LMFDB - Embedded newform 4018.2.a.bj.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.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:	$32.0838915322$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.11348.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + x + 2 $ x^4 - x^3 - 5*x^2 + x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 574)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.77571$ of defining polynomial
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.12631 q^{3} +1.00000 q^{4} +3.70458 q^{5} -1.12631 q^{6} -1.00000 q^{8} -1.73143 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.12631 q^{3} +1.00000 q^{4} +3.70458 q^{5} -1.12631 q^{6} -1.00000 q^{8} -1.73143 q^{9} -3.70458 q^{10} +4.57827 q^{11} +1.12631 q^{12} +5.55143 q^{13} +4.17250 q^{15} +1.00000 q^{16} -1.43262 q^{17} +1.73143 q^{18} +3.55143 q^{19} +3.70458 q^{20} -4.57827 q^{22} +5.55143 q^{23} -1.12631 q^{24} +8.72393 q^{25} -5.55143 q^{26} -5.32905 q^{27} +6.40577 q^{29} -4.17250 q^{30} +0.172501 q^{31} -1.00000 q^{32} +5.15655 q^{33} +1.43262 q^{34} -1.73143 q^{36} +0.252616 q^{37} -3.55143 q^{38} +6.25262 q^{39} -3.70458 q^{40} -1.00000 q^{41} -6.42512 q^{43} +4.57827 q^{44} -6.41422 q^{45} -5.55143 q^{46} -8.11035 q^{47} +1.12631 q^{48} -8.72393 q^{50} -1.61357 q^{51} +5.55143 q^{52} -8.41255 q^{53} +5.32905 q^{54} +16.9606 q^{55} +4.00000 q^{57} -6.40577 q^{58} -9.87708 q^{59} +4.17250 q^{60} -14.3022 q^{61} -0.172501 q^{62} +1.00000 q^{64} +20.5657 q^{65} -5.15655 q^{66} +7.13720 q^{67} -1.43262 q^{68} +6.25262 q^{69} +5.81249 q^{71} +1.73143 q^{72} -1.38738 q^{73} -0.252616 q^{74} +9.82583 q^{75} +3.55143 q^{76} -6.25262 q^{78} -10.7314 q^{79} +3.70458 q^{80} -0.807862 q^{81} +1.00000 q^{82} +12.1297 q^{83} -5.30726 q^{85} +6.42512 q^{86} +7.21487 q^{87} -4.57827 q^{88} -14.9840 q^{89} +6.41422 q^{90} +5.55143 q^{92} +0.194289 q^{93} +8.11035 q^{94} +13.1565 q^{95} -1.12631 q^{96} -9.58166 q^{97} -7.92696 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + q^{3} + 4 q^{4} - 3 q^{5} - q^{6} - 4 q^{8} + 9 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + q^3 + 4 * q^4 - 3 * q^5 - q^6 - 4 * q^8 + 9 * q^9	$ 4 q - 4 q^{2} + q^{3} + 4 q^{4} - 3 q^{5} - q^{6} - 4 q^{8} + 9 q^{9} + 3 q^{10} + 4 q^{11} + q^{12} + 6 q^{13} + 11 q^{15} + 4 q^{16} + q^{17} - 9 q^{18} - 2 q^{19} - 3 q^{20} - 4 q^{22} + 6 q^{23} - q^{24} + 13 q^{25} - 6 q^{26} + 13 q^{27} + 17 q^{29} - 11 q^{30} - 5 q^{31} - 4 q^{32} - 8 q^{33} - q^{34} + 9 q^{36} - 6 q^{37} + 2 q^{38} + 18 q^{39} + 3 q^{40} - 4 q^{41} - 13 q^{43} + 4 q^{44} - 34 q^{45} - 6 q^{46} - 6 q^{47} + q^{48} - 13 q^{50} - 11 q^{51} + 6 q^{52} + 29 q^{53} - 13 q^{54} + 16 q^{55} + 16 q^{57} - 17 q^{58} - 16 q^{59} + 11 q^{60} - 21 q^{61} + 5 q^{62} + 4 q^{64} + 18 q^{65} + 8 q^{66} + 4 q^{67} + q^{68} + 18 q^{69} + 17 q^{71} - 9 q^{72} - 12 q^{73} + 6 q^{74} - 26 q^{75} - 2 q^{76} - 18 q^{78} - 27 q^{79} - 3 q^{80} + 40 q^{81} + 4 q^{82} + 18 q^{83} - 29 q^{85} + 13 q^{86} + 41 q^{87} - 4 q^{88} - 37 q^{89} + 34 q^{90} + 6 q^{92} - 47 q^{93} + 6 q^{94} + 24 q^{95} - q^{96} + 3 q^{97} - 32 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + q^3 + 4 * q^4 - 3 * q^5 - q^6 - 4 * q^8 + 9 * q^9 + 3 * q^10 + 4 * q^11 + q^12 + 6 * q^13 + 11 * q^15 + 4 * q^16 + q^17 - 9 * q^18 - 2 * q^19 - 3 * q^20 - 4 * q^22 + 6 * q^23 - q^24 + 13 * q^25 - 6 * q^26 + 13 * q^27 + 17 * q^29 - 11 * q^30 - 5 * q^31 - 4 * q^32 - 8 * q^33 - q^34 + 9 * q^36 - 6 * q^37 + 2 * q^38 + 18 * q^39 + 3 * q^40 - 4 * q^41 - 13 * q^43 + 4 * q^44 - 34 * q^45 - 6 * q^46 - 6 * q^47 + q^48 - 13 * q^50 - 11 * q^51 + 6 * q^52 + 29 * q^53 - 13 * q^54 + 16 * q^55 + 16 * q^57 - 17 * q^58 - 16 * q^59 + 11 * q^60 - 21 * q^61 + 5 * q^62 + 4 * q^64 + 18 * q^65 + 8 * q^66 + 4 * q^67 + q^68 + 18 * q^69 + 17 * q^71 - 9 * q^72 - 12 * q^73 + 6 * q^74 - 26 * q^75 - 2 * q^76 - 18 * q^78 - 27 * q^79 - 3 * q^80 + 40 * q^81 + 4 * q^82 + 18 * q^83 - 29 * q^85 + 13 * q^86 + 41 * q^87 - 4 * q^88 - 37 * q^89 + 34 * q^90 + 6 * q^92 - 47 * q^93 + 6 * q^94 + 24 * q^95 - q^96 + 3 * q^97 - 32 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.12631	0.650274	0.325137	−	0.945667i	$-0.394590\pi$
$3$	1.12631	0.650274	0.325137	+	0.945667i	$0.394590\pi$
$4$	1.00000	0.500000
$5$	3.70458	1.65674	0.828370	−	0.560182i	$-0.189269\pi$
$5$	3.70458	1.65674	0.828370	+	0.560182i	$0.189269\pi$
$6$	−1.12631	−0.459813
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	−1.73143	−0.577143
$10$	−3.70458	−1.17149
$11$	4.57827	1.38040	0.690201	−	0.723618i	$-0.257522\pi$
$11$	4.57827	1.38040	0.690201	+	0.723618i	$0.257522\pi$
$12$	1.12631	0.325137
$13$	5.55143	1.53969	0.769844	−	0.638232i	$-0.220334\pi$
$13$	5.55143	1.53969	0.769844	+	0.638232i	$0.220334\pi$
$14$	0	0
$15$	4.17250	1.07734
$16$	1.00000	0.250000
$17$	−1.43262	−0.347462	−0.173731	−	0.984793i	$-0.555582\pi$
$17$	−1.43262	−0.347462	−0.173731	+	0.984793i	$0.555582\pi$
$18$	1.73143	0.408102
$19$	3.55143	0.814753	0.407376	−	0.913260i	$-0.366444\pi$
$19$	3.55143	0.814753	0.407376	+	0.913260i	$0.366444\pi$
$20$	3.70458	0.828370
$21$	0	0
$22$	−4.57827	−0.976091
$23$	5.55143	1.15755	0.578776	−	0.815486i	$-0.303531\pi$
$23$	5.55143	1.15755	0.578776	+	0.815486i	$0.303531\pi$
$24$	−1.12631	−0.229907
$25$	8.72393	1.74479
$26$	−5.55143	−1.08872
$27$	−5.32905	−1.02558
$28$	0	0
$29$	6.40577	1.18952	0.594761	−	0.803903i	$-0.297247\pi$
$29$	6.40577	1.18952	0.594761	+	0.803903i	$0.297247\pi$
$30$	−4.17250	−0.761791
$31$	0.172501	0.0309821	0.0154910	−	0.999880i	$-0.495069\pi$
$31$	0.172501	0.0309821	0.0154910	+	0.999880i	$0.495069\pi$
$32$	−1.00000	−0.176777
$33$	5.15655	0.897640
$34$	1.43262	0.245692
$35$	0	0
$36$	−1.73143	−0.288572
$37$	0.252616	0.0415299	0.0207649	−	0.999784i	$-0.493390\pi$
$37$	0.252616	0.0415299	0.0207649	+	0.999784i	$0.493390\pi$
$38$	−3.55143	−0.576117
$39$	6.25262	1.00122
$40$	−3.70458	−0.585746
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−6.42512	−0.979821	−0.489911	−	0.871773i	$-0.662971\pi$
$43$	−6.42512	−0.979821	−0.489911	+	0.871773i	$0.662971\pi$
$44$	4.57827	0.690201
$45$	−6.41422	−0.956176
$46$	−5.55143	−0.818513
$47$	−8.11035	−1.18302	−0.591508	−	0.806299i	$-0.701467\pi$
$47$	−8.11035	−1.18302	−0.591508	+	0.806299i	$0.701467\pi$
$48$	1.12631	0.162569
$49$	0	0
$50$	−8.72393	−1.23375
$51$	−1.61357	−0.225945
$52$	5.55143	0.769844
$53$	−8.41255	−1.15555	−0.577777	−	0.816195i	$-0.696080\pi$
$53$	−8.41255	−1.15555	−0.577777	+	0.816195i	$0.696080\pi$
$54$	5.32905	0.725192
$55$	16.9606	2.28697
$56$	0	0
$57$	4.00000	0.529813
$58$	−6.40577	−0.841119
$59$	−9.87708	−1.28589	−0.642943	−	0.765914i	$-0.722287\pi$
$59$	−9.87708	−1.28589	−0.642943	+	0.765914i	$0.722287\pi$
$60$	4.17250	0.538668
$61$	−14.3022	−1.83121	−0.915605	−	0.402080i	$-0.868287\pi$
$61$	−14.3022	−1.83121	−0.915605	+	0.402080i	$0.868287\pi$
$62$	−0.172501	−0.0219077
$63$	0	0
$64$	1.00000	0.125000
$65$	20.5657	2.55086
$66$	−5.15655	−0.634727
$67$	7.13720	0.871948	0.435974	−	0.899959i	$-0.356404\pi$
$67$	7.13720	0.871948	0.435974	+	0.899959i	$0.356404\pi$
$68$	−1.43262	−0.173731
$69$	6.25262	0.752727
$70$	0	0
$71$	5.81249	0.689816	0.344908	−	0.938636i	$-0.387910\pi$
$71$	5.81249	0.689816	0.344908	+	0.938636i	$0.387910\pi$
$72$	1.73143	0.204051
$73$	−1.38738	−0.162380	−0.0811900	−	0.996699i	$-0.525872\pi$
$73$	−1.38738	−0.162380	−0.0811900	+	0.996699i	$0.525872\pi$
$74$	−0.252616	−0.0293661
$75$	9.82583	1.13459
$76$	3.55143	0.407376
$77$	0	0
$78$	−6.25262	−0.707969
$79$	−10.7314	−1.20738	−0.603690	−	0.797219i	$-0.706304\pi$
$79$	−10.7314	−1.20738	−0.603690	+	0.797219i	$0.706304\pi$
$80$	3.70458	0.414185
$81$	−0.807862	−0.0897624
$82$	1.00000	0.110432
$83$	12.1297	1.33141	0.665704	−	0.746216i	$-0.268131\pi$
$83$	12.1297	1.33141	0.665704	+	0.746216i	$0.268131\pi$
$84$	0	0
$85$	−5.30726	−0.575653
$86$	6.42512	0.692838
$87$	7.21487	0.773516
$88$	−4.57827	−0.488046
$89$	−14.9840	−1.58831	−0.794153	−	0.607718i	$-0.792085\pi$
$89$	−14.9840	−1.58831	−0.794153	+	0.607718i	$0.792085\pi$
$90$	6.41422	0.676119
$91$	0	0
$92$	5.55143	0.578776
$93$	0.194289	0.0201469
$94$	8.11035	0.836519
$95$	13.1565	1.34983
$96$	−1.12631	−0.114953
$97$	−9.58166	−0.972871	−0.486435	−	0.873717i	$-0.661703\pi$
$97$	−9.58166	−0.972871	−0.486435	+	0.873717i	$0.661703\pi$
$98$	0	0
$99$	−7.92696	−0.796689
$100$	8.72393	0.872393
$101$	10.7080	1.06548	0.532742	−	0.846278i	$-0.321162\pi$
$101$	10.7080	1.06548	0.532742	+	0.846278i	$0.321162\pi$
$102$	1.61357	0.159767
$103$	15.8880	1.56549	0.782744	−	0.622343i	$-0.213819\pi$
$103$	15.8880	1.56549	0.782744	+	0.622343i	$0.213819\pi$
$104$	−5.55143	−0.544362
$105$	0	0
$106$	8.41255	0.817100
$107$	−15.2971	−1.47883	−0.739415	−	0.673250i	$-0.764898\pi$
$107$	−15.2971	−1.47883	−0.739415	+	0.673250i	$0.764898\pi$
$108$	−5.32905	−0.512788
$109$	−1.92696	−0.184569	−0.0922846	−	0.995733i	$-0.529417\pi$
$109$	−1.92696	−0.184569	−0.0922846	+	0.995733i	$0.529417\pi$
$110$	−16.9606	−1.61713
$111$	0.284524	0.0270058
$112$	0	0
$113$	9.97654	0.938514	0.469257	−	0.883062i	$-0.344522\pi$
$113$	9.97654	0.938514	0.469257	+	0.883062i	$0.344522\pi$
$114$	−4.00000	−0.374634
$115$	20.5657	1.91776
$116$	6.40577	0.594761
$117$	−9.61190	−0.888621
$118$	9.87708	0.909259
$119$	0	0
$120$	−4.17250	−0.380895
$121$	9.96059	0.905508
$122$	14.3022	1.29486
$123$	−1.12631	−0.101556
$124$	0.172501	0.0154910
$125$	13.7956	1.23392
$126$	0	0
$127$	−9.04619	−0.802720	−0.401360	−	0.915920i	$-0.631462\pi$
$127$	−9.04619	−0.802720	−0.401360	+	0.915920i	$0.631462\pi$
$128$	−1.00000	−0.0883883
$129$	−7.23666	−0.637153
$130$	−20.5657	−1.80373
$131$	5.22577	0.456578	0.228289	−	0.973593i	$-0.426687\pi$
$131$	5.22577	0.456578	0.228289	+	0.973593i	$0.426687\pi$
$132$	5.15655	0.448820
$133$	0	0
$134$	−7.13720	−0.616560
$135$	−19.7419	−1.69911
$136$	1.43262	0.122846
$137$	6.65131	0.568260	0.284130	−	0.958786i	$-0.408295\pi$
$137$	6.65131	0.568260	0.284130	+	0.958786i	$0.408295\pi$
$138$	−6.25262	−0.532258
$139$	−15.5389	−1.31799	−0.658995	−	0.752148i	$-0.729018\pi$
$139$	−15.5389	−1.31799	−0.658995	+	0.752148i	$0.729018\pi$
$140$	0	0
$141$	−9.13476	−0.769285
$142$	−5.81249	−0.487774
$143$	25.4159	2.12539
$144$	−1.73143	−0.144286
$145$	23.7307	1.97073
$146$	1.38738	0.114820
$147$	0	0
$148$	0.252616	0.0207649
$149$	−19.0102	−1.55737	−0.778687	−	0.627413i	$-0.784114\pi$
$149$	−19.0102	−1.55737	−0.778687	+	0.627413i	$0.784114\pi$
$150$	−9.82583	−0.802276
$151$	16.2858	1.32532	0.662661	−	0.748920i	$-0.269427\pi$
$151$	16.2858	1.32532	0.662661	+	0.748920i	$0.269427\pi$
$152$	−3.55143	−0.288059
$153$	2.48048	0.200535
$154$	0	0
$155$	0.639044	0.0513293
$156$	6.25262	0.500610
$157$	10.4017	0.830143	0.415071	−	0.909789i	$-0.363757\pi$
$157$	10.4017	0.830143	0.415071	+	0.909789i	$0.363757\pi$
$158$	10.7314	0.853747
$159$	−9.47513	−0.751427
$160$	−3.70458	−0.292873
$161$	0	0
$162$	0.807862	0.0634716
$163$	8.54392	0.669212	0.334606	−	0.942358i	$-0.391397\pi$
$163$	8.54392	0.669212	0.334606	+	0.942358i	$0.391397\pi$
$164$	−1.00000	−0.0780869
$165$	19.1029	1.48715
$166$	−12.1297	−0.941447
$167$	0.107392	0.00831022	0.00415511	−	0.999991i	$-0.498677\pi$
$167$	0.107392	0.00831022	0.00415511	+	0.999991i	$0.498677\pi$
$168$	0	0
$169$	17.8183	1.37064
$170$	5.30726	0.407048
$171$	−6.14904	−0.470229
$172$	−6.42512	−0.489911
$173$	−17.0987	−1.29999	−0.649997	−	0.759937i	$-0.725230\pi$
$173$	−17.0987	−1.29999	−0.649997	+	0.759937i	$0.725230\pi$
$174$	−7.21487	−0.546958
$175$	0	0
$176$	4.57827	0.345100
$177$	−11.1246	−0.836179
$178$	14.9840	1.12310
$179$	13.9807	1.04496	0.522482	−	0.852651i	$-0.325006\pi$
$179$	13.9807	1.04496	0.522482	+	0.852651i	$0.325006\pi$
$180$	−6.41422	−0.478088
$181$	16.4554	1.22312	0.611559	−	0.791199i	$-0.290543\pi$
$181$	16.4554	1.22312	0.611559	+	0.791199i	$0.290543\pi$
$182$	0	0
$183$	−16.1087	−1.19079
$184$	−5.55143	−0.409257
$185$	0.935838	0.0688042
$186$	−0.194289	−0.0142460
$187$	−6.55893	−0.479636
$188$	−8.11035	−0.591508
$189$	0	0
$190$	−13.1565	−0.954476
$191$	−17.8730	−1.29324	−0.646621	−	0.762811i	$-0.723819\pi$
$191$	−17.8730	−1.29324	−0.646621	+	0.762811i	$0.723819\pi$
$192$	1.12631	0.0812843
$193$	25.1633	1.81130	0.905648	−	0.424030i	$-0.139385\pi$
$193$	25.1633	1.81130	0.905648	+	0.424030i	$0.139385\pi$
$194$	9.58166	0.687923
$195$	23.1633	1.65876
$196$	0	0
$197$	−2.02179	−0.144046	−0.0720232	−	0.997403i	$-0.522946\pi$
$197$	−2.02179	−0.144046	−0.0720232	+	0.997403i	$0.522946\pi$
$198$	7.92696	0.563344
$199$	−8.45536	−0.599384	−0.299692	−	0.954036i	$-0.596884\pi$
$199$	−8.45536	−0.599384	−0.299692	+	0.954036i	$0.596884\pi$
$200$	−8.72393	−0.616875
$201$	8.03869	0.567005
$202$	−10.7080	−0.753410
$203$	0	0
$204$	−1.61357	−0.112973
$205$	−3.70458	−0.258739
$206$	−15.8880	−1.10697
$207$	−9.61190	−0.668073
$208$	5.55143	0.384922
$209$	16.2594	1.12469
$210$	0	0
$211$	15.7198	1.08220	0.541098	−	0.840959i	$-0.318009\pi$
$211$	15.7198	1.08220	0.541098	+	0.840959i	$0.318009\pi$
$212$	−8.41255	−0.577777
$213$	6.54666	0.448570
$214$	15.2971	1.04569
$215$	−23.8024	−1.62331
$216$	5.32905	0.362596
$217$	0	0
$218$	1.92696	0.130510
$219$	−1.56261	−0.105592
$220$	16.9606	1.14348
$221$	−7.95309	−0.534982
$222$	−0.284524	−0.0190960
$223$	−15.1897	−1.01718	−0.508590	−	0.861009i	$-0.669833\pi$
$223$	−15.1897	−1.01718	−0.508590	+	0.861009i	$0.669833\pi$
$224$	0	0
$225$	−15.1049	−1.00699
$226$	−9.97654	−0.663630
$227$	−13.7307	−0.911339	−0.455670	−	0.890149i	$-0.650600\pi$
$227$	−13.7307	−0.911339	−0.455670	+	0.890149i	$0.650600\pi$
$228$	4.00000	0.264906
$229$	−21.5732	−1.42560	−0.712799	−	0.701368i	$-0.752573\pi$
$229$	−21.5732	−1.42560	−0.712799	+	0.701368i	$0.752573\pi$
$230$	−20.5657	−1.35606
$231$	0	0
$232$	−6.40577	−0.420560
$233$	−7.13476	−0.467414	−0.233707	−	0.972307i	$-0.575086\pi$
$233$	−7.13476	−0.467414	−0.233707	+	0.972307i	$0.575086\pi$
$234$	9.61190	0.628350
$235$	−30.0455	−1.95995
$236$	−9.87708	−0.642943
$237$	−12.0869	−0.785128
$238$	0	0
$239$	3.45608	0.223555	0.111778	−	0.993733i	$-0.464346\pi$
$239$	3.45608	0.223555	0.111778	+	0.993733i	$0.464346\pi$
$240$	4.17250	0.269334
$241$	−11.7474	−0.756715	−0.378358	−	0.925659i	$-0.623511\pi$
$241$	−11.7474	−0.756715	−0.378358	+	0.925659i	$0.623511\pi$
$242$	−9.96059	−0.640291
$243$	15.0772	0.967206
$244$	−14.3022	−0.915605
$245$	0	0
$246$	1.12631	0.0718108
$247$	19.7155	1.25447
$248$	−0.172501	−0.0109538
$249$	13.6618	0.865780
$250$	−13.7956	−0.872510
$251$	2.14471	0.135373	0.0676863	−	0.997707i	$-0.478438\pi$
$251$	2.14471	0.135373	0.0676863	+	0.997707i	$0.478438\pi$
$252$	0	0
$253$	25.4159	1.59789
$254$	9.04619	0.567609
$255$	−5.97761	−0.374332
$256$	1.00000	0.0625000
$257$	−15.7269	−0.981016	−0.490508	−	0.871437i	$-0.663189\pi$
$257$	−15.7269	−0.981016	−0.490508	+	0.871437i	$0.663189\pi$
$258$	7.23666	0.450535
$259$	0	0
$260$	20.5657	1.27543
$261$	−11.0911	−0.686525
$262$	−5.22577	−0.322849
$263$	2.31309	0.142632	0.0713158	−	0.997454i	$-0.477280\pi$
$263$	2.31309	0.142632	0.0713158	+	0.997454i	$0.477280\pi$
$264$	−5.15655	−0.317364
$265$	−31.1650	−1.91445
$266$	0	0
$267$	−16.8767	−1.03283
$268$	7.13720	0.435974
$269$	−30.7810	−1.87675	−0.938376	−	0.345617i	$-0.887670\pi$
$269$	−30.7810	−1.87675	−0.938376	+	0.345617i	$0.887670\pi$
$270$	19.7419	1.20145
$271$	3.38738	0.205768	0.102884	−	0.994693i	$-0.467193\pi$
$271$	3.38738	0.205768	0.102884	+	0.994693i	$0.467193\pi$
$272$	−1.43262	−0.0868654
$273$	0	0
$274$	−6.65131	−0.401821
$275$	39.9405	2.40850
$276$	6.25262	0.376363
$277$	−4.21393	−0.253190	−0.126595	−	0.991954i	$-0.540405\pi$
$277$	−4.21393	−0.253190	−0.126595	+	0.991954i	$0.540405\pi$
$278$	15.5389	0.931959
$279$	−0.298673	−0.0178811
$280$	0	0
$281$	20.3131	1.21178	0.605889	−	0.795549i	$-0.292818\pi$
$281$	20.3131	1.21178	0.605889	+	0.795549i	$0.292818\pi$
$282$	9.13476	0.543967
$283$	3.87030	0.230065	0.115033	−	0.993362i	$-0.463303\pi$
$283$	3.87030	0.230065	0.115033	+	0.993362i	$0.463303\pi$
$284$	5.81249	0.344908
$285$	14.8183	0.877762
$286$	−25.4159	−1.50288
$287$	0	0
$288$	1.73143	0.102025
$289$	−14.9476	−0.879270
$290$	−23.7307	−1.39352
$291$	−10.7919	−0.632633
$292$	−1.38738	−0.0811900
$293$	13.7890	0.805564	0.402782	−	0.915296i	$-0.368043\pi$
$293$	13.7890	0.805564	0.402782	+	0.915296i	$0.368043\pi$
$294$	0	0
$295$	−36.5905	−2.13038
$296$	−0.252616	−0.0146830
$297$	−24.3978	−1.41571
$298$	19.0102	1.10123
$299$	30.8183	1.78227
$300$	9.82583	0.567295
$301$	0	0
$302$	−16.2858	−0.937144
$303$	12.0605	0.692856
$304$	3.55143	0.203688
$305$	−52.9837	−3.03384
$306$	−2.48048	−0.141800
$307$	−2.42923	−0.138643	−0.0693217	−	0.997594i	$-0.522084\pi$
$307$	−2.42923	−0.138643	−0.0693217	+	0.997594i	$0.522084\pi$
$308$	0	0
$309$	17.8948	1.01800
$310$	−0.639044	−0.0362953
$311$	−10.0180	−0.568067	−0.284033	−	0.958814i	$-0.591673\pi$
$311$	−10.0180	−0.568067	−0.284033	+	0.958814i	$0.591673\pi$
$312$	−6.25262	−0.353985
$313$	0.509052	0.0287733	0.0143867	−	0.999897i	$-0.495420\pi$
$313$	0.509052	0.0287733	0.0143867	+	0.999897i	$0.495420\pi$
$314$	−10.4017	−0.587000
$315$	0	0
$316$	−10.7314	−0.603690
$317$	25.9405	1.45696	0.728482	−	0.685064i	$-0.240226\pi$
$317$	25.9405	1.45696	0.728482	+	0.685064i	$0.240226\pi$
$318$	9.47513	0.531339
$319$	29.3274	1.64202
$320$	3.70458	0.207092
$321$	−17.2293	−0.961645
$322$	0	0
$323$	−5.08785	−0.283095
$324$	−0.807862	−0.0448812
$325$	48.4302	2.68643
$326$	−8.54392	−0.473204
$327$	−2.17035	−0.120021
$328$	1.00000	0.0552158
$329$	0	0
$330$	−19.1029	−1.05158
$331$	−6.65376	−0.365724	−0.182862	−	0.983139i	$-0.558536\pi$
$331$	−6.65376	−0.365724	−0.182862	+	0.983139i	$0.558536\pi$
$332$	12.1297	0.665704
$333$	−0.437388	−0.0239687
$334$	−0.107392	−0.00587621
$335$	26.4404	1.44459
$336$	0	0
$337$	21.2367	1.15683	0.578417	−	0.815741i	$-0.303671\pi$
$337$	21.2367	1.15683	0.578417	+	0.815741i	$0.303671\pi$
$338$	−17.8183	−0.969189
$339$	11.2367	0.610292
$340$	−5.30726	−0.287827
$341$	0.789757	0.0427677
$342$	6.14904	0.332502
$343$	0	0
$344$	6.42512	0.346419
$345$	23.1633	1.24707
$346$	17.0987	0.919234
$347$	34.3861	1.84594	0.922972	−	0.384867i	$-0.125753\pi$
$347$	34.3861	1.84594	0.922972	+	0.384867i	$0.125753\pi$
$348$	7.21487	0.386758
$349$	11.6095	0.621440	0.310720	−	0.950501i	$-0.399430\pi$
$349$	11.6095	0.621440	0.310720	+	0.950501i	$0.399430\pi$
$350$	0	0
$351$	−29.5838	−1.57907
$352$	−4.57827	−0.244023
$353$	−2.82845	−0.150543	−0.0752715	−	0.997163i	$-0.523982\pi$
$353$	−2.82845	−0.150543	−0.0752715	+	0.997163i	$0.523982\pi$
$354$	11.1246	0.591268
$355$	21.5329	1.14285
$356$	−14.9840	−0.794153
$357$	0	0
$358$	−13.9807	−0.738901
$359$	8.22071	0.433872	0.216936	−	0.976186i	$-0.430394\pi$
$359$	8.22071	0.433872	0.216936	+	0.976186i	$0.430394\pi$
$360$	6.41422	0.338059
$361$	−6.38738	−0.336178
$362$	−16.4554	−0.864874
$363$	11.2187	0.588829
$364$	0	0
$365$	−5.13965	−0.269021
$366$	16.1087	0.842015
$367$	8.47881	0.442590	0.221295	−	0.975207i	$-0.428972\pi$
$367$	8.47881	0.442590	0.221295	+	0.975207i	$0.428972\pi$
$368$	5.55143	0.289388
$369$	1.73143	0.0901346
$370$	−0.935838	−0.0486519
$371$	0	0
$372$	0.194289	0.0100734
$373$	−22.4583	−1.16285	−0.581424	−	0.813601i	$-0.697504\pi$
$373$	−22.4583	−1.16285	−0.581424	+	0.813601i	$0.697504\pi$
$374$	6.55893	0.339154
$375$	15.5381	0.802383
$376$	8.11035	0.418260
$377$	35.5612	1.83149
$378$	0	0
$379$	−22.2321	−1.14199	−0.570994	−	0.820954i	$-0.693442\pi$
$379$	−22.2321	−1.14199	−0.570994	+	0.820954i	$0.693442\pi$
$380$	13.1565	0.674917
$381$	−10.1888	−0.521988
$382$	17.8730	0.914461
$383$	4.00000	0.204390	0.102195	−	0.994764i	$-0.467413\pi$
$383$	4.00000	0.204390	0.102195	+	0.994764i	$0.467413\pi$
$384$	−1.12631	−0.0574767
$385$	0	0
$386$	−25.1633	−1.28078
$387$	11.1246	0.565497
$388$	−9.58166	−0.486435
$389$	25.1633	1.27583	0.637916	−	0.770106i	$-0.279797\pi$
$389$	25.1633	1.27583	0.637916	+	0.770106i	$0.279797\pi$
$390$	−23.1633	−1.17292
$391$	−7.95309	−0.402205
$392$	0	0
$393$	5.88583	0.296901
$394$	2.02179	0.101856
$395$	−39.7555	−2.00031
$396$	−7.92696	−0.398345
$397$	−10.6006	−0.532028	−0.266014	−	0.963969i	$-0.585707\pi$
$397$	−10.6006	−0.532028	−0.266014	+	0.963969i	$0.585707\pi$
$398$	8.45536	0.423829
$399$	0	0
$400$	8.72393	0.436196
$401$	22.6496	1.13107	0.565535	−	0.824725i	$-0.308670\pi$
$401$	22.6496	1.13107	0.565535	+	0.824725i	$0.308670\pi$
$402$	−8.03869	−0.400933
$403$	0.957627	0.0477028
$404$	10.7080	0.532742
$405$	−2.99279	−0.148713
$406$	0	0
$407$	1.15655	0.0573279
$408$	1.61357	0.0798837
$409$	−7.24215	−0.358101	−0.179051	−	0.983840i	$-0.557303\pi$
$409$	−7.24215	−0.358101	−0.179051	+	0.983840i	$0.557303\pi$
$410$	3.70458	0.182956
$411$	7.49143	0.369525
$412$	15.8880	0.782744
$413$	0	0
$414$	9.61190	0.472399
$415$	44.9355	2.20580
$416$	−5.55143	−0.272181
$417$	−17.5015	−0.857055
$418$	−16.2594	−0.795273
$419$	27.3617	1.33671	0.668354	−	0.743843i	$-0.266999\pi$
$419$	27.3617	1.33671	0.668354	+	0.743843i	$0.266999\pi$
$420$	0	0
$421$	−18.1986	−0.886947	−0.443473	−	0.896288i	$-0.646254\pi$
$421$	−18.1986	−0.886947	−0.443473	+	0.896288i	$0.646254\pi$
$422$	−15.7198	−0.765229
$423$	14.0425	0.682770
$424$	8.41255	0.408550
$425$	−12.4981	−0.606246
$426$	−6.54666	−0.317187
$427$	0	0
$428$	−15.2971	−0.739415
$429$	28.6262	1.38209
$430$	23.8024	1.14785
$431$	28.8919	1.39167	0.695837	−	0.718200i	$-0.255034\pi$
$431$	28.8919	1.39167	0.695837	+	0.718200i	$0.255034\pi$
$432$	−5.32905	−0.256394
$433$	−38.6262	−1.85626	−0.928128	−	0.372261i	$-0.878583\pi$
$433$	−38.6262	−1.85626	−0.928128	+	0.372261i	$0.878583\pi$
$434$	0	0
$435$	26.7281	1.28151
$436$	−1.92696	−0.0922846
$437$	19.7155	0.943119
$438$	1.56261	0.0746645
$439$	36.6761	1.75045	0.875227	−	0.483713i	$-0.160712\pi$
$439$	36.6761	1.75045	0.875227	+	0.483713i	$0.160712\pi$
$440$	−16.9606	−0.808564
$441$	0	0
$442$	7.95309	0.378290
$443$	2.99083	0.142099	0.0710493	−	0.997473i	$-0.477365\pi$
$443$	2.99083	0.142099	0.0710493	+	0.997473i	$0.477365\pi$
$444$	0.284524	0.0135029
$445$	−55.5096	−2.63141
$446$	15.1897	0.719255
$447$	−21.4113	−1.01272
$448$	0	0
$449$	18.8069	0.887553	0.443777	−	0.896137i	$-0.353638\pi$
$449$	18.8069	0.887553	0.443777	+	0.896137i	$0.353638\pi$
$450$	15.1049	0.712050
$451$	−4.57827	−0.215582
$452$	9.97654	0.469257
$453$	18.3429	0.861822
$454$	13.7307	0.644414
$455$	0	0
$456$	−4.00000	−0.187317
$457$	−23.9986	−1.12261	−0.561303	−	0.827611i	$-0.689700\pi$
$457$	−23.9986	−1.12261	−0.561303	+	0.827611i	$0.689700\pi$
$458$	21.5732	1.00805
$459$	7.63450	0.356348
$460$	20.5657	0.958881
$461$	6.22482	0.289919	0.144959	−	0.989438i	$-0.453695\pi$
$461$	6.22482	0.289919	0.144959	+	0.989438i	$0.453695\pi$
$462$	0	0
$463$	23.2162	1.07895	0.539473	−	0.842003i	$-0.318623\pi$
$463$	23.2162	1.07895	0.539473	+	0.842003i	$0.318623\pi$
$464$	6.40577	0.297381
$465$	0.719761	0.0333781
$466$	7.13476	0.330511
$467$	−14.6499	−0.677918	−0.338959	−	0.940801i	$-0.610075\pi$
$467$	−14.6499	−0.677918	−0.338959	+	0.940801i	$0.610075\pi$
$468$	−9.61190	−0.444310
$469$	0	0
$470$	30.0455	1.38589
$471$	11.7155	0.539821
$472$	9.87708	0.454630
$473$	−29.4159	−1.35255
$474$	12.0869	0.555170
$475$	30.9824	1.42157
$476$	0	0
$477$	14.5657	0.666920
$478$	−3.45608	−0.158077
$479$	−11.9032	−0.543872	−0.271936	−	0.962315i	$-0.587664\pi$
$479$	−11.9032	−0.543872	−0.271936	+	0.962315i	$0.587664\pi$
$480$	−4.17250	−0.190448
$481$	1.40238	0.0639431
$482$	11.7474	0.535079
$483$	0	0
$484$	9.96059	0.452754
$485$	−35.4961	−1.61179
$486$	−15.0772	−0.683918
$487$	−41.0845	−1.86172	−0.930858	−	0.365380i	$-0.880939\pi$
$487$	−41.0845	−1.86172	−0.930858	+	0.365380i	$0.880939\pi$
$488$	14.3022	0.647430
$489$	9.62309	0.435171
$490$	0	0
$491$	14.5325	0.655843	0.327921	−	0.944705i	$-0.393652\pi$
$491$	14.5325	0.655843	0.327921	+	0.944705i	$0.393652\pi$
$492$	−1.12631	−0.0507779
$493$	−9.17704	−0.413313
$494$	−19.7155	−0.887041
$495$	−29.3661	−1.31991
$496$	0.172501	0.00774552
$497$	0	0
$498$	−13.6618	−0.612199
$499$	−3.37481	−0.151077	−0.0755387	−	0.997143i	$-0.524068\pi$
$499$	−3.37481	−0.151077	−0.0755387	+	0.997143i	$0.524068\pi$
$500$	13.7956	0.616958
$501$	0.120956	0.00540392
$502$	−2.14471	−0.0957229
$503$	−16.1738	−0.721154	−0.360577	−	0.932729i	$-0.617420\pi$
$503$	−16.1738	−0.721154	−0.360577	+	0.932729i	$0.617420\pi$
$504$	0	0
$505$	39.6686	1.76523
$506$	−25.4159	−1.12988
$507$	20.0689	0.891292
$508$	−9.04619	−0.401360
$509$	34.2463	1.51794	0.758971	−	0.651125i	$-0.225703\pi$
$509$	34.2463	1.51794	0.758971	+	0.651125i	$0.225703\pi$
$510$	5.97761	0.264693
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−18.9257	−0.835591
$514$	15.7269	0.693683
$515$	58.8583	2.59361
$516$	−7.23666	−0.318576
$517$	−37.1314	−1.63304
$518$	0	0
$519$	−19.2585	−0.845352
$520$	−20.5657	−0.901866
$521$	−7.92644	−0.347264	−0.173632	−	0.984811i	$-0.555550\pi$
$521$	−7.92644	−0.347264	−0.173632	+	0.984811i	$0.555550\pi$
$522$	11.0911	0.485446
$523$	31.4004	1.37304	0.686522	−	0.727109i	$-0.259136\pi$
$523$	31.4004	1.37304	0.686522	+	0.727109i	$0.259136\pi$
$524$	5.22577	0.228289
$525$	0	0
$526$	−2.31309	−0.100856
$527$	−0.247129	−0.0107651
$528$	5.15655	0.224410
$529$	7.81833	0.339927
$530$	31.1650	1.35372
$531$	17.1015	0.742141
$532$	0	0
$533$	−5.55143	−0.240459
$534$	16.8767	0.730324
$535$	−56.6695	−2.45004
$536$	−7.13720	−0.308280
$537$	15.7465	0.679513
$538$	30.7810	1.32706
$539$	0	0
$540$	−19.7419	−0.849556
$541$	−8.07548	−0.347192	−0.173596	−	0.984817i	$-0.555539\pi$
$541$	−8.07548	−0.347192	−0.173596	+	0.984817i	$0.555539\pi$
$542$	−3.38738	−0.145500
$543$	18.5338	0.795362
$544$	1.43262	0.0614231
$545$	−7.13858	−0.305783
$546$	0	0
$547$	2.41126	0.103098	0.0515490	−	0.998670i	$-0.483584\pi$
$547$	2.41126	0.103098	0.0515490	+	0.998670i	$0.483584\pi$
$548$	6.65131	0.284130
$549$	24.7633	1.05687
$550$	−39.9405	−1.70307
$551$	22.7496	0.969167
$552$	−6.25262	−0.266129
$553$	0	0
$554$	4.21393	0.179033
$555$	1.05404	0.0447416
$556$	−15.5389	−0.658995
$557$	−17.8367	−0.755766	−0.377883	−	0.925853i	$-0.623348\pi$
$557$	−17.8367	−0.755766	−0.377883	+	0.925853i	$0.623348\pi$
$558$	0.298673	0.0126439
$559$	−35.6686	−1.50862
$560$	0	0
$561$	−7.38738	−0.311895
$562$	−20.3131	−0.856856
$563$	18.6543	0.786184	0.393092	−	0.919499i	$-0.371405\pi$
$563$	18.6543	0.786184	0.393092	+	0.919499i	$0.371405\pi$
$564$	−9.13476	−0.384643
$565$	36.9589	1.55487
$566$	−3.87030	−0.162681
$567$	0	0
$568$	−5.81249	−0.243887
$569$	35.6301	1.49369	0.746846	−	0.664997i	$-0.231567\pi$
$569$	35.6301	1.49369	0.746846	+	0.664997i	$0.231567\pi$
$570$	−14.8183	−0.620671
$571$	4.96197	0.207652	0.103826	−	0.994595i	$-0.466892\pi$
$571$	4.96197	0.207652	0.103826	+	0.994595i	$0.466892\pi$
$572$	25.4159	1.06269
$573$	−20.1305	−0.840963
$574$	0	0
$575$	48.4302	2.01968
$576$	−1.73143	−0.0721429
$577$	9.41213	0.391832	0.195916	−	0.980621i	$-0.437232\pi$
$577$	9.41213	0.391832	0.195916	+	0.980621i	$0.437232\pi$
$578$	14.9476	0.621738
$579$	28.3417	1.17784
$580$	23.7307	0.985364
$581$	0	0
$582$	10.7919	0.447339
$583$	−38.5150	−1.59513
$584$	1.38738	0.0574100
$585$	−35.6081	−1.47221
$586$	−13.7890	−0.569620
$587$	12.5742	0.518991	0.259496	−	0.965744i	$-0.416444\pi$
$587$	12.5742	0.518991	0.259496	+	0.965744i	$0.416444\pi$
$588$	0	0
$589$	0.612625	0.0252428
$590$	36.5905	1.50641
$591$	−2.27716	−0.0936697
$592$	0.252616	0.0103825
$593$	31.6102	1.29808	0.649038	−	0.760756i	$-0.275171\pi$
$593$	31.6102	1.29808	0.649038	+	0.760756i	$0.275171\pi$
$594$	24.3978	1.00106
$595$	0	0
$596$	−19.0102	−0.778687
$597$	−9.52334	−0.389764
$598$	−30.8183	−1.26026
$599$	−24.9636	−1.01998	−0.509992	−	0.860179i	$-0.670351\pi$
$599$	−24.9636	−1.01998	−0.509992	+	0.860179i	$0.670351\pi$
$600$	−9.82583	−0.401138
$601$	−11.3402	−0.462578	−0.231289	−	0.972885i	$-0.574294\pi$
$601$	−11.3402	−0.462578	−0.231289	+	0.972885i	$0.574294\pi$
$602$	0	0
$603$	−12.3576	−0.503239
$604$	16.2858	0.662661
$605$	36.8998	1.50019
$606$	−12.0605	−0.489923
$607$	−25.0974	−1.01867	−0.509335	−	0.860568i	$-0.670109\pi$
$607$	−25.0974	−1.01867	−0.509335	+	0.860568i	$0.670109\pi$
$608$	−3.55143	−0.144029
$609$	0	0
$610$	52.9837	2.14525
$611$	−45.0240	−1.82148
$612$	2.48048	0.100268
$613$	1.80700	0.0729842	0.0364921	−	0.999334i	$-0.488382\pi$
$613$	1.80700	0.0729842	0.0364921	+	0.999334i	$0.488382\pi$
$614$	2.42923	0.0980357
$615$	−4.17250	−0.168251
$616$	0	0
$617$	−35.7639	−1.43980	−0.719900	−	0.694077i	$-0.755813\pi$
$617$	−35.7639	−1.43980	−0.719900	+	0.694077i	$0.755813\pi$
$618$	−17.8948	−0.719833
$619$	28.1046	1.12962	0.564809	−	0.825222i	$-0.308950\pi$
$619$	28.1046	1.12962	0.564809	+	0.825222i	$0.308950\pi$
$620$	0.639044	0.0256646
$621$	−29.5838	−1.18716
$622$	10.0180	0.401684
$623$	0	0
$624$	6.25262	0.250305
$625$	7.48726	0.299491
$626$	−0.509052	−0.0203458
$627$	18.3131	0.731355
$628$	10.4017	0.415071
$629$	−0.361904	−0.0144300
$630$	0	0
$631$	13.3307	0.530687	0.265344	−	0.964154i	$-0.414515\pi$
$631$	13.3307	0.530687	0.265344	+	0.964154i	$0.414515\pi$
$632$	10.7314	0.426873
$633$	17.7054	0.703725
$634$	−25.9405	−1.03023
$635$	−33.5124	−1.32990
$636$	−9.47513	−0.375713
$637$	0	0
$638$	−29.3274	−1.16108
$639$	−10.0639	−0.398123
$640$	−3.70458	−0.146436
$641$	−45.1164	−1.78199	−0.890996	−	0.454012i	$-0.849992\pi$
$641$	−45.1164	−1.78199	−0.890996	+	0.454012i	$0.849992\pi$
$642$	17.2293	0.679986
$643$	48.2176	1.90152	0.950758	−	0.309933i	$-0.100307\pi$
$643$	48.2176	1.90152	0.950758	+	0.309933i	$0.100307\pi$
$644$	0	0
$645$	−26.8088	−1.05560
$646$	5.08785	0.200179
$647$	−18.4251	−0.724366	−0.362183	−	0.932107i	$-0.617968\pi$
$647$	−18.4251	−0.724366	−0.362183	+	0.932107i	$0.617968\pi$
$648$	0.807862	0.0317358
$649$	−45.2200	−1.77504
$650$	−48.4302	−1.89959
$651$	0	0
$652$	8.54392	0.334606
$653$	−10.8195	−0.423399	−0.211699	−	0.977335i	$-0.567900\pi$
$653$	−10.8195	−0.423399	−0.211699	+	0.977335i	$0.567900\pi$
$654$	2.17035	0.0848674
$655$	19.3593	0.756430
$656$	−1.00000	−0.0390434
$657$	2.40214	0.0937165
$658$	0	0
$659$	27.0129	1.05227	0.526137	−	0.850400i	$-0.323640\pi$
$659$	27.0129	1.05227	0.526137	+	0.850400i	$0.323640\pi$
$660$	19.1029	0.743577
$661$	−24.2221	−0.942130	−0.471065	−	0.882099i	$-0.656130\pi$
$661$	−24.2221	−0.942130	−0.471065	+	0.882099i	$0.656130\pi$
$662$	6.65376	0.258606
$663$	−8.95763	−0.347885
$664$	−12.1297	−0.470724
$665$	0	0
$666$	0.437388	0.0169484
$667$	35.5612	1.37693
$668$	0.107392	0.00415511
$669$	−17.1083	−0.661447
$670$	−26.4404	−1.02148
$671$	−65.4794	−2.52780
$672$	0	0
$673$	−27.1396	−1.04616	−0.523078	−	0.852285i	$-0.675216\pi$
$673$	−27.1396	−1.04616	−0.523078	+	0.852285i	$0.675216\pi$
$674$	−21.2367	−0.818006
$675$	−46.4902	−1.78941
$676$	17.8183	0.685320
$677$	−18.6098	−0.715233	−0.357616	−	0.933869i	$-0.616410\pi$
$677$	−18.6098	−0.715233	−0.357616	+	0.933869i	$0.616410\pi$
$678$	−11.2367	−0.431541
$679$	0	0
$680$	5.30726	0.203524
$681$	−15.4650	−0.592620
$682$	−0.789757	−0.0302414
$683$	−30.3534	−1.16144	−0.580720	−	0.814104i	$-0.697229\pi$
$683$	−30.3534	−1.16144	−0.580720	+	0.814104i	$0.697229\pi$
$684$	−6.14904	−0.235115
$685$	24.6403	0.941459
$686$	0	0
$687$	−24.2981	−0.927030
$688$	−6.42512	−0.244955
$689$	−46.7017	−1.77919
$690$	−23.1633	−0.881813
$691$	−9.29418	−0.353567	−0.176784	−	0.984250i	$-0.556569\pi$
$691$	−9.29418	−0.353567	−0.176784	+	0.984250i	$0.556569\pi$
$692$	−17.0987	−0.649997
$693$	0	0
$694$	−34.3861	−1.30528
$695$	−57.5650	−2.18356
$696$	−7.21487	−0.273479
$697$	1.43262	0.0542644
$698$	−11.6095	−0.439425
$699$	−8.03594	−0.303947
$700$	0	0
$701$	25.9062	0.978463	0.489231	−	0.872154i	$-0.337277\pi$
$701$	25.9062	0.978463	0.489231	+	0.872154i	$0.337277\pi$
$702$	29.5838	1.11657
$703$	0.897149	0.0338366
$704$	4.57827	0.172550
$705$	−33.8405	−1.27451
$706$	2.82845	0.106450
$707$	0	0
$708$	−11.1246	−0.418090
$709$	−42.3637	−1.59100	−0.795502	−	0.605951i	$-0.792793\pi$
$709$	−42.3637	−1.59100	−0.795502	+	0.605951i	$0.792793\pi$
$710$	−21.5329	−0.808114
$711$	18.5807	0.696831
$712$	14.9840	0.561551
$713$	0.957627	0.0358634
$714$	0	0
$715$	94.1555	3.52121
$716$	13.9807	0.522482
$717$	3.89261	0.145372
$718$	−8.22071	−0.306794
$719$	4.95763	0.184888	0.0924441	−	0.995718i	$-0.470532\pi$
$719$	4.95763	0.184888	0.0924441	+	0.995718i	$0.470532\pi$
$720$	−6.41422	−0.239044
$721$	0	0
$722$	6.38738	0.237713
$723$	−13.2312	−0.492073
$724$	16.4554	0.611559
$725$	55.8835	2.07546
$726$	−11.2187	−0.416365
$727$	10.7748	0.399613	0.199807	−	0.979835i	$-0.435969\pi$
$727$	10.7748	0.399613	0.199807	+	0.979835i	$0.435969\pi$
$728$	0	0
$729$	19.4052	0.718711
$730$	5.13965	0.190227
$731$	9.20476	0.340450
$732$	−16.1087	−0.595394
$733$	−34.1310	−1.26066	−0.630329	−	0.776329i	$-0.717080\pi$
$733$	−34.1310	−1.26066	−0.630329	+	0.776329i	$0.717080\pi$
$734$	−8.47881	−0.312959
$735$	0	0
$736$	−5.55143	−0.204628
$737$	32.6761	1.20364
$738$	−1.73143	−0.0637348
$739$	−11.0077	−0.404926	−0.202463	−	0.979290i	$-0.564895\pi$
$739$	−11.0077	−0.404926	−0.202463	+	0.979290i	$0.564895\pi$
$740$	0.935838	0.0344021
$741$	22.2057	0.815747
$742$	0	0
$743$	32.7428	1.20122	0.600609	−	0.799543i	$-0.294925\pi$
$743$	32.7428	1.20122	0.600609	+	0.799543i	$0.294925\pi$
$744$	−0.194289	−0.00712299
$745$	−70.4247	−2.58016
$746$	22.4583	0.822257
$747$	−21.0017	−0.768413
$748$	−6.55893	−0.239818
$749$	0	0
$750$	−15.5381	−0.567371
$751$	25.4846	0.929948	0.464974	−	0.885324i	$-0.346064\pi$
$751$	25.4846	0.929948	0.464974	+	0.885324i	$0.346064\pi$
$752$	−8.11035	−0.295754
$753$	2.41560	0.0880293
$754$	−35.5612	−1.29506
$755$	60.3321	2.19571
$756$	0	0
$757$	15.4162	0.560313	0.280156	−	0.959954i	$-0.409614\pi$
$757$	15.4162	0.560313	0.280156	+	0.959954i	$0.409614\pi$
$758$	22.2321	0.807507
$759$	28.6262	1.03906
$760$	−13.1565	−0.477238
$761$	−22.5439	−0.817217	−0.408608	−	0.912710i	$-0.633986\pi$
$761$	−22.5439	−0.817217	−0.408608	+	0.912710i	$0.633986\pi$
$762$	10.1888	0.369101
$763$	0	0
$764$	−17.8730	−0.646621
$765$	9.18915	0.332234
$766$	−4.00000	−0.144526
$767$	−54.8319	−1.97986
$768$	1.12631	0.0406421
$769$	−46.1520	−1.66428	−0.832142	−	0.554563i	$-0.812886\pi$
$769$	−46.1520	−1.66428	−0.832142	+	0.554563i	$0.812886\pi$
$770$	0	0
$771$	−17.7133	−0.637930
$772$	25.1633	0.905648
$773$	−2.55597	−0.0919317	−0.0459659	−	0.998943i	$-0.514637\pi$
$773$	−2.55597	−0.0919317	−0.0459659	+	0.998943i	$0.514637\pi$
$774$	−11.1246	−0.399867
$775$	1.50489	0.0540571
$776$	9.58166	0.343962
$777$	0	0
$778$	−25.1633	−0.902149
$779$	−3.55143	−0.127243
$780$	23.1633	0.829380
$781$	26.6112	0.952223
$782$	7.95309	0.284402
$783$	−34.1367	−1.21995
$784$	0	0
$785$	38.5338	1.37533
$786$	−5.88583	−0.209940
$787$	6.25314	0.222900	0.111450	−	0.993770i	$-0.464450\pi$
$787$	6.25314	0.222900	0.111450	+	0.993770i	$0.464450\pi$
$788$	−2.02179	−0.0720232
$789$	2.60526	0.0927496
$790$	39.7555	1.41444
$791$	0	0
$792$	7.92696	0.281672
$793$	−79.3976	−2.81949
$794$	10.6006	0.376201
$795$	−35.1014	−1.24492
$796$	−8.45536	−0.299692
$797$	−33.8329	−1.19842	−0.599211	−	0.800591i	$-0.704519\pi$
$797$	−33.8329	−1.19842	−0.599211	+	0.800591i	$0.704519\pi$
$798$	0	0
$799$	11.6191	0.411053
$800$	−8.72393	−0.308437
$801$	25.9438	0.916680
$802$	−22.6496	−0.799787
$803$	−6.35178	−0.224150
$804$	8.03869	0.283503
$805$	0	0
$806$	−0.957627	−0.0337310
$807$	−34.6689	−1.22040
$808$	−10.7080	−0.376705
$809$	−46.7864	−1.64492	−0.822461	−	0.568821i	$-0.807400\pi$
$809$	−46.7864	−1.64492	−0.822461	+	0.568821i	$0.807400\pi$
$810$	2.99279	0.105156
$811$	6.92624	0.243213	0.121607	−	0.992578i	$-0.461195\pi$
$811$	6.92624	0.243213	0.121607	+	0.992578i	$0.461195\pi$
$812$	0	0
$813$	3.81523	0.133806
$814$	−1.15655	−0.0405370
$815$	31.6517	1.10871
$816$	−1.61357	−0.0564863
$817$	−22.8183	−0.798312
$818$	7.24215	0.253216
$819$	0	0
$820$	−3.70458	−0.129370
$821$	26.4273	0.922318	0.461159	−	0.887318i	$-0.347434\pi$
$821$	26.4273	0.922318	0.461159	+	0.887318i	$0.347434\pi$
$822$	−7.49143	−0.261294
$823$	−4.27989	−0.149188	−0.0745938	−	0.997214i	$-0.523766\pi$
$823$	−4.27989	−0.149188	−0.0745938	+	0.997214i	$0.523766\pi$
$824$	−15.8880	−0.553484
$825$	44.9853	1.56619
$826$	0	0
$827$	41.1140	1.42967	0.714836	−	0.699292i	$-0.246501\pi$
$827$	41.1140	1.42967	0.714836	+	0.699292i	$0.246501\pi$
$828$	−9.61190	−0.334037
$829$	−16.3090	−0.566434	−0.283217	−	0.959056i	$-0.591402\pi$
$829$	−16.3090	−0.566434	−0.283217	+	0.959056i	$0.591402\pi$
$830$	−44.9355	−1.55973
$831$	−4.74618	−0.164643
$832$	5.55143	0.192461
$833$	0	0
$834$	17.5015	0.606029
$835$	0.397841	0.0137679
$836$	16.2594	0.562343
$837$	−0.919266	−0.0317745
$838$	−27.3617	−0.945195
$839$	−35.9937	−1.24264	−0.621320	−	0.783557i	$-0.713403\pi$
$839$	−35.9937	−1.24264	−0.621320	+	0.783557i	$0.713403\pi$
$840$	0	0
$841$	12.0339	0.414963
$842$	18.1986	0.627166
$843$	22.8788	0.787988
$844$	15.7198	0.541098
$845$	66.0095	2.27079
$846$	−14.0425	−0.482791
$847$	0	0
$848$	−8.41255	−0.288888
$849$	4.35915	0.149606
$850$	12.4981	0.428680
$851$	1.40238	0.0480730
$852$	6.54666	0.224285
$853$	−30.2940	−1.03725	−0.518623	−	0.855003i	$-0.673555\pi$
$853$	−30.2940	−1.03725	−0.518623	+	0.855003i	$0.673555\pi$
$854$	0	0
$855$	−22.7796	−0.779047
$856$	15.2971	0.522846
$857$	34.2283	1.16922	0.584609	−	0.811315i	$-0.301248\pi$
$857$	34.2283	1.16922	0.584609	+	0.811315i	$0.301248\pi$
$858$	−28.6262	−0.977282
$859$	−39.3677	−1.34321	−0.671604	−	0.740911i	$-0.734394\pi$
$859$	−39.3677	−1.34321	−0.671604	+	0.740911i	$0.734394\pi$
$860$	−23.8024	−0.811654
$861$	0	0
$862$	−28.8919	−0.984062
$863$	2.43739	0.0829696	0.0414848	−	0.999139i	$-0.486791\pi$
$863$	2.43739	0.0829696	0.0414848	+	0.999139i	$0.486791\pi$
$864$	5.32905	0.181298
$865$	−63.3437	−2.15375
$866$	38.6262	1.31257
$867$	−16.8356	−0.571767
$868$	0	0
$869$	−49.1314	−1.66667
$870$	−26.7281	−0.906167
$871$	39.6216	1.34253
$872$	1.92696	0.0652551
$873$	16.5900	0.561486
$874$	−19.7155	−0.666886
$875$	0	0
$876$	−1.56261	−0.0527958
$877$	49.8506	1.68333	0.841667	−	0.539996i	$-0.181574\pi$
$877$	49.8506	1.68333	0.841667	+	0.539996i	$0.181574\pi$
$878$	−36.6761	−1.23776
$879$	15.5307	0.523838
$880$	16.9606	0.571741
$881$	−38.5406	−1.29847	−0.649233	−	0.760590i	$-0.724910\pi$
$881$	−38.5406	−1.29847	−0.649233	+	0.760590i	$0.724910\pi$
$882$	0	0
$883$	6.39206	0.215110	0.107555	−	0.994199i	$-0.465698\pi$
$883$	6.39206	0.215110	0.107555	+	0.994199i	$0.465698\pi$
$884$	−7.95309	−0.267491
$885$	−41.2121	−1.38533
$886$	−2.99083	−0.100479
$887$	15.5413	0.521826	0.260913	−	0.965362i	$-0.415976\pi$
$887$	15.5413	0.521826	0.260913	+	0.965362i	$0.415976\pi$
$888$	−0.284524	−0.00954800
$889$	0	0
$890$	55.5096	1.86069
$891$	−3.69861	−0.123908
$892$	−15.1897	−0.508590
$893$	−28.8033	−0.963866
$894$	21.4113	0.716101
$895$	51.7925	1.73123
$896$	0	0
$897$	34.7109	1.15896
$898$	−18.8069	−0.627595
$899$	1.10500	0.0368539
$900$	−15.1049	−0.503496
$901$	12.0520	0.401510
$902$	4.57827	0.152440
$903$	0	0
$904$	−9.97654	−0.331815
$905$	60.9602	2.02639
$906$	−18.3429	−0.609400
$907$	3.60345	0.119651	0.0598253	−	0.998209i	$-0.480946\pi$
$907$	3.60345	0.119651	0.0598253	+	0.998209i	$0.480946\pi$
$908$	−13.7307	−0.455670
$909$	−18.5401	−0.614936
$910$	0	0
$911$	−45.3274	−1.50176	−0.750882	−	0.660437i	$-0.770371\pi$
$911$	−45.3274	−1.50176	−0.750882	+	0.660437i	$0.770371\pi$
$912$	4.00000	0.132453
$913$	55.5331	1.83788
$914$	23.9986	0.793802
$915$	−59.6759	−1.97283
$916$	−21.5732	−0.712799
$917$	0	0
$918$	−7.63450	−0.251976
$919$	−46.3313	−1.52833	−0.764164	−	0.645022i	$-0.776848\pi$
$919$	−46.3313	−1.52833	−0.764164	+	0.645022i	$0.776848\pi$
$920$	−20.5657	−0.678031
$921$	−2.73606	−0.0901563
$922$	−6.22482	−0.205004
$923$	32.2676	1.06210
$924$	0	0
$925$	2.20381	0.0724607
$926$	−23.2162	−0.762931
$927$	−27.5089	−0.903511
$928$	−6.40577	−0.210280
$929$	50.9467	1.67151	0.835753	−	0.549106i	$-0.185032\pi$
$929$	50.9467	1.67151	0.835753	+	0.549106i	$0.185032\pi$
$930$	−0.719761	−0.0236019
$931$	0	0
$932$	−7.13476	−0.233707
$933$	−11.2833	−0.369399
$934$	14.6499	0.479361
$935$	−24.2981	−0.794632
$936$	9.61190	0.314175
$937$	−47.4593	−1.55043	−0.775213	−	0.631700i	$-0.782358\pi$
$937$	−47.4593	−1.55043	−0.775213	+	0.631700i	$0.782358\pi$
$938$	0	0
$939$	0.573350	0.0187106
$940$	−30.0455	−0.979975
$941$	42.1433	1.37383	0.686916	−	0.726737i	$-0.258964\pi$
$941$	42.1433	1.37383	0.686916	+	0.726737i	$0.258964\pi$
$942$	−11.7155	−0.381711
$943$	−5.55143	−0.180779
$944$	−9.87708	−0.321472
$945$	0	0
$946$	29.4159	0.956395
$947$	57.2583	1.86064	0.930322	−	0.366743i	$-0.119527\pi$
$947$	57.2583	1.86064	0.930322	+	0.366743i	$0.119527\pi$
$948$	−12.0869	−0.392564
$949$	−7.70191	−0.250015
$950$	−30.9824	−1.00520
$951$	29.2170	0.947427
$952$	0	0
$953$	−15.0739	−0.488292	−0.244146	−	0.969739i	$-0.578508\pi$
$953$	−15.0739	−0.488292	−0.244146	+	0.969739i	$0.578508\pi$
$954$	−14.5657	−0.471584
$955$	−66.2119	−2.14257
$956$	3.45608	0.111778
$957$	33.0317	1.06776
$958$	11.9032	0.384575
$959$	0	0
$960$	4.17250	0.134667
$961$	−30.9702	−0.999040
$962$	−1.40238	−0.0452146
$963$	26.4859	0.853497
$964$	−11.7474	−0.378358
$965$	93.2196	3.00085
$966$	0	0
$967$	−16.2171	−0.521507	−0.260754	−	0.965405i	$-0.583971\pi$
$967$	−16.2171	−0.521507	−0.260754	+	0.965405i	$0.583971\pi$
$968$	−9.96059	−0.320145
$969$	−5.73048	−0.184090
$970$	35.4961	1.13971
$971$	−4.12999	−0.132538	−0.0662689	−	0.997802i	$-0.521110\pi$
$971$	−4.12999	−0.132538	−0.0662689	+	0.997802i	$0.521110\pi$
$972$	15.0772	0.483603
$973$	0	0
$974$	41.0845	1.31643
$975$	54.5474	1.74691
$976$	−14.3022	−0.457802
$977$	54.6070	1.74703	0.873516	−	0.486795i	$-0.161834\pi$
$977$	54.6070	1.74703	0.873516	+	0.486795i	$0.161834\pi$
$978$	−9.62309	−0.307712
$979$	−68.6011	−2.19250
$980$	0	0
$981$	3.33639	0.106523
$982$	−14.5325	−0.463751
$983$	18.0937	0.577099	0.288549	−	0.957465i	$-0.406827\pi$
$983$	18.0937	0.577099	0.288549	+	0.957465i	$0.406827\pi$
$984$	1.12631	0.0359054
$985$	−7.48988	−0.238647
$986$	9.17704	0.292257
$987$	0	0
$988$	19.7155	0.627233
$989$	−35.6686	−1.13419
$990$	29.3661	0.933315
$991$	−41.9899	−1.33385	−0.666926	−	0.745124i	$-0.732390\pi$
$991$	−41.9899	−1.33385	−0.666926	+	0.745124i	$0.732390\pi$
$992$	−0.172501	−0.00547691
$993$	−7.49418	−0.237821
$994$	0	0
$995$	−31.3236	−0.993024
$996$	13.6618	0.432890
$997$	−22.9984	−0.728367	−0.364184	−	0.931327i	$-0.618652\pi$
$997$	−22.9984	−0.728367	−0.364184	+	0.931327i	$0.618652\pi$
$998$	3.37481	0.106828
$999$	−1.34621	−0.0425921

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bj.1.3		4
7.6	odd	2		574.2.a.m.1.2	✓	4
21.20	even	2		5166.2.a.bx.1.4		4
28.27	even	2		4592.2.a.ba.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.a.m.1.2	✓	4	7.6	odd	2
4018.2.a.bj.1.3		4	1.1	even	1	trivial
4592.2.a.ba.1.3		4	28.27	even	2
5166.2.a.bx.1.4		4	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.12631 q^{3} +1.00000 q^{4} +3.70458 q^{5} -1.12631 q^{6} -1.00000 q^{8} -1.73143 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.12631 q^{3} +1.00000 q^{4} +3.70458 q^{5} -1.12631 q^{6} -1.00000 q^{8} -1.73143 q^{9} -3.70458 q^{10} +4.57827 q^{11} +1.12631 q^{12} +5.55143 q^{13} +4.17250 q^{15} +1.00000 q^{16} -1.43262 q^{17} +1.73143 q^{18} +3.55143 q^{19} +3.70458 q^{20} -4.57827 q^{22} +5.55143 q^{23} -1.12631 q^{24} +8.72393 q^{25} -5.55143 q^{26} -5.32905 q^{27} +6.40577 q^{29} -4.17250 q^{30} +0.172501 q^{31} -1.00000 q^{32} +5.15655 q^{33} +1.43262 q^{34} -1.73143 q^{36} +0.252616 q^{37} -3.55143 q^{38} +6.25262 q^{39} -3.70458 q^{40} -1.00000 q^{41} -6.42512 q^{43} +4.57827 q^{44} -6.41422 q^{45} -5.55143 q^{46} -8.11035 q^{47} +1.12631 q^{48} -8.72393 q^{50} -1.61357 q^{51} +5.55143 q^{52} -8.41255 q^{53} +5.32905 q^{54} +16.9606 q^{55} +4.00000 q^{57} -6.40577 q^{58} -9.87708 q^{59} +4.17250 q^{60} -14.3022 q^{61} -0.172501 q^{62} +1.00000 q^{64} +20.5657 q^{65} -5.15655 q^{66} +7.13720 q^{67} -1.43262 q^{68} +6.25262 q^{69} +5.81249 q^{71} +1.73143 q^{72} -1.38738 q^{73} -0.252616 q^{74} +9.82583 q^{75} +3.55143 q^{76} -6.25262 q^{78} -10.7314 q^{79} +3.70458 q^{80} -0.807862 q^{81} +1.00000 q^{82} +12.1297 q^{83} -5.30726 q^{85} +6.42512 q^{86} +7.21487 q^{87} -4.57827 q^{88} -14.9840 q^{89} +6.41422 q^{90} +5.55143 q^{92} +0.194289 q^{93} +8.11035 q^{94} +13.1565 q^{95} -1.12631 q^{96} -9.58166 q^{97} -7.92696 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + q^{3} + 4 q^{4} - 3 q^{5} - q^{6} - 4 q^{8} + 9 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + q^3 + 4 * q^4 - 3 * q^5 - q^6 - 4 * q^8 + 9 * q^9	\( 4 q - 4 q^{2} + q^{3} + 4 q^{4} - 3 q^{5} - q^{6} - 4 q^{8} + 9 q^{9} + 3 q^{10} + 4 q^{11} + q^{12} + 6 q^{13} + 11 q^{15} + 4 q^{16} + q^{17} - 9 q^{18} - 2 q^{19} - 3 q^{20} - 4 q^{22} + 6 q^{23} - q^{24} + 13 q^{25} - 6 q^{26} + 13 q^{27} + 17 q^{29} - 11 q^{30} - 5 q^{31} - 4 q^{32} - 8 q^{33} - q^{34} + 9 q^{36} - 6 q^{37} + 2 q^{38} + 18 q^{39} + 3 q^{40} - 4 q^{41} - 13 q^{43} + 4 q^{44} - 34 q^{45} - 6 q^{46} - 6 q^{47} + q^{48} - 13 q^{50} - 11 q^{51} + 6 q^{52} + 29 q^{53} - 13 q^{54} + 16 q^{55} + 16 q^{57} - 17 q^{58} - 16 q^{59} + 11 q^{60} - 21 q^{61} + 5 q^{62} + 4 q^{64} + 18 q^{65} + 8 q^{66} + 4 q^{67} + q^{68} + 18 q^{69} + 17 q^{71} - 9 q^{72} - 12 q^{73} + 6 q^{74} - 26 q^{75} - 2 q^{76} - 18 q^{78} - 27 q^{79} - 3 q^{80} + 40 q^{81} + 4 q^{82} + 18 q^{83} - 29 q^{85} + 13 q^{86} + 41 q^{87} - 4 q^{88} - 37 q^{89} + 34 q^{90} + 6 q^{92} - 47 q^{93} + 6 q^{94} + 24 q^{95} - q^{96} + 3 q^{97} - 32 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + q^3 + 4 * q^4 - 3 * q^5 - q^6 - 4 * q^8 + 9 * q^9 + 3 * q^10 + 4 * q^11 + q^12 + 6 * q^13 + 11 * q^15 + 4 * q^16 + q^17 - 9 * q^18 - 2 * q^19 - 3 * q^20 - 4 * q^22 + 6 * q^23 - q^24 + 13 * q^25 - 6 * q^26 + 13 * q^27 + 17 * q^29 - 11 * q^30 - 5 * q^31 - 4 * q^32 - 8 * q^33 - q^34 + 9 * q^36 - 6 * q^37 + 2 * q^38 + 18 * q^39 + 3 * q^40 - 4 * q^41 - 13 * q^43 + 4 * q^44 - 34 * q^45 - 6 * q^46 - 6 * q^47 + q^48 - 13 * q^50 - 11 * q^51 + 6 * q^52 + 29 * q^53 - 13 * q^54 + 16 * q^55 + 16 * q^57 - 17 * q^58 - 16 * q^59 + 11 * q^60 - 21 * q^61 + 5 * q^62 + 4 * q^64 + 18 * q^65 + 8 * q^66 + 4 * q^67 + q^68 + 18 * q^69 + 17 * q^71 - 9 * q^72 - 12 * q^73 + 6 * q^74 - 26 * q^75 - 2 * q^76 - 18 * q^78 - 27 * q^79 - 3 * q^80 + 40 * q^81 + 4 * q^82 + 18 * q^83 - 29 * q^85 + 13 * q^86 + 41 * q^87 - 4 * q^88 - 37 * q^89 + 34 * q^90 + 6 * q^92 - 47 * q^93 + 6 * q^94 + 24 * q^95 - q^96 + 3 * q^97 - 32 * q^99

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