LMFDB - Embedded newform 833.2.a.h.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(1,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, 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("833.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.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:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 8x^{5} + 29x^{4} + x^{3} - 53x^{2} + 34x - 5 $ x^7 - 3x^6 - 8x^5 + 29x^4 + x^3 - 53x^2 + 34*x - 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 119)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$2.21321$ of defining polynomial
Character	$\chi$	$=$	833.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.21321 q^{2} +2.17950 q^{3} +2.89829 q^{4} -0.435315 q^{5} +4.82369 q^{6} +1.98810 q^{8} +1.75024 q^{9} +O(q^{10})$	\(q+2.21321 q^{2} +2.17950 q^{3} +2.89829 q^{4} -0.435315 q^{5} +4.82369 q^{6} +1.98810 q^{8} +1.75024 q^{9} -0.963443 q^{10} +5.13561 q^{11} +6.31683 q^{12} -3.38709 q^{13} -0.948771 q^{15} -1.39650 q^{16} -1.00000 q^{17} +3.87363 q^{18} -1.17388 q^{19} -1.26167 q^{20} +11.3662 q^{22} +5.18122 q^{23} +4.33306 q^{24} -4.81050 q^{25} -7.49633 q^{26} -2.72387 q^{27} +5.60030 q^{29} -2.09983 q^{30} -6.00545 q^{31} -7.06695 q^{32} +11.1931 q^{33} -2.21321 q^{34} +5.07268 q^{36} -0.651526 q^{37} -2.59804 q^{38} -7.38217 q^{39} -0.865448 q^{40} -1.97717 q^{41} -6.47351 q^{43} +14.8845 q^{44} -0.761904 q^{45} +11.4671 q^{46} +3.80372 q^{47} -3.04369 q^{48} -10.6466 q^{50} -2.17950 q^{51} -9.81676 q^{52} +7.93165 q^{53} -6.02848 q^{54} -2.23561 q^{55} -2.55848 q^{57} +12.3946 q^{58} +3.67918 q^{59} -2.74981 q^{60} +12.5031 q^{61} -13.2913 q^{62} -12.8476 q^{64} +1.47445 q^{65} +24.7726 q^{66} +0.00890004 q^{67} -2.89829 q^{68} +11.2925 q^{69} -13.3916 q^{71} +3.47964 q^{72} -15.3206 q^{73} -1.44196 q^{74} -10.4845 q^{75} -3.40225 q^{76} -16.3383 q^{78} -5.73816 q^{79} +0.607919 q^{80} -11.1874 q^{81} -4.37590 q^{82} -10.6195 q^{83} +0.435315 q^{85} -14.3272 q^{86} +12.2059 q^{87} +10.2101 q^{88} +14.6869 q^{89} -1.68625 q^{90} +15.0167 q^{92} -13.0889 q^{93} +8.41843 q^{94} +0.511008 q^{95} -15.4024 q^{96} +15.3730 q^{97} +8.98852 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 3 q^{2} - q^{3} + 11 q^{4} - 2 q^{5} - 5 q^{6} + 8 q^{9}+O(q^{10}) $ 7 * q + 3 * q^2 - q^3 + 11 * q^4 - 2 * q^5 - 5 * q^6 + 8 * q^9	$ 7 q + 3 q^{2} - q^{3} + 11 q^{4} - 2 q^{5} - 5 q^{6} + 8 q^{9} + 10 q^{10} + 4 q^{11} - 2 q^{12} + 2 q^{13} + 8 q^{15} + 23 q^{16} - 7 q^{17} + 15 q^{18} + 5 q^{19} - 27 q^{20} + 9 q^{22} + 22 q^{23} + 7 q^{24} + 7 q^{25} + 10 q^{26} - 10 q^{27} + q^{29} + 15 q^{30} - 2 q^{31} + 8 q^{32} + 27 q^{33} - 3 q^{34} - 18 q^{36} + 19 q^{37} + 35 q^{38} + 2 q^{39} + 25 q^{40} - 12 q^{41} + 19 q^{43} - 2 q^{44} - 9 q^{45} + 7 q^{47} - 30 q^{48} - 22 q^{50} + q^{51} + 7 q^{52} - 8 q^{53} - 11 q^{54} + 9 q^{55} - 3 q^{57} + 15 q^{58} - 5 q^{59} - q^{60} + 4 q^{61} - 17 q^{62} + 40 q^{64} + 2 q^{65} + 16 q^{66} + 24 q^{67} - 11 q^{68} - 16 q^{69} - q^{71} - 19 q^{73} - 18 q^{74} + 2 q^{75} + 13 q^{76} - 45 q^{78} + 15 q^{79} + 9 q^{80} - 29 q^{81} - 41 q^{82} + 2 q^{83} + 2 q^{85} - 21 q^{86} - 7 q^{87} + 62 q^{88} + 32 q^{89} - 49 q^{90} + 8 q^{92} - q^{93} + 15 q^{94} + 12 q^{95} - 18 q^{96} + 23 q^{97} + 10 q^{99}+O(q^{100}) $ 7 * q + 3 * q^2 - q^3 + 11 * q^4 - 2 * q^5 - 5 * q^6 + 8 * q^9 + 10 * q^10 + 4 * q^11 - 2 * q^12 + 2 * q^13 + 8 * q^15 + 23 * q^16 - 7 * q^17 + 15 * q^18 + 5 * q^19 - 27 * q^20 + 9 * q^22 + 22 * q^23 + 7 * q^24 + 7 * q^25 + 10 * q^26 - 10 * q^27 + q^29 + 15 * q^30 - 2 * q^31 + 8 * q^32 + 27 * q^33 - 3 * q^34 - 18 * q^36 + 19 * q^37 + 35 * q^38 + 2 * q^39 + 25 * q^40 - 12 * q^41 + 19 * q^43 - 2 * q^44 - 9 * q^45 + 7 * q^47 - 30 * q^48 - 22 * q^50 + q^51 + 7 * q^52 - 8 * q^53 - 11 * q^54 + 9 * q^55 - 3 * q^57 + 15 * q^58 - 5 * q^59 - q^60 + 4 * q^61 - 17 * q^62 + 40 * q^64 + 2 * q^65 + 16 * q^66 + 24 * q^67 - 11 * q^68 - 16 * q^69 - q^71 - 19 * q^73 - 18 * q^74 + 2 * q^75 + 13 * q^76 - 45 * q^78 + 15 * q^79 + 9 * q^80 - 29 * q^81 - 41 * q^82 + 2 * q^83 + 2 * q^85 - 21 * q^86 - 7 * q^87 + 62 * q^88 + 32 * q^89 - 49 * q^90 + 8 * q^92 - q^93 + 15 * q^94 + 12 * q^95 - 18 * q^96 + 23 * q^97 + 10 * 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 $

$2$	2.21321	1.56497	0.782487	−	0.622667i	$-0.213951\pi$
$2$	2.21321	1.56497	0.782487	+	0.622667i	$0.213951\pi$
$3$	2.17950	1.25834	0.629168	−	0.777269i	$-0.283396\pi$
$3$	2.17950	1.25834	0.629168	+	0.777269i	$0.283396\pi$
$4$	2.89829	1.44914
$5$	−0.435315	−0.194679	−0.0973394	−	0.995251i	$-0.531033\pi$
$5$	−0.435315	−0.194679	−0.0973394	+	0.995251i	$0.531033\pi$
$6$	4.82369	1.96926
$7$	0	0
$7$	0	0
$8$	1.98810	0.702898
$9$	1.75024	0.583412
$10$	−0.963443	−0.304667
$11$	5.13561	1.54844	0.774222	−	0.632914i	$-0.218141\pi$
$11$	5.13561	1.54844	0.774222	+	0.632914i	$0.218141\pi$
$12$	6.31683	1.82351
$13$	−3.38709	−0.939409	−0.469705	−	0.882824i	$-0.655640\pi$
$13$	−3.38709	−0.939409	−0.469705	+	0.882824i	$0.655640\pi$
$14$	0	0
$15$	−0.948771	−0.244972
$16$	−1.39650	−0.349126
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	3.87363	0.913024
$19$	−1.17388	−0.269307	−0.134653	−	0.990893i	$-0.542992\pi$
$19$	−1.17388	−0.269307	−0.134653	+	0.990893i	$0.542992\pi$
$20$	−1.26167	−0.282118
$21$	0	0
$22$	11.3662	2.42328
$23$	5.18122	1.08036	0.540179	−	0.841550i	$-0.318356\pi$
$23$	5.18122	1.08036	0.540179	+	0.841550i	$0.318356\pi$
$24$	4.33306	0.884483
$25$	−4.81050	−0.962100
$26$	−7.49633	−1.47015
$27$	−2.72387	−0.524208
$28$	0	0
$29$	5.60030	1.03995	0.519974	−	0.854182i	$-0.325941\pi$
$29$	5.60030	1.03995	0.519974	+	0.854182i	$0.325941\pi$
$30$	−2.09983	−0.383374
$31$	−6.00545	−1.07861	−0.539305	−	0.842110i	$-0.681313\pi$
$31$	−6.00545	−1.07861	−0.539305	+	0.842110i	$0.681313\pi$
$32$	−7.06695	−1.24927
$33$	11.1931	1.94847
$34$	−2.21321	−0.379562
$35$	0	0
$36$	5.07268	0.845447
$37$	−0.651526	−0.107110	−0.0535551	−	0.998565i	$-0.517055\pi$
$37$	−0.651526	−0.107110	−0.0535551	+	0.998565i	$0.517055\pi$
$38$	−2.59804	−0.421458
$39$	−7.38217	−1.18209
$40$	−0.865448	−0.136839
$41$	−1.97717	−0.308783	−0.154391	−	0.988010i	$-0.549342\pi$
$41$	−1.97717	−0.308783	−0.154391	+	0.988010i	$0.549342\pi$
$42$	0	0
$43$	−6.47351	−0.987200	−0.493600	−	0.869689i	$-0.664319\pi$
$43$	−6.47351	−0.987200	−0.493600	+	0.869689i	$0.664319\pi$
$44$	14.8845	2.24392
$45$	−0.761904	−0.113578
$46$	11.4671	1.69073
$47$	3.80372	0.554830	0.277415	−	0.960750i	$-0.410522\pi$
$47$	3.80372	0.554830	0.277415	+	0.960750i	$0.410522\pi$
$48$	−3.04369	−0.439318
$49$	0	0
$50$	−10.6466	−1.50566
$51$	−2.17950	−0.305192
$52$	−9.81676	−1.36134
$53$	7.93165	1.08950	0.544748	−	0.838600i	$-0.316625\pi$
$53$	7.93165	1.08950	0.544748	+	0.838600i	$0.316625\pi$
$54$	−6.02848	−0.820373
$55$	−2.23561	−0.301449
$56$	0	0
$57$	−2.55848	−0.338879
$58$	12.3946	1.62749
$59$	3.67918	0.478989	0.239494	−	0.970898i	$-0.423018\pi$
$59$	3.67918	0.478989	0.239494	+	0.970898i	$0.423018\pi$
$60$	−2.74981	−0.354999
$61$	12.5031	1.60086	0.800430	−	0.599427i	$-0.204605\pi$
$61$	12.5031	1.60086	0.800430	+	0.599427i	$0.204605\pi$
$62$	−13.2913	−1.68800
$63$	0	0
$64$	−12.8476	−1.60595
$65$	1.47445	0.182883
$66$	24.7726	3.04930
$67$	0.00890004	0.00108731	0.000543656	−	1.00000i	$-0.499827\pi$
$67$	0.00890004	0.00108731	0.000543656		1.00000i	$0.499827\pi$
$68$	−2.89829	−0.351469
$69$	11.2925	1.35945
$70$	0	0
$71$	−13.3916	−1.58929	−0.794644	−	0.607076i	$-0.792342\pi$
$71$	−13.3916	−1.58929	−0.794644	+	0.607076i	$0.792342\pi$
$72$	3.47964	0.410079
$73$	−15.3206	−1.79314	−0.896568	−	0.442906i	$-0.853948\pi$
$73$	−15.3206	−1.79314	−0.896568	+	0.442906i	$0.853948\pi$
$74$	−1.44196	−0.167625
$75$	−10.4845	−1.21065
$76$	−3.40225	−0.390264
$77$	0	0
$78$	−16.3383	−1.84995
$79$	−5.73816	−0.645593	−0.322797	−	0.946468i	$-0.604623\pi$
$79$	−5.73816	−0.645593	−0.322797	+	0.946468i	$0.604623\pi$
$80$	0.607919	0.0679675
$81$	−11.1874	−1.24304
$82$	−4.37590	−0.483237
$83$	−10.6195	−1.16564	−0.582820	−	0.812601i	$-0.698051\pi$
$83$	−10.6195	−1.16564	−0.582820	+	0.812601i	$0.698051\pi$
$84$	0	0
$85$	0.435315	0.0472165
$86$	−14.3272	−1.54494
$87$	12.2059	1.30861
$88$	10.2101	1.08840
$89$	14.6869	1.55681	0.778407	−	0.627760i	$-0.216028\pi$
$89$	14.6869	1.55681	0.778407	+	0.627760i	$0.216028\pi$
$90$	−1.68625	−0.177746
$91$	0	0
$92$	15.0167	1.56559
$93$	−13.0889	−1.35726
$94$	8.41843	0.868294
$95$	0.511008	0.0524283
$96$	−15.4024	−1.57200
$97$	15.3730	1.56089	0.780444	−	0.625225i	$-0.214993\pi$
$97$	15.3730	1.56089	0.780444	+	0.625225i	$0.214993\pi$
$98$	0	0
$99$	8.98852	0.903381
$100$	−13.9422	−1.39422
$101$	7.40577	0.736902	0.368451	−	0.929647i	$-0.379888\pi$
$101$	7.40577	0.736902	0.368451	+	0.929647i	$0.379888\pi$
$102$	−4.82369	−0.477617
$103$	0.377439	0.0371902	0.0185951	−	0.999827i	$-0.494081\pi$
$103$	0.377439	0.0371902	0.0185951	+	0.999827i	$0.494081\pi$
$104$	−6.73386	−0.660309
$105$	0	0
$106$	17.5544	1.70503
$107$	12.4112	1.19983	0.599917	−	0.800062i	$-0.295200\pi$
$107$	12.4112	1.19983	0.599917	+	0.800062i	$0.295200\pi$
$108$	−7.89455	−0.759653
$109$	−7.90429	−0.757094	−0.378547	−	0.925582i	$-0.623576\pi$
$109$	−7.90429	−0.757094	−0.378547	+	0.925582i	$0.623576\pi$
$110$	−4.94787	−0.471760
$111$	−1.42000	−0.134781
$112$	0	0
$113$	−13.1390	−1.23601	−0.618005	−	0.786175i	$-0.712059\pi$
$113$	−13.1390	−1.23601	−0.618005	+	0.786175i	$0.712059\pi$
$114$	−5.66244	−0.530337
$115$	−2.25546	−0.210323
$116$	16.2313	1.50704
$117$	−5.92820	−0.548062
$118$	8.14280	0.749605
$119$	0	0
$120$	−1.88625	−0.172190
$121$	15.3745	1.39768
$122$	27.6720	2.50530
$123$	−4.30926	−0.388553
$124$	−17.4055	−1.56306
$125$	4.27066	0.381979
$126$	0	0
$127$	13.8456	1.22859	0.614297	−	0.789075i	$-0.289440\pi$
$127$	13.8456	1.22859	0.614297	+	0.789075i	$0.289440\pi$
$128$	−14.3005	−1.26400
$129$	−14.1090	−1.24223
$130$	3.26327	0.286207
$131$	−16.9371	−1.47980	−0.739900	−	0.672716i	$-0.765127\pi$
$131$	−16.9371	−1.47980	−0.739900	+	0.672716i	$0.765127\pi$
$132$	32.4408	2.82361
$133$	0	0
$134$	0.0196976	0.00170162
$135$	1.18574	0.102052
$136$	−1.98810	−0.170478
$137$	0.191231	0.0163380	0.00816900	−	0.999967i	$-0.497400\pi$
$137$	0.191231	0.0163380	0.00816900	+	0.999967i	$0.497400\pi$
$138$	24.9926	2.12751
$139$	5.44958	0.462227	0.231114	−	0.972927i	$-0.425763\pi$
$139$	5.44958	0.462227	0.231114	+	0.972927i	$0.425763\pi$
$140$	0	0
$141$	8.29022	0.698163
$142$	−29.6383	−2.48719
$143$	−17.3948	−1.45462
$144$	−2.44421	−0.203684
$145$	−2.43789	−0.202456
$146$	−33.9076	−2.80621
$147$	0	0
$148$	−1.88831	−0.155218
$149$	−12.1986	−0.999347	−0.499674	−	0.866214i	$-0.666547\pi$
$149$	−12.1986	−0.999347	−0.499674	+	0.866214i	$0.666547\pi$
$150$	−23.2044	−1.89463
$151$	20.7907	1.69192	0.845961	−	0.533245i	$-0.179028\pi$
$151$	20.7907	1.69192	0.845961	+	0.533245i	$0.179028\pi$
$152$	−2.33379	−0.189295
$153$	−1.75024	−0.141498
$154$	0	0
$155$	2.61426	0.209983
$156$	−21.3957	−1.71302
$157$	17.2113	1.37361	0.686807	−	0.726840i	$-0.259012\pi$
$157$	17.2113	1.37361	0.686807	+	0.726840i	$0.259012\pi$
$158$	−12.6997	−1.01034
$159$	17.2870	1.37095
$160$	3.07635	0.243207
$161$	0	0
$162$	−24.7600	−1.94533
$163$	19.9532	1.56285	0.781426	−	0.623997i	$-0.214492\pi$
$163$	19.9532	1.56285	0.781426	+	0.623997i	$0.214492\pi$
$164$	−5.73042	−0.447471
$165$	−4.87252	−0.379325
$166$	−23.5031	−1.82420
$167$	0.626149	0.0484529	0.0242264	−	0.999706i	$-0.492288\pi$
$167$	0.626149	0.0484529	0.0242264	+	0.999706i	$0.492288\pi$
$168$	0	0
$169$	−1.52763	−0.117510
$170$	0.963443	0.0738927
$171$	−2.05457	−0.157117
$172$	−18.7621	−1.43060
$173$	21.4072	1.62756	0.813780	−	0.581173i	$-0.197406\pi$
$173$	21.4072	1.62756	0.813780	+	0.581173i	$0.197406\pi$
$174$	27.0141	2.04793
$175$	0	0
$176$	−7.17190	−0.540602
$177$	8.01879	0.602729
$178$	32.5053	2.43637
$179$	−8.89113	−0.664554	−0.332277	−	0.943182i	$-0.607817\pi$
$179$	−8.89113	−0.664554	−0.332277	+	0.943182i	$0.607817\pi$
$180$	−2.20822	−0.164591
$181$	0.427555	0.0317799	0.0158900	−	0.999874i	$-0.494942\pi$
$181$	0.427555	0.0317799	0.0158900	+	0.999874i	$0.494942\pi$
$182$	0	0
$183$	27.2506	2.01442
$184$	10.3008	0.759382
$185$	0.283619	0.0208521
$186$	−28.9684	−2.12407
$187$	−5.13561	−0.375553
$188$	11.0243	0.804028
$189$	0	0
$190$	1.13097	0.0820490
$191$	2.75499	0.199344	0.0996721	−	0.995020i	$-0.468221\pi$
$191$	2.75499	0.199344	0.0996721	+	0.995020i	$0.468221\pi$
$192$	−28.0014	−2.02083
$193$	−2.69450	−0.193954	−0.0969770	−	0.995287i	$-0.530917\pi$
$193$	−2.69450	−0.193954	−0.0969770	+	0.995287i	$0.530917\pi$
$194$	34.0236	2.44275
$195$	3.21357	0.230129
$196$	0	0
$197$	5.91919	0.421724	0.210862	−	0.977516i	$-0.432373\pi$
$197$	5.91919	0.421724	0.210862	+	0.977516i	$0.432373\pi$
$198$	19.8935	1.41377
$199$	1.07895	0.0764847	0.0382423	−	0.999268i	$-0.487824\pi$
$199$	1.07895	0.0764847	0.0382423	+	0.999268i	$0.487824\pi$
$200$	−9.56374	−0.676259
$201$	0.0193977	0.00136821
$202$	16.3905	1.15323
$203$	0	0
$204$	−6.31683	−0.442266
$205$	0.860694	0.0601135
$206$	0.835351	0.0582016
$207$	9.06835	0.630294
$208$	4.73009	0.327972
$209$	−6.02860	−0.417007
$210$	0	0
$211$	−3.59621	−0.247574	−0.123787	−	0.992309i	$-0.539504\pi$
$211$	−3.59621	−0.247574	−0.123787	+	0.992309i	$0.539504\pi$
$212$	22.9882	1.57884
$213$	−29.1870	−1.99986
$214$	27.4685	1.87771
$215$	2.81801	0.192187
$216$	−5.41531	−0.368465
$217$	0	0
$218$	−17.4938	−1.18483
$219$	−33.3912	−2.25637
$220$	−6.47944	−0.436843
$221$	3.38709	0.227840
$222$	−3.14276	−0.210928
$223$	13.5306	0.906077	0.453038	−	0.891491i	$-0.350340\pi$
$223$	13.5306	0.906077	0.453038	+	0.891491i	$0.350340\pi$
$224$	0	0
$225$	−8.41951	−0.561300
$226$	−29.0792	−1.93432
$227$	6.21373	0.412419	0.206210	−	0.978508i	$-0.433887\pi$
$227$	6.21373	0.412419	0.206210	+	0.978508i	$0.433887\pi$
$228$	−7.41521	−0.491084
$229$	−3.69030	−0.243862	−0.121931	−	0.992539i	$-0.538909\pi$
$229$	−3.69030	−0.243862	−0.121931	+	0.992539i	$0.538909\pi$
$230$	−4.99181	−0.329150
$231$	0	0
$232$	11.1339	0.730978
$233$	−2.94964	−0.193237	−0.0966186	−	0.995321i	$-0.530803\pi$
$233$	−2.94964	−0.193237	−0.0966186	+	0.995321i	$0.530803\pi$
$234$	−13.1203	−0.857704
$235$	−1.65582	−0.108014
$236$	10.6633	0.694124
$237$	−12.5063	−0.812374
$238$	0	0
$239$	−2.88136	−0.186380	−0.0931899	−	0.995648i	$-0.529706\pi$
$239$	−2.88136	−0.186380	−0.0931899	+	0.995648i	$0.529706\pi$
$240$	1.32496	0.0855260
$241$	−12.6531	−0.815055	−0.407527	−	0.913193i	$-0.633609\pi$
$241$	−12.6531	−0.815055	−0.407527	+	0.913193i	$0.633609\pi$
$242$	34.0269	2.18733
$243$	−16.2113	−1.03996
$244$	36.2376	2.31988
$245$	0	0
$246$	−9.53728	−0.608075
$247$	3.97604	0.252989
$248$	−11.9394	−0.758154
$249$	−23.1452	−1.46677
$250$	9.45185	0.597788
$251$	−2.53970	−0.160305	−0.0801523	−	0.996783i	$-0.525541\pi$
$251$	−2.53970	−0.160305	−0.0801523	+	0.996783i	$0.525541\pi$
$252$	0	0
$253$	26.6087	1.67288
$254$	30.6431	1.92272
$255$	0.948771	0.0594143
$256$	−5.95483	−0.372177
$257$	−7.10514	−0.443206	−0.221603	−	0.975137i	$-0.571129\pi$
$257$	−7.10514	−0.443206	−0.221603	+	0.975137i	$0.571129\pi$
$258$	−31.2262	−1.94406
$259$	0	0
$260$	4.27338	0.265024
$261$	9.80184	0.606718
$262$	−37.4853	−2.31585
$263$	13.6507	0.841741	0.420870	−	0.907121i	$-0.361725\pi$
$263$	13.6507	0.841741	0.420870	+	0.907121i	$0.361725\pi$
$264$	22.2529	1.36957
$265$	−3.45277	−0.212102
$266$	0	0
$267$	32.0103	1.95900
$268$	0.0257949	0.00157567
$269$	9.76980	0.595675	0.297838	−	0.954617i	$-0.403735\pi$
$269$	9.76980	0.595675	0.297838	+	0.954617i	$0.403735\pi$
$270$	2.62429	0.159709
$271$	−9.48740	−0.576318	−0.288159	−	0.957583i	$-0.593043\pi$
$271$	−9.48740	−0.576318	−0.288159	+	0.957583i	$0.593043\pi$
$272$	1.39650	0.0846755
$273$	0	0
$274$	0.423235	0.0255686
$275$	−24.7049	−1.48976
$276$	32.7289	1.97005
$277$	−7.29865	−0.438533	−0.219267	−	0.975665i	$-0.570366\pi$
$277$	−7.29865	−0.438533	−0.219267	+	0.975665i	$0.570366\pi$
$278$	12.0611	0.723374
$279$	−10.5109	−0.629274
$280$	0	0
$281$	−8.48449	−0.506142	−0.253071	−	0.967448i	$-0.581441\pi$
$281$	−8.48449	−0.506142	−0.253071	+	0.967448i	$0.581441\pi$
$282$	18.3480	1.09261
$283$	0.258470	0.0153645	0.00768224	−	0.999970i	$-0.497555\pi$
$283$	0.258470	0.0153645	0.00768224	+	0.999970i	$0.497555\pi$
$284$	−38.8126	−2.30311
$285$	1.11374	0.0659725
$286$	−38.4982	−2.27645
$287$	0	0
$288$	−12.3688	−0.728840
$289$	1.00000	0.0588235
$290$	−5.39556	−0.316838
$291$	33.5054	1.96412
$292$	−44.4034	−2.59851
$293$	−9.96481	−0.582150	−0.291075	−	0.956700i	$-0.594013\pi$
$293$	−9.96481	−0.582150	−0.291075	+	0.956700i	$0.594013\pi$
$294$	0	0
$295$	−1.60160	−0.0932490
$296$	−1.29530	−0.0752876
$297$	−13.9887	−0.811708
$298$	−26.9980	−1.56395
$299$	−17.5492	−1.01490
$300$	−30.3871	−1.75440
$301$	0	0
$302$	46.0141	2.64781
$303$	16.1409	0.927271
$304$	1.63933	0.0940221
$305$	−5.44279	−0.311653
$306$	−3.87363	−0.221441
$307$	−3.43626	−0.196117	−0.0980587	−	0.995181i	$-0.531263\pi$
$307$	−3.43626	−0.196117	−0.0980587	+	0.995181i	$0.531263\pi$
$308$	0	0
$309$	0.822629	0.0467977
$310$	5.78591	0.328617
$311$	−5.37278	−0.304663	−0.152331	−	0.988329i	$-0.548678\pi$
$311$	−5.37278	−0.304663	−0.152331	+	0.988329i	$0.548678\pi$
$312$	−14.6765	−0.830892
$313$	−16.5795	−0.937131	−0.468566	−	0.883429i	$-0.655229\pi$
$313$	−16.5795	−0.937131	−0.468566	+	0.883429i	$0.655229\pi$
$314$	38.0922	2.14967
$315$	0	0
$316$	−16.6308	−0.935558
$317$	25.2458	1.41794	0.708972	−	0.705237i	$-0.249159\pi$
$317$	25.2458	1.41794	0.708972	+	0.705237i	$0.249159\pi$
$318$	38.2598	2.14550
$319$	28.7609	1.61030
$320$	5.59276	0.312645
$321$	27.0502	1.50980
$322$	0	0
$323$	1.17388	0.0653165
$324$	−32.4243	−1.80135
$325$	16.2936	0.903806
$326$	44.1605	2.44582
$327$	−17.2274	−0.952679
$328$	−3.93081	−0.217043
$329$	0	0
$330$	−10.7839	−0.593634
$331$	1.21366	0.0667087	0.0333543	−	0.999444i	$-0.489381\pi$
$331$	1.21366	0.0667087	0.0333543	+	0.999444i	$0.489381\pi$
$332$	−30.7783	−1.68918
$333$	−1.14032	−0.0624893
$334$	1.38580	0.0758275
$335$	−0.00387432	−0.000211677 0
$336$	0	0
$337$	13.3691	0.728260	0.364130	−	0.931348i	$-0.381366\pi$
$337$	13.3691	0.728260	0.364130	+	0.931348i	$0.381366\pi$
$338$	−3.38096	−0.183900
$339$	−28.6364	−1.55532
$340$	1.26167	0.0684236
$341$	−30.8416	−1.67017
$342$	−4.54719	−0.245884
$343$	0	0
$344$	−12.8700	−0.693901
$345$	−4.91579	−0.264657
$346$	47.3786	2.54709
$347$	−8.48242	−0.455360	−0.227680	−	0.973736i	$-0.573114\pi$
$347$	−8.48242	−0.455360	−0.227680	+	0.973736i	$0.573114\pi$
$348$	35.3761	1.89636
$349$	−7.84573	−0.419972	−0.209986	−	0.977704i	$-0.567342\pi$
$349$	−7.84573	−0.419972	−0.209986	+	0.977704i	$0.567342\pi$
$350$	0	0
$351$	9.22598	0.492446
$352$	−36.2931	−1.93443
$353$	30.3066	1.61306	0.806530	−	0.591194i	$-0.201343\pi$
$353$	30.3066	1.61306	0.806530	+	0.591194i	$0.201343\pi$
$354$	17.7473	0.943256
$355$	5.82955	0.309401
$356$	42.5670	2.25605
$357$	0	0
$358$	−19.6779	−1.04001
$359$	−15.5543	−0.820926	−0.410463	−	0.911877i	$-0.634633\pi$
$359$	−15.5543	−0.820926	−0.410463	+	0.911877i	$0.634633\pi$
$360$	−1.51474	−0.0798337
$361$	−17.6220	−0.927474
$362$	0.946268	0.0497347
$363$	33.5088	1.75875
$364$	0	0
$365$	6.66927	0.349086
$366$	60.3112	3.15252
$367$	−2.05841	−0.107448	−0.0537241	−	0.998556i	$-0.517109\pi$
$367$	−2.05841	−0.107448	−0.0537241	+	0.998556i	$0.517109\pi$
$368$	−7.23559	−0.377181
$369$	−3.46052	−0.180147
$370$	0.627708	0.0326330
$371$	0	0
$372$	−37.9354	−1.96686
$373$	6.88552	0.356519	0.178259	−	0.983984i	$-0.442953\pi$
$373$	6.88552	0.356519	0.178259	+	0.983984i	$0.442953\pi$
$374$	−11.3662	−0.587731
$375$	9.30792	0.480659
$376$	7.56217	0.389989
$377$	−18.9687	−0.976938
$378$	0	0
$379$	−32.2704	−1.65762	−0.828810	−	0.559530i	$-0.810982\pi$
$379$	−32.2704	−1.65762	−0.828810	+	0.559530i	$0.810982\pi$
$380$	1.48105	0.0759762
$381$	30.1764	1.54599
$382$	6.09737	0.311969
$383$	−7.28072	−0.372027	−0.186014	−	0.982547i	$-0.559557\pi$
$383$	−7.28072	−0.372027	−0.186014	+	0.982547i	$0.559557\pi$
$384$	−31.1681	−1.59054
$385$	0	0
$386$	−5.96348	−0.303533
$387$	−11.3302	−0.575944
$388$	44.5553	2.26195
$389$	15.2330	0.772344	0.386172	−	0.922427i	$-0.373797\pi$
$389$	15.2330	0.772344	0.386172	+	0.922427i	$0.373797\pi$
$390$	7.11230	0.360145
$391$	−5.18122	−0.262025
$392$	0	0
$393$	−36.9145	−1.86209
$394$	13.1004	0.659988
$395$	2.49791	0.125683
$396$	26.0513	1.30913
$397$	22.7519	1.14189	0.570944	−	0.820989i	$-0.306577\pi$
$397$	22.7519	1.14189	0.570944	+	0.820989i	$0.306577\pi$
$398$	2.38794	0.119697
$399$	0	0
$400$	6.71789	0.335894
$401$	22.2975	1.11349	0.556743	−	0.830685i	$-0.312051\pi$
$401$	22.2975	1.11349	0.556743	+	0.830685i	$0.312051\pi$
$402$	0.0429310	0.00214121
$403$	20.3410	1.01326
$404$	21.4641	1.06788
$405$	4.87004	0.241994
$406$	0	0
$407$	−3.34598	−0.165854
$408$	−4.33306	−0.214519
$409$	31.6032	1.56268	0.781338	−	0.624108i	$-0.214537\pi$
$409$	31.6032	1.56268	0.781338	+	0.624108i	$0.214537\pi$
$410$	1.90489	0.0940760
$411$	0.416790	0.0205587
$412$	1.09393	0.0538939
$413$	0	0
$414$	20.0701	0.986393
$415$	4.62283	0.226926
$416$	23.9364	1.17358
$417$	11.8774	0.581638
$418$	−13.3425	−0.652605
$419$	9.30199	0.454432	0.227216	−	0.973844i	$-0.427038\pi$
$419$	9.30199	0.454432	0.227216	+	0.973844i	$0.427038\pi$
$420$	0	0
$421$	−24.2939	−1.18401	−0.592006	−	0.805933i	$-0.701664\pi$
$421$	−24.2939	−1.18401	−0.592006	+	0.805933i	$0.701664\pi$
$422$	−7.95917	−0.387446
$423$	6.65741	0.323694
$424$	15.7689	0.765804
$425$	4.81050	0.233344
$426$	−64.5969	−3.12973
$427$	0	0
$428$	35.9712	1.73873
$429$	−37.9120	−1.83041
$430$	6.23685	0.300768
$431$	−7.50789	−0.361643	−0.180821	−	0.983516i	$-0.557876\pi$
$431$	−7.50789	−0.361643	−0.180821	+	0.983516i	$0.557876\pi$
$432$	3.80389	0.183015
$433$	−32.4721	−1.56051	−0.780254	−	0.625463i	$-0.784910\pi$
$433$	−32.4721	−1.56051	−0.780254	+	0.625463i	$0.784910\pi$
$434$	0	0
$435$	−5.31340	−0.254758
$436$	−22.9089	−1.09714
$437$	−6.08214	−0.290948
$438$	−73.9017	−3.53116
$439$	−23.3252	−1.11325	−0.556625	−	0.830764i	$-0.687904\pi$
$439$	−23.3252	−1.11325	−0.556625	+	0.830764i	$0.687904\pi$
$440$	−4.44461	−0.211888
$441$	0	0
$442$	7.49633	0.356564
$443$	−21.0423	−0.999749	−0.499874	−	0.866098i	$-0.666620\pi$
$443$	−21.0423	−0.999749	−0.499874	+	0.866098i	$0.666620\pi$
$444$	−4.11558	−0.195317
$445$	−6.39345	−0.303079
$446$	29.9460	1.41799
$447$	−26.5869	−1.25752
$448$	0	0
$449$	−12.3665	−0.583610	−0.291805	−	0.956478i	$-0.594256\pi$
$449$	−12.3665	−0.583610	−0.291805	+	0.956478i	$0.594256\pi$
$450$	−18.6341	−0.878421
$451$	−10.1540	−0.478133
$452$	−38.0805	−1.79115
$453$	45.3134	2.12901
$454$	13.7523	0.645426
$455$	0	0
$456$	−5.08650	−0.238197
$457$	14.0506	0.657261	0.328630	−	0.944459i	$-0.393413\pi$
$457$	14.0506	0.657261	0.328630	+	0.944459i	$0.393413\pi$
$458$	−8.16739	−0.381637
$459$	2.72387	0.127139
$460$	−6.53698	−0.304788
$461$	9.07553	0.422690	0.211345	−	0.977412i	$-0.432216\pi$
$461$	9.07553	0.422690	0.211345	+	0.977412i	$0.432216\pi$
$462$	0	0
$463$	−27.9220	−1.29765	−0.648823	−	0.760939i	$-0.724738\pi$
$463$	−27.9220	−1.29765	−0.648823	+	0.760939i	$0.724738\pi$
$464$	−7.82084	−0.363073
$465$	5.69779	0.264229
$466$	−6.52816	−0.302411
$467$	32.5646	1.50691	0.753455	−	0.657500i	$-0.228386\pi$
$467$	32.5646	1.50691	0.753455	+	0.657500i	$0.228386\pi$
$468$	−17.1816	−0.794221
$469$	0	0
$470$	−3.66467	−0.169038
$471$	37.5122	1.72847
$472$	7.31457	0.336680
$473$	−33.2454	−1.52863
$474$	−27.6791	−1.27134
$475$	5.64696	0.259100
$476$	0	0
$477$	13.8822	0.635624
$478$	−6.37705	−0.291680
$479$	31.3730	1.43347	0.716735	−	0.697346i	$-0.245636\pi$
$479$	31.3730	1.43347	0.716735	+	0.697346i	$0.245636\pi$
$480$	6.70491	0.306036
$481$	2.20678	0.100620
$482$	−28.0038	−1.27554
$483$	0	0
$484$	44.5597	2.02544
$485$	−6.69208	−0.303872
$486$	−35.8791	−1.62751
$487$	42.5869	1.92980	0.964899	−	0.262622i	$-0.0845871\pi$
$487$	42.5869	1.92980	0.964899	+	0.262622i	$0.0845871\pi$
$488$	24.8574	1.12524
$489$	43.4880	1.96660
$490$	0	0
$491$	28.9293	1.30556	0.652781	−	0.757547i	$-0.273602\pi$
$491$	28.9293	1.30556	0.652781	+	0.757547i	$0.273602\pi$
$492$	−12.4895	−0.563069
$493$	−5.60030	−0.252225
$494$	8.79980	0.395922
$495$	−3.91284	−0.175869
$496$	8.38664	0.376571
$497$	0	0
$498$	−51.2252	−2.29546
$499$	2.22626	0.0996612	0.0498306	−	0.998758i	$-0.484132\pi$
$499$	2.22626	0.0996612	0.0498306	+	0.998758i	$0.484132\pi$
$500$	12.3776	0.553543
$501$	1.36469	0.0609701
$502$	−5.62089	−0.250873
$503$	−30.3553	−1.35348	−0.676738	−	0.736224i	$-0.736607\pi$
$503$	−30.3553	−1.35348	−0.676738	+	0.736224i	$0.736607\pi$
$504$	0	0
$505$	−3.22384	−0.143459
$506$	58.8906	2.61801
$507$	−3.32947	−0.147867
$508$	40.1284	1.78041
$509$	9.83979	0.436141	0.218070	−	0.975933i	$-0.430024\pi$
$509$	9.83979	0.436141	0.218070	+	0.975933i	$0.430024\pi$
$510$	2.09983	0.0929819
$511$	0	0
$512$	15.4218	0.681554
$513$	3.19750	0.141173
$514$	−15.7251	−0.693606
$515$	−0.164305	−0.00724014
$516$	−40.8920	−1.80017
$517$	19.5344	0.859123
$518$	0	0
$519$	46.6571	2.04802
$520$	2.93135	0.128548
$521$	−43.8582	−1.92146	−0.960731	−	0.277480i	$-0.910501\pi$
$521$	−43.8582	−1.92146	−0.960731	+	0.277480i	$0.910501\pi$
$522$	21.6935	0.949499
$523$	38.9834	1.70462	0.852312	−	0.523033i	$-0.175200\pi$
$523$	38.9834	1.70462	0.852312	+	0.523033i	$0.175200\pi$
$524$	−49.0886	−2.14444
$525$	0	0
$526$	30.2119	1.31730
$527$	6.00545	0.261602
$528$	−15.6312	−0.680260
$529$	3.84501	0.167175
$530$	−7.64169	−0.331934
$531$	6.43944	0.279448
$532$	0	0
$533$	6.69687	0.290073
$534$	70.8453	3.06578
$535$	−5.40277	−0.233582
$536$	0.0176941	0.000764270 0
$537$	−19.3782	−0.836233
$538$	21.6226	0.932217
$539$	0	0
$540$	3.43662	0.147888
$541$	−25.9902	−1.11740	−0.558702	−	0.829368i	$-0.688701\pi$
$541$	−25.9902	−1.11740	−0.558702	+	0.829368i	$0.688701\pi$
$542$	−20.9976	−0.901923
$543$	0.931857	0.0399898
$544$	7.06695	0.302993
$545$	3.44086	0.147390
$546$	0	0
$547$	−0.645862	−0.0276150	−0.0138075	−	0.999905i	$-0.504395\pi$
$547$	−0.645862	−0.0276150	−0.0138075	+	0.999905i	$0.504395\pi$
$548$	0.554244	0.0236761
$549$	21.8834	0.933960
$550$	−54.6770	−2.33143
$551$	−6.57408	−0.280065
$552$	22.4505	0.955559
$553$	0	0
$554$	−16.1534	−0.686293
$555$	0.618149	0.0262389
$556$	15.7945	0.669834
$557$	−7.13504	−0.302321	−0.151161	−	0.988509i	$-0.548301\pi$
$557$	−7.13504	−0.302321	−0.151161	+	0.988509i	$0.548301\pi$
$558$	−23.2629	−0.984798
$559$	21.9263	0.927385
$560$	0	0
$561$	−11.1931	−0.472572
$562$	−18.7779	−0.792099
$563$	19.2071	0.809484	0.404742	−	0.914431i	$-0.367361\pi$
$563$	19.2071	0.809484	0.404742	+	0.914431i	$0.367361\pi$
$564$	24.0275	1.01174
$565$	5.71959	0.240625
$566$	0.572049	0.0240450
$567$	0	0
$568$	−26.6237	−1.11711
$569$	3.28293	0.137628	0.0688139	−	0.997630i	$-0.478079\pi$
$569$	3.28293	0.137628	0.0688139	+	0.997630i	$0.478079\pi$
$570$	2.46495	0.103245
$571$	15.0551	0.630038	0.315019	−	0.949085i	$-0.397989\pi$
$571$	15.0551	0.630038	0.315019	+	0.949085i	$0.397989\pi$
$572$	−50.4150	−2.10796
$573$	6.00451	0.250842
$574$	0	0
$575$	−24.9243	−1.03941
$576$	−22.4863	−0.936931
$577$	−43.5312	−1.81223	−0.906113	−	0.423036i	$-0.860964\pi$
$577$	−43.5312	−1.81223	−0.906113	+	0.423036i	$0.860964\pi$
$578$	2.21321	0.0920573
$579$	−5.87266	−0.244060
$580$	−7.06572	−0.293388
$581$	0	0
$582$	74.1545	3.07380
$583$	40.7338	1.68702
$584$	−30.4588	−1.26039
$585$	2.58064	0.106696
$586$	−22.0542	−0.911050
$587$	20.0288	0.826676	0.413338	−	0.910578i	$-0.364363\pi$
$587$	20.0288	0.826676	0.413338	+	0.910578i	$0.364363\pi$
$588$	0	0
$589$	7.04969	0.290477
$590$	−3.54468	−0.145932
$591$	12.9009	0.530671
$592$	0.909859	0.0373950
$593$	−12.8851	−0.529127	−0.264563	−	0.964368i	$-0.585228\pi$
$593$	−12.8851	−0.529127	−0.264563	+	0.964368i	$0.585228\pi$
$594$	−30.9599	−1.27030
$595$	0	0
$596$	−35.3550	−1.44820
$597$	2.35157	0.0962435
$598$	−38.8401	−1.58829
$599$	−41.8801	−1.71118	−0.855588	−	0.517658i	$-0.826804\pi$
$599$	−41.8801	−1.71118	−0.855588	+	0.517658i	$0.826804\pi$
$600$	−20.8442	−0.850961
$601$	−0.766470	−0.0312650	−0.0156325	−	0.999878i	$-0.504976\pi$
$601$	−0.766470	−0.0312650	−0.0156325	+	0.999878i	$0.504976\pi$
$602$	0	0
$603$	0.0155772	0.000634351 0
$604$	60.2574	2.45184
$605$	−6.69275	−0.272099
$606$	35.7232	1.45115
$607$	−15.0134	−0.609374	−0.304687	−	0.952452i	$-0.598552\pi$
$607$	−15.0134	−0.609374	−0.304687	+	0.952452i	$0.598552\pi$
$608$	8.29576	0.336437
$609$	0	0
$610$	−12.0460	−0.487729
$611$	−12.8835	−0.521212
$612$	−5.07268	−0.205051
$613$	−13.1252	−0.530120	−0.265060	−	0.964232i	$-0.585392\pi$
$613$	−13.1252	−0.530120	−0.265060	+	0.964232i	$0.585392\pi$
$614$	−7.60515	−0.306919
$615$	1.87588	0.0756430
$616$	0	0
$617$	−17.9291	−0.721799	−0.360900	−	0.932605i	$-0.617530\pi$
$617$	−17.9291	−0.721799	−0.360900	+	0.932605i	$0.617530\pi$
$618$	1.82065	0.0732373
$619$	10.4317	0.419284	0.209642	−	0.977778i	$-0.432770\pi$
$619$	10.4317	0.419284	0.209642	+	0.977778i	$0.432770\pi$
$620$	7.57689	0.304295
$621$	−14.1129	−0.566333
$622$	−11.8911	−0.476789
$623$	0	0
$624$	10.3092	0.412700
$625$	22.1934	0.887737
$626$	−36.6940	−1.46659
$627$	−13.1393	−0.524735
$628$	49.8834	1.99056
$629$	0.651526	0.0259780
$630$	0	0
$631$	37.9512	1.51081	0.755406	−	0.655257i	$-0.227440\pi$
$631$	37.9512	1.51081	0.755406	+	0.655257i	$0.227440\pi$
$632$	−11.4080	−0.453787
$633$	−7.83796	−0.311531
$634$	55.8741	2.21904
$635$	−6.02718	−0.239181
$636$	50.1028	1.98671
$637$	0	0
$638$	63.6539	2.52008
$639$	−23.4384	−0.927209
$640$	6.22524	0.246074
$641$	9.27723	0.366429	0.183214	−	0.983073i	$-0.441350\pi$
$641$	9.27723	0.366429	0.183214	+	0.983073i	$0.441350\pi$
$642$	59.8677	2.36279
$643$	−26.6175	−1.04969	−0.524845	−	0.851198i	$-0.675877\pi$
$643$	−26.6175	−1.04969	−0.524845	+	0.851198i	$0.675877\pi$
$644$	0	0
$645$	6.14187	0.241836
$646$	2.59804	0.102219
$647$	36.9044	1.45086	0.725431	−	0.688295i	$-0.241640\pi$
$647$	36.9044	1.45086	0.725431	+	0.688295i	$0.241640\pi$
$648$	−22.2416	−0.873732
$649$	18.8949	0.741688
$650$	36.0611	1.41443
$651$	0	0
$652$	57.8300	2.26480
$653$	−35.4506	−1.38729	−0.693645	−	0.720317i	$-0.743996\pi$
$653$	−35.4506	−1.38729	−0.693645	+	0.720317i	$0.743996\pi$
$654$	−38.1279	−1.49092
$655$	7.37297	0.288086
$656$	2.76113	0.107804
$657$	−26.8146	−1.04614
$658$	0	0
$659$	−44.3138	−1.72622	−0.863111	−	0.505014i	$-0.831487\pi$
$659$	−44.3138	−1.72622	−0.863111	+	0.505014i	$0.831487\pi$
$660$	−14.1220	−0.549696
$661$	26.6563	1.03681	0.518405	−	0.855135i	$-0.326526\pi$
$661$	26.6563	1.03681	0.518405	+	0.855135i	$0.326526\pi$
$662$	2.68608	0.104397
$663$	7.38217	0.286700
$664$	−21.1126	−0.819327
$665$	0	0
$666$	−2.52377	−0.0977942
$667$	29.0164	1.12352
$668$	1.81476	0.0702152
$669$	29.4900	1.14015
$670$	−0.00857467	−0.000331269 0
$671$	64.2111	2.47884
$672$	0	0
$673$	−10.0653	−0.387991	−0.193995	−	0.981002i	$-0.562145\pi$
$673$	−10.0653	−0.387991	−0.193995	+	0.981002i	$0.562145\pi$
$674$	29.5885	1.13971
$675$	13.1032	0.504341
$676$	−4.42750	−0.170289
$677$	1.09682	0.0421542	0.0210771	−	0.999778i	$-0.493290\pi$
$677$	1.09682	0.0421542	0.0210771	+	0.999778i	$0.493290\pi$
$678$	−63.3783	−2.43403
$679$	0	0
$680$	0.865448	0.0331884
$681$	13.5428	0.518963
$682$	−68.2590	−2.61377
$683$	−18.1508	−0.694521	−0.347260	−	0.937769i	$-0.612888\pi$
$683$	−18.1508	−0.694521	−0.347260	+	0.937769i	$0.612888\pi$
$684$	−5.95473	−0.227685
$685$	−0.0832459	−0.00318066
$686$	0	0
$687$	−8.04301	−0.306860
$688$	9.04028	0.344657
$689$	−26.8652	−1.02348
$690$	−10.8797	−0.414181
$691$	3.75568	0.142873	0.0714364	−	0.997445i	$-0.477242\pi$
$691$	3.75568	0.142873	0.0714364	+	0.997445i	$0.477242\pi$
$692$	62.0442	2.35857
$693$	0	0
$694$	−18.7734	−0.712627
$695$	−2.37228	−0.0899859
$696$	24.2664	0.919817
$697$	1.97717	0.0748908
$698$	−17.3642	−0.657245
$699$	−6.42874	−0.243157
$700$	0	0
$701$	−20.3765	−0.769610	−0.384805	−	0.922998i	$-0.625731\pi$
$701$	−20.3765	−0.769610	−0.384805	+	0.922998i	$0.625731\pi$
$702$	20.4190	0.770666
$703$	0.764814	0.0288455
$704$	−65.9803	−2.48673
$705$	−3.60886	−0.135918
$706$	67.0749	2.52440
$707$	0	0
$708$	23.2408	0.873441
$709$	−15.3846	−0.577782	−0.288891	−	0.957362i	$-0.593286\pi$
$709$	−15.3846	−0.577782	−0.288891	+	0.957362i	$0.593286\pi$
$710$	12.9020	0.484204
$711$	−10.0431	−0.376647
$712$	29.1991	1.09428
$713$	−31.1155	−1.16529
$714$	0	0
$715$	7.57220	0.283184
$716$	−25.7690	−0.963035
$717$	−6.27994	−0.234529
$718$	−34.4250	−1.28473
$719$	30.7961	1.14850	0.574251	−	0.818679i	$-0.305293\pi$
$719$	30.7961	1.14850	0.574251	+	0.818679i	$0.305293\pi$
$720$	1.06400	0.0396530
$721$	0	0
$722$	−39.0011	−1.45147
$723$	−27.5774	−1.02561
$724$	1.23918	0.0460537
$725$	−26.9402	−1.00054
$726$	74.1618	2.75240
$727$	7.37569	0.273549	0.136775	−	0.990602i	$-0.456326\pi$
$727$	7.37569	0.273549	0.136775	+	0.990602i	$0.456326\pi$
$728$	0	0
$729$	−1.77052	−0.0655747
$730$	14.7605	0.546310
$731$	6.47351	0.239431
$732$	78.9800	2.91918
$733$	−6.97329	−0.257564	−0.128782	−	0.991673i	$-0.541107\pi$
$733$	−6.97329	−0.257564	−0.128782	+	0.991673i	$0.541107\pi$
$734$	−4.55569	−0.168154
$735$	0	0
$736$	−36.6154	−1.34966
$737$	0.0457071	0.00168364
$738$	−7.65885	−0.281926
$739$	−0.184137	−0.00677358	−0.00338679	−	0.999994i	$-0.501078\pi$
$739$	−0.184137	−0.00677358	−0.00338679	+	0.999994i	$0.501078\pi$
$740$	0.822009	0.0302177
$741$	8.66580	0.318346
$742$	0	0
$743$	−20.6128	−0.756209	−0.378104	−	0.925763i	$-0.623424\pi$
$743$	−20.6128	−0.756209	−0.378104	+	0.925763i	$0.623424\pi$
$744$	−26.0220	−0.954013
$745$	5.31023	0.194552
$746$	15.2391	0.557943
$747$	−18.5866	−0.680049
$748$	−14.8845	−0.544230
$749$	0	0
$750$	20.6003	0.752218
$751$	−13.9163	−0.507813	−0.253907	−	0.967229i	$-0.581716\pi$
$751$	−13.9163	−0.507813	−0.253907	+	0.967229i	$0.581716\pi$
$752$	−5.31191	−0.193706
$753$	−5.53529	−0.201717
$754$	−41.9817	−1.52888
$755$	−9.05050	−0.329381
$756$	0	0
$757$	9.46275	0.343929	0.171965	−	0.985103i	$-0.444988\pi$
$757$	9.46275	0.343929	0.171965	+	0.985103i	$0.444988\pi$
$758$	−71.4211	−2.59413
$759$	57.9938	2.10504
$760$	1.01593	0.0368518
$761$	1.73691	0.0629628	0.0314814	−	0.999504i	$-0.489978\pi$
$761$	1.73691	0.0629628	0.0314814	+	0.999504i	$0.489978\pi$
$762$	66.7867	2.41943
$763$	0	0
$764$	7.98476	0.288878
$765$	0.761904	0.0275467
$766$	−16.1137	−0.582213
$767$	−12.4617	−0.449967
$768$	−12.9786	−0.468324
$769$	−39.3101	−1.41756	−0.708780	−	0.705430i	$-0.750754\pi$
$769$	−39.3101	−1.41756	−0.708780	+	0.705430i	$0.750754\pi$
$770$	0	0
$771$	−15.4857	−0.557703
$772$	−7.80942	−0.281067
$773$	−9.40778	−0.338374	−0.169187	−	0.985584i	$-0.554114\pi$
$773$	−9.40778	−0.338374	−0.169187	+	0.985584i	$0.554114\pi$
$774$	−25.0760	−0.901338
$775$	28.8892	1.03773
$776$	30.5629	1.09715
$777$	0	0
$778$	33.7138	1.20870
$779$	2.32097	0.0831573
$780$	9.31385	0.333489
$781$	−68.7739	−2.46092
$782$	−11.4671	−0.410063
$783$	−15.2545	−0.545150
$784$	0	0
$785$	−7.49235	−0.267414
$786$	−81.6994	−2.91412
$787$	−4.63422	−0.165192	−0.0825960	−	0.996583i	$-0.526321\pi$
$787$	−4.63422	−0.165192	−0.0825960	+	0.996583i	$0.526321\pi$
$788$	17.1555	0.611139
$789$	29.7518	1.05919
$790$	5.52839	0.196691
$791$	0	0
$792$	17.8701	0.634985
$793$	−42.3491	−1.50386
$794$	50.3548	1.78702
$795$	−7.52531	−0.266895
$796$	3.12711	0.110837
$797$	−15.0811	−0.534200	−0.267100	−	0.963669i	$-0.586065\pi$
$797$	−15.0811	−0.534200	−0.267100	+	0.963669i	$0.586065\pi$
$798$	0	0
$799$	−3.80372	−0.134566
$800$	33.9956	1.20192
$801$	25.7056	0.908263
$802$	49.3491	1.74258
$803$	−78.6804	−2.77657
$804$	0.0562200	0.00198273
$805$	0	0
$806$	45.0188	1.58572
$807$	21.2933	0.749560
$808$	14.7234	0.517967
$809$	19.5485	0.687290	0.343645	−	0.939100i	$-0.388338\pi$
$809$	19.5485	0.687290	0.343645	+	0.939100i	$0.388338\pi$
$810$	10.7784	0.378714
$811$	−53.9778	−1.89542	−0.947708	−	0.319138i	$-0.896607\pi$
$811$	−53.9778	−1.89542	−0.947708	+	0.319138i	$0.896607\pi$
$812$	0	0
$813$	−20.6778	−0.725203
$814$	−7.40535	−0.259558
$815$	−8.68592	−0.304254
$816$	3.04369	0.106550
$817$	7.59913	0.265860
$818$	69.9444	2.44555
$819$	0	0
$820$	2.49454	0.0871130
$821$	−44.9653	−1.56930	−0.784649	−	0.619940i	$-0.787157\pi$
$821$	−44.9653	−1.56930	−0.784649	+	0.619940i	$0.787157\pi$
$822$	0.922442	0.0321739
$823$	0.0731139	0.00254859	0.00127429	−	0.999999i	$-0.499594\pi$
$823$	0.0731139	0.00254859	0.00127429	+	0.999999i	$0.499594\pi$
$824$	0.750385	0.0261409
$825$	−53.8443	−1.87462
$826$	0	0
$827$	−45.7266	−1.59007	−0.795035	−	0.606564i	$-0.792547\pi$
$827$	−45.7266	−1.59007	−0.795035	+	0.606564i	$0.792547\pi$
$828$	26.2827	0.913386
$829$	−16.1331	−0.560326	−0.280163	−	0.959952i	$-0.590389\pi$
$829$	−16.1331	−0.560326	−0.280163	+	0.959952i	$0.590389\pi$
$830$	10.2313	0.355133
$831$	−15.9074	−0.551823
$832$	43.5160	1.50865
$833$	0	0
$834$	26.2871	0.910248
$835$	−0.272572	−0.00943275
$836$	−17.4726	−0.604303
$837$	16.3580	0.565417
$838$	20.5872	0.711175
$839$	−26.3488	−0.909661	−0.454830	−	0.890578i	$-0.650300\pi$
$839$	−26.3488	−0.909661	−0.454830	+	0.890578i	$0.650300\pi$
$840$	0	0
$841$	2.36332	0.0814938
$842$	−53.7675	−1.85295
$843$	−18.4920	−0.636897
$844$	−10.4229	−0.358770
$845$	0.664999	0.0228767
$846$	14.7342	0.506573
$847$	0	0
$848$	−11.0766	−0.380371
$849$	0.563337	0.0193337
$850$	10.6466	0.365177
$851$	−3.37570	−0.115717
$852$	−84.5923	−2.89808
$853$	−45.0125	−1.54120	−0.770600	−	0.637320i	$-0.780043\pi$
$853$	−45.0125	−1.54120	−0.770600	+	0.637320i	$0.780043\pi$
$854$	0	0
$855$	0.894385	0.0305873
$856$	24.6746	0.843361
$857$	11.1927	0.382334	0.191167	−	0.981557i	$-0.438773\pi$
$857$	11.1927	0.382334	0.191167	+	0.981557i	$0.438773\pi$
$858$	−83.9070	−2.86454
$859$	−4.76318	−0.162518	−0.0812588	−	0.996693i	$-0.525894\pi$
$859$	−4.76318	−0.162518	−0.0812588	+	0.996693i	$0.525894\pi$
$860$	8.16742	0.278507
$861$	0	0
$862$	−16.6165	−0.565961
$863$	−0.912014	−0.0310453	−0.0155227	−	0.999880i	$-0.504941\pi$
$863$	−0.912014	−0.0310453	−0.0155227	+	0.999880i	$0.504941\pi$
$864$	19.2494	0.654879
$865$	−9.31888	−0.316851
$866$	−71.8674	−2.44215
$867$	2.17950	0.0740198
$868$	0	0
$869$	−29.4690	−0.999666
$870$	−11.7597	−0.398689
$871$	−0.0301452	−0.00102143
$872$	−15.7145	−0.532160
$873$	26.9063	0.910641
$874$	−13.4610	−0.455326
$875$	0	0
$876$	−96.7774	−3.26980
$877$	26.4891	0.894475	0.447237	−	0.894415i	$-0.352408\pi$
$877$	26.4891	0.894475	0.447237	+	0.894415i	$0.352408\pi$
$878$	−51.6235	−1.74221
$879$	−21.7183	−0.732541
$880$	3.12204	0.105244
$881$	0.914651	0.0308154	0.0154077	−	0.999881i	$-0.495095\pi$
$881$	0.914651	0.0308154	0.0154077	+	0.999881i	$0.495095\pi$
$882$	0	0
$883$	44.8471	1.50922	0.754612	−	0.656172i	$-0.227825\pi$
$883$	44.8471	1.50922	0.754612	+	0.656172i	$0.227825\pi$
$884$	9.81676	0.330173
$885$	−3.49070	−0.117339
$886$	−46.5709	−1.56458
$887$	−23.8806	−0.801834	−0.400917	−	0.916114i	$-0.631308\pi$
$887$	−23.8806	−0.801834	−0.400917	+	0.916114i	$0.631308\pi$
$888$	−2.82310	−0.0947371
$889$	0	0
$890$	−14.1500	−0.474310
$891$	−57.4540	−1.92478
$892$	39.2156	1.31304
$893$	−4.46512	−0.149419
$894$	−58.8422	−1.96798
$895$	3.87044	0.129375
$896$	0	0
$897$	−38.2486	−1.27708
$898$	−27.3696	−0.913335
$899$	−33.6323	−1.12170
$900$	−24.4022	−0.813405
$901$	−7.93165	−0.264241
$902$	−22.4729	−0.748266
$903$	0	0
$904$	−26.1215	−0.868789
$905$	−0.186121	−0.00618688
$906$	100.288	3.33184
$907$	−5.40248	−0.179386	−0.0896932	−	0.995969i	$-0.528589\pi$
$907$	−5.40248	−0.179386	−0.0896932	+	0.995969i	$0.528589\pi$
$908$	18.0092	0.597655
$909$	12.9618	0.429917
$910$	0	0
$911$	29.7868	0.986879	0.493440	−	0.869780i	$-0.335739\pi$
$911$	29.7868	0.986879	0.493440	+	0.869780i	$0.335739\pi$
$912$	3.57293	0.118311
$913$	−54.5376	−1.80493
$914$	31.0970	1.02860
$915$	−11.8626	−0.392165
$916$	−10.6955	−0.353391
$917$	0	0
$918$	6.02848	0.198970
$919$	−7.93712	−0.261821	−0.130911	−	0.991394i	$-0.541790\pi$
$919$	−7.93712	−0.261821	−0.130911	+	0.991394i	$0.541790\pi$
$920$	−4.48408	−0.147836
$921$	−7.48933	−0.246782
$922$	20.0860	0.661498
$923$	45.3585	1.49299
$924$	0	0
$925$	3.13417	0.103051
$926$	−61.7972	−2.03078
$927$	0.660607	0.0216972
$928$	−39.5770	−1.29918
$929$	2.95851	0.0970657	0.0485329	−	0.998822i	$-0.484545\pi$
$929$	2.95851	0.0970657	0.0485329	+	0.998822i	$0.484545\pi$
$930$	12.6104	0.413511
$931$	0	0
$932$	−8.54890	−0.280028
$933$	−11.7100	−0.383368
$934$	72.0722	2.35827
$935$	2.23561	0.0731122
$936$	−11.7858	−0.385232
$937$	4.99430	0.163157	0.0815784	−	0.996667i	$-0.474004\pi$
$937$	4.99430	0.163157	0.0815784	+	0.996667i	$0.474004\pi$
$938$	0	0
$939$	−36.1352	−1.17923
$940$	−4.79903	−0.156527
$941$	−33.4788	−1.09138	−0.545689	−	0.837988i	$-0.683732\pi$
$941$	−33.4788	−1.09138	−0.545689	+	0.837988i	$0.683732\pi$
$942$	83.0222	2.70501
$943$	−10.2442	−0.333596
$944$	−5.13800	−0.167228
$945$	0	0
$946$	−73.5790	−2.39226
$947$	−10.0421	−0.326323	−0.163162	−	0.986599i	$-0.552169\pi$
$947$	−10.0421	−0.326323	−0.163162	+	0.986599i	$0.552169\pi$
$948$	−36.2470	−1.17725
$949$	51.8921	1.68449
$950$	12.4979	0.405485
$951$	55.0232	1.78425
$952$	0	0
$953$	−19.5150	−0.632153	−0.316076	−	0.948734i	$-0.602366\pi$
$953$	−19.5150	−0.632153	−0.316076	+	0.948734i	$0.602366\pi$
$954$	30.7243	0.994736
$955$	−1.19929	−0.0388081
$956$	−8.35102	−0.270091
$957$	62.6846	2.02630
$958$	69.4350	2.24334
$959$	0	0
$960$	12.1894	0.393412
$961$	5.06543	0.163401
$962$	4.88405	0.157468
$963$	21.7225	0.699997
$964$	−36.6722	−1.18113
$965$	1.17295	0.0377587
$966$	0	0
$967$	24.6812	0.793693	0.396847	−	0.917885i	$-0.370104\pi$
$967$	24.6812	0.793693	0.396847	+	0.917885i	$0.370104\pi$
$968$	30.5660	0.982428
$969$	2.55848	0.0821902
$970$	−14.8110	−0.475552
$971$	49.1078	1.57594	0.787972	−	0.615711i	$-0.211131\pi$
$971$	49.1078	1.57594	0.787972	+	0.615711i	$0.211131\pi$
$972$	−46.9851	−1.50705
$973$	0	0
$974$	94.2537	3.02008
$975$	35.5119	1.13729
$976$	−17.4606	−0.558902
$977$	−43.7340	−1.39917	−0.699587	−	0.714548i	$-0.746633\pi$
$977$	−43.7340	−1.39917	−0.699587	+	0.714548i	$0.746633\pi$
$978$	96.2480	3.07767
$979$	75.4264	2.41064
$980$	0	0
$981$	−13.8344	−0.441698
$982$	64.0266	2.04317
$983$	−39.7211	−1.26691	−0.633453	−	0.773781i	$-0.718363\pi$
$983$	−39.7211	−1.26691	−0.633453	+	0.773781i	$0.718363\pi$
$984$	−8.56722	−0.273113
$985$	−2.57671	−0.0821008
$986$	−12.3946	−0.394725
$987$	0	0
$988$	11.5237	0.366618
$989$	−33.5406	−1.06653
$990$	−8.65993	−0.275231
$991$	−12.1775	−0.386830	−0.193415	−	0.981117i	$-0.561956\pi$
$991$	−12.1775	−0.386830	−0.193415	+	0.981117i	$0.561956\pi$
$992$	42.4402	1.34748
$993$	2.64517	0.0839420
$994$	0	0
$995$	−0.469683	−0.0148899
$996$	−67.0815	−2.12556
$997$	49.4341	1.56559	0.782797	−	0.622278i	$-0.213793\pi$
$997$	49.4341	1.56559	0.782797	+	0.622278i	$0.213793\pi$
$998$	4.92718	0.155967
$999$	1.77467	0.0561481

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.a.h.1.6		7
3.2	odd	2		7497.2.a.ca.1.2		7
7.2	even	3		833.2.e.j.18.2		14
7.3	odd	6		119.2.e.b.86.2	yes	14
7.4	even	3		833.2.e.j.324.2		14
7.5	odd	6		119.2.e.b.18.2	✓	14
7.6	odd	2		833.2.a.i.1.6		7
21.5	even	6		1071.2.i.i.613.6		14
21.17	even	6		1071.2.i.i.919.6		14
21.20	even	2		7497.2.a.bz.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.e.b.18.2	✓	14	7.5	odd	6
119.2.e.b.86.2	yes	14	7.3	odd	6
833.2.a.h.1.6		7	1.1	even	1	trivial
833.2.a.i.1.6		7	7.6	odd	2
833.2.e.j.18.2		14	7.2	even	3
833.2.e.j.324.2		14	7.4	even	3
1071.2.i.i.613.6		14	21.5	even	6
1071.2.i.i.919.6		14	21.17	even	6
7497.2.a.bz.1.2		7	21.20	even	2
7497.2.a.ca.1.2		7	3.2	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:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.a (trivial)

\(f(q)\)	\(=\)	\(q+2.21321 q^{2} +2.17950 q^{3} +2.89829 q^{4} -0.435315 q^{5} +4.82369 q^{6} +1.98810 q^{8} +1.75024 q^{9} +O(q^{10})\)	\(q+2.21321 q^{2} +2.17950 q^{3} +2.89829 q^{4} -0.435315 q^{5} +4.82369 q^{6} +1.98810 q^{8} +1.75024 q^{9} -0.963443 q^{10} +5.13561 q^{11} +6.31683 q^{12} -3.38709 q^{13} -0.948771 q^{15} -1.39650 q^{16} -1.00000 q^{17} +3.87363 q^{18} -1.17388 q^{19} -1.26167 q^{20} +11.3662 q^{22} +5.18122 q^{23} +4.33306 q^{24} -4.81050 q^{25} -7.49633 q^{26} -2.72387 q^{27} +5.60030 q^{29} -2.09983 q^{30} -6.00545 q^{31} -7.06695 q^{32} +11.1931 q^{33} -2.21321 q^{34} +5.07268 q^{36} -0.651526 q^{37} -2.59804 q^{38} -7.38217 q^{39} -0.865448 q^{40} -1.97717 q^{41} -6.47351 q^{43} +14.8845 q^{44} -0.761904 q^{45} +11.4671 q^{46} +3.80372 q^{47} -3.04369 q^{48} -10.6466 q^{50} -2.17950 q^{51} -9.81676 q^{52} +7.93165 q^{53} -6.02848 q^{54} -2.23561 q^{55} -2.55848 q^{57} +12.3946 q^{58} +3.67918 q^{59} -2.74981 q^{60} +12.5031 q^{61} -13.2913 q^{62} -12.8476 q^{64} +1.47445 q^{65} +24.7726 q^{66} +0.00890004 q^{67} -2.89829 q^{68} +11.2925 q^{69} -13.3916 q^{71} +3.47964 q^{72} -15.3206 q^{73} -1.44196 q^{74} -10.4845 q^{75} -3.40225 q^{76} -16.3383 q^{78} -5.73816 q^{79} +0.607919 q^{80} -11.1874 q^{81} -4.37590 q^{82} -10.6195 q^{83} +0.435315 q^{85} -14.3272 q^{86} +12.2059 q^{87} +10.2101 q^{88} +14.6869 q^{89} -1.68625 q^{90} +15.0167 q^{92} -13.0889 q^{93} +8.41843 q^{94} +0.511008 q^{95} -15.4024 q^{96} +15.3730 q^{97} +8.98852 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3 q^{2} - q^{3} + 11 q^{4} - 2 q^{5} - 5 q^{6} + 8 q^{9}+O(q^{10}) \) 7 * q + 3 * q^2 - q^3 + 11 * q^4 - 2 * q^5 - 5 * q^6 + 8 * q^9	\( 7 q + 3 q^{2} - q^{3} + 11 q^{4} - 2 q^{5} - 5 q^{6} + 8 q^{9} + 10 q^{10} + 4 q^{11} - 2 q^{12} + 2 q^{13} + 8 q^{15} + 23 q^{16} - 7 q^{17} + 15 q^{18} + 5 q^{19} - 27 q^{20} + 9 q^{22} + 22 q^{23} + 7 q^{24} + 7 q^{25} + 10 q^{26} - 10 q^{27} + q^{29} + 15 q^{30} - 2 q^{31} + 8 q^{32} + 27 q^{33} - 3 q^{34} - 18 q^{36} + 19 q^{37} + 35 q^{38} + 2 q^{39} + 25 q^{40} - 12 q^{41} + 19 q^{43} - 2 q^{44} - 9 q^{45} + 7 q^{47} - 30 q^{48} - 22 q^{50} + q^{51} + 7 q^{52} - 8 q^{53} - 11 q^{54} + 9 q^{55} - 3 q^{57} + 15 q^{58} - 5 q^{59} - q^{60} + 4 q^{61} - 17 q^{62} + 40 q^{64} + 2 q^{65} + 16 q^{66} + 24 q^{67} - 11 q^{68} - 16 q^{69} - q^{71} - 19 q^{73} - 18 q^{74} + 2 q^{75} + 13 q^{76} - 45 q^{78} + 15 q^{79} + 9 q^{80} - 29 q^{81} - 41 q^{82} + 2 q^{83} + 2 q^{85} - 21 q^{86} - 7 q^{87} + 62 q^{88} + 32 q^{89} - 49 q^{90} + 8 q^{92} - q^{93} + 15 q^{94} + 12 q^{95} - 18 q^{96} + 23 q^{97} + 10 q^{99}+O(q^{100}) \) 7 * q + 3 * q^2 - q^3 + 11 * q^4 - 2 * q^5 - 5 * q^6 + 8 * q^9 + 10 * q^10 + 4 * q^11 - 2 * q^12 + 2 * q^13 + 8 * q^15 + 23 * q^16 - 7 * q^17 + 15 * q^18 + 5 * q^19 - 27 * q^20 + 9 * q^22 + 22 * q^23 + 7 * q^24 + 7 * q^25 + 10 * q^26 - 10 * q^27 + q^29 + 15 * q^30 - 2 * q^31 + 8 * q^32 + 27 * q^33 - 3 * q^34 - 18 * q^36 + 19 * q^37 + 35 * q^38 + 2 * q^39 + 25 * q^40 - 12 * q^41 + 19 * q^43 - 2 * q^44 - 9 * q^45 + 7 * q^47 - 30 * q^48 - 22 * q^50 + q^51 + 7 * q^52 - 8 * q^53 - 11 * q^54 + 9 * q^55 - 3 * q^57 + 15 * q^58 - 5 * q^59 - q^60 + 4 * q^61 - 17 * q^62 + 40 * q^64 + 2 * q^65 + 16 * q^66 + 24 * q^67 - 11 * q^68 - 16 * q^69 - q^71 - 19 * q^73 - 18 * q^74 + 2 * q^75 + 13 * q^76 - 45 * q^78 + 15 * q^79 + 9 * q^80 - 29 * q^81 - 41 * q^82 + 2 * q^83 + 2 * q^85 - 21 * q^86 - 7 * q^87 + 62 * q^88 + 32 * q^89 - 49 * q^90 + 8 * q^92 - q^93 + 15 * q^94 + 12 * q^95 - 18 * q^96 + 23 * q^97 + 10 * q^99

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