LMFDB - Embedded newform 4018.2.a.bu.1.9

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 23x^{8} + 19x^{7} + 181x^{6} - 109x^{5} - 579x^{4} + 231x^{3} + 608x^{2} - 204x - 12 $ x^10 - x^9 - 23x^8 + 19x^7 + 181x^6 - 109x^5 - 579x^4 + 231x^3 + 608x^2 - 204x - 12
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 574)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$2.71108$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.71108 q^{3} +1.00000 q^{4} +0.432605 q^{5} +2.71108 q^{6} +1.00000 q^{8} +4.34997 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.71108 q^{3} +1.00000 q^{4} +0.432605 q^{5} +2.71108 q^{6} +1.00000 q^{8} +4.34997 q^{9} +0.432605 q^{10} -4.46491 q^{11} +2.71108 q^{12} +6.22838 q^{13} +1.17283 q^{15} +1.00000 q^{16} +3.78258 q^{17} +4.34997 q^{18} -2.18592 q^{19} +0.432605 q^{20} -4.46491 q^{22} -0.639400 q^{23} +2.71108 q^{24} -4.81285 q^{25} +6.22838 q^{26} +3.65989 q^{27} +3.86873 q^{29} +1.17283 q^{30} -0.411452 q^{31} +1.00000 q^{32} -12.1047 q^{33} +3.78258 q^{34} +4.34997 q^{36} +7.45770 q^{37} -2.18592 q^{38} +16.8857 q^{39} +0.432605 q^{40} +1.00000 q^{41} +2.67133 q^{43} -4.46491 q^{44} +1.88182 q^{45} -0.639400 q^{46} +11.8552 q^{47} +2.71108 q^{48} -4.81285 q^{50} +10.2549 q^{51} +6.22838 q^{52} +11.5160 q^{53} +3.65989 q^{54} -1.93154 q^{55} -5.92622 q^{57} +3.86873 q^{58} -10.4298 q^{59} +1.17283 q^{60} +10.9393 q^{61} -0.411452 q^{62} +1.00000 q^{64} +2.69443 q^{65} -12.1047 q^{66} -5.53641 q^{67} +3.78258 q^{68} -1.73347 q^{69} -9.40984 q^{71} +4.34997 q^{72} -6.26918 q^{73} +7.45770 q^{74} -13.0480 q^{75} -2.18592 q^{76} +16.8857 q^{78} -0.703406 q^{79} +0.432605 q^{80} -3.12765 q^{81} +1.00000 q^{82} -10.8852 q^{83} +1.63636 q^{85} +2.67133 q^{86} +10.4884 q^{87} -4.46491 q^{88} -1.59618 q^{89} +1.88182 q^{90} -0.639400 q^{92} -1.11548 q^{93} +11.8552 q^{94} -0.945641 q^{95} +2.71108 q^{96} -15.6752 q^{97} -19.4222 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + q^{3} + 10 q^{4} - 2 q^{5} + q^{6} + 10 q^{8} + 17 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + q^3 + 10 * q^4 - 2 * q^5 + q^6 + 10 * q^8 + 17 * q^9	$ 10 q + 10 q^{2} + q^{3} + 10 q^{4} - 2 q^{5} + q^{6} + 10 q^{8} + 17 q^{9} - 2 q^{10} + 11 q^{11} + q^{12} + 4 q^{13} + 4 q^{15} + 10 q^{16} + 5 q^{17} + 17 q^{18} - q^{19} - 2 q^{20} + 11 q^{22} + 9 q^{23} + q^{24} + 24 q^{25} + 4 q^{26} + 7 q^{27} + 23 q^{29} + 4 q^{30} - 5 q^{31} + 10 q^{32} - 5 q^{33} + 5 q^{34} + 17 q^{36} + 16 q^{37} - q^{38} - 7 q^{39} - 2 q^{40} + 10 q^{41} + 20 q^{43} + 11 q^{44} - 42 q^{45} + 9 q^{46} - 16 q^{47} + q^{48} + 24 q^{50} + 13 q^{51} + 4 q^{52} + 26 q^{53} + 7 q^{54} + 7 q^{55} + 37 q^{57} + 23 q^{58} - 10 q^{59} + 4 q^{60} - 5 q^{62} + 10 q^{64} + 18 q^{65} - 5 q^{66} + 7 q^{67} + 5 q^{68} + 39 q^{69} + 5 q^{71} + 17 q^{72} - 13 q^{73} + 16 q^{74} + 19 q^{75} - q^{76} - 7 q^{78} - q^{79} - 2 q^{80} + 18 q^{81} + 10 q^{82} + 21 q^{83} + 34 q^{85} + 20 q^{86} + 2 q^{87} + 11 q^{88} + 6 q^{89} - 42 q^{90} + 9 q^{92} - 5 q^{93} - 16 q^{94} + 24 q^{95} + q^{96} + 29 q^{97} + 48 q^{99}+O(q^{100}) $ 10 * q + 10 * q^2 + q^3 + 10 * q^4 - 2 * q^5 + q^6 + 10 * q^8 + 17 * q^9 - 2 * q^10 + 11 * q^11 + q^12 + 4 * q^13 + 4 * q^15 + 10 * q^16 + 5 * q^17 + 17 * q^18 - q^19 - 2 * q^20 + 11 * q^22 + 9 * q^23 + q^24 + 24 * q^25 + 4 * q^26 + 7 * q^27 + 23 * q^29 + 4 * q^30 - 5 * q^31 + 10 * q^32 - 5 * q^33 + 5 * q^34 + 17 * q^36 + 16 * q^37 - q^38 - 7 * q^39 - 2 * q^40 + 10 * q^41 + 20 * q^43 + 11 * q^44 - 42 * q^45 + 9 * q^46 - 16 * q^47 + q^48 + 24 * q^50 + 13 * q^51 + 4 * q^52 + 26 * q^53 + 7 * q^54 + 7 * q^55 + 37 * q^57 + 23 * q^58 - 10 * q^59 + 4 * q^60 - 5 * q^62 + 10 * q^64 + 18 * q^65 - 5 * q^66 + 7 * q^67 + 5 * q^68 + 39 * q^69 + 5 * q^71 + 17 * q^72 - 13 * q^73 + 16 * q^74 + 19 * q^75 - q^76 - 7 * q^78 - q^79 - 2 * q^80 + 18 * q^81 + 10 * q^82 + 21 * q^83 + 34 * q^85 + 20 * q^86 + 2 * q^87 + 11 * q^88 + 6 * q^89 - 42 * q^90 + 9 * q^92 - 5 * q^93 - 16 * q^94 + 24 * q^95 + q^96 + 29 * q^97 + 48 * 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
$3$	2.71108	1.56524	0.782622	−	0.622497i	$-0.213882\pi$
$3$	2.71108	1.56524	0.782622	+	0.622497i	$0.213882\pi$
$4$	1.00000	0.500000
$5$	0.432605	0.193467	0.0967334	−	0.995310i	$-0.469161\pi$
$5$	0.432605	0.193467	0.0967334	+	0.995310i	$0.469161\pi$
$6$	2.71108	1.10680
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	4.34997	1.44999
$10$	0.432605	0.136802
$11$	−4.46491	−1.34622	−0.673111	−	0.739542i	$-0.735042\pi$
$11$	−4.46491	−1.34622	−0.673111	+	0.739542i	$0.735042\pi$
$12$	2.71108	0.782622
$13$	6.22838	1.72744	0.863721	−	0.503971i	$-0.168128\pi$
$13$	6.22838	1.72744	0.863721	+	0.503971i	$0.168128\pi$
$14$	0	0
$15$	1.17283	0.302823
$16$	1.00000	0.250000
$17$	3.78258	0.917410	0.458705	−	0.888589i	$-0.348313\pi$
$17$	3.78258	0.917410	0.458705	+	0.888589i	$0.348313\pi$
$18$	4.34997	1.02530
$19$	−2.18592	−0.501485	−0.250743	−	0.968054i	$-0.580675\pi$
$19$	−2.18592	−0.501485	−0.250743	+	0.968054i	$0.580675\pi$
$20$	0.432605	0.0967334
$21$	0	0
$22$	−4.46491	−0.951922
$23$	−0.639400	−0.133324	−0.0666620	−	0.997776i	$-0.521235\pi$
$23$	−0.639400	−0.133324	−0.0666620	+	0.997776i	$0.521235\pi$
$24$	2.71108	0.553398
$25$	−4.81285	−0.962571
$26$	6.22838	1.22149
$27$	3.65989	0.704346
$28$	0	0
$29$	3.86873	0.718404	0.359202	−	0.933260i	$-0.383049\pi$
$29$	3.86873	0.718404	0.359202	+	0.933260i	$0.383049\pi$
$30$	1.17283	0.214128
$31$	−0.411452	−0.0738989	−0.0369495	−	0.999317i	$-0.511764\pi$
$31$	−0.411452	−0.0738989	−0.0369495	+	0.999317i	$0.511764\pi$
$32$	1.00000	0.176777
$33$	−12.1047	−2.10717
$34$	3.78258	0.648707
$35$	0	0
$36$	4.34997	0.724996
$37$	7.45770	1.22604	0.613020	−	0.790068i	$-0.289955\pi$
$37$	7.45770	1.22604	0.613020	+	0.790068i	$0.289955\pi$
$38$	−2.18592	−0.354604
$39$	16.8857	2.70387
$40$	0.432605	0.0684008
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	2.67133	0.407375	0.203687	−	0.979036i	$-0.434707\pi$
$43$	2.67133	0.407375	0.203687	+	0.979036i	$0.434707\pi$
$44$	−4.46491	−0.673111
$45$	1.88182	0.280525
$46$	−0.639400	−0.0942744
$47$	11.8552	1.72925	0.864627	−	0.502415i	$-0.167555\pi$
$47$	11.8552	1.72925	0.864627	+	0.502415i	$0.167555\pi$
$48$	2.71108	0.391311
$49$	0	0
$50$	−4.81285	−0.680640
$51$	10.2549	1.43597
$52$	6.22838	0.863721
$53$	11.5160	1.58185	0.790925	−	0.611913i	$-0.209600\pi$
$53$	11.5160	1.58185	0.790925	+	0.611913i	$0.209600\pi$
$54$	3.65989	0.498048
$55$	−1.93154	−0.260449
$56$	0	0
$57$	−5.92622	−0.784947
$58$	3.86873	0.507989
$59$	−10.4298	−1.35785	−0.678923	−	0.734210i	$-0.737553\pi$
$59$	−10.4298	−1.35785	−0.678923	+	0.734210i	$0.737553\pi$
$60$	1.17283	0.151411
$61$	10.9393	1.40064	0.700318	−	0.713831i	$-0.253042\pi$
$61$	10.9393	1.40064	0.700318	+	0.713831i	$0.253042\pi$
$62$	−0.411452	−0.0522544
$63$	0	0
$64$	1.00000	0.125000
$65$	2.69443	0.334203
$66$	−12.1047	−1.48999
$67$	−5.53641	−0.676380	−0.338190	−	0.941078i	$-0.609815\pi$
$67$	−5.53641	−0.676380	−0.338190	+	0.941078i	$0.609815\pi$
$68$	3.78258	0.458705
$69$	−1.73347	−0.208685
$70$	0	0
$71$	−9.40984	−1.11674	−0.558371	−	0.829591i	$-0.688574\pi$
$71$	−9.40984	−1.11674	−0.558371	+	0.829591i	$0.688574\pi$
$72$	4.34997	0.512649
$73$	−6.26918	−0.733752	−0.366876	−	0.930270i	$-0.619573\pi$
$73$	−6.26918	−0.733752	−0.366876	+	0.930270i	$0.619573\pi$
$74$	7.45770	0.866941
$75$	−13.0480	−1.50666
$76$	−2.18592	−0.250743
$77$	0	0
$78$	16.8857	1.91192
$79$	−0.703406	−0.0791394	−0.0395697	−	0.999217i	$-0.512599\pi$
$79$	−0.703406	−0.0791394	−0.0395697	+	0.999217i	$0.512599\pi$
$80$	0.432605	0.0483667
$81$	−3.12765	−0.347517
$82$	1.00000	0.110432
$83$	−10.8852	−1.19480	−0.597402	−	0.801942i	$-0.703800\pi$
$83$	−10.8852	−1.19480	−0.597402	+	0.801942i	$0.703800\pi$
$84$	0	0
$85$	1.63636	0.177488
$86$	2.67133	0.288057
$87$	10.4884	1.12448
$88$	−4.46491	−0.475961
$89$	−1.59618	−0.169194	−0.0845972	−	0.996415i	$-0.526960\pi$
$89$	−1.59618	−0.169194	−0.0845972	+	0.996415i	$0.526960\pi$
$90$	1.88182	0.198361
$91$	0	0
$92$	−0.639400	−0.0666620
$93$	−1.11548	−0.115670
$94$	11.8552	1.22277
$95$	−0.945641	−0.0970207
$96$	2.71108	0.276699
$97$	−15.6752	−1.59158	−0.795788	−	0.605575i	$-0.792943\pi$
$97$	−15.6752	−1.59158	−0.795788	+	0.605575i	$0.792943\pi$
$98$	0	0
$99$	−19.4222	−1.95201
$100$	−4.81285	−0.481285
$101$	−0.215041	−0.0213974	−0.0106987	−	0.999943i	$-0.503406\pi$
$101$	−0.215041	−0.0213974	−0.0106987	+	0.999943i	$0.503406\pi$
$102$	10.2549	1.01539
$103$	1.83039	0.180354	0.0901770	−	0.995926i	$-0.471257\pi$
$103$	1.83039	0.180354	0.0901770	+	0.995926i	$0.471257\pi$
$104$	6.22838	0.610743
$105$	0	0
$106$	11.5160	1.11854
$107$	−3.38165	−0.326916	−0.163458	−	0.986550i	$-0.552265\pi$
$107$	−3.38165	−0.326916	−0.163458	+	0.986550i	$0.552265\pi$
$108$	3.65989	0.352173
$109$	−11.7484	−1.12529	−0.562647	−	0.826697i	$-0.690217\pi$
$109$	−11.7484	−1.12529	−0.562647	+	0.826697i	$0.690217\pi$
$110$	−1.93154	−0.184165
$111$	20.2185	1.91905
$112$	0	0
$113$	10.9142	1.02672	0.513362	−	0.858172i	$-0.328400\pi$
$113$	10.9142	1.02672	0.513362	+	0.858172i	$0.328400\pi$
$114$	−5.92622	−0.555041
$115$	−0.276607	−0.0257938
$116$	3.86873	0.359202
$117$	27.0933	2.50477
$118$	−10.4298	−0.960142
$119$	0	0
$120$	1.17283	0.107064
$121$	8.93543	0.812312
$122$	10.9393	0.990399
$123$	2.71108	0.244450
$124$	−0.411452	−0.0369495
$125$	−4.24509	−0.379692
$126$	0	0
$127$	−12.8088	−1.13660	−0.568300	−	0.822821i	$-0.692399\pi$
$127$	−12.8088	−1.13660	−0.568300	+	0.822821i	$0.692399\pi$
$128$	1.00000	0.0883883
$129$	7.24221	0.637641
$130$	2.69443	0.236317
$131$	0.182242	0.0159226	0.00796129	−	0.999968i	$-0.497466\pi$
$131$	0.182242	0.0159226	0.00796129	+	0.999968i	$0.497466\pi$
$132$	−12.1047	−1.05358
$133$	0	0
$134$	−5.53641	−0.478273
$135$	1.58329	0.136268
$136$	3.78258	0.324353
$137$	22.3635	1.91064	0.955322	−	0.295566i	$-0.0955083\pi$
$137$	22.3635	1.91064	0.955322	+	0.295566i	$0.0955083\pi$
$138$	−1.73347	−0.147562
$139$	−4.52022	−0.383400	−0.191700	−	0.981454i	$-0.561400\pi$
$139$	−4.52022	−0.383400	−0.191700	+	0.981454i	$0.561400\pi$
$140$	0	0
$141$	32.1403	2.70670
$142$	−9.40984	−0.789656
$143$	−27.8092	−2.32552
$144$	4.34997	0.362498
$145$	1.67363	0.138987
$146$	−6.26918	−0.518841
$147$	0	0
$148$	7.45770	0.613020
$149$	1.27269	0.104263	0.0521314	−	0.998640i	$-0.483399\pi$
$149$	1.27269	0.104263	0.0521314	+	0.998640i	$0.483399\pi$
$150$	−13.0480	−1.06537
$151$	−4.40229	−0.358253	−0.179127	−	0.983826i	$-0.557327\pi$
$151$	−4.40229	−0.358253	−0.179127	+	0.983826i	$0.557327\pi$
$152$	−2.18592	−0.177302
$153$	16.4541	1.33024
$154$	0	0
$155$	−0.177996	−0.0142970
$156$	16.8857	1.35193
$157$	−23.5110	−1.87638	−0.938189	−	0.346123i	$-0.887498\pi$
$157$	−23.5110	−1.87638	−0.938189	+	0.346123i	$0.887498\pi$
$158$	−0.703406	−0.0559600
$159$	31.2210	2.47598
$160$	0.432605	0.0342004
$161$	0	0
$162$	−3.12765	−0.245731
$163$	15.5629	1.21898	0.609491	−	0.792793i	$-0.291374\pi$
$163$	15.5629	1.21898	0.609491	+	0.792793i	$0.291374\pi$
$164$	1.00000	0.0780869
$165$	−5.23657	−0.407667
$166$	−10.8852	−0.844854
$167$	−13.1662	−1.01883	−0.509414	−	0.860521i	$-0.670138\pi$
$167$	−13.1662	−1.01883	−0.509414	+	0.860521i	$0.670138\pi$
$168$	0	0
$169$	25.7927	1.98405
$170$	1.63636	0.125503
$171$	−9.50871	−0.727149
$172$	2.67133	0.203687
$173$	−13.4387	−1.02173	−0.510863	−	0.859662i	$-0.670674\pi$
$173$	−13.4387	−1.02173	−0.510863	+	0.859662i	$0.670674\pi$
$174$	10.4884	0.795127
$175$	0	0
$176$	−4.46491	−0.336555
$177$	−28.2761	−2.12536
$178$	−1.59618	−0.119639
$179$	−19.5256	−1.45941	−0.729705	−	0.683762i	$-0.760343\pi$
$179$	−19.5256	−1.45941	−0.729705	+	0.683762i	$0.760343\pi$
$180$	1.88182	0.140263
$181$	12.1688	0.904503	0.452251	−	0.891891i	$-0.350621\pi$
$181$	12.1688	0.904503	0.452251	+	0.891891i	$0.350621\pi$
$182$	0	0
$183$	29.6574	2.19234
$184$	−0.639400	−0.0471372
$185$	3.22624	0.237198
$186$	−1.11548	−0.0817910
$187$	−16.8889	−1.23504
$188$	11.8552	0.864627
$189$	0	0
$190$	−0.945641	−0.0686040
$191$	−11.6757	−0.844822	−0.422411	−	0.906404i	$-0.638816\pi$
$191$	−11.6757	−0.844822	−0.422411	+	0.906404i	$0.638816\pi$
$192$	2.71108	0.195656
$193$	9.46460	0.681277	0.340639	−	0.940194i	$-0.389357\pi$
$193$	9.46460	0.681277	0.340639	+	0.940194i	$0.389357\pi$
$194$	−15.6752	−1.12541
$195$	7.30482	0.523109
$196$	0	0
$197$	27.1676	1.93561	0.967805	−	0.251701i	$-0.0809899\pi$
$197$	27.1676	1.93561	0.967805	+	0.251701i	$0.0809899\pi$
$198$	−19.4222	−1.38028
$199$	−21.0478	−1.49204	−0.746020	−	0.665924i	$-0.768038\pi$
$199$	−21.0478	−1.49204	−0.746020	+	0.665924i	$0.768038\pi$
$200$	−4.81285	−0.340320
$201$	−15.0097	−1.05870
$202$	−0.215041	−0.0151303
$203$	0	0
$204$	10.2549	0.717986
$205$	0.432605	0.0302144
$206$	1.83039	0.127529
$207$	−2.78137	−0.193319
$208$	6.22838	0.431860
$209$	9.75995	0.675110
$210$	0	0
$211$	−22.4317	−1.54426	−0.772130	−	0.635465i	$-0.780808\pi$
$211$	−22.4317	−1.54426	−0.772130	+	0.635465i	$0.780808\pi$
$212$	11.5160	0.790925
$213$	−25.5109	−1.74798
$214$	−3.38165	−0.231165
$215$	1.15563	0.0788135
$216$	3.65989	0.249024
$217$	0	0
$218$	−11.7484	−0.795703
$219$	−16.9963	−1.14850
$220$	−1.93154	−0.130225
$221$	23.5593	1.58477
$222$	20.2185	1.35697
$223$	17.6934	1.18484	0.592419	−	0.805630i	$-0.298173\pi$
$223$	17.6934	1.18484	0.592419	+	0.805630i	$0.298173\pi$
$224$	0	0
$225$	−20.9358	−1.39572
$226$	10.9142	0.726003
$227$	−4.36249	−0.289549	−0.144774	−	0.989465i	$-0.546246\pi$
$227$	−4.36249	−0.289549	−0.144774	+	0.989465i	$0.546246\pi$
$228$	−5.92622	−0.392474
$229$	−12.7505	−0.842577	−0.421289	−	0.906927i	$-0.638422\pi$
$229$	−12.7505	−0.842577	−0.421289	+	0.906927i	$0.638422\pi$
$230$	−0.276607	−0.0182390
$231$	0	0
$232$	3.86873	0.253994
$233$	−2.29536	−0.150374	−0.0751871	−	0.997169i	$-0.523955\pi$
$233$	−2.29536	−0.150374	−0.0751871	+	0.997169i	$0.523955\pi$
$234$	27.0933	1.77114
$235$	5.12860	0.334553
$236$	−10.4298	−0.678923
$237$	−1.90699	−0.123872
$238$	0	0
$239$	−0.0315757	−0.00204246	−0.00102123	−	0.999999i	$-0.500325\pi$
$239$	−0.0315757	−0.00204246	−0.00102123	+	0.999999i	$0.500325\pi$
$240$	1.17283	0.0757057
$241$	−2.52792	−0.162838	−0.0814189	−	0.996680i	$-0.525945\pi$
$241$	−2.52792	−0.162838	−0.0814189	+	0.996680i	$0.525945\pi$
$242$	8.93543	0.574392
$243$	−19.4590	−1.24830
$244$	10.9393	0.700318
$245$	0	0
$246$	2.71108	0.172852
$247$	−13.6148	−0.866286
$248$	−0.411452	−0.0261272
$249$	−29.5107	−1.87016
$250$	−4.24509	−0.268483
$251$	20.0206	1.26369	0.631846	−	0.775094i	$-0.282298\pi$
$251$	20.0206	1.26369	0.631846	+	0.775094i	$0.282298\pi$
$252$	0	0
$253$	2.85486	0.179484
$254$	−12.8088	−0.803698
$255$	4.43631	0.277813
$256$	1.00000	0.0625000
$257$	1.66960	0.104147	0.0520733	−	0.998643i	$-0.483417\pi$
$257$	1.66960	0.104147	0.0520733	+	0.998643i	$0.483417\pi$
$258$	7.24221	0.450880
$259$	0	0
$260$	2.69443	0.167101
$261$	16.8289	1.04168
$262$	0.182242	0.0112590
$263$	17.9495	1.10681	0.553406	−	0.832912i	$-0.313328\pi$
$263$	17.9495	1.10681	0.553406	+	0.832912i	$0.313328\pi$
$264$	−12.1047	−0.744996
$265$	4.98190	0.306036
$266$	0	0
$267$	−4.32737	−0.264831
$268$	−5.53641	−0.338190
$269$	−0.00980080	−0.000597565 0	−0.000298783	−	1.00000i	$-0.500095\pi$
$269$	−0.00980080	−0.000597565 0	−0.000298783		1.00000i	$0.500095\pi$
$270$	1.58329	0.0963558
$271$	−20.6636	−1.25523	−0.627614	−	0.778525i	$-0.715968\pi$
$271$	−20.6636	−1.25523	−0.627614	+	0.778525i	$0.715968\pi$
$272$	3.78258	0.229353
$273$	0	0
$274$	22.3635	1.35103
$275$	21.4890	1.29583
$276$	−1.73347	−0.104342
$277$	−26.8349	−1.61235	−0.806176	−	0.591676i	$-0.798467\pi$
$277$	−26.8349	−1.61235	−0.806176	+	0.591676i	$0.798467\pi$
$278$	−4.52022	−0.271105
$279$	−1.78980	−0.107153
$280$	0	0
$281$	12.3726	0.738090	0.369045	−	0.929412i	$-0.379685\pi$
$281$	12.3726	0.738090	0.369045	+	0.929412i	$0.379685\pi$
$282$	32.1403	1.91393
$283$	−12.8737	−0.765260	−0.382630	−	0.923902i	$-0.624982\pi$
$283$	−12.8737	−0.765260	−0.382630	+	0.923902i	$0.624982\pi$
$284$	−9.40984	−0.558371
$285$	−2.56371	−0.151861
$286$	−27.8092	−1.64439
$287$	0	0
$288$	4.34997	0.256325
$289$	−2.69210	−0.158359
$290$	1.67363	0.0982789
$291$	−42.4968	−2.49121
$292$	−6.26918	−0.366876
$293$	−12.8345	−0.749801	−0.374901	−	0.927065i	$-0.622323\pi$
$293$	−12.8345	−0.749801	−0.374901	+	0.927065i	$0.622323\pi$
$294$	0	0
$295$	−4.51199	−0.262698
$296$	7.45770	0.433470
$297$	−16.3411	−0.948206
$298$	1.27269	0.0737249
$299$	−3.98242	−0.230309
$300$	−13.0480	−0.753329
$301$	0	0
$302$	−4.40229	−0.253323
$303$	−0.582995	−0.0334922
$304$	−2.18592	−0.125371
$305$	4.73240	0.270977
$306$	16.4541	0.940619
$307$	−23.4010	−1.33556	−0.667782	−	0.744357i	$-0.732756\pi$
$307$	−23.4010	−1.33556	−0.667782	+	0.744357i	$0.732756\pi$
$308$	0	0
$309$	4.96235	0.282298
$310$	−0.177996	−0.0101095
$311$	7.18058	0.407174	0.203587	−	0.979057i	$-0.434740\pi$
$311$	7.18058	0.407174	0.203587	+	0.979057i	$0.434740\pi$
$312$	16.8857	0.955962
$313$	19.0891	1.07898	0.539491	−	0.841992i	$-0.318617\pi$
$313$	19.0891	1.07898	0.539491	+	0.841992i	$0.318617\pi$
$314$	−23.5110	−1.32680
$315$	0	0
$316$	−0.703406	−0.0395697
$317$	−0.713584	−0.0400789	−0.0200394	−	0.999799i	$-0.506379\pi$
$317$	−0.713584	−0.0400789	−0.0200394	+	0.999799i	$0.506379\pi$
$318$	31.2210	1.75078
$319$	−17.2735	−0.967132
$320$	0.432605	0.0241834
$321$	−9.16793	−0.511704
$322$	0	0
$323$	−8.26843	−0.460068
$324$	−3.12765	−0.173758
$325$	−29.9763	−1.66278
$326$	15.5629	0.861951
$327$	−31.8509	−1.76136
$328$	1.00000	0.0552158
$329$	0	0
$330$	−5.23657	−0.288264
$331$	18.0121	0.990035	0.495018	−	0.868883i	$-0.335162\pi$
$331$	18.0121	0.990035	0.495018	+	0.868883i	$0.335162\pi$
$332$	−10.8852	−0.597402
$333$	32.4408	1.77775
$334$	−13.1662	−0.720421
$335$	−2.39508	−0.130857
$336$	0	0
$337$	6.12270	0.333525	0.166762	−	0.985997i	$-0.446669\pi$
$337$	6.12270	0.333525	0.166762	+	0.985997i	$0.446669\pi$
$338$	25.7927	1.40294
$339$	29.5894	1.60707
$340$	1.63636	0.0887442
$341$	1.83710	0.0994843
$342$	−9.50871	−0.514172
$343$	0	0
$344$	2.67133	0.144029
$345$	−0.749906	−0.0403736
$346$	−13.4387	−0.722469
$347$	9.46217	0.507956	0.253978	−	0.967210i	$-0.418261\pi$
$347$	9.46217	0.507956	0.253978	+	0.967210i	$0.418261\pi$
$348$	10.4884	0.562239
$349$	8.24410	0.441297	0.220648	−	0.975353i	$-0.429183\pi$
$349$	8.24410	0.441297	0.220648	+	0.975353i	$0.429183\pi$
$350$	0	0
$351$	22.7952	1.21672
$352$	−4.46491	−0.237981
$353$	−21.9621	−1.16892	−0.584462	−	0.811421i	$-0.698695\pi$
$353$	−21.9621	−1.16892	−0.584462	+	0.811421i	$0.698695\pi$
$354$	−28.2761	−1.50286
$355$	−4.07074	−0.216053
$356$	−1.59618	−0.0845972
$357$	0	0
$358$	−19.5256	−1.03196
$359$	15.2090	0.802699	0.401349	−	0.915925i	$-0.368541\pi$
$359$	15.2090	0.802699	0.401349	+	0.915925i	$0.368541\pi$
$360$	1.88182	0.0991806
$361$	−14.2217	−0.748513
$362$	12.1688	0.639580
$363$	24.2247	1.27147
$364$	0	0
$365$	−2.71208	−0.141957
$366$	29.6574	1.55022
$367$	15.0798	0.787159	0.393579	−	0.919291i	$-0.371237\pi$
$367$	15.0798	0.787159	0.393579	+	0.919291i	$0.371237\pi$
$368$	−0.639400	−0.0333310
$369$	4.34997	0.226451
$370$	3.22624	0.167724
$371$	0	0
$372$	−1.11548	−0.0578350
$373$	10.2695	0.531733	0.265867	−	0.964010i	$-0.414342\pi$
$373$	10.2695	0.531733	0.265867	+	0.964010i	$0.414342\pi$
$374$	−16.8889	−0.873303
$375$	−11.5088	−0.594311
$376$	11.8552	0.611383
$377$	24.0959	1.24100
$378$	0	0
$379$	15.2591	0.783810	0.391905	−	0.920006i	$-0.371816\pi$
$379$	15.2591	0.783810	0.391905	+	0.920006i	$0.371816\pi$
$380$	−0.945641	−0.0485104
$381$	−34.7258	−1.77906
$382$	−11.6757	−0.597379
$383$	11.7125	0.598482	0.299241	−	0.954178i	$-0.403266\pi$
$383$	11.7125	0.598482	0.299241	+	0.954178i	$0.403266\pi$
$384$	2.71108	0.138349
$385$	0	0
$386$	9.46460	0.481736
$387$	11.6202	0.590690
$388$	−15.6752	−0.795788
$389$	13.1032	0.664357	0.332179	−	0.943216i	$-0.392216\pi$
$389$	13.1032	0.664357	0.332179	+	0.943216i	$0.392216\pi$
$390$	7.30482	0.369894
$391$	−2.41858	−0.122313
$392$	0	0
$393$	0.494074	0.0249227
$394$	27.1676	1.36868
$395$	−0.304297	−0.0153108
$396$	−19.4222	−0.976005
$397$	−27.2224	−1.36625	−0.683126	−	0.730300i	$-0.739380\pi$
$397$	−27.2224	−1.36625	−0.683126	+	0.730300i	$0.739380\pi$
$398$	−21.0478	−1.05503
$399$	0	0
$400$	−4.81285	−0.240643
$401$	−5.73076	−0.286181	−0.143090	−	0.989710i	$-0.545704\pi$
$401$	−5.73076	−0.286181	−0.143090	+	0.989710i	$0.545704\pi$
$402$	−15.0097	−0.748614
$403$	−2.56268	−0.127656
$404$	−0.215041	−0.0106987
$405$	−1.35304	−0.0672330
$406$	0	0
$407$	−33.2980	−1.65052
$408$	10.2549	0.507693
$409$	0.572141	0.0282905	0.0141453	−	0.999900i	$-0.495497\pi$
$409$	0.572141	0.0282905	0.0141453	+	0.999900i	$0.495497\pi$
$410$	0.432605	0.0213648
$411$	60.6294	2.99063
$412$	1.83039	0.0901770
$413$	0	0
$414$	−2.78137	−0.136697
$415$	−4.70899	−0.231155
$416$	6.22838	0.305371
$417$	−12.2547	−0.600115
$418$	9.75995	0.477375
$419$	34.3458	1.67790	0.838951	−	0.544208i	$-0.183170\pi$
$419$	34.3458	1.67790	0.838951	+	0.544208i	$0.183170\pi$
$420$	0	0
$421$	−20.9602	−1.02154	−0.510768	−	0.859719i	$-0.670639\pi$
$421$	−20.9602	−1.02154	−0.510768	+	0.859719i	$0.670639\pi$
$422$	−22.4317	−1.09196
$423$	51.5696	2.50740
$424$	11.5160	0.559269
$425$	−18.2050	−0.883072
$426$	−25.5109	−1.23601
$427$	0	0
$428$	−3.38165	−0.163458
$429$	−75.3929	−3.64001
$430$	1.15563	0.0557295
$431$	−20.8479	−1.00421	−0.502104	−	0.864807i	$-0.667440\pi$
$431$	−20.8479	−1.00421	−0.502104	+	0.864807i	$0.667440\pi$
$432$	3.65989	0.176087
$433$	17.6824	0.849762	0.424881	−	0.905249i	$-0.360316\pi$
$433$	17.6824	0.849762	0.424881	+	0.905249i	$0.360316\pi$
$434$	0	0
$435$	4.53735	0.217549
$436$	−11.7484	−0.562647
$437$	1.39768	0.0668600
$438$	−16.9963	−0.812113
$439$	35.8181	1.70951	0.854753	−	0.519035i	$-0.173709\pi$
$439$	35.8181	1.70951	0.854753	+	0.519035i	$0.173709\pi$
$440$	−1.93154	−0.0920827
$441$	0	0
$442$	23.5593	1.12060
$443$	−21.6372	−1.02802	−0.514008	−	0.857786i	$-0.671840\pi$
$443$	−21.6372	−1.02802	−0.514008	+	0.857786i	$0.671840\pi$
$444$	20.2185	0.959526
$445$	−0.690514	−0.0327335
$446$	17.6934	0.837807
$447$	3.45037	0.163197
$448$	0	0
$449$	21.3140	1.00587	0.502935	−	0.864324i	$-0.332253\pi$
$449$	21.3140	1.00587	0.502935	+	0.864324i	$0.332253\pi$
$450$	−20.9358	−0.986922
$451$	−4.46491	−0.210244
$452$	10.9142	0.513362
$453$	−11.9350	−0.560754
$454$	−4.36249	−0.204742
$455$	0	0
$456$	−5.92622	−0.277521
$457$	−39.7713	−1.86042	−0.930210	−	0.367027i	$-0.880376\pi$
$457$	−39.7713	−1.86042	−0.930210	+	0.367027i	$0.880376\pi$
$458$	−12.7505	−0.595792
$459$	13.8438	0.646174
$460$	−0.276607	−0.0128969
$461$	−36.3299	−1.69205	−0.846026	−	0.533142i	$-0.821011\pi$
$461$	−36.3299	−1.69205	−0.846026	+	0.533142i	$0.821011\pi$
$462$	0	0
$463$	−26.2255	−1.21880	−0.609400	−	0.792863i	$-0.708590\pi$
$463$	−26.2255	−1.21880	−0.609400	+	0.792863i	$0.708590\pi$
$464$	3.86873	0.179601
$465$	−0.482562	−0.0223783
$466$	−2.29536	−0.106331
$467$	36.9752	1.71101	0.855504	−	0.517796i	$-0.173247\pi$
$467$	36.9752	1.71101	0.855504	+	0.517796i	$0.173247\pi$
$468$	27.0933	1.25239
$469$	0	0
$470$	5.12860	0.236565
$471$	−63.7402	−2.93699
$472$	−10.4298	−0.480071
$473$	−11.9273	−0.548417
$474$	−1.90699	−0.0875911
$475$	10.5205	0.482715
$476$	0	0
$477$	50.0945	2.29367
$478$	−0.0315757	−0.00144424
$479$	18.8993	0.863529	0.431764	−	0.901986i	$-0.357891\pi$
$479$	18.8993	0.863529	0.431764	+	0.901986i	$0.357891\pi$
$480$	1.17283	0.0535320
$481$	46.4494	2.11791
$482$	−2.52792	−0.115144
$483$	0	0
$484$	8.93543	0.406156
$485$	−6.78117	−0.307917
$486$	−19.4590	−0.882678
$487$	−4.29089	−0.194439	−0.0972193	−	0.995263i	$-0.530995\pi$
$487$	−4.29089	−0.194439	−0.0972193	+	0.995263i	$0.530995\pi$
$488$	10.9393	0.495200
$489$	42.1924	1.90801
$490$	0	0
$491$	22.3383	1.00811	0.504056	−	0.863671i	$-0.331840\pi$
$491$	22.3383	1.00811	0.504056	+	0.863671i	$0.331840\pi$
$492$	2.71108	0.122225
$493$	14.6338	0.659071
$494$	−13.6148	−0.612557
$495$	−8.40216	−0.377649
$496$	−0.411452	−0.0184747
$497$	0	0
$498$	−29.5107	−1.32240
$499$	32.3208	1.44688	0.723438	−	0.690389i	$-0.242561\pi$
$499$	32.3208	1.44688	0.723438	+	0.690389i	$0.242561\pi$
$500$	−4.24509	−0.189846
$501$	−35.6946	−1.59472
$502$	20.0206	0.893565
$503$	2.57125	0.114646	0.0573232	−	0.998356i	$-0.481743\pi$
$503$	2.57125	0.114646	0.0573232	+	0.998356i	$0.481743\pi$
$504$	0	0
$505$	−0.0930280	−0.00413969
$506$	2.85486	0.126914
$507$	69.9261	3.10553
$508$	−12.8088	−0.568300
$509$	−34.4699	−1.52785	−0.763926	−	0.645304i	$-0.776731\pi$
$509$	−34.4699	−1.52785	−0.763926	+	0.645304i	$0.776731\pi$
$510$	4.43631	0.196443
$511$	0	0
$512$	1.00000	0.0441942
$513$	−8.00024	−0.353219
$514$	1.66960	0.0736428
$515$	0.791837	0.0348925
$516$	7.24221	0.318821
$517$	−52.9322	−2.32796
$518$	0	0
$519$	−36.4334	−1.59925
$520$	2.69443	0.118158
$521$	−29.0569	−1.27301	−0.636504	−	0.771274i	$-0.719620\pi$
$521$	−29.0569	−1.27301	−0.636504	+	0.771274i	$0.719620\pi$
$522$	16.8289	0.736579
$523$	−15.5368	−0.679375	−0.339688	−	0.940538i	$-0.610321\pi$
$523$	−15.5368	−0.679375	−0.339688	+	0.940538i	$0.610321\pi$
$524$	0.182242	0.00796129
$525$	0	0
$526$	17.9495	0.782634
$527$	−1.55635	−0.0677956
$528$	−12.1047	−0.526792
$529$	−22.5912	−0.982225
$530$	4.98190	0.216400
$531$	−45.3694	−1.96886
$532$	0	0
$533$	6.22838	0.269781
$534$	−4.32737	−0.187264
$535$	−1.46292	−0.0632474
$536$	−5.53641	−0.239136
$537$	−52.9355	−2.28433
$538$	−0.00980080	−0.000422542 0
$539$	0	0
$540$	1.58329	0.0681338
$541$	33.4773	1.43930	0.719652	−	0.694335i	$-0.244301\pi$
$541$	33.4773	1.43930	0.719652	+	0.694335i	$0.244301\pi$
$542$	−20.6636	−0.887580
$543$	32.9907	1.41577
$544$	3.78258	0.162177
$545$	−5.08242	−0.217707
$546$	0	0
$547$	−25.1799	−1.07662	−0.538308	−	0.842748i	$-0.680936\pi$
$547$	−25.1799	−1.07662	−0.538308	+	0.842748i	$0.680936\pi$
$548$	22.3635	0.955322
$549$	47.5857	2.03091
$550$	21.4890	0.916292
$551$	−8.45674	−0.360269
$552$	−1.73347	−0.0737812
$553$	0	0
$554$	−26.8349	−1.14011
$555$	8.74660	0.371273
$556$	−4.52022	−0.191700
$557$	−20.0159	−0.848101	−0.424051	−	0.905638i	$-0.639392\pi$
$557$	−20.0159	−0.848101	−0.424051	+	0.905638i	$0.639392\pi$
$558$	−1.78980	−0.0757685
$559$	16.6381	0.703716
$560$	0	0
$561$	−45.7872	−1.93314
$562$	12.3726	0.521908
$563$	37.8795	1.59643	0.798216	−	0.602372i	$-0.205778\pi$
$563$	37.8795	1.59643	0.798216	+	0.602372i	$0.205778\pi$
$564$	32.1403	1.35335
$565$	4.72154	0.198637
$566$	−12.8737	−0.541120
$567$	0	0
$568$	−9.40984	−0.394828
$569$	18.7751	0.787092	0.393546	−	0.919305i	$-0.371248\pi$
$569$	18.7751	0.787092	0.393546	+	0.919305i	$0.371248\pi$
$570$	−2.56371	−0.107382
$571$	35.3809	1.48065	0.740323	−	0.672251i	$-0.234672\pi$
$571$	35.3809	1.48065	0.740323	+	0.672251i	$0.234672\pi$
$572$	−27.8092	−1.16276
$573$	−31.6537	−1.32235
$574$	0	0
$575$	3.07734	0.128334
$576$	4.34997	0.181249
$577$	−17.0906	−0.711492	−0.355746	−	0.934583i	$-0.615773\pi$
$577$	−17.0906	−0.711492	−0.355746	+	0.934583i	$0.615773\pi$
$578$	−2.69210	−0.111977
$579$	25.6593	1.06637
$580$	1.67363	0.0694937
$581$	0	0
$582$	−42.4968	−1.76155
$583$	−51.4181	−2.12952
$584$	−6.26918	−0.259421
$585$	11.7207	0.484591
$586$	−12.8345	−0.530189
$587$	−27.0670	−1.11717	−0.558587	−	0.829446i	$-0.688656\pi$
$587$	−27.0670	−1.11717	−0.558587	+	0.829446i	$0.688656\pi$
$588$	0	0
$589$	0.899402	0.0370592
$590$	−4.51199	−0.185756
$591$	73.6536	3.02970
$592$	7.45770	0.306510
$593$	−1.60013	−0.0657095	−0.0328548	−	0.999460i	$-0.510460\pi$
$593$	−1.60013	−0.0657095	−0.0328548	+	0.999460i	$0.510460\pi$
$594$	−16.3411	−0.670483
$595$	0	0
$596$	1.27269	0.0521314
$597$	−57.0624	−2.33541
$598$	−3.98242	−0.162853
$599$	−7.91830	−0.323533	−0.161767	−	0.986829i	$-0.551719\pi$
$599$	−7.91830	−0.323533	−0.161767	+	0.986829i	$0.551719\pi$
$600$	−13.0480	−0.532684
$601$	20.1626	0.822449	0.411225	−	0.911534i	$-0.365101\pi$
$601$	20.1626	0.822449	0.411225	+	0.911534i	$0.365101\pi$
$602$	0	0
$603$	−24.0832	−0.980745
$604$	−4.40229	−0.179127
$605$	3.86551	0.157155
$606$	−0.582995	−0.0236826
$607$	19.2752	0.782356	0.391178	−	0.920315i	$-0.372068\pi$
$607$	19.2752	0.782356	0.391178	+	0.920315i	$0.372068\pi$
$608$	−2.18592	−0.0886509
$609$	0	0
$610$	4.73240	0.191609
$611$	73.8384	2.98718
$612$	16.4541	0.665118
$613$	−30.4096	−1.22823	−0.614115	−	0.789216i	$-0.710487\pi$
$613$	−30.4096	−1.22823	−0.614115	+	0.789216i	$0.710487\pi$
$614$	−23.4010	−0.944386
$615$	1.17283	0.0472930
$616$	0	0
$617$	−14.3424	−0.577405	−0.288702	−	0.957419i	$-0.593224\pi$
$617$	−14.3424	−0.577405	−0.288702	+	0.957419i	$0.593224\pi$
$618$	4.96235	0.199615
$619$	−38.6625	−1.55398	−0.776989	−	0.629515i	$-0.783254\pi$
$619$	−38.6625	−1.55398	−0.776989	+	0.629515i	$0.783254\pi$
$620$	−0.177996	−0.00714850
$621$	−2.34013	−0.0939063
$622$	7.18058	0.287915
$623$	0	0
$624$	16.8857	0.675967
$625$	22.2278	0.889113
$626$	19.0891	0.762955
$627$	26.4600	1.05671
$628$	−23.5110	−0.938189
$629$	28.2094	1.12478
$630$	0	0
$631$	−19.9520	−0.794278	−0.397139	−	0.917759i	$-0.629997\pi$
$631$	−19.9520	−0.794278	−0.397139	+	0.917759i	$0.629997\pi$
$632$	−0.703406	−0.0279800
$633$	−60.8141	−2.41714
$634$	−0.713584	−0.0283400
$635$	−5.54117	−0.219895
$636$	31.2210	1.23799
$637$	0	0
$638$	−17.2735	−0.683865
$639$	−40.9326	−1.61927
$640$	0.432605	0.0171002
$641$	−4.67522	−0.184660	−0.0923301	−	0.995728i	$-0.529431\pi$
$641$	−4.67522	−0.184660	−0.0923301	+	0.995728i	$0.529431\pi$
$642$	−9.16793	−0.361829
$643$	7.54167	0.297414	0.148707	−	0.988881i	$-0.452489\pi$
$643$	7.54167	0.297414	0.148707	+	0.988881i	$0.452489\pi$
$644$	0	0
$645$	3.13302	0.123362
$646$	−8.26843	−0.325317
$647$	−11.8846	−0.467231	−0.233616	−	0.972329i	$-0.575056\pi$
$647$	−11.8846	−0.467231	−0.233616	+	0.972329i	$0.575056\pi$
$648$	−3.12765	−0.122866
$649$	46.5682	1.82796
$650$	−29.9763	−1.17577
$651$	0	0
$652$	15.5629	0.609491
$653$	2.87055	0.112333	0.0561666	−	0.998421i	$-0.482112\pi$
$653$	2.87055	0.112333	0.0561666	+	0.998421i	$0.482112\pi$
$654$	−31.8509	−1.24547
$655$	0.0788389	0.00308049
$656$	1.00000	0.0390434
$657$	−27.2708	−1.06393
$658$	0	0
$659$	−35.2499	−1.37314	−0.686570	−	0.727064i	$-0.740884\pi$
$659$	−35.2499	−1.37314	−0.686570	+	0.727064i	$0.740884\pi$
$660$	−5.23657	−0.203833
$661$	31.0531	1.20782	0.603912	−	0.797051i	$-0.293608\pi$
$661$	31.0531	1.20782	0.603912	+	0.797051i	$0.293608\pi$
$662$	18.0121	0.700061
$663$	63.8713	2.48056
$664$	−10.8852	−0.422427
$665$	0	0
$666$	32.4408	1.25706
$667$	−2.47366	−0.0957806
$668$	−13.1662	−0.509414
$669$	47.9683	1.85456
$670$	−2.39508	−0.0925299
$671$	−48.8431	−1.88557
$672$	0	0
$673$	0.0605684	0.00233474	0.00116737	−	0.999999i	$-0.499628\pi$
$673$	0.0605684	0.00233474	0.00116737	+	0.999999i	$0.499628\pi$
$674$	6.12270	0.235838
$675$	−17.6145	−0.677983
$676$	25.7927	0.992026
$677$	−6.45732	−0.248175	−0.124088	−	0.992271i	$-0.539600\pi$
$677$	−6.45732	−0.248175	−0.124088	+	0.992271i	$0.539600\pi$
$678$	29.5894	1.13637
$679$	0	0
$680$	1.63636	0.0627516
$681$	−11.8271	−0.453215
$682$	1.83710	0.0703461
$683$	35.7058	1.36624	0.683121	−	0.730305i	$-0.260622\pi$
$683$	35.7058	1.36624	0.683121	+	0.730305i	$0.260622\pi$
$684$	−9.50871	−0.363575
$685$	9.67457	0.369646
$686$	0	0
$687$	−34.5677	−1.31884
$688$	2.67133	0.101844
$689$	71.7263	2.73255
$690$	−0.749906	−0.0285484
$691$	−9.25593	−0.352112	−0.176056	−	0.984380i	$-0.556334\pi$
$691$	−9.25593	−0.352112	−0.176056	+	0.984380i	$0.556334\pi$
$692$	−13.4387	−0.510863
$693$	0	0
$694$	9.46217	0.359179
$695$	−1.95547	−0.0741752
$696$	10.4884	0.397563
$697$	3.78258	0.143275
$698$	8.24410	0.312044
$699$	−6.22292	−0.235373
$700$	0	0
$701$	42.4460	1.60316	0.801582	−	0.597884i	$-0.203992\pi$
$701$	42.4460	1.60316	0.801582	+	0.597884i	$0.203992\pi$
$702$	22.7952	0.860349
$703$	−16.3020	−0.614840
$704$	−4.46491	−0.168278
$705$	13.9041	0.523657
$706$	−21.9621	−0.826555
$707$	0	0
$708$	−28.2761	−1.06268
$709$	−3.43774	−0.129107	−0.0645535	−	0.997914i	$-0.520562\pi$
$709$	−3.43774	−0.129107	−0.0645535	+	0.997914i	$0.520562\pi$
$710$	−4.07074	−0.152772
$711$	−3.05980	−0.114751
$712$	−1.59618	−0.0598193
$713$	0.263082	0.00985251
$714$	0	0
$715$	−12.0304	−0.449911
$716$	−19.5256	−0.729705
$717$	−0.0856043	−0.00319695
$718$	15.2090	0.567594
$719$	2.19109	0.0817138	0.0408569	−	0.999165i	$-0.486991\pi$
$719$	2.19109	0.0817138	0.0408569	+	0.999165i	$0.486991\pi$
$720$	1.88182	0.0701313
$721$	0	0
$722$	−14.2217	−0.529278
$723$	−6.85341	−0.254881
$724$	12.1688	0.452251
$725$	−18.6196	−0.691515
$726$	24.2247	0.899063
$727$	30.5344	1.13246	0.566230	−	0.824247i	$-0.308401\pi$
$727$	30.5344	1.13246	0.566230	+	0.824247i	$0.308401\pi$
$728$	0	0
$729$	−43.3720	−1.60637
$730$	−2.71208	−0.100379
$731$	10.1045	0.373730
$732$	29.6574	1.09617
$733$	−41.4480	−1.53092	−0.765459	−	0.643485i	$-0.777488\pi$
$733$	−41.4480	−1.53092	−0.765459	+	0.643485i	$0.777488\pi$
$734$	15.0798	0.556605
$735$	0	0
$736$	−0.639400	−0.0235686
$737$	24.7196	0.910557
$738$	4.34997	0.160125
$739$	19.3397	0.711422	0.355711	−	0.934596i	$-0.384239\pi$
$739$	19.3397	0.711422	0.355711	+	0.934596i	$0.384239\pi$
$740$	3.22624	0.118599
$741$	−36.9107	−1.35595
$742$	0	0
$743$	−4.77787	−0.175283	−0.0876415	−	0.996152i	$-0.527933\pi$
$743$	−4.77787	−0.175283	−0.0876415	+	0.996152i	$0.527933\pi$
$744$	−1.11548	−0.0408955
$745$	0.550572	0.0201714
$746$	10.2695	0.375992
$747$	−47.3503	−1.73246
$748$	−16.8889	−0.617519
$749$	0	0
$750$	−11.5088	−0.420242
$751$	9.24125	0.337218	0.168609	−	0.985683i	$-0.446073\pi$
$751$	9.24125	0.337218	0.168609	+	0.985683i	$0.446073\pi$
$752$	11.8552	0.432313
$753$	54.2776	1.97799
$754$	24.0959	0.877521
$755$	−1.90445	−0.0693101
$756$	0	0
$757$	43.3591	1.57591	0.787956	−	0.615732i	$-0.211139\pi$
$757$	43.3591	1.57591	0.787956	+	0.615732i	$0.211139\pi$
$758$	15.2591	0.554237
$759$	7.73977	0.280936
$760$	−0.945641	−0.0343020
$761$	4.79444	0.173798	0.0868991	−	0.996217i	$-0.472304\pi$
$761$	4.79444	0.173798	0.0868991	+	0.996217i	$0.472304\pi$
$762$	−34.7258	−1.25798
$763$	0	0
$764$	−11.6757	−0.422411
$765$	7.11813	0.257357
$766$	11.7125	0.423191
$767$	−64.9608	−2.34560
$768$	2.71108	0.0978278
$769$	37.9248	1.36760	0.683801	−	0.729669i	$-0.260326\pi$
$769$	37.9248	1.36760	0.683801	+	0.729669i	$0.260326\pi$
$770$	0	0
$771$	4.52642	0.163015
$772$	9.46460	0.340639
$773$	38.0012	1.36681	0.683405	−	0.730040i	$-0.260498\pi$
$773$	38.0012	1.36681	0.683405	+	0.730040i	$0.260498\pi$
$774$	11.6202	0.417681
$775$	1.98026	0.0711329
$776$	−15.6752	−0.562707
$777$	0	0
$778$	13.1032	0.469772
$779$	−2.18592	−0.0783188
$780$	7.30482	0.261554
$781$	42.0141	1.50338
$782$	−2.41858	−0.0864882
$783$	14.1591	0.506006
$784$	0	0
$785$	−10.1710	−0.363017
$786$	0.494074	0.0176230
$787$	−11.0635	−0.394370	−0.197185	−	0.980366i	$-0.563180\pi$
$787$	−11.0635	−0.394370	−0.197185	+	0.980366i	$0.563180\pi$
$788$	27.1676	0.967805
$789$	48.6625	1.73243
$790$	−0.304297	−0.0108264
$791$	0	0
$792$	−19.4222	−0.690139
$793$	68.1342	2.41952
$794$	−27.2224	−0.966086
$795$	13.5063	0.479021
$796$	−21.0478	−0.746020
$797$	−5.91737	−0.209604	−0.104802	−	0.994493i	$-0.533421\pi$
$797$	−5.91737	−0.209604	−0.104802	+	0.994493i	$0.533421\pi$
$798$	0	0
$799$	44.8431	1.58643
$800$	−4.81285	−0.170160
$801$	−6.94333	−0.245330
$802$	−5.73076	−0.202360
$803$	27.9913	0.987793
$804$	−15.0097	−0.529350
$805$	0	0
$806$	−2.56268	−0.0902665
$807$	−0.0265708	−0.000935336 0
$808$	−0.215041	−0.00756513
$809$	−27.3012	−0.959858	−0.479929	−	0.877307i	$-0.659338\pi$
$809$	−27.3012	−0.959858	−0.479929	+	0.877307i	$0.659338\pi$
$810$	−1.35304	−0.0475409
$811$	21.5991	0.758448	0.379224	−	0.925305i	$-0.376191\pi$
$811$	21.5991	0.758448	0.379224	+	0.925305i	$0.376191\pi$
$812$	0	0
$813$	−56.0209	−1.96474
$814$	−33.2980	−1.16709
$815$	6.73260	0.235833
$816$	10.2549	0.358993
$817$	−5.83933	−0.204292
$818$	0.572141	0.0200044
$819$	0	0
$820$	0.432605	0.0151072
$821$	−4.15647	−0.145062	−0.0725309	−	0.997366i	$-0.523108\pi$
$821$	−4.15647	−0.145062	−0.0725309	+	0.997366i	$0.523108\pi$
$822$	60.6294	2.11469
$823$	21.6022	0.753005	0.376502	−	0.926416i	$-0.377127\pi$
$823$	21.6022	0.753005	0.376502	+	0.926416i	$0.377127\pi$
$824$	1.83039	0.0637647
$825$	58.2584	2.02830
$826$	0	0
$827$	−23.3536	−0.812086	−0.406043	−	0.913854i	$-0.633092\pi$
$827$	−23.3536	−0.812086	−0.406043	+	0.913854i	$0.633092\pi$
$828$	−2.78137	−0.0966594
$829$	32.3236	1.12264	0.561322	−	0.827597i	$-0.310293\pi$
$829$	32.3236	1.12264	0.561322	+	0.827597i	$0.310293\pi$
$830$	−4.70899	−0.163451
$831$	−72.7516	−2.52373
$832$	6.22838	0.215930
$833$	0	0
$834$	−12.2547	−0.424345
$835$	−5.69575	−0.197110
$836$	9.75995	0.337555
$837$	−1.50587	−0.0520504
$838$	34.3458	1.18646
$839$	43.7298	1.50972	0.754861	−	0.655885i	$-0.227704\pi$
$839$	43.7298	1.50972	0.754861	+	0.655885i	$0.227704\pi$
$840$	0	0
$841$	−14.0330	−0.483895
$842$	−20.9602	−0.722335
$843$	33.5433	1.15529
$844$	−22.4317	−0.772130
$845$	11.1580	0.383848
$846$	51.5696	1.77300
$847$	0	0
$848$	11.5160	0.395463
$849$	−34.9016	−1.19782
$850$	−18.2050	−0.624426
$851$	−4.76845	−0.163461
$852$	−25.5109	−0.873988
$853$	25.4770	0.872316	0.436158	−	0.899870i	$-0.356339\pi$
$853$	25.4770	0.872316	0.436158	+	0.899870i	$0.356339\pi$
$854$	0	0
$855$	−4.11351	−0.140679
$856$	−3.38165	−0.115582
$857$	−26.7072	−0.912299	−0.456150	−	0.889903i	$-0.650772\pi$
$857$	−26.7072	−0.912299	−0.456150	+	0.889903i	$0.650772\pi$
$858$	−75.3929	−2.57387
$859$	−12.7019	−0.433385	−0.216692	−	0.976240i	$-0.569527\pi$
$859$	−12.7019	−0.433385	−0.216692	+	0.976240i	$0.569527\pi$
$860$	1.15563	0.0394067
$861$	0	0
$862$	−20.8479	−0.710082
$863$	16.4689	0.560609	0.280305	−	0.959911i	$-0.409565\pi$
$863$	16.4689	0.560609	0.280305	+	0.959911i	$0.409565\pi$
$864$	3.65989	0.124512
$865$	−5.81365	−0.197670
$866$	17.6824	0.600873
$867$	−7.29851	−0.247870
$868$	0	0
$869$	3.14065	0.106539
$870$	4.53735	0.153831
$871$	−34.4828	−1.16841
$872$	−11.7484	−0.397851
$873$	−68.1867	−2.30777
$874$	1.39768	0.0472772
$875$	0	0
$876$	−16.9963	−0.574251
$877$	−12.3777	−0.417966	−0.208983	−	0.977919i	$-0.567015\pi$
$877$	−12.3777	−0.417966	−0.208983	+	0.977919i	$0.567015\pi$
$878$	35.8181	1.20880
$879$	−34.7955	−1.17362
$880$	−1.93154	−0.0651123
$881$	−11.0114	−0.370982	−0.185491	−	0.982646i	$-0.559388\pi$
$881$	−11.0114	−0.370982	−0.185491	+	0.982646i	$0.559388\pi$
$882$	0	0
$883$	−6.03453	−0.203078	−0.101539	−	0.994832i	$-0.532377\pi$
$883$	−6.03453	−0.203078	−0.101539	+	0.994832i	$0.532377\pi$
$884$	23.5593	0.792386
$885$	−12.2324	−0.411187
$886$	−21.6372	−0.726917
$887$	−50.4579	−1.69421	−0.847106	−	0.531425i	$-0.821657\pi$
$887$	−50.4579	−1.69421	−0.847106	+	0.531425i	$0.821657\pi$
$888$	20.2185	0.678487
$889$	0	0
$890$	−0.690514	−0.0231461
$891$	13.9647	0.467835
$892$	17.6934	0.592419
$893$	−25.9145	−0.867195
$894$	3.45037	0.115398
$895$	−8.44686	−0.282347
$896$	0	0
$897$	−10.7967	−0.360491
$898$	21.3140	0.711258
$899$	−1.59179	−0.0530893
$900$	−20.9358	−0.697859
$901$	43.5603	1.45121
$902$	−4.46491	−0.148665
$903$	0	0
$904$	10.9142	0.363001
$905$	5.26430	0.174991
$906$	−11.9350	−0.396513
$907$	27.7605	0.921773	0.460886	−	0.887459i	$-0.347532\pi$
$907$	27.7605	0.921773	0.460886	+	0.887459i	$0.347532\pi$
$908$	−4.36249	−0.144774
$909$	−0.935424	−0.0310261
$910$	0	0
$911$	3.53758	0.117205	0.0586026	−	0.998281i	$-0.481336\pi$
$911$	3.53758	0.117205	0.0586026	+	0.998281i	$0.481336\pi$
$912$	−5.92622	−0.196237
$913$	48.6014	1.60847
$914$	−39.7713	−1.31552
$915$	12.8299	0.424145
$916$	−12.7505	−0.421289
$917$	0	0
$918$	13.8438	0.456914
$919$	−5.03510	−0.166093	−0.0830464	−	0.996546i	$-0.526465\pi$
$919$	−5.03510	−0.166093	−0.0830464	+	0.996546i	$0.526465\pi$
$920$	−0.276607	−0.00911948
$921$	−63.4420	−2.09048
$922$	−36.3299	−1.19646
$923$	−58.6080	−1.92911
$924$	0	0
$925$	−35.8928	−1.18015
$926$	−26.2255	−0.861822
$927$	7.96216	0.261512
$928$	3.86873	0.126997
$929$	−46.1718	−1.51485	−0.757424	−	0.652924i	$-0.773542\pi$
$929$	−46.1718	−1.51485	−0.757424	+	0.652924i	$0.773542\pi$
$930$	−0.482562	−0.0158238
$931$	0	0
$932$	−2.29536	−0.0751871
$933$	19.4672	0.637326
$934$	36.9752	1.20987
$935$	−7.30621	−0.238939
$936$	27.0933	0.885571
$937$	−12.8163	−0.418689	−0.209345	−	0.977842i	$-0.567133\pi$
$937$	−12.8163	−0.418689	−0.209345	+	0.977842i	$0.567133\pi$
$938$	0	0
$939$	51.7522	1.68887
$940$	5.12860	0.167277
$941$	−35.9752	−1.17276	−0.586379	−	0.810037i	$-0.699447\pi$
$941$	−35.9752	−1.17276	−0.586379	+	0.810037i	$0.699447\pi$
$942$	−63.7402	−2.07677
$943$	−0.639400	−0.0208217
$944$	−10.4298	−0.339461
$945$	0	0
$946$	−11.9273	−0.387789
$947$	−20.4015	−0.662959	−0.331479	−	0.943462i	$-0.607548\pi$
$947$	−20.4015	−0.662959	−0.331479	+	0.943462i	$0.607548\pi$
$948$	−1.90699	−0.0619362
$949$	−39.0468	−1.26751
$950$	10.5205	0.341331
$951$	−1.93459	−0.0627332
$952$	0	0
$953$	38.5523	1.24883	0.624416	−	0.781092i	$-0.285337\pi$
$953$	38.5523	1.24883	0.624416	+	0.781092i	$0.285337\pi$
$954$	50.0945	1.62187
$955$	−5.05095	−0.163445
$956$	−0.0315757	−0.00102123
$957$	−46.8300	−1.51380
$958$	18.8993	0.610607
$959$	0	0
$960$	1.17283	0.0378529
$961$	−30.8307	−0.994539
$962$	46.4494	1.49759
$963$	−14.7101	−0.474026
$964$	−2.52792	−0.0814189
$965$	4.09443	0.131804
$966$	0	0
$967$	42.6090	1.37021	0.685107	−	0.728442i	$-0.259755\pi$
$967$	42.6090	1.37021	0.685107	+	0.728442i	$0.259755\pi$
$968$	8.93543	0.287196
$969$	−22.4164	−0.720118
$970$	−6.78117	−0.217730
$971$	31.3959	1.00754	0.503772	−	0.863837i	$-0.331945\pi$
$971$	31.3959	1.00754	0.503772	+	0.863837i	$0.331945\pi$
$972$	−19.4590	−0.624148
$973$	0	0
$974$	−4.29089	−0.137489
$975$	−81.2682	−2.60266
$976$	10.9393	0.350159
$977$	2.24534	0.0718349	0.0359175	−	0.999355i	$-0.488565\pi$
$977$	2.24534	0.0718349	0.0359175	+	0.999355i	$0.488565\pi$
$978$	42.1924	1.34916
$979$	7.12679	0.227773
$980$	0	0
$981$	−51.1053	−1.63167
$982$	22.3383	0.712843
$983$	−34.5877	−1.10317	−0.551587	−	0.834117i	$-0.685978\pi$
$983$	−34.5877	−1.10317	−0.551587	+	0.834117i	$0.685978\pi$
$984$	2.71108	0.0864262
$985$	11.7528	0.374476
$986$	14.6338	0.466034
$987$	0	0
$988$	−13.6148	−0.433143
$989$	−1.70805	−0.0543129
$990$	−8.40216	−0.267038
$991$	24.8716	0.790071	0.395036	−	0.918666i	$-0.370732\pi$
$991$	24.8716	0.790071	0.395036	+	0.918666i	$0.370732\pi$
$992$	−0.411452	−0.0130636
$993$	48.8323	1.54965
$994$	0	0
$995$	−9.10539	−0.288660
$996$	−29.5107	−0.935081
$997$	−23.5051	−0.744414	−0.372207	−	0.928150i	$-0.621399\pi$
$997$	−23.5051	−0.744414	−0.372207	+	0.928150i	$0.621399\pi$
$998$	32.3208	1.02310
$999$	27.2944	0.863556

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bu.1.9		10
7.3	odd	6		574.2.e.h.247.9	yes	20
7.5	odd	6		574.2.e.h.165.9	✓	20
7.6	odd	2		4018.2.a.bt.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.h.165.9	✓	20	7.5	odd	6
574.2.e.h.247.9	yes	20	7.3	odd	6
4018.2.a.bt.1.2		10	7.6	odd	2
4018.2.a.bu.1.9		10	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.71108 q^{3} +1.00000 q^{4} +0.432605 q^{5} +2.71108 q^{6} +1.00000 q^{8} +4.34997 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.71108 q^{3} +1.00000 q^{4} +0.432605 q^{5} +2.71108 q^{6} +1.00000 q^{8} +4.34997 q^{9} +0.432605 q^{10} -4.46491 q^{11} +2.71108 q^{12} +6.22838 q^{13} +1.17283 q^{15} +1.00000 q^{16} +3.78258 q^{17} +4.34997 q^{18} -2.18592 q^{19} +0.432605 q^{20} -4.46491 q^{22} -0.639400 q^{23} +2.71108 q^{24} -4.81285 q^{25} +6.22838 q^{26} +3.65989 q^{27} +3.86873 q^{29} +1.17283 q^{30} -0.411452 q^{31} +1.00000 q^{32} -12.1047 q^{33} +3.78258 q^{34} +4.34997 q^{36} +7.45770 q^{37} -2.18592 q^{38} +16.8857 q^{39} +0.432605 q^{40} +1.00000 q^{41} +2.67133 q^{43} -4.46491 q^{44} +1.88182 q^{45} -0.639400 q^{46} +11.8552 q^{47} +2.71108 q^{48} -4.81285 q^{50} +10.2549 q^{51} +6.22838 q^{52} +11.5160 q^{53} +3.65989 q^{54} -1.93154 q^{55} -5.92622 q^{57} +3.86873 q^{58} -10.4298 q^{59} +1.17283 q^{60} +10.9393 q^{61} -0.411452 q^{62} +1.00000 q^{64} +2.69443 q^{65} -12.1047 q^{66} -5.53641 q^{67} +3.78258 q^{68} -1.73347 q^{69} -9.40984 q^{71} +4.34997 q^{72} -6.26918 q^{73} +7.45770 q^{74} -13.0480 q^{75} -2.18592 q^{76} +16.8857 q^{78} -0.703406 q^{79} +0.432605 q^{80} -3.12765 q^{81} +1.00000 q^{82} -10.8852 q^{83} +1.63636 q^{85} +2.67133 q^{86} +10.4884 q^{87} -4.46491 q^{88} -1.59618 q^{89} +1.88182 q^{90} -0.639400 q^{92} -1.11548 q^{93} +11.8552 q^{94} -0.945641 q^{95} +2.71108 q^{96} -15.6752 q^{97} -19.4222 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + q^{3} + 10 q^{4} - 2 q^{5} + q^{6} + 10 q^{8} + 17 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 + q^3 + 10 * q^4 - 2 * q^5 + q^6 + 10 * q^8 + 17 * q^9	\( 10 q + 10 q^{2} + q^{3} + 10 q^{4} - 2 q^{5} + q^{6} + 10 q^{8} + 17 q^{9} - 2 q^{10} + 11 q^{11} + q^{12} + 4 q^{13} + 4 q^{15} + 10 q^{16} + 5 q^{17} + 17 q^{18} - q^{19} - 2 q^{20} + 11 q^{22} + 9 q^{23} + q^{24} + 24 q^{25} + 4 q^{26} + 7 q^{27} + 23 q^{29} + 4 q^{30} - 5 q^{31} + 10 q^{32} - 5 q^{33} + 5 q^{34} + 17 q^{36} + 16 q^{37} - q^{38} - 7 q^{39} - 2 q^{40} + 10 q^{41} + 20 q^{43} + 11 q^{44} - 42 q^{45} + 9 q^{46} - 16 q^{47} + q^{48} + 24 q^{50} + 13 q^{51} + 4 q^{52} + 26 q^{53} + 7 q^{54} + 7 q^{55} + 37 q^{57} + 23 q^{58} - 10 q^{59} + 4 q^{60} - 5 q^{62} + 10 q^{64} + 18 q^{65} - 5 q^{66} + 7 q^{67} + 5 q^{68} + 39 q^{69} + 5 q^{71} + 17 q^{72} - 13 q^{73} + 16 q^{74} + 19 q^{75} - q^{76} - 7 q^{78} - q^{79} - 2 q^{80} + 18 q^{81} + 10 q^{82} + 21 q^{83} + 34 q^{85} + 20 q^{86} + 2 q^{87} + 11 q^{88} + 6 q^{89} - 42 q^{90} + 9 q^{92} - 5 q^{93} - 16 q^{94} + 24 q^{95} + q^{96} + 29 q^{97} + 48 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + q^3 + 10 * q^4 - 2 * q^5 + q^6 + 10 * q^8 + 17 * q^9 - 2 * q^10 + 11 * q^11 + q^12 + 4 * q^13 + 4 * q^15 + 10 * q^16 + 5 * q^17 + 17 * q^18 - q^19 - 2 * q^20 + 11 * q^22 + 9 * q^23 + q^24 + 24 * q^25 + 4 * q^26 + 7 * q^27 + 23 * q^29 + 4 * q^30 - 5 * q^31 + 10 * q^32 - 5 * q^33 + 5 * q^34 + 17 * q^36 + 16 * q^37 - q^38 - 7 * q^39 - 2 * q^40 + 10 * q^41 + 20 * q^43 + 11 * q^44 - 42 * q^45 + 9 * q^46 - 16 * q^47 + q^48 + 24 * q^50 + 13 * q^51 + 4 * q^52 + 26 * q^53 + 7 * q^54 + 7 * q^55 + 37 * q^57 + 23 * q^58 - 10 * q^59 + 4 * q^60 - 5 * q^62 + 10 * q^64 + 18 * q^65 - 5 * q^66 + 7 * q^67 + 5 * q^68 + 39 * q^69 + 5 * q^71 + 17 * q^72 - 13 * q^73 + 16 * q^74 + 19 * q^75 - q^76 - 7 * q^78 - q^79 - 2 * q^80 + 18 * q^81 + 10 * q^82 + 21 * q^83 + 34 * q^85 + 20 * q^86 + 2 * q^87 + 11 * q^88 + 6 * q^89 - 42 * q^90 + 9 * q^92 - 5 * q^93 - 16 * q^94 + 24 * q^95 + q^96 + 29 * q^97 + 48 * q^99

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