LMFDB - Embedded newform 1183.2.a.n.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:	$6$
Coefficient field:	6.6.1279733.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 6x^{4} + 10x^{3} + 10x^{2} - 11x - 1 $ x^6 - 2x^5 - 6x^4 + 10x^3 + 10x^2 - 11*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.0849355$ 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)

$f(q)$	$=$	$q-1.10591 q^{2} +1.33192 q^{3} -0.776957 q^{4} +1.90785 q^{5} -1.47298 q^{6} +1.00000 q^{7} +3.07107 q^{8} -1.22600 q^{9} +O(q^{10})$	\(q-1.10591 q^{2} +1.33192 q^{3} -0.776957 q^{4} +1.90785 q^{5} -1.47298 q^{6} +1.00000 q^{7} +3.07107 q^{8} -1.22600 q^{9} -2.10992 q^{10} -6.49608 q^{11} -1.03484 q^{12} -1.10591 q^{14} +2.54109 q^{15} -1.84242 q^{16} -7.14583 q^{17} +1.35585 q^{18} +4.93001 q^{19} -1.48232 q^{20} +1.33192 q^{21} +7.18410 q^{22} -6.24377 q^{23} +4.09041 q^{24} -1.36011 q^{25} -5.62868 q^{27} -0.776957 q^{28} -0.505701 q^{29} -2.81023 q^{30} -5.66349 q^{31} -4.10458 q^{32} -8.65223 q^{33} +7.90267 q^{34} +1.90785 q^{35} +0.952551 q^{36} -0.0345893 q^{37} -5.45216 q^{38} +5.85915 q^{40} +2.58588 q^{41} -1.47298 q^{42} +0.374663 q^{43} +5.04718 q^{44} -2.33903 q^{45} +6.90506 q^{46} +10.3893 q^{47} -2.45395 q^{48} +1.00000 q^{49} +1.50416 q^{50} -9.51764 q^{51} +2.66712 q^{53} +6.22482 q^{54} -12.3936 q^{55} +3.07107 q^{56} +6.56635 q^{57} +0.559261 q^{58} -1.28549 q^{59} -1.97432 q^{60} -5.66025 q^{61} +6.26333 q^{62} -1.22600 q^{63} +8.22416 q^{64} +9.56861 q^{66} +12.8913 q^{67} +5.55201 q^{68} -8.31617 q^{69} -2.10992 q^{70} -9.38877 q^{71} -3.76514 q^{72} -4.37566 q^{73} +0.0382527 q^{74} -1.81155 q^{75} -3.83040 q^{76} -6.49608 q^{77} +0.870391 q^{79} -3.51507 q^{80} -3.81891 q^{81} -2.85976 q^{82} -7.76117 q^{83} -1.03484 q^{84} -13.6332 q^{85} -0.414344 q^{86} -0.673550 q^{87} -19.9499 q^{88} -9.16906 q^{89} +2.58676 q^{90} +4.85114 q^{92} -7.54329 q^{93} -11.4896 q^{94} +9.40571 q^{95} -5.46696 q^{96} -1.40381 q^{97} -1.10591 q^{98} +7.96421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 8 q^{6} + 6 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 8 * q^6 + 6 * q^7 - 3 * q^8	$ 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 8 q^{6} + 6 q^{7} - 3 q^{8} - 14 q^{10} - 8 q^{11} - 23 q^{12} - 2 q^{14} - 3 q^{15} - 23 q^{17} - 26 q^{18} + 13 q^{19} + 4 q^{20} - 4 q^{21} - 4 q^{22} - 18 q^{23} + 26 q^{24} - 10 q^{25} - 10 q^{27} + 8 q^{28} - 15 q^{29} + 14 q^{30} - 3 q^{31} - 28 q^{32} - 3 q^{33} + 29 q^{34} - 2 q^{35} + 22 q^{36} + 13 q^{37} - 11 q^{38} - 14 q^{40} + 4 q^{41} + 8 q^{42} - 18 q^{43} + 19 q^{45} - 10 q^{46} + 16 q^{47} - 11 q^{48} + 6 q^{49} + 10 q^{50} + 14 q^{51} - 25 q^{53} + 31 q^{54} - 3 q^{56} + 4 q^{57} + 13 q^{58} - 18 q^{59} - 22 q^{60} + 16 q^{61} - 9 q^{62} - 7 q^{64} + 16 q^{66} - 16 q^{67} - 34 q^{68} - q^{69} - 14 q^{70} - 25 q^{71} - 39 q^{72} + 5 q^{73} - 14 q^{74} + 15 q^{75} - 7 q^{76} - 8 q^{77} + 2 q^{79} + 27 q^{80} - 6 q^{81} - 10 q^{82} + 7 q^{83} - 23 q^{84} - 9 q^{85} + 3 q^{86} + 13 q^{87} - 48 q^{88} + 10 q^{89} - 32 q^{92} - 35 q^{93} - 14 q^{94} - 7 q^{95} + 14 q^{96} + 5 q^{97} - 2 q^{98} + 15 q^{99}+O(q^{100}) $ 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 8 * q^6 + 6 * q^7 - 3 * q^8 - 14 * q^10 - 8 * q^11 - 23 * q^12 - 2 * q^14 - 3 * q^15 - 23 * q^17 - 26 * q^18 + 13 * q^19 + 4 * q^20 - 4 * q^21 - 4 * q^22 - 18 * q^23 + 26 * q^24 - 10 * q^25 - 10 * q^27 + 8 * q^28 - 15 * q^29 + 14 * q^30 - 3 * q^31 - 28 * q^32 - 3 * q^33 + 29 * q^34 - 2 * q^35 + 22 * q^36 + 13 * q^37 - 11 * q^38 - 14 * q^40 + 4 * q^41 + 8 * q^42 - 18 * q^43 + 19 * q^45 - 10 * q^46 + 16 * q^47 - 11 * q^48 + 6 * q^49 + 10 * q^50 + 14 * q^51 - 25 * q^53 + 31 * q^54 - 3 * q^56 + 4 * q^57 + 13 * q^58 - 18 * q^59 - 22 * q^60 + 16 * q^61 - 9 * q^62 - 7 * q^64 + 16 * q^66 - 16 * q^67 - 34 * q^68 - q^69 - 14 * q^70 - 25 * q^71 - 39 * q^72 + 5 * q^73 - 14 * q^74 + 15 * q^75 - 7 * q^76 - 8 * q^77 + 2 * q^79 + 27 * q^80 - 6 * q^81 - 10 * q^82 + 7 * q^83 - 23 * q^84 - 9 * q^85 + 3 * q^86 + 13 * q^87 - 48 * q^88 + 10 * q^89 - 32 * q^92 - 35 * q^93 - 14 * q^94 - 7 * q^95 + 14 * q^96 + 5 * q^97 - 2 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.10591	−0.781998	−0.390999	−	0.920391i	$-0.627870\pi$
$2$	−1.10591	−0.781998	−0.390999	+	0.920391i	$0.627870\pi$
$3$	1.33192	0.768982	0.384491	−	0.923129i	$-0.374377\pi$
$3$	1.33192	0.768982	0.384491	+	0.923129i	$0.374377\pi$
$4$	−0.776957	−0.388478
$5$	1.90785	0.853217	0.426608	−	0.904436i	$-0.359708\pi$
$5$	1.90785	0.853217	0.426608	+	0.904436i	$0.359708\pi$
$6$	−1.47298	−0.601342
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.07107	1.08579
$9$	−1.22600	−0.408667
$10$	−2.10992	−0.667214
$11$	−6.49608	−1.95864	−0.979321	−	0.202312i	$-0.935154\pi$
$11$	−6.49608	−1.95864	−0.979321	+	0.202312i	$0.935154\pi$
$12$	−1.03484	−0.298733
$13$	0	0
$13$	0	0
$14$	−1.10591	−0.295568
$15$	2.54109	0.656108
$16$	−1.84242	−0.460606
$17$	−7.14583	−1.73312	−0.866560	−	0.499073i	$-0.833674\pi$
$17$	−7.14583	−1.73312	−0.866560	+	0.499073i	$0.833674\pi$
$18$	1.35585	0.319577
$19$	4.93001	1.13102	0.565510	−	0.824741i	$-0.308679\pi$
$19$	4.93001	1.13102	0.565510	+	0.824741i	$0.308679\pi$
$20$	−1.48232	−0.331456
$21$	1.33192	0.290648
$22$	7.18410	1.53166
$23$	−6.24377	−1.30192	−0.650958	−	0.759114i	$-0.725633\pi$
$23$	−6.24377	−1.30192	−0.650958	+	0.759114i	$0.725633\pi$
$24$	4.09041	0.834951
$25$	−1.36011	−0.272021
$26$	0	0
$27$	−5.62868	−1.08324
$28$	−0.776957	−0.146831
$29$	−0.505701	−0.0939063	−0.0469531	−	0.998897i	$-0.514951\pi$
$29$	−0.505701	−0.0939063	−0.0469531	+	0.998897i	$0.514951\pi$
$30$	−2.81023	−0.513075
$31$	−5.66349	−1.01719	−0.508596	−	0.861005i	$-0.669835\pi$
$31$	−5.66349	−1.01719	−0.508596	+	0.861005i	$0.669835\pi$
$32$	−4.10458	−0.725595
$33$	−8.65223	−1.50616
$34$	7.90267	1.35530
$35$	1.90785	0.322486
$36$	0.952551	0.158758
$37$	−0.0345893	−0.00568644	−0.00284322	−	0.999996i	$-0.500905\pi$
$37$	−0.0345893	−0.00568644	−0.00284322	+	0.999996i	$0.500905\pi$
$38$	−5.45216	−0.884456
$39$	0	0
$40$	5.85915	0.926412
$41$	2.58588	0.403847	0.201924	−	0.979401i	$-0.435281\pi$
$41$	2.58588	0.403847	0.201924	+	0.979401i	$0.435281\pi$
$42$	−1.47298	−0.227286
$43$	0.374663	0.0571355	0.0285678	−	0.999592i	$-0.490905\pi$
$43$	0.374663	0.0571355	0.0285678	+	0.999592i	$0.490905\pi$
$44$	5.04718	0.760890
$45$	−2.33903	−0.348682
$46$	6.90506	1.01810
$47$	10.3893	1.51543	0.757715	−	0.652586i	$-0.226316\pi$
$47$	10.3893	1.51543	0.757715	+	0.652586i	$0.226316\pi$
$48$	−2.45395	−0.354198
$49$	1.00000	0.142857
$50$	1.50416	0.212720
$51$	−9.51764	−1.33274
$52$	0	0
$53$	2.66712	0.366357	0.183179	−	0.983080i	$-0.441361\pi$
$53$	2.66712	0.366357	0.183179	+	0.983080i	$0.441361\pi$
$54$	6.22482	0.847091
$55$	−12.3936	−1.67115
$56$	3.07107	0.410389
$57$	6.56635	0.869734
$58$	0.559261	0.0734346
$59$	−1.28549	−0.167357	−0.0836784	−	0.996493i	$-0.526667\pi$
$59$	−1.28549	−0.167357	−0.0836784	+	0.996493i	$0.526667\pi$
$60$	−1.97432	−0.254884
$61$	−5.66025	−0.724720	−0.362360	−	0.932038i	$-0.618029\pi$
$61$	−5.66025	−0.724720	−0.362360	+	0.932038i	$0.618029\pi$
$62$	6.26333	0.795443
$63$	−1.22600	−0.154462
$64$	8.22416	1.02802
$65$	0	0
$66$	9.56861	1.17781
$67$	12.8913	1.57492	0.787461	−	0.616365i	$-0.211395\pi$
$67$	12.8913	1.57492	0.787461	+	0.616365i	$0.211395\pi$
$68$	5.55201	0.673280
$69$	−8.31617	−1.00115
$70$	−2.10992	−0.252183
$71$	−9.38877	−1.11424	−0.557121	−	0.830431i	$-0.688094\pi$
$71$	−9.38877	−1.11424	−0.557121	+	0.830431i	$0.688094\pi$
$72$	−3.76514	−0.443726
$73$	−4.37566	−0.512132	−0.256066	−	0.966659i	$-0.582426\pi$
$73$	−4.37566	−0.512132	−0.256066	+	0.966659i	$0.582426\pi$
$74$	0.0382527	0.00444679
$75$	−1.81155	−0.209179
$76$	−3.83040	−0.439377
$77$	−6.49608	−0.740297
$78$	0	0
$79$	0.870391	0.0979266	0.0489633	−	0.998801i	$-0.484408\pi$
$79$	0.870391	0.0979266	0.0489633	+	0.998801i	$0.484408\pi$
$80$	−3.51507	−0.392997
$81$	−3.81891	−0.424324
$82$	−2.85976	−0.315808
$83$	−7.76117	−0.851899	−0.425950	−	0.904747i	$-0.640060\pi$
$83$	−7.76117	−0.851899	−0.425950	+	0.904747i	$0.640060\pi$
$84$	−1.03484	−0.112910
$85$	−13.6332	−1.47873
$86$	−0.414344	−0.0446799
$87$	−0.673550	−0.0722122
$88$	−19.9499	−2.12667
$89$	−9.16906	−0.971918	−0.485959	−	0.873982i	$-0.661530\pi$
$89$	−9.16906	−0.971918	−0.485959	+	0.873982i	$0.661530\pi$
$90$	2.58676	0.272669
$91$	0	0
$92$	4.85114	0.505766
$93$	−7.54329	−0.782202
$94$	−11.4896	−1.18506
$95$	9.40571	0.965006
$96$	−5.46696	−0.557969
$97$	−1.40381	−0.142535	−0.0712675	−	0.997457i	$-0.522704\pi$
$97$	−1.40381	−0.142535	−0.0712675	+	0.997457i	$0.522704\pi$
$98$	−1.10591	−0.111714
$99$	7.96421	0.800433
$100$	1.05674	0.105674
$101$	7.91948	0.788018	0.394009	−	0.919107i	$-0.371088\pi$
$101$	7.91948	0.788018	0.394009	+	0.919107i	$0.371088\pi$
$102$	10.5257	1.04220
$103$	5.39342	0.531429	0.265715	−	0.964052i	$-0.414392\pi$
$103$	5.39342	0.531429	0.265715	+	0.964052i	$0.414392\pi$
$104$	0	0
$105$	2.54109	0.247985
$106$	−2.94960	−0.286491
$107$	−1.27332	−0.123096	−0.0615482	−	0.998104i	$-0.519604\pi$
$107$	−1.27332	−0.123096	−0.0615482	+	0.998104i	$0.519604\pi$
$108$	4.37324	0.420815
$109$	−12.6746	−1.21401	−0.607004	−	0.794699i	$-0.707629\pi$
$109$	−12.6746	−1.21401	−0.607004	+	0.794699i	$0.707629\pi$
$110$	13.7062	1.30683
$111$	−0.0460700	−0.00437277
$112$	−1.84242	−0.174093
$113$	0.833601	0.0784186	0.0392093	−	0.999231i	$-0.487516\pi$
$113$	0.833601	0.0784186	0.0392093	+	0.999231i	$0.487516\pi$
$114$	−7.26181	−0.680131
$115$	−11.9122	−1.11082
$116$	0.392908	0.0364806
$117$	0	0
$118$	1.42164	0.130873
$119$	−7.14583	−0.655058
$120$	7.80389	0.712394
$121$	31.1991	2.83628
$122$	6.25974	0.566730
$123$	3.44418	0.310551
$124$	4.40029	0.395158
$125$	−12.1341	−1.08531
$126$	1.35585	0.120789
$127$	−7.97017	−0.707238	−0.353619	−	0.935390i	$-0.615049\pi$
$127$	−7.97017	−0.707238	−0.353619	+	0.935390i	$0.615049\pi$
$128$	−0.886036	−0.0783152
$129$	0.499019	0.0439362
$130$	0	0
$131$	−15.5538	−1.35894	−0.679472	−	0.733702i	$-0.737791\pi$
$131$	−15.5538	−1.35894	−0.679472	+	0.733702i	$0.737791\pi$
$132$	6.72241	0.585111
$133$	4.93001	0.427486
$134$	−14.2566	−1.23159
$135$	−10.7387	−0.924238
$136$	−21.9454	−1.88180
$137$	17.7435	1.51593	0.757965	−	0.652295i	$-0.226194\pi$
$137$	17.7435	1.51593	0.757965	+	0.652295i	$0.226194\pi$
$138$	9.19696	0.782897
$139$	−17.3421	−1.47094	−0.735468	−	0.677560i	$-0.763038\pi$
$139$	−17.3421	−1.47094	−0.735468	+	0.677560i	$0.763038\pi$
$140$	−1.48232	−0.125279
$141$	13.8376	1.16534
$142$	10.3832	0.871335
$143$	0	0
$144$	2.25882	0.188235
$145$	−0.964801	−0.0801224
$146$	4.83910	0.400487
$147$	1.33192	0.109855
$148$	0.0268744	0.00220906
$149$	−3.45543	−0.283080	−0.141540	−	0.989933i	$-0.545205\pi$
$149$	−3.45543	−0.283080	−0.141540	+	0.989933i	$0.545205\pi$
$150$	2.00341	0.163578
$151$	−4.65219	−0.378590	−0.189295	−	0.981920i	$-0.560620\pi$
$151$	−4.65219	−0.378590	−0.189295	+	0.981920i	$0.560620\pi$
$152$	15.1404	1.22805
$153$	8.76081	0.708269
$154$	7.18410	0.578911
$155$	−10.8051	−0.867886
$156$	0	0
$157$	−2.24284	−0.178998	−0.0894992	−	0.995987i	$-0.528527\pi$
$157$	−2.24284	−0.178998	−0.0894992	+	0.995987i	$0.528527\pi$
$158$	−0.962576	−0.0765785
$159$	3.55238	0.281722
$160$	−7.83093	−0.619090
$161$	−6.24377	−0.492078
$162$	4.22338	0.331820
$163$	9.85924	0.772235	0.386118	−	0.922450i	$-0.373816\pi$
$163$	9.85924	0.772235	0.386118	+	0.922450i	$0.373816\pi$
$164$	−2.00912	−0.156886
$165$	−16.5072	−1.28508
$166$	8.58318	0.666184
$167$	8.60457	0.665841	0.332921	−	0.942955i	$-0.391966\pi$
$167$	8.60457	0.665841	0.332921	+	0.942955i	$0.391966\pi$
$168$	4.09041	0.315582
$169$	0	0
$170$	15.0771	1.15636
$171$	−6.04420	−0.462211
$172$	−0.291097	−0.0221959
$173$	−15.0786	−1.14640	−0.573202	−	0.819414i	$-0.694299\pi$
$173$	−15.0786	−1.14640	−0.573202	+	0.819414i	$0.694299\pi$
$174$	0.744888	0.0564698
$175$	−1.36011	−0.102814
$176$	11.9685	0.902162
$177$	−1.71217	−0.128694
$178$	10.1402	0.760039
$179$	2.60788	0.194922	0.0974610	−	0.995239i	$-0.468928\pi$
$179$	2.60788	0.194922	0.0974610	+	0.995239i	$0.468928\pi$
$180$	1.81732	0.135455
$181$	−16.2821	−1.21024	−0.605119	−	0.796135i	$-0.706874\pi$
$181$	−16.2821	−1.21024	−0.605119	+	0.796135i	$0.706874\pi$
$182$	0	0
$183$	−7.53897	−0.557297
$184$	−19.1751	−1.41360
$185$	−0.0659912	−0.00485177
$186$	8.34222	0.611681
$187$	46.4199	3.39456
$188$	−8.07201	−0.588712
$189$	−5.62868	−0.409426
$190$	−10.4019	−0.754633
$191$	12.8226	0.927811	0.463906	−	0.885885i	$-0.346448\pi$
$191$	12.8226	0.927811	0.463906	+	0.885885i	$0.346448\pi$
$192$	10.9539	0.790528
$193$	−3.15790	−0.227311	−0.113655	−	0.993520i	$-0.536256\pi$
$193$	−3.15790	−0.227311	−0.113655	+	0.993520i	$0.536256\pi$
$194$	1.55249	0.111462
$195$	0	0
$196$	−0.776957	−0.0554969
$197$	−13.9283	−0.992350	−0.496175	−	0.868223i	$-0.665263\pi$
$197$	−13.9283	−0.992350	−0.496175	+	0.868223i	$0.665263\pi$
$198$	−8.80772	−0.625938
$199$	22.9738	1.62857	0.814285	−	0.580465i	$-0.197129\pi$
$199$	22.9738	1.62857	0.814285	+	0.580465i	$0.197129\pi$
$200$	−4.17698	−0.295357
$201$	17.1701	1.21109
$202$	−8.75825	−0.616229
$203$	−0.505701	−0.0354932
$204$	7.39480	0.517740
$205$	4.93348	0.344569
$206$	−5.96465	−0.415577
$207$	7.65488	0.532051
$208$	0	0
$209$	−32.0257	−2.21526
$210$	−2.81023	−0.193924
$211$	23.8461	1.64164	0.820818	−	0.571190i	$-0.193518\pi$
$211$	23.8461	1.64164	0.820818	+	0.571190i	$0.193518\pi$
$212$	−2.07224	−0.142322
$213$	−12.5050	−0.856831
$214$	1.40818	0.0962611
$215$	0.714800	0.0487490
$216$	−17.2861	−1.17617
$217$	−5.66349	−0.384463
$218$	14.0170	0.949352
$219$	−5.82801	−0.393820
$220$	9.62926	0.649204
$221$	0	0
$222$	0.0509494	0.00341950
$223$	19.3348	1.29475	0.647375	−	0.762171i	$-0.275867\pi$
$223$	19.3348	1.29475	0.647375	+	0.762171i	$0.275867\pi$
$224$	−4.10458	−0.274249
$225$	1.66749	0.111166
$226$	−0.921890	−0.0613232
$227$	9.40454	0.624201	0.312100	−	0.950049i	$-0.398967\pi$
$227$	9.40454	0.624201	0.312100	+	0.950049i	$0.398967\pi$
$228$	−5.10177	−0.337873
$229$	−7.01784	−0.463752	−0.231876	−	0.972745i	$-0.574486\pi$
$229$	−7.01784	−0.463752	−0.231876	+	0.972745i	$0.574486\pi$
$230$	13.1738	0.868657
$231$	−8.65223	−0.569275
$232$	−1.55304	−0.101962
$233$	−1.34066	−0.0878293	−0.0439147	−	0.999035i	$-0.513983\pi$
$233$	−1.34066	−0.0878293	−0.0439147	+	0.999035i	$0.513983\pi$
$234$	0	0
$235$	19.8212	1.29299
$236$	0.998772	0.0650145
$237$	1.15929	0.0753038
$238$	7.90267	0.512254
$239$	4.15222	0.268585	0.134293	−	0.990942i	$-0.457124\pi$
$239$	4.15222	0.268585	0.134293	+	0.990942i	$0.457124\pi$
$240$	−4.68177	−0.302207
$241$	4.32286	0.278460	0.139230	−	0.990260i	$-0.455537\pi$
$241$	4.32286	0.278460	0.139230	+	0.990260i	$0.455537\pi$
$242$	−34.5034	−2.21797
$243$	11.7996	0.756942
$244$	4.39777	0.281538
$245$	1.90785	0.121888
$246$	−3.80896	−0.242850
$247$	0	0
$248$	−17.3930	−1.10446
$249$	−10.3372	−0.655095
$250$	13.4193	0.848711
$251$	−20.2440	−1.27779	−0.638895	−	0.769294i	$-0.720608\pi$
$251$	−20.2440	−1.27779	−0.638895	+	0.769294i	$0.720608\pi$
$252$	0.952551	0.0600051
$253$	40.5600	2.54999
$254$	8.81431	0.553059
$255$	−18.1582	−1.13711
$256$	−15.4684	−0.966778
$257$	−4.03630	−0.251778	−0.125889	−	0.992044i	$-0.540178\pi$
$257$	−4.03630	−0.251778	−0.125889	+	0.992044i	$0.540178\pi$
$258$	−0.551871	−0.0343580
$259$	−0.0345893	−0.00214927
$260$	0	0
$261$	0.619990	0.0383764
$262$	17.2012	1.06269
$263$	−23.7353	−1.46358	−0.731792	−	0.681528i	$-0.761316\pi$
$263$	−23.7353	−1.46358	−0.731792	+	0.681528i	$0.761316\pi$
$264$	−26.5716	−1.63537
$265$	5.08847	0.312582
$266$	−5.45216	−0.334293
$267$	−12.2124	−0.747387
$268$	−10.0160	−0.611823
$269$	−21.2888	−1.29800	−0.649000	−	0.760789i	$-0.724812\pi$
$269$	−21.2888	−1.29800	−0.649000	+	0.760789i	$0.724812\pi$
$270$	11.8760	0.722752
$271$	−9.20572	−0.559208	−0.279604	−	0.960115i	$-0.590203\pi$
$271$	−9.20572	−0.559208	−0.279604	+	0.960115i	$0.590203\pi$
$272$	13.1657	0.798285
$273$	0	0
$274$	−19.6228	−1.18545
$275$	8.83536	0.532792
$276$	6.46131	0.388925
$277$	4.85993	0.292005	0.146002	−	0.989284i	$-0.453359\pi$
$277$	4.85993	0.292005	0.146002	+	0.989284i	$0.453359\pi$
$278$	19.1788	1.15027
$279$	6.94345	0.415694
$280$	5.85915	0.350151
$281$	25.1410	1.49979	0.749894	−	0.661558i	$-0.230105\pi$
$281$	25.1410	1.49979	0.749894	+	0.661558i	$0.230105\pi$
$282$	−15.3032	−0.911292
$283$	10.1245	0.601838	0.300919	−	0.953650i	$-0.402707\pi$
$283$	10.1245	0.601838	0.300919	+	0.953650i	$0.402707\pi$
$284$	7.29467	0.432859
$285$	12.5276	0.742072
$286$	0	0
$287$	2.58588	0.152640
$288$	5.03223	0.296527
$289$	34.0629	2.00370
$290$	1.06699	0.0626556
$291$	−1.86975	−0.109607
$292$	3.39970	0.198952
$293$	25.0544	1.46369	0.731846	−	0.681470i	$-0.238659\pi$
$293$	25.0544	1.46369	0.731846	+	0.681470i	$0.238659\pi$
$294$	−1.47298	−0.0859060
$295$	−2.45253	−0.142792
$296$	−0.106226	−0.00617427
$297$	36.5643	2.12168
$298$	3.82140	0.221368
$299$	0	0
$300$	1.40749	0.0812617
$301$	0.374663	0.0215952
$302$	5.14491	0.296057
$303$	10.5481	0.605971
$304$	−9.08316	−0.520955
$305$	−10.7989	−0.618343
$306$	−9.68869	−0.553866
$307$	31.8849	1.81977	0.909883	−	0.414864i	$-0.136171\pi$
$307$	31.8849	1.81977	0.909883	+	0.414864i	$0.136171\pi$
$308$	5.04718	0.287589
$309$	7.18357	0.408659
$310$	11.9495	0.678685
$311$	−2.23201	−0.126566	−0.0632828	−	0.997996i	$-0.520157\pi$
$311$	−2.23201	−0.126566	−0.0632828	+	0.997996i	$0.520157\pi$
$312$	0	0
$313$	−16.1644	−0.913668	−0.456834	−	0.889552i	$-0.651017\pi$
$313$	−16.1644	−0.913668	−0.456834	+	0.889552i	$0.651017\pi$
$314$	2.48039	0.139976
$315$	−2.33903	−0.131789
$316$	−0.676256	−0.0380424
$317$	−7.95078	−0.446560	−0.223280	−	0.974754i	$-0.571676\pi$
$317$	−7.95078	−0.446560	−0.223280	+	0.974754i	$0.571676\pi$
$318$	−3.92862	−0.220306
$319$	3.28507	0.183929
$320$	15.6905	0.877124
$321$	−1.69595	−0.0946588
$322$	6.90506	0.384804
$323$	−35.2290	−1.96019
$324$	2.96713	0.164841
$325$	0	0
$326$	−10.9035	−0.603887
$327$	−16.8815	−0.933550
$328$	7.94144	0.438492
$329$	10.3893	0.572779
$330$	18.2555	1.00493
$331$	14.0809	0.773954	0.386977	−	0.922089i	$-0.373519\pi$
$331$	14.0809	0.773954	0.386977	+	0.922089i	$0.373519\pi$
$332$	6.03010	0.330944
$333$	0.0424065	0.00232386
$334$	−9.51590	−0.520687
$335$	24.5947	1.34375
$336$	−2.45395	−0.133874
$337$	21.3763	1.16444	0.582220	−	0.813032i	$-0.302184\pi$
$337$	21.3763	1.16444	0.582220	+	0.813032i	$0.302184\pi$
$338$	0	0
$339$	1.11029	0.0603024
$340$	10.5924	0.574453
$341$	36.7905	1.99232
$342$	6.68436	0.361449
$343$	1.00000	0.0539949
$344$	1.15062	0.0620371
$345$	−15.8660	−0.854197
$346$	16.6756	0.896487
$347$	8.96438	0.481233	0.240617	−	0.970620i	$-0.422650\pi$
$347$	8.96438	0.481233	0.240617	+	0.970620i	$0.422650\pi$
$348$	0.523320	0.0280529
$349$	5.83019	0.312083	0.156041	−	0.987751i	$-0.450127\pi$
$349$	5.83019	0.312083	0.156041	+	0.987751i	$0.450127\pi$
$350$	1.50416	0.0804007
$351$	0	0
$352$	26.6637	1.42118
$353$	−22.1854	−1.18081	−0.590406	−	0.807107i	$-0.701032\pi$
$353$	−22.1854	−1.18081	−0.590406	+	0.807107i	$0.701032\pi$
$354$	1.89351	0.100639
$355$	−17.9124	−0.950689
$356$	7.12396	0.377569
$357$	−9.51764	−0.503727
$358$	−2.88409	−0.152429
$359$	−14.3644	−0.758123	−0.379062	−	0.925371i	$-0.623753\pi$
$359$	−14.3644	−0.758123	−0.379062	+	0.925371i	$0.623753\pi$
$360$	−7.18333	−0.378595
$361$	5.30495	0.279208
$362$	18.0066	0.946404
$363$	41.5545	2.18105
$364$	0	0
$365$	−8.34811	−0.436960
$366$	8.33744	0.435805
$367$	−22.0395	−1.15045	−0.575226	−	0.817994i	$-0.695086\pi$
$367$	−22.0395	−1.15045	−0.575226	+	0.817994i	$0.695086\pi$
$368$	11.5037	0.599670
$369$	−3.17030	−0.165039
$370$	0.0729805	0.00379408
$371$	2.66712	0.138470
$372$	5.86081	0.303869
$373$	10.5232	0.544873	0.272436	−	0.962174i	$-0.412171\pi$
$373$	10.5232	0.544873	0.272436	+	0.962174i	$0.412171\pi$
$374$	−51.3364	−2.65454
$375$	−16.1616	−0.834583
$376$	31.9062	1.64544
$377$	0	0
$378$	6.22482	0.320170
$379$	2.24826	0.115485	0.0577427	−	0.998331i	$-0.481610\pi$
$379$	2.24826	0.115485	0.0577427	+	0.998331i	$0.481610\pi$
$380$	−7.30783	−0.374884
$381$	−10.6156	−0.543853
$382$	−14.1807	−0.725547
$383$	8.17316	0.417629	0.208815	−	0.977955i	$-0.433039\pi$
$383$	8.17316	0.417629	0.208815	+	0.977955i	$0.433039\pi$
$384$	−1.18012	−0.0602230
$385$	−12.3936	−0.631634
$386$	3.49237	0.177757
$387$	−0.459337	−0.0233494
$388$	1.09070	0.0553718
$389$	−21.0561	−1.06758	−0.533792	−	0.845616i	$-0.679234\pi$
$389$	−21.0561	−1.06758	−0.533792	+	0.845616i	$0.679234\pi$
$390$	0	0
$391$	44.6169	2.25638
$392$	3.07107	0.155113
$393$	−20.7164	−1.04500
$394$	15.4035	0.776016
$395$	1.66058	0.0835526
$396$	−6.18785	−0.310951
$397$	−28.4290	−1.42681	−0.713405	−	0.700752i	$-0.752848\pi$
$397$	−28.4290	−1.42681	−0.713405	+	0.700752i	$0.752848\pi$
$398$	−25.4070	−1.27354
$399$	6.56635	0.328729
$400$	2.50589	0.125295
$401$	26.8409	1.34037	0.670185	−	0.742194i	$-0.266215\pi$
$401$	26.8409	1.34037	0.670185	+	0.742194i	$0.266215\pi$
$402$	−18.9886	−0.947067
$403$	0	0
$404$	−6.15310	−0.306128
$405$	−7.28591	−0.362040
$406$	0.559261	0.0277557
$407$	0.224695	0.0111377
$408$	−29.2294	−1.44707
$409$	18.9796	0.938483	0.469242	−	0.883070i	$-0.344527\pi$
$409$	18.9796	0.938483	0.469242	+	0.883070i	$0.344527\pi$
$410$	−5.45600	−0.269453
$411$	23.6328	1.16572
$412$	−4.19045	−0.206449
$413$	−1.28549	−0.0632549
$414$	−8.46562	−0.416063
$415$	−14.8072	−0.726855
$416$	0	0
$417$	−23.0982	−1.13112
$418$	35.4176	1.73233
$419$	−14.7355	−0.719874	−0.359937	−	0.932977i	$-0.617202\pi$
$419$	−14.7355	−0.719874	−0.359937	+	0.932977i	$0.617202\pi$
$420$	−1.97432	−0.0963370
$421$	1.07189	0.0522408	0.0261204	−	0.999659i	$-0.491685\pi$
$421$	1.07189	0.0522408	0.0261204	+	0.999659i	$0.491685\pi$
$422$	−26.3717	−1.28376
$423$	−12.7373	−0.619307
$424$	8.19092	0.397786
$425$	9.71910	0.471445
$426$	13.8295	0.670041
$427$	−5.66025	−0.273919
$428$	0.989313	0.0478203
$429$	0	0
$430$	−0.790507	−0.0381216
$431$	−28.0271	−1.35002	−0.675008	−	0.737810i	$-0.735860\pi$
$431$	−28.0271	−1.35002	−0.675008	+	0.737810i	$0.735860\pi$
$432$	10.3704	0.498947
$433$	−17.9880	−0.864446	−0.432223	−	0.901767i	$-0.642271\pi$
$433$	−17.9880	−0.864446	−0.432223	+	0.901767i	$0.642271\pi$
$434$	6.26333	0.300649
$435$	−1.28503	−0.0616126
$436$	9.84763	0.471616
$437$	−30.7818	−1.47249
$438$	6.44527	0.307967
$439$	33.5023	1.59898	0.799489	−	0.600681i	$-0.205104\pi$
$439$	33.5023	1.59898	0.799489	+	0.600681i	$0.205104\pi$
$440$	−38.0615	−1.81451
$441$	−1.22600	−0.0583811
$442$	0	0
$443$	−29.2578	−1.39008	−0.695040	−	0.718971i	$-0.744613\pi$
$443$	−29.2578	−1.39008	−0.695040	+	0.718971i	$0.744613\pi$
$444$	0.0357944	0.00169873
$445$	−17.4932	−0.829257
$446$	−21.3826	−1.01249
$447$	−4.60233	−0.217683
$448$	8.22416	0.388555
$449$	−19.3050	−0.911058	−0.455529	−	0.890221i	$-0.650550\pi$
$449$	−19.3050	−0.911058	−0.455529	+	0.890221i	$0.650550\pi$
$450$	−1.84410	−0.0869318
$451$	−16.7981	−0.790992
$452$	−0.647672	−0.0304639
$453$	−6.19632	−0.291129
$454$	−10.4006	−0.488124
$455$	0	0
$456$	20.1657	0.944347
$457$	−17.4861	−0.817964	−0.408982	−	0.912542i	$-0.634116\pi$
$457$	−17.4861	−0.817964	−0.408982	+	0.912542i	$0.634116\pi$
$458$	7.76112	0.362653
$459$	40.2216	1.87738
$460$	9.25525	0.431528
$461$	18.5263	0.862858	0.431429	−	0.902147i	$-0.358010\pi$
$461$	18.5263	0.862858	0.431429	+	0.902147i	$0.358010\pi$
$462$	9.56861	0.445172
$463$	2.68708	0.124879	0.0624395	−	0.998049i	$-0.480112\pi$
$463$	2.68708	0.124879	0.0624395	+	0.998049i	$0.480112\pi$
$464$	0.931715	0.0432538
$465$	−14.3915	−0.667388
$466$	1.48265	0.0686824
$467$	−16.0186	−0.741251	−0.370625	−	0.928782i	$-0.620857\pi$
$467$	−16.0186	−0.741251	−0.370625	+	0.928782i	$0.620857\pi$
$468$	0	0
$469$	12.8913	0.595264
$470$	−21.9205	−1.01112
$471$	−2.98728	−0.137646
$472$	−3.94784	−0.181714
$473$	−2.43384	−0.111908
$474$	−1.28207	−0.0588874
$475$	−6.70533	−0.307662
$476$	5.55201	0.254476
$477$	−3.26990	−0.149718
$478$	−4.59200	−0.210033
$479$	4.25810	0.194557	0.0972787	−	0.995257i	$-0.468986\pi$
$479$	4.25810	0.194557	0.0972787	+	0.995257i	$0.468986\pi$
$480$	−10.4301	−0.476068
$481$	0	0
$482$	−4.78070	−0.217755
$483$	−8.31617	−0.378399
$484$	−24.2403	−1.10183
$485$	−2.67825	−0.121613
$486$	−13.0493	−0.591928
$487$	−43.0637	−1.95140	−0.975702	−	0.219103i	$-0.929687\pi$
$487$	−43.0637	−1.95140	−0.975702	+	0.219103i	$0.929687\pi$
$488$	−17.3830	−0.786893
$489$	13.1317	0.593835
$490$	−2.10992	−0.0953163
$491$	9.44176	0.426101	0.213050	−	0.977041i	$-0.431660\pi$
$491$	9.44176	0.426101	0.213050	+	0.977041i	$0.431660\pi$
$492$	−2.67598	−0.120642
$493$	3.61365	0.162751
$494$	0	0
$495$	15.1945	0.682943
$496$	10.4346	0.468525
$497$	−9.38877	−0.421144
$498$	11.4321	0.512283
$499$	−0.400211	−0.0179159	−0.00895795	−	0.999960i	$-0.502851\pi$
$499$	−0.400211	−0.0179159	−0.00895795	+	0.999960i	$0.502851\pi$
$500$	9.42770	0.421619
$501$	11.4606	0.512020
$502$	22.3881	0.999229
$503$	18.5562	0.827378	0.413689	−	0.910418i	$-0.364240\pi$
$503$	18.5562	0.827378	0.413689	+	0.910418i	$0.364240\pi$
$504$	−3.76514	−0.167713
$505$	15.1092	0.672350
$506$	−44.8559	−1.99409
$507$	0	0
$508$	6.19248	0.274747
$509$	39.7624	1.76244	0.881219	−	0.472709i	$-0.156724\pi$
$509$	39.7624	1.76244	0.881219	+	0.472709i	$0.156724\pi$
$510$	20.0814	0.889221
$511$	−4.37566	−0.193568
$512$	18.8788	0.834334
$513$	−27.7494	−1.22517
$514$	4.46380	0.196890
$515$	10.2898	0.453424
$516$	−0.387716	−0.0170683
$517$	−67.4895	−2.96818
$518$	0.0382527	0.00168073
$519$	−20.0834	−0.881564
$520$	0	0
$521$	22.7880	0.998359	0.499180	−	0.866499i	$-0.333635\pi$
$521$	22.7880	0.998359	0.499180	+	0.866499i	$0.333635\pi$
$522$	−0.685655	−0.0300103
$523$	−26.9862	−1.18003	−0.590013	−	0.807394i	$-0.700877\pi$
$523$	−26.9862	−1.18003	−0.590013	+	0.807394i	$0.700877\pi$
$524$	12.0847	0.527920
$525$	−1.81155	−0.0790624
$526$	26.2492	1.14452
$527$	40.4704	1.76292
$528$	15.9411	0.693746
$529$	15.9847	0.694985
$530$	−5.62740	−0.244439
$531$	1.57602	0.0683933
$532$	−3.83040	−0.166069
$533$	0	0
$534$	13.5059	0.584456
$535$	−2.42930	−0.105028
$536$	39.5901	1.71003
$537$	3.47347	0.149891
$538$	23.5435	1.01503
$539$	−6.49608	−0.279806
$540$	8.34349	0.359046
$541$	1.35736	0.0583574	0.0291787	−	0.999574i	$-0.490711\pi$
$541$	1.35736	0.0583574	0.0291787	+	0.999574i	$0.490711\pi$
$542$	10.1807	0.437299
$543$	−21.6864	−0.930651
$544$	29.3307	1.25754
$545$	−24.1813	−1.03581
$546$	0	0
$547$	4.66512	0.199466	0.0997330	−	0.995014i	$-0.468201\pi$
$547$	4.66512	0.199466	0.0997330	+	0.995014i	$0.468201\pi$
$548$	−13.7859	−0.588906
$549$	6.93948	0.296170
$550$	−9.77114	−0.416643
$551$	−2.49311	−0.106210
$552$	−25.5396	−1.08704
$553$	0.870391	0.0370128
$554$	−5.37466	−0.228347
$555$	−0.0878947	−0.00373092
$556$	13.4740	0.571427
$557$	9.60851	0.407126	0.203563	−	0.979062i	$-0.434748\pi$
$557$	9.60851	0.407126	0.203563	+	0.979062i	$0.434748\pi$
$558$	−7.67885	−0.325072
$559$	0	0
$560$	−3.51507	−0.148539
$561$	61.8274	2.61035
$562$	−27.8038	−1.17283
$563$	33.1683	1.39788	0.698938	−	0.715183i	$-0.253656\pi$
$563$	33.1683	1.39788	0.698938	+	0.715183i	$0.253656\pi$
$564$	−10.7512	−0.452709
$565$	1.59039	0.0669080
$566$	−11.1968	−0.470636
$567$	−3.81891	−0.160379
$568$	−28.8336	−1.20983
$569$	−44.4353	−1.86282	−0.931411	−	0.363968i	$-0.881422\pi$
$569$	−44.4353	−1.86282	−0.931411	+	0.363968i	$0.881422\pi$
$570$	−13.8544	−0.580299
$571$	−15.0146	−0.628341	−0.314170	−	0.949367i	$-0.601726\pi$
$571$	−15.0146	−0.628341	−0.314170	+	0.949367i	$0.601726\pi$
$572$	0	0
$573$	17.0786	0.713470
$574$	−2.85976	−0.119364
$575$	8.49219	0.354149
$576$	−10.0828	−0.420118
$577$	−11.7372	−0.488625	−0.244312	−	0.969697i	$-0.578562\pi$
$577$	−11.7372	−0.488625	−0.244312	+	0.969697i	$0.578562\pi$
$578$	−37.6707	−1.56689
$579$	−4.20606	−0.174798
$580$	0.749609	0.0311258
$581$	−7.76117	−0.321988
$582$	2.06778	0.0857123
$583$	−17.3258	−0.717563
$584$	−13.4380	−0.556067
$585$	0	0
$586$	−27.7079	−1.14460
$587$	−1.87115	−0.0772306	−0.0386153	−	0.999254i	$-0.512295\pi$
$587$	−1.87115	−0.0772306	−0.0386153	+	0.999254i	$0.512295\pi$
$588$	−1.03484	−0.0426761
$589$	−27.9210	−1.15047
$590$	2.71228	0.111663
$591$	−18.5513	−0.763099
$592$	0.0637281	0.00261921
$593$	−5.06081	−0.207823	−0.103911	−	0.994587i	$-0.533136\pi$
$593$	−5.06081	−0.207823	−0.103911	+	0.994587i	$0.533136\pi$
$594$	−40.4370	−1.65915
$595$	−13.6332	−0.558906
$596$	2.68472	0.109970
$597$	30.5992	1.25234
$598$	0	0
$599$	3.98581	0.162856	0.0814280	−	0.996679i	$-0.474052\pi$
$599$	3.98581	0.162856	0.0814280	+	0.996679i	$0.474052\pi$
$600$	−5.56339	−0.227124
$601$	−12.2004	−0.497666	−0.248833	−	0.968546i	$-0.580047\pi$
$601$	−12.2004	−0.497666	−0.248833	+	0.968546i	$0.580047\pi$
$602$	−0.414344	−0.0168874
$603$	−15.8048	−0.643619
$604$	3.61455	0.147074
$605$	59.5232	2.41996
$606$	−11.6653	−0.473868
$607$	11.0021	0.446560	0.223280	−	0.974754i	$-0.428324\pi$
$607$	11.0021	0.446560	0.223280	+	0.974754i	$0.428324\pi$
$608$	−20.2356	−0.820663
$609$	−0.673550	−0.0272936
$610$	11.9426	0.483544
$611$	0	0
$612$	−6.80677	−0.275147
$613$	−23.9685	−0.968080	−0.484040	−	0.875046i	$-0.660831\pi$
$613$	−23.9685	−0.968080	−0.484040	+	0.875046i	$0.660831\pi$
$614$	−35.2619	−1.42305
$615$	6.57098	0.264967
$616$	−19.9499	−0.803806
$617$	−7.63127	−0.307223	−0.153612	−	0.988131i	$-0.549090\pi$
$617$	−7.63127	−0.307223	−0.153612	+	0.988131i	$0.549090\pi$
$618$	−7.94441	−0.319571
$619$	12.1904	0.489972	0.244986	−	0.969527i	$-0.421217\pi$
$619$	12.1904	0.489972	0.244986	+	0.969527i	$0.421217\pi$
$620$	8.39509	0.337155
$621$	35.1442	1.41029
$622$	2.46841	0.0989740
$623$	−9.16906	−0.367351
$624$	0	0
$625$	−16.3496	−0.653983
$626$	17.8764	0.714487
$627$	−42.6555	−1.70350
$628$	1.74259	0.0695370
$629$	0.247169	0.00985529
$630$	2.58676	0.103059
$631$	12.1308	0.482921	0.241461	−	0.970411i	$-0.422374\pi$
$631$	12.1308	0.482921	0.241461	+	0.970411i	$0.422374\pi$
$632$	2.67303	0.106328
$633$	31.7610	1.26239
$634$	8.79287	0.349209
$635$	−15.2059	−0.603427
$636$	−2.76005	−0.109443
$637$	0	0
$638$	−3.63300	−0.143832
$639$	11.5106	0.455354
$640$	−1.69042	−0.0668199
$641$	−49.5578	−1.95742	−0.978708	−	0.205259i	$-0.934196\pi$
$641$	−49.5578	−1.95742	−0.978708	+	0.205259i	$0.934196\pi$
$642$	1.87557	0.0740230
$643$	27.1873	1.07216	0.536080	−	0.844167i	$-0.319904\pi$
$643$	27.1873	1.07216	0.536080	+	0.844167i	$0.319904\pi$
$644$	4.85114	0.191162
$645$	0.952053	0.0374871
$646$	38.9602	1.53287
$647$	−23.1148	−0.908738	−0.454369	−	0.890814i	$-0.650135\pi$
$647$	−23.1148	−0.908738	−0.454369	+	0.890814i	$0.650135\pi$
$648$	−11.7282	−0.460725
$649$	8.35066	0.327792
$650$	0	0
$651$	−7.54329	−0.295645
$652$	−7.66021	−0.299997
$653$	−35.9335	−1.40619	−0.703093	−	0.711098i	$-0.748198\pi$
$653$	−35.9335	−1.40619	−0.703093	+	0.711098i	$0.748198\pi$
$654$	18.6695	0.730034
$655$	−29.6744	−1.15947
$656$	−4.76429	−0.186014
$657$	5.36457	0.209292
$658$	−11.4896	−0.447912
$659$	0.915223	0.0356520	0.0178260	−	0.999841i	$-0.494326\pi$
$659$	0.915223	0.0356520	0.0178260	+	0.999841i	$0.494326\pi$
$660$	12.8254	0.499226
$661$	−44.7114	−1.73907	−0.869536	−	0.493869i	$-0.835582\pi$
$661$	−44.7114	−1.73907	−0.869536	+	0.493869i	$0.835582\pi$
$662$	−15.5722	−0.605231
$663$	0	0
$664$	−23.8351	−0.924982
$665$	9.40571	0.364738
$666$	−0.0468979	−0.00181726
$667$	3.15748	0.122258
$668$	−6.68538	−0.258665
$669$	25.7522	0.995639
$670$	−27.1995	−1.05081
$671$	36.7694	1.41947
$672$	−5.46696	−0.210892
$673$	−34.0405	−1.31216	−0.656082	−	0.754690i	$-0.727787\pi$
$673$	−34.0405	−1.31216	−0.656082	+	0.754690i	$0.727787\pi$
$674$	−23.6403	−0.910590
$675$	7.65560	0.294664
$676$	0	0
$677$	36.9457	1.41994	0.709969	−	0.704233i	$-0.248709\pi$
$677$	36.9457	1.41994	0.709969	+	0.704233i	$0.248709\pi$
$678$	−1.22788	−0.0471564
$679$	−1.40381	−0.0538732
$680$	−41.8685	−1.60558
$681$	12.5260	0.479999
$682$	−40.6871	−1.55799
$683$	−22.6057	−0.864982	−0.432491	−	0.901638i	$-0.642365\pi$
$683$	−22.6057	−0.864982	−0.432491	+	0.901638i	$0.642365\pi$
$684$	4.69608	0.179559
$685$	33.8519	1.29342
$686$	−1.10591	−0.0422239
$687$	−9.34716	−0.356617
$688$	−0.690287	−0.0263170
$689$	0	0
$690$	17.5464	0.667981
$691$	5.83440	0.221951	0.110976	−	0.993823i	$-0.464602\pi$
$691$	5.83440	0.221951	0.110976	+	0.993823i	$0.464602\pi$
$692$	11.7154	0.445354
$693$	7.96421	0.302535
$694$	−9.91382	−0.376324
$695$	−33.0861	−1.25503
$696$	−2.06852	−0.0784071
$697$	−18.4783	−0.699915
$698$	−6.44768	−0.244048
$699$	−1.78564	−0.0675391
$700$	1.05674	0.0399412
$701$	−17.5715	−0.663667	−0.331834	−	0.943338i	$-0.607667\pi$
$701$	−17.5715	−0.663667	−0.331834	+	0.943338i	$0.607667\pi$
$702$	0	0
$703$	−0.170525	−0.00643149
$704$	−53.4248	−2.01352
$705$	26.4001	0.994285
$706$	24.5352	0.923393
$707$	7.91948	0.297843
$708$	1.33028	0.0499950
$709$	−41.7153	−1.56665	−0.783325	−	0.621612i	$-0.786478\pi$
$709$	−41.7153	−1.56665	−0.783325	+	0.621612i	$0.786478\pi$
$710$	19.8095	0.743438
$711$	−1.06710	−0.0400194
$712$	−28.1588	−1.05530
$713$	35.3615	1.32430
$714$	10.5257	0.393914
$715$	0	0
$716$	−2.02621	−0.0757230
$717$	5.53041	0.206537
$718$	15.8858	0.592851
$719$	−36.1319	−1.34749	−0.673746	−	0.738963i	$-0.735316\pi$
$719$	−36.1319	−1.34749	−0.673746	+	0.738963i	$0.735316\pi$
$720$	4.30948	0.160605
$721$	5.39342	0.200861
$722$	−5.86681	−0.218340
$723$	5.75768	0.214130
$724$	12.6505	0.470151
$725$	0.687807	0.0255445
$726$	−45.9557	−1.70557
$727$	23.7414	0.880520	0.440260	−	0.897870i	$-0.354886\pi$
$727$	23.7414	0.880520	0.440260	+	0.897870i	$0.354886\pi$
$728$	0	0
$729$	27.1727	1.00640
$730$	9.23228	0.341702
$731$	−2.67728	−0.0990227
$732$	5.85745	0.216498
$733$	−18.1355	−0.669849	−0.334925	−	0.942245i	$-0.608711\pi$
$733$	−18.1355	−0.669849	−0.334925	+	0.942245i	$0.608711\pi$
$734$	24.3738	0.899652
$735$	2.54109	0.0937297
$736$	25.6281	0.944663
$737$	−83.7429	−3.08471
$738$	3.50607	0.129060
$739$	33.8316	1.24451	0.622257	−	0.782813i	$-0.286216\pi$
$739$	33.8316	1.24451	0.622257	+	0.782813i	$0.286216\pi$
$740$	0.0512723	0.00188481
$741$	0	0
$742$	−2.94960	−0.108283
$743$	16.6098	0.609353	0.304677	−	0.952456i	$-0.401452\pi$
$743$	16.6098	0.609353	0.304677	+	0.952456i	$0.401452\pi$
$744$	−23.1660	−0.849306
$745$	−6.59244	−0.241528
$746$	−11.6378	−0.426090
$747$	9.51521	0.348143
$748$	−36.0663	−1.31871
$749$	−1.27332	−0.0465260
$750$	17.8734	0.652643
$751$	41.9317	1.53011	0.765054	−	0.643966i	$-0.222712\pi$
$751$	41.9317	1.53011	0.765054	+	0.643966i	$0.222712\pi$
$752$	−19.1414	−0.698016
$753$	−26.9633	−0.982596
$754$	0	0
$755$	−8.87568	−0.323019
$756$	4.37324	0.159053
$757$	46.3278	1.68381	0.841907	−	0.539623i	$-0.181433\pi$
$757$	46.3278	1.68381	0.841907	+	0.539623i	$0.181433\pi$
$758$	−2.48638	−0.0903094
$759$	54.0225	1.96089
$760$	28.8856	1.04779
$761$	29.5269	1.07035	0.535174	−	0.844742i	$-0.320246\pi$
$761$	29.5269	1.07035	0.535174	+	0.844742i	$0.320246\pi$
$762$	11.7399	0.425292
$763$	−12.6746	−0.458852
$764$	−9.96261	−0.360435
$765$	16.7143	0.604307
$766$	−9.03880	−0.326585
$767$	0	0
$768$	−20.6027	−0.743434
$769$	−39.4542	−1.42275	−0.711377	−	0.702811i	$-0.751928\pi$
$769$	−39.4542	−1.42275	−0.711377	+	0.702811i	$0.751928\pi$
$770$	13.7062	0.493937
$771$	−5.37601	−0.193612
$772$	2.45356	0.0883054
$773$	−3.97395	−0.142933	−0.0714666	−	0.997443i	$-0.522768\pi$
$773$	−3.97395	−0.142933	−0.0714666	+	0.997443i	$0.522768\pi$
$774$	0.507987	0.0182592
$775$	7.70295	0.276698
$776$	−4.31119	−0.154763
$777$	−0.0460700	−0.00165275
$778$	23.2862	0.834849
$779$	12.7484	0.456760
$780$	0	0
$781$	60.9902	2.18240
$782$	−49.3424	−1.76448
$783$	2.84643	0.101723
$784$	−1.84242	−0.0658009
$785$	−4.27901	−0.152724
$786$	22.9105	0.817190
$787$	0.698671	0.0249049	0.0124525	−	0.999922i	$-0.496036\pi$
$787$	0.698671	0.0249049	0.0124525	+	0.999922i	$0.496036\pi$
$788$	10.8217	0.385507
$789$	−31.6134	−1.12547
$790$	−1.83645	−0.0653380
$791$	0.833601	0.0296394
$792$	24.4587	0.869101
$793$	0	0
$794$	31.4400	1.11576
$795$	6.77741	0.240370
$796$	−17.8497	−0.632664
$797$	−6.12095	−0.216815	−0.108408	−	0.994107i	$-0.534575\pi$
$797$	−6.12095	−0.216815	−0.108408	+	0.994107i	$0.534575\pi$
$798$	−7.26181	−0.257065
$799$	−74.2400	−2.62642
$800$	5.58267	0.197377
$801$	11.2413	0.397191
$802$	−29.6837	−1.04817
$803$	28.4246	1.00308
$804$	−13.3404	−0.470481
$805$	−11.9122	−0.419849
$806$	0	0
$807$	−28.3548	−0.998137
$808$	24.3213	0.855620
$809$	−21.8694	−0.768886	−0.384443	−	0.923149i	$-0.625606\pi$
$809$	−21.8694	−0.768886	−0.384443	+	0.923149i	$0.625606\pi$
$810$	8.05758	0.283115
$811$	−4.38772	−0.154074	−0.0770368	−	0.997028i	$-0.524546\pi$
$811$	−4.38772	−0.154074	−0.0770368	+	0.997028i	$0.524546\pi$
$812$	0.392908	0.0137884
$813$	−12.2612	−0.430020
$814$	−0.248493	−0.00870967
$815$	18.8100	0.658884
$816$	17.5355	0.613867
$817$	1.84709	0.0646215
$818$	−20.9898	−0.733892
$819$	0	0
$820$	−3.83310	−0.133858
$821$	31.5599	1.10145	0.550724	−	0.834687i	$-0.314352\pi$
$821$	31.5599	1.10145	0.550724	+	0.834687i	$0.314352\pi$
$822$	−26.1359	−0.911593
$823$	−13.6727	−0.476600	−0.238300	−	0.971192i	$-0.576590\pi$
$823$	−13.6727	−0.476600	−0.238300	+	0.971192i	$0.576590\pi$
$824$	16.5636	0.577020
$825$	11.7680	0.409707
$826$	1.42164	0.0494653
$827$	−13.5727	−0.471970	−0.235985	−	0.971757i	$-0.575832\pi$
$827$	−13.5727	−0.471970	−0.235985	+	0.971757i	$0.575832\pi$
$828$	−5.94751	−0.206690
$829$	51.0839	1.77422	0.887109	−	0.461560i	$-0.152710\pi$
$829$	51.0839	1.77422	0.887109	+	0.461560i	$0.152710\pi$
$830$	16.3754	0.568399
$831$	6.47301	0.224546
$832$	0	0
$833$	−7.14583	−0.247588
$834$	25.5446	0.884536
$835$	16.4162	0.568107
$836$	24.8826	0.860583
$837$	31.8780	1.10186
$838$	16.2961	0.562940
$839$	−7.39574	−0.255329	−0.127665	−	0.991817i	$-0.540748\pi$
$839$	−7.39574	−0.255329	−0.127665	+	0.991817i	$0.540748\pi$
$840$	7.80389	0.269260
$841$	−28.7443	−0.991182
$842$	−1.18542	−0.0408522
$843$	33.4857	1.15331
$844$	−18.5274	−0.637740
$845$	0	0
$846$	14.0863	0.484297
$847$	31.1991	1.07201
$848$	−4.91397	−0.168746
$849$	13.4849	0.462802
$850$	−10.7485	−0.368670
$851$	0.215968	0.00740327
$852$	9.71588	0.332860
$853$	−12.0552	−0.412762	−0.206381	−	0.978472i	$-0.566169\pi$
$853$	−12.0552	−0.412762	−0.206381	+	0.978472i	$0.566169\pi$
$854$	6.25974	0.214204
$855$	−11.5314	−0.394366
$856$	−3.91045	−0.133656
$857$	46.7924	1.59840	0.799199	−	0.601066i	$-0.205257\pi$
$857$	46.7924	1.59840	0.799199	+	0.601066i	$0.205257\pi$
$858$	0	0
$859$	−43.5870	−1.48717	−0.743585	−	0.668641i	$-0.766876\pi$
$859$	−43.5870	−1.48717	−0.743585	+	0.668641i	$0.766876\pi$
$860$	−0.555369	−0.0189379
$861$	3.44418	0.117377
$862$	30.9955	1.05571
$863$	−0.0785410	−0.00267357	−0.00133678	−	0.999999i	$-0.500426\pi$
$863$	−0.0785410	−0.00267357	−0.00133678	+	0.999999i	$0.500426\pi$
$864$	23.1034	0.785993
$865$	−28.7677	−0.978132
$866$	19.8931	0.675995
$867$	45.3690	1.54081
$868$	4.40029	0.149356
$869$	−5.65413	−0.191803
$870$	1.42114	0.0481810
$871$	0	0
$872$	−38.9247	−1.31816
$873$	1.72107	0.0582494
$874$	34.0420	1.15149
$875$	−12.1341	−0.410209
$876$	4.52811	0.152991
$877$	−32.1903	−1.08699	−0.543495	−	0.839413i	$-0.682899\pi$
$877$	−32.1903	−1.08699	−0.543495	+	0.839413i	$0.682899\pi$
$878$	−37.0506	−1.25040
$879$	33.3703	1.12555
$880$	22.8342	0.769740
$881$	−10.4114	−0.350770	−0.175385	−	0.984500i	$-0.556117\pi$
$881$	−10.4114	−0.350770	−0.175385	+	0.984500i	$0.556117\pi$
$882$	1.35585	0.0456539
$883$	21.5238	0.724334	0.362167	−	0.932113i	$-0.382037\pi$
$883$	21.5238	0.724334	0.362167	+	0.932113i	$0.382037\pi$
$884$	0	0
$885$	−3.26656	−0.109804
$886$	32.3566	1.08704
$887$	45.5964	1.53098	0.765489	−	0.643449i	$-0.222497\pi$
$887$	45.5964	1.53098	0.765489	+	0.643449i	$0.222497\pi$
$888$	−0.141484	−0.00474790
$889$	−7.97017	−0.267311
$890$	19.3459	0.648478
$891$	24.8080	0.831098
$892$	−15.0223	−0.502983
$893$	51.2191	1.71398
$894$	5.08978	0.170228
$895$	4.97544	0.166311
$896$	−0.886036	−0.0296004
$897$	0	0
$898$	21.3496	0.712446
$899$	2.86403	0.0955208
$900$	−1.29557	−0.0431857
$901$	−19.0588	−0.634941
$902$	18.5772	0.618555
$903$	0.499019	0.0166063
$904$	2.56005	0.0851460
$905$	−31.0638	−1.03260
$906$	6.85259	0.227662
$907$	19.0080	0.631150	0.315575	−	0.948901i	$-0.397803\pi$
$907$	19.0080	0.631150	0.315575	+	0.948901i	$0.397803\pi$
$908$	−7.30692	−0.242489
$909$	−9.70930	−0.322037
$910$	0	0
$911$	−33.6010	−1.11325	−0.556626	−	0.830763i	$-0.687904\pi$
$911$	−33.6010	−1.11325	−0.556626	+	0.830763i	$0.687904\pi$
$912$	−12.0980	−0.400605
$913$	50.4172	1.66857
$914$	19.3381	0.639647
$915$	−14.3832	−0.475495
$916$	5.45256	0.180158
$917$	−15.5538	−0.513632
$918$	−44.4816	−1.46811
$919$	19.9752	0.658921	0.329461	−	0.944169i	$-0.393133\pi$
$919$	19.9752	0.658921	0.329461	+	0.944169i	$0.393133\pi$
$920$	−36.5832	−1.20611
$921$	42.4680	1.39937
$922$	−20.4885	−0.674754
$923$	0	0
$924$	6.72241	0.221151
$925$	0.0470451	0.00154683
$926$	−2.97167	−0.0976552
$927$	−6.61234	−0.217178
$928$	2.07569	0.0681379
$929$	1.73612	0.0569602	0.0284801	−	0.999594i	$-0.490933\pi$
$929$	1.73612	0.0569602	0.0284801	+	0.999594i	$0.490933\pi$
$930$	15.9157	0.521897
$931$	4.93001	0.161574
$932$	1.04163	0.0341198
$933$	−2.97284	−0.0973265
$934$	17.7151	0.579657
$935$	88.5623	2.89630
$936$	0	0
$937$	4.46161	0.145754	0.0728772	−	0.997341i	$-0.476782\pi$
$937$	4.46161	0.145754	0.0728772	+	0.997341i	$0.476782\pi$
$938$	−14.2566	−0.465496
$939$	−21.5296	−0.702593
$940$	−15.4002	−0.502299
$941$	5.31110	0.173137	0.0865685	−	0.996246i	$-0.472410\pi$
$941$	5.31110	0.173137	0.0865685	+	0.996246i	$0.472410\pi$
$942$	3.30367	0.107639
$943$	−16.1457	−0.525775
$944$	2.36842	0.0770856
$945$	−10.7387	−0.349329
$946$	2.69161	0.0875119
$947$	−15.0901	−0.490364	−0.245182	−	0.969477i	$-0.578848\pi$
$947$	−15.0901	−0.490364	−0.245182	+	0.969477i	$0.578848\pi$
$948$	−0.900716	−0.0292539
$949$	0	0
$950$	7.41551	0.240591
$951$	−10.5898	−0.343397
$952$	−21.9454	−0.711254
$953$	−38.5139	−1.24759	−0.623794	−	0.781589i	$-0.714409\pi$
$953$	−38.5139	−1.24759	−0.623794	+	0.781589i	$0.714409\pi$
$954$	3.61622	0.117079
$955$	24.4636	0.791624
$956$	−3.22610	−0.104339
$957$	4.37544	0.141438
$958$	−4.70909	−0.152144
$959$	17.7435	0.572968
$960$	20.8984	0.674492
$961$	1.07512	0.0346813
$962$	0	0
$963$	1.56109	0.0503055
$964$	−3.35868	−0.108176
$965$	−6.02481	−0.193945
$966$	9.19696	0.295907
$967$	46.8859	1.50775	0.753874	−	0.657019i	$-0.228183\pi$
$967$	46.8859	1.50775	0.753874	+	0.657019i	$0.228183\pi$
$968$	95.8146	3.07960
$969$	−46.9220	−1.50735
$970$	2.96191	0.0951014
$971$	2.39329	0.0768045	0.0384022	−	0.999262i	$-0.487773\pi$
$971$	2.39329	0.0768045	0.0384022	+	0.999262i	$0.487773\pi$
$972$	−9.16775	−0.294056
$973$	−17.3421	−0.555961
$974$	47.6247	1.52599
$975$	0	0
$976$	10.4286	0.333811
$977$	33.4315	1.06957	0.534784	−	0.844988i	$-0.320393\pi$
$977$	33.4315	1.06957	0.534784	+	0.844988i	$0.320393\pi$
$978$	−14.5225	−0.464378
$979$	59.5629	1.90364
$980$	−1.48232	−0.0473509
$981$	15.5391	0.496125
$982$	−10.4418	−0.333210
$983$	−48.2644	−1.53940	−0.769698	−	0.638408i	$-0.779593\pi$
$983$	−48.2644	−1.53940	−0.769698	+	0.638408i	$0.779593\pi$
$984$	10.5773	0.337193
$985$	−26.5731	−0.846689
$986$	−3.99639	−0.127271
$987$	13.8376	0.440456
$988$	0	0
$989$	−2.33931	−0.0743856
$990$	−16.8038	−0.534060
$991$	57.0084	1.81093	0.905466	−	0.424418i	$-0.139521\pi$
$991$	57.0084	1.81093	0.905466	+	0.424418i	$0.139521\pi$
$992$	23.2463	0.738070
$993$	18.7545	0.595157
$994$	10.3832	0.329334
$995$	43.8306	1.38952
$996$	8.03158	0.254490
$997$	−42.4795	−1.34534	−0.672670	−	0.739943i	$-0.734853\pi$
$997$	−42.4795	−1.34534	−0.672670	+	0.739943i	$0.734853\pi$
$998$	0.442598	0.0140102
$999$	0.194692	0.00615978

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.n.1.3	✓	6
7.6	odd	2		8281.2.a.cb.1.3		6
13.5	odd	4		1183.2.c.h.337.8		12
13.8	odd	4		1183.2.c.h.337.5		12
13.12	even	2		1183.2.a.o.1.4	yes	6
91.90	odd	2		8281.2.a.cg.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.n.1.3	✓	6	1.1	even	1	trivial
1183.2.a.o.1.4	yes	6	13.12	even	2
1183.2.c.h.337.5		12	13.8	odd	4
1183.2.c.h.337.8		12	13.5	odd	4
8281.2.a.cb.1.3		6	7.6	odd	2
8281.2.a.cg.1.4		6	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)

\(f(q)\)	\(=\)	\(q-1.10591 q^{2} +1.33192 q^{3} -0.776957 q^{4} +1.90785 q^{5} -1.47298 q^{6} +1.00000 q^{7} +3.07107 q^{8} -1.22600 q^{9} +O(q^{10})\)	\(q-1.10591 q^{2} +1.33192 q^{3} -0.776957 q^{4} +1.90785 q^{5} -1.47298 q^{6} +1.00000 q^{7} +3.07107 q^{8} -1.22600 q^{9} -2.10992 q^{10} -6.49608 q^{11} -1.03484 q^{12} -1.10591 q^{14} +2.54109 q^{15} -1.84242 q^{16} -7.14583 q^{17} +1.35585 q^{18} +4.93001 q^{19} -1.48232 q^{20} +1.33192 q^{21} +7.18410 q^{22} -6.24377 q^{23} +4.09041 q^{24} -1.36011 q^{25} -5.62868 q^{27} -0.776957 q^{28} -0.505701 q^{29} -2.81023 q^{30} -5.66349 q^{31} -4.10458 q^{32} -8.65223 q^{33} +7.90267 q^{34} +1.90785 q^{35} +0.952551 q^{36} -0.0345893 q^{37} -5.45216 q^{38} +5.85915 q^{40} +2.58588 q^{41} -1.47298 q^{42} +0.374663 q^{43} +5.04718 q^{44} -2.33903 q^{45} +6.90506 q^{46} +10.3893 q^{47} -2.45395 q^{48} +1.00000 q^{49} +1.50416 q^{50} -9.51764 q^{51} +2.66712 q^{53} +6.22482 q^{54} -12.3936 q^{55} +3.07107 q^{56} +6.56635 q^{57} +0.559261 q^{58} -1.28549 q^{59} -1.97432 q^{60} -5.66025 q^{61} +6.26333 q^{62} -1.22600 q^{63} +8.22416 q^{64} +9.56861 q^{66} +12.8913 q^{67} +5.55201 q^{68} -8.31617 q^{69} -2.10992 q^{70} -9.38877 q^{71} -3.76514 q^{72} -4.37566 q^{73} +0.0382527 q^{74} -1.81155 q^{75} -3.83040 q^{76} -6.49608 q^{77} +0.870391 q^{79} -3.51507 q^{80} -3.81891 q^{81} -2.85976 q^{82} -7.76117 q^{83} -1.03484 q^{84} -13.6332 q^{85} -0.414344 q^{86} -0.673550 q^{87} -19.9499 q^{88} -9.16906 q^{89} +2.58676 q^{90} +4.85114 q^{92} -7.54329 q^{93} -11.4896 q^{94} +9.40571 q^{95} -5.46696 q^{96} -1.40381 q^{97} -1.10591 q^{98} +7.96421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 8 q^{6} + 6 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 8 * q^6 + 6 * q^7 - 3 * q^8	\( 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 8 q^{6} + 6 q^{7} - 3 q^{8} - 14 q^{10} - 8 q^{11} - 23 q^{12} - 2 q^{14} - 3 q^{15} - 23 q^{17} - 26 q^{18} + 13 q^{19} + 4 q^{20} - 4 q^{21} - 4 q^{22} - 18 q^{23} + 26 q^{24} - 10 q^{25} - 10 q^{27} + 8 q^{28} - 15 q^{29} + 14 q^{30} - 3 q^{31} - 28 q^{32} - 3 q^{33} + 29 q^{34} - 2 q^{35} + 22 q^{36} + 13 q^{37} - 11 q^{38} - 14 q^{40} + 4 q^{41} + 8 q^{42} - 18 q^{43} + 19 q^{45} - 10 q^{46} + 16 q^{47} - 11 q^{48} + 6 q^{49} + 10 q^{50} + 14 q^{51} - 25 q^{53} + 31 q^{54} - 3 q^{56} + 4 q^{57} + 13 q^{58} - 18 q^{59} - 22 q^{60} + 16 q^{61} - 9 q^{62} - 7 q^{64} + 16 q^{66} - 16 q^{67} - 34 q^{68} - q^{69} - 14 q^{70} - 25 q^{71} - 39 q^{72} + 5 q^{73} - 14 q^{74} + 15 q^{75} - 7 q^{76} - 8 q^{77} + 2 q^{79} + 27 q^{80} - 6 q^{81} - 10 q^{82} + 7 q^{83} - 23 q^{84} - 9 q^{85} + 3 q^{86} + 13 q^{87} - 48 q^{88} + 10 q^{89} - 32 q^{92} - 35 q^{93} - 14 q^{94} - 7 q^{95} + 14 q^{96} + 5 q^{97} - 2 q^{98} + 15 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 8 * q^6 + 6 * q^7 - 3 * q^8 - 14 * q^10 - 8 * q^11 - 23 * q^12 - 2 * q^14 - 3 * q^15 - 23 * q^17 - 26 * q^18 + 13 * q^19 + 4 * q^20 - 4 * q^21 - 4 * q^22 - 18 * q^23 + 26 * q^24 - 10 * q^25 - 10 * q^27 + 8 * q^28 - 15 * q^29 + 14 * q^30 - 3 * q^31 - 28 * q^32 - 3 * q^33 + 29 * q^34 - 2 * q^35 + 22 * q^36 + 13 * q^37 - 11 * q^38 - 14 * q^40 + 4 * q^41 + 8 * q^42 - 18 * q^43 + 19 * q^45 - 10 * q^46 + 16 * q^47 - 11 * q^48 + 6 * q^49 + 10 * q^50 + 14 * q^51 - 25 * q^53 + 31 * q^54 - 3 * q^56 + 4 * q^57 + 13 * q^58 - 18 * q^59 - 22 * q^60 + 16 * q^61 - 9 * q^62 - 7 * q^64 + 16 * q^66 - 16 * q^67 - 34 * q^68 - q^69 - 14 * q^70 - 25 * q^71 - 39 * q^72 + 5 * q^73 - 14 * q^74 + 15 * q^75 - 7 * q^76 - 8 * q^77 + 2 * q^79 + 27 * q^80 - 6 * q^81 - 10 * q^82 + 7 * q^83 - 23 * q^84 - 9 * q^85 + 3 * q^86 + 13 * q^87 - 48 * q^88 + 10 * q^89 - 32 * q^92 - 35 * q^93 - 14 * q^94 - 7 * q^95 + 14 * q^96 + 5 * q^97 - 2 * q^98 + 15 * q^99

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