LMFDB - Embedded newform 6014.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
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			$1.41421$ of defining polynomial
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.82843 q^{3} +1.00000 q^{4} +3.41421 q^{5} -2.82843 q^{6} -0.585786 q^{7} -1.00000 q^{8} +5.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.82843 q^{3} +1.00000 q^{4} +3.41421 q^{5} -2.82843 q^{6} -0.585786 q^{7} -1.00000 q^{8} +5.00000 q^{9} -3.41421 q^{10} +4.00000 q^{11} +2.82843 q^{12} +0.585786 q^{14} +9.65685 q^{15} +1.00000 q^{16} -1.41421 q^{17} -5.00000 q^{18} -6.00000 q^{19} +3.41421 q^{20} -1.65685 q^{21} -4.00000 q^{22} +5.65685 q^{23} -2.82843 q^{24} +6.65685 q^{25} +5.65685 q^{27} -0.585786 q^{28} -1.65685 q^{29} -9.65685 q^{30} -1.00000 q^{31} -1.00000 q^{32} +11.3137 q^{33} +1.41421 q^{34} -2.00000 q^{35} +5.00000 q^{36} -9.65685 q^{37} +6.00000 q^{38} -3.41421 q^{40} +3.17157 q^{41} +1.65685 q^{42} +8.48528 q^{43} +4.00000 q^{44} +17.0711 q^{45} -5.65685 q^{46} +4.00000 q^{47} +2.82843 q^{48} -6.65685 q^{49} -6.65685 q^{50} -4.00000 q^{51} +10.8284 q^{53} -5.65685 q^{54} +13.6569 q^{55} +0.585786 q^{56} -16.9706 q^{57} +1.65685 q^{58} +12.8284 q^{59} +9.65685 q^{60} -12.4853 q^{61} +1.00000 q^{62} -2.92893 q^{63} +1.00000 q^{64} -11.3137 q^{66} +10.4853 q^{67} -1.41421 q^{68} +16.0000 q^{69} +2.00000 q^{70} -2.24264 q^{71} -5.00000 q^{72} +7.65685 q^{73} +9.65685 q^{74} +18.8284 q^{75} -6.00000 q^{76} -2.34315 q^{77} +0.828427 q^{79} +3.41421 q^{80} +1.00000 q^{81} -3.17157 q^{82} +8.72792 q^{83} -1.65685 q^{84} -4.82843 q^{85} -8.48528 q^{86} -4.68629 q^{87} -4.00000 q^{88} +6.48528 q^{89} -17.0711 q^{90} +5.65685 q^{92} -2.82843 q^{93} -4.00000 q^{94} -20.4853 q^{95} -2.82843 q^{96} +1.00000 q^{97} +6.65685 q^{98} +20.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} + 4 q^{5} - 4 q^{7} - 2 q^{8} + 10 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 + 4 * q^5 - 4 * q^7 - 2 * q^8 + 10 * q^9	$ 2 q - 2 q^{2} + 2 q^{4} + 4 q^{5} - 4 q^{7} - 2 q^{8} + 10 q^{9} - 4 q^{10} + 8 q^{11} + 4 q^{14} + 8 q^{15} + 2 q^{16} - 10 q^{18} - 12 q^{19} + 4 q^{20} + 8 q^{21} - 8 q^{22} + 2 q^{25} - 4 q^{28} + 8 q^{29} - 8 q^{30} - 2 q^{31} - 2 q^{32} - 4 q^{35} + 10 q^{36} - 8 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 8 q^{42} + 8 q^{44} + 20 q^{45} + 8 q^{47} - 2 q^{49} - 2 q^{50} - 8 q^{51} + 16 q^{53} + 16 q^{55} + 4 q^{56} - 8 q^{58} + 20 q^{59} + 8 q^{60} - 8 q^{61} + 2 q^{62} - 20 q^{63} + 2 q^{64} + 4 q^{67} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 10 q^{72} + 4 q^{73} + 8 q^{74} + 32 q^{75} - 12 q^{76} - 16 q^{77} - 4 q^{79} + 4 q^{80} + 2 q^{81} - 12 q^{82} - 8 q^{83} + 8 q^{84} - 4 q^{85} - 32 q^{87} - 8 q^{88} - 4 q^{89} - 20 q^{90} - 8 q^{94} - 24 q^{95} + 2 q^{97} + 2 q^{98} + 40 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 + 4 * q^5 - 4 * q^7 - 2 * q^8 + 10 * q^9 - 4 * q^10 + 8 * q^11 + 4 * q^14 + 8 * q^15 + 2 * q^16 - 10 * q^18 - 12 * q^19 + 4 * q^20 + 8 * q^21 - 8 * q^22 + 2 * q^25 - 4 * q^28 + 8 * q^29 - 8 * q^30 - 2 * q^31 - 2 * q^32 - 4 * q^35 + 10 * q^36 - 8 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 8 * q^42 + 8 * q^44 + 20 * q^45 + 8 * q^47 - 2 * q^49 - 2 * q^50 - 8 * q^51 + 16 * q^53 + 16 * q^55 + 4 * q^56 - 8 * q^58 + 20 * q^59 + 8 * q^60 - 8 * q^61 + 2 * q^62 - 20 * q^63 + 2 * q^64 + 4 * q^67 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 10 * q^72 + 4 * q^73 + 8 * q^74 + 32 * q^75 - 12 * q^76 - 16 * q^77 - 4 * q^79 + 4 * q^80 + 2 * q^81 - 12 * q^82 - 8 * q^83 + 8 * q^84 - 4 * q^85 - 32 * q^87 - 8 * q^88 - 4 * q^89 - 20 * q^90 - 8 * q^94 - 24 * q^95 + 2 * q^97 + 2 * q^98 + 40 * 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
$3$	2.82843	1.63299	0.816497	−	0.577350i	$-0.195913\pi$
$3$	2.82843	1.63299	0.816497	+	0.577350i	$0.195913\pi$
$4$	1.00000	0.500000
$5$	3.41421	1.52688	0.763441	−	0.645877i	$-0.223508\pi$
$5$	3.41421	1.52688	0.763441	+	0.645877i	$0.223508\pi$
$6$	−2.82843	−1.15470
$7$	−0.585786	−0.221406	−0.110703	−	0.993854i	$-0.535310\pi$
$7$	−0.585786	−0.221406	−0.110703	+	0.993854i	$0.535310\pi$
$8$	−1.00000	−0.353553
$9$	5.00000	1.66667
$10$	−3.41421	−1.07967
$11$	4.00000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	2.82843	0.816497
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	0.585786	0.156558
$15$	9.65685	2.49339
$16$	1.00000	0.250000
$17$	−1.41421	−0.342997	−0.171499	−	0.985184i	$-0.554861\pi$
$17$	−1.41421	−0.342997	−0.171499	+	0.985184i	$0.554861\pi$
$18$	−5.00000	−1.17851
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	3.41421	0.763441
$21$	−1.65685	−0.361555
$22$	−4.00000	−0.852803
$23$	5.65685	1.17954	0.589768	−	0.807573i	$-0.299219\pi$
$23$	5.65685	1.17954	0.589768	+	0.807573i	$0.299219\pi$
$24$	−2.82843	−0.577350
$25$	6.65685	1.33137
$26$	0	0
$27$	5.65685	1.08866
$28$	−0.585786	−0.110703
$29$	−1.65685	−0.307670	−0.153835	−	0.988097i	$-0.549162\pi$
$29$	−1.65685	−0.307670	−0.153835	+	0.988097i	$0.549162\pi$
$30$	−9.65685	−1.76309
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	11.3137	1.96946
$34$	1.41421	0.242536
$35$	−2.00000	−0.338062
$36$	5.00000	0.833333
$37$	−9.65685	−1.58758	−0.793789	−	0.608194i	$-0.791894\pi$
$37$	−9.65685	−1.58758	−0.793789	+	0.608194i	$0.791894\pi$
$38$	6.00000	0.973329
$39$	0	0
$40$	−3.41421	−0.539835
$41$	3.17157	0.495316	0.247658	−	0.968847i	$-0.420339\pi$
$41$	3.17157	0.495316	0.247658	+	0.968847i	$0.420339\pi$
$42$	1.65685	0.255658
$43$	8.48528	1.29399	0.646997	−	0.762493i	$-0.276025\pi$
$43$	8.48528	1.29399	0.646997	+	0.762493i	$0.276025\pi$
$44$	4.00000	0.603023
$45$	17.0711	2.54480
$46$	−5.65685	−0.834058
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	2.82843	0.408248
$49$	−6.65685	−0.950979
$50$	−6.65685	−0.941421
$51$	−4.00000	−0.560112
$52$	0	0
$53$	10.8284	1.48740	0.743699	−	0.668514i	$-0.233069\pi$
$53$	10.8284	1.48740	0.743699	+	0.668514i	$0.233069\pi$
$54$	−5.65685	−0.769800
$55$	13.6569	1.84149
$56$	0.585786	0.0782790
$57$	−16.9706	−2.24781
$58$	1.65685	0.217556
$59$	12.8284	1.67012	0.835059	−	0.550160i	$-0.185433\pi$
$59$	12.8284	1.67012	0.835059	+	0.550160i	$0.185433\pi$
$60$	9.65685	1.24669
$61$	−12.4853	−1.59858	−0.799288	−	0.600948i	$-0.794790\pi$
$61$	−12.4853	−1.59858	−0.799288	+	0.600948i	$0.794790\pi$
$62$	1.00000	0.127000
$63$	−2.92893	−0.369011
$64$	1.00000	0.125000
$65$	0	0
$66$	−11.3137	−1.39262
$67$	10.4853	1.28098	0.640490	−	0.767966i	$-0.278731\pi$
$67$	10.4853	1.28098	0.640490	+	0.767966i	$0.278731\pi$
$68$	−1.41421	−0.171499
$69$	16.0000	1.92617
$70$	2.00000	0.239046
$71$	−2.24264	−0.266152	−0.133076	−	0.991106i	$-0.542486\pi$
$71$	−2.24264	−0.266152	−0.133076	+	0.991106i	$0.542486\pi$
$72$	−5.00000	−0.589256
$73$	7.65685	0.896167	0.448084	−	0.893992i	$-0.352107\pi$
$73$	7.65685	0.896167	0.448084	+	0.893992i	$0.352107\pi$
$74$	9.65685	1.12259
$75$	18.8284	2.17412
$76$	−6.00000	−0.688247
$77$	−2.34315	−0.267026
$78$	0	0
$79$	0.828427	0.0932053	0.0466027	−	0.998914i	$-0.485161\pi$
$79$	0.828427	0.0932053	0.0466027	+	0.998914i	$0.485161\pi$
$80$	3.41421	0.381721
$81$	1.00000	0.111111
$82$	−3.17157	−0.350242
$83$	8.72792	0.958014	0.479007	−	0.877811i	$-0.340997\pi$
$83$	8.72792	0.958014	0.479007	+	0.877811i	$0.340997\pi$
$84$	−1.65685	−0.180778
$85$	−4.82843	−0.523716
$86$	−8.48528	−0.914991
$87$	−4.68629	−0.502423
$88$	−4.00000	−0.426401
$89$	6.48528	0.687438	0.343719	−	0.939072i	$-0.388313\pi$
$89$	6.48528	0.687438	0.343719	+	0.939072i	$0.388313\pi$
$90$	−17.0711	−1.79945
$91$	0	0
$92$	5.65685	0.589768
$93$	−2.82843	−0.293294
$94$	−4.00000	−0.412568
$95$	−20.4853	−2.10175
$96$	−2.82843	−0.288675
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	6.65685	0.672444
$99$	20.0000	2.01008
$100$	6.65685	0.665685
$101$	0.828427	0.0824316	0.0412158	−	0.999150i	$-0.486877\pi$
$101$	0.828427	0.0824316	0.0412158	+	0.999150i	$0.486877\pi$
$102$	4.00000	0.396059
$103$	−2.82843	−0.278693	−0.139347	−	0.990244i	$-0.544500\pi$
$103$	−2.82843	−0.278693	−0.139347	+	0.990244i	$0.544500\pi$
$104$	0	0
$105$	−5.65685	−0.552052
$106$	−10.8284	−1.05175
$107$	−0.828427	−0.0800871	−0.0400435	−	0.999198i	$-0.512750\pi$
$107$	−0.828427	−0.0800871	−0.0400435	+	0.999198i	$0.512750\pi$
$108$	5.65685	0.544331
$109$	−11.1716	−1.07004	−0.535021	−	0.844839i	$-0.679696\pi$
$109$	−11.1716	−1.07004	−0.535021	+	0.844839i	$0.679696\pi$
$110$	−13.6569	−1.30213
$111$	−27.3137	−2.59250
$112$	−0.585786	−0.0553516
$113$	13.6569	1.28473	0.642364	−	0.766399i	$-0.277954\pi$
$113$	13.6569	1.28473	0.642364	+	0.766399i	$0.277954\pi$
$114$	16.9706	1.58944
$115$	19.3137	1.80101
$116$	−1.65685	−0.153835
$117$	0	0
$118$	−12.8284	−1.18095
$119$	0.828427	0.0759418
$120$	−9.65685	−0.881546
$121$	5.00000	0.454545
$122$	12.4853	1.13036
$123$	8.97056	0.808848
$124$	−1.00000	−0.0898027
$125$	5.65685	0.505964
$126$	2.92893	0.260930
$127$	−5.17157	−0.458903	−0.229451	−	0.973320i	$-0.573693\pi$
$127$	−5.17157	−0.458903	−0.229451	+	0.973320i	$0.573693\pi$
$128$	−1.00000	−0.0883883
$129$	24.0000	2.11308
$130$	0	0
$131$	−1.31371	−0.114779	−0.0573896	−	0.998352i	$-0.518278\pi$
$131$	−1.31371	−0.114779	−0.0573896	+	0.998352i	$0.518278\pi$
$132$	11.3137	0.984732
$133$	3.51472	0.304765
$134$	−10.4853	−0.905790
$135$	19.3137	1.66226
$136$	1.41421	0.121268
$137$	−9.41421	−0.804311	−0.402155	−	0.915571i	$-0.631739\pi$
$137$	−9.41421	−0.804311	−0.402155	+	0.915571i	$0.631739\pi$
$138$	−16.0000	−1.36201
$139$	−7.75736	−0.657971	−0.328985	−	0.944335i	$-0.606707\pi$
$139$	−7.75736	−0.657971	−0.328985	+	0.944335i	$0.606707\pi$
$140$	−2.00000	−0.169031
$141$	11.3137	0.952786
$142$	2.24264	0.188198
$143$	0	0
$144$	5.00000	0.416667
$145$	−5.65685	−0.469776
$146$	−7.65685	−0.633686
$147$	−18.8284	−1.55294
$148$	−9.65685	−0.793789
$149$	3.41421	0.279703	0.139852	−	0.990172i	$-0.455337\pi$
$149$	3.41421	0.279703	0.139852	+	0.990172i	$0.455337\pi$
$150$	−18.8284	−1.53733
$151$	−5.65685	−0.460348	−0.230174	−	0.973149i	$-0.573930\pi$
$151$	−5.65685	−0.460348	−0.230174	+	0.973149i	$0.573930\pi$
$152$	6.00000	0.486664
$153$	−7.07107	−0.571662
$154$	2.34315	0.188816
$155$	−3.41421	−0.274236
$156$	0	0
$157$	17.5563	1.40115	0.700575	−	0.713579i	$-0.252927\pi$
$157$	17.5563	1.40115	0.700575	+	0.713579i	$0.252927\pi$
$158$	−0.828427	−0.0659061
$159$	30.6274	2.42891
$160$	−3.41421	−0.269917
$161$	−3.31371	−0.261157
$162$	−1.00000	−0.0785674
$163$	−7.31371	−0.572854	−0.286427	−	0.958102i	$-0.592468\pi$
$163$	−7.31371	−0.572854	−0.286427	+	0.958102i	$0.592468\pi$
$164$	3.17157	0.247658
$165$	38.6274	3.00714
$166$	−8.72792	−0.677418
$167$	1.51472	0.117212	0.0586062	−	0.998281i	$-0.481334\pi$
$167$	1.51472	0.117212	0.0586062	+	0.998281i	$0.481334\pi$
$168$	1.65685	0.127829
$169$	−13.0000	−1.00000
$170$	4.82843	0.370323
$171$	−30.0000	−2.29416
$172$	8.48528	0.646997
$173$	11.4142	0.867807	0.433903	−	0.900959i	$-0.357136\pi$
$173$	11.4142	0.867807	0.433903	+	0.900959i	$0.357136\pi$
$174$	4.68629	0.355267
$175$	−3.89949	−0.294774
$176$	4.00000	0.301511
$177$	36.2843	2.72729
$178$	−6.48528	−0.486092
$179$	−5.41421	−0.404677	−0.202339	−	0.979316i	$-0.564854\pi$
$179$	−5.41421	−0.404677	−0.202339	+	0.979316i	$0.564854\pi$
$180$	17.0711	1.27240
$181$	−10.1421	−0.753859	−0.376930	−	0.926242i	$-0.623020\pi$
$181$	−10.1421	−0.753859	−0.376930	+	0.926242i	$0.623020\pi$
$182$	0	0
$183$	−35.3137	−2.61046
$184$	−5.65685	−0.417029
$185$	−32.9706	−2.42404
$186$	2.82843	0.207390
$187$	−5.65685	−0.413670
$188$	4.00000	0.291730
$189$	−3.31371	−0.241037
$190$	20.4853	1.48616
$191$	8.48528	0.613973	0.306987	−	0.951714i	$-0.400679\pi$
$191$	8.48528	0.613973	0.306987	+	0.951714i	$0.400679\pi$
$192$	2.82843	0.204124
$193$	−6.00000	−0.431889	−0.215945	−	0.976406i	$-0.569283\pi$
$193$	−6.00000	−0.431889	−0.215945	+	0.976406i	$0.569283\pi$
$194$	−1.00000	−0.0717958
$195$	0	0
$196$	−6.65685	−0.475490
$197$	−14.1421	−1.00759	−0.503793	−	0.863825i	$-0.668062\pi$
$197$	−14.1421	−1.00759	−0.503793	+	0.863825i	$0.668062\pi$
$198$	−20.0000	−1.42134
$199$	−8.00000	−0.567105	−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000	−0.567105	−0.283552	+	0.958957i	$0.591513\pi$
$200$	−6.65685	−0.470711
$201$	29.6569	2.09183
$202$	−0.828427	−0.0582879
$203$	0.970563	0.0681202
$204$	−4.00000	−0.280056
$205$	10.8284	0.756290
$206$	2.82843	0.197066
$207$	28.2843	1.96589
$208$	0	0
$209$	−24.0000	−1.66011
$210$	5.65685	0.390360
$211$	−3.65685	−0.251748	−0.125874	−	0.992046i	$-0.540174\pi$
$211$	−3.65685	−0.251748	−0.125874	+	0.992046i	$0.540174\pi$
$212$	10.8284	0.743699
$213$	−6.34315	−0.434625
$214$	0.828427	0.0566301
$215$	28.9706	1.97578
$216$	−5.65685	−0.384900
$217$	0.585786	0.0397658
$218$	11.1716	0.756634
$219$	21.6569	1.46343
$220$	13.6569	0.920745
$221$	0	0
$222$	27.3137	1.83318
$223$	1.17157	0.0784543	0.0392272	−	0.999230i	$-0.487510\pi$
$223$	1.17157	0.0784543	0.0392272	+	0.999230i	$0.487510\pi$
$224$	0.585786	0.0391395
$225$	33.2843	2.21895
$226$	−13.6569	−0.908440
$227$	−4.00000	−0.265489	−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000	−0.265489	−0.132745	+	0.991150i	$0.542379\pi$
$228$	−16.9706	−1.12390
$229$	14.1421	0.934539	0.467269	−	0.884115i	$-0.345238\pi$
$229$	14.1421	0.934539	0.467269	+	0.884115i	$0.345238\pi$
$230$	−19.3137	−1.27351
$231$	−6.62742	−0.436052
$232$	1.65685	0.108778
$233$	12.1421	0.795458	0.397729	−	0.917503i	$-0.369798\pi$
$233$	12.1421	0.795458	0.397729	+	0.917503i	$0.369798\pi$
$234$	0	0
$235$	13.6569	0.890875
$236$	12.8284	0.835059
$237$	2.34315	0.152204
$238$	−0.828427	−0.0536990
$239$	4.48528	0.290129	0.145064	−	0.989422i	$-0.453661\pi$
$239$	4.48528	0.290129	0.145064	+	0.989422i	$0.453661\pi$
$240$	9.65685	0.623347
$241$	−16.3431	−1.05275	−0.526377	−	0.850251i	$-0.676450\pi$
$241$	−16.3431	−1.05275	−0.526377	+	0.850251i	$0.676450\pi$
$242$	−5.00000	−0.321412
$243$	−14.1421	−0.907218
$244$	−12.4853	−0.799288
$245$	−22.7279	−1.45203
$246$	−8.97056	−0.571942
$247$	0	0
$248$	1.00000	0.0635001
$249$	24.6863	1.56443
$250$	−5.65685	−0.357771
$251$	17.8995	1.12981	0.564903	−	0.825157i	$-0.308914\pi$
$251$	17.8995	1.12981	0.564903	+	0.825157i	$0.308914\pi$
$252$	−2.92893	−0.184505
$253$	22.6274	1.42257
$254$	5.17157	0.324493
$255$	−13.6569	−0.855225
$256$	1.00000	0.0625000
$257$	−14.4853	−0.903567	−0.451784	−	0.892128i	$-0.649212\pi$
$257$	−14.4853	−0.903567	−0.451784	+	0.892128i	$0.649212\pi$
$258$	−24.0000	−1.49417
$259$	5.65685	0.351500
$260$	0	0
$261$	−8.28427	−0.512784
$262$	1.31371	0.0811612
$263$	30.1421	1.85864	0.929322	−	0.369271i	$-0.120393\pi$
$263$	30.1421	1.85864	0.929322	+	0.369271i	$0.120393\pi$
$264$	−11.3137	−0.696311
$265$	36.9706	2.27108
$266$	−3.51472	−0.215501
$267$	18.3431	1.12258
$268$	10.4853	0.640490
$269$	−1.31371	−0.0800982	−0.0400491	−	0.999198i	$-0.512751\pi$
$269$	−1.31371	−0.0800982	−0.0400491	+	0.999198i	$0.512751\pi$
$270$	−19.3137	−1.17539
$271$	−16.4853	−1.00141	−0.500705	−	0.865618i	$-0.666926\pi$
$271$	−16.4853	−1.00141	−0.500705	+	0.865618i	$0.666926\pi$
$272$	−1.41421	−0.0857493
$273$	0	0
$274$	9.41421	0.568733
$275$	26.6274	1.60569
$276$	16.0000	0.963087
$277$	13.6569	0.820561	0.410280	−	0.911959i	$-0.365431\pi$
$277$	13.6569	0.820561	0.410280	+	0.911959i	$0.365431\pi$
$278$	7.75736	0.465255
$279$	−5.00000	−0.299342
$280$	2.00000	0.119523
$281$	22.4853	1.34136	0.670680	−	0.741747i	$-0.266003\pi$
$281$	22.4853	1.34136	0.670680	+	0.741747i	$0.266003\pi$
$282$	−11.3137	−0.673722
$283$	−24.6274	−1.46395	−0.731974	−	0.681333i	$-0.761401\pi$
$283$	−24.6274	−1.46395	−0.731974	+	0.681333i	$0.761401\pi$
$284$	−2.24264	−0.133076
$285$	−57.9411	−3.43214
$286$	0	0
$287$	−1.85786	−0.109666
$288$	−5.00000	−0.294628
$289$	−15.0000	−0.882353
$290$	5.65685	0.332182
$291$	2.82843	0.165805
$292$	7.65685	0.448084
$293$	−28.8284	−1.68417	−0.842087	−	0.539341i	$-0.818673\pi$
$293$	−28.8284	−1.68417	−0.842087	+	0.539341i	$0.818673\pi$
$294$	18.8284	1.09810
$295$	43.7990	2.55008
$296$	9.65685	0.561293
$297$	22.6274	1.31298
$298$	−3.41421	−0.197780
$299$	0	0
$300$	18.8284	1.08706
$301$	−4.97056	−0.286498
$302$	5.65685	0.325515
$303$	2.34315	0.134610
$304$	−6.00000	−0.344124
$305$	−42.6274	−2.44084
$306$	7.07107	0.404226
$307$	−24.6274	−1.40556	−0.702780	−	0.711407i	$-0.748058\pi$
$307$	−24.6274	−1.40556	−0.702780	+	0.711407i	$0.748058\pi$
$308$	−2.34315	−0.133513
$309$	−8.00000	−0.455104
$310$	3.41421	0.193914
$311$	−28.3848	−1.60955	−0.804776	−	0.593578i	$-0.797715\pi$
$311$	−28.3848	−1.60955	−0.804776	+	0.593578i	$0.797715\pi$
$312$	0	0
$313$	11.1716	0.631455	0.315727	−	0.948850i	$-0.397752\pi$
$313$	11.1716	0.631455	0.315727	+	0.948850i	$0.397752\pi$
$314$	−17.5563	−0.990762
$315$	−10.0000	−0.563436
$316$	0.828427	0.0466027
$317$	−10.7279	−0.602540	−0.301270	−	0.953539i	$-0.597411\pi$
$317$	−10.7279	−0.602540	−0.301270	+	0.953539i	$0.597411\pi$
$318$	−30.6274	−1.71750
$319$	−6.62742	−0.371064
$320$	3.41421	0.190860
$321$	−2.34315	−0.130782
$322$	3.31371	0.184666
$323$	8.48528	0.472134
$324$	1.00000	0.0555556
$325$	0	0
$326$	7.31371	0.405069
$327$	−31.5980	−1.74737
$328$	−3.17157	−0.175121
$329$	−2.34315	−0.129182
$330$	−38.6274	−2.12637
$331$	−13.8995	−0.763985	−0.381993	−	0.924165i	$-0.624762\pi$
$331$	−13.8995	−0.763985	−0.381993	+	0.924165i	$0.624762\pi$
$332$	8.72792	0.479007
$333$	−48.2843	−2.64596
$334$	−1.51472	−0.0828817
$335$	35.7990	1.95591
$336$	−1.65685	−0.0903888
$337$	−21.4142	−1.16651	−0.583253	−	0.812290i	$-0.698220\pi$
$337$	−21.4142	−1.16651	−0.583253	+	0.812290i	$0.698220\pi$
$338$	13.0000	0.707107
$339$	38.6274	2.09795
$340$	−4.82843	−0.261858
$341$	−4.00000	−0.216612
$342$	30.0000	1.62221
$343$	8.00000	0.431959
$344$	−8.48528	−0.457496
$345$	54.6274	2.94104
$346$	−11.4142	−0.613632
$347$	−32.7279	−1.75693	−0.878463	−	0.477810i	$-0.841431\pi$
$347$	−32.7279	−1.75693	−0.878463	+	0.477810i	$0.841431\pi$
$348$	−4.68629	−0.251212
$349$	−10.7279	−0.574253	−0.287126	−	0.957893i	$-0.592700\pi$
$349$	−10.7279	−0.574253	−0.287126	+	0.957893i	$0.592700\pi$
$350$	3.89949	0.208437
$351$	0	0
$352$	−4.00000	−0.213201
$353$	6.68629	0.355875	0.177938	−	0.984042i	$-0.443057\pi$
$353$	6.68629	0.355875	0.177938	+	0.984042i	$0.443057\pi$
$354$	−36.2843	−1.92849
$355$	−7.65685	−0.406384
$356$	6.48528	0.343719
$357$	2.34315	0.124012
$358$	5.41421	0.286150
$359$	−29.5563	−1.55992	−0.779962	−	0.625827i	$-0.784762\pi$
$359$	−29.5563	−1.55992	−0.779962	+	0.625827i	$0.784762\pi$
$360$	−17.0711	−0.899724
$361$	17.0000	0.894737
$362$	10.1421	0.533059
$363$	14.1421	0.742270
$364$	0	0
$365$	26.1421	1.36834
$366$	35.3137	1.84588
$367$	6.14214	0.320617	0.160308	−	0.987067i	$-0.448751\pi$
$367$	6.14214	0.320617	0.160308	+	0.987067i	$0.448751\pi$
$368$	5.65685	0.294884
$369$	15.8579	0.825527
$370$	32.9706	1.71406
$371$	−6.34315	−0.329320
$372$	−2.82843	−0.146647
$373$	−12.3848	−0.641259	−0.320630	−	0.947205i	$-0.603895\pi$
$373$	−12.3848	−0.641259	−0.320630	+	0.947205i	$0.603895\pi$
$374$	5.65685	0.292509
$375$	16.0000	0.826236
$376$	−4.00000	−0.206284
$377$	0	0
$378$	3.31371	0.170439
$379$	−22.9706	−1.17992	−0.589959	−	0.807433i	$-0.700856\pi$
$379$	−22.9706	−1.17992	−0.589959	+	0.807433i	$0.700856\pi$
$380$	−20.4853	−1.05087
$381$	−14.6274	−0.749385
$382$	−8.48528	−0.434145
$383$	−16.9706	−0.867155	−0.433578	−	0.901116i	$-0.642749\pi$
$383$	−16.9706	−0.867155	−0.433578	+	0.901116i	$0.642749\pi$
$384$	−2.82843	−0.144338
$385$	−8.00000	−0.407718
$386$	6.00000	0.305392
$387$	42.4264	2.15666
$388$	1.00000	0.0507673
$389$	−6.97056	−0.353422	−0.176711	−	0.984263i	$-0.556546\pi$
$389$	−6.97056	−0.353422	−0.176711	+	0.984263i	$0.556546\pi$
$390$	0	0
$391$	−8.00000	−0.404577
$392$	6.65685	0.336222
$393$	−3.71573	−0.187434
$394$	14.1421	0.712470
$395$	2.82843	0.142314
$396$	20.0000	1.00504
$397$	27.1716	1.36370	0.681851	−	0.731491i	$-0.261175\pi$
$397$	27.1716	1.36370	0.681851	+	0.731491i	$0.261175\pi$
$398$	8.00000	0.401004
$399$	9.94113	0.497679
$400$	6.65685	0.332843
$401$	33.8995	1.69286	0.846430	−	0.532500i	$-0.178747\pi$
$401$	33.8995	1.69286	0.846430	+	0.532500i	$0.178747\pi$
$402$	−29.6569	−1.47915
$403$	0	0
$404$	0.828427	0.0412158
$405$	3.41421	0.169654
$406$	−0.970563	−0.0481682
$407$	−38.6274	−1.91469
$408$	4.00000	0.198030
$409$	14.3848	0.711281	0.355641	−	0.934623i	$-0.384263\pi$
$409$	14.3848	0.711281	0.355641	+	0.934623i	$0.384263\pi$
$410$	−10.8284	−0.534778
$411$	−26.6274	−1.31343
$412$	−2.82843	−0.139347
$413$	−7.51472	−0.369775
$414$	−28.2843	−1.39010
$415$	29.7990	1.46277
$416$	0	0
$417$	−21.9411	−1.07446
$418$	24.0000	1.17388
$419$	−23.6569	−1.15571	−0.577856	−	0.816138i	$-0.696111\pi$
$419$	−23.6569	−1.15571	−0.577856	+	0.816138i	$0.696111\pi$
$420$	−5.65685	−0.276026
$421$	−15.1716	−0.739417	−0.369709	−	0.929148i	$-0.620542\pi$
$421$	−15.1716	−0.739417	−0.369709	+	0.929148i	$0.620542\pi$
$422$	3.65685	0.178013
$423$	20.0000	0.972433
$424$	−10.8284	−0.525875
$425$	−9.41421	−0.456656
$426$	6.34315	0.307326
$427$	7.31371	0.353935
$428$	−0.828427	−0.0400435
$429$	0	0
$430$	−28.9706	−1.39708
$431$	23.7990	1.14636	0.573179	−	0.819431i	$-0.305710\pi$
$431$	23.7990	1.14636	0.573179	+	0.819431i	$0.305710\pi$
$432$	5.65685	0.272166
$433$	−13.2132	−0.634986	−0.317493	−	0.948261i	$-0.602841\pi$
$433$	−13.2132	−0.634986	−0.317493	+	0.948261i	$0.602841\pi$
$434$	−0.585786	−0.0281186
$435$	−16.0000	−0.767141
$436$	−11.1716	−0.535021
$437$	−33.9411	−1.62362
$438$	−21.6569	−1.03480
$439$	−12.3848	−0.591093	−0.295547	−	0.955328i	$-0.595502\pi$
$439$	−12.3848	−0.591093	−0.295547	+	0.955328i	$0.595502\pi$
$440$	−13.6569	−0.651065
$441$	−33.2843	−1.58497
$442$	0	0
$443$	−21.3137	−1.01264	−0.506322	−	0.862344i	$-0.668995\pi$
$443$	−21.3137	−1.01264	−0.506322	+	0.862344i	$0.668995\pi$
$444$	−27.3137	−1.29625
$445$	22.1421	1.04964
$446$	−1.17157	−0.0554756
$447$	9.65685	0.456754
$448$	−0.585786	−0.0276758
$449$	−8.82843	−0.416639	−0.208320	−	0.978061i	$-0.566799\pi$
$449$	−8.82843	−0.416639	−0.208320	+	0.978061i	$0.566799\pi$
$450$	−33.2843	−1.56904
$451$	12.6863	0.597374
$452$	13.6569	0.642364
$453$	−16.0000	−0.751746
$454$	4.00000	0.187729
$455$	0	0
$456$	16.9706	0.794719
$457$	14.1005	0.659594	0.329797	−	0.944052i	$-0.393020\pi$
$457$	14.1005	0.659594	0.329797	+	0.944052i	$0.393020\pi$
$458$	−14.1421	−0.660819
$459$	−8.00000	−0.373408
$460$	19.3137	0.900506
$461$	31.6569	1.47441	0.737203	−	0.675671i	$-0.236146\pi$
$461$	31.6569	1.47441	0.737203	+	0.675671i	$0.236146\pi$
$462$	6.62742	0.308335
$463$	−36.1421	−1.67967	−0.839834	−	0.542844i	$-0.817348\pi$
$463$	−36.1421	−1.67967	−0.839834	+	0.542844i	$0.817348\pi$
$464$	−1.65685	−0.0769175
$465$	−9.65685	−0.447826
$466$	−12.1421	−0.562474
$467$	−30.9706	−1.43315	−0.716573	−	0.697512i	$-0.754291\pi$
$467$	−30.9706	−1.43315	−0.716573	+	0.697512i	$0.754291\pi$
$468$	0	0
$469$	−6.14214	−0.283617
$470$	−13.6569	−0.629944
$471$	49.6569	2.28807
$472$	−12.8284	−0.590476
$473$	33.9411	1.56061
$474$	−2.34315	−0.107624
$475$	−39.9411	−1.83262
$476$	0.828427	0.0379709
$477$	54.1421	2.47900
$478$	−4.48528	−0.205152
$479$	33.1716	1.51565	0.757824	−	0.652459i	$-0.226263\pi$
$479$	33.1716	1.51565	0.757824	+	0.652459i	$0.226263\pi$
$480$	−9.65685	−0.440773
$481$	0	0
$482$	16.3431	0.744410
$483$	−9.37258	−0.426467
$484$	5.00000	0.227273
$485$	3.41421	0.155031
$486$	14.1421	0.641500
$487$	−31.4558	−1.42540	−0.712700	−	0.701469i	$-0.752528\pi$
$487$	−31.4558	−1.42540	−0.712700	+	0.701469i	$0.752528\pi$
$488$	12.4853	0.565182
$489$	−20.6863	−0.935466
$490$	22.7279	1.02674
$491$	−15.3137	−0.691098	−0.345549	−	0.938401i	$-0.612307\pi$
$491$	−15.3137	−0.691098	−0.345549	+	0.938401i	$0.612307\pi$
$492$	8.97056	0.404424
$493$	2.34315	0.105530
$494$	0	0
$495$	68.2843	3.06915
$496$	−1.00000	−0.0449013
$497$	1.31371	0.0589279
$498$	−24.6863	−1.10622
$499$	−5.89949	−0.264098	−0.132049	−	0.991243i	$-0.542156\pi$
$499$	−5.89949	−0.264098	−0.132049	+	0.991243i	$0.542156\pi$
$500$	5.65685	0.252982
$501$	4.28427	0.191407
$502$	−17.8995	−0.798894
$503$	−3.51472	−0.156714	−0.0783568	−	0.996925i	$-0.524967\pi$
$503$	−3.51472	−0.156714	−0.0783568	+	0.996925i	$0.524967\pi$
$504$	2.92893	0.130465
$505$	2.82843	0.125863
$506$	−22.6274	−1.00591
$507$	−36.7696	−1.63299
$508$	−5.17157	−0.229451
$509$	−35.1127	−1.55634	−0.778171	−	0.628052i	$-0.783853\pi$
$509$	−35.1127	−1.55634	−0.778171	+	0.628052i	$0.783853\pi$
$510$	13.6569	0.604736
$511$	−4.48528	−0.198417
$512$	−1.00000	−0.0441942
$513$	−33.9411	−1.49854
$514$	14.4853	0.638918
$515$	−9.65685	−0.425532
$516$	24.0000	1.05654
$517$	16.0000	0.703679
$518$	−5.65685	−0.248548
$519$	32.2843	1.41712
$520$	0	0
$521$	6.68629	0.292932	0.146466	−	0.989216i	$-0.453210\pi$
$521$	6.68629	0.292932	0.146466	+	0.989216i	$0.453210\pi$
$522$	8.28427	0.362593
$523$	−29.8995	−1.30741	−0.653707	−	0.756748i	$-0.726787\pi$
$523$	−29.8995	−1.30741	−0.653707	+	0.756748i	$0.726787\pi$
$524$	−1.31371	−0.0573896
$525$	−11.0294	−0.481364
$526$	−30.1421	−1.31426
$527$	1.41421	0.0616041
$528$	11.3137	0.492366
$529$	9.00000	0.391304
$530$	−36.9706	−1.60590
$531$	64.1421	2.78353
$532$	3.51472	0.152382
$533$	0	0
$534$	−18.3431	−0.793786
$535$	−2.82843	−0.122284
$536$	−10.4853	−0.452895
$537$	−15.3137	−0.660835
$538$	1.31371	0.0566380
$539$	−26.6274	−1.14692
$540$	19.3137	0.831130
$541$	25.5563	1.09875	0.549377	−	0.835575i	$-0.314865\pi$
$541$	25.5563	1.09875	0.549377	+	0.835575i	$0.314865\pi$
$542$	16.4853	0.708103
$543$	−28.6863	−1.23105
$544$	1.41421	0.0606339
$545$	−38.1421	−1.63383
$546$	0	0
$547$	2.34315	0.100186	0.0500928	−	0.998745i	$-0.484048\pi$
$547$	2.34315	0.100186	0.0500928	+	0.998745i	$0.484048\pi$
$548$	−9.41421	−0.402155
$549$	−62.4264	−2.66429
$550$	−26.6274	−1.13540
$551$	9.94113	0.423506
$552$	−16.0000	−0.681005
$553$	−0.485281	−0.0206363
$554$	−13.6569	−0.580224
$555$	−93.2548	−3.95845
$556$	−7.75736	−0.328985
$557$	15.6569	0.663402	0.331701	−	0.943385i	$-0.392377\pi$
$557$	15.6569	0.663402	0.331701	+	0.943385i	$0.392377\pi$
$558$	5.00000	0.211667
$559$	0	0
$560$	−2.00000	−0.0845154
$561$	−16.0000	−0.675521
$562$	−22.4853	−0.948484
$563$	21.5147	0.906737	0.453369	−	0.891323i	$-0.350222\pi$
$563$	21.5147	0.906737	0.453369	+	0.891323i	$0.350222\pi$
$564$	11.3137	0.476393
$565$	46.6274	1.96163
$566$	24.6274	1.03517
$567$	−0.585786	−0.0246007
$568$	2.24264	0.0940991
$569$	34.3848	1.44148	0.720742	−	0.693203i	$-0.243801\pi$
$569$	34.3848	1.44148	0.720742	+	0.693203i	$0.243801\pi$
$570$	57.9411	2.42689
$571$	−27.5147	−1.15146	−0.575728	−	0.817642i	$-0.695281\pi$
$571$	−27.5147	−1.15146	−0.575728	+	0.817642i	$0.695281\pi$
$572$	0	0
$573$	24.0000	1.00261
$574$	1.85786	0.0775458
$575$	37.6569	1.57040
$576$	5.00000	0.208333
$577$	17.3137	0.720779	0.360390	−	0.932802i	$-0.382644\pi$
$577$	17.3137	0.720779	0.360390	+	0.932802i	$0.382644\pi$
$578$	15.0000	0.623918
$579$	−16.9706	−0.705273
$580$	−5.65685	−0.234888
$581$	−5.11270	−0.212110
$582$	−2.82843	−0.117242
$583$	43.3137	1.79387
$584$	−7.65685	−0.316843
$585$	0	0
$586$	28.8284	1.19089
$587$	−30.3848	−1.25411	−0.627057	−	0.778973i	$-0.715741\pi$
$587$	−30.3848	−1.25411	−0.627057	+	0.778973i	$0.715741\pi$
$588$	−18.8284	−0.776471
$589$	6.00000	0.247226
$590$	−43.7990	−1.80318
$591$	−40.0000	−1.64538
$592$	−9.65685	−0.396894
$593$	−6.00000	−0.246390	−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000	−0.246390	−0.123195	+	0.992382i	$0.539314\pi$
$594$	−22.6274	−0.928414
$595$	2.82843	0.115954
$596$	3.41421	0.139852
$597$	−22.6274	−0.926079
$598$	0	0
$599$	24.3848	0.996335	0.498167	−	0.867081i	$-0.334006\pi$
$599$	24.3848	0.996335	0.498167	+	0.867081i	$0.334006\pi$
$600$	−18.8284	−0.768667
$601$	−29.8995	−1.21963	−0.609813	−	0.792545i	$-0.708755\pi$
$601$	−29.8995	−1.21963	−0.609813	+	0.792545i	$0.708755\pi$
$602$	4.97056	0.202585
$603$	52.4264	2.13497
$604$	−5.65685	−0.230174
$605$	17.0711	0.694038
$606$	−2.34315	−0.0951838
$607$	−14.3431	−0.582170	−0.291085	−	0.956697i	$-0.594016\pi$
$607$	−14.3431	−0.582170	−0.291085	+	0.956697i	$0.594016\pi$
$608$	6.00000	0.243332
$609$	2.74517	0.111240
$610$	42.6274	1.72593
$611$	0	0
$612$	−7.07107	−0.285831
$613$	31.6569	1.27861	0.639304	−	0.768954i	$-0.279222\pi$
$613$	31.6569	1.27861	0.639304	+	0.768954i	$0.279222\pi$
$614$	24.6274	0.993882
$615$	30.6274	1.23502
$616$	2.34315	0.0944080
$617$	41.6569	1.67704	0.838521	−	0.544869i	$-0.183421\pi$
$617$	41.6569	1.67704	0.838521	+	0.544869i	$0.183421\pi$
$618$	8.00000	0.321807
$619$	43.3553	1.74260	0.871299	−	0.490752i	$-0.163278\pi$
$619$	43.3553	1.74260	0.871299	+	0.490752i	$0.163278\pi$
$620$	−3.41421	−0.137118
$621$	32.0000	1.28412
$622$	28.3848	1.13813
$623$	−3.79899	−0.152203
$624$	0	0
$625$	−13.9706	−0.558823
$626$	−11.1716	−0.446506
$627$	−67.8823	−2.71096
$628$	17.5563	0.700575
$629$	13.6569	0.544534
$630$	10.0000	0.398410
$631$	25.5147	1.01572	0.507862	−	0.861438i	$-0.330436\pi$
$631$	25.5147	1.01572	0.507862	+	0.861438i	$0.330436\pi$
$632$	−0.828427	−0.0329531
$633$	−10.3431	−0.411103
$634$	10.7279	0.426060
$635$	−17.6569	−0.700691
$636$	30.6274	1.21446
$637$	0	0
$638$	6.62742	0.262382
$639$	−11.2132	−0.443587
$640$	−3.41421	−0.134959
$641$	−0.242641	−0.00958373	−0.00479187	−	0.999989i	$-0.501525\pi$
$641$	−0.242641	−0.00958373	−0.00479187	+	0.999989i	$0.501525\pi$
$642$	2.34315	0.0924766
$643$	18.1421	0.715456	0.357728	−	0.933826i	$-0.383552\pi$
$643$	18.1421	0.715456	0.357728	+	0.933826i	$0.383552\pi$
$644$	−3.31371	−0.130578
$645$	81.9411	3.22643
$646$	−8.48528	−0.333849
$647$	−3.31371	−0.130275	−0.0651377	−	0.997876i	$-0.520749\pi$
$647$	−3.31371	−0.130275	−0.0651377	+	0.997876i	$0.520749\pi$
$648$	−1.00000	−0.0392837
$649$	51.3137	2.01424
$650$	0	0
$651$	1.65685	0.0649372
$652$	−7.31371	−0.286427
$653$	7.41421	0.290141	0.145070	−	0.989421i	$-0.453659\pi$
$653$	7.41421	0.290141	0.145070	+	0.989421i	$0.453659\pi$
$654$	31.5980	1.23558
$655$	−4.48528	−0.175254
$656$	3.17157	0.123829
$657$	38.2843	1.49361
$658$	2.34315	0.0913453
$659$	39.9411	1.55589	0.777943	−	0.628335i	$-0.216263\pi$
$659$	39.9411	1.55589	0.777943	+	0.628335i	$0.216263\pi$
$660$	38.6274	1.50357
$661$	34.7696	1.35238	0.676189	−	0.736728i	$-0.263630\pi$
$661$	34.7696	1.35238	0.676189	+	0.736728i	$0.263630\pi$
$662$	13.8995	0.540219
$663$	0	0
$664$	−8.72792	−0.338709
$665$	12.0000	0.465340
$666$	48.2843	1.87098
$667$	−9.37258	−0.362908
$668$	1.51472	0.0586062
$669$	3.31371	0.128115
$670$	−35.7990	−1.38304
$671$	−49.9411	−1.92796
$672$	1.65685	0.0639145
$673$	−13.7990	−0.531912	−0.265956	−	0.963985i	$-0.585688\pi$
$673$	−13.7990	−0.531912	−0.265956	+	0.963985i	$0.585688\pi$
$674$	21.4142	0.824845
$675$	37.6569	1.44941
$676$	−13.0000	−0.500000
$677$	−41.3137	−1.58781	−0.793907	−	0.608039i	$-0.791957\pi$
$677$	−41.3137	−1.58781	−0.793907	+	0.608039i	$0.791957\pi$
$678$	−38.6274	−1.48348
$679$	−0.585786	−0.0224804
$680$	4.82843	0.185162
$681$	−11.3137	−0.433542
$682$	4.00000	0.153168
$683$	−34.9706	−1.33811	−0.669056	−	0.743212i	$-0.733301\pi$
$683$	−34.9706	−1.33811	−0.669056	+	0.743212i	$0.733301\pi$
$684$	−30.0000	−1.14708
$685$	−32.1421	−1.22809
$686$	−8.00000	−0.305441
$687$	40.0000	1.52610
$688$	8.48528	0.323498
$689$	0	0
$690$	−54.6274	−2.07963
$691$	36.2843	1.38032	0.690159	−	0.723657i	$-0.257540\pi$
$691$	36.2843	1.38032	0.690159	+	0.723657i	$0.257540\pi$
$692$	11.4142	0.433903
$693$	−11.7157	−0.445044
$694$	32.7279	1.24233
$695$	−26.4853	−1.00464
$696$	4.68629	0.177633
$697$	−4.48528	−0.169892
$698$	10.7279	0.406058
$699$	34.3431	1.29898
$700$	−3.89949	−0.147387
$701$	10.4853	0.396024	0.198012	−	0.980200i	$-0.436552\pi$
$701$	10.4853	0.396024	0.198012	+	0.980200i	$0.436552\pi$
$702$	0	0
$703$	57.9411	2.18529
$704$	4.00000	0.150756
$705$	38.6274	1.45479
$706$	−6.68629	−0.251642
$707$	−0.485281	−0.0182509
$708$	36.2843	1.36365
$709$	−14.8284	−0.556893	−0.278447	−	0.960452i	$-0.589820\pi$
$709$	−14.8284	−0.556893	−0.278447	+	0.960452i	$0.589820\pi$
$710$	7.65685	0.287357
$711$	4.14214	0.155342
$712$	−6.48528	−0.243046
$713$	−5.65685	−0.211851
$714$	−2.34315	−0.0876900
$715$	0	0
$716$	−5.41421	−0.202339
$717$	12.6863	0.473778
$718$	29.5563	1.10303
$719$	49.6569	1.85189	0.925944	−	0.377661i	$-0.123271\pi$
$719$	49.6569	1.85189	0.925944	+	0.377661i	$0.123271\pi$
$720$	17.0711	0.636201
$721$	1.65685	0.0617045
$722$	−17.0000	−0.632674
$723$	−46.2254	−1.71914
$724$	−10.1421	−0.376930
$725$	−11.0294	−0.409623
$726$	−14.1421	−0.524864
$727$	−20.2843	−0.752302	−0.376151	−	0.926558i	$-0.622753\pi$
$727$	−20.2843	−0.752302	−0.376151	+	0.926558i	$0.622753\pi$
$728$	0	0
$729$	−43.0000	−1.59259
$730$	−26.1421	−0.967564
$731$	−12.0000	−0.443836
$732$	−35.3137	−1.30523
$733$	3.45584	0.127645	0.0638223	−	0.997961i	$-0.479671\pi$
$733$	3.45584	0.127645	0.0638223	+	0.997961i	$0.479671\pi$
$734$	−6.14214	−0.226710
$735$	−64.2843	−2.37116
$736$	−5.65685	−0.208514
$737$	41.9411	1.54492
$738$	−15.8579	−0.583736
$739$	13.4142	0.493450	0.246725	−	0.969086i	$-0.420646\pi$
$739$	13.4142	0.493450	0.246725	+	0.969086i	$0.420646\pi$
$740$	−32.9706	−1.21202
$741$	0	0
$742$	6.34315	0.232864
$743$	−30.6274	−1.12361	−0.561805	−	0.827269i	$-0.689893\pi$
$743$	−30.6274	−1.12361	−0.561805	+	0.827269i	$0.689893\pi$
$744$	2.82843	0.103695
$745$	11.6569	0.427074
$746$	12.3848	0.453439
$747$	43.6396	1.59669
$748$	−5.65685	−0.206835
$749$	0.485281	0.0177318
$750$	−16.0000	−0.584237
$751$	20.9706	0.765227	0.382613	−	0.923909i	$-0.375024\pi$
$751$	20.9706	0.765227	0.382613	+	0.923909i	$0.375024\pi$
$752$	4.00000	0.145865
$753$	50.6274	1.84497
$754$	0	0
$755$	−19.3137	−0.702898
$756$	−3.31371	−0.120518
$757$	10.1421	0.368622	0.184311	−	0.982868i	$-0.440995\pi$
$757$	10.1421	0.368622	0.184311	+	0.982868i	$0.440995\pi$
$758$	22.9706	0.834328
$759$	64.0000	2.32305
$760$	20.4853	0.743079
$761$	36.2426	1.31379	0.656897	−	0.753980i	$-0.271868\pi$
$761$	36.2426	1.31379	0.656897	+	0.753980i	$0.271868\pi$
$762$	14.6274	0.529895
$763$	6.54416	0.236914
$764$	8.48528	0.306987
$765$	−24.1421	−0.872861
$766$	16.9706	0.613171
$767$	0	0
$768$	2.82843	0.102062
$769$	22.6863	0.818089	0.409044	−	0.912515i	$-0.365862\pi$
$769$	22.6863	0.818089	0.409044	+	0.912515i	$0.365862\pi$
$770$	8.00000	0.288300
$771$	−40.9706	−1.47552
$772$	−6.00000	−0.215945
$773$	7.79899	0.280510	0.140255	−	0.990115i	$-0.455208\pi$
$773$	7.79899	0.280510	0.140255	+	0.990115i	$0.455208\pi$
$774$	−42.4264	−1.52499
$775$	−6.65685	−0.239121
$776$	−1.00000	−0.0358979
$777$	16.0000	0.573997
$778$	6.97056	0.249907
$779$	−19.0294	−0.681800
$780$	0	0
$781$	−8.97056	−0.320992
$782$	8.00000	0.286079
$783$	−9.37258	−0.334949
$784$	−6.65685	−0.237745
$785$	59.9411	2.13939
$786$	3.71573	0.132536
$787$	−27.5147	−0.980794	−0.490397	−	0.871499i	$-0.663148\pi$
$787$	−27.5147	−0.980794	−0.490397	+	0.871499i	$0.663148\pi$
$788$	−14.1421	−0.503793
$789$	85.2548	3.03515
$790$	−2.82843	−0.100631
$791$	−8.00000	−0.284447
$792$	−20.0000	−0.710669
$793$	0	0
$794$	−27.1716	−0.964283
$795$	104.569	3.70866
$796$	−8.00000	−0.283552
$797$	−36.9706	−1.30956	−0.654782	−	0.755818i	$-0.727240\pi$
$797$	−36.9706	−1.30956	−0.654782	+	0.755818i	$0.727240\pi$
$798$	−9.94113	−0.351912
$799$	−5.65685	−0.200125
$800$	−6.65685	−0.235355
$801$	32.4264	1.14573
$802$	−33.8995	−1.19703
$803$	30.6274	1.08082
$804$	29.6569	1.04592
$805$	−11.3137	−0.398756
$806$	0	0
$807$	−3.71573	−0.130800
$808$	−0.828427	−0.0291440
$809$	29.5147	1.03768	0.518841	−	0.854871i	$-0.326364\pi$
$809$	29.5147	1.03768	0.518841	+	0.854871i	$0.326364\pi$
$810$	−3.41421	−0.119963
$811$	9.37258	0.329116	0.164558	−	0.986367i	$-0.447380\pi$
$811$	9.37258	0.329116	0.164558	+	0.986367i	$0.447380\pi$
$812$	0.970563	0.0340601
$813$	−46.6274	−1.63529
$814$	38.6274	1.35389
$815$	−24.9706	−0.874681
$816$	−4.00000	−0.140028
$817$	−50.9117	−1.78117
$818$	−14.3848	−0.502952
$819$	0	0
$820$	10.8284	0.378145
$821$	−5.65685	−0.197426	−0.0987128	−	0.995116i	$-0.531473\pi$
$821$	−5.65685	−0.197426	−0.0987128	+	0.995116i	$0.531473\pi$
$822$	26.6274	0.928738
$823$	−27.4558	−0.957051	−0.478525	−	0.878074i	$-0.658829\pi$
$823$	−27.4558	−0.957051	−0.478525	+	0.878074i	$0.658829\pi$
$824$	2.82843	0.0985329
$825$	75.3137	2.62209
$826$	7.51472	0.261471
$827$	17.4142	0.605552	0.302776	−	0.953062i	$-0.402087\pi$
$827$	17.4142	0.605552	0.302776	+	0.953062i	$0.402087\pi$
$828$	28.2843	0.982946
$829$	6.68629	0.232225	0.116112	−	0.993236i	$-0.462957\pi$
$829$	6.68629	0.232225	0.116112	+	0.993236i	$0.462957\pi$
$830$	−29.7990	−1.03434
$831$	38.6274	1.33997
$832$	0	0
$833$	9.41421	0.326183
$834$	21.9411	0.759759
$835$	5.17157	0.178970
$836$	−24.0000	−0.830057
$837$	−5.65685	−0.195529
$838$	23.6569	0.817212
$839$	18.2426	0.629806	0.314903	−	0.949124i	$-0.398028\pi$
$839$	18.2426	0.629806	0.314903	+	0.949124i	$0.398028\pi$
$840$	5.65685	0.195180
$841$	−26.2548	−0.905339
$842$	15.1716	0.522847
$843$	63.5980	2.19043
$844$	−3.65685	−0.125874
$845$	−44.3848	−1.52688
$846$	−20.0000	−0.687614
$847$	−2.92893	−0.100639
$848$	10.8284	0.371850
$849$	−69.6569	−2.39062
$850$	9.41421	0.322905
$851$	−54.6274	−1.87260
$852$	−6.34315	−0.217313
$853$	16.1005	0.551271	0.275635	−	0.961262i	$-0.411112\pi$
$853$	16.1005	0.551271	0.275635	+	0.961262i	$0.411112\pi$
$854$	−7.31371	−0.250270
$855$	−102.426	−3.50291
$856$	0.828427	0.0283151
$857$	13.6569	0.466509	0.233255	−	0.972416i	$-0.425062\pi$
$857$	13.6569	0.466509	0.233255	+	0.972416i	$0.425062\pi$
$858$	0	0
$859$	25.8995	0.883679	0.441840	−	0.897094i	$-0.354326\pi$
$859$	25.8995	0.883679	0.441840	+	0.897094i	$0.354326\pi$
$860$	28.9706	0.987888
$861$	−5.25483	−0.179084
$862$	−23.7990	−0.810597
$863$	−39.7990	−1.35477	−0.677387	−	0.735627i	$-0.736888\pi$
$863$	−39.7990	−1.35477	−0.677387	+	0.735627i	$0.736888\pi$
$864$	−5.65685	−0.192450
$865$	38.9706	1.32504
$866$	13.2132	0.449003
$867$	−42.4264	−1.44088
$868$	0.585786	0.0198829
$869$	3.31371	0.112410
$870$	16.0000	0.542451
$871$	0	0
$872$	11.1716	0.378317
$873$	5.00000	0.169224
$874$	33.9411	1.14808
$875$	−3.31371	−0.112024
$876$	21.6569	0.731717
$877$	−31.9411	−1.07858	−0.539288	−	0.842122i	$-0.681306\pi$
$877$	−31.9411	−1.07858	−0.539288	+	0.842122i	$0.681306\pi$
$878$	12.3848	0.417966
$879$	−81.5391	−2.75025
$880$	13.6569	0.460372
$881$	17.0294	0.573736	0.286868	−	0.957970i	$-0.407386\pi$
$881$	17.0294	0.573736	0.286868	+	0.957970i	$0.407386\pi$
$882$	33.2843	1.12074
$883$	55.3553	1.86286	0.931428	−	0.363926i	$-0.118564\pi$
$883$	55.3553	1.86286	0.931428	+	0.363926i	$0.118564\pi$
$884$	0	0
$885$	123.882	4.16426
$886$	21.3137	0.716048
$887$	−17.5563	−0.589485	−0.294742	−	0.955577i	$-0.595234\pi$
$887$	−17.5563	−0.589485	−0.294742	+	0.955577i	$0.595234\pi$
$888$	27.3137	0.916588
$889$	3.02944	0.101604
$890$	−22.1421	−0.742206
$891$	4.00000	0.134005
$892$	1.17157	0.0392272
$893$	−24.0000	−0.803129
$894$	−9.65685	−0.322974
$895$	−18.4853	−0.617895
$896$	0.585786	0.0195698
$897$	0	0
$898$	8.82843	0.294608
$899$	1.65685	0.0552592
$900$	33.2843	1.10948
$901$	−15.3137	−0.510174
$902$	−12.6863	−0.422407
$903$	−14.0589	−0.467850
$904$	−13.6569	−0.454220
$905$	−34.6274	−1.15105
$906$	16.0000	0.531564
$907$	40.3431	1.33957	0.669786	−	0.742554i	$-0.266386\pi$
$907$	40.3431	1.33957	0.669786	+	0.742554i	$0.266386\pi$
$908$	−4.00000	−0.132745
$909$	4.14214	0.137386
$910$	0	0
$911$	7.11270	0.235654	0.117827	−	0.993034i	$-0.462407\pi$
$911$	7.11270	0.235654	0.117827	+	0.993034i	$0.462407\pi$
$912$	−16.9706	−0.561951
$913$	34.9117	1.15541
$914$	−14.1005	−0.466403
$915$	−120.569	−3.98587
$916$	14.1421	0.467269
$917$	0.769553	0.0254129
$918$	8.00000	0.264039
$919$	−42.7279	−1.40946	−0.704732	−	0.709474i	$-0.748933\pi$
$919$	−42.7279	−1.40946	−0.704732	+	0.709474i	$0.748933\pi$
$920$	−19.3137	−0.636754
$921$	−69.6569	−2.29527
$922$	−31.6569	−1.04256
$923$	0	0
$924$	−6.62742	−0.218026
$925$	−64.2843	−2.11365
$926$	36.1421	1.18770
$927$	−14.1421	−0.464489
$928$	1.65685	0.0543889
$929$	−24.0416	−0.788780	−0.394390	−	0.918943i	$-0.629044\pi$
$929$	−24.0416	−0.788780	−0.394390	+	0.918943i	$0.629044\pi$
$930$	9.65685	0.316661
$931$	39.9411	1.30902
$932$	12.1421	0.397729
$933$	−80.2843	−2.62839
$934$	30.9706	1.01339
$935$	−19.3137	−0.631626
$936$	0	0
$937$	−24.2843	−0.793333	−0.396666	−	0.917963i	$-0.629833\pi$
$937$	−24.2843	−0.793333	−0.396666	+	0.917963i	$0.629833\pi$
$938$	6.14214	0.200548
$939$	31.5980	1.03116
$940$	13.6569	0.445437
$941$	−30.6274	−0.998425	−0.499213	−	0.866480i	$-0.666377\pi$
$941$	−30.6274	−0.998425	−0.499213	+	0.866480i	$0.666377\pi$
$942$	−49.6569	−1.61791
$943$	17.9411	0.584243
$944$	12.8284	0.417530
$945$	−11.3137	−0.368035
$946$	−33.9411	−1.10352
$947$	−12.9289	−0.420134	−0.210067	−	0.977687i	$-0.567368\pi$
$947$	−12.9289	−0.420134	−0.210067	+	0.977687i	$0.567368\pi$
$948$	2.34315	0.0761018
$949$	0	0
$950$	39.9411	1.29586
$951$	−30.3431	−0.983944
$952$	−0.828427	−0.0268495
$953$	−3.27208	−0.105993	−0.0529965	−	0.998595i	$-0.516877\pi$
$953$	−3.27208	−0.105993	−0.0529965	+	0.998595i	$0.516877\pi$
$954$	−54.1421	−1.75292
$955$	28.9706	0.937465
$956$	4.48528	0.145064
$957$	−18.7452	−0.605945
$958$	−33.1716	−1.07172
$959$	5.51472	0.178080
$960$	9.65685	0.311674
$961$	1.00000	0.0322581
$962$	0	0
$963$	−4.14214	−0.133478
$964$	−16.3431	−0.526377
$965$	−20.4853	−0.659445
$966$	9.37258	0.301558
$967$	32.1421	1.03362	0.516811	−	0.856100i	$-0.327119\pi$
$967$	32.1421	1.03362	0.516811	+	0.856100i	$0.327119\pi$
$968$	−5.00000	−0.160706
$969$	24.0000	0.770991
$970$	−3.41421	−0.109624
$971$	−16.0000	−0.513464	−0.256732	−	0.966483i	$-0.582646\pi$
$971$	−16.0000	−0.513464	−0.256732	+	0.966483i	$0.582646\pi$
$972$	−14.1421	−0.453609
$973$	4.54416	0.145679
$974$	31.4558	1.00791
$975$	0	0
$976$	−12.4853	−0.399644
$977$	30.7696	0.984405	0.492203	−	0.870481i	$-0.336192\pi$
$977$	30.7696	0.984405	0.492203	+	0.870481i	$0.336192\pi$
$978$	20.6863	0.661475
$979$	25.9411	0.829082
$980$	−22.7279	−0.726017
$981$	−55.8579	−1.78340
$982$	15.3137	0.488680
$983$	−16.0000	−0.510321	−0.255160	−	0.966899i	$-0.582128\pi$
$983$	−16.0000	−0.510321	−0.255160	+	0.966899i	$0.582128\pi$
$984$	−8.97056	−0.285971
$985$	−48.2843	−1.53846
$986$	−2.34315	−0.0746210
$987$	−6.62742	−0.210953
$988$	0	0
$989$	48.0000	1.52631
$990$	−68.2843	−2.17022
$991$	46.4264	1.47478	0.737392	−	0.675465i	$-0.236057\pi$
$991$	46.4264	1.47478	0.737392	+	0.675465i	$0.236057\pi$
$992$	1.00000	0.0317500
$993$	−39.3137	−1.24758
$994$	−1.31371	−0.0416683
$995$	−27.3137	−0.865903
$996$	24.6863	0.782215
$997$	−8.62742	−0.273233	−0.136617	−	0.990624i	$-0.543623\pi$
$997$	−8.62742	−0.273233	−0.136617	+	0.990624i	$0.543623\pi$
$998$	5.89949	0.186745
$999$	−54.6274	−1.72833

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.c.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.c.1.2	✓	2	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.82843 q^{3} +1.00000 q^{4} +3.41421 q^{5} -2.82843 q^{6} -0.585786 q^{7} -1.00000 q^{8} +5.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.82843 q^{3} +1.00000 q^{4} +3.41421 q^{5} -2.82843 q^{6} -0.585786 q^{7} -1.00000 q^{8} +5.00000 q^{9} -3.41421 q^{10} +4.00000 q^{11} +2.82843 q^{12} +0.585786 q^{14} +9.65685 q^{15} +1.00000 q^{16} -1.41421 q^{17} -5.00000 q^{18} -6.00000 q^{19} +3.41421 q^{20} -1.65685 q^{21} -4.00000 q^{22} +5.65685 q^{23} -2.82843 q^{24} +6.65685 q^{25} +5.65685 q^{27} -0.585786 q^{28} -1.65685 q^{29} -9.65685 q^{30} -1.00000 q^{31} -1.00000 q^{32} +11.3137 q^{33} +1.41421 q^{34} -2.00000 q^{35} +5.00000 q^{36} -9.65685 q^{37} +6.00000 q^{38} -3.41421 q^{40} +3.17157 q^{41} +1.65685 q^{42} +8.48528 q^{43} +4.00000 q^{44} +17.0711 q^{45} -5.65685 q^{46} +4.00000 q^{47} +2.82843 q^{48} -6.65685 q^{49} -6.65685 q^{50} -4.00000 q^{51} +10.8284 q^{53} -5.65685 q^{54} +13.6569 q^{55} +0.585786 q^{56} -16.9706 q^{57} +1.65685 q^{58} +12.8284 q^{59} +9.65685 q^{60} -12.4853 q^{61} +1.00000 q^{62} -2.92893 q^{63} +1.00000 q^{64} -11.3137 q^{66} +10.4853 q^{67} -1.41421 q^{68} +16.0000 q^{69} +2.00000 q^{70} -2.24264 q^{71} -5.00000 q^{72} +7.65685 q^{73} +9.65685 q^{74} +18.8284 q^{75} -6.00000 q^{76} -2.34315 q^{77} +0.828427 q^{79} +3.41421 q^{80} +1.00000 q^{81} -3.17157 q^{82} +8.72792 q^{83} -1.65685 q^{84} -4.82843 q^{85} -8.48528 q^{86} -4.68629 q^{87} -4.00000 q^{88} +6.48528 q^{89} -17.0711 q^{90} +5.65685 q^{92} -2.82843 q^{93} -4.00000 q^{94} -20.4853 q^{95} -2.82843 q^{96} +1.00000 q^{97} +6.65685 q^{98} +20.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} + 4 q^{5} - 4 q^{7} - 2 q^{8} + 10 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 + 4 * q^5 - 4 * q^7 - 2 * q^8 + 10 * q^9	\( 2 q - 2 q^{2} + 2 q^{4} + 4 q^{5} - 4 q^{7} - 2 q^{8} + 10 q^{9} - 4 q^{10} + 8 q^{11} + 4 q^{14} + 8 q^{15} + 2 q^{16} - 10 q^{18} - 12 q^{19} + 4 q^{20} + 8 q^{21} - 8 q^{22} + 2 q^{25} - 4 q^{28} + 8 q^{29} - 8 q^{30} - 2 q^{31} - 2 q^{32} - 4 q^{35} + 10 q^{36} - 8 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 8 q^{42} + 8 q^{44} + 20 q^{45} + 8 q^{47} - 2 q^{49} - 2 q^{50} - 8 q^{51} + 16 q^{53} + 16 q^{55} + 4 q^{56} - 8 q^{58} + 20 q^{59} + 8 q^{60} - 8 q^{61} + 2 q^{62} - 20 q^{63} + 2 q^{64} + 4 q^{67} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 10 q^{72} + 4 q^{73} + 8 q^{74} + 32 q^{75} - 12 q^{76} - 16 q^{77} - 4 q^{79} + 4 q^{80} + 2 q^{81} - 12 q^{82} - 8 q^{83} + 8 q^{84} - 4 q^{85} - 32 q^{87} - 8 q^{88} - 4 q^{89} - 20 q^{90} - 8 q^{94} - 24 q^{95} + 2 q^{97} + 2 q^{98} + 40 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 + 4 * q^5 - 4 * q^7 - 2 * q^8 + 10 * q^9 - 4 * q^10 + 8 * q^11 + 4 * q^14 + 8 * q^15 + 2 * q^16 - 10 * q^18 - 12 * q^19 + 4 * q^20 + 8 * q^21 - 8 * q^22 + 2 * q^25 - 4 * q^28 + 8 * q^29 - 8 * q^30 - 2 * q^31 - 2 * q^32 - 4 * q^35 + 10 * q^36 - 8 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 8 * q^42 + 8 * q^44 + 20 * q^45 + 8 * q^47 - 2 * q^49 - 2 * q^50 - 8 * q^51 + 16 * q^53 + 16 * q^55 + 4 * q^56 - 8 * q^58 + 20 * q^59 + 8 * q^60 - 8 * q^61 + 2 * q^62 - 20 * q^63 + 2 * q^64 + 4 * q^67 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 10 * q^72 + 4 * q^73 + 8 * q^74 + 32 * q^75 - 12 * q^76 - 16 * q^77 - 4 * q^79 + 4 * q^80 + 2 * q^81 - 12 * q^82 - 8 * q^83 + 8 * q^84 - 4 * q^85 - 32 * q^87 - 8 * q^88 - 4 * q^89 - 20 * q^90 - 8 * q^94 - 24 * q^95 + 2 * q^97 + 2 * q^98 + 40 * q^99

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