LMFDB - Embedded newform 1078.4.a.v.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,4,Mod(1,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, 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("1078.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1078.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:	$63.6040589862$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 105x^{3} + 196x^{2} + 2156x - 3381 $ x^5 - x^4 - 105x^3 + 196x^2 + 2156*x - 3381
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$6.37816$ of defining polynomial
Character	$\chi$	$=$	1078.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} +6.37816 q^{3} +4.00000 q^{4} -17.2424 q^{5} -12.7563 q^{6} -8.00000 q^{8} +13.6809 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +6.37816 q^{3} +4.00000 q^{4} -17.2424 q^{5} -12.7563 q^{6} -8.00000 q^{8} +13.6809 q^{9} +34.4848 q^{10} +11.0000 q^{11} +25.5126 q^{12} +45.7422 q^{13} -109.975 q^{15} +16.0000 q^{16} -67.2619 q^{17} -27.3619 q^{18} +98.2710 q^{19} -68.9696 q^{20} -22.0000 q^{22} +9.11089 q^{23} -51.0253 q^{24} +172.301 q^{25} -91.4844 q^{26} -84.9511 q^{27} -8.89814 q^{29} +219.950 q^{30} -219.310 q^{31} -32.0000 q^{32} +70.1598 q^{33} +134.524 q^{34} +54.7238 q^{36} -86.5420 q^{37} -196.542 q^{38} +291.751 q^{39} +137.939 q^{40} +21.1006 q^{41} +499.901 q^{43} +44.0000 q^{44} -235.892 q^{45} -18.2218 q^{46} +171.289 q^{47} +102.051 q^{48} -344.601 q^{50} -429.007 q^{51} +182.969 q^{52} -301.223 q^{53} +169.902 q^{54} -189.666 q^{55} +626.788 q^{57} +17.7963 q^{58} +503.472 q^{59} -439.899 q^{60} -461.964 q^{61} +438.620 q^{62} +64.0000 q^{64} -788.706 q^{65} -140.320 q^{66} -208.991 q^{67} -269.048 q^{68} +58.1107 q^{69} -1102.50 q^{71} -109.448 q^{72} -470.798 q^{73} +173.084 q^{74} +1098.96 q^{75} +393.084 q^{76} -583.503 q^{78} -111.260 q^{79} -275.878 q^{80} -911.217 q^{81} -42.2013 q^{82} -1001.87 q^{83} +1159.76 q^{85} -999.803 q^{86} -56.7538 q^{87} -88.0000 q^{88} -936.186 q^{89} +471.785 q^{90} +36.4436 q^{92} -1398.79 q^{93} -342.579 q^{94} -1694.43 q^{95} -204.101 q^{96} -692.904 q^{97} +150.490 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 10 q^{2} + q^{3} + 20 q^{4} - 10 q^{5} - 2 q^{6} - 40 q^{8} + 76 q^{9}+O(q^{10}) $ 5 * q - 10 * q^2 + q^3 + 20 * q^4 - 10 * q^5 - 2 * q^6 - 40 * q^8 + 76 * q^9	\( 5 q - 10 q^{2} + q^{3} + 20 q^{4} - 10 q^{5} - 2 q^{6} - 40 q^{8} + 76 q^{9} + 20 q^{10} + 55 q^{11} + 4 q^{12} - 95 q^{13} - 3 q^{15} + 80 q^{16} - 91 q^{17} - 152 q^{18} - 97 q^{19} - 40 q^{20} - 110 q^{22} + 70 q^{23} - 8 q^{24} - 75 q^{25} + 190 q^{26} - 326 q^{27} + 181 q^{29} + 6 q^{30} - 117 q^{31} - 160 q^{32} + 11 q^{33} + 182 q^{34} + 304 q^{36} - 396 q^{37} + 194 q^{38} - 277 q^{39} + 80 q^{40} - 287 q^{41} + 666 q^{43} + 220 q^{44} + 15 q^{45} - 140 q^{46} + 251 q^{47} + 16 q^{48} + 150 q^{50} - 798 q^{51} - 380 q^{52} + 285 q^{53} + 652 q^{54} - 110 q^{55} + 1898 q^{57} - 362 q^{58} - 198 q^{59} - 12 q^{60} + 54 q^{61} + 234 q^{62} + 320 q^{64} - 2111 q^{65} - 22 q^{66} - 634 q^{67} - 364 q^{68} - 1203 q^{69} + 1921 q^{71} - 608 q^{72} - 936 q^{73} + 792 q^{74} + 1753 q^{75} - 388 q^{76} + 554 q^{78} - 997 q^{79} - 160 q^{80} - 383 q^{81} + 574 q^{82} - 3069 q^{83} + 1081 q^{85} - 1332 q^{86} - 2028 q^{87} - 440 q^{88} + 237 q^{89} - 30 q^{90} + 280 q^{92} - 2266 q^{93} - 502 q^{94} - 891 q^{95} - 32 q^{96} + 1203 q^{97} + 836 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 + q^3 + 20 * q^4 - 10 * q^5 - 2 * q^6 - 40 * q^8 + 76 * q^9 + 20 * q^10 + 55 * q^11 + 4 * q^12 - 95 * q^13 - 3 * q^15 + 80 * q^16 - 91 * q^17 - 152 * q^18 - 97 * q^19 - 40 * q^20 - 110 * q^22 + 70 * q^23 - 8 * q^24 - 75 * q^25 + 190 * q^26 - 326 * q^27 + 181 * q^29 + 6 * q^30 - 117 * q^31 - 160 * q^32 + 11 * q^33 + 182 * q^34 + 304 * q^36 - 396 * q^37 + 194 * q^38 - 277 * q^39 + 80 * q^40 - 287 * q^41 + 666 * q^43 + 220 * q^44 + 15 * q^45 - 140 * q^46 + 251 * q^47 + 16 * q^48 + 150 * q^50 - 798 * q^51 - 380 * q^52 + 285 * q^53 + 652 * q^54 - 110 * q^55 + 1898 * q^57 - 362 * q^58 - 198 * q^59 - 12 * q^60 + 54 * q^61 + 234 * q^62 + 320 * q^64 - 2111 * q^65 - 22 * q^66 - 634 * q^67 - 364 * q^68 - 1203 * q^69 + 1921 * q^71 - 608 * q^72 - 936 * q^73 + 792 * q^74 + 1753 * q^75 - 388 * q^76 + 554 * q^78 - 997 * q^79 - 160 * q^80 - 383 * q^81 + 574 * q^82 - 3069 * q^83 + 1081 * q^85 - 1332 * q^86 - 2028 * q^87 - 440 * q^88 + 237 * q^89 - 30 * q^90 + 280 * q^92 - 2266 * q^93 - 502 * q^94 - 891 * q^95 - 32 * q^96 + 1203 * q^97 + 836 * 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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	6.37816	1.22748	0.613739	−	0.789509i	$-0.289665\pi$
$3$	6.37816	1.22748	0.613739	+	0.789509i	$0.289665\pi$
$4$	4.00000	0.500000
$5$	−17.2424	−1.54221	−0.771104	−	0.636709i	$-0.780295\pi$
$5$	−17.2424	−1.54221	−0.771104	+	0.636709i	$0.780295\pi$
$6$	−12.7563	−0.867958
$7$	0	0
$7$	0	0
$8$	−8.00000	−0.353553
$9$	13.6809	0.506702
$10$	34.4848	1.09051
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	25.5126	0.613739
$13$	45.7422	0.975893	0.487947	−	0.872874i	$-0.337746\pi$
$13$	45.7422	0.975893	0.487947	+	0.872874i	$0.337746\pi$
$14$	0	0
$15$	−109.975	−1.89303
$16$	16.0000	0.250000
$17$	−67.2619	−0.959612	−0.479806	−	0.877375i	$-0.659293\pi$
$17$	−67.2619	−0.959612	−0.479806	+	0.877375i	$0.659293\pi$
$18$	−27.3619	−0.358292
$19$	98.2710	1.18657	0.593287	−	0.804991i	$-0.297830\pi$
$19$	98.2710	1.18657	0.593287	+	0.804991i	$0.297830\pi$
$20$	−68.9696	−0.771104
$21$	0	0
$22$	−22.0000	−0.213201
$23$	9.11089	0.0825979	0.0412990	−	0.999147i	$-0.486850\pi$
$23$	9.11089	0.0825979	0.0412990	+	0.999147i	$0.486850\pi$
$24$	−51.0253	−0.433979
$25$	172.301	1.37840
$26$	−91.4844	−0.690061
$27$	−84.9511	−0.605513
$28$	0	0
$29$	−8.89814	−0.0569773	−0.0284887	−	0.999594i	$-0.509069\pi$
$29$	−8.89814	−0.0569773	−0.0284887	+	0.999594i	$0.509069\pi$
$30$	219.950	1.33857
$31$	−219.310	−1.27062	−0.635310	−	0.772257i	$-0.719128\pi$
$31$	−219.310	−1.27062	−0.635310	+	0.772257i	$0.719128\pi$
$32$	−32.0000	−0.176777
$33$	70.1598	0.370098
$34$	134.524	0.678548
$35$	0	0
$36$	54.7238	0.253351
$37$	−86.5420	−0.384525	−0.192262	−	0.981344i	$-0.561582\pi$
$37$	−86.5420	−0.384525	−0.192262	+	0.981344i	$0.561582\pi$
$38$	−196.542	−0.839035
$39$	291.751	1.19789
$40$	137.939	0.545253
$41$	21.1006	0.0803748	0.0401874	−	0.999192i	$-0.487205\pi$
$41$	21.1006	0.0803748	0.0401874	+	0.999192i	$0.487205\pi$
$42$	0	0
$43$	499.901	1.77289	0.886445	−	0.462835i	$-0.153168\pi$
$43$	499.901	1.77289	0.886445	+	0.462835i	$0.153168\pi$
$44$	44.0000	0.150756
$45$	−235.892	−0.781439
$46$	−18.2218	−0.0584056
$47$	171.289	0.531598	0.265799	−	0.964028i	$-0.414364\pi$
$47$	171.289	0.531598	0.265799	+	0.964028i	$0.414364\pi$
$48$	102.051	0.306869
$49$	0	0
$50$	−344.601	−0.974679
$51$	−429.007	−1.17790
$52$	182.969	0.487947
$53$	−301.223	−0.780683	−0.390342	−	0.920670i	$-0.627643\pi$
$53$	−301.223	−0.780683	−0.390342	+	0.920670i	$0.627643\pi$
$54$	169.902	0.428162
$55$	−189.666	−0.464993
$56$	0	0
$57$	626.788	1.45649
$58$	17.7963	0.0402891
$59$	503.472	1.11096	0.555479	−	0.831531i	$-0.312535\pi$
$59$	503.472	1.11096	0.555479	+	0.831531i	$0.312535\pi$
$60$	−439.899	−0.946513
$61$	−461.964	−0.969647	−0.484823	−	0.874612i	$-0.661116\pi$
$61$	−461.964	−0.969647	−0.484823	+	0.874612i	$0.661116\pi$
$62$	438.620	0.898464
$63$	0	0
$64$	64.0000	0.125000
$65$	−788.706	−1.50503
$66$	−140.320	−0.261699
$67$	−208.991	−0.381080	−0.190540	−	0.981679i	$-0.561024\pi$
$67$	−208.991	−0.381080	−0.190540	+	0.981679i	$0.561024\pi$
$68$	−269.048	−0.479806
$69$	58.1107	0.101387
$70$	0	0
$71$	−1102.50	−1.84285	−0.921425	−	0.388556i	$-0.872974\pi$
$71$	−1102.50	−1.84285	−0.921425	+	0.388556i	$0.872974\pi$
$72$	−109.448	−0.179146
$73$	−470.798	−0.754831	−0.377416	−	0.926044i	$-0.623187\pi$
$73$	−470.798	−0.754831	−0.377416	+	0.926044i	$0.623187\pi$
$74$	173.084	0.271900
$75$	1098.96	1.69196
$76$	393.084	0.593287
$77$	0	0
$78$	−583.503	−0.847034
$79$	−111.260	−0.158452	−0.0792259	−	0.996857i	$-0.525245\pi$
$79$	−111.260	−0.158452	−0.0792259	+	0.996857i	$0.525245\pi$
$80$	−275.878	−0.385552
$81$	−911.217	−1.24996
$82$	−42.2013	−0.0568335
$83$	−1001.87	−1.32493	−0.662464	−	0.749094i	$-0.730489\pi$
$83$	−1001.87	−1.32493	−0.662464	+	0.749094i	$0.730489\pi$
$84$	0	0
$85$	1159.76	1.47992
$86$	−999.803	−1.25362
$87$	−56.7538	−0.0699384
$88$	−88.0000	−0.106600
$89$	−936.186	−1.11501	−0.557503	−	0.830175i	$-0.688240\pi$
$89$	−936.186	−1.11501	−0.557503	+	0.830175i	$0.688240\pi$
$90$	471.785	0.552561
$91$	0	0
$92$	36.4436	0.0412990
$93$	−1398.79	−1.55966
$94$	−342.579	−0.375897
$95$	−1694.43	−1.82994
$96$	−204.101	−0.216989
$97$	−692.904	−0.725297	−0.362648	−	0.931926i	$-0.618127\pi$
$97$	−692.904	−0.725297	−0.362648	+	0.931926i	$0.618127\pi$
$98$	0	0
$99$	150.490	0.152776
$100$	689.202	0.689202
$101$	−1660.05	−1.63546	−0.817730	−	0.575603i	$-0.804768\pi$
$101$	−1660.05	−1.63546	−0.817730	+	0.575603i	$0.804768\pi$
$102$	858.015	0.832903
$103$	1607.82	1.53809	0.769043	−	0.639197i	$-0.220733\pi$
$103$	1607.82	1.53809	0.769043	+	0.639197i	$0.220733\pi$
$104$	−365.938	−0.345030
$105$	0	0
$106$	602.447	0.552027
$107$	−2032.59	−1.83643	−0.918215	−	0.396083i	$-0.870369\pi$
$107$	−2032.59	−1.83643	−0.918215	+	0.396083i	$0.870369\pi$
$108$	−339.804	−0.302756
$109$	1320.27	1.16017	0.580086	−	0.814555i	$-0.303019\pi$
$109$	1320.27	1.16017	0.580086	+	0.814555i	$0.303019\pi$
$110$	379.333	0.328800
$111$	−551.979	−0.471996
$112$	0	0
$113$	125.281	0.104296	0.0521482	−	0.998639i	$-0.483393\pi$
$113$	125.281	0.104296	0.0521482	+	0.998639i	$0.483393\pi$
$114$	−1253.58	−1.02990
$115$	−157.094	−0.127383
$116$	−35.5925	−0.0284887
$117$	625.797	0.494487
$118$	−1006.94	−0.785565
$119$	0	0
$120$	879.799	0.669286
$121$	121.000	0.0909091
$122$	923.928	0.685644
$123$	134.583	0.0986582
$124$	−877.240	−0.635310
$125$	−815.576	−0.583578
$126$	0	0
$127$	−1710.45	−1.19510	−0.597549	−	0.801832i	$-0.703859\pi$
$127$	−1710.45	−1.19510	−0.597549	+	0.801832i	$0.703859\pi$
$128$	−128.000	−0.0883883
$129$	3188.45	2.17618
$130$	1577.41	1.06422
$131$	1249.20	0.833151	0.416576	−	0.909101i	$-0.363230\pi$
$131$	1249.20	0.833151	0.416576	+	0.909101i	$0.363230\pi$
$132$	280.639	0.185049
$133$	0	0
$134$	417.982	0.269464
$135$	1464.76	0.933826
$136$	538.095	0.339274
$137$	2706.79	1.68801	0.844004	−	0.536338i	$-0.180193\pi$
$137$	2706.79	1.68801	0.844004	+	0.536338i	$0.180193\pi$
$138$	−116.221	−0.0716915
$139$	−1281.80	−0.782163	−0.391082	−	0.920356i	$-0.627899\pi$
$139$	−1281.80	−0.782163	−0.391082	+	0.920356i	$0.627899\pi$
$140$	0	0
$141$	1092.51	0.652525
$142$	2204.99	1.30309
$143$	503.164	0.294243
$144$	218.895	0.126675
$145$	153.425	0.0878709
$146$	941.595	0.533746
$147$	0	0
$148$	−346.168	−0.192262
$149$	1533.31	0.843045	0.421522	−	0.906818i	$-0.361496\pi$
$149$	1533.31	0.843045	0.421522	+	0.906818i	$0.361496\pi$
$150$	−2197.92	−1.19640
$151$	58.8282	0.0317045	0.0158522	−	0.999874i	$-0.494954\pi$
$151$	58.8282	0.0317045	0.0158522	+	0.999874i	$0.494954\pi$
$152$	−786.168	−0.419517
$153$	−920.207	−0.486237
$154$	0	0
$155$	3781.43	1.95956
$156$	1167.01	0.598944
$157$	−3709.27	−1.88556	−0.942778	−	0.333421i	$-0.891797\pi$
$157$	−3709.27	−1.88556	−0.942778	+	0.333421i	$0.891797\pi$
$158$	222.519	0.112042
$159$	−1921.25	−0.958272
$160$	551.757	0.272626
$161$	0	0
$162$	1822.43	0.883852
$163$	−108.625	−0.0521973	−0.0260986	−	0.999659i	$-0.508308\pi$
$163$	−108.625	−0.0521973	−0.0260986	+	0.999659i	$0.508308\pi$
$164$	84.4025	0.0401874
$165$	−1209.72	−0.570769
$166$	2003.73	0.936866
$167$	−3283.50	−1.52146	−0.760732	−	0.649066i	$-0.775160\pi$
$167$	−3283.50	−1.52146	−0.760732	+	0.649066i	$0.775160\pi$
$168$	0	0
$169$	−104.649	−0.0476328
$170$	−2319.51	−1.04646
$171$	1344.44	0.601239
$172$	1999.61	0.886445
$173$	−3904.63	−1.71597	−0.857987	−	0.513671i	$-0.828285\pi$
$173$	−3904.63	−1.71597	−0.857987	+	0.513671i	$0.828285\pi$
$174$	113.508	0.0494539
$175$	0	0
$176$	176.000	0.0753778
$177$	3211.23	1.36368
$178$	1872.37	0.788428
$179$	625.063	0.261002	0.130501	−	0.991448i	$-0.458341\pi$
$179$	625.063	0.261002	0.130501	+	0.991448i	$0.458341\pi$
$180$	−943.570	−0.390720
$181$	2153.12	0.884198	0.442099	−	0.896966i	$-0.354234\pi$
$181$	2153.12	0.884198	0.442099	+	0.896966i	$0.354234\pi$
$182$	0	0
$183$	−2946.48	−1.19022
$184$	−72.8871	−0.0292028
$185$	1492.19	0.593017
$186$	2797.59	1.10285
$187$	−739.881	−0.289334
$188$	685.157	0.265799
$189$	0	0
$190$	3388.86	1.29397
$191$	−4382.47	−1.66023	−0.830116	−	0.557590i	$-0.811726\pi$
$191$	−4382.47	−1.66023	−0.830116	+	0.557590i	$0.811726\pi$
$192$	408.202	0.153435
$193$	−1315.95	−0.490797	−0.245399	−	0.969422i	$-0.578919\pi$
$193$	−1315.95	−0.490797	−0.245399	+	0.969422i	$0.578919\pi$
$194$	1385.81	0.512862
$195$	−5030.49	−1.84739
$196$	0	0
$197$	3274.72	1.18433	0.592167	−	0.805815i	$-0.298273\pi$
$197$	3274.72	1.18433	0.592167	+	0.805815i	$0.298273\pi$
$198$	−300.981	−0.108029
$199$	−4660.90	−1.66031	−0.830156	−	0.557531i	$-0.811749\pi$
$199$	−4660.90	−1.66031	−0.830156	+	0.557531i	$0.811749\pi$
$200$	−1378.40	−0.487340
$201$	−1332.98	−0.467767
$202$	3320.10	1.15644
$203$	0	0
$204$	−1716.03	−0.588951
$205$	−363.826	−0.123955
$206$	−3215.63	−1.08759
$207$	124.646	0.0418525
$208$	731.876	0.243973
$209$	1080.98	0.357766
$210$	0	0
$211$	3197.75	1.04333	0.521665	−	0.853151i	$-0.325311\pi$
$211$	3197.75	1.04333	0.521665	+	0.853151i	$0.325311\pi$
$212$	−1204.89	−0.390342
$213$	−7031.91	−2.26206
$214$	4065.18	1.29855
$215$	−8619.50	−2.73416
$216$	679.609	0.214081
$217$	0	0
$218$	−2640.54	−0.820365
$219$	−3002.82	−0.926539
$220$	−758.666	−0.232497
$221$	−3076.71	−0.936479
$222$	1103.96	0.333751
$223$	−1887.58	−0.566822	−0.283411	−	0.958998i	$-0.591466\pi$
$223$	−1887.58	−0.566822	−0.283411	+	0.958998i	$0.591466\pi$
$224$	0	0
$225$	2357.24	0.698440
$226$	−250.563	−0.0737487
$227$	−5218.58	−1.52586	−0.762928	−	0.646484i	$-0.776239\pi$
$227$	−5218.58	−1.52586	−0.762928	+	0.646484i	$0.776239\pi$
$228$	2507.15	0.728247
$229$	1628.17	0.469837	0.234919	−	0.972015i	$-0.424518\pi$
$229$	1628.17	0.469837	0.234919	+	0.972015i	$0.424518\pi$
$230$	314.187	0.0900735
$231$	0	0
$232$	71.1851	0.0201445
$233$	2147.25	0.603737	0.301868	−	0.953350i	$-0.402390\pi$
$233$	2147.25	0.603737	0.301868	+	0.953350i	$0.402390\pi$
$234$	−1251.59	−0.349655
$235$	−2953.44	−0.819835
$236$	2013.89	0.555479
$237$	−709.632	−0.194496
$238$	0	0
$239$	555.544	0.150356	0.0751781	−	0.997170i	$-0.476047\pi$
$239$	555.544	0.150356	0.0751781	+	0.997170i	$0.476047\pi$
$240$	−1759.60	−0.473256
$241$	−5327.31	−1.42391	−0.711955	−	0.702225i	$-0.752190\pi$
$241$	−5327.31	−1.42391	−0.711955	+	0.702225i	$0.752190\pi$
$242$	−242.000	−0.0642824
$243$	−3518.21	−0.928780
$244$	−1847.86	−0.484823
$245$	0	0
$246$	−269.167	−0.0697619
$247$	4495.13	1.15797
$248$	1754.48	0.449232
$249$	−6390.06	−1.62632
$250$	1631.15	0.412652
$251$	5473.69	1.37648	0.688240	−	0.725483i	$-0.258384\pi$
$251$	5473.69	1.37648	0.688240	+	0.725483i	$0.258384\pi$
$252$	0	0
$253$	100.220	0.0249042
$254$	3420.89	0.845062
$255$	7397.12	1.81657
$256$	256.000	0.0625000
$257$	−3195.02	−0.775485	−0.387742	−	0.921768i	$-0.626745\pi$
$257$	−3195.02	−0.775485	−0.387742	+	0.921768i	$0.626745\pi$
$258$	−6376.90	−1.53879
$259$	0	0
$260$	−3154.82	−0.752515
$261$	−121.735	−0.0288705
$262$	−2498.39	−0.589127
$263$	4686.32	1.09875	0.549374	−	0.835577i	$-0.314866\pi$
$263$	4686.32	1.09875	0.549374	+	0.835577i	$0.314866\pi$
$264$	−561.278	−0.130850
$265$	5193.82	1.20398
$266$	0	0
$267$	−5971.14	−1.36864
$268$	−835.965	−0.190540
$269$	3617.95	0.820039	0.410019	−	0.912077i	$-0.365522\pi$
$269$	3617.95	0.820039	0.410019	+	0.912077i	$0.365522\pi$
$270$	−2929.52	−0.660315
$271$	4146.66	0.929489	0.464745	−	0.885445i	$-0.346146\pi$
$271$	4146.66	0.929489	0.464745	+	0.885445i	$0.346146\pi$
$272$	−1076.19	−0.239903
$273$	0	0
$274$	−5413.59	−1.19360
$275$	1895.31	0.415605
$276$	232.443	0.0506936
$277$	5691.81	1.23461	0.617307	−	0.786723i	$-0.288224\pi$
$277$	5691.81	1.23461	0.617307	+	0.786723i	$0.288224\pi$
$278$	2563.60	0.553073
$279$	−3000.37	−0.643826
$280$	0	0
$281$	−4443.74	−0.943385	−0.471693	−	0.881763i	$-0.656357\pi$
$281$	−4443.74	−0.943385	−0.471693	+	0.881763i	$0.656357\pi$
$282$	−2185.02	−0.461405
$283$	6169.69	1.29594	0.647969	−	0.761667i	$-0.275619\pi$
$283$	6169.69	1.29594	0.647969	+	0.761667i	$0.275619\pi$
$284$	−4409.99	−0.921425
$285$	−10807.3	−2.24622
$286$	−1006.33	−0.208061
$287$	0	0
$288$	−437.790	−0.0895731
$289$	−388.836	−0.0791444
$290$	−306.851	−0.0621341
$291$	−4419.46	−0.890286
$292$	−1883.19	−0.377416
$293$	−125.115	−0.0249464	−0.0124732	−	0.999922i	$-0.503970\pi$
$293$	−125.115	−0.0249464	−0.0124732	+	0.999922i	$0.503970\pi$
$294$	0	0
$295$	−8681.07	−1.71333
$296$	692.336	0.135950
$297$	−934.462	−0.182569
$298$	−3066.62	−0.596123
$299$	416.752	0.0806067
$300$	4395.84	0.845980
$301$	0	0
$302$	−117.656	−0.0224184
$303$	−10588.1	−2.00749
$304$	1572.34	0.296643
$305$	7965.38	1.49540
$306$	1840.41	0.343822
$307$	−4396.63	−0.817358	−0.408679	−	0.912678i	$-0.634011\pi$
$307$	−4396.63	−0.817358	−0.408679	+	0.912678i	$0.634011\pi$
$308$	0	0
$309$	10254.9	1.88797
$310$	−7562.86	−1.38562
$311$	−10407.0	−1.89752	−0.948761	−	0.315995i	$-0.897662\pi$
$311$	−10407.0	−1.89752	−0.948761	+	0.315995i	$0.897662\pi$
$312$	−2334.01	−0.423517
$313$	2622.60	0.473604	0.236802	−	0.971558i	$-0.423901\pi$
$313$	2622.60	0.473604	0.236802	+	0.971558i	$0.423901\pi$
$314$	7418.55	1.33329
$315$	0	0
$316$	−445.039	−0.0792259
$317$	5081.47	0.900328	0.450164	−	0.892946i	$-0.351366\pi$
$317$	5081.47	0.900328	0.450164	+	0.892946i	$0.351366\pi$
$318$	3842.50	0.677600
$319$	−97.8795	−0.0171793
$320$	−1103.51	−0.192776
$321$	−12964.2	−2.25418
$322$	0	0
$323$	−6609.89	−1.13865
$324$	−3644.87	−0.624978
$325$	7881.41	1.34518
$326$	217.250	0.0369090
$327$	8420.88	1.42409
$328$	−168.805	−0.0284168
$329$	0	0
$330$	2419.45	0.403594
$331$	−1598.00	−0.265360	−0.132680	−	0.991159i	$-0.542358\pi$
$331$	−1598.00	−0.265360	−0.132680	+	0.991159i	$0.542358\pi$
$332$	−4007.46	−0.662464
$333$	−1183.98	−0.194839
$334$	6566.99	1.07584
$335$	3603.51	0.587704
$336$	0	0
$337$	−5279.54	−0.853398	−0.426699	−	0.904394i	$-0.640324\pi$
$337$	−5279.54	−0.853398	−0.426699	+	0.904394i	$0.640324\pi$
$338$	209.299	0.0336815
$339$	799.066	0.128021
$340$	4639.03	0.739961
$341$	−2412.41	−0.383107
$342$	−2688.88	−0.425140
$343$	0	0
$344$	−3999.21	−0.626811
$345$	−1001.97	−0.156360
$346$	7809.26	1.21338
$347$	−2805.64	−0.434048	−0.217024	−	0.976166i	$-0.569635\pi$
$347$	−2805.64	−0.434048	−0.217024	+	0.976166i	$0.569635\pi$
$348$	−227.015	−0.0349692
$349$	−1798.24	−0.275810	−0.137905	−	0.990445i	$-0.544037\pi$
$349$	−1798.24	−0.275810	−0.137905	+	0.990445i	$0.544037\pi$
$350$	0	0
$351$	−3885.85	−0.590916
$352$	−352.000	−0.0533002
$353$	5298.51	0.798898	0.399449	−	0.916755i	$-0.369201\pi$
$353$	5298.51	0.798898	0.399449	+	0.916755i	$0.369201\pi$
$354$	−6422.45	−0.964264
$355$	19009.7	2.84206
$356$	−3744.74	−0.557503
$357$	0	0
$358$	−1250.13	−0.184556
$359$	−8292.12	−1.21906	−0.609528	−	0.792764i	$-0.708641\pi$
$359$	−8292.12	−1.21906	−0.609528	+	0.792764i	$0.708641\pi$
$360$	1887.14	0.276281
$361$	2798.18	0.407958
$362$	−4306.23	−0.625222
$363$	771.758	0.111589
$364$	0	0
$365$	8117.68	1.16411
$366$	5892.97	0.841613
$367$	−12309.9	−1.75088	−0.875438	−	0.483330i	$-0.839427\pi$
$367$	−12309.9	−1.75088	−0.875438	+	0.483330i	$0.839427\pi$
$368$	145.774	0.0206495
$369$	288.677	0.0407260
$370$	−2984.38	−0.419326
$371$	0	0
$372$	−5595.18	−0.779829
$373$	7605.12	1.05570	0.527852	−	0.849336i	$-0.322997\pi$
$373$	7605.12	1.05570	0.527852	+	0.849336i	$0.322997\pi$
$374$	1479.76	0.204590
$375$	−5201.87	−0.716329
$376$	−1370.31	−0.187948
$377$	−407.021	−0.0556038
$378$	0	0
$379$	4264.11	0.577923	0.288961	−	0.957341i	$-0.406690\pi$
$379$	4264.11	0.577923	0.288961	+	0.957341i	$0.406690\pi$
$380$	−6777.71	−0.914972
$381$	−10909.5	−1.46696
$382$	8764.94	1.17396
$383$	−10579.2	−1.41142	−0.705710	−	0.708501i	$-0.749372\pi$
$383$	−10579.2	−1.41142	−0.705710	+	0.708501i	$0.749372\pi$
$384$	−816.405	−0.108495
$385$	0	0
$386$	2631.89	0.347046
$387$	6839.12	0.898326
$388$	−2771.62	−0.362648
$389$	10055.1	1.31058	0.655288	−	0.755379i	$-0.272547\pi$
$389$	10055.1	1.31058	0.655288	+	0.755379i	$0.272547\pi$
$390$	10061.0	1.30630
$391$	−612.816	−0.0792620
$392$	0	0
$393$	7967.58	1.02267
$394$	−6549.43	−0.837451
$395$	1918.39	0.244366
$396$	601.962	0.0763882
$397$	11276.4	1.42556	0.712778	−	0.701390i	$-0.247437\pi$
$397$	11276.4	1.42556	0.712778	+	0.701390i	$0.247437\pi$
$398$	9321.79	1.17402
$399$	0	0
$400$	2756.81	0.344601
$401$	12016.6	1.49646	0.748228	−	0.663441i	$-0.230905\pi$
$401$	12016.6	1.49646	0.748228	+	0.663441i	$0.230905\pi$
$402$	2665.96	0.330761
$403$	−10031.7	−1.23999
$404$	−6640.21	−0.817730
$405$	15711.6	1.92769
$406$	0	0
$407$	−951.962	−0.115939
$408$	3432.06	0.416451
$409$	2781.52	0.336278	0.168139	−	0.985763i	$-0.446224\pi$
$409$	2781.52	0.336278	0.168139	+	0.985763i	$0.446224\pi$
$410$	727.651	0.0876491
$411$	17264.4	2.07199
$412$	6431.27	0.769043
$413$	0	0
$414$	−249.291	−0.0295942
$415$	17274.6	2.04331
$416$	−1463.75	−0.172515
$417$	−8175.52	−0.960088
$418$	−2161.96	−0.252978
$419$	790.602	0.0921801	0.0460900	−	0.998937i	$-0.485324\pi$
$419$	790.602	0.0921801	0.0460900	+	0.998937i	$0.485324\pi$
$420$	0	0
$421$	231.084	0.0267514	0.0133757	−	0.999911i	$-0.495742\pi$
$421$	231.084	0.0267514	0.0133757	+	0.999911i	$0.495742\pi$
$422$	−6395.51	−0.737745
$423$	2343.40	0.269362
$424$	2409.79	0.276013
$425$	−11589.3	−1.32273
$426$	14063.8	1.59952
$427$	0	0
$428$	−8130.36	−0.918215
$429$	3209.26	0.361177
$430$	17239.0	1.93335
$431$	−13739.2	−1.53549	−0.767743	−	0.640757i	$-0.778620\pi$
$431$	−13739.2	−1.53549	−0.767743	+	0.640757i	$0.778620\pi$
$432$	−1359.22	−0.151378
$433$	79.5912	0.00883350	0.00441675	−	0.999990i	$-0.498594\pi$
$433$	79.5912	0.00883350	0.00441675	+	0.999990i	$0.498594\pi$
$434$	0	0
$435$	978.571	0.107860
$436$	5281.07	0.580086
$437$	895.336	0.0980085
$438$	6005.65	0.655162
$439$	−14180.2	−1.54165	−0.770823	−	0.637049i	$-0.780155\pi$
$439$	−14180.2	−1.54165	−0.770823	+	0.637049i	$0.780155\pi$
$440$	1517.33	0.164400
$441$	0	0
$442$	6153.42	0.662191
$443$	15459.0	1.65797	0.828985	−	0.559271i	$-0.188919\pi$
$443$	15459.0	1.65797	0.828985	+	0.559271i	$0.188919\pi$
$444$	−2207.92	−0.235998
$445$	16142.1	1.71957
$446$	3775.15	0.400804
$447$	9779.70	1.03482
$448$	0	0
$449$	9274.48	0.974811	0.487405	−	0.873176i	$-0.337943\pi$
$449$	9274.48	0.974811	0.487405	+	0.873176i	$0.337943\pi$
$450$	−4714.47	−0.493872
$451$	232.107	0.0242339
$452$	501.126	0.0521482
$453$	375.216	0.0389165
$454$	10437.2	1.07894
$455$	0	0
$456$	−5014.30	−0.514948
$457$	9260.28	0.947872	0.473936	−	0.880559i	$-0.342833\pi$
$457$	9260.28	0.947872	0.473936	+	0.880559i	$0.342833\pi$
$458$	−3256.35	−0.332225
$459$	5713.97	0.581057
$460$	−628.375	−0.0636916
$461$	−7535.30	−0.761288	−0.380644	−	0.924722i	$-0.624298\pi$
$461$	−7535.30	−0.761288	−0.380644	+	0.924722i	$0.624298\pi$
$462$	0	0
$463$	−2247.46	−0.225590	−0.112795	−	0.993618i	$-0.535980\pi$
$463$	−2247.46	−0.225590	−0.112795	+	0.993618i	$0.535980\pi$
$464$	−142.370	−0.0142443
$465$	24118.6	2.40532
$466$	−4294.49	−0.426906
$467$	−2848.26	−0.282231	−0.141115	−	0.989993i	$-0.545069\pi$
$467$	−2848.26	−0.282231	−0.141115	+	0.989993i	$0.545069\pi$
$468$	2503.19	0.247243
$469$	0	0
$470$	5906.88	0.579711
$471$	−23658.3	−2.31448
$472$	−4027.78	−0.392783
$473$	5498.91	0.534546
$474$	1419.26	0.137530
$475$	16932.1	1.63558
$476$	0	0
$477$	−4121.02	−0.395574
$478$	−1111.09	−0.106318
$479$	7631.16	0.727926	0.363963	−	0.931413i	$-0.381423\pi$
$479$	7631.16	0.727926	0.363963	+	0.931413i	$0.381423\pi$
$480$	3519.20	0.334643
$481$	−3958.62	−0.375255
$482$	10654.6	1.00686
$483$	0	0
$484$	484.000	0.0454545
$485$	11947.3	1.11856
$486$	7036.42	0.656746
$487$	15417.6	1.43458	0.717288	−	0.696776i	$-0.245383\pi$
$487$	15417.6	1.43458	0.717288	+	0.696776i	$0.245383\pi$
$488$	3695.71	0.342822
$489$	−692.827	−0.0640710
$490$	0	0
$491$	169.404	0.0155705	0.00778525	−	0.999970i	$-0.497522\pi$
$491$	169.404	0.0155705	0.00778525	+	0.999970i	$0.497522\pi$
$492$	538.333	0.0493291
$493$	598.506	0.0546761
$494$	−8990.26	−0.818808
$495$	−2594.82	−0.235613
$496$	−3508.96	−0.317655
$497$	0	0
$498$	12780.1	1.14998
$499$	5717.15	0.512895	0.256448	−	0.966558i	$-0.417448\pi$
$499$	5717.15	0.512895	0.256448	+	0.966558i	$0.417448\pi$
$500$	−3262.30	−0.291789
$501$	−20942.7	−1.86756
$502$	−10947.4	−0.973318
$503$	−14801.4	−1.31205	−0.656024	−	0.754740i	$-0.727763\pi$
$503$	−14801.4	−1.31205	−0.656024	+	0.754740i	$0.727763\pi$
$504$	0	0
$505$	28623.3	2.52222
$506$	−200.440	−0.0176099
$507$	−667.470	−0.0584682
$508$	−6841.78	−0.597549
$509$	11334.2	0.986995	0.493498	−	0.869747i	$-0.335718\pi$
$509$	11334.2	0.986995	0.493498	+	0.869747i	$0.335718\pi$
$510$	−14794.2	−1.28451
$511$	0	0
$512$	−512.000	−0.0441942
$513$	−8348.22	−0.718486
$514$	6390.03	0.548351
$515$	−27722.6	−2.37205
$516$	12753.8	1.08809
$517$	1884.18	0.160283
$518$	0	0
$519$	−24904.4	−2.10632
$520$	6309.65	0.532108
$521$	10060.3	0.845969	0.422985	−	0.906137i	$-0.360982\pi$
$521$	10060.3	0.845969	0.422985	+	0.906137i	$0.360982\pi$
$522$	243.470	0.0204145
$523$	−11068.9	−0.925447	−0.462724	−	0.886503i	$-0.653128\pi$
$523$	−11068.9	−0.925447	−0.462724	+	0.886503i	$0.653128\pi$
$524$	4996.79	0.416576
$525$	0	0
$526$	−9372.63	−0.776932
$527$	14751.2	1.21930
$528$	1122.56	0.0925246
$529$	−12084.0	−0.993178
$530$	−10387.6	−0.851340
$531$	6887.97	0.562924
$532$	0	0
$533$	965.190	0.0784372
$534$	11942.3	0.967778
$535$	35046.8	2.83216
$536$	1671.93	0.134732
$537$	3986.75	0.320374
$538$	−7235.90	−0.579855
$539$	0	0
$540$	5859.04	0.466913
$541$	2391.97	0.190091	0.0950453	−	0.995473i	$-0.469700\pi$
$541$	2391.97	0.190091	0.0950453	+	0.995473i	$0.469700\pi$
$542$	−8293.32	−0.657248
$543$	13732.9	1.08533
$544$	2152.38	0.169637
$545$	−22764.6	−1.78923
$546$	0	0
$547$	22233.3	1.73790	0.868948	−	0.494904i	$-0.164797\pi$
$547$	22233.3	1.73790	0.868948	+	0.494904i	$0.164797\pi$
$548$	10827.2	0.844004
$549$	−6320.11	−0.491322
$550$	−3790.61	−0.293877
$551$	−874.429	−0.0676078
$552$	−464.886	−0.0358458
$553$	0	0
$554$	−11383.6	−0.873003
$555$	9517.44	0.727915
$556$	−5127.19	−0.391082
$557$	−3649.75	−0.277639	−0.138820	−	0.990318i	$-0.544331\pi$
$557$	−3649.75	−0.277639	−0.138820	+	0.990318i	$0.544331\pi$
$558$	6000.74	0.455254
$559$	22866.6	1.73015
$560$	0	0
$561$	−4719.08	−0.355151
$562$	8887.48	0.667074
$563$	7504.26	0.561753	0.280876	−	0.959744i	$-0.409375\pi$
$563$	7504.26	0.561753	0.280876	+	0.959744i	$0.409375\pi$
$564$	4370.04	0.326262
$565$	−2160.15	−0.160847
$566$	−12339.4	−0.916366
$567$	0	0
$568$	8819.98	0.651546
$569$	−8011.38	−0.590254	−0.295127	−	0.955458i	$-0.595362\pi$
$569$	−8011.38	−0.590254	−0.295127	+	0.955458i	$0.595362\pi$
$570$	21614.7	1.58831
$571$	−11679.1	−0.855964	−0.427982	−	0.903787i	$-0.640775\pi$
$571$	−11679.1	−0.855964	−0.427982	+	0.903787i	$0.640775\pi$
$572$	2012.66	0.147121
$573$	−27952.1	−2.03790
$574$	0	0
$575$	1569.81	0.113853
$576$	875.581	0.0633377
$577$	−5831.24	−0.420724	−0.210362	−	0.977624i	$-0.567464\pi$
$577$	−5831.24	−0.420724	−0.210362	+	0.977624i	$0.567464\pi$
$578$	777.673	0.0559635
$579$	−8393.31	−0.602443
$580$	613.701	0.0439354
$581$	0	0
$582$	8838.91	0.629527
$583$	−3313.46	−0.235385
$584$	3766.38	0.266873
$585$	−10790.2	−0.762601
$586$	250.230	0.0176398
$587$	−1286.10	−0.0904308	−0.0452154	−	0.998977i	$-0.514397\pi$
$587$	−1286.10	−0.0904308	−0.0452154	+	0.998977i	$0.514397\pi$
$588$	0	0
$589$	−21551.8	−1.50769
$590$	17362.1	1.21150
$591$	20886.7	1.45374
$592$	−1384.67	−0.0961312
$593$	15491.0	1.07275	0.536375	−	0.843980i	$-0.319793\pi$
$593$	15491.0	1.07275	0.536375	+	0.843980i	$0.319793\pi$
$594$	1868.92	0.129096
$595$	0	0
$596$	6133.24	0.421522
$597$	−29728.0	−2.03800
$598$	−833.505	−0.0569976
$599$	5945.16	0.405531	0.202765	−	0.979227i	$-0.435007\pi$
$599$	5945.16	0.405531	0.202765	+	0.979227i	$0.435007\pi$
$600$	−8791.69	−0.598199
$601$	−1726.11	−0.117154	−0.0585770	−	0.998283i	$-0.518656\pi$
$601$	−1726.11	−0.117154	−0.0585770	+	0.998283i	$0.518656\pi$
$602$	0	0
$603$	−2859.20	−0.193094
$604$	235.313	0.0158522
$605$	−2086.33	−0.140201
$606$	21176.2	1.41951
$607$	1697.59	0.113514	0.0567570	−	0.998388i	$-0.481924\pi$
$607$	1697.59	0.113514	0.0567570	+	0.998388i	$0.481924\pi$
$608$	−3144.67	−0.209759
$609$	0	0
$610$	−15930.8	−1.05741
$611$	7835.15	0.518783
$612$	−3680.83	−0.243119
$613$	−8908.59	−0.586973	−0.293486	−	0.955963i	$-0.594816\pi$
$613$	−8908.59	−0.586973	−0.293486	+	0.955963i	$0.594816\pi$
$614$	8793.26	0.577960
$615$	−2320.54	−0.152151
$616$	0	0
$617$	2213.41	0.144422	0.0722112	−	0.997389i	$-0.476994\pi$
$617$	2213.41	0.144422	0.0722112	+	0.997389i	$0.476994\pi$
$618$	−20509.8	−1.33499
$619$	−12936.8	−0.840023	−0.420011	−	0.907519i	$-0.637974\pi$
$619$	−12936.8	−0.840023	−0.420011	+	0.907519i	$0.637974\pi$
$620$	15125.7	0.979780
$621$	−773.980	−0.0500141
$622$	20814.1	1.34175
$623$	0	0
$624$	4668.02	0.299472
$625$	−7475.09	−0.478406
$626$	−5245.20	−0.334889
$627$	6894.67	0.439149
$628$	−14837.1	−0.942778
$629$	5820.98	0.368995
$630$	0	0
$631$	13707.4	0.864789	0.432394	−	0.901685i	$-0.357669\pi$
$631$	13707.4	0.864789	0.432394	+	0.901685i	$0.357669\pi$
$632$	890.078	0.0560212
$633$	20395.8	1.28066
$634$	−10162.9	−0.636628
$635$	29492.2	1.84309
$636$	−7685.01	−0.479136
$637$	0	0
$638$	195.759	0.0121476
$639$	−15083.2	−0.933775
$640$	2207.03	0.136313
$641$	15321.5	0.944092	0.472046	−	0.881574i	$-0.343516\pi$
$641$	15321.5	0.944092	0.472046	+	0.881574i	$0.343516\pi$
$642$	25928.4	1.59394
$643$	20997.2	1.28779	0.643894	−	0.765115i	$-0.277318\pi$
$643$	20997.2	1.28779	0.643894	+	0.765115i	$0.277318\pi$
$644$	0	0
$645$	−54976.6	−3.35612
$646$	13219.8	0.805148
$647$	726.893	0.0441686	0.0220843	−	0.999756i	$-0.492970\pi$
$647$	726.893	0.0441686	0.0220843	+	0.999756i	$0.492970\pi$
$648$	7289.74	0.441926
$649$	5538.19	0.334966
$650$	−15762.8	−0.951183
$651$	0	0
$652$	−434.499	−0.0260986
$653$	−8589.09	−0.514727	−0.257364	−	0.966315i	$-0.582854\pi$
$653$	−8589.09	−0.514727	−0.257364	+	0.966315i	$0.582854\pi$
$654$	−16841.8	−1.00698
$655$	−21539.2	−1.28489
$656$	337.610	0.0200937
$657$	−6440.96	−0.382474
$658$	0	0
$659$	−6692.43	−0.395599	−0.197800	−	0.980242i	$-0.563380\pi$
$659$	−6692.43	−0.395599	−0.197800	+	0.980242i	$0.563380\pi$
$660$	−4838.89	−0.285384
$661$	14382.9	0.846339	0.423169	−	0.906051i	$-0.360918\pi$
$661$	14382.9	0.846339	0.423169	+	0.906051i	$0.360918\pi$
$662$	3196.01	0.187638
$663$	−19623.7	−1.14951
$664$	8014.93	0.468433
$665$	0	0
$666$	2367.95	0.137772
$667$	−81.0700	−0.00470621
$668$	−13134.0	−0.760732
$669$	−12039.3	−0.695762
$670$	−7207.02	−0.415569
$671$	−5081.61	−0.292360
$672$	0	0
$673$	−6350.71	−0.363747	−0.181874	−	0.983322i	$-0.558216\pi$
$673$	−6350.71	−0.363747	−0.181874	+	0.983322i	$0.558216\pi$
$674$	10559.1	0.603443
$675$	−14637.1	−0.834641
$676$	−418.597	−0.0238164
$677$	−16349.3	−0.928147	−0.464073	−	0.885797i	$-0.653613\pi$
$677$	−16349.3	−0.928147	−0.464073	+	0.885797i	$0.653613\pi$
$678$	−1598.13	−0.0905249
$679$	0	0
$680$	−9278.06	−0.523231
$681$	−33284.9	−1.87295
$682$	4824.82	0.270897
$683$	−9321.38	−0.522215	−0.261107	−	0.965310i	$-0.584088\pi$
$683$	−9321.38	−0.522215	−0.261107	+	0.965310i	$0.584088\pi$
$684$	5377.76	0.300620
$685$	−46671.6	−2.60326
$686$	0	0
$687$	10384.8	0.576715
$688$	7998.42	0.443222
$689$	−13778.6	−0.761863
$690$	2003.94	0.110563
$691$	20852.3	1.14799	0.573994	−	0.818860i	$-0.305393\pi$
$691$	20852.3	1.14799	0.573994	+	0.818860i	$0.305393\pi$
$692$	−15618.5	−0.857987
$693$	0	0
$694$	5611.28	0.306918
$695$	22101.3	1.20626
$696$	454.030	0.0247270
$697$	−1419.27	−0.0771286
$698$	3596.48	0.195027
$699$	13695.5	0.741074
$700$	0	0
$701$	−1869.40	−0.100722	−0.0503611	−	0.998731i	$-0.516037\pi$
$701$	−1869.40	−0.100722	−0.0503611	+	0.998731i	$0.516037\pi$
$702$	7771.70	0.417840
$703$	−8504.57	−0.456267
$704$	704.000	0.0376889
$705$	−18837.5	−1.00633
$706$	−10597.0	−0.564906
$707$	0	0
$708$	12844.9	0.681838
$709$	4631.17	0.245314	0.122657	−	0.992449i	$-0.460859\pi$
$709$	4631.17	0.245314	0.122657	+	0.992449i	$0.460859\pi$
$710$	−38019.4	−2.00964
$711$	−1522.14	−0.0802878
$712$	7489.49	0.394214
$713$	−1998.11	−0.104951
$714$	0	0
$715$	−8675.77	−0.453784
$716$	2500.25	0.130501
$717$	3543.35	0.184559
$718$	16584.2	0.862003
$719$	10554.0	0.547423	0.273711	−	0.961812i	$-0.411749\pi$
$719$	10554.0	0.547423	0.273711	+	0.961812i	$0.411749\pi$
$720$	−3774.28	−0.195360
$721$	0	0
$722$	−5596.36	−0.288470
$723$	−33978.5	−1.74782
$724$	8612.46	0.442099
$725$	−1533.15	−0.0785378
$726$	−1543.52	−0.0789053
$727$	32270.9	1.64630	0.823151	−	0.567823i	$-0.192214\pi$
$727$	32270.9	1.64630	0.823151	+	0.567823i	$0.192214\pi$
$728$	0	0
$729$	2163.14	0.109899
$730$	−16235.4	−0.823148
$731$	−33624.3	−1.70129
$732$	−11785.9	−0.595110
$733$	−23666.9	−1.19258	−0.596288	−	0.802770i	$-0.703358\pi$
$733$	−23666.9	−1.19258	−0.596288	+	0.802770i	$0.703358\pi$
$734$	24619.8	1.23806
$735$	0	0
$736$	−291.549	−0.0146014
$737$	−2298.90	−0.114900
$738$	−577.353	−0.0287977
$739$	19978.4	0.994473	0.497237	−	0.867615i	$-0.334348\pi$
$739$	19978.4	0.994473	0.497237	+	0.867615i	$0.334348\pi$
$740$	5968.77	0.296509
$741$	28670.7	1.42138
$742$	0	0
$743$	5487.04	0.270929	0.135464	−	0.990782i	$-0.456747\pi$
$743$	5487.04	0.270929	0.135464	+	0.990782i	$0.456747\pi$
$744$	11190.4	0.551423
$745$	−26438.0	−1.30015
$746$	−15210.2	−0.746496
$747$	−13706.5	−0.671344
$748$	−2959.52	−0.144667
$749$	0	0
$750$	10403.7	0.506521
$751$	−22697.1	−1.10283	−0.551417	−	0.834230i	$-0.685913\pi$
$751$	−22697.1	−1.10283	−0.551417	+	0.834230i	$0.685913\pi$
$752$	2740.63	0.132900
$753$	34912.1	1.68960
$754$	814.041	0.0393178
$755$	−1014.34	−0.0488949
$756$	0	0
$757$	−26520.6	−1.27332	−0.636662	−	0.771143i	$-0.719685\pi$
$757$	−26520.6	−1.27332	−0.636662	+	0.771143i	$0.719685\pi$
$758$	−8528.22	−0.408653
$759$	639.218	0.0305694
$760$	13555.4	0.646983
$761$	−24067.0	−1.14642	−0.573212	−	0.819407i	$-0.694303\pi$
$761$	−24067.0	−1.14642	−0.573212	+	0.819407i	$0.694303\pi$
$762$	21819.0	1.03729
$763$	0	0
$764$	−17529.9	−0.830116
$765$	15866.6	0.749879
$766$	21158.5	0.998025
$767$	23029.9	1.08418
$768$	1632.81	0.0767174
$769$	17700.1	0.830017	0.415009	−	0.909817i	$-0.363779\pi$
$769$	17700.1	0.830017	0.415009	+	0.909817i	$0.363779\pi$
$770$	0	0
$771$	−20378.3	−0.951890
$772$	−5263.78	−0.245399
$773$	−5478.59	−0.254917	−0.127459	−	0.991844i	$-0.540682\pi$
$773$	−5478.59	−0.254917	−0.127459	+	0.991844i	$0.540682\pi$
$774$	−13678.2	−0.635212
$775$	−37787.2	−1.75143
$776$	5543.23	0.256431
$777$	0	0
$778$	−20110.2	−0.926717
$779$	2073.58	0.0953706
$780$	−20122.0	−0.923695
$781$	−12127.5	−0.555640
$782$	1225.63	0.0560467
$783$	755.906	0.0345005
$784$	0	0
$785$	63956.8	2.90792
$786$	−15935.2	−0.723140
$787$	−21224.8	−0.961351	−0.480675	−	0.876899i	$-0.659608\pi$
$787$	−21224.8	−0.961351	−0.480675	+	0.876899i	$0.659608\pi$
$788$	13098.9	0.592167
$789$	29890.1	1.34869
$790$	−3836.77	−0.172793
$791$	0	0
$792$	−1203.92	−0.0540146
$793$	−21131.3	−0.946272
$794$	−22552.8	−1.00802
$795$	33127.0	1.47785
$796$	−18643.6	−0.830156
$797$	−23592.1	−1.04853	−0.524264	−	0.851556i	$-0.675659\pi$
$797$	−23592.1	−1.04853	−0.524264	+	0.851556i	$0.675659\pi$
$798$	0	0
$799$	−11521.2	−0.510128
$800$	−5513.62	−0.243670
$801$	−12807.9	−0.564975
$802$	−24033.2	−1.05815
$803$	−5178.77	−0.227590
$804$	−5331.92	−0.233883
$805$	0	0
$806$	20063.5	0.876805
$807$	23075.9	1.00658
$808$	13280.4	0.578222
$809$	−19365.6	−0.841606	−0.420803	−	0.907152i	$-0.638252\pi$
$809$	−19365.6	−0.841606	−0.420803	+	0.907152i	$0.638252\pi$
$810$	−31423.2	−1.36308
$811$	31768.3	1.37551	0.687753	−	0.725945i	$-0.258597\pi$
$811$	31768.3	1.37551	0.687753	+	0.725945i	$0.258597\pi$
$812$	0	0
$813$	26448.1	1.14093
$814$	1903.92	0.0819810
$815$	1872.95	0.0804990
$816$	−6864.12	−0.294476
$817$	49125.8	2.10366
$818$	−5563.05	−0.237784
$819$	0	0
$820$	−1455.30	−0.0619773
$821$	−21046.9	−0.894691	−0.447346	−	0.894361i	$-0.647631\pi$
$821$	−21046.9	−0.894691	−0.447346	+	0.894361i	$0.647631\pi$
$822$	−34528.7	−1.46512
$823$	−51.2685	−0.00217146	−0.00108573	−	0.999999i	$-0.500346\pi$
$823$	−51.2685	−0.00217146	−0.00108573	+	0.999999i	$0.500346\pi$
$824$	−12862.5	−0.543796
$825$	12088.6	0.510145
$826$	0	0
$827$	8706.43	0.366085	0.183042	−	0.983105i	$-0.441405\pi$
$827$	8706.43	0.366085	0.183042	+	0.983105i	$0.441405\pi$
$828$	498.583	0.0209263
$829$	22314.2	0.934868	0.467434	−	0.884028i	$-0.345179\pi$
$829$	22314.2	0.934868	0.467434	+	0.884028i	$0.345179\pi$
$830$	−34549.2	−1.44484
$831$	36303.3	1.51546
$832$	2927.50	0.121987
$833$	0	0
$834$	16351.0	0.678885
$835$	56615.4	2.34641
$836$	4323.92	0.178883
$837$	18630.6	0.769377
$838$	−1581.20	−0.0651811
$839$	−21575.0	−0.887785	−0.443893	−	0.896080i	$-0.646403\pi$
$839$	−21575.0	−0.887785	−0.443893	+	0.896080i	$0.646403\pi$
$840$	0	0
$841$	−24309.8	−0.996754
$842$	−462.168	−0.0189161
$843$	−28342.9	−1.15798
$844$	12791.0	0.521665
$845$	1804.41	0.0734597
$846$	−4686.80	−0.190467
$847$	0	0
$848$	−4819.57	−0.195171
$849$	39351.3	1.59073
$850$	23178.5	0.935314
$851$	−788.475	−0.0317609
$852$	−28127.6	−1.13103
$853$	36125.8	1.45009	0.725043	−	0.688703i	$-0.241820\pi$
$853$	36125.8	1.45009	0.725043	+	0.688703i	$0.241820\pi$
$854$	0	0
$855$	−23181.4	−0.927236
$856$	16260.7	0.649276
$857$	7474.98	0.297947	0.148973	−	0.988841i	$-0.452403\pi$
$857$	7474.98	0.297947	0.148973	+	0.988841i	$0.452403\pi$
$858$	−6418.53	−0.255390
$859$	−17681.3	−0.702302	−0.351151	−	0.936319i	$-0.614210\pi$
$859$	−17681.3	−0.702302	−0.351151	+	0.936319i	$0.614210\pi$
$860$	−34478.0	−1.36708
$861$	0	0
$862$	27478.4	1.08575
$863$	34752.5	1.37079	0.685393	−	0.728174i	$-0.259631\pi$
$863$	34752.5	1.37079	0.685393	+	0.728174i	$0.259631\pi$
$864$	2718.43	0.107041
$865$	67325.2	2.64639
$866$	−159.182	−0.00624623
$867$	−2480.06	−0.0971480
$868$	0	0
$869$	−1223.86	−0.0477750
$870$	−1957.14	−0.0762682
$871$	−9559.72	−0.371893
$872$	−10562.1	−0.410183
$873$	−9479.59	−0.367509
$874$	−1790.67	−0.0693025
$875$	0	0
$876$	−12011.3	−0.463269
$877$	−19756.6	−0.760697	−0.380349	−	0.924843i	$-0.624196\pi$
$877$	−19756.6	−0.760697	−0.380349	+	0.924843i	$0.624196\pi$
$878$	28360.4	1.09011
$879$	−798.005	−0.0306212
$880$	−3034.66	−0.116248
$881$	3449.87	0.131929	0.0659643	−	0.997822i	$-0.478988\pi$
$881$	3449.87	0.131929	0.0659643	+	0.997822i	$0.478988\pi$
$882$	0	0
$883$	−26337.1	−1.00375	−0.501877	−	0.864939i	$-0.667357\pi$
$883$	−26337.1	−1.00375	−0.501877	+	0.864939i	$0.667357\pi$
$884$	−12306.8	−0.468239
$885$	−55369.3	−2.10307
$886$	−30918.1	−1.17236
$887$	10617.4	0.401913	0.200957	−	0.979600i	$-0.435595\pi$
$887$	10617.4	0.401913	0.200957	+	0.979600i	$0.435595\pi$
$888$	4415.83	0.166876
$889$	0	0
$890$	−32284.2	−1.21592
$891$	−10023.4	−0.376876
$892$	−7550.30	−0.283411
$893$	16832.8	0.630780
$894$	−19559.4	−0.731728
$895$	−10777.6	−0.402519
$896$	0	0
$897$	2658.11	0.0989430
$898$	−18549.0	−0.689295
$899$	1951.45	0.0723966
$900$	9428.94	0.349220
$901$	20260.9	0.749153
$902$	−464.214	−0.0171360
$903$	0	0
$904$	−1002.25	−0.0368743
$905$	−37124.9	−1.36362
$906$	−750.432	−0.0275181
$907$	31855.2	1.16619	0.583094	−	0.812404i	$-0.301842\pi$
$907$	31855.2	1.16619	0.583094	+	0.812404i	$0.301842\pi$
$908$	−20874.3	−0.762928
$909$	−22711.1	−0.828690
$910$	0	0
$911$	14353.0	0.521992	0.260996	−	0.965340i	$-0.415949\pi$
$911$	14353.0	0.521992	0.260996	+	0.965340i	$0.415949\pi$
$912$	10028.6	0.364123
$913$	−11020.5	−0.399481
$914$	−18520.6	−0.670247
$915$	50804.5	1.83557
$916$	6512.69	0.234919
$917$	0	0
$918$	−11427.9	−0.410870
$919$	−15227.0	−0.546565	−0.273282	−	0.961934i	$-0.588109\pi$
$919$	−15227.0	−0.546565	−0.273282	+	0.961934i	$0.588109\pi$
$920$	1256.75	0.0450367
$921$	−28042.4	−1.00329
$922$	15070.6	0.538312
$923$	−50430.7	−1.79842
$924$	0	0
$925$	−14911.2	−0.530031
$926$	4494.91	0.159516
$927$	21996.5	0.779351
$928$	284.740	0.0100723
$929$	12897.7	0.455500	0.227750	−	0.973720i	$-0.426863\pi$
$929$	12897.7	0.455500	0.227750	+	0.973720i	$0.426863\pi$
$930$	−48237.2	−1.70082
$931$	0	0
$932$	8588.98	0.301868
$933$	−66377.8	−2.32917
$934$	5696.52	0.199567
$935$	12757.3	0.446213
$936$	−5006.38	−0.174827
$937$	−13880.0	−0.483929	−0.241964	−	0.970285i	$-0.577792\pi$
$937$	−13880.0	−0.483929	−0.241964	+	0.970285i	$0.577792\pi$
$938$	0	0
$939$	16727.4	0.581338
$940$	−11813.8	−0.409917
$941$	−30211.8	−1.04663	−0.523314	−	0.852140i	$-0.675305\pi$
$941$	−30211.8	−1.04663	−0.523314	+	0.852140i	$0.675305\pi$
$942$	47316.7	1.63658
$943$	192.246	0.00663879
$944$	8055.55	0.277739
$945$	0	0
$946$	−10997.8	−0.377981
$947$	−12031.1	−0.412838	−0.206419	−	0.978464i	$-0.566181\pi$
$947$	−12031.1	−0.412838	−0.206419	+	0.978464i	$0.566181\pi$
$948$	−2838.53	−0.0972481
$949$	−21535.3	−0.736635
$950$	−33864.3	−1.15653
$951$	32410.4	1.10513
$952$	0	0
$953$	6203.82	0.210872	0.105436	−	0.994426i	$-0.466376\pi$
$953$	6203.82	0.210872	0.105436	+	0.994426i	$0.466376\pi$
$954$	8242.04	0.279713
$955$	75564.3	2.56042
$956$	2222.17	0.0751781
$957$	−624.291	−0.0210872
$958$	−15262.3	−0.514721
$959$	0	0
$960$	−7038.39	−0.236628
$961$	18305.9	0.614477
$962$	7917.25	0.265345
$963$	−27807.8	−0.930522
$964$	−21309.2	−0.711955
$965$	22690.1	0.756911
$966$	0	0
$967$	−46127.3	−1.53398	−0.766988	−	0.641662i	$-0.778245\pi$
$967$	−46127.3	−1.53398	−0.766988	+	0.641662i	$0.778245\pi$
$968$	−968.000	−0.0321412
$969$	−42159.0	−1.39767
$970$	−23894.7	−0.790940
$971$	−10694.2	−0.353442	−0.176721	−	0.984261i	$-0.556549\pi$
$971$	−10694.2	−0.353442	−0.176721	+	0.984261i	$0.556549\pi$
$972$	−14072.8	−0.464390
$973$	0	0
$974$	−30835.2	−1.01440
$975$	50268.9	1.65117
$976$	−7391.43	−0.242412
$977$	48580.0	1.59080	0.795401	−	0.606084i	$-0.207260\pi$
$977$	48580.0	1.59080	0.795401	+	0.606084i	$0.207260\pi$
$978$	1385.65	0.0453050
$979$	−10298.0	−0.336187
$980$	0	0
$981$	18062.5	0.587861
$982$	−338.809	−0.0110100
$983$	38257.1	1.24131	0.620657	−	0.784082i	$-0.286866\pi$
$983$	38257.1	1.24131	0.620657	+	0.784082i	$0.286866\pi$
$984$	−1076.67	−0.0348810
$985$	−56464.0	−1.82649
$986$	−1197.01	−0.0386619
$987$	0	0
$988$	17980.5	0.578985
$989$	4554.55	0.146437
$990$	5189.63	0.166603
$991$	−13997.0	−0.448666	−0.224333	−	0.974513i	$-0.572020\pi$
$991$	−13997.0	−0.448666	−0.224333	+	0.974513i	$0.572020\pi$
$992$	7017.92	0.224616
$993$	−10192.3	−0.325724
$994$	0	0
$995$	80365.1	2.56055
$996$	−25560.3	−0.813160
$997$	−57785.8	−1.83560	−0.917801	−	0.397042i	$-0.870037\pi$
$997$	−57785.8	−1.83560	−0.917801	+	0.397042i	$0.870037\pi$
$998$	−11434.3	−0.362672
$999$	7351.84	0.232835

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.4.a.v.1.4		5
7.2	even	3		154.4.e.d.67.2	yes	10
7.4	even	3		154.4.e.d.23.2	✓	10
7.6	odd	2		1078.4.a.u.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.4.e.d.23.2	✓	10	7.4	even	3
154.4.e.d.67.2	yes	10	7.2	even	3
1078.4.a.u.1.2		5	7.6	odd	2
1078.4.a.v.1.4		5	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1078.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +6.37816 q^{3} +4.00000 q^{4} -17.2424 q^{5} -12.7563 q^{6} -8.00000 q^{8} +13.6809 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +6.37816 q^{3} +4.00000 q^{4} -17.2424 q^{5} -12.7563 q^{6} -8.00000 q^{8} +13.6809 q^{9} +34.4848 q^{10} +11.0000 q^{11} +25.5126 q^{12} +45.7422 q^{13} -109.975 q^{15} +16.0000 q^{16} -67.2619 q^{17} -27.3619 q^{18} +98.2710 q^{19} -68.9696 q^{20} -22.0000 q^{22} +9.11089 q^{23} -51.0253 q^{24} +172.301 q^{25} -91.4844 q^{26} -84.9511 q^{27} -8.89814 q^{29} +219.950 q^{30} -219.310 q^{31} -32.0000 q^{32} +70.1598 q^{33} +134.524 q^{34} +54.7238 q^{36} -86.5420 q^{37} -196.542 q^{38} +291.751 q^{39} +137.939 q^{40} +21.1006 q^{41} +499.901 q^{43} +44.0000 q^{44} -235.892 q^{45} -18.2218 q^{46} +171.289 q^{47} +102.051 q^{48} -344.601 q^{50} -429.007 q^{51} +182.969 q^{52} -301.223 q^{53} +169.902 q^{54} -189.666 q^{55} +626.788 q^{57} +17.7963 q^{58} +503.472 q^{59} -439.899 q^{60} -461.964 q^{61} +438.620 q^{62} +64.0000 q^{64} -788.706 q^{65} -140.320 q^{66} -208.991 q^{67} -269.048 q^{68} +58.1107 q^{69} -1102.50 q^{71} -109.448 q^{72} -470.798 q^{73} +173.084 q^{74} +1098.96 q^{75} +393.084 q^{76} -583.503 q^{78} -111.260 q^{79} -275.878 q^{80} -911.217 q^{81} -42.2013 q^{82} -1001.87 q^{83} +1159.76 q^{85} -999.803 q^{86} -56.7538 q^{87} -88.0000 q^{88} -936.186 q^{89} +471.785 q^{90} +36.4436 q^{92} -1398.79 q^{93} -342.579 q^{94} -1694.43 q^{95} -204.101 q^{96} -692.904 q^{97} +150.490 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 10 q^{2} + q^{3} + 20 q^{4} - 10 q^{5} - 2 q^{6} - 40 q^{8} + 76 q^{9}+O(q^{10}) \) 5 * q - 10 * q^2 + q^3 + 20 * q^4 - 10 * q^5 - 2 * q^6 - 40 * q^8 + 76 * q^9	\( 5 q - 10 q^{2} + q^{3} + 20 q^{4} - 10 q^{5} - 2 q^{6} - 40 q^{8} + 76 q^{9} + 20 q^{10} + 55 q^{11} + 4 q^{12} - 95 q^{13} - 3 q^{15} + 80 q^{16} - 91 q^{17} - 152 q^{18} - 97 q^{19} - 40 q^{20} - 110 q^{22} + 70 q^{23} - 8 q^{24} - 75 q^{25} + 190 q^{26} - 326 q^{27} + 181 q^{29} + 6 q^{30} - 117 q^{31} - 160 q^{32} + 11 q^{33} + 182 q^{34} + 304 q^{36} - 396 q^{37} + 194 q^{38} - 277 q^{39} + 80 q^{40} - 287 q^{41} + 666 q^{43} + 220 q^{44} + 15 q^{45} - 140 q^{46} + 251 q^{47} + 16 q^{48} + 150 q^{50} - 798 q^{51} - 380 q^{52} + 285 q^{53} + 652 q^{54} - 110 q^{55} + 1898 q^{57} - 362 q^{58} - 198 q^{59} - 12 q^{60} + 54 q^{61} + 234 q^{62} + 320 q^{64} - 2111 q^{65} - 22 q^{66} - 634 q^{67} - 364 q^{68} - 1203 q^{69} + 1921 q^{71} - 608 q^{72} - 936 q^{73} + 792 q^{74} + 1753 q^{75} - 388 q^{76} + 554 q^{78} - 997 q^{79} - 160 q^{80} - 383 q^{81} + 574 q^{82} - 3069 q^{83} + 1081 q^{85} - 1332 q^{86} - 2028 q^{87} - 440 q^{88} + 237 q^{89} - 30 q^{90} + 280 q^{92} - 2266 q^{93} - 502 q^{94} - 891 q^{95} - 32 q^{96} + 1203 q^{97} + 836 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 + q^3 + 20 * q^4 - 10 * q^5 - 2 * q^6 - 40 * q^8 + 76 * q^9 + 20 * q^10 + 55 * q^11 + 4 * q^12 - 95 * q^13 - 3 * q^15 + 80 * q^16 - 91 * q^17 - 152 * q^18 - 97 * q^19 - 40 * q^20 - 110 * q^22 + 70 * q^23 - 8 * q^24 - 75 * q^25 + 190 * q^26 - 326 * q^27 + 181 * q^29 + 6 * q^30 - 117 * q^31 - 160 * q^32 + 11 * q^33 + 182 * q^34 + 304 * q^36 - 396 * q^37 + 194 * q^38 - 277 * q^39 + 80 * q^40 - 287 * q^41 + 666 * q^43 + 220 * q^44 + 15 * q^45 - 140 * q^46 + 251 * q^47 + 16 * q^48 + 150 * q^50 - 798 * q^51 - 380 * q^52 + 285 * q^53 + 652 * q^54 - 110 * q^55 + 1898 * q^57 - 362 * q^58 - 198 * q^59 - 12 * q^60 + 54 * q^61 + 234 * q^62 + 320 * q^64 - 2111 * q^65 - 22 * q^66 - 634 * q^67 - 364 * q^68 - 1203 * q^69 + 1921 * q^71 - 608 * q^72 - 936 * q^73 + 792 * q^74 + 1753 * q^75 - 388 * q^76 + 554 * q^78 - 997 * q^79 - 160 * q^80 - 383 * q^81 + 574 * q^82 - 3069 * q^83 + 1081 * q^85 - 1332 * q^86 - 2028 * q^87 - 440 * q^88 + 237 * q^89 - 30 * q^90 + 280 * q^92 - 2266 * q^93 - 502 * q^94 - 891 * q^95 - 32 * q^96 + 1203 * q^97 + 836 * q^99

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