LMFDB - Embedded newform 275.6.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,6,Mod(1,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, 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("275.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	275.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:	$44.1055504486$
Analytic rank:	$1$
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} - x^{4} - 129x^{3} + 45x^{2} + 2924x - 5216 $ x^5 - x^4 - 129x^3 + 45x^2 + 2924*x - 5216
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-9.07964$ of defining polynomial
Character	$\chi$	$=$	275.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.0796 q^{2} +26.0567 q^{3} +90.7584 q^{4} -288.699 q^{6} -153.562 q^{7} -651.022 q^{8} +435.954 q^{9} +O(q^{10})$	\(q-11.0796 q^{2} +26.0567 q^{3} +90.7584 q^{4} -288.699 q^{6} -153.562 q^{7} -651.022 q^{8} +435.954 q^{9} -121.000 q^{11} +2364.87 q^{12} +20.2038 q^{13} +1701.41 q^{14} +4308.82 q^{16} +604.838 q^{17} -4830.21 q^{18} -858.829 q^{19} -4001.32 q^{21} +1340.64 q^{22} +1570.47 q^{23} -16963.5 q^{24} -223.851 q^{26} +5027.74 q^{27} -13937.0 q^{28} -547.596 q^{29} -10633.6 q^{31} -26907.4 q^{32} -3152.87 q^{33} -6701.39 q^{34} +39566.4 q^{36} +1771.64 q^{37} +9515.52 q^{38} +526.446 q^{39} +9789.24 q^{41} +44333.2 q^{42} +358.676 q^{43} -10981.8 q^{44} -17400.2 q^{46} -8121.29 q^{47} +112274. q^{48} +6774.25 q^{49} +15760.1 q^{51} +1833.67 q^{52} -13731.4 q^{53} -55705.6 q^{54} +99972.1 q^{56} -22378.3 q^{57} +6067.16 q^{58} -16885.1 q^{59} -51723.5 q^{61} +117816. q^{62} -66945.9 q^{63} +160243. q^{64} +34932.6 q^{66} -5045.11 q^{67} +54894.1 q^{68} +40921.2 q^{69} -44395.0 q^{71} -283815. q^{72} -76489.4 q^{73} -19629.1 q^{74} -77945.9 q^{76} +18581.0 q^{77} -5832.83 q^{78} -12136.5 q^{79} +25069.8 q^{81} -108461. q^{82} +101872. q^{83} -363154. q^{84} -3974.01 q^{86} -14268.6 q^{87} +78773.6 q^{88} +96433.2 q^{89} -3102.54 q^{91} +142533. q^{92} -277076. q^{93} +89981.0 q^{94} -701120. q^{96} -33752.1 q^{97} -75056.3 q^{98} -52750.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 9 q^{2} + 115 q^{4} - 237 q^{6} - 70 q^{7} - 753 q^{8} + 1059 q^{9}+O(q^{10}) $ 5 * q - 9 * q^2 + 115 * q^4 - 237 * q^6 - 70 * q^7 - 753 * q^8 + 1059 * q^9	\( 5 q - 9 q^{2} + 115 q^{4} - 237 q^{6} - 70 q^{7} - 753 q^{8} + 1059 q^{9} - 605 q^{11} + 1605 q^{12} - 1498 q^{13} + 2113 q^{14} + 4883 q^{16} - 3874 q^{17} - 5838 q^{18} + 882 q^{19} + 1092 q^{21} + 1089 q^{22} + 5344 q^{23} - 13119 q^{24} - 4478 q^{26} + 2160 q^{27} - 12565 q^{28} + 5318 q^{29} - 7916 q^{31} - 21385 q^{32} - 18605 q^{34} + 5628 q^{36} + 1788 q^{37} + 34421 q^{38} - 29760 q^{39} + 5854 q^{41} + 46725 q^{42} + 4364 q^{43} - 13915 q^{44} - 33834 q^{46} - 46452 q^{47} + 127545 q^{48} - 34217 q^{49} + 19842 q^{51} - 3222 q^{52} - 4412 q^{53} - 86535 q^{54} + 115575 q^{56} - 137160 q^{57} + 58221 q^{58} + 17896 q^{59} - 35930 q^{61} + 19627 q^{62} - 100980 q^{63} + 14779 q^{64} + 28677 q^{66} - 73136 q^{67} + 83409 q^{68} + 34296 q^{69} + 43612 q^{71} - 372276 q^{72} - 142306 q^{73} - 95609 q^{74} - 6617 q^{76} + 8470 q^{77} - 15750 q^{78} - 46504 q^{79} + 79101 q^{81} - 175798 q^{82} - 81604 q^{83} - 532533 q^{84} - 101788 q^{86} - 219750 q^{87} + 91113 q^{88} + 8664 q^{89} - 203380 q^{91} - 251174 q^{92} + 46470 q^{93} - 71458 q^{94} - 925479 q^{96} + 22230 q^{97} - 59962 q^{98} - 128139 q^{99}+O(q^{100}) \) 5 * q - 9 * q^2 + 115 * q^4 - 237 * q^6 - 70 * q^7 - 753 * q^8 + 1059 * q^9 - 605 * q^11 + 1605 * q^12 - 1498 * q^13 + 2113 * q^14 + 4883 * q^16 - 3874 * q^17 - 5838 * q^18 + 882 * q^19 + 1092 * q^21 + 1089 * q^22 + 5344 * q^23 - 13119 * q^24 - 4478 * q^26 + 2160 * q^27 - 12565 * q^28 + 5318 * q^29 - 7916 * q^31 - 21385 * q^32 - 18605 * q^34 + 5628 * q^36 + 1788 * q^37 + 34421 * q^38 - 29760 * q^39 + 5854 * q^41 + 46725 * q^42 + 4364 * q^43 - 13915 * q^44 - 33834 * q^46 - 46452 * q^47 + 127545 * q^48 - 34217 * q^49 + 19842 * q^51 - 3222 * q^52 - 4412 * q^53 - 86535 * q^54 + 115575 * q^56 - 137160 * q^57 + 58221 * q^58 + 17896 * q^59 - 35930 * q^61 + 19627 * q^62 - 100980 * q^63 + 14779 * q^64 + 28677 * q^66 - 73136 * q^67 + 83409 * q^68 + 34296 * q^69 + 43612 * q^71 - 372276 * q^72 - 142306 * q^73 - 95609 * q^74 - 6617 * q^76 + 8470 * q^77 - 15750 * q^78 - 46504 * q^79 + 79101 * q^81 - 175798 * q^82 - 81604 * q^83 - 532533 * q^84 - 101788 * q^86 - 219750 * q^87 + 91113 * q^88 + 8664 * q^89 - 203380 * q^91 - 251174 * q^92 + 46470 * q^93 - 71458 * q^94 - 925479 * q^96 + 22230 * q^97 - 59962 * q^98 - 128139 * 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 $

$2$	−11.0796	−1.95862	−0.979311	−	0.202361i	$-0.935138\pi$
$2$	−11.0796	−1.95862	−0.979311	+	0.202361i	$0.935138\pi$
$3$	26.0567	1.67154	0.835770	−	0.549079i	$-0.185022\pi$
$3$	26.0567	1.67154	0.835770	+	0.549079i	$0.185022\pi$
$4$	90.7584	2.83620
$5$	0	0
$5$	0	0
$6$	−288.699	−3.27392
$7$	−153.562	−1.18451	−0.592254	−	0.805751i	$-0.701762\pi$
$7$	−153.562	−1.18451	−0.592254	+	0.805751i	$0.701762\pi$
$8$	−651.022	−3.59642
$9$	435.954	1.79405
$10$	0	0
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	2364.87	4.74082
$13$	20.2038	0.0331570	0.0165785	−	0.999863i	$-0.494723\pi$
$13$	20.2038	0.0331570	0.0165785	+	0.999863i	$0.494723\pi$
$14$	1701.41	2.32001
$15$	0	0
$16$	4308.82	4.20783
$17$	604.838	0.507594	0.253797	−	0.967257i	$-0.418320\pi$
$17$	604.838	0.507594	0.253797	+	0.967257i	$0.418320\pi$
$18$	−4830.21	−3.51386
$19$	−858.829	−0.545786	−0.272893	−	0.962044i	$-0.587981\pi$
$19$	−858.829	−0.545786	−0.272893	+	0.962044i	$0.587981\pi$
$20$	0	0
$21$	−4001.32	−1.97995
$22$	1340.64	0.590547
$23$	1570.47	0.619026	0.309513	−	0.950895i	$-0.399834\pi$
$23$	1570.47	0.619026	0.309513	+	0.950895i	$0.399834\pi$
$24$	−16963.5	−6.01156
$25$	0	0
$26$	−223.851	−0.0649420
$27$	5027.74	1.32728
$28$	−13937.0	−3.35950
$29$	−547.596	−0.120911	−0.0604554	−	0.998171i	$-0.519255\pi$
$29$	−547.596	−0.120911	−0.0604554	+	0.998171i	$0.519255\pi$
$30$	0	0
$31$	−10633.6	−1.98735	−0.993676	−	0.112285i	$-0.964183\pi$
$31$	−10633.6	−1.98735	−0.993676	+	0.112285i	$0.964183\pi$
$32$	−26907.4	−4.64512
$33$	−3152.87	−0.503988
$34$	−6701.39	−0.994185
$35$	0	0
$36$	39566.4	5.08828
$37$	1771.64	0.212751	0.106375	−	0.994326i	$-0.466075\pi$
$37$	1771.64	0.212751	0.106375	+	0.994326i	$0.466075\pi$
$38$	9515.52	1.06899
$39$	526.446	0.0554232
$40$	0	0
$41$	9789.24	0.909472	0.454736	−	0.890626i	$-0.349734\pi$
$41$	9789.24	0.909472	0.454736	+	0.890626i	$0.349734\pi$
$42$	44333.2	3.87798
$43$	358.676	0.0295823	0.0147911	−	0.999891i	$-0.495292\pi$
$43$	358.676	0.0295823	0.0147911	+	0.999891i	$0.495292\pi$
$44$	−10981.8	−0.855146
$45$	0	0
$46$	−17400.2	−1.21244
$47$	−8121.29	−0.536266	−0.268133	−	0.963382i	$-0.586407\pi$
$47$	−8121.29	−0.536266	−0.268133	+	0.963382i	$0.586407\pi$
$48$	112274.	7.03356
$49$	6774.25	0.403062
$50$	0	0
$51$	15760.1	0.848464
$52$	1833.67	0.0940398
$53$	−13731.4	−0.671467	−0.335733	−	0.941957i	$-0.608984\pi$
$53$	−13731.4	−0.671467	−0.335733	+	0.941957i	$0.608984\pi$
$54$	−55705.6	−2.59965
$55$	0	0
$56$	99972.1	4.25999
$57$	−22378.3	−0.912304
$58$	6067.16	0.236819
$59$	−16885.1	−0.631500	−0.315750	−	0.948842i	$-0.602256\pi$
$59$	−16885.1	−0.631500	−0.315750	+	0.948842i	$0.602256\pi$
$60$	0	0
$61$	−51723.5	−1.77977	−0.889885	−	0.456186i	$-0.849215\pi$
$61$	−51723.5	−1.77977	−0.889885	+	0.456186i	$0.849215\pi$
$62$	117816.	3.89247
$63$	−66945.9	−2.12507
$64$	160243.	4.89021
$65$	0	0
$66$	34932.6	0.987123
$67$	−5045.11	−0.137304	−0.0686521	−	0.997641i	$-0.521870\pi$
$67$	−5045.11	−0.137304	−0.0686521	+	0.997641i	$0.521870\pi$
$68$	54894.1	1.43964
$69$	40921.2	1.03473
$70$	0	0
$71$	−44395.0	−1.04517	−0.522587	−	0.852586i	$-0.675033\pi$
$71$	−44395.0	−1.04517	−0.522587	+	0.852586i	$0.675033\pi$
$72$	−283815.	−6.45215
$73$	−76489.4	−1.67994	−0.839971	−	0.542632i	$-0.817428\pi$
$73$	−76489.4	−1.67994	−0.839971	+	0.542632i	$0.817428\pi$
$74$	−19629.1	−0.416698
$75$	0	0
$76$	−77945.9	−1.54796
$77$	18581.0	0.357143
$78$	−5832.83	−0.108553
$79$	−12136.5	−0.218788	−0.109394	−	0.993998i	$-0.534891\pi$
$79$	−12136.5	−0.218788	−0.109394	+	0.993998i	$0.534891\pi$
$80$	0	0
$81$	25069.8	0.424560
$82$	−108461.	−1.78131
$83$	101872.	1.62316	0.811578	−	0.584244i	$-0.198609\pi$
$83$	101872.	1.62316	0.811578	+	0.584244i	$0.198609\pi$
$84$	−363154.	−5.61555
$85$	0	0
$86$	−3974.01	−0.0579405
$87$	−14268.6	−0.202107
$88$	78773.6	1.08436
$89$	96433.2	1.29048	0.645240	−	0.763980i	$-0.276757\pi$
$89$	96433.2	1.29048	0.645240	+	0.763980i	$0.276757\pi$
$90$	0	0
$91$	−3102.54	−0.0392747
$92$	142533.	1.75568
$93$	−277076.	−3.32194
$94$	89981.0	1.05034
$95$	0	0
$96$	−701120.	−7.76451
$97$	−33752.1	−0.364226	−0.182113	−	0.983278i	$-0.558294\pi$
$97$	−33752.1	−0.364226	−0.182113	+	0.983278i	$0.558294\pi$
$98$	−75056.3	−0.789445
$99$	−52750.4	−0.540926
$100$	0	0
$101$	−62440.0	−0.609060	−0.304530	−	0.952503i	$-0.598499\pi$
$101$	−62440.0	−0.609060	−0.304530	+	0.952503i	$0.598499\pi$
$102$	−174616.	−1.66182
$103$	−41795.3	−0.388181	−0.194090	−	0.980984i	$-0.562175\pi$
$103$	−41795.3	−0.388181	−0.194090	+	0.980984i	$0.562175\pi$
$104$	−13153.1	−0.119246
$105$	0	0
$106$	152139.	1.31515
$107$	25461.2	0.214990	0.107495	−	0.994206i	$-0.465717\pi$
$107$	25461.2	0.214990	0.107495	+	0.994206i	$0.465717\pi$
$108$	456310.	3.76444
$109$	45320.8	0.365369	0.182684	−	0.983172i	$-0.441521\pi$
$109$	45320.8	0.365369	0.182684	+	0.983172i	$0.441521\pi$
$110$	0	0
$111$	46163.2	0.355622
$112$	−661670.	−4.98421
$113$	−102583.	−0.755755	−0.377877	−	0.925856i	$-0.623346\pi$
$113$	−102583.	−0.755755	−0.377877	+	0.925856i	$0.623346\pi$
$114$	247943.	1.78686
$115$	0	0
$116$	−49698.9	−0.342927
$117$	8807.93	0.0594852
$118$	187081.	1.23687
$119$	−92880.1	−0.601250
$120$	0	0
$121$	14641.0	0.0909091
$122$	573078.	3.48589
$123$	255076.	1.52022
$124$	−965086.	−5.63653
$125$	0	0
$126$	741736.	4.16220
$127$	123640.	0.680219	0.340110	−	0.940386i	$-0.389536\pi$
$127$	123640.	0.680219	0.340110	+	0.940386i	$0.389536\pi$
$128$	−914391.	−4.93295
$129$	9345.94	0.0494480
$130$	0	0
$131$	204656.	1.04195	0.520974	−	0.853573i	$-0.325569\pi$
$131$	204656.	1.04195	0.520974	+	0.853573i	$0.325569\pi$
$132$	−286149.	−1.42941
$133$	131883.	0.646489
$134$	55898.0	0.268927
$135$	0	0
$136$	−393763.	−1.82552
$137$	−402047.	−1.83010	−0.915051	−	0.403337i	$-0.867850\pi$
$137$	−402047.	−1.83010	−0.915051	+	0.403337i	$0.867850\pi$
$138$	−453392.	−2.02664
$139$	−296295.	−1.30073	−0.650365	−	0.759622i	$-0.725384\pi$
$139$	−296295.	−1.30073	−0.650365	+	0.759622i	$0.725384\pi$
$140$	0	0
$141$	−211614.	−0.896391
$142$	491881.	2.04710
$143$	−2444.66	−0.00999721
$144$	1.87844e6	7.54905
$145$	0	0
$146$	847475.	3.29037
$147$	176515.	0.673734
$148$	160791.	0.603404
$149$	−422066.	−1.55745	−0.778726	−	0.627364i	$-0.784134\pi$
$149$	−422066.	−1.55745	−0.778726	+	0.627364i	$0.784134\pi$
$150$	0	0
$151$	361831.	1.29141	0.645703	−	0.763588i	$-0.276564\pi$
$151$	361831.	1.29141	0.645703	+	0.763588i	$0.276564\pi$
$152$	559116.	1.96288
$153$	263681.	0.910648
$154$	−205871.	−0.699508
$155$	0	0
$156$	47779.4	0.157191
$157$	−524227.	−1.69734	−0.848672	−	0.528919i	$-0.822597\pi$
$157$	−524227.	−1.69734	−0.848672	+	0.528919i	$0.822597\pi$
$158$	134468.	0.428524
$159$	−357795.	−1.12238
$160$	0	0
$161$	−241164.	−0.733242
$162$	−277765.	−0.831552
$163$	361032.	1.06433	0.532165	−	0.846641i	$-0.321379\pi$
$163$	361032.	1.06433	0.532165	+	0.846641i	$0.321379\pi$
$164$	888456.	2.57944
$165$	0	0
$166$	−1.12871e6	−3.17915
$167$	−160164.	−0.444400	−0.222200	−	0.975001i	$-0.571324\pi$
$167$	−160164.	−0.444400	−0.222200	+	0.975001i	$0.571324\pi$
$168$	2.60495e6	7.12075
$169$	−370885.	−0.998901
$170$	0	0
$171$	−374410.	−0.979167
$172$	32552.9	0.0839013
$173$	−198093.	−0.503216	−0.251608	−	0.967829i	$-0.580959\pi$
$173$	−198093.	−0.503216	−0.251608	+	0.967829i	$0.580959\pi$
$174$	158090.	0.395852
$175$	0	0
$176$	−521367.	−1.26871
$177$	−439970.	−1.05558
$178$	−1.06844e6	−2.52756
$179$	623165.	1.45369	0.726843	−	0.686804i	$-0.240987\pi$
$179$	623165.	1.45369	0.726843	+	0.686804i	$0.240987\pi$
$180$	0	0
$181$	−492504.	−1.11741	−0.558706	−	0.829366i	$-0.688702\pi$
$181$	−492504.	−1.11741	−0.558706	+	0.829366i	$0.688702\pi$
$182$	34375.0	0.0769244
$183$	−1.34775e6	−2.97496
$184$	−1.02241e6	−2.22628
$185$	0	0
$186$	3.06990e6	6.50642
$187$	−73185.4	−0.153045
$188$	−737076.	−1.52096
$189$	−772070.	−1.57218
$190$	0	0
$191$	600899.	1.19184	0.595920	−	0.803044i	$-0.296788\pi$
$191$	600899.	1.19184	0.595920	+	0.803044i	$0.296788\pi$
$192$	4.17540e6	8.17419
$193$	−476437.	−0.920688	−0.460344	−	0.887741i	$-0.652274\pi$
$193$	−476437.	−0.920688	−0.460344	+	0.887741i	$0.652274\pi$
$194$	373961.	0.713381
$195$	0	0
$196$	614820.	1.14316
$197$	676730.	1.24237	0.621184	−	0.783665i	$-0.286652\pi$
$197$	676730.	1.24237	0.621184	+	0.783665i	$0.286652\pi$
$198$	584455.	1.05947
$199$	−208206.	−0.372701	−0.186351	−	0.982483i	$-0.559666\pi$
$199$	−208206.	−0.372701	−0.186351	+	0.982483i	$0.559666\pi$
$200$	0	0
$201$	−131459.	−0.229510
$202$	691813.	1.19292
$203$	84089.8	0.143220
$204$	1.43036e6	2.40641
$205$	0	0
$206$	463076.	0.760299
$207$	684650.	1.11056
$208$	87054.5	0.139519
$209$	103918.	0.164561
$210$	0	0
$211$	−629495.	−0.973389	−0.486694	−	0.873572i	$-0.661797\pi$
$211$	−629495.	−0.973389	−0.486694	+	0.873572i	$0.661797\pi$
$212$	−1.24624e6	−1.90441
$213$	−1.15679e6	−1.74705
$214$	−282101.	−0.421085
$215$	0	0
$216$	−3.27317e6	−4.77347
$217$	1.63291e6	2.35404
$218$	−502138.	−0.715619
$219$	−1.99306e6	−2.80809
$220$	0	0
$221$	12220.0	0.0168303
$222$	−511471.	−0.696528
$223$	−424632.	−0.571809	−0.285904	−	0.958258i	$-0.592294\pi$
$223$	−424632.	−0.571809	−0.285904	+	0.958258i	$0.592294\pi$
$224$	4.13196e6	5.50219
$225$	0	0
$226$	1.13659e6	1.48024
$227$	−547745.	−0.705528	−0.352764	−	0.935712i	$-0.614758\pi$
$227$	−547745.	−0.705528	−0.352764	+	0.935712i	$0.614758\pi$
$228$	−2.03102e6	−2.58748
$229$	621853.	0.783609	0.391804	−	0.920049i	$-0.371851\pi$
$229$	621853.	0.783609	0.391804	+	0.920049i	$0.371851\pi$
$230$	0	0
$231$	484160.	0.596979
$232$	356497.	0.434846
$233$	183035.	0.220874	0.110437	−	0.993883i	$-0.464775\pi$
$233$	183035.	0.220874	0.110437	+	0.993883i	$0.464775\pi$
$234$	−97588.7	−0.116509
$235$	0	0
$236$	−1.53246e6	−1.79106
$237$	−316236.	−0.365713
$238$	1.02908e6	1.17762
$239$	830633.	0.940621	0.470311	−	0.882501i	$-0.344142\pi$
$239$	830633.	0.940621	0.470311	+	0.882501i	$0.344142\pi$
$240$	0	0
$241$	755578.	0.837986	0.418993	−	0.907990i	$-0.362383\pi$
$241$	755578.	0.837986	0.418993	+	0.907990i	$0.362383\pi$
$242$	−162217.	−0.178057
$243$	−568503.	−0.617614
$244$	−4.69435e6	−5.04778
$245$	0	0
$246$	−2.82615e6	−2.97753
$247$	−17351.6	−0.0180966
$248$	6.92268e6	7.14735
$249$	2.65446e6	2.71317
$250$	0	0
$251$	254381.	0.254859	0.127430	−	0.991848i	$-0.459327\pi$
$251$	254381.	0.254859	0.127430	+	0.991848i	$0.459327\pi$
$252$	−6.07590e6	−6.02711
$253$	−190026.	−0.186643
$254$	−1.36988e6	−1.33229
$255$	0	0
$256$	5.00336e6	4.77158
$257$	152437.	0.143966	0.0719828	−	0.997406i	$-0.477067\pi$
$257$	152437.	0.143966	0.0719828	+	0.997406i	$0.477067\pi$
$258$	−103550.	−0.0968499
$259$	−272056.	−0.252005
$260$	0	0
$261$	−238726.	−0.216920
$262$	−2.26751e6	−2.04078
$263$	−522887.	−0.466142	−0.233071	−	0.972460i	$-0.574877\pi$
$263$	−522887.	−0.466142	−0.233071	+	0.972460i	$0.574877\pi$
$264$	2.05258e6	1.81255
$265$	0	0
$266$	−1.46122e6	−1.26623
$267$	2.51273e6	2.15709
$268$	−457886.	−0.389422
$269$	1.89754e6	1.59886	0.799429	−	0.600761i	$-0.205136\pi$
$269$	1.89754e6	1.59886	0.799429	+	0.600761i	$0.205136\pi$
$270$	0	0
$271$	296344.	0.245116	0.122558	−	0.992461i	$-0.460890\pi$
$271$	296344.	0.245116	0.122558	+	0.992461i	$0.460890\pi$
$272$	2.60614e6	2.13587
$273$	−80842.0	−0.0656493
$274$	4.45454e6	3.58448
$275$	0	0
$276$	3.71394e6	2.93469
$277$	−1.30959e6	−1.02550	−0.512750	−	0.858538i	$-0.671373\pi$
$277$	−1.30959e6	−1.02550	−0.512750	+	0.858538i	$0.671373\pi$
$278$	3.28284e6	2.54764
$279$	−4.63574e6	−3.56540
$280$	0	0
$281$	−1.21106e6	−0.914958	−0.457479	−	0.889220i	$-0.651247\pi$
$281$	−1.21106e6	−0.914958	−0.457479	+	0.889220i	$0.651247\pi$
$282$	2.34461e6	1.75569
$283$	105844.	0.0785598	0.0392799	−	0.999228i	$-0.487494\pi$
$283$	105844.	0.0785598	0.0392799	+	0.999228i	$0.487494\pi$
$284$	−4.02922e6	−2.96432
$285$	0	0
$286$	27086.0	0.0195808
$287$	−1.50325e6	−1.07728
$288$	−1.17304e7	−8.33358
$289$	−1.05403e6	−0.742348
$290$	0	0
$291$	−879469.	−0.608819
$292$	−6.94205e6	−4.76465
$293$	−2.49688e6	−1.69914	−0.849570	−	0.527476i	$-0.823138\pi$
$293$	−2.49688e6	−1.69914	−0.849570	+	0.527476i	$0.823138\pi$
$294$	−1.95572e6	−1.31959
$295$	0	0
$296$	−1.15338e6	−0.765141
$297$	−608357.	−0.400191
$298$	4.67634e6	3.05046
$299$	31729.4	0.0205250
$300$	0	0
$301$	−55079.0	−0.0350405
$302$	−4.00895e6	−2.52938
$303$	−1.62698e6	−1.01807
$304$	−3.70054e6	−2.29658
$305$	0	0
$306$	−2.92149e6	−1.78362
$307$	512223.	0.310179	0.155090	−	0.987900i	$-0.450433\pi$
$307$	512223.	0.310179	0.155090	+	0.987900i	$0.450433\pi$
$308$	1.68638e6	1.01293
$309$	−1.08905e6	−0.648860
$310$	0	0
$311$	−308722.	−0.180995	−0.0904976	−	0.995897i	$-0.528846\pi$
$311$	−308722.	−0.180995	−0.0904976	+	0.995897i	$0.528846\pi$
$312$	−342728.	−0.199325
$313$	1.16137e6	0.670052	0.335026	−	0.942209i	$-0.391255\pi$
$313$	1.16137e6	0.670052	0.335026	+	0.942209i	$0.391255\pi$
$314$	5.80824e6	3.32446
$315$	0	0
$316$	−1.10148e6	−0.620527
$317$	954197.	0.533323	0.266661	−	0.963790i	$-0.414080\pi$
$317$	954197.	0.533323	0.266661	+	0.963790i	$0.414080\pi$
$318$	3.96424e6	2.19833
$319$	66259.1	0.0364560
$320$	0	0
$321$	663435.	0.359365
$322$	2.67201e6	1.43614
$323$	−519452.	−0.277038
$324$	2.27530e6	1.20414
$325$	0	0
$326$	−4.00010e6	−2.08462
$327$	1.18091e6	0.610729
$328$	−6.37301e6	−3.27084
$329$	1.24712e6	0.635212
$330$	0	0
$331$	−486364.	−0.244001	−0.122000	−	0.992530i	$-0.538931\pi$
$331$	−486364.	−0.244001	−0.122000	+	0.992530i	$0.538931\pi$
$332$	9.24575e6	4.60359
$333$	772353.	0.381685
$334$	1.77456e6	0.870411
$335$	0	0
$336$	−1.72410e7	−8.33131
$337$	1.86376e6	0.893954	0.446977	−	0.894546i	$-0.352501\pi$
$337$	1.86376e6	0.893954	0.446977	+	0.894546i	$0.352501\pi$
$338$	4.10927e6	1.95647
$339$	−2.67299e6	−1.26327
$340$	0	0
$341$	1.28666e6	0.599209
$342$	4.14832e6	1.91782
$343$	1.54065e6	0.707079
$344$	−233506.	−0.106390
$345$	0	0
$346$	2.19480e6	0.985609
$347$	−382061.	−0.170337	−0.0851685	−	0.996367i	$-0.527143\pi$
$347$	−382061.	−0.170337	−0.0851685	+	0.996367i	$0.527143\pi$
$348$	−1.29499e6	−0.573217
$349$	1.03124e6	0.453205	0.226603	−	0.973987i	$-0.427238\pi$
$349$	1.03124e6	0.453205	0.226603	+	0.973987i	$0.427238\pi$
$350$	0	0
$351$	101580.	0.0440087
$352$	3.25580e6	1.40056
$353$	3.36046e6	1.43536	0.717682	−	0.696371i	$-0.245203\pi$
$353$	3.36046e6	1.43536	0.717682	+	0.696371i	$0.245203\pi$
$354$	4.87471e6	2.06748
$355$	0	0
$356$	8.75212e6	3.66006
$357$	−2.42015e6	−1.00501
$358$	−6.90444e6	−2.84722
$359$	3.18957e6	1.30616	0.653080	−	0.757289i	$-0.273477\pi$
$359$	3.18957e6	1.30616	0.653080	+	0.757289i	$0.273477\pi$
$360$	0	0
$361$	−1.73851e6	−0.702117
$362$	5.45677e6	2.18859
$363$	381497.	0.151958
$364$	−281581.	−0.111391
$365$	0	0
$366$	1.49325e7	5.82681
$367$	4.17400e6	1.61766	0.808830	−	0.588043i	$-0.200101\pi$
$367$	4.17400e6	1.61766	0.808830	+	0.588043i	$0.200101\pi$
$368$	6.76685e6	2.60476
$369$	4.26765e6	1.63164
$370$	0	0
$371$	2.10862e6	0.795358
$372$	−2.51470e7	−9.42168
$373$	2.96206e6	1.10235	0.551177	−	0.834388i	$-0.314179\pi$
$373$	2.96206e6	1.10235	0.551177	+	0.834388i	$0.314179\pi$
$374$	810868.	0.299758
$375$	0	0
$376$	5.28714e6	1.92864
$377$	−11063.5	−0.00400904
$378$	8.55425e6	3.07930
$379$	−2.70460e6	−0.967173	−0.483587	−	0.875297i	$-0.660666\pi$
$379$	−2.70460e6	−0.967173	−0.483587	+	0.875297i	$0.660666\pi$
$380$	0	0
$381$	3.22165e6	1.13701
$382$	−6.65774e6	−2.33436
$383$	−3.33727e6	−1.16250	−0.581252	−	0.813723i	$-0.697437\pi$
$383$	−3.33727e6	−1.16250	−0.581252	+	0.813723i	$0.697437\pi$
$384$	−2.38261e7	−8.24563
$385$	0	0
$386$	5.27875e6	1.80328
$387$	156366.	0.0530720
$388$	−3.06328e6	−1.03302
$389$	2.20346e6	0.738297	0.369148	−	0.929370i	$-0.379649\pi$
$389$	2.20346e6	0.738297	0.369148	+	0.929370i	$0.379649\pi$
$390$	0	0
$391$	949877.	0.314214
$392$	−4.41019e6	−1.44958
$393$	5.33266e6	1.74166
$394$	−7.49793e6	−2.43333
$395$	0	0
$396$	−4.78754e6	−1.53417
$397$	1.85514e6	0.590745	0.295372	−	0.955382i	$-0.404556\pi$
$397$	1.85514e6	0.590745	0.295372	+	0.955382i	$0.404556\pi$
$398$	2.30685e6	0.729980
$399$	3.43645e6	1.08063
$400$	0	0
$401$	4.24705e6	1.31895	0.659473	−	0.751729i	$-0.270780\pi$
$401$	4.24705e6	1.31895	0.659473	+	0.751729i	$0.270780\pi$
$402$	1.45652e6	0.449523
$403$	−214839.	−0.0658946
$404$	−5.66696e6	−1.72741
$405$	0	0
$406$	−931685.	−0.280514
$407$	−214368.	−0.0641468
$408$	−1.02602e7	−3.05143
$409$	3.52881e6	1.04309	0.521543	−	0.853225i	$-0.325357\pi$
$409$	3.52881e6	1.04309	0.521543	+	0.853225i	$0.325357\pi$
$410$	0	0
$411$	−1.04760e7	−3.05909
$412$	−3.79327e6	−1.10096
$413$	2.59291e6	0.748018
$414$	−7.58568e6	−2.17517
$415$	0	0
$416$	−543633.	−0.154018
$417$	−7.72048e6	−2.17422
$418$	−1.15138e6	−0.322312
$419$	1.26874e6	0.353051	0.176525	−	0.984296i	$-0.443514\pi$
$419$	1.26874e6	0.353051	0.176525	+	0.984296i	$0.443514\pi$
$420$	0	0
$421$	−5.82708e6	−1.60231	−0.801153	−	0.598460i	$-0.795780\pi$
$421$	−5.82708e6	−1.60231	−0.801153	+	0.598460i	$0.795780\pi$
$422$	6.97458e6	1.90650
$423$	−3.54051e6	−0.962088
$424$	8.93943e6	2.41488
$425$	0	0
$426$	1.28168e7	3.42181
$427$	7.94276e6	2.10815
$428$	2.31082e6	0.609756
$429$	−63699.9	−0.0167107
$430$	0	0
$431$	−1.26237e6	−0.327335	−0.163668	−	0.986516i	$-0.552332\pi$
$431$	−1.26237e6	−0.327335	−0.163668	+	0.986516i	$0.552332\pi$
$432$	2.16636e7	5.58498
$433$	−7.32365e6	−1.87719	−0.938594	−	0.345024i	$-0.887871\pi$
$433$	−7.32365e6	−1.87719	−0.938594	+	0.345024i	$0.887871\pi$
$434$	−1.80921e7	−4.61067
$435$	0	0
$436$	4.11324e6	1.03626
$437$	−1.34876e6	−0.337856
$438$	2.20824e7	5.49999
$439$	2.49650e6	0.618259	0.309129	−	0.951020i	$-0.399962\pi$
$439$	2.49650e6	0.618259	0.309129	+	0.951020i	$0.399962\pi$
$440$	0	0
$441$	2.95326e6	0.723112
$442$	−135394.	−0.0329642
$443$	−3.36722e6	−0.815197	−0.407598	−	0.913161i	$-0.633634\pi$
$443$	−3.36722e6	−0.815197	−0.407598	+	0.913161i	$0.633634\pi$
$444$	4.18969e6	1.00861
$445$	0	0
$446$	4.70477e6	1.11996
$447$	−1.09977e7	−2.60334
$448$	−2.46071e7	−5.79250
$449$	4.81330e6	1.12675	0.563374	−	0.826202i	$-0.309503\pi$
$449$	4.81330e6	1.12675	0.563374	+	0.826202i	$0.309503\pi$
$450$	0	0
$451$	−1.18450e6	−0.274216
$452$	−9.31030e6	−2.14347
$453$	9.42813e6	2.15864
$454$	6.06882e6	1.38186
$455$	0	0
$456$	1.45687e7	3.28103
$457$	2.85415e6	0.639273	0.319636	−	0.947540i	$-0.396439\pi$
$457$	2.85415e6	0.639273	0.319636	+	0.947540i	$0.396439\pi$
$458$	−6.88991e6	−1.53479
$459$	3.04097e6	0.673721
$460$	0	0
$461$	−7.32110e6	−1.60444	−0.802221	−	0.597027i	$-0.796348\pi$
$461$	−7.32110e6	−1.60444	−0.802221	+	0.597027i	$0.796348\pi$
$462$	−5.36432e6	−1.16926
$463$	5.43131e6	1.17748	0.588738	−	0.808324i	$-0.299625\pi$
$463$	5.43131e6	1.17748	0.588738	+	0.808324i	$0.299625\pi$
$464$	−2.35949e6	−0.508772
$465$	0	0
$466$	−2.02796e6	−0.432608
$467$	6.93403e6	1.47127	0.735637	−	0.677376i	$-0.236883\pi$
$467$	6.93403e6	1.47127	0.735637	+	0.677376i	$0.236883\pi$
$468$	799393.	0.168712
$469$	774737.	0.162638
$470$	0	0
$471$	−1.36596e7	−2.83718
$472$	1.09926e7	2.27114
$473$	−43399.8	−0.00891939
$474$	3.50378e6	0.716294
$475$	0	0
$476$	−8.42964e6	−1.70526
$477$	−5.98624e6	−1.20464
$478$	−9.20312e6	−1.84232
$479$	−5.25866e6	−1.04722	−0.523608	−	0.851960i	$-0.675414\pi$
$479$	−5.25866e6	−1.04722	−0.523608	+	0.851960i	$0.675414\pi$
$480$	0	0
$481$	35793.9	0.00705418
$482$	−8.37153e6	−1.64130
$483$	−6.28394e6	−1.22564
$484$	1.32879e6	0.257836
$485$	0	0
$486$	6.29881e6	1.20967
$487$	6.20820e6	1.18616	0.593080	−	0.805143i	$-0.297912\pi$
$487$	6.20820e6	1.18616	0.593080	+	0.805143i	$0.297912\pi$
$488$	3.36731e7	6.40080
$489$	9.40731e6	1.77907
$490$	0	0
$491$	−7.17776e6	−1.34365	−0.671824	−	0.740711i	$-0.734489\pi$
$491$	−7.17776e6	−1.34365	−0.671824	+	0.740711i	$0.734489\pi$
$492$	2.31503e7	4.31164
$493$	−331207.	−0.0613736
$494$	192250.	0.0354445
$495$	0	0
$496$	−4.58181e7	−8.36244
$497$	6.81738e6	1.23802
$498$	−2.94104e7	−5.31407
$499$	−105515.	−0.0189698	−0.00948492	−	0.999955i	$-0.503019\pi$
$499$	−105515.	−0.0189698	−0.00948492	+	0.999955i	$0.503019\pi$
$500$	0	0
$501$	−4.17335e6	−0.742832
$502$	−2.81845e6	−0.499173
$503$	−2.72221e6	−0.479735	−0.239868	−	0.970806i	$-0.577104\pi$
$503$	−2.72221e6	−0.479735	−0.239868	+	0.970806i	$0.577104\pi$
$504$	4.35832e7	7.64263
$505$	0	0
$506$	2.10542e6	0.365564
$507$	−9.66405e6	−1.66970
$508$	1.12213e7	1.92924
$509$	−4.81964e6	−0.824556	−0.412278	−	0.911058i	$-0.635267\pi$
$509$	−4.81964e6	−0.824556	−0.412278	+	0.911058i	$0.635267\pi$
$510$	0	0
$511$	1.17459e7	1.98991
$512$	−2.61749e7	−4.41277
$513$	−4.31797e6	−0.724413
$514$	−1.68895e6	−0.281974
$515$	0	0
$516$	848222.	0.140244
$517$	982677.	0.161690
$518$	3.01429e6	0.493583
$519$	−5.16166e6	−0.841145
$520$	0	0
$521$	−1.49556e6	−0.241385	−0.120692	−	0.992690i	$-0.538511\pi$
$521$	−1.49556e6	−0.241385	−0.120692	+	0.992690i	$0.538511\pi$
$522$	2.64500e6	0.424864
$523$	3.78410e6	0.604934	0.302467	−	0.953160i	$-0.402190\pi$
$523$	3.78410e6	0.604934	0.302467	+	0.953160i	$0.402190\pi$
$524$	1.85742e7	2.95517
$525$	0	0
$526$	5.79340e6	0.912996
$527$	−6.43159e6	−1.00877
$528$	−1.35851e7	−2.12070
$529$	−3.96998e6	−0.616807
$530$	0	0
$531$	−7.36112e6	−1.13294
$532$	1.19695e7	1.83357
$533$	197780.	0.0301553
$534$	−2.78402e7	−4.22492
$535$	0	0
$536$	3.28448e6	0.493804
$537$	1.62376e7	2.42989
$538$	−2.10240e7	−3.13156
$539$	−819685.	−0.121528
$540$	0	0
$541$	−3.06349e6	−0.450011	−0.225005	−	0.974358i	$-0.572240\pi$
$541$	−3.06349e6	−0.450011	−0.225005	+	0.974358i	$0.572240\pi$
$542$	−3.28338e6	−0.480090
$543$	−1.28330e7	−1.86780
$544$	−1.62746e7	−2.35784
$545$	0	0
$546$	895700.	0.128582
$547$	−6.60146e6	−0.943347	−0.471674	−	0.881773i	$-0.656350\pi$
$547$	−6.60146e6	−0.943347	−0.471674	+	0.881773i	$0.656350\pi$
$548$	−3.64891e7	−5.19054
$549$	−2.25491e7	−3.19299
$550$	0	0
$551$	470291.	0.0659915
$552$	−2.66406e7	−3.72131
$553$	1.86370e6	0.259157
$554$	1.45098e7	2.00857
$555$	0	0
$556$	−2.68912e7	−3.68913
$557$	711079.	0.0971136	0.0485568	−	0.998820i	$-0.484538\pi$
$557$	711079.	0.0971136	0.0485568	+	0.998820i	$0.484538\pi$
$558$	5.13624e7	6.98328
$559$	7246.63	0.000980859 0
$560$	0	0
$561$	−1.90697e6	−0.255822
$562$	1.34181e7	1.79206
$563$	−4.81549e6	−0.640279	−0.320140	−	0.947370i	$-0.603730\pi$
$563$	−4.81549e6	−0.640279	−0.320140	+	0.947370i	$0.603730\pi$
$564$	−1.92058e7	−2.54234
$565$	0	0
$566$	−1.17271e6	−0.153869
$567$	−3.84977e6	−0.502895
$568$	2.89021e7	3.75888
$569$	4.55361e6	0.589624	0.294812	−	0.955555i	$-0.404743\pi$
$569$	4.55361e6	0.589624	0.294812	+	0.955555i	$0.404743\pi$
$570$	0	0
$571$	1.27456e7	1.63596	0.817978	−	0.575250i	$-0.195095\pi$
$571$	1.27456e7	1.63596	0.817978	+	0.575250i	$0.195095\pi$
$572$	−221874.	−0.0283541
$573$	1.56575e7	1.99221
$574$	1.66555e7	2.10998
$575$	0	0
$576$	6.98583e7	8.77328
$577$	7.00292e6	0.875668	0.437834	−	0.899056i	$-0.355746\pi$
$577$	7.00292e6	0.875668	0.437834	+	0.899056i	$0.355746\pi$
$578$	1.16783e7	1.45398
$579$	−1.24144e7	−1.53897
$580$	0	0
$581$	−1.56437e7	−1.92264
$582$	9.74420e6	1.19245
$583$	1.66150e6	0.202455
$584$	4.97963e7	6.04177
$585$	0	0
$586$	2.76646e7	3.32797
$587$	−1.68605e6	−0.201965	−0.100982	−	0.994888i	$-0.532199\pi$
$587$	−1.68605e6	−0.201965	−0.100982	+	0.994888i	$0.532199\pi$
$588$	1.60202e7	1.91084
$589$	9.13242e6	1.08467
$590$	0	0
$591$	1.76334e7	2.07667
$592$	7.63367e6	0.895219
$593$	−5.21950e6	−0.609525	−0.304763	−	0.952428i	$-0.598577\pi$
$593$	−5.21950e6	−0.609525	−0.304763	+	0.952428i	$0.598577\pi$
$594$	6.74037e6	0.783823
$595$	0	0
$596$	−3.83060e7	−4.41724
$597$	−5.42517e6	−0.622985
$598$	−351550.	−0.0402008
$599$	1.40361e7	1.59838	0.799189	−	0.601079i	$-0.205262\pi$
$599$	1.40361e7	1.59838	0.799189	+	0.601079i	$0.205262\pi$
$600$	0	0
$601$	−4.77582e6	−0.539339	−0.269670	−	0.962953i	$-0.586914\pi$
$601$	−4.77582e6	−0.539339	−0.269670	+	0.962953i	$0.586914\pi$
$602$	610256.	0.0686311
$603$	−2.19944e6	−0.246330
$604$	3.28392e7	3.66269
$605$	0	0
$606$	1.80264e7	1.99401
$607$	−1.73953e7	−1.91629	−0.958144	−	0.286286i	$-0.907579\pi$
$607$	−1.73953e7	−1.91629	−0.958144	+	0.286286i	$0.907579\pi$
$608$	2.31089e7	2.53525
$609$	2.19111e6	0.239398
$610$	0	0
$611$	−164081.	−0.0177810
$612$	2.39313e7	2.58278
$613$	9.73991e6	1.04690	0.523448	−	0.852057i	$-0.324645\pi$
$613$	9.73991e6	1.04690	0.523448	+	0.852057i	$0.324645\pi$
$614$	−5.67524e6	−0.607524
$615$	0	0
$616$	−1.20966e7	−1.28444
$617$	3.85043e6	0.407190	0.203595	−	0.979055i	$-0.434737\pi$
$617$	3.85043e6	0.407190	0.203595	+	0.979055i	$0.434737\pi$
$618$	1.20663e7	1.27087
$619$	4.73416e6	0.496611	0.248306	−	0.968682i	$-0.420126\pi$
$619$	4.73416e6	0.496611	0.248306	+	0.968682i	$0.420126\pi$
$620$	0	0
$621$	7.89590e6	0.821623
$622$	3.42053e6	0.354501
$623$	−1.48085e7	−1.52859
$624$	2.26836e6	0.233212
$625$	0	0
$626$	−1.28675e7	−1.31238
$627$	2.70777e6	0.275070
$628$	−4.75780e7	−4.81401
$629$	1.07156e6	0.107991
$630$	0	0
$631$	5.50991e6	0.550898	0.275449	−	0.961316i	$-0.411173\pi$
$631$	5.50991e6	0.550898	0.275449	+	0.961316i	$0.411173\pi$
$632$	7.90109e6	0.786855
$633$	−1.64026e7	−1.62706
$634$	−1.05722e7	−1.04458
$635$	0	0
$636$	−3.24729e7	−3.18330
$637$	136866.	0.0133643
$638$	−734127.	−0.0714035
$639$	−1.93542e7	−1.87509
$640$	0	0
$641$	−1.05924e7	−1.01824	−0.509119	−	0.860696i	$-0.670029\pi$
$641$	−1.05924e7	−1.01824	−0.509119	+	0.860696i	$0.670029\pi$
$642$	−7.35062e6	−0.703861
$643$	−1.86539e6	−0.177927	−0.0889636	−	0.996035i	$-0.528355\pi$
$643$	−1.86539e6	−0.177927	−0.0889636	+	0.996035i	$0.528355\pi$
$644$	−2.18876e7	−2.07962
$645$	0	0
$646$	5.75534e6	0.542613
$647$	−1.35325e7	−1.27092	−0.635460	−	0.772134i	$-0.719190\pi$
$647$	−1.35325e7	−1.27092	−0.635460	+	0.772134i	$0.719190\pi$
$648$	−1.63210e7	−1.52690
$649$	2.04310e6	0.190404
$650$	0	0
$651$	4.25483e7	3.93487
$652$	3.27667e7	3.01865
$653$	816578.	0.0749402	0.0374701	−	0.999298i	$-0.488070\pi$
$653$	816578.	0.0749402	0.0374701	+	0.999298i	$0.488070\pi$
$654$	−1.30841e7	−1.19619
$655$	0	0
$656$	4.21800e7	3.82690
$657$	−3.33458e7	−3.01389
$658$	−1.38177e7	−1.24414
$659$	1.69927e7	1.52422	0.762110	−	0.647447i	$-0.224163\pi$
$659$	1.69927e7	1.52422	0.762110	+	0.647447i	$0.224163\pi$
$660$	0	0
$661$	1.85049e7	1.64734	0.823669	−	0.567071i	$-0.191924\pi$
$661$	1.85049e7	1.64734	0.823669	+	0.567071i	$0.191924\pi$
$662$	5.38874e6	0.477906
$663$	318414.	0.0281325
$664$	−6.63210e7	−5.83755
$665$	0	0
$666$	−8.55739e6	−0.747577
$667$	−859980.	−0.0748469
$668$	−1.45362e7	−1.26041
$669$	−1.10645e7	−0.955802
$670$	0	0
$671$	6.25855e6	0.536621
$672$	1.07665e8	9.19714
$673$	1.03983e7	0.884961	0.442481	−	0.896778i	$-0.354099\pi$
$673$	1.03983e7	0.884961	0.442481	+	0.896778i	$0.354099\pi$
$674$	−2.06498e7	−1.75092
$675$	0	0
$676$	−3.36609e7	−2.83308
$677$	−7.71661e6	−0.647076	−0.323538	−	0.946215i	$-0.604872\pi$
$677$	−7.71661e6	−0.647076	−0.323538	+	0.946215i	$0.604872\pi$
$678$	2.96157e7	2.47428
$679$	5.18303e6	0.431429
$680$	0	0
$681$	−1.42725e7	−1.17932
$682$	−1.42557e7	−1.17362
$683$	1.59699e7	1.30994	0.654970	−	0.755655i	$-0.272681\pi$
$683$	1.59699e7	1.30994	0.654970	+	0.755655i	$0.272681\pi$
$684$	−3.39808e7	−2.77711
$685$	0	0
$686$	−1.70698e7	−1.38490
$687$	1.62035e7	1.30983
$688$	1.54547e6	0.124477
$689$	−277426.	−0.0222638
$690$	0	0
$691$	2.50729e7	1.99760	0.998801	−	0.0489546i	$-0.0155890\pi$
$691$	2.50729e7	1.99760	0.998801	+	0.0489546i	$0.0155890\pi$
$692$	−1.79786e7	−1.42722
$693$	8.10045e6	0.640731
$694$	4.23310e6	0.333626
$695$	0	0
$696$	9.28914e6	0.726863
$697$	5.92090e6	0.461643
$698$	−1.14257e7	−0.887657
$699$	4.76929e6	0.369199
$700$	0	0
$701$	1.76005e7	1.35279	0.676396	−	0.736538i	$-0.263541\pi$
$701$	1.76005e7	1.35279	0.676396	+	0.736538i	$0.263541\pi$
$702$	−1.12547e6	−0.0861964
$703$	−1.52154e6	−0.116117
$704$	−1.93893e7	−1.47445
$705$	0	0
$706$	−3.72327e7	−2.81134
$707$	9.58841e6	0.721437
$708$	−3.99310e7	−2.99383
$709$	−1.82170e7	−1.36101	−0.680503	−	0.732745i	$-0.738239\pi$
$709$	−1.82170e7	−1.36101	−0.680503	+	0.732745i	$0.738239\pi$
$710$	0	0
$711$	−5.29093e6	−0.392517
$712$	−6.27801e7	−4.64111
$713$	−1.66997e7	−1.23022
$714$	2.68144e7	1.96844
$715$	0	0
$716$	5.65575e7	4.12294
$717$	2.16436e7	1.57229
$718$	−3.53393e7	−2.55827
$719$	−1.21425e7	−0.875963	−0.437982	−	0.898984i	$-0.644306\pi$
$719$	−1.21425e7	−0.875963	−0.437982	+	0.898984i	$0.644306\pi$
$720$	0	0
$721$	6.41816e6	0.459804
$722$	1.92621e7	1.37518
$723$	1.96879e7	1.40073
$724$	−4.46989e7	−3.16920
$725$	0	0
$726$	−4.22685e6	−0.297629
$727$	7.34160e6	0.515175	0.257587	−	0.966255i	$-0.417072\pi$
$727$	7.34160e6	0.515175	0.257587	+	0.966255i	$0.417072\pi$
$728$	2.01982e6	0.141249
$729$	−2.09053e7	−1.45693
$730$	0	0
$731$	216941.	0.0150158
$732$	−1.22319e8	−8.43757
$733$	7.08726e6	0.487212	0.243606	−	0.969874i	$-0.421670\pi$
$733$	7.08726e6	0.487212	0.243606	+	0.969874i	$0.421670\pi$
$734$	−4.62464e7	−3.16838
$735$	0	0
$736$	−4.22572e7	−2.87545
$737$	610459.	0.0413988
$738$	−4.72841e7	−3.19576
$739$	1.81412e7	1.22196	0.610979	−	0.791647i	$-0.290776\pi$
$739$	1.81412e7	1.22196	0.610979	+	0.791647i	$0.290776\pi$
$740$	0	0
$741$	−452127.	−0.0302493
$742$	−2.33627e7	−1.55781
$743$	2.11218e7	1.40365	0.701825	−	0.712349i	$-0.252369\pi$
$743$	2.11218e7	1.40365	0.701825	+	0.712349i	$0.252369\pi$
$744$	1.80383e8	11.9471
$745$	0	0
$746$	−3.28185e7	−2.15910
$747$	4.44115e7	2.91202
$748$	−6.64219e6	−0.434067
$749$	−3.90987e6	−0.254658
$750$	0	0
$751$	−1.58356e7	−1.02456	−0.512278	−	0.858820i	$-0.671198\pi$
$751$	−1.58356e7	−1.02456	−0.512278	+	0.858820i	$0.671198\pi$
$752$	−3.49932e7	−2.25652
$753$	6.62834e6	0.426007
$754$	122580.	0.00785219
$755$	0	0
$756$	−7.00718e7	−4.45901
$757$	−3.31626e6	−0.210334	−0.105167	−	0.994455i	$-0.533538\pi$
$757$	−3.31626e6	−0.210334	−0.105167	+	0.994455i	$0.533538\pi$
$758$	2.99659e7	1.89433
$759$	−4.95147e6	−0.311982
$760$	0	0
$761$	3.32163e6	0.207917	0.103959	−	0.994582i	$-0.466849\pi$
$761$	3.32163e6	0.207917	0.103959	+	0.994582i	$0.466849\pi$
$762$	−3.56947e7	−2.22698
$763$	−6.95955e6	−0.432783
$764$	5.45366e7	3.38029
$765$	0	0
$766$	3.69758e7	2.27691
$767$	−341143.	−0.0209386
$768$	1.30371e8	7.97589
$769$	−6.94773e6	−0.423669	−0.211835	−	0.977306i	$-0.567944\pi$
$769$	−6.94773e6	−0.423669	−0.211835	+	0.977306i	$0.567944\pi$
$770$	0	0
$771$	3.97202e6	0.240644
$772$	−4.32407e7	−2.61126
$773$	−3.94568e6	−0.237505	−0.118753	−	0.992924i	$-0.537890\pi$
$773$	−3.94568e6	−0.237505	−0.118753	+	0.992924i	$0.537890\pi$
$774$	−1.73248e6	−0.103948
$775$	0	0
$776$	2.19733e7	1.30991
$777$	−7.08890e6	−0.421237
$778$	−2.44135e7	−1.44604
$779$	−8.40728e6	−0.496377
$780$	0	0
$781$	5.37180e6	0.315132
$782$	−1.05243e7	−0.615426
$783$	−2.75317e6	−0.160483
$784$	2.91890e7	1.69601
$785$	0	0
$786$	−5.90840e7	−3.41125
$787$	−2.23224e6	−0.128471	−0.0642354	−	0.997935i	$-0.520461\pi$
$787$	−2.23224e6	−0.128471	−0.0642354	+	0.997935i	$0.520461\pi$
$788$	6.14190e7	3.52360
$789$	−1.36247e7	−0.779175
$790$	0	0
$791$	1.57529e7	0.895198
$792$	3.43416e7	1.94540
$793$	−1.04501e6	−0.0590118
$794$	−2.05542e7	−1.15705
$795$	0	0
$796$	−1.88964e7	−1.05705
$797$	8.44785e6	0.471086	0.235543	−	0.971864i	$-0.424313\pi$
$797$	8.44785e6	0.471086	0.235543	+	0.971864i	$0.424313\pi$
$798$	−3.80746e7	−2.11655
$799$	−4.91207e6	−0.272206
$800$	0	0
$801$	4.20404e7	2.31518
$802$	−4.70558e7	−2.58331
$803$	9.25522e6	0.506521
$804$	−1.19310e7	−0.650935
$805$	0	0
$806$	2.38034e6	0.129063
$807$	4.94437e7	2.67256
$808$	4.06498e7	2.19043
$809$	2.52205e7	1.35482	0.677410	−	0.735606i	$-0.263102\pi$
$809$	2.52205e7	1.35482	0.677410	+	0.735606i	$0.263102\pi$
$810$	0	0
$811$	−4.88349e6	−0.260723	−0.130361	−	0.991467i	$-0.541614\pi$
$811$	−4.88349e6	−0.260723	−0.130361	+	0.991467i	$0.541614\pi$
$812$	7.63186e6	0.406200
$813$	7.72175e6	0.409722
$814$	2.37513e6	0.125639
$815$	0	0
$816$	6.79074e7	3.57019
$817$	−308042.	−0.0161456
$818$	−3.90980e7	−2.04301
$819$	−1.35256e6	−0.0704608
$820$	0	0
$821$	−1.72115e7	−0.891171	−0.445586	−	0.895239i	$-0.647005\pi$
$821$	−1.72115e7	−0.891171	−0.445586	+	0.895239i	$0.647005\pi$
$822$	1.16071e8	5.99160
$823$	−3.40762e7	−1.75369	−0.876843	−	0.480777i	$-0.840355\pi$
$823$	−3.40762e7	−1.75369	−0.876843	+	0.480777i	$0.840355\pi$
$824$	2.72096e7	1.39606
$825$	0	0
$826$	−2.87285e7	−1.46508
$827$	−3.25969e6	−0.165734	−0.0828671	−	0.996561i	$-0.526408\pi$
$827$	−3.25969e6	−0.165734	−0.0828671	+	0.996561i	$0.526408\pi$
$828$	6.21377e7	3.14978
$829$	1.21342e6	0.0613232	0.0306616	−	0.999530i	$-0.490239\pi$
$829$	1.21342e6	0.0613232	0.0306616	+	0.999530i	$0.490239\pi$
$830$	0	0
$831$	−3.41236e7	−1.71416
$832$	3.23751e6	0.162145
$833$	4.09733e6	0.204592
$834$	8.55401e7	4.25848
$835$	0	0
$836$	9.43146e6	0.466727
$837$	−5.34628e7	−2.63778
$838$	−1.40572e7	−0.691493
$839$	679712.	0.0333365	0.0166682	−	0.999861i	$-0.494694\pi$
$839$	679712.	0.0333365	0.0166682	+	0.999861i	$0.494694\pi$
$840$	0	0
$841$	−2.02113e7	−0.985381
$842$	6.45619e7	3.13831
$843$	−3.15564e7	−1.52939
$844$	−5.71320e7	−2.76072
$845$	0	0
$846$	3.92275e7	1.88437
$847$	−2.24830e6	−0.107683
$848$	−5.91660e7	−2.82542
$849$	2.75795e6	0.131316
$850$	0	0
$851$	2.78230e6	0.131698
$852$	−1.04988e8	−4.95498
$853$	−2.32575e6	−0.109444	−0.0547219	−	0.998502i	$-0.517427\pi$
$853$	−2.32575e6	−0.109444	−0.0547219	+	0.998502i	$0.517427\pi$
$854$	−8.80030e7	−4.12907
$855$	0	0
$856$	−1.65758e7	−0.773196
$857$	1.06934e7	0.497350	0.248675	−	0.968587i	$-0.420005\pi$
$857$	1.06934e7	0.497350	0.248675	+	0.968587i	$0.420005\pi$
$858$	705772.	0.0327300
$859$	3.36097e7	1.55411	0.777056	−	0.629432i	$-0.216712\pi$
$859$	3.36097e7	1.55411	0.777056	+	0.629432i	$0.216712\pi$
$860$	0	0
$861$	−3.91699e7	−1.80071
$862$	1.39866e7	0.641126
$863$	−1.13378e7	−0.518206	−0.259103	−	0.965850i	$-0.583427\pi$
$863$	−1.13378e7	−0.518206	−0.259103	+	0.965850i	$0.583427\pi$
$864$	−1.35284e8	−6.16540
$865$	0	0
$866$	8.11434e7	3.67670
$867$	−2.74645e7	−1.24086
$868$	1.48200e8	6.67652
$869$	1.46851e6	0.0659672
$870$	0	0
$871$	−101931.	−0.00455260
$872$	−2.95048e7	−1.31402
$873$	−1.47143e7	−0.653439
$874$	1.49438e7	0.661732
$875$	0	0
$876$	−1.80887e8	−7.96430
$877$	−1.61696e7	−0.709906	−0.354953	−	0.934884i	$-0.615503\pi$
$877$	−1.61696e7	−0.709906	−0.354953	+	0.934884i	$0.615503\pi$
$878$	−2.76603e7	−1.21094
$879$	−6.50606e7	−2.84018
$880$	0	0
$881$	5.99273e6	0.260127	0.130063	−	0.991506i	$-0.458482\pi$
$881$	5.99273e6	0.260127	0.130063	+	0.991506i	$0.458482\pi$
$882$	−3.27211e7	−1.41630
$883$	3.74933e7	1.61827	0.809136	−	0.587621i	$-0.199935\pi$
$883$	3.74933e7	1.61827	0.809136	+	0.587621i	$0.199935\pi$
$884$	1.10907e6	0.0477341
$885$	0	0
$886$	3.73076e7	1.59666
$887$	−2.77752e6	−0.118535	−0.0592676	−	0.998242i	$-0.518877\pi$
$887$	−2.77752e6	−0.118535	−0.0592676	+	0.998242i	$0.518877\pi$
$888$	−3.00532e7	−1.27896
$889$	−1.89864e7	−0.805726
$890$	0	0
$891$	−3.03345e6	−0.128010
$892$	−3.85389e7	−1.62176
$893$	6.97480e6	0.292687
$894$	1.21850e8	5.09897
$895$	0	0
$896$	1.40416e8	5.84313
$897$	826765.	0.0343084
$898$	−5.33296e7	−2.20687
$899$	5.82290e6	0.240292
$900$	0	0
$901$	−8.30526e6	−0.340833
$902$	1.31238e7	0.537086
$903$	−1.43518e6	−0.0585716
$904$	6.67840e7	2.71801
$905$	0	0
$906$	−1.04460e8	−4.22796
$907$	2.48102e7	1.00141	0.500706	−	0.865617i	$-0.333074\pi$
$907$	2.48102e7	1.00141	0.500706	+	0.865617i	$0.333074\pi$
$908$	−4.97125e7	−2.00102
$909$	−2.72210e7	−1.09268
$910$	0	0
$911$	−2.18540e6	−0.0872438	−0.0436219	−	0.999048i	$-0.513890\pi$
$911$	−2.18540e6	−0.0872438	−0.0436219	+	0.999048i	$0.513890\pi$
$912$	−9.64239e7	−3.83882
$913$	−1.23265e7	−0.489400
$914$	−3.16229e7	−1.25209
$915$	0	0
$916$	5.64384e7	2.22247
$917$	−3.14273e7	−1.23420
$918$	−3.36928e7	−1.31957
$919$	1.10244e7	0.430592	0.215296	−	0.976549i	$-0.430928\pi$
$919$	1.10244e7	0.430592	0.215296	+	0.976549i	$0.430928\pi$
$920$	0	0
$921$	1.33469e7	0.518477
$922$	8.11151e7	3.14249
$923$	−896949.	−0.0346548
$924$	4.39416e7	1.69315
$925$	0	0
$926$	−6.01769e7	−2.30623
$927$	−1.82208e7	−0.696415
$928$	1.47344e7	0.561646
$929$	−1.85237e7	−0.704189	−0.352094	−	0.935965i	$-0.614530\pi$
$929$	−1.85237e7	−0.704189	−0.352094	+	0.935965i	$0.614530\pi$
$930$	0	0
$931$	−5.81793e6	−0.219986
$932$	1.66119e7	0.626442
$933$	−8.04430e6	−0.302541
$934$	−7.68266e7	−2.88167
$935$	0	0
$936$	−5.73415e6	−0.213934
$937$	−3.43378e6	−0.127769	−0.0638843	−	0.997957i	$-0.520349\pi$
$937$	−3.43378e6	−0.127769	−0.0638843	+	0.997957i	$0.520349\pi$
$938$	−8.58381e6	−0.318547
$939$	3.02614e7	1.12002
$940$	0	0
$941$	−1.51701e7	−0.558490	−0.279245	−	0.960220i	$-0.590084\pi$
$941$	−1.51701e7	−0.558490	−0.279245	+	0.960220i	$0.590084\pi$
$942$	1.51344e8	5.55696
$943$	1.53737e7	0.562987
$944$	−7.27548e7	−2.65724
$945$	0	0
$946$	480855.	0.0174697
$947$	−1.73131e7	−0.627334	−0.313667	−	0.949533i	$-0.601558\pi$
$947$	−1.73131e7	−0.627334	−0.313667	+	0.949533i	$0.601558\pi$
$948$	−2.87011e7	−1.03724
$949$	−1.54538e6	−0.0557018
$950$	0	0
$951$	2.48633e7	0.891470
$952$	6.04669e7	2.16235
$953$	1.57049e7	0.560150	0.280075	−	0.959978i	$-0.409641\pi$
$953$	1.57049e7	0.560150	0.280075	+	0.959978i	$0.409641\pi$
$954$	6.63254e7	2.35944
$955$	0	0
$956$	7.53870e7	2.66779
$957$	1.72650e6	0.0609376
$958$	5.82640e7	2.05110
$959$	6.17391e7	2.16777
$960$	0	0
$961$	8.44436e7	2.94957
$962$	−396583.	−0.0138165
$963$	1.10999e7	0.385703
$964$	6.85750e7	2.37669
$965$	0	0
$966$	6.96238e7	2.40057
$967$	6.15278e6	0.211595	0.105797	−	0.994388i	$-0.466260\pi$
$967$	6.15278e6	0.211595	0.105797	+	0.994388i	$0.466260\pi$
$968$	−9.53161e6	−0.326947
$969$	−1.35352e7	−0.463080
$970$	0	0
$971$	−8.69711e6	−0.296024	−0.148012	−	0.988986i	$-0.547287\pi$
$971$	−8.69711e6	−0.296024	−0.148012	+	0.988986i	$0.547287\pi$
$972$	−5.15964e7	−1.75168
$973$	4.54996e7	1.54073
$974$	−6.87846e7	−2.32324
$975$	0	0
$976$	−2.22867e8	−7.48896
$977$	−1.79321e6	−0.0601028	−0.0300514	−	0.999548i	$-0.509567\pi$
$977$	−1.79321e6	−0.0601028	−0.0300514	+	0.999548i	$0.509567\pi$
$978$	−1.04230e8	−3.48453
$979$	−1.16684e7	−0.389094
$980$	0	0
$981$	1.97578e7	0.655489
$982$	7.95270e7	2.63170
$983$	−1.89388e7	−0.625129	−0.312564	−	0.949897i	$-0.601188\pi$
$983$	−1.89388e7	−0.625129	−0.312564	+	0.949897i	$0.601188\pi$
$984$	−1.66060e8	−5.46735
$985$	0	0
$986$	3.66965e6	0.120208
$987$	3.24959e7	1.06178
$988$	−1.57481e6	−0.0513257
$989$	563289.	0.0183122
$990$	0	0
$991$	−4.62568e7	−1.49621	−0.748103	−	0.663582i	$-0.769035\pi$
$991$	−4.62568e7	−1.49621	−0.748103	+	0.663582i	$0.769035\pi$
$992$	2.86122e8	9.23150
$993$	−1.26731e7	−0.407858
$994$	−7.55342e7	−2.42481
$995$	0	0
$996$	2.40914e8	7.69509
$997$	−3.50783e7	−1.11764	−0.558819	−	0.829290i	$-0.688745\pi$
$997$	−3.50783e7	−1.11764	−0.558819	+	0.829290i	$0.688745\pi$
$998$	1.16907e6	0.0371547
$999$	8.90735e6	0.282381

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.6.a.e.1.1		5
5.2	odd	4		275.6.b.e.199.1		10
5.3	odd	4		275.6.b.e.199.10		10
5.4	even	2		55.6.a.c.1.5	✓	5
15.14	odd	2		495.6.a.h.1.1		5
20.19	odd	2		880.6.a.r.1.5		5
55.54	odd	2		605.6.a.d.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.a.c.1.5	✓	5	5.4	even	2
275.6.a.e.1.1		5	1.1	even	1	trivial
275.6.b.e.199.1		10	5.2	odd	4
275.6.b.e.199.10		10	5.3	odd	4
495.6.a.h.1.1		5	15.14	odd	2
605.6.a.d.1.1		5	55.54	odd	2
880.6.a.r.1.5		5	20.19	odd	2

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	275.a (trivial)

\(f(q)\)	\(=\)	\(q-11.0796 q^{2} +26.0567 q^{3} +90.7584 q^{4} -288.699 q^{6} -153.562 q^{7} -651.022 q^{8} +435.954 q^{9} +O(q^{10})\)	\(q-11.0796 q^{2} +26.0567 q^{3} +90.7584 q^{4} -288.699 q^{6} -153.562 q^{7} -651.022 q^{8} +435.954 q^{9} -121.000 q^{11} +2364.87 q^{12} +20.2038 q^{13} +1701.41 q^{14} +4308.82 q^{16} +604.838 q^{17} -4830.21 q^{18} -858.829 q^{19} -4001.32 q^{21} +1340.64 q^{22} +1570.47 q^{23} -16963.5 q^{24} -223.851 q^{26} +5027.74 q^{27} -13937.0 q^{28} -547.596 q^{29} -10633.6 q^{31} -26907.4 q^{32} -3152.87 q^{33} -6701.39 q^{34} +39566.4 q^{36} +1771.64 q^{37} +9515.52 q^{38} +526.446 q^{39} +9789.24 q^{41} +44333.2 q^{42} +358.676 q^{43} -10981.8 q^{44} -17400.2 q^{46} -8121.29 q^{47} +112274. q^{48} +6774.25 q^{49} +15760.1 q^{51} +1833.67 q^{52} -13731.4 q^{53} -55705.6 q^{54} +99972.1 q^{56} -22378.3 q^{57} +6067.16 q^{58} -16885.1 q^{59} -51723.5 q^{61} +117816. q^{62} -66945.9 q^{63} +160243. q^{64} +34932.6 q^{66} -5045.11 q^{67} +54894.1 q^{68} +40921.2 q^{69} -44395.0 q^{71} -283815. q^{72} -76489.4 q^{73} -19629.1 q^{74} -77945.9 q^{76} +18581.0 q^{77} -5832.83 q^{78} -12136.5 q^{79} +25069.8 q^{81} -108461. q^{82} +101872. q^{83} -363154. q^{84} -3974.01 q^{86} -14268.6 q^{87} +78773.6 q^{88} +96433.2 q^{89} -3102.54 q^{91} +142533. q^{92} -277076. q^{93} +89981.0 q^{94} -701120. q^{96} -33752.1 q^{97} -75056.3 q^{98} -52750.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 9 q^{2} + 115 q^{4} - 237 q^{6} - 70 q^{7} - 753 q^{8} + 1059 q^{9}+O(q^{10}) \) 5 * q - 9 * q^2 + 115 * q^4 - 237 * q^6 - 70 * q^7 - 753 * q^8 + 1059 * q^9	\( 5 q - 9 q^{2} + 115 q^{4} - 237 q^{6} - 70 q^{7} - 753 q^{8} + 1059 q^{9} - 605 q^{11} + 1605 q^{12} - 1498 q^{13} + 2113 q^{14} + 4883 q^{16} - 3874 q^{17} - 5838 q^{18} + 882 q^{19} + 1092 q^{21} + 1089 q^{22} + 5344 q^{23} - 13119 q^{24} - 4478 q^{26} + 2160 q^{27} - 12565 q^{28} + 5318 q^{29} - 7916 q^{31} - 21385 q^{32} - 18605 q^{34} + 5628 q^{36} + 1788 q^{37} + 34421 q^{38} - 29760 q^{39} + 5854 q^{41} + 46725 q^{42} + 4364 q^{43} - 13915 q^{44} - 33834 q^{46} - 46452 q^{47} + 127545 q^{48} - 34217 q^{49} + 19842 q^{51} - 3222 q^{52} - 4412 q^{53} - 86535 q^{54} + 115575 q^{56} - 137160 q^{57} + 58221 q^{58} + 17896 q^{59} - 35930 q^{61} + 19627 q^{62} - 100980 q^{63} + 14779 q^{64} + 28677 q^{66} - 73136 q^{67} + 83409 q^{68} + 34296 q^{69} + 43612 q^{71} - 372276 q^{72} - 142306 q^{73} - 95609 q^{74} - 6617 q^{76} + 8470 q^{77} - 15750 q^{78} - 46504 q^{79} + 79101 q^{81} - 175798 q^{82} - 81604 q^{83} - 532533 q^{84} - 101788 q^{86} - 219750 q^{87} + 91113 q^{88} + 8664 q^{89} - 203380 q^{91} - 251174 q^{92} + 46470 q^{93} - 71458 q^{94} - 925479 q^{96} + 22230 q^{97} - 59962 q^{98} - 128139 q^{99}+O(q^{100}) \) 5 * q - 9 * q^2 + 115 * q^4 - 237 * q^6 - 70 * q^7 - 753 * q^8 + 1059 * q^9 - 605 * q^11 + 1605 * q^12 - 1498 * q^13 + 2113 * q^14 + 4883 * q^16 - 3874 * q^17 - 5838 * q^18 + 882 * q^19 + 1092 * q^21 + 1089 * q^22 + 5344 * q^23 - 13119 * q^24 - 4478 * q^26 + 2160 * q^27 - 12565 * q^28 + 5318 * q^29 - 7916 * q^31 - 21385 * q^32 - 18605 * q^34 + 5628 * q^36 + 1788 * q^37 + 34421 * q^38 - 29760 * q^39 + 5854 * q^41 + 46725 * q^42 + 4364 * q^43 - 13915 * q^44 - 33834 * q^46 - 46452 * q^47 + 127545 * q^48 - 34217 * q^49 + 19842 * q^51 - 3222 * q^52 - 4412 * q^53 - 86535 * q^54 + 115575 * q^56 - 137160 * q^57 + 58221 * q^58 + 17896 * q^59 - 35930 * q^61 + 19627 * q^62 - 100980 * q^63 + 14779 * q^64 + 28677 * q^66 - 73136 * q^67 + 83409 * q^68 + 34296 * q^69 + 43612 * q^71 - 372276 * q^72 - 142306 * q^73 - 95609 * q^74 - 6617 * q^76 + 8470 * q^77 - 15750 * q^78 - 46504 * q^79 + 79101 * q^81 - 175798 * q^82 - 81604 * q^83 - 532533 * q^84 - 101788 * q^86 - 219750 * q^87 + 91113 * q^88 + 8664 * q^89 - 203380 * q^91 - 251174 * q^92 + 46470 * q^93 - 71458 * q^94 - 925479 * q^96 + 22230 * q^97 - 59962 * q^98 - 128139 * q^99

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