LMFDB - Embedded newform 1421.4.a.e.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1421,4,Mod(1,1421)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1421, 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("1421.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1421 = 7^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1421.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:	$83.8417141182$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.13458092.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 14x^{3} + 18x^{2} + 20x - 8 $ x^5 - x^4 - 14x^3 + 18x^2 + 20*x - 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 29)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-3.68360$ of defining polynomial
Character	$\chi$	$=$	1421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.47236 q^{2} +1.90549 q^{3} +12.0020 q^{4} +6.52855 q^{5} +8.52204 q^{6} +17.8986 q^{8} -23.3691 q^{9} +O(q^{10})$	\(q+4.47236 q^{2} +1.90549 q^{3} +12.0020 q^{4} +6.52855 q^{5} +8.52204 q^{6} +17.8986 q^{8} -23.3691 q^{9} +29.1981 q^{10} -21.1299 q^{11} +22.8697 q^{12} -83.4615 q^{13} +12.4401 q^{15} -15.9674 q^{16} -11.3273 q^{17} -104.515 q^{18} +7.68096 q^{19} +78.3559 q^{20} -94.5005 q^{22} +153.169 q^{23} +34.1055 q^{24} -82.3780 q^{25} -373.270 q^{26} -95.9778 q^{27} -29.0000 q^{29} +55.6366 q^{30} -270.530 q^{31} -214.601 q^{32} -40.2628 q^{33} -50.6597 q^{34} -280.477 q^{36} -298.404 q^{37} +34.3520 q^{38} -159.035 q^{39} +116.852 q^{40} +184.710 q^{41} +208.337 q^{43} -253.602 q^{44} -152.566 q^{45} +685.028 q^{46} +553.098 q^{47} -30.4258 q^{48} -368.424 q^{50} -21.5840 q^{51} -1001.71 q^{52} -321.465 q^{53} -429.248 q^{54} -137.948 q^{55} +14.6360 q^{57} -129.699 q^{58} -104.930 q^{59} +149.306 q^{60} -464.230 q^{61} -1209.91 q^{62} -832.032 q^{64} -544.883 q^{65} -180.070 q^{66} +745.813 q^{67} -135.950 q^{68} +291.862 q^{69} -509.252 q^{71} -418.273 q^{72} +0.374979 q^{73} -1334.57 q^{74} -156.970 q^{75} +92.1871 q^{76} -711.262 q^{78} +610.912 q^{79} -104.244 q^{80} +448.081 q^{81} +826.092 q^{82} -791.431 q^{83} -73.9507 q^{85} +931.757 q^{86} -55.2592 q^{87} -378.194 q^{88} +342.011 q^{89} -682.333 q^{90} +1838.34 q^{92} -515.491 q^{93} +2473.65 q^{94} +50.1455 q^{95} -408.919 q^{96} -601.476 q^{97} +493.787 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 8 q^{3} + 26 q^{4} - 10 q^{5} - 34 q^{6} - 84 q^{8} + 33 q^{9}+O(q^{10}) $ 5 * q - 8 * q^3 + 26 * q^4 - 10 * q^5 - 34 * q^6 - 84 * q^8 + 33 * q^9	\( 5 q - 8 q^{3} + 26 q^{4} - 10 q^{5} - 34 q^{6} - 84 q^{8} + 33 q^{9} + 64 q^{10} + 12 q^{11} + 224 q^{12} - 14 q^{13} - 74 q^{15} + 146 q^{16} - 66 q^{17} - 108 q^{18} - 214 q^{19} - 6 q^{20} - 98 q^{22} + 164 q^{23} - 314 q^{24} + 207 q^{25} - 56 q^{26} - 362 q^{27} - 145 q^{29} - 234 q^{30} - 420 q^{31} - 652 q^{32} + 576 q^{33} - 204 q^{34} - 260 q^{36} + 378 q^{37} + 496 q^{38} - 374 q^{39} + 80 q^{40} + 1158 q^{41} - 204 q^{43} + 784 q^{44} + 1506 q^{45} + 580 q^{46} - 248 q^{47} + 1880 q^{48} + 908 q^{50} + 228 q^{51} - 1482 q^{52} - 554 q^{53} - 918 q^{54} - 546 q^{55} + 44 q^{57} - 440 q^{59} + 636 q^{60} - 618 q^{61} - 1250 q^{62} + 2594 q^{64} - 1656 q^{65} - 2940 q^{66} + 1164 q^{67} - 356 q^{68} + 1968 q^{69} - 692 q^{71} - 2648 q^{72} + 1950 q^{73} - 1832 q^{74} - 3074 q^{75} - 1376 q^{76} - 1302 q^{78} + 272 q^{79} + 890 q^{80} + 1801 q^{81} - 92 q^{82} - 512 q^{83} - 1628 q^{85} + 2446 q^{86} + 232 q^{87} - 6954 q^{88} - 866 q^{89} + 2200 q^{90} + 3468 q^{92} - 40 q^{93} + 5942 q^{94} + 2244 q^{95} - 7386 q^{96} - 1562 q^{97} - 238 q^{99}+O(q^{100}) \) 5 * q - 8 * q^3 + 26 * q^4 - 10 * q^5 - 34 * q^6 - 84 * q^8 + 33 * q^9 + 64 * q^10 + 12 * q^11 + 224 * q^12 - 14 * q^13 - 74 * q^15 + 146 * q^16 - 66 * q^17 - 108 * q^18 - 214 * q^19 - 6 * q^20 - 98 * q^22 + 164 * q^23 - 314 * q^24 + 207 * q^25 - 56 * q^26 - 362 * q^27 - 145 * q^29 - 234 * q^30 - 420 * q^31 - 652 * q^32 + 576 * q^33 - 204 * q^34 - 260 * q^36 + 378 * q^37 + 496 * q^38 - 374 * q^39 + 80 * q^40 + 1158 * q^41 - 204 * q^43 + 784 * q^44 + 1506 * q^45 + 580 * q^46 - 248 * q^47 + 1880 * q^48 + 908 * q^50 + 228 * q^51 - 1482 * q^52 - 554 * q^53 - 918 * q^54 - 546 * q^55 + 44 * q^57 - 440 * q^59 + 636 * q^60 - 618 * q^61 - 1250 * q^62 + 2594 * q^64 - 1656 * q^65 - 2940 * q^66 + 1164 * q^67 - 356 * q^68 + 1968 * q^69 - 692 * q^71 - 2648 * q^72 + 1950 * q^73 - 1832 * q^74 - 3074 * q^75 - 1376 * q^76 - 1302 * q^78 + 272 * q^79 + 890 * q^80 + 1801 * q^81 - 92 * q^82 - 512 * q^83 - 1628 * q^85 + 2446 * q^86 + 232 * q^87 - 6954 * q^88 - 866 * q^89 + 2200 * q^90 + 3468 * q^92 - 40 * q^93 + 5942 * q^94 + 2244 * q^95 - 7386 * q^96 - 1562 * q^97 - 238 * 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 $

$2$	4.47236	1.58122	0.790610	−	0.612321i	$-0.209764\pi$
$2$	4.47236	1.58122	0.790610	+	0.612321i	$0.209764\pi$
$3$	1.90549	0.366712	0.183356	−	0.983047i	$-0.441304\pi$
$3$	1.90549	0.366712	0.183356	+	0.983047i	$0.441304\pi$
$4$	12.0020	1.50025
$5$	6.52855	0.583931	0.291966	−	0.956429i	$-0.405691\pi$
$5$	6.52855	0.583931	0.291966	+	0.956429i	$0.405691\pi$
$6$	8.52204	0.579851
$7$	0	0
$7$	0	0
$8$	17.8986	0.791012
$9$	−23.3691	−0.865523
$10$	29.1981	0.923324
$11$	−21.1299	−0.579173	−0.289586	−	0.957152i	$-0.593518\pi$
$11$	−21.1299	−0.579173	−0.289586	+	0.957152i	$0.593518\pi$
$12$	22.8697	0.550161
$13$	−83.4615	−1.78062	−0.890310	−	0.455355i	$-0.849512\pi$
$13$	−83.4615	−1.78062	−0.890310	+	0.455355i	$0.849512\pi$
$14$	0	0
$15$	12.4401	0.214134
$16$	−15.9674	−0.249491
$17$	−11.3273	−0.161604	−0.0808020	−	0.996730i	$-0.525748\pi$
$17$	−11.3273	−0.161604	−0.0808020	+	0.996730i	$0.525748\pi$
$18$	−104.515	−1.36858
$19$	7.68096	0.0927438	0.0463719	−	0.998924i	$-0.485234\pi$
$19$	7.68096	0.0927438	0.0463719	+	0.998924i	$0.485234\pi$
$20$	78.3559	0.876046
$21$	0	0
$22$	−94.5005	−0.915799
$23$	153.169	1.38861	0.694303	−	0.719683i	$-0.255713\pi$
$23$	153.169	1.38861	0.694303	+	0.719683i	$0.255713\pi$
$24$	34.1055	0.290073
$25$	−82.3780	−0.659024
$26$	−373.270	−2.81555
$27$	−95.9778	−0.684109
$28$	0	0
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	55.6366	0.338593
$31$	−270.530	−1.56737	−0.783687	−	0.621156i	$-0.786663\pi$
$31$	−270.530	−1.56737	−0.783687	+	0.621156i	$0.786663\pi$
$32$	−214.601	−1.18551
$33$	−40.2628	−0.212389
$34$	−50.6597	−0.255531
$35$	0	0
$36$	−280.477	−1.29850
$37$	−298.404	−1.32587	−0.662936	−	0.748676i	$-0.730690\pi$
$37$	−298.404	−1.32587	−0.662936	+	0.748676i	$0.730690\pi$
$38$	34.3520	0.146648
$39$	−159.035	−0.652974
$40$	116.852	0.461897
$41$	184.710	0.703584	0.351792	−	0.936078i	$-0.385573\pi$
$41$	184.710	0.703584	0.351792	+	0.936078i	$0.385573\pi$
$42$	0	0
$43$	208.337	0.738861	0.369430	−	0.929258i	$-0.379553\pi$
$43$	208.337	0.738861	0.369430	+	0.929258i	$0.379553\pi$
$44$	−253.602	−0.868906
$45$	−152.566	−0.505406
$46$	685.028	2.19569
$47$	553.098	1.71654	0.858272	−	0.513194i	$-0.171538\pi$
$47$	553.098	1.71654	0.858272	+	0.513194i	$0.171538\pi$
$48$	−30.4258	−0.0914913
$49$	0	0
$50$	−368.424	−1.04206
$51$	−21.5840	−0.0592620
$52$	−1001.71	−2.67138
$53$	−321.465	−0.833144	−0.416572	−	0.909103i	$-0.636769\pi$
$53$	−321.465	−0.833144	−0.416572	+	0.909103i	$0.636769\pi$
$54$	−429.248	−1.08173
$55$	−137.948	−0.338197
$56$	0	0
$57$	14.6360	0.0340102
$58$	−129.699	−0.293625
$59$	−104.930	−0.231538	−0.115769	−	0.993276i	$-0.536933\pi$
$59$	−104.930	−0.231538	−0.115769	+	0.993276i	$0.536933\pi$
$60$	149.306	0.321256
$61$	−464.230	−0.974403	−0.487201	−	0.873290i	$-0.661982\pi$
$61$	−464.230	−0.974403	−0.487201	+	0.873290i	$0.661982\pi$
$62$	−1209.91	−2.47836
$63$	0	0
$64$	−832.032	−1.62506
$65$	−544.883	−1.03976
$66$	−180.070	−0.335834
$67$	745.813	1.35993	0.679967	−	0.733243i	$-0.261994\pi$
$67$	745.813	1.35993	0.679967	+	0.733243i	$0.261994\pi$
$68$	−135.950	−0.242447
$69$	291.862	0.509218
$70$	0	0
$71$	−509.252	−0.851227	−0.425613	−	0.904905i	$-0.639942\pi$
$71$	−509.252	−0.851227	−0.425613	+	0.904905i	$0.639942\pi$
$72$	−418.273	−0.684639
$73$	0.374979	0.000601205 0	0.000300603	−	1.00000i	$-0.499904\pi$
$73$	0.374979	0.000601205 0	0.000300603		1.00000i	$0.499904\pi$
$74$	−1334.57	−2.09649
$75$	−156.970	−0.241672
$76$	92.1871	0.139139
$77$	0	0
$78$	−711.262	−1.03249
$79$	610.912	0.870037	0.435018	−	0.900422i	$-0.356742\pi$
$79$	610.912	0.870037	0.435018	+	0.900422i	$0.356742\pi$
$80$	−104.244	−0.145686
$81$	448.081	0.614652
$82$	826.092	1.11252
$83$	−791.431	−1.04664	−0.523319	−	0.852137i	$-0.675306\pi$
$83$	−791.431	−1.04664	−0.523319	+	0.852137i	$0.675306\pi$
$84$	0	0
$85$	−73.9507	−0.0943656
$86$	931.757	1.16830
$87$	−55.2592	−0.0680966
$88$	−378.194	−0.458132
$89$	342.011	0.407338	0.203669	−	0.979040i	$-0.434713\pi$
$89$	342.011	0.407338	0.203669	+	0.979040i	$0.434713\pi$
$90$	−682.333	−0.799157
$91$	0	0
$92$	1838.34	2.08326
$93$	−515.491	−0.574774
$94$	2473.65	2.71423
$95$	50.1455	0.0541560
$96$	−408.919	−0.434741
$97$	−601.476	−0.629594	−0.314797	−	0.949159i	$-0.601937\pi$
$97$	−601.476	−0.629594	−0.314797	+	0.949159i	$0.601937\pi$
$98$	0	0
$99$	493.787	0.501287
$100$	−988.704	−0.988704
$101$	−402.327	−0.396367	−0.198183	−	0.980165i	$-0.563504\pi$
$101$	−402.327	−0.396367	−0.198183	+	0.980165i	$0.563504\pi$
$102$	−96.5314	−0.0937063
$103$	1338.38	1.28033	0.640166	−	0.768236i	$-0.278866\pi$
$103$	1338.38	1.28033	0.640166	+	0.768236i	$0.278866\pi$
$104$	−1493.84	−1.40849
$105$	0	0
$106$	−1437.71	−1.31738
$107$	500.501	0.452199	0.226099	−	0.974104i	$-0.427403\pi$
$107$	500.501	0.452199	0.226099	+	0.974104i	$0.427403\pi$
$108$	−1151.93	−1.02634
$109$	1274.80	1.12022	0.560108	−	0.828420i	$-0.310760\pi$
$109$	1274.80	1.12022	0.560108	+	0.828420i	$0.310760\pi$
$110$	−616.951	−0.534764
$111$	−568.605	−0.486212
$112$	0	0
$113$	335.278	0.279118	0.139559	−	0.990214i	$-0.455432\pi$
$113$	335.278	0.279118	0.139559	+	0.990214i	$0.455432\pi$
$114$	65.4574	0.0537776
$115$	999.972	0.810851
$116$	−348.059	−0.278590
$117$	1950.42	1.54117
$118$	−469.287	−0.366113
$119$	0	0
$120$	222.660	0.169383
$121$	−884.528	−0.664559
$122$	−2076.21	−1.54074
$123$	351.964	0.258012
$124$	−3246.91	−2.35146
$125$	−1353.88	−0.968756
$126$	0	0
$127$	755.312	0.527741	0.263870	−	0.964558i	$-0.415001\pi$
$127$	755.312	0.527741	0.263870	+	0.964558i	$0.415001\pi$
$128$	−2004.35	−1.38407
$129$	396.983	0.270949
$130$	−2436.91	−1.64409
$131$	253.351	0.168973	0.0844863	−	0.996425i	$-0.473075\pi$
$131$	253.351	0.168973	0.0844863	+	0.996425i	$0.473075\pi$
$132$	−483.235	−0.318638
$133$	0	0
$134$	3335.55	2.15035
$135$	−626.596	−0.399473
$136$	−202.742	−0.127831
$137$	−2477.49	−1.54501	−0.772504	−	0.635010i	$-0.780996\pi$
$137$	−2477.49	−1.54501	−0.772504	+	0.635010i	$0.780996\pi$
$138$	1305.31	0.805185
$139$	−423.114	−0.258187	−0.129094	−	0.991632i	$-0.541207\pi$
$139$	−423.114	−0.258187	−0.129094	+	0.991632i	$0.541207\pi$
$140$	0	0
$141$	1053.92	0.629477
$142$	−2277.56	−1.34598
$143$	1763.53	1.03129
$144$	373.145	0.215940
$145$	−189.328	−0.108433
$146$	1.67704	0.000950637 0
$147$	0	0
$148$	−3581.45	−1.98914
$149$	−1263.82	−0.694873	−0.347437	−	0.937703i	$-0.612948\pi$
$149$	−1263.82	−0.694873	−0.347437	+	0.937703i	$0.612948\pi$
$150$	−702.029	−0.382136
$151$	3369.67	1.81603	0.908013	−	0.418943i	$-0.137599\pi$
$151$	3369.67	1.81603	0.908013	+	0.418943i	$0.137599\pi$
$152$	137.478	0.0733615
$153$	264.708	0.139872
$154$	0	0
$155$	−1766.17	−0.915238
$156$	−1908.74	−0.979627
$157$	3688.61	1.87505	0.937527	−	0.347914i	$-0.113110\pi$
$157$	3688.61	1.87505	0.937527	+	0.347914i	$0.113110\pi$
$158$	2732.22	1.37572
$159$	−612.548	−0.305523
$160$	−1401.03	−0.692258
$161$	0	0
$162$	2003.98	0.971900
$163$	−1975.81	−0.949432	−0.474716	−	0.880139i	$-0.657449\pi$
$163$	−1975.81	−0.949432	−0.474716	+	0.880139i	$0.657449\pi$
$164$	2216.90	1.05555
$165$	−262.857	−0.124021
$166$	−3539.57	−1.65496
$167$	1608.44	0.745297	0.372649	−	0.927973i	$-0.378450\pi$
$167$	1608.44	0.745297	0.372649	+	0.927973i	$0.378450\pi$
$168$	0	0
$169$	4768.82	2.17061
$170$	−330.734	−0.149213
$171$	−179.497	−0.0802719
$172$	2500.46	1.10848
$173$	−4445.71	−1.95376	−0.976881	−	0.213784i	$-0.931421\pi$
$173$	−4445.71	−1.95376	−0.976881	+	0.213784i	$0.931421\pi$
$174$	−247.139	−0.107676
$175$	0	0
$176$	337.390	0.144498
$177$	−199.944	−0.0849078
$178$	1529.60	0.644091
$179$	1461.35	0.610203	0.305101	−	0.952320i	$-0.401310\pi$
$179$	1461.35	0.610203	0.305101	+	0.952320i	$0.401310\pi$
$180$	−1831.11	−0.758237
$181$	−3789.62	−1.55624	−0.778122	−	0.628113i	$-0.783828\pi$
$181$	−3789.62	−1.55624	−0.778122	+	0.628113i	$0.783828\pi$
$182$	0	0
$183$	−884.585	−0.357325
$184$	2741.50	1.09840
$185$	−1948.14	−0.774218
$186$	−2305.46	−0.908843
$187$	239.344	0.0935966
$188$	6638.30	2.57525
$189$	0	0
$190$	224.269	0.0856326
$191$	−4782.10	−1.81163	−0.905813	−	0.423678i	$-0.860739\pi$
$191$	−4782.10	−1.81163	−0.905813	+	0.423678i	$0.860739\pi$
$192$	−1585.43	−0.595929
$193$	−3557.27	−1.32673	−0.663363	−	0.748298i	$-0.730871\pi$
$193$	−3557.27	−1.32673	−0.663363	+	0.748298i	$0.730871\pi$
$194$	−2690.02	−0.995527
$195$	−1038.27	−0.381292
$196$	0	0
$197$	−2290.24	−0.828290	−0.414145	−	0.910211i	$-0.635919\pi$
$197$	−2290.24	−0.828290	−0.414145	+	0.910211i	$0.635919\pi$
$198$	2208.39	0.792645
$199$	2788.00	0.993146	0.496573	−	0.867995i	$-0.334591\pi$
$199$	2788.00	0.993146	0.496573	+	0.867995i	$0.334591\pi$
$200$	−1474.45	−0.521296
$201$	1421.14	0.498703
$202$	−1799.35	−0.626742
$203$	0	0
$204$	−259.052	−0.0889081
$205$	1205.89	0.410845
$206$	5985.71	2.02449
$207$	−3579.42	−1.20187
$208$	1332.67	0.444249
$209$	−162.298	−0.0537147
$210$	0	0
$211$	628.449	0.205044	0.102522	−	0.994731i	$-0.467309\pi$
$211$	628.449	0.205044	0.102522	+	0.994731i	$0.467309\pi$
$212$	−3858.24	−1.24993
$213$	−970.374	−0.312155
$214$	2238.42	0.715025
$215$	1360.14	0.431444
$216$	−1717.86	−0.541138
$217$	0	0
$218$	5701.36	1.77131
$219$	0.714519	0.000220469 0
$220$	−1655.65	−0.507382
$221$	945.391	0.287755
$222$	−2543.01	−0.768808
$223$	−136.439	−0.0409714	−0.0204857	−	0.999790i	$-0.506521\pi$
$223$	−136.439	−0.0409714	−0.0204857	+	0.999790i	$0.506521\pi$
$224$	0	0
$225$	1925.10	0.570400
$226$	1499.49	0.441347
$227$	−4180.45	−1.22232	−0.611159	−	0.791508i	$-0.709296\pi$
$227$	−4180.45	−1.22232	−0.611159	+	0.791508i	$0.709296\pi$
$228$	175.662	0.0510240
$229$	1352.95	0.390417	0.195209	−	0.980762i	$-0.437462\pi$
$229$	1352.95	0.390417	0.195209	+	0.980762i	$0.437462\pi$
$230$	4472.24	1.28213
$231$	0	0
$232$	−519.058	−0.146887
$233$	2175.34	0.611635	0.305818	−	0.952090i	$-0.401070\pi$
$233$	2175.34	0.611635	0.305818	+	0.952090i	$0.401070\pi$
$234$	8722.99	2.43692
$235$	3610.93	1.00234
$236$	−1259.38	−0.347367
$237$	1164.09	0.319053
$238$	0	0
$239$	−4512.18	−1.22121	−0.610604	−	0.791936i	$-0.709073\pi$
$239$	−4512.18	−1.22121	−0.610604	+	0.791936i	$0.709073\pi$
$240$	−198.636	−0.0534246
$241$	−1950.53	−0.521346	−0.260673	−	0.965427i	$-0.583944\pi$
$241$	−1950.53	−0.521346	−0.260673	+	0.965427i	$0.583944\pi$
$242$	−3955.93	−1.05081
$243$	3445.21	0.909509
$244$	−5571.70	−1.46185
$245$	0	0
$246$	1574.11	0.407974
$247$	−641.064	−0.165141
$248$	−4842.09	−1.23981
$249$	−1508.06	−0.383814
$250$	−6055.03	−1.53182
$251$	−27.4143	−0.00689393	−0.00344696	−	0.999994i	$-0.501097\pi$
$251$	−27.4143	−0.00689393	−0.00344696	+	0.999994i	$0.501097\pi$
$252$	0	0
$253$	−3236.44	−0.804243
$254$	3378.03	0.834474
$255$	−140.912	−0.0346050
$256$	−2307.91	−0.563454
$257$	−4458.31	−1.08211	−0.541053	−	0.840988i	$-0.681974\pi$
$257$	−4458.31	−1.08211	−0.541053	+	0.840988i	$0.681974\pi$
$258$	1775.45	0.428429
$259$	0	0
$260$	−6539.70	−1.55990
$261$	677.704	0.160724
$262$	1133.08	0.267183
$263$	4641.08	1.08814	0.544071	−	0.839039i	$-0.316882\pi$
$263$	4641.08	1.08814	0.544071	+	0.839039i	$0.316882\pi$
$264$	−720.645	−0.168002
$265$	−2098.70	−0.486499
$266$	0	0
$267$	651.699	0.149376
$268$	8951.28	2.04025
$269$	235.021	0.0532694	0.0266347	−	0.999645i	$-0.491521\pi$
$269$	235.021	0.0532694	0.0266347	+	0.999645i	$0.491521\pi$
$270$	−2802.36	−0.631654
$271$	−3816.09	−0.855392	−0.427696	−	0.903923i	$-0.640675\pi$
$271$	−3816.09	−0.855392	−0.427696	+	0.903923i	$0.640675\pi$
$272$	180.867	0.0403188
$273$	0	0
$274$	−11080.2	−2.44300
$275$	1740.64	0.381689
$276$	3502.94	0.763957
$277$	−2024.79	−0.439198	−0.219599	−	0.975590i	$-0.570475\pi$
$277$	−2024.79	−0.439198	−0.219599	+	0.975590i	$0.570475\pi$
$278$	−1892.32	−0.408251
$279$	6322.04	1.35660
$280$	0	0
$281$	5451.81	1.15739	0.578697	−	0.815543i	$-0.303561\pi$
$281$	5451.81	1.15739	0.578697	+	0.815543i	$0.303561\pi$
$282$	4713.52	0.995341
$283$	−5026.80	−1.05587	−0.527937	−	0.849284i	$-0.677034\pi$
$283$	−5026.80	−1.05587	−0.527937	+	0.849284i	$0.677034\pi$
$284$	−6112.06	−1.27706
$285$	95.5517	0.0198596
$286$	7887.16	1.63069
$287$	0	0
$288$	5015.03	1.02609
$289$	−4784.69	−0.973884
$290$	−846.744	−0.171457
$291$	−1146.11	−0.230880
$292$	4.50051	0.000901961 0
$293$	−6160.34	−1.22830	−0.614148	−	0.789191i	$-0.710500\pi$
$293$	−6160.34	−1.22830	−0.614148	+	0.789191i	$0.710500\pi$
$294$	0	0
$295$	−685.043	−0.135203
$296$	−5340.99	−1.04878
$297$	2028.00	0.396217
$298$	−5652.26	−1.09875
$299$	−12783.7	−2.47258
$300$	−1883.96	−0.362569
$301$	0	0
$302$	15070.4	2.87153
$303$	−766.629	−0.145352
$304$	−122.645	−0.0231388
$305$	−3030.75	−0.568984
$306$	1183.87	0.221168
$307$	4329.54	0.804885	0.402443	−	0.915445i	$-0.368161\pi$
$307$	4329.54	0.804885	0.402443	+	0.915445i	$0.368161\pi$
$308$	0	0
$309$	2550.26	0.469513
$310$	−7898.94	−1.44719
$311$	6411.83	1.16907	0.584536	−	0.811368i	$-0.301276\pi$
$311$	6411.83	1.16907	0.584536	+	0.811368i	$0.301276\pi$
$312$	−2846.50	−0.516510
$313$	19.5263	0.00352617	0.00176309	−	0.999998i	$-0.499439\pi$
$313$	19.5263	0.00352617	0.00176309	+	0.999998i	$0.499439\pi$
$314$	16496.8	2.96487
$315$	0	0
$316$	7332.18	1.30528
$317$	−8198.11	−1.45253	−0.726265	−	0.687415i	$-0.758745\pi$
$317$	−8198.11	−1.45253	−0.726265	+	0.687415i	$0.758745\pi$
$318$	−2739.54	−0.483100
$319$	612.767	0.107550
$320$	−5431.97	−0.948926
$321$	953.699	0.165826
$322$	0	0
$323$	−87.0043	−0.0149878
$324$	5377.89	0.922135
$325$	6875.39	1.17347
$326$	−8836.54	−1.50126
$327$	2429.11	0.410796
$328$	3306.05	0.556543
$329$	0	0
$330$	−1175.59	−0.196104
$331$	2374.46	0.394297	0.197148	−	0.980374i	$-0.436832\pi$
$331$	2374.46	0.394297	0.197148	+	0.980374i	$0.436832\pi$
$332$	−9498.79	−1.57022
$333$	6973.43	1.14757
$334$	7193.52	1.17848
$335$	4869.08	0.794108
$336$	0	0
$337$	−4985.34	−0.805842	−0.402921	−	0.915235i	$-0.632005\pi$
$337$	−4985.34	−0.805842	−0.402921	+	0.915235i	$0.632005\pi$
$338$	21327.9	3.43221
$339$	638.869	0.102356
$340$	−887.559	−0.141572
$341$	5716.26	0.907780
$342$	−802.777	−0.126927
$343$	0	0
$344$	3728.92	0.584448
$345$	1905.44	0.297348
$346$	−19882.8	−3.08933
$347$	−2023.98	−0.313121	−0.156560	−	0.987668i	$-0.550041\pi$
$347$	−2023.98	−0.313121	−0.156560	+	0.987668i	$0.550041\pi$
$348$	−663.223	−0.102162
$349$	2651.99	0.406755	0.203378	−	0.979100i	$-0.434808\pi$
$349$	2651.99	0.406755	0.203378	+	0.979100i	$0.434808\pi$
$350$	0	0
$351$	8010.45	1.21814
$352$	4534.49	0.686616
$353$	1729.22	0.260729	0.130364	−	0.991466i	$-0.458385\pi$
$353$	1729.22	0.260729	0.130364	+	0.991466i	$0.458385\pi$
$354$	−894.220	−0.134258
$355$	−3324.68	−0.497058
$356$	4104.83	0.611111
$357$	0	0
$358$	6535.68	0.964864
$359$	6875.38	1.01078	0.505388	−	0.862892i	$-0.331349\pi$
$359$	6875.38	1.01078	0.505388	+	0.862892i	$0.331349\pi$
$360$	−2730.72	−0.399782
$361$	−6800.00	−0.991399
$362$	−16948.6	−2.46076
$363$	−1685.46	−0.243701
$364$	0	0
$365$	2.44807	0.000351063 0
$366$	−3956.19	−0.565009
$367$	7435.15	1.05753	0.528763	−	0.848770i	$-0.322656\pi$
$367$	7435.15	1.05753	0.528763	+	0.848770i	$0.322656\pi$
$368$	−2445.72	−0.346445
$369$	−4316.52	−0.608968
$370$	−8712.80	−1.22421
$371$	0	0
$372$	−6186.95	−0.862307
$373$	1397.48	0.193991	0.0969954	−	0.995285i	$-0.469077\pi$
$373$	1397.48	0.193991	0.0969954	+	0.995285i	$0.469077\pi$
$374$	1070.43	0.147997
$375$	−2579.80	−0.355254
$376$	9899.65	1.35781
$377$	2420.38	0.330653
$378$	0	0
$379$	7009.57	0.950020	0.475010	−	0.879980i	$-0.342444\pi$
$379$	7009.57	0.950020	0.475010	+	0.879980i	$0.342444\pi$
$380$	601.848	0.0812478
$381$	1439.24	0.193529
$382$	−21387.3	−2.86458
$383$	11728.7	1.56477	0.782387	−	0.622792i	$-0.214002\pi$
$383$	11728.7	1.56477	0.782387	+	0.622792i	$0.214002\pi$
$384$	−3819.26	−0.507554
$385$	0	0
$386$	−15909.4	−2.09784
$387$	−4868.64	−0.639501
$388$	−7218.94	−0.944552
$389$	−4367.15	−0.569212	−0.284606	−	0.958645i	$-0.591863\pi$
$389$	−4367.15	−0.569212	−0.284606	+	0.958645i	$0.591863\pi$
$390$	−4643.51	−0.602906
$391$	−1734.99	−0.224404
$392$	0	0
$393$	482.758	0.0619642
$394$	−10242.8	−1.30971
$395$	3988.37	0.508042
$396$	5926.44	0.752058
$397$	−1632.74	−0.206410	−0.103205	−	0.994660i	$-0.532910\pi$
$397$	−1632.74	−0.206410	−0.103205	+	0.994660i	$0.532910\pi$
$398$	12469.0	1.57038
$399$	0	0
$400$	1315.37	0.164421
$401$	5028.65	0.626232	0.313116	−	0.949715i	$-0.398627\pi$
$401$	5028.65	0.626232	0.313116	+	0.949715i	$0.398627\pi$
$402$	6355.85	0.788559
$403$	22578.8	2.79090
$404$	−4828.74	−0.594651
$405$	2925.32	0.358915
$406$	0	0
$407$	6305.23	0.767908
$408$	−386.322	−0.0468770
$409$	2497.21	0.301904	0.150952	−	0.988541i	$-0.451766\pi$
$409$	2497.21	0.301904	0.150952	+	0.988541i	$0.451766\pi$
$410$	5393.19	0.649635
$411$	−4720.82	−0.566572
$412$	16063.3	1.92082
$413$	0	0
$414$	−16008.5	−1.90042
$415$	−5166.90	−0.611164
$416$	17910.9	2.11095
$417$	−806.239	−0.0946803
$418$	−725.854	−0.0849347
$419$	−12909.4	−1.50517	−0.752585	−	0.658496i	$-0.771193\pi$
$419$	−12909.4	−1.50517	−0.752585	+	0.658496i	$0.771193\pi$
$420$	0	0
$421$	−4019.30	−0.465293	−0.232647	−	0.972561i	$-0.574739\pi$
$421$	−4019.30	−0.465293	−0.232647	+	0.972561i	$0.574739\pi$
$422$	2810.65	0.324219
$423$	−12925.4	−1.48571
$424$	−5753.76	−0.659027
$425$	933.118	0.106501
$426$	−4339.86	−0.493585
$427$	0	0
$428$	6007.03	0.678413
$429$	3360.39	0.378185
$430$	6083.02	0.682208
$431$	8768.94	0.980012	0.490006	−	0.871719i	$-0.336995\pi$
$431$	8768.94	0.980012	0.490006	+	0.871719i	$0.336995\pi$
$432$	1532.52	0.170679
$433$	−4496.26	−0.499021	−0.249511	−	0.968372i	$-0.580270\pi$
$433$	−4496.26	−0.499021	−0.249511	+	0.968372i	$0.580270\pi$
$434$	0	0
$435$	−360.762	−0.0397638
$436$	15300.2	1.68061
$437$	1176.48	0.128785
$438$	3.19559	0.000348610 0
$439$	7316.62	0.795451	0.397725	−	0.917504i	$-0.369800\pi$
$439$	7316.62	0.795451	0.397725	+	0.917504i	$0.369800\pi$
$440$	−2469.06	−0.267518
$441$	0	0
$442$	4228.13	0.455004
$443$	−12801.1	−1.37291	−0.686454	−	0.727173i	$-0.740834\pi$
$443$	−12801.1	−1.37291	−0.686454	+	0.727173i	$0.740834\pi$
$444$	−6824.41	−0.729442
$445$	2232.84	0.237858
$446$	−610.204	−0.0647847
$447$	−2408.19	−0.254818
$448$	0	0
$449$	6412.22	0.673968	0.336984	−	0.941510i	$-0.390593\pi$
$449$	6412.22	0.673968	0.336984	+	0.941510i	$0.390593\pi$
$450$	8609.75	0.901928
$451$	−3902.91	−0.407496
$452$	4024.02	0.418748
$453$	6420.87	0.665957
$454$	−18696.5	−1.93275
$455$	0	0
$456$	261.963	0.0269025
$457$	−2153.32	−0.220412	−0.110206	−	0.993909i	$-0.535151\pi$
$457$	−2153.32	−0.220412	−0.110206	+	0.993909i	$0.535151\pi$
$458$	6050.89	0.617336
$459$	1087.17	0.110555
$460$	12001.7	1.21648
$461$	1850.55	0.186960	0.0934800	−	0.995621i	$-0.470201\pi$
$461$	1850.55	0.186960	0.0934800	+	0.995621i	$0.470201\pi$
$462$	0	0
$463$	1892.04	0.189914	0.0949572	−	0.995481i	$-0.469729\pi$
$463$	1892.04	0.189914	0.0949572	+	0.995481i	$0.469729\pi$
$464$	463.056	0.0463293
$465$	−3365.41	−0.335628
$466$	9728.89	0.967129
$467$	3739.40	0.370533	0.185267	−	0.982688i	$-0.440685\pi$
$467$	3739.40	0.370533	0.185267	+	0.982688i	$0.440685\pi$
$468$	23409.0	2.31214
$469$	0	0
$470$	16149.4	1.58493
$471$	7028.61	0.687604
$472$	−1878.10	−0.183150
$473$	−4402.13	−0.427928
$474$	5206.21	0.504492
$475$	−632.742	−0.0611204
$476$	0	0
$477$	7512.35	0.721105
$478$	−20180.1	−1.93100
$479$	7260.30	0.692550	0.346275	−	0.938133i	$-0.387446\pi$
$479$	7260.30	0.692550	0.346275	+	0.938133i	$0.387446\pi$
$480$	−2669.65	−0.253859
$481$	24905.2	2.36087
$482$	−8723.46	−0.824363
$483$	0	0
$484$	−10616.1	−0.997008
$485$	−3926.77	−0.367640
$486$	15408.3	1.43813
$487$	4756.40	0.442573	0.221287	−	0.975209i	$-0.428974\pi$
$487$	4756.40	0.442573	0.221287	+	0.975209i	$0.428974\pi$
$488$	−8309.05	−0.770764
$489$	−3764.88	−0.348168
$490$	0	0
$491$	−2007.83	−0.184546	−0.0922730	−	0.995734i	$-0.529413\pi$
$491$	−2007.83	−0.184546	−0.0922730	+	0.995734i	$0.529413\pi$
$492$	4224.28	0.387084
$493$	328.491	0.0300091
$494$	−2867.07	−0.261125
$495$	3223.71	0.292717
$496$	4319.66	0.391046
$497$	0	0
$498$	−6744.61	−0.606894
$499$	−8952.55	−0.803149	−0.401574	−	0.915826i	$-0.631537\pi$
$499$	−8952.55	−0.803149	−0.401574	+	0.915826i	$0.631537\pi$
$500$	−16249.3	−1.45338
$501$	3064.86	0.273309
$502$	−122.607	−0.0109008
$503$	−20564.9	−1.82295	−0.911477	−	0.411351i	$-0.865057\pi$
$503$	−20564.9	−1.82295	−0.911477	+	0.411351i	$0.865057\pi$
$504$	0	0
$505$	−2626.61	−0.231451
$506$	−14474.6	−1.27168
$507$	9086.94	0.795987
$508$	9065.28	0.791746
$509$	−13321.9	−1.16008	−0.580041	−	0.814587i	$-0.696964\pi$
$509$	−13321.9	−1.16008	−0.580041	+	0.814587i	$0.696964\pi$
$510$	−630.211	−0.0547180
$511$	0	0
$512$	5712.97	0.493125
$513$	−737.201	−0.0634468
$514$	−19939.2	−1.71105
$515$	8737.66	0.747626
$516$	4764.60	0.406492
$517$	−11686.9	−0.994176
$518$	0	0
$519$	−8471.24	−0.716467
$520$	−9752.62	−0.822462
$521$	13047.0	1.09712	0.548558	−	0.836113i	$-0.315177\pi$
$521$	13047.0	1.09712	0.548558	+	0.836113i	$0.315177\pi$
$522$	3030.94	0.254139
$523$	20207.4	1.68950	0.844750	−	0.535161i	$-0.179749\pi$
$523$	20207.4	1.68950	0.844750	+	0.535161i	$0.179749\pi$
$524$	3040.73	0.253502
$525$	0	0
$526$	20756.6	1.72059
$527$	3064.36	0.253294
$528$	642.893	0.0529892
$529$	11293.8	0.928228
$530$	−9386.16	−0.769262
$531$	2452.13	0.200402
$532$	0	0
$533$	−15416.2	−1.25281
$534$	2914.63	0.236196
$535$	3267.55	0.264053
$536$	13349.0	1.07572
$537$	2784.58	0.223768
$538$	1051.10	0.0842306
$539$	0	0
$540$	−7520.43	−0.599310
$541$	−17866.0	−1.41981	−0.709906	−	0.704297i	$-0.751263\pi$
$541$	−17866.0	−1.41981	−0.709906	+	0.704297i	$0.751263\pi$
$542$	−17067.0	−1.35256
$543$	−7221.08	−0.570693
$544$	2430.84	0.191583
$545$	8322.59	0.654129
$546$	0	0
$547$	−8027.79	−0.627502	−0.313751	−	0.949505i	$-0.601586\pi$
$547$	−8027.79	−0.627502	−0.313751	+	0.949505i	$0.601586\pi$
$548$	−29734.9	−2.31790
$549$	10848.6	0.843367
$550$	7784.76	0.603534
$551$	−222.748	−0.0172221
$552$	5223.91	0.402797
$553$	0	0
$554$	−9055.59	−0.694468
$555$	−3712.16	−0.283915
$556$	−5078.23	−0.387347
$557$	17357.6	1.32040	0.660201	−	0.751089i	$-0.270471\pi$
$557$	17357.6	1.32040	0.660201	+	0.751089i	$0.270471\pi$
$558$	28274.5	2.14508
$559$	−17388.1	−1.31563
$560$	0	0
$561$	456.067	0.0343229
$562$	24382.5	1.83009
$563$	6073.90	0.454679	0.227340	−	0.973816i	$-0.426997\pi$
$563$	6073.90	0.454679	0.227340	+	0.973816i	$0.426997\pi$
$564$	12649.2	0.944375
$565$	2188.88	0.162986
$566$	−22481.7	−1.66957
$567$	0	0
$568$	−9114.87	−0.673330
$569$	5084.04	0.374577	0.187288	−	0.982305i	$-0.440030\pi$
$569$	5084.04	0.374577	0.187288	+	0.982305i	$0.440030\pi$
$570$	427.342	0.0314024
$571$	15552.3	1.13983	0.569914	−	0.821704i	$-0.306976\pi$
$571$	15552.3	1.13983	0.569914	+	0.821704i	$0.306976\pi$
$572$	21166.0	1.54719
$573$	−9112.24	−0.664344
$574$	0	0
$575$	−12617.8	−0.915125
$576$	19443.9	1.40653
$577$	20714.3	1.49454	0.747269	−	0.664521i	$-0.231365\pi$
$577$	20714.3	1.49454	0.747269	+	0.664521i	$0.231365\pi$
$578$	−21398.9	−1.53992
$579$	−6778.34	−0.486526
$580$	−2272.32	−0.162678
$581$	0	0
$582$	−5125.80	−0.365071
$583$	6792.52	0.482534
$584$	6.71159	0.000475561 0
$585$	12733.4	0.899936
$586$	−27551.3	−1.94221
$587$	1015.03	0.0713711	0.0356856	−	0.999363i	$-0.488639\pi$
$587$	1015.03	0.0713711	0.0356856	+	0.999363i	$0.488639\pi$
$588$	0	0
$589$	−2077.93	−0.145364
$590$	−3063.76	−0.213785
$591$	−4364.03	−0.303744
$592$	4764.74	0.330793
$593$	−3831.39	−0.265323	−0.132661	−	0.991161i	$-0.542352\pi$
$593$	−3831.39	−0.265323	−0.132661	+	0.991161i	$0.542352\pi$
$594$	9069.95	0.626506
$595$	0	0
$596$	−15168.4	−1.04249
$597$	5312.50	0.364198
$598$	−57173.4	−3.90969
$599$	−16703.5	−1.13938	−0.569688	−	0.821861i	$-0.692936\pi$
$599$	−16703.5	−1.13938	−0.569688	+	0.821861i	$0.692936\pi$
$600$	−2809.54	−0.191165
$601$	−17781.6	−1.20686	−0.603432	−	0.797414i	$-0.706201\pi$
$601$	−17781.6	−1.20686	−0.603432	+	0.797414i	$0.706201\pi$
$602$	0	0
$603$	−17429.0	−1.17705
$604$	40442.9	2.72450
$605$	−5774.69	−0.388057
$606$	−3428.65	−0.229834
$607$	−7610.08	−0.508869	−0.254435	−	0.967090i	$-0.581889\pi$
$607$	−7610.08	−0.508869	−0.254435	+	0.967090i	$0.581889\pi$
$608$	−1648.34	−0.109949
$609$	0	0
$610$	−13554.6	−0.899689
$611$	−46162.4	−3.05651
$612$	3177.04	0.209843
$613$	4207.29	0.277212	0.138606	−	0.990348i	$-0.455738\pi$
$613$	4207.29	0.277212	0.138606	+	0.990348i	$0.455738\pi$
$614$	19363.3	1.27270
$615$	2297.81	0.150661
$616$	0	0
$617$	28539.4	1.86216	0.931082	−	0.364810i	$-0.118866\pi$
$617$	28539.4	1.86216	0.931082	+	0.364810i	$0.118866\pi$
$618$	11405.7	0.742402
$619$	−16799.9	−1.09086	−0.545432	−	0.838155i	$-0.683634\pi$
$619$	−16799.9	−1.09086	−0.545432	+	0.838155i	$0.683634\pi$
$620$	−21197.6	−1.37309
$621$	−14700.8	−0.949958
$622$	28676.0	1.84856
$623$	0	0
$624$	2539.38	0.162911
$625$	1458.39	0.0933369
$626$	87.3288	0.00557565
$627$	−309.256	−0.0196978
$628$	44270.9	2.81306
$629$	3380.10	0.214266
$630$	0	0
$631$	−16207.1	−1.02249	−0.511247	−	0.859434i	$-0.670816\pi$
$631$	−16207.1	−1.02249	−0.511247	+	0.859434i	$0.670816\pi$
$632$	10934.4	0.688210
$633$	1197.50	0.0751919
$634$	−36664.9	−2.29677
$635$	4931.09	0.308164
$636$	−7351.83	−0.458363
$637$	0	0
$638$	2740.51	0.170060
$639$	11900.8	0.736756
$640$	−13085.5	−0.808202
$641$	10697.0	0.659133	0.329567	−	0.944132i	$-0.393097\pi$
$641$	10697.0	0.659133	0.329567	+	0.944132i	$0.393097\pi$
$642$	4265.29	0.262208
$643$	−7901.34	−0.484601	−0.242300	−	0.970201i	$-0.577902\pi$
$643$	−7901.34	−0.484601	−0.242300	+	0.970201i	$0.577902\pi$
$644$	0	0
$645$	2591.72	0.158216
$646$	−389.115	−0.0236989
$647$	312.370	0.0189807	0.00949036	−	0.999955i	$-0.496979\pi$
$647$	312.370	0.0189807	0.00949036	+	0.999955i	$0.496979\pi$
$648$	8020.01	0.486197
$649$	2217.17	0.134101
$650$	30749.3	1.85552
$651$	0	0
$652$	−23713.7	−1.42439
$653$	13732.3	0.822950	0.411475	−	0.911421i	$-0.365014\pi$
$653$	13732.3	0.822950	0.411475	+	0.911421i	$0.365014\pi$
$654$	10863.9	0.649559
$655$	1654.02	0.0986684
$656$	−2949.35	−0.175538
$657$	−8.76293	−0.000520357 0
$658$	0	0
$659$	19869.0	1.17449	0.587244	−	0.809410i	$-0.300213\pi$
$659$	19869.0	1.17449	0.587244	+	0.809410i	$0.300213\pi$
$660$	−3154.82	−0.186063
$661$	11047.2	0.650057	0.325029	−	0.945704i	$-0.394626\pi$
$661$	11047.2	0.650057	0.325029	+	0.945704i	$0.394626\pi$
$662$	10619.5	0.623470
$663$	1801.43	0.105523
$664$	−14165.5	−0.827902
$665$	0	0
$666$	31187.7	1.81456
$667$	−4441.90	−0.257858
$668$	19304.5	1.11814
$669$	−259.983	−0.0150247
$670$	21776.3	1.25566
$671$	9809.12	0.564347
$672$	0	0
$673$	−25673.8	−1.47051	−0.735253	−	0.677793i	$-0.762937\pi$
$673$	−25673.8	−1.47051	−0.735253	+	0.677793i	$0.762937\pi$
$674$	−22296.2	−1.27421
$675$	7906.46	0.450844
$676$	57235.6	3.25646
$677$	−4268.79	−0.242338	−0.121169	−	0.992632i	$-0.538664\pi$
$677$	−4268.79	−0.242338	−0.121169	+	0.992632i	$0.538664\pi$
$678$	2857.25	0.161847
$679$	0	0
$680$	−1323.61	−0.0746443
$681$	−7965.79	−0.448238
$682$	25565.2	1.43540
$683$	7370.85	0.412940	0.206470	−	0.978453i	$-0.433802\pi$
$683$	7370.85	0.412940	0.206470	+	0.978453i	$0.433802\pi$
$684$	−2154.33	−0.120428
$685$	−16174.4	−0.902178
$686$	0	0
$687$	2578.04	0.143171
$688$	−3326.60	−0.184339
$689$	26830.0	1.48351
$690$	8521.80	0.470173
$691$	−2112.00	−0.116272	−0.0581361	−	0.998309i	$-0.518516\pi$
$691$	−2112.00	−0.116272	−0.0581361	+	0.998309i	$0.518516\pi$
$692$	−53357.5	−2.93114
$693$	0	0
$694$	−9051.97	−0.495113
$695$	−2762.32	−0.150764
$696$	−989.059	−0.0538652
$697$	−2092.27	−0.113702
$698$	11860.6	0.643169
$699$	4145.08	0.224294
$700$	0	0
$701$	20945.5	1.12853	0.564266	−	0.825593i	$-0.309159\pi$
$701$	20945.5	1.12853	0.564266	+	0.825593i	$0.309159\pi$
$702$	35825.6	1.92614
$703$	−2292.02	−0.122966
$704$	17580.7	0.941192
$705$	6880.58	0.367571
$706$	7733.71	0.412269
$707$	0	0
$708$	−2399.73	−0.127383
$709$	7826.11	0.414550	0.207275	−	0.978283i	$-0.433541\pi$
$709$	7826.11	0.414550	0.207275	+	0.978283i	$0.433541\pi$
$710$	−14869.2	−0.785958
$711$	−14276.5	−0.753037
$712$	6121.51	0.322210
$713$	−41436.8	−2.17646
$714$	0	0
$715$	11513.3	0.602200
$716$	17539.1	0.915459
$717$	−8597.91	−0.447831
$718$	30749.2	1.59826
$719$	−23373.7	−1.21237	−0.606183	−	0.795325i	$-0.707300\pi$
$719$	−23373.7	−1.21237	−0.606183	+	0.795325i	$0.707300\pi$
$720$	2436.09	0.126094
$721$	0	0
$722$	−30412.1	−1.56762
$723$	−3716.71	−0.191184
$724$	−45483.2	−2.33476
$725$	2388.96	0.122378
$726$	−7537.98	−0.385345
$727$	−31240.8	−1.59375	−0.796875	−	0.604145i	$-0.793515\pi$
$727$	−31240.8	−1.59375	−0.796875	+	0.604145i	$0.793515\pi$
$728$	0	0
$729$	−5533.38	−0.281125
$730$	10.9487	0.000555107 0
$731$	−2359.88	−0.119403
$732$	−10616.8	−0.536078
$733$	4426.59	0.223056	0.111528	−	0.993761i	$-0.464426\pi$
$733$	4426.59	0.223056	0.111528	+	0.993761i	$0.464426\pi$
$734$	33252.7	1.67218
$735$	0	0
$736$	−32870.2	−1.64621
$737$	−15758.9	−0.787636
$738$	−19305.0	−0.962911
$739$	−32119.5	−1.59883	−0.799414	−	0.600781i	$-0.794856\pi$
$739$	−32119.5	−1.59883	−0.799414	+	0.600781i	$0.794856\pi$
$740$	−23381.7	−1.16152
$741$	−1221.54	−0.0605593
$742$	0	0
$743$	−19215.0	−0.948763	−0.474382	−	0.880319i	$-0.657328\pi$
$743$	−19215.0	−0.948763	−0.474382	+	0.880319i	$0.657328\pi$
$744$	−9226.55	−0.454653
$745$	−8250.91	−0.405758
$746$	6250.02	0.306742
$747$	18495.0	0.905888
$748$	2872.61	0.140419
$749$	0	0
$750$	−11537.8	−0.561735
$751$	3593.57	0.174609	0.0873045	−	0.996182i	$-0.472175\pi$
$751$	3593.57	0.174609	0.0873045	+	0.996182i	$0.472175\pi$
$752$	−8831.55	−0.428263
$753$	−52.2377	−0.00252808
$754$	10824.8	0.522835
$755$	21999.1	1.06043
$756$	0	0
$757$	−32956.7	−1.58234	−0.791169	−	0.611598i	$-0.790527\pi$
$757$	−32956.7	−1.58234	−0.791169	+	0.611598i	$0.790527\pi$
$758$	31349.4	1.50219
$759$	−6167.01	−0.294925
$760$	897.532	0.0428381
$761$	−15689.7	−0.747373	−0.373687	−	0.927555i	$-0.621906\pi$
$761$	−15689.7	−0.747373	−0.373687	+	0.927555i	$0.621906\pi$
$762$	6436.80	0.306011
$763$	0	0
$764$	−57394.9	−2.71790
$765$	1728.16	0.0816756
$766$	52455.0	2.47425
$767$	8757.64	0.412282
$768$	−4397.69	−0.206625
$769$	−2134.77	−0.100106	−0.0500532	−	0.998747i	$-0.515939\pi$
$769$	−2134.77	−0.100106	−0.0500532	+	0.998747i	$0.515939\pi$
$770$	0	0
$771$	−8495.25	−0.396821
$772$	−42694.5	−1.99043
$773$	−14780.2	−0.687721	−0.343861	−	0.939021i	$-0.611735\pi$
$773$	−14780.2	−0.687721	−0.343861	+	0.939021i	$0.611735\pi$
$774$	−21774.3	−1.01119
$775$	22285.7	1.03294
$776$	−10765.6	−0.498017
$777$	0	0
$778$	−19531.5	−0.900049
$779$	1418.75	0.0652530
$780$	−12461.3	−0.572035
$781$	10760.4	0.493007
$782$	−7759.49	−0.354832
$783$	2783.36	0.127036
$784$	0	0
$785$	24081.3	1.09490
$786$	2159.07	0.0979790
$787$	−35525.7	−1.60909	−0.804545	−	0.593892i	$-0.797591\pi$
$787$	−35525.7	−1.60909	−0.804545	+	0.593892i	$0.797591\pi$
$788$	−27487.6	−1.24265
$789$	8843.53	0.399034
$790$	17837.4	0.803326
$791$	0	0
$792$	8838.07	0.396524
$793$	38745.3	1.73504
$794$	−7302.21	−0.326380
$795$	−3999.05	−0.178405
$796$	33461.7	1.48997
$797$	−2190.00	−0.0973321	−0.0486660	−	0.998815i	$-0.515497\pi$
$797$	−2190.00	−0.0973321	−0.0486660	+	0.998815i	$0.515497\pi$
$798$	0	0
$799$	−6265.09	−0.277400
$800$	17678.4	0.781281
$801$	−7992.50	−0.352561
$802$	22490.0	0.990210
$803$	−7.92326	−0.000348202 0
$804$	17056.6	0.748182
$805$	0	0
$806$	100981.	4.41302
$807$	447.830	0.0195345
$808$	−7201.07	−0.313531
$809$	21464.6	0.932824	0.466412	−	0.884568i	$-0.345546\pi$
$809$	21464.6	0.932824	0.466412	+	0.884568i	$0.345546\pi$
$810$	13083.1	0.567523
$811$	32288.8	1.39804	0.699021	−	0.715101i	$-0.253620\pi$
$811$	32288.8	1.39804	0.699021	+	0.715101i	$0.253620\pi$
$812$	0	0
$813$	−7271.52	−0.313682
$814$	28199.3	1.21423
$815$	−12899.2	−0.554403
$816$	344.641	0.0147853
$817$	1600.22	0.0685248
$818$	11168.4	0.477377
$819$	0	0
$820$	14473.2	0.616371
$821$	−40334.4	−1.71459	−0.857296	−	0.514825i	$-0.827857\pi$
$821$	−40334.4	−1.71459	−0.857296	+	0.514825i	$0.827857\pi$
$822$	−21113.2	−0.895874
$823$	8188.53	0.346822	0.173411	−	0.984850i	$-0.444521\pi$
$823$	8188.53	0.346822	0.173411	+	0.984850i	$0.444521\pi$
$824$	23955.0	1.01276
$825$	3316.77	0.139970
$826$	0	0
$827$	−7630.74	−0.320855	−0.160427	−	0.987048i	$-0.551287\pi$
$827$	−7630.74	−0.320855	−0.160427	+	0.987048i	$0.551287\pi$
$828$	−42960.4	−1.80311
$829$	−12637.7	−0.529462	−0.264731	−	0.964322i	$-0.585283\pi$
$829$	−12637.7	−0.529462	−0.264731	+	0.964322i	$0.585283\pi$
$830$	−23108.3	−0.966385
$831$	−3858.21	−0.161059
$832$	69442.7	2.89362
$833$	0	0
$834$	−3605.79	−0.149710
$835$	10500.8	0.435203
$836$	−1947.90	−0.0805857
$837$	25964.8	1.07225
$838$	−57735.6	−2.38000
$839$	−24059.1	−0.990005	−0.495002	−	0.868892i	$-0.664833\pi$
$839$	−24059.1	−0.990005	−0.495002	+	0.868892i	$0.664833\pi$
$840$	0	0
$841$	841.000	0.0344828
$842$	−17975.8	−0.735731
$843$	10388.4	0.424430
$844$	7542.67	0.307618
$845$	31133.5	1.26749
$846$	−57807.1	−2.34923
$847$	0	0
$848$	5132.97	0.207862
$849$	−9578.51	−0.387201
$850$	4173.24	0.168401
$851$	−45706.2	−1.84111
$852$	−11646.5	−0.468311
$853$	18588.4	0.746138	0.373069	−	0.927804i	$-0.378305\pi$
$853$	18588.4	0.746138	0.373069	+	0.927804i	$0.378305\pi$
$854$	0	0
$855$	−1171.86	−0.0468733
$856$	8958.25	0.357695
$857$	−28616.2	−1.14062	−0.570310	−	0.821430i	$-0.693177\pi$
$857$	−28616.2	−1.14062	−0.570310	+	0.821430i	$0.693177\pi$
$858$	15028.9	0.597993
$859$	31968.9	1.26981	0.634904	−	0.772591i	$-0.281040\pi$
$859$	31968.9	1.26981	0.634904	+	0.772591i	$0.281040\pi$
$860$	16324.4	0.647276
$861$	0	0
$862$	39217.9	1.54961
$863$	15417.8	0.608145	0.304072	−	0.952649i	$-0.401654\pi$
$863$	15417.8	0.608145	0.304072	+	0.952649i	$0.401654\pi$
$864$	20596.9	0.811019
$865$	−29024.0	−1.14086
$866$	−20108.9	−0.789062
$867$	−9117.18	−0.357135
$868$	0	0
$869$	−12908.5	−0.503902
$870$	−1613.46	−0.0628752
$871$	−62246.7	−2.42153
$872$	22817.0	0.886104
$873$	14056.0	0.544928
$874$	5261.67	0.203637
$875$	0	0
$876$	8.57568	0.000330759 0
$877$	−41961.0	−1.61565	−0.807824	−	0.589424i	$-0.799355\pi$
$877$	−41961.0	−1.61565	−0.807824	+	0.589424i	$0.799355\pi$
$878$	32722.6	1.25778
$879$	−11738.5	−0.450430
$880$	2202.67	0.0843772
$881$	22884.6	0.875145	0.437573	−	0.899183i	$-0.355838\pi$
$881$	22884.6	0.875145	0.437573	+	0.899183i	$0.355838\pi$
$882$	0	0
$883$	29611.7	1.12855	0.564277	−	0.825585i	$-0.309155\pi$
$883$	29611.7	1.12855	0.564277	+	0.825585i	$0.309155\pi$
$884$	11346.6	0.431706
$885$	−1305.34	−0.0495803
$886$	−57251.1	−2.17087
$887$	−27117.7	−1.02652	−0.513259	−	0.858234i	$-0.671562\pi$
$887$	−27117.7	−1.02652	−0.513259	+	0.858234i	$0.671562\pi$
$888$	−10177.2	−0.384600
$889$	0	0
$890$	9986.06	0.376105
$891$	−9467.91	−0.355990
$892$	−1637.54	−0.0614675
$893$	4248.32	0.159199
$894$	−10770.3	−0.402923
$895$	9540.48	0.356316
$896$	0	0
$897$	−24359.2	−0.906724
$898$	28677.8	1.06569
$899$	7845.36	0.291054
$900$	23105.1	0.855746
$901$	3641.32	0.134639
$902$	−17455.2	−0.644341
$903$	0	0
$904$	6001.00	0.220786
$905$	−24740.7	−0.908740
$906$	28716.5	1.05302
$907$	10010.9	0.366491	0.183245	−	0.983067i	$-0.441340\pi$
$907$	10010.9	0.366491	0.183245	+	0.983067i	$0.441340\pi$
$908$	−50173.9	−1.83379
$909$	9402.02	0.343064
$910$	0	0
$911$	40394.1	1.46906	0.734532	−	0.678575i	$-0.237402\pi$
$911$	40394.1	1.46906	0.734532	+	0.678575i	$0.237402\pi$
$912$	−233.699	−0.00848525
$913$	16722.8	0.606183
$914$	−9630.44	−0.348519
$915$	−5775.06	−0.208653
$916$	16238.2	0.585725
$917$	0	0
$918$	4862.20	0.174811
$919$	2392.98	0.0858945	0.0429472	−	0.999077i	$-0.486325\pi$
$919$	2392.98	0.0858945	0.0429472	+	0.999077i	$0.486325\pi$
$920$	17898.1	0.641393
$921$	8249.89	0.295161
$922$	8276.32	0.295625
$923$	42502.9	1.51571
$924$	0	0
$925$	24581.9	0.873781
$926$	8461.87	0.300296
$927$	−31276.7	−1.10816
$928$	6223.42	0.220144
$929$	21920.3	0.774148	0.387074	−	0.922049i	$-0.373486\pi$
$929$	21920.3	0.774148	0.387074	+	0.922049i	$0.373486\pi$
$930$	−15051.3	−0.530702
$931$	0	0
$932$	26108.5	0.917608
$933$	12217.7	0.428712
$934$	16724.0	0.585894
$935$	1562.57	0.0546540
$936$	34909.7	1.21908
$937$	−4891.90	−0.170556	−0.0852782	−	0.996357i	$-0.527178\pi$
$937$	−4891.90	−0.170556	−0.0852782	+	0.996357i	$0.527178\pi$
$938$	0	0
$939$	37.2072	0.00129309
$940$	43338.5	1.50377
$941$	40152.3	1.39100	0.695499	−	0.718527i	$-0.255183\pi$
$941$	40152.3	1.39100	0.695499	+	0.718527i	$0.255183\pi$
$942$	31434.5	1.08725
$943$	28291.9	0.977001
$944$	1675.47	0.0577668
$945$	0	0
$946$	−19687.9	−0.676648
$947$	−16057.5	−0.551002	−0.275501	−	0.961301i	$-0.588844\pi$
$947$	−16057.5	−0.551002	−0.275501	+	0.961301i	$0.588844\pi$
$948$	13971.4	0.478660
$949$	−31.2963	−0.00107052
$950$	−2829.85	−0.0966448
$951$	−15621.4	−0.532659
$952$	0	0
$953$	−21912.3	−0.744815	−0.372408	−	0.928069i	$-0.621468\pi$
$953$	−21912.3	−0.744815	−0.372408	+	0.928069i	$0.621468\pi$
$954$	33598.0	1.14023
$955$	−31220.2	−1.05787
$956$	−54155.4	−1.83212
$957$	1167.62	0.0394397
$958$	32470.7	1.09507
$959$	0	0
$960$	−10350.6	−0.347982
$961$	43395.3	1.45666
$962$	111385.	3.73306
$963$	−11696.3	−0.391388
$964$	−23410.3	−0.782152
$965$	−23223.8	−0.774717
$966$	0	0
$967$	17618.1	0.585895	0.292948	−	0.956129i	$-0.405364\pi$
$967$	17618.1	0.585895	0.292948	+	0.956129i	$0.405364\pi$
$968$	−15831.8	−0.525674
$969$	−165.786	−0.00549619
$970$	−17561.9	−0.581319
$971$	−24152.9	−0.798252	−0.399126	−	0.916896i	$-0.630686\pi$
$971$	−24152.9	−0.798252	−0.399126	+	0.916896i	$0.630686\pi$
$972$	41349.6	1.36449
$973$	0	0
$974$	21272.4	0.699805
$975$	13101.0	0.430325
$976$	7412.56	0.243105
$977$	−43754.7	−1.43279	−0.716395	−	0.697695i	$-0.754209\pi$
$977$	−43754.7	−1.43279	−0.716395	+	0.697695i	$0.754209\pi$
$978$	−16837.9	−0.550529
$979$	−7226.66	−0.235919
$980$	0	0
$981$	−29790.9	−0.969572
$982$	−8979.74	−0.291808
$983$	51651.4	1.67591	0.837957	−	0.545736i	$-0.183750\pi$
$983$	51651.4	1.67591	0.837957	+	0.545736i	$0.183750\pi$
$984$	6299.64	0.204091
$985$	−14952.0	−0.483665
$986$	1469.13	0.0474510
$987$	0	0
$988$	−7694.08	−0.247754
$989$	31910.7	1.02599
$990$	14417.6	0.462850
$991$	23894.0	0.765911	0.382956	−	0.923767i	$-0.374906\pi$
$991$	23894.0	0.765911	0.382956	+	0.923767i	$0.374906\pi$
$992$	58055.8	1.85814
$993$	4524.51	0.144593
$994$	0	0
$995$	18201.6	0.579929
$996$	−18099.8	−0.575818
$997$	−5951.47	−0.189052	−0.0945261	−	0.995522i	$-0.530134\pi$
$997$	−5951.47	−0.189052	−0.0945261	+	0.995522i	$0.530134\pi$
$998$	−40039.1	−1.26995
$999$	28640.1	0.907040

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1421.4.a.e.1.5		5
7.6	odd	2		29.4.a.b.1.5	✓	5
21.20	even	2		261.4.a.f.1.1		5
28.27	even	2		464.4.a.l.1.4		5
35.34	odd	2		725.4.a.c.1.1		5
56.13	odd	2		1856.4.a.y.1.4		5
56.27	even	2		1856.4.a.bb.1.2		5
203.202	odd	2		841.4.a.b.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.4.a.b.1.5	✓	5	7.6	odd	2
261.4.a.f.1.1		5	21.20	even	2
464.4.a.l.1.4		5	28.27	even	2
725.4.a.c.1.1		5	35.34	odd	2
841.4.a.b.1.1		5	203.202	odd	2
1421.4.a.e.1.5		5	1.1	even	1	trivial
1856.4.a.y.1.4		5	56.13	odd	2
1856.4.a.bb.1.2		5	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:	\( N \)	\(=\)	\( 1421 = 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1421.a (trivial)

\(f(q)\)	\(=\)	\(q+4.47236 q^{2} +1.90549 q^{3} +12.0020 q^{4} +6.52855 q^{5} +8.52204 q^{6} +17.8986 q^{8} -23.3691 q^{9} +O(q^{10})\)	\(q+4.47236 q^{2} +1.90549 q^{3} +12.0020 q^{4} +6.52855 q^{5} +8.52204 q^{6} +17.8986 q^{8} -23.3691 q^{9} +29.1981 q^{10} -21.1299 q^{11} +22.8697 q^{12} -83.4615 q^{13} +12.4401 q^{15} -15.9674 q^{16} -11.3273 q^{17} -104.515 q^{18} +7.68096 q^{19} +78.3559 q^{20} -94.5005 q^{22} +153.169 q^{23} +34.1055 q^{24} -82.3780 q^{25} -373.270 q^{26} -95.9778 q^{27} -29.0000 q^{29} +55.6366 q^{30} -270.530 q^{31} -214.601 q^{32} -40.2628 q^{33} -50.6597 q^{34} -280.477 q^{36} -298.404 q^{37} +34.3520 q^{38} -159.035 q^{39} +116.852 q^{40} +184.710 q^{41} +208.337 q^{43} -253.602 q^{44} -152.566 q^{45} +685.028 q^{46} +553.098 q^{47} -30.4258 q^{48} -368.424 q^{50} -21.5840 q^{51} -1001.71 q^{52} -321.465 q^{53} -429.248 q^{54} -137.948 q^{55} +14.6360 q^{57} -129.699 q^{58} -104.930 q^{59} +149.306 q^{60} -464.230 q^{61} -1209.91 q^{62} -832.032 q^{64} -544.883 q^{65} -180.070 q^{66} +745.813 q^{67} -135.950 q^{68} +291.862 q^{69} -509.252 q^{71} -418.273 q^{72} +0.374979 q^{73} -1334.57 q^{74} -156.970 q^{75} +92.1871 q^{76} -711.262 q^{78} +610.912 q^{79} -104.244 q^{80} +448.081 q^{81} +826.092 q^{82} -791.431 q^{83} -73.9507 q^{85} +931.757 q^{86} -55.2592 q^{87} -378.194 q^{88} +342.011 q^{89} -682.333 q^{90} +1838.34 q^{92} -515.491 q^{93} +2473.65 q^{94} +50.1455 q^{95} -408.919 q^{96} -601.476 q^{97} +493.787 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 8 q^{3} + 26 q^{4} - 10 q^{5} - 34 q^{6} - 84 q^{8} + 33 q^{9}+O(q^{10}) \) 5 * q - 8 * q^3 + 26 * q^4 - 10 * q^5 - 34 * q^6 - 84 * q^8 + 33 * q^9	\( 5 q - 8 q^{3} + 26 q^{4} - 10 q^{5} - 34 q^{6} - 84 q^{8} + 33 q^{9} + 64 q^{10} + 12 q^{11} + 224 q^{12} - 14 q^{13} - 74 q^{15} + 146 q^{16} - 66 q^{17} - 108 q^{18} - 214 q^{19} - 6 q^{20} - 98 q^{22} + 164 q^{23} - 314 q^{24} + 207 q^{25} - 56 q^{26} - 362 q^{27} - 145 q^{29} - 234 q^{30} - 420 q^{31} - 652 q^{32} + 576 q^{33} - 204 q^{34} - 260 q^{36} + 378 q^{37} + 496 q^{38} - 374 q^{39} + 80 q^{40} + 1158 q^{41} - 204 q^{43} + 784 q^{44} + 1506 q^{45} + 580 q^{46} - 248 q^{47} + 1880 q^{48} + 908 q^{50} + 228 q^{51} - 1482 q^{52} - 554 q^{53} - 918 q^{54} - 546 q^{55} + 44 q^{57} - 440 q^{59} + 636 q^{60} - 618 q^{61} - 1250 q^{62} + 2594 q^{64} - 1656 q^{65} - 2940 q^{66} + 1164 q^{67} - 356 q^{68} + 1968 q^{69} - 692 q^{71} - 2648 q^{72} + 1950 q^{73} - 1832 q^{74} - 3074 q^{75} - 1376 q^{76} - 1302 q^{78} + 272 q^{79} + 890 q^{80} + 1801 q^{81} - 92 q^{82} - 512 q^{83} - 1628 q^{85} + 2446 q^{86} + 232 q^{87} - 6954 q^{88} - 866 q^{89} + 2200 q^{90} + 3468 q^{92} - 40 q^{93} + 5942 q^{94} + 2244 q^{95} - 7386 q^{96} - 1562 q^{97} - 238 q^{99}+O(q^{100}) \) 5 * q - 8 * q^3 + 26 * q^4 - 10 * q^5 - 34 * q^6 - 84 * q^8 + 33 * q^9 + 64 * q^10 + 12 * q^11 + 224 * q^12 - 14 * q^13 - 74 * q^15 + 146 * q^16 - 66 * q^17 - 108 * q^18 - 214 * q^19 - 6 * q^20 - 98 * q^22 + 164 * q^23 - 314 * q^24 + 207 * q^25 - 56 * q^26 - 362 * q^27 - 145 * q^29 - 234 * q^30 - 420 * q^31 - 652 * q^32 + 576 * q^33 - 204 * q^34 - 260 * q^36 + 378 * q^37 + 496 * q^38 - 374 * q^39 + 80 * q^40 + 1158 * q^41 - 204 * q^43 + 784 * q^44 + 1506 * q^45 + 580 * q^46 - 248 * q^47 + 1880 * q^48 + 908 * q^50 + 228 * q^51 - 1482 * q^52 - 554 * q^53 - 918 * q^54 - 546 * q^55 + 44 * q^57 - 440 * q^59 + 636 * q^60 - 618 * q^61 - 1250 * q^62 + 2594 * q^64 - 1656 * q^65 - 2940 * q^66 + 1164 * q^67 - 356 * q^68 + 1968 * q^69 - 692 * q^71 - 2648 * q^72 + 1950 * q^73 - 1832 * q^74 - 3074 * q^75 - 1376 * q^76 - 1302 * q^78 + 272 * q^79 + 890 * q^80 + 1801 * q^81 - 92 * q^82 - 512 * q^83 - 1628 * q^85 + 2446 * q^86 + 232 * q^87 - 6954 * q^88 - 866 * q^89 + 2200 * q^90 + 3468 * q^92 - 40 * q^93 + 5942 * q^94 + 2244 * q^95 - 7386 * q^96 - 1562 * q^97 - 238 * q^99

Introduction

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