LMFDB - Embedded newform 4018.2.a.bt.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0838915322$
Analytic rank:	$0$
Dimension:	$10$
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			1.2
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	$-0.786118\pi$
$3$	−2.71108	−1.56524	−0.782622	+	0.622497i	$0.786118\pi$
$4$	1.00000	0.500000
$5$	−0.432605	−0.193467	−0.0967334	−	0.995310i	$-0.530839\pi$
$5$	−0.432605	−0.193467	−0.0967334	+	0.995310i	$0.530839\pi$
$6$	−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	$-0.831872\pi$
$13$	−6.22838	−1.72744	−0.863721	+	0.503971i	$0.831872\pi$
$14$	0	0
$15$	1.17283	0.302823
$16$	1.00000	0.250000
$17$	−3.78258	−0.917410	−0.458705	−	0.888589i	$-0.651687\pi$
$17$	−3.78258	−0.917410	−0.458705	+	0.888589i	$0.651687\pi$
$18$	4.34997	1.02530
$19$	2.18592	0.501485	0.250743	−	0.968054i	$-0.419325\pi$
$19$	2.18592	0.501485	0.250743	+	0.968054i	$0.419325\pi$
$20$	−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	$-0.488236\pi$
$31$	0.411452	0.0738989	0.0369495	+	0.999317i	$0.488236\pi$
$32$	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	$-0.832445\pi$
$47$	−11.8552	−1.72925	−0.864627	+	0.502415i	$0.832445\pi$
$48$	−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	$-0.262447\pi$
$59$	10.4298	1.35785	0.678923	+	0.734210i	$0.262447\pi$
$60$	1.17283	0.151411
$61$	−10.9393	−1.40064	−0.700318	−	0.713831i	$-0.746958\pi$
$61$	−10.9393	−1.40064	−0.700318	+	0.713831i	$0.746958\pi$
$62$	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	$-0.380427\pi$
$73$	6.26918	0.733752	0.366876	+	0.930270i	$0.380427\pi$
$74$	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	$-0.296200\pi$
$83$	10.8852	1.19480	0.597402	+	0.801942i	$0.296200\pi$
$84$	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	$-0.473040\pi$
$89$	1.59618	0.169194	0.0845972	+	0.996415i	$0.473040\pi$
$90$	−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	$-0.207057\pi$
$97$	15.6752	1.59158	0.795788	+	0.605575i	$0.207057\pi$
$98$	0	0
$99$	−19.4222	−1.95201
$100$	−4.81285	−0.481285
$101$	0.215041	0.0213974	0.0106987	−	0.999943i	$-0.496594\pi$
$101$	0.215041	0.0213974	0.0106987	+	0.999943i	$0.496594\pi$
$102$	10.2549	1.01539
$103$	−1.83039	−0.180354	−0.0901770	−	0.995926i	$-0.528743\pi$
$103$	−1.83039	−0.180354	−0.0901770	+	0.995926i	$0.528743\pi$
$104$	−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	$-0.502534\pi$
$131$	−0.182242	−0.0159226	−0.00796129	+	0.999968i	$0.502534\pi$
$132$	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	$-0.438600\pi$
$139$	4.52022	0.383400	0.191700	+	0.981454i	$0.438600\pi$
$140$	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	$-0.112502\pi$
$157$	23.5110	1.87638	0.938189	+	0.346123i	$0.112502\pi$
$158$	−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	$-0.329862\pi$
$167$	13.1662	1.01883	0.509414	+	0.860521i	$0.329862\pi$
$168$	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	$-0.329326\pi$
$173$	13.4387	1.02173	0.510863	+	0.859662i	$0.329326\pi$
$174$	−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	$-0.649379\pi$
$181$	−12.1688	−0.904503	−0.452251	+	0.891891i	$0.649379\pi$
$182$	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	$-0.231962\pi$
$199$	21.0478	1.49204	0.746020	+	0.665924i	$0.231962\pi$
$200$	−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	$-0.701827\pi$
$223$	−17.6934	−1.18484	−0.592419	+	0.805630i	$0.701827\pi$
$224$	0	0
$225$	−20.9358	−1.39572
$226$	10.9142	0.726003
$227$	4.36249	0.289549	0.144774	−	0.989465i	$-0.453754\pi$
$227$	4.36249	0.289549	0.144774	+	0.989465i	$0.453754\pi$
$228$	−5.92622	−0.392474
$229$	12.7505	0.842577	0.421289	−	0.906927i	$-0.361578\pi$
$229$	12.7505	0.842577	0.421289	+	0.906927i	$0.361578\pi$
$230$	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	$-0.474055\pi$
$241$	2.52792	0.162838	0.0814189	+	0.996680i	$0.474055\pi$
$242$	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	$-0.717702\pi$
$251$	−20.0206	−1.26369	−0.631846	+	0.775094i	$0.717702\pi$
$252$	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	$-0.516583\pi$
$257$	−1.66960	−0.104147	−0.0520733	+	0.998643i	$0.516583\pi$
$258$	−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	$-0.499905\pi$
$269$	0.00980080	0.000597565 0	0.000298783		1.00000i	$0.499905\pi$
$270$	1.58329	0.0963558
$271$	20.6636	1.25523	0.627614	−	0.778525i	$-0.284032\pi$
$271$	20.6636	1.25523	0.627614	+	0.778525i	$0.284032\pi$
$272$	−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	$-0.375018\pi$
$283$	12.8737	0.765260	0.382630	+	0.923902i	$0.375018\pi$
$284$	−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	$-0.377677\pi$
$293$	12.8345	0.749801	0.374901	+	0.927065i	$0.377677\pi$
$294$	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	$-0.267244\pi$
$307$	23.4010	1.33556	0.667782	+	0.744357i	$0.267244\pi$
$308$	0	0
$309$	4.96235	0.282298
$310$	−0.177996	−0.0101095
$311$	−7.18058	−0.407174	−0.203587	−	0.979057i	$-0.565260\pi$
$311$	−7.18058	−0.407174	−0.203587	+	0.979057i	$0.565260\pi$
$312$	16.8857	0.955962
$313$	−19.0891	−1.07898	−0.539491	−	0.841992i	$-0.681383\pi$
$313$	−19.0891	−1.07898	−0.539491	+	0.841992i	$0.681383\pi$
$314$	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	$-0.570817\pi$
$349$	−8.24410	−0.441297	−0.220648	+	0.975353i	$0.570817\pi$
$350$	0	0
$351$	22.7952	1.21672
$352$	−4.46491	−0.237981
$353$	21.9621	1.16892	0.584462	−	0.811421i	$-0.301305\pi$
$353$	21.9621	1.16892	0.584462	+	0.811421i	$0.301305\pi$
$354$	−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	$-0.628763\pi$
$367$	−15.0798	−0.787159	−0.393579	+	0.919291i	$0.628763\pi$
$368$	−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	$-0.596734\pi$
$383$	−11.7125	−0.598482	−0.299241	+	0.954178i	$0.596734\pi$
$384$	−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	$-0.260620\pi$
$397$	27.2224	1.36625	0.683126	+	0.730300i	$0.260620\pi$
$398$	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	$-0.504503\pi$
$409$	−0.572141	−0.0282905	−0.0141453	+	0.999900i	$0.504503\pi$
$410$	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	$-0.816830\pi$
$419$	−34.3458	−1.67790	−0.838951	+	0.544208i	$0.816830\pi$
$420$	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	$-0.639684\pi$
$433$	−17.6824	−0.849762	−0.424881	+	0.905249i	$0.639684\pi$
$434$	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	$-0.826291\pi$
$439$	−35.8181	−1.70951	−0.854753	+	0.519035i	$0.826291\pi$
$440$	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	$-0.178989\pi$
$461$	36.3299	1.69205	0.846026	+	0.533142i	$0.178989\pi$
$462$	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	$-0.826753\pi$
$467$	−36.9752	−1.71101	−0.855504	+	0.517796i	$0.826753\pi$
$468$	−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	$-0.642109\pi$
$479$	−18.8993	−0.863529	−0.431764	+	0.901986i	$0.642109\pi$
$480$	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	$-0.518257\pi$
$503$	−2.57125	−0.114646	−0.0573232	+	0.998356i	$0.518257\pi$
$504$	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	$-0.223269\pi$
$509$	34.4699	1.52785	0.763926	+	0.645304i	$0.223269\pi$
$510$	−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	$-0.280380\pi$
$521$	29.0569	1.27301	0.636504	+	0.771274i	$0.280380\pi$
$522$	16.8289	0.736579
$523$	15.5368	0.679375	0.339688	−	0.940538i	$-0.389679\pi$
$523$	15.5368	0.679375	0.339688	+	0.940538i	$0.389679\pi$
$524$	−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	$-0.794222\pi$
$563$	−37.8795	−1.59643	−0.798216	+	0.602372i	$0.794222\pi$
$564$	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	$-0.384227\pi$
$577$	17.0906	0.711492	0.355746	+	0.934583i	$0.384227\pi$
$578$	−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	$-0.311344\pi$
$587$	27.0670	1.11717	0.558587	+	0.829446i	$0.311344\pi$
$588$	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	$-0.489540\pi$
$593$	1.60013	0.0657095	0.0328548	+	0.999460i	$0.489540\pi$
$594$	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	$-0.634899\pi$
$601$	−20.1626	−0.822449	−0.411225	+	0.911534i	$0.634899\pi$
$602$	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	$-0.627932\pi$
$607$	−19.2752	−0.782356	−0.391178	+	0.920315i	$0.627932\pi$
$608$	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	$-0.216746\pi$
$619$	38.6625	1.55398	0.776989	+	0.629515i	$0.216746\pi$
$620$	−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	$-0.547511\pi$
$643$	−7.54167	−0.297414	−0.148707	+	0.988881i	$0.547511\pi$
$644$	0	0
$645$	3.13302	0.123362
$646$	−8.26843	−0.325317
$647$	11.8846	0.467231	0.233616	−	0.972329i	$-0.424944\pi$
$647$	11.8846	0.467231	0.233616	+	0.972329i	$0.424944\pi$
$648$	−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	$-0.706392\pi$
$661$	−31.0531	−1.20782	−0.603912	+	0.797051i	$0.706392\pi$
$662$	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	$-0.460400\pi$
$677$	6.45732	0.248175	0.124088	+	0.992271i	$0.460400\pi$
$678$	−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	$-0.443666\pi$
$691$	9.25593	0.352112	0.176056	+	0.984380i	$0.443666\pi$
$692$	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	$-0.513009\pi$
$719$	−2.19109	−0.0817138	−0.0408569	+	0.999165i	$0.513009\pi$
$720$	−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	$-0.691599\pi$
$727$	−30.5344	−1.13246	−0.566230	+	0.824247i	$0.691599\pi$
$728$	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	$-0.222512\pi$
$733$	41.4480	1.53092	0.765459	+	0.643485i	$0.222512\pi$
$734$	−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	$-0.527696\pi$
$761$	−4.79444	−0.173798	−0.0868991	+	0.996217i	$0.527696\pi$
$762$	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	$-0.739674\pi$
$769$	−37.9248	−1.36760	−0.683801	+	0.729669i	$0.739674\pi$
$770$	0	0
$771$	4.52642	0.163015
$772$	9.46460	0.340639
$773$	−38.0012	−1.36681	−0.683405	−	0.730040i	$-0.739502\pi$
$773$	−38.0012	−1.36681	−0.683405	+	0.730040i	$0.739502\pi$
$774$	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	$-0.436820\pi$
$787$	11.0635	0.394370	0.197185	+	0.980366i	$0.436820\pi$
$788$	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	$-0.466579\pi$
$797$	5.91737	0.209604	0.104802	+	0.994493i	$0.466579\pi$
$798$	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	$-0.623809\pi$
$811$	−21.5991	−0.758448	−0.379224	+	0.925305i	$0.623809\pi$
$812$	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	$-0.689707\pi$
$829$	−32.3236	−1.12264	−0.561322	+	0.827597i	$0.689707\pi$
$830$	−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	$-0.772296\pi$
$839$	−43.7298	−1.50972	−0.754861	+	0.655885i	$0.772296\pi$
$840$	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	$-0.643661\pi$
$853$	−25.4770	−0.872316	−0.436158	+	0.899870i	$0.643661\pi$
$854$	0	0
$855$	−4.11351	−0.140679
$856$	−3.38165	−0.115582
$857$	26.7072	0.912299	0.456150	−	0.889903i	$-0.349228\pi$
$857$	26.7072	0.912299	0.456150	+	0.889903i	$0.349228\pi$
$858$	−75.3929	−2.57387
$859$	12.7019	0.433385	0.216692	−	0.976240i	$-0.430473\pi$
$859$	12.7019	0.433385	0.216692	+	0.976240i	$0.430473\pi$
$860$	−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	$-0.440612\pi$
$881$	11.0114	0.370982	0.185491	+	0.982646i	$0.440612\pi$
$882$	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	$-0.178343\pi$
$887$	50.4579	1.69421	0.847106	+	0.531425i	$0.178343\pi$
$888$	−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	$-0.226458\pi$
$929$	46.1718	1.51485	0.757424	+	0.652924i	$0.226458\pi$
$930$	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	$-0.432867\pi$
$937$	12.8163	0.418689	0.209345	+	0.977842i	$0.432867\pi$
$938$	0	0
$939$	51.7522	1.68887
$940$	5.12860	0.167277
$941$	35.9752	1.17276	0.586379	−	0.810037i	$-0.300553\pi$
$941$	35.9752	1.17276	0.586379	+	0.810037i	$0.300553\pi$
$942$	−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	$-0.668055\pi$
$971$	−31.3959	−1.00754	−0.503772	+	0.863837i	$0.668055\pi$
$972$	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	$-0.314022\pi$
$983$	34.5877	1.10317	0.551587	+	0.834117i	$0.314022\pi$
$984$	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	$-0.378601\pi$
$997$	23.5051	0.744414	0.372207	+	0.928150i	$0.378601\pi$
$998$	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.bt.1.2		10
7.2	even	3		574.2.e.h.165.9	✓	20
7.4	even	3		574.2.e.h.247.9	yes	20
7.6	odd	2		4018.2.a.bu.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.h.165.9	✓	20	7.2	even	3
574.2.e.h.247.9	yes	20	7.4	even	3
4018.2.a.bt.1.2		10	1.1	even	1	trivial
4018.2.a.bu.1.9		10	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
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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