LMFDB - Embedded newform 735.4.a.p.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,4,Mod(1,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("735.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	735.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:	$43.3664038542$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{65}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 16 $ x^2 - x - 16
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$4.53113$ of defining polynomial
Character	$\chi$	$=$	735.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.53113 q^{2} -3.00000 q^{3} +12.5311 q^{4} -5.00000 q^{5} -13.5934 q^{6} +20.5311 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+4.53113 q^{2} -3.00000 q^{3} +12.5311 q^{4} -5.00000 q^{5} -13.5934 q^{6} +20.5311 q^{8} +9.00000 q^{9} -22.6556 q^{10} -19.0623 q^{11} -37.5934 q^{12} +2.93774 q^{13} +15.0000 q^{15} -7.21984 q^{16} +6.49806 q^{17} +40.7802 q^{18} +5.43580 q^{19} -62.6556 q^{20} -86.3735 q^{22} +49.3774 q^{23} -61.5934 q^{24} +25.0000 q^{25} +13.3113 q^{26} -27.0000 q^{27} -291.494 q^{29} +67.9669 q^{30} -244.307 q^{31} -196.963 q^{32} +57.1868 q^{33} +29.4436 q^{34} +112.780 q^{36} -193.121 q^{37} +24.6303 q^{38} -8.81323 q^{39} -102.656 q^{40} -315.113 q^{41} -300.996 q^{43} -238.872 q^{44} -45.0000 q^{45} +223.735 q^{46} -86.5058 q^{47} +21.6595 q^{48} +113.278 q^{50} -19.4942 q^{51} +36.8132 q^{52} +509.677 q^{53} -122.340 q^{54} +95.3113 q^{55} -16.3074 q^{57} -1320.80 q^{58} +83.3852 q^{59} +187.967 q^{60} +5.25291 q^{61} -1106.99 q^{62} -834.706 q^{64} -14.6887 q^{65} +259.121 q^{66} +205.992 q^{67} +81.4281 q^{68} -148.132 q^{69} +1004.31 q^{71} +184.780 q^{72} +1007.29 q^{73} -875.055 q^{74} -75.0000 q^{75} +68.1168 q^{76} -39.9339 q^{78} -863.237 q^{79} +36.0992 q^{80} +81.0000 q^{81} -1427.82 q^{82} -1334.72 q^{83} -32.4903 q^{85} -1363.85 q^{86} +874.483 q^{87} -391.370 q^{88} -326.249 q^{89} -203.901 q^{90} +618.755 q^{92} +732.922 q^{93} -391.969 q^{94} -27.1790 q^{95} +590.889 q^{96} -1526.77 q^{97} -171.560 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 6 q^{3} + 17 q^{4} - 10 q^{5} - 3 q^{6} + 33 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + q^2 - 6 * q^3 + 17 * q^4 - 10 * q^5 - 3 * q^6 + 33 * q^8 + 18 * q^9	\( 2 q + q^{2} - 6 q^{3} + 17 q^{4} - 10 q^{5} - 3 q^{6} + 33 q^{8} + 18 q^{9} - 5 q^{10} - 22 q^{11} - 51 q^{12} + 22 q^{13} + 30 q^{15} - 87 q^{16} - 116 q^{17} + 9 q^{18} - 102 q^{19} - 85 q^{20} - 76 q^{22} + 260 q^{23} - 99 q^{24} + 50 q^{25} - 54 q^{26} - 54 q^{27} - 196 q^{29} + 15 q^{30} - 150 q^{31} - 15 q^{32} + 66 q^{33} + 462 q^{34} + 153 q^{36} - 96 q^{37} + 404 q^{38} - 66 q^{39} - 165 q^{40} + 176 q^{41} - 344 q^{43} - 252 q^{44} - 90 q^{45} - 520 q^{46} - 560 q^{47} + 261 q^{48} + 25 q^{50} + 348 q^{51} + 122 q^{52} + 326 q^{53} - 27 q^{54} + 110 q^{55} + 306 q^{57} - 1658 q^{58} + 844 q^{59} + 255 q^{60} + 204 q^{61} - 1440 q^{62} - 839 q^{64} - 110 q^{65} + 228 q^{66} - 104 q^{67} - 466 q^{68} - 780 q^{69} + 1670 q^{71} + 297 q^{72} + 386 q^{73} - 1218 q^{74} - 150 q^{75} - 412 q^{76} + 162 q^{78} - 888 q^{79} + 435 q^{80} + 162 q^{81} - 3162 q^{82} - 928 q^{83} + 580 q^{85} - 1212 q^{86} + 588 q^{87} - 428 q^{88} - 588 q^{89} - 45 q^{90} + 1560 q^{92} + 450 q^{93} + 1280 q^{94} + 510 q^{95} + 45 q^{96} - 522 q^{97} - 198 q^{99}+O(q^{100}) \) 2 * q + q^2 - 6 * q^3 + 17 * q^4 - 10 * q^5 - 3 * q^6 + 33 * q^8 + 18 * q^9 - 5 * q^10 - 22 * q^11 - 51 * q^12 + 22 * q^13 + 30 * q^15 - 87 * q^16 - 116 * q^17 + 9 * q^18 - 102 * q^19 - 85 * q^20 - 76 * q^22 + 260 * q^23 - 99 * q^24 + 50 * q^25 - 54 * q^26 - 54 * q^27 - 196 * q^29 + 15 * q^30 - 150 * q^31 - 15 * q^32 + 66 * q^33 + 462 * q^34 + 153 * q^36 - 96 * q^37 + 404 * q^38 - 66 * q^39 - 165 * q^40 + 176 * q^41 - 344 * q^43 - 252 * q^44 - 90 * q^45 - 520 * q^46 - 560 * q^47 + 261 * q^48 + 25 * q^50 + 348 * q^51 + 122 * q^52 + 326 * q^53 - 27 * q^54 + 110 * q^55 + 306 * q^57 - 1658 * q^58 + 844 * q^59 + 255 * q^60 + 204 * q^61 - 1440 * q^62 - 839 * q^64 - 110 * q^65 + 228 * q^66 - 104 * q^67 - 466 * q^68 - 780 * q^69 + 1670 * q^71 + 297 * q^72 + 386 * q^73 - 1218 * q^74 - 150 * q^75 - 412 * q^76 + 162 * q^78 - 888 * q^79 + 435 * q^80 + 162 * q^81 - 3162 * q^82 - 928 * q^83 + 580 * q^85 - 1212 * q^86 + 588 * q^87 - 428 * q^88 - 588 * q^89 - 45 * q^90 + 1560 * q^92 + 450 * q^93 + 1280 * q^94 + 510 * q^95 + 45 * q^96 - 522 * q^97 - 198 * 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 $

$2$	4.53113	1.60200	0.800998	−	0.598667i	$-0.204303\pi$
$2$	4.53113	1.60200	0.800998	+	0.598667i	$0.204303\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	12.5311	1.56639
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−13.5934	−0.924913
$7$	0	0
$7$	0	0
$8$	20.5311	0.907356
$9$	9.00000	0.333333
$10$	−22.6556	−0.716434
$11$	−19.0623	−0.522499	−0.261249	−	0.965271i	$-0.584135\pi$
$11$	−19.0623	−0.522499	−0.261249	+	0.965271i	$0.584135\pi$
$12$	−37.5934	−0.904356
$13$	2.93774	0.0626756	0.0313378	−	0.999509i	$-0.490023\pi$
$13$	2.93774	0.0626756	0.0313378	+	0.999509i	$0.490023\pi$
$14$	0	0
$15$	15.0000	0.258199
$16$	−7.21984	−0.112810
$17$	6.49806	0.0927066	0.0463533	−	0.998925i	$-0.485240\pi$
$17$	6.49806	0.0927066	0.0463533	+	0.998925i	$0.485240\pi$
$18$	40.7802	0.533999
$19$	5.43580	0.0656347	0.0328173	−	0.999461i	$-0.489552\pi$
$19$	5.43580	0.0656347	0.0328173	+	0.999461i	$0.489552\pi$
$20$	−62.6556	−0.700511
$21$	0	0
$22$	−86.3735	−0.837041
$23$	49.3774	0.447648	0.223824	−	0.974630i	$-0.428146\pi$
$23$	49.3774	0.447648	0.223824	+	0.974630i	$0.428146\pi$
$24$	−61.5934	−0.523862
$25$	25.0000	0.200000
$26$	13.3113	0.100406
$27$	−27.0000	−0.192450
$28$	0	0
$29$	−291.494	−1.86652	−0.933261	−	0.359200i	$-0.883050\pi$
$29$	−291.494	−1.86652	−0.933261	+	0.359200i	$0.883050\pi$
$30$	67.9669	0.413634
$31$	−244.307	−1.41545	−0.707724	−	0.706489i	$-0.750278\pi$
$31$	−244.307	−1.41545	−0.707724	+	0.706489i	$0.750278\pi$
$32$	−196.963	−1.08808
$33$	57.1868	0.301665
$34$	29.4436	0.148516
$35$	0	0
$36$	112.780	0.522130
$37$	−193.121	−0.858077	−0.429038	−	0.903286i	$-0.641147\pi$
$37$	−193.121	−0.858077	−0.429038	+	0.903286i	$0.641147\pi$
$38$	24.6303	0.105147
$39$	−8.81323	−0.0361858
$40$	−102.656	−0.405782
$41$	−315.113	−1.20030	−0.600151	−	0.799887i	$-0.704893\pi$
$41$	−315.113	−1.20030	−0.600151	+	0.799887i	$0.704893\pi$
$42$	0	0
$43$	−300.996	−1.06748	−0.533738	−	0.845650i	$-0.679213\pi$
$43$	−300.996	−1.06748	−0.533738	+	0.845650i	$0.679213\pi$
$44$	−238.872	−0.818437
$45$	−45.0000	−0.149071
$46$	223.735	0.717130
$47$	−86.5058	−0.268472	−0.134236	−	0.990949i	$-0.542858\pi$
$47$	−86.5058	−0.268472	−0.134236	+	0.990949i	$0.542858\pi$
$48$	21.6595	0.0651309
$49$	0	0
$50$	113.278	0.320399
$51$	−19.4942	−0.0535242
$52$	36.8132	0.0981745
$53$	509.677	1.32093	0.660467	−	0.750855i	$-0.270358\pi$
$53$	509.677	1.32093	0.660467	+	0.750855i	$0.270358\pi$
$54$	−122.340	−0.308304
$55$	95.3113	0.233669
$56$	0	0
$57$	−16.3074	−0.0378942
$58$	−1320.80	−2.99016
$59$	83.3852	0.183997	0.0919985	−	0.995759i	$-0.470674\pi$
$59$	83.3852	0.183997	0.0919985	+	0.995759i	$0.470674\pi$
$60$	187.967	0.404440
$61$	5.25291	0.0110257	0.00551283	−	0.999985i	$-0.498245\pi$
$61$	5.25291	0.0110257	0.00551283	+	0.999985i	$0.498245\pi$
$62$	−1106.99	−2.26754
$63$	0	0
$64$	−834.706	−1.63029
$65$	−14.6887	−0.0280294
$66$	259.121	0.483266
$67$	205.992	0.375611	0.187806	−	0.982206i	$-0.439862\pi$
$67$	205.992	0.375611	0.187806	+	0.982206i	$0.439862\pi$
$68$	81.4281	0.145215
$69$	−148.132	−0.258450
$70$	0	0
$71$	1004.31	1.67872	0.839362	−	0.543573i	$-0.182929\pi$
$71$	1004.31	1.67872	0.839362	+	0.543573i	$0.182929\pi$
$72$	184.780	0.302452
$73$	1007.29	1.61499	0.807494	−	0.589876i	$-0.200823\pi$
$73$	1007.29	1.61499	0.807494	+	0.589876i	$0.200823\pi$
$74$	−875.055	−1.37464
$75$	−75.0000	−0.115470
$76$	68.1168	0.102810
$77$	0	0
$78$	−39.9339	−0.0579695
$79$	−863.237	−1.22939	−0.614695	−	0.788765i	$-0.710721\pi$
$79$	−863.237	−1.22939	−0.614695	+	0.788765i	$0.710721\pi$
$80$	36.0992	0.0504502
$81$	81.0000	0.111111
$82$	−1427.82	−1.92288
$83$	−1334.72	−1.76512	−0.882560	−	0.470200i	$-0.844182\pi$
$83$	−1334.72	−1.76512	−0.882560	+	0.470200i	$0.844182\pi$
$84$	0	0
$85$	−32.4903	−0.0414596
$86$	−1363.85	−1.71009
$87$	874.483	1.07764
$88$	−391.370	−0.474093
$89$	−326.249	−0.388565	−0.194283	−	0.980946i	$-0.562238\pi$
$89$	−326.249	−0.388565	−0.194283	+	0.980946i	$0.562238\pi$
$90$	−203.901	−0.238811
$91$	0	0
$92$	618.755	0.701192
$93$	732.922	0.817210
$94$	−391.969	−0.430091
$95$	−27.1790	−0.0293527
$96$	590.889	0.628202
$97$	−1526.77	−1.59815	−0.799075	−	0.601232i	$-0.794677\pi$
$97$	−1526.77	−1.59815	−0.799075	+	0.601232i	$0.794677\pi$
$98$	0	0
$99$	−171.560	−0.174166
$100$	313.278	0.313278
$101$	−96.8716	−0.0954365	−0.0477182	−	0.998861i	$-0.515195\pi$
$101$	−96.8716	−0.0954365	−0.0477182	+	0.998861i	$0.515195\pi$
$102$	−88.3307	−0.0857455
$103$	−1321.99	−1.26466	−0.632329	−	0.774700i	$-0.717901\pi$
$103$	−1321.99	−1.26466	−0.632329	+	0.774700i	$0.717901\pi$
$104$	60.3152	0.0568691
$105$	0	0
$106$	2309.41	2.11613
$107$	1745.71	1.57724	0.788619	−	0.614883i	$-0.210797\pi$
$107$	1745.71	1.57724	0.788619	+	0.614883i	$0.210797\pi$
$108$	−338.340	−0.301452
$109$	476.856	0.419032	0.209516	−	0.977805i	$-0.432811\pi$
$109$	476.856	0.419032	0.209516	+	0.977805i	$0.432811\pi$
$110$	431.868	0.374336
$111$	579.362	0.495411
$112$	0	0
$113$	1641.65	1.36666	0.683332	−	0.730108i	$-0.260530\pi$
$113$	1641.65	1.36666	0.683332	+	0.730108i	$0.260530\pi$
$114$	−73.8910	−0.0607064
$115$	−246.887	−0.200194
$116$	−3652.75	−2.92370
$117$	26.4397	0.0208919
$118$	377.829	0.294763
$119$	0	0
$120$	307.967	0.234278
$121$	−967.630	−0.726995
$122$	23.8016	0.0176631
$123$	945.339	0.692994
$124$	−3061.45	−2.21715
$125$	−125.000	−0.0894427
$126$	0	0
$127$	−844.016	−0.589719	−0.294859	−	0.955541i	$-0.595273\pi$
$127$	−844.016	−0.589719	−0.294859	+	0.955541i	$0.595273\pi$
$128$	−2206.46	−1.52363
$129$	902.988	0.616308
$130$	−66.5564	−0.0449030
$131$	2796.20	1.86493	0.932463	−	0.361265i	$-0.117655\pi$
$131$	2796.20	1.86493	0.932463	+	0.361265i	$0.117655\pi$
$132$	716.615	0.472525
$133$	0	0
$134$	933.377	0.601728
$135$	135.000	0.0860663
$136$	133.413	0.0841179
$137$	−2057.13	−1.28287	−0.641433	−	0.767179i	$-0.721660\pi$
$137$	−2057.13	−1.28287	−0.641433	+	0.767179i	$0.721660\pi$
$138$	−671.206	−0.414035
$139$	1745.12	1.06489	0.532444	−	0.846465i	$-0.321274\pi$
$139$	1745.12	1.06489	0.532444	+	0.846465i	$0.321274\pi$
$140$	0	0
$141$	259.517	0.155002
$142$	4550.65	2.68931
$143$	−56.0000	−0.0327479
$144$	−64.9786	−0.0376033
$145$	1457.47	0.834734
$146$	4564.15	2.58720
$147$	0	0
$148$	−2420.02	−1.34408
$149$	−1173.57	−0.645254	−0.322627	−	0.946526i	$-0.604566\pi$
$149$	−1173.57	−0.645254	−0.322627	+	0.946526i	$0.604566\pi$
$150$	−339.835	−0.184983
$151$	1540.07	0.829994	0.414997	−	0.909823i	$-0.363783\pi$
$151$	1540.07	0.829994	0.414997	+	0.909823i	$0.363783\pi$
$152$	111.603	0.0595540
$153$	58.4826	0.0309022
$154$	0	0
$155$	1221.54	0.633008
$156$	−110.440	−0.0566811
$157$	2544.53	1.29348	0.646738	−	0.762712i	$-0.276133\pi$
$157$	2544.53	1.29348	0.646738	+	0.762712i	$0.276133\pi$
$158$	−3911.44	−1.96948
$159$	−1529.03	−0.762642
$160$	984.815	0.486603
$161$	0	0
$162$	367.021	0.178000
$163$	−594.708	−0.285774	−0.142887	−	0.989739i	$-0.545639\pi$
$163$	−594.708	−0.285774	−0.142887	+	0.989739i	$0.545639\pi$
$164$	−3948.72	−1.88014
$165$	−285.934	−0.134909
$166$	−6047.81	−2.82772
$167$	−928.498	−0.430236	−0.215118	−	0.976588i	$-0.569014\pi$
$167$	−928.498	−0.430236	−0.215118	+	0.976588i	$0.569014\pi$
$168$	0	0
$169$	−2188.37	−0.996072
$170$	−147.218	−0.0664182
$171$	48.9222	0.0218782
$172$	−3771.82	−1.67209
$173$	315.642	0.138716	0.0693578	−	0.997592i	$-0.477905\pi$
$173$	315.642	0.138716	0.0693578	+	0.997592i	$0.477905\pi$
$174$	3962.39	1.72637
$175$	0	0
$176$	137.626	0.0589431
$177$	−250.156	−0.106231
$178$	−1478.28	−0.622480
$179$	−1445.49	−0.603581	−0.301791	−	0.953374i	$-0.597584\pi$
$179$	−1445.49	−0.603581	−0.301791	+	0.953374i	$0.597584\pi$
$180$	−563.901	−0.233504
$181$	1843.81	0.757180	0.378590	−	0.925564i	$-0.376409\pi$
$181$	1843.81	0.757180	0.378590	+	0.925564i	$0.376409\pi$
$182$	0	0
$183$	−15.7587	−0.00636567
$184$	1013.77	0.406176
$185$	965.603	0.383744
$186$	3320.97	1.30917
$187$	−123.868	−0.0484391
$188$	−1084.02	−0.420532
$189$	0	0
$190$	−123.152	−0.0470229
$191$	−244.074	−0.0924637	−0.0462318	−	0.998931i	$-0.514721\pi$
$191$	−244.074	−0.0924637	−0.0462318	+	0.998931i	$0.514721\pi$
$192$	2504.12	0.941246
$193$	−1733.03	−0.646355	−0.323178	−	0.946338i	$-0.604751\pi$
$193$	−1733.03	−0.646355	−0.323178	+	0.946338i	$0.604751\pi$
$194$	−6918.01	−2.56023
$195$	44.0661	0.0161828
$196$	0	0
$197$	358.230	0.129557	0.0647787	−	0.997900i	$-0.479366\pi$
$197$	358.230	0.129557	0.0647787	+	0.997900i	$0.479366\pi$
$198$	−777.362	−0.279014
$199$	3203.63	1.14120	0.570601	−	0.821227i	$-0.306710\pi$
$199$	3203.63	1.14120	0.570601	+	0.821227i	$0.306710\pi$
$200$	513.278	0.181471
$201$	−617.977	−0.216859
$202$	−438.938	−0.152889
$203$	0	0
$204$	−244.284	−0.0838398
$205$	1575.56	0.536791
$206$	−5990.12	−2.02598
$207$	444.397	0.149216
$208$	−21.2100	−0.00707044
$209$	−103.619	−0.0342940
$210$	0	0
$211$	4943.16	1.61280	0.806401	−	0.591369i	$-0.201412\pi$
$211$	4943.16	1.61280	0.806401	+	0.591369i	$0.201412\pi$
$212$	6386.83	2.06910
$213$	−3012.92	−0.969211
$214$	7910.05	2.52673
$215$	1504.98	0.477390
$216$	−554.340	−0.174621
$217$	0	0
$218$	2160.70	0.671288
$219$	−3021.86	−0.932414
$220$	1194.36	0.366016
$221$	19.0896	0.00581044
$222$	2625.16	0.793646
$223$	−3160.15	−0.948965	−0.474482	−	0.880265i	$-0.657365\pi$
$223$	−3160.15	−0.948965	−0.474482	+	0.880265i	$0.657365\pi$
$224$	0	0
$225$	225.000	0.0666667
$226$	7438.51	2.18939
$227$	3651.11	1.06755	0.533773	−	0.845628i	$-0.320774\pi$
$227$	3651.11	1.06755	0.533773	+	0.845628i	$0.320774\pi$
$228$	−204.350	−0.0593571
$229$	4083.70	1.17842	0.589210	−	0.807980i	$-0.299439\pi$
$229$	4083.70	1.17842	0.589210	+	0.807980i	$0.299439\pi$
$230$	−1118.68	−0.320710
$231$	0	0
$232$	−5984.70	−1.69360
$233$	−3682.51	−1.03540	−0.517702	−	0.855561i	$-0.673212\pi$
$233$	−3682.51	−1.03540	−0.517702	+	0.855561i	$0.673212\pi$
$234$	119.802	0.0334687
$235$	432.529	0.120064
$236$	1044.91	0.288211
$237$	2589.71	0.709789
$238$	0	0
$239$	2658.78	0.719591	0.359796	−	0.933031i	$-0.382846\pi$
$239$	2658.78	0.719591	0.359796	+	0.933031i	$0.382846\pi$
$240$	−108.298	−0.0291274
$241$	4820.39	1.28842	0.644209	−	0.764850i	$-0.277187\pi$
$241$	4820.39	1.28842	0.644209	+	0.764850i	$0.277187\pi$
$242$	−4384.46	−1.16464
$243$	−243.000	−0.0641500
$244$	65.8249	0.0172705
$245$	0	0
$246$	4283.45	1.11017
$247$	15.9690	0.00411369
$248$	−5015.91	−1.28432
$249$	4004.17	1.01909
$250$	−566.391	−0.143287
$251$	−1672.27	−0.420530	−0.210265	−	0.977644i	$-0.567433\pi$
$251$	−1672.27	−0.420530	−0.210265	+	0.977644i	$0.567433\pi$
$252$	0	0
$253$	−941.245	−0.233896
$254$	−3824.34	−0.944727
$255$	97.4709	0.0239367
$256$	−3320.09	−0.810569
$257$	3697.74	0.897506	0.448753	−	0.893656i	$-0.351868\pi$
$257$	3697.74	0.897506	0.448753	+	0.893656i	$0.351868\pi$
$258$	4091.56	0.987322
$259$	0	0
$260$	−184.066	−0.0439050
$261$	−2623.45	−0.622174
$262$	12670.0	2.98760
$263$	7319.00	1.71600	0.858002	−	0.513646i	$-0.171706\pi$
$263$	7319.00	1.71600	0.858002	+	0.513646i	$0.171706\pi$
$264$	1174.11	0.273717
$265$	−2548.39	−0.590740
$266$	0	0
$267$	978.747	0.224338
$268$	2581.32	0.588354
$269$	815.097	0.184749	0.0923743	−	0.995724i	$-0.470554\pi$
$269$	815.097	0.184749	0.0923743	+	0.995724i	$0.470554\pi$
$270$	611.702	0.137878
$271$	5106.02	1.14453	0.572267	−	0.820068i	$-0.306064\pi$
$271$	5106.02	1.14453	0.572267	+	0.820068i	$0.306064\pi$
$272$	−46.9150	−0.0104582
$273$	0	0
$274$	−9321.13	−2.05515
$275$	−476.556	−0.104500
$276$	−1856.26	−0.404833
$277$	1398.72	0.303398	0.151699	−	0.988427i	$-0.451526\pi$
$277$	1398.72	0.303398	0.151699	+	0.988427i	$0.451526\pi$
$278$	7907.39	1.70595
$279$	−2198.77	−0.471816
$280$	0	0
$281$	−7102.38	−1.50780	−0.753901	−	0.656988i	$-0.771830\pi$
$281$	−7102.38	−1.50780	−0.753901	+	0.656988i	$0.771830\pi$
$282$	1175.91	0.248313
$283$	−4465.18	−0.937907	−0.468953	−	0.883223i	$-0.655369\pi$
$283$	−4465.18	−0.937907	−0.468953	+	0.883223i	$0.655369\pi$
$284$	12585.1	2.62954
$285$	81.5371	0.0169468
$286$	−253.743	−0.0524621
$287$	0	0
$288$	−1772.67	−0.362692
$289$	−4870.78	−0.991405
$290$	6603.99	1.33724
$291$	4580.32	0.922692
$292$	12622.5	2.52970
$293$	−7590.61	−1.51348	−0.756738	−	0.653718i	$-0.773208\pi$
$293$	−7590.61	−1.51348	−0.756738	+	0.653718i	$0.773208\pi$
$294$	0	0
$295$	−416.926	−0.0822860
$296$	−3964.98	−0.778581
$297$	514.681	0.100555
$298$	−5317.61	−1.03369
$299$	145.058	0.0280566
$300$	−939.835	−0.180871
$301$	0	0
$302$	6978.26	1.32965
$303$	290.615	0.0551003
$304$	−39.2456	−0.00740425
$305$	−26.2645	−0.00493083
$306$	264.992	0.0495052
$307$	−9480.12	−1.76241	−0.881203	−	0.472737i	$-0.843266\pi$
$307$	−9480.12	−1.76241	−0.881203	+	0.472737i	$0.843266\pi$
$308$	0	0
$309$	3965.98	0.730151
$310$	5534.94	1.01408
$311$	−7078.01	−1.29054	−0.645268	−	0.763956i	$-0.723254\pi$
$311$	−7078.01	−1.29054	−0.645268	+	0.763956i	$0.723254\pi$
$312$	−180.945	−0.0328334
$313$	−5593.84	−1.01017	−0.505084	−	0.863070i	$-0.668539\pi$
$313$	−5593.84	−1.01017	−0.505084	+	0.863070i	$0.668539\pi$
$314$	11529.6	2.07214
$315$	0	0
$316$	−10817.3	−1.92571
$317$	3567.81	0.632139	0.316070	−	0.948736i	$-0.397637\pi$
$317$	3567.81	0.632139	0.316070	+	0.948736i	$0.397637\pi$
$318$	−6928.24	−1.22175
$319$	5556.54	0.975255
$320$	4173.53	0.729086
$321$	−5237.14	−0.910618
$322$	0	0
$323$	35.3222	0.00608477
$324$	1015.02	0.174043
$325$	73.4436	0.0125351
$326$	−2694.70	−0.457809
$327$	−1430.57	−0.241928
$328$	−6469.62	−1.08910
$329$	0	0
$330$	−1295.60	−0.216123
$331$	−4389.67	−0.728936	−0.364468	−	0.931216i	$-0.618749\pi$
$331$	−4389.67	−0.728936	−0.364468	+	0.931216i	$0.618749\pi$
$332$	−16725.6	−2.76487
$333$	−1738.09	−0.286026
$334$	−4207.14	−0.689236
$335$	−1029.96	−0.167978
$336$	0	0
$337$	2348.83	0.379671	0.189835	−	0.981816i	$-0.439205\pi$
$337$	2348.83	0.379671	0.189835	+	0.981816i	$0.439205\pi$
$338$	−9915.79	−1.59570
$339$	−4924.94	−0.789044
$340$	−407.140	−0.0649420
$341$	4657.05	0.739570
$342$	221.673	0.0350488
$343$	0	0
$344$	−6179.79	−0.968581
$345$	740.661	0.115582
$346$	1430.21	0.222222
$347$	558.436	0.0863931	0.0431965	−	0.999067i	$-0.486246\pi$
$347$	558.436	0.0863931	0.0431965	+	0.999067i	$0.486246\pi$
$348$	10958.3	1.68800
$349$	−3233.89	−0.496006	−0.248003	−	0.968759i	$-0.579774\pi$
$349$	−3233.89	−0.496006	−0.248003	+	0.968759i	$0.579774\pi$
$350$	0	0
$351$	−79.3190	−0.0120619
$352$	3754.56	0.568519
$353$	7516.35	1.13330	0.566650	−	0.823959i	$-0.308239\pi$
$353$	7516.35	1.13330	0.566650	+	0.823959i	$0.308239\pi$
$354$	−1133.49	−0.170181
$355$	−5021.54	−0.750748
$356$	−4088.27	−0.608646
$357$	0	0
$358$	−6549.70	−0.966935
$359$	−6577.76	−0.967021	−0.483511	−	0.875338i	$-0.660639\pi$
$359$	−6577.76	−0.967021	−0.483511	+	0.875338i	$0.660639\pi$
$360$	−923.901	−0.135261
$361$	−6829.45	−0.995692
$362$	8354.56	1.21300
$363$	2902.89	0.419731
$364$	0	0
$365$	−5036.44	−0.722245
$366$	−71.4048	−0.0101978
$367$	−8307.17	−1.18155	−0.590777	−	0.806835i	$-0.701179\pi$
$367$	−8307.17	−1.18155	−0.590777	+	0.806835i	$0.701179\pi$
$368$	−356.497	−0.0504992
$369$	−2836.02	−0.400101
$370$	4375.27	0.614756
$371$	0	0
$372$	9184.34	1.28007
$373$	−4551.09	−0.631760	−0.315880	−	0.948799i	$-0.602300\pi$
$373$	−4551.09	−0.631760	−0.315880	+	0.948799i	$0.602300\pi$
$374$	−561.261	−0.0775992
$375$	375.000	0.0516398
$376$	−1776.06	−0.243599
$377$	−856.335	−0.116985
$378$	0	0
$379$	−1788.29	−0.242370	−0.121185	−	0.992630i	$-0.538669\pi$
$379$	−1788.29	−0.242370	−0.121185	+	0.992630i	$0.538669\pi$
$380$	−340.584	−0.0459778
$381$	2532.05	0.340474
$382$	−1105.93	−0.148126
$383$	1358.47	0.181240	0.0906199	−	0.995886i	$-0.471115\pi$
$383$	1358.47	0.181240	0.0906199	+	0.995886i	$0.471115\pi$
$384$	6619.37	0.879670
$385$	0	0
$386$	−7852.60	−1.03546
$387$	−2708.97	−0.355825
$388$	−19132.2	−2.50333
$389$	9722.54	1.26723	0.633615	−	0.773649i	$-0.281570\pi$
$389$	9722.54	1.26723	0.633615	+	0.773649i	$0.281570\pi$
$390$	199.669	0.0259247
$391$	320.858	0.0414999
$392$	0	0
$393$	−8388.61	−1.07672
$394$	1623.19	0.207551
$395$	4316.19	0.549800
$396$	−2149.84	−0.272812
$397$	4788.04	0.605302	0.302651	−	0.953101i	$-0.402128\pi$
$397$	4788.04	0.605302	0.302651	+	0.953101i	$0.402128\pi$
$398$	14516.1	1.82820
$399$	0	0
$400$	−180.496	−0.0225620
$401$	9681.41	1.20565	0.602826	−	0.797873i	$-0.294041\pi$
$401$	9681.41	1.20565	0.602826	+	0.797873i	$0.294041\pi$
$402$	−2800.13	−0.347408
$403$	−717.712	−0.0887141
$404$	−1213.91	−0.149491
$405$	−405.000	−0.0496904
$406$	0	0
$407$	3681.32	0.448344
$408$	−400.238	−0.0485655
$409$	−11113.1	−1.34353	−0.671767	−	0.740763i	$-0.734464\pi$
$409$	−11113.1	−1.34353	−0.671767	+	0.740763i	$0.734464\pi$
$410$	7139.09	0.859937
$411$	6171.40	0.740663
$412$	−16566.1	−1.98095
$413$	0	0
$414$	2013.62	0.239043
$415$	6673.62	0.789386
$416$	−578.627	−0.0681959
$417$	−5235.37	−0.614814
$418$	−469.510	−0.0549389
$419$	1230.09	0.143421	0.0717107	−	0.997425i	$-0.477154\pi$
$419$	1230.09	0.143421	0.0717107	+	0.997425i	$0.477154\pi$
$420$	0	0
$421$	−12356.5	−1.43044	−0.715222	−	0.698897i	$-0.753674\pi$
$421$	−12356.5	−1.43044	−0.715222	+	0.698897i	$0.753674\pi$
$422$	22398.1	2.58370
$423$	−778.552	−0.0894906
$424$	10464.2	1.19856
$425$	162.452	0.0185413
$426$	−13651.9	−1.55267
$427$	0	0
$428$	21875.7	2.47057
$429$	168.000	0.0189070
$430$	6819.26	0.764777
$431$	−7375.27	−0.824256	−0.412128	−	0.911126i	$-0.635214\pi$
$431$	−7375.27	−0.824256	−0.412128	+	0.911126i	$0.635214\pi$
$432$	194.936	0.0217103
$433$	690.067	0.0765877	0.0382939	−	0.999267i	$-0.487808\pi$
$433$	690.067	0.0765877	0.0382939	+	0.999267i	$0.487808\pi$
$434$	0	0
$435$	−4372.41	−0.481934
$436$	5975.55	0.656369
$437$	268.406	0.0293812
$438$	−13692.5	−1.49372
$439$	−8408.79	−0.914191	−0.457095	−	0.889418i	$-0.651110\pi$
$439$	−8408.79	−0.914191	−0.457095	+	0.889418i	$0.651110\pi$
$440$	1956.85	0.212021
$441$	0	0
$442$	86.4976	0.00930830
$443$	6568.55	0.704473	0.352236	−	0.935911i	$-0.385421\pi$
$443$	6568.55	0.704473	0.352236	+	0.935911i	$0.385421\pi$
$444$	7260.06	0.776007
$445$	1631.25	0.173772
$446$	−14319.0	−1.52024
$447$	3520.72	0.372537
$448$	0	0
$449$	2954.55	0.310543	0.155271	−	0.987872i	$-0.450375\pi$
$449$	2954.55	0.310543	0.155271	+	0.987872i	$0.450375\pi$
$450$	1019.50	0.106800
$451$	6006.76	0.627156
$452$	20571.7	2.14073
$453$	−4620.21	−0.479197
$454$	16543.7	1.71020
$455$	0	0
$456$	−334.810	−0.0343835
$457$	−8144.84	−0.833697	−0.416849	−	0.908976i	$-0.636865\pi$
$457$	−8144.84	−0.833697	−0.416849	+	0.908976i	$0.636865\pi$
$458$	18503.8	1.88782
$459$	−175.448	−0.0178414
$460$	−3093.77	−0.313583
$461$	−2495.26	−0.252095	−0.126048	−	0.992024i	$-0.540229\pi$
$461$	−2495.26	−0.252095	−0.126048	+	0.992024i	$0.540229\pi$
$462$	0	0
$463$	−5755.66	−0.577728	−0.288864	−	0.957370i	$-0.593278\pi$
$463$	−5755.66	−0.577728	−0.288864	+	0.957370i	$0.593278\pi$
$464$	2104.54	0.210562
$465$	−3664.61	−0.365467
$466$	−16685.9	−1.65871
$467$	4143.73	0.410598	0.205299	−	0.978699i	$-0.434183\pi$
$467$	4143.73	0.410598	0.205299	+	0.978699i	$0.434183\pi$
$468$	331.319	0.0327248
$469$	0	0
$470$	1959.84	0.192342
$471$	−7633.60	−0.746789
$472$	1711.99	0.166951
$473$	5737.67	0.557755
$474$	11734.3	1.13708
$475$	135.895	0.0131269
$476$	0	0
$477$	4587.09	0.440312
$478$	12047.3	1.15278
$479$	6765.96	0.645396	0.322698	−	0.946502i	$-0.395410\pi$
$479$	6765.96	0.645396	0.322698	+	0.946502i	$0.395410\pi$
$480$	−2954.45	−0.280940
$481$	−567.339	−0.0537805
$482$	21841.8	2.06404
$483$	0	0
$484$	−12125.5	−1.13876
$485$	7633.87	0.714714
$486$	−1101.06	−0.102768
$487$	6360.42	0.591824	0.295912	−	0.955215i	$-0.404377\pi$
$487$	6360.42	0.591824	0.295912	+	0.955215i	$0.404377\pi$
$488$	107.848	0.0100042
$489$	1784.12	0.164992
$490$	0	0
$491$	−7072.54	−0.650060	−0.325030	−	0.945704i	$-0.605374\pi$
$491$	−7072.54	−0.650060	−0.325030	+	0.945704i	$0.605374\pi$
$492$	11846.2	1.08550
$493$	−1894.15	−0.173039
$494$	72.3576	0.00659012
$495$	857.802	0.0778895
$496$	1763.86	0.159677
$497$	0	0
$498$	18143.4	1.63258
$499$	−18473.9	−1.65732	−0.828661	−	0.559751i	$-0.810897\pi$
$499$	−18473.9	−1.65732	−0.828661	+	0.559751i	$0.810897\pi$
$500$	−1566.39	−0.140102
$501$	2785.49	0.248397
$502$	−7577.28	−0.673687
$503$	−11379.2	−1.00869	−0.504347	−	0.863501i	$-0.668267\pi$
$503$	−11379.2	−1.00869	−0.504347	+	0.863501i	$0.668267\pi$
$504$	0	0
$505$	484.358	0.0426805
$506$	−4264.90	−0.374700
$507$	6565.11	0.575082
$508$	−10576.5	−0.923730
$509$	−6064.48	−0.528101	−0.264051	−	0.964509i	$-0.585059\pi$
$509$	−6064.48	−0.528101	−0.264051	+	0.964509i	$0.585059\pi$
$510$	441.653	0.0383465
$511$	0	0
$512$	2607.89	0.225105
$513$	−146.767	−0.0126314
$514$	16755.0	1.43780
$515$	6609.96	0.565572
$516$	11315.5	0.965379
$517$	1649.00	0.140276
$518$	0	0
$519$	−946.926	−0.0800875
$520$	−301.576	−0.0254326
$521$	−2682.88	−0.225603	−0.112801	−	0.993618i	$-0.535982\pi$
$521$	−2682.88	−0.225603	−0.112801	+	0.993618i	$0.535982\pi$
$522$	−11887.2	−0.996720
$523$	4309.02	0.360268	0.180134	−	0.983642i	$-0.442347\pi$
$523$	4309.02	0.360268	0.180134	+	0.983642i	$0.442347\pi$
$524$	35039.6	2.92120
$525$	0	0
$526$	33163.3	2.74903
$527$	−1587.52	−0.131221
$528$	−412.879	−0.0340308
$529$	−9728.87	−0.799611
$530$	−11547.1	−0.946363
$531$	750.467	0.0613323
$532$	0	0
$533$	−925.720	−0.0752296
$534$	4434.83	0.359389
$535$	−8728.56	−0.705362
$536$	4229.25	0.340813
$537$	4336.47	0.348478
$538$	3693.31	0.295966
$539$	0	0
$540$	1691.70	0.134813
$541$	4081.47	0.324355	0.162178	−	0.986762i	$-0.448148\pi$
$541$	4081.47	0.324355	0.162178	+	0.986762i	$0.448148\pi$
$542$	23136.0	1.83354
$543$	−5531.44	−0.437158
$544$	−1279.88	−0.100872
$545$	−2384.28	−0.187397
$546$	0	0
$547$	8844.82	0.691366	0.345683	−	0.938351i	$-0.387647\pi$
$547$	8844.82	0.691366	0.345683	+	0.938351i	$0.387647\pi$
$548$	−25778.2	−2.00947
$549$	47.2762	0.00367522
$550$	−2159.34	−0.167408
$551$	−1584.51	−0.122509
$552$	−3041.32	−0.234506
$553$	0	0
$554$	6337.80	0.486042
$555$	−2896.81	−0.221554
$556$	21868.4	1.66803
$557$	−11144.7	−0.847787	−0.423894	−	0.905712i	$-0.639337\pi$
$557$	−11144.7	−0.847787	−0.423894	+	0.905712i	$0.639337\pi$
$558$	−9962.90	−0.755848
$559$	−884.249	−0.0669047
$560$	0	0
$561$	371.603	0.0279663
$562$	−32181.8	−2.41549
$563$	21857.5	1.63621	0.818104	−	0.575071i	$-0.195025\pi$
$563$	21857.5	1.63621	0.818104	+	0.575071i	$0.195025\pi$
$564$	3252.05	0.242794
$565$	−8208.23	−0.611191
$566$	−20232.3	−1.50252
$567$	0	0
$568$	20619.6	1.52320
$569$	23496.4	1.73115	0.865573	−	0.500783i	$-0.166954\pi$
$569$	23496.4	1.73115	0.865573	+	0.500783i	$0.166954\pi$
$570$	369.455	0.0271487
$571$	11067.8	0.811164	0.405582	−	0.914059i	$-0.367069\pi$
$571$	11067.8	0.811164	0.405582	+	0.914059i	$0.367069\pi$
$572$	−701.743	−0.0512961
$573$	732.222	0.0533839
$574$	0	0
$575$	1234.44	0.0895296
$576$	−7512.36	−0.543429
$577$	−20482.9	−1.47784	−0.738922	−	0.673791i	$-0.764665\pi$
$577$	−20482.9	−1.47784	−0.738922	+	0.673791i	$0.764665\pi$
$578$	−22070.1	−1.58823
$579$	5199.10	0.373173
$580$	18263.8	1.30752
$581$	0	0
$582$	20754.0	1.47815
$583$	−9715.60	−0.690187
$584$	20680.8	1.46537
$585$	−132.198	−0.00934313
$586$	−34394.1	−2.42458
$587$	23444.3	1.64847	0.824235	−	0.566248i	$-0.191606\pi$
$587$	23444.3	1.64847	0.824235	+	0.566248i	$0.191606\pi$
$588$	0	0
$589$	−1328.01	−0.0929025
$590$	−1889.14	−0.131822
$591$	−1074.69	−0.0748000
$592$	1394.30	0.0967996
$593$	−4404.69	−0.305024	−0.152512	−	0.988302i	$-0.548736\pi$
$593$	−4404.69	−0.305024	−0.152512	+	0.988302i	$0.548736\pi$
$594$	2332.09	0.161089
$595$	0	0
$596$	−14706.2	−1.01072
$597$	−9610.89	−0.658874
$598$	657.277	0.0449466
$599$	3327.05	0.226945	0.113472	−	0.993541i	$-0.463803\pi$
$599$	3327.05	0.226945	0.113472	+	0.993541i	$0.463803\pi$
$600$	−1539.83	−0.104772
$601$	14244.8	0.966818	0.483409	−	0.875395i	$-0.339398\pi$
$601$	14244.8	0.966818	0.483409	+	0.875395i	$0.339398\pi$
$602$	0	0
$603$	1853.93	0.125204
$604$	19298.8	1.30010
$605$	4838.15	0.325122
$606$	1316.81	0.0882704
$607$	−11446.5	−0.765402	−0.382701	−	0.923872i	$-0.625006\pi$
$607$	−11446.5	−0.765402	−0.382701	+	0.923872i	$0.625006\pi$
$608$	−1070.65	−0.0714156
$609$	0	0
$610$	−119.008	−0.00789917
$611$	−254.132	−0.0168266
$612$	732.852	0.0484049
$613$	−19436.4	−1.28063	−0.640316	−	0.768111i	$-0.721197\pi$
$613$	−19436.4	−1.28063	−0.640316	+	0.768111i	$0.721197\pi$
$614$	−42955.6	−2.82337
$615$	−4726.69	−0.309917
$616$	0	0
$617$	−20530.1	−1.33956	−0.669781	−	0.742558i	$-0.733612\pi$
$617$	−20530.1	−1.33956	−0.669781	+	0.742558i	$0.733612\pi$
$618$	17970.4	1.16970
$619$	−5833.35	−0.378776	−0.189388	−	0.981902i	$-0.560650\pi$
$619$	−5833.35	−0.378776	−0.189388	+	0.981902i	$0.560650\pi$
$620$	15307.2	0.991538
$621$	−1333.19	−0.0861499
$622$	−32071.4	−2.06744
$623$	0	0
$624$	63.6301	0.00408212
$625$	625.000	0.0400000
$626$	−25346.4	−1.61829
$627$	310.856	0.0197997
$628$	31885.9	2.02609
$629$	−1254.91	−0.0795493
$630$	0	0
$631$	24776.6	1.56314	0.781568	−	0.623820i	$-0.214420\pi$
$631$	24776.6	1.56314	0.781568	+	0.623820i	$0.214420\pi$
$632$	−17723.2	−1.11549
$633$	−14829.5	−0.931152
$634$	16166.2	1.01268
$635$	4220.08	0.263730
$636$	−19160.5	−1.19460
$637$	0	0
$638$	25177.4	1.56235
$639$	9038.77	0.559574
$640$	11032.3	0.681390
$641$	27219.4	1.67723	0.838613	−	0.544728i	$-0.183367\pi$
$641$	27219.4	1.67723	0.838613	+	0.544728i	$0.183367\pi$
$642$	−23730.1	−1.45881
$643$	−7091.79	−0.434950	−0.217475	−	0.976066i	$-0.569782\pi$
$643$	−7091.79	−0.434950	−0.217475	+	0.976066i	$0.569782\pi$
$644$	0	0
$645$	−4514.94	−0.275621
$646$	160.049	0.00974777
$647$	−27773.0	−1.68758	−0.843792	−	0.536670i	$-0.819682\pi$
$647$	−27773.0	−1.68758	−0.843792	+	0.536670i	$0.819682\pi$
$648$	1663.02	0.100817
$649$	−1589.51	−0.0961382
$650$	332.782	0.0200812
$651$	0	0
$652$	−7452.37	−0.447634
$653$	21380.4	1.28129	0.640643	−	0.767839i	$-0.278668\pi$
$653$	21380.4	1.28129	0.640643	+	0.767839i	$0.278668\pi$
$654$	−6482.09	−0.387568
$655$	−13981.0	−0.834020
$656$	2275.06	0.135406
$657$	9065.59	0.538329
$658$	0	0
$659$	−17232.3	−1.01863	−0.509315	−	0.860580i	$-0.670101\pi$
$659$	−17232.3	−1.01863	−0.509315	+	0.860580i	$0.670101\pi$
$660$	−3583.07	−0.211320
$661$	−26577.7	−1.56392	−0.781962	−	0.623326i	$-0.785781\pi$
$661$	−26577.7	−1.56392	−0.781962	+	0.623326i	$0.785781\pi$
$662$	−19890.1	−1.16775
$663$	−57.2689	−0.00335466
$664$	−27403.4	−1.60159
$665$	0	0
$666$	−7875.49	−0.458212
$667$	−14393.2	−0.835544
$668$	−11635.1	−0.673917
$669$	9480.44	0.547885
$670$	−4666.89	−0.269101
$671$	−100.132	−0.00576090
$672$	0	0
$673$	−31695.2	−1.81540	−0.907698	−	0.419624i	$-0.862162\pi$
$673$	−31695.2	−1.81540	−0.907698	+	0.419624i	$0.862162\pi$
$674$	10642.9	0.608231
$675$	−675.000	−0.0384900
$676$	−27422.7	−1.56024
$677$	−20440.3	−1.16039	−0.580195	−	0.814477i	$-0.697024\pi$
$677$	−20440.3	−1.16039	−0.580195	+	0.814477i	$0.697024\pi$
$678$	−22315.5	−1.26405
$679$	0	0
$680$	−667.063	−0.0376187
$681$	−10953.3	−0.616348
$682$	21101.7	1.18479
$683$	−22896.9	−1.28276	−0.641381	−	0.767223i	$-0.721638\pi$
$683$	−22896.9	−1.28276	−0.641381	+	0.767223i	$0.721638\pi$
$684$	613.051	0.0342699
$685$	10285.7	0.573715
$686$	0	0
$687$	−12251.1	−0.680361
$688$	2173.14	0.120422
$689$	1497.30	0.0827904
$690$	3356.03	0.185162
$691$	23764.0	1.30829	0.654143	−	0.756371i	$-0.273029\pi$
$691$	23764.0	1.30829	0.654143	+	0.756371i	$0.273029\pi$
$692$	3955.35	0.217283
$693$	0	0
$694$	2530.34	0.138401
$695$	−8725.62	−0.476233
$696$	17954.1	0.977800
$697$	−2047.62	−0.111276
$698$	−14653.2	−0.794600
$699$	11047.5	0.597791
$700$	0	0
$701$	26259.5	1.41485	0.707423	−	0.706791i	$-0.249858\pi$
$701$	26259.5	1.41485	0.707423	+	0.706791i	$0.249858\pi$
$702$	−359.405	−0.0193232
$703$	−1049.77	−0.0563196
$704$	15911.4	0.851822
$705$	−1297.59	−0.0693191
$706$	34057.6	1.81554
$707$	0	0
$708$	−3134.73	−0.166399
$709$	12783.0	0.677116	0.338558	−	0.940945i	$-0.390061\pi$
$709$	12783.0	0.677116	0.338558	+	0.940945i	$0.390061\pi$
$710$	−22753.2	−1.20270
$711$	−7769.14	−0.409797
$712$	−6698.26	−0.352567
$713$	−12063.3	−0.633623
$714$	0	0
$715$	280.000	0.0146453
$716$	−18113.6	−0.945444
$717$	−7976.35	−0.415456
$718$	−29804.7	−1.54916
$719$	27609.0	1.43205	0.716025	−	0.698075i	$-0.245960\pi$
$719$	27609.0	1.43205	0.716025	+	0.698075i	$0.245960\pi$
$720$	324.893	0.0168167
$721$	0	0
$722$	−30945.1	−1.59509
$723$	−14461.2	−0.743868
$724$	23105.1	1.18604
$725$	−7287.35	−0.373304
$726$	13153.4	0.672407
$727$	−31306.2	−1.59709	−0.798544	−	0.601937i	$-0.794396\pi$
$727$	−31306.2	−1.59709	−0.798544	+	0.601937i	$0.794396\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−22820.8	−1.15703
$731$	−1955.89	−0.0989621
$732$	−197.475	−0.00997113
$733$	15765.8	0.794441	0.397220	−	0.917723i	$-0.369975\pi$
$733$	15765.8	0.794441	0.397220	+	0.917723i	$0.369975\pi$
$734$	−37640.8	−1.89285
$735$	0	0
$736$	−9725.53	−0.487076
$737$	−3926.68	−0.196256
$738$	−12850.4	−0.640959
$739$	3966.51	0.197443	0.0987216	−	0.995115i	$-0.468525\pi$
$739$	3966.51	0.197443	0.0987216	+	0.995115i	$0.468525\pi$
$740$	12100.1	0.601093
$741$	−47.9070	−0.00237504
$742$	0	0
$743$	8224.50	0.406094	0.203047	−	0.979169i	$-0.434916\pi$
$743$	8224.50	0.406094	0.203047	+	0.979169i	$0.434916\pi$
$744$	15047.7	0.741500
$745$	5867.86	0.288566
$746$	−20621.6	−1.01208
$747$	−12012.5	−0.588373
$748$	−1552.20	−0.0758745
$749$	0	0
$750$	1699.17	0.0827267
$751$	18929.2	0.919754	0.459877	−	0.887983i	$-0.347894\pi$
$751$	18929.2	0.919754	0.459877	+	0.887983i	$0.347894\pi$
$752$	624.558	0.0302863
$753$	5016.82	0.242793
$754$	−3880.16	−0.187410
$755$	−7700.35	−0.371185
$756$	0	0
$757$	−34906.8	−1.67597	−0.837984	−	0.545695i	$-0.816266\pi$
$757$	−34906.8	−1.67597	−0.837984	+	0.545695i	$0.816266\pi$
$758$	−8102.96	−0.388276
$759$	2823.74	0.135040
$760$	−558.016	−0.0266334
$761$	13683.4	0.651803	0.325902	−	0.945404i	$-0.394332\pi$
$761$	13683.4	0.651803	0.325902	+	0.945404i	$0.394332\pi$
$762$	11473.0	0.545438
$763$	0	0
$764$	−3058.52	−0.144834
$765$	−292.413	−0.0138199
$766$	6155.42	0.290345
$767$	244.964	0.0115321
$768$	9960.28	0.467982
$769$	−41837.3	−1.96189	−0.980943	−	0.194294i	$-0.937758\pi$
$769$	−41837.3	−1.96189	−0.980943	+	0.194294i	$0.937758\pi$
$770$	0	0
$771$	−11093.2	−0.518175
$772$	−21716.9	−1.01245
$773$	−19640.0	−0.913843	−0.456921	−	0.889507i	$-0.651048\pi$
$773$	−19640.0	−0.913843	−0.456921	+	0.889507i	$0.651048\pi$
$774$	−12274.7	−0.570031
$775$	−6107.69	−0.283090
$776$	−31346.4	−1.45009
$777$	0	0
$778$	44054.1	2.03010
$779$	−1712.89	−0.0787814
$780$	552.198	0.0253486
$781$	−19144.4	−0.877131
$782$	1453.85	0.0664827
$783$	7870.34	0.359212
$784$	0	0
$785$	−12722.7	−0.578460
$786$	−38009.9	−1.72489
$787$	−24935.3	−1.12941	−0.564705	−	0.825293i	$-0.691010\pi$
$787$	−24935.3	−1.12941	−0.564705	+	0.825293i	$0.691010\pi$
$788$	4489.02	0.202938
$789$	−21957.0	−0.990736
$790$	19557.2	0.880777
$791$	0	0
$792$	−3522.33	−0.158031
$793$	15.4317	0.000691041 0
$794$	21695.2	0.969692
$795$	7645.16	0.341064
$796$	40145.1	1.78757
$797$	1168.33	0.0519251	0.0259625	−	0.999663i	$-0.491735\pi$
$797$	1168.33	0.0519251	0.0259625	+	0.999663i	$0.491735\pi$
$798$	0	0
$799$	−562.120	−0.0248891
$800$	−4924.08	−0.217615
$801$	−2936.24	−0.129522
$802$	43867.7	1.93145
$803$	−19201.2	−0.843829
$804$	−7743.95	−0.339686
$805$	0	0
$806$	−3252.05	−0.142120
$807$	−2445.29	−0.106665
$808$	−1988.88	−0.0865949
$809$	−35175.7	−1.52869	−0.764345	−	0.644807i	$-0.776938\pi$
$809$	−35175.7	−1.52869	−0.764345	+	0.644807i	$0.776938\pi$
$810$	−1835.11	−0.0796038
$811$	15256.5	0.660577	0.330288	−	0.943880i	$-0.392854\pi$
$811$	15256.5	0.660577	0.330288	+	0.943880i	$0.392854\pi$
$812$	0	0
$813$	−15318.1	−0.660797
$814$	16680.5	0.718245
$815$	2973.54	0.127802
$816$	140.745	0.00603806
$817$	−1636.16	−0.0700635
$818$	−50354.7	−2.15233
$819$	0	0
$820$	19743.6	0.840825
$821$	−15971.9	−0.678956	−0.339478	−	0.940614i	$-0.610250\pi$
$821$	−15971.9	−0.678956	−0.339478	+	0.940614i	$0.610250\pi$
$822$	27963.4	1.18654
$823$	2312.41	0.0979409	0.0489705	−	0.998800i	$-0.484406\pi$
$823$	2312.41	0.0979409	0.0489705	+	0.998800i	$0.484406\pi$
$824$	−27142.0	−1.14750
$825$	1429.67	0.0603330
$826$	0	0
$827$	10422.4	0.438238	0.219119	−	0.975698i	$-0.429682\pi$
$827$	10422.4	0.438238	0.219119	+	0.975698i	$0.429682\pi$
$828$	5568.79	0.233731
$829$	13213.4	0.553584	0.276792	−	0.960930i	$-0.410729\pi$
$829$	13213.4	0.553584	0.276792	+	0.960930i	$0.410729\pi$
$830$	30239.0	1.26459
$831$	−4196.17	−0.175167
$832$	−2452.15	−0.102179
$833$	0	0
$834$	−23722.2	−0.984929
$835$	4642.49	0.192407
$836$	−1298.46	−0.0537179
$837$	6596.30	0.272403
$838$	5573.67	0.229761
$839$	10119.6	0.416409	0.208205	−	0.978085i	$-0.433238\pi$
$839$	10119.6	0.416409	0.208205	+	0.978085i	$0.433238\pi$
$840$	0	0
$841$	60579.9	2.48390
$842$	−55988.7	−2.29157
$843$	21307.1	0.870530
$844$	61943.4	2.52628
$845$	10941.8	0.445457
$846$	−3527.72	−0.143364
$847$	0	0
$848$	−3679.79	−0.149015
$849$	13395.5	0.541501
$850$	736.089	0.0297031
$851$	−9535.80	−0.384116
$852$	−37755.3	−1.51816
$853$	−35378.1	−1.42007	−0.710037	−	0.704165i	$-0.751322\pi$
$853$	−35378.1	−1.42007	−0.710037	+	0.704165i	$0.751322\pi$
$854$	0	0
$855$	−244.611	−0.00978424
$856$	35841.4	1.43112
$857$	−6697.57	−0.266960	−0.133480	−	0.991052i	$-0.542615\pi$
$857$	−6697.57	−0.266960	−0.133480	+	0.991052i	$0.542615\pi$
$858$	761.230	0.0302890
$859$	24298.4	0.965135	0.482568	−	0.875859i	$-0.339704\pi$
$859$	24298.4	0.965135	0.482568	+	0.875859i	$0.339704\pi$
$860$	18859.1	0.747779
$861$	0	0
$862$	−33418.3	−1.32045
$863$	24942.9	0.983853	0.491926	−	0.870637i	$-0.336293\pi$
$863$	24942.9	0.983853	0.491926	+	0.870637i	$0.336293\pi$
$864$	5318.00	0.209401
$865$	−1578.21	−0.0620355
$866$	3126.78	0.122693
$867$	14612.3	0.572388
$868$	0	0
$869$	16455.3	0.642355
$870$	−19812.0	−0.772056
$871$	605.152	0.0235417
$872$	9790.39	0.380212
$873$	−13741.0	−0.532716
$874$	1216.18	0.0470686
$875$	0	0
$876$	−37867.4	−1.46052
$877$	−16276.6	−0.626705	−0.313353	−	0.949637i	$-0.601452\pi$
$877$	−16276.6	−0.626705	−0.313353	+	0.949637i	$0.601452\pi$
$878$	−38101.3	−1.46453
$879$	22771.8	0.873806
$880$	−688.132	−0.0263602
$881$	−26636.5	−1.01862	−0.509311	−	0.860582i	$-0.670100\pi$
$881$	−26636.5	−1.01862	−0.509311	+	0.860582i	$0.670100\pi$
$882$	0	0
$883$	−21788.3	−0.830392	−0.415196	−	0.909732i	$-0.636287\pi$
$883$	−21788.3	−0.830392	−0.415196	+	0.909732i	$0.636287\pi$
$884$	239.215	0.00910142
$885$	1250.78	0.0475078
$886$	29763.0	1.12856
$887$	26813.2	1.01499	0.507496	−	0.861654i	$-0.330571\pi$
$887$	26813.2	1.01499	0.507496	+	0.861654i	$0.330571\pi$
$888$	11895.0	0.449514
$889$	0	0
$890$	7391.38	0.278382
$891$	−1544.04	−0.0580554
$892$	−39600.2	−1.48645
$893$	−470.229	−0.0176211
$894$	15952.8	0.596803
$895$	7227.45	0.269930
$896$	0	0
$897$	−435.174	−0.0161985
$898$	13387.4	0.497488
$899$	71214.2	2.64196
$900$	2819.50	0.104426
$901$	3311.91	0.122459
$902$	27217.4	1.00470
$903$	0	0
$904$	33704.8	1.24005
$905$	−9219.07	−0.338621
$906$	−20934.8	−0.767672
$907$	15543.0	0.569014	0.284507	−	0.958674i	$-0.408170\pi$
$907$	15543.0	0.569014	0.284507	+	0.958674i	$0.408170\pi$
$908$	45752.6	1.67219
$909$	−871.844	−0.0318122
$910$	0	0
$911$	48711.1	1.77154	0.885768	−	0.464128i	$-0.153632\pi$
$911$	48711.1	1.77154	0.885768	+	0.464128i	$0.153632\pi$
$912$	117.737	0.00427485
$913$	25442.8	0.922273
$914$	−36905.3	−1.33558
$915$	78.7936	0.00284682
$916$	51173.3	1.84587
$917$	0	0
$918$	−794.976	−0.0285818
$919$	1030.47	0.0369883	0.0184941	−	0.999829i	$-0.494113\pi$
$919$	1030.47	0.0369883	0.0184941	+	0.999829i	$0.494113\pi$
$920$	−5068.87	−0.181648
$921$	28440.4	1.01753
$922$	−11306.3	−0.403855
$923$	2950.40	0.105215
$924$	0	0
$925$	−4828.02	−0.171615
$926$	−26079.6	−0.925518
$927$	−11897.9	−0.421553
$928$	57413.6	2.03092
$929$	−879.756	−0.0310698	−0.0155349	−	0.999879i	$-0.504945\pi$
$929$	−879.756	−0.0310698	−0.0155349	+	0.999879i	$0.504945\pi$
$930$	−16604.8	−0.585477
$931$	0	0
$932$	−46146.0	−1.62185
$933$	21234.0	0.745092
$934$	18775.8	0.657776
$935$	619.339	0.0216626
$936$	542.836	0.0189564
$937$	18668.1	0.650864	0.325432	−	0.945565i	$-0.394490\pi$
$937$	18668.1	0.650864	0.325432	+	0.945565i	$0.394490\pi$
$938$	0	0
$939$	16781.5	0.583221
$940$	5420.08	0.188067
$941$	−29613.4	−1.02590	−0.512948	−	0.858420i	$-0.671447\pi$
$941$	−29613.4	−1.02590	−0.512948	+	0.858420i	$0.671447\pi$
$942$	−34588.8	−1.19635
$943$	−15559.5	−0.537313
$944$	−602.028	−0.0207567
$945$	0	0
$946$	25998.1	0.893521
$947$	20738.9	0.711640	0.355820	−	0.934554i	$-0.384202\pi$
$947$	20738.9	0.711640	0.355820	+	0.934554i	$0.384202\pi$
$948$	32452.0	1.11181
$949$	2959.15	0.101220
$950$	615.758	0.0210293
$951$	−10703.4	−0.364966
$952$	0	0
$953$	−45776.5	−1.55598	−0.777988	−	0.628279i	$-0.783760\pi$
$953$	−45776.5	−1.55598	−0.777988	+	0.628279i	$0.783760\pi$
$954$	20784.7	0.705377
$955$	1220.37	0.0413510
$956$	33317.5	1.12716
$957$	−16669.6	−0.563064
$958$	30657.4	1.03392
$959$	0	0
$960$	−12520.6	−0.420938
$961$	29895.1	1.00349
$962$	−2570.68	−0.0861561
$963$	15711.4	0.525746
$964$	60404.9	2.01817
$965$	8665.17	0.289059
$966$	0	0
$967$	34461.0	1.14601	0.573005	−	0.819552i	$-0.305778\pi$
$967$	34461.0	1.14601	0.573005	+	0.819552i	$0.305778\pi$
$968$	−19866.5	−0.659643
$969$	−105.967	−0.00351304
$970$	34590.1	1.14497
$971$	22762.8	0.752309	0.376154	−	0.926557i	$-0.377246\pi$
$971$	22762.8	0.752309	0.376154	+	0.926557i	$0.377246\pi$
$972$	−3045.06	−0.100484
$973$	0	0
$974$	28819.9	0.948099
$975$	−220.331	−0.00723716
$976$	−37.9251	−0.00124381
$977$	4809.57	0.157494	0.0787470	−	0.996895i	$-0.474908\pi$
$977$	4809.57	0.157494	0.0787470	+	0.996895i	$0.474908\pi$
$978$	8084.10	0.264316
$979$	6219.04	0.203025
$980$	0	0
$981$	4291.70	0.139677
$982$	−32046.6	−1.04139
$983$	27591.6	0.895256	0.447628	−	0.894220i	$-0.352269\pi$
$983$	27591.6	0.895256	0.447628	+	0.894220i	$0.352269\pi$
$984$	19408.9	0.628793
$985$	−1791.15	−0.0579399
$986$	−8582.63	−0.277207
$987$	0	0
$988$	200.109	0.00644365
$989$	−14862.4	−0.477854
$990$	3886.81	0.124779
$991$	−22263.4	−0.713643	−0.356822	−	0.934173i	$-0.616140\pi$
$991$	−22263.4	−0.713643	−0.356822	+	0.934173i	$0.616140\pi$
$992$	48119.5	1.54012
$993$	13169.0	0.420851
$994$	0	0
$995$	−16018.2	−0.510361
$996$	50176.8	1.59630
$997$	−30378.2	−0.964983	−0.482491	−	0.875901i	$-0.660268\pi$
$997$	−30378.2	−0.964983	−0.482491	+	0.875901i	$0.660268\pi$
$998$	−83707.4	−2.65502
$999$	5214.26	0.165137

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.4.a.p.1.2		2
3.2	odd	2		2205.4.a.z.1.1		2
7.6	odd	2		105.4.a.f.1.2	✓	2
21.20	even	2		315.4.a.i.1.1		2
28.27	even	2		1680.4.a.bg.1.2		2
35.13	even	4		525.4.d.h.274.1		4
35.27	even	4		525.4.d.h.274.4		4
35.34	odd	2		525.4.a.k.1.1		2
105.104	even	2		1575.4.a.w.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.a.f.1.2	✓	2	7.6	odd	2
315.4.a.i.1.1		2	21.20	even	2
525.4.a.k.1.1		2	35.34	odd	2
525.4.d.h.274.1		4	35.13	even	4
525.4.d.h.274.4		4	35.27	even	4
735.4.a.p.1.2		2	1.1	even	1	trivial
1575.4.a.w.1.2		2	105.104	even	2
1680.4.a.bg.1.2		2	28.27	even	2
2205.4.a.z.1.1		2	3.2	odd	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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	735.a (trivial)

\(f(q)\)	\(=\)	\(q+4.53113 q^{2} -3.00000 q^{3} +12.5311 q^{4} -5.00000 q^{5} -13.5934 q^{6} +20.5311 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+4.53113 q^{2} -3.00000 q^{3} +12.5311 q^{4} -5.00000 q^{5} -13.5934 q^{6} +20.5311 q^{8} +9.00000 q^{9} -22.6556 q^{10} -19.0623 q^{11} -37.5934 q^{12} +2.93774 q^{13} +15.0000 q^{15} -7.21984 q^{16} +6.49806 q^{17} +40.7802 q^{18} +5.43580 q^{19} -62.6556 q^{20} -86.3735 q^{22} +49.3774 q^{23} -61.5934 q^{24} +25.0000 q^{25} +13.3113 q^{26} -27.0000 q^{27} -291.494 q^{29} +67.9669 q^{30} -244.307 q^{31} -196.963 q^{32} +57.1868 q^{33} +29.4436 q^{34} +112.780 q^{36} -193.121 q^{37} +24.6303 q^{38} -8.81323 q^{39} -102.656 q^{40} -315.113 q^{41} -300.996 q^{43} -238.872 q^{44} -45.0000 q^{45} +223.735 q^{46} -86.5058 q^{47} +21.6595 q^{48} +113.278 q^{50} -19.4942 q^{51} +36.8132 q^{52} +509.677 q^{53} -122.340 q^{54} +95.3113 q^{55} -16.3074 q^{57} -1320.80 q^{58} +83.3852 q^{59} +187.967 q^{60} +5.25291 q^{61} -1106.99 q^{62} -834.706 q^{64} -14.6887 q^{65} +259.121 q^{66} +205.992 q^{67} +81.4281 q^{68} -148.132 q^{69} +1004.31 q^{71} +184.780 q^{72} +1007.29 q^{73} -875.055 q^{74} -75.0000 q^{75} +68.1168 q^{76} -39.9339 q^{78} -863.237 q^{79} +36.0992 q^{80} +81.0000 q^{81} -1427.82 q^{82} -1334.72 q^{83} -32.4903 q^{85} -1363.85 q^{86} +874.483 q^{87} -391.370 q^{88} -326.249 q^{89} -203.901 q^{90} +618.755 q^{92} +732.922 q^{93} -391.969 q^{94} -27.1790 q^{95} +590.889 q^{96} -1526.77 q^{97} -171.560 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 6 q^{3} + 17 q^{4} - 10 q^{5} - 3 q^{6} + 33 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + q^2 - 6 * q^3 + 17 * q^4 - 10 * q^5 - 3 * q^6 + 33 * q^8 + 18 * q^9	\( 2 q + q^{2} - 6 q^{3} + 17 q^{4} - 10 q^{5} - 3 q^{6} + 33 q^{8} + 18 q^{9} - 5 q^{10} - 22 q^{11} - 51 q^{12} + 22 q^{13} + 30 q^{15} - 87 q^{16} - 116 q^{17} + 9 q^{18} - 102 q^{19} - 85 q^{20} - 76 q^{22} + 260 q^{23} - 99 q^{24} + 50 q^{25} - 54 q^{26} - 54 q^{27} - 196 q^{29} + 15 q^{30} - 150 q^{31} - 15 q^{32} + 66 q^{33} + 462 q^{34} + 153 q^{36} - 96 q^{37} + 404 q^{38} - 66 q^{39} - 165 q^{40} + 176 q^{41} - 344 q^{43} - 252 q^{44} - 90 q^{45} - 520 q^{46} - 560 q^{47} + 261 q^{48} + 25 q^{50} + 348 q^{51} + 122 q^{52} + 326 q^{53} - 27 q^{54} + 110 q^{55} + 306 q^{57} - 1658 q^{58} + 844 q^{59} + 255 q^{60} + 204 q^{61} - 1440 q^{62} - 839 q^{64} - 110 q^{65} + 228 q^{66} - 104 q^{67} - 466 q^{68} - 780 q^{69} + 1670 q^{71} + 297 q^{72} + 386 q^{73} - 1218 q^{74} - 150 q^{75} - 412 q^{76} + 162 q^{78} - 888 q^{79} + 435 q^{80} + 162 q^{81} - 3162 q^{82} - 928 q^{83} + 580 q^{85} - 1212 q^{86} + 588 q^{87} - 428 q^{88} - 588 q^{89} - 45 q^{90} + 1560 q^{92} + 450 q^{93} + 1280 q^{94} + 510 q^{95} + 45 q^{96} - 522 q^{97} - 198 q^{99}+O(q^{100}) \) 2 * q + q^2 - 6 * q^3 + 17 * q^4 - 10 * q^5 - 3 * q^6 + 33 * q^8 + 18 * q^9 - 5 * q^10 - 22 * q^11 - 51 * q^12 + 22 * q^13 + 30 * q^15 - 87 * q^16 - 116 * q^17 + 9 * q^18 - 102 * q^19 - 85 * q^20 - 76 * q^22 + 260 * q^23 - 99 * q^24 + 50 * q^25 - 54 * q^26 - 54 * q^27 - 196 * q^29 + 15 * q^30 - 150 * q^31 - 15 * q^32 + 66 * q^33 + 462 * q^34 + 153 * q^36 - 96 * q^37 + 404 * q^38 - 66 * q^39 - 165 * q^40 + 176 * q^41 - 344 * q^43 - 252 * q^44 - 90 * q^45 - 520 * q^46 - 560 * q^47 + 261 * q^48 + 25 * q^50 + 348 * q^51 + 122 * q^52 + 326 * q^53 - 27 * q^54 + 110 * q^55 + 306 * q^57 - 1658 * q^58 + 844 * q^59 + 255 * q^60 + 204 * q^61 - 1440 * q^62 - 839 * q^64 - 110 * q^65 + 228 * q^66 - 104 * q^67 - 466 * q^68 - 780 * q^69 + 1670 * q^71 + 297 * q^72 + 386 * q^73 - 1218 * q^74 - 150 * q^75 - 412 * q^76 + 162 * q^78 - 888 * q^79 + 435 * q^80 + 162 * q^81 - 3162 * q^82 - 928 * q^83 + 580 * q^85 - 1212 * q^86 + 588 * q^87 - 428 * q^88 - 588 * q^89 - 45 * q^90 + 1560 * q^92 + 450 * q^93 + 1280 * q^94 + 510 * q^95 + 45 * q^96 - 522 * q^97 - 198 * q^99

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