LMFDB - Embedded newform 1075.6.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,6,Mod(1,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, 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("1075.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1075.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:	$172.412606299$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} - 256 x^{8} + 266 x^{7} + 21986 x^{6} - 10450 x^{5} - 719484 x^{4} + 384582 x^{3} + \cdots - 22734604 $ x^10 - 2x^9 - 256x^8 + 266x^7 + 21986x^6 - 10450x^5 - 719484x^4 + 384582x^3 + 8437093x^2 - 5752252*x - 22734604
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-9.70631$ of defining polynomial
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.7063 q^{2} -18.3440 q^{3} +82.6251 q^{4} +196.397 q^{6} +96.4803 q^{7} -542.008 q^{8} +93.5034 q^{9} +O(q^{10})$	\(q-10.7063 q^{2} -18.3440 q^{3} +82.6251 q^{4} +196.397 q^{6} +96.4803 q^{7} -542.008 q^{8} +93.5034 q^{9} -684.136 q^{11} -1515.68 q^{12} -344.655 q^{13} -1032.95 q^{14} +3158.90 q^{16} -1319.32 q^{17} -1001.08 q^{18} +739.016 q^{19} -1769.84 q^{21} +7324.58 q^{22} -3165.85 q^{23} +9942.61 q^{24} +3689.99 q^{26} +2742.37 q^{27} +7971.70 q^{28} +7073.21 q^{29} -3791.93 q^{31} -16476.0 q^{32} +12549.8 q^{33} +14125.1 q^{34} +7725.73 q^{36} +12682.3 q^{37} -7912.13 q^{38} +6322.37 q^{39} -10882.5 q^{41} +18948.4 q^{42} -1849.00 q^{43} -56526.8 q^{44} +33894.6 q^{46} -3873.59 q^{47} -57947.0 q^{48} -7498.54 q^{49} +24201.7 q^{51} -28477.2 q^{52} -6479.38 q^{53} -29360.7 q^{54} -52293.1 q^{56} -13556.5 q^{57} -75728.0 q^{58} +34750.3 q^{59} +26452.9 q^{61} +40597.6 q^{62} +9021.24 q^{63} +75311.8 q^{64} -134362. q^{66} +58007.3 q^{67} -109009. q^{68} +58074.5 q^{69} -23477.7 q^{71} -50679.6 q^{72} -45184.4 q^{73} -135781. q^{74} +61061.3 q^{76} -66005.7 q^{77} -67689.2 q^{78} +17895.9 q^{79} -73027.4 q^{81} +116512. q^{82} -39799.2 q^{83} -146233. q^{84} +19796.0 q^{86} -129751. q^{87} +370808. q^{88} -30802.0 q^{89} -33252.5 q^{91} -261579. q^{92} +69559.2 q^{93} +41471.9 q^{94} +302235. q^{96} -22524.5 q^{97} +80281.7 q^{98} -63969.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 8 q^{2} - 28 q^{3} + 202 q^{4} + 75 q^{6} - 60 q^{7} - 294 q^{8} + 1356 q^{9}+O(q^{10}) $ 10 * q - 8 * q^2 - 28 * q^3 + 202 * q^4 + 75 * q^6 - 60 * q^7 - 294 * q^8 + 1356 * q^9	\( 10 q - 8 q^{2} - 28 q^{3} + 202 q^{4} + 75 q^{6} - 60 q^{7} - 294 q^{8} + 1356 q^{9} + 745 q^{11} - 4627 q^{12} - 1917 q^{13} + 1936 q^{14} + 5354 q^{16} - 4017 q^{17} + 2725 q^{18} - 2404 q^{19} - 228 q^{21} + 5836 q^{22} - 1733 q^{23} - 10711 q^{24} - 1484 q^{26} + 2324 q^{27} + 15028 q^{28} + 6996 q^{29} - 4899 q^{31} + 7554 q^{32} + 15734 q^{33} - 27033 q^{34} + 4433 q^{36} - 1466 q^{37} - 13905 q^{38} - 26542 q^{39} + 10297 q^{41} + 37642 q^{42} - 18490 q^{43} - 36140 q^{44} + 17991 q^{46} - 48592 q^{47} - 83607 q^{48} + 29458 q^{49} + 92972 q^{51} - 14232 q^{52} - 127165 q^{53} - 92002 q^{54} - 7780 q^{56} - 34060 q^{57} + 10305 q^{58} + 99372 q^{59} + 17408 q^{61} - 28265 q^{62} - 2244 q^{63} + 47202 q^{64} - 150292 q^{66} + 2021 q^{67} - 192151 q^{68} + 1654 q^{69} + 11286 q^{71} + 298365 q^{72} - 49892 q^{73} - 125431 q^{74} - 249803 q^{76} - 98144 q^{77} + 28494 q^{78} - 91524 q^{79} - 26450 q^{81} + 158909 q^{82} + 105203 q^{83} - 357682 q^{84} + 14792 q^{86} - 181200 q^{87} + 461824 q^{88} - 62682 q^{89} - 295304 q^{91} - 183783 q^{92} + 238430 q^{93} + 7259 q^{94} - 162399 q^{96} - 108383 q^{97} - 354656 q^{98} - 270499 q^{99}+O(q^{100}) \) 10 * q - 8 * q^2 - 28 * q^3 + 202 * q^4 + 75 * q^6 - 60 * q^7 - 294 * q^8 + 1356 * q^9 + 745 * q^11 - 4627 * q^12 - 1917 * q^13 + 1936 * q^14 + 5354 * q^16 - 4017 * q^17 + 2725 * q^18 - 2404 * q^19 - 228 * q^21 + 5836 * q^22 - 1733 * q^23 - 10711 * q^24 - 1484 * q^26 + 2324 * q^27 + 15028 * q^28 + 6996 * q^29 - 4899 * q^31 + 7554 * q^32 + 15734 * q^33 - 27033 * q^34 + 4433 * q^36 - 1466 * q^37 - 13905 * q^38 - 26542 * q^39 + 10297 * q^41 + 37642 * q^42 - 18490 * q^43 - 36140 * q^44 + 17991 * q^46 - 48592 * q^47 - 83607 * q^48 + 29458 * q^49 + 92972 * q^51 - 14232 * q^52 - 127165 * q^53 - 92002 * q^54 - 7780 * q^56 - 34060 * q^57 + 10305 * q^58 + 99372 * q^59 + 17408 * q^61 - 28265 * q^62 - 2244 * q^63 + 47202 * q^64 - 150292 * q^66 + 2021 * q^67 - 192151 * q^68 + 1654 * q^69 + 11286 * q^71 + 298365 * q^72 - 49892 * q^73 - 125431 * q^74 - 249803 * q^76 - 98144 * q^77 + 28494 * q^78 - 91524 * q^79 - 26450 * q^81 + 158909 * q^82 + 105203 * q^83 - 357682 * q^84 + 14792 * q^86 - 181200 * q^87 + 461824 * q^88 - 62682 * q^89 - 295304 * q^91 - 183783 * q^92 + 238430 * q^93 + 7259 * q^94 - 162399 * q^96 - 108383 * q^97 - 354656 * q^98 - 270499 * 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 $

$2$	−10.7063	−1.89263	−0.946313	−	0.323251i	$-0.895224\pi$
$2$	−10.7063	−1.89263	−0.946313	+	0.323251i	$0.895224\pi$
$3$	−18.3440	−1.17677	−0.588385	−	0.808581i	$-0.700236\pi$
$3$	−18.3440	−1.17677	−0.588385	+	0.808581i	$0.700236\pi$
$4$	82.6251	2.58203
$5$	0	0
$5$	0	0
$6$	196.397	2.22719
$7$	96.4803	0.744207	0.372103	−	0.928191i	$-0.378637\pi$
$7$	96.4803	0.744207	0.372103	+	0.928191i	$0.378637\pi$
$8$	−542.008	−2.99420
$9$	93.5034	0.384788
$10$	0	0
$11$	−684.136	−1.70475	−0.852376	−	0.522930i	$-0.824839\pi$
$11$	−684.136	−1.70475	−0.852376	+	0.522930i	$0.824839\pi$
$12$	−1515.68	−3.03846
$13$	−344.655	−0.565622	−0.282811	−	0.959176i	$-0.591267\pi$
$13$	−344.655	−0.565622	−0.282811	+	0.959176i	$0.591267\pi$
$14$	−1032.95	−1.40851
$15$	0	0
$16$	3158.90	3.08487
$17$	−1319.32	−1.10721	−0.553604	−	0.832780i	$-0.686748\pi$
$17$	−1319.32	−1.10721	−0.553604	+	0.832780i	$0.686748\pi$
$18$	−1001.08	−0.728260
$19$	739.016	0.469645	0.234823	−	0.972038i	$-0.424549\pi$
$19$	739.016	0.469645	0.234823	+	0.972038i	$0.424549\pi$
$20$	0	0
$21$	−1769.84	−0.875760
$22$	7324.58	3.22646
$23$	−3165.85	−1.24787	−0.623937	−	0.781474i	$-0.714468\pi$
$23$	−3165.85	−1.24787	−0.623937	+	0.781474i	$0.714468\pi$
$24$	9942.61	3.52349
$25$	0	0
$26$	3689.99	1.07051
$27$	2742.37	0.723963
$28$	7971.70	1.92157
$29$	7073.21	1.56179	0.780893	−	0.624665i	$-0.214765\pi$
$29$	7073.21	1.56179	0.780893	+	0.624665i	$0.214765\pi$
$30$	0	0
$31$	−3791.93	−0.708689	−0.354345	−	0.935115i	$-0.615296\pi$
$31$	−3791.93	−0.708689	−0.354345	+	0.935115i	$0.615296\pi$
$32$	−16476.0	−2.84430
$33$	12549.8	2.00610
$34$	14125.1	2.09553
$35$	0	0
$36$	7725.73	0.993536
$37$	12682.3	1.52298	0.761489	−	0.648177i	$-0.224469\pi$
$37$	12682.3	1.52298	0.761489	+	0.648177i	$0.224469\pi$
$38$	−7912.13	−0.888863
$39$	6322.37	0.665607
$40$	0	0
$41$	−10882.5	−1.01105	−0.505523	−	0.862813i	$-0.668700\pi$
$41$	−10882.5	−1.01105	−0.505523	+	0.862813i	$0.668700\pi$
$42$	18948.4	1.65749
$43$	−1849.00	−0.152499
$43$	−1849.00	−0.152499
$44$	−56526.8	−4.40173
$45$	0	0
$46$	33894.6	2.36176
$47$	−3873.59	−0.255782	−0.127891	−	0.991788i	$-0.540821\pi$
$47$	−3873.59	−0.255782	−0.127891	+	0.991788i	$0.540821\pi$
$48$	−57947.0	−3.63018
$49$	−7498.54	−0.446156
$50$	0	0
$51$	24201.7	1.30293
$52$	−28477.2	−1.46046
$53$	−6479.38	−0.316843	−0.158421	−	0.987372i	$-0.550640\pi$
$53$	−6479.38	−0.316843	−0.158421	+	0.987372i	$0.550640\pi$
$54$	−29360.7	−1.37019
$55$	0	0
$56$	−52293.1	−2.22830
$57$	−13556.5	−0.552664
$58$	−75728.0	−2.95588
$59$	34750.3	1.29966	0.649829	−	0.760081i	$-0.274841\pi$
$59$	34750.3	1.29966	0.649829	+	0.760081i	$0.274841\pi$
$60$	0	0
$61$	26452.9	0.910224	0.455112	−	0.890434i	$-0.349599\pi$
$61$	26452.9	0.910224	0.455112	+	0.890434i	$0.349599\pi$
$62$	40597.6	1.34128
$63$	9021.24	0.286362
$64$	75311.8	2.29833
$65$	0	0
$66$	−134362.	−3.79680
$67$	58007.3	1.57868	0.789342	−	0.613953i	$-0.210422\pi$
$67$	58007.3	1.57868	0.789342	+	0.613953i	$0.210422\pi$
$68$	−109009.	−2.85885
$69$	58074.5	1.46846
$70$	0	0
$71$	−23477.7	−0.552726	−0.276363	−	0.961053i	$-0.589129\pi$
$71$	−23477.7	−0.552726	−0.276363	+	0.961053i	$0.589129\pi$
$72$	−50679.6	−1.15213
$73$	−45184.4	−0.992388	−0.496194	−	0.868212i	$-0.665269\pi$
$73$	−45184.4	−0.992388	−0.496194	+	0.868212i	$0.665269\pi$
$74$	−135781.	−2.88243
$75$	0	0
$76$	61061.3	1.21264
$77$	−66005.7	−1.26869
$78$	−67689.2	−1.25975
$79$	17895.9	0.322617	0.161308	−	0.986904i	$-0.448429\pi$
$79$	17895.9	0.322617	0.161308	+	0.986904i	$0.448429\pi$
$80$	0	0
$81$	−73027.4	−1.23673
$82$	116512.	1.91353
$83$	−39799.2	−0.634132	−0.317066	−	0.948403i	$-0.602698\pi$
$83$	−39799.2	−0.634132	−0.317066	+	0.948403i	$0.602698\pi$
$84$	−146233.	−2.26124
$85$	0	0
$86$	19796.0	0.288623
$87$	−129751.	−1.83786
$88$	370808.	5.10437
$89$	−30802.0	−0.412197	−0.206098	−	0.978531i	$-0.566077\pi$
$89$	−30802.0	−0.412197	−0.206098	+	0.978531i	$0.566077\pi$
$90$	0	0
$91$	−33252.5	−0.420940
$92$	−261579.	−3.22206
$93$	69559.2	0.833964
$94$	41471.9	0.484099
$95$	0	0
$96$	302235.	3.34709
$97$	−22524.5	−0.243067	−0.121533	−	0.992587i	$-0.538781\pi$
$97$	−22524.5	−0.243067	−0.121533	+	0.992587i	$0.538781\pi$
$98$	80281.7	0.844407
$99$	−63969.1	−0.655968
$100$	0	0
$101$	70592.5	0.688581	0.344290	−	0.938863i	$-0.388120\pi$
$101$	70592.5	0.688581	0.344290	+	0.938863i	$0.388120\pi$
$102$	−259111.	−2.46596
$103$	36628.5	0.340193	0.170097	−	0.985427i	$-0.445592\pi$
$103$	36628.5	0.340193	0.170097	+	0.985427i	$0.445592\pi$
$104$	186806.	1.69359
$105$	0	0
$106$	69370.2	0.599665
$107$	48388.9	0.408588	0.204294	−	0.978910i	$-0.434510\pi$
$107$	48388.9	0.408588	0.204294	+	0.978910i	$0.434510\pi$
$108$	226589.	1.86930
$109$	−75896.0	−0.611861	−0.305930	−	0.952054i	$-0.598967\pi$
$109$	−75896.0	−0.611861	−0.305930	+	0.952054i	$0.598967\pi$
$110$	0	0
$111$	−232645.	−1.79220
$112$	304772.	2.29578
$113$	212156.	1.56300	0.781500	−	0.623905i	$-0.214455\pi$
$113$	212156.	1.56300	0.781500	+	0.623905i	$0.214455\pi$
$114$	145140.	1.04599
$115$	0	0
$116$	584424.	4.03258
$117$	−32226.4	−0.217645
$118$	−372048.	−2.45977
$119$	−127289.	−0.823992
$120$	0	0
$121$	306992.	1.90618
$122$	−283213.	−1.72271
$123$	199630.	1.18977
$124$	−313308.	−1.82986
$125$	0	0
$126$	−96584.3	−0.541976
$127$	74547.8	0.410134	0.205067	−	0.978748i	$-0.434259\pi$
$127$	74547.8	0.410134	0.205067	+	0.978748i	$0.434259\pi$
$128$	−279081.	−1.50558
$129$	33918.1	0.179456
$130$	0	0
$131$	−57691.8	−0.293722	−0.146861	−	0.989157i	$-0.546917\pi$
$131$	−57691.8	−0.293722	−0.146861	+	0.989157i	$0.546917\pi$
$132$	1.03693e6	5.17982
$133$	71300.5	0.349513
$134$	−621044.	−2.98786
$135$	0	0
$136$	715084.	3.31520
$137$	23674.0	0.107763	0.0538815	−	0.998547i	$-0.482841\pi$
$137$	23674.0	0.107763	0.0538815	+	0.998547i	$0.482841\pi$
$138$	−621763.	−2.77925
$139$	234996.	1.03163	0.515815	−	0.856700i	$-0.327489\pi$
$139$	234996.	1.03163	0.515815	+	0.856700i	$0.327489\pi$
$140$	0	0
$141$	71057.3	0.300996
$142$	251360.	1.04610
$143$	235791.	0.964245
$144$	295368.	1.18702
$145$	0	0
$146$	483758.	1.87822
$147$	137554.	0.525023
$148$	1.04788e6	3.93238
$149$	236660.	0.873292	0.436646	−	0.899633i	$-0.356166\pi$
$149$	236660.	0.873292	0.436646	+	0.899633i	$0.356166\pi$
$150$	0	0
$151$	−106852.	−0.381363	−0.190681	−	0.981652i	$-0.561070\pi$
$151$	−106852.	−0.381363	−0.190681	+	0.981652i	$0.561070\pi$
$152$	−400553.	−1.40621
$153$	−123361.	−0.426040
$154$	706678.	2.40115
$155$	0	0
$156$	522386.	1.71862
$157$	−316009.	−1.02318	−0.511588	−	0.859231i	$-0.670943\pi$
$157$	−316009.	−1.02318	−0.511588	+	0.859231i	$0.670943\pi$
$158$	−191599.	−0.610593
$159$	118858.	0.372851
$160$	0	0
$161$	−305442.	−0.928677
$162$	781855.	2.34066
$163$	467943.	1.37951	0.689753	−	0.724045i	$-0.257719\pi$
$163$	467943.	1.37951	0.689753	+	0.724045i	$0.257719\pi$
$164$	−899172.	−2.61056
$165$	0	0
$166$	426103.	1.20017
$167$	−329143.	−0.913258	−0.456629	−	0.889657i	$-0.650943\pi$
$167$	−329143.	−0.913258	−0.456629	+	0.889657i	$0.650943\pi$
$168$	959267.	2.62220
$169$	−252506.	−0.680072
$170$	0	0
$171$	69100.5	0.180714
$172$	−152774.	−0.393757
$173$	−197867.	−0.502641	−0.251321	−	0.967904i	$-0.580865\pi$
$173$	−197867.	−0.502641	−0.251321	+	0.967904i	$0.580865\pi$
$174$	1.38916e6	3.47839
$175$	0	0
$176$	−2.16112e6	−5.25893
$177$	−637461.	−1.52940
$178$	329776.	0.780134
$179$	71110.2	0.165882	0.0829410	−	0.996554i	$-0.473569\pi$
$179$	71110.2	0.165882	0.0829410	+	0.996554i	$0.473569\pi$
$180$	0	0
$181$	111059.	0.251975	0.125987	−	0.992032i	$-0.459790\pi$
$181$	111059.	0.251975	0.125987	+	0.992032i	$0.459790\pi$
$182$	356011.	0.796682
$183$	−485252.	−1.07112
$184$	1.71592e6	3.73639
$185$	0	0
$186$	−744723.	−1.57838
$187$	902597.	1.88751
$188$	−320056.	−0.660437
$189$	264585.	0.538779
$190$	0	0
$191$	620980.	1.23167	0.615835	−	0.787875i	$-0.288819\pi$
$191$	620980.	1.23167	0.615835	+	0.787875i	$0.288819\pi$
$192$	−1.38152e6	−2.70461
$193$	725314.	1.40163	0.700814	−	0.713344i	$-0.252820\pi$
$193$	725314.	1.40163	0.700814	+	0.713344i	$0.252820\pi$
$194$	241154.	0.460035
$195$	0	0
$196$	−619568.	−1.15199
$197$	−273782.	−0.502619	−0.251310	−	0.967907i	$-0.580861\pi$
$197$	−273782.	−0.502619	−0.251310	+	0.967907i	$0.580861\pi$
$198$	684873.	1.24150
$199$	−314223.	−0.562477	−0.281239	−	0.959638i	$-0.590745\pi$
$199$	−314223.	−0.562477	−0.281239	+	0.959638i	$0.590745\pi$
$200$	0	0
$201$	−1.06409e6	−1.85775
$202$	−755785.	−1.30323
$203$	682425.	1.16229
$204$	1.99967e6	3.36421
$205$	0	0
$206$	−392156.	−0.643859
$207$	−296018.	−0.480167
$208$	−1.08873e6	−1.74487
$209$	−505588.	−0.800628
$210$	0	0
$211$	−540561.	−0.835869	−0.417935	−	0.908477i	$-0.637246\pi$
$211$	−540561.	−0.835869	−0.417935	+	0.908477i	$0.637246\pi$
$212$	−535359.	−0.818099
$213$	430676.	0.650432
$214$	−518066.	−0.773305
$215$	0	0
$216$	−1.48639e6	−2.16769
$217$	−365846.	−0.527411
$218$	812566.	1.15802
$219$	828864.	1.16781
$220$	0	0
$221$	454712.	0.626261
$222$	2.49076e6	3.39196
$223$	231856.	0.312216	0.156108	−	0.987740i	$-0.450105\pi$
$223$	231856.	0.312216	0.156108	+	0.987740i	$0.450105\pi$
$224$	−1.58961e6	−2.11675
$225$	0	0
$226$	−2.27141e6	−2.95818
$227$	1.39293e6	1.79418	0.897090	−	0.441848i	$-0.145677\pi$
$227$	1.39293e6	1.79418	0.897090	+	0.441848i	$0.145677\pi$
$228$	−1.12011e6	−1.42700
$229$	−565105.	−0.712099	−0.356050	−	0.934467i	$-0.615877\pi$
$229$	−565105.	−0.712099	−0.356050	+	0.934467i	$0.615877\pi$
$230$	0	0
$231$	1.21081e6	1.49295
$232$	−3.83374e6	−4.67630
$233$	−237550.	−0.286658	−0.143329	−	0.989675i	$-0.545781\pi$
$233$	−237550.	−0.286658	−0.143329	+	0.989675i	$0.545781\pi$
$234$	345026.	0.411920
$235$	0	0
$236$	2.87125e6	3.35576
$237$	−328284.	−0.379645
$238$	1.36279e6	1.55951
$239$	1.31472e6	1.48881	0.744403	−	0.667731i	$-0.232734\pi$
$239$	1.31472e6	1.48881	0.744403	+	0.667731i	$0.232734\pi$
$240$	0	0
$241$	1.03644e6	1.14948	0.574739	−	0.818337i	$-0.305104\pi$
$241$	1.03644e6	1.14948	0.574739	+	0.818337i	$0.305104\pi$
$242$	−3.28675e6	−3.60768
$243$	673222.	0.731379
$244$	2.18567e6	2.35023
$245$	0	0
$246$	−2.13730e6	−2.25179
$247$	−254706.	−0.265642
$248$	2.05526e6	2.12196
$249$	730079.	0.746227
$250$	0	0
$251$	−1.67030e6	−1.67344	−0.836720	−	0.547632i	$-0.815530\pi$
$251$	−1.67030e6	−1.67344	−0.836720	+	0.547632i	$0.815530\pi$
$252$	745381.	0.739396
$253$	2.16587e6	2.12732
$254$	−798132.	−0.776230
$255$	0	0
$256$	577949.	0.551175
$257$	−311852.	−0.294521	−0.147261	−	0.989098i	$-0.547046\pi$
$257$	−311852.	−0.294521	−0.147261	+	0.989098i	$0.547046\pi$
$258$	−363138.	−0.339643
$259$	1.22359e6	1.13341
$260$	0	0
$261$	661369.	0.600956
$262$	617666.	0.555905
$263$	341600.	0.304529	0.152264	−	0.988340i	$-0.451343\pi$
$263$	341600.	0.304529	0.152264	+	0.988340i	$0.451343\pi$
$264$	−6.80210e6	−6.00667
$265$	0	0
$266$	−763365.	−0.661498
$267$	565034.	0.485061
$268$	4.79286e6	4.07622
$269$	865544.	0.729304	0.364652	−	0.931144i	$-0.381188\pi$
$269$	865544.	0.729304	0.364652	+	0.931144i	$0.381188\pi$
$270$	0	0
$271$	1.49244e6	1.23445	0.617226	−	0.786786i	$-0.288256\pi$
$271$	1.49244e6	1.23445	0.617226	+	0.786786i	$0.288256\pi$
$272$	−4.16762e6	−3.41559
$273$	609984.	0.495350
$274$	−253461.	−0.203955
$275$	0	0
$276$	4.79841e6	3.79162
$277$	395961.	0.310065	0.155033	−	0.987909i	$-0.450452\pi$
$277$	395961.	0.310065	0.155033	+	0.987909i	$0.450452\pi$
$278$	−2.51595e6	−1.95249
$279$	−354558.	−0.272695
$280$	0	0
$281$	2.19634e6	1.65934	0.829668	−	0.558257i	$-0.188530\pi$
$281$	2.19634e6	1.65934	0.829668	+	0.558257i	$0.188530\pi$
$282$	−760761.	−0.569673
$283$	−562659.	−0.417618	−0.208809	−	0.977956i	$-0.566959\pi$
$283$	−562659.	−0.417618	−0.208809	+	0.977956i	$0.566959\pi$
$284$	−1.93985e6	−1.42716
$285$	0	0
$286$	−2.52445e6	−1.82496
$287$	−1.04995e6	−0.752427
$288$	−1.54056e6	−1.09445
$289$	320758.	0.225909
$290$	0	0
$291$	413190.	0.286034
$292$	−3.73337e6	−2.56238
$293$	−2.24866e6	−1.53022	−0.765111	−	0.643898i	$-0.777316\pi$
$293$	−2.24866e6	−1.53022	−0.765111	+	0.643898i	$0.777316\pi$
$294$	−1.47269e6	−0.993672
$295$	0	0
$296$	−6.87391e6	−4.56010
$297$	−1.87615e6	−1.23418
$298$	−2.53376e6	−1.65282
$299$	1.09113e6	0.705826
$300$	0	0
$301$	−178392.	−0.113490
$302$	1.14399e6	0.721778
$303$	−1.29495e6	−0.810301
$304$	2.33448e6	1.44879
$305$	0	0
$306$	1.32074e6	0.806335
$307$	−2.14795e6	−1.30070	−0.650352	−	0.759633i	$-0.725379\pi$
$307$	−2.14795e6	−1.30070	−0.650352	+	0.759633i	$0.725379\pi$
$308$	−5.45373e6	−3.27580
$309$	−671914.	−0.400329
$310$	0	0
$311$	−2.61384e6	−1.53242	−0.766210	−	0.642590i	$-0.777860\pi$
$311$	−2.61384e6	−1.53242	−0.766210	+	0.642590i	$0.777860\pi$
$312$	−3.42677e6	−1.99296
$313$	−968697.	−0.558891	−0.279445	−	0.960162i	$-0.590151\pi$
$313$	−968697.	−0.558891	−0.279445	+	0.960162i	$0.590151\pi$
$314$	3.38329e6	1.93649
$315$	0	0
$316$	1.47865e6	0.833007
$317$	−289378.	−0.161740	−0.0808700	−	0.996725i	$-0.525770\pi$
$317$	−289378.	−0.161740	−0.0808700	+	0.996725i	$0.525770\pi$
$318$	−1.27253e6	−0.705667
$319$	−4.83904e6	−2.66246
$320$	0	0
$321$	−887647.	−0.480815
$322$	3.27016e6	1.75764
$323$	−975001.	−0.519995
$324$	−6.03390e6	−3.19327
$325$	0	0
$326$	−5.00994e6	−2.61089
$327$	1.39224e6	0.720019
$328$	5.89843e6	3.02727
$329$	−373725.	−0.190354
$330$	0	0
$331$	2.74453e6	1.37689	0.688443	−	0.725291i	$-0.258295\pi$
$331$	2.74453e6	1.37689	0.688443	+	0.725291i	$0.258295\pi$
$332$	−3.28842e6	−1.63735
$333$	1.18584e6	0.586024
$334$	3.52391e6	1.72846
$335$	0	0
$336$	−5.59075e6	−2.70161
$337$	1.03816e6	0.497956	0.248978	−	0.968509i	$-0.419905\pi$
$337$	1.03816e6	0.497956	0.248978	+	0.968509i	$0.419905\pi$
$338$	2.70341e6	1.28712
$339$	−3.89180e6	−1.83929
$340$	0	0
$341$	2.59420e6	1.20814
$342$	−739812.	−0.342023
$343$	−2.34501e6	−1.07624
$344$	1.00217e6	0.456611
$345$	0	0
$346$	2.11843e6	0.951312
$347$	1.87377e6	0.835396	0.417698	−	0.908586i	$-0.362837\pi$
$347$	1.87377e6	0.835396	0.417698	+	0.908586i	$0.362837\pi$
$348$	−1.07207e7	−4.74542
$349$	46712.6	0.0205291	0.0102646	−	0.999947i	$-0.496733\pi$
$349$	46712.6	0.0205291	0.0102646	+	0.999947i	$0.496733\pi$
$350$	0	0
$351$	−945172.	−0.409490
$352$	1.12718e7	4.84883
$353$	−643022.	−0.274656	−0.137328	−	0.990526i	$-0.543851\pi$
$353$	−643022.	−0.274656	−0.137328	+	0.990526i	$0.543851\pi$
$354$	6.82486e6	2.89458
$355$	0	0
$356$	−2.54502e6	−1.06431
$357$	2.33499e6	0.969649
$358$	−761328.	−0.313953
$359$	361451.	0.148017	0.0740087	−	0.997258i	$-0.476421\pi$
$359$	361451.	0.148017	0.0740087	+	0.997258i	$0.476421\pi$
$360$	0	0
$361$	−1.92995e6	−0.779434
$362$	−1.18903e6	−0.476894
$363$	−5.63146e6	−2.24313
$364$	−2.74749e6	−1.08688
$365$	0	0
$366$	5.19526e6	2.02724
$367$	1.12671e6	0.436663	0.218332	−	0.975875i	$-0.429939\pi$
$367$	1.12671e6	0.436663	0.218332	+	0.975875i	$0.429939\pi$
$368$	−1.00006e7	−3.84953
$369$	−1.01756e6	−0.389038
$370$	0	0
$371$	−625132.	−0.235796
$372$	5.74734e6	2.15332
$373$	1.98041e6	0.737027	0.368514	−	0.929622i	$-0.379867\pi$
$373$	1.98041e6	0.737027	0.368514	+	0.929622i	$0.379867\pi$
$374$	−9.66349e6	−3.57236
$375$	0	0
$376$	2.09952e6	0.765861
$377$	−2.43782e6	−0.883380
$378$	−2.83273e6	−1.01971
$379$	−870212.	−0.311191	−0.155596	−	0.987821i	$-0.549730\pi$
$379$	−870212.	−0.311191	−0.155596	+	0.987821i	$0.549730\pi$
$380$	0	0
$381$	−1.36751e6	−0.482633
$382$	−6.64841e6	−2.33109
$383$	2.78192e6	0.969055	0.484527	−	0.874776i	$-0.338992\pi$
$383$	2.78192e6	0.969055	0.484527	+	0.874776i	$0.338992\pi$
$384$	5.11947e6	1.77173
$385$	0	0
$386$	−7.76544e6	−2.65276
$387$	−172888.	−0.0586796
$388$	−1.86109e6	−0.627607
$389$	5.01979e6	1.68195	0.840973	−	0.541077i	$-0.181983\pi$
$389$	5.01979e6	1.68195	0.840973	+	0.541077i	$0.181983\pi$
$390$	0	0
$391$	4.17678e6	1.38166
$392$	4.06427e6	1.33588
$393$	1.05830e6	0.345643
$394$	2.93119e6	0.951270
$395$	0	0
$396$	−5.28545e6	−1.69373
$397$	3.26819e6	1.04071	0.520357	−	0.853949i	$-0.325799\pi$
$397$	3.26819e6	1.04071	0.520357	+	0.853949i	$0.325799\pi$
$398$	3.36417e6	1.06456
$399$	−1.30794e6	−0.411297
$400$	0	0
$401$	3.63270e6	1.12815	0.564077	−	0.825722i	$-0.309232\pi$
$401$	3.63270e6	1.12815	0.564077	+	0.825722i	$0.309232\pi$
$402$	1.13924e7	3.51603
$403$	1.30691e6	0.400850
$404$	5.83271e6	1.77794
$405$	0	0
$406$	−7.30626e6	−2.19978
$407$	−8.67643e6	−2.59630
$408$	−1.31175e7	−3.90123
$409$	−4.93318e6	−1.45821	−0.729103	−	0.684404i	$-0.760063\pi$
$409$	−4.93318e6	−1.45821	−0.729103	+	0.684404i	$0.760063\pi$
$410$	0	0
$411$	−434276.	−0.126812
$412$	3.02643e6	0.878391
$413$	3.35272e6	0.967214
$414$	3.16926e6	0.908777
$415$	0	0
$416$	5.67852e6	1.60880
$417$	−4.31078e6	−1.21399
$418$	5.41298e6	1.51529
$419$	412864.	0.114887	0.0574437	−	0.998349i	$-0.481705\pi$
$419$	412864.	0.114887	0.0574437	+	0.998349i	$0.481705\pi$
$420$	0	0
$421$	−2.27168e6	−0.624656	−0.312328	−	0.949974i	$-0.601109\pi$
$421$	−2.27168e6	−0.624656	−0.312328	+	0.949974i	$0.601109\pi$
$422$	5.78741e6	1.58199
$423$	−362194.	−0.0984216
$424$	3.51188e6	0.948690
$425$	0	0
$426$	−4.61095e6	−1.23102
$427$	2.55218e6	0.677395
$428$	3.99814e6	1.05499
$429$	−4.32536e6	−1.13469
$430$	0	0
$431$	−1.37855e6	−0.357461	−0.178731	−	0.983898i	$-0.557199\pi$
$431$	−1.37855e6	−0.357461	−0.178731	+	0.983898i	$0.557199\pi$
$432$	8.66288e6	2.23333
$433$	4.50720e6	1.15528	0.577639	−	0.816292i	$-0.303974\pi$
$433$	4.50720e6	1.15528	0.577639	+	0.816292i	$0.303974\pi$
$434$	3.91687e6	0.998193
$435$	0	0
$436$	−6.27091e6	−1.57985
$437$	−2.33961e6	−0.586058
$438$	−8.87408e6	−2.21023
$439$	−1.97588e6	−0.489327	−0.244663	−	0.969608i	$-0.578677\pi$
$439$	−1.97588e6	−0.489327	−0.244663	+	0.969608i	$0.578677\pi$
$440$	0	0
$441$	−701140.	−0.171675
$442$	−4.86829e6	−1.18528
$443$	2.75707e6	0.667481	0.333740	−	0.942665i	$-0.391689\pi$
$443$	2.75707e6	0.667481	0.333740	+	0.942665i	$0.391689\pi$
$444$	−1.92223e7	−4.62751
$445$	0	0
$446$	−2.48232e6	−0.590909
$447$	−4.34130e6	−1.02766
$448$	7.26611e6	1.71044
$449$	5.19837e6	1.21689	0.608445	−	0.793596i	$-0.291794\pi$
$449$	5.19837e6	1.21689	0.608445	+	0.793596i	$0.291794\pi$
$450$	0	0
$451$	7.44515e6	1.72358
$452$	1.75294e7	4.03572
$453$	1.96009e6	0.448777
$454$	−1.49132e7	−3.39571
$455$	0	0
$456$	7.34775e6	1.65479
$457$	−7.85140e6	−1.75856	−0.879279	−	0.476307i	$-0.841975\pi$
$457$	−7.85140e6	−1.75856	−0.879279	+	0.476307i	$0.841975\pi$
$458$	6.05019e6	1.34774
$459$	−3.61807e6	−0.801578
$460$	0	0
$461$	528436.	0.115808	0.0579042	−	0.998322i	$-0.481558\pi$
$461$	528436.	0.115808	0.0579042	+	0.998322i	$0.481558\pi$
$462$	−1.29633e7	−2.82560
$463$	−825321.	−0.178925	−0.0894624	−	0.995990i	$-0.528515\pi$
$463$	−825321.	−0.178925	−0.0894624	+	0.995990i	$0.528515\pi$
$464$	2.23436e7	4.81790
$465$	0	0
$466$	2.54328e6	0.542537
$467$	−4.03618e6	−0.856404	−0.428202	−	0.903683i	$-0.640853\pi$
$467$	−4.03618e6	−0.856404	−0.428202	+	0.903683i	$0.640853\pi$
$468$	−2.66271e6	−0.561966
$469$	5.59656e6	1.17487
$470$	0	0
$471$	5.79688e6	1.20404
$472$	−1.88350e7	−3.89144
$473$	1.26497e6	0.259972
$474$	3.51471e6	0.718527
$475$	0	0
$476$	−1.05173e7	−2.12758
$477$	−605844.	−0.121917
$478$	−1.40758e7	−2.81775
$479$	−6.39933e6	−1.27437	−0.637186	−	0.770710i	$-0.719902\pi$
$479$	−6.39933e6	−1.27437	−0.637186	+	0.770710i	$0.719902\pi$
$480$	0	0
$481$	−4.37102e6	−0.861431
$482$	−1.10964e7	−2.17553
$483$	5.60305e6	1.09284
$484$	2.53652e7	4.92181
$485$	0	0
$486$	−7.20772e6	−1.38423
$487$	−4.00561e6	−0.765326	−0.382663	−	0.923888i	$-0.624993\pi$
$487$	−4.00561e6	−0.765326	−0.382663	+	0.923888i	$0.624993\pi$
$488$	−1.43377e7	−2.72539
$489$	−8.58395e6	−1.62336
$490$	0	0
$491$	−5.31835e6	−0.995573	−0.497786	−	0.867300i	$-0.665854\pi$
$491$	−5.31835e6	−0.995573	−0.497786	+	0.867300i	$0.665854\pi$
$492$	1.64944e7	3.07202
$493$	−9.33185e6	−1.72922
$494$	2.72696e6	0.502760
$495$	0	0
$496$	−1.19783e7	−2.18621
$497$	−2.26514e6	−0.411343
$498$	−7.81645e6	−1.41233
$499$	172551.	0.0310217	0.0155108	−	0.999880i	$-0.495063\pi$
$499$	172551.	0.0310217	0.0155108	+	0.999880i	$0.495063\pi$
$500$	0	0
$501$	6.03781e6	1.07470
$502$	1.78827e7	3.16719
$503$	−1.54456e6	−0.272198	−0.136099	−	0.990695i	$-0.543457\pi$
$503$	−1.54456e6	−0.272198	−0.136099	+	0.990695i	$0.543457\pi$
$504$	−4.88959e6	−0.857425
$505$	0	0
$506$	−2.31885e7	−4.02621
$507$	4.63197e6	0.800288
$508$	6.15952e6	1.05898
$509$	3.51269e6	0.600960	0.300480	−	0.953788i	$-0.402853\pi$
$509$	3.51269e6	0.600960	0.300480	+	0.953788i	$0.402853\pi$
$510$	0	0
$511$	−4.35941e6	−0.738542
$512$	2.74289e6	0.462416
$513$	2.02665e6	0.340006
$514$	3.33879e6	0.557418
$515$	0	0
$516$	2.80249e6	0.463361
$517$	2.65007e6	0.436044
$518$	−1.31002e7	−2.14512
$519$	3.62968e6	0.591493
$520$	0	0
$521$	−1.33669e6	−0.215743	−0.107871	−	0.994165i	$-0.534403\pi$
$521$	−1.33669e6	−0.215743	−0.107871	+	0.994165i	$0.534403\pi$
$522$	−7.08082e6	−1.13739
$523$	1.35607e6	0.216784	0.108392	−	0.994108i	$-0.465430\pi$
$523$	1.35607e6	0.216784	0.108392	+	0.994108i	$0.465430\pi$
$524$	−4.76679e6	−0.758399
$525$	0	0
$526$	−3.65728e6	−0.576359
$527$	5.00278e6	0.784666
$528$	3.96437e7	6.18855
$529$	3.58627e6	0.557191
$530$	0	0
$531$	3.24928e6	0.500092
$532$	5.89121e6	0.902455
$533$	3.75073e6	0.571870
$534$	−6.04943e6	−0.918039
$535$	0	0
$536$	−3.14404e7	−4.72690
$537$	−1.30445e6	−0.195205
$538$	−9.26678e6	−1.38030
$539$	5.13003e6	0.760585
$540$	0	0
$541$	1.28068e6	0.188125	0.0940625	−	0.995566i	$-0.470015\pi$
$541$	1.28068e6	0.188125	0.0940625	+	0.995566i	$0.470015\pi$
$542$	−1.59785e7	−2.33636
$543$	−2.03727e6	−0.296516
$544$	2.17371e7	3.14923
$545$	0	0
$546$	−6.53068e6	−0.937512
$547$	−1.13222e7	−1.61793	−0.808967	−	0.587854i	$-0.799973\pi$
$547$	−1.13222e7	−1.61793	−0.808967	+	0.587854i	$0.799973\pi$
$548$	1.95606e6	0.278248
$549$	2.47343e6	0.350243
$550$	0	0
$551$	5.22721e6	0.733485
$552$	−3.14768e7	−4.39687
$553$	1.72661e6	0.240093
$554$	−4.23928e6	−0.586838
$555$	0	0
$556$	1.94166e7	2.66371
$557$	1.13494e7	1.55002	0.775008	−	0.631952i	$-0.217746\pi$
$557$	1.13494e7	1.55002	0.775008	+	0.631952i	$0.217746\pi$
$558$	3.79601e6	0.516110
$559$	637267.	0.0862566
$560$	0	0
$561$	−1.65573e7	−2.22117
$562$	−2.35147e7	−3.14050
$563$	8.01199e6	1.06529	0.532647	−	0.846338i	$-0.321198\pi$
$563$	8.01199e6	1.06529	0.532647	+	0.846338i	$0.321198\pi$
$564$	5.87112e6	0.777182
$565$	0	0
$566$	6.02401e6	0.790395
$567$	−7.04571e6	−0.920380
$568$	1.27251e7	1.65497
$569$	−6.18179e6	−0.800448	−0.400224	−	0.916417i	$-0.631068\pi$
$569$	−6.18179e6	−0.800448	−0.400224	+	0.916417i	$0.631068\pi$
$570$	0	0
$571$	4.84960e6	0.622466	0.311233	−	0.950334i	$-0.399258\pi$
$571$	4.84960e6	0.622466	0.311233	+	0.950334i	$0.399258\pi$
$572$	1.94823e7	2.48971
$573$	−1.13913e7	−1.44939
$574$	1.12411e7	1.42406
$575$	0	0
$576$	7.04191e6	0.884371
$577$	1.20012e6	0.150067	0.0750335	−	0.997181i	$-0.476094\pi$
$577$	1.20012e6	0.150067	0.0750335	+	0.997181i	$0.476094\pi$
$578$	−3.43414e6	−0.427561
$579$	−1.33052e7	−1.64939
$580$	0	0
$581$	−3.83984e6	−0.471925
$582$	−4.42374e6	−0.541355
$583$	4.43278e6	0.540138
$584$	2.44903e7	2.97141
$585$	0	0
$586$	2.40748e7	2.89614
$587$	−2.03492e6	−0.243754	−0.121877	−	0.992545i	$-0.538891\pi$
$587$	−2.03492e6	−0.243754	−0.121877	+	0.992545i	$0.538891\pi$
$588$	1.13654e7	1.35563
$589$	−2.80229e6	−0.332832
$590$	0	0
$591$	5.02226e6	0.591467
$592$	4.00622e7	4.69819
$593$	1.38521e7	1.61762	0.808812	−	0.588067i	$-0.200111\pi$
$593$	1.38521e7	1.61762	0.808812	+	0.588067i	$0.200111\pi$
$594$	2.00867e7	2.33584
$595$	0	0
$596$	1.95541e7	2.25487
$597$	5.76411e6	0.661906
$598$	−1.16819e7	−1.33586
$599$	−1.64523e7	−1.87352	−0.936760	−	0.349972i	$-0.886191\pi$
$599$	−1.64523e7	−1.87352	−0.936760	+	0.349972i	$0.886191\pi$
$600$	0	0
$601$	1.48314e7	1.67493	0.837465	−	0.546491i	$-0.184037\pi$
$601$	1.48314e7	1.67493	0.837465	+	0.546491i	$0.184037\pi$
$602$	1.90992e6	0.214795
$603$	5.42388e6	0.607459
$604$	−8.82862e6	−0.984692
$605$	0	0
$606$	1.38641e7	1.53360
$607$	1.64197e7	1.80881	0.904404	−	0.426677i	$-0.140316\pi$
$607$	1.64197e7	1.80881	0.904404	+	0.426677i	$0.140316\pi$
$608$	−1.21760e7	−1.33581
$609$	−1.25184e7	−1.36775
$610$	0	0
$611$	1.33505e6	0.144676
$612$	−1.01927e7	−1.10005
$613$	−8.77423e6	−0.943100	−0.471550	−	0.881839i	$-0.656305\pi$
$613$	−8.77423e6	−0.943100	−0.471550	+	0.881839i	$0.656305\pi$
$614$	2.29966e7	2.46175
$615$	0	0
$616$	3.57756e7	3.79871
$617$	−1.23910e7	−1.31037	−0.655183	−	0.755470i	$-0.727409\pi$
$617$	−1.23910e7	−1.31037	−0.655183	+	0.755470i	$0.727409\pi$
$618$	7.19372e6	0.757674
$619$	−1.58048e6	−0.165791	−0.0828957	−	0.996558i	$-0.526417\pi$
$619$	−1.58048e6	−0.165791	−0.0828957	+	0.996558i	$0.526417\pi$
$620$	0	0
$621$	−8.68193e6	−0.903415
$622$	2.79846e7	2.90030
$623$	−2.97179e6	−0.306760
$624$	1.99718e7	2.05331
$625$	0	0
$626$	1.03712e7	1.05777
$627$	9.27451e6	0.942155
$628$	−2.61103e7	−2.64188
$629$	−1.67321e7	−1.68625
$630$	0	0
$631$	−3.95881e6	−0.395814	−0.197907	−	0.980221i	$-0.563414\pi$
$631$	−3.95881e6	−0.395814	−0.197907	+	0.980221i	$0.563414\pi$
$632$	−9.69974e6	−0.965979
$633$	9.91606e6	0.983626
$634$	3.09817e6	0.306113
$635$	0	0
$636$	9.82065e6	0.962714
$637$	2.58441e6	0.252356
$638$	5.18082e7	5.03903
$639$	−2.19525e6	−0.212682
$640$	0	0
$641$	8.19225e6	0.787514	0.393757	−	0.919215i	$-0.371175\pi$
$641$	8.19225e6	0.787514	0.393757	+	0.919215i	$0.371175\pi$
$642$	9.50343e6	0.910003
$643$	9.53703e6	0.909674	0.454837	−	0.890575i	$-0.349697\pi$
$643$	9.53703e6	0.909674	0.454837	+	0.890575i	$0.349697\pi$
$644$	−2.52372e7	−2.39788
$645$	0	0
$646$	1.04387e7	0.984155
$647$	1.17034e7	1.09913	0.549566	−	0.835450i	$-0.314793\pi$
$647$	1.17034e7	1.09913	0.549566	+	0.835450i	$0.314793\pi$
$648$	3.95815e7	3.70301
$649$	−2.37740e7	−2.21559
$650$	0	0
$651$	6.71110e6	0.620642
$652$	3.86638e7	3.56193
$653$	−9.87401e6	−0.906172	−0.453086	−	0.891467i	$-0.649677\pi$
$653$	−9.87401e6	−0.906172	−0.453086	+	0.891467i	$0.649677\pi$
$654$	−1.49057e7	−1.36273
$655$	0	0
$656$	−3.43769e7	−3.11894
$657$	−4.22490e6	−0.381859
$658$	4.00122e6	0.360270
$659$	1.87688e7	1.68354	0.841770	−	0.539836i	$-0.181514\pi$
$659$	1.87688e7	1.68354	0.841770	+	0.539836i	$0.181514\pi$
$660$	0	0
$661$	1.84811e6	0.164522	0.0822612	−	0.996611i	$-0.473786\pi$
$661$	1.84811e6	0.164522	0.0822612	+	0.996611i	$0.473786\pi$
$662$	−2.93838e7	−2.60593
$663$	−8.34125e6	−0.736966
$664$	2.15715e7	1.89872
$665$	0	0
$666$	−1.26960e7	−1.10912
$667$	−2.23927e7	−1.94891
$668$	−2.71955e7	−2.35806
$669$	−4.25317e6	−0.367407
$670$	0	0
$671$	−1.80974e7	−1.55171
$672$	2.91598e7	2.49093
$673$	3.40289e6	0.289608	0.144804	−	0.989460i	$-0.453745\pi$
$673$	3.40289e6	0.289608	0.144804	+	0.989460i	$0.453745\pi$
$674$	−1.11149e7	−0.942445
$675$	0	0
$676$	−2.08633e7	−1.75597
$677$	−2.23309e7	−1.87255	−0.936276	−	0.351266i	$-0.885751\pi$
$677$	−2.23309e7	−1.87255	−0.936276	+	0.351266i	$0.885751\pi$
$678$	4.16668e7	3.48109
$679$	−2.17317e6	−0.180892
$680$	0	0
$681$	−2.55520e7	−2.11134
$682$	−2.77743e7	−2.28655
$683$	−7.78181e6	−0.638306	−0.319153	−	0.947703i	$-0.603398\pi$
$683$	−7.78181e6	−0.638306	−0.319153	+	0.947703i	$0.603398\pi$
$684$	5.70944e6	0.466609
$685$	0	0
$686$	2.51064e7	2.03692
$687$	1.03663e7	0.837977
$688$	−5.84082e6	−0.470438
$689$	2.23315e6	0.179213
$690$	0	0
$691$	2.39450e7	1.90775	0.953873	−	0.300211i	$-0.0970570\pi$
$691$	2.39450e7	1.90775	0.953873	+	0.300211i	$0.0970570\pi$
$692$	−1.63488e7	−1.29784
$693$	−6.17176e6	−0.488176
$694$	−2.00612e7	−1.58109
$695$	0	0
$696$	7.03262e7	5.50293
$697$	1.43576e7	1.11944
$698$	−500120.	−0.0388540
$699$	4.35762e6	0.337331
$700$	0	0
$701$	−6.24393e6	−0.479914	−0.239957	−	0.970784i	$-0.577133\pi$
$701$	−6.24393e6	−0.479914	−0.239957	+	0.970784i	$0.577133\pi$
$702$	1.01193e7	0.775011
$703$	9.37242e6	0.715259
$704$	−5.15235e7	−3.91809
$705$	0	0
$706$	6.88439e6	0.519821
$707$	6.81079e6	0.512447
$708$	−5.26703e7	−3.94896
$709$	−9.29599e6	−0.694513	−0.347256	−	0.937770i	$-0.612887\pi$
$709$	−9.29599e6	−0.694513	−0.347256	+	0.937770i	$0.612887\pi$
$710$	0	0
$711$	1.67333e6	0.124139
$712$	1.66950e7	1.23420
$713$	1.20047e7	0.884355
$714$	−2.49991e7	−1.83518
$715$	0	0
$716$	5.87549e6	0.428313
$717$	−2.41172e7	−1.75198
$718$	−3.86980e6	−0.280142
$719$	1.77934e7	1.28362	0.641811	−	0.766863i	$-0.278184\pi$
$719$	1.77934e7	1.28362	0.641811	+	0.766863i	$0.278184\pi$
$720$	0	0
$721$	3.53393e6	0.253174
$722$	2.06627e7	1.47518
$723$	−1.90124e7	−1.35267
$724$	9.17626e6	0.650608
$725$	0	0
$726$	6.02922e7	4.24541
$727$	1.60920e7	1.12921	0.564604	−	0.825362i	$-0.309029\pi$
$727$	1.60920e7	1.12921	0.564604	+	0.825362i	$0.309029\pi$
$728$	1.80231e7	1.26038
$729$	5.39607e6	0.376061
$730$	0	0
$731$	2.43943e6	0.168848
$732$	−4.00940e7	−2.76568
$733$	−2.32899e7	−1.60106	−0.800529	−	0.599295i	$-0.795448\pi$
$733$	−2.32899e7	−1.60106	−0.800529	+	0.599295i	$0.795448\pi$
$734$	−1.20629e7	−0.826441
$735$	0	0
$736$	5.21604e7	3.54933
$737$	−3.96849e7	−2.69126
$738$	1.08943e7	0.736304
$739$	−1.68335e7	−1.13387	−0.566934	−	0.823763i	$-0.691871\pi$
$739$	−1.68335e7	−1.13387	−0.566934	+	0.823763i	$0.691871\pi$
$740$	0	0
$741$	4.67233e6	0.312599
$742$	6.69286e6	0.446275
$743$	−5.88483e6	−0.391077	−0.195538	−	0.980696i	$-0.562645\pi$
$743$	−5.88483e6	−0.391077	−0.195538	+	0.980696i	$0.562645\pi$
$744$	−3.77017e7	−2.49706
$745$	0	0
$746$	−2.12029e7	−1.39492
$747$	−3.72137e6	−0.244006
$748$	7.45772e7	4.87363
$749$	4.66858e6	0.304074
$750$	0	0
$751$	−2.45954e7	−1.59131	−0.795655	−	0.605750i	$-0.792873\pi$
$751$	−2.45954e7	−1.59131	−0.795655	+	0.605750i	$0.792873\pi$
$752$	−1.22363e7	−0.789052
$753$	3.06400e7	1.96925
$754$	2.61000e7	1.67191
$755$	0	0
$756$	2.18613e7	1.39114
$757$	−1.55533e7	−0.986467	−0.493233	−	0.869897i	$-0.664185\pi$
$757$	−1.55533e7	−0.986467	−0.493233	+	0.869897i	$0.664185\pi$
$758$	9.31676e6	0.588969
$759$	−3.97309e7	−2.50336
$760$	0	0
$761$	−1.20979e7	−0.757264	−0.378632	−	0.925547i	$-0.623605\pi$
$761$	−1.20979e7	−0.757264	−0.378632	+	0.925547i	$0.623605\pi$
$762$	1.46410e7	0.913445
$763$	−7.32247e6	−0.455351
$764$	5.13086e7	3.18022
$765$	0	0
$766$	−2.97841e7	−1.83406
$767$	−1.19769e7	−0.735115
$768$	−1.06019e7	−0.648606
$769$	6.89705e6	0.420579	0.210289	−	0.977639i	$-0.432559\pi$
$769$	6.89705e6	0.420579	0.210289	+	0.977639i	$0.432559\pi$
$770$	0	0
$771$	5.72063e6	0.346584
$772$	5.99291e7	3.61905
$773$	−2.76899e7	−1.66676	−0.833380	−	0.552701i	$-0.813597\pi$
$773$	−2.76899e7	−1.66676	−0.833380	+	0.552701i	$0.813597\pi$
$774$	1.85099e6	0.111059
$775$	0	0
$776$	1.22085e7	0.727791
$777$	−2.24456e7	−1.33376
$778$	−5.37435e7	−3.18329
$779$	−8.04237e6	−0.474833
$780$	0	0
$781$	1.60620e7	0.942261
$782$	−4.47179e7	−2.61496
$783$	1.93973e7	1.13068
$784$	−2.36872e7	−1.37633
$785$	0	0
$786$	−1.13305e7	−0.654173
$787$	−2.46071e6	−0.141620	−0.0708098	−	0.997490i	$-0.522558\pi$
$787$	−2.46071e6	−0.141620	−0.0708098	+	0.997490i	$0.522558\pi$
$788$	−2.26213e7	−1.29778
$789$	−6.26632e6	−0.358360
$790$	0	0
$791$	2.04689e7	1.16320
$792$	3.46718e7	1.96410
$793$	−9.11712e6	−0.514843
$794$	−3.49903e7	−1.96968
$795$	0	0
$796$	−2.59627e7	−1.45234
$797$	−1.86050e7	−1.03749	−0.518746	−	0.854928i	$-0.673601\pi$
$797$	−1.86050e7	−1.03749	−0.518746	+	0.854928i	$0.673601\pi$
$798$	1.40032e7	0.778431
$799$	5.11052e6	0.283203
$800$	0	0
$801$	−2.88010e6	−0.158608
$802$	−3.88928e7	−2.13517
$803$	3.09123e7	1.69177
$804$	−8.79203e7	−4.79677
$805$	0	0
$806$	−1.39922e7	−0.758660
$807$	−1.58776e7	−0.858223
$808$	−3.82617e7	−2.06175
$809$	−2.26776e7	−1.21822	−0.609110	−	0.793085i	$-0.708473\pi$
$809$	−2.26776e7	−1.21822	−0.609110	+	0.793085i	$0.708473\pi$
$810$	0	0
$811$	−1.84184e7	−0.983329	−0.491665	−	0.870785i	$-0.663611\pi$
$811$	−1.84184e7	−0.983329	−0.491665	+	0.870785i	$0.663611\pi$
$812$	5.63855e7	3.00108
$813$	−2.73774e7	−1.45267
$814$	9.28925e7	4.91382
$815$	0	0
$816$	7.64509e7	4.01936
$817$	−1.36644e6	−0.0716202
$818$	5.28162e7	2.75984
$819$	−3.10922e6	−0.161973
$820$	0	0
$821$	1.39401e7	0.721783	0.360891	−	0.932608i	$-0.382472\pi$
$821$	1.39401e7	0.721783	0.360891	+	0.932608i	$0.382472\pi$
$822$	4.64949e6	0.240008
$823$	−1.86303e6	−0.0958781	−0.0479391	−	0.998850i	$-0.515265\pi$
$823$	−1.86303e6	−0.0958781	−0.0479391	+	0.998850i	$0.515265\pi$
$824$	−1.98529e7	−1.01861
$825$	0	0
$826$	−3.58953e7	−1.83058
$827$	−1.84625e7	−0.938698	−0.469349	−	0.883013i	$-0.655511\pi$
$827$	−1.84625e7	−0.938698	−0.469349	+	0.883013i	$0.655511\pi$
$828$	−2.44585e7	−1.23981
$829$	6.01093e6	0.303777	0.151889	−	0.988398i	$-0.451464\pi$
$829$	6.01093e6	0.303777	0.151889	+	0.988398i	$0.451464\pi$
$830$	0	0
$831$	−7.26353e6	−0.364876
$832$	−2.59566e7	−1.29999
$833$	9.89301e6	0.493987
$834$	4.61526e7	2.29763
$835$	0	0
$836$	−4.17742e7	−2.06725
$837$	−1.03989e7	−0.513065
$838$	−4.42025e6	−0.217439
$839$	−2.60373e7	−1.27700	−0.638500	−	0.769622i	$-0.720445\pi$
$839$	−2.60373e7	−1.27700	−0.638500	+	0.769622i	$0.720445\pi$
$840$	0	0
$841$	2.95191e7	1.43917
$842$	2.43213e7	1.18224
$843$	−4.02898e7	−1.95266
$844$	−4.46639e7	−2.15824
$845$	0	0
$846$	3.87776e6	0.186275
$847$	2.96187e7	1.41859
$848$	−2.04677e7	−0.977418
$849$	1.03214e7	0.491441
$850$	0	0
$851$	−4.01503e7	−1.90049
$852$	3.55847e7	1.67944
$853$	−1.81066e7	−0.852050	−0.426025	−	0.904711i	$-0.640086\pi$
$853$	−1.81066e7	−0.852050	−0.426025	+	0.904711i	$0.640086\pi$
$854$	−2.73245e7	−1.28206
$855$	0	0
$856$	−2.62272e7	−1.22340
$857$	−2.48924e7	−1.15775	−0.578874	−	0.815417i	$-0.696508\pi$
$857$	−2.48924e7	−1.15775	−0.578874	+	0.815417i	$0.696508\pi$
$858$	4.63087e7	2.14755
$859$	−8.53406e6	−0.394614	−0.197307	−	0.980342i	$-0.563220\pi$
$859$	−8.53406e6	−0.394614	−0.197307	+	0.980342i	$0.563220\pi$
$860$	0	0
$861$	1.92603e7	0.885434
$862$	1.47592e7	0.676541
$863$	2.14592e7	0.980815	0.490407	−	0.871493i	$-0.336848\pi$
$863$	2.14592e7	0.980815	0.490407	+	0.871493i	$0.336848\pi$
$864$	−4.51832e7	−2.05917
$865$	0	0
$866$	−4.82555e7	−2.18651
$867$	−5.88400e6	−0.265843
$868$	−3.02281e7	−1.36179
$869$	−1.22433e7	−0.549981
$870$	0	0
$871$	−1.99925e7	−0.892939
$872$	4.11363e7	1.83203
$873$	−2.10612e6	−0.0935292
$874$	2.50486e7	1.10919
$875$	0	0
$876$	6.84850e7	3.01533
$877$	−3.45569e7	−1.51717	−0.758587	−	0.651572i	$-0.774110\pi$
$877$	−3.45569e7	−1.51717	−0.758587	+	0.651572i	$0.774110\pi$
$878$	2.11544e7	0.926112
$879$	4.12495e7	1.80072
$880$	0	0
$881$	780223.	0.0338672	0.0169336	−	0.999857i	$-0.494610\pi$
$881$	780223.	0.0338672	0.0169336	+	0.999857i	$0.494610\pi$
$882$	7.50662e6	0.324917
$883$	1.51541e7	0.654077	0.327039	−	0.945011i	$-0.393949\pi$
$883$	1.51541e7	0.654077	0.327039	+	0.945011i	$0.393949\pi$
$884$	3.75706e7	1.61703
$885$	0	0
$886$	−2.95181e7	−1.26329
$887$	2.42062e7	1.03304	0.516520	−	0.856275i	$-0.327227\pi$
$887$	2.42062e7	1.03304	0.516520	+	0.856275i	$0.327227\pi$
$888$	1.26095e8	5.36619
$889$	7.19240e6	0.305225
$890$	0	0
$891$	4.99607e7	2.10831
$892$	1.91571e7	0.806153
$893$	−2.86265e6	−0.120127
$894$	4.64793e7	1.94498
$895$	0	0
$896$	−2.69258e7	−1.12047
$897$	−2.00157e7	−0.830594
$898$	−5.56554e7	−2.30312
$899$	−2.68211e7	−1.10682
$900$	0	0
$901$	8.54840e6	0.350811
$902$	−7.97101e7	−3.26210
$903$	3.27243e6	0.133552
$904$	−1.14990e8	−4.67994
$905$	0	0
$906$	−2.09853e7	−0.849366
$907$	3.38285e7	1.36541	0.682706	−	0.730693i	$-0.260803\pi$
$907$	3.38285e7	1.36541	0.682706	+	0.730693i	$0.260803\pi$
$908$	1.15091e8	4.63264
$909$	6.60064e6	0.264958
$910$	0	0
$911$	−3.51743e7	−1.40420	−0.702101	−	0.712077i	$-0.747755\pi$
$911$	−3.51743e7	−1.40420	−0.702101	+	0.712077i	$0.747755\pi$
$912$	−4.28238e7	−1.70490
$913$	2.72281e7	1.08104
$914$	8.40595e7	3.32829
$915$	0	0
$916$	−4.66919e7	−1.83866
$917$	−5.56612e6	−0.218590
$918$	3.87362e7	1.51709
$919$	7.15839e6	0.279593	0.139797	−	0.990180i	$-0.455355\pi$
$919$	7.15839e6	0.279593	0.139797	+	0.990180i	$0.455355\pi$
$920$	0	0
$921$	3.94021e7	1.53063
$922$	−5.65760e6	−0.219182
$923$	8.09172e6	0.312634
$924$	1.00043e8	3.85486
$925$	0	0
$926$	8.83615e6	0.338638
$927$	3.42489e6	0.130902
$928$	−1.16538e8	−4.44219
$929$	−4.60865e7	−1.75200	−0.876000	−	0.482311i	$-0.839798\pi$
$929$	−4.60865e7	−1.75200	−0.876000	+	0.482311i	$0.839798\pi$
$930$	0	0
$931$	−5.54154e6	−0.209535
$932$	−1.96276e7	−0.740162
$933$	4.79484e7	1.80331
$934$	4.32126e7	1.62085
$935$	0	0
$936$	1.74670e7	0.651671
$937$	−2.18537e7	−0.813160	−0.406580	−	0.913615i	$-0.633279\pi$
$937$	−2.18537e7	−0.813160	−0.406580	+	0.913615i	$0.633279\pi$
$938$	−5.99185e7	−2.22359
$939$	1.77698e7	0.657686
$940$	0	0
$941$	−1.41230e7	−0.519941	−0.259970	−	0.965617i	$-0.583713\pi$
$941$	−1.41230e7	−0.519941	−0.259970	+	0.965617i	$0.583713\pi$
$942$	−6.20632e7	−2.27880
$943$	3.44525e7	1.26166
$944$	1.09773e8	4.00927
$945$	0	0
$946$	−1.35431e7	−0.492030
$947$	1.31237e6	0.0475535	0.0237768	−	0.999717i	$-0.492431\pi$
$947$	1.31237e6	0.0475535	0.0237768	+	0.999717i	$0.492431\pi$
$948$	−2.71245e7	−0.980258
$949$	1.55730e7	0.561316
$950$	0	0
$951$	5.30836e6	0.190331
$952$	6.89916e7	2.46720
$953$	−2.64202e7	−0.942333	−0.471167	−	0.882044i	$-0.656167\pi$
$953$	−2.64202e7	−0.942333	−0.471167	+	0.882044i	$0.656167\pi$
$954$	6.48636e6	0.230744
$955$	0	0
$956$	1.08629e8	3.84415
$957$	8.87675e7	3.13310
$958$	6.85133e7	2.41191
$959$	2.28407e6	0.0801979
$960$	0	0
$961$	−1.42504e7	−0.497760
$962$	4.67975e7	1.63037
$963$	4.52453e6	0.157220
$964$	8.56358e7	2.96799
$965$	0	0
$966$	−5.99880e7	−2.06834
$967$	−1.50682e7	−0.518199	−0.259099	−	0.965851i	$-0.583426\pi$
$967$	−1.50682e7	−0.518199	−0.259099	+	0.965851i	$0.583426\pi$
$968$	−1.66392e8	−5.70747
$969$	1.78855e7	0.611914
$970$	0	0
$971$	−5.19475e7	−1.76814	−0.884070	−	0.467354i	$-0.845207\pi$
$971$	−5.19475e7	−1.76814	−0.884070	+	0.467354i	$0.845207\pi$
$972$	5.56250e7	1.88845
$973$	2.26725e7	0.767747
$974$	4.28853e7	1.44848
$975$	0	0
$976$	8.35621e7	2.80792
$977$	3.80206e7	1.27433	0.637166	−	0.770727i	$-0.280107\pi$
$977$	3.80206e7	1.27433	0.637166	+	0.770727i	$0.280107\pi$
$978$	9.19025e7	3.07242
$979$	2.10728e7	0.702693
$980$	0	0
$981$	−7.09654e6	−0.235437
$982$	5.69399e7	1.88425
$983$	−4.43240e7	−1.46304	−0.731518	−	0.681822i	$-0.761188\pi$
$983$	−4.43240e7	−1.46304	−0.731518	+	0.681822i	$0.761188\pi$
$984$	−1.08201e8	−3.56241
$985$	0	0
$986$	9.99097e7	3.27277
$987$	6.85563e6	0.224003
$988$	−2.10451e7	−0.685896
$989$	5.85366e6	0.190299
$990$	0	0
$991$	1.06776e7	0.345373	0.172687	−	0.984977i	$-0.444755\pi$
$991$	1.06776e7	0.345373	0.172687	+	0.984977i	$0.444755\pi$
$992$	6.24756e7	2.01573
$993$	−5.03457e7	−1.62028
$994$	2.42513e7	0.778518
$995$	0	0
$996$	6.03228e7	1.92679
$997$	2.28612e7	0.728386	0.364193	−	0.931324i	$-0.381345\pi$
$997$	2.28612e7	0.728386	0.364193	+	0.931324i	$0.381345\pi$
$998$	−1.84738e6	−0.0587124
$999$	3.47796e7	1.10258

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.6.a.b.1.1		10
5.4	even	2		43.6.a.b.1.10	✓	10
15.14	odd	2		387.6.a.e.1.1		10
20.19	odd	2		688.6.a.h.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.a.b.1.10	✓	10	5.4	even	2
387.6.a.e.1.1		10	15.14	odd	2
688.6.a.h.1.3		10	20.19	odd	2
1075.6.a.b.1.1		10	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:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q-10.7063 q^{2} -18.3440 q^{3} +82.6251 q^{4} +196.397 q^{6} +96.4803 q^{7} -542.008 q^{8} +93.5034 q^{9} +O(q^{10})\)	\(q-10.7063 q^{2} -18.3440 q^{3} +82.6251 q^{4} +196.397 q^{6} +96.4803 q^{7} -542.008 q^{8} +93.5034 q^{9} -684.136 q^{11} -1515.68 q^{12} -344.655 q^{13} -1032.95 q^{14} +3158.90 q^{16} -1319.32 q^{17} -1001.08 q^{18} +739.016 q^{19} -1769.84 q^{21} +7324.58 q^{22} -3165.85 q^{23} +9942.61 q^{24} +3689.99 q^{26} +2742.37 q^{27} +7971.70 q^{28} +7073.21 q^{29} -3791.93 q^{31} -16476.0 q^{32} +12549.8 q^{33} +14125.1 q^{34} +7725.73 q^{36} +12682.3 q^{37} -7912.13 q^{38} +6322.37 q^{39} -10882.5 q^{41} +18948.4 q^{42} -1849.00 q^{43} -56526.8 q^{44} +33894.6 q^{46} -3873.59 q^{47} -57947.0 q^{48} -7498.54 q^{49} +24201.7 q^{51} -28477.2 q^{52} -6479.38 q^{53} -29360.7 q^{54} -52293.1 q^{56} -13556.5 q^{57} -75728.0 q^{58} +34750.3 q^{59} +26452.9 q^{61} +40597.6 q^{62} +9021.24 q^{63} +75311.8 q^{64} -134362. q^{66} +58007.3 q^{67} -109009. q^{68} +58074.5 q^{69} -23477.7 q^{71} -50679.6 q^{72} -45184.4 q^{73} -135781. q^{74} +61061.3 q^{76} -66005.7 q^{77} -67689.2 q^{78} +17895.9 q^{79} -73027.4 q^{81} +116512. q^{82} -39799.2 q^{83} -146233. q^{84} +19796.0 q^{86} -129751. q^{87} +370808. q^{88} -30802.0 q^{89} -33252.5 q^{91} -261579. q^{92} +69559.2 q^{93} +41471.9 q^{94} +302235. q^{96} -22524.5 q^{97} +80281.7 q^{98} -63969.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 8 q^{2} - 28 q^{3} + 202 q^{4} + 75 q^{6} - 60 q^{7} - 294 q^{8} + 1356 q^{9}+O(q^{10}) \) 10 * q - 8 * q^2 - 28 * q^3 + 202 * q^4 + 75 * q^6 - 60 * q^7 - 294 * q^8 + 1356 * q^9	\( 10 q - 8 q^{2} - 28 q^{3} + 202 q^{4} + 75 q^{6} - 60 q^{7} - 294 q^{8} + 1356 q^{9} + 745 q^{11} - 4627 q^{12} - 1917 q^{13} + 1936 q^{14} + 5354 q^{16} - 4017 q^{17} + 2725 q^{18} - 2404 q^{19} - 228 q^{21} + 5836 q^{22} - 1733 q^{23} - 10711 q^{24} - 1484 q^{26} + 2324 q^{27} + 15028 q^{28} + 6996 q^{29} - 4899 q^{31} + 7554 q^{32} + 15734 q^{33} - 27033 q^{34} + 4433 q^{36} - 1466 q^{37} - 13905 q^{38} - 26542 q^{39} + 10297 q^{41} + 37642 q^{42} - 18490 q^{43} - 36140 q^{44} + 17991 q^{46} - 48592 q^{47} - 83607 q^{48} + 29458 q^{49} + 92972 q^{51} - 14232 q^{52} - 127165 q^{53} - 92002 q^{54} - 7780 q^{56} - 34060 q^{57} + 10305 q^{58} + 99372 q^{59} + 17408 q^{61} - 28265 q^{62} - 2244 q^{63} + 47202 q^{64} - 150292 q^{66} + 2021 q^{67} - 192151 q^{68} + 1654 q^{69} + 11286 q^{71} + 298365 q^{72} - 49892 q^{73} - 125431 q^{74} - 249803 q^{76} - 98144 q^{77} + 28494 q^{78} - 91524 q^{79} - 26450 q^{81} + 158909 q^{82} + 105203 q^{83} - 357682 q^{84} + 14792 q^{86} - 181200 q^{87} + 461824 q^{88} - 62682 q^{89} - 295304 q^{91} - 183783 q^{92} + 238430 q^{93} + 7259 q^{94} - 162399 q^{96} - 108383 q^{97} - 354656 q^{98} - 270499 q^{99}+O(q^{100}) \) 10 * q - 8 * q^2 - 28 * q^3 + 202 * q^4 + 75 * q^6 - 60 * q^7 - 294 * q^8 + 1356 * q^9 + 745 * q^11 - 4627 * q^12 - 1917 * q^13 + 1936 * q^14 + 5354 * q^16 - 4017 * q^17 + 2725 * q^18 - 2404 * q^19 - 228 * q^21 + 5836 * q^22 - 1733 * q^23 - 10711 * q^24 - 1484 * q^26 + 2324 * q^27 + 15028 * q^28 + 6996 * q^29 - 4899 * q^31 + 7554 * q^32 + 15734 * q^33 - 27033 * q^34 + 4433 * q^36 - 1466 * q^37 - 13905 * q^38 - 26542 * q^39 + 10297 * q^41 + 37642 * q^42 - 18490 * q^43 - 36140 * q^44 + 17991 * q^46 - 48592 * q^47 - 83607 * q^48 + 29458 * q^49 + 92972 * q^51 - 14232 * q^52 - 127165 * q^53 - 92002 * q^54 - 7780 * q^56 - 34060 * q^57 + 10305 * q^58 + 99372 * q^59 + 17408 * q^61 - 28265 * q^62 - 2244 * q^63 + 47202 * q^64 - 150292 * q^66 + 2021 * q^67 - 192151 * q^68 + 1654 * q^69 + 11286 * q^71 + 298365 * q^72 - 49892 * q^73 - 125431 * q^74 - 249803 * q^76 - 98144 * q^77 + 28494 * q^78 - 91524 * q^79 - 26450 * q^81 + 158909 * q^82 + 105203 * q^83 - 357682 * q^84 + 14792 * q^86 - 181200 * q^87 + 461824 * q^88 - 62682 * q^89 - 295304 * q^91 - 183783 * q^92 + 238430 * q^93 + 7259 * q^94 - 162399 * q^96 - 108383 * q^97 - 354656 * q^98 - 270499 * q^99

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