LMFDB - Embedded newform 7742.2.a.bj.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7742,2,Mod(1,7742)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7742, 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("7742.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7742 = 2 \cdot 7^{2} \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7742.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:	$61.8201812449$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 2x^{8} - 18x^{7} + 34x^{6} + 105x^{5} - 184x^{4} - 212x^{3} + 342x^{2} + 72x - 108 $ x^9 - 2x^8 - 18x^7 + 34x^6 + 105x^5 - 184x^4 - 212x^3 + 342x^2 + 72x - 108
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 1106)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.633348$ of defining polynomial
Character	$\chi$	$=$	7742.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.633348 q^{3} +1.00000 q^{4} +2.25697 q^{5} +0.633348 q^{6} +1.00000 q^{8} -2.59887 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.633348 q^{3} +1.00000 q^{4} +2.25697 q^{5} +0.633348 q^{6} +1.00000 q^{8} -2.59887 q^{9} +2.25697 q^{10} +5.27893 q^{11} +0.633348 q^{12} +4.66074 q^{13} +1.42945 q^{15} +1.00000 q^{16} -3.55123 q^{17} -2.59887 q^{18} -7.07412 q^{19} +2.25697 q^{20} +5.27893 q^{22} +6.63757 q^{23} +0.633348 q^{24} +0.0939338 q^{25} +4.66074 q^{26} -3.54603 q^{27} +1.34429 q^{29} +1.42945 q^{30} +1.28906 q^{31} +1.00000 q^{32} +3.34340 q^{33} -3.55123 q^{34} -2.59887 q^{36} +9.57042 q^{37} -7.07412 q^{38} +2.95187 q^{39} +2.25697 q^{40} +1.11390 q^{41} +3.92241 q^{43} +5.27893 q^{44} -5.86558 q^{45} +6.63757 q^{46} -0.906066 q^{47} +0.633348 q^{48} +0.0939338 q^{50} -2.24916 q^{51} +4.66074 q^{52} -12.8356 q^{53} -3.54603 q^{54} +11.9144 q^{55} -4.48038 q^{57} +1.34429 q^{58} -6.91021 q^{59} +1.42945 q^{60} +11.0404 q^{61} +1.28906 q^{62} +1.00000 q^{64} +10.5192 q^{65} +3.34340 q^{66} +12.8944 q^{67} -3.55123 q^{68} +4.20389 q^{69} +11.3640 q^{71} -2.59887 q^{72} +6.49512 q^{73} +9.57042 q^{74} +0.0594928 q^{75} -7.07412 q^{76} +2.95187 q^{78} +1.00000 q^{79} +2.25697 q^{80} +5.55074 q^{81} +1.11390 q^{82} +8.31051 q^{83} -8.01503 q^{85} +3.92241 q^{86} +0.851403 q^{87} +5.27893 q^{88} -6.45124 q^{89} -5.86558 q^{90} +6.63757 q^{92} +0.816422 q^{93} -0.906066 q^{94} -15.9661 q^{95} +0.633348 q^{96} -2.03031 q^{97} -13.7193 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} - 2 q^{3} + 9 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{8} + 13 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^8 + 13 * q^9	$ 9 q + 9 q^{2} - 2 q^{3} + 9 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{8} + 13 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{15} + 9 q^{16} - 6 q^{17} + 13 q^{18} - 2 q^{19} - 4 q^{20} + 8 q^{22} - 2 q^{24} + 23 q^{25} - 2 q^{26} - 2 q^{27} + 10 q^{29} - 2 q^{30} + 6 q^{31} + 9 q^{32} + 2 q^{33} - 6 q^{34} + 13 q^{36} + 10 q^{37} - 2 q^{38} - 6 q^{39} - 4 q^{40} - 10 q^{41} + 22 q^{43} + 8 q^{44} + 10 q^{45} + 14 q^{47} - 2 q^{48} + 23 q^{50} + 4 q^{51} - 2 q^{52} + 12 q^{53} - 2 q^{54} + 14 q^{55} + 22 q^{57} + 10 q^{58} + 2 q^{59} - 2 q^{60} - 6 q^{61} + 6 q^{62} + 9 q^{64} - 12 q^{65} + 2 q^{66} + 24 q^{67} - 6 q^{68} + 26 q^{69} + 20 q^{71} + 13 q^{72} + 12 q^{73} + 10 q^{74} - 6 q^{75} - 2 q^{76} - 6 q^{78} + 9 q^{79} - 4 q^{80} - 19 q^{81} - 10 q^{82} + 22 q^{83} + 32 q^{85} + 22 q^{86} + 54 q^{87} + 8 q^{88} - 20 q^{89} + 10 q^{90} - 18 q^{93} + 14 q^{94} - 40 q^{95} - 2 q^{96} + 6 q^{97} + 24 q^{99}+O(q^{100}) $ 9 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^8 + 13 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^15 + 9 * q^16 - 6 * q^17 + 13 * q^18 - 2 * q^19 - 4 * q^20 + 8 * q^22 - 2 * q^24 + 23 * q^25 - 2 * q^26 - 2 * q^27 + 10 * q^29 - 2 * q^30 + 6 * q^31 + 9 * q^32 + 2 * q^33 - 6 * q^34 + 13 * q^36 + 10 * q^37 - 2 * q^38 - 6 * q^39 - 4 * q^40 - 10 * q^41 + 22 * q^43 + 8 * q^44 + 10 * q^45 + 14 * q^47 - 2 * q^48 + 23 * q^50 + 4 * q^51 - 2 * q^52 + 12 * q^53 - 2 * q^54 + 14 * q^55 + 22 * q^57 + 10 * q^58 + 2 * q^59 - 2 * q^60 - 6 * q^61 + 6 * q^62 + 9 * q^64 - 12 * q^65 + 2 * q^66 + 24 * q^67 - 6 * q^68 + 26 * q^69 + 20 * q^71 + 13 * q^72 + 12 * q^73 + 10 * q^74 - 6 * q^75 - 2 * q^76 - 6 * q^78 + 9 * q^79 - 4 * q^80 - 19 * q^81 - 10 * q^82 + 22 * q^83 + 32 * q^85 + 22 * q^86 + 54 * q^87 + 8 * q^88 - 20 * q^89 + 10 * q^90 - 18 * q^93 + 14 * q^94 - 40 * q^95 - 2 * q^96 + 6 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.633348	0.365664	0.182832	−	0.983144i	$-0.441474\pi$
$3$	0.633348	0.365664	0.182832	+	0.983144i	$0.441474\pi$
$4$	1.00000	0.500000
$5$	2.25697	1.00935	0.504675	−	0.863310i	$-0.331612\pi$
$5$	2.25697	1.00935	0.504675	+	0.863310i	$0.331612\pi$
$6$	0.633348	0.258563
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−2.59887	−0.866290
$10$	2.25697	0.713718
$11$	5.27893	1.59166	0.795829	−	0.605522i	$-0.207036\pi$
$11$	5.27893	1.59166	0.795829	+	0.605522i	$0.207036\pi$
$12$	0.633348	0.182832
$13$	4.66074	1.29266	0.646328	−	0.763060i	$-0.276304\pi$
$13$	4.66074	1.29266	0.646328	+	0.763060i	$0.276304\pi$
$14$	0	0
$15$	1.42945	0.369082
$16$	1.00000	0.250000
$17$	−3.55123	−0.861300	−0.430650	−	0.902519i	$-0.641716\pi$
$17$	−3.55123	−0.861300	−0.430650	+	0.902519i	$0.641716\pi$
$18$	−2.59887	−0.612560
$19$	−7.07412	−1.62292	−0.811458	−	0.584411i	$-0.801325\pi$
$19$	−7.07412	−1.62292	−0.811458	+	0.584411i	$0.801325\pi$
$20$	2.25697	0.504675
$21$	0	0
$22$	5.27893	1.12547
$23$	6.63757	1.38403	0.692014	−	0.721884i	$-0.256724\pi$
$23$	6.63757	1.38403	0.692014	+	0.721884i	$0.256724\pi$
$24$	0.633348	0.129282
$25$	0.0939338	0.0187868
$26$	4.66074	0.914046
$27$	−3.54603	−0.682434
$28$	0	0
$29$	1.34429	0.249628	0.124814	−	0.992180i	$-0.460167\pi$
$29$	1.34429	0.249628	0.124814	+	0.992180i	$0.460167\pi$
$30$	1.42945	0.260981
$31$	1.28906	0.231522	0.115761	−	0.993277i	$-0.463069\pi$
$31$	1.28906	0.231522	0.115761	+	0.993277i	$0.463069\pi$
$32$	1.00000	0.176777
$33$	3.34340	0.582011
$34$	−3.55123	−0.609031
$35$	0	0
$36$	−2.59887	−0.433145
$37$	9.57042	1.57337	0.786684	−	0.617356i	$-0.211796\pi$
$37$	9.57042	1.57337	0.786684	+	0.617356i	$0.211796\pi$
$38$	−7.07412	−1.14757
$39$	2.95187	0.472677
$40$	2.25697	0.356859
$41$	1.11390	0.173961	0.0869807	−	0.996210i	$-0.472278\pi$
$41$	1.11390	0.173961	0.0869807	+	0.996210i	$0.472278\pi$
$42$	0	0
$43$	3.92241	0.598161	0.299081	−	0.954228i	$-0.403320\pi$
$43$	3.92241	0.598161	0.299081	+	0.954228i	$0.403320\pi$
$44$	5.27893	0.795829
$45$	−5.86558	−0.874390
$46$	6.63757	0.978656
$47$	−0.906066	−0.132163	−0.0660817	−	0.997814i	$-0.521050\pi$
$47$	−0.906066	−0.132163	−0.0660817	+	0.997814i	$0.521050\pi$
$48$	0.633348	0.0914159
$49$	0	0
$50$	0.0939338	0.0132842
$51$	−2.24916	−0.314946
$52$	4.66074	0.646328
$53$	−12.8356	−1.76311	−0.881555	−	0.472081i	$-0.843503\pi$
$53$	−12.8356	−1.76311	−0.881555	+	0.472081i	$0.843503\pi$
$54$	−3.54603	−0.482554
$55$	11.9144	1.60654
$56$	0	0
$57$	−4.48038	−0.593441
$58$	1.34429	0.176514
$59$	−6.91021	−0.899632	−0.449816	−	0.893121i	$-0.648510\pi$
$59$	−6.91021	−0.899632	−0.449816	+	0.893121i	$0.648510\pi$
$60$	1.42945	0.184541
$61$	11.0404	1.41358	0.706792	−	0.707422i	$-0.250142\pi$
$61$	11.0404	1.41358	0.706792	+	0.707422i	$0.250142\pi$
$62$	1.28906	0.163711
$63$	0	0
$64$	1.00000	0.125000
$65$	10.5192	1.30474
$66$	3.34340	0.411544
$67$	12.8944	1.57530	0.787650	−	0.616124i	$-0.211298\pi$
$67$	12.8944	1.57530	0.787650	+	0.616124i	$0.211298\pi$
$68$	−3.55123	−0.430650
$69$	4.20389	0.506089
$70$	0	0
$71$	11.3640	1.34866	0.674328	−	0.738432i	$-0.264433\pi$
$71$	11.3640	1.34866	0.674328	+	0.738432i	$0.264433\pi$
$72$	−2.59887	−0.306280
$73$	6.49512	0.760196	0.380098	−	0.924946i	$-0.375890\pi$
$73$	6.49512	0.760196	0.380098	+	0.924946i	$0.375890\pi$
$74$	9.57042	1.11254
$75$	0.0594928	0.00686964
$76$	−7.07412	−0.811458
$77$	0	0
$78$	2.95187	0.334233
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	2.25697	0.252337
$81$	5.55074	0.616749
$82$	1.11390	0.123009
$83$	8.31051	0.912196	0.456098	−	0.889929i	$-0.349247\pi$
$83$	8.31051	0.912196	0.456098	+	0.889929i	$0.349247\pi$
$84$	0	0
$85$	−8.01503	−0.869353
$86$	3.92241	0.422964
$87$	0.851403	0.0912800
$88$	5.27893	0.562736
$89$	−6.45124	−0.683830	−0.341915	−	0.939731i	$-0.611076\pi$
$89$	−6.45124	−0.683830	−0.341915	+	0.939731i	$0.611076\pi$
$90$	−5.86558	−0.618287
$91$	0	0
$92$	6.63757	0.692014
$93$	0.816422	0.0846590
$94$	−0.906066	−0.0934536
$95$	−15.9661	−1.63809
$96$	0.633348	0.0646408
$97$	−2.03031	−0.206147	−0.103074	−	0.994674i	$-0.532868\pi$
$97$	−2.03031	−0.206147	−0.103074	+	0.994674i	$0.532868\pi$
$98$	0	0
$99$	−13.7193	−1.37884
$100$	0.0939338	0.00939338
$101$	14.1083	1.40383	0.701913	−	0.712263i	$-0.252329\pi$
$101$	14.1083	1.40383	0.701913	+	0.712263i	$0.252329\pi$
$102$	−2.24916	−0.222700
$103$	−15.1959	−1.49729	−0.748647	−	0.662969i	$-0.769296\pi$
$103$	−15.1959	−1.49729	−0.748647	+	0.662969i	$0.769296\pi$
$104$	4.66074	0.457023
$105$	0	0
$106$	−12.8356	−1.24671
$107$	−15.9173	−1.53878	−0.769391	−	0.638778i	$-0.779440\pi$
$107$	−15.9173	−1.53878	−0.769391	+	0.638778i	$0.779440\pi$
$108$	−3.54603	−0.341217
$109$	9.28757	0.889588	0.444794	−	0.895633i	$-0.353277\pi$
$109$	9.28757	0.889588	0.444794	+	0.895633i	$0.353277\pi$
$110$	11.9144	1.13599
$111$	6.06141	0.575323
$112$	0	0
$113$	6.40056	0.602114	0.301057	−	0.953606i	$-0.402661\pi$
$113$	6.40056	0.602114	0.301057	+	0.953606i	$0.402661\pi$
$114$	−4.48038	−0.419626
$115$	14.9808	1.39697
$116$	1.34429	0.124814
$117$	−12.1127	−1.11982
$118$	−6.91021	−0.636136
$119$	0	0
$120$	1.42945	0.130490
$121$	16.8671	1.53337
$122$	11.0404	0.999555
$123$	0.705484	0.0636114
$124$	1.28906	0.115761
$125$	−11.0729	−0.990387
$126$	0	0
$127$	−19.3182	−1.71422	−0.857109	−	0.515136i	$-0.827741\pi$
$127$	−19.3182	−1.71422	−0.857109	+	0.515136i	$0.827741\pi$
$128$	1.00000	0.0883883
$129$	2.48425	0.218726
$130$	10.5192	0.922592
$131$	2.11002	0.184353	0.0921766	−	0.995743i	$-0.470618\pi$
$131$	2.11002	0.184353	0.0921766	+	0.995743i	$0.470618\pi$
$132$	3.34340	0.291006
$133$	0	0
$134$	12.8944	1.11390
$135$	−8.00330	−0.688815
$136$	−3.55123	−0.304515
$137$	−14.8831	−1.27155	−0.635775	−	0.771875i	$-0.719319\pi$
$137$	−14.8831	−1.27155	−0.635775	+	0.771875i	$0.719319\pi$
$138$	4.20389	0.357859
$139$	−0.661630	−0.0561187	−0.0280594	−	0.999606i	$-0.508933\pi$
$139$	−0.661630	−0.0561187	−0.0280594	+	0.999606i	$0.508933\pi$
$140$	0	0
$141$	−0.573855	−0.0483273
$142$	11.3640	0.953644
$143$	24.6037	2.05747
$144$	−2.59887	−0.216573
$145$	3.03403	0.251962
$146$	6.49512	0.537540
$147$	0	0
$148$	9.57042	0.786684
$149$	−14.6199	−1.19771	−0.598853	−	0.800859i	$-0.704377\pi$
$149$	−14.6199	−1.19771	−0.598853	+	0.800859i	$0.704377\pi$
$150$	0.0594928	0.00485757
$151$	−14.5083	−1.18067	−0.590336	−	0.807157i	$-0.701005\pi$
$151$	−14.5083	−1.18067	−0.590336	+	0.807157i	$0.701005\pi$
$152$	−7.07412	−0.573787
$153$	9.22919	0.746135
$154$	0	0
$155$	2.90937	0.233686
$156$	2.95187	0.236339
$157$	8.55607	0.682849	0.341425	−	0.939909i	$-0.389091\pi$
$157$	8.55607	0.682849	0.341425	+	0.939909i	$0.389091\pi$
$158$	1.00000	0.0795557
$159$	−8.12942	−0.644705
$160$	2.25697	0.178429
$161$	0	0
$162$	5.55074	0.436107
$163$	23.6056	1.84894	0.924468	−	0.381259i	$-0.124509\pi$
$163$	23.6056	1.84894	0.924468	+	0.381259i	$0.124509\pi$
$164$	1.11390	0.0869807
$165$	7.54597	0.587453
$166$	8.31051	0.645020
$167$	24.1103	1.86571	0.932854	−	0.360255i	$-0.117310\pi$
$167$	24.1103	1.86571	0.932854	+	0.360255i	$0.117310\pi$
$168$	0	0
$169$	8.72249	0.670961
$170$	−8.01503	−0.614725
$171$	18.3847	1.40592
$172$	3.92241	0.299081
$173$	2.97020	0.225820	0.112910	−	0.993605i	$-0.463983\pi$
$173$	2.97020	0.225820	0.112910	+	0.993605i	$0.463983\pi$
$174$	0.851403	0.0645447
$175$	0	0
$176$	5.27893	0.397914
$177$	−4.37656	−0.328963
$178$	−6.45124	−0.483541
$179$	2.08550	0.155878	0.0779388	−	0.996958i	$-0.475166\pi$
$179$	2.08550	0.155878	0.0779388	+	0.996958i	$0.475166\pi$
$180$	−5.86558	−0.437195
$181$	−22.6586	−1.68420	−0.842100	−	0.539322i	$-0.818681\pi$
$181$	−22.6586	−1.68420	−0.842100	+	0.539322i	$0.818681\pi$
$182$	0	0
$183$	6.99244	0.516896
$184$	6.63757	0.489328
$185$	21.6002	1.58808
$186$	0.816422	0.0598630
$187$	−18.7467	−1.37089
$188$	−0.906066	−0.0660817
$189$	0	0
$190$	−15.9661	−1.15830
$191$	−20.1756	−1.45986	−0.729929	−	0.683523i	$-0.760447\pi$
$191$	−20.1756	−1.45986	−0.729929	+	0.683523i	$0.760447\pi$
$192$	0.633348	0.0457079
$193$	−16.0563	−1.15576	−0.577880	−	0.816122i	$-0.696120\pi$
$193$	−16.0563	−1.15576	−0.577880	+	0.816122i	$0.696120\pi$
$194$	−2.03031	−0.145768
$195$	6.66229	0.477097
$196$	0	0
$197$	14.6290	1.04227	0.521135	−	0.853474i	$-0.325509\pi$
$197$	14.6290	1.04227	0.521135	+	0.853474i	$0.325509\pi$
$198$	−13.7193	−0.974985
$199$	−17.6802	−1.25332	−0.626659	−	0.779293i	$-0.715578\pi$
$199$	−17.6802	−1.25332	−0.626659	+	0.779293i	$0.715578\pi$
$200$	0.0939338	0.00664212
$201$	8.16663	0.576029
$202$	14.1083	0.992655
$203$	0	0
$204$	−2.24916	−0.157473
$205$	2.51404	0.175588
$206$	−15.1959	−1.05875
$207$	−17.2502	−1.19897
$208$	4.66074	0.323164
$209$	−37.3438	−2.58312
$210$	0	0
$211$	17.1046	1.17753	0.588766	−	0.808304i	$-0.299614\pi$
$211$	17.1046	1.17753	0.588766	+	0.808304i	$0.299614\pi$
$212$	−12.8356	−0.881555
$213$	7.19735	0.493154
$214$	−15.9173	−1.08808
$215$	8.85277	0.603754
$216$	−3.54603	−0.241277
$217$	0	0
$218$	9.28757	0.629034
$219$	4.11367	0.277976
$220$	11.9144	0.803269
$221$	−16.5514	−1.11336
$222$	6.06141	0.406815
$223$	17.0518	1.14187	0.570935	−	0.820995i	$-0.306581\pi$
$223$	17.0518	1.14187	0.570935	+	0.820995i	$0.306581\pi$
$224$	0	0
$225$	−0.244122	−0.0162748
$226$	6.40056	0.425759
$227$	−16.5151	−1.09615	−0.548074	−	0.836430i	$-0.684639\pi$
$227$	−16.5151	−1.09615	−0.548074	+	0.836430i	$0.684639\pi$
$228$	−4.48038	−0.296720
$229$	−10.5070	−0.694323	−0.347161	−	0.937805i	$-0.612854\pi$
$229$	−10.5070	−0.694323	−0.347161	+	0.937805i	$0.612854\pi$
$230$	14.9808	0.987806
$231$	0	0
$232$	1.34429	0.0882569
$233$	0.700264	0.0458758	0.0229379	−	0.999737i	$-0.492698\pi$
$233$	0.700264	0.0458758	0.0229379	+	0.999737i	$0.492698\pi$
$234$	−12.1127	−0.791829
$235$	−2.04497	−0.133399
$236$	−6.91021	−0.449816
$237$	0.633348	0.0411404
$238$	0	0
$239$	20.6480	1.33561	0.667803	−	0.744338i	$-0.267235\pi$
$239$	20.6480	1.33561	0.667803	+	0.744338i	$0.267235\pi$
$240$	1.42945	0.0922706
$241$	5.70325	0.367379	0.183689	−	0.982984i	$-0.441196\pi$
$241$	5.70325	0.367379	0.183689	+	0.982984i	$0.441196\pi$
$242$	16.8671	1.08426
$243$	14.1536	0.907957
$244$	11.0404	0.706792
$245$	0	0
$246$	0.705484	0.0449800
$247$	−32.9706	−2.09787
$248$	1.28906	0.0818553
$249$	5.26344	0.333557
$250$	−11.0729	−0.700310
$251$	12.9005	0.814273	0.407136	−	0.913367i	$-0.366527\pi$
$251$	12.9005	0.814273	0.407136	+	0.913367i	$0.366527\pi$
$252$	0	0
$253$	35.0393	2.20290
$254$	−19.3182	−1.21213
$255$	−5.07630	−0.317891
$256$	1.00000	0.0625000
$257$	14.9567	0.932974	0.466487	−	0.884528i	$-0.345519\pi$
$257$	14.9567	0.932974	0.466487	+	0.884528i	$0.345519\pi$
$258$	2.48425	0.154662
$259$	0	0
$260$	10.5192	0.652371
$261$	−3.49364	−0.216251
$262$	2.11002	0.130357
$263$	−25.9031	−1.59726	−0.798628	−	0.601826i	$-0.794440\pi$
$263$	−25.9031	−1.59726	−0.798628	+	0.601826i	$0.794440\pi$
$264$	3.34340	0.205772
$265$	−28.9697	−1.77959
$266$	0	0
$267$	−4.08588	−0.250052
$268$	12.8944	0.787650
$269$	12.5068	0.762553	0.381277	−	0.924461i	$-0.375485\pi$
$269$	12.5068	0.762553	0.381277	+	0.924461i	$0.375485\pi$
$270$	−8.00330	−0.487066
$271$	−23.0355	−1.39931	−0.699654	−	0.714482i	$-0.746662\pi$
$271$	−23.0355	−1.39931	−0.699654	+	0.714482i	$0.746662\pi$
$272$	−3.55123	−0.215325
$273$	0	0
$274$	−14.8831	−0.899121
$275$	0.495870	0.0299021
$276$	4.20389	0.253044
$277$	−7.43340	−0.446630	−0.223315	−	0.974746i	$-0.571688\pi$
$277$	−7.43340	−0.446630	−0.223315	+	0.974746i	$0.571688\pi$
$278$	−0.661630	−0.0396819
$279$	−3.35009	−0.200565
$280$	0	0
$281$	−9.74518	−0.581348	−0.290674	−	0.956822i	$-0.593880\pi$
$281$	−9.74518	−0.581348	−0.290674	+	0.956822i	$0.593880\pi$
$282$	−0.573855	−0.0341726
$283$	−9.77448	−0.581033	−0.290516	−	0.956870i	$-0.593827\pi$
$283$	−9.77448	−0.581033	−0.290516	+	0.956870i	$0.593827\pi$
$284$	11.3640	0.674328
$285$	−10.1121	−0.598989
$286$	24.6037	1.45485
$287$	0	0
$288$	−2.59887	−0.153140
$289$	−4.38877	−0.258163
$290$	3.03403	0.178164
$291$	−1.28589	−0.0753805
$292$	6.49512	0.380098
$293$	18.8142	1.09914	0.549568	−	0.835449i	$-0.314792\pi$
$293$	18.8142	1.09914	0.549568	+	0.835449i	$0.314792\pi$
$294$	0	0
$295$	−15.5962	−0.908043
$296$	9.57042	0.556269
$297$	−18.7193	−1.08620
$298$	−14.6199	−0.846906
$299$	30.9360	1.78907
$300$	0.0594928	0.00343482
$301$	0	0
$302$	−14.5083	−0.834862
$303$	8.93545	0.513328
$304$	−7.07412	−0.405729
$305$	24.9180	1.42680
$306$	9.22919	0.527597
$307$	−10.3194	−0.588956	−0.294478	−	0.955658i	$-0.595146\pi$
$307$	−10.3194	−0.588956	−0.294478	+	0.955658i	$0.595146\pi$
$308$	0	0
$309$	−9.62427	−0.547506
$310$	2.90937	0.165241
$311$	22.3945	1.26988	0.634938	−	0.772563i	$-0.281026\pi$
$311$	22.3945	1.26988	0.634938	+	0.772563i	$0.281026\pi$
$312$	2.95187	0.167117
$313$	−4.09573	−0.231504	−0.115752	−	0.993278i	$-0.536928\pi$
$313$	−4.09573	−0.231504	−0.115752	+	0.993278i	$0.536928\pi$
$314$	8.55607	0.482847
$315$	0	0
$316$	1.00000	0.0562544
$317$	20.9717	1.17789	0.588945	−	0.808173i	$-0.299543\pi$
$317$	20.9717	1.17789	0.588945	+	0.808173i	$0.299543\pi$
$318$	−8.12942	−0.455875
$319$	7.09641	0.397323
$320$	2.25697	0.126169
$321$	−10.0812	−0.562676
$322$	0	0
$323$	25.1218	1.39782
$324$	5.55074	0.308374
$325$	0.437801	0.0242848
$326$	23.6056	1.30740
$327$	5.88226	0.325290
$328$	1.11390	0.0615047
$329$	0	0
$330$	7.54597	0.415392
$331$	16.3424	0.898260	0.449130	−	0.893466i	$-0.351734\pi$
$331$	16.3424	0.898260	0.449130	+	0.893466i	$0.351734\pi$
$332$	8.31051	0.456098
$333$	−24.8723	−1.36299
$334$	24.1103	1.31925
$335$	29.1023	1.59003
$336$	0	0
$337$	−8.99311	−0.489886	−0.244943	−	0.969538i	$-0.578769\pi$
$337$	−8.99311	−0.489886	−0.244943	+	0.969538i	$0.578769\pi$
$338$	8.72249	0.474441
$339$	4.05378	0.220171
$340$	−8.01503	−0.434676
$341$	6.80485	0.368503
$342$	18.3847	0.994132
$343$	0	0
$344$	3.92241	0.211482
$345$	9.48807	0.510820
$346$	2.97020	0.159679
$347$	10.4471	0.560830	0.280415	−	0.959879i	$-0.409528\pi$
$347$	10.4471	0.560830	0.280415	+	0.959879i	$0.409528\pi$
$348$	0.851403	0.0456400
$349$	−18.6072	−0.996021	−0.498011	−	0.867171i	$-0.665936\pi$
$349$	−18.6072	−0.996021	−0.498011	+	0.867171i	$0.665936\pi$
$350$	0	0
$351$	−16.5271	−0.882153
$352$	5.27893	0.281368
$353$	−5.30241	−0.282219	−0.141109	−	0.989994i	$-0.545067\pi$
$353$	−5.30241	−0.282219	−0.141109	+	0.989994i	$0.545067\pi$
$354$	−4.37656	−0.232612
$355$	25.6482	1.36127
$356$	−6.45124	−0.341915
$357$	0	0
$358$	2.08550	0.110222
$359$	13.7769	0.727117	0.363558	−	0.931571i	$-0.381562\pi$
$359$	13.7769	0.727117	0.363558	+	0.931571i	$0.381562\pi$
$360$	−5.86558	−0.309143
$361$	31.0432	1.63385
$362$	−22.6586	−1.19091
$363$	10.6827	0.560699
$364$	0	0
$365$	14.6593	0.767304
$366$	6.99244	0.365501
$367$	18.0162	0.940440	0.470220	−	0.882549i	$-0.344175\pi$
$367$	18.0162	0.940440	0.470220	+	0.882549i	$0.344175\pi$
$368$	6.63757	0.346007
$369$	−2.89487	−0.150701
$370$	21.6002	1.12294
$371$	0	0
$372$	0.816422	0.0423295
$373$	−35.9695	−1.86243	−0.931214	−	0.364473i	$-0.881249\pi$
$373$	−35.9695	−1.86243	−0.931214	+	0.364473i	$0.881249\pi$
$374$	−18.7467	−0.969368
$375$	−7.01298	−0.362149
$376$	−0.906066	−0.0467268
$377$	6.26538	0.322684
$378$	0	0
$379$	−16.8266	−0.864326	−0.432163	−	0.901795i	$-0.642250\pi$
$379$	−16.8266	−0.864326	−0.432163	+	0.901795i	$0.642250\pi$
$380$	−15.9661	−0.819044
$381$	−12.2352	−0.626827
$382$	−20.1756	−1.03228
$383$	−28.2129	−1.44161	−0.720806	−	0.693137i	$-0.756228\pi$
$383$	−28.2129	−1.44161	−0.720806	+	0.693137i	$0.756228\pi$
$384$	0.633348	0.0323204
$385$	0	0
$386$	−16.0563	−0.817245
$387$	−10.1938	−0.518181
$388$	−2.03031	−0.103074
$389$	−16.1937	−0.821056	−0.410528	−	0.911848i	$-0.634656\pi$
$389$	−16.1937	−0.821056	−0.410528	+	0.911848i	$0.634656\pi$
$390$	6.66229	0.337358
$391$	−23.5715	−1.19206
$392$	0	0
$393$	1.33638	0.0674113
$394$	14.6290	0.736997
$395$	2.25697	0.113561
$396$	−13.7193	−0.689419
$397$	−30.3540	−1.52343	−0.761713	−	0.647915i	$-0.775641\pi$
$397$	−30.3540	−1.52343	−0.761713	+	0.647915i	$0.775641\pi$
$398$	−17.6802	−0.886230
$399$	0	0
$400$	0.0939338	0.00469669
$401$	13.2769	0.663017	0.331509	−	0.943452i	$-0.392442\pi$
$401$	13.2769	0.663017	0.331509	+	0.943452i	$0.392442\pi$
$402$	8.16663	0.407314
$403$	6.00796	0.299278
$404$	14.1083	0.701913
$405$	12.5279	0.622515
$406$	0	0
$407$	50.5216	2.50426
$408$	−2.24916	−0.111350
$409$	16.5441	0.818051	0.409025	−	0.912523i	$-0.365869\pi$
$409$	16.5441	0.818051	0.409025	+	0.912523i	$0.365869\pi$
$410$	2.51404	0.124159
$411$	−9.42618	−0.464959
$412$	−15.1959	−0.748647
$413$	0	0
$414$	−17.2502	−0.847800
$415$	18.7566	0.920725
$416$	4.66074	0.228512
$417$	−0.419042	−0.0205206
$418$	−37.3438	−1.82655
$419$	−5.10448	−0.249370	−0.124685	−	0.992196i	$-0.539792\pi$
$419$	−5.10448	−0.249370	−0.124685	+	0.992196i	$0.539792\pi$
$420$	0	0
$421$	11.3403	0.552691	0.276346	−	0.961058i	$-0.410877\pi$
$421$	11.3403	0.552691	0.276346	+	0.961058i	$0.410877\pi$
$422$	17.1046	0.832641
$423$	2.35475	0.114492
$424$	−12.8356	−0.623353
$425$	−0.333581	−0.0161810
$426$	7.19735	0.348713
$427$	0	0
$428$	−15.9173	−0.769391
$429$	15.5827	0.752340
$430$	8.85277	0.426918
$431$	−22.1586	−1.06734	−0.533670	−	0.845693i	$-0.679188\pi$
$431$	−22.1586	−1.06734	−0.533670	+	0.845693i	$0.679188\pi$
$432$	−3.54603	−0.170609
$433$	34.8399	1.67430	0.837149	−	0.546975i	$-0.184221\pi$
$433$	34.8399	1.67430	0.837149	+	0.546975i	$0.184221\pi$
$434$	0	0
$435$	1.92159	0.0921334
$436$	9.28757	0.444794
$437$	−46.9550	−2.24616
$438$	4.11367	0.196559
$439$	4.73739	0.226103	0.113052	−	0.993589i	$-0.463937\pi$
$439$	4.73739	0.226103	0.113052	+	0.993589i	$0.463937\pi$
$440$	11.9144	0.567997
$441$	0	0
$442$	−16.5514	−0.787268
$443$	18.9012	0.898021	0.449011	−	0.893526i	$-0.351777\pi$
$443$	18.9012	0.898021	0.449011	+	0.893526i	$0.351777\pi$
$444$	6.06141	0.287662
$445$	−14.5603	−0.690224
$446$	17.0518	0.807424
$447$	−9.25946	−0.437958
$448$	0	0
$449$	5.17789	0.244360	0.122180	−	0.992508i	$-0.461012\pi$
$449$	5.17789	0.244360	0.122180	+	0.992508i	$0.461012\pi$
$450$	−0.244122	−0.0115080
$451$	5.88018	0.276887
$452$	6.40056	0.301057
$453$	−9.18883	−0.431729
$454$	−16.5151	−0.775093
$455$	0	0
$456$	−4.48038	−0.209813
$457$	−16.6714	−0.779854	−0.389927	−	0.920846i	$-0.627500\pi$
$457$	−16.6714	−0.779854	−0.389927	+	0.920846i	$0.627500\pi$
$458$	−10.5070	−0.490960
$459$	12.5928	0.587780
$460$	14.9808	0.698484
$461$	6.97526	0.324870	0.162435	−	0.986719i	$-0.448065\pi$
$461$	6.97526	0.324870	0.162435	+	0.986719i	$0.448065\pi$
$462$	0	0
$463$	−19.2141	−0.892957	−0.446478	−	0.894794i	$-0.647322\pi$
$463$	−19.2141	−0.892957	−0.446478	+	0.894794i	$0.647322\pi$
$464$	1.34429	0.0624071
$465$	1.84264	0.0854506
$466$	0.700264	0.0324391
$467$	−30.2224	−1.39853	−0.699263	−	0.714864i	$-0.746488\pi$
$467$	−30.2224	−1.39853	−0.699263	+	0.714864i	$0.746488\pi$
$468$	−12.1127	−0.559908
$469$	0	0
$470$	−2.04497	−0.0943274
$471$	5.41897	0.249693
$472$	−6.91021	−0.318068
$473$	20.7061	0.952068
$474$	0.633348	0.0290906
$475$	−0.664499	−0.0304893
$476$	0	0
$477$	33.3581	1.52736
$478$	20.6480	0.944417
$479$	−4.82161	−0.220305	−0.110153	−	0.993915i	$-0.535134\pi$
$479$	−4.82161	−0.220305	−0.110153	+	0.993915i	$0.535134\pi$
$480$	1.42945	0.0652452
$481$	44.6052	2.03382
$482$	5.70325	0.259776
$483$	0	0
$484$	16.8671	0.766687
$485$	−4.58237	−0.208074
$486$	14.1536	0.642022
$487$	11.4363	0.518226	0.259113	−	0.965847i	$-0.416570\pi$
$487$	11.4363	0.518226	0.259113	+	0.965847i	$0.416570\pi$
$488$	11.0404	0.499777
$489$	14.9506	0.676089
$490$	0	0
$491$	10.9993	0.496389	0.248195	−	0.968710i	$-0.420163\pi$
$491$	10.9993	0.496389	0.248195	+	0.968710i	$0.420163\pi$
$492$	0.705484	0.0318057
$493$	−4.77388	−0.215005
$494$	−32.9706	−1.48342
$495$	−30.9640	−1.39173
$496$	1.28906	0.0578804
$497$	0	0
$498$	5.26344	0.235860
$499$	−5.27154	−0.235987	−0.117993	−	0.993014i	$-0.537646\pi$
$499$	−5.27154	−0.235987	−0.117993	+	0.993014i	$0.537646\pi$
$500$	−11.0729	−0.495194
$501$	15.2702	0.682221
$502$	12.9005	0.575778
$503$	−6.11100	−0.272476	−0.136238	−	0.990676i	$-0.543501\pi$
$503$	−6.11100	−0.272476	−0.136238	+	0.990676i	$0.543501\pi$
$504$	0	0
$505$	31.8420	1.41695
$506$	35.0393	1.55768
$507$	5.52437	0.245346
$508$	−19.3182	−0.857109
$509$	−29.8727	−1.32409	−0.662043	−	0.749466i	$-0.730310\pi$
$509$	−29.8727	−1.32409	−0.662043	+	0.749466i	$0.730310\pi$
$510$	−5.07630	−0.224783
$511$	0	0
$512$	1.00000	0.0441942
$513$	25.0851	1.10753
$514$	14.9567	0.659712
$515$	−34.2967	−1.51129
$516$	2.48425	0.109363
$517$	−4.78306	−0.210359
$518$	0	0
$519$	1.88117	0.0825742
$520$	10.5192	0.461296
$521$	18.2345	0.798866	0.399433	−	0.916762i	$-0.369207\pi$
$521$	18.2345	0.798866	0.399433	+	0.916762i	$0.369207\pi$
$522$	−3.49364	−0.152912
$523$	−27.5397	−1.20423	−0.602113	−	0.798411i	$-0.705674\pi$
$523$	−27.5397	−1.20423	−0.602113	+	0.798411i	$0.705674\pi$
$524$	2.11002	0.0921766
$525$	0	0
$526$	−25.9031	−1.12943
$527$	−4.57774	−0.199410
$528$	3.34340	0.145503
$529$	21.0573	0.915534
$530$	−28.9697	−1.25836
$531$	17.9587	0.779343
$532$	0	0
$533$	5.19158	0.224872
$534$	−4.08588	−0.176813
$535$	−35.9249	−1.55317
$536$	12.8944	0.556952
$537$	1.32085	0.0569988
$538$	12.5068	0.539207
$539$	0	0
$540$	−8.00330	−0.344407
$541$	29.3228	1.26068	0.630342	−	0.776318i	$-0.282915\pi$
$541$	29.3228	1.26068	0.630342	+	0.776318i	$0.282915\pi$
$542$	−23.0355	−0.989460
$543$	−14.3508	−0.615850
$544$	−3.55123	−0.152258
$545$	20.9618	0.897905
$546$	0	0
$547$	12.0449	0.515002	0.257501	−	0.966278i	$-0.417101\pi$
$547$	12.0449	0.515002	0.257501	+	0.966278i	$0.417101\pi$
$548$	−14.8831	−0.635775
$549$	−28.6927	−1.22457
$550$	0.495870	0.0211440
$551$	−9.50967	−0.405126
$552$	4.20389	0.178929
$553$	0	0
$554$	−7.43340	−0.315815
$555$	13.6804	0.580702
$556$	−0.661630	−0.0280594
$557$	−33.1102	−1.40292	−0.701461	−	0.712708i	$-0.747469\pi$
$557$	−33.1102	−1.40292	−0.701461	+	0.712708i	$0.747469\pi$
$558$	−3.35009	−0.141821
$559$	18.2813	0.773217
$560$	0	0
$561$	−11.8732	−0.501286
$562$	−9.74518	−0.411075
$563$	14.2794	0.601804	0.300902	−	0.953655i	$-0.402712\pi$
$563$	14.2794	0.601804	0.300902	+	0.953655i	$0.402712\pi$
$564$	−0.573855	−0.0241637
$565$	14.4459	0.607743
$566$	−9.77448	−0.410852
$567$	0	0
$568$	11.3640	0.476822
$569$	−23.8262	−0.998847	−0.499424	−	0.866358i	$-0.666455\pi$
$569$	−23.8262	−0.998847	−0.499424	+	0.866358i	$0.666455\pi$
$570$	−10.1121	−0.423549
$571$	−14.2721	−0.597267	−0.298633	−	0.954368i	$-0.596531\pi$
$571$	−14.2721	−0.597267	−0.298633	+	0.954368i	$0.596531\pi$
$572$	24.6037	1.02873
$573$	−12.7782	−0.533817
$574$	0	0
$575$	0.623492	0.0260014
$576$	−2.59887	−0.108286
$577$	−19.7394	−0.821761	−0.410880	−	0.911689i	$-0.634779\pi$
$577$	−19.7394	−0.821761	−0.410880	+	0.911689i	$0.634779\pi$
$578$	−4.38877	−0.182549
$579$	−10.1692	−0.422619
$580$	3.03403	0.125981
$581$	0	0
$582$	−1.28589	−0.0533020
$583$	−67.7584	−2.80627
$584$	6.49512	0.268770
$585$	−27.3380	−1.13029
$586$	18.8142	0.777207
$587$	21.2081	0.875354	0.437677	−	0.899132i	$-0.355801\pi$
$587$	21.2081	0.875354	0.437677	+	0.899132i	$0.355801\pi$
$588$	0	0
$589$	−9.11896	−0.375740
$590$	−15.5962	−0.642084
$591$	9.26523	0.381120
$592$	9.57042	0.393342
$593$	21.5515	0.885015	0.442507	−	0.896765i	$-0.354089\pi$
$593$	21.5515	0.885015	0.442507	+	0.896765i	$0.354089\pi$
$594$	−18.7193	−0.768060
$595$	0	0
$596$	−14.6199	−0.598853
$597$	−11.1977	−0.458293
$598$	30.9360	1.26507
$599$	26.2745	1.07355	0.536774	−	0.843726i	$-0.319643\pi$
$599$	26.2745	1.07355	0.536774	+	0.843726i	$0.319643\pi$
$600$	0.0594928	0.00242878
$601$	48.0945	1.96182	0.980908	−	0.194471i	$-0.0622990\pi$
$601$	48.0945	1.96182	0.980908	+	0.194471i	$0.0622990\pi$
$602$	0	0
$603$	−33.5108	−1.36467
$604$	−14.5083	−0.590336
$605$	38.0686	1.54771
$606$	8.93545	0.362978
$607$	−5.92545	−0.240507	−0.120253	−	0.992743i	$-0.538371\pi$
$607$	−5.92545	−0.240507	−0.120253	+	0.992743i	$0.538371\pi$
$608$	−7.07412	−0.286894
$609$	0	0
$610$	24.9180	1.00890
$611$	−4.22294	−0.170842
$612$	9.22919	0.373068
$613$	−17.6660	−0.713522	−0.356761	−	0.934196i	$-0.616119\pi$
$613$	−17.6660	−0.713522	−0.356761	+	0.934196i	$0.616119\pi$
$614$	−10.3194	−0.416455
$615$	1.59226	0.0642061
$616$	0	0
$617$	−16.3592	−0.658599	−0.329299	−	0.944226i	$-0.606813\pi$
$617$	−16.3592	−0.658599	−0.329299	+	0.944226i	$0.606813\pi$
$618$	−9.62427	−0.387145
$619$	14.3951	0.578587	0.289293	−	0.957240i	$-0.406580\pi$
$619$	14.3951	0.578587	0.289293	+	0.957240i	$0.406580\pi$
$620$	2.90937	0.116843
$621$	−23.5370	−0.944508
$622$	22.3945	0.897938
$623$	0	0
$624$	2.95187	0.118169
$625$	−25.4608	−1.01843
$626$	−4.09573	−0.163698
$627$	−23.6516	−0.944555
$628$	8.55607	0.341425
$629$	−33.9868	−1.35514
$630$	0	0
$631$	36.4529	1.45117	0.725583	−	0.688135i	$-0.241570\pi$
$631$	36.4529	1.45117	0.725583	+	0.688135i	$0.241570\pi$
$632$	1.00000	0.0397779
$633$	10.8332	0.430581
$634$	20.9717	0.832894
$635$	−43.6008	−1.73024
$636$	−8.12942	−0.322353
$637$	0	0
$638$	7.09641	0.280950
$639$	−29.5335	−1.16833
$640$	2.25697	0.0892147
$641$	−13.7629	−0.543601	−0.271801	−	0.962354i	$-0.587619\pi$
$641$	−13.7629	−0.543601	−0.271801	+	0.962354i	$0.587619\pi$
$642$	−10.0812	−0.397872
$643$	−46.2943	−1.82567	−0.912835	−	0.408329i	$-0.866112\pi$
$643$	−46.2943	−1.82567	−0.912835	+	0.408329i	$0.866112\pi$
$644$	0	0
$645$	5.60688	0.220771
$646$	25.1218	0.988405
$647$	−9.20407	−0.361849	−0.180925	−	0.983497i	$-0.557909\pi$
$647$	−9.20407	−0.361849	−0.180925	+	0.983497i	$0.557909\pi$
$648$	5.55074	0.218054
$649$	−36.4785	−1.43191
$650$	0.437801	0.0171720
$651$	0	0
$652$	23.6056	0.924468
$653$	−20.9889	−0.821360	−0.410680	−	0.911780i	$-0.634709\pi$
$653$	−20.9889	−0.821360	−0.410680	+	0.911780i	$0.634709\pi$
$654$	5.88226	0.230015
$655$	4.76226	0.186077
$656$	1.11390	0.0434904
$657$	−16.8800	−0.658550
$658$	0	0
$659$	−6.02589	−0.234735	−0.117368	−	0.993089i	$-0.537446\pi$
$659$	−6.02589	−0.234735	−0.117368	+	0.993089i	$0.537446\pi$
$660$	7.54597	0.293726
$661$	−41.5313	−1.61538	−0.807690	−	0.589607i	$-0.799282\pi$
$661$	−41.5313	−1.61538	−0.807690	+	0.589607i	$0.799282\pi$
$662$	16.3424	0.635166
$663$	−10.4828	−0.407117
$664$	8.31051	0.322510
$665$	0	0
$666$	−24.8723	−0.963781
$667$	8.92281	0.345493
$668$	24.1103	0.932854
$669$	10.7997	0.417540
$670$	29.1023	1.12432
$671$	58.2817	2.24994
$672$	0	0
$673$	−5.43414	−0.209471	−0.104735	−	0.994500i	$-0.533400\pi$
$673$	−5.43414	−0.209471	−0.104735	+	0.994500i	$0.533400\pi$
$674$	−8.99311	−0.346401
$675$	−0.333092	−0.0128207
$676$	8.72249	0.335480
$677$	−32.9253	−1.26542	−0.632710	−	0.774389i	$-0.718058\pi$
$677$	−32.9253	−1.26542	−0.632710	+	0.774389i	$0.718058\pi$
$678$	4.05378	0.155684
$679$	0	0
$680$	−8.01503	−0.307363
$681$	−10.4598	−0.400821
$682$	6.80485	0.260571
$683$	−28.1822	−1.07836	−0.539180	−	0.842190i	$-0.681266\pi$
$683$	−28.1822	−1.07836	−0.539180	+	0.842190i	$0.681266\pi$
$684$	18.3847	0.702958
$685$	−33.5908	−1.28344
$686$	0	0
$687$	−6.65459	−0.253889
$688$	3.92241	0.149540
$689$	−59.8235	−2.27910
$690$	9.48807	0.361205
$691$	−32.0321	−1.21856	−0.609280	−	0.792955i	$-0.708541\pi$
$691$	−32.0321	−1.21856	−0.609280	+	0.792955i	$0.708541\pi$
$692$	2.97020	0.112910
$693$	0	0
$694$	10.4471	0.396567
$695$	−1.49328	−0.0566434
$696$	0.851403	0.0322723
$697$	−3.95570	−0.149833
$698$	−18.6072	−0.704294
$699$	0.443511	0.0167751
$700$	0	0
$701$	−13.5538	−0.511919	−0.255959	−	0.966688i	$-0.582391\pi$
$701$	−13.5538	−0.511919	−0.255959	+	0.966688i	$0.582391\pi$
$702$	−16.5271	−0.623776
$703$	−67.7023	−2.55344
$704$	5.27893	0.198957
$705$	−1.29518	−0.0487792
$706$	−5.30241	−0.199559
$707$	0	0
$708$	−4.37656	−0.164481
$709$	−11.8457	−0.444876	−0.222438	−	0.974947i	$-0.571401\pi$
$709$	−11.8457	−0.444876	−0.222438	+	0.974947i	$0.571401\pi$
$710$	25.6482	0.962560
$711$	−2.59887	−0.0974653
$712$	−6.45124	−0.241771
$713$	8.55621	0.320433
$714$	0	0
$715$	55.5300	2.07670
$716$	2.08550	0.0779388
$717$	13.0774	0.488383
$718$	13.7769	0.514149
$719$	−8.03579	−0.299684	−0.149842	−	0.988710i	$-0.547877\pi$
$719$	−8.03579	−0.299684	−0.149842	+	0.988710i	$0.547877\pi$
$720$	−5.86558	−0.218597
$721$	0	0
$722$	31.0432	1.15531
$723$	3.61214	0.134337
$724$	−22.6586	−0.842100
$725$	0.126274	0.00468971
$726$	10.6827	0.396474
$727$	39.0901	1.44977	0.724886	−	0.688869i	$-0.241892\pi$
$727$	39.0901	1.44977	0.724886	+	0.688869i	$0.241892\pi$
$728$	0	0
$729$	−7.68804	−0.284742
$730$	14.6593	0.542566
$731$	−13.9294	−0.515196
$732$	6.99244	0.258448
$733$	3.59760	0.132880	0.0664402	−	0.997790i	$-0.478836\pi$
$733$	3.59760	0.132880	0.0664402	+	0.997790i	$0.478836\pi$
$734$	18.0162	0.664991
$735$	0	0
$736$	6.63757	0.244664
$737$	68.0685	2.50734
$738$	−2.89487	−0.106562
$739$	23.8388	0.876926	0.438463	−	0.898749i	$-0.355523\pi$
$739$	23.8388	0.876926	0.438463	+	0.898749i	$0.355523\pi$
$740$	21.6002	0.794039
$741$	−20.8819	−0.767115
$742$	0	0
$743$	−23.7807	−0.872430	−0.436215	−	0.899842i	$-0.643681\pi$
$743$	−23.7807	−0.872430	−0.436215	+	0.899842i	$0.643681\pi$
$744$	0.816422	0.0299315
$745$	−32.9967	−1.20890
$746$	−35.9695	−1.31694
$747$	−21.5979	−0.790227
$748$	−18.7467	−0.685447
$749$	0	0
$750$	−7.01298	−0.256078
$751$	−3.08127	−0.112437	−0.0562185	−	0.998418i	$-0.517904\pi$
$751$	−3.08127	−0.112437	−0.0562185	+	0.998418i	$0.517904\pi$
$752$	−0.906066	−0.0330408
$753$	8.17051	0.297750
$754$	6.26538	0.228172
$755$	−32.7450	−1.19171
$756$	0	0
$757$	−2.53457	−0.0921205	−0.0460603	−	0.998939i	$-0.514667\pi$
$757$	−2.53457	−0.0921205	−0.0460603	+	0.998939i	$0.514667\pi$
$758$	−16.8266	−0.611171
$759$	22.1920	0.805520
$760$	−15.9661	−0.579152
$761$	−21.3414	−0.773624	−0.386812	−	0.922159i	$-0.626424\pi$
$761$	−21.3414	−0.773624	−0.386812	+	0.922159i	$0.626424\pi$
$762$	−12.2352	−0.443233
$763$	0	0
$764$	−20.1756	−0.729929
$765$	20.8300	0.753112
$766$	−28.2129	−1.01937
$767$	−32.2067	−1.16292
$768$	0.633348	0.0228540
$769$	−16.8050	−0.606003	−0.303002	−	0.952990i	$-0.597989\pi$
$769$	−16.8050	−0.606003	−0.303002	+	0.952990i	$0.597989\pi$
$770$	0	0
$771$	9.47280	0.341155
$772$	−16.0563	−0.577880
$773$	−32.4095	−1.16569	−0.582845	−	0.812583i	$-0.698061\pi$
$773$	−32.4095	−1.16569	−0.582845	+	0.812583i	$0.698061\pi$
$774$	−10.1938	−0.366409
$775$	0.121086	0.00434954
$776$	−2.03031	−0.0728840
$777$	0	0
$778$	−16.1937	−0.580574
$779$	−7.87984	−0.282325
$780$	6.66229	0.238548
$781$	59.9896	2.14660
$782$	−23.5715	−0.842916
$783$	−4.76690	−0.170355
$784$	0	0
$785$	19.3108	0.689233
$786$	1.33638	0.0476670
$787$	30.7240	1.09519	0.547595	−	0.836743i	$-0.315543\pi$
$787$	30.7240	1.09519	0.547595	+	0.836743i	$0.315543\pi$
$788$	14.6290	0.521135
$789$	−16.4057	−0.584058
$790$	2.25697	0.0802995
$791$	0	0
$792$	−13.7193	−0.487493
$793$	51.4566	1.82728
$794$	−30.3540	−1.07722
$795$	−18.3479	−0.650733
$796$	−17.6802	−0.626659
$797$	21.2682	0.753359	0.376680	−	0.926344i	$-0.377066\pi$
$797$	21.2682	0.753359	0.376680	+	0.926344i	$0.377066\pi$
$798$	0	0
$799$	3.21765	0.113832
$800$	0.0939338	0.00332106
$801$	16.7659	0.592396
$802$	13.2769	0.468824
$803$	34.2873	1.20997
$804$	8.16663	0.288015
$805$	0	0
$806$	6.00796	0.211621
$807$	7.92116	0.278838
$808$	14.1083	0.496328
$809$	−11.2417	−0.395235	−0.197618	−	0.980279i	$-0.563320\pi$
$809$	−11.2417	−0.395235	−0.197618	+	0.980279i	$0.563320\pi$
$810$	12.5279	0.440185
$811$	6.84725	0.240439	0.120220	−	0.992747i	$-0.461640\pi$
$811$	6.84725	0.240439	0.120220	+	0.992747i	$0.461640\pi$
$812$	0	0
$813$	−14.5895	−0.511676
$814$	50.5216	1.77078
$815$	53.2773	1.86622
$816$	−2.24916	−0.0787365
$817$	−27.7476	−0.970765
$818$	16.5441	0.578449
$819$	0	0
$820$	2.51404	0.0877940
$821$	−26.6354	−0.929580	−0.464790	−	0.885421i	$-0.653870\pi$
$821$	−26.6354	−0.929580	−0.464790	+	0.885421i	$0.653870\pi$
$822$	−9.42618	−0.328776
$823$	30.3563	1.05815	0.529077	−	0.848574i	$-0.322538\pi$
$823$	30.3563	1.05815	0.529077	+	0.848574i	$0.322538\pi$
$824$	−15.1959	−0.529373
$825$	0.314058	0.0109341
$826$	0	0
$827$	−19.6578	−0.683570	−0.341785	−	0.939778i	$-0.611031\pi$
$827$	−19.6578	−0.683570	−0.341785	+	0.939778i	$0.611031\pi$
$828$	−17.2502	−0.599485
$829$	28.6799	0.996095	0.498047	−	0.867150i	$-0.334051\pi$
$829$	28.6799	0.996095	0.498047	+	0.867150i	$0.334051\pi$
$830$	18.7566	0.651051
$831$	−4.70793	−0.163316
$832$	4.66074	0.161582
$833$	0	0
$834$	−0.419042	−0.0145102
$835$	54.4162	1.88315
$836$	−37.3438	−1.29156
$837$	−4.57104	−0.157998
$838$	−5.10448	−0.176331
$839$	26.7592	0.923830	0.461915	−	0.886924i	$-0.347163\pi$
$839$	26.7592	0.923830	0.461915	+	0.886924i	$0.347163\pi$
$840$	0	0
$841$	−27.1929	−0.937686
$842$	11.3403	0.390812
$843$	−6.17209	−0.212578
$844$	17.1046	0.588766
$845$	19.6864	0.677234
$846$	2.35475	0.0809579
$847$	0	0
$848$	−12.8356	−0.440777
$849$	−6.19065	−0.212462
$850$	−0.333581	−0.0114417
$851$	63.5243	2.17759
$852$	7.19735	0.246577
$853$	43.6102	1.49319	0.746593	−	0.665281i	$-0.231688\pi$
$853$	43.6102	1.49319	0.746593	+	0.665281i	$0.231688\pi$
$854$	0	0
$855$	41.4939	1.41906
$856$	−15.9173	−0.544042
$857$	−51.7778	−1.76870	−0.884348	−	0.466828i	$-0.845397\pi$
$857$	−51.7778	−1.76870	−0.884348	+	0.466828i	$0.845397\pi$
$858$	15.5827	0.531985
$859$	6.97440	0.237963	0.118982	−	0.992896i	$-0.462037\pi$
$859$	6.97440	0.237963	0.118982	+	0.992896i	$0.462037\pi$
$860$	8.85277	0.301877
$861$	0	0
$862$	−22.1586	−0.754723
$863$	12.5428	0.426963	0.213481	−	0.976947i	$-0.431520\pi$
$863$	12.5428	0.426963	0.213481	+	0.976947i	$0.431520\pi$
$864$	−3.54603	−0.120638
$865$	6.70367	0.227932
$866$	34.8399	1.18391
$867$	−2.77962	−0.0944008
$868$	0	0
$869$	5.27893	0.179075
$870$	1.92159	0.0651482
$871$	60.0973	2.03632
$872$	9.28757	0.314517
$873$	5.27652	0.178583
$874$	−46.9550	−1.58828
$875$	0	0
$876$	4.11367	0.138988
$877$	−45.0646	−1.52172	−0.760861	−	0.648914i	$-0.775223\pi$
$877$	−45.0646	−1.52172	−0.760861	+	0.648914i	$0.775223\pi$
$878$	4.73739	0.159879
$879$	11.9159	0.401914
$880$	11.9144	0.401635
$881$	26.5981	0.896111	0.448056	−	0.894006i	$-0.352117\pi$
$881$	26.5981	0.896111	0.448056	+	0.894006i	$0.352117\pi$
$882$	0	0
$883$	−23.3156	−0.784634	−0.392317	−	0.919830i	$-0.628326\pi$
$883$	−23.3156	−0.784634	−0.392317	+	0.919830i	$0.628326\pi$
$884$	−16.5514	−0.556682
$885$	−9.87779	−0.332038
$886$	18.9012	0.634997
$887$	39.3232	1.32034	0.660172	−	0.751115i	$-0.270483\pi$
$887$	39.3232	1.32034	0.660172	+	0.751115i	$0.270483\pi$
$888$	6.06141	0.203407
$889$	0	0
$890$	−14.5603	−0.488062
$891$	29.3020	0.981653
$892$	17.0518	0.570935
$893$	6.40962	0.214490
$894$	−9.25946	−0.309683
$895$	4.70692	0.157335
$896$	0	0
$897$	19.5932	0.654199
$898$	5.17789	0.172789
$899$	1.73287	0.0577944
$900$	−0.244122	−0.00813740
$901$	45.5823	1.51857
$902$	5.88018	0.195789
$903$	0	0
$904$	6.40056	0.212879
$905$	−51.1398	−1.69995
$906$	−9.18883	−0.305278
$907$	9.27873	0.308095	0.154048	−	0.988063i	$-0.450769\pi$
$907$	9.27873	0.308095	0.154048	+	0.988063i	$0.450769\pi$
$908$	−16.5151	−0.548074
$909$	−36.6656	−1.21612
$910$	0	0
$911$	−50.5835	−1.67590	−0.837952	−	0.545743i	$-0.816247\pi$
$911$	−50.5835	−1.67590	−0.837952	+	0.545743i	$0.816247\pi$
$912$	−4.48038	−0.148360
$913$	43.8706	1.45190
$914$	−16.6714	−0.551440
$915$	15.7818	0.521729
$916$	−10.5070	−0.347161
$917$	0	0
$918$	12.5928	0.415624
$919$	8.43707	0.278313	0.139157	−	0.990270i	$-0.455561\pi$
$919$	8.43707	0.278313	0.139157	+	0.990270i	$0.455561\pi$
$920$	14.9808	0.493903
$921$	−6.53574	−0.215360
$922$	6.97526	0.229718
$923$	52.9645	1.74335
$924$	0	0
$925$	0.898986	0.0295585
$926$	−19.2141	−0.631416
$927$	39.4921	1.29709
$928$	1.34429	0.0441285
$929$	−3.50026	−0.114840	−0.0574198	−	0.998350i	$-0.518287\pi$
$929$	−3.50026	−0.114840	−0.0574198	+	0.998350i	$0.518287\pi$
$930$	1.84264	0.0604227
$931$	0	0
$932$	0.700264	0.0229379
$933$	14.1835	0.464347
$934$	−30.2224	−0.988908
$935$	−42.3108	−1.38371
$936$	−12.1127	−0.395915
$937$	44.1708	1.44300	0.721498	−	0.692416i	$-0.243454\pi$
$937$	44.1708	1.44300	0.721498	+	0.692416i	$0.243454\pi$
$938$	0	0
$939$	−2.59402	−0.0846526
$940$	−2.04497	−0.0666995
$941$	−10.6221	−0.346269	−0.173135	−	0.984898i	$-0.555390\pi$
$941$	−10.6221	−0.346269	−0.173135	+	0.984898i	$0.555390\pi$
$942$	5.41897	0.176560
$943$	7.39356	0.240768
$944$	−6.91021	−0.224908
$945$	0	0
$946$	20.7061	0.673214
$947$	−14.3300	−0.465662	−0.232831	−	0.972517i	$-0.574799\pi$
$947$	−14.3300	−0.465662	−0.232831	+	0.972517i	$0.574799\pi$
$948$	0.633348	0.0205702
$949$	30.2721	0.982672
$950$	−0.664499	−0.0215592
$951$	13.2824	0.430712
$952$	0	0
$953$	−16.3091	−0.528304	−0.264152	−	0.964481i	$-0.585092\pi$
$953$	−16.3091	−0.528304	−0.264152	+	0.964481i	$0.585092\pi$
$954$	33.3581	1.08001
$955$	−45.5359	−1.47351
$956$	20.6480	0.667803
$957$	4.49450	0.145286
$958$	−4.82161	−0.155779
$959$	0	0
$960$	1.42945	0.0461353
$961$	−29.3383	−0.946398
$962$	44.6052	1.43813
$963$	41.3670	1.33303
$964$	5.70325	0.183689
$965$	−36.2387	−1.16657
$966$	0	0
$967$	−7.91647	−0.254576	−0.127288	−	0.991866i	$-0.540627\pi$
$967$	−7.91647	−0.254576	−0.127288	+	0.991866i	$0.540627\pi$
$968$	16.8671	0.542129
$969$	15.9109	0.511130
$970$	−4.58237	−0.147131
$971$	55.0534	1.76675	0.883374	−	0.468669i	$-0.155266\pi$
$971$	55.0534	1.76675	0.883374	+	0.468669i	$0.155266\pi$
$972$	14.1536	0.453978
$973$	0	0
$974$	11.4363	0.366441
$975$	0.277280	0.00888008
$976$	11.0404	0.353396
$977$	11.3005	0.361535	0.180767	−	0.983526i	$-0.442142\pi$
$977$	11.3005	0.361535	0.180767	+	0.983526i	$0.442142\pi$
$978$	14.9506	0.478067
$979$	−34.0557	−1.08842
$980$	0	0
$981$	−24.1372	−0.770641
$982$	10.9993	0.351000
$983$	−4.29649	−0.137037	−0.0685184	−	0.997650i	$-0.521827\pi$
$983$	−4.29649	−0.137037	−0.0685184	+	0.997650i	$0.521827\pi$
$984$	0.705484	0.0224900
$985$	33.0172	1.05202
$986$	−4.77388	−0.152031
$987$	0	0
$988$	−32.9706	−1.04894
$989$	26.0352	0.827872
$990$	−30.9640	−0.984101
$991$	32.7076	1.03899	0.519496	−	0.854473i	$-0.326120\pi$
$991$	32.7076	1.03899	0.519496	+	0.854473i	$0.326120\pi$
$992$	1.28906	0.0409276
$993$	10.3504	0.328461
$994$	0	0
$995$	−39.9038	−1.26504
$996$	5.26344	0.166779
$997$	47.9783	1.51949	0.759743	−	0.650223i	$-0.225325\pi$
$997$	47.9783	1.51949	0.759743	+	0.650223i	$0.225325\pi$
$998$	−5.27154	−0.166868
$999$	−33.9370	−1.07372

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7742.2.a.bj.1.6		9
7.6	odd	2		1106.2.a.l.1.4	✓	9
21.20	even	2		9954.2.a.bn.1.7		9
28.27	even	2		8848.2.a.t.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1106.2.a.l.1.4	✓	9	7.6	odd	2
7742.2.a.bj.1.6		9	1.1	even	1	trivial
8848.2.a.t.1.6		9	28.27	even	2
9954.2.a.bn.1.7		9	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7742 = 2 \cdot 7^{2} \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7742.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.633348 q^{3} +1.00000 q^{4} +2.25697 q^{5} +0.633348 q^{6} +1.00000 q^{8} -2.59887 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.633348 q^{3} +1.00000 q^{4} +2.25697 q^{5} +0.633348 q^{6} +1.00000 q^{8} -2.59887 q^{9} +2.25697 q^{10} +5.27893 q^{11} +0.633348 q^{12} +4.66074 q^{13} +1.42945 q^{15} +1.00000 q^{16} -3.55123 q^{17} -2.59887 q^{18} -7.07412 q^{19} +2.25697 q^{20} +5.27893 q^{22} +6.63757 q^{23} +0.633348 q^{24} +0.0939338 q^{25} +4.66074 q^{26} -3.54603 q^{27} +1.34429 q^{29} +1.42945 q^{30} +1.28906 q^{31} +1.00000 q^{32} +3.34340 q^{33} -3.55123 q^{34} -2.59887 q^{36} +9.57042 q^{37} -7.07412 q^{38} +2.95187 q^{39} +2.25697 q^{40} +1.11390 q^{41} +3.92241 q^{43} +5.27893 q^{44} -5.86558 q^{45} +6.63757 q^{46} -0.906066 q^{47} +0.633348 q^{48} +0.0939338 q^{50} -2.24916 q^{51} +4.66074 q^{52} -12.8356 q^{53} -3.54603 q^{54} +11.9144 q^{55} -4.48038 q^{57} +1.34429 q^{58} -6.91021 q^{59} +1.42945 q^{60} +11.0404 q^{61} +1.28906 q^{62} +1.00000 q^{64} +10.5192 q^{65} +3.34340 q^{66} +12.8944 q^{67} -3.55123 q^{68} +4.20389 q^{69} +11.3640 q^{71} -2.59887 q^{72} +6.49512 q^{73} +9.57042 q^{74} +0.0594928 q^{75} -7.07412 q^{76} +2.95187 q^{78} +1.00000 q^{79} +2.25697 q^{80} +5.55074 q^{81} +1.11390 q^{82} +8.31051 q^{83} -8.01503 q^{85} +3.92241 q^{86} +0.851403 q^{87} +5.27893 q^{88} -6.45124 q^{89} -5.86558 q^{90} +6.63757 q^{92} +0.816422 q^{93} -0.906066 q^{94} -15.9661 q^{95} +0.633348 q^{96} -2.03031 q^{97} -13.7193 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 2 q^{3} + 9 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{8} + 13 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^8 + 13 * q^9	\( 9 q + 9 q^{2} - 2 q^{3} + 9 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{8} + 13 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{15} + 9 q^{16} - 6 q^{17} + 13 q^{18} - 2 q^{19} - 4 q^{20} + 8 q^{22} - 2 q^{24} + 23 q^{25} - 2 q^{26} - 2 q^{27} + 10 q^{29} - 2 q^{30} + 6 q^{31} + 9 q^{32} + 2 q^{33} - 6 q^{34} + 13 q^{36} + 10 q^{37} - 2 q^{38} - 6 q^{39} - 4 q^{40} - 10 q^{41} + 22 q^{43} + 8 q^{44} + 10 q^{45} + 14 q^{47} - 2 q^{48} + 23 q^{50} + 4 q^{51} - 2 q^{52} + 12 q^{53} - 2 q^{54} + 14 q^{55} + 22 q^{57} + 10 q^{58} + 2 q^{59} - 2 q^{60} - 6 q^{61} + 6 q^{62} + 9 q^{64} - 12 q^{65} + 2 q^{66} + 24 q^{67} - 6 q^{68} + 26 q^{69} + 20 q^{71} + 13 q^{72} + 12 q^{73} + 10 q^{74} - 6 q^{75} - 2 q^{76} - 6 q^{78} + 9 q^{79} - 4 q^{80} - 19 q^{81} - 10 q^{82} + 22 q^{83} + 32 q^{85} + 22 q^{86} + 54 q^{87} + 8 q^{88} - 20 q^{89} + 10 q^{90} - 18 q^{93} + 14 q^{94} - 40 q^{95} - 2 q^{96} + 6 q^{97} + 24 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^8 + 13 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^15 + 9 * q^16 - 6 * q^17 + 13 * q^18 - 2 * q^19 - 4 * q^20 + 8 * q^22 - 2 * q^24 + 23 * q^25 - 2 * q^26 - 2 * q^27 + 10 * q^29 - 2 * q^30 + 6 * q^31 + 9 * q^32 + 2 * q^33 - 6 * q^34 + 13 * q^36 + 10 * q^37 - 2 * q^38 - 6 * q^39 - 4 * q^40 - 10 * q^41 + 22 * q^43 + 8 * q^44 + 10 * q^45 + 14 * q^47 - 2 * q^48 + 23 * q^50 + 4 * q^51 - 2 * q^52 + 12 * q^53 - 2 * q^54 + 14 * q^55 + 22 * q^57 + 10 * q^58 + 2 * q^59 - 2 * q^60 - 6 * q^61 + 6 * q^62 + 9 * q^64 - 12 * q^65 + 2 * q^66 + 24 * q^67 - 6 * q^68 + 26 * q^69 + 20 * q^71 + 13 * q^72 + 12 * q^73 + 10 * q^74 - 6 * q^75 - 2 * q^76 - 6 * q^78 + 9 * q^79 - 4 * q^80 - 19 * q^81 - 10 * q^82 + 22 * q^83 + 32 * q^85 + 22 * q^86 + 54 * q^87 + 8 * q^88 - 20 * q^89 + 10 * q^90 - 18 * q^93 + 14 * q^94 - 40 * q^95 - 2 * q^96 + 6 * q^97 + 24 * q^99

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