LMFDB - Embedded newform 1183.2.a.k.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(1,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, 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("1183.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.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:	$9.44630255912$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.27004.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 3x + 1 $ x^4 - x^3 - 6x^2 + 3x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.231361$ of defining polynomial
Character	$\chi$	$=$	1183.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.231361 q^{2} -3.32225 q^{3} -1.94647 q^{4} -2.23136 q^{5} -0.768639 q^{6} -1.00000 q^{7} -0.913059 q^{8} +8.03736 q^{9} +O(q^{10})$	\(q+0.231361 q^{2} -3.32225 q^{3} -1.94647 q^{4} -2.23136 q^{5} -0.768639 q^{6} -1.00000 q^{7} -0.913059 q^{8} +8.03736 q^{9} -0.516249 q^{10} +3.32225 q^{11} +6.46667 q^{12} -0.231361 q^{14} +7.41314 q^{15} +3.68170 q^{16} -1.37578 q^{17} +1.85953 q^{18} +3.23531 q^{19} +4.34328 q^{20} +3.32225 q^{21} +0.768639 q^{22} +0.838502 q^{23} +3.03341 q^{24} -0.0210289 q^{25} -16.7354 q^{27} +1.94647 q^{28} -0.607142 q^{29} +1.71511 q^{30} +1.71511 q^{31} +2.67792 q^{32} -11.0374 q^{33} -0.318302 q^{34} +2.23136 q^{35} -15.6445 q^{36} +1.55361 q^{37} +0.748524 q^{38} +2.03736 q^{40} -9.17783 q^{41} +0.768639 q^{42} +1.23136 q^{43} -6.46667 q^{44} -17.9343 q^{45} +0.193997 q^{46} -1.62817 q^{47} -12.2315 q^{48} +1.00000 q^{49} -0.00486525 q^{50} +4.57069 q^{51} +8.39607 q^{53} -3.87192 q^{54} -7.41314 q^{55} +0.913059 q^{56} -10.7485 q^{57} -0.140469 q^{58} +8.82234 q^{59} -14.4295 q^{60} +5.46667 q^{61} +0.396810 q^{62} -8.03736 q^{63} -6.74383 q^{64} -2.55361 q^{66} -10.1857 q^{67} +2.67792 q^{68} -2.78572 q^{69} +0.516249 q^{70} -5.21428 q^{71} -7.33859 q^{72} -3.96355 q^{73} +0.359445 q^{74} +0.0698632 q^{75} -6.29744 q^{76} -3.32225 q^{77} +6.45051 q^{79} -8.21520 q^{80} +31.4871 q^{81} -2.12339 q^{82} -4.64055 q^{83} -6.46667 q^{84} +3.06986 q^{85} +0.284889 q^{86} +2.01708 q^{87} -3.03341 q^{88} +9.12826 q^{89} -4.14929 q^{90} -1.63212 q^{92} -5.69803 q^{93} -0.376695 q^{94} -7.21915 q^{95} -8.89672 q^{96} -15.3589 q^{97} +0.231361 q^{98} +26.7022 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} - 4 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 4 * q - q^2 + q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 - 4 * q^7 - 6 * q^8 + 7 * q^9	$ 4 q - q^{2} + q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} - 4 q^{7} - 6 q^{8} + 7 q^{9} - 11 q^{10} - q^{11} + 12 q^{12} + q^{14} + 3 q^{15} + 19 q^{16} - 4 q^{17} - 3 q^{18} + q^{19} - 2 q^{20} - q^{21} + 5 q^{22} - 2 q^{23} - 3 q^{24} + 5 q^{25} - 26 q^{27} - 5 q^{28} + q^{29} - 4 q^{30} - 4 q^{31} - 33 q^{32} - 19 q^{33} + 3 q^{34} + 7 q^{35} - 34 q^{36} - 10 q^{37} - 23 q^{38} - 17 q^{40} - 22 q^{41} + 5 q^{42} + 3 q^{43} - 12 q^{44} - 11 q^{45} + 24 q^{46} + 2 q^{47} + 11 q^{48} + 4 q^{49} + 43 q^{50} + 7 q^{51} + 2 q^{53} + 5 q^{54} - 3 q^{55} + 6 q^{56} - 17 q^{57} - 11 q^{58} - 8 q^{59} - 11 q^{60} + 8 q^{61} - 5 q^{62} - 7 q^{63} + 14 q^{64} + 6 q^{66} - 6 q^{67} - 33 q^{68} - 18 q^{69} + 11 q^{70} - 14 q^{71} + 5 q^{72} - 8 q^{73} + 20 q^{74} - 7 q^{75} + 32 q^{76} + q^{77} - 26 q^{79} + 7 q^{80} + 24 q^{81} - 14 q^{82} - 12 q^{84} + 5 q^{85} + 12 q^{86} + 13 q^{87} + 3 q^{88} - q^{89} + 26 q^{90} + 12 q^{92} - 7 q^{93} + 33 q^{94} + 21 q^{95} - 58 q^{96} + 3 q^{97} - q^{98} + 23 q^{99}+O(q^{100}) $ 4 * q - q^2 + q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 - 4 * q^7 - 6 * q^8 + 7 * q^9 - 11 * q^10 - q^11 + 12 * q^12 + q^14 + 3 * q^15 + 19 * q^16 - 4 * q^17 - 3 * q^18 + q^19 - 2 * q^20 - q^21 + 5 * q^22 - 2 * q^23 - 3 * q^24 + 5 * q^25 - 26 * q^27 - 5 * q^28 + q^29 - 4 * q^30 - 4 * q^31 - 33 * q^32 - 19 * q^33 + 3 * q^34 + 7 * q^35 - 34 * q^36 - 10 * q^37 - 23 * q^38 - 17 * q^40 - 22 * q^41 + 5 * q^42 + 3 * q^43 - 12 * q^44 - 11 * q^45 + 24 * q^46 + 2 * q^47 + 11 * q^48 + 4 * q^49 + 43 * q^50 + 7 * q^51 + 2 * q^53 + 5 * q^54 - 3 * q^55 + 6 * q^56 - 17 * q^57 - 11 * q^58 - 8 * q^59 - 11 * q^60 + 8 * q^61 - 5 * q^62 - 7 * q^63 + 14 * q^64 + 6 * q^66 - 6 * q^67 - 33 * q^68 - 18 * q^69 + 11 * q^70 - 14 * q^71 + 5 * q^72 - 8 * q^73 + 20 * q^74 - 7 * q^75 + 32 * q^76 + q^77 - 26 * q^79 + 7 * q^80 + 24 * q^81 - 14 * q^82 - 12 * q^84 + 5 * q^85 + 12 * q^86 + 13 * q^87 + 3 * q^88 - q^89 + 26 * q^90 + 12 * q^92 - 7 * q^93 + 33 * q^94 + 21 * q^95 - 58 * q^96 + 3 * q^97 - q^98 + 23 * 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 $

$2$	0.231361	0.163597	0.0817984	−	0.996649i	$-0.473934\pi$
$2$	0.231361	0.163597	0.0817984	+	0.996649i	$0.473934\pi$
$3$	−3.32225	−1.91810	−0.959052	−	0.283231i	$-0.908594\pi$
$3$	−3.32225	−1.91810	−0.959052	+	0.283231i	$0.908594\pi$
$4$	−1.94647	−0.973236
$5$	−2.23136	−0.997895	−0.498947	−	0.866632i	$-0.666280\pi$
$5$	−2.23136	−0.997895	−0.498947	+	0.866632i	$0.666280\pi$
$6$	−0.768639	−0.313796
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.913059	−0.322815
$9$	8.03736	2.67912
$10$	−0.516249	−0.163252
$11$	3.32225	1.00170	0.500848	−	0.865535i	$-0.333021\pi$
$11$	3.32225	1.00170	0.500848	+	0.865535i	$0.333021\pi$
$12$	6.46667	1.86677
$13$	0	0
$13$	0	0
$14$	−0.231361	−0.0618338
$15$	7.41314	1.91407
$16$	3.68170	0.920425
$17$	−1.37578	−0.333676	−0.166838	−	0.985984i	$-0.553356\pi$
$17$	−1.37578	−0.333676	−0.166838	+	0.985984i	$0.553356\pi$
$18$	1.85953	0.438296
$19$	3.23531	0.742231	0.371116	−	0.928587i	$-0.378975\pi$
$19$	3.23531	0.742231	0.371116	+	0.928587i	$0.378975\pi$
$20$	4.34328	0.971187
$21$	3.32225	0.724975
$22$	0.768639	0.163874
$23$	0.838502	0.174840	0.0874199	−	0.996172i	$-0.472138\pi$
$23$	0.838502	0.174840	0.0874199	+	0.996172i	$0.472138\pi$
$24$	3.03341	0.619193
$25$	−0.0210289	−0.00420577
$26$	0	0
$27$	−16.7354	−3.22073
$28$	1.94647	0.367849
$29$	−0.607142	−0.112743	−0.0563717	−	0.998410i	$-0.517953\pi$
$29$	−0.607142	−0.112743	−0.0563717	+	0.998410i	$0.517953\pi$
$30$	1.71511	0.313135
$31$	1.71511	0.308043	0.154022	−	0.988067i	$-0.450777\pi$
$31$	1.71511	0.308043	0.154022	+	0.988067i	$0.450777\pi$
$32$	2.67792	0.473394
$33$	−11.0374	−1.92136
$34$	−0.318302	−0.0545883
$35$	2.23136	0.377169
$36$	−15.6445	−2.60742
$37$	1.55361	0.255413	0.127706	−	0.991812i	$-0.459239\pi$
$37$	1.55361	0.255413	0.127706	+	0.991812i	$0.459239\pi$
$38$	0.748524	0.121427
$39$	0	0
$40$	2.03736	0.322136
$41$	−9.17783	−1.43334	−0.716668	−	0.697414i	$-0.754334\pi$
$41$	−9.17783	−1.43334	−0.716668	+	0.697414i	$0.754334\pi$
$42$	0.768639	0.118604
$43$	1.23136	0.187781	0.0938904	−	0.995583i	$-0.470070\pi$
$43$	1.23136	0.187781	0.0938904	+	0.995583i	$0.470070\pi$
$44$	−6.46667	−0.974888
$45$	−17.9343	−2.67348
$46$	0.193997	0.0286032
$47$	−1.62817	−0.237493	−0.118747	−	0.992925i	$-0.537888\pi$
$47$	−1.62817	−0.237493	−0.118747	+	0.992925i	$0.537888\pi$
$48$	−12.2315	−1.76547
$49$	1.00000	0.142857
$50$	−0.00486525	−0.000688051 0
$51$	4.57069	0.640025
$52$	0	0
$53$	8.39607	1.15329	0.576644	−	0.816995i	$-0.304362\pi$
$53$	8.39607	1.15329	0.576644	+	0.816995i	$0.304362\pi$
$54$	−3.87192	−0.526901
$55$	−7.41314	−0.999588
$56$	0.913059	0.122013
$57$	−10.7485	−1.42368
$58$	−0.140469	−0.0184445
$59$	8.82234	1.14857	0.574285	−	0.818655i	$-0.305280\pi$
$59$	8.82234	1.14857	0.574285	+	0.818655i	$0.305280\pi$
$60$	−14.4295	−1.86284
$61$	5.46667	0.699936	0.349968	−	0.936762i	$-0.386193\pi$
$61$	5.46667	0.699936	0.349968	+	0.936762i	$0.386193\pi$
$62$	0.396810	0.0503949
$63$	−8.03736	−1.01261
$64$	−6.74383	−0.842979
$65$	0	0
$66$	−2.55361	−0.314328
$67$	−10.1857	−1.24439	−0.622193	−	0.782864i	$-0.713758\pi$
$67$	−10.1857	−1.24439	−0.622193	+	0.782864i	$0.713758\pi$
$68$	2.67792	0.324745
$69$	−2.78572	−0.335361
$70$	0.516249	0.0617036
$71$	−5.21428	−0.618822	−0.309411	−	0.950928i	$-0.600132\pi$
$71$	−5.21428	−0.618822	−0.309411	+	0.950928i	$0.600132\pi$
$72$	−7.33859	−0.864861
$73$	−3.96355	−0.463898	−0.231949	−	0.972728i	$-0.574510\pi$
$73$	−3.96355	−0.463898	−0.231949	+	0.972728i	$0.574510\pi$
$74$	0.359445	0.0417847
$75$	0.0698632	0.00806711
$76$	−6.29744	−0.722366
$77$	−3.32225	−0.378606
$78$	0	0
$79$	6.45051	0.725739	0.362869	−	0.931840i	$-0.381797\pi$
$79$	6.45051	0.725739	0.362869	+	0.931840i	$0.381797\pi$
$80$	−8.21520	−0.918487
$81$	31.4871	3.49857
$82$	−2.12339	−0.234489
$83$	−4.64055	−0.509367	−0.254684	−	0.967024i	$-0.581971\pi$
$83$	−4.64055	−0.509367	−0.254684	+	0.967024i	$0.581971\pi$
$84$	−6.46667	−0.705572
$85$	3.06986	0.332973
$86$	0.284889	0.0307203
$87$	2.01708	0.216253
$88$	−3.03341	−0.323363
$89$	9.12826	0.967593	0.483797	−	0.875180i	$-0.339257\pi$
$89$	9.12826	0.967593	0.483797	+	0.875180i	$0.339257\pi$
$90$	−4.14929	−0.437373
$91$	0	0
$92$	−1.63212	−0.170160
$93$	−5.69803	−0.590859
$94$	−0.376695	−0.0388531
$95$	−7.21915	−0.740669
$96$	−8.89672	−0.908018
$97$	−15.3589	−1.55946	−0.779729	−	0.626117i	$-0.784643\pi$
$97$	−15.3589	−1.55946	−0.779729	+	0.626117i	$0.784643\pi$
$98$	0.231361	0.0233710
$99$	26.7022	2.68367
$100$	0.0409321	0.00409321
$101$	−7.95042	−0.791097	−0.395548	−	0.918445i	$-0.629445\pi$
$101$	−7.95042	−0.791097	−0.395548	+	0.918445i	$0.629445\pi$
$102$	1.05748	0.104706
$103$	0.694825	0.0684631	0.0342316	−	0.999414i	$-0.489102\pi$
$103$	0.694825	0.0684631	0.0342316	+	0.999414i	$0.489102\pi$
$104$	0	0
$105$	−7.41314	−0.723449
$106$	1.94252	0.188674
$107$	8.94647	0.864888	0.432444	−	0.901661i	$-0.357651\pi$
$107$	8.94647	0.864888	0.432444	+	0.901661i	$0.357651\pi$
$108$	32.5750	3.13453
$109$	−2.27268	−0.217683	−0.108841	−	0.994059i	$-0.534714\pi$
$109$	−2.27268	−0.217683	−0.108841	+	0.994059i	$0.534714\pi$
$110$	−1.71511	−0.163529
$111$	−5.16150	−0.489908
$112$	−3.68170	−0.347888
$113$	−9.50478	−0.894134	−0.447067	−	0.894500i	$-0.647532\pi$
$113$	−9.50478	−0.894134	−0.447067	+	0.894500i	$0.647532\pi$
$114$	−2.48679	−0.232909
$115$	−1.87100	−0.174472
$116$	1.18178	0.109726
$117$	0	0
$118$	2.04114	0.187902
$119$	1.37578	0.126118
$120$	−6.76864	−0.617889
$121$	0.0373642	0.00339675
$122$	1.26477	0.114507
$123$	30.4911	2.74929
$124$	−3.33842	−0.299799
$125$	11.2037	1.00209
$126$	−1.85953	−0.165660
$127$	18.4334	1.63570	0.817851	−	0.575430i	$-0.195165\pi$
$127$	18.4334	1.63570	0.817851	+	0.575430i	$0.195165\pi$
$128$	−6.91610	−0.611302
$129$	−4.09089	−0.360183
$130$	0	0
$131$	−1.74835	−0.152754	−0.0763771	−	0.997079i	$-0.524335\pi$
$131$	−1.74835	−0.152754	−0.0763771	+	0.997079i	$0.524335\pi$
$132$	21.4839	1.86994
$133$	−3.23531	−0.280537
$134$	−2.35658	−0.203578
$135$	37.3427	3.21395
$136$	1.25617	0.107716
$137$	−18.0032	−1.53812	−0.769059	−	0.639178i	$-0.779275\pi$
$137$	−18.0032	−1.53812	−0.769059	+	0.639178i	$0.779275\pi$
$138$	−0.644506	−0.0548640
$139$	13.9179	1.18050	0.590251	−	0.807219i	$-0.299029\pi$
$139$	13.9179	1.18050	0.590251	+	0.807219i	$0.299029\pi$
$140$	−4.34328	−0.367074
$141$	5.40919	0.455536
$142$	−1.20638	−0.101237
$143$	0	0
$144$	29.5911	2.46593
$145$	1.35475	0.112506
$146$	−0.917010	−0.0758923
$147$	−3.32225	−0.274015
$148$	−3.02407	−0.248577
$149$	−15.9303	−1.30506	−0.652531	−	0.757762i	$-0.726293\pi$
$149$	−15.9303	−1.30506	−0.652531	+	0.757762i	$0.726293\pi$
$150$	0.0161636	0.00131975
$151$	−13.9497	−1.13521	−0.567604	−	0.823301i	$-0.692130\pi$
$151$	−13.9497	−1.13521	−0.567604	+	0.823301i	$0.692130\pi$
$152$	−2.95403	−0.239604
$153$	−11.0577	−0.893958
$154$	−0.768639	−0.0619387
$155$	−3.82703	−0.307395
$156$	0	0
$157$	−12.9747	−1.03549	−0.517745	−	0.855535i	$-0.673229\pi$
$157$	−12.9747	−1.03549	−0.517745	+	0.855535i	$0.673229\pi$
$158$	1.49240	0.118729
$159$	−27.8939	−2.21213
$160$	−5.97540	−0.472397
$161$	−0.838502	−0.0660832
$162$	7.28489	0.572355
$163$	18.4085	1.44186	0.720931	−	0.693007i	$-0.243715\pi$
$163$	18.4085	1.44186	0.720931	+	0.693007i	$0.243715\pi$
$164$	17.8644	1.39498
$165$	24.6283	1.91731
$166$	−1.07364	−0.0833308
$167$	−18.4993	−1.43152	−0.715761	−	0.698345i	$-0.753920\pi$
$167$	−18.4993	−1.43152	−0.715761	+	0.698345i	$0.753920\pi$
$168$	−3.03341	−0.234033
$169$	0	0
$170$	0.710246	0.0544734
$171$	26.0034	1.98853
$172$	−2.39681	−0.182755
$173$	−17.1981	−1.30755	−0.653774	−	0.756690i	$-0.726815\pi$
$173$	−17.1981	−1.30755	−0.653774	+	0.756690i	$0.726815\pi$
$174$	0.466673	0.0353784
$175$	0.0210289	0.00158963
$176$	12.2315	0.921986
$177$	−29.3100	−2.20308
$178$	2.11192	0.158295
$179$	14.4886	1.08293	0.541465	−	0.840723i	$-0.317870\pi$
$179$	14.4886	1.08293	0.541465	+	0.840723i	$0.317870\pi$
$180$	34.9085	2.60193
$181$	6.85484	0.509516	0.254758	−	0.967005i	$-0.418004\pi$
$181$	6.85484	0.509516	0.254758	+	0.967005i	$0.418004\pi$
$182$	0	0
$183$	−18.1617	−1.34255
$184$	−0.765602	−0.0564409
$185$	−3.46667	−0.254875
$186$	−1.31830	−0.0966626
$187$	−4.57069	−0.334242
$188$	3.16919	0.231137
$189$	16.7354	1.21732
$190$	−1.67023	−0.121171
$191$	−2.85163	−0.206337	−0.103168	−	0.994664i	$-0.532898\pi$
$191$	−2.85163	−0.206337	−0.103168	+	0.994664i	$0.532898\pi$
$192$	22.4047	1.61692
$193$	−10.0505	−0.723450	−0.361725	−	0.932285i	$-0.617812\pi$
$193$	−10.0505	−0.723450	−0.361725	+	0.932285i	$0.617812\pi$
$194$	−3.55344	−0.255122
$195$	0	0
$196$	−1.94647	−0.139034
$197$	−25.4171	−1.81089	−0.905447	−	0.424460i	$-0.860464\pi$
$197$	−25.4171	−1.81089	−0.905447	+	0.424460i	$0.860464\pi$
$198$	6.17783	0.439039
$199$	−12.4466	−0.882313	−0.441157	−	0.897430i	$-0.645432\pi$
$199$	−12.4466	−0.882313	−0.441157	+	0.897430i	$0.645432\pi$
$200$	0.0192006	0.00135769
$201$	33.8396	2.38686
$202$	−1.83942	−0.129421
$203$	0.607142	0.0426130
$204$	−8.89672	−0.622895
$205$	20.4791	1.43032
$206$	0.160755	0.0112003
$207$	6.73935	0.468417
$208$	0	0
$209$	10.7485	0.743491
$210$	−1.71511	−0.118354
$211$	−24.3923	−1.67923	−0.839617	−	0.543179i	$-0.817221\pi$
$211$	−24.3923	−1.67923	−0.839617	+	0.543179i	$0.817221\pi$
$212$	−16.3427	−1.12242
$213$	17.3232	1.18696
$214$	2.06986	0.141493
$215$	−2.74761	−0.187385
$216$	15.2804	1.03970
$217$	−1.71511	−0.116429
$218$	−0.525808	−0.0356122
$219$	13.1679	0.889805
$220$	14.4295	0.972835
$221$	0	0
$222$	−1.19417	−0.0801473
$223$	22.6494	1.51671	0.758357	−	0.651839i	$-0.226002\pi$
$223$	22.6494	1.51671	0.758357	+	0.651839i	$0.226002\pi$
$224$	−2.67792	−0.178926
$225$	−0.169017	−0.0112678
$226$	−2.19903	−0.146278
$227$	1.28506	0.0852925	0.0426462	−	0.999090i	$-0.486421\pi$
$227$	1.28506	0.0852925	0.0426462	+	0.999090i	$0.486421\pi$
$228$	20.9217	1.38557
$229$	−4.64451	−0.306918	−0.153459	−	0.988155i	$-0.549041\pi$
$229$	−4.64451	−0.306918	−0.153459	+	0.988155i	$0.549041\pi$
$230$	−0.432876	−0.0285430
$231$	11.0374	0.726205
$232$	0.554356	0.0363953
$233$	11.8877	0.778790	0.389395	−	0.921071i	$-0.372684\pi$
$233$	11.8877	0.778790	0.389395	+	0.921071i	$0.372684\pi$
$234$	0	0
$235$	3.63304	0.236993
$236$	−17.1724	−1.11783
$237$	−21.4302	−1.39204
$238$	0.318302	0.0206324
$239$	−4.17783	−0.270242	−0.135121	−	0.990829i	$-0.543142\pi$
$239$	−4.17783	−0.270242	−0.135121	+	0.990829i	$0.543142\pi$
$240$	27.2930	1.76175
$241$	4.03341	0.259815	0.129907	−	0.991526i	$-0.458532\pi$
$241$	4.03341	0.259815	0.129907	+	0.991526i	$0.458532\pi$
$242$	0.00864462	0.000555697 0
$243$	−54.4020	−3.48989
$244$	−10.6407	−0.681203
$245$	−2.23136	−0.142556
$246$	7.05444	0.449775
$247$	0	0
$248$	−1.56600	−0.0994410
$249$	15.4171	0.977019
$250$	2.59210	0.163939
$251$	27.8685	1.75905	0.879523	−	0.475857i	$-0.157862\pi$
$251$	27.8685	1.75905	0.879523	+	0.475857i	$0.157862\pi$
$252$	15.6445	0.985511
$253$	2.78572	0.175137
$254$	4.26477	0.267596
$255$	−10.1989	−0.638678
$256$	11.8875	0.742972
$257$	−7.14064	−0.445421	−0.222710	−	0.974885i	$-0.571490\pi$
$257$	−7.14064	−0.445421	−0.222710	+	0.974885i	$0.571490\pi$
$258$	−0.946472	−0.0589248
$259$	−1.55361	−0.0965369
$260$	0	0
$261$	−4.87982	−0.302053
$262$	−0.404500	−0.0249901
$263$	21.3192	1.31460	0.657300	−	0.753629i	$-0.271699\pi$
$263$	21.3192	1.31460	0.657300	+	0.753629i	$0.271699\pi$
$264$	10.0778	0.620244
$265$	−18.7347	−1.15086
$266$	−0.748524	−0.0458950
$267$	−30.3264	−1.85594
$268$	19.8263	1.21108
$269$	2.78875	0.170033	0.0850167	−	0.996380i	$-0.472906\pi$
$269$	2.78875	0.170033	0.0850167	+	0.996380i	$0.472906\pi$
$270$	8.63964	0.525792
$271$	−15.4747	−0.940024	−0.470012	−	0.882660i	$-0.655750\pi$
$271$	−15.4747	−0.940024	−0.470012	+	0.882660i	$0.655750\pi$
$272$	−5.06521	−0.307123
$273$	0	0
$274$	−4.16524	−0.251631
$275$	−0.0698632	−0.00421291
$276$	5.42232	0.326385
$277$	5.52955	0.332238	0.166119	−	0.986106i	$-0.446876\pi$
$277$	5.52955	0.332238	0.166119	+	0.986106i	$0.446876\pi$
$278$	3.22006	0.193127
$279$	13.7850	0.825285
$280$	−2.03736	−0.121756
$281$	−31.4871	−1.87836	−0.939182	−	0.343419i	$-0.888415\pi$
$281$	−31.4871	−1.87836	−0.939182	+	0.343419i	$0.888415\pi$
$282$	1.25148	0.0745243
$283$	−7.35118	−0.436983	−0.218491	−	0.975839i	$-0.570114\pi$
$283$	−7.35118	−0.436983	−0.218491	+	0.975839i	$0.570114\pi$
$284$	10.1495	0.602259
$285$	23.9838	1.42068
$286$	0	0
$287$	9.17783	0.541750
$288$	21.5234	1.26828
$289$	−15.1072	−0.888660
$290$	0.313437	0.0184056
$291$	51.0261	2.99120
$292$	7.71494	0.451483
$293$	−13.5335	−0.790635	−0.395318	−	0.918544i	$-0.629366\pi$
$293$	−13.5335	−0.790635	−0.395318	+	0.918544i	$0.629366\pi$
$294$	−0.768639	−0.0448279
$295$	−19.6858	−1.14615
$296$	−1.41854	−0.0824510
$297$	−55.5992	−3.22619
$298$	−3.68565	−0.213504
$299$	0	0
$300$	−0.135987	−0.00785120
$301$	−1.23136	−0.0709745
$302$	−3.22741	−0.185717
$303$	26.4133	1.51741
$304$	11.9114	0.683168
$305$	−12.1981	−0.698462
$306$	−2.55831	−0.146249
$307$	−3.30609	−0.188688	−0.0943442	−	0.995540i	$-0.530075\pi$
$307$	−3.30609	−0.188688	−0.0943442	+	0.995540i	$0.530075\pi$
$308$	6.46667	0.368473
$309$	−2.30838	−0.131319
$310$	−0.885425	−0.0502888
$311$	−34.3063	−1.94533	−0.972665	−	0.232214i	$-0.925403\pi$
$311$	−34.3063	−1.94533	−0.972665	+	0.232214i	$0.925403\pi$
$312$	0	0
$313$	7.21428	0.407775	0.203888	−	0.978994i	$-0.434642\pi$
$313$	7.21428	0.407775	0.203888	+	0.978994i	$0.434642\pi$
$314$	−3.00183	−0.169403
$315$	17.9343	1.01048
$316$	−12.5557	−0.706315
$317$	−8.04040	−0.451594	−0.225797	−	0.974174i	$-0.572499\pi$
$317$	−8.04040	−0.451594	−0.225797	+	0.974174i	$0.572499\pi$
$318$	−6.45355	−0.361897
$319$	−2.01708	−0.112935
$320$	15.0479	0.841204
$321$	−29.7224	−1.65894
$322$	−0.193997	−0.0108110
$323$	−4.45108	−0.247665
$324$	−61.2888	−3.40493
$325$	0	0
$326$	4.25899	0.235884
$327$	7.55040	0.417538
$328$	8.37990	0.462703
$329$	1.62817	0.0897639
$330$	5.69803	0.313666
$331$	0.893687	0.0491215	0.0245607	−	0.999698i	$-0.492181\pi$
$331$	0.893687	0.0491215	0.0245607	+	0.999698i	$0.492181\pi$
$332$	9.03271	0.495734
$333$	12.4870	0.684281
$334$	−4.28002	−0.234192
$335$	22.7281	1.24177
$336$	12.2315	0.667285
$337$	15.0717	0.821007	0.410504	−	0.911859i	$-0.365353\pi$
$337$	15.0717	0.821007	0.410504	+	0.911859i	$0.365353\pi$
$338$	0	0
$339$	31.5773	1.71504
$340$	−5.97540	−0.324062
$341$	5.69803	0.308566
$342$	6.01616	0.325317
$343$	−1.00000	−0.0539949
$344$	−1.12431	−0.0606185
$345$	6.21594	0.334655
$346$	−3.97897	−0.213911
$347$	−16.4164	−0.881276	−0.440638	−	0.897685i	$-0.645248\pi$
$347$	−16.4164	−0.881276	−0.440638	+	0.897685i	$0.645248\pi$
$348$	−3.92619	−0.210466
$349$	34.3722	1.83990	0.919950	−	0.392035i	$-0.128229\pi$
$349$	34.3722	1.83990	0.919950	+	0.392035i	$0.128229\pi$
$350$	0.00486525	0.000260059 0
$351$	0	0
$352$	8.89672	0.474197
$353$	−23.9163	−1.27293	−0.636467	−	0.771304i	$-0.719605\pi$
$353$	−23.9163	−1.27293	−0.636467	+	0.771304i	$0.719605\pi$
$354$	−6.78120	−0.360416
$355$	11.6349	0.617519
$356$	−17.7679	−0.941697
$357$	−4.57069	−0.241907
$358$	3.35210	0.177164
$359$	−6.17875	−0.326102	−0.163051	−	0.986618i	$-0.552133\pi$
$359$	−6.17875	−0.326102	−0.163051	+	0.986618i	$0.552133\pi$
$360$	16.3750	0.863040
$361$	−8.53276	−0.449092
$362$	1.58594	0.0833552
$363$	−0.124133	−0.00651531
$364$	0	0
$365$	8.84411	0.462922
$366$	−4.20190	−0.219637
$367$	19.8560	1.03647	0.518236	−	0.855237i	$-0.326589\pi$
$367$	19.8560	1.03647	0.518236	+	0.855237i	$0.326589\pi$
$368$	3.08711	0.160927
$369$	−73.7656	−3.84008
$370$	−0.802052	−0.0416967
$371$	−8.39607	−0.435902
$372$	11.0911	0.575045
$373$	30.1951	1.56344	0.781721	−	0.623628i	$-0.214342\pi$
$373$	30.1951	1.56344	0.781721	+	0.623628i	$0.214342\pi$
$374$	−1.05748	−0.0546809
$375$	−37.2216	−1.92212
$376$	1.48662	0.0766664
$377$	0	0
$378$	3.87192	0.199150
$379$	−4.32242	−0.222028	−0.111014	−	0.993819i	$-0.535410\pi$
$379$	−4.32242	−0.222028	−0.111014	+	0.993819i	$0.535410\pi$
$380$	14.0519	0.720846
$381$	−61.2405	−3.13745
$382$	−0.659755	−0.0337560
$383$	−17.3481	−0.886449	−0.443224	−	0.896411i	$-0.646166\pi$
$383$	−17.3481	−0.886449	−0.443224	+	0.896411i	$0.646166\pi$
$384$	22.9770	1.17254
$385$	7.41314	0.377809
$386$	−2.32529	−0.118354
$387$	9.89690	0.503087
$388$	29.8956	1.51772
$389$	−25.3474	−1.28516	−0.642582	−	0.766217i	$-0.722137\pi$
$389$	−25.3474	−1.28516	−0.642582	+	0.766217i	$0.722137\pi$
$390$	0	0
$391$	−1.15360	−0.0583398
$392$	−0.913059	−0.0461164
$393$	5.80847	0.292999
$394$	−5.88052	−0.296256
$395$	−14.3934	−0.724211
$396$	−51.9750	−2.61184
$397$	−27.0749	−1.35885	−0.679425	−	0.733745i	$-0.737771\pi$
$397$	−27.0749	−1.35885	−0.679425	+	0.733745i	$0.737771\pi$
$398$	−2.87965	−0.144344
$399$	10.7485	0.538099
$400$	−0.0774219	−0.00387110
$401$	−29.2858	−1.46246	−0.731232	−	0.682129i	$-0.761054\pi$
$401$	−29.2858	−1.46246	−0.731232	+	0.682129i	$0.761054\pi$
$402$	7.82916	0.390483
$403$	0	0
$404$	15.4753	0.769924
$405$	−70.2592	−3.49121
$406$	0.140469	0.00697135
$407$	5.16150	0.255846
$408$	−4.17331	−0.206610
$409$	23.3713	1.15563	0.577817	−	0.816166i	$-0.303905\pi$
$409$	23.3713	1.15563	0.577817	+	0.816166i	$0.303905\pi$
$410$	4.73805	0.233996
$411$	59.8112	2.95027
$412$	−1.35246	−0.0666308
$413$	−8.82234	−0.434119
$414$	1.55922	0.0766315
$415$	10.3548	0.508295
$416$	0	0
$417$	−46.2389	−2.26433
$418$	2.48679	0.121633
$419$	14.6064	0.713569	0.356785	−	0.934187i	$-0.383873\pi$
$419$	14.6064	0.713569	0.356785	+	0.934187i	$0.383873\pi$
$420$	14.4295	0.704087
$421$	10.2728	0.500668	0.250334	−	0.968160i	$-0.419460\pi$
$421$	10.2728	0.500668	0.250334	+	0.968160i	$0.419460\pi$
$422$	−5.64342	−0.274717
$423$	−13.0862	−0.636273
$424$	−7.66611	−0.372299
$425$	0.0289311	0.00140336
$426$	4.00790	0.194183
$427$	−5.46667	−0.264551
$428$	−17.4141	−0.841740
$429$	0	0
$430$	−0.635689	−0.0306557
$431$	−12.5017	−0.602188	−0.301094	−	0.953595i	$-0.597352\pi$
$431$	−12.5017	−0.602188	−0.301094	+	0.953595i	$0.597352\pi$
$432$	−61.6147	−2.96444
$433$	−10.9472	−0.526090	−0.263045	−	0.964784i	$-0.584727\pi$
$433$	−10.9472	−0.526090	−0.263045	+	0.964784i	$0.584727\pi$
$434$	−0.396810	−0.0190475
$435$	−4.50083	−0.215798
$436$	4.42370	0.211857
$437$	2.71282	0.129772
$438$	3.04654	0.145569
$439$	−17.9179	−0.855176	−0.427588	−	0.903974i	$-0.640637\pi$
$439$	−17.9179	−0.855176	−0.427588	+	0.903974i	$0.640637\pi$
$440$	6.76864	0.322682
$441$	8.03736	0.382732
$442$	0	0
$443$	27.7194	1.31699	0.658494	−	0.752586i	$-0.271194\pi$
$443$	27.7194	1.31699	0.658494	+	0.752586i	$0.271194\pi$
$444$	10.0467	0.476796
$445$	−20.3684	−0.965556
$446$	5.24018	0.248130
$447$	52.9245	2.50324
$448$	6.74383	0.318616
$449$	−0.165980	−0.00783306	−0.00391653	−	0.999992i	$-0.501247\pi$
$449$	−0.165980	−0.00783306	−0.00391653	+	0.999992i	$0.501247\pi$
$450$	−0.0391038	−0.00184337
$451$	−30.4911	−1.43577
$452$	18.5008	0.870204
$453$	46.3444	2.17745
$454$	0.297313	0.0139536
$455$	0	0
$456$	9.81404	0.459584
$457$	31.7354	1.48452	0.742260	−	0.670112i	$-0.233754\pi$
$457$	31.7354	1.48452	0.742260	+	0.670112i	$0.233754\pi$
$458$	−1.07456	−0.0502107
$459$	23.0242	1.07468
$460$	3.64185	0.169802
$461$	29.0656	1.35372	0.676859	−	0.736113i	$-0.263341\pi$
$461$	29.0656	1.35372	0.676859	+	0.736113i	$0.263341\pi$
$462$	2.55361	0.118805
$463$	6.31904	0.293671	0.146835	−	0.989161i	$-0.453091\pi$
$463$	6.31904	0.293671	0.146835	+	0.989161i	$0.453091\pi$
$464$	−2.23531	−0.103772
$465$	12.7144	0.589615
$466$	2.75035	0.127408
$467$	−34.6409	−1.60299	−0.801495	−	0.598002i	$-0.795962\pi$
$467$	−34.6409	−1.60299	−0.801495	+	0.598002i	$0.795962\pi$
$468$	0	0
$469$	10.1857	0.470334
$470$	0.840542	0.0387713
$471$	43.1051	1.98618
$472$	−8.05532	−0.370776
$473$	4.09089	0.188099
$474$	−4.95811	−0.227734
$475$	−0.0680349	−0.00312166
$476$	−2.67792	−0.122742
$477$	67.4823	3.08980
$478$	−0.966587	−0.0442107
$479$	−7.14230	−0.326340	−0.163170	−	0.986598i	$-0.552172\pi$
$479$	−7.14230	−0.326340	−0.163170	+	0.986598i	$0.552172\pi$
$480$	19.8518	0.906107
$481$	0	0
$482$	0.933174	0.0425049
$483$	2.78572	0.126755
$484$	−0.0727284	−0.00330584
$485$	34.2712	1.55617
$486$	−12.5865	−0.570935
$487$	−18.5003	−0.838327	−0.419163	−	0.907911i	$-0.637677\pi$
$487$	−18.5003	−0.838327	−0.419163	+	0.907911i	$0.637677\pi$
$488$	−4.99140	−0.225950
$489$	−61.1575	−2.76564
$490$	−0.516249	−0.0233218
$491$	−15.2781	−0.689490	−0.344745	−	0.938696i	$-0.612035\pi$
$491$	−15.2781	−0.689490	−0.344745	+	0.938696i	$0.612035\pi$
$492$	−59.3500	−2.67571
$493$	0.835294	0.0376197
$494$	0	0
$495$	−59.5821	−2.67802
$496$	6.31452	0.283530
$497$	5.21428	0.233893
$498$	3.56691	0.159837
$499$	12.4783	0.558606	0.279303	−	0.960203i	$-0.409897\pi$
$499$	12.4783	0.558606	0.279303	+	0.960203i	$0.409897\pi$
$500$	−21.8077	−0.975272
$501$	61.4595	2.74581
$502$	6.44768	0.287774
$503$	−2.58008	−0.115040	−0.0575200	−	0.998344i	$-0.518319\pi$
$503$	−2.58008	−0.115040	−0.0575200	+	0.998344i	$0.518319\pi$
$504$	7.33859	0.326887
$505$	17.7403	0.789431
$506$	0.644506	0.0286518
$507$	0	0
$508$	−35.8802	−1.59192
$509$	35.6808	1.58152	0.790761	−	0.612125i	$-0.209685\pi$
$509$	35.6808	1.58152	0.790761	+	0.612125i	$0.209685\pi$
$510$	−2.35962	−0.104486
$511$	3.96355	0.175337
$512$	16.5825	0.732850
$513$	−54.1442	−2.39053
$514$	−1.65206	−0.0728694
$515$	−1.55040	−0.0683190
$516$	7.96281	0.350543
$517$	−5.40919	−0.237896
$518$	−0.359445	−0.0157931
$519$	57.1365	2.50801
$520$	0	0
$521$	−20.9637	−0.918437	−0.459219	−	0.888323i	$-0.651871\pi$
$521$	−20.9637	−0.918437	−0.459219	+	0.888323i	$0.651871\pi$
$522$	−1.12900	−0.0494149
$523$	−22.8263	−0.998124	−0.499062	−	0.866566i	$-0.666322\pi$
$523$	−22.8263	−0.998124	−0.499062	+	0.866566i	$0.666322\pi$
$524$	3.40312	0.148666
$525$	−0.0698632	−0.00304908
$526$	4.93243	0.215064
$527$	−2.35962	−0.102787
$528$	−40.6362	−1.76847
$529$	−22.2969	−0.969431
$530$	−4.33447	−0.188277
$531$	70.9083	3.07716
$532$	6.29744	0.273029
$533$	0	0
$534$	−7.01634	−0.303627
$535$	−19.9628	−0.863067
$536$	9.30018	0.401707
$537$	−48.1348	−2.07717
$538$	0.645208	0.0278169
$539$	3.32225	0.143100
$540$	−72.6865	−3.12793
$541$	30.2191	1.29922	0.649611	−	0.760266i	$-0.274932\pi$
$541$	30.2191	1.29922	0.649611	+	0.760266i	$0.274932\pi$
$542$	−3.58025	−0.153785
$543$	−22.7735	−0.977305
$544$	−3.68423	−0.157960
$545$	5.07116	0.217225
$546$	0	0
$547$	−16.8223	−0.719271	−0.359636	−	0.933093i	$-0.617099\pi$
$547$	−16.8223	−0.719271	−0.359636	+	0.933093i	$0.617099\pi$
$548$	35.0427	1.49695
$549$	43.9376	1.87521
$550$	−0.0161636	−0.000689219 0
$551$	−1.96429	−0.0836817
$552$	2.54352	0.108260
$553$	−6.45051	−0.274304
$554$	1.27932	0.0543531
$555$	11.5172	0.488876
$556$	−27.0909	−1.14891
$557$	−10.4918	−0.444553	−0.222276	−	0.974984i	$-0.571349\pi$
$557$	−10.4918	−0.444553	−0.222276	+	0.974984i	$0.571349\pi$
$558$	3.18930	0.135014
$559$	0	0
$560$	8.21520	0.347155
$561$	15.1850	0.641111
$562$	−7.28489	−0.307294
$563$	30.9474	1.30428	0.652138	−	0.758100i	$-0.273872\pi$
$563$	30.9474	1.30428	0.652138	+	0.758100i	$0.273872\pi$
$564$	−10.5288	−0.443344
$565$	21.2086	0.892252
$566$	−1.70078	−0.0714889
$567$	−31.4871	−1.32234
$568$	4.76095	0.199765
$569$	−36.9089	−1.54730	−0.773651	−	0.633612i	$-0.781572\pi$
$569$	−36.9089	−1.54730	−0.773651	+	0.633612i	$0.781572\pi$
$570$	5.54892	0.232419
$571$	−1.77093	−0.0741113	−0.0370556	−	0.999313i	$-0.511798\pi$
$571$	−1.77093	−0.0741113	−0.0370556	+	0.999313i	$0.511798\pi$
$572$	0	0
$573$	9.47383	0.395775
$574$	2.12339	0.0886286
$575$	−0.0176328	−0.000735337 0
$576$	−54.2026	−2.25844
$577$	−9.83999	−0.409644	−0.204822	−	0.978799i	$-0.565662\pi$
$577$	−9.83999	−0.409644	−0.204822	+	0.978799i	$0.565662\pi$
$578$	−3.49522	−0.145382
$579$	33.3903	1.38765
$580$	−2.63699	−0.109495
$581$	4.64055	0.192523
$582$	11.8054	0.489351
$583$	27.8939	1.15525
$584$	3.61896	0.149753
$585$	0	0
$586$	−3.13112	−0.129345
$587$	−15.1383	−0.624826	−0.312413	−	0.949946i	$-0.601137\pi$
$587$	−15.1383	−0.624826	−0.312413	+	0.949946i	$0.601137\pi$
$588$	6.46667	0.266681
$589$	5.54892	0.228639
$590$	−4.55453	−0.187507
$591$	84.4420	3.47348
$592$	5.71994	0.235088
$593$	9.17148	0.376628	0.188314	−	0.982109i	$-0.439698\pi$
$593$	9.17148	0.376628	0.188314	+	0.982109i	$0.439698\pi$
$594$	−12.8635	−0.527795
$595$	−3.06986	−0.125852
$596$	31.0079	1.27013
$597$	41.3506	1.69237
$598$	0	0
$599$	−18.5811	−0.759202	−0.379601	−	0.925150i	$-0.623939\pi$
$599$	−18.5811	−0.759202	−0.379601	+	0.925150i	$0.623939\pi$
$600$	−0.0637892	−0.00260418
$601$	−13.4036	−0.546744	−0.273372	−	0.961908i	$-0.588139\pi$
$601$	−13.4036	−0.546744	−0.273372	+	0.961908i	$0.588139\pi$
$602$	−0.284889	−0.0116112
$603$	−81.8665	−3.33386
$604$	27.1527	1.10483
$605$	−0.0833731	−0.00338960
$606$	6.11101	0.248243
$607$	12.6362	0.512889	0.256445	−	0.966559i	$-0.417449\pi$
$607$	12.6362	0.512889	0.256445	+	0.966559i	$0.417449\pi$
$608$	8.66390	0.351368
$609$	−2.01708	−0.0817361
$610$	−2.82217	−0.114266
$611$	0	0
$612$	21.5234	0.870032
$613$	25.7079	1.03833	0.519167	−	0.854673i	$-0.326242\pi$
$613$	25.7079	1.03833	0.519167	+	0.854673i	$0.326242\pi$
$614$	−0.764900	−0.0308688
$615$	−68.0366	−2.74350
$616$	3.03341	0.122220
$617$	−6.59620	−0.265553	−0.132777	−	0.991146i	$-0.542389\pi$
$617$	−6.59620	−0.265553	−0.132777	+	0.991146i	$0.542389\pi$
$618$	−0.534070	−0.0214834
$619$	−21.0124	−0.844559	−0.422280	−	0.906466i	$-0.638770\pi$
$619$	−21.0124	−0.844559	−0.422280	+	0.906466i	$0.638770\pi$
$620$	7.44921	0.299168
$621$	−14.0327	−0.563112
$622$	−7.93712	−0.318250
$623$	−9.12826	−0.365716
$624$	0	0
$625$	−24.8944	−0.995777
$626$	1.66910	0.0667108
$627$	−35.7093	−1.42609
$628$	25.2548	1.00778
$629$	−2.13743	−0.0852250
$630$	4.14929	0.165311
$631$	26.0210	1.03588	0.517940	−	0.855417i	$-0.326699\pi$
$631$	26.0210	1.03588	0.517940	+	0.855417i	$0.326699\pi$
$632$	−5.88970	−0.234280
$633$	81.0373	3.22095
$634$	−1.86023	−0.0738793
$635$	−41.1316	−1.63226
$636$	54.2946	2.15292
$637$	0	0
$638$	−0.466673	−0.0184758
$639$	−41.9091	−1.65790
$640$	15.4323	0.610015
$641$	18.5339	0.732044	0.366022	−	0.930606i	$-0.380719\pi$
$641$	18.5339	0.732044	0.366022	+	0.930606i	$0.380719\pi$
$642$	−6.87661	−0.271398
$643$	−14.4466	−0.569717	−0.284858	−	0.958570i	$-0.591947\pi$
$643$	−14.4466	−0.569717	−0.284858	+	0.958570i	$0.591947\pi$
$644$	1.63212	0.0643146
$645$	9.12826	0.359425
$646$	−1.02981	−0.0405172
$647$	29.2875	1.15141	0.575706	−	0.817657i	$-0.304727\pi$
$647$	29.2875	1.15141	0.575706	+	0.817657i	$0.304727\pi$
$648$	−28.7496	−1.12939
$649$	29.3100	1.15052
$650$	0	0
$651$	5.69803	0.223324
$652$	−35.8315	−1.40327
$653$	−30.9615	−1.21162	−0.605808	−	0.795611i	$-0.707150\pi$
$653$	−30.9615	−1.21162	−0.605808	+	0.795611i	$0.707150\pi$
$654$	1.74687	0.0683079
$655$	3.90121	0.152433
$656$	−33.7900	−1.31928
$657$	−31.8565	−1.24284
$658$	0.376695	0.0146851
$659$	−37.0828	−1.44454	−0.722270	−	0.691611i	$-0.756901\pi$
$659$	−37.0828	−1.44454	−0.722270	+	0.691611i	$0.756901\pi$
$660$	−47.9384	−1.86600
$661$	−20.4018	−0.793540	−0.396770	−	0.917918i	$-0.629869\pi$
$661$	−20.4018	−0.793540	−0.396770	+	0.917918i	$0.629869\pi$
$662$	0.206764	0.00803611
$663$	0	0
$664$	4.23710	0.164431
$665$	7.21915	0.279947
$666$	2.88899	0.111946
$667$	−0.509090	−0.0197120
$668$	36.0085	1.39321
$669$	−75.2469	−2.90921
$670$	5.25838	0.203149
$671$	18.1617	0.701123
$672$	8.89672	0.343199
$673$	14.5110	0.559359	0.279679	−	0.960093i	$-0.409772\pi$
$673$	14.5110	0.559359	0.279679	+	0.960093i	$0.409772\pi$
$674$	3.48700	0.134314
$675$	0.351926	0.0135457
$676$	0	0
$677$	−3.51476	−0.135083	−0.0675417	−	0.997716i	$-0.521516\pi$
$677$	−3.51476	−0.135083	−0.0675417	+	0.997716i	$0.521516\pi$
$678$	7.30575	0.280575
$679$	15.3589	0.589420
$680$	−2.80297	−0.107489
$681$	−4.26930	−0.163600
$682$	1.31830	0.0504804
$683$	−27.0753	−1.03601	−0.518003	−	0.855379i	$-0.673324\pi$
$683$	−27.0753	−1.03601	−0.518003	+	0.855379i	$0.673324\pi$
$684$	−50.6149	−1.93531
$685$	40.1717	1.53488
$686$	−0.231361	−0.00883340
$687$	15.4302	0.588700
$688$	4.53350	0.172838
$689$	0	0
$690$	1.43812	0.0547485
$691$	29.7404	1.13138	0.565690	−	0.824618i	$-0.308610\pi$
$691$	29.7404	1.13138	0.565690	+	0.824618i	$0.308610\pi$
$692$	33.4757	1.27255
$693$	−26.7022	−1.01433
$694$	−3.79810	−0.144174
$695$	−31.0559	−1.17802
$696$	−1.84171	−0.0698099
$697$	12.6267	0.478270
$698$	7.95237	0.301002
$699$	−39.4940	−1.49380
$700$	−0.0409321	−0.00154709
$701$	18.2888	0.690760	0.345380	−	0.938463i	$-0.387750\pi$
$701$	18.2888	0.690760	0.345380	+	0.938463i	$0.387750\pi$
$702$	0	0
$703$	5.02642	0.189575
$704$	−22.4047	−0.844409
$705$	−12.0699	−0.454577
$706$	−5.53329	−0.208248
$707$	7.95042	0.299006
$708$	57.0512	2.14411
$709$	−28.6804	−1.07711	−0.538557	−	0.842589i	$-0.681030\pi$
$709$	−28.6804	−1.07711	−0.538557	+	0.842589i	$0.681030\pi$
$710$	2.69187	0.101024
$711$	51.8451	1.94434
$712$	−8.33464	−0.312354
$713$	1.43812	0.0538582
$714$	−1.05748	−0.0395752
$715$	0	0
$716$	−28.2017	−1.05395
$717$	13.8798	0.518351
$718$	−1.42952	−0.0533492
$719$	25.4762	0.950103	0.475052	−	0.879958i	$-0.342429\pi$
$719$	25.4762	0.950103	0.475052	+	0.879958i	$0.342429\pi$
$720$	−66.0285	−2.46074
$721$	−0.694825	−0.0258766
$722$	−1.97415	−0.0734701
$723$	−13.4000	−0.498352
$724$	−13.3428	−0.495879
$725$	0.0127675	0.000474173 0
$726$	−0.0287196	−0.00106588
$727$	−9.02572	−0.334746	−0.167373	−	0.985894i	$-0.553528\pi$
$727$	−9.02572	−0.334746	−0.167373	+	0.985894i	$0.553528\pi$
$728$	0	0
$729$	86.2759	3.19540
$730$	2.04618	0.0757325
$731$	−1.69408	−0.0626579
$732$	35.3512	1.30662
$733$	−7.57069	−0.279630	−0.139815	−	0.990178i	$-0.544651\pi$
$733$	−7.57069	−0.279630	−0.139815	+	0.990178i	$0.544651\pi$
$734$	4.59389	0.169564
$735$	7.41314	0.273438
$736$	2.24544	0.0827681
$737$	−33.8396	−1.24650
$738$	−17.0665	−0.628225
$739$	−6.37296	−0.234433	−0.117216	−	0.993106i	$-0.537397\pi$
$739$	−6.37296	−0.234433	−0.117216	+	0.993106i	$0.537397\pi$
$740$	6.74778	0.248053
$741$	0	0
$742$	−1.94252	−0.0713122
$743$	−22.8297	−0.837539	−0.418770	−	0.908092i	$-0.637539\pi$
$743$	−22.8297	−0.837539	−0.418770	+	0.908092i	$0.637539\pi$
$744$	5.20264	0.190738
$745$	35.5463	1.30231
$746$	6.98596	0.255774
$747$	−37.2978	−1.36466
$748$	8.89672	0.325296
$749$	−8.94647	−0.326897
$750$	−8.61162	−0.314452
$751$	39.3695	1.43661	0.718307	−	0.695726i	$-0.244917\pi$
$751$	39.3695	1.43661	0.718307	+	0.695726i	$0.244917\pi$
$752$	−5.99443	−0.218594
$753$	−92.5863	−3.37403
$754$	0	0
$755$	31.1268	1.13282
$756$	−32.5750	−1.18474
$757$	8.72714	0.317193	0.158597	−	0.987343i	$-0.449303\pi$
$757$	8.72714	0.317193	0.158597	+	0.987343i	$0.449303\pi$
$758$	−1.00004	−0.0363231
$759$	−9.25486	−0.335930
$760$	6.59151	0.239099
$761$	−22.8391	−0.827915	−0.413958	−	0.910296i	$-0.635854\pi$
$761$	−22.8391	−0.827915	−0.413958	+	0.910296i	$0.635854\pi$
$762$	−14.1687	−0.513276
$763$	2.27268	0.0822764
$764$	5.55062	0.200814
$765$	24.6736	0.892076
$766$	−4.01368	−0.145020
$767$	0	0
$768$	−39.4934	−1.42510
$769$	34.8349	1.25618	0.628089	−	0.778141i	$-0.283837\pi$
$769$	34.8349	1.25618	0.628089	+	0.778141i	$0.283837\pi$
$770$	1.71511	0.0618083
$771$	23.7230	0.854363
$772$	19.5630	0.704088
$773$	−33.2743	−1.19679	−0.598397	−	0.801200i	$-0.704196\pi$
$773$	−33.2743	−1.19679	−0.598397	+	0.801200i	$0.704196\pi$
$774$	2.28975	0.0823035
$775$	−0.0360668	−0.00129556
$776$	14.0236	0.503416
$777$	5.16150	0.185168
$778$	−5.86440	−0.210249
$779$	−29.6932	−1.06387
$780$	0	0
$781$	−17.3232	−0.619872
$782$	−0.266897	−0.00954421
$783$	10.1608	0.363116
$784$	3.68170	0.131489
$785$	28.9512	1.03331
$786$	1.34385	0.0479336
$787$	−27.8157	−0.991524	−0.495762	−	0.868458i	$-0.665111\pi$
$787$	−27.8157	−0.991524	−0.495762	+	0.868458i	$0.665111\pi$
$788$	49.4737	1.76243
$789$	−70.8278	−2.52154
$790$	−3.33007	−0.118479
$791$	9.50478	0.337951
$792$	−24.3806	−0.866329
$793$	0	0
$794$	−6.26407	−0.222304
$795$	62.2413	2.20747
$796$	24.2269	0.858699
$797$	35.8685	1.27053	0.635264	−	0.772295i	$-0.280891\pi$
$797$	35.8685	1.27053	0.635264	+	0.772295i	$0.280891\pi$
$798$	2.48679	0.0880313
$799$	2.24001	0.0792457
$800$	−0.0563136	−0.00199099
$801$	73.3671	2.59230
$802$	−6.77559	−0.239254
$803$	−13.1679	−0.464686
$804$	−65.8678	−2.32298
$805$	1.87100	0.0659441
$806$	0	0
$807$	−9.26495	−0.326142
$808$	7.25921	0.255378
$809$	−17.8245	−0.626675	−0.313337	−	0.949642i	$-0.601447\pi$
$809$	−17.8245	−0.626675	−0.313337	+	0.949642i	$0.601447\pi$
$810$	−16.2552	−0.571150
$811$	25.2152	0.885425	0.442713	−	0.896664i	$-0.354016\pi$
$811$	25.2152	0.885425	0.442713	+	0.896664i	$0.354016\pi$
$812$	−1.18178	−0.0414725
$813$	51.4110	1.80306
$814$	1.19417	0.0418556
$815$	−41.0759	−1.43883
$816$	16.8279	0.589095
$817$	3.98384	0.139377
$818$	5.40719	0.189058
$819$	0	0
$820$	−39.8619	−1.39204
$821$	−10.4559	−0.364915	−0.182457	−	0.983214i	$-0.558405\pi$
$821$	−10.4559	−0.364915	−0.182457	+	0.983214i	$0.558405\pi$
$822$	13.8380	0.482655
$823$	−33.2405	−1.15869	−0.579346	−	0.815082i	$-0.696692\pi$
$823$	−33.2405	−1.15869	−0.579346	+	0.815082i	$0.696692\pi$
$824$	−0.634416	−0.0221009
$825$	0.232103	0.00808080
$826$	−2.04114	−0.0710205
$827$	−37.9927	−1.32113	−0.660567	−	0.750767i	$-0.729684\pi$
$827$	−37.9927	−1.32113	−0.660567	+	0.750767i	$0.729684\pi$
$828$	−13.1180	−0.455880
$829$	16.6944	0.579821	0.289911	−	0.957054i	$-0.406374\pi$
$829$	16.6944	0.579821	0.289911	+	0.957054i	$0.406374\pi$
$830$	2.39568	0.0831554
$831$	−18.3706	−0.637268
$832$	0	0
$833$	−1.37578	−0.0476680
$834$	−10.6979	−0.370437
$835$	41.2787	1.42851
$836$	−20.9217	−0.723592
$837$	−28.7031	−0.992123
$838$	3.37935	0.116738
$839$	−46.6411	−1.61023	−0.805115	−	0.593119i	$-0.797896\pi$
$839$	−46.6411	−1.61023	−0.805115	+	0.593119i	$0.797896\pi$
$840$	6.76864	0.233540
$841$	−28.6314	−0.987289
$842$	2.37673	0.0819077
$843$	104.608	3.60290
$844$	47.4789	1.63429
$845$	0	0
$846$	−3.02763	−0.104092
$847$	−0.0373642	−0.00128385
$848$	30.9118	1.06152
$849$	24.4225	0.838178
$850$	0.00669352	0.000229586 0
$851$	1.30271	0.0446563
$852$	−33.7191	−1.15520
$853$	39.5640	1.35464	0.677322	−	0.735686i	$-0.263140\pi$
$853$	39.5640	1.35464	0.677322	+	0.735686i	$0.263140\pi$
$854$	−1.26477	−0.0432797
$855$	−58.0229	−1.98434
$856$	−8.16866	−0.279199
$857$	−19.5613	−0.668201	−0.334101	−	0.942537i	$-0.608433\pi$
$857$	−19.5613	−0.668201	−0.334101	+	0.942537i	$0.608433\pi$
$858$	0	0
$859$	−10.1632	−0.346762	−0.173381	−	0.984855i	$-0.555469\pi$
$859$	−10.1632	−0.346762	−0.173381	+	0.984855i	$0.555469\pi$
$860$	5.34815	0.182370
$861$	−30.4911	−1.03913
$862$	−2.89241	−0.0985160
$863$	26.8903	0.915356	0.457678	−	0.889118i	$-0.348681\pi$
$863$	26.8903	0.915356	0.457678	+	0.889118i	$0.348681\pi$
$864$	−44.8160	−1.52467
$865$	38.3752	1.30480
$866$	−2.53276	−0.0860666
$867$	50.1900	1.70454
$868$	3.33842	0.113313
$869$	21.4302	0.726971
$870$	−1.04132	−0.0353039
$871$	0	0
$872$	2.07509	0.0702713
$873$	−123.445	−4.17798
$874$	0.627640	0.0212302
$875$	−11.2037	−0.378755
$876$	−25.6310	−0.865991
$877$	−1.70160	−0.0574590	−0.0287295	−	0.999587i	$-0.509146\pi$
$877$	−1.70160	−0.0574590	−0.0287295	+	0.999587i	$0.509146\pi$
$878$	−4.14551	−0.139904
$879$	44.9617	1.51652
$880$	−27.2930	−0.920046
$881$	−11.3090	−0.381008	−0.190504	−	0.981686i	$-0.561012\pi$
$881$	−11.3090	−0.381008	−0.190504	+	0.981686i	$0.561012\pi$
$882$	1.85953	0.0626137
$883$	−46.9068	−1.57854	−0.789270	−	0.614047i	$-0.789541\pi$
$883$	−46.9068	−1.57854	−0.789270	+	0.614047i	$0.789541\pi$
$884$	0	0
$885$	65.4013	2.19844
$886$	6.41318	0.215455
$887$	−2.44692	−0.0821594	−0.0410797	−	0.999156i	$-0.513080\pi$
$887$	−2.44692	−0.0821594	−0.0410797	+	0.999156i	$0.513080\pi$
$888$	4.71275	0.158150
$889$	−18.4334	−0.618237
$890$	−4.71246	−0.157962
$891$	104.608	3.50451
$892$	−44.0864	−1.47612
$893$	−5.26764	−0.176275
$894$	12.2447	0.409523
$895$	−32.3293	−1.08065
$896$	6.91610	0.231051
$897$	0	0
$898$	−0.0384012	−0.00128146
$899$	−1.04132	−0.0347298
$900$	0.328986	0.0109662
$901$	−11.5511	−0.384825
$902$	−7.05444	−0.234887
$903$	4.09089	0.136136
$904$	8.67842	0.288640
$905$	−15.2956	−0.508443
$906$	10.7223	0.356224
$907$	−41.4165	−1.37521	−0.687607	−	0.726083i	$-0.741339\pi$
$907$	−41.4165	−1.37521	−0.687607	+	0.726083i	$0.741339\pi$
$908$	−2.50133	−0.0830097
$909$	−63.9004	−2.11944
$910$	0	0
$911$	−11.9951	−0.397416	−0.198708	−	0.980059i	$-0.563675\pi$
$911$	−11.9951	−0.397416	−0.198708	+	0.980059i	$0.563675\pi$
$912$	−39.5728	−1.31039
$913$	−15.4171	−0.510231
$914$	7.34233	0.242863
$915$	40.5252	1.33972
$916$	9.04040	0.298703
$917$	1.74835	0.0577357
$918$	5.32691	0.175814
$919$	44.9416	1.48249	0.741243	−	0.671237i	$-0.234237\pi$
$919$	44.9416	1.48249	0.741243	+	0.671237i	$0.234237\pi$
$920$	1.70833	0.0563221
$921$	10.9837	0.361924
$922$	6.72463	0.221464
$923$	0	0
$924$	−21.4839	−0.706769
$925$	−0.0326707	−0.00107421
$926$	1.46198	0.0480436
$927$	5.58456	0.183421
$928$	−1.62588	−0.0533720
$929$	28.2595	0.927164	0.463582	−	0.886054i	$-0.346564\pi$
$929$	28.2595	0.927164	0.463582	+	0.886054i	$0.346564\pi$
$930$	2.94161	0.0964591
$931$	3.23531	0.106033
$932$	−23.1391	−0.757947
$933$	113.974	3.73134
$934$	−8.01455	−0.262244
$935$	10.1989	0.333538
$936$	0	0
$937$	32.4601	1.06042	0.530212	−	0.847865i	$-0.322112\pi$
$937$	32.4601	1.06042	0.530212	+	0.847865i	$0.322112\pi$
$938$	2.35658	0.0769451
$939$	−23.9677	−0.782155
$940$	−7.07160	−0.230650
$941$	−12.6051	−0.410913	−0.205457	−	0.978666i	$-0.565868\pi$
$941$	−12.6051	−0.410913	−0.205457	+	0.978666i	$0.565868\pi$
$942$	9.97283	0.324932
$943$	−7.69563	−0.250604
$944$	32.4812	1.05717
$945$	−37.3427	−1.21476
$946$	0.946472	0.0307725
$947$	−13.2802	−0.431548	−0.215774	−	0.976443i	$-0.569228\pi$
$947$	−13.2802	−0.431548	−0.215774	+	0.976443i	$0.569228\pi$
$948$	41.7133	1.35479
$949$	0	0
$950$	−0.0157406	−0.000510693 0
$951$	26.7122	0.866204
$952$	−1.25617	−0.0407127
$953$	−58.4319	−1.89279	−0.946397	−	0.323006i	$-0.895307\pi$
$953$	−58.4319	−1.89279	−0.946397	+	0.323006i	$0.895307\pi$
$954$	15.6127	0.505481
$955$	6.36301	0.205902
$956$	8.13204	0.263009
$957$	6.70124	0.216620
$958$	−1.65245	−0.0533882
$959$	18.0032	0.581354
$960$	−49.9930	−1.61352
$961$	−28.0584	−0.905109
$962$	0	0
$963$	71.9061	2.31714
$964$	−7.85093	−0.252861
$965$	22.4263	0.721927
$966$	0.644506	0.0207366
$967$	33.2182	1.06823	0.534113	−	0.845413i	$-0.320646\pi$
$967$	33.2182	1.06823	0.534113	+	0.845413i	$0.320646\pi$
$968$	−0.0341157	−0.00109652
$969$	14.7876	0.475047
$970$	7.92901	0.254585
$971$	16.7778	0.538425	0.269213	−	0.963081i	$-0.413237\pi$
$971$	16.7778	0.538425	0.269213	+	0.963081i	$0.413237\pi$
$972$	105.892	3.39649
$973$	−13.9179	−0.446188
$974$	−4.28023	−0.137148
$975$	0	0
$976$	20.1266	0.644238
$977$	−50.0422	−1.60099	−0.800496	−	0.599338i	$-0.795431\pi$
$977$	−50.0422	−1.60099	−0.800496	+	0.599338i	$0.795431\pi$
$978$	−14.1495	−0.452450
$979$	30.3264	0.969235
$980$	4.34328	0.138741
$981$	−18.2663	−0.583199
$982$	−3.53475	−0.112798
$983$	16.6741	0.531822	0.265911	−	0.963998i	$-0.414327\pi$
$983$	16.6741	0.531822	0.265911	+	0.963998i	$0.414327\pi$
$984$	−27.8402	−0.887512
$985$	56.7147	1.80708
$986$	0.193254	0.00615447
$987$	−5.40919	−0.172177
$988$	0	0
$989$	1.03250	0.0328316
$990$	−13.7850	−0.438115
$991$	20.3285	0.645756	0.322878	−	0.946441i	$-0.395350\pi$
$991$	20.3285	0.645756	0.322878	+	0.946441i	$0.395350\pi$
$992$	4.59293	0.145826
$993$	−2.96905	−0.0942201
$994$	1.20638	0.0382641
$995$	27.7728	0.880456
$996$	−30.0089	−0.950870
$997$	6.27646	0.198777	0.0993887	−	0.995049i	$-0.468311\pi$
$997$	6.27646	0.198777	0.0993887	+	0.995049i	$0.468311\pi$
$998$	2.88699	0.0913862
$999$	−26.0003	−0.822614

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.k.1.3		4
7.6	odd	2		8281.2.a.bp.1.3		4
13.3	even	3		91.2.f.c.22.2	✓	8
13.5	odd	4		1183.2.c.g.337.4		8
13.8	odd	4		1183.2.c.g.337.5		8
13.9	even	3		91.2.f.c.29.2	yes	8
13.12	even	2		1183.2.a.l.1.2		4
39.29	odd	6		819.2.o.h.568.3		8
39.35	odd	6		819.2.o.h.757.3		8
52.3	odd	6		1456.2.s.q.113.1		8
52.35	odd	6		1456.2.s.q.1121.1		8
91.3	odd	6		637.2.g.j.373.2		8
91.9	even	3		637.2.g.k.263.2		8
91.16	even	3		637.2.h.h.165.3		8
91.48	odd	6		637.2.f.i.393.2		8
91.55	odd	6		637.2.f.i.295.2		8
91.61	odd	6		637.2.g.j.263.2		8
91.68	odd	6		637.2.h.i.165.3		8
91.74	even	3		637.2.h.h.471.3		8
91.81	even	3		637.2.g.k.373.2		8
91.87	odd	6		637.2.h.i.471.3		8
91.90	odd	2		8281.2.a.bt.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.2	✓	8	13.3	even	3
91.2.f.c.29.2	yes	8	13.9	even	3
637.2.f.i.295.2		8	91.55	odd	6
637.2.f.i.393.2		8	91.48	odd	6
637.2.g.j.263.2		8	91.61	odd	6
637.2.g.j.373.2		8	91.3	odd	6
637.2.g.k.263.2		8	91.9	even	3
637.2.g.k.373.2		8	91.81	even	3
637.2.h.h.165.3		8	91.16	even	3
637.2.h.h.471.3		8	91.74	even	3
637.2.h.i.165.3		8	91.68	odd	6
637.2.h.i.471.3		8	91.87	odd	6
819.2.o.h.568.3		8	39.29	odd	6
819.2.o.h.757.3		8	39.35	odd	6
1183.2.a.k.1.3		4	1.1	even	1	trivial
1183.2.a.l.1.2		4	13.12	even	2
1183.2.c.g.337.4		8	13.5	odd	4
1183.2.c.g.337.5		8	13.8	odd	4
1456.2.s.q.113.1		8	52.3	odd	6
1456.2.s.q.1121.1		8	52.35	odd	6
8281.2.a.bp.1.3		4	7.6	odd	2
8281.2.a.bt.1.2		4	91.90	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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.a (trivial)

\(f(q)\)	\(=\)	\(q+0.231361 q^{2} -3.32225 q^{3} -1.94647 q^{4} -2.23136 q^{5} -0.768639 q^{6} -1.00000 q^{7} -0.913059 q^{8} +8.03736 q^{9} +O(q^{10})\)	\(q+0.231361 q^{2} -3.32225 q^{3} -1.94647 q^{4} -2.23136 q^{5} -0.768639 q^{6} -1.00000 q^{7} -0.913059 q^{8} +8.03736 q^{9} -0.516249 q^{10} +3.32225 q^{11} +6.46667 q^{12} -0.231361 q^{14} +7.41314 q^{15} +3.68170 q^{16} -1.37578 q^{17} +1.85953 q^{18} +3.23531 q^{19} +4.34328 q^{20} +3.32225 q^{21} +0.768639 q^{22} +0.838502 q^{23} +3.03341 q^{24} -0.0210289 q^{25} -16.7354 q^{27} +1.94647 q^{28} -0.607142 q^{29} +1.71511 q^{30} +1.71511 q^{31} +2.67792 q^{32} -11.0374 q^{33} -0.318302 q^{34} +2.23136 q^{35} -15.6445 q^{36} +1.55361 q^{37} +0.748524 q^{38} +2.03736 q^{40} -9.17783 q^{41} +0.768639 q^{42} +1.23136 q^{43} -6.46667 q^{44} -17.9343 q^{45} +0.193997 q^{46} -1.62817 q^{47} -12.2315 q^{48} +1.00000 q^{49} -0.00486525 q^{50} +4.57069 q^{51} +8.39607 q^{53} -3.87192 q^{54} -7.41314 q^{55} +0.913059 q^{56} -10.7485 q^{57} -0.140469 q^{58} +8.82234 q^{59} -14.4295 q^{60} +5.46667 q^{61} +0.396810 q^{62} -8.03736 q^{63} -6.74383 q^{64} -2.55361 q^{66} -10.1857 q^{67} +2.67792 q^{68} -2.78572 q^{69} +0.516249 q^{70} -5.21428 q^{71} -7.33859 q^{72} -3.96355 q^{73} +0.359445 q^{74} +0.0698632 q^{75} -6.29744 q^{76} -3.32225 q^{77} +6.45051 q^{79} -8.21520 q^{80} +31.4871 q^{81} -2.12339 q^{82} -4.64055 q^{83} -6.46667 q^{84} +3.06986 q^{85} +0.284889 q^{86} +2.01708 q^{87} -3.03341 q^{88} +9.12826 q^{89} -4.14929 q^{90} -1.63212 q^{92} -5.69803 q^{93} -0.376695 q^{94} -7.21915 q^{95} -8.89672 q^{96} -15.3589 q^{97} +0.231361 q^{98} +26.7022 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} - 4 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 4 * q - q^2 + q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 - 4 * q^7 - 6 * q^8 + 7 * q^9	\( 4 q - q^{2} + q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} - 4 q^{7} - 6 q^{8} + 7 q^{9} - 11 q^{10} - q^{11} + 12 q^{12} + q^{14} + 3 q^{15} + 19 q^{16} - 4 q^{17} - 3 q^{18} + q^{19} - 2 q^{20} - q^{21} + 5 q^{22} - 2 q^{23} - 3 q^{24} + 5 q^{25} - 26 q^{27} - 5 q^{28} + q^{29} - 4 q^{30} - 4 q^{31} - 33 q^{32} - 19 q^{33} + 3 q^{34} + 7 q^{35} - 34 q^{36} - 10 q^{37} - 23 q^{38} - 17 q^{40} - 22 q^{41} + 5 q^{42} + 3 q^{43} - 12 q^{44} - 11 q^{45} + 24 q^{46} + 2 q^{47} + 11 q^{48} + 4 q^{49} + 43 q^{50} + 7 q^{51} + 2 q^{53} + 5 q^{54} - 3 q^{55} + 6 q^{56} - 17 q^{57} - 11 q^{58} - 8 q^{59} - 11 q^{60} + 8 q^{61} - 5 q^{62} - 7 q^{63} + 14 q^{64} + 6 q^{66} - 6 q^{67} - 33 q^{68} - 18 q^{69} + 11 q^{70} - 14 q^{71} + 5 q^{72} - 8 q^{73} + 20 q^{74} - 7 q^{75} + 32 q^{76} + q^{77} - 26 q^{79} + 7 q^{80} + 24 q^{81} - 14 q^{82} - 12 q^{84} + 5 q^{85} + 12 q^{86} + 13 q^{87} + 3 q^{88} - q^{89} + 26 q^{90} + 12 q^{92} - 7 q^{93} + 33 q^{94} + 21 q^{95} - 58 q^{96} + 3 q^{97} - q^{98} + 23 q^{99}+O(q^{100}) \) 4 * q - q^2 + q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 - 4 * q^7 - 6 * q^8 + 7 * q^9 - 11 * q^10 - q^11 + 12 * q^12 + q^14 + 3 * q^15 + 19 * q^16 - 4 * q^17 - 3 * q^18 + q^19 - 2 * q^20 - q^21 + 5 * q^22 - 2 * q^23 - 3 * q^24 + 5 * q^25 - 26 * q^27 - 5 * q^28 + q^29 - 4 * q^30 - 4 * q^31 - 33 * q^32 - 19 * q^33 + 3 * q^34 + 7 * q^35 - 34 * q^36 - 10 * q^37 - 23 * q^38 - 17 * q^40 - 22 * q^41 + 5 * q^42 + 3 * q^43 - 12 * q^44 - 11 * q^45 + 24 * q^46 + 2 * q^47 + 11 * q^48 + 4 * q^49 + 43 * q^50 + 7 * q^51 + 2 * q^53 + 5 * q^54 - 3 * q^55 + 6 * q^56 - 17 * q^57 - 11 * q^58 - 8 * q^59 - 11 * q^60 + 8 * q^61 - 5 * q^62 - 7 * q^63 + 14 * q^64 + 6 * q^66 - 6 * q^67 - 33 * q^68 - 18 * q^69 + 11 * q^70 - 14 * q^71 + 5 * q^72 - 8 * q^73 + 20 * q^74 - 7 * q^75 + 32 * q^76 + q^77 - 26 * q^79 + 7 * q^80 + 24 * q^81 - 14 * q^82 - 12 * q^84 + 5 * q^85 + 12 * q^86 + 13 * q^87 + 3 * q^88 - q^89 + 26 * q^90 + 12 * q^92 - 7 * q^93 + 33 * q^94 + 21 * q^95 - 58 * q^96 + 3 * q^97 - q^98 + 23 * q^99

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