LMFDB - Embedded newform 245.4.a.o.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:	$6$
Coefficient field:	6.6.1163891200.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 23x^{4} + 12x^{3} + 154x^{2} + 152x + 28 $ x^6 - 2x^5 - 23x^4 + 12x^3 + 154x^2 + 152*x + 28
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.04490$ 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)

$f(q)$	$=$	$q-0.369315 q^{2} -9.74070 q^{3} -7.86361 q^{4} +5.00000 q^{5} +3.59738 q^{6} +5.85867 q^{8} +67.8812 q^{9} +O(q^{10})$	\(q-0.369315 q^{2} -9.74070 q^{3} -7.86361 q^{4} +5.00000 q^{5} +3.59738 q^{6} +5.85867 q^{8} +67.8812 q^{9} -1.84657 q^{10} +30.6361 q^{11} +76.5970 q^{12} +36.4622 q^{13} -48.7035 q^{15} +60.7452 q^{16} -79.7341 q^{17} -25.0695 q^{18} -152.418 q^{19} -39.3180 q^{20} -11.3144 q^{22} +22.2207 q^{23} -57.0675 q^{24} +25.0000 q^{25} -13.4660 q^{26} -398.211 q^{27} +101.285 q^{29} +17.9869 q^{30} +249.956 q^{31} -69.3034 q^{32} -298.417 q^{33} +29.4470 q^{34} -533.791 q^{36} +7.55765 q^{37} +56.2904 q^{38} -355.168 q^{39} +29.2933 q^{40} +142.280 q^{41} -237.530 q^{43} -240.910 q^{44} +339.406 q^{45} -8.20644 q^{46} -331.129 q^{47} -591.700 q^{48} -9.23287 q^{50} +776.666 q^{51} -286.725 q^{52} -487.337 q^{53} +147.065 q^{54} +153.180 q^{55} +1484.66 q^{57} -37.4059 q^{58} -717.355 q^{59} +382.985 q^{60} +354.592 q^{61} -92.3126 q^{62} -460.367 q^{64} +182.311 q^{65} +110.210 q^{66} +57.5883 q^{67} +626.997 q^{68} -216.445 q^{69} -696.174 q^{71} +397.693 q^{72} -261.035 q^{73} -2.79115 q^{74} -243.517 q^{75} +1198.56 q^{76} +131.169 q^{78} +271.344 q^{79} +303.726 q^{80} +2046.06 q^{81} -52.5460 q^{82} +681.441 q^{83} -398.670 q^{85} +87.7234 q^{86} -986.584 q^{87} +179.487 q^{88} +160.668 q^{89} -125.348 q^{90} -174.735 q^{92} -2434.75 q^{93} +122.291 q^{94} -762.092 q^{95} +675.063 q^{96} -167.841 q^{97} +2079.61 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 16 q^{3} + 14 q^{4} + 30 q^{5} - 24 q^{6} - 66 q^{8} + 70 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 16 * q^3 + 14 * q^4 + 30 * q^5 - 24 * q^6 - 66 * q^8 + 70 * q^9	\( 6 q - 2 q^{2} - 16 q^{3} + 14 q^{4} + 30 q^{5} - 24 q^{6} - 66 q^{8} + 70 q^{9} - 10 q^{10} - 16 q^{11} - 160 q^{12} - 168 q^{13} - 80 q^{15} + 298 q^{16} + 4 q^{17} + 354 q^{18} - 308 q^{19} + 70 q^{20} - 236 q^{22} - 336 q^{23} + 92 q^{24} + 150 q^{25} - 56 q^{26} - 964 q^{27} + 176 q^{29} - 120 q^{30} - 392 q^{31} - 770 q^{32} - 188 q^{33} - 812 q^{34} + 230 q^{36} - 140 q^{37} - 20 q^{38} + 140 q^{39} - 330 q^{40} - 656 q^{41} - 388 q^{43} - 160 q^{44} + 350 q^{45} - 388 q^{46} - 628 q^{47} - 1396 q^{48} - 50 q^{50} + 744 q^{51} - 1520 q^{52} - 676 q^{53} - 2284 q^{54} - 80 q^{55} + 1468 q^{57} - 2012 q^{58} - 996 q^{59} - 800 q^{60} - 740 q^{61} + 364 q^{62} + 1426 q^{64} - 840 q^{65} + 3620 q^{66} + 1768 q^{67} + 2940 q^{68} + 1048 q^{69} - 224 q^{71} + 2858 q^{72} - 2640 q^{73} + 928 q^{74} - 400 q^{75} + 1340 q^{76} + 8 q^{78} + 1636 q^{79} + 1490 q^{80} + 4442 q^{81} + 1756 q^{82} - 140 q^{83} + 20 q^{85} + 1180 q^{86} - 1940 q^{87} - 5652 q^{88} + 1904 q^{89} + 1770 q^{90} - 1952 q^{92} - 1592 q^{93} + 3332 q^{94} - 1540 q^{95} + 6460 q^{96} - 516 q^{97} - 2804 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 16 * q^3 + 14 * q^4 + 30 * q^5 - 24 * q^6 - 66 * q^8 + 70 * q^9 - 10 * q^10 - 16 * q^11 - 160 * q^12 - 168 * q^13 - 80 * q^15 + 298 * q^16 + 4 * q^17 + 354 * q^18 - 308 * q^19 + 70 * q^20 - 236 * q^22 - 336 * q^23 + 92 * q^24 + 150 * q^25 - 56 * q^26 - 964 * q^27 + 176 * q^29 - 120 * q^30 - 392 * q^31 - 770 * q^32 - 188 * q^33 - 812 * q^34 + 230 * q^36 - 140 * q^37 - 20 * q^38 + 140 * q^39 - 330 * q^40 - 656 * q^41 - 388 * q^43 - 160 * q^44 + 350 * q^45 - 388 * q^46 - 628 * q^47 - 1396 * q^48 - 50 * q^50 + 744 * q^51 - 1520 * q^52 - 676 * q^53 - 2284 * q^54 - 80 * q^55 + 1468 * q^57 - 2012 * q^58 - 996 * q^59 - 800 * q^60 - 740 * q^61 + 364 * q^62 + 1426 * q^64 - 840 * q^65 + 3620 * q^66 + 1768 * q^67 + 2940 * q^68 + 1048 * q^69 - 224 * q^71 + 2858 * q^72 - 2640 * q^73 + 928 * q^74 - 400 * q^75 + 1340 * q^76 + 8 * q^78 + 1636 * q^79 + 1490 * q^80 + 4442 * q^81 + 1756 * q^82 - 140 * q^83 + 20 * q^85 + 1180 * q^86 - 1940 * q^87 - 5652 * q^88 + 1904 * q^89 + 1770 * q^90 - 1952 * q^92 - 1592 * q^93 + 3332 * q^94 - 1540 * q^95 + 6460 * q^96 - 516 * q^97 - 2804 * 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 $

$2$	−0.369315	−0.130573	−0.0652863	−	0.997867i	$-0.520796\pi$
$2$	−0.369315	−0.130573	−0.0652863	+	0.997867i	$0.520796\pi$
$3$	−9.74070	−1.87460	−0.937299	−	0.348526i	$-0.886682\pi$
$3$	−9.74070	−1.87460	−0.937299	+	0.348526i	$0.886682\pi$
$4$	−7.86361	−0.982951
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	3.59738	0.244771
$7$	0	0
$7$	0	0
$8$	5.85867	0.258919
$9$	67.8812	2.51412
$10$	−1.84657	−0.0583938
$11$	30.6361	0.839739	0.419870	−	0.907584i	$-0.362076\pi$
$11$	30.6361	0.839739	0.419870	+	0.907584i	$0.362076\pi$
$12$	76.5970	1.84264
$13$	36.4622	0.777908	0.388954	−	0.921257i	$-0.372836\pi$
$13$	36.4622	0.777908	0.388954	+	0.921257i	$0.372836\pi$
$14$	0	0
$15$	−48.7035	−0.838346
$16$	60.7452	0.949143
$17$	−79.7341	−1.13755	−0.568775	−	0.822493i	$-0.692583\pi$
$17$	−79.7341	−1.13755	−0.568775	+	0.822493i	$0.692583\pi$
$18$	−25.0695	−0.328275
$19$	−152.418	−1.84038	−0.920189	−	0.391474i	$-0.871965\pi$
$19$	−152.418	−1.84038	−0.920189	+	0.391474i	$0.871965\pi$
$20$	−39.3180	−0.439589
$21$	0	0
$22$	−11.3144	−0.109647
$23$	22.2207	0.201450	0.100725	−	0.994914i	$-0.467884\pi$
$23$	22.2207	0.201450	0.100725	+	0.994914i	$0.467884\pi$
$24$	−57.0675	−0.485369
$25$	25.0000	0.200000
$26$	−13.4660	−0.101573
$27$	−398.211	−2.83836
$28$	0	0
$29$	101.285	0.648555	0.324278	−	0.945962i	$-0.394879\pi$
$29$	101.285	0.648555	0.324278	+	0.945962i	$0.394879\pi$
$30$	17.9869	0.109465
$31$	249.956	1.44818	0.724089	−	0.689707i	$-0.242261\pi$
$31$	249.956	1.44818	0.724089	+	0.689707i	$0.242261\pi$
$32$	−69.3034	−0.382851
$33$	−298.417	−1.57417
$34$	29.4470	0.148533
$35$	0	0
$36$	−533.791	−2.47125
$37$	7.55765	0.0335803	0.0167901	−	0.999859i	$-0.494655\pi$
$37$	7.55765	0.0335803	0.0167901	+	0.999859i	$0.494655\pi$
$38$	56.2904	0.240303
$39$	−355.168	−1.45826
$40$	29.2933	0.115792
$41$	142.280	0.541960	0.270980	−	0.962585i	$-0.412652\pi$
$41$	142.280	0.541960	0.270980	+	0.962585i	$0.412652\pi$
$42$	0	0
$43$	−237.530	−0.842396	−0.421198	−	0.906969i	$-0.638390\pi$
$43$	−237.530	−0.842396	−0.421198	+	0.906969i	$0.638390\pi$
$44$	−240.910	−0.825422
$45$	339.406	1.12435
$46$	−8.20644	−0.0263038
$47$	−331.129	−1.02766	−0.513830	−	0.857892i	$-0.671774\pi$
$47$	−331.129	−1.02766	−0.513830	+	0.857892i	$0.671774\pi$
$48$	−591.700	−1.77926
$49$	0	0
$50$	−9.23287	−0.0261145
$51$	776.666	2.13245
$52$	−286.725	−0.764645
$53$	−487.337	−1.26303	−0.631517	−	0.775362i	$-0.717568\pi$
$53$	−487.337	−1.26303	−0.631517	+	0.775362i	$0.717568\pi$
$54$	147.065	0.370612
$55$	153.180	0.375543
$56$	0	0
$57$	1484.66	3.44997
$58$	−37.4059	−0.0846835
$59$	−717.355	−1.58291	−0.791454	−	0.611228i	$-0.790676\pi$
$59$	−717.355	−1.58291	−0.791454	+	0.611228i	$0.790676\pi$
$60$	382.985	0.824053
$61$	354.592	0.744276	0.372138	−	0.928177i	$-0.378625\pi$
$61$	354.592	0.744276	0.372138	+	0.928177i	$0.378625\pi$
$62$	−92.3126	−0.189092
$63$	0	0
$64$	−460.367	−0.899153
$65$	182.311	0.347891
$66$	110.210	0.205544
$67$	57.5883	0.105008	0.0525040	−	0.998621i	$-0.483280\pi$
$67$	57.5883	0.105008	0.0525040	+	0.998621i	$0.483280\pi$
$68$	626.997	1.11816
$69$	−216.445	−0.377637
$70$	0	0
$71$	−696.174	−1.16367	−0.581836	−	0.813306i	$-0.697665\pi$
$71$	−696.174	−1.16367	−0.581836	+	0.813306i	$0.697665\pi$
$72$	397.693	0.650952
$73$	−261.035	−0.418518	−0.209259	−	0.977860i	$-0.567105\pi$
$73$	−261.035	−0.418518	−0.209259	+	0.977860i	$0.567105\pi$
$74$	−2.79115	−0.00438466
$75$	−243.517	−0.374920
$76$	1198.56	1.80900
$77$	0	0
$78$	131.169	0.190409
$79$	271.344	0.386438	0.193219	−	0.981156i	$-0.438107\pi$
$79$	271.344	0.386438	0.193219	+	0.981156i	$0.438107\pi$
$80$	303.726	0.424470
$81$	2046.06	2.80667
$82$	−52.5460	−0.0707651
$83$	681.441	0.901179	0.450590	−	0.892731i	$-0.351214\pi$
$83$	681.441	0.901179	0.450590	+	0.892731i	$0.351214\pi$
$84$	0	0
$85$	−398.670	−0.508728
$86$	87.7234	0.109994
$87$	−986.584	−1.21578
$88$	179.487	0.217424
$89$	160.668	0.191357	0.0956784	−	0.995412i	$-0.469498\pi$
$89$	160.668	0.191357	0.0956784	+	0.995412i	$0.469498\pi$
$90$	−125.348	−0.146809
$91$	0	0
$92$	−174.735	−0.198015
$93$	−2434.75	−2.71475
$94$	122.291	0.134184
$95$	−762.092	−0.823042
$96$	675.063	0.717691
$97$	−167.841	−0.175687	−0.0878436	−	0.996134i	$-0.527998\pi$
$97$	−167.841	−0.175687	−0.0878436	+	0.996134i	$0.527998\pi$
$98$	0	0
$99$	2079.61	2.11120
$100$	−196.590	−0.196590
$101$	−413.394	−0.407270	−0.203635	−	0.979047i	$-0.565276\pi$
$101$	−413.394	−0.407270	−0.203635	+	0.979047i	$0.565276\pi$
$102$	−286.834	−0.278439
$103$	−1451.11	−1.38817	−0.694086	−	0.719892i	$-0.744191\pi$
$103$	−1451.11	−1.38817	−0.694086	+	0.719892i	$0.744191\pi$
$104$	213.620	0.201415
$105$	0	0
$106$	179.981	0.164918
$107$	−1780.63	−1.60878	−0.804391	−	0.594100i	$-0.797508\pi$
$107$	−1780.63	−1.60878	−0.804391	+	0.594100i	$0.797508\pi$
$108$	3131.38	2.78997
$109$	37.8920	0.0332972	0.0166486	−	0.999861i	$-0.494700\pi$
$109$	37.8920	0.0332972	0.0166486	+	0.999861i	$0.494700\pi$
$110$	−56.5718	−0.0490356
$111$	−73.6168	−0.0629495
$112$	0	0
$113$	457.320	0.380717	0.190359	−	0.981715i	$-0.439035\pi$
$113$	457.320	0.380717	0.190359	+	0.981715i	$0.439035\pi$
$114$	−548.308	−0.450471
$115$	111.104	0.0900910
$116$	−796.463	−0.637498
$117$	2475.10	1.95575
$118$	264.930	0.206684
$119$	0	0
$120$	−285.337	−0.217064
$121$	−392.430	−0.294838
$122$	−130.956	−0.0971820
$123$	−1385.90	−1.01596
$124$	−1965.56	−1.42349
$125$	125.000	0.0894427
$126$	0	0
$127$	−2545.41	−1.77849	−0.889246	−	0.457429i	$-0.848771\pi$
$127$	−2545.41	−1.77849	−0.889246	+	0.457429i	$0.848771\pi$
$128$	724.447	0.500256
$129$	2313.71	1.57915
$130$	−67.3302	−0.0454250
$131$	970.873	0.647523	0.323762	−	0.946139i	$-0.395052\pi$
$131$	970.873	0.647523	0.323762	+	0.946139i	$0.395052\pi$
$132$	2346.63	1.54733
$133$	0	0
$134$	−21.2682	−0.0137112
$135$	−1991.06	−1.26935
$136$	−467.135	−0.294533
$137$	183.635	0.114518	0.0572592	−	0.998359i	$-0.481764\pi$
$137$	183.635	0.114518	0.0572592	+	0.998359i	$0.481764\pi$
$138$	79.9365	0.0493090
$139$	1078.90	0.658356	0.329178	−	0.944268i	$-0.393228\pi$
$139$	1078.90	0.658356	0.329178	+	0.944268i	$0.393228\pi$
$140$	0	0
$141$	3225.42	1.92645
$142$	257.108	0.151944
$143$	1117.06	0.653240
$144$	4123.45	2.38626
$145$	506.424	0.290043
$146$	96.4040	0.0546469
$147$	0	0
$148$	−59.4304	−0.0330077
$149$	1211.24	0.665962	0.332981	−	0.942934i	$-0.391946\pi$
$149$	1211.24	0.665962	0.332981	+	0.942934i	$0.391946\pi$
$150$	89.9346	0.0489542
$151$	−602.244	−0.324569	−0.162285	−	0.986744i	$-0.551886\pi$
$151$	−602.244	−0.324569	−0.162285	+	0.986744i	$0.551886\pi$
$152$	−892.969	−0.476509
$153$	−5412.44	−2.85994
$154$	0	0
$155$	1249.78	0.647644
$156$	2792.90	1.43340
$157$	−1602.07	−0.814389	−0.407195	−	0.913341i	$-0.633493\pi$
$157$	−1602.07	−0.814389	−0.407195	+	0.913341i	$0.633493\pi$
$158$	−100.212	−0.0504582
$159$	4747.00	2.36768
$160$	−346.517	−0.171216
$161$	0	0
$162$	−755.641	−0.366474
$163$	−3091.61	−1.48561	−0.742803	−	0.669510i	$-0.766504\pi$
$163$	−3091.61	−1.48561	−0.742803	+	0.669510i	$0.766504\pi$
$164$	−1118.83	−0.532720
$165$	−1492.08	−0.703992
$166$	−251.666	−0.117669
$167$	3251.19	1.50649	0.753247	−	0.657738i	$-0.228487\pi$
$167$	3251.19	1.50649	0.753247	+	0.657738i	$0.228487\pi$
$168$	0	0
$169$	−867.505	−0.394859
$170$	147.235	0.0664259
$171$	−10346.3	−4.62693
$172$	1867.84	0.828034
$173$	−2254.55	−0.990809	−0.495405	−	0.868662i	$-0.664980\pi$
$173$	−2254.55	−0.990809	−0.495405	+	0.868662i	$0.664980\pi$
$174$	364.360	0.158747
$175$	0	0
$176$	1860.99	0.797033
$177$	6987.53	2.96732
$178$	−59.3370	−0.0249859
$179$	−2685.46	−1.12135	−0.560673	−	0.828038i	$-0.689457\pi$
$179$	−2685.46	−1.12135	−0.560673	+	0.828038i	$0.689457\pi$
$180$	−2668.95	−1.10518
$181$	−1293.25	−0.531087	−0.265543	−	0.964099i	$-0.585551\pi$
$181$	−1293.25	−0.531087	−0.265543	+	0.964099i	$0.585551\pi$
$182$	0	0
$183$	−3453.97	−1.39522
$184$	130.184	0.0521591
$185$	37.7882	0.0150175
$186$	899.189	0.354472
$187$	−2442.74	−0.955245
$188$	2603.86	1.01014
$189$	0	0
$190$	281.452	0.107467
$191$	−139.878	−0.0529905	−0.0264953	−	0.999649i	$-0.508435\pi$
$191$	−139.878	−0.0529905	−0.0264953	+	0.999649i	$0.508435\pi$
$192$	4484.29	1.68555
$193$	2384.81	0.889442	0.444721	−	0.895669i	$-0.353303\pi$
$193$	2384.81	0.889442	0.444721	+	0.895669i	$0.353303\pi$
$194$	61.9861	0.0229399
$195$	−1775.84	−0.652156
$196$	0	0
$197$	−1008.67	−0.364797	−0.182399	−	0.983225i	$-0.558386\pi$
$197$	−1008.67	−0.364797	−0.182399	+	0.983225i	$0.558386\pi$
$198$	−768.032	−0.275665
$199$	−995.036	−0.354453	−0.177227	−	0.984170i	$-0.556713\pi$
$199$	−995.036	−0.354453	−0.177227	+	0.984170i	$0.556713\pi$
$200$	146.467	0.0517838
$201$	−560.950	−0.196848
$202$	152.672	0.0531782
$203$	0	0
$204$	−6107.39	−2.09609
$205$	711.399	0.242372
$206$	535.915	0.181257
$207$	1508.37	0.506468
$208$	2214.90	0.738346
$209$	−4669.51	−1.54544
$210$	0	0
$211$	2307.30	0.752802	0.376401	−	0.926457i	$-0.377161\pi$
$211$	2307.30	0.752802	0.376401	+	0.926457i	$0.377161\pi$
$212$	3832.22	1.24150
$213$	6781.22	2.18142
$214$	657.612	0.210063
$215$	−1187.65	−0.376731
$216$	−2332.99	−0.734905
$217$	0	0
$218$	−13.9941	−0.00434770
$219$	2542.66	0.784552
$220$	−1204.55	−0.369140
$221$	−2907.28	−0.884910
$222$	27.1878	0.00821947
$223$	−1629.00	−0.489173	−0.244587	−	0.969627i	$-0.578652\pi$
$223$	−1629.00	−0.489173	−0.244587	+	0.969627i	$0.578652\pi$
$224$	0	0
$225$	1697.03	0.502824
$226$	−168.895	−0.0497112
$227$	2410.92	0.704926	0.352463	−	0.935826i	$-0.385344\pi$
$227$	2410.92	0.704926	0.352463	+	0.935826i	$0.385344\pi$
$228$	−11674.8	−3.39115
$229$	−3666.59	−1.05806	−0.529028	−	0.848604i	$-0.677443\pi$
$229$	−3666.59	−1.05806	−0.529028	+	0.848604i	$0.677443\pi$
$230$	−41.0322	−0.0117634
$231$	0	0
$232$	593.393	0.167923
$233$	−3018.33	−0.848658	−0.424329	−	0.905508i	$-0.639490\pi$
$233$	−3018.33	−0.848658	−0.424329	+	0.905508i	$0.639490\pi$
$234$	−914.091	−0.255367
$235$	−1655.64	−0.459584
$236$	5640.99	1.55592
$237$	−2643.08	−0.724417
$238$	0	0
$239$	−546.873	−0.148010	−0.0740048	−	0.997258i	$-0.523578\pi$
$239$	−546.873	−0.148010	−0.0740048	+	0.997258i	$0.523578\pi$
$240$	−2958.50	−0.795710
$241$	−3135.27	−0.838010	−0.419005	−	0.907984i	$-0.637621\pi$
$241$	−3135.27	−0.838010	−0.419005	+	0.907984i	$0.637621\pi$
$242$	144.930	0.0384978
$243$	−9178.37	−2.42302
$244$	−2788.37	−0.731587
$245$	0	0
$246$	511.835	0.132656
$247$	−5557.52	−1.43165
$248$	1464.41	0.374960
$249$	−6637.71	−1.68935
$250$	−46.1644	−0.0116788
$251$	914.967	0.230088	0.115044	−	0.993360i	$-0.463299\pi$
$251$	914.967	0.230088	0.115044	+	0.993360i	$0.463299\pi$
$252$	0	0
$253$	680.756	0.169165
$254$	940.058	0.232222
$255$	3883.33	0.953660
$256$	3415.38	0.833834
$257$	6334.18	1.53741	0.768707	−	0.639602i	$-0.220901\pi$
$257$	6334.18	1.53741	0.768707	+	0.639602i	$0.220901\pi$
$258$	−854.487	−0.206194
$259$	0	0
$260$	−1433.62	−0.341960
$261$	6875.33	1.63054
$262$	−358.558	−0.0845487
$263$	4126.75	0.967553	0.483777	−	0.875191i	$-0.339265\pi$
$263$	4126.75	0.967553	0.483777	+	0.875191i	$0.339265\pi$
$264$	−1748.32	−0.407583
$265$	−2436.68	−0.564846
$266$	0	0
$267$	−1565.02	−0.358717
$268$	−452.852	−0.103218
$269$	5887.07	1.33435	0.667176	−	0.744900i	$-0.267503\pi$
$269$	5887.07	1.33435	0.667176	+	0.744900i	$0.267503\pi$
$270$	735.326	0.165743
$271$	−7237.72	−1.62236	−0.811181	−	0.584795i	$-0.801175\pi$
$271$	−7237.72	−1.62236	−0.811181	+	0.584795i	$0.801175\pi$
$272$	−4843.46	−1.07970
$273$	0	0
$274$	−67.8192	−0.0149530
$275$	765.902	0.167948
$276$	1702.04	0.371199
$277$	5640.17	1.22341	0.611705	−	0.791086i	$-0.290484\pi$
$277$	5640.17	1.22341	0.611705	+	0.791086i	$0.290484\pi$
$278$	−398.456	−0.0859632
$279$	16967.3	3.64089
$280$	0	0
$281$	−2593.05	−0.550492	−0.275246	−	0.961374i	$-0.588759\pi$
$281$	−2593.05	−0.550492	−0.275246	+	0.961374i	$0.588759\pi$
$282$	−1191.20	−0.251542
$283$	−2533.26	−0.532109	−0.266054	−	0.963958i	$-0.585720\pi$
$283$	−2533.26	−0.532109	−0.266054	+	0.963958i	$0.585720\pi$
$284$	5474.44	1.14383
$285$	7423.31	1.54287
$286$	−412.547	−0.0852952
$287$	0	0
$288$	−4704.40	−0.962532
$289$	1444.52	0.294021
$290$	−187.030	−0.0378716
$291$	1634.89	0.329343
$292$	2052.67	0.411382
$293$	589.215	0.117482	0.0587411	−	0.998273i	$-0.481291\pi$
$293$	589.215	0.117482	0.0587411	+	0.998273i	$0.481291\pi$
$294$	0	0
$295$	−3586.77	−0.707898
$296$	44.2777	0.00869456
$297$	−12199.6	−2.38348
$298$	−447.327	−0.0869563
$299$	810.217	0.156709
$300$	1914.93	0.368528
$301$	0	0
$302$	222.418	0.0423798
$303$	4026.74	0.763467
$304$	−9258.68	−1.74678
$305$	1772.96	0.332851
$306$	1998.90	0.373429
$307$	−5273.75	−0.980420	−0.490210	−	0.871604i	$-0.663080\pi$
$307$	−5273.75	−0.980420	−0.490210	+	0.871604i	$0.663080\pi$
$308$	0	0
$309$	14134.8	2.60226
$310$	−461.563	−0.0845646
$311$	3295.08	0.600795	0.300397	−	0.953814i	$-0.402881\pi$
$311$	3295.08	0.600795	0.300397	+	0.953814i	$0.402881\pi$
$312$	−2080.81	−0.377572
$313$	1819.37	0.328553	0.164276	−	0.986414i	$-0.447471\pi$
$313$	1819.37	0.328553	0.164276	+	0.986414i	$0.447471\pi$
$314$	591.668	0.106337
$315$	0	0
$316$	−2133.75	−0.379850
$317$	1887.91	0.334496	0.167248	−	0.985915i	$-0.446512\pi$
$317$	1887.91	0.334496	0.167248	+	0.985915i	$0.446512\pi$
$318$	−1753.14	−0.309154
$319$	3102.97	0.544617
$320$	−2301.83	−0.402114
$321$	17344.6	3.01582
$322$	0	0
$323$	12152.9	2.09352
$324$	−16089.4	−2.75882
$325$	911.556	0.155582
$326$	1141.78	0.193979
$327$	−369.094	−0.0624188
$328$	833.569	0.140324
$329$	0	0
$330$	551.049	0.0919220
$331$	−456.387	−0.0757863	−0.0378932	−	0.999282i	$-0.512065\pi$
$331$	−456.387	−0.0757863	−0.0378932	+	0.999282i	$0.512065\pi$
$332$	−5358.58	−0.885815
$333$	513.022	0.0844247
$334$	−1200.71	−0.196707
$335$	287.942	0.0469610
$336$	0	0
$337$	8174.42	1.32133	0.660666	−	0.750680i	$-0.270274\pi$
$337$	8174.42	1.32133	0.660666	+	0.750680i	$0.270274\pi$
$338$	320.383	0.0515577
$339$	−4454.61	−0.713691
$340$	3134.99	0.500055
$341$	7657.69	1.21609
$342$	3821.06	0.604150
$343$	0	0
$344$	−1391.61	−0.218112
$345$	−1082.23	−0.168884
$346$	832.637	0.129372
$347$	−7935.70	−1.22770	−0.613849	−	0.789424i	$-0.710379\pi$
$347$	−7935.70	−1.22770	−0.613849	+	0.789424i	$0.710379\pi$
$348$	7758.11	1.19505
$349$	−8649.40	−1.32662	−0.663312	−	0.748343i	$-0.730850\pi$
$349$	−8649.40	−1.32662	−0.663312	+	0.748343i	$0.730850\pi$
$350$	0	0
$351$	−14519.7	−2.20798
$352$	−2123.19	−0.321495
$353$	4931.06	0.743495	0.371747	−	0.928334i	$-0.378759\pi$
$353$	4931.06	0.743495	0.371747	+	0.928334i	$0.378759\pi$
$354$	−2580.60	−0.387450
$355$	−3480.87	−0.520410
$356$	−1263.43	−0.188094
$357$	0	0
$358$	991.781	0.146417
$359$	8243.64	1.21193	0.605965	−	0.795491i	$-0.292787\pi$
$359$	8243.64	1.21193	0.605965	+	0.795491i	$0.292787\pi$
$360$	1988.47	0.291115
$361$	16372.4	2.38699
$362$	477.617	0.0693453
$363$	3822.54	0.552703
$364$	0	0
$365$	−1305.17	−0.187167
$366$	1275.60	0.182177
$367$	8179.11	1.16334	0.581670	−	0.813425i	$-0.302399\pi$
$367$	8179.11	1.16334	0.581670	+	0.813425i	$0.302399\pi$
$368$	1349.80	0.191204
$369$	9658.12	1.36255
$370$	−13.9558	−0.00196088
$371$	0	0
$372$	19145.9	2.66847
$373$	−12795.5	−1.77620	−0.888102	−	0.459646i	$-0.847976\pi$
$373$	−12795.5	−1.77620	−0.888102	+	0.459646i	$0.847976\pi$
$374$	902.140	0.124729
$375$	−1217.59	−0.167669
$376$	−1939.97	−0.266081
$377$	3693.07	0.504516
$378$	0	0
$379$	−5735.40	−0.777329	−0.388664	−	0.921379i	$-0.627063\pi$
$379$	−5735.40	−0.777329	−0.388664	+	0.921379i	$0.627063\pi$
$380$	5992.79	0.809010
$381$	24794.1	3.33396
$382$	51.6589	0.00691910
$383$	−737.841	−0.0984384	−0.0492192	−	0.998788i	$-0.515673\pi$
$383$	−737.841	−0.0984384	−0.0492192	+	0.998788i	$0.515673\pi$
$384$	−7056.62	−0.937778
$385$	0	0
$386$	−880.745	−0.116137
$387$	−16123.8	−2.11788
$388$	1319.83	0.172692
$389$	−13034.0	−1.69884	−0.849419	−	0.527718i	$-0.823048\pi$
$389$	−13034.0	−1.69884	−0.849419	+	0.527718i	$0.823048\pi$
$390$	655.843	0.0851536
$391$	−1771.75	−0.229159
$392$	0	0
$393$	−9456.98	−1.21385
$394$	372.518	0.0476325
$395$	1356.72	0.172821
$396$	−16353.3	−2.07521
$397$	−8313.64	−1.05101	−0.525503	−	0.850792i	$-0.676123\pi$
$397$	−8313.64	−1.05101	−0.525503	+	0.850792i	$0.676123\pi$
$398$	367.481	0.0462819
$399$	0	0
$400$	1518.63	0.189829
$401$	−14341.4	−1.78598	−0.892988	−	0.450080i	$-0.851396\pi$
$401$	−14341.4	−1.78598	−0.892988	+	0.450080i	$0.851396\pi$
$402$	207.167	0.0257029
$403$	9113.97	1.12655
$404$	3250.77	0.400326
$405$	10230.3	1.25518
$406$	0	0
$407$	231.537	0.0281987
$408$	4550.22	0.552131
$409$	6282.35	0.759517	0.379758	−	0.925086i	$-0.376007\pi$
$409$	6282.35	0.759517	0.379758	+	0.925086i	$0.376007\pi$
$410$	−262.730	−0.0316471
$411$	−1788.74	−0.214676
$412$	11410.9	1.36450
$413$	0	0
$414$	−557.063	−0.0661308
$415$	3407.21	0.403020
$416$	−2526.96	−0.297823
$417$	−10509.3	−1.23415
$418$	1724.52	0.201792
$419$	−15226.1	−1.77528	−0.887640	−	0.460538i	$-0.847656\pi$
$419$	−15226.1	−1.77528	−0.887640	+	0.460538i	$0.847656\pi$
$420$	0	0
$421$	−2026.55	−0.234603	−0.117302	−	0.993096i	$-0.537424\pi$
$421$	−2026.55	−0.234603	−0.117302	+	0.993096i	$0.537424\pi$
$422$	−852.121	−0.0982953
$423$	−22477.4	−2.58366
$424$	−2855.14	−0.327024
$425$	−1993.35	−0.227510
$426$	−2504.41	−0.284833
$427$	0	0
$428$	14002.2	1.58135
$429$	−10880.9	−1.22456
$430$	438.617	0.0491907
$431$	8983.56	1.00400	0.501999	−	0.864868i	$-0.332598\pi$
$431$	8983.56	1.00400	0.501999	+	0.864868i	$0.332598\pi$
$432$	−24189.4	−2.69401
$433$	6836.59	0.758766	0.379383	−	0.925240i	$-0.376136\pi$
$433$	6836.59	0.758766	0.379383	+	0.925240i	$0.376136\pi$
$434$	0	0
$435$	−4932.92	−0.543713
$436$	−297.968	−0.0327295
$437$	−3386.85	−0.370743
$438$	−939.042	−0.102441
$439$	−7802.96	−0.848325	−0.424163	−	0.905586i	$-0.639432\pi$
$439$	−7802.96	−0.848325	−0.424163	+	0.905586i	$0.639432\pi$
$440$	897.433	0.0972351
$441$	0	0
$442$	1073.70	0.115545
$443$	5184.37	0.556020	0.278010	−	0.960578i	$-0.410325\pi$
$443$	5184.37	0.556020	0.278010	+	0.960578i	$0.410325\pi$
$444$	578.893	0.0618762
$445$	803.339	0.0855773
$446$	601.612	0.0638726
$447$	−11798.3	−1.24841
$448$	0	0
$449$	−772.951	−0.0812424	−0.0406212	−	0.999175i	$-0.512934\pi$
$449$	−772.951	−0.0812424	−0.0406212	+	0.999175i	$0.512934\pi$
$450$	−626.738	−0.0656549
$451$	4358.90	0.455105
$452$	−3596.18	−0.374226
$453$	5866.28	0.608437
$454$	−890.387	−0.0920439
$455$	0	0
$456$	8698.14	0.893262
$457$	11532.7	1.18048	0.590239	−	0.807228i	$-0.299033\pi$
$457$	11532.7	1.18048	0.590239	+	0.807228i	$0.299033\pi$
$458$	1354.13	0.138153
$459$	31751.0	3.22878
$460$	−873.675	−0.0885550
$461$	−10400.7	−1.05078	−0.525391	−	0.850861i	$-0.676081\pi$
$461$	−10400.7	−1.05078	−0.525391	+	0.850861i	$0.676081\pi$
$462$	0	0
$463$	−13855.4	−1.39075	−0.695374	−	0.718648i	$-0.744761\pi$
$463$	−13855.4	−1.39075	−0.695374	+	0.718648i	$0.744761\pi$
$464$	6152.56	0.615572
$465$	−12173.7	−1.21407
$466$	1114.71	0.110811
$467$	14734.5	1.46002	0.730011	−	0.683435i	$-0.239515\pi$
$467$	14734.5	1.46002	0.730011	+	0.683435i	$0.239515\pi$
$468$	−19463.2	−1.92241
$469$	0	0
$470$	611.453	0.0600090
$471$	15605.3	1.52665
$472$	−4202.74	−0.409845
$473$	−7277.00	−0.707393
$474$	976.130	0.0945889
$475$	−3810.46	−0.368076
$476$	0	0
$477$	−33081.0	−3.17542
$478$	201.968	0.0193260
$479$	1471.23	0.140338	0.0701691	−	0.997535i	$-0.477646\pi$
$479$	1471.23	0.140338	0.0701691	+	0.997535i	$0.477646\pi$
$480$	3375.32	0.320961
$481$	275.569	0.0261224
$482$	1157.90	0.109421
$483$	0	0
$484$	3085.91	0.289812
$485$	−839.204	−0.0785697
$486$	3389.71	0.316379
$487$	5610.00	0.521998	0.260999	−	0.965339i	$-0.415948\pi$
$487$	5610.00	0.521998	0.260999	+	0.965339i	$0.415948\pi$
$488$	2077.44	0.192707
$489$	30114.5	2.78491
$490$	0	0
$491$	−3193.98	−0.293569	−0.146784	−	0.989169i	$-0.546892\pi$
$491$	−3193.98	−0.293569	−0.146784	+	0.989169i	$0.546892\pi$
$492$	10898.2	0.998636
$493$	−8075.85	−0.737764
$494$	2052.47	0.186933
$495$	10398.1	0.944159
$496$	15183.6	1.37453
$497$	0	0
$498$	2451.41	0.220583
$499$	8724.32	0.782673	0.391337	−	0.920248i	$-0.372013\pi$
$499$	8724.32	0.782673	0.391337	+	0.920248i	$0.372013\pi$
$500$	−982.951	−0.0879178
$501$	−31668.8	−2.82407
$502$	−337.911	−0.0300432
$503$	14636.7	1.29745	0.648726	−	0.761022i	$-0.275302\pi$
$503$	14636.7	1.29745	0.648726	+	0.761022i	$0.275302\pi$
$504$	0	0
$505$	−2066.97	−0.182136
$506$	−251.413	−0.0220883
$507$	8450.11	0.740202
$508$	20016.1	1.74817
$509$	−8530.56	−0.742850	−0.371425	−	0.928463i	$-0.621131\pi$
$509$	−8530.56	−0.742850	−0.371425	+	0.928463i	$0.621131\pi$
$510$	−1434.17	−0.124522
$511$	0	0
$512$	−7056.93	−0.609131
$513$	60694.7	5.22366
$514$	−2339.31	−0.200744
$515$	−7255.53	−0.620809
$516$	−18194.1	−1.55223
$517$	−10144.5	−0.862967
$518$	0	0
$519$	21960.9	1.85737
$520$	1068.10	0.0900756
$521$	−13743.0	−1.15564	−0.577822	−	0.816163i	$-0.696097\pi$
$521$	−13743.0	−1.15564	−0.577822	+	0.816163i	$0.696097\pi$
$522$	−2539.16	−0.212904
$523$	2236.17	0.186961	0.0934806	−	0.995621i	$-0.470201\pi$
$523$	2236.17	0.186961	0.0934806	+	0.995621i	$0.470201\pi$
$524$	−7634.56	−0.636483
$525$	0	0
$526$	−1524.07	−0.126336
$527$	−19930.0	−1.64737
$528$	−18127.4	−1.49412
$529$	−11673.2	−0.959418
$530$	899.903	0.0737534
$531$	−48694.9	−3.97962
$532$	0	0
$533$	5187.84	0.421595
$534$	577.984	0.0468386
$535$	−8903.14	−0.719470
$536$	337.391	0.0271885
$537$	26158.3	2.10207
$538$	−2174.18	−0.174230
$539$	0	0
$540$	15656.9	1.24771
$541$	−19487.9	−1.54870	−0.774352	−	0.632755i	$-0.781924\pi$
$541$	−19487.9	−1.54870	−0.774352	+	0.632755i	$0.781924\pi$
$542$	2673.00	0.211836
$543$	12597.2	0.995574
$544$	5525.84	0.435512
$545$	189.460	0.0148910
$546$	0	0
$547$	−15949.3	−1.24670	−0.623349	−	0.781944i	$-0.714228\pi$
$547$	−15949.3	−1.24670	−0.623349	+	0.781944i	$0.714228\pi$
$548$	−1444.04	−0.112566
$549$	24070.1	1.87120
$550$	−282.859	−0.0219294
$551$	−15437.7	−1.19359
$552$	−1268.08	−0.0977773
$553$	0	0
$554$	−2083.00	−0.159744
$555$	−368.084	−0.0281519
$556$	−8484.08	−0.647132
$557$	−6349.74	−0.483029	−0.241514	−	0.970397i	$-0.577644\pi$
$557$	−6349.74	−0.483029	−0.241514	+	0.970397i	$0.577644\pi$
$558$	−6266.29	−0.475400
$559$	−8660.88	−0.655306
$560$	0	0
$561$	23794.0	1.79070
$562$	957.651	0.0718791
$563$	14805.0	1.10827	0.554135	−	0.832427i	$-0.313049\pi$
$563$	14805.0	1.10827	0.554135	+	0.832427i	$0.313049\pi$
$564$	−25363.5	−1.89361
$565$	2286.60	0.170262
$566$	935.571	0.0694788
$567$	0	0
$568$	−4078.65	−0.301297
$569$	24578.7	1.81088	0.905442	−	0.424469i	$-0.139539\pi$
$569$	24578.7	1.81088	0.905442	+	0.424469i	$0.139539\pi$
$570$	−2741.54	−0.201457
$571$	−15609.9	−1.14405	−0.572027	−	0.820235i	$-0.693843\pi$
$571$	−15609.9	−1.14405	−0.572027	+	0.820235i	$0.693843\pi$
$572$	−8784.12	−0.642103
$573$	1362.51	0.0993359
$574$	0	0
$575$	555.518	0.0402899
$576$	−31250.2	−2.26058
$577$	15111.3	1.09028	0.545141	−	0.838344i	$-0.316476\pi$
$577$	15111.3	1.09028	0.545141	+	0.838344i	$0.316476\pi$
$578$	−533.484	−0.0383910
$579$	−23229.7	−1.66735
$580$	−3982.32	−0.285098
$581$	0	0
$582$	−603.788	−0.0430031
$583$	−14930.1	−1.06062
$584$	−1529.31	−0.108362
$585$	12375.5	0.874639
$586$	−217.606	−0.0153399
$587$	14983.2	1.05353	0.526766	−	0.850010i	$-0.323404\pi$
$587$	14983.2	1.05353	0.526766	+	0.850010i	$0.323404\pi$
$588$	0	0
$589$	−38098.0	−2.66519
$590$	1324.65	0.0924320
$591$	9825.18	0.683848
$592$	459.090	0.0318725
$593$	6931.01	0.479971	0.239985	−	0.970777i	$-0.422857\pi$
$593$	6931.01	0.479971	0.239985	+	0.970777i	$0.422857\pi$
$594$	4505.51	0.311217
$595$	0	0
$596$	−9524.68	−0.654608
$597$	9692.34	0.664457
$598$	−299.225	−0.0204619
$599$	12309.2	0.839632	0.419816	−	0.907609i	$-0.362095\pi$
$599$	12309.2	0.839632	0.419816	+	0.907609i	$0.362095\pi$
$600$	−1426.69	−0.0970738
$601$	15293.6	1.03800	0.519001	−	0.854774i	$-0.326304\pi$
$601$	15293.6	1.03800	0.519001	+	0.854774i	$0.326304\pi$
$602$	0	0
$603$	3909.16	0.264002
$604$	4735.81	0.319036
$605$	−1962.15	−0.131856
$606$	−1487.14	−0.0996878
$607$	−5338.80	−0.356994	−0.178497	−	0.983940i	$-0.557123\pi$
$607$	−5338.80	−0.356994	−0.178497	+	0.983940i	$0.557123\pi$
$608$	10563.1	0.704590
$609$	0	0
$610$	−654.780	−0.0434611
$611$	−12073.7	−0.799426
$612$	42561.3	2.81118
$613$	−28848.6	−1.90079	−0.950396	−	0.311043i	$-0.899322\pi$
$613$	−28848.6	−1.90079	−0.950396	+	0.311043i	$0.899322\pi$
$614$	1947.68	0.128016
$615$	−6929.52	−0.454350
$616$	0	0
$617$	−12346.6	−0.805602	−0.402801	−	0.915287i	$-0.631963\pi$
$617$	−12346.6	−0.805602	−0.402801	+	0.915287i	$0.631963\pi$
$618$	−5220.18	−0.339784
$619$	−6383.16	−0.414477	−0.207238	−	0.978290i	$-0.566448\pi$
$619$	−6383.16	−0.414477	−0.207238	+	0.978290i	$0.566448\pi$
$620$	−9827.79	−0.636603
$621$	−8848.54	−0.571787
$622$	−1216.92	−0.0784473
$623$	0	0
$624$	−21574.7	−1.38410
$625$	625.000	0.0400000
$626$	−671.921	−0.0429000
$627$	45484.2	2.89707
$628$	12598.1	0.800505
$629$	−602.602	−0.0381992
$630$	0	0
$631$	25708.6	1.62194	0.810969	−	0.585090i	$-0.198941\pi$
$631$	25708.6	1.62194	0.810969	+	0.585090i	$0.198941\pi$
$632$	1589.72	0.100056
$633$	−22474.7	−1.41120
$634$	−697.232	−0.0436760
$635$	−12727.0	−0.795366
$636$	−37328.5	−2.32732
$637$	0	0
$638$	−1145.97	−0.0711120
$639$	−47257.1	−2.92561
$640$	3622.24	0.223721
$641$	−18617.5	−1.14719	−0.573594	−	0.819139i	$-0.694451\pi$
$641$	−18617.5	−1.14719	−0.573594	+	0.819139i	$0.694451\pi$
$642$	−6405.60	−0.393783
$643$	21168.8	1.29832	0.649158	−	0.760654i	$-0.275121\pi$
$643$	21168.8	1.29832	0.649158	+	0.760654i	$0.275121\pi$
$644$	0	0
$645$	11568.5	0.706219
$646$	−4488.26	−0.273357
$647$	5952.47	0.361693	0.180847	−	0.983511i	$-0.442116\pi$
$647$	5952.47	0.361693	0.180847	+	0.983511i	$0.442116\pi$
$648$	11987.2	0.726700
$649$	−21976.9	−1.32923
$650$	−336.651	−0.0203147
$651$	0	0
$652$	24311.2	1.46028
$653$	−3040.63	−0.182219	−0.0911096	−	0.995841i	$-0.529041\pi$
$653$	−3040.63	−0.182219	−0.0911096	+	0.995841i	$0.529041\pi$
$654$	136.312	0.00815018
$655$	4854.36	0.289581
$656$	8642.81	0.514398
$657$	−17719.3	−1.05220
$658$	0	0
$659$	−3335.95	−0.197193	−0.0985966	−	0.995127i	$-0.531435\pi$
$659$	−3335.95	−0.197193	−0.0985966	+	0.995127i	$0.531435\pi$
$660$	11733.2	0.691989
$661$	1547.90	0.0910838	0.0455419	−	0.998962i	$-0.485499\pi$
$661$	1547.90	0.0910838	0.0455419	+	0.998962i	$0.485499\pi$
$662$	168.550	0.00989561
$663$	28319.0	1.65885
$664$	3992.34	0.233332
$665$	0	0
$666$	−189.467	−0.0110235
$667$	2250.62	0.130651
$668$	−25566.0	−1.48081
$669$	15867.5	0.917003
$670$	−106.341	−0.00613181
$671$	10863.3	0.624998
$672$	0	0
$673$	19632.4	1.12448	0.562239	−	0.826975i	$-0.309940\pi$
$673$	19632.4	1.12448	0.562239	+	0.826975i	$0.309940\pi$
$674$	−3018.94	−0.172530
$675$	−9955.28	−0.567672
$676$	6821.72	0.388127
$677$	−30318.2	−1.72116	−0.860579	−	0.509317i	$-0.829898\pi$
$677$	−30318.2	−1.72116	−0.860579	+	0.509317i	$0.829898\pi$
$678$	1645.15	0.0931885
$679$	0	0
$680$	−2335.68	−0.131719
$681$	−23484.0	−1.32145
$682$	−2828.10	−0.158788
$683$	28970.8	1.62304	0.811520	−	0.584325i	$-0.198641\pi$
$683$	28970.8	1.62304	0.811520	+	0.584325i	$0.198641\pi$
$684$	81359.6	4.54804
$685$	918.176	0.0512142
$686$	0	0
$687$	35715.1	1.98343
$688$	−14428.8	−0.799554
$689$	−17769.4	−0.982525
$690$	399.682	0.0220517
$691$	3434.91	0.189103	0.0945514	−	0.995520i	$-0.469858\pi$
$691$	3434.91	0.189103	0.0945514	+	0.995520i	$0.469858\pi$
$692$	17728.9	0.973917
$693$	0	0
$694$	2930.77	0.160304
$695$	5394.52	0.294426
$696$	−5780.06	−0.314788
$697$	−11344.5	−0.616507
$698$	3194.35	0.173221
$699$	29400.6	1.59089
$700$	0	0
$701$	16304.4	0.878471	0.439235	−	0.898372i	$-0.355249\pi$
$701$	16304.4	0.878471	0.439235	+	0.898372i	$0.355249\pi$
$702$	5362.33	0.288302
$703$	−1151.92	−0.0618004
$704$	−14103.8	−0.755054
$705$	16127.1	0.861535
$706$	−1821.11	−0.0970800
$707$	0	0
$708$	−54947.2	−2.91673
$709$	16094.4	0.852519	0.426260	−	0.904601i	$-0.359831\pi$
$709$	16094.4	0.852519	0.426260	+	0.904601i	$0.359831\pi$
$710$	1285.54	0.0679512
$711$	18419.2	0.971552
$712$	941.299	0.0495459
$713$	5554.21	0.291735
$714$	0	0
$715$	5585.30	0.292138
$716$	21117.4	1.10223
$717$	5326.93	0.277458
$718$	−3044.50	−0.158245
$719$	−8651.93	−0.448766	−0.224383	−	0.974501i	$-0.572037\pi$
$719$	−8651.93	−0.448766	−0.224383	+	0.974501i	$0.572037\pi$
$720$	20617.3	1.06717
$721$	0	0
$722$	−6046.56	−0.311676
$723$	30539.7	1.57093
$724$	10169.6	0.522032
$725$	2532.12	0.129711
$726$	−1411.72	−0.0721679
$727$	6999.43	0.357076	0.178538	−	0.983933i	$-0.442863\pi$
$727$	6999.43	0.357076	0.178538	+	0.983933i	$0.442863\pi$
$728$	0	0
$729$	34160.1	1.73551
$730$	482.020	0.0244388
$731$	18939.3	0.958268
$732$	27160.7	1.37143
$733$	−5167.74	−0.260402	−0.130201	−	0.991488i	$-0.541562\pi$
$733$	−5167.74	−0.260402	−0.130201	+	0.991488i	$0.541562\pi$
$734$	−3020.67	−0.151900
$735$	0	0
$736$	−1539.97	−0.0771251
$737$	1764.28	0.0881793
$738$	−3566.89	−0.177912
$739$	−12319.1	−0.613214	−0.306607	−	0.951836i	$-0.599194\pi$
$739$	−12319.1	−0.613214	−0.306607	+	0.951836i	$0.599194\pi$
$740$	−297.152	−0.0147615
$741$	54134.1	2.68376
$742$	0	0
$743$	16942.4	0.836548	0.418274	−	0.908321i	$-0.362635\pi$
$743$	16942.4	0.836548	0.418274	+	0.908321i	$0.362635\pi$
$744$	−14264.4	−0.702900
$745$	6056.18	0.297827
$746$	4725.56	0.231923
$747$	46257.0	2.26567
$748$	19208.8	0.938959
$749$	0	0
$750$	449.673	0.0218930
$751$	32917.9	1.59946	0.799728	−	0.600363i	$-0.204977\pi$
$751$	32917.9	1.59946	0.799728	+	0.600363i	$0.204977\pi$
$752$	−20114.5	−0.975397
$753$	−8912.41	−0.431323
$754$	−1363.90	−0.0658760
$755$	−3011.22	−0.145152
$756$	0	0
$757$	−9433.45	−0.452926	−0.226463	−	0.974020i	$-0.572716\pi$
$757$	−9433.45	−0.452926	−0.226463	+	0.974020i	$0.572716\pi$
$758$	2118.17	0.101498
$759$	−6631.04	−0.317117
$760$	−4464.84	−0.213101
$761$	34551.0	1.64582	0.822912	−	0.568170i	$-0.192348\pi$
$761$	34551.0	1.64582	0.822912	+	0.568170i	$0.192348\pi$
$762$	−9156.82	−0.435323
$763$	0	0
$764$	1099.94	0.0520871
$765$	−27062.2	−1.27900
$766$	272.495	0.0128533
$767$	−26156.4	−1.23136
$768$	−33268.2	−1.56310
$769$	348.011	0.0163194	0.00815970	−	0.999967i	$-0.497403\pi$
$769$	348.011	0.0163194	0.00815970	+	0.999967i	$0.497403\pi$
$770$	0	0
$771$	−61699.3	−2.88203
$772$	−18753.2	−0.874277
$773$	30083.9	1.39979	0.699897	−	0.714243i	$-0.253229\pi$
$773$	30083.9	1.39979	0.699897	+	0.714243i	$0.253229\pi$
$774$	5954.77	0.276537
$775$	6248.91	0.289635
$776$	−983.323	−0.0454887
$777$	0	0
$778$	4813.64	0.221822
$779$	−21686.1	−0.997412
$780$	13964.5	0.641037
$781$	−21328.1	−0.977181
$782$	654.333	0.0299219
$783$	−40332.7	−1.84083
$784$	0	0
$785$	−8010.35	−0.364206
$786$	3492.60	0.158495
$787$	−31958.4	−1.44751	−0.723757	−	0.690055i	$-0.757587\pi$
$787$	−31958.4	−1.44751	−0.723757	+	0.690055i	$0.757587\pi$
$788$	7931.81	0.358578
$789$	−40197.5	−1.81377
$790$	−501.058	−0.0225656
$791$	0	0
$792$	12183.8	0.546630
$793$	12929.2	0.578979
$794$	3070.35	0.137233
$795$	23735.0	1.05886
$796$	7824.57	0.348410
$797$	364.165	0.0161849	0.00809247	−	0.999967i	$-0.497424\pi$
$797$	364.165	0.0161849	0.00809247	+	0.999967i	$0.497424\pi$
$798$	0	0
$799$	26402.2	1.16902
$800$	−1732.59	−0.0765702
$801$	10906.3	0.481093
$802$	5296.50	0.233199
$803$	−7997.08	−0.351446
$804$	4411.09	0.193492
$805$	0	0
$806$	−3365.92	−0.147096
$807$	−57344.2	−2.50138
$808$	−2421.94	−0.105450
$809$	30714.8	1.33482	0.667412	−	0.744688i	$-0.267402\pi$
$809$	30714.8	1.33482	0.667412	+	0.744688i	$0.267402\pi$
$810$	−3778.21	−0.163892
$811$	−18967.6	−0.821260	−0.410630	−	0.911802i	$-0.634691\pi$
$811$	−18967.6	−0.821260	−0.410630	+	0.911802i	$0.634691\pi$
$812$	0	0
$813$	70500.4	3.04128
$814$	−85.5100	−0.00368197
$815$	−15458.1	−0.664383
$816$	47178.7	2.02400
$817$	36204.0	1.55033
$818$	−2320.17	−0.0991720
$819$	0	0
$820$	−5594.16	−0.238240
$821$	−14817.0	−0.629860	−0.314930	−	0.949115i	$-0.601981\pi$
$821$	−14817.0	−0.629860	−0.314930	+	0.949115i	$0.601981\pi$
$822$	660.606	0.0280308
$823$	−26588.1	−1.12613	−0.563063	−	0.826414i	$-0.690377\pi$
$823$	−26588.1	−1.12613	−0.563063	+	0.826414i	$0.690377\pi$
$824$	−8501.54	−0.359424
$825$	−7460.42	−0.314835
$826$	0	0
$827$	−11287.0	−0.474592	−0.237296	−	0.971437i	$-0.576261\pi$
$827$	−11287.0	−0.474592	−0.237296	+	0.971437i	$0.576261\pi$
$828$	−11861.2	−0.497833
$829$	−14448.6	−0.605332	−0.302666	−	0.953097i	$-0.597877\pi$
$829$	−14448.6	−0.605332	−0.302666	+	0.953097i	$0.597877\pi$
$830$	−1258.33	−0.0526233
$831$	−54939.2	−2.29340
$832$	−16786.0	−0.699459
$833$	0	0
$834$	3881.23	0.161146
$835$	16255.9	0.673724
$836$	36719.2	1.51909
$837$	−99535.4	−4.11045
$838$	5623.21	0.231803
$839$	−40032.0	−1.64727	−0.823635	−	0.567120i	$-0.808057\pi$
$839$	−40032.0	−1.64727	−0.823635	+	0.567120i	$0.808057\pi$
$840$	0	0
$841$	−14130.4	−0.579376
$842$	748.434	0.0306327
$843$	25258.1	1.03195
$844$	−18143.7	−0.739967
$845$	−4337.53	−0.176586
$846$	8301.23	0.337355
$847$	0	0
$848$	−29603.3	−1.19880
$849$	24675.7	0.997490
$850$	736.175	0.0297066
$851$	167.936	0.00676473
$852$	−53324.9	−2.14423
$853$	−10864.4	−0.436098	−0.218049	−	0.975938i	$-0.569969\pi$
$853$	−10864.4	−0.436098	−0.218049	+	0.975938i	$0.569969\pi$
$854$	0	0
$855$	−51731.7	−2.06922
$856$	−10432.1	−0.416544
$857$	−42013.7	−1.67463	−0.837316	−	0.546719i	$-0.815877\pi$
$857$	−42013.7	−1.67463	−0.837316	+	0.546719i	$0.815877\pi$
$858$	4018.50	0.159894
$859$	−16135.6	−0.640908	−0.320454	−	0.947264i	$-0.603835\pi$
$859$	−16135.6	−0.640908	−0.320454	+	0.947264i	$0.603835\pi$
$860$	9339.22	0.370308
$861$	0	0
$862$	−3317.76	−0.131094
$863$	−46246.8	−1.82417	−0.912086	−	0.409998i	$-0.865529\pi$
$863$	−46246.8	−1.82417	−0.912086	+	0.409998i	$0.865529\pi$
$864$	27597.4	1.08667
$865$	−11272.7	−0.443103
$866$	−2524.85	−0.0990739
$867$	−14070.7	−0.551171
$868$	0	0
$869$	8312.93	0.324507
$870$	1821.80	0.0709940
$871$	2099.80	0.0816865
$872$	221.996	0.00862127
$873$	−11393.2	−0.441698
$874$	1250.81	0.0484089
$875$	0	0
$876$	−19994.5	−0.771177
$877$	−25094.1	−0.966212	−0.483106	−	0.875562i	$-0.660491\pi$
$877$	−25094.1	−0.966212	−0.483106	+	0.875562i	$0.660491\pi$
$878$	2881.75	0.110768
$879$	−5739.36	−0.220232
$880$	9304.97	0.356444
$881$	27546.6	1.05342	0.526712	−	0.850044i	$-0.323424\pi$
$881$	27546.6	1.05342	0.526712	+	0.850044i	$0.323424\pi$
$882$	0	0
$883$	5825.31	0.222013	0.111006	−	0.993820i	$-0.464593\pi$
$883$	5825.31	0.222013	0.111006	+	0.993820i	$0.464593\pi$
$884$	22861.7	0.869823
$885$	34937.7	1.32702
$886$	−1914.67	−0.0726010
$887$	−6214.29	−0.235237	−0.117619	−	0.993059i	$-0.537526\pi$
$887$	−6214.29	−0.235237	−0.117619	+	0.993059i	$0.537526\pi$
$888$	−431.296	−0.0162988
$889$	0	0
$890$	−296.685	−0.0111740
$891$	62683.4	2.35687
$892$	12809.8	0.480833
$893$	50470.1	1.89128
$894$	4357.28	0.163008
$895$	−13427.3	−0.501481
$896$	0	0
$897$	−7892.08	−0.293767
$898$	285.462	0.0106080
$899$	25316.8	0.939223
$900$	−13344.8	−0.494251
$901$	38857.3	1.43677
$902$	−1609.80	−0.0594242
$903$	0	0
$904$	2679.28	0.0985748
$905$	−6466.26	−0.237509
$906$	−2166.50	−0.0794451
$907$	24415.9	0.893845	0.446923	−	0.894573i	$-0.352520\pi$
$907$	24415.9	0.893845	0.446923	+	0.894573i	$0.352520\pi$
$908$	−18958.5	−0.692907
$909$	−28061.7	−1.02392
$910$	0	0
$911$	−3493.35	−0.127047	−0.0635236	−	0.997980i	$-0.520234\pi$
$911$	−3493.35	−0.127047	−0.0635236	+	0.997980i	$0.520234\pi$
$912$	90186.0	3.27451
$913$	20876.7	0.756755
$914$	−4259.21	−0.154138
$915$	−17269.9	−0.623961
$916$	28832.6	1.04002
$917$	0	0
$918$	−11726.1	−0.421590
$919$	15656.7	0.561989	0.280995	−	0.959709i	$-0.409336\pi$
$919$	15656.7	0.561989	0.280995	+	0.959709i	$0.409336\pi$
$920$	650.919	0.0233263
$921$	51370.0	1.83789
$922$	3841.14	0.137203
$923$	−25384.1	−0.905230
$924$	0	0
$925$	188.941	0.00671605
$926$	5117.02	0.181594
$927$	−98502.8	−3.49003
$928$	−7019.38	−0.248300
$929$	30504.5	1.07731	0.538654	−	0.842527i	$-0.318933\pi$
$929$	30504.5	1.07731	0.538654	+	0.842527i	$0.318933\pi$
$930$	4495.94	0.158525
$931$	0	0
$932$	23735.0	0.834189
$933$	−32096.4	−1.12625
$934$	−5441.66	−0.190639
$935$	−12213.7	−0.427199
$936$	14500.8	0.506381
$937$	−50290.7	−1.75339	−0.876694	−	0.481049i	$-0.840256\pi$
$937$	−50290.7	−1.75339	−0.876694	+	0.481049i	$0.840256\pi$
$938$	0	0
$939$	−17722.0	−0.615904
$940$	13019.3	0.451748
$941$	−18681.7	−0.647189	−0.323595	−	0.946196i	$-0.604891\pi$
$941$	−18681.7	−0.647189	−0.323595	+	0.946196i	$0.604891\pi$
$942$	−5763.26	−0.199339
$943$	3161.56	0.109178
$944$	−43575.8	−1.50241
$945$	0	0
$946$	2687.50	0.0923660
$947$	16332.6	0.560440	0.280220	−	0.959936i	$-0.409593\pi$
$947$	16332.6	0.560440	0.280220	+	0.959936i	$0.409593\pi$
$948$	20784.2	0.712066
$949$	−9517.91	−0.325568
$950$	1407.26	0.0480606
$951$	−18389.5	−0.627046
$952$	0	0
$953$	−34233.6	−1.16362	−0.581812	−	0.813323i	$-0.697656\pi$
$953$	−34233.6	−1.16362	−0.581812	+	0.813323i	$0.697656\pi$
$954$	12217.3	0.414622
$955$	−699.388	−0.0236981
$956$	4300.40	0.145486
$957$	−30225.1	−1.02094
$958$	−543.345	−0.0183243
$959$	0	0
$960$	22421.5	0.753801
$961$	32687.2	1.09722
$962$	−101.772	−0.00341086
$963$	−120871.	−4.04467
$964$	24654.5	0.823723
$965$	11924.0	0.397770
$966$	0	0
$967$	53792.0	1.78887	0.894434	−	0.447200i	$-0.147579\pi$
$967$	53792.0	1.78887	0.894434	+	0.447200i	$0.147579\pi$
$968$	−2299.11	−0.0763392
$969$	−118378.	−3.92451
$970$	309.931	0.0102590
$971$	−826.331	−0.0273102	−0.0136551	−	0.999907i	$-0.504347\pi$
$971$	−826.331	−0.0273102	−0.0136551	+	0.999907i	$0.504347\pi$
$972$	72175.1	2.38171
$973$	0	0
$974$	−2071.85	−0.0681586
$975$	−8879.19	−0.291653
$976$	21539.8	0.706425
$977$	8703.52	0.285005	0.142503	−	0.989794i	$-0.454485\pi$
$977$	8703.52	0.285005	0.142503	+	0.989794i	$0.454485\pi$
$978$	−11121.7	−0.363633
$979$	4922.23	0.160690
$980$	0	0
$981$	2572.15	0.0837130
$982$	1179.58	0.0383320
$983$	−41000.9	−1.33034	−0.665170	−	0.746692i	$-0.731641\pi$
$983$	−41000.9	−1.33034	−0.665170	+	0.746692i	$0.731641\pi$
$984$	−8119.55	−0.263051
$985$	−5043.37	−0.163142
$986$	2982.53	0.0963317
$987$	0	0
$988$	43702.1	1.40724
$989$	−5278.09	−0.169700
$990$	−3840.16	−0.123281
$991$	−18341.0	−0.587912	−0.293956	−	0.955819i	$-0.594972\pi$
$991$	−18341.0	−0.587912	−0.293956	+	0.955819i	$0.594972\pi$
$992$	−17322.8	−0.554436
$993$	4445.52	0.142069
$994$	0	0
$995$	−4975.18	−0.158516
$996$	52196.3	1.66055
$997$	57335.4	1.82129	0.910646	−	0.413187i	$-0.135584\pi$
$997$	57335.4	1.82129	0.910646	+	0.413187i	$0.135584\pi$
$998$	−3222.02	−0.102196
$999$	−3009.54	−0.0953129

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.a.o.1.3	✓	6
3.2	odd	2		2205.4.a.bz.1.4		6
5.4	even	2		1225.4.a.bj.1.4		6
7.2	even	3		245.4.e.q.116.4		12
7.3	odd	6		245.4.e.p.226.4		12
7.4	even	3		245.4.e.q.226.4		12
7.5	odd	6		245.4.e.p.116.4		12
7.6	odd	2		245.4.a.p.1.3	yes	6
21.20	even	2		2205.4.a.ca.1.4		6
35.34	odd	2		1225.4.a.bi.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.4.a.o.1.3	✓	6	1.1	even	1	trivial
245.4.a.p.1.3	yes	6	7.6	odd	2
245.4.e.p.116.4		12	7.5	odd	6
245.4.e.p.226.4		12	7.3	odd	6
245.4.e.q.116.4		12	7.2	even	3
245.4.e.q.226.4		12	7.4	even	3
1225.4.a.bi.1.4		6	35.34	odd	2
1225.4.a.bj.1.4		6	5.4	even	2
2205.4.a.bz.1.4		6	3.2	odd	2
2205.4.a.ca.1.4		6	21.20	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)

\(f(q)\)	\(=\)	\(q-0.369315 q^{2} -9.74070 q^{3} -7.86361 q^{4} +5.00000 q^{5} +3.59738 q^{6} +5.85867 q^{8} +67.8812 q^{9} +O(q^{10})\)	\(q-0.369315 q^{2} -9.74070 q^{3} -7.86361 q^{4} +5.00000 q^{5} +3.59738 q^{6} +5.85867 q^{8} +67.8812 q^{9} -1.84657 q^{10} +30.6361 q^{11} +76.5970 q^{12} +36.4622 q^{13} -48.7035 q^{15} +60.7452 q^{16} -79.7341 q^{17} -25.0695 q^{18} -152.418 q^{19} -39.3180 q^{20} -11.3144 q^{22} +22.2207 q^{23} -57.0675 q^{24} +25.0000 q^{25} -13.4660 q^{26} -398.211 q^{27} +101.285 q^{29} +17.9869 q^{30} +249.956 q^{31} -69.3034 q^{32} -298.417 q^{33} +29.4470 q^{34} -533.791 q^{36} +7.55765 q^{37} +56.2904 q^{38} -355.168 q^{39} +29.2933 q^{40} +142.280 q^{41} -237.530 q^{43} -240.910 q^{44} +339.406 q^{45} -8.20644 q^{46} -331.129 q^{47} -591.700 q^{48} -9.23287 q^{50} +776.666 q^{51} -286.725 q^{52} -487.337 q^{53} +147.065 q^{54} +153.180 q^{55} +1484.66 q^{57} -37.4059 q^{58} -717.355 q^{59} +382.985 q^{60} +354.592 q^{61} -92.3126 q^{62} -460.367 q^{64} +182.311 q^{65} +110.210 q^{66} +57.5883 q^{67} +626.997 q^{68} -216.445 q^{69} -696.174 q^{71} +397.693 q^{72} -261.035 q^{73} -2.79115 q^{74} -243.517 q^{75} +1198.56 q^{76} +131.169 q^{78} +271.344 q^{79} +303.726 q^{80} +2046.06 q^{81} -52.5460 q^{82} +681.441 q^{83} -398.670 q^{85} +87.7234 q^{86} -986.584 q^{87} +179.487 q^{88} +160.668 q^{89} -125.348 q^{90} -174.735 q^{92} -2434.75 q^{93} +122.291 q^{94} -762.092 q^{95} +675.063 q^{96} -167.841 q^{97} +2079.61 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 16 q^{3} + 14 q^{4} + 30 q^{5} - 24 q^{6} - 66 q^{8} + 70 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 16 * q^3 + 14 * q^4 + 30 * q^5 - 24 * q^6 - 66 * q^8 + 70 * q^9	\( 6 q - 2 q^{2} - 16 q^{3} + 14 q^{4} + 30 q^{5} - 24 q^{6} - 66 q^{8} + 70 q^{9} - 10 q^{10} - 16 q^{11} - 160 q^{12} - 168 q^{13} - 80 q^{15} + 298 q^{16} + 4 q^{17} + 354 q^{18} - 308 q^{19} + 70 q^{20} - 236 q^{22} - 336 q^{23} + 92 q^{24} + 150 q^{25} - 56 q^{26} - 964 q^{27} + 176 q^{29} - 120 q^{30} - 392 q^{31} - 770 q^{32} - 188 q^{33} - 812 q^{34} + 230 q^{36} - 140 q^{37} - 20 q^{38} + 140 q^{39} - 330 q^{40} - 656 q^{41} - 388 q^{43} - 160 q^{44} + 350 q^{45} - 388 q^{46} - 628 q^{47} - 1396 q^{48} - 50 q^{50} + 744 q^{51} - 1520 q^{52} - 676 q^{53} - 2284 q^{54} - 80 q^{55} + 1468 q^{57} - 2012 q^{58} - 996 q^{59} - 800 q^{60} - 740 q^{61} + 364 q^{62} + 1426 q^{64} - 840 q^{65} + 3620 q^{66} + 1768 q^{67} + 2940 q^{68} + 1048 q^{69} - 224 q^{71} + 2858 q^{72} - 2640 q^{73} + 928 q^{74} - 400 q^{75} + 1340 q^{76} + 8 q^{78} + 1636 q^{79} + 1490 q^{80} + 4442 q^{81} + 1756 q^{82} - 140 q^{83} + 20 q^{85} + 1180 q^{86} - 1940 q^{87} - 5652 q^{88} + 1904 q^{89} + 1770 q^{90} - 1952 q^{92} - 1592 q^{93} + 3332 q^{94} - 1540 q^{95} + 6460 q^{96} - 516 q^{97} - 2804 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 16 * q^3 + 14 * q^4 + 30 * q^5 - 24 * q^6 - 66 * q^8 + 70 * q^9 - 10 * q^10 - 16 * q^11 - 160 * q^12 - 168 * q^13 - 80 * q^15 + 298 * q^16 + 4 * q^17 + 354 * q^18 - 308 * q^19 + 70 * q^20 - 236 * q^22 - 336 * q^23 + 92 * q^24 + 150 * q^25 - 56 * q^26 - 964 * q^27 + 176 * q^29 - 120 * q^30 - 392 * q^31 - 770 * q^32 - 188 * q^33 - 812 * q^34 + 230 * q^36 - 140 * q^37 - 20 * q^38 + 140 * q^39 - 330 * q^40 - 656 * q^41 - 388 * q^43 - 160 * q^44 + 350 * q^45 - 388 * q^46 - 628 * q^47 - 1396 * q^48 - 50 * q^50 + 744 * q^51 - 1520 * q^52 - 676 * q^53 - 2284 * q^54 - 80 * q^55 + 1468 * q^57 - 2012 * q^58 - 996 * q^59 - 800 * q^60 - 740 * q^61 + 364 * q^62 + 1426 * q^64 - 840 * q^65 + 3620 * q^66 + 1768 * q^67 + 2940 * q^68 + 1048 * q^69 - 224 * q^71 + 2858 * q^72 - 2640 * q^73 + 928 * q^74 - 400 * q^75 + 1340 * q^76 + 8 * q^78 + 1636 * q^79 + 1490 * q^80 + 4442 * q^81 + 1756 * q^82 - 140 * q^83 + 20 * q^85 + 1180 * q^86 - 1940 * q^87 - 5652 * q^88 + 1904 * q^89 + 1770 * q^90 - 1952 * q^92 - 1592 * q^93 + 3332 * q^94 - 1540 * q^95 + 6460 * q^96 - 516 * q^97 - 2804 * q^99

Introduction

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