LMFDB - Embedded newform 245.4.a.l.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(1,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("245.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$14.4554679514$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.14360.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 17x - 14 $ x^3 - 17*x - 14
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$4.48565$ of defining polynomial
Character	$\chi$	$=$	245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.48565 q^{2} -0.850238 q^{3} +4.14976 q^{4} -5.00000 q^{5} -2.96363 q^{6} -13.4206 q^{8} -26.2771 q^{9} +O(q^{10})$	\(q+3.48565 q^{2} -0.850238 q^{3} +4.14976 q^{4} -5.00000 q^{5} -2.96363 q^{6} -13.4206 q^{8} -26.2771 q^{9} -17.4283 q^{10} -6.90764 q^{11} -3.52829 q^{12} +22.1364 q^{13} +4.25119 q^{15} -79.9776 q^{16} -88.3030 q^{17} -91.5928 q^{18} -36.9560 q^{19} -20.7488 q^{20} -24.0776 q^{22} -95.5283 q^{23} +11.4107 q^{24} +25.0000 q^{25} +77.1598 q^{26} +45.2982 q^{27} +269.029 q^{29} +14.8182 q^{30} -197.114 q^{31} -171.409 q^{32} +5.87314 q^{33} -307.793 q^{34} -109.044 q^{36} +2.14546 q^{37} -128.816 q^{38} -18.8212 q^{39} +67.1029 q^{40} -174.127 q^{41} -17.0345 q^{43} -28.6650 q^{44} +131.385 q^{45} -332.978 q^{46} +528.029 q^{47} +68.0000 q^{48} +87.1413 q^{50} +75.0786 q^{51} +91.8608 q^{52} -641.114 q^{53} +157.894 q^{54} +34.5382 q^{55} +31.4214 q^{57} +937.742 q^{58} +642.975 q^{59} +17.6414 q^{60} -142.967 q^{61} -687.070 q^{62} +42.3480 q^{64} -110.682 q^{65} +20.4717 q^{66} +478.797 q^{67} -366.436 q^{68} +81.2218 q^{69} +105.550 q^{71} +352.654 q^{72} -986.512 q^{73} +7.47834 q^{74} -21.2560 q^{75} -153.358 q^{76} -65.6042 q^{78} -1099.86 q^{79} +399.888 q^{80} +670.967 q^{81} -606.947 q^{82} +1236.62 q^{83} +441.515 q^{85} -59.3763 q^{86} -228.739 q^{87} +92.7045 q^{88} +711.698 q^{89} +457.964 q^{90} -396.420 q^{92} +167.594 q^{93} +1840.52 q^{94} +184.780 q^{95} +145.739 q^{96} +636.553 q^{97} +181.513 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 2 q^{3} + 13 q^{4} - 15 q^{5} - 24 q^{6} - 15 q^{8} + 81 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 2 * q^3 + 13 * q^4 - 15 * q^5 - 24 * q^6 - 15 * q^8 + 81 * q^9	\( 3 q - 3 q^{2} - 2 q^{3} + 13 q^{4} - 15 q^{5} - 24 q^{6} - 15 q^{8} + 81 q^{9} + 15 q^{10} - 74 q^{11} + 152 q^{12} - 44 q^{13} + 10 q^{15} - 79 q^{16} + 52 q^{17} - 411 q^{18} - 168 q^{19} - 65 q^{20} + 184 q^{22} - 124 q^{23} - 420 q^{24} + 75 q^{25} + 446 q^{26} - 170 q^{27} + 332 q^{29} + 120 q^{30} - 320 q^{31} - 183 q^{32} + 106 q^{33} - 582 q^{34} + 181 q^{36} - 54 q^{37} + 460 q^{38} - 982 q^{39} + 75 q^{40} - 362 q^{41} - 16 q^{43} - 264 q^{44} - 405 q^{45} - 336 q^{46} + 730 q^{47} + 204 q^{48} - 75 q^{50} - 1178 q^{51} - 1202 q^{52} + 110 q^{53} + 180 q^{54} + 370 q^{55} - 956 q^{57} + 450 q^{58} + 180 q^{59} - 760 q^{60} - 1222 q^{61} - 464 q^{62} - 391 q^{64} + 220 q^{65} + 532 q^{66} + 204 q^{67} - 918 q^{68} + 716 q^{69} - 136 q^{71} + 765 q^{72} - 310 q^{73} + 502 q^{74} - 50 q^{75} - 1796 q^{76} + 3788 q^{78} - 1034 q^{79} + 395 q^{80} + 2283 q^{81} + 6 q^{82} + 1660 q^{83} - 260 q^{85} + 764 q^{86} + 1574 q^{87} - 20 q^{88} - 242 q^{89} + 2055 q^{90} + 96 q^{92} + 1376 q^{93} + 1108 q^{94} + 840 q^{95} + 3156 q^{96} - 100 q^{97} - 3488 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 2 * q^3 + 13 * q^4 - 15 * q^5 - 24 * q^6 - 15 * q^8 + 81 * q^9 + 15 * q^10 - 74 * q^11 + 152 * q^12 - 44 * q^13 + 10 * q^15 - 79 * q^16 + 52 * q^17 - 411 * q^18 - 168 * q^19 - 65 * q^20 + 184 * q^22 - 124 * q^23 - 420 * q^24 + 75 * q^25 + 446 * q^26 - 170 * q^27 + 332 * q^29 + 120 * q^30 - 320 * q^31 - 183 * q^32 + 106 * q^33 - 582 * q^34 + 181 * q^36 - 54 * q^37 + 460 * q^38 - 982 * q^39 + 75 * q^40 - 362 * q^41 - 16 * q^43 - 264 * q^44 - 405 * q^45 - 336 * q^46 + 730 * q^47 + 204 * q^48 - 75 * q^50 - 1178 * q^51 - 1202 * q^52 + 110 * q^53 + 180 * q^54 + 370 * q^55 - 956 * q^57 + 450 * q^58 + 180 * q^59 - 760 * q^60 - 1222 * q^61 - 464 * q^62 - 391 * q^64 + 220 * q^65 + 532 * q^66 + 204 * q^67 - 918 * q^68 + 716 * q^69 - 136 * q^71 + 765 * q^72 - 310 * q^73 + 502 * q^74 - 50 * q^75 - 1796 * q^76 + 3788 * q^78 - 1034 * q^79 + 395 * q^80 + 2283 * q^81 + 6 * q^82 + 1660 * q^83 - 260 * q^85 + 764 * q^86 + 1574 * q^87 - 20 * q^88 - 242 * q^89 + 2055 * q^90 + 96 * q^92 + 1376 * q^93 + 1108 * q^94 + 840 * q^95 + 3156 * q^96 - 100 * q^97 - 3488 * 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 $

$2$	3.48565	1.23236	0.616182	−	0.787604i	$-0.288679\pi$
$2$	3.48565	1.23236	0.616182	+	0.787604i	$0.288679\pi$
$3$	−0.850238	−0.163628	−0.0818142	−	0.996648i	$-0.526071\pi$
$3$	−0.850238	−0.163628	−0.0818142	+	0.996648i	$0.526071\pi$
$4$	4.14976	0.518720
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−2.96363	−0.201650
$7$	0	0
$7$	0	0
$8$	−13.4206	−0.593112
$9$	−26.2771	−0.973226
$10$	−17.4283	−0.551130
$11$	−6.90764	−0.189339	−0.0946696	−	0.995509i	$-0.530179\pi$
$11$	−6.90764	−0.189339	−0.0946696	+	0.995509i	$0.530179\pi$
$12$	−3.52829	−0.0848774
$13$	22.1364	0.472272	0.236136	−	0.971720i	$-0.424119\pi$
$13$	22.1364	0.472272	0.236136	+	0.971720i	$0.424119\pi$
$14$	0	0
$15$	4.25119	0.0731769
$16$	−79.9776	−1.24965
$17$	−88.3030	−1.25980	−0.629901	−	0.776676i	$-0.716904\pi$
$17$	−88.3030	−1.25980	−0.629901	+	0.776676i	$0.716904\pi$
$18$	−91.5928	−1.19937
$19$	−36.9560	−0.446225	−0.223113	−	0.974793i	$-0.571622\pi$
$19$	−36.9560	−0.446225	−0.223113	+	0.974793i	$0.571622\pi$
$20$	−20.7488	−0.231979
$21$	0	0
$22$	−24.0776	−0.233335
$23$	−95.5283	−0.866045	−0.433022	−	0.901383i	$-0.642553\pi$
$23$	−95.5283	−0.866045	−0.433022	+	0.901383i	$0.642553\pi$
$24$	11.4107	0.0970500
$25$	25.0000	0.200000
$26$	77.1598	0.582010
$27$	45.2982	0.322876
$28$	0	0
$29$	269.029	1.72267	0.861336	−	0.508035i	$-0.169628\pi$
$29$	269.029	1.72267	0.861336	+	0.508035i	$0.169628\pi$
$30$	14.8182	0.0901805
$31$	−197.114	−1.14202	−0.571012	−	0.820942i	$-0.693449\pi$
$31$	−197.114	−1.14202	−0.571012	+	0.820942i	$0.693449\pi$
$32$	−171.409	−0.946911
$33$	5.87314	0.0309813
$34$	−307.793	−1.55253
$35$	0	0
$36$	−109.044	−0.504832
$37$	2.14546	0.00953276	0.00476638	−	0.999989i	$-0.498483\pi$
$37$	2.14546	0.00953276	0.00476638	+	0.999989i	$0.498483\pi$
$38$	−128.816	−0.549912
$39$	−18.8212	−0.0772771
$40$	67.1029	0.265248
$41$	−174.127	−0.663271	−0.331636	−	0.943408i	$-0.607600\pi$
$41$	−174.127	−0.663271	−0.331636	+	0.943408i	$0.607600\pi$
$42$	0	0
$43$	−17.0345	−0.0604125	−0.0302062	−	0.999544i	$-0.509616\pi$
$43$	−17.0345	−0.0604125	−0.0302062	+	0.999544i	$0.509616\pi$
$44$	−28.6650	−0.0982140
$45$	131.385	0.435240
$46$	−332.978	−1.06728
$47$	528.029	1.63874	0.819371	−	0.573264i	$-0.194323\pi$
$47$	528.029	1.63874	0.819371	+	0.573264i	$0.194323\pi$
$48$	68.0000	0.204478
$49$	0	0
$50$	87.1413	0.246473
$51$	75.0786	0.206139
$52$	91.8608	0.244977
$53$	−641.114	−1.66158	−0.830790	−	0.556586i	$-0.812111\pi$
$53$	−641.114	−1.66158	−0.830790	+	0.556586i	$0.812111\pi$
$54$	157.894	0.397900
$55$	34.5382	0.0846750
$56$	0	0
$57$	31.4214	0.0730151
$58$	937.742	2.12296
$59$	642.975	1.41878	0.709391	−	0.704815i	$-0.248970\pi$
$59$	642.975	1.41878	0.709391	+	0.704815i	$0.248970\pi$
$60$	17.6414	0.0379583
$61$	−142.967	−0.300083	−0.150042	−	0.988680i	$-0.547941\pi$
$61$	−142.967	−0.300083	−0.150042	+	0.988680i	$0.547941\pi$
$62$	−687.070	−1.40739
$63$	0	0
$64$	42.3480	0.0827109
$65$	−110.682	−0.211206
$66$	20.4717	0.0381802
$67$	478.797	0.873050	0.436525	−	0.899692i	$-0.356209\pi$
$67$	478.797	0.873050	0.436525	+	0.899692i	$0.356209\pi$
$68$	−366.436	−0.653484
$69$	81.2218	0.141710
$70$	0	0
$71$	105.550	0.176430	0.0882150	−	0.996101i	$-0.471884\pi$
$71$	105.550	0.176430	0.0882150	+	0.996101i	$0.471884\pi$
$72$	352.654	0.577232
$73$	−986.512	−1.58168	−0.790839	−	0.612024i	$-0.790356\pi$
$73$	−986.512	−1.58168	−0.790839	+	0.612024i	$0.790356\pi$
$74$	7.47834	0.0117478
$75$	−21.2560	−0.0327257
$76$	−153.358	−0.231466
$77$	0	0
$78$	−65.6042	−0.0952335
$79$	−1099.86	−1.56638	−0.783190	−	0.621783i	$-0.786409\pi$
$79$	−1099.86	−1.56638	−0.783190	+	0.621783i	$0.786409\pi$
$80$	399.888	0.558860
$81$	670.967	0.920394
$82$	−606.947	−0.817391
$83$	1236.62	1.63538	0.817691	−	0.575657i	$-0.195254\pi$
$83$	1236.62	1.63538	0.817691	+	0.575657i	$0.195254\pi$
$84$	0	0
$85$	441.515	0.563400
$86$	−59.3763	−0.0744501
$87$	−228.739	−0.281878
$88$	92.7045	0.112299
$89$	711.698	0.847638	0.423819	−	0.905747i	$-0.360689\pi$
$89$	711.698	0.847638	0.423819	+	0.905747i	$0.360689\pi$
$90$	457.964	0.536374
$91$	0	0
$92$	−396.420	−0.449235
$93$	167.594	0.186867
$94$	1840.52	2.01953
$95$	184.780	0.199558
$96$	145.739	0.154942
$97$	636.553	0.666311	0.333156	−	0.942872i	$-0.391887\pi$
$97$	636.553	0.666311	0.333156	+	0.942872i	$0.391887\pi$
$98$	0	0
$99$	181.513	0.184270
$100$	103.744	0.103744
$101$	−1742.05	−1.71624	−0.858121	−	0.513448i	$-0.828368\pi$
$101$	−1742.05	−1.71624	−0.858121	+	0.513448i	$0.828368\pi$
$102$	261.698	0.254039
$103$	−1454.62	−1.39154	−0.695769	−	0.718266i	$-0.744936\pi$
$103$	−1454.62	−1.39154	−0.695769	+	0.718266i	$0.744936\pi$
$104$	−297.083	−0.280110
$105$	0	0
$106$	−2234.70	−2.04767
$107$	−1181.67	−1.06763	−0.533813	−	0.845603i	$-0.679241\pi$
$107$	−1181.67	−1.06763	−0.533813	+	0.845603i	$0.679241\pi$
$108$	187.977	0.167482
$109$	2204.43	1.93712	0.968559	−	0.248784i	$-0.0800310\pi$
$109$	2204.43	1.93712	0.968559	+	0.248784i	$0.0800310\pi$
$110$	120.388	0.104350
$111$	−1.82416	−0.00155983
$112$	0	0
$113$	236.886	0.197207	0.0986034	−	0.995127i	$-0.468562\pi$
$113$	236.886	0.197207	0.0986034	+	0.995127i	$0.468562\pi$
$114$	109.524	0.0899812
$115$	477.641	0.387307
$116$	1116.41	0.893585
$117$	−581.680	−0.459627
$118$	2241.19	1.74846
$119$	0	0
$120$	−57.0535	−0.0434021
$121$	−1283.28	−0.964151
$122$	−498.334	−0.369811
$123$	148.050	0.108530
$124$	−817.976	−0.592390
$125$	−125.000	−0.0894427
$126$	0	0
$127$	−1667.21	−1.16489	−0.582446	−	0.812869i	$-0.697904\pi$
$127$	−1667.21	−1.16489	−0.582446	+	0.812869i	$0.697904\pi$
$128$	1518.88	1.04884
$129$	14.4834	0.00988520
$130$	−385.799	−0.260283
$131$	−891.722	−0.594733	−0.297367	−	0.954763i	$-0.596108\pi$
$131$	−891.722	−0.594733	−0.297367	+	0.954763i	$0.596108\pi$
$132$	24.3721	0.0160706
$133$	0	0
$134$	1668.92	1.07591
$135$	−226.491	−0.144394
$136$	1185.08	0.747203
$137$	−400.425	−0.249713	−0.124856	−	0.992175i	$-0.539847\pi$
$137$	−400.425	−0.249713	−0.124856	+	0.992175i	$0.539847\pi$
$138$	283.111	0.174638
$139$	−515.050	−0.314287	−0.157144	−	0.987576i	$-0.550229\pi$
$139$	−515.050	−0.314287	−0.157144	+	0.987576i	$0.550229\pi$
$140$	0	0
$141$	−448.950	−0.268145
$142$	367.912	0.217426
$143$	−152.910	−0.0894195
$144$	2101.58	1.21619
$145$	−1345.15	−0.770403
$146$	−3438.64	−1.94920
$147$	0	0
$148$	8.90316	0.00494483
$149$	218.374	0.120066	0.0600332	−	0.998196i	$-0.480879\pi$
$149$	218.374	0.120066	0.0600332	+	0.998196i	$0.480879\pi$
$150$	−74.0909	−0.0403300
$151$	−175.011	−0.0943190	−0.0471595	−	0.998887i	$-0.515017\pi$
$151$	−175.011	−0.0943190	−0.0471595	+	0.998887i	$0.515017\pi$
$152$	495.971	0.264661
$153$	2320.35	1.22607
$154$	0	0
$155$	985.570	0.510728
$156$	−78.1036	−0.0400852
$157$	919.642	0.467487	0.233743	−	0.972298i	$-0.424902\pi$
$157$	919.642	0.467487	0.233743	+	0.972298i	$0.424902\pi$
$158$	−3833.73	−1.93035
$159$	545.099	0.271882
$160$	857.046	0.423471
$161$	0	0
$162$	2338.76	1.13426
$163$	2368.51	1.13813	0.569067	−	0.822291i	$-0.307305\pi$
$163$	2368.51	1.13813	0.569067	+	0.822291i	$0.307305\pi$
$164$	−722.587	−0.344052
$165$	−29.3657	−0.0138552
$166$	4310.43	2.01539
$167$	−1079.37	−0.500144	−0.250072	−	0.968227i	$-0.580454\pi$
$167$	−1079.37	−0.500144	−0.250072	+	0.968227i	$0.580454\pi$
$168$	0	0
$169$	−1706.98	−0.776959
$170$	1538.97	0.694314
$171$	971.095	0.434278
$172$	−70.6891	−0.0313372
$173$	881.271	0.387294	0.193647	−	0.981071i	$-0.437968\pi$
$173$	881.271	0.387294	0.193647	+	0.981071i	$0.437968\pi$
$174$	−797.305	−0.347376
$175$	0	0
$176$	552.456	0.236608
$177$	−546.682	−0.232153
$178$	2480.73	1.04460
$179$	−3377.72	−1.41041	−0.705203	−	0.709006i	$-0.749144\pi$
$179$	−3377.72	−1.41041	−0.705203	+	0.709006i	$0.749144\pi$
$180$	545.218	0.225768
$181$	−1435.58	−0.589533	−0.294767	−	0.955569i	$-0.595242\pi$
$181$	−1435.58	−0.589533	−0.294767	+	0.955569i	$0.595242\pi$
$182$	0	0
$183$	121.556	0.0491021
$184$	1282.05	0.513661
$185$	−10.7273	−0.00426318
$186$	584.174	0.230289
$187$	609.965	0.238530
$188$	2191.19	0.850049
$189$	0	0
$190$	644.078	0.245928
$191$	−1588.14	−0.601642	−0.300821	−	0.953681i	$-0.597261\pi$
$191$	−1588.14	−0.601642	−0.300821	+	0.953681i	$0.597261\pi$
$192$	−36.0059	−0.0135339
$193$	−977.704	−0.364646	−0.182323	−	0.983239i	$-0.558362\pi$
$193$	−977.704	−0.364646	−0.182323	+	0.983239i	$0.558362\pi$
$194$	2218.80	0.821138
$195$	94.1061	0.0345594
$196$	0	0
$197$	359.682	0.130083	0.0650413	−	0.997883i	$-0.479282\pi$
$197$	359.682	0.130083	0.0650413	+	0.997883i	$0.479282\pi$
$198$	632.689	0.227087
$199$	−2818.38	−1.00397	−0.501983	−	0.864877i	$-0.667396\pi$
$199$	−2818.38	−1.00397	−0.501983	+	0.864877i	$0.667396\pi$
$200$	−335.515	−0.118622
$201$	−407.091	−0.142856
$202$	−6072.18	−2.11503
$203$	0	0
$204$	311.558	0.106929
$205$	870.637	0.296624
$206$	−5070.31	−1.71488
$207$	2510.21	0.842857
$208$	−1770.42	−0.590174
$209$	255.278	0.0844879
$210$	0	0
$211$	−1009.64	−0.329415	−0.164708	−	0.986342i	$-0.552668\pi$
$211$	−1009.64	−0.329415	−0.164708	+	0.986342i	$0.552668\pi$
$212$	−2660.47	−0.861895
$213$	−89.7430	−0.0288690
$214$	−4118.88	−1.31570
$215$	85.1725	0.0270173
$216$	−607.929	−0.191501
$217$	0	0
$218$	7683.86	2.38723
$219$	838.770	0.258808
$220$	143.325	0.0439226
$221$	−1954.71	−0.594969
$222$	−6.35837	−0.00192228
$223$	−1277.28	−0.383555	−0.191778	−	0.981438i	$-0.561425\pi$
$223$	−1277.28	−0.383555	−0.191778	+	0.981438i	$0.561425\pi$
$224$	0	0
$225$	−656.927	−0.194645
$226$	825.702	0.243030
$227$	−1399.87	−0.409307	−0.204654	−	0.978834i	$-0.565607\pi$
$227$	−1399.87	−0.409307	−0.204654	+	0.978834i	$0.565607\pi$
$228$	130.391	0.0378744
$229$	−3182.00	−0.918222	−0.459111	−	0.888379i	$-0.651832\pi$
$229$	−3182.00	−0.918222	−0.459111	+	0.888379i	$0.651832\pi$
$230$	1664.89	0.477303
$231$	0	0
$232$	−3610.53	−1.02174
$233$	−3027.84	−0.851332	−0.425666	−	0.904880i	$-0.639960\pi$
$233$	−3027.84	−0.851332	−0.425666	+	0.904880i	$0.639960\pi$
$234$	−2027.53	−0.566428
$235$	−2640.14	−0.732868
$236$	2668.19	0.735951
$237$	935.144	0.256304
$238$	0	0
$239$	−4995.69	−1.35207	−0.676034	−	0.736870i	$-0.736303\pi$
$239$	−4995.69	−1.35207	−0.676034	+	0.736870i	$0.736303\pi$
$240$	−340.000	−0.0914454
$241$	3756.52	1.00406	0.502030	−	0.864850i	$-0.332587\pi$
$241$	3756.52	1.00406	0.502030	+	0.864850i	$0.332587\pi$
$242$	−4473.08	−1.18818
$243$	−1793.53	−0.473479
$244$	−593.280	−0.155659
$245$	0	0
$246$	516.050	0.133748
$247$	−818.072	−0.210740
$248$	2645.39	0.677347
$249$	−1051.42	−0.267595
$250$	−435.706	−0.110226
$251$	−6565.46	−1.65103	−0.825514	−	0.564381i	$-0.809115\pi$
$251$	−6565.46	−1.65103	−0.825514	+	0.564381i	$0.809115\pi$
$252$	0	0
$253$	659.875	0.163976
$254$	−5811.33	−1.43557
$255$	−375.393	−0.0921883
$256$	4955.51	1.20984
$257$	6879.44	1.66976	0.834879	−	0.550433i	$-0.185537\pi$
$257$	6879.44	1.66976	0.834879	+	0.550433i	$0.185537\pi$
$258$	50.4840	0.0121822
$259$	0	0
$260$	−459.304	−0.109557
$261$	−7069.31	−1.67655
$262$	−3108.23	−0.732928
$263$	3080.15	0.722169	0.361084	−	0.932533i	$-0.382407\pi$
$263$	3080.15	0.722169	0.361084	+	0.932533i	$0.382407\pi$
$264$	−78.8209	−0.0183754
$265$	3205.57	0.743081
$266$	0	0
$267$	−605.113	−0.138698
$268$	1986.89	0.452869
$269$	−6710.33	−1.52095	−0.760476	−	0.649366i	$-0.775034\pi$
$269$	−6710.33	−1.52095	−0.760476	+	0.649366i	$0.775034\pi$
$270$	−789.469	−0.177947
$271$	−7842.95	−1.75803	−0.879014	−	0.476796i	$-0.841798\pi$
$271$	−7842.95	−1.75803	−0.879014	+	0.476796i	$0.841798\pi$
$272$	7062.26	1.57431
$273$	0	0
$274$	−1395.74	−0.307737
$275$	−172.691	−0.0378678
$276$	337.051	0.0735076
$277$	5446.87	1.18148	0.590742	−	0.806861i	$-0.298835\pi$
$277$	5446.87	1.18148	0.590742	+	0.806861i	$0.298835\pi$
$278$	−1795.28	−0.387316
$279$	5179.58	1.11145
$280$	0	0
$281$	2126.76	0.451501	0.225751	−	0.974185i	$-0.427517\pi$
$281$	2126.76	0.451501	0.225751	+	0.974185i	$0.427517\pi$
$282$	−1564.88	−0.330452
$283$	3426.38	0.719707	0.359853	−	0.933009i	$-0.382827\pi$
$283$	3426.38	0.719707	0.359853	+	0.933009i	$0.382827\pi$
$284$	438.009	0.0915178
$285$	−157.107	−0.0326534
$286$	−532.991	−0.110197
$287$	0	0
$288$	4504.14	0.921558
$289$	2884.42	0.587099
$290$	−4688.71	−0.949416
$291$	−541.222	−0.109028
$292$	−4093.79	−0.820448
$293$	1749.82	0.348894	0.174447	−	0.984667i	$-0.444186\pi$
$293$	1749.82	0.348894	0.174447	+	0.984667i	$0.444186\pi$
$294$	0	0
$295$	−3214.87	−0.634499
$296$	−28.7934	−0.00565399
$297$	−312.904	−0.0611330
$298$	761.176	0.147966
$299$	−2114.65	−0.409008
$300$	−88.2072	−0.0169755
$301$	0	0
$302$	−610.026	−0.116235
$303$	1481.16	0.280826
$304$	2955.65	0.557625
$305$	714.836	0.134201
$306$	8087.92	1.51097
$307$	−7970.33	−1.48173	−0.740864	−	0.671655i	$-0.765584\pi$
$307$	−7970.33	−1.48173	−0.740864	+	0.671655i	$0.765584\pi$
$308$	0	0
$309$	1236.78	0.227695
$310$	3435.35	0.629403
$311$	2560.72	0.466898	0.233449	−	0.972369i	$-0.424999\pi$
$311$	2560.72	0.466898	0.233449	+	0.972369i	$0.424999\pi$
$312$	252.592	0.0458339
$313$	4861.11	0.877848	0.438924	−	0.898524i	$-0.355360\pi$
$313$	4861.11	0.877848	0.438924	+	0.898524i	$0.355360\pi$
$314$	3205.55	0.576114
$315$	0	0
$316$	−4564.16	−0.812513
$317$	8166.16	1.44687	0.723434	−	0.690394i	$-0.242563\pi$
$317$	8166.16	1.44687	0.723434	+	0.690394i	$0.242563\pi$
$318$	1900.03	0.335057
$319$	−1858.36	−0.326169
$320$	−211.740	−0.0369894
$321$	1004.70	0.174694
$322$	0	0
$323$	3263.32	0.562155
$324$	2784.35	0.477427
$325$	553.410	0.0944543
$326$	8255.79	1.40259
$327$	−1874.29	−0.316968
$328$	2336.89	0.393394
$329$	0	0
$330$	−102.359	−0.0170747
$331$	2974.89	0.494002	0.247001	−	0.969015i	$-0.420555\pi$
$331$	2974.89	0.494002	0.247001	+	0.969015i	$0.420555\pi$
$332$	5131.68	0.848306
$333$	−56.3766	−0.00927753
$334$	−3762.30	−0.616359
$335$	−2393.98	−0.390440
$336$	0	0
$337$	3496.34	0.565157	0.282578	−	0.959244i	$-0.408810\pi$
$337$	3496.34	0.565157	0.282578	+	0.959244i	$0.408810\pi$
$338$	−5949.94	−0.957497
$339$	−201.410	−0.0322686
$340$	1832.18	0.292247
$341$	1361.59	0.216230
$342$	3384.90	0.535188
$343$	0	0
$344$	228.613	0.0358314
$345$	−406.109	−0.0633744
$346$	3071.80	0.477287
$347$	3959.08	0.612491	0.306246	−	0.951953i	$-0.400927\pi$
$347$	3959.08	0.612491	0.306246	+	0.951953i	$0.400927\pi$
$348$	−949.213	−0.146216
$349$	−5581.65	−0.856099	−0.428050	−	0.903755i	$-0.640799\pi$
$349$	−5581.65	−0.856099	−0.428050	+	0.903755i	$0.640799\pi$
$350$	0	0
$351$	1002.74	0.152485
$352$	1184.03	0.179287
$353$	9896.43	1.49216	0.746082	−	0.665854i	$-0.231933\pi$
$353$	9896.43	1.49216	0.746082	+	0.665854i	$0.231933\pi$
$354$	−1905.54	−0.286097
$355$	−527.752	−0.0789019
$356$	2953.38	0.439687
$357$	0	0
$358$	−11773.5	−1.73813
$359$	11917.6	1.75205	0.876025	−	0.482265i	$-0.160186\pi$
$359$	11917.6	1.75205	0.876025	+	0.482265i	$0.160186\pi$
$360$	−1763.27	−0.258146
$361$	−5493.26	−0.800883
$362$	−5003.92	−0.726519
$363$	1091.10	0.157762
$364$	0	0
$365$	4932.56	0.707348
$366$	423.702	0.0605117
$367$	7101.58	1.01008	0.505040	−	0.863096i	$-0.331478\pi$
$367$	7101.58	1.01008	0.505040	+	0.863096i	$0.331478\pi$
$368$	7640.12	1.08225
$369$	4575.56	0.645513
$370$	−37.3917	−0.00525379
$371$	0	0
$372$	695.475	0.0969319
$373$	294.316	0.0408555	0.0204277	−	0.999791i	$-0.493497\pi$
$373$	294.316	0.0408555	0.0204277	+	0.999791i	$0.493497\pi$
$374$	2126.12	0.293955
$375$	106.280	0.0146354
$376$	−7086.45	−0.971957
$377$	5955.34	0.813569
$378$	0	0
$379$	−9436.57	−1.27896	−0.639478	−	0.768810i	$-0.720849\pi$
$379$	−9436.57	−1.27896	−0.639478	+	0.768810i	$0.720849\pi$
$380$	766.792	0.103515
$381$	1417.53	0.190610
$382$	−5535.70	−0.741442
$383$	3160.82	0.421699	0.210849	−	0.977519i	$-0.432377\pi$
$383$	3160.82	0.421699	0.210849	+	0.977519i	$0.432377\pi$
$384$	−1291.41	−0.171620
$385$	0	0
$386$	−3407.93	−0.449376
$387$	447.617	0.0587950
$388$	2641.55	0.345629
$389$	7822.76	1.01961	0.509807	−	0.860289i	$-0.329717\pi$
$389$	7822.76	1.01961	0.509807	+	0.860289i	$0.329717\pi$
$390$	328.021	0.0425897
$391$	8435.43	1.09104
$392$	0	0
$393$	758.176	0.0973153
$394$	1253.73	0.160309
$395$	5499.30	0.700506
$396$	753.234	0.0955844
$397$	7935.18	1.00316	0.501581	−	0.865111i	$-0.332752\pi$
$397$	7935.18	1.00316	0.501581	+	0.865111i	$0.332752\pi$
$398$	−9823.87	−1.23725
$399$	0	0
$400$	−1999.44	−0.249930
$401$	−488.380	−0.0608193	−0.0304097	−	0.999538i	$-0.509681\pi$
$401$	−488.380	−0.0608193	−0.0304097	+	0.999538i	$0.509681\pi$
$402$	−1418.98	−0.176050
$403$	−4363.39	−0.539345
$404$	−7229.09	−0.890249
$405$	−3354.84	−0.411613
$406$	0	0
$407$	−14.8201	−0.00180492
$408$	−1007.60	−0.122264
$409$	−11230.6	−1.35775	−0.678874	−	0.734254i	$-0.737532\pi$
$409$	−11230.6	−1.35775	−0.678874	+	0.734254i	$0.737532\pi$
$410$	3034.74	0.365549
$411$	340.457	0.0408601
$412$	−6036.34	−0.721818
$413$	0	0
$414$	8749.70	1.03871
$415$	−6183.10	−0.731365
$416$	−3794.38	−0.447199
$417$	437.915	0.0514263
$418$	889.811	0.104120
$419$	7369.62	0.859259	0.429629	−	0.903005i	$-0.358644\pi$
$419$	7369.62	0.859259	0.429629	+	0.903005i	$0.358644\pi$
$420$	0	0
$421$	11972.5	1.38599	0.692997	−	0.720941i	$-0.256290\pi$
$421$	11972.5	1.38599	0.692997	+	0.720941i	$0.256290\pi$
$422$	−3519.26	−0.405959
$423$	−13875.1	−1.59487
$424$	8604.12	0.985503
$425$	−2207.57	−0.251960
$426$	−312.813	−0.0355770
$427$	0	0
$428$	−4903.63	−0.553799
$429$	130.010	0.0146316
$430$	296.882	0.0332951
$431$	−3568.60	−0.398825	−0.199412	−	0.979916i	$-0.563903\pi$
$431$	−3568.60	−0.398825	−0.199412	+	0.979916i	$0.563903\pi$
$432$	−3622.84	−0.403482
$433$	−2291.60	−0.254335	−0.127168	−	0.991881i	$-0.540589\pi$
$433$	−2291.60	−0.254335	−0.127168	+	0.991881i	$0.540589\pi$
$434$	0	0
$435$	1143.70	0.126060
$436$	9147.85	1.00482
$437$	3530.34	0.386451
$438$	2923.66	0.318945
$439$	7329.66	0.796870	0.398435	−	0.917197i	$-0.369554\pi$
$439$	7329.66	0.796870	0.398435	+	0.917197i	$0.369554\pi$
$440$	−463.523	−0.0502218
$441$	0	0
$442$	−6813.44	−0.733218
$443$	8297.38	0.889889	0.444944	−	0.895558i	$-0.353223\pi$
$443$	8297.38	0.889889	0.444944	+	0.895558i	$0.353223\pi$
$444$	−7.56981	−0.000809116 0
$445$	−3558.49	−0.379075
$446$	−4452.14	−0.472679
$447$	−185.670	−0.0196463
$448$	0	0
$449$	9758.62	1.02570	0.512848	−	0.858479i	$-0.328590\pi$
$449$	9758.62	1.02570	0.512848	+	0.858479i	$0.328590\pi$
$450$	−2289.82	−0.239874
$451$	1202.81	0.125583
$452$	983.021	0.102295
$453$	148.801	0.0154333
$454$	−4879.47	−0.504416
$455$	0	0
$456$	−421.693	−0.0433061
$457$	−11745.0	−1.20220	−0.601102	−	0.799172i	$-0.705272\pi$
$457$	−11745.0	−1.20220	−0.601102	+	0.799172i	$0.705272\pi$
$458$	−11091.4	−1.13158
$459$	−3999.97	−0.406759
$460$	1982.10	0.200904
$461$	10748.6	1.08593	0.542963	−	0.839756i	$-0.317302\pi$
$461$	10748.6	1.08593	0.542963	+	0.839756i	$0.317302\pi$
$462$	0	0
$463$	−9862.51	−0.989957	−0.494978	−	0.868905i	$-0.664824\pi$
$463$	−9862.51	−0.989957	−0.494978	+	0.868905i	$0.664824\pi$
$464$	−21516.3	−2.15274
$465$	−837.969	−0.0835697
$466$	−10554.0	−1.04915
$467$	4660.78	0.461831	0.230916	−	0.972974i	$-0.425828\pi$
$467$	4660.78	0.461831	0.230916	+	0.972974i	$0.425828\pi$
$468$	−2413.83	−0.238418
$469$	0	0
$470$	−9202.62	−0.903160
$471$	−781.915	−0.0764941
$472$	−8629.10	−0.841497
$473$	117.668	0.0114384
$474$	3259.58	0.315860
$475$	−923.899	−0.0892451
$476$	0	0
$477$	16846.6	1.61709
$478$	−17413.2	−1.66624
$479$	16293.2	1.55419	0.777094	−	0.629385i	$-0.216693\pi$
$479$	16293.2	1.55419	0.777094	+	0.629385i	$0.216693\pi$
$480$	−728.693	−0.0692920
$481$	47.4928	0.00450205
$482$	13093.9	1.23737
$483$	0	0
$484$	−5325.33	−0.500124
$485$	−3182.77	−0.297984
$486$	−6251.63	−0.583498
$487$	−3515.00	−0.327063	−0.163531	−	0.986538i	$-0.552289\pi$
$487$	−3515.00	−0.327063	−0.163531	+	0.986538i	$0.552289\pi$
$488$	1918.70	0.177983
$489$	−2013.80	−0.186231
$490$	0	0
$491$	−2516.79	−0.231326	−0.115663	−	0.993288i	$-0.536899\pi$
$491$	−2516.79	−0.231326	−0.115663	+	0.993288i	$0.536899\pi$
$492$	614.371	0.0562967
$493$	−23756.1	−2.17023
$494$	−2851.51	−0.259708
$495$	−907.563	−0.0824079
$496$	15764.7	1.42713
$497$	0	0
$498$	−3664.89	−0.329775
$499$	−8747.48	−0.784751	−0.392376	−	0.919805i	$-0.628347\pi$
$499$	−8747.48	−0.784751	−0.392376	+	0.919805i	$0.628347\pi$
$500$	−518.720	−0.0463957
$501$	917.720	0.0818377
$502$	−22884.9	−2.03467
$503$	−11426.1	−1.01285	−0.506426	−	0.862284i	$-0.669034\pi$
$503$	−11426.1	−1.01285	−0.506426	+	0.862284i	$0.669034\pi$
$504$	0	0
$505$	8710.25	0.767526
$506$	2300.09	0.202078
$507$	1451.34	0.127133
$508$	−6918.54	−0.604254
$509$	8078.44	0.703478	0.351739	−	0.936098i	$-0.385590\pi$
$509$	8078.44	0.703478	0.351739	+	0.936098i	$0.385590\pi$
$510$	−1308.49	−0.113610
$511$	0	0
$512$	5122.12	0.442125
$513$	−1674.04	−0.144075
$514$	23979.3	2.05775
$515$	7273.12	0.622314
$516$	60.1026	0.00512765
$517$	−3647.43	−0.310278
$518$	0	0
$519$	−749.290	−0.0633723
$520$	1485.42	0.125269
$521$	−7226.14	−0.607645	−0.303822	−	0.952729i	$-0.598263\pi$
$521$	−7226.14	−0.607645	−0.303822	+	0.952729i	$0.598263\pi$
$522$	−24641.1	−2.06612
$523$	−9333.06	−0.780318	−0.390159	−	0.920748i	$-0.627580\pi$
$523$	−9333.06	−0.780318	−0.390159	+	0.920748i	$0.627580\pi$
$524$	−3700.43	−0.308500
$525$	0	0
$526$	10736.3	0.889974
$527$	17405.8	1.43872
$528$	−469.719	−0.0387157
$529$	−3041.35	−0.249967
$530$	11173.5	0.915746
$531$	−16895.5	−1.38080
$532$	0	0
$533$	−3854.55	−0.313244
$534$	−2109.21	−0.170926
$535$	5908.33	0.477457
$536$	−6425.73	−0.517816
$537$	2871.87	0.230782
$538$	−23389.9	−1.87437
$539$	0	0
$540$	−939.884	−0.0749003
$541$	15263.1	1.21296	0.606482	−	0.795097i	$-0.292580\pi$
$541$	15263.1	1.21296	0.606482	+	0.795097i	$0.292580\pi$
$542$	−27337.8	−2.16653
$543$	1220.58	0.0964644
$544$	15135.9	1.19292
$545$	−11022.1	−0.866305
$546$	0	0
$547$	−13226.0	−1.03382	−0.516912	−	0.856039i	$-0.672918\pi$
$547$	−13226.0	−1.03382	−0.516912	+	0.856039i	$0.672918\pi$
$548$	−1661.67	−0.129531
$549$	3756.76	0.292049
$550$	−601.940	−0.0466669
$551$	−9942.24	−0.768700
$552$	−1090.04	−0.0840496
$553$	0	0
$554$	18985.9	1.45602
$555$	9.12078	0.000697577 0
$556$	−2137.33	−0.163027
$557$	6993.63	0.532010	0.266005	−	0.963972i	$-0.414296\pi$
$557$	6993.63	0.532010	0.266005	+	0.963972i	$0.414296\pi$
$558$	18054.2	1.36971
$559$	−377.082	−0.0285311
$560$	0	0
$561$	−518.616	−0.0390302
$562$	7413.14	0.556413
$563$	−392.197	−0.0293590	−0.0146795	−	0.999892i	$-0.504673\pi$
$563$	−392.197	−0.0293590	−0.0146795	+	0.999892i	$0.504673\pi$
$564$	−1863.04	−0.139092
$565$	−1184.43	−0.0881935
$566$	11943.2	0.886940
$567$	0	0
$568$	−1416.55	−0.104643
$569$	8811.72	0.649221	0.324610	−	0.945848i	$-0.394767\pi$
$569$	8811.72	0.649221	0.324610	+	0.945848i	$0.394767\pi$
$570$	−547.620	−0.0402408
$571$	−24775.6	−1.81581	−0.907905	−	0.419175i	$-0.862319\pi$
$571$	−24775.6	−1.81581	−0.907905	+	0.419175i	$0.862319\pi$
$572$	−634.541	−0.0463837
$573$	1350.30	0.0984458
$574$	0	0
$575$	−2388.21	−0.173209
$576$	−1112.78	−0.0804964
$577$	8850.62	0.638572	0.319286	−	0.947658i	$-0.396557\pi$
$577$	8850.62	0.638572	0.319286	+	0.947658i	$0.396557\pi$
$578$	10054.1	0.723520
$579$	831.281	0.0596664
$580$	−5582.04	−0.399623
$581$	0	0
$582$	−1886.51	−0.134362
$583$	4428.58	0.314602
$584$	13239.6	0.938112
$585$	2908.40	0.205551
$586$	6099.28	0.429964
$587$	46.0232	0.00323608	0.00161804	−	0.999999i	$-0.499485\pi$
$587$	46.0232	0.00323608	0.00161804	+	0.999999i	$0.499485\pi$
$588$	0	0
$589$	7284.54	0.509600
$590$	−11205.9	−0.781933
$591$	−305.815	−0.0212852
$592$	−171.589	−0.0119126
$593$	2729.93	0.189047	0.0945235	−	0.995523i	$-0.469867\pi$
$593$	2729.93	0.189047	0.0945235	+	0.995523i	$0.469867\pi$
$594$	−1090.67	−0.0753381
$595$	0	0
$596$	906.200	0.0622809
$597$	2396.29	0.164277
$598$	−7370.94	−0.504047
$599$	−5505.07	−0.375511	−0.187756	−	0.982216i	$-0.560121\pi$
$599$	−5505.07	−0.375511	−0.187756	+	0.982216i	$0.560121\pi$
$600$	285.267	0.0194100
$601$	7446.97	0.505438	0.252719	−	0.967540i	$-0.418675\pi$
$601$	7446.97	0.505438	0.252719	+	0.967540i	$0.418675\pi$
$602$	0	0
$603$	−12581.4	−0.849674
$604$	−726.253	−0.0489252
$605$	6416.42	0.431181
$606$	5162.80	0.346080
$607$	24071.4	1.60960	0.804799	−	0.593547i	$-0.202273\pi$
$607$	24071.4	1.60960	0.804799	+	0.593547i	$0.202273\pi$
$608$	6334.59	0.422536
$609$	0	0
$610$	2491.67	0.165385
$611$	11688.7	0.773932
$612$	9628.88	0.635988
$613$	−4108.61	−0.270710	−0.135355	−	0.990797i	$-0.543218\pi$
$613$	−4108.61	−0.270710	−0.135355	+	0.990797i	$0.543218\pi$
$614$	−27781.8	−1.82603
$615$	−740.249	−0.0485361
$616$	0	0
$617$	3542.46	0.231141	0.115571	−	0.993299i	$-0.463130\pi$
$617$	3542.46	0.231141	0.115571	+	0.993299i	$0.463130\pi$
$618$	4310.97	0.280603
$619$	−6484.81	−0.421077	−0.210538	−	0.977586i	$-0.567522\pi$
$619$	−6484.81	−0.421077	−0.210538	+	0.977586i	$0.567522\pi$
$620$	4089.88	0.264925
$621$	−4327.26	−0.279625
$622$	8925.79	0.575388
$623$	0	0
$624$	1505.28	0.0965693
$625$	625.000	0.0400000
$626$	16944.1	1.08183
$627$	−217.047	−0.0138246
$628$	3816.29	0.242495
$629$	−189.451	−0.0120094
$630$	0	0
$631$	3250.84	0.205094	0.102547	−	0.994728i	$-0.467301\pi$
$631$	3250.84	0.205094	0.102547	+	0.994728i	$0.467301\pi$
$632$	14760.8	0.929038
$633$	858.436	0.0539017
$634$	28464.4	1.78307
$635$	8336.07	0.520956
$636$	2262.03	0.141031
$637$	0	0
$638$	−6477.58	−0.401959
$639$	−2773.56	−0.171706
$640$	−7594.42	−0.469056
$641$	2800.61	0.172570	0.0862852	−	0.996270i	$-0.472500\pi$
$641$	2800.61	0.172570	0.0862852	+	0.996270i	$0.472500\pi$
$642$	3502.03	0.215287
$643$	−18910.6	−1.15982	−0.579908	−	0.814682i	$-0.696911\pi$
$643$	−18910.6	−1.15982	−0.579908	+	0.814682i	$0.696911\pi$
$644$	0	0
$645$	−72.4169	−0.00442080
$646$	11374.8	0.692780
$647$	24522.7	1.49009	0.745043	−	0.667016i	$-0.232429\pi$
$647$	24522.7	1.49009	0.745043	+	0.667016i	$0.232429\pi$
$648$	−9004.77	−0.545897
$649$	−4441.43	−0.268631
$650$	1928.99	0.116402
$651$	0	0
$652$	9828.74	0.590373
$653$	−15299.6	−0.916875	−0.458438	−	0.888727i	$-0.651591\pi$
$653$	−15299.6	−0.916875	−0.458438	+	0.888727i	$0.651591\pi$
$654$	−6533.12	−0.390619
$655$	4458.61	0.265973
$656$	13926.3	0.828857
$657$	25922.7	1.53933
$658$	0	0
$659$	−2203.13	−0.130230	−0.0651151	−	0.997878i	$-0.520741\pi$
$659$	−2203.13	−0.130230	−0.0651151	+	0.997878i	$0.520741\pi$
$660$	−121.861	−0.00718699
$661$	3162.36	0.186084	0.0930421	−	0.995662i	$-0.470341\pi$
$661$	3162.36	0.186084	0.0930421	+	0.995662i	$0.470341\pi$
$662$	10369.4	0.608790
$663$	1661.97	0.0973538
$664$	−16596.2	−0.969965
$665$	0	0
$666$	−196.509	−0.0114333
$667$	−25699.9	−1.49191
$668$	−4479.12	−0.259435
$669$	1085.99	0.0627605
$670$	−8344.59	−0.481164
$671$	987.565	0.0568175
$672$	0	0
$673$	−4443.07	−0.254484	−0.127242	−	0.991872i	$-0.540613\pi$
$673$	−4443.07	−0.254484	−0.127242	+	0.991872i	$0.540613\pi$
$674$	12187.0	0.696479
$675$	1132.46	0.0645752
$676$	−7083.56	−0.403025
$677$	−4456.32	−0.252984	−0.126492	−	0.991968i	$-0.540372\pi$
$677$	−4456.32	−0.252984	−0.126492	+	0.991968i	$0.540372\pi$
$678$	−702.044	−0.0397667
$679$	0	0
$680$	−5925.39	−0.334159
$681$	1190.23	0.0669743
$682$	4746.03	0.266474
$683$	−10046.8	−0.562858	−0.281429	−	0.959582i	$-0.590808\pi$
$683$	−10046.8	−0.562858	−0.281429	+	0.959582i	$0.590808\pi$
$684$	4029.81	0.225269
$685$	2002.13	0.111675
$686$	0	0
$687$	2705.46	0.150247
$688$	1362.38	0.0754944
$689$	−14191.9	−0.784717
$690$	−1415.55	−0.0781003
$691$	−31811.2	−1.75131	−0.875655	−	0.482938i	$-0.839570\pi$
$691$	−31811.2	−1.75131	−0.875655	+	0.482938i	$0.839570\pi$
$692$	3657.06	0.200897
$693$	0	0
$694$	13800.0	0.754812
$695$	2575.25	0.140554
$696$	3069.81	0.167185
$697$	15376.0	0.835590
$698$	−19455.7	−1.05503
$699$	2574.39	0.139302
$700$	0	0
$701$	−13907.2	−0.749312	−0.374656	−	0.927164i	$-0.622239\pi$
$701$	−13907.2	−0.749312	−0.374656	+	0.927164i	$0.622239\pi$
$702$	3495.20	0.187917
$703$	−79.2877	−0.00425376
$704$	−292.524	−0.0156604
$705$	2244.75	0.119918
$706$	34495.5	1.83889
$707$	0	0
$708$	−2268.60	−0.120423
$709$	−228.952	−0.0121276	−0.00606381	−	0.999982i	$-0.501930\pi$
$709$	−228.952	−0.0121276	−0.00606381	+	0.999982i	$0.501930\pi$
$710$	−1839.56	−0.0972358
$711$	28901.1	1.52444
$712$	−9551.40	−0.502744
$713$	18830.0	0.989043
$714$	0	0
$715$	764.551	0.0399896
$716$	−14016.7	−0.731606
$717$	4247.53	0.221237
$718$	41540.5	2.15916
$719$	−36162.2	−1.87569	−0.937846	−	0.347052i	$-0.887183\pi$
$719$	−36162.2	−1.87569	−0.937846	+	0.347052i	$0.887183\pi$
$720$	−10507.9	−0.543897
$721$	0	0
$722$	−19147.6	−0.986979
$723$	−3193.93	−0.164293
$724$	−5957.30	−0.305803
$725$	6725.73	0.344534
$726$	3803.19	0.194421
$727$	−22268.3	−1.13602	−0.568010	−	0.823021i	$-0.692287\pi$
$727$	−22268.3	−1.13602	−0.568010	+	0.823021i	$0.692287\pi$
$728$	0	0
$729$	−16591.2	−0.842919
$730$	17193.2	0.871710
$731$	1504.20	0.0761077
$732$	504.429	0.0254703
$733$	2333.20	0.117570	0.0587848	−	0.998271i	$-0.481277\pi$
$733$	2333.20	0.117570	0.0587848	+	0.998271i	$0.481277\pi$
$734$	24753.6	1.24479
$735$	0	0
$736$	16374.4	0.820067
$737$	−3307.35	−0.165302
$738$	15948.8	0.795506
$739$	−4829.15	−0.240383	−0.120192	−	0.992751i	$-0.538351\pi$
$739$	−4829.15	−0.240383	−0.120192	+	0.992751i	$0.538351\pi$
$740$	−44.5158	−0.00221140
$741$	695.556	0.0344830
$742$	0	0
$743$	−25459.0	−1.25707	−0.628533	−	0.777783i	$-0.716344\pi$
$743$	−25459.0	−1.25707	−0.628533	+	0.777783i	$0.716344\pi$
$744$	−2249.21	−0.110833
$745$	−1091.87	−0.0536953
$746$	1025.88	0.0503488
$747$	−32494.8	−1.59160
$748$	2531.21	0.123730
$749$	0	0
$750$	370.454	0.0180361
$751$	−5707.08	−0.277303	−0.138651	−	0.990341i	$-0.544277\pi$
$751$	−5707.08	−0.277303	−0.138651	+	0.990341i	$0.544277\pi$
$752$	−42230.4	−2.04785
$753$	5582.21	0.270155
$754$	20758.2	1.00261
$755$	875.054	0.0421808
$756$	0	0
$757$	−1900.91	−0.0912677	−0.0456339	−	0.998958i	$-0.514531\pi$
$757$	−1900.91	−0.0912677	−0.0456339	+	0.998958i	$0.514531\pi$
$758$	−32892.6	−1.57614
$759$	−561.051	−0.0268312
$760$	−2479.85	−0.118360
$761$	11583.8	0.551791	0.275896	−	0.961188i	$-0.411026\pi$
$761$	11583.8	0.551791	0.275896	+	0.961188i	$0.411026\pi$
$762$	4941.01	0.234900
$763$	0	0
$764$	−6590.40	−0.312084
$765$	−11601.7	−0.548316
$766$	11017.5	0.519686
$767$	14233.1	0.670051
$768$	−4213.37	−0.197965
$769$	26059.7	1.22202	0.611012	−	0.791622i	$-0.290763\pi$
$769$	26059.7	1.22202	0.611012	+	0.791622i	$0.290763\pi$
$770$	0	0
$771$	−5849.17	−0.273220
$772$	−4057.24	−0.189149
$773$	16213.6	0.754413	0.377206	−	0.926129i	$-0.376885\pi$
$773$	16213.6	0.754413	0.377206	+	0.926129i	$0.376885\pi$
$774$	1560.24	0.0724568
$775$	−4927.85	−0.228405
$776$	−8542.92	−0.395197
$777$	0	0
$778$	27267.4	1.25653
$779$	6435.04	0.295968
$780$	390.518	0.0179266
$781$	−729.103	−0.0334051
$782$	29403.0	1.34456
$783$	12186.6	0.556209
$784$	0	0
$785$	−4598.21	−0.209066
$786$	2642.74	0.119928
$787$	1371.34	0.0621131	0.0310565	−	0.999518i	$-0.490113\pi$
$787$	1371.34	0.0621131	0.0310565	+	0.999518i	$0.490113\pi$
$788$	1492.59	0.0674765
$789$	−2618.86	−0.118167
$790$	19168.7	0.863279
$791$	0	0
$792$	−2436.01	−0.109293
$793$	−3164.78	−0.141721
$794$	27659.3	1.23626
$795$	−2725.50	−0.121589
$796$	−11695.6	−0.520778
$797$	−7991.49	−0.355173	−0.177587	−	0.984105i	$-0.556829\pi$
$797$	−7991.49	−0.355173	−0.177587	+	0.984105i	$0.556829\pi$
$798$	0	0
$799$	−46626.5	−2.06449
$800$	−4285.23	−0.189382
$801$	−18701.3	−0.824943
$802$	−1702.32	−0.0749515
$803$	6814.47	0.299474
$804$	−1689.33	−0.0741022
$805$	0	0
$806$	−15209.3	−0.664669
$807$	5705.38	0.248871
$808$	23379.3	1.01792
$809$	−17661.4	−0.767542	−0.383771	−	0.923428i	$-0.625375\pi$
$809$	−17661.4	−0.767542	−0.383771	+	0.923428i	$0.625375\pi$
$810$	−11693.8	−0.507257
$811$	24180.6	1.04697	0.523486	−	0.852034i	$-0.324631\pi$
$811$	24180.6	1.04697	0.523486	+	0.852034i	$0.324631\pi$
$812$	0	0
$813$	6668.38	0.287663
$814$	−51.6576	−0.00222432
$815$	−11842.5	−0.508989
$816$	−6004.60	−0.257602
$817$	629.526	0.0269576
$818$	−39146.1	−1.67324
$819$	0	0
$820$	3612.93	0.153865
$821$	−23340.9	−0.992208	−0.496104	−	0.868263i	$-0.665237\pi$
$821$	−23340.9	−0.992208	−0.496104	+	0.868263i	$0.665237\pi$
$822$	1186.71	0.0503545
$823$	20630.4	0.873792	0.436896	−	0.899512i	$-0.356078\pi$
$823$	20630.4	0.873792	0.436896	+	0.899512i	$0.356078\pi$
$824$	19521.9	0.825337
$825$	146.828	0.00619625
$826$	0	0
$827$	24113.7	1.01393	0.506963	−	0.861968i	$-0.330768\pi$
$827$	24113.7	1.01393	0.506963	+	0.861968i	$0.330768\pi$
$828$	10416.8	0.437207
$829$	−41738.9	−1.74868	−0.874338	−	0.485317i	$-0.838704\pi$
$829$	−41738.9	−1.74868	−0.874338	+	0.485317i	$0.838704\pi$
$830$	−21552.1	−0.901308
$831$	−4631.14	−0.193324
$832$	937.432	0.0390620
$833$	0	0
$834$	1526.42	0.0633760
$835$	5396.84	0.223671
$836$	1059.34	0.0438256
$837$	−8928.91	−0.368732
$838$	25687.9	1.05892
$839$	−30403.0	−1.25105	−0.625523	−	0.780205i	$-0.715114\pi$
$839$	−30403.0	−1.25105	−0.625523	+	0.780205i	$0.715114\pi$
$840$	0	0
$841$	47987.8	1.96760
$842$	41731.9	1.70805
$843$	−1808.25	−0.0738784
$844$	−4189.77	−0.170874
$845$	8534.90	0.347467
$846$	−48363.6	−1.96545
$847$	0	0
$848$	51274.7	2.07639
$849$	−2913.24	−0.117764
$850$	−7694.84	−0.310507
$851$	−204.952	−0.00825579
$852$	−372.412	−0.0149749
$853$	−5900.43	−0.236843	−0.118421	−	0.992963i	$-0.537783\pi$
$853$	−5900.43	−0.236843	−0.118421	+	0.992963i	$0.537783\pi$
$854$	0	0
$855$	−4855.48	−0.194215
$856$	15858.7	0.633221
$857$	18226.2	0.726480	0.363240	−	0.931696i	$-0.381670\pi$
$857$	18226.2	0.726480	0.363240	+	0.931696i	$0.381670\pi$
$858$	453.170	0.0180314
$859$	19944.2	0.792186	0.396093	−	0.918210i	$-0.370366\pi$
$859$	19944.2	0.792186	0.396093	+	0.918210i	$0.370366\pi$
$860$	353.446	0.0140144
$861$	0	0
$862$	−12438.9	−0.491497
$863$	30830.3	1.21608	0.608038	−	0.793908i	$-0.291957\pi$
$863$	30830.3	1.21608	0.608038	+	0.793908i	$0.291957\pi$
$864$	−7764.53	−0.305735
$865$	−4406.36	−0.173203
$866$	−7987.70	−0.313433
$867$	−2452.44	−0.0960662
$868$	0	0
$869$	7597.44	0.296577
$870$	3986.52	0.155351
$871$	10598.8	0.412317
$872$	−29584.7	−1.14893
$873$	−16726.8	−0.648471
$874$	12305.5	0.476248
$875$	0	0
$876$	3480.70	0.134249
$877$	−45885.6	−1.76676	−0.883379	−	0.468659i	$-0.844737\pi$
$877$	−45885.6	−1.76676	−0.883379	+	0.468659i	$0.844737\pi$
$878$	25548.6	0.982033
$879$	−1487.77	−0.0570889
$880$	−2762.28	−0.105814
$881$	−41132.6	−1.57298	−0.786489	−	0.617605i	$-0.788103\pi$
$881$	−41132.6	−1.57298	−0.786489	+	0.617605i	$0.788103\pi$
$882$	0	0
$883$	19850.0	0.756520	0.378260	−	0.925699i	$-0.376523\pi$
$883$	19850.0	0.756520	0.378260	+	0.925699i	$0.376523\pi$
$884$	−8111.58	−0.308622
$885$	2733.41	0.103822
$886$	28921.8	1.09667
$887$	−29029.3	−1.09888	−0.549441	−	0.835532i	$-0.685159\pi$
$887$	−29029.3	−1.09888	−0.549441	+	0.835532i	$0.685159\pi$
$888$	24.4812	0.000925154 0
$889$	0	0
$890$	−12403.6	−0.467159
$891$	−4634.80	−0.174267
$892$	−5300.40	−0.198958
$893$	−19513.8	−0.731248
$894$	−647.181	−0.0242114
$895$	16888.6	0.630752
$896$	0	0
$897$	1797.96	0.0669254
$898$	34015.2	1.26403
$899$	−53029.4	−1.96733
$900$	−2726.09	−0.100966
$901$	56612.3	2.09326
$902$	4192.57	0.154764
$903$	0	0
$904$	−3179.15	−0.116966
$905$	7177.88	0.263647
$906$	518.668	0.0190194
$907$	−21029.1	−0.769856	−0.384928	−	0.922947i	$-0.625774\pi$
$907$	−21029.1	−0.769856	−0.384928	+	0.922947i	$0.625774\pi$
$908$	−5809.14	−0.212316
$909$	45776.0	1.67029
$910$	0	0
$911$	−19225.5	−0.699198	−0.349599	−	0.936899i	$-0.613682\pi$
$911$	−19225.5	−0.699198	−0.349599	+	0.936899i	$0.613682\pi$
$912$	−2513.01	−0.0912433
$913$	−8542.13	−0.309642
$914$	−40938.9	−1.48155
$915$	−607.781	−0.0219591
$916$	−13204.6	−0.476300
$917$	0	0
$918$	−13942.5	−0.501276
$919$	21316.8	0.765154	0.382577	−	0.923924i	$-0.375037\pi$
$919$	21316.8	0.765154	0.382577	+	0.923924i	$0.375037\pi$
$920$	−6410.23	−0.229716
$921$	6776.68	0.242453
$922$	37465.9	1.33826
$923$	2336.50	0.0833229
$924$	0	0
$925$	53.6366	0.00190655
$926$	−34377.3	−1.21999
$927$	38223.3	1.35428
$928$	−46114.1	−1.63122
$929$	−19989.6	−0.705959	−0.352979	−	0.935631i	$-0.614831\pi$
$929$	−19989.6	−0.705959	−0.352979	+	0.935631i	$0.614831\pi$
$930$	−2920.87	−0.102988
$931$	0	0
$932$	−12564.8	−0.441603
$933$	−2177.23	−0.0763978
$934$	16245.9	0.569144
$935$	−3049.82	−0.106674
$936$	7806.49	0.272610
$937$	−55676.4	−1.94116	−0.970580	−	0.240779i	$-0.922597\pi$
$937$	−55676.4	−1.94116	−0.970580	+	0.240779i	$0.922597\pi$
$938$	0	0
$939$	−4133.10	−0.143641
$940$	−10956.0	−0.380153
$941$	108.842	0.00377062	0.00188531	−	0.999998i	$-0.499400\pi$
$941$	108.842	0.00377062	0.00188531	+	0.999998i	$0.499400\pi$
$942$	−2725.48	−0.0942686
$943$	16634.1	0.574422
$944$	−51423.6	−1.77298
$945$	0	0
$946$	410.150	0.0140963
$947$	−7785.95	−0.267169	−0.133585	−	0.991037i	$-0.542649\pi$
$947$	−7785.95	−0.267169	−0.133585	+	0.991037i	$0.542649\pi$
$948$	3880.62	0.132950
$949$	−21837.8	−0.746982
$950$	−3220.39	−0.109982
$951$	−6943.18	−0.236749
$952$	0	0
$953$	41445.5	1.40876	0.704381	−	0.709822i	$-0.251224\pi$
$953$	41445.5	1.40876	0.704381	+	0.709822i	$0.251224\pi$
$954$	58721.4	1.99285
$955$	7940.69	0.269063
$956$	−20730.9	−0.701345
$957$	1580.05	0.0533706
$958$	56792.5	1.91532
$959$	0	0
$960$	180.029	0.00605252
$961$	9062.92	0.304217
$962$	165.543	0.00554817
$963$	31050.8	1.03904
$964$	15588.7	0.520826
$965$	4888.52	0.163075
$966$	0	0
$967$	39155.0	1.30211	0.651055	−	0.759030i	$-0.274327\pi$
$967$	39155.0	1.30211	0.651055	+	0.759030i	$0.274327\pi$
$968$	17222.4	0.571849
$969$	−2774.60	−0.0919846
$970$	−11094.0	−0.367224
$971$	43440.8	1.43572	0.717859	−	0.696189i	$-0.245122\pi$
$971$	43440.8	1.43572	0.717859	+	0.696189i	$0.245122\pi$
$972$	−7442.74	−0.245603
$973$	0	0
$974$	−12252.0	−0.403061
$975$	−470.530	−0.0154554
$976$	11434.2	0.374999
$977$	11297.8	0.369957	0.184978	−	0.982743i	$-0.440778\pi$
$977$	11297.8	0.369957	0.184978	+	0.982743i	$0.440778\pi$
$978$	−7019.39	−0.229504
$979$	−4916.15	−0.160491
$980$	0	0
$981$	−57925.9	−1.88525
$982$	−8772.66	−0.285078
$983$	−10865.9	−0.352563	−0.176282	−	0.984340i	$-0.556407\pi$
$983$	−10865.9	−0.352563	−0.176282	+	0.984340i	$0.556407\pi$
$984$	−1986.91	−0.0643704
$985$	−1798.41	−0.0581747
$986$	−82805.5	−2.67451
$987$	0	0
$988$	−3394.80	−0.109315
$989$	1627.28	0.0523199
$990$	−3163.45	−0.101557
$991$	13884.1	0.445048	0.222524	−	0.974927i	$-0.428570\pi$
$991$	13884.1	0.445048	0.222524	+	0.974927i	$0.428570\pi$
$992$	33787.1	1.08139
$993$	−2529.36	−0.0808328
$994$	0	0
$995$	14091.9	0.448987
$996$	−4363.15	−0.138807
$997$	−31665.7	−1.00588	−0.502940	−	0.864321i	$-0.667748\pi$
$997$	−31665.7	−1.00588	−0.502940	+	0.864321i	$0.667748\pi$
$998$	−30490.7	−0.967099
$999$	97.1857	0.00307790

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.a.l.1.3		3
3.2	odd	2		2205.4.a.bm.1.1		3
5.4	even	2		1225.4.a.y.1.1		3
7.2	even	3		245.4.e.n.116.1		6
7.3	odd	6		245.4.e.m.226.1		6
7.4	even	3		245.4.e.n.226.1		6
7.5	odd	6		245.4.e.m.116.1		6
7.6	odd	2		35.4.a.c.1.3	✓	3
21.20	even	2		315.4.a.p.1.1		3
28.27	even	2		560.4.a.u.1.2		3
35.13	even	4		175.4.b.e.99.2		6
35.27	even	4		175.4.b.e.99.5		6
35.34	odd	2		175.4.a.f.1.1		3
56.13	odd	2		2240.4.a.bt.1.2		3
56.27	even	2		2240.4.a.bv.1.2		3
105.104	even	2		1575.4.a.ba.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.a.c.1.3	✓	3	7.6	odd	2
175.4.a.f.1.1		3	35.34	odd	2
175.4.b.e.99.2		6	35.13	even	4
175.4.b.e.99.5		6	35.27	even	4
245.4.a.l.1.3		3	1.1	even	1	trivial
245.4.e.m.116.1		6	7.5	odd	6
245.4.e.m.226.1		6	7.3	odd	6
245.4.e.n.116.1		6	7.2	even	3
245.4.e.n.226.1		6	7.4	even	3
315.4.a.p.1.1		3	21.20	even	2
560.4.a.u.1.2		3	28.27	even	2
1225.4.a.y.1.1		3	5.4	even	2
1575.4.a.ba.1.3		3	105.104	even	2
2205.4.a.bm.1.1		3	3.2	odd	2
2240.4.a.bt.1.2		3	56.13	odd	2
2240.4.a.bv.1.2		3	56.27	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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

\(f(q)\)	\(=\)	\(q+3.48565 q^{2} -0.850238 q^{3} +4.14976 q^{4} -5.00000 q^{5} -2.96363 q^{6} -13.4206 q^{8} -26.2771 q^{9} +O(q^{10})\)	\(q+3.48565 q^{2} -0.850238 q^{3} +4.14976 q^{4} -5.00000 q^{5} -2.96363 q^{6} -13.4206 q^{8} -26.2771 q^{9} -17.4283 q^{10} -6.90764 q^{11} -3.52829 q^{12} +22.1364 q^{13} +4.25119 q^{15} -79.9776 q^{16} -88.3030 q^{17} -91.5928 q^{18} -36.9560 q^{19} -20.7488 q^{20} -24.0776 q^{22} -95.5283 q^{23} +11.4107 q^{24} +25.0000 q^{25} +77.1598 q^{26} +45.2982 q^{27} +269.029 q^{29} +14.8182 q^{30} -197.114 q^{31} -171.409 q^{32} +5.87314 q^{33} -307.793 q^{34} -109.044 q^{36} +2.14546 q^{37} -128.816 q^{38} -18.8212 q^{39} +67.1029 q^{40} -174.127 q^{41} -17.0345 q^{43} -28.6650 q^{44} +131.385 q^{45} -332.978 q^{46} +528.029 q^{47} +68.0000 q^{48} +87.1413 q^{50} +75.0786 q^{51} +91.8608 q^{52} -641.114 q^{53} +157.894 q^{54} +34.5382 q^{55} +31.4214 q^{57} +937.742 q^{58} +642.975 q^{59} +17.6414 q^{60} -142.967 q^{61} -687.070 q^{62} +42.3480 q^{64} -110.682 q^{65} +20.4717 q^{66} +478.797 q^{67} -366.436 q^{68} +81.2218 q^{69} +105.550 q^{71} +352.654 q^{72} -986.512 q^{73} +7.47834 q^{74} -21.2560 q^{75} -153.358 q^{76} -65.6042 q^{78} -1099.86 q^{79} +399.888 q^{80} +670.967 q^{81} -606.947 q^{82} +1236.62 q^{83} +441.515 q^{85} -59.3763 q^{86} -228.739 q^{87} +92.7045 q^{88} +711.698 q^{89} +457.964 q^{90} -396.420 q^{92} +167.594 q^{93} +1840.52 q^{94} +184.780 q^{95} +145.739 q^{96} +636.553 q^{97} +181.513 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 2 q^{3} + 13 q^{4} - 15 q^{5} - 24 q^{6} - 15 q^{8} + 81 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 2 * q^3 + 13 * q^4 - 15 * q^5 - 24 * q^6 - 15 * q^8 + 81 * q^9	\( 3 q - 3 q^{2} - 2 q^{3} + 13 q^{4} - 15 q^{5} - 24 q^{6} - 15 q^{8} + 81 q^{9} + 15 q^{10} - 74 q^{11} + 152 q^{12} - 44 q^{13} + 10 q^{15} - 79 q^{16} + 52 q^{17} - 411 q^{18} - 168 q^{19} - 65 q^{20} + 184 q^{22} - 124 q^{23} - 420 q^{24} + 75 q^{25} + 446 q^{26} - 170 q^{27} + 332 q^{29} + 120 q^{30} - 320 q^{31} - 183 q^{32} + 106 q^{33} - 582 q^{34} + 181 q^{36} - 54 q^{37} + 460 q^{38} - 982 q^{39} + 75 q^{40} - 362 q^{41} - 16 q^{43} - 264 q^{44} - 405 q^{45} - 336 q^{46} + 730 q^{47} + 204 q^{48} - 75 q^{50} - 1178 q^{51} - 1202 q^{52} + 110 q^{53} + 180 q^{54} + 370 q^{55} - 956 q^{57} + 450 q^{58} + 180 q^{59} - 760 q^{60} - 1222 q^{61} - 464 q^{62} - 391 q^{64} + 220 q^{65} + 532 q^{66} + 204 q^{67} - 918 q^{68} + 716 q^{69} - 136 q^{71} + 765 q^{72} - 310 q^{73} + 502 q^{74} - 50 q^{75} - 1796 q^{76} + 3788 q^{78} - 1034 q^{79} + 395 q^{80} + 2283 q^{81} + 6 q^{82} + 1660 q^{83} - 260 q^{85} + 764 q^{86} + 1574 q^{87} - 20 q^{88} - 242 q^{89} + 2055 q^{90} + 96 q^{92} + 1376 q^{93} + 1108 q^{94} + 840 q^{95} + 3156 q^{96} - 100 q^{97} - 3488 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 2 * q^3 + 13 * q^4 - 15 * q^5 - 24 * q^6 - 15 * q^8 + 81 * q^9 + 15 * q^10 - 74 * q^11 + 152 * q^12 - 44 * q^13 + 10 * q^15 - 79 * q^16 + 52 * q^17 - 411 * q^18 - 168 * q^19 - 65 * q^20 + 184 * q^22 - 124 * q^23 - 420 * q^24 + 75 * q^25 + 446 * q^26 - 170 * q^27 + 332 * q^29 + 120 * q^30 - 320 * q^31 - 183 * q^32 + 106 * q^33 - 582 * q^34 + 181 * q^36 - 54 * q^37 + 460 * q^38 - 982 * q^39 + 75 * q^40 - 362 * q^41 - 16 * q^43 - 264 * q^44 - 405 * q^45 - 336 * q^46 + 730 * q^47 + 204 * q^48 - 75 * q^50 - 1178 * q^51 - 1202 * q^52 + 110 * q^53 + 180 * q^54 + 370 * q^55 - 956 * q^57 + 450 * q^58 + 180 * q^59 - 760 * q^60 - 1222 * q^61 - 464 * q^62 - 391 * q^64 + 220 * q^65 + 532 * q^66 + 204 * q^67 - 918 * q^68 + 716 * q^69 - 136 * q^71 + 765 * q^72 - 310 * q^73 + 502 * q^74 - 50 * q^75 - 1796 * q^76 + 3788 * q^78 - 1034 * q^79 + 395 * q^80 + 2283 * q^81 + 6 * q^82 + 1660 * q^83 - 260 * q^85 + 764 * q^86 + 1574 * q^87 - 20 * q^88 - 242 * q^89 + 2055 * q^90 + 96 * q^92 + 1376 * q^93 + 1108 * q^94 + 840 * q^95 + 3156 * q^96 - 100 * q^97 - 3488 * q^99

Introduction

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