LMFDB - Embedded newform 825.6.a.t.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,6,Mod(1,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("825.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	825.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:	$132.316651346$
Analytic rank:	$0$
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} - x^{9} - 271 x^{8} + 309 x^{7} + 24456 x^{6} - 33410 x^{5} - 822204 x^{4} + 1367872 x^{3} + \cdots - 7036608 $ x^10 - x^9 - 271x^8 + 309x^7 + 24456x^6 - 33410x^5 - 822204x^4 + 1367872x^3 + 7443872x^2 - 12856224x - 7036608
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 5^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-3.54519$ of defining polynomial
Character	$\chi$	$=$	825.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.54519 q^{2} +9.00000 q^{3} -19.4316 q^{4} +31.9067 q^{6} +15.4153 q^{7} -182.335 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+3.54519 q^{2} +9.00000 q^{3} -19.4316 q^{4} +31.9067 q^{6} +15.4153 q^{7} -182.335 q^{8} +81.0000 q^{9} +121.000 q^{11} -174.885 q^{12} -9.16464 q^{13} +54.6502 q^{14} -24.6000 q^{16} -1481.22 q^{17} +287.160 q^{18} +1058.30 q^{19} +138.738 q^{21} +428.968 q^{22} -3006.99 q^{23} -1641.01 q^{24} -32.4904 q^{26} +729.000 q^{27} -299.544 q^{28} +3763.09 q^{29} +1375.47 q^{31} +5747.51 q^{32} +1089.00 q^{33} -5251.22 q^{34} -1573.96 q^{36} +2015.66 q^{37} +3751.87 q^{38} -82.4818 q^{39} +16545.7 q^{41} +491.852 q^{42} -13647.3 q^{43} -2351.23 q^{44} -10660.4 q^{46} +6638.58 q^{47} -221.400 q^{48} -16569.4 q^{49} -13331.0 q^{51} +178.084 q^{52} -7719.83 q^{53} +2584.44 q^{54} -2810.75 q^{56} +9524.68 q^{57} +13340.9 q^{58} +39159.4 q^{59} -8220.98 q^{61} +4876.30 q^{62} +1248.64 q^{63} +21163.2 q^{64} +3860.71 q^{66} +38209.1 q^{67} +28782.6 q^{68} -27062.9 q^{69} -48470.8 q^{71} -14769.1 q^{72} +49320.4 q^{73} +7145.91 q^{74} -20564.5 q^{76} +1865.25 q^{77} -292.414 q^{78} +16423.9 q^{79} +6561.00 q^{81} +58657.8 q^{82} -419.670 q^{83} -2695.90 q^{84} -48382.3 q^{86} +33867.8 q^{87} -22062.5 q^{88} -17081.2 q^{89} -141.276 q^{91} +58430.7 q^{92} +12379.2 q^{93} +23535.0 q^{94} +51727.5 q^{96} -3464.57 q^{97} -58741.6 q^{98} +9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} + 90 q^{3} + 223 q^{4} - 9 q^{6} + 188 q^{7} + 177 q^{8} + 810 q^{9}+O(q^{10}) $ 10 * q - q^2 + 90 * q^3 + 223 * q^4 - 9 * q^6 + 188 * q^7 + 177 * q^8 + 810 * q^9	\( 10 q - q^{2} + 90 q^{3} + 223 q^{4} - 9 q^{6} + 188 q^{7} + 177 q^{8} + 810 q^{9} + 1210 q^{11} + 2007 q^{12} - 1102 q^{13} + 684 q^{14} + 7019 q^{16} + 1106 q^{17} - 81 q^{18} + 2586 q^{19} + 1692 q^{21} - 121 q^{22} + 2206 q^{23} + 1593 q^{24} + 12001 q^{26} + 7290 q^{27} + 14452 q^{28} + 5824 q^{29} - 4586 q^{31} - 10627 q^{32} + 10890 q^{33} + 7426 q^{34} + 18063 q^{36} - 18362 q^{37} + 44001 q^{38} - 9918 q^{39} - 5474 q^{41} + 6156 q^{42} + 20496 q^{43} + 26983 q^{44} + 19981 q^{46} - 14970 q^{47} + 63171 q^{48} + 68582 q^{49} + 9954 q^{51} - 58603 q^{52} + 61980 q^{53} - 729 q^{54} + 7132 q^{56} + 23274 q^{57} + 7161 q^{58} + 61190 q^{59} + 8230 q^{61} - 4509 q^{62} + 15228 q^{63} + 152223 q^{64} - 1089 q^{66} - 11930 q^{67} + 105598 q^{68} + 19854 q^{69} + 59822 q^{71} + 14337 q^{72} - 20680 q^{73} + 132564 q^{74} + 68165 q^{76} + 22748 q^{77} + 108009 q^{78} + 234494 q^{79} + 65610 q^{81} + 151948 q^{82} + 185478 q^{83} + 130068 q^{84} - 17825 q^{86} + 52416 q^{87} + 21417 q^{88} + 181834 q^{89} + 206274 q^{91} + 98373 q^{92} - 41274 q^{93} - 64998 q^{94} - 95643 q^{96} + 304358 q^{97} + 153453 q^{98} + 98010 q^{99}+O(q^{100}) \) 10 * q - q^2 + 90 * q^3 + 223 * q^4 - 9 * q^6 + 188 * q^7 + 177 * q^8 + 810 * q^9 + 1210 * q^11 + 2007 * q^12 - 1102 * q^13 + 684 * q^14 + 7019 * q^16 + 1106 * q^17 - 81 * q^18 + 2586 * q^19 + 1692 * q^21 - 121 * q^22 + 2206 * q^23 + 1593 * q^24 + 12001 * q^26 + 7290 * q^27 + 14452 * q^28 + 5824 * q^29 - 4586 * q^31 - 10627 * q^32 + 10890 * q^33 + 7426 * q^34 + 18063 * q^36 - 18362 * q^37 + 44001 * q^38 - 9918 * q^39 - 5474 * q^41 + 6156 * q^42 + 20496 * q^43 + 26983 * q^44 + 19981 * q^46 - 14970 * q^47 + 63171 * q^48 + 68582 * q^49 + 9954 * q^51 - 58603 * q^52 + 61980 * q^53 - 729 * q^54 + 7132 * q^56 + 23274 * q^57 + 7161 * q^58 + 61190 * q^59 + 8230 * q^61 - 4509 * q^62 + 15228 * q^63 + 152223 * q^64 - 1089 * q^66 - 11930 * q^67 + 105598 * q^68 + 19854 * q^69 + 59822 * q^71 + 14337 * q^72 - 20680 * q^73 + 132564 * q^74 + 68165 * q^76 + 22748 * q^77 + 108009 * q^78 + 234494 * q^79 + 65610 * q^81 + 151948 * q^82 + 185478 * q^83 + 130068 * q^84 - 17825 * q^86 + 52416 * q^87 + 21417 * q^88 + 181834 * q^89 + 206274 * q^91 + 98373 * q^92 - 41274 * q^93 - 64998 * q^94 - 95643 * q^96 + 304358 * q^97 + 153453 * q^98 + 98010 * 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 $

$2$	3.54519	0.626707	0.313354	−	0.949637i	$-0.398548\pi$
$2$	3.54519	0.626707	0.313354	+	0.949637i	$0.398548\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	−19.4316	−0.607238
$5$	0	0
$5$	0	0
$6$	31.9067	0.361829
$7$	15.4153	0.118907	0.0594534	−	0.998231i	$-0.481064\pi$
$7$	15.4153	0.118907	0.0594534	+	0.998231i	$0.481064\pi$
$8$	−182.335	−1.00727
$9$	81.0000	0.333333
$10$	0	0
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−174.885	−0.350589
$13$	−9.16464	−0.0150403	−0.00752016	−	0.999972i	$-0.502394\pi$
$13$	−9.16464	−0.0150403	−0.00752016	+	0.999972i	$0.502394\pi$
$14$	54.6502	0.0745198
$15$	0	0
$16$	−24.6000	−0.0240234
$17$	−1481.22	−1.24308	−0.621539	−	0.783383i	$-0.713492\pi$
$17$	−1481.22	−1.24308	−0.621539	+	0.783383i	$0.713492\pi$
$18$	287.160	0.208902
$19$	1058.30	0.672549	0.336275	−	0.941764i	$-0.390833\pi$
$19$	1058.30	0.672549	0.336275	+	0.941764i	$0.390833\pi$
$20$	0	0
$21$	138.738	0.0686509
$22$	428.968	0.188959
$23$	−3006.99	−1.18526	−0.592629	−	0.805476i	$-0.701910\pi$
$23$	−3006.99	−1.18526	−0.592629	+	0.805476i	$0.701910\pi$
$24$	−1641.01	−0.581546
$25$	0	0
$26$	−32.4904	−0.00942587
$27$	729.000	0.192450
$28$	−299.544	−0.0722048
$29$	3763.09	0.830901	0.415450	−	0.909616i	$-0.363624\pi$
$29$	3763.09	0.830901	0.415450	+	0.909616i	$0.363624\pi$
$30$	0	0
$31$	1375.47	0.257067	0.128534	−	0.991705i	$-0.458973\pi$
$31$	1375.47	0.257067	0.128534	+	0.991705i	$0.458973\pi$
$32$	5747.51	0.992212
$33$	1089.00	0.174078
$34$	−5251.22	−0.779046
$35$	0	0
$36$	−1573.96	−0.202413
$37$	2015.66	0.242055	0.121027	−	0.992649i	$-0.461381\pi$
$37$	2015.66	0.242055	0.121027	+	0.992649i	$0.461381\pi$
$38$	3751.87	0.421491
$39$	−82.4818	−0.00868353
$40$	0	0
$41$	16545.7	1.53719	0.768593	−	0.639738i	$-0.220957\pi$
$41$	16545.7	1.53719	0.768593	+	0.639738i	$0.220957\pi$
$42$	491.852	0.0430240
$43$	−13647.3	−1.12558	−0.562790	−	0.826600i	$-0.690272\pi$
$43$	−13647.3	−1.12558	−0.562790	+	0.826600i	$0.690272\pi$
$44$	−2351.23	−0.183089
$45$	0	0
$46$	−10660.4	−0.742809
$47$	6638.58	0.438360	0.219180	−	0.975684i	$-0.429662\pi$
$47$	6638.58	0.438360	0.219180	+	0.975684i	$0.429662\pi$
$48$	−221.400	−0.0138699
$49$	−16569.4	−0.985861
$50$	0	0
$51$	−13331.0	−0.717691
$52$	178.084	0.00913306
$53$	−7719.83	−0.377501	−0.188751	−	0.982025i	$-0.560444\pi$
$53$	−7719.83	−0.377501	−0.188751	+	0.982025i	$0.560444\pi$
$54$	2584.44	0.120610
$55$	0	0
$56$	−2810.75	−0.119771
$57$	9524.68	0.388296
$58$	13340.9	0.520731
$59$	39159.4	1.46455	0.732277	−	0.681007i	$-0.238458\pi$
$59$	39159.4	1.46455	0.732277	+	0.681007i	$0.238458\pi$
$60$	0	0
$61$	−8220.98	−0.282878	−0.141439	−	0.989947i	$-0.545173\pi$
$61$	−8220.98	−0.282878	−0.141439	+	0.989947i	$0.545173\pi$
$62$	4876.30	0.161106
$63$	1248.64	0.0396356
$64$	21163.2	0.645850
$65$	0	0
$66$	3860.71	0.109096
$67$	38209.1	1.03987	0.519936	−	0.854205i	$-0.325956\pi$
$67$	38209.1	1.03987	0.519936	+	0.854205i	$0.325956\pi$
$68$	28782.6	0.754845
$69$	−27062.9	−0.684308
$70$	0	0
$71$	−48470.8	−1.14113	−0.570564	−	0.821253i	$-0.693275\pi$
$71$	−48470.8	−1.14113	−0.570564	+	0.821253i	$0.693275\pi$
$72$	−14769.1	−0.335756
$73$	49320.4	1.08323	0.541613	−	0.840628i	$-0.317814\pi$
$73$	49320.4	1.08323	0.541613	+	0.840628i	$0.317814\pi$
$74$	7145.91	0.151698
$75$	0	0
$76$	−20564.5	−0.408398
$77$	1865.25	0.0358518
$78$	−292.414	−0.00544203
$79$	16423.9	0.296079	0.148040	−	0.988981i	$-0.452704\pi$
$79$	16423.9	0.296079	0.148040	+	0.988981i	$0.452704\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	58657.8	0.963365
$83$	−419.670	−0.00668671	−0.00334336	−	0.999994i	$-0.501064\pi$
$83$	−419.670	−0.00668671	−0.00334336	+	0.999994i	$0.501064\pi$
$84$	−2695.90	−0.0416875
$85$	0	0
$86$	−48382.3	−0.705409
$87$	33867.8	0.479721
$88$	−22062.5	−0.303703
$89$	−17081.2	−0.228583	−0.114291	−	0.993447i	$-0.536460\pi$
$89$	−17081.2	−0.228583	−0.114291	+	0.993447i	$0.536460\pi$
$90$	0	0
$91$	−141.276	−0.00178840
$92$	58430.7	0.719733
$93$	12379.2	0.148418
$94$	23535.0	0.274723
$95$	0	0
$96$	51727.5	0.572854
$97$	−3464.57	−0.0373870	−0.0186935	−	0.999825i	$-0.505951\pi$
$97$	−3464.57	−0.0373870	−0.0186935	+	0.999825i	$0.505951\pi$
$98$	−58741.6	−0.617846
$99$	9801.00	0.100504
$100$	0	0
$101$	118690.	1.15774	0.578868	−	0.815421i	$-0.303495\pi$
$101$	118690.	1.15774	0.578868	+	0.815421i	$0.303495\pi$
$102$	−47261.0	−0.449782
$103$	107513.	0.998544	0.499272	−	0.866445i	$-0.333601\pi$
$103$	107513.	0.998544	0.499272	+	0.866445i	$0.333601\pi$
$104$	1671.03	0.0151496
$105$	0	0
$106$	−27368.3	−0.236583
$107$	187147.	1.58024	0.790120	−	0.612952i	$-0.210018\pi$
$107$	187147.	1.58024	0.790120	+	0.612952i	$0.210018\pi$
$108$	−14165.7	−0.116863
$109$	−496.203	−0.00400031	−0.00200015	−	0.999998i	$-0.500637\pi$
$109$	−496.203	−0.00400031	−0.00200015	+	0.999998i	$0.500637\pi$
$110$	0	0
$111$	18141.0	0.139750
$112$	−379.216	−0.00285655
$113$	−109520.	−0.806859	−0.403429	−	0.915011i	$-0.632182\pi$
$113$	−109520.	−0.806859	−0.403429	+	0.915011i	$0.632182\pi$
$114$	33766.8	0.243348
$115$	0	0
$116$	−73122.9	−0.504555
$117$	−742.336	−0.00501344
$118$	138827.	0.917847
$119$	−22833.5	−0.147811
$120$	0	0
$121$	14641.0	0.0909091
$122$	−29144.9	−0.177281
$123$	148912.	0.887495
$124$	−26727.6	−0.156101
$125$	0	0
$126$	4426.66	0.0248399
$127$	1438.91	0.00791634	0.00395817	−	0.999992i	$-0.498740\pi$
$127$	1438.91	0.00791634	0.00395817	+	0.999992i	$0.498740\pi$
$128$	−108893.	−0.587453
$129$	−122826.	−0.649854
$130$	0	0
$131$	289785.	1.47536	0.737680	−	0.675151i	$-0.235921\pi$
$131$	289785.	1.47536	0.737680	+	0.675151i	$0.235921\pi$
$132$	−21161.0	−0.105707
$133$	16314.0	0.0799707
$134$	135459.	0.651695
$135$	0	0
$136$	270079.	1.25211
$137$	283421.	1.29012	0.645062	−	0.764130i	$-0.276832\pi$
$137$	283421.	1.29012	0.645062	+	0.764130i	$0.276832\pi$
$138$	−95943.2	−0.428861
$139$	200510.	0.880238	0.440119	−	0.897940i	$-0.354936\pi$
$139$	200510.	0.880238	0.440119	+	0.897940i	$0.354936\pi$
$140$	0	0
$141$	59747.3	0.253087
$142$	−171838.	−0.715153
$143$	−1108.92	−0.00453483
$144$	−1992.60	−0.00800780
$145$	0	0
$146$	174850.	0.678865
$147$	−149124.	−0.569187
$148$	−39167.6	−0.146985
$149$	350853.	1.29467	0.647336	−	0.762205i	$-0.275883\pi$
$149$	350853.	1.29467	0.647336	+	0.762205i	$0.275883\pi$
$150$	0	0
$151$	−66420.6	−0.237061	−0.118531	−	0.992950i	$-0.537818\pi$
$151$	−66420.6	−0.237061	−0.118531	+	0.992950i	$0.537818\pi$
$152$	−192965.	−0.677437
$153$	−119979.	−0.414359
$154$	6612.67	0.0224686
$155$	0	0
$156$	1602.75	0.00527297
$157$	507303.	1.64255	0.821275	−	0.570533i	$-0.193263\pi$
$157$	507303.	1.64255	0.821275	+	0.570533i	$0.193263\pi$
$158$	58225.8	0.185555
$159$	−69478.5	−0.217950
$160$	0	0
$161$	−46353.7	−0.140935
$162$	23260.0	0.0696341
$163$	−402141.	−1.18552	−0.592761	−	0.805379i	$-0.701962\pi$
$163$	−402141.	−1.18552	−0.592761	+	0.805379i	$0.701962\pi$
$164$	−321511.	−0.933438
$165$	0	0
$166$	−1487.81	−0.00419061
$167$	293252.	0.813672	0.406836	−	0.913501i	$-0.366632\pi$
$167$	293252.	0.813672	0.406836	+	0.913501i	$0.366632\pi$
$168$	−25296.7	−0.0691498
$169$	−371209.	−0.999774
$170$	0	0
$171$	85722.2	0.224183
$172$	265190.	0.683495
$173$	−69667.0	−0.176975	−0.0884875	−	0.996077i	$-0.528203\pi$
$173$	−69667.0	−0.176975	−0.0884875	+	0.996077i	$0.528203\pi$
$174$	120068.	0.300644
$175$	0	0
$176$	−2976.60	−0.00724333
$177$	352434.	0.845561
$178$	−60556.1	−0.143254
$179$	137994.	0.321904	0.160952	−	0.986962i	$-0.448544\pi$
$179$	137994.	0.321904	0.160952	+	0.986962i	$0.448544\pi$
$180$	0	0
$181$	365502.	0.829264	0.414632	−	0.909989i	$-0.363910\pi$
$181$	365502.	0.829264	0.414632	+	0.909989i	$0.363910\pi$
$182$	−500.849	−0.00112080
$183$	−73988.8	−0.163320
$184$	548279.	1.19387
$185$	0	0
$186$	43886.7	0.0930145
$187$	−179228.	−0.374802
$188$	−128998.	−0.266189
$189$	11237.8	0.0228836
$190$	0	0
$191$	339173.	0.672725	0.336363	−	0.941733i	$-0.390803\pi$
$191$	339173.	0.672725	0.336363	+	0.941733i	$0.390803\pi$
$192$	190469.	0.372881
$193$	−84815.0	−0.163900	−0.0819500	−	0.996636i	$-0.526115\pi$
$193$	−84815.0	−0.163900	−0.0819500	+	0.996636i	$0.526115\pi$
$194$	−12282.6	−0.0234307
$195$	0	0
$196$	321970.	0.598653
$197$	−15771.8	−0.0289545	−0.0144772	−	0.999895i	$-0.504608\pi$
$197$	−15771.8	−0.0289545	−0.0144772	+	0.999895i	$0.504608\pi$
$198$	34746.4	0.0629864
$199$	937964.	1.67901	0.839505	−	0.543351i	$-0.182845\pi$
$199$	937964.	1.67901	0.839505	+	0.543351i	$0.182845\pi$
$200$	0	0
$201$	343882.	0.600371
$202$	420777.	0.725561
$203$	58009.1	0.0987998
$204$	259043.	0.435810
$205$	0	0
$206$	381154.	0.625795
$207$	−243566.	−0.395086
$208$	225.450	0.000361320 0
$209$	128054.	0.202781
$210$	0	0
$211$	−680076.	−1.05160	−0.525801	−	0.850608i	$-0.676234\pi$
$211$	−680076.	−1.05160	−0.525801	+	0.850608i	$0.676234\pi$
$212$	150009.	0.229233
$213$	−436237.	−0.658831
$214$	663471.	0.990348
$215$	0	0
$216$	−132922.	−0.193849
$217$	21203.3	0.0305671
$218$	−1759.14	−0.00250702
$219$	443883.	0.625401
$220$	0	0
$221$	13574.9	0.0186963
$222$	64313.2	0.0875826
$223$	398926.	0.537193	0.268596	−	0.963253i	$-0.413440\pi$
$223$	398926.	0.537193	0.268596	+	0.963253i	$0.413440\pi$
$224$	88599.5	0.117981
$225$	0	0
$226$	−388269.	−0.505664
$227$	327010.	0.421208	0.210604	−	0.977571i	$-0.432457\pi$
$227$	327010.	0.421208	0.210604	+	0.977571i	$0.432457\pi$
$228$	−185080.	−0.235788
$229$	855131.	1.07757	0.538783	−	0.842445i	$-0.318884\pi$
$229$	855131.	1.07757	0.538783	+	0.842445i	$0.318884\pi$
$230$	0	0
$231$	16787.3	0.0206990
$232$	−686142.	−0.836940
$233$	−1.30246e6	−1.57172	−0.785858	−	0.618407i	$-0.787778\pi$
$233$	−1.30246e6	−1.57172	−0.785858	+	0.618407i	$0.787778\pi$
$234$	−2631.72	−0.00314196
$235$	0	0
$236$	−760930.	−0.889333
$237$	147815.	0.170941
$238$	−80949.2	−0.0926339
$239$	−887999.	−1.00558	−0.502791	−	0.864408i	$-0.667694\pi$
$239$	−887999.	−1.00558	−0.502791	+	0.864408i	$0.667694\pi$
$240$	0	0
$241$	787905.	0.873838	0.436919	−	0.899501i	$-0.356070\pi$
$241$	787905.	0.873838	0.436919	+	0.899501i	$0.356070\pi$
$242$	51905.1	0.0569734
$243$	59049.0	0.0641500
$244$	159747.	0.171774
$245$	0	0
$246$	527920.	0.556199
$247$	−9698.92	−0.0101154
$248$	−250796.	−0.258936
$249$	−3777.03	−0.00386057
$250$	0	0
$251$	−1.07431e6	−1.07633	−0.538167	−	0.842838i	$-0.680883\pi$
$251$	−1.07431e6	−1.07633	−0.538167	+	0.842838i	$0.680883\pi$
$252$	−24263.1	−0.0240683
$253$	−363846.	−0.357368
$254$	5101.21	0.00496123
$255$	0	0
$256$	−1.06327e6	−1.01401
$257$	183068.	0.172894	0.0864471	−	0.996256i	$-0.472449\pi$
$257$	183068.	0.172894	0.0864471	+	0.996256i	$0.472449\pi$
$258$	−435441.	−0.407268
$259$	31072.1	0.0287820
$260$	0	0
$261$	304810.	0.276967
$262$	1.02734e6	0.924618
$263$	−1.79693e6	−1.60193	−0.800963	−	0.598714i	$-0.795679\pi$
$263$	−1.79693e6	−1.60193	−0.800963	+	0.598714i	$0.795679\pi$
$264$	−198563.	−0.175343
$265$	0	0
$266$	57836.2	0.0501182
$267$	−153731.	−0.131972
$268$	−742465.	−0.631450
$269$	−198575.	−0.167319	−0.0836593	−	0.996494i	$-0.526661\pi$
$269$	−198575.	−0.167319	−0.0836593	+	0.996494i	$0.526661\pi$
$270$	0	0
$271$	2.09316e6	1.73133	0.865663	−	0.500627i	$-0.166897\pi$
$271$	2.09316e6	1.73133	0.865663	+	0.500627i	$0.166897\pi$
$272$	36438.1	0.0298630
$273$	−1271.48	−0.00103253
$274$	1.00478e6	0.808530
$275$	0	0
$276$	525876.	0.415538
$277$	634155.	0.496588	0.248294	−	0.968685i	$-0.420130\pi$
$277$	634155.	0.496588	0.248294	+	0.968685i	$0.420130\pi$
$278$	710848.	0.551651
$279$	111413.	0.0856891
$280$	0	0
$281$	724201.	0.547133	0.273567	−	0.961853i	$-0.411797\pi$
$281$	724201.	0.547133	0.273567	+	0.961853i	$0.411797\pi$
$282$	211815.	0.158612
$283$	−2.42288e6	−1.79831	−0.899157	−	0.437626i	$-0.855819\pi$
$283$	−2.42288e6	−1.79831	−0.899157	+	0.437626i	$0.855819\pi$
$284$	941867.	0.692937
$285$	0	0
$286$	−3931.34	−0.00284201
$287$	255058.	0.182782
$288$	465548.	0.330737
$289$	774167.	0.545243
$290$	0	0
$291$	−31181.2	−0.0215854
$292$	−958375.	−0.657776
$293$	−742942.	−0.505575	−0.252788	−	0.967522i	$-0.581347\pi$
$293$	−742942.	−0.505575	−0.252788	+	0.967522i	$0.581347\pi$
$294$	−528674.	−0.356714
$295$	0	0
$296$	−367526.	−0.243814
$297$	88209.0	0.0580259
$298$	1.24384e6	0.811379
$299$	27558.0	0.0178266
$300$	0	0
$301$	−210378.	−0.133839
$302$	−235474.	−0.148568
$303$	1.06821e6	0.668419
$304$	−26034.1	−0.0161569
$305$	0	0
$306$	−425349.	−0.259682
$307$	−1.25868e6	−0.762203	−0.381102	−	0.924533i	$-0.624455\pi$
$307$	−1.25868e6	−0.762203	−0.381102	+	0.924533i	$0.624455\pi$
$308$	−36244.9	−0.0217706
$309$	967616.	0.576510
$310$	0	0
$311$	−1.71512e6	−1.00553	−0.502763	−	0.864424i	$-0.667683\pi$
$311$	−1.71512e6	−1.00553	−0.502763	+	0.864424i	$0.667683\pi$
$312$	15039.3	0.00874664
$313$	2.85909e6	1.64956	0.824778	−	0.565457i	$-0.191300\pi$
$313$	2.85909e6	1.64956	0.824778	+	0.565457i	$0.191300\pi$
$314$	1.79849e6	1.02940
$315$	0	0
$316$	−319143.	−0.179791
$317$	1.60936e6	0.899510	0.449755	−	0.893152i	$-0.351511\pi$
$317$	1.60936e6	0.899510	0.449755	+	0.893152i	$0.351511\pi$
$318$	−246315.	−0.136591
$319$	455334.	0.250526
$320$	0	0
$321$	1.68432e6	0.912352
$322$	−164333.	−0.0883251
$323$	−1.56758e6	−0.836031
$324$	−127491.	−0.0674709
$325$	0	0
$326$	−1.42567e6	−0.742975
$327$	−4465.83	−0.00230958
$328$	−3.01687e6	−1.54836
$329$	102336.	0.0521240
$330$	0	0
$331$	−1.21843e6	−0.611264	−0.305632	−	0.952150i	$-0.598868\pi$
$331$	−1.21843e6	−0.611264	−0.305632	+	0.952150i	$0.598868\pi$
$332$	8154.87	0.00406043
$333$	163269.	0.0806850
$334$	1.03963e6	0.509934
$335$	0	0
$336$	−3412.94	−0.00164923
$337$	−1.59524e6	−0.765160	−0.382580	−	0.923922i	$-0.624964\pi$
$337$	−1.59524e6	−0.765160	−0.382580	+	0.923922i	$0.624964\pi$
$338$	−1.31601e6	−0.626565
$339$	−985681.	−0.465840
$340$	0	0
$341$	166432.	0.0775087
$342$	303901.	0.140497
$343$	−514507.	−0.236133
$344$	2.48838e6	1.13376
$345$	0	0
$346$	−246983.	−0.110911
$347$	2.98284e6	1.32986	0.664930	−	0.746906i	$-0.268462\pi$
$347$	2.98284e6	1.32986	0.664930	+	0.746906i	$0.268462\pi$
$348$	−658106.	−0.291305
$349$	1.45121e6	0.637775	0.318887	−	0.947793i	$-0.396691\pi$
$349$	1.45121e6	0.637775	0.318887	+	0.947793i	$0.396691\pi$
$350$	0	0
$351$	−6681.02	−0.00289451
$352$	695448.	0.299163
$353$	373296.	0.159447	0.0797235	−	0.996817i	$-0.474596\pi$
$353$	373296.	0.159447	0.0797235	+	0.996817i	$0.474596\pi$
$354$	1.24945e6	0.529919
$355$	0	0
$356$	331915.	0.138804
$357$	−205502.	−0.0853384
$358$	489213.	0.201739
$359$	1.59973e6	0.655103	0.327551	−	0.944833i	$-0.393777\pi$
$359$	1.59973e6	0.655103	0.327551	+	0.944833i	$0.393777\pi$
$360$	0	0
$361$	−1.35610e6	−0.547678
$362$	1.29577e6	0.519706
$363$	131769.	0.0524864
$364$	2745.22	0.00108598
$365$	0	0
$366$	−262304.	−0.102354
$367$	−3.67213e6	−1.42316	−0.711578	−	0.702607i	$-0.752019\pi$
$367$	−3.67213e6	−1.42316	−0.711578	+	0.702607i	$0.752019\pi$
$368$	73971.9	0.0284739
$369$	1.34020e6	0.512395
$370$	0	0
$371$	−119004.	−0.0448875
$372$	−240549.	−0.0901250
$373$	−290636.	−0.108163	−0.0540814	−	0.998537i	$-0.517223\pi$
$373$	−290636.	−0.108163	−0.0540814	+	0.998537i	$0.517223\pi$
$374$	−635398.	−0.234891
$375$	0	0
$376$	−1.21045e6	−0.441546
$377$	−34487.3	−0.0124970
$378$	39840.0	0.0143413
$379$	4.72607e6	1.69006	0.845031	−	0.534718i	$-0.179582\pi$
$379$	4.72607e6	1.69006	0.845031	+	0.534718i	$0.179582\pi$
$380$	0	0
$381$	12950.2	0.00457050
$382$	1.20243e6	0.421602
$383$	1.69814e6	0.591531	0.295766	−	0.955261i	$-0.404425\pi$
$383$	1.69814e6	0.591531	0.295766	+	0.955261i	$0.404425\pi$
$384$	−980033.	−0.339166
$385$	0	0
$386$	−300685.	−0.102717
$387$	−1.10543e6	−0.375193
$388$	67322.3	0.0227028
$389$	−614215.	−0.205800	−0.102900	−	0.994692i	$-0.532812\pi$
$389$	−614215.	−0.205800	−0.102900	+	0.994692i	$0.532812\pi$
$390$	0	0
$391$	4.45403e6	1.47337
$392$	3.02117e6	0.993026
$393$	2.60807e6	0.851799
$394$	−55914.0	−0.0181460
$395$	0	0
$396$	−190449.	−0.0610297
$397$	151925.	0.0483786	0.0241893	−	0.999707i	$-0.492300\pi$
$397$	151925.	0.0483786	0.0241893	+	0.999707i	$0.492300\pi$
$398$	3.32526e6	1.05225
$399$	146826.	0.0461711
$400$	0	0
$401$	−411747.	−0.127870	−0.0639350	−	0.997954i	$-0.520365\pi$
$401$	−411747.	−0.127870	−0.0639350	+	0.997954i	$0.520365\pi$
$402$	1.21913e6	0.376256
$403$	−12605.7	−0.00386637
$404$	−2.30633e6	−0.703021
$405$	0	0
$406$	205653.	0.0619186
$407$	243895.	0.0729823
$408$	2.43071e6	0.722907
$409$	−522118.	−0.154334	−0.0771668	−	0.997018i	$-0.524587\pi$
$409$	−522118.	−0.154334	−0.0771668	+	0.997018i	$0.524587\pi$
$410$	0	0
$411$	2.55079e6	0.744853
$412$	−2.08915e6	−0.606354
$413$	603653.	0.174146
$414$	−863489.	−0.247603
$415$	0	0
$416$	−52673.8	−0.0149232
$417$	1.80459e6	0.508205
$418$	453976.	0.127084
$419$	4.42421e6	1.23112	0.615561	−	0.788090i	$-0.288930\pi$
$419$	4.42421e6	1.23112	0.615561	+	0.788090i	$0.288930\pi$
$420$	0	0
$421$	41986.3	0.0115452	0.00577261	−	0.999983i	$-0.498163\pi$
$421$	41986.3	0.0115452	0.00577261	+	0.999983i	$0.498163\pi$
$422$	−2.41100e6	−0.659047
$423$	537725.	0.146120
$424$	1.40760e6	0.380245
$425$	0	0
$426$	−1.54654e6	−0.412894
$427$	−126729.	−0.0336361
$428$	−3.63657e6	−0.959582
$429$	−9980.29	−0.00261818
$430$	0	0
$431$	2.90650e6	0.753664	0.376832	−	0.926282i	$-0.377013\pi$
$431$	2.90650e6	0.753664	0.376832	+	0.926282i	$0.377013\pi$
$432$	−17933.4	−0.00462331
$433$	−1.49232e6	−0.382508	−0.191254	−	0.981541i	$-0.561255\pi$
$433$	−1.49232e6	−0.382508	−0.191254	+	0.981541i	$0.561255\pi$
$434$	75169.7	0.0191566
$435$	0	0
$436$	9642.04	0.00242914
$437$	−3.18229e6	−0.797144
$438$	1.57365e6	0.391943
$439$	−6.08351e6	−1.50658	−0.753291	−	0.657687i	$-0.771535\pi$
$439$	−6.08351e6	−1.50658	−0.753291	+	0.657687i	$0.771535\pi$
$440$	0	0
$441$	−1.34212e6	−0.328620
$442$	48125.5	0.0117171
$443$	1.20270e6	0.291171	0.145586	−	0.989346i	$-0.453493\pi$
$443$	1.20270e6	0.291171	0.145586	+	0.989346i	$0.453493\pi$
$444$	−352509.	−0.0848618
$445$	0	0
$446$	1.41427e6	0.336662
$447$	3.15768e6	0.747479
$448$	326237.	0.0767960
$449$	−935321.	−0.218950	−0.109475	−	0.993990i	$-0.534917\pi$
$449$	−935321.	−0.218950	−0.109475	+	0.993990i	$0.534917\pi$
$450$	0	0
$451$	2.00203e6	0.463479
$452$	2.12815e6	0.489956
$453$	−597786.	−0.136867
$454$	1.15931e6	0.263974
$455$	0	0
$456$	−1.73668e6	−0.391118
$457$	−530855.	−0.118901	−0.0594504	−	0.998231i	$-0.518935\pi$
$457$	−530855.	−0.118901	−0.0594504	+	0.998231i	$0.518935\pi$
$458$	3.03160e6	0.675318
$459$	−1.07981e6	−0.239230
$460$	0	0
$461$	2.26064e6	0.495426	0.247713	−	0.968833i	$-0.420321\pi$
$461$	2.26064e6	0.495426	0.247713	+	0.968833i	$0.420321\pi$
$462$	59514.1	0.0129722
$463$	3.48143e6	0.754753	0.377376	−	0.926060i	$-0.376826\pi$
$463$	3.48143e6	0.754753	0.377376	+	0.926060i	$0.376826\pi$
$464$	−92571.8	−0.0199611
$465$	0	0
$466$	−4.61746e6	−0.985006
$467$	6.14838e6	1.30457	0.652287	−	0.757972i	$-0.273810\pi$
$467$	6.14838e6	1.30457	0.652287	+	0.757972i	$0.273810\pi$
$468$	14424.8	0.00304435
$469$	589005.	0.123648
$470$	0	0
$471$	4.56573e6	0.948326
$472$	−7.14012e6	−1.47520
$473$	−1.65133e6	−0.339375
$474$	524032.	0.107130
$475$	0	0
$476$	443692.	0.0897562
$477$	−625307.	−0.125834
$478$	−3.14813e6	−0.630206
$479$	−5.92932e6	−1.18077	−0.590386	−	0.807121i	$-0.701024\pi$
$479$	−5.92932e6	−1.18077	−0.590386	+	0.807121i	$0.701024\pi$
$480$	0	0
$481$	−18472.8	−0.00364058
$482$	2.79327e6	0.547641
$483$	−417183.	−0.0813690
$484$	−284498.	−0.0552035
$485$	0	0
$486$	209340.	0.0402033
$487$	−8.99316e6	−1.71826	−0.859132	−	0.511754i	$-0.828996\pi$
$487$	−8.99316e6	−1.71826	−0.859132	+	0.511754i	$0.828996\pi$
$488$	1.49897e6	0.284934
$489$	−3.61927e6	−0.684461
$490$	0	0
$491$	−2.74306e6	−0.513489	−0.256745	−	0.966479i	$-0.582650\pi$
$491$	−2.74306e6	−0.513489	−0.256745	+	0.966479i	$0.582650\pi$
$492$	−2.89359e6	−0.538921
$493$	−5.57397e6	−1.03287
$494$	−34384.5	−0.00633936
$495$	0	0
$496$	−33836.5	−0.00617563
$497$	−747192.	−0.135688
$498$	−13390.3	−0.00241945
$499$	−6.85332e6	−1.23211	−0.616055	−	0.787703i	$-0.711270\pi$
$499$	−6.85332e6	−1.23211	−0.616055	+	0.787703i	$0.711270\pi$
$500$	0	0
$501$	2.63927e6	0.469774
$502$	−3.80865e6	−0.674546
$503$	−3.53279e6	−0.622583	−0.311292	−	0.950314i	$-0.600762\pi$
$503$	−3.53279e6	−0.622583	−0.311292	+	0.950314i	$0.600762\pi$
$504$	−227671.	−0.0399237
$505$	0	0
$506$	−1.28990e6	−0.223965
$507$	−3.34088e6	−0.577220
$508$	−27960.4	−0.00480711
$509$	−8.42114e6	−1.44071	−0.720354	−	0.693606i	$-0.756021\pi$
$509$	−8.42114e6	−1.44071	−0.720354	+	0.693606i	$0.756021\pi$
$510$	0	0
$511$	760288.	0.128803
$512$	−284922.	−0.0480343
$513$	771499.	0.129432
$514$	649012.	0.108354
$515$	0	0
$516$	2.38671e6	0.394616
$517$	803269.	0.132170
$518$	110156.	0.0180379
$519$	−627003.	−0.102177
$520$	0	0
$521$	1.11375e6	0.179761	0.0898804	−	0.995953i	$-0.471352\pi$
$521$	1.11375e6	0.179761	0.0898804	+	0.995953i	$0.471352\pi$
$522$	1.08061e6	0.173577
$523$	−1.22565e6	−0.195935	−0.0979674	−	0.995190i	$-0.531234\pi$
$523$	−1.22565e6	−0.195935	−0.0979674	+	0.995190i	$0.531234\pi$
$524$	−5.63100e6	−0.895895
$525$	0	0
$526$	−6.37047e6	−1.00394
$527$	−2.03738e6	−0.319555
$528$	−26789.4	−0.00418194
$529$	2.60565e6	0.404834
$530$	0	0
$531$	3.17191e6	0.488185
$532$	−317007.	−0.0485613
$533$	−151636.	−0.0231198
$534$	−545005.	−0.0827080
$535$	0	0
$536$	−6.96686e6	−1.04743
$537$	1.24194e6	0.185851
$538$	−703987.	−0.104860
$539$	−2.00489e6	−0.297248
$540$	0	0
$541$	−47884.8	−0.00703403	−0.00351701	−	0.999994i	$-0.501120\pi$
$541$	−47884.8	−0.00703403	−0.00351701	+	0.999994i	$0.501120\pi$
$542$	7.42065e6	1.08503
$543$	3.28951e6	0.478776
$544$	−8.51334e6	−1.23340
$545$	0	0
$546$	−4507.64	−0.000647095 0
$547$	1.04705e6	0.149624	0.0748118	−	0.997198i	$-0.476164\pi$
$547$	1.04705e6	0.149624	0.0748118	+	0.997198i	$0.476164\pi$
$548$	−5.50734e6	−0.783412
$549$	−665899.	−0.0942926
$550$	0	0
$551$	3.98247e6	0.558822
$552$	4.93451e6	0.689282
$553$	253179.	0.0352059
$554$	2.24820e6	0.311215
$555$	0	0
$556$	−3.89624e6	−0.534514
$557$	8.54477e6	1.16698	0.583488	−	0.812121i	$-0.301687\pi$
$557$	8.54477e6	1.16698	0.583488	+	0.812121i	$0.301687\pi$
$558$	394980.	0.0537020
$559$	125073.	0.0169291
$560$	0	0
$561$	−1.61305e6	−0.216392
$562$	2.56743e6	0.342892
$563$	3.21883e6	0.427984	0.213992	−	0.976835i	$-0.431353\pi$
$563$	3.21883e6	0.427984	0.213992	+	0.976835i	$0.431353\pi$
$564$	−1.16099e6	−0.153684
$565$	0	0
$566$	−8.58957e6	−1.12702
$567$	101140.	0.0132119
$568$	8.83792e6	1.14942
$569$	−9.31971e6	−1.20676	−0.603381	−	0.797453i	$-0.706180\pi$
$569$	−9.31971e6	−1.20676	−0.603381	+	0.797453i	$0.706180\pi$
$570$	0	0
$571$	1.38799e7	1.78154	0.890769	−	0.454457i	$-0.150167\pi$
$571$	1.38799e7	1.78154	0.890769	+	0.454457i	$0.150167\pi$
$572$	21548.1	0.00275372
$573$	3.05256e6	0.388398
$574$	904228.	0.114551
$575$	0	0
$576$	1.71422e6	0.215283
$577$	−4.91293e6	−0.614330	−0.307165	−	0.951656i	$-0.599380\pi$
$577$	−4.91293e6	−0.614330	−0.307165	+	0.951656i	$0.599380\pi$
$578$	2.74457e6	0.341708
$579$	−763335.	−0.0946278
$580$	0	0
$581$	−6469.34	−0.000795096 0
$582$	−110543.	−0.0135277
$583$	−934100.	−0.113821
$584$	−8.99282e6	−1.09110
$585$	0	0
$586$	−2.63387e6	−0.316848
$587$	5.36479e6	0.642624	0.321312	−	0.946973i	$-0.395876\pi$
$587$	5.36479e6	0.642624	0.321312	+	0.946973i	$0.395876\pi$
$588$	2.89773e6	0.345632
$589$	1.45566e6	0.172890
$590$	0	0
$591$	−141946.	−0.0167169
$592$	−49585.3	−0.00581498
$593$	8.86855e6	1.03566	0.517829	−	0.855484i	$-0.326741\pi$
$593$	8.86855e6	1.03566	0.517829	+	0.855484i	$0.326741\pi$
$594$	312718.	0.0363652
$595$	0	0
$596$	−6.81764e6	−0.786174
$597$	8.44168e6	0.969377
$598$	97698.3	0.0111721
$599$	−1.10799e7	−1.26174	−0.630869	−	0.775889i	$-0.717302\pi$
$599$	−1.10799e7	−1.26174	−0.630869	+	0.775889i	$0.717302\pi$
$600$	0	0
$601$	−5.50666e6	−0.621873	−0.310937	−	0.950431i	$-0.600643\pi$
$601$	−5.50666e6	−0.621873	−0.310937	+	0.950431i	$0.600643\pi$
$602$	−745828.	−0.0838779
$603$	3.09494e6	0.346624
$604$	1.29066e6	0.143953
$605$	0	0
$606$	3.78700e6	0.418903
$607$	−1.29430e7	−1.42581	−0.712906	−	0.701259i	$-0.752621\pi$
$607$	−1.29430e7	−1.42581	−0.712906	+	0.701259i	$0.752621\pi$
$608$	6.08257e6	0.667311
$609$	522082.	0.0570421
$610$	0	0
$611$	−60840.2	−0.00659307
$612$	2.33139e6	0.251615
$613$	−3.41360e6	−0.366911	−0.183456	−	0.983028i	$-0.558728\pi$
$613$	−3.41360e6	−0.366911	−0.183456	+	0.983028i	$0.558728\pi$
$614$	−4.46227e6	−0.477678
$615$	0	0
$616$	−340100.	−0.0361123
$617$	−1.36370e7	−1.44213	−0.721067	−	0.692865i	$-0.756348\pi$
$617$	−1.36370e7	−1.44213	−0.721067	+	0.692865i	$0.756348\pi$
$618$	3.43038e6	0.361303
$619$	−6.21254e6	−0.651692	−0.325846	−	0.945423i	$-0.605649\pi$
$619$	−6.21254e6	−0.651692	−0.325846	+	0.945423i	$0.605649\pi$
$620$	0	0
$621$	−2.19210e6	−0.228103
$622$	−6.08042e6	−0.630170
$623$	−263312.	−0.0271801
$624$	2029.05	0.000208608 0
$625$	0	0
$626$	1.01360e7	1.03379
$627$	1.15249e6	0.117076
$628$	−9.85772e6	−0.997419
$629$	−2.98565e6	−0.300893
$630$	0	0
$631$	−3.32349e6	−0.332293	−0.166146	−	0.986101i	$-0.553132\pi$
$631$	−3.32349e6	−0.332293	−0.166146	+	0.986101i	$0.553132\pi$
$632$	−2.99465e6	−0.298231
$633$	−6.12069e6	−0.607143
$634$	5.70550e6	0.563729
$635$	0	0
$636$	1.35008e6	0.132348
$637$	151852.	0.0148277
$638$	1.61424e6	0.157006
$639$	−3.92614e6	−0.380376
$640$	0	0
$641$	−1.81780e6	−0.174744	−0.0873720	−	0.996176i	$-0.527847\pi$
$641$	−1.81780e6	−0.174744	−0.0873720	+	0.996176i	$0.527847\pi$
$642$	5.97124e6	0.571777
$643$	−421961.	−0.0402481	−0.0201240	−	0.999797i	$-0.506406\pi$
$643$	−421961.	−0.0402481	−0.0201240	+	0.999797i	$0.506406\pi$
$644$	900727.	0.0855813
$645$	0	0
$646$	−5.55736e6	−0.523947
$647$	−5.62498e6	−0.528275	−0.264138	−	0.964485i	$-0.585087\pi$
$647$	−5.62498e6	−0.528275	−0.264138	+	0.964485i	$0.585087\pi$
$648$	−1.19630e6	−0.111919
$649$	4.73828e6	0.441580
$650$	0	0
$651$	190830.	0.0176479
$652$	7.81426e6	0.719894
$653$	1.69247e7	1.55324	0.776619	−	0.629970i	$-0.216933\pi$
$653$	1.69247e7	1.55324	0.776619	+	0.629970i	$0.216933\pi$
$654$	−15832.2	−0.00144743
$655$	0	0
$656$	−407025.	−0.0369285
$657$	3.99495e6	0.361075
$658$	362800.	0.0326665
$659$	−480657.	−0.0431144	−0.0215572	−	0.999768i	$-0.506862\pi$
$659$	−480657.	−0.0431144	−0.0215572	+	0.999768i	$0.506862\pi$
$660$	0	0
$661$	−1.53510e7	−1.36657	−0.683285	−	0.730151i	$-0.739449\pi$
$661$	−1.53510e7	−1.36657	−0.683285	+	0.730151i	$0.739449\pi$
$662$	−4.31955e6	−0.383083
$663$	122174.	0.0107943
$664$	76520.5	0.00673531
$665$	0	0
$666$	578819.	0.0505658
$667$	−1.13156e7	−0.984831
$668$	−5.69836e6	−0.494093
$669$	3.59033e6	0.310148
$670$	0	0
$671$	−994738.	−0.0852909
$672$	797396.	0.0681163
$673$	−3.83589e6	−0.326459	−0.163229	−	0.986588i	$-0.552191\pi$
$673$	−3.83589e6	−0.326459	−0.163229	+	0.986588i	$0.552191\pi$
$674$	−5.65545e6	−0.479531
$675$	0	0
$676$	7.21319e6	0.607101
$677$	−5.74417e6	−0.481676	−0.240838	−	0.970565i	$-0.577422\pi$
$677$	−5.74417e6	−0.481676	−0.240838	+	0.970565i	$0.577422\pi$
$678$	−3.49443e6	−0.291945
$679$	−53407.5	−0.00444557
$680$	0	0
$681$	2.94309e6	0.243185
$682$	590033.	0.0485753
$683$	2.11651e7	1.73608	0.868038	−	0.496498i	$-0.165381\pi$
$683$	2.11651e7	1.73608	0.868038	+	0.496498i	$0.165381\pi$
$684$	−1.66572e6	−0.136133
$685$	0	0
$686$	−1.82402e6	−0.147986
$687$	7.69618e6	0.622133
$688$	335724.	0.0270403
$689$	70749.5	0.00567774
$690$	0	0
$691$	−2.20475e7	−1.75657	−0.878283	−	0.478142i	$-0.841311\pi$
$691$	−2.20475e7	−1.75657	−0.878283	+	0.478142i	$0.841311\pi$
$692$	1.35374e6	0.107466
$693$	151085.	0.0119506
$694$	1.05747e7	0.833432
$695$	0	0
$696$	−6.17528e6	−0.483207
$697$	−2.45079e7	−1.91084
$698$	5.14482e6	0.399698
$699$	−1.17221e7	−0.907431
$700$	0	0
$701$	1.26680e7	0.973676	0.486838	−	0.873492i	$-0.338150\pi$
$701$	1.26680e7	0.973676	0.486838	+	0.873492i	$0.338150\pi$
$702$	−23685.5	−0.00181401
$703$	2.13317e6	0.162794
$704$	2.56075e6	0.194731
$705$	0	0
$706$	1.32341e6	0.0999266
$707$	1.82964e6	0.137663
$708$	−6.84837e6	−0.513457
$709$	−6.24919e6	−0.466883	−0.233441	−	0.972371i	$-0.574999\pi$
$709$	−6.24919e6	−0.466883	−0.233441	+	0.972371i	$0.574999\pi$
$710$	0	0
$711$	1.33033e6	0.0986931
$712$	3.11450e6	0.230244
$713$	−4.13603e6	−0.304691
$714$	−728542.	−0.0534822
$715$	0	0
$716$	−2.68144e6	−0.195472
$717$	−7.99199e6	−0.580573
$718$	5.67133e6	0.410558
$719$	2.29008e6	0.165207	0.0826036	−	0.996582i	$-0.473676\pi$
$719$	2.29008e6	0.165207	0.0826036	+	0.996582i	$0.473676\pi$
$720$	0	0
$721$	1.65734e6	0.118734
$722$	−4.80765e6	−0.343233
$723$	7.09114e6	0.504511
$724$	−7.10229e6	−0.503561
$725$	0	0
$726$	467146.	0.0328936
$727$	−5.32482e6	−0.373653	−0.186827	−	0.982393i	$-0.559820\pi$
$727$	−5.32482e6	−0.373653	−0.186827	+	0.982393i	$0.559820\pi$
$728$	25759.5	0.00180139
$729$	531441.	0.0370370
$730$	0	0
$731$	2.02147e7	1.39918
$732$	1.43772e6	0.0991739
$733$	2.07826e7	1.42870	0.714348	−	0.699790i	$-0.246723\pi$
$733$	2.07826e7	1.42870	0.714348	+	0.699790i	$0.246723\pi$
$734$	−1.30184e7	−0.891902
$735$	0	0
$736$	−1.72827e7	−1.17603
$737$	4.62330e6	0.313533
$738$	4.75128e6	0.321122
$739$	1.24923e7	0.841454	0.420727	−	0.907187i	$-0.361775\pi$
$739$	1.24923e7	0.841454	0.420727	+	0.907187i	$0.361775\pi$
$740$	0	0
$741$	−87290.3	−0.00584010
$742$	−421890.	−0.0281313
$743$	−2.39696e7	−1.59290	−0.796450	−	0.604705i	$-0.793291\pi$
$743$	−2.39696e7	−1.59290	−0.796450	+	0.604705i	$0.793291\pi$
$744$	−2.25717e6	−0.149497
$745$	0	0
$746$	−1.03036e6	−0.0677864
$747$	−33993.3	−0.00222890
$748$	3.48269e6	0.227594
$749$	2.88493e6	0.187901
$750$	0	0
$751$	1.76984e6	0.114508	0.0572539	−	0.998360i	$-0.481766\pi$
$751$	1.76984e6	0.114508	0.0572539	+	0.998360i	$0.481766\pi$
$752$	−163309.	−0.0105309
$753$	−9.66883e6	−0.621422
$754$	−122264.	−0.00783197
$755$	0	0
$756$	−218368.	−0.0138958
$757$	−1.88709e7	−1.19689	−0.598443	−	0.801165i	$-0.704214\pi$
$757$	−1.88709e7	−1.19689	−0.598443	+	0.801165i	$0.704214\pi$
$758$	1.67548e7	1.05917
$759$	−3.27461e6	−0.206327
$760$	0	0
$761$	9.56502e6	0.598721	0.299360	−	0.954140i	$-0.403227\pi$
$761$	9.56502e6	0.598721	0.299360	+	0.954140i	$0.403227\pi$
$762$	45910.9	0.00286437
$763$	−7649.12	−0.000475664 0
$764$	−6.59068e6	−0.408504
$765$	0	0
$766$	6.02025e6	0.370717
$767$	−358881.	−0.0220274
$768$	−9.56941e6	−0.585439
$769$	2.63227e7	1.60514	0.802572	−	0.596556i	$-0.203464\pi$
$769$	2.63227e7	1.60514	0.802572	+	0.596556i	$0.203464\pi$
$770$	0	0
$771$	1.64761e6	0.0998205
$772$	1.64809e6	0.0995264
$773$	−1.07241e7	−0.645525	−0.322762	−	0.946480i	$-0.604611\pi$
$773$	−1.07241e7	−0.645525	−0.322762	+	0.946480i	$0.604611\pi$
$774$	−3.91897e6	−0.235136
$775$	0	0
$776$	631713.	0.0376587
$777$	279649.	0.0166173
$778$	−2.17751e6	−0.128977
$779$	1.75103e7	1.03383
$780$	0	0
$781$	−5.86497e6	−0.344063
$782$	1.57904e7	0.923369
$783$	2.74329e6	0.159907
$784$	407606.	0.0236837
$785$	0	0
$786$	9.24609e6	0.533829
$787$	−2.31773e7	−1.33391	−0.666954	−	0.745099i	$-0.732402\pi$
$787$	−2.31773e7	−1.33391	−0.666954	+	0.745099i	$0.732402\pi$
$788$	306472.	0.0175823
$789$	−1.61724e7	−0.924873
$790$	0	0
$791$	−1.68828e6	−0.0959411
$792$	−1.78706e6	−0.101234
$793$	75342.3	0.00425457
$794$	538604.	0.0303192
$795$	0	0
$796$	−1.82262e7	−1.01956
$797$	5.94831e6	0.331702	0.165851	−	0.986151i	$-0.446963\pi$
$797$	5.94831e6	0.331702	0.165851	+	0.986151i	$0.446963\pi$
$798$	520526.	0.0289358
$799$	−9.83323e6	−0.544916
$800$	0	0
$801$	−1.38358e6	−0.0761942
$802$	−1.45972e6	−0.0801371
$803$	5.96776e6	0.326605
$804$	−6.68219e6	−0.364568
$805$	0	0
$806$	−44689.6	−0.00242308
$807$	−1.78718e6	−0.0966014
$808$	−2.16413e7	−1.16615
$809$	2.46026e6	0.132163	0.0660815	−	0.997814i	$-0.478950\pi$
$809$	2.46026e6	0.132163	0.0660815	+	0.997814i	$0.478950\pi$
$810$	0	0
$811$	−1.67473e7	−0.894112	−0.447056	−	0.894506i	$-0.647528\pi$
$811$	−1.67473e7	−0.894112	−0.447056	+	0.894506i	$0.647528\pi$
$812$	−1.12721e6	−0.0599950
$813$	1.88384e7	0.999582
$814$	864655.	0.0457385
$815$	0	0
$816$	327943.	0.0172414
$817$	−1.44429e7	−0.757008
$818$	−1.85101e6	−0.0967220
$819$	−11443.3	−0.000596132 0
$820$	0	0
$821$	2.04537e7	1.05904	0.529521	−	0.848297i	$-0.322372\pi$
$821$	2.04537e7	1.05904	0.529521	+	0.848297i	$0.322372\pi$
$822$	9.04305e6	0.466805
$823$	6.10386e6	0.314127	0.157063	−	0.987589i	$-0.449797\pi$
$823$	6.10386e6	0.314127	0.157063	+	0.987589i	$0.449797\pi$
$824$	−1.96033e7	−1.00580
$825$	0	0
$826$	2.14007e6	0.109138
$827$	−1.25743e7	−0.639321	−0.319661	−	0.947532i	$-0.603569\pi$
$827$	−1.25743e7	−0.639321	−0.319661	+	0.947532i	$0.603569\pi$
$828$	4.73289e6	0.239911
$829$	−3.64808e6	−0.184365	−0.0921824	−	0.995742i	$-0.529384\pi$
$829$	−3.64808e6	−0.184365	−0.0921824	+	0.995742i	$0.529384\pi$
$830$	0	0
$831$	5.70740e6	0.286705
$832$	−193953.	−0.00971378
$833$	2.45429e7	1.22550
$834$	6.39763e6	0.318496
$835$	0	0
$836$	−2.48830e6	−0.123137
$837$	1.00272e6	0.0494726
$838$	1.56847e7	0.771552
$839$	3.98638e7	1.95512	0.977560	−	0.210657i	$-0.0675602\pi$
$839$	3.98638e7	1.95512	0.977560	+	0.210657i	$0.0675602\pi$
$840$	0	0
$841$	−6.35033e6	−0.309604
$842$	148849.	0.00723547
$843$	6.51781e6	0.315888
$844$	1.32150e7	0.638573
$845$	0	0
$846$	1.90634e6	0.0915744
$847$	225695.	0.0108097
$848$	189908.	0.00906886
$849$	−2.18059e7	−1.03826
$850$	0	0
$851$	−6.06108e6	−0.286897
$852$	8.47680e6	0.400067
$853$	−7.03128e6	−0.330873	−0.165437	−	0.986220i	$-0.552903\pi$
$853$	−7.03128e6	−0.330873	−0.165437	+	0.986220i	$0.552903\pi$
$854$	−449278.	−0.0210800
$855$	0	0
$856$	−3.41234e7	−1.59172
$857$	5.35026e6	0.248842	0.124421	−	0.992230i	$-0.460293\pi$
$857$	5.35026e6	0.248842	0.124421	+	0.992230i	$0.460293\pi$
$858$	−35382.0	−0.00164083
$859$	3.74127e7	1.72996	0.864981	−	0.501805i	$-0.167331\pi$
$859$	3.74127e7	1.72996	0.864981	+	0.501805i	$0.167331\pi$
$860$	0	0
$861$	2.29552e6	0.105529
$862$	1.03041e7	0.472326
$863$	−2.03619e7	−0.930661	−0.465331	−	0.885137i	$-0.654065\pi$
$863$	−2.03619e7	−0.930661	−0.465331	+	0.885137i	$0.654065\pi$
$864$	4.18993e6	0.190951
$865$	0	0
$866$	−5.29054e6	−0.239721
$867$	6.96750e6	0.314796
$868$	−412014.	−0.0185615
$869$	1.98729e6	0.0892713
$870$	0	0
$871$	−350173.	−0.0156400
$872$	90475.2	0.00402938
$873$	−280630.	−0.0124623
$874$	−1.12818e7	−0.499576
$875$	0	0
$876$	−8.62537e6	−0.379767
$877$	−2.69907e7	−1.18499	−0.592497	−	0.805573i	$-0.701858\pi$
$877$	−2.69907e7	−1.18499	−0.592497	+	0.805573i	$0.701858\pi$
$878$	−2.15672e7	−0.944186
$879$	−6.68648e6	−0.291894
$880$	0	0
$881$	−5.82848e6	−0.252997	−0.126499	−	0.991967i	$-0.540374\pi$
$881$	−5.82848e6	−0.252997	−0.126499	+	0.991967i	$0.540374\pi$
$882$	−4.75807e6	−0.205949
$883$	4.30317e6	0.185732	0.0928661	−	0.995679i	$-0.470397\pi$
$883$	4.30317e6	0.185732	0.0928661	+	0.995679i	$0.470397\pi$
$884$	−263782.	−0.0113531
$885$	0	0
$886$	4.26381e6	0.182479
$887$	5.28627e6	0.225601	0.112800	−	0.993618i	$-0.464018\pi$
$887$	5.28627e6	0.225601	0.112800	+	0.993618i	$0.464018\pi$
$888$	−3.30773e6	−0.140766
$889$	22181.2	0.000941308 0
$890$	0	0
$891$	793881.	0.0335013
$892$	−7.75178e6	−0.326204
$893$	7.02560e6	0.294819
$894$	1.11946e7	0.468450
$895$	0	0
$896$	−1.67861e6	−0.0698522
$897$	248022.	0.0102922
$898$	−3.31589e6	−0.137217
$899$	5.17601e6	0.213597
$900$	0	0
$901$	1.14348e7	0.469263
$902$	7.09759e6	0.290466
$903$	−1.89340e6	−0.0772721
$904$	1.99693e7	0.812723
$905$	0	0
$906$	−2.11926e6	−0.0857758
$907$	−1.24628e6	−0.0503035	−0.0251518	−	0.999684i	$-0.508007\pi$
$907$	−1.24628e6	−0.0503035	−0.0251518	+	0.999684i	$0.508007\pi$
$908$	−6.35434e6	−0.255774
$909$	9.61386e6	0.385912
$910$	0	0
$911$	−7.11472e6	−0.284028	−0.142014	−	0.989865i	$-0.545358\pi$
$911$	−7.11472e6	−0.284028	−0.142014	+	0.989865i	$0.545358\pi$
$912$	−234307.	−0.00932820
$913$	−50780.1	−0.00201612
$914$	−1.88198e6	−0.0745160
$915$	0	0
$916$	−1.66166e7	−0.654339
$917$	4.46713e6	0.175430
$918$	−3.82814e6	−0.149927
$919$	8.70813e6	0.340123	0.170061	−	0.985433i	$-0.445603\pi$
$919$	8.70813e6	0.340123	0.170061	+	0.985433i	$0.445603\pi$
$920$	0	0
$921$	−1.13282e7	−0.440058
$922$	8.01440e6	0.310487
$923$	444218.	0.0171629
$924$	−326204.	−0.0125692
$925$	0	0
$926$	1.23423e7	0.473009
$927$	8.70854e6	0.332848
$928$	2.16284e7	0.824430
$929$	−1.65935e6	−0.0630809	−0.0315405	−	0.999502i	$-0.510041\pi$
$929$	−1.65935e6	−0.0630809	−0.0315405	+	0.999502i	$0.510041\pi$
$930$	0	0
$931$	−1.75353e7	−0.663040
$932$	2.53089e7	0.954406
$933$	−1.54361e7	−0.580541
$934$	2.17972e7	0.817585
$935$	0	0
$936$	135354.	0.00504987
$937$	−3.17616e7	−1.18183	−0.590913	−	0.806735i	$-0.701232\pi$
$937$	−3.17616e7	−1.18183	−0.590913	+	0.806735i	$0.701232\pi$
$938$	2.08814e6	0.0774911
$939$	2.57318e7	0.952371
$940$	0	0
$941$	4.87851e7	1.79603	0.898014	−	0.439966i	$-0.145010\pi$
$941$	4.87851e7	1.79603	0.898014	+	0.439966i	$0.145010\pi$
$942$	1.61864e7	0.594323
$943$	−4.97529e7	−1.82196
$944$	−963319.	−0.0351836
$945$	0	0
$946$	−5.85426e6	−0.212689
$947$	−9.76025e6	−0.353660	−0.176830	−	0.984241i	$-0.556584\pi$
$947$	−9.76025e6	−0.353660	−0.176830	+	0.984241i	$0.556584\pi$
$948$	−2.87228e6	−0.103802
$949$	−452003.	−0.0162921
$950$	0	0
$951$	1.44843e7	0.519332
$952$	4.16335e6	0.148885
$953$	3.78772e7	1.35097	0.675485	−	0.737374i	$-0.263934\pi$
$953$	3.78772e7	1.35097	0.675485	+	0.737374i	$0.263934\pi$
$954$	−2.21683e6	−0.0788609
$955$	0	0
$956$	1.72553e7	0.610628
$957$	4.09800e6	0.144641
$958$	−2.10206e7	−0.739998
$959$	4.36903e6	0.153405
$960$	0	0
$961$	−2.67372e7	−0.933916
$962$	−65489.7	−0.00228158
$963$	1.51589e7	0.526747
$964$	−1.53103e7	−0.530628
$965$	0	0
$966$	−1.47899e6	−0.0509945
$967$	1.59962e7	0.550113	0.275056	−	0.961428i	$-0.411304\pi$
$967$	1.59962e7	0.550113	0.275056	+	0.961428i	$0.411304\pi$
$968$	−2.66957e6	−0.0915698
$969$	−1.41082e7	−0.482683
$970$	0	0
$971$	5.23637e7	1.78231	0.891153	−	0.453703i	$-0.149897\pi$
$971$	5.23637e7	1.78231	0.891153	+	0.453703i	$0.149897\pi$
$972$	−1.14742e6	−0.0389544
$973$	3.09093e6	0.104666
$974$	−3.18825e7	−1.07685
$975$	0	0
$976$	202236.	0.00679569
$977$	5.78033e6	0.193739	0.0968693	−	0.995297i	$-0.469117\pi$
$977$	5.78033e6	0.193739	0.0968693	+	0.995297i	$0.469117\pi$
$978$	−1.28310e7	−0.428957
$979$	−2.06683e6	−0.0689203
$980$	0	0
$981$	−40192.5	−0.00133344
$982$	−9.72467e6	−0.321807
$983$	−2.58942e7	−0.854709	−0.427355	−	0.904084i	$-0.640554\pi$
$983$	−2.58942e7	−0.854709	−0.427355	+	0.904084i	$0.640554\pi$
$984$	−2.71518e7	−0.893945
$985$	0	0
$986$	−1.97608e7	−0.647310
$987$	921022.	0.0300938
$988$	188466.	0.00614243
$989$	4.10374e7	1.33410
$990$	0	0
$991$	3.10539e7	1.00446	0.502230	−	0.864734i	$-0.332513\pi$
$991$	3.10539e7	1.00446	0.502230	+	0.864734i	$0.332513\pi$
$992$	7.90552e6	0.255065
$993$	−1.09658e7	−0.352913
$994$	−2.64894e6	−0.0850366
$995$	0	0
$996$	73393.8	0.00234429
$997$	5.56862e7	1.77423	0.887115	−	0.461549i	$-0.152706\pi$
$997$	5.56862e7	1.77423	0.887115	+	0.461549i	$0.152706\pi$
$998$	−2.42963e7	−0.772172
$999$	1.46942e6	0.0465835

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.6.a.t.1.7	✓	10
5.4	even	2		825.6.a.u.1.4	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.6.a.t.1.7	✓	10	1.1	even	1	trivial
825.6.a.u.1.4	yes	10	5.4	even	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	825.a (trivial)

\(f(q)\)	\(=\)	\(q+3.54519 q^{2} +9.00000 q^{3} -19.4316 q^{4} +31.9067 q^{6} +15.4153 q^{7} -182.335 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+3.54519 q^{2} +9.00000 q^{3} -19.4316 q^{4} +31.9067 q^{6} +15.4153 q^{7} -182.335 q^{8} +81.0000 q^{9} +121.000 q^{11} -174.885 q^{12} -9.16464 q^{13} +54.6502 q^{14} -24.6000 q^{16} -1481.22 q^{17} +287.160 q^{18} +1058.30 q^{19} +138.738 q^{21} +428.968 q^{22} -3006.99 q^{23} -1641.01 q^{24} -32.4904 q^{26} +729.000 q^{27} -299.544 q^{28} +3763.09 q^{29} +1375.47 q^{31} +5747.51 q^{32} +1089.00 q^{33} -5251.22 q^{34} -1573.96 q^{36} +2015.66 q^{37} +3751.87 q^{38} -82.4818 q^{39} +16545.7 q^{41} +491.852 q^{42} -13647.3 q^{43} -2351.23 q^{44} -10660.4 q^{46} +6638.58 q^{47} -221.400 q^{48} -16569.4 q^{49} -13331.0 q^{51} +178.084 q^{52} -7719.83 q^{53} +2584.44 q^{54} -2810.75 q^{56} +9524.68 q^{57} +13340.9 q^{58} +39159.4 q^{59} -8220.98 q^{61} +4876.30 q^{62} +1248.64 q^{63} +21163.2 q^{64} +3860.71 q^{66} +38209.1 q^{67} +28782.6 q^{68} -27062.9 q^{69} -48470.8 q^{71} -14769.1 q^{72} +49320.4 q^{73} +7145.91 q^{74} -20564.5 q^{76} +1865.25 q^{77} -292.414 q^{78} +16423.9 q^{79} +6561.00 q^{81} +58657.8 q^{82} -419.670 q^{83} -2695.90 q^{84} -48382.3 q^{86} +33867.8 q^{87} -22062.5 q^{88} -17081.2 q^{89} -141.276 q^{91} +58430.7 q^{92} +12379.2 q^{93} +23535.0 q^{94} +51727.5 q^{96} -3464.57 q^{97} -58741.6 q^{98} +9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} + 90 q^{3} + 223 q^{4} - 9 q^{6} + 188 q^{7} + 177 q^{8} + 810 q^{9}+O(q^{10}) \) 10 * q - q^2 + 90 * q^3 + 223 * q^4 - 9 * q^6 + 188 * q^7 + 177 * q^8 + 810 * q^9	\( 10 q - q^{2} + 90 q^{3} + 223 q^{4} - 9 q^{6} + 188 q^{7} + 177 q^{8} + 810 q^{9} + 1210 q^{11} + 2007 q^{12} - 1102 q^{13} + 684 q^{14} + 7019 q^{16} + 1106 q^{17} - 81 q^{18} + 2586 q^{19} + 1692 q^{21} - 121 q^{22} + 2206 q^{23} + 1593 q^{24} + 12001 q^{26} + 7290 q^{27} + 14452 q^{28} + 5824 q^{29} - 4586 q^{31} - 10627 q^{32} + 10890 q^{33} + 7426 q^{34} + 18063 q^{36} - 18362 q^{37} + 44001 q^{38} - 9918 q^{39} - 5474 q^{41} + 6156 q^{42} + 20496 q^{43} + 26983 q^{44} + 19981 q^{46} - 14970 q^{47} + 63171 q^{48} + 68582 q^{49} + 9954 q^{51} - 58603 q^{52} + 61980 q^{53} - 729 q^{54} + 7132 q^{56} + 23274 q^{57} + 7161 q^{58} + 61190 q^{59} + 8230 q^{61} - 4509 q^{62} + 15228 q^{63} + 152223 q^{64} - 1089 q^{66} - 11930 q^{67} + 105598 q^{68} + 19854 q^{69} + 59822 q^{71} + 14337 q^{72} - 20680 q^{73} + 132564 q^{74} + 68165 q^{76} + 22748 q^{77} + 108009 q^{78} + 234494 q^{79} + 65610 q^{81} + 151948 q^{82} + 185478 q^{83} + 130068 q^{84} - 17825 q^{86} + 52416 q^{87} + 21417 q^{88} + 181834 q^{89} + 206274 q^{91} + 98373 q^{92} - 41274 q^{93} - 64998 q^{94} - 95643 q^{96} + 304358 q^{97} + 153453 q^{98} + 98010 q^{99}+O(q^{100}) \) 10 * q - q^2 + 90 * q^3 + 223 * q^4 - 9 * q^6 + 188 * q^7 + 177 * q^8 + 810 * q^9 + 1210 * q^11 + 2007 * q^12 - 1102 * q^13 + 684 * q^14 + 7019 * q^16 + 1106 * q^17 - 81 * q^18 + 2586 * q^19 + 1692 * q^21 - 121 * q^22 + 2206 * q^23 + 1593 * q^24 + 12001 * q^26 + 7290 * q^27 + 14452 * q^28 + 5824 * q^29 - 4586 * q^31 - 10627 * q^32 + 10890 * q^33 + 7426 * q^34 + 18063 * q^36 - 18362 * q^37 + 44001 * q^38 - 9918 * q^39 - 5474 * q^41 + 6156 * q^42 + 20496 * q^43 + 26983 * q^44 + 19981 * q^46 - 14970 * q^47 + 63171 * q^48 + 68582 * q^49 + 9954 * q^51 - 58603 * q^52 + 61980 * q^53 - 729 * q^54 + 7132 * q^56 + 23274 * q^57 + 7161 * q^58 + 61190 * q^59 + 8230 * q^61 - 4509 * q^62 + 15228 * q^63 + 152223 * q^64 - 1089 * q^66 - 11930 * q^67 + 105598 * q^68 + 19854 * q^69 + 59822 * q^71 + 14337 * q^72 - 20680 * q^73 + 132564 * q^74 + 68165 * q^76 + 22748 * q^77 + 108009 * q^78 + 234494 * q^79 + 65610 * q^81 + 151948 * q^82 + 185478 * q^83 + 130068 * q^84 - 17825 * q^86 + 52416 * q^87 + 21417 * q^88 + 181834 * q^89 + 206274 * q^91 + 98373 * q^92 - 41274 * q^93 - 64998 * q^94 - 95643 * q^96 + 304358 * q^97 + 153453 * q^98 + 98010 * q^99

Introduction

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