09543
$375$	354958.	0.130346
$376$	2.62583e6	0.957848
$377$	−2.27329e6	−0.823761
$378$	0	0
$379$	5.54663e6	1.98350	0.991748	−	0.128205i	$-0.0409214\pi$
$379$	5.54663e6	1.98350	0.991748	+	0.128205i	$0.0409214\pi$
$380$	−5.08067e6	−1.80494
$381$	−4.16966e6	−1.47160
$382$	−2.99893e6	−1.05150
$383$	541761.	0.188717	0.0943584	−	0.995538i	$-0.469920\pi$
$383$	541761.	0.188717	0.0943584	+	0.995538i	$0.469920\pi$
$384$	4.80598e6	1.66324
$385$	0	0
$386$	−600958.	−0.205294
$387$	−1.38777e6	−0.471020
$388$	1.27815e7	4.31025
$389$	−4.09886e6	−1.37338	−0.686688	−	0.726953i	$-0.740936\pi$
$389$	−4.09886e6	−1.37338	−0.686688	+	0.726953i	$0.740936\pi$
$390$	−3.20895e6	−1.06832
$391$	−7.09197e6	−2.34598
$392$	0	0
$393$	2.93916e6	0.959936
$394$	6.30232e6	2.04531
$395$	−1.71337e6	−0.552533
$396$	1.16073e7	3.71957
$397$	4.55573e6	1.45071	0.725357	−	0.688373i	$-0.241675\pi$
$397$	4.55573e6	1.45071	0.725357	+	0.688373i	$0.241675\pi$
$398$	9.33781e6	2.95486
$399$	0	0
$400$	1.88059e6	0.587684
$401$	−1.70845e6	−0.530569	−0.265285	−	0.964170i	$-0.585466\pi$
$401$	−1.70845e6	−0.530569	−0.265285	+	0.964170i	$0.585466\pi$
$402$	−817214.	−0.252215
$403$	2.67192e6	0.819522
$404$	−6.12468e6	−1.86694
$405$	1.27089e6	0.385008
$406$	0	0
$407$	−1.36687e6	−0.409018
$408$	2.38788e7	7.10171
$409$	3.59252e6	1.06192	0.530958	−	0.847398i	$-0.321832\pi$
$409$	3.59252e6	1.06192	0.530958	+	0.847398i	$0.321832\pi$
$410$	487250.	0.143150
$411$	4.39078e6	1.28215
$412$	4.72491e6	1.37136
$413$	0	0
$414$	1.03484e7	2.96737
$415$	638774.	0.182065
$416$	−8.05305e6	−2.28154
$417$	−4.55938e6	−1.28400
$418$	−1.38578e7	−3.87931
$419$	6.02602e6	1.67686	0.838428	−	0.545012i	$-0.183475\pi$
$419$	6.02602e6	1.67686	0.838428	+	0.545012i	$0.183475\pi$
$420$	0	0
$421$	−6.37071e6	−1.75179	−0.875896	−	0.482500i	$-0.839729\pi$
$421$	−6.37071e6	−1.75179	−0.875896	+	0.482500i	$0.839729\pi$
$422$	3.46487e6	0.947122
$423$	−1.36005e6	−0.369577
$424$	−1.00456e7	−2.71371
$425$	1.24606e6	0.334632
$426$	1.13601e7	3.03291
$427$	0	0
$428$	−6.14041e6	−1.62027
$429$	−6.28470e6	−1.64870
$430$	−1.35347e6	−0.353003
$431$	4.65069e6	1.20594	0.602968	−	0.797765i	$-0.293985\pi$
$431$	4.65069e6	1.20594	0.602968	+	0.797765i	$0.293985\pi$
$432$	−2.05595e6	−0.530034
$433$	−940843.	−0.241156	−0.120578	−	0.992704i	$-0.538475\pi$
$433$	−940843.	−0.241156	−0.120578	+	0.992704i	$0.538475\pi$
$434$	0	0
$435$	−2.43425e6	−0.616796
$436$	−5.66368e6	−1.42686
$437$	−8.87123e6	−2.22219
$438$	2.37149e6	0.590659
$439$	−1.16009e6	−0.287297	−0.143649	−	0.989629i	$-0.545883\pi$
$439$	−1.16009e6	−0.287297	−0.143649	+	0.989629i	$0.545883\pi$
$440$	6.87506e6	1.69295
$441$	0	0
$442$	−1.12648e7	−2.74264
$443$	5.18593e6	1.25550	0.627751	−	0.778415i	$-0.283976\pi$
$443$	5.18593e6	1.25550	0.627751	+	0.778415i	$0.283976\pi$
$444$	4.85121e6	1.16786
$445$	2.80502e6	0.671485
$446$	−2.92873e6	−0.697176
$447$	1.86134e6	0.440612
$448$	0	0
$449$	−7.56677e6	−1.77131	−0.885655	−	0.464344i	$-0.846290\pi$
$449$	−7.56677e6	−1.77131	−0.885655	+	0.464344i	$0.846290\pi$
$450$	−1.81821e6	−0.423266
$451$	954274.	0.220918
$452$	1.55743e7	3.58561
$453$	3.93674e6	0.901345
$454$	−8.49198e6	−1.93361
$455$	0	0
$456$	2.98697e7	6.72695
$457$	−6.61968e6	−1.48268	−0.741338	−	0.671132i	$-0.765808\pi$
$457$	−6.61968e6	−1.48268	−0.741338	+	0.671132i	$0.765808\pi$
$458$	2.65255e6	0.590881
$459$	−1.36226e6	−0.301805
$460$	7.24690e6	1.59683
$461$	869895.	0.190640	0.0953202	−	0.995447i	$-0.469613\pi$
$461$	869895.	0.190640	0.0953202	+	0.995447i	$0.469613\pi$
$462$	0	0
$463$	−2.81299e6	−0.609840	−0.304920	−	0.952378i	$-0.598630\pi$
$463$	−2.81299e6	−0.609840	−0.304920	+	0.952378i	$0.598630\pi$
$464$	−1.28968e7	−2.78091
$465$	2.86111e6	0.613623
$466$	6.28393e6	1.34050
$467$	−1.98975e6	−0.422188	−0.211094	−	0.977466i	$-0.567703\pi$
$467$	−1.98975e6	−0.422188	−0.211094	+	0.977466i	$0.567703\pi$
$468$	1.18026e7	2.49094
$469$	0	0
$470$	−1.32644e6	−0.276977
$471$	−9.91324e6	−2.05903
$472$	4.71209e6	0.973551
$473$	−2.65077e6	−0.544777
$474$	1.65862e7	3.39080
$475$	1.55868e6	0.316973
$476$	0	0
$477$	5.20316e6	1.04706
$478$	3.23538e6	0.647672
$479$	9.97073e6	1.98558	0.992792	−	0.119849i	$-0.0382409\pi$
$479$	9.97073e6	1.98558	0.992792	+	0.119849i	$0.0382409\pi$
$480$	−8.62325e6	−1.70831
$481$	−1.38987e6	−0.273913
$482$	5.94351e6	1.16527
$483$	0	0
$484$	9.04693e6	1.75545
$485$	−3.92118e6	−0.756942
$486$	−1.40716e7	−2.70242
$487$	−9.19578e6	−1.75698	−0.878489	−	0.477763i	$-0.841448\pi$
$487$	−9.19578e6	−1.75698	−0.878489	+	0.477763i	$0.841448\pi$
$488$	−7.16972e6	−1.36286
$489$	4.28967e6	0.811245
$490$	0	0
$491$	−2.52488e6	−0.472648	−0.236324	−	0.971674i	$-0.575943\pi$
$491$	−2.52488e6	−0.472648	−0.236324	+	0.971674i	$0.575943\pi$
$492$	−3.38684e6	−0.630786
$493$	−8.54529e6	−1.58347
$494$	−1.40910e7	−2.59791
$495$	−3.56095e6	−0.653211
$496$	1.51583e7	2.76660
$497$	0	0
$498$	−6.18363e6	−1.11730
$499$	461817.	0.0830268	0.0415134	−	0.999138i	$-0.486782\pi$
$499$	461817.	0.0830268	0.0415134	+	0.999138i	$0.486782\pi$
$500$	−1.27328e6	−0.227772
$501$	−1.73561e6	−0.308929
$502$	−1.34916e7	−2.38948
$503$	−2.01939e6	−0.355876	−0.177938	−	0.984042i	$-0.556943\pi$
$503$	−2.01939e6	−0.355876	−0.177938	+	0.984042i	$0.556943\pi$
$504$	0	0
$505$	1.87897e6	0.327862
$506$	1.97664e7	3.43202
$507$	2.04434e6	0.353210
$508$	1.49571e7	2.57151
$509$	4.01050e6	0.686127	0.343063	−	0.939312i	$-0.388535\pi$
$509$	4.01050e6	0.686127	0.343063	+	0.939312i	$0.388535\pi$
$510$	−1.20624e7	−2.05357
$511$	0	0
$512$	5.07807e6	0.856099
$513$	−1.70402e6	−0.285879
$514$	−1.42271e7	−2.37524
$515$	−1.44954e6	−0.240830
$516$	9.40790e6	1.55550
$517$	−2.59783e6	−0.427449
$518$	0	0
$519$	1.18591e7	1.93257
$520$	6.99074e6	1.13374
$521$	458812.	0.0740526	0.0370263	−	0.999314i	$-0.488211\pi$
$521$	458812.	0.0740526	0.0370263	+	0.999314i	$0.488211\pi$
$522$	1.24690e7	2.00289
$523$	1.16085e7	1.85576	0.927879	−	0.372881i	$-0.121630\pi$
$523$	1.16085e7	1.85576	0.927879	+	0.372881i	$0.121630\pi$
$524$	−1.05432e7	−1.67742
$525$	0	0
$526$	−9.08772e6	−1.43216
$527$	1.00437e7	1.57532
$528$	−3.56543e7	−5.56579
$529$	6.21729e6	0.965966
$530$	5.07457e6	0.784711
$531$	−2.44064e6	−0.375636
$532$	0	0
$533$	970330.	0.147945
$534$	−2.71539e7	−4.12078
$535$	1.88379e6	0.284544
$536$	1.78031e6	0.267660
$537$	−1.76374e7	−2.63936
$538$	−1.54810e7	−2.30591
$539$	0	0
$540$	1.39202e6	0.205428
$541$	4.23130e6	0.621557	0.310779	−	0.950482i	$-0.399410\pi$
$541$	4.23130e6	0.621557	0.310779	+	0.950482i	$0.399410\pi$
$542$	1.29094e6	0.188759
$543$	−256873.	−0.0373868
$544$	−3.02714e7	−4.38567
$545$	1.73754e6	0.250578
$546$	0	0
$547$	5.93158e6	0.847622	0.423811	−	0.905751i	$-0.360692\pi$
$547$	5.93158e6	0.847622	0.423811	+	0.905751i	$0.360692\pi$
$548$	−1.57503e7	−2.24046
$549$	3.71357e6	0.525849
$550$	−3.47295e6	−0.489545
$551$	−1.06892e7	−1.49991
$552$	−4.26051e7	−5.95133
$553$	0	0
$554$	−2.07858e7	−2.87734
$555$	−1.48828e6	−0.205094
$556$	1.63551e7	2.24371
$557$	1.11020e7	1.51623	0.758113	−	0.652123i	$-0.226122\pi$
$557$	1.11020e7	1.51623	0.758113	+	0.652123i	$0.226122\pi$
$558$	−1.46555e7	−1.99258
$559$	−2.69537e6	−0.364828
$560$	0	0
$561$	−2.36242e7	−3.16920
$562$	1.67988e7	2.24356
$563$	9.30268e6	1.23691	0.618454	−	0.785821i	$-0.287759\pi$
$563$	9.30268e6	1.23691	0.618454	+	0.785821i	$0.287759\pi$
$564$	9.22002e6	1.22049
$565$	−4.77799e6	−0.629686
$566$	2.62395e7	3.44282
$567$	0	0
$568$	−2.47482e7	−3.21864
$569$	6.55304e6	0.848521	0.424260	−	0.905540i	$-0.360534\pi$
$569$	6.55304e6	0.848521	0.424260	+	0.905540i	$0.360534\pi$
$570$	−1.50887e7	−1.94521
$571$	−3.67926e6	−0.472249	−0.236124	−	0.971723i	$-0.575877\pi$
$571$	−3.67926e6	−0.472249	−0.236124	+	0.971723i	$0.575877\pi$
$572$	2.25440e7	2.88099
$573$	−6.39506e6	−0.813688
$574$	0	0
$575$	−2.22325e6	−0.280426
$576$	1.78775e7	2.24518
$577$	−3.60398e6	−0.450653	−0.225327	−	0.974283i	$-0.572345\pi$
$577$	−3.60398e6	−0.450653	−0.225327	+	0.974283i	$0.572345\pi$
$578$	−2.72185e7	−3.38880
$579$	−1.28151e6	−0.158864
$580$	8.73196e6	1.07781
$581$	0	0
$582$	3.79589e7	4.64522
$583$	9.93851e6	1.21102
$584$	−5.16633e6	−0.626831
$585$	−3.62087e6	−0.437445
$586$	3.57354e6	0.429888
$587$	1.02724e7	1.23048	0.615241	−	0.788339i	$-0.289059\pi$
$587$	1.02724e7	1.23048	0.615241	+	0.788339i	$0.289059\pi$
$588$	0	0
$589$	1.25636e7	1.49219
$590$	−2.38032e6	−0.281518
$591$	1.34394e7	1.58274
$592$	−7.88500e6	−0.924693
$593$	9.26511e6	1.08197	0.540983	−	0.841034i	$-0.318052\pi$
$593$	9.26511e6	1.08197	0.540983	+	0.841034i	$0.318052\pi$
$594$	3.79681e6	0.441522
$595$	0	0
$596$	−6.67686e6	−0.769939
$597$	1.99124e7	2.28659
$598$	2.00990e7	2.29837
$599$	1.25992e7	1.43475	0.717376	−	0.696686i	$-0.245343\pi$
$599$	1.25992e7	1.43475	0.717376	+	0.696686i	$0.245343\pi$
$600$	7.48573e6	0.848899
$601$	2.27047e6	0.256407	0.128204	−	0.991748i	$-0.459079\pi$
$601$	2.27047e6	0.256407	0.128204	+	0.991748i	$0.459079\pi$
$602$	0	0
$603$	−922116.	−0.103274
$604$	−1.41216e7	−1.57504
$605$	−2.77547e6	−0.308282
$606$	−1.81893e7	−2.01203
$607$	−1.57067e6	−0.173027	−0.0865134	−	0.996251i	$-0.527573\pi$
$607$	−1.57067e6	−0.173027	−0.0865134	+	0.996251i	$0.527573\pi$
$608$	−3.78660e7	−4.15423
$609$	0	0
$610$	3.62180e6	0.394094
$611$	−2.64154e6	−0.286256
$612$	4.43659e7	4.78819
$613$	5.43708e6	0.584406	0.292203	−	0.956356i	$-0.405612\pi$
$613$	5.43708e6	0.584406	0.292203	+	0.956356i	$0.405612\pi$
$614$	−1.87846e7	−2.01085
$615$	1.03903e6	0.110775
$616$	0	0
$617$	1.47526e7	1.56011	0.780057	−	0.625709i	$-0.215190\pi$
$617$	1.47526e7	1.56011	0.780057	+	0.625709i	$0.215190\pi$
$618$	1.40322e7	1.47793
$619$	1.72859e7	1.81329	0.906643	−	0.421900i	$-0.138637\pi$
$619$	1.72859e7	1.81329	0.906643	+	0.421900i	$0.138637\pi$
$620$	−1.02632e7	−1.07226
$621$	2.43056e6	0.252917
$622$	3.48023e7	3.60688
$623$	0	0
$624$	−3.62542e7	−3.72732
$625$	390625.	0.0400000
$626$	1.53756e7	1.56818
$627$	−2.95511e7	−3.00196
$628$	3.55601e7	3.59802
$629$	−5.22453e6	−0.526527
$630$	0	0
$631$	6.78983e6	0.678868	0.339434	−	0.940630i	$-0.389764\pi$
$631$	6.78983e6	0.678868	0.339434	+	0.940630i	$0.389764\pi$
$632$	−3.61333e7	−3.59845
$633$	7.38866e6	0.732920
$634$	−2.48353e6	−0.245384
$635$	−4.58864e6	−0.451595
$636$	−3.52730e7	−3.45780
$637$	0	0
$638$	2.38170e7	2.31651
$639$	1.28184e7	1.24188
$640$	5.28889e6	0.510405
$641$	5.60185e6	0.538501	0.269251	−	0.963070i	$-0.413224\pi$
$641$	5.60185e6	0.538501	0.269251	+	0.963070i	$0.413224\pi$
$642$	−1.82360e7	−1.74619
$643$	1.19459e6	0.113944	0.0569721	−	0.998376i	$-0.481855\pi$
$643$	1.19459e6	0.113944	0.0569721	+	0.998376i	$0.481855\pi$
$644$	0	0
$645$	−2.88621e6	−0.273168
$646$	−5.29681e7	−4.99382
$647$	−1.21183e7	−1.13811	−0.569053	−	0.822301i	$-0.692690\pi$
$647$	−1.21183e7	−1.13811	−0.569053	+	0.822301i	$0.692690\pi$
$648$	2.68018e7	2.50741
$649$	−4.66184e6	−0.434456
$650$	−3.53139e6	−0.327840
$651$	0	0
$652$	−1.53876e7	−1.41760
$653$	−1.82241e7	−1.67249	−0.836246	−	0.548354i	$-0.815254\pi$
$653$	−1.82241e7	−1.67249	−0.836246	+	0.548354i	$0.815254\pi$
$654$	−1.68202e7	−1.53775
$655$	3.23449e6	0.294580
$656$	5.50486e6	0.499444
$657$	2.67591e6	0.241857
$658$	0	0
$659$	−7.05291e6	−0.632638	−0.316319	−	0.948653i	$-0.602447\pi$
$659$	−7.05291e6	−0.632638	−0.316319	+	0.948653i	$0.602447\pi$
$660$	2.41403e7	2.15716
$661$	7.25490e6	0.645844	0.322922	−	0.946426i	$-0.395335\pi$
$661$	7.25490e6	0.645844	0.322922	+	0.946426i	$0.395335\pi$
$662$	−2.23521e6	−0.198231
$663$	−2.40217e7	−2.12236
$664$	1.34711e7	1.18572
$665$	0	0
$666$	7.62347e6	0.665989
$667$	1.52467e7	1.32697
$668$	6.22587e6	0.539832
$669$	−6.24537e6	−0.539502
$670$	−899329.	−0.0773983
$671$	7.09327e6	0.608191
$672$	0	0
$673$	−9.68815e6	−0.824524	−0.412262	−	0.911065i	$-0.635261\pi$
$673$	−9.68815e6	−0.824524	−0.412262	+	0.911065i	$0.635261\pi$
$674$	431193.	0.0365613
$675$	−427051.	−0.0360761
$676$	−7.33331e6	−0.617211
$677$	−1.30038e7	−1.09043	−0.545216	−	0.838296i	$-0.683552\pi$
$677$	−1.30038e7	−1.09043	−0.545216	+	0.838296i	$0.683552\pi$
$678$	4.62532e7	3.86427
$679$	0	0
$680$	2.62782e7	2.17933
$681$	−1.81087e7	−1.49630
$682$	−2.79934e7	−2.30460
$683$	2.08435e7	1.70969	0.854846	−	0.518881i	$-0.173651\pi$
$683$	2.08435e7	1.70969	0.854846	+	0.518881i	$0.173651\pi$
$684$	5.54966e7	4.53551
$685$	4.83197e6	0.393458
$686$	0	0
$687$	5.65643e6	0.457246
$688$	−1.52913e7	−1.23161
$689$	1.01057e7	0.810998
$690$	2.15221e7	1.72092
$691$	−322717.	−0.0257114	−0.0128557	−	0.999917i	$-0.504092\pi$
$691$	−322717.	−0.0257114	−0.0128557	+	0.999917i	$0.504092\pi$
$692$	−4.25402e7	−3.37703
$693$	0	0
$694$	−6.81084e6	−0.536787
$695$	−5.01751e6	−0.394028
$696$	−5.13359e7	−4.01697
$697$	3.64747e6	0.284387
$698$	1.15237e7	0.895265
$699$	1.34002e7	1.03733
$700$	0	0
$701$	3.05080e6	0.234487	0.117244	−	0.993103i	$-0.462594\pi$
$701$	3.05080e6	0.234487	0.117244	+	0.993103i	$0.462594\pi$
$702$	3.86069e6	0.295680
$703$	−6.53528e6	−0.498742
$704$	3.41477e7	2.59675
$705$	−2.82857e6	−0.214336
$706$	2.24769e7	1.69716
$707$	0	0
$708$	1.65455e7	1.24050
$709$	7.46074e6	0.557400	0.278700	−	0.960378i	$-0.410097\pi$
$709$	7.46074e6	0.557400	0.278700	+	0.960378i	$0.410097\pi$
$710$	1.25016e7	0.930721
$711$	1.87153e7	1.38843
$712$	5.91552e7	4.37314
$713$	−1.79203e7	−1.32014
$714$	0	0
$715$	−6.91619e6	−0.505944
$716$	6.32676e7	4.61210
$717$	6.89928e6	0.501194
$718$	−1.95828e7	−1.41763
$719$	2.36672e7	1.70735	0.853677	−	0.520802i	$-0.174367\pi$
$719$	2.36672e7	1.70735	0.853677	+	0.520802i	$0.174367\pi$
$720$	−2.05419e7	−1.47676
$721$	0	0
$722$	−3.98787e7	−2.84707
$723$	1.26742e7	0.901729
$724$	921435.	0.0653309
$725$	−2.67884e6	−0.189279
$726$	2.68679e7	1.89187
$727$	−4.49081e6	−0.315129	−0.157565	−	0.987509i	$-0.550364\pi$
$727$	−4.49081e6	−0.315129	−0.157565	+	0.987509i	$0.550364\pi$
$728$	0	0
$729$	−1.76540e7	−1.23033
$730$	2.60978e6	0.181258
$731$	−1.01319e7	−0.701289
$732$	−2.51749e7	−1.73656
$733$	−2.04848e7	−1.40822	−0.704111	−	0.710090i	$-0.748654\pi$
$733$	−2.04848e7	−1.40822	−0.704111	+	0.710090i	$0.748654\pi$
$734$	−2.43957e7	−1.67137
$735$	0	0
$736$	5.40109e7	3.67525
$737$	−1.76133e6	−0.119446
$738$	−5.32228e6	−0.359713
$739$	4.52276e6	0.304644	0.152322	−	0.988331i	$-0.451325\pi$
$739$	4.52276e6	0.304644	0.152322	+	0.988331i	$0.451325\pi$
$740$	5.33866e6	0.358388
$741$	−3.00484e7	−2.01037
$742$	0	0
$743$	3.74564e6	0.248917	0.124458	−	0.992225i	$-0.460281\pi$
$743$	3.74564e6	0.248917	0.124458	+	0.992225i	$0.460281\pi$
$744$	6.03379e7	3.99630
$745$	2.04837e6	0.135213
$746$	1.97928e7	1.30215
$747$	−6.97739e6	−0.457501
$748$	8.47430e7	5.53796
$749$	0	0
$750$	−3.78143e6	−0.245473
$751$	−1.99005e7	−1.28755	−0.643775	−	0.765215i	$-0.722633\pi$
$751$	−1.99005e7	−1.28755	−0.643775	+	0.765215i	$0.722633\pi$
$752$	−1.49859e7	−0.966361
$753$	−2.87702e7	−1.84908
$754$	2.42177e7	1.55133
$755$	4.33231e6	0.276600
$756$	0	0
$757$	2.47334e7	1.56872	0.784359	−	0.620307i	$-0.212992\pi$
$757$	2.47334e7	1.56872	0.784359	+	0.620307i	$0.212992\pi$
$758$	−5.90892e7	−3.73538
$759$	4.21508e7	2.65583
$760$	3.28710e7	2.06433
$761$	2.14534e7	1.34287	0.671435	−	0.741064i	$-0.265678\pi$
$761$	2.14534e7	1.34287	0.671435	+	0.741064i	$0.265678\pi$
$762$	4.44201e7	2.77136
$763$	0	0
$764$	2.29399e7	1.42186
$765$	−1.36108e7	−0.840875
$766$	−5.77147e6	−0.355397
$767$	−4.74028e6	−0.290948
$768$	−3.60747e6	−0.220699
$769$	−1.60988e7	−0.981696	−0.490848	−	0.871245i	$-0.663313\pi$
$769$	−1.60988e7	−0.981696	−0.490848	+	0.871245i	$0.663313\pi$
$770$	0	0
$771$	−3.03385e7	−1.83806
$772$	4.59695e6	0.277605
$773$	−7.48739e6	−0.450694	−0.225347	−	0.974279i	$-0.572352\pi$
$773$	−7.48739e6	−0.450694	−0.225347	+	0.974279i	$0.572352\pi$
$774$	1.47841e7	0.887040
$775$	3.14859e6	0.188305
$776$	−8.26939e7	−4.92969
$777$	0	0
$778$	4.36659e7	2.58638
$779$	4.56256e6	0.269380
$780$	2.45465e7	1.44462
$781$	2.44843e7	1.43635
$782$	7.55519e7	4.41803
$783$	2.92865e6	0.170711
$784$	0	0
$785$	−1.09093e7	−0.631864
$786$	−3.13114e7	−1.80778
$787$	−911554.	−0.0524621	−0.0262310	−	0.999656i	$-0.508351\pi$
$787$	−911554.	−0.0524621	−0.0262310	+	0.999656i	$0.508351\pi$
$788$	−4.82088e7	−2.76574
$789$	−1.93791e7	−1.10826
$790$	1.82528e7	1.04055
$791$	0	0
$792$	−7.50970e7	−4.25412
$793$	7.21262e6	0.407296
$794$	−4.85329e7	−2.73203
$795$	1.08213e7	0.607240
$796$	−7.14284e7	−3.99566
$797$	2.62845e7	1.46573	0.732864	−	0.680375i	$-0.238183\pi$
$797$	2.62845e7	1.46573	0.732864	+	0.680375i	$0.238183\pi$
$798$	0	0
$799$	−9.92954e6	−0.550253
$800$	−9.48972e6	−0.524238
$801$	−3.06396e7	−1.68733
$802$	1.82004e7	0.999185
$803$	5.11124e6	0.279729
$804$	6.25117e6	0.341053
$805$	0	0
$806$	−2.84644e7	−1.54335
$807$	−3.30124e7	−1.78440
$808$	3.96256e7	2.13524
$809$	−2.30873e7	−1.24023	−0.620114	−	0.784512i	$-0.712914\pi$
$809$	−2.30873e7	−1.24023	−0.620114	+	0.784512i	$0.712914\pi$
$810$	−1.35390e7	−0.725059
$811$	3.22681e7	1.72274	0.861372	−	0.507975i	$-0.169606\pi$
$811$	3.22681e7	1.72274	0.861372	+	0.507975i	$0.169606\pi$
$812$	0	0
$813$	2.75287e6	0.146069
$814$	1.45615e7	0.770276
$815$	4.72070e6	0.248950
$816$	−1.36280e8	−7.16482
$817$	−1.26738e7	−0.664282
$818$	−3.82717e7	−1.99984
$819$	0	0
$820$	−3.72715e6	−0.193572
$821$	7.91982e6	0.410070	0.205035	−	0.978755i	$-0.434269\pi$
$821$	7.91982e6	0.410070	0.205035	+	0.978755i	$0.434269\pi$
$822$	−4.67758e7	−2.41458
$823$	7.48092e6	0.384995	0.192498	−	0.981297i	$-0.438341\pi$
$823$	7.48092e6	0.384995	0.192498	+	0.981297i	$0.438341\pi$
$824$	−3.05693e7	−1.56844
$825$	−7.40590e6	−0.378829
$826$	0	0
$827$	2.38814e6	0.121422	0.0607109	−	0.998155i	$-0.480663\pi$
$827$	2.38814e6	0.121422	0.0607109	+	0.998155i	$0.480663\pi$
$828$	−7.91586e7	−4.01257
$829$	−2.19954e7	−1.11159	−0.555796	−	0.831319i	$-0.687586\pi$
$829$	−2.19954e7	−1.11159	−0.555796	+	0.831319i	$0.687586\pi$
$830$	−6.80497e6	−0.342871
$831$	−4.43246e7	−2.22660
$832$	3.47223e7	1.73900
$833$	0	0
$834$	4.85719e7	2.41807
$835$	−1.91001e6	−0.0948024
$836$	1.06004e8	5.24572
$837$	−3.44220e6	−0.169833
$838$	−6.41963e7	−3.15791
$839$	8.59396e6	0.421491	0.210746	−	0.977541i	$-0.432411\pi$
$839$	8.59396e6	0.421491	0.210746	+	0.977541i	$0.432411\pi$
$840$	0	0
$841$	−2.14005e6	−0.104336
$842$	6.78683e7	3.29903
$843$	3.58226e7	1.73615
$844$	−2.65041e7	−1.28073
$845$	2.24976e6	0.108391
$846$	1.44889e7	0.695999
$847$	0	0
$848$	5.73317e7	2.73782
$849$	5.59544e7	2.66419
$850$	−1.32745e7	−0.630189
$851$	9.32171e6	0.441237
$852$	−8.68978e7	−4.10119
$853$	−1.27571e7	−0.600316	−0.300158	−	0.953889i	$-0.597039\pi$
$853$	−1.27571e7	−0.600316	−0.300158	+	0.953889i	$0.597039\pi$
$854$	0	0
$855$	−1.70256e7	−0.796502
$856$	3.97274e7	1.85313
$857$	1.39381e7	0.648265	0.324133	−	0.946012i	$-0.394928\pi$
$857$	1.39381e7	0.648265	0.324133	+	0.946012i	$0.394928\pi$
$858$	6.69520e7	3.10488
$859$	−2.82949e7	−1.30836	−0.654178	−	0.756341i	$-0.726985\pi$
$859$	−2.82949e7	−1.30836	−0.654178	+	0.756341i	$0.726985\pi$
$860$	1.03532e7	0.477342
$861$	0	0
$862$	−4.95446e7	−2.27106
$863$	−3.92969e7	−1.79610	−0.898052	−	0.439889i	$-0.855018\pi$
$863$	−3.92969e7	−1.79610	−0.898052	+	0.439889i	$0.855018\pi$
$864$	1.03746e7	0.472812
$865$	1.30508e7	0.593055
$866$	1.00230e7	0.454152
$867$	−5.80422e7	−2.62238
$868$	0	0
$869$	3.57480e7	1.60584
$870$	2.59325e7	1.16157
$871$	−1.79096e6	−0.0799910
$872$	3.66430e7	1.63192
$873$	4.28315e7	1.90207
$874$	9.45067e7	4.18489
$875$	0	0
$876$	−1.81404e7	−0.798707
$877$	−3.88777e7	−1.70687	−0.853436	−	0.521197i	$-0.825486\pi$
$877$	−3.88777e7	−1.70687	−0.853436	+	0.521197i	$0.825486\pi$
$878$	1.23587e7	0.541047
$879$	7.62040e6	0.332664
$880$	−3.92369e7	−1.70800
$881$	−3.50457e7	−1.52123	−0.760615	−	0.649203i	$-0.775102\pi$
$881$	−3.50457e7	−1.52123	−0.760615	+	0.649203i	$0.775102\pi$
$882$	0	0
$883$	−4.91508e6	−0.212143	−0.106071	−	0.994359i	$-0.533827\pi$
$883$	−4.91508e6	−0.212143	−0.106071	+	0.994359i	$0.533827\pi$
$884$	8.61689e7	3.70868
$885$	−5.07592e6	−0.217849
$886$	−5.52466e7	−2.36440
$887$	−1.33480e6	−0.0569650	−0.0284825	−	0.999594i	$-0.509067\pi$
$887$	−1.33480e6	−0.0569650	−0.0284825	+	0.999594i	$0.509067\pi$
$888$	−3.13864e7	−1.33570
$889$	0	0
$890$	−2.98824e7	−1.26456
$891$	−2.65160e7	−1.11896
$892$	2.24030e7	0.942743
$893$	−1.24207e7	−0.521216
$894$	−1.98291e7	−0.829775
$895$	−1.94096e7	−0.809952
$896$	0	0
$897$	4.28600e7	1.77857
$898$	8.06101e7	3.33579
$899$	−2.15926e7	−0.891056
$900$	1.39082e7	0.572353
$901$	3.79874e7	1.55894
$902$	−1.01660e7	−0.416040
$903$	0	0
$904$	−1.00763e8	−4.10091
$905$	−282684.	−0.0114731
$906$	−4.19388e7	−1.69744
$907$	−2.17668e7	−0.878571	−0.439285	−	0.898348i	$-0.644768\pi$
$907$	−2.17668e7	−0.878571	−0.439285	+	0.898348i	$0.644768\pi$
$908$	6.49583e7	2.61469
$909$	−2.05241e7	−0.823864
$910$	0	0
$911$	−3.93270e7	−1.56998	−0.784991	−	0.619507i	$-0.787333\pi$
$911$	−3.93270e7	−1.56998	−0.784991	+	0.619507i	$0.787333\pi$
$912$	−1.70470e8	−6.78673
$913$	−1.33275e7	−0.529140
$914$	7.05205e7	2.79222
$915$	7.72331e6	0.304965
$916$	−2.02903e7	−0.799007
$917$	0	0
$918$	1.45123e7	0.568370
$919$	−2.67596e7	−1.04518	−0.522589	−	0.852585i	$-0.675034\pi$
$919$	−2.67596e7	−1.04518	−0.522589	+	0.852585i	$0.675034\pi$
$920$	−4.68861e7	−1.82631
$921$	−4.00571e7	−1.55608
$922$	−9.26714e6	−0.359020
$923$	2.48962e7	0.961899
$924$	0	0
$925$	−1.63783e6	−0.0629381
$926$	2.99673e7	1.14847
$927$	1.58334e7	0.605168
$928$	6.50790e7	2.48068
$929$	2.19549e7	0.834627	0.417314	−	0.908762i	$-0.362972\pi$
$929$	2.19549e7	0.834627	0.417314	+	0.908762i	$0.362972\pi$
$930$	−3.04798e7	−1.15559
$931$	0	0
$932$	−4.80681e7	−1.81266
$933$	7.42141e7	2.79114
$934$	2.11971e7	0.795078
$935$	−2.59980e7	−0.972547
$936$	−7.63606e7	−2.84892
$937$	−4.24909e7	−1.58106	−0.790528	−	0.612426i	$-0.790194\pi$
$937$	−4.24909e7	−1.58106	−0.790528	+	0.612426i	$0.790194\pi$
$938$	0	0
$939$	3.27877e7	1.21352
$940$	1.01465e7	0.374537
$941$	3.16745e7	1.16610	0.583049	−	0.812437i	$-0.301860\pi$
$941$	3.16745e7	1.16610	0.583049	+	0.812437i	$0.301860\pi$
$942$	1.05607e8	3.87764
$943$	−6.50789e6	−0.238320
$944$	−2.68925e7	−0.982202
$945$	0	0
$946$	2.82391e7	1.02594
$947$	1.19386e7	0.432591	0.216296	−	0.976328i	$-0.430603\pi$
$947$	1.19386e7	0.432591	0.216296	+	0.976328i	$0.430603\pi$
$948$	−1.26874e8	−4.58514
$949$	5.19724e6	0.187330
$950$	−1.66049e7	−0.596934
$951$	−5.29600e6	−0.189888
$952$	0	0
$953$	3.86319e7	1.37789	0.688943	−	0.724815i	$-0.258075\pi$
$953$	3.86319e7	1.37789	0.688943	+	0.724815i	$0.258075\pi$
$954$	−5.54301e7	−1.97185
$955$	−7.03764e6	−0.249700
$956$	−2.47486e7	−0.875801
$957$	5.07885e7	1.79261
$958$	−1.06220e8	−3.73932
$959$	0	0
$960$	3.71808e7	1.30209
$961$	−3.25024e6	−0.113529
$962$	1.48065e7	0.515841
$963$	−2.05769e7	−0.715012
$964$	−4.54641e7	−1.57571
$965$	−1.41028e6	−0.0487514
$966$	0	0
$967$	2.82154e7	0.970330	0.485165	−	0.874423i	$-0.338760\pi$
$967$	2.82154e7	0.970330	0.485165	+	0.874423i	$0.338760\pi$
$968$	−5.85320e7	−2.00773
$969$	−1.12952e8	−3.86441
$970$	4.17730e7	1.42550
$971$	−6.54166e6	−0.222659	−0.111329	−	0.993784i	$-0.535511\pi$
$971$	−6.54166e6	−0.222659	−0.111329	+	0.993784i	$0.535511\pi$
$972$	1.07639e8	3.65430
$973$	0	0
$974$	9.79642e7	3.30880
$975$	−7.53051e6	−0.253696
$976$	4.09185e7	1.37498
$977$	−2.54615e7	−0.853391	−0.426695	−	0.904395i	$-0.640322\pi$
$977$	−2.54615e7	−0.853391	−0.426695	+	0.904395i	$0.640322\pi$
$978$	−4.56986e7	−1.52776
$979$	−5.85244e7	−1.95155
$980$	0	0
$981$	−1.89793e7	−0.629662
$982$	2.68980e7	0.890106
$983$	−5.70076e7	−1.88169	−0.940846	−	0.338834i	$-0.889968\pi$
$983$	−5.70076e7	−1.88169	−0.940846	+	0.338834i	$0.889968\pi$
$984$	2.19122e7	0.721438
$985$	1.47898e7	0.485703
$986$	9.10344e7	2.98204
$987$	0	0
$988$	1.07787e8	3.51298
$989$	1.80775e7	0.587689
$990$	3.79354e7	1.23015
$991$	−1.17123e7	−0.378843	−0.189421	−	0.981896i	$-0.560661\pi$
$991$	−1.17123e7	−0.378843	−0.189421	+	0.981896i	$0.560661\pi$
$992$	−7.64909e7	−2.46792
$993$	−4.76646e6	−0.153399
$994$	0	0
$995$	2.19132e7	0.701695
$996$	4.73009e7	1.51085
$997$	−1.50849e7	−0.480622	−0.240311	−	0.970696i	$-0.577249\pi$
$997$	−1.50849e7	−0.480622	−0.240311	+	0.970696i	$0.577249\pi$
$998$	−4.91981e6	−0.156359
$999$	1.79055e6	0.0567641

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.6.a.g.1.1	yes	5
7.6	odd	2		245.6.a.f.1.1	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.6.a.f.1.1	✓	5	7.6	odd	2
245.6.a.g.1.1	yes	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

\(f(q)\)	\(=\)	\(q-10.6532 q^{2} -22.7173 q^{3} +81.4900 q^{4} -25.0000 q^{5} +242.012 q^{6} -527.226 q^{8} +273.078 q^{9} +O(q^{10})\)	\(q-10.6532 q^{2} -22.7173 q^{3} +81.4900 q^{4} -25.0000 q^{5} +242.012 q^{6} -527.226 q^{8} +273.078 q^{9} +266.329 q^{10} +521.603 q^{11} -1851.24 q^{12} +530.380 q^{13} +567.933 q^{15} +3008.94 q^{16} +1993.70 q^{17} -2909.14 q^{18} +2493.88 q^{19} -2037.25 q^{20} -5556.73 q^{22} -3557.19 q^{23} +11977.2 q^{24} +625.000 q^{25} -5650.23 q^{26} -683.281 q^{27} -4286.15 q^{29} -6050.29 q^{30} +5037.75 q^{31} -15183.6 q^{32} -11849.4 q^{33} -21239.2 q^{34} +22253.1 q^{36} -2620.52 q^{37} -26567.8 q^{38} -12048.8 q^{39} +13180.6 q^{40} +1829.50 q^{41} -5081.96 q^{43} +42505.5 q^{44} -6826.94 q^{45} +37895.4 q^{46} -4980.47 q^{47} -68355.2 q^{48} -6658.23 q^{50} -45291.5 q^{51} +43220.7 q^{52} +19053.8 q^{53} +7279.11 q^{54} -13040.1 q^{55} -56654.4 q^{57} +45661.1 q^{58} -8937.52 q^{59} +46280.9 q^{60} +13599.0 q^{61} -53668.0 q^{62} +65466.8 q^{64} -13259.5 q^{65} +126234. q^{66} -3376.76 q^{67} +162466. q^{68} +80810.0 q^{69} +46940.4 q^{71} -143973. q^{72} +9799.09 q^{73} +27916.9 q^{74} -14198.3 q^{75} +203227. q^{76} +128358. q^{78} +68534.8 q^{79} -75223.6 q^{80} -50835.5 q^{81} -19490.0 q^{82} -25551.0 q^{83} -49842.4 q^{85} +54139.0 q^{86} +97370.0 q^{87} -275003. q^{88} -112201. q^{89} +72728.5 q^{90} -289876. q^{92} -114444. q^{93} +53057.7 q^{94} -62347.1 q^{95} +344930. q^{96} +156847. q^{97} +142438. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 3 q^{2} + 7 q^{3} + 101 q^{4} - 125 q^{5} + 304 q^{6} - 675 q^{8} + 284 q^{9}+O(q^{10}) \) 5 * q - 3 * q^2 + 7 * q^3 + 101 * q^4 - 125 * q^5 + 304 * q^6 - 675 * q^8 + 284 * q^9	\( 5 q - 3 q^{2} + 7 q^{3} + 101 q^{4} - 125 q^{5} + 304 q^{6} - 675 q^{8} + 284 q^{9} + 75 q^{10} + 1033 q^{11} - 1226 q^{12} + 1117 q^{13} - 175 q^{15} + 297 q^{16} + 3403 q^{17} + 887 q^{18} + 2846 q^{19} - 2525 q^{20} - 1858 q^{22} - 2756 q^{23} + 13290 q^{24} + 3125 q^{25} + 2544 q^{26} + 3661 q^{27} + 485 q^{29} - 7600 q^{30} + 10726 q^{31} - 17383 q^{32} + 12597 q^{33} - 16414 q^{34} + 38165 q^{36} - 2660 q^{37} - 14378 q^{38} - 13171 q^{39} + 16875 q^{40} - 8334 q^{41} - 17294 q^{43} + 42876 q^{44} - 7100 q^{45} + 45724 q^{46} + 59799 q^{47} - 94218 q^{48} - 1875 q^{50} - 12049 q^{51} + 87974 q^{52} - 9250 q^{53} + 106342 q^{54} - 25825 q^{55} - 121778 q^{57} + 35868 q^{58} + 52994 q^{59} + 30650 q^{60} + 81540 q^{61} - 74048 q^{62} + 39745 q^{64} - 27925 q^{65} + 311614 q^{66} - 726 q^{67} + 276216 q^{68} + 21388 q^{69} + 3760 q^{71} - 154815 q^{72} + 90634 q^{73} - 57342 q^{74} + 4375 q^{75} + 43902 q^{76} + 152598 q^{78} + 68243 q^{79} - 7425 q^{80} + 17645 q^{81} + 191552 q^{82} - 133292 q^{83} - 85075 q^{85} - 88352 q^{86} + 216813 q^{87} - 273040 q^{88} + 102852 q^{89} - 22175 q^{90} - 140852 q^{92} + 184862 q^{93} + 332618 q^{94} - 71150 q^{95} + 245574 q^{96} + 186175 q^{97} + 454710 q^{99}+O(q^{100}) \) 5 * q - 3 * q^2 + 7 * q^3 + 101 * q^4 - 125 * q^5 + 304 * q^6 - 675 * q^8 + 284 * q^9 + 75 * q^10 + 1033 * q^11 - 1226 * q^12 + 1117 * q^13 - 175 * q^15 + 297 * q^16 + 3403 * q^17 + 887 * q^18 + 2846 * q^19 - 2525 * q^20 - 1858 * q^22 - 2756 * q^23 + 13290 * q^24 + 3125 * q^25 + 2544 * q^26 + 3661 * q^27 + 485 * q^29 - 7600 * q^30 + 10726 * q^31 - 17383 * q^32 + 12597 * q^33 - 16414 * q^34 + 38165 * q^36 - 2660 * q^37 - 14378 * q^38 - 13171 * q^39 + 16875 * q^40 - 8334 * q^41 - 17294 * q^43 + 42876 * q^44 - 7100 * q^45 + 45724 * q^46 + 59799 * q^47 - 94218 * q^48 - 1875 * q^50 - 12049 * q^51 + 87974 * q^52 - 9250 * q^53 + 106342 * q^54 - 25825 * q^55 - 121778 * q^57 + 35868 * q^58 + 52994 * q^59 + 30650 * q^60 + 81540 * q^61 - 74048 * q^62 + 39745 * q^64 - 27925 * q^65 + 311614 * q^66 - 726 * q^67 + 276216 * q^68 + 21388 * q^69 + 3760 * q^71 - 154815 * q^72 + 90634 * q^73 - 57342 * q^74 + 4375 * q^75 + 43902 * q^76 + 152598 * q^78 + 68243 * q^79 - 7425 * q^80 + 17645 * q^81 + 191552 * q^82 - 133292 * q^83 - 85075 * q^85 - 88352 * q^86 + 216813 * q^87 - 273040 * q^88 + 102852 * q^89 - 22175 * q^90 - 140852 * q^92 + 184862 * q^93 + 332618 * q^94 - 71150 * q^95 + 245574 * q^96 + 186175 * q^97 + 454710 * q^99

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