LMFDB - Embedded newform 4018.2.a.bm.1.2

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:	4.4.37108.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 7x^{2} + 5x + 8 $ x^4 - x^3 - 7x^2 + 5x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.66364$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.232297 q^{3} +1.00000 q^{4} -0.663642 q^{5} -0.232297 q^{6} +1.00000 q^{8} -2.94604 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.232297 q^{3} +1.00000 q^{4} -0.663642 q^{5} -0.232297 q^{6} +1.00000 q^{8} -2.94604 q^{9} -0.663642 q^{10} +0.431345 q^{11} -0.232297 q^{12} -1.71374 q^{13} +0.154162 q^{15} +1.00000 q^{16} +3.55958 q^{17} -2.94604 q^{18} +7.71374 q^{19} -0.663642 q^{20} +0.431345 q^{22} +0.386458 q^{23} -0.232297 q^{24} -4.55958 q^{25} -1.71374 q^{26} +1.38124 q^{27} -6.37738 q^{29} +0.154162 q^{30} +5.94604 q^{31} +1.00000 q^{32} -0.100200 q^{33} +3.55958 q^{34} -2.94604 q^{36} -1.53541 q^{37} +7.71374 q^{38} +0.398096 q^{39} -0.663642 q^{40} +1.00000 q^{41} +2.61876 q^{43} +0.431345 q^{44} +1.95511 q^{45} +0.386458 q^{46} +2.85105 q^{47} -0.232297 q^{48} -4.55958 q^{50} -0.826879 q^{51} -1.71374 q^{52} +9.24007 q^{53} +1.38124 q^{54} -0.286258 q^{55} -1.79188 q^{57} -6.37738 q^{58} +0.509480 q^{59} +0.154162 q^{60} +7.99092 q^{61} +5.94604 q^{62} +1.00000 q^{64} +1.13731 q^{65} -0.100200 q^{66} -3.36053 q^{67} +3.55958 q^{68} -0.0897730 q^{69} +0.518555 q^{71} -2.94604 q^{72} -7.42748 q^{73} -1.53541 q^{74} +1.05918 q^{75} +7.71374 q^{76} +0.398096 q^{78} +13.7379 q^{79} -0.663642 q^{80} +8.51726 q^{81} +1.00000 q^{82} +3.95511 q^{83} -2.36229 q^{85} +2.61876 q^{86} +1.48144 q^{87} +0.431345 q^{88} +13.9460 q^{89} +1.95511 q^{90} +0.386458 q^{92} -1.38124 q^{93} +2.85105 q^{94} -5.11916 q^{95} -0.232297 q^{96} -12.0462 q^{97} -1.27076 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 3 q^{3} + 4 q^{4} + 3 q^{5} + 3 q^{6} + 4 q^{8} + 9 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 3 * q^3 + 4 * q^4 + 3 * q^5 + 3 * q^6 + 4 * q^8 + 9 * q^9	$ 4 q + 4 q^{2} + 3 q^{3} + 4 q^{4} + 3 q^{5} + 3 q^{6} + 4 q^{8} + 9 q^{9} + 3 q^{10} + 3 q^{12} + 10 q^{13} - q^{15} + 4 q^{16} - q^{17} + 9 q^{18} + 14 q^{19} + 3 q^{20} - 4 q^{23} + 3 q^{24} - 3 q^{25} + 10 q^{26} + 15 q^{27} - 3 q^{29} - q^{30} + 3 q^{31} + 4 q^{32} + 22 q^{33} - q^{34} + 9 q^{36} - 14 q^{37} + 14 q^{38} + 6 q^{39} + 3 q^{40} + 4 q^{41} + q^{43} + 4 q^{45} - 4 q^{46} - 2 q^{47} + 3 q^{48} - 3 q^{50} - 13 q^{51} + 10 q^{52} + 11 q^{53} + 15 q^{54} - 18 q^{55} + 12 q^{57} - 3 q^{58} - 2 q^{59} - q^{60} + 15 q^{61} + 3 q^{62} + 4 q^{64} + 8 q^{65} + 22 q^{66} + 4 q^{67} - q^{68} - 8 q^{69} + 15 q^{71} + 9 q^{72} + 4 q^{73} - 14 q^{74} + 10 q^{75} + 14 q^{76} + 6 q^{78} + 15 q^{79} + 3 q^{80} + 8 q^{81} + 4 q^{82} + 12 q^{83} - 27 q^{85} + q^{86} - 7 q^{87} + 35 q^{89} + 4 q^{90} - 4 q^{92} - 15 q^{93} - 2 q^{94} + 10 q^{95} + 3 q^{96} - 5 q^{97} + 20 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 3 * q^3 + 4 * q^4 + 3 * q^5 + 3 * q^6 + 4 * q^8 + 9 * q^9 + 3 * q^10 + 3 * q^12 + 10 * q^13 - q^15 + 4 * q^16 - q^17 + 9 * q^18 + 14 * q^19 + 3 * q^20 - 4 * q^23 + 3 * q^24 - 3 * q^25 + 10 * q^26 + 15 * q^27 - 3 * q^29 - q^30 + 3 * q^31 + 4 * q^32 + 22 * q^33 - q^34 + 9 * q^36 - 14 * q^37 + 14 * q^38 + 6 * q^39 + 3 * q^40 + 4 * q^41 + q^43 + 4 * q^45 - 4 * q^46 - 2 * q^47 + 3 * q^48 - 3 * q^50 - 13 * q^51 + 10 * q^52 + 11 * q^53 + 15 * q^54 - 18 * q^55 + 12 * q^57 - 3 * q^58 - 2 * q^59 - q^60 + 15 * q^61 + 3 * q^62 + 4 * q^64 + 8 * q^65 + 22 * q^66 + 4 * q^67 - q^68 - 8 * q^69 + 15 * q^71 + 9 * q^72 + 4 * q^73 - 14 * q^74 + 10 * q^75 + 14 * q^76 + 6 * q^78 + 15 * q^79 + 3 * q^80 + 8 * q^81 + 4 * q^82 + 12 * q^83 - 27 * q^85 + q^86 - 7 * q^87 + 35 * q^89 + 4 * q^90 - 4 * q^92 - 15 * q^93 - 2 * q^94 + 10 * q^95 + 3 * q^96 - 5 * q^97 + 20 * 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
$3$	−0.232297	−0.134117	−0.0670583	−	0.997749i	$-0.521361\pi$
$3$	−0.232297	−0.134117	−0.0670583	+	0.997749i	$0.521361\pi$
$4$	1.00000	0.500000
$5$	−0.663642	−0.296790	−0.148395	−	0.988928i	$-0.547411\pi$
$5$	−0.663642	−0.296790	−0.148395	+	0.988928i	$0.547411\pi$
$6$	−0.232297	−0.0948347
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−2.94604	−0.982013
$10$	−0.663642	−0.209862
$11$	0.431345	0.130055	0.0650277	−	0.997883i	$-0.479286\pi$
$11$	0.431345	0.130055	0.0650277	+	0.997883i	$0.479286\pi$
$12$	−0.232297	−0.0670583
$13$	−1.71374	−0.475306	−0.237653	−	0.971350i	$-0.576378\pi$
$13$	−1.71374	−0.475306	−0.237653	+	0.971350i	$0.576378\pi$
$14$	0	0
$15$	0.154162	0.0398044
$16$	1.00000	0.250000
$17$	3.55958	0.863325	0.431662	−	0.902035i	$-0.357927\pi$
$17$	3.55958	0.863325	0.431662	+	0.902035i	$0.357927\pi$
$18$	−2.94604	−0.694388
$19$	7.71374	1.76965	0.884827	−	0.465920i	$-0.154277\pi$
$19$	7.71374	1.76965	0.884827	+	0.465920i	$0.154277\pi$
$20$	−0.663642	−0.148395
$21$	0	0
$22$	0.431345	0.0919630
$23$	0.386458	0.0805821	0.0402911	−	0.999188i	$-0.487171\pi$
$23$	0.386458	0.0805821	0.0402911	+	0.999188i	$0.487171\pi$
$24$	−0.232297	−0.0474174
$25$	−4.55958	−0.911916
$26$	−1.71374	−0.336092
$27$	1.38124	0.265821
$28$	0	0
$29$	−6.37738	−1.18425	−0.592125	−	0.805846i	$-0.701711\pi$
$29$	−6.37738	−1.18425	−0.592125	+	0.805846i	$0.701711\pi$
$30$	0.154162	0.0281460
$31$	5.94604	1.06794	0.533970	−	0.845503i	$-0.320700\pi$
$31$	5.94604	1.06794	0.533970	+	0.845503i	$0.320700\pi$
$32$	1.00000	0.176777
$33$	−0.100200	−0.0174426
$34$	3.55958	0.610463
$35$	0	0
$36$	−2.94604	−0.491006
$37$	−1.53541	−0.252419	−0.126210	−	0.992004i	$-0.540281\pi$
$37$	−1.53541	−0.252419	−0.126210	+	0.992004i	$0.540281\pi$
$38$	7.71374	1.25133
$39$	0.398096	0.0637465
$40$	−0.663642	−0.104931
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	2.61876	0.399356	0.199678	−	0.979862i	$-0.436010\pi$
$43$	2.61876	0.399356	0.199678	+	0.979862i	$0.436010\pi$
$44$	0.431345	0.0650277
$45$	1.95511	0.291451
$46$	0.386458	0.0569802
$47$	2.85105	0.415869	0.207934	−	0.978143i	$-0.433326\pi$
$47$	2.85105	0.415869	0.207934	+	0.978143i	$0.433326\pi$
$48$	−0.232297	−0.0335291
$49$	0	0
$50$	−4.55958	−0.644822
$51$	−0.826879	−0.115786
$52$	−1.71374	−0.237653
$53$	9.24007	1.26922	0.634611	−	0.772832i	$-0.281160\pi$
$53$	9.24007	1.26922	0.634611	+	0.772832i	$0.281160\pi$
$54$	1.38124	0.187964
$55$	−0.286258	−0.0385991
$56$	0	0
$57$	−1.79188	−0.237340
$58$	−6.37738	−0.837391
$59$	0.509480	0.0663286	0.0331643	−	0.999450i	$-0.489442\pi$
$59$	0.509480	0.0663286	0.0331643	+	0.999450i	$0.489442\pi$
$60$	0.154162	0.0199022
$61$	7.99092	1.02313	0.511567	−	0.859244i	$-0.329065\pi$
$61$	7.99092	1.02313	0.511567	+	0.859244i	$0.329065\pi$
$62$	5.94604	0.755148
$63$	0	0
$64$	1.00000	0.125000
$65$	1.13731	0.141066
$66$	−0.100200	−0.0123338
$67$	−3.36053	−0.410554	−0.205277	−	0.978704i	$-0.565810\pi$
$67$	−3.36053	−0.410554	−0.205277	+	0.978704i	$0.565810\pi$
$68$	3.55958	0.431662
$69$	−0.0897730	−0.0108074
$70$	0	0
$71$	0.518555	0.0615412	0.0307706	−	0.999526i	$-0.490204\pi$
$71$	0.518555	0.0615412	0.0307706	+	0.999526i	$0.490204\pi$
$72$	−2.94604	−0.347194
$73$	−7.42748	−0.869321	−0.434661	−	0.900594i	$-0.643132\pi$
$73$	−7.42748	−0.869321	−0.434661	+	0.900594i	$0.643132\pi$
$74$	−1.53541	−0.178487
$75$	1.05918	0.122303
$76$	7.71374	0.884827
$77$	0	0
$78$	0.398096	0.0450755
$79$	13.7379	1.54564	0.772818	−	0.634628i	$-0.218847\pi$
$79$	13.7379	1.54564	0.772818	+	0.634628i	$0.218847\pi$
$80$	−0.663642	−0.0741974
$81$	8.51726	0.946362
$82$	1.00000	0.110432
$83$	3.95511	0.434130	0.217065	−	0.976157i	$-0.430352\pi$
$83$	3.95511	0.434130	0.217065	+	0.976157i	$0.430352\pi$
$84$	0	0
$85$	−2.36229	−0.256226
$86$	2.61876	0.282388
$87$	1.48144	0.158828
$88$	0.431345	0.0459815
$89$	13.9460	1.47828	0.739139	−	0.673553i	$-0.235233\pi$
$89$	13.9460	1.47828	0.739139	+	0.673553i	$0.235233\pi$
$90$	1.95511	0.206087
$91$	0	0
$92$	0.386458	0.0402911
$93$	−1.38124	−0.143228
$94$	2.85105	0.294064
$95$	−5.11916	−0.525215
$96$	−0.232297	−0.0237087
$97$	−12.0462	−1.22311	−0.611555	−	0.791202i	$-0.709456\pi$
$97$	−12.0462	−1.22311	−0.611555	+	0.791202i	$0.709456\pi$
$98$	0	0
$99$	−1.27076	−0.127716
$100$	−4.55958	−0.455958
$101$	−4.36831	−0.434663	−0.217331	−	0.976098i	$-0.569735\pi$
$101$	−4.36831	−0.434663	−0.217331	+	0.976098i	$0.569735\pi$
$102$	−0.826879	−0.0818732
$103$	14.9089	1.46902	0.734510	−	0.678598i	$-0.237412\pi$
$103$	14.9089	1.46902	0.734510	+	0.678598i	$0.237412\pi$
$104$	−1.71374	−0.168046
$105$	0	0
$106$	9.24007	0.897475
$107$	14.4927	1.40106	0.700530	−	0.713623i	$-0.252947\pi$
$107$	14.4927	1.40106	0.700530	+	0.713623i	$0.252947\pi$
$108$	1.38124	0.132910
$109$	−11.3942	−1.09137	−0.545685	−	0.837990i	$-0.683730\pi$
$109$	−11.3942	−1.09137	−0.545685	+	0.837990i	$0.683730\pi$
$110$	−0.286258	−0.0272937
$111$	0.356670	0.0338536
$112$	0	0
$113$	10.4888	0.986700	0.493350	−	0.869831i	$-0.335772\pi$
$113$	10.4888	0.986700	0.493350	+	0.869831i	$0.335772\pi$
$114$	−1.79188	−0.167825
$115$	−0.256470	−0.0239159
$116$	−6.37738	−0.592125
$117$	5.04875	0.466757
$118$	0.509480	0.0469014
$119$	0	0
$120$	0.154162	0.0140730
$121$	−10.8139	−0.983086
$122$	7.99092	0.723464
$123$	−0.232297	−0.0209455
$124$	5.94604	0.533970
$125$	6.34413	0.567437
$126$	0	0
$127$	10.4685	0.928930	0.464465	−	0.885592i	$-0.346247\pi$
$127$	10.4685	0.928930	0.464465	+	0.885592i	$0.346247\pi$
$128$	1.00000	0.0883883
$129$	−0.608328	−0.0535603
$130$	1.13731	0.0997487
$131$	9.38260	0.819761	0.409881	−	0.912139i	$-0.365570\pi$
$131$	9.38260	0.819761	0.409881	+	0.912139i	$0.365570\pi$
$132$	−0.100200	−0.00872129
$133$	0	0
$134$	−3.36053	−0.290306
$135$	−0.916652	−0.0788928
$136$	3.55958	0.305231
$137$	8.25647	0.705398	0.352699	−	0.935737i	$-0.385264\pi$
$137$	8.25647	0.705398	0.352699	+	0.935737i	$0.385264\pi$
$138$	−0.0897730	−0.00764199
$139$	16.8999	1.43343	0.716713	−	0.697368i	$-0.245646\pi$
$139$	16.8999	1.43343	0.716713	+	0.697368i	$0.245646\pi$
$140$	0	0
$141$	−0.662290	−0.0557749
$142$	0.518555	0.0435162
$143$	−0.739214	−0.0618162
$144$	−2.94604	−0.245503
$145$	4.23230	0.351473
$146$	−7.42748	−0.614703
$147$	0	0
$148$	−1.53541	−0.126210
$149$	2.39553	0.196250	0.0981249	−	0.995174i	$-0.468716\pi$
$149$	2.39553	0.196250	0.0981249	+	0.995174i	$0.468716\pi$
$150$	1.05918	0.0864813
$151$	0.927079	0.0754446	0.0377223	−	0.999288i	$-0.487990\pi$
$151$	0.927079	0.0754446	0.0377223	+	0.999288i	$0.487990\pi$
$152$	7.71374	0.625667
$153$	−10.4867	−0.847796
$154$	0	0
$155$	−3.94604	−0.316953
$156$	0.398096	0.0318732
$157$	18.6248	1.48642	0.743210	−	0.669059i	$-0.233303\pi$
$157$	18.6248	1.48642	0.743210	+	0.669059i	$0.233303\pi$
$158$	13.7379	1.09293
$159$	−2.14644	−0.170224
$160$	−0.663642	−0.0524655
$161$	0	0
$162$	8.51726	0.669179
$163$	1.79188	0.140351	0.0701753	−	0.997535i	$-0.477644\pi$
$163$	1.79188	0.140351	0.0701753	+	0.997535i	$0.477644\pi$
$164$	1.00000	0.0780869
$165$	0.0664969	0.00517678
$166$	3.95511	0.306976
$167$	1.01896	0.0788495	0.0394247	−	0.999223i	$-0.487447\pi$
$167$	1.01896	0.0788495	0.0394247	+	0.999223i	$0.487447\pi$
$168$	0	0
$169$	−10.0631	−0.774084
$170$	−2.36229	−0.181179
$171$	−22.7250	−1.73782
$172$	2.61876	0.199678
$173$	11.2362	0.854269	0.427135	−	0.904188i	$-0.359523\pi$
$173$	11.2362	0.854269	0.427135	+	0.904188i	$0.359523\pi$
$174$	1.48144	0.112308
$175$	0	0
$176$	0.431345	0.0325138
$177$	−0.118350	−0.00889577
$178$	13.9460	1.04530
$179$	−0.839868	−0.0627747	−0.0313874	−	0.999507i	$-0.509993\pi$
$179$	−0.839868	−0.0627747	−0.0313874	+	0.999507i	$0.509993\pi$
$180$	1.95511	0.145726
$181$	−25.7621	−1.91488	−0.957440	−	0.288631i	$-0.906800\pi$
$181$	−25.7621	−1.91488	−0.957440	+	0.288631i	$0.906800\pi$
$182$	0	0
$183$	−1.85627	−0.137219
$184$	0.386458	0.0284901
$185$	1.01896	0.0749154
$186$	−1.38124	−0.101278
$187$	1.53541	0.112280
$188$	2.85105	0.207934
$189$	0	0
$190$	−5.11916	−0.371383
$191$	−15.6818	−1.13470	−0.567349	−	0.823477i	$-0.692031\pi$
$191$	−15.6818	−1.13470	−0.567349	+	0.823477i	$0.692031\pi$
$192$	−0.232297	−0.0167646
$193$	−5.52768	−0.397891	−0.198946	−	0.980011i	$-0.563752\pi$
$193$	−5.52768	−0.397891	−0.198946	+	0.980011i	$0.563752\pi$
$194$	−12.0462	−0.864870
$195$	−0.264193	−0.0189193
$196$	0	0
$197$	−3.32728	−0.237059	−0.118530	−	0.992951i	$-0.537818\pi$
$197$	−3.32728	−0.237059	−0.118530	+	0.992951i	$0.537818\pi$
$198$	−1.27076	−0.0903089
$199$	3.78024	0.267974	0.133987	−	0.990983i	$-0.457222\pi$
$199$	3.78024	0.267974	0.133987	+	0.990983i	$0.457222\pi$
$200$	−4.55958	−0.322411
$201$	0.780640	0.0550621
$202$	−4.36831	−0.307353
$203$	0	0
$204$	−0.826879	−0.0578931
$205$	−0.663642	−0.0463507
$206$	14.9089	1.03875
$207$	−1.13852	−0.0791327
$208$	−1.71374	−0.118827
$209$	3.32728	0.230153
$210$	0	0
$211$	6.57989	0.452978	0.226489	−	0.974014i	$-0.427275\pi$
$211$	6.57989	0.452978	0.226489	+	0.974014i	$0.427275\pi$
$212$	9.24007	0.634611
$213$	−0.120459	−0.00825369
$214$	14.4927	0.990699
$215$	−1.73791	−0.118525
$216$	1.38124	0.0939818
$217$	0	0
$218$	−11.3942	−0.771715
$219$	1.72538	0.116590
$220$	−0.286258	−0.0192995
$221$	−6.10020	−0.410344
$222$	0.356670	0.0239381
$223$	−20.8087	−1.39346	−0.696728	−	0.717336i	$-0.745361\pi$
$223$	−20.8087	−1.39346	−0.696728	+	0.717336i	$0.745361\pi$
$224$	0	0
$225$	13.4327	0.895513
$226$	10.4888	0.697702
$227$	−12.6122	−0.837104	−0.418552	−	0.908193i	$-0.637462\pi$
$227$	−12.6122	−0.837104	−0.418552	+	0.908193i	$0.637462\pi$
$228$	−1.79188	−0.118670
$229$	−9.29749	−0.614396	−0.307198	−	0.951646i	$-0.599391\pi$
$229$	−9.29749	−0.614396	−0.307198	+	0.951646i	$0.599391\pi$
$230$	−0.256470	−0.0169111
$231$	0	0
$232$	−6.37738	−0.418696
$233$	−10.0483	−0.658289	−0.329145	−	0.944280i	$-0.606760\pi$
$233$	−10.0483	−0.658289	−0.329145	+	0.944280i	$0.606760\pi$
$234$	5.04875	0.330047
$235$	−1.89208	−0.123425
$236$	0.509480	0.0331643
$237$	−3.19127	−0.207295
$238$	0	0
$239$	−25.6995	−1.66236	−0.831181	−	0.556001i	$-0.812335\pi$
$239$	−25.6995	−1.66236	−0.831181	+	0.556001i	$0.812335\pi$
$240$	0.154162	0.00995110
$241$	17.1192	1.10274	0.551371	−	0.834260i	$-0.314105\pi$
$241$	17.1192	1.10274	0.551371	+	0.834260i	$0.314105\pi$
$242$	−10.8139	−0.695146
$243$	−6.12227	−0.392743
$244$	7.99092	0.511567
$245$	0	0
$246$	−0.232297	−0.0148107
$247$	−13.2194	−0.841128
$248$	5.94604	0.377574
$249$	−0.918760	−0.0582240
$250$	6.34413	0.401238
$251$	−13.4828	−0.851027	−0.425513	−	0.904952i	$-0.639906\pi$
$251$	−13.4828	−0.851027	−0.425513	+	0.904952i	$0.639906\pi$
$252$	0	0
$253$	0.166697	0.0104801
$254$	10.4685	0.656853
$255$	0.548751	0.0343641
$256$	1.00000	0.0625000
$257$	27.5635	1.71936	0.859682	−	0.510830i	$-0.170662\pi$
$257$	27.5635	1.71936	0.859682	+	0.510830i	$0.170662\pi$
$258$	−0.608328	−0.0378729
$259$	0	0
$260$	1.13731	0.0705330
$261$	18.7880	1.16295
$262$	9.38260	0.579659
$263$	−4.15627	−0.256287	−0.128143	−	0.991756i	$-0.540902\pi$
$263$	−4.15627	−0.256287	−0.128143	+	0.991756i	$0.540902\pi$
$264$	−0.100200	−0.00616688
$265$	−6.13210	−0.376692
$266$	0	0
$267$	−3.23962	−0.198261
$268$	−3.36053	−0.205277
$269$	0.419707	0.0255900	0.0127950	−	0.999918i	$-0.495927\pi$
$269$	0.419707	0.0255900	0.0127950	+	0.999918i	$0.495927\pi$
$270$	−0.916652	−0.0557856
$271$	17.2754	1.04941	0.524704	−	0.851285i	$-0.324176\pi$
$271$	17.2754	1.04941	0.524704	+	0.851285i	$0.324176\pi$
$272$	3.55958	0.215831
$273$	0	0
$274$	8.25647	0.498792
$275$	−1.96675	−0.118600
$276$	−0.0897730	−0.00540370
$277$	2.22277	0.133553	0.0667766	−	0.997768i	$-0.478729\pi$
$277$	2.22277	0.133553	0.0667766	+	0.997768i	$0.478729\pi$
$278$	16.8999	1.01359
$279$	−17.5173	−1.04873
$280$	0	0
$281$	17.9404	1.07024	0.535118	−	0.844777i	$-0.320267\pi$
$281$	17.9404	1.07024	0.535118	+	0.844777i	$0.320267\pi$
$282$	−0.662290	−0.0394388
$283$	−22.1857	−1.31880	−0.659402	−	0.751791i	$-0.729190\pi$
$283$	−22.1857	−1.31880	−0.659402	+	0.751791i	$0.729190\pi$
$284$	0.518555	0.0307706
$285$	1.18916	0.0704400
$286$	−0.739214	−0.0437106
$287$	0	0
$288$	−2.94604	−0.173597
$289$	−4.32939	−0.254670
$290$	4.23230	0.248529
$291$	2.79830	0.164039
$292$	−7.42748	−0.434661
$293$	−31.6697	−1.85016	−0.925082	−	0.379767i	$-0.876004\pi$
$293$	−31.6697	−1.85016	−0.925082	+	0.379767i	$0.876004\pi$
$294$	0	0
$295$	−0.338112	−0.0196856
$296$	−1.53541	−0.0892437
$297$	0.595793	0.0345714
$298$	2.39553	0.138770
$299$	−0.662290	−0.0383012
$300$	1.05918	0.0611515
$301$	0	0
$302$	0.927079	0.0533474
$303$	1.01474	0.0582955
$304$	7.71374	0.442413
$305$	−5.30311	−0.303655
$306$	−10.4867	−0.599482
$307$	−22.7099	−1.29612	−0.648061	−	0.761589i	$-0.724420\pi$
$307$	−22.7099	−1.29612	−0.648061	+	0.761589i	$0.724420\pi$
$308$	0	0
$309$	−3.46329	−0.197020
$310$	−3.94604	−0.224120
$311$	10.3865	0.588962	0.294481	−	0.955657i	$-0.404853\pi$
$311$	10.3865	0.588962	0.294481	+	0.955657i	$0.404853\pi$
$312$	0.398096	0.0225378
$313$	−0.368308	−0.0208180	−0.0104090	−	0.999946i	$-0.503313\pi$
$313$	−0.368308	−0.0208180	−0.0104090	+	0.999946i	$0.503313\pi$
$314$	18.6248	1.05106
$315$	0	0
$316$	13.7379	0.772818
$317$	6.43134	0.361220	0.180610	−	0.983555i	$-0.442193\pi$
$317$	6.43134	0.361220	0.180610	+	0.983555i	$0.442193\pi$
$318$	−2.14644	−0.120366
$319$	−2.75085	−0.154018
$320$	−0.663642	−0.0370987
$321$	−3.36660	−0.187905
$322$	0	0
$323$	27.4577	1.52779
$324$	8.51726	0.473181
$325$	7.81394	0.433439
$326$	1.79188	0.0992429
$327$	2.64684	0.146371
$328$	1.00000	0.0552158
$329$	0	0
$330$	0.0664969	0.00366053
$331$	26.1257	1.43600	0.718000	−	0.696043i	$-0.245058\pi$
$331$	26.1257	1.43600	0.718000	+	0.696043i	$0.245058\pi$
$332$	3.95511	0.217065
$333$	4.52337	0.247879
$334$	1.01896	0.0557550
$335$	2.23019	0.121848
$336$	0	0
$337$	13.4633	0.733392	0.366696	−	0.930341i	$-0.380489\pi$
$337$	13.4633	0.733392	0.366696	+	0.930341i	$0.380489\pi$
$338$	−10.0631	−0.547360
$339$	−2.43651	−0.132333
$340$	−2.36229	−0.128113
$341$	2.56479	0.138891
$342$	−22.7250	−1.22883
$343$	0	0
$344$	2.61876	0.141194
$345$	0.0595771	0.00320752
$346$	11.2362	0.604060
$347$	21.5246	1.15550	0.577751	−	0.816213i	$-0.303930\pi$
$347$	21.5246	1.15550	0.577751	+	0.816213i	$0.303930\pi$
$348$	1.48144	0.0794138
$349$	20.5838	1.10183	0.550913	−	0.834563i	$-0.314280\pi$
$349$	20.5838	1.10183	0.550913	+	0.834563i	$0.314280\pi$
$350$	0	0
$351$	−2.36710	−0.126346
$352$	0.431345	0.0229908
$353$	−1.98185	−0.105483	−0.0527416	−	0.998608i	$-0.516796\pi$
$353$	−1.98185	−0.105483	−0.0527416	+	0.998608i	$0.516796\pi$
$354$	−0.118350	−0.00629026
$355$	−0.344135	−0.0182648
$356$	13.9460	0.739139
$357$	0	0
$358$	−0.839868	−0.0443884
$359$	−25.7281	−1.35788	−0.678938	−	0.734195i	$-0.737560\pi$
$359$	−25.7281	−1.35788	−0.678938	+	0.734195i	$0.737560\pi$
$360$	1.95511	0.103044
$361$	40.5018	2.13167
$362$	−25.7621	−1.35403
$363$	2.51204	0.131848
$364$	0	0
$365$	4.92919	0.258005
$366$	−1.85627	−0.0970285
$367$	−1.08335	−0.0565503	−0.0282752	−	0.999600i	$-0.509001\pi$
$367$	−1.08335	−0.0565503	−0.0282752	+	0.999600i	$0.509001\pi$
$368$	0.386458	0.0201455
$369$	−2.94604	−0.153365
$370$	1.01896	0.0529732
$371$	0	0
$372$	−1.38124	−0.0716142
$373$	7.37141	0.381677	0.190839	−	0.981621i	$-0.438879\pi$
$373$	7.37141	0.381677	0.190839	+	0.981621i	$0.438879\pi$
$374$	1.53541	0.0793940
$375$	−1.47372	−0.0761026
$376$	2.85105	0.147032
$377$	10.9292	0.562882
$378$	0	0
$379$	−14.6188	−0.750915	−0.375458	−	0.926840i	$-0.622514\pi$
$379$	−14.6188	−0.750915	−0.375458	+	0.926840i	$0.622514\pi$
$380$	−5.11916	−0.262607
$381$	−2.43180	−0.124585
$382$	−15.6818	−0.802353
$383$	−25.2194	−1.28865	−0.644325	−	0.764752i	$-0.722861\pi$
$383$	−25.2194	−1.28865	−0.644325	+	0.764752i	$0.722861\pi$
$384$	−0.232297	−0.0118543
$385$	0	0
$386$	−5.52768	−0.281352
$387$	−7.71495	−0.392173
$388$	−12.0462	−0.611555
$389$	−14.9292	−0.756940	−0.378470	−	0.925614i	$-0.623550\pi$
$389$	−14.9292	−0.756940	−0.378470	+	0.925614i	$0.623550\pi$
$390$	−0.264193	−0.0133780
$391$	1.37563	0.0695686
$392$	0	0
$393$	−2.17955	−0.109944
$394$	−3.32728	−0.167626
$395$	−9.11705	−0.458729
$396$	−1.27076	−0.0638580
$397$	38.4945	1.93198	0.965991	−	0.258574i	$-0.0832526\pi$
$397$	38.4945	1.93198	0.965991	+	0.258574i	$0.0832526\pi$
$398$	3.78024	0.189486
$399$	0	0
$400$	−4.55958	−0.227979
$401$	−0.763387	−0.0381217	−0.0190609	−	0.999818i	$-0.506068\pi$
$401$	−0.763387	−0.0381217	−0.0190609	+	0.999818i	$0.506068\pi$
$402$	0.780640	0.0389348
$403$	−10.1900	−0.507599
$404$	−4.36831	−0.217331
$405$	−5.65241	−0.280870
$406$	0	0
$407$	−0.662290	−0.0328285
$408$	−0.826879	−0.0409366
$409$	13.1633	0.650883	0.325441	−	0.945562i	$-0.394487\pi$
$409$	13.1633	0.650883	0.325441	+	0.945562i	$0.394487\pi$
$410$	−0.663642	−0.0327749
$411$	−1.91795	−0.0946055
$412$	14.9089	0.734510
$413$	0	0
$414$	−1.13852	−0.0559553
$415$	−2.62478	−0.128845
$416$	−1.71374	−0.0840231
$417$	−3.92578	−0.192246
$418$	3.32728	0.162743
$419$	33.8955	1.65591	0.827953	−	0.560798i	$-0.189506\pi$
$419$	33.8955	1.65591	0.827953	+	0.560798i	$0.189506\pi$
$420$	0	0
$421$	−31.8688	−1.55319	−0.776594	−	0.630001i	$-0.783054\pi$
$421$	−31.8688	−1.55319	−0.776594	+	0.630001i	$0.783054\pi$
$422$	6.57989	0.320304
$423$	−8.39931	−0.408388
$424$	9.24007	0.448738
$425$	−16.2302	−0.787280
$426$	−0.120459	−0.00583624
$427$	0	0
$428$	14.4927	0.700530
$429$	0.171717	0.00829057
$430$	−1.73791	−0.0838097
$431$	7.61354	0.366731	0.183366	−	0.983045i	$-0.441301\pi$
$431$	7.61354	0.366731	0.183366	+	0.983045i	$0.441301\pi$
$432$	1.38124	0.0664552
$433$	−36.9033	−1.77346	−0.886730	−	0.462288i	$-0.847029\pi$
$433$	−36.9033	−1.77346	−0.886730	+	0.462288i	$0.847029\pi$
$434$	0	0
$435$	−0.983148	−0.0471384
$436$	−11.3942	−0.545685
$437$	2.98104	0.142602
$438$	1.72538	0.0824418
$439$	−16.2448	−0.775324	−0.387662	−	0.921802i	$-0.626717\pi$
$439$	−16.2448	−0.775324	−0.387662	+	0.921802i	$0.626717\pi$
$440$	−0.286258	−0.0136468
$441$	0	0
$442$	−6.10020	−0.290157
$443$	−29.1058	−1.38286	−0.691430	−	0.722444i	$-0.743019\pi$
$443$	−29.1058	−1.38286	−0.691430	+	0.722444i	$0.743019\pi$
$444$	0.356670	0.0169268
$445$	−9.25517	−0.438737
$446$	−20.8087	−0.985322
$447$	−0.556475	−0.0263203
$448$	0	0
$449$	−5.01685	−0.236760	−0.118380	−	0.992968i	$-0.537770\pi$
$449$	−5.01685	−0.236760	−0.118380	+	0.992968i	$0.537770\pi$
$450$	13.4327	0.633223
$451$	0.431345	0.0203112
$452$	10.4888	0.493350
$453$	−0.215357	−0.0101184
$454$	−12.6122	−0.591922
$455$	0	0
$456$	−1.79188	−0.0839123
$457$	−1.79188	−0.0838204	−0.0419102	−	0.999121i	$-0.513344\pi$
$457$	−1.79188	−0.0838204	−0.0419102	+	0.999121i	$0.513344\pi$
$458$	−9.29749	−0.434443
$459$	4.91665	0.229490
$460$	−0.256470	−0.0119580
$461$	−2.32162	−0.108128	−0.0540642	−	0.998537i	$-0.517218\pi$
$461$	−2.32162	−0.108128	−0.0540642	+	0.998537i	$0.517218\pi$
$462$	0	0
$463$	23.6279	1.09808	0.549040	−	0.835796i	$-0.314993\pi$
$463$	23.6279	1.09808	0.549040	+	0.835796i	$0.314993\pi$
$464$	−6.37738	−0.296063
$465$	0.916652	0.0425087
$466$	−10.0483	−0.465481
$467$	10.7245	0.496272	0.248136	−	0.968725i	$-0.420182\pi$
$467$	10.7245	0.496272	0.248136	+	0.968725i	$0.420182\pi$
$468$	5.04875	0.233378
$469$	0	0
$470$	−1.89208	−0.0872750
$471$	−4.32647	−0.199353
$472$	0.509480	0.0234507
$473$	1.12959	0.0519385
$474$	−3.19127	−0.146580
$475$	−35.1714	−1.61378
$476$	0	0
$477$	−27.2216	−1.24639
$478$	−25.6995	−1.17547
$479$	16.2043	0.740394	0.370197	−	0.928953i	$-0.379290\pi$
$479$	16.2043	0.740394	0.370197	+	0.928953i	$0.379290\pi$
$480$	0.154162	0.00703649
$481$	2.63129	0.119977
$482$	17.1192	0.779756
$483$	0	0
$484$	−10.8139	−0.491543
$485$	7.99438	0.363006
$486$	−6.12227	−0.277712
$487$	3.08896	0.139974	0.0699872	−	0.997548i	$-0.477704\pi$
$487$	3.08896	0.139974	0.0699872	+	0.997548i	$0.477704\pi$
$488$	7.99092	0.361732
$489$	−0.416247	−0.0188233
$490$	0	0
$491$	−7.76379	−0.350375	−0.175187	−	0.984535i	$-0.556053\pi$
$491$	−7.76379	−0.350375	−0.175187	+	0.984535i	$0.556053\pi$
$492$	−0.232297	−0.0104727
$493$	−22.7008	−1.02239
$494$	−13.2194	−0.594767
$495$	0.843328	0.0379048
$496$	5.94604	0.266985
$497$	0	0
$498$	−0.918760	−0.0411706
$499$	14.7880	0.662002	0.331001	−	0.943630i	$-0.392614\pi$
$499$	14.7880	0.662002	0.331001	+	0.943630i	$0.392614\pi$
$500$	6.34413	0.283718
$501$	−0.236701	−0.0105750
$502$	−13.4828	−0.601767
$503$	27.6512	1.23290	0.616452	−	0.787392i	$-0.288569\pi$
$503$	27.6512	1.23290	0.616452	+	0.787392i	$0.288569\pi$
$504$	0	0
$505$	2.89899	0.129003
$506$	0.166697	0.00741058
$507$	2.33762	0.103817
$508$	10.4685	0.464465
$509$	−13.0929	−0.580332	−0.290166	−	0.956976i	$-0.593710\pi$
$509$	−13.0929	−0.580332	−0.290166	+	0.956976i	$0.593710\pi$
$510$	0.548751	0.0242991
$511$	0	0
$512$	1.00000	0.0441942
$513$	10.6546	0.470411
$514$	27.5635	1.21577
$515$	−9.89418	−0.435990
$516$	−0.608328	−0.0267802
$517$	1.22979	0.0540860
$518$	0	0
$519$	−2.61012	−0.114572
$520$	1.13731	0.0498744
$521$	4.98495	0.218395	0.109197	−	0.994020i	$-0.465172\pi$
$521$	4.98495	0.218395	0.109197	+	0.994020i	$0.465172\pi$
$522$	18.7880	0.822329
$523$	8.90758	0.389501	0.194751	−	0.980853i	$-0.437610\pi$
$523$	8.90758	0.389501	0.194751	+	0.980853i	$0.437610\pi$
$524$	9.38260	0.409881
$525$	0	0
$526$	−4.15627	−0.181222
$527$	21.1654	0.921979
$528$	−0.100200	−0.00436064
$529$	−22.8506	−0.993507
$530$	−6.13210	−0.266361
$531$	−1.50095	−0.0651356
$532$	0	0
$533$	−1.71374	−0.0742304
$534$	−3.23962	−0.140192
$535$	−9.61795	−0.415820
$536$	−3.36053	−0.145153
$537$	0.195099	0.00841913
$538$	0.419707	0.0180948
$539$	0	0
$540$	−0.916652	−0.0394464
$541$	−21.9637	−0.944293	−0.472147	−	0.881520i	$-0.656521\pi$
$541$	−21.9637	−0.944293	−0.472147	+	0.881520i	$0.656521\pi$
$542$	17.2754	0.742043
$543$	5.98445	0.256817
$544$	3.55958	0.152616
$545$	7.56169	0.323907
$546$	0	0
$547$	−24.0634	−1.02888	−0.514439	−	0.857527i	$-0.672000\pi$
$547$	−24.0634	−1.02888	−0.514439	+	0.857527i	$0.672000\pi$
$548$	8.25647	0.352699
$549$	−23.5416	−1.00473
$550$	−1.96675	−0.0838626
$551$	−49.1935	−2.09571
$552$	−0.0897730	−0.00382099
$553$	0	0
$554$	2.22277	0.0944363
$555$	−0.236701	−0.0100474
$556$	16.8999	0.716713
$557$	−25.4405	−1.07795	−0.538974	−	0.842323i	$-0.681188\pi$
$557$	−25.4405	−1.07795	−0.538974	+	0.842323i	$0.681188\pi$
$558$	−17.5173	−0.741565
$559$	−4.48787	−0.189817
$560$	0	0
$561$	−0.356670	−0.0150586
$562$	17.9404	0.756771
$563$	9.14895	0.385582	0.192791	−	0.981240i	$-0.438246\pi$
$563$	9.14895	0.385582	0.192791	+	0.981240i	$0.438246\pi$
$564$	−0.662290	−0.0278874
$565$	−6.96078	−0.292842
$566$	−22.1857	−0.932535
$567$	0	0
$568$	0.518555	0.0217581
$569$	−7.63380	−0.320026	−0.160013	−	0.987115i	$-0.551154\pi$
$569$	−7.63380	−0.320026	−0.160013	+	0.987115i	$0.551154\pi$
$570$	1.18916	0.0498086
$571$	21.4607	0.898104	0.449052	−	0.893506i	$-0.351762\pi$
$571$	21.4607	0.898104	0.449052	+	0.893506i	$0.351762\pi$
$572$	−0.739214	−0.0309081
$573$	3.64284	0.152182
$574$	0	0
$575$	−1.76209	−0.0734841
$576$	−2.94604	−0.122752
$577$	12.2120	0.508394	0.254197	−	0.967152i	$-0.418189\pi$
$577$	12.2120	0.508394	0.254197	+	0.967152i	$0.418189\pi$
$578$	−4.32939	−0.180079
$579$	1.28406	0.0533638
$580$	4.23230	0.175737
$581$	0	0
$582$	2.79830	0.115993
$583$	3.98566	0.165069
$584$	−7.42748	−0.307351
$585$	−3.35056	−0.138529
$586$	−31.6697	−1.30826
$587$	−3.06911	−0.126676	−0.0633379	−	0.997992i	$-0.520175\pi$
$587$	−3.06911	−0.126676	−0.0633379	+	0.997992i	$0.520175\pi$
$588$	0	0
$589$	45.8662	1.88988
$590$	−0.338112	−0.0139199
$591$	0.772917	0.0317935
$592$	−1.53541	−0.0631048
$593$	13.9279	0.571950	0.285975	−	0.958237i	$-0.407683\pi$
$593$	13.9279	0.571950	0.285975	+	0.958237i	$0.407683\pi$
$594$	0.595793	0.0244457
$595$	0	0
$596$	2.39553	0.0981249
$597$	−0.878137	−0.0359397
$598$	−0.662290	−0.0270830
$599$	−29.6607	−1.21190	−0.605951	−	0.795502i	$-0.707207\pi$
$599$	−29.6607	−1.21190	−0.605951	+	0.795502i	$0.707207\pi$
$600$	1.05918	0.0432406
$601$	−17.1096	−0.697916	−0.348958	−	0.937138i	$-0.613464\pi$
$601$	−17.1096	−0.697916	−0.348958	+	0.937138i	$0.613464\pi$
$602$	0	0
$603$	9.90025	0.403170
$604$	0.927079	0.0377223
$605$	7.17658	0.291770
$606$	1.01474	0.0412211
$607$	−34.3520	−1.39430	−0.697152	−	0.716924i	$-0.745550\pi$
$607$	−34.3520	−1.39430	−0.697152	+	0.716924i	$0.745550\pi$
$608$	7.71374	0.312834
$609$	0	0
$610$	−5.30311	−0.214717
$611$	−4.88597	−0.197665
$612$	−10.4867	−0.423898
$613$	−5.07081	−0.204808	−0.102404	−	0.994743i	$-0.532653\pi$
$613$	−5.07081	−0.204808	−0.102404	+	0.994743i	$0.532653\pi$
$614$	−22.7099	−0.916496
$615$	0.154162	0.00621640
$616$	0	0
$617$	25.8674	1.04138	0.520691	−	0.853745i	$-0.325674\pi$
$617$	25.8674	1.04138	0.520691	+	0.853745i	$0.325674\pi$
$618$	−3.46329	−0.139314
$619$	−36.0709	−1.44981	−0.724905	−	0.688849i	$-0.758116\pi$
$619$	−36.0709	−1.44981	−0.724905	+	0.688849i	$0.758116\pi$
$620$	−3.94604	−0.158477
$621$	0.533794	0.0214204
$622$	10.3865	0.416459
$623$	0	0
$624$	0.398096	0.0159366
$625$	18.5877	0.743507
$626$	−0.368308	−0.0147205
$627$	−0.772917	−0.0308673
$628$	18.6248	0.743210
$629$	−5.46540	−0.217920
$630$	0	0
$631$	−11.1749	−0.444867	−0.222433	−	0.974948i	$-0.571400\pi$
$631$	−11.1749	−0.444867	−0.222433	+	0.974948i	$0.571400\pi$
$632$	13.7379	0.546465
$633$	−1.52849	−0.0607519
$634$	6.43134	0.255421
$635$	−6.94734	−0.275697
$636$	−2.14644	−0.0851118
$637$	0	0
$638$	−2.75085	−0.108907
$639$	−1.52768	−0.0604342
$640$	−0.663642	−0.0262327
$641$	11.1814	0.441640	0.220820	−	0.975315i	$-0.429127\pi$
$641$	11.1814	0.441640	0.220820	+	0.975315i	$0.429127\pi$
$642$	−3.36660	−0.132869
$643$	−20.2401	−0.798193	−0.399096	−	0.916909i	$-0.630676\pi$
$643$	−20.2401	−0.798193	−0.399096	+	0.916909i	$0.630676\pi$
$644$	0	0
$645$	0.403712	0.0158961
$646$	27.4577	1.08031
$647$	−7.24053	−0.284655	−0.142327	−	0.989820i	$-0.545459\pi$
$647$	−7.24053	−0.284655	−0.142327	+	0.989820i	$0.545459\pi$
$648$	8.51726	0.334589
$649$	0.219762	0.00862640
$650$	7.81394	0.306488
$651$	0	0
$652$	1.79188	0.0701753
$653$	32.0018	1.25233	0.626163	−	0.779692i	$-0.284625\pi$
$653$	32.0018	1.25233	0.626163	+	0.779692i	$0.284625\pi$
$654$	2.64684	0.103500
$655$	−6.22668	−0.243297
$656$	1.00000	0.0390434
$657$	21.8816	0.853684
$658$	0	0
$659$	48.1231	1.87461	0.937305	−	0.348509i	$-0.113312\pi$
$659$	48.1231	1.87461	0.937305	+	0.348509i	$0.113312\pi$
$660$	0.0664969	0.00258839
$661$	−3.81089	−0.148226	−0.0741132	−	0.997250i	$-0.523613\pi$
$661$	−3.81089	−0.148226	−0.0741132	+	0.997250i	$0.523613\pi$
$662$	26.1257	1.01541
$663$	1.41706	0.0550339
$664$	3.95511	0.153488
$665$	0	0
$666$	4.52337	0.175277
$667$	−2.46459	−0.0954294
$668$	1.01896	0.0394247
$669$	4.83380	0.186885
$670$	2.23019	0.0861597
$671$	3.44684	0.133064
$672$	0	0
$673$	−46.3463	−1.78652	−0.893260	−	0.449540i	$-0.851588\pi$
$673$	−46.3463	−1.78652	−0.893260	+	0.449540i	$0.851588\pi$
$674$	13.4633	0.518587
$675$	−6.29790	−0.242406
$676$	−10.0631	−0.387042
$677$	−1.12262	−0.0431458	−0.0215729	−	0.999767i	$-0.506867\pi$
$677$	−1.12262	−0.0431458	−0.0215729	+	0.999767i	$0.506867\pi$
$678$	−2.43651	−0.0935734
$679$	0	0
$680$	−2.36229	−0.0905895
$681$	2.92978	0.112269
$682$	2.56479	0.0982110
$683$	24.7854	0.948388	0.474194	−	0.880420i	$-0.342740\pi$
$683$	24.7854	0.948388	0.474194	+	0.880420i	$0.342740\pi$
$684$	−22.7250	−0.868911
$685$	−5.47934	−0.209355
$686$	0	0
$687$	2.15978	0.0824006
$688$	2.61876	0.0998391
$689$	−15.8351	−0.603269
$690$	0.0595771	0.00226806
$691$	−7.54915	−0.287183	−0.143592	−	0.989637i	$-0.545865\pi$
$691$	−7.54915	−0.287183	−0.143592	+	0.989637i	$0.545865\pi$
$692$	11.2362	0.427135
$693$	0	0
$694$	21.5246	0.817064
$695$	−11.2154	−0.425426
$696$	1.48144	0.0561540
$697$	3.55958	0.134829
$698$	20.5838	0.779109
$699$	2.33420	0.0882875
$700$	0	0
$701$	6.69519	0.252874	0.126437	−	0.991975i	$-0.459646\pi$
$701$	6.69519	0.252874	0.126437	+	0.991975i	$0.459646\pi$
$702$	−2.36710	−0.0893403
$703$	−11.8437	−0.446695
$704$	0.431345	0.0162569
$705$	0.439523	0.0165534
$706$	−1.98185	−0.0745879
$707$	0	0
$708$	−0.118350	−0.00444788
$709$	−37.5553	−1.41042	−0.705210	−	0.708999i	$-0.749147\pi$
$709$	−37.5553	−1.41042	−0.705210	+	0.708999i	$0.749147\pi$
$710$	−0.344135	−0.0129151
$711$	−40.4724	−1.51783
$712$	13.9460	0.522650
$713$	2.29790	0.0860569
$714$	0	0
$715$	0.490573	0.0183464
$716$	−0.839868	−0.0313874
$717$	5.96991	0.222950
$718$	−25.7281	−0.960164
$719$	−42.0406	−1.56785	−0.783925	−	0.620855i	$-0.786786\pi$
$719$	−42.0406	−1.56785	−0.783925	+	0.620855i	$0.786786\pi$
$720$	1.95511	0.0728628
$721$	0	0
$722$	40.5018	1.50732
$723$	−3.97672	−0.147896
$724$	−25.7621	−0.957440
$725$	29.0782	1.07994
$726$	2.51204	0.0932306
$727$	−3.08896	−0.114563	−0.0572817	−	0.998358i	$-0.518243\pi$
$727$	−3.08896	−0.114563	−0.0572817	+	0.998358i	$0.518243\pi$
$728$	0	0
$729$	−24.1296	−0.893688
$730$	4.92919	0.182437
$731$	9.32167	0.344774
$732$	−1.85627	−0.0686095
$733$	−3.71630	−0.137265	−0.0686324	−	0.997642i	$-0.521864\pi$
$733$	−3.71630	−0.137265	−0.0686324	+	0.997642i	$0.521864\pi$
$734$	−1.08335	−0.0399871
$735$	0	0
$736$	0.386458	0.0142450
$737$	−1.44955	−0.0533948
$738$	−2.94604	−0.108445
$739$	28.4115	1.04514	0.522568	−	0.852598i	$-0.324974\pi$
$739$	28.4115	1.04514	0.522568	+	0.852598i	$0.324974\pi$
$740$	1.01896	0.0374577
$741$	3.07081	0.112809
$742$	0	0
$743$	−9.09329	−0.333600	−0.166800	−	0.985991i	$-0.553343\pi$
$743$	−9.09329	−0.333600	−0.166800	+	0.985991i	$0.553343\pi$
$744$	−1.38124	−0.0506389
$745$	−1.58978	−0.0582449
$746$	7.37141	0.269887
$747$	−11.6519	−0.426321
$748$	1.53541	0.0561400
$749$	0	0
$750$	−1.47372	−0.0538127
$751$	6.24875	0.228020	0.114010	−	0.993480i	$-0.463630\pi$
$751$	6.24875	0.228020	0.114010	+	0.993480i	$0.463630\pi$
$752$	2.85105	0.103967
$753$	3.13201	0.114137
$754$	10.9292	0.398018
$755$	−0.615248	−0.0223912
$756$	0	0
$757$	−20.1762	−0.733316	−0.366658	−	0.930356i	$-0.619498\pi$
$757$	−20.1762	−0.733316	−0.366658	+	0.930356i	$0.619498\pi$
$758$	−14.6188	−0.530977
$759$	−0.0387231	−0.00140556
$760$	−5.11916	−0.185691
$761$	−24.8031	−0.899112	−0.449556	−	0.893252i	$-0.648418\pi$
$761$	−24.8031	−0.899112	−0.449556	+	0.893252i	$0.648418\pi$
$762$	−2.43180	−0.0880948
$763$	0	0
$764$	−15.6818	−0.567349
$765$	6.95938	0.251617
$766$	−25.2194	−0.911213
$767$	−0.873117	−0.0315264
$768$	−0.232297	−0.00838228
$769$	−35.0735	−1.26478	−0.632392	−	0.774649i	$-0.717927\pi$
$769$	−35.0735	−1.26478	−0.632392	+	0.774649i	$0.717927\pi$
$770$	0	0
$771$	−6.40291	−0.230595
$772$	−5.52768	−0.198946
$773$	−12.8770	−0.463155	−0.231577	−	0.972817i	$-0.574389\pi$
$773$	−12.8770	−0.463155	−0.231577	+	0.972817i	$0.574389\pi$
$774$	−7.71495	−0.277308
$775$	−27.1114	−0.973872
$776$	−12.0462	−0.432435
$777$	0	0
$778$	−14.9292	−0.535237
$779$	7.71374	0.276373
$780$	−0.264193	−0.00945964
$781$	0.223676	0.00800376
$782$	1.37563	0.0491924
$783$	−8.80873	−0.314798
$784$	0	0
$785$	−12.3602	−0.441154
$786$	−2.17955	−0.0777418
$787$	−46.1339	−1.64449	−0.822247	−	0.569131i	$-0.807280\pi$
$787$	−46.1339	−1.64449	−0.822247	+	0.569131i	$0.807280\pi$
$788$	−3.32728	−0.118530
$789$	0.965488	0.0343723
$790$	−9.11705	−0.324370
$791$	0	0
$792$	−1.27076	−0.0451544
$793$	−13.6944	−0.486302
$794$	38.4945	1.36612
$795$	1.42447	0.0505206
$796$	3.78024	0.133987
$797$	33.1205	1.17319	0.586594	−	0.809881i	$-0.300468\pi$
$797$	33.1205	1.17319	0.586594	+	0.809881i	$0.300468\pi$
$798$	0	0
$799$	10.1485	0.359030
$800$	−4.55958	−0.161205
$801$	−41.0856	−1.45169
$802$	−0.763387	−0.0269561
$803$	−3.20381	−0.113060
$804$	0.780640	0.0275311
$805$	0	0
$806$	−10.1900	−0.358926
$807$	−0.0974965	−0.00343204
$808$	−4.36831	−0.153677
$809$	10.8480	0.381397	0.190699	−	0.981649i	$-0.438925\pi$
$809$	10.8480	0.381397	0.190699	+	0.981649i	$0.438925\pi$
$810$	−5.65241	−0.198605
$811$	37.8360	1.32860	0.664300	−	0.747466i	$-0.268730\pi$
$811$	37.8360	1.32860	0.664300	+	0.747466i	$0.268730\pi$
$812$	0	0
$813$	−4.01302	−0.140743
$814$	−0.662290	−0.0232132
$815$	−1.18916	−0.0416546
$816$	−0.826879	−0.0289465
$817$	20.2004	0.706723
$818$	13.1633	0.460244
$819$	0	0
$820$	−0.663642	−0.0231754
$821$	−4.69870	−0.163986	−0.0819928	−	0.996633i	$-0.526128\pi$
$821$	−4.69870	−0.163986	−0.0819928	+	0.996633i	$0.526128\pi$
$822$	−1.91795	−0.0668962
$823$	−10.6853	−0.372464	−0.186232	−	0.982506i	$-0.559628\pi$
$823$	−10.6853	−0.372464	−0.186232	+	0.982506i	$0.559628\pi$
$824$	14.9089	0.519377
$825$	0.456870	0.0159062
$826$	0	0
$827$	−26.6541	−0.926854	−0.463427	−	0.886135i	$-0.653380\pi$
$827$	−26.6541	−0.926854	−0.463427	+	0.886135i	$0.653380\pi$
$828$	−1.13852	−0.0395663
$829$	9.55140	0.331734	0.165867	−	0.986148i	$-0.446958\pi$
$829$	9.55140	0.331734	0.165867	+	0.986148i	$0.446958\pi$
$830$	−2.62478	−0.0911074
$831$	−0.516341	−0.0179117
$832$	−1.71374	−0.0594133
$833$	0	0
$834$	−3.92578	−0.135939
$835$	−0.676224	−0.0234017
$836$	3.32728	0.115076
$837$	8.21294	0.283881
$838$	33.8955	1.17090
$839$	37.1610	1.28294	0.641470	−	0.767148i	$-0.278325\pi$
$839$	37.1610	1.28294	0.641470	+	0.767148i	$0.278325\pi$
$840$	0	0
$841$	11.6710	0.402449
$842$	−31.8688	−1.09827
$843$	−4.16750	−0.143536
$844$	6.57989	0.226489
$845$	6.67828	0.229740
$846$	−8.39931	−0.288774
$847$	0	0
$848$	9.24007	0.317305
$849$	5.15367	0.176873
$850$	−16.2302	−0.556691
$851$	−0.593371	−0.0203405
$852$	−0.120459	−0.00412684
$853$	11.4003	0.390337	0.195169	−	0.980770i	$-0.437475\pi$
$853$	11.4003	0.390337	0.195169	+	0.980770i	$0.437475\pi$
$854$	0	0
$855$	15.0812	0.515768
$856$	14.4927	0.495350
$857$	−0.943830	−0.0322406	−0.0161203	−	0.999870i	$-0.505131\pi$
$857$	−0.943830	−0.0322406	−0.0161203	+	0.999870i	$0.505131\pi$
$858$	0.171717	0.00586232
$859$	−13.1589	−0.448977	−0.224488	−	0.974477i	$-0.572071\pi$
$859$	−13.1589	−0.448977	−0.224488	+	0.974477i	$0.572071\pi$
$860$	−1.73791	−0.0592624
$861$	0	0
$862$	7.61354	0.259318
$863$	40.1459	1.36658	0.683292	−	0.730145i	$-0.260548\pi$
$863$	40.1459	1.36658	0.683292	+	0.730145i	$0.260548\pi$
$864$	1.38124	0.0469909
$865$	−7.45678	−0.253538
$866$	−36.9033	−1.25403
$867$	1.00570	0.0341555
$868$	0	0
$869$	5.92578	0.201018
$870$	−0.983148	−0.0333319
$871$	5.75908	0.195139
$872$	−11.3942	−0.385857
$873$	35.4887	1.20111
$874$	2.98104	0.100835
$875$	0	0
$876$	1.72538	0.0582952
$877$	−34.7989	−1.17508	−0.587538	−	0.809197i	$-0.699903\pi$
$877$	−34.7989	−1.17508	−0.587538	+	0.809197i	$0.699903\pi$
$878$	−16.2448	−0.548237
$879$	7.35677	0.248138
$880$	−0.286258	−0.00964977
$881$	46.2747	1.55904	0.779518	−	0.626380i	$-0.215464\pi$
$881$	46.2747	1.55904	0.779518	+	0.626380i	$0.215464\pi$
$882$	0	0
$883$	22.9339	0.771786	0.385893	−	0.922544i	$-0.373893\pi$
$883$	22.9339	0.771786	0.385893	+	0.922544i	$0.373893\pi$
$884$	−6.10020	−0.205172
$885$	0.0785423	0.00264017
$886$	−29.1058	−0.977829
$887$	−36.8735	−1.23809	−0.619046	−	0.785355i	$-0.712481\pi$
$887$	−36.8735	−1.23809	−0.619046	+	0.785355i	$0.712481\pi$
$888$	0.356670	0.0119691
$889$	0	0
$890$	−9.25517	−0.310234
$891$	3.67388	0.123079
$892$	−20.8087	−0.696728
$893$	21.9923	0.735943
$894$	−0.556475	−0.0186113
$895$	0.557372	0.0186309
$896$	0	0
$897$	0.153848	0.00513683
$898$	−5.01685	−0.167415
$899$	−37.9202	−1.26471
$900$	13.4327	0.447757
$901$	32.8908	1.09575
$902$	0.431345	0.0143622
$903$	0	0
$904$	10.4888	0.348851
$905$	17.0968	0.568317
$906$	−0.215357	−0.00715477
$907$	−33.7379	−1.12025	−0.560125	−	0.828408i	$-0.689247\pi$
$907$	−33.7379	−1.12025	−0.560125	+	0.828408i	$0.689247\pi$
$908$	−12.6122	−0.418552
$909$	12.8692	0.426844
$910$	0	0
$911$	−57.7881	−1.91460	−0.957302	−	0.289090i	$-0.906647\pi$
$911$	−57.7881	−1.91460	−0.957302	+	0.289090i	$0.906647\pi$
$912$	−1.79188	−0.0593350
$913$	1.70602	0.0564610
$914$	−1.79188	−0.0592700
$915$	1.23189	0.0407252
$916$	−9.29749	−0.307198
$917$	0	0
$918$	4.91665	0.162274
$919$	−18.2285	−0.601302	−0.300651	−	0.953734i	$-0.597204\pi$
$919$	−18.2285	−0.601302	−0.300651	+	0.953734i	$0.597204\pi$
$920$	−0.256470	−0.00845556
$921$	5.27543	0.173831
$922$	−2.32162	−0.0764583
$923$	−0.888669	−0.0292509
$924$	0	0
$925$	7.00081	0.230185
$926$	23.6279	0.776460
$927$	−43.9223	−1.44260
$928$	−6.37738	−0.209348
$929$	24.5130	0.804247	0.402123	−	0.915585i	$-0.368272\pi$
$929$	24.5130	0.804247	0.402123	+	0.915585i	$0.368272\pi$
$930$	0.916652	0.0300582
$931$	0	0
$932$	−10.0483	−0.329145
$933$	−2.41274	−0.0789896
$934$	10.7245	0.350917
$935$	−1.01896	−0.0333235
$936$	5.04875	0.165023
$937$	25.7078	0.839838	0.419919	−	0.907562i	$-0.362058\pi$
$937$	25.7078	0.839838	0.419919	+	0.907562i	$0.362058\pi$
$938$	0	0
$939$	0.0855567	0.00279204
$940$	−1.89208	−0.0617127
$941$	19.2901	0.628840	0.314420	−	0.949284i	$-0.398190\pi$
$941$	19.2901	0.628840	0.314420	+	0.949284i	$0.398190\pi$
$942$	−4.32647	−0.140964
$943$	0.386458	0.0125848
$944$	0.509480	0.0165822
$945$	0	0
$946$	1.12959	0.0367260
$947$	41.4863	1.34812	0.674061	−	0.738676i	$-0.264548\pi$
$947$	41.4863	1.34812	0.674061	+	0.738676i	$0.264548\pi$
$948$	−3.19127	−0.103648
$949$	12.7288	0.413194
$950$	−35.1714	−1.14111
$951$	−1.49398	−0.0484456
$952$	0	0
$953$	−19.8519	−0.643065	−0.321532	−	0.946899i	$-0.604198\pi$
$953$	−19.8519	−0.643065	−0.321532	+	0.946899i	$0.604198\pi$
$954$	−27.2216	−0.881332
$955$	10.4071	0.336767
$956$	−25.6995	−0.831181
$957$	0.639014	0.0206564
$958$	16.2043	0.523538
$959$	0	0
$960$	0.154162	0.00497555
$961$	4.35537	0.140496
$962$	2.63129	0.0848362
$963$	−42.6960	−1.37586
$964$	17.1192	0.551371
$965$	3.66840	0.118090
$966$	0	0
$967$	24.2923	0.781187	0.390594	−	0.920563i	$-0.372270\pi$
$967$	24.2923	0.781187	0.390594	+	0.920563i	$0.372270\pi$
$968$	−10.8139	−0.347573
$969$	−6.37833	−0.204901
$970$	7.99438	0.256684
$971$	−31.5104	−1.01122	−0.505609	−	0.862763i	$-0.668732\pi$
$971$	−31.5104	−1.01122	−0.505609	+	0.862763i	$0.668732\pi$
$972$	−6.12227	−0.196372
$973$	0	0
$974$	3.08896	0.0989768
$975$	−1.81515	−0.0581314
$976$	7.99092	0.255783
$977$	40.4922	1.29546	0.647730	−	0.761870i	$-0.275718\pi$
$977$	40.4922	1.29546	0.647730	+	0.761870i	$0.275718\pi$
$978$	−0.416247	−0.0133101
$979$	6.01555	0.192258
$980$	0	0
$981$	33.5679	1.07174
$982$	−7.76379	−0.247752
$983$	−40.5894	−1.29460	−0.647300	−	0.762235i	$-0.724102\pi$
$983$	−40.5894	−1.29460	−0.647300	+	0.762235i	$0.724102\pi$
$984$	−0.232297	−0.00740535
$985$	2.20812	0.0703567
$986$	−22.7008	−0.722941
$987$	0	0
$988$	−13.2194	−0.420564
$989$	1.01204	0.0321810
$990$	0.843328	0.0268027
$991$	18.4085	0.584766	0.292383	−	0.956301i	$-0.405552\pi$
$991$	18.4085	0.584766	0.292383	+	0.956301i	$0.405552\pi$
$992$	5.94604	0.188787
$993$	−6.06892	−0.192591
$994$	0	0
$995$	−2.50872	−0.0795319
$996$	−0.918760	−0.0291120
$997$	−4.07392	−0.129022	−0.0645111	−	0.997917i	$-0.520549\pi$
$997$	−4.07392	−0.129022	−0.0645111	+	0.997917i	$0.520549\pi$
$998$	14.7880	0.468106
$999$	−2.12077	−0.0670983

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bm.1.2	yes	4
7.6	odd	2		4018.2.a.bl.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4018.2.a.bl.1.3	✓	4	7.6	odd	2
4018.2.a.bm.1.2	yes	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.232297 q^{3} +1.00000 q^{4} -0.663642 q^{5} -0.232297 q^{6} +1.00000 q^{8} -2.94604 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.232297 q^{3} +1.00000 q^{4} -0.663642 q^{5} -0.232297 q^{6} +1.00000 q^{8} -2.94604 q^{9} -0.663642 q^{10} +0.431345 q^{11} -0.232297 q^{12} -1.71374 q^{13} +0.154162 q^{15} +1.00000 q^{16} +3.55958 q^{17} -2.94604 q^{18} +7.71374 q^{19} -0.663642 q^{20} +0.431345 q^{22} +0.386458 q^{23} -0.232297 q^{24} -4.55958 q^{25} -1.71374 q^{26} +1.38124 q^{27} -6.37738 q^{29} +0.154162 q^{30} +5.94604 q^{31} +1.00000 q^{32} -0.100200 q^{33} +3.55958 q^{34} -2.94604 q^{36} -1.53541 q^{37} +7.71374 q^{38} +0.398096 q^{39} -0.663642 q^{40} +1.00000 q^{41} +2.61876 q^{43} +0.431345 q^{44} +1.95511 q^{45} +0.386458 q^{46} +2.85105 q^{47} -0.232297 q^{48} -4.55958 q^{50} -0.826879 q^{51} -1.71374 q^{52} +9.24007 q^{53} +1.38124 q^{54} -0.286258 q^{55} -1.79188 q^{57} -6.37738 q^{58} +0.509480 q^{59} +0.154162 q^{60} +7.99092 q^{61} +5.94604 q^{62} +1.00000 q^{64} +1.13731 q^{65} -0.100200 q^{66} -3.36053 q^{67} +3.55958 q^{68} -0.0897730 q^{69} +0.518555 q^{71} -2.94604 q^{72} -7.42748 q^{73} -1.53541 q^{74} +1.05918 q^{75} +7.71374 q^{76} +0.398096 q^{78} +13.7379 q^{79} -0.663642 q^{80} +8.51726 q^{81} +1.00000 q^{82} +3.95511 q^{83} -2.36229 q^{85} +2.61876 q^{86} +1.48144 q^{87} +0.431345 q^{88} +13.9460 q^{89} +1.95511 q^{90} +0.386458 q^{92} -1.38124 q^{93} +2.85105 q^{94} -5.11916 q^{95} -0.232297 q^{96} -12.0462 q^{97} -1.27076 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 3 q^{3} + 4 q^{4} + 3 q^{5} + 3 q^{6} + 4 q^{8} + 9 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 3 * q^3 + 4 * q^4 + 3 * q^5 + 3 * q^6 + 4 * q^8 + 9 * q^9	\( 4 q + 4 q^{2} + 3 q^{3} + 4 q^{4} + 3 q^{5} + 3 q^{6} + 4 q^{8} + 9 q^{9} + 3 q^{10} + 3 q^{12} + 10 q^{13} - q^{15} + 4 q^{16} - q^{17} + 9 q^{18} + 14 q^{19} + 3 q^{20} - 4 q^{23} + 3 q^{24} - 3 q^{25} + 10 q^{26} + 15 q^{27} - 3 q^{29} - q^{30} + 3 q^{31} + 4 q^{32} + 22 q^{33} - q^{34} + 9 q^{36} - 14 q^{37} + 14 q^{38} + 6 q^{39} + 3 q^{40} + 4 q^{41} + q^{43} + 4 q^{45} - 4 q^{46} - 2 q^{47} + 3 q^{48} - 3 q^{50} - 13 q^{51} + 10 q^{52} + 11 q^{53} + 15 q^{54} - 18 q^{55} + 12 q^{57} - 3 q^{58} - 2 q^{59} - q^{60} + 15 q^{61} + 3 q^{62} + 4 q^{64} + 8 q^{65} + 22 q^{66} + 4 q^{67} - q^{68} - 8 q^{69} + 15 q^{71} + 9 q^{72} + 4 q^{73} - 14 q^{74} + 10 q^{75} + 14 q^{76} + 6 q^{78} + 15 q^{79} + 3 q^{80} + 8 q^{81} + 4 q^{82} + 12 q^{83} - 27 q^{85} + q^{86} - 7 q^{87} + 35 q^{89} + 4 q^{90} - 4 q^{92} - 15 q^{93} - 2 q^{94} + 10 q^{95} + 3 q^{96} - 5 q^{97} + 20 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 3 * q^3 + 4 * q^4 + 3 * q^5 + 3 * q^6 + 4 * q^8 + 9 * q^9 + 3 * q^10 + 3 * q^12 + 10 * q^13 - q^15 + 4 * q^16 - q^17 + 9 * q^18 + 14 * q^19 + 3 * q^20 - 4 * q^23 + 3 * q^24 - 3 * q^25 + 10 * q^26 + 15 * q^27 - 3 * q^29 - q^30 + 3 * q^31 + 4 * q^32 + 22 * q^33 - q^34 + 9 * q^36 - 14 * q^37 + 14 * q^38 + 6 * q^39 + 3 * q^40 + 4 * q^41 + q^43 + 4 * q^45 - 4 * q^46 - 2 * q^47 + 3 * q^48 - 3 * q^50 - 13 * q^51 + 10 * q^52 + 11 * q^53 + 15 * q^54 - 18 * q^55 + 12 * q^57 - 3 * q^58 - 2 * q^59 - q^60 + 15 * q^61 + 3 * q^62 + 4 * q^64 + 8 * q^65 + 22 * q^66 + 4 * q^67 - q^68 - 8 * q^69 + 15 * q^71 + 9 * q^72 + 4 * q^73 - 14 * q^74 + 10 * q^75 + 14 * q^76 + 6 * q^78 + 15 * q^79 + 3 * q^80 + 8 * q^81 + 4 * q^82 + 12 * q^83 - 27 * q^85 + q^86 - 7 * q^87 + 35 * q^89 + 4 * q^90 - 4 * q^92 - 15 * q^93 - 2 * q^94 + 10 * q^95 + 3 * q^96 - 5 * q^97 + 20 * q^99

Introduction

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Database

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