LMFDB - Embedded newform 5415.2.a.z.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5415,2,Mod(1,5415)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5415, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("5415.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5415 = 3 \cdot 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5415.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:	$43.2389926945$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.8797896.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 8x^{3} + 5x^{2} + 13x - 4 $ x^5 - x^4 - 8x^3 + 5x^2 + 13*x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 285)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.24750$ of defining polynomial
Character	$\chi$	$=$	5415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.24750 q^{2} +1.00000 q^{3} +3.05123 q^{4} +1.00000 q^{5} -2.24750 q^{6} +3.16638 q^{7} -2.36264 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.24750 q^{2} +1.00000 q^{3} +3.05123 q^{4} +1.00000 q^{5} -2.24750 q^{6} +3.16638 q^{7} -2.36264 q^{8} +1.00000 q^{9} -2.24750 q^{10} +4.81770 q^{11} +3.05123 q^{12} -1.16638 q^{13} -7.11643 q^{14} +1.00000 q^{15} -0.792439 q^{16} +5.84367 q^{17} -2.24750 q^{18} +3.05123 q^{20} +3.16638 q^{21} -10.8278 q^{22} -8.59746 q^{23} -2.36264 q^{24} +1.00000 q^{25} +2.62144 q^{26} +1.00000 q^{27} +9.66137 q^{28} -7.31269 q^{29} -2.24750 q^{30} +5.10247 q^{31} +6.50629 q^{32} +4.81770 q^{33} -13.1336 q^{34} +3.16638 q^{35} +3.05123 q^{36} -7.26885 q^{37} -1.16638 q^{39} -2.36264 q^{40} +2.49499 q^{41} -7.11643 q^{42} +1.16638 q^{43} +14.6999 q^{44} +1.00000 q^{45} +19.3227 q^{46} +9.37660 q^{47} -0.792439 q^{48} +3.02597 q^{49} -2.24750 q^{50} +5.84367 q^{51} -3.55890 q^{52} +2.75378 q^{53} -2.24750 q^{54} +4.81770 q^{55} -7.48103 q^{56} +16.4352 q^{58} +10.1125 q^{59} +3.05123 q^{60} -5.10837 q^{61} -11.4678 q^{62} +3.16638 q^{63} -13.0380 q^{64} -1.16638 q^{65} -10.8278 q^{66} -1.03855 q^{67} +17.8304 q^{68} -8.59746 q^{69} -7.11643 q^{70} +4.32271 q^{71} -2.36264 q^{72} +3.63345 q^{73} +16.3367 q^{74} +1.00000 q^{75} +15.2547 q^{77} +2.62144 q^{78} +15.0765 q^{79} -0.792439 q^{80} +1.00000 q^{81} -5.60748 q^{82} -8.98408 q^{83} +9.66137 q^{84} +5.84367 q^{85} -2.62144 q^{86} -7.31269 q^{87} -11.3825 q^{88} -4.17228 q^{89} -2.24750 q^{90} -3.69321 q^{91} -26.2329 q^{92} +5.10247 q^{93} -21.0739 q^{94} +6.50629 q^{96} -2.00000 q^{97} -6.80086 q^{98} +4.81770 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} + 5 q^{3} + 7 q^{4} + 5 q^{5} + q^{6} + 2 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + q^2 + 5 * q^3 + 7 * q^4 + 5 * q^5 + q^6 + 2 * q^7 + 6 * q^8 + 5 * q^9	\( 5 q + q^{2} + 5 q^{3} + 7 q^{4} + 5 q^{5} + q^{6} + 2 q^{7} + 6 q^{8} + 5 q^{9} + q^{10} + 5 q^{11} + 7 q^{12} + 8 q^{13} + 4 q^{14} + 5 q^{15} + 7 q^{16} + 10 q^{17} + q^{18} + 7 q^{20} + 2 q^{21} - 2 q^{22} - 2 q^{23} + 6 q^{24} + 5 q^{25} - 2 q^{26} + 5 q^{27} + 10 q^{28} + 7 q^{29} + q^{30} + 9 q^{31} + 23 q^{32} + 5 q^{33} - 25 q^{34} + 2 q^{35} + 7 q^{36} - 6 q^{37} + 8 q^{39} + 6 q^{40} - 12 q^{41} + 4 q^{42} - 8 q^{43} + 16 q^{44} + 5 q^{45} + 20 q^{46} + 6 q^{47} + 7 q^{48} + 15 q^{49} + q^{50} + 10 q^{51} + 4 q^{52} - 8 q^{53} + q^{54} + 5 q^{55} - 36 q^{56} + 38 q^{58} + q^{59} + 7 q^{60} + 7 q^{61} + 15 q^{62} + 2 q^{63} + 14 q^{64} + 8 q^{65} - 2 q^{66} + 14 q^{67} - q^{68} - 2 q^{69} + 4 q^{70} + 27 q^{71} + 6 q^{72} + 26 q^{73} - 18 q^{74} + 5 q^{75} + 14 q^{77} - 2 q^{78} - 23 q^{79} + 7 q^{80} + 5 q^{81} - 36 q^{82} - 12 q^{83} + 10 q^{84} + 10 q^{85} + 2 q^{86} + 7 q^{87} + 9 q^{89} + q^{90} - 46 q^{91} - 52 q^{92} + 9 q^{93} - 45 q^{94} + 23 q^{96} - 10 q^{97} - 21 q^{98} + 5 q^{99}+O(q^{100}) \) 5 * q + q^2 + 5 * q^3 + 7 * q^4 + 5 * q^5 + q^6 + 2 * q^7 + 6 * q^8 + 5 * q^9 + q^10 + 5 * q^11 + 7 * q^12 + 8 * q^13 + 4 * q^14 + 5 * q^15 + 7 * q^16 + 10 * q^17 + q^18 + 7 * q^20 + 2 * q^21 - 2 * q^22 - 2 * q^23 + 6 * q^24 + 5 * q^25 - 2 * q^26 + 5 * q^27 + 10 * q^28 + 7 * q^29 + q^30 + 9 * q^31 + 23 * q^32 + 5 * q^33 - 25 * q^34 + 2 * q^35 + 7 * q^36 - 6 * q^37 + 8 * q^39 + 6 * q^40 - 12 * q^41 + 4 * q^42 - 8 * q^43 + 16 * q^44 + 5 * q^45 + 20 * q^46 + 6 * q^47 + 7 * q^48 + 15 * q^49 + q^50 + 10 * q^51 + 4 * q^52 - 8 * q^53 + q^54 + 5 * q^55 - 36 * q^56 + 38 * q^58 + q^59 + 7 * q^60 + 7 * q^61 + 15 * q^62 + 2 * q^63 + 14 * q^64 + 8 * q^65 - 2 * q^66 + 14 * q^67 - q^68 - 2 * q^69 + 4 * q^70 + 27 * q^71 + 6 * q^72 + 26 * q^73 - 18 * q^74 + 5 * q^75 + 14 * q^77 - 2 * q^78 - 23 * q^79 + 7 * q^80 + 5 * q^81 - 36 * q^82 - 12 * q^83 + 10 * q^84 + 10 * q^85 + 2 * q^86 + 7 * q^87 + 9 * q^89 + q^90 - 46 * q^91 - 52 * q^92 + 9 * q^93 - 45 * q^94 + 23 * q^96 - 10 * q^97 - 21 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.24750	−1.58922	−0.794609	−	0.607121i	$-0.792324\pi$
$2$	−2.24750	−1.58922	−0.794609	+	0.607121i	$0.792324\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.05123	1.52562
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.24750	−0.917536
$7$	3.16638	1.19678	0.598390	−	0.801205i	$-0.295807\pi$
$7$	3.16638	1.19678	0.598390	+	0.801205i	$0.295807\pi$
$8$	−2.36264	−0.835320
$9$	1.00000	0.333333
$10$	−2.24750	−0.710720
$11$	4.81770	1.45259	0.726295	−	0.687383i	$-0.241240\pi$
$11$	4.81770	1.45259	0.726295	+	0.687383i	$0.241240\pi$
$12$	3.05123	0.880815
$13$	−1.16638	−0.323496	−0.161748	−	0.986832i	$-0.551713\pi$
$13$	−1.16638	−0.323496	−0.161748	+	0.986832i	$0.551713\pi$
$14$	−7.11643	−1.90195
$15$	1.00000	0.258199
$16$	−0.792439	−0.198110
$17$	5.84367	1.41730	0.708649	−	0.705561i	$-0.249305\pi$
$17$	5.84367	1.41730	0.708649	+	0.705561i	$0.249305\pi$
$18$	−2.24750	−0.529740
$19$	0	0
$19$	0	0
$20$	3.05123	0.682277
$21$	3.16638	0.690961
$22$	−10.8278	−2.30848
$23$	−8.59746	−1.79269	−0.896347	−	0.443353i	$-0.853789\pi$
$23$	−8.59746	−1.79269	−0.896347	+	0.443353i	$0.853789\pi$
$24$	−2.36264	−0.482272
$25$	1.00000	0.200000
$26$	2.62144	0.514106
$27$	1.00000	0.192450
$28$	9.66137	1.82583
$29$	−7.31269	−1.35793	−0.678966	−	0.734170i	$-0.737572\pi$
$29$	−7.31269	−1.35793	−0.678966	+	0.734170i	$0.737572\pi$
$30$	−2.24750	−0.410335
$31$	5.10247	0.916430	0.458215	−	0.888841i	$-0.348489\pi$
$31$	5.10247	0.916430	0.458215	+	0.888841i	$0.348489\pi$
$32$	6.50629	1.15016
$33$	4.81770	0.838654
$34$	−13.1336	−2.25240
$35$	3.16638	0.535216
$36$	3.05123	0.508539
$37$	−7.26885	−1.19499	−0.597496	−	0.801872i	$-0.703838\pi$
$37$	−7.26885	−1.19499	−0.597496	+	0.801872i	$0.703838\pi$
$38$	0	0
$39$	−1.16638	−0.186771
$40$	−2.36264	−0.373567
$41$	2.49499	0.389652	0.194826	−	0.980838i	$-0.437586\pi$
$41$	2.49499	0.389652	0.194826	+	0.980838i	$0.437586\pi$
$42$	−7.11643	−1.09809
$43$	1.16638	0.177872	0.0889358	−	0.996037i	$-0.471653\pi$
$43$	1.16638	0.177872	0.0889358	+	0.996037i	$0.471653\pi$
$44$	14.6999	2.21610
$45$	1.00000	0.149071
$46$	19.3227	2.84898
$47$	9.37660	1.36772	0.683859	−	0.729614i	$-0.260300\pi$
$47$	9.37660	1.36772	0.683859	+	0.729614i	$0.260300\pi$
$48$	−0.792439	−0.114379
$49$	3.02597	0.432282
$50$	−2.24750	−0.317844
$51$	5.84367	0.818278
$52$	−3.55890	−0.493531
$53$	2.75378	0.378261	0.189131	−	0.981952i	$-0.439433\pi$
$53$	2.75378	0.378261	0.189131	+	0.981952i	$0.439433\pi$
$54$	−2.24750	−0.305845
$55$	4.81770	0.649618
$56$	−7.48103	−0.999695
$57$	0	0
$58$	16.4352	2.15805
$59$	10.1125	1.31654	0.658269	−	0.752783i	$-0.271289\pi$
$59$	10.1125	1.31654	0.658269	+	0.752783i	$0.271289\pi$
$60$	3.05123	0.393913
$61$	−5.10837	−0.654059	−0.327030	−	0.945014i	$-0.606048\pi$
$61$	−5.10837	−0.654059	−0.327030	+	0.945014i	$0.606048\pi$
$62$	−11.4678	−1.45641
$63$	3.16638	0.398927
$64$	−13.0380	−1.62975
$65$	−1.16638	−0.144672
$66$	−10.8278	−1.33280
$67$	−1.03855	−0.126880	−0.0634398	−	0.997986i	$-0.520207\pi$
$67$	−1.03855	−0.126880	−0.0634398	+	0.997986i	$0.520207\pi$
$68$	17.8304	2.16226
$69$	−8.59746	−1.03501
$70$	−7.11643	−0.850576
$71$	4.32271	0.513011	0.256506	−	0.966543i	$-0.417429\pi$
$71$	4.32271	0.513011	0.256506	+	0.966543i	$0.417429\pi$
$72$	−2.36264	−0.278440
$73$	3.63345	0.425263	0.212632	−	0.977132i	$-0.431797\pi$
$73$	3.63345	0.425263	0.212632	+	0.977132i	$0.431797\pi$
$74$	16.3367	1.89910
$75$	1.00000	0.115470
$76$	0	0
$77$	15.2547	1.73843
$78$	2.62144	0.296819
$79$	15.0765	1.69624	0.848121	−	0.529803i	$-0.177734\pi$
$79$	15.0765	1.69624	0.848121	+	0.529803i	$0.177734\pi$
$80$	−0.792439	−0.0885974
$81$	1.00000	0.111111
$82$	−5.60748	−0.619242
$83$	−8.98408	−0.986131	−0.493065	−	0.869992i	$-0.664124\pi$
$83$	−8.98408	−0.986131	−0.493065	+	0.869992i	$0.664124\pi$
$84$	9.66137	1.05414
$85$	5.84367	0.633835
$86$	−2.62144	−0.282677
$87$	−7.31269	−0.784003
$88$	−11.3825	−1.21338
$89$	−4.17228	−0.442261	−0.221130	−	0.975244i	$-0.570975\pi$
$89$	−4.17228	−0.442261	−0.221130	+	0.975244i	$0.570975\pi$
$90$	−2.24750	−0.236907
$91$	−3.69321	−0.387154
$92$	−26.2329	−2.73496
$93$	5.10247	0.529101
$94$	−21.0739	−2.17360
$95$	0	0
$96$	6.50629	0.664045
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	−6.80086	−0.686991
$99$	4.81770	0.484197
$100$	3.05123	0.305123
$101$	10.9202	1.08660	0.543299	−	0.839540i	$-0.317175\pi$
$101$	10.9202	1.08660	0.543299	+	0.839540i	$0.317175\pi$
$102$	−13.1336	−1.30042
$103$	5.72113	0.563720	0.281860	−	0.959456i	$-0.409049\pi$
$103$	5.72113	0.563720	0.281860	+	0.959456i	$0.409049\pi$
$104$	2.75574	0.270223
$105$	3.16638	0.309007
$106$	−6.18912	−0.601140
$107$	2.98408	0.288482	0.144241	−	0.989543i	$-0.453926\pi$
$107$	2.98408	0.288482	0.144241	+	0.989543i	$0.453926\pi$
$108$	3.05123	0.293605
$109$	−12.8663	−1.23237	−0.616184	−	0.787602i	$-0.711322\pi$
$109$	−12.8663	−1.23237	−0.616184	+	0.787602i	$0.711322\pi$
$110$	−10.8278	−1.03239
$111$	−7.26885	−0.689929
$112$	−2.50917	−0.237094
$113$	16.7739	1.57796	0.788978	−	0.614422i	$-0.210611\pi$
$113$	16.7739	1.57796	0.788978	+	0.614422i	$0.210611\pi$
$114$	0	0
$115$	−8.59746	−0.801717
$116$	−22.3127	−2.07168
$117$	−1.16638	−0.107832
$118$	−22.7278	−2.09227
$119$	18.5033	1.69619
$120$	−2.36264	−0.215679
$121$	12.2102	1.11002
$122$	11.4810	1.03944
$123$	2.49499	0.224966
$124$	15.5688	1.39812
$125$	1.00000	0.0894427
$126$	−7.11643	−0.633982
$127$	−0.102468	−0.00909255	−0.00454628	−	0.999990i	$-0.501447\pi$
$127$	−0.102468	−0.00909255	−0.00454628	+	0.999990i	$0.501447\pi$
$128$	16.2902	1.43986
$129$	1.16638	0.102694
$130$	2.62144	0.229915
$131$	13.5673	1.18538	0.592691	−	0.805430i	$-0.298065\pi$
$131$	13.5673	1.18538	0.592691	+	0.805430i	$0.298065\pi$
$132$	14.6999	1.27946
$133$	0	0
$134$	2.33414	0.201639
$135$	1.00000	0.0860663
$136$	−13.8065	−1.18390
$137$	15.8437	1.35362	0.676808	−	0.736159i	$-0.263363\pi$
$137$	15.8437	1.35362	0.676808	+	0.736159i	$0.263363\pi$
$138$	19.3227	1.64486
$139$	−4.31269	−0.365797	−0.182899	−	0.983132i	$-0.558548\pi$
$139$	−4.31269	−0.365797	−0.182899	+	0.983132i	$0.558548\pi$
$140$	9.66137	0.816535
$141$	9.37660	0.789652
$142$	−9.71527	−0.815287
$143$	−5.61928	−0.469908
$144$	−0.792439	−0.0660366
$145$	−7.31269	−0.607286
$146$	−8.16617	−0.675837
$147$	3.02597	0.249578
$148$	−22.1790	−1.82310
$149$	9.57738	0.784610	0.392305	−	0.919835i	$-0.371678\pi$
$149$	9.57738	0.784610	0.392305	+	0.919835i	$0.371678\pi$
$150$	−2.24750	−0.183507
$151$	−1.90169	−0.154757	−0.0773786	−	0.997002i	$-0.524655\pi$
$151$	−1.90169	−0.154757	−0.0773786	+	0.997002i	$0.524655\pi$
$152$	0	0
$153$	5.84367	0.472433
$154$	−34.2848	−2.76275
$155$	5.10247	0.409840
$156$	−3.55890	−0.284940
$157$	−18.3867	−1.46742	−0.733708	−	0.679465i	$-0.762212\pi$
$157$	−18.3867	−1.46742	−0.733708	+	0.679465i	$0.762212\pi$
$158$	−33.8844	−2.69570
$159$	2.75378	0.218389
$160$	6.50629	0.514367
$161$	−27.2228	−2.14546
$162$	−2.24750	−0.176580
$163$	−10.6234	−0.832091	−0.416046	−	0.909344i	$-0.636584\pi$
$163$	−10.6234	−0.832091	−0.416046	+	0.909344i	$0.636584\pi$
$164$	7.61280	0.594460
$165$	4.81770	0.375057
$166$	20.1917	1.56718
$167$	−14.6195	−1.13129	−0.565645	−	0.824649i	$-0.691373\pi$
$167$	−14.6195	−1.13129	−0.565645	+	0.824649i	$0.691373\pi$
$168$	−7.48103	−0.577174
$169$	−11.6396	−0.895350
$170$	−13.1336	−1.00730
$171$	0	0
$172$	3.55890	0.271364
$173$	0.657216	0.0499672	0.0249836	−	0.999688i	$-0.492047\pi$
$173$	0.657216	0.0499672	0.0249836	+	0.999688i	$0.492047\pi$
$174$	16.4352	1.24595
$175$	3.16638	0.239356
$176$	−3.81773	−0.287773
$177$	10.1125	0.760104
$178$	9.37718	0.702849
$179$	23.2647	1.73889	0.869444	−	0.494032i	$-0.164477\pi$
$179$	23.2647	1.73889	0.869444	+	0.494032i	$0.164477\pi$
$180$	3.05123	0.227426
$181$	−1.45115	−0.107863	−0.0539316	−	0.998545i	$-0.517175\pi$
$181$	−1.45115	−0.107863	−0.0539316	+	0.998545i	$0.517175\pi$
$182$	8.30047	0.615272
$183$	−5.10837	−0.377621
$184$	20.3127	1.49747
$185$	−7.26885	−0.534416
$186$	−11.4678	−0.840858
$187$	28.1531	2.05876
$188$	28.6102	2.08661
$189$	3.16638	0.230320
$190$	0	0
$191$	19.0598	1.37912	0.689559	−	0.724229i	$-0.257804\pi$
$191$	19.0598	1.37912	0.689559	+	0.724229i	$0.257804\pi$
$192$	−13.0380	−0.940935
$193$	−15.6958	−1.12981	−0.564903	−	0.825157i	$-0.691086\pi$
$193$	−15.6958	−1.12981	−0.564903	+	0.825157i	$0.691086\pi$
$194$	4.49499	0.322721
$195$	−1.16638	−0.0835263
$196$	9.23296	0.659497
$197$	8.23620	0.586805	0.293402	−	0.955989i	$-0.405212\pi$
$197$	8.23620	0.586805	0.293402	+	0.955989i	$0.405212\pi$
$198$	−10.8278	−0.769495
$199$	17.3892	1.23269	0.616343	−	0.787478i	$-0.288613\pi$
$199$	17.3892	1.23269	0.616343	+	0.787478i	$0.288613\pi$
$200$	−2.36264	−0.167064
$201$	−1.03855	−0.0732539
$202$	−24.5430	−1.72684
$203$	−23.1548	−1.62515
$204$	17.8304	1.24838
$205$	2.49499	0.174258
$206$	−12.8582	−0.895874
$207$	−8.59746	−0.597565
$208$	0.924287	0.0640878
$209$	0	0
$210$	−7.11643	−0.491080
$211$	−21.0824	−1.45137	−0.725687	−	0.688025i	$-0.758478\pi$
$211$	−21.0824	−1.45137	−0.725687	+	0.688025i	$0.758478\pi$
$212$	8.40244	0.577082
$213$	4.32271	0.296187
$214$	−6.70671	−0.458461
$215$	1.16638	0.0795466
$216$	−2.36264	−0.160757
$217$	16.1564	1.09677
$218$	28.9170	1.95850
$219$	3.63345	0.245526
$220$	14.6999	0.991069
$221$	−6.81595	−0.458491
$222$	16.3367	1.09645
$223$	−0.929608	−0.0622511	−0.0311256	−	0.999515i	$-0.509909\pi$
$223$	−0.929608	−0.0622511	−0.0311256	+	0.999515i	$0.509909\pi$
$224$	20.6014	1.37649
$225$	1.00000	0.0666667
$226$	−37.6992	−2.50772
$227$	−2.53770	−0.168433	−0.0842165	−	0.996447i	$-0.526839\pi$
$227$	−2.53770	−0.168433	−0.0842165	+	0.996447i	$0.526839\pi$
$228$	0	0
$229$	−0.912322	−0.0602879	−0.0301440	−	0.999546i	$-0.509597\pi$
$229$	−0.912322	−0.0602879	−0.0301440	+	0.999546i	$0.509597\pi$
$230$	19.3227	1.27410
$231$	15.2547	1.00368
$232$	17.2773	1.13431
$233$	−22.9788	−1.50539	−0.752697	−	0.658368i	$-0.771247\pi$
$233$	−22.9788	−1.50539	−0.752697	+	0.658368i	$0.771247\pi$
$234$	2.62144	0.171369
$235$	9.37660	0.611662
$236$	30.8557	2.00853
$237$	15.0765	0.979326
$238$	−41.5861	−2.69563
$239$	21.1849	1.37033	0.685167	−	0.728386i	$-0.259729\pi$
$239$	21.1849	1.37033	0.685167	+	0.728386i	$0.259729\pi$
$240$	−0.792439	−0.0511517
$241$	4.30263	0.277157	0.138578	−	0.990351i	$-0.455747\pi$
$241$	4.30263	0.277157	0.138578	+	0.990351i	$0.455747\pi$
$242$	−27.4424	−1.76406
$243$	1.00000	0.0641500
$244$	−15.5868	−0.997844
$245$	3.02597	0.193322
$246$	−5.60748	−0.357520
$247$	0	0
$248$	−12.0553	−0.765513
$249$	−8.98408	−0.569343
$250$	−2.24750	−0.142144
$251$	−13.5430	−0.854826	−0.427413	−	0.904057i	$-0.640575\pi$
$251$	−13.5430	−0.854826	−0.427413	+	0.904057i	$0.640575\pi$
$252$	9.66137	0.608609
$253$	−41.4200	−2.60405
$254$	0.230296	0.0144501
$255$	5.84367	0.365945
$256$	−10.5362	−0.658513
$257$	21.9202	1.36734	0.683672	−	0.729789i	$-0.260382\pi$
$257$	21.9202	1.36734	0.683672	+	0.729789i	$0.260382\pi$
$258$	−2.62144	−0.163204
$259$	−23.0160	−1.43014
$260$	−3.55890	−0.220714
$261$	−7.31269	−0.452644
$262$	−30.4925	−1.88383
$263$	−19.1729	−1.18225	−0.591126	−	0.806579i	$-0.701316\pi$
$263$	−19.1729	−1.18225	−0.591126	+	0.806579i	$0.701316\pi$
$264$	−11.3825	−0.700545
$265$	2.75378	0.169164
$266$	0	0
$267$	−4.17228	−0.255339
$268$	−3.16887	−0.193570
$269$	−20.4051	−1.24412	−0.622062	−	0.782968i	$-0.713705\pi$
$269$	−20.4051	−1.24412	−0.622062	+	0.782968i	$0.713705\pi$
$270$	−2.24750	−0.136778
$271$	16.3221	0.991499	0.495749	−	0.868466i	$-0.334893\pi$
$271$	16.3221	0.991499	0.495749	+	0.868466i	$0.334893\pi$
$272$	−4.63076	−0.280781
$273$	−3.69321	−0.223523
$274$	−35.6086	−2.15119
$275$	4.81770	0.290518
$276$	−26.2329	−1.57903
$277$	7.08065	0.425435	0.212717	−	0.977114i	$-0.431769\pi$
$277$	7.08065	0.425435	0.212717	+	0.977114i	$0.431769\pi$
$278$	9.69275	0.581332
$279$	5.10247	0.305477
$280$	−7.48103	−0.447077
$281$	10.1226	0.603862	0.301931	−	0.953330i	$-0.402369\pi$
$281$	10.1226	0.603862	0.301931	+	0.953330i	$0.402369\pi$
$282$	−21.0739	−1.25493
$283$	14.5111	0.862596	0.431298	−	0.902210i	$-0.358056\pi$
$283$	14.5111	0.862596	0.431298	+	0.902210i	$0.358056\pi$
$284$	13.1896	0.782658
$285$	0	0
$286$	12.6293	0.746786
$287$	7.90009	0.466328
$288$	6.50629	0.383387
$289$	17.1485	1.00874
$290$	16.4352	0.965110
$291$	−2.00000	−0.117242
$292$	11.0865	0.648789
$293$	−6.10837	−0.356855	−0.178427	−	0.983953i	$-0.557101\pi$
$293$	−6.10837	−0.356855	−0.178427	+	0.983953i	$0.557101\pi$
$294$	−6.80086	−0.396634
$295$	10.1125	0.588774
$296$	17.1737	0.998201
$297$	4.81770	0.279551
$298$	−21.5251	−1.24692
$299$	10.0279	0.579930
$300$	3.05123	0.176163
$301$	3.69321	0.212873
$302$	4.27403	0.245943
$303$	10.9202	0.627347
$304$	0	0
$305$	−5.10837	−0.292504
$306$	−13.1336	−0.750799
$307$	−12.5429	−0.715864	−0.357932	−	0.933748i	$-0.616518\pi$
$307$	−12.5429	−0.715864	−0.357932	+	0.933748i	$0.616518\pi$
$308$	46.5456	2.65218
$309$	5.72113	0.325464
$310$	−11.4678	−0.651326
$311$	−17.9682	−1.01888	−0.509440	−	0.860506i	$-0.670148\pi$
$311$	−17.9682	−1.01888	−0.509440	+	0.860506i	$0.670148\pi$
$312$	2.75574	0.156013
$313$	7.54473	0.426453	0.213227	−	0.977003i	$-0.431603\pi$
$313$	7.54473	0.426453	0.213227	+	0.977003i	$0.431603\pi$
$314$	41.3239	2.33204
$315$	3.16638	0.178405
$316$	46.0020	2.58782
$317$	−4.51701	−0.253701	−0.126850	−	0.991922i	$-0.540487\pi$
$317$	−4.51701	−0.253701	−0.126850	+	0.991922i	$0.540487\pi$
$318$	−6.18912	−0.347068
$319$	−35.2303	−1.97252
$320$	−13.0380	−0.728845
$321$	2.98408	0.166555
$322$	61.1832	3.40961
$323$	0	0
$324$	3.05123	0.169513
$325$	−1.16638	−0.0646992
$326$	23.8761	1.32238
$327$	−12.8663	−0.711508
$328$	−5.89477	−0.325484
$329$	29.6899	1.63686
$330$	−10.8278	−0.596048
$331$	−16.7674	−0.921619	−0.460809	−	0.887499i	$-0.652441\pi$
$331$	−16.7674	−0.921619	−0.460809	+	0.887499i	$0.652441\pi$
$332$	−27.4125	−1.50446
$333$	−7.26885	−0.398331
$334$	32.8572	1.79787
$335$	−1.03855	−0.0567423
$336$	−2.50917	−0.136886
$337$	17.4336	0.949671	0.474835	−	0.880075i	$-0.342508\pi$
$337$	17.4336	0.949671	0.474835	+	0.880075i	$0.342508\pi$
$338$	26.1598	1.42291
$339$	16.7739	0.911033
$340$	17.8304	0.966990
$341$	24.5822	1.33120
$342$	0	0
$343$	−12.5833	−0.679433
$344$	−2.75574	−0.148580
$345$	−8.59746	−0.462872
$346$	−1.47709	−0.0794089
$347$	−31.0891	−1.66895	−0.834475	−	0.551045i	$-0.814229\pi$
$347$	−31.0891	−1.66895	−0.834475	+	0.551045i	$0.814229\pi$
$348$	−22.3127	−1.19609
$349$	0.887477	0.0475055	0.0237528	−	0.999718i	$-0.492439\pi$
$349$	0.887477	0.0475055	0.0237528	+	0.999718i	$0.492439\pi$
$350$	−7.11643	−0.380389
$351$	−1.16638	−0.0622569
$352$	31.3453	1.67071
$353$	−5.27079	−0.280536	−0.140268	−	0.990114i	$-0.544796\pi$
$353$	−5.27079	−0.280536	−0.140268	+	0.990114i	$0.544796\pi$
$354$	−22.7278	−1.20797
$355$	4.32271	0.229426
$356$	−12.7306	−0.674721
$357$	18.5033	0.979299
$358$	−52.2874	−2.76347
$359$	−27.2630	−1.43889	−0.719443	−	0.694552i	$-0.755603\pi$
$359$	−27.2630	−1.43889	−0.719443	+	0.694552i	$0.755603\pi$
$360$	−2.36264	−0.124522
$361$	0	0
$362$	3.26145	0.171418
$363$	12.2102	0.640870
$364$	−11.2688	−0.590648
$365$	3.63345	0.190184
$366$	11.4810	0.600123
$367$	1.37132	0.0715822	0.0357911	−	0.999359i	$-0.488605\pi$
$367$	1.37132	0.0715822	0.0357911	+	0.999359i	$0.488605\pi$
$368$	6.81296	0.355150
$369$	2.49499	0.129884
$370$	16.3367	0.849305
$371$	8.71953	0.452696
$372$	15.5688	0.807206
$373$	−33.1801	−1.71800	−0.859001	−	0.511974i	$-0.828914\pi$
$373$	−33.1801	−1.71800	−0.859001	+	0.511974i	$0.828914\pi$
$374$	−63.2739	−3.27181
$375$	1.00000	0.0516398
$376$	−22.1536	−1.14248
$377$	8.52939	0.439286
$378$	−7.11643	−0.366030
$379$	31.1642	1.60080	0.800399	−	0.599468i	$-0.204621\pi$
$379$	31.1642	1.60080	0.800399	+	0.599468i	$0.204621\pi$
$380$	0	0
$381$	−0.102468	−0.00524959
$382$	−42.8368	−2.19172
$383$	−29.6614	−1.51563	−0.757814	−	0.652471i	$-0.773732\pi$
$383$	−29.6614	−1.51563	−0.757814	+	0.652471i	$0.773732\pi$
$384$	16.2902	0.831306
$385$	15.2547	0.777450
$386$	35.2762	1.79551
$387$	1.16638	0.0592905
$388$	−6.10247	−0.309806
$389$	−20.0380	−1.01597	−0.507983	−	0.861367i	$-0.669609\pi$
$389$	−20.0380	−1.01597	−0.507983	+	0.861367i	$0.669609\pi$
$390$	2.62144	0.132742
$391$	−50.2407	−2.54078
$392$	−7.14930	−0.361094
$393$	13.5673	0.684381
$394$	−18.5108	−0.932561
$395$	15.0765	0.758582
$396$	14.6999	0.738699
$397$	−19.4708	−0.977211	−0.488606	−	0.872505i	$-0.662494\pi$
$397$	−19.4708	−0.977211	−0.488606	+	0.872505i	$0.662494\pi$
$398$	−39.0821	−1.95901
$399$	0	0
$400$	−0.792439	−0.0396220
$401$	36.7633	1.83587	0.917935	−	0.396731i	$-0.129855\pi$
$401$	36.7633	1.83587	0.917935	+	0.396731i	$0.129855\pi$
$402$	2.33414	0.116417
$403$	−5.95143	−0.296462
$404$	33.3200	1.65773
$405$	1.00000	0.0496904
$406$	52.0402	2.58271
$407$	−35.0191	−1.73583
$408$	−13.8065	−0.683524
$409$	12.5648	0.621290	0.310645	−	0.950526i	$-0.399455\pi$
$409$	12.5648	0.621290	0.310645	+	0.950526i	$0.399455\pi$
$410$	−5.60748	−0.276934
$411$	15.8437	0.781511
$412$	17.4565	0.860020
$413$	32.0201	1.57561
$414$	19.3227	0.949661
$415$	−8.98408	−0.441011
$416$	−7.58882	−0.372072
$417$	−4.31269	−0.211193
$418$	0	0
$419$	23.8674	1.16600	0.583000	−	0.812472i	$-0.301879\pi$
$419$	23.8674	1.16600	0.583000	+	0.812472i	$0.301879\pi$
$420$	9.66137	0.471427
$421$	6.61007	0.322155	0.161078	−	0.986942i	$-0.448503\pi$
$421$	6.61007	0.322155	0.161078	+	0.986942i	$0.448503\pi$
$422$	47.3827	2.30655
$423$	9.37660	0.455906
$424$	−6.50621	−0.315969
$425$	5.84367	0.283460
$426$	−9.71527	−0.470706
$427$	−16.1750	−0.782765
$428$	9.10513	0.440113
$429$	−5.61928	−0.271301
$430$	−2.62144	−0.126417
$431$	7.46312	0.359486	0.179743	−	0.983714i	$-0.442473\pi$
$431$	7.46312	0.359486	0.179743	+	0.983714i	$0.442473\pi$
$432$	−0.792439	−0.0381263
$433$	−21.5951	−1.03780	−0.518898	−	0.854836i	$-0.673658\pi$
$433$	−21.5951	−1.03780	−0.518898	+	0.854836i	$0.673658\pi$
$434$	−36.3113	−1.74300
$435$	−7.31269	−0.350617
$436$	−39.2581	−1.88012
$437$	0	0
$438$	−8.16617	−0.390195
$439$	33.7480	1.61070	0.805351	−	0.592798i	$-0.201977\pi$
$439$	33.7480	1.61070	0.805351	+	0.592798i	$0.201977\pi$
$440$	−11.3825	−0.542640
$441$	3.02597	0.144094
$442$	15.3188	0.728642
$443$	−7.70106	−0.365888	−0.182944	−	0.983123i	$-0.558563\pi$
$443$	−7.70106	−0.365888	−0.182944	+	0.983123i	$0.558563\pi$
$444$	−22.1790	−1.05257
$445$	−4.17228	−0.197785
$446$	2.08929	0.0989307
$447$	9.57738	0.452995
$448$	−41.2832	−1.95045
$449$	−4.84306	−0.228558	−0.114279	−	0.993449i	$-0.536456\pi$
$449$	−4.84306	−0.228558	−0.114279	+	0.993449i	$0.536456\pi$
$450$	−2.24750	−0.105948
$451$	12.0201	0.566005
$452$	51.1811	2.40736
$453$	−1.90169	−0.0893491
$454$	5.70347	0.267677
$455$	−3.69321	−0.173140
$456$	0	0
$457$	−18.2322	−0.852868	−0.426434	−	0.904519i	$-0.640230\pi$
$457$	−18.2322	−0.852868	−0.426434	+	0.904519i	$0.640230\pi$
$458$	2.05044	0.0958107
$459$	5.84367	0.272759
$460$	−26.2329	−1.22311
$461$	−32.5556	−1.51627	−0.758134	−	0.652099i	$-0.773888\pi$
$461$	−32.5556	−1.51627	−0.758134	+	0.652099i	$0.773888\pi$
$462$	−34.2848	−1.59507
$463$	−30.9666	−1.43914	−0.719569	−	0.694421i	$-0.755661\pi$
$463$	−30.9666	−1.43914	−0.719569	+	0.694421i	$0.755661\pi$
$464$	5.79486	0.269020
$465$	5.10247	0.236621
$466$	51.6448	2.39240
$467$	−26.4956	−1.22607	−0.613036	−	0.790055i	$-0.710052\pi$
$467$	−26.4956	−1.22607	−0.613036	+	0.790055i	$0.710052\pi$
$468$	−3.55890	−0.164510
$469$	−3.28846	−0.151847
$470$	−21.0739	−0.972065
$471$	−18.3867	−0.847212
$472$	−23.8923	−1.09973
$473$	5.61928	0.258375
$474$	−33.8844	−1.55636
$475$	0	0
$476$	56.4579	2.58774
$477$	2.75378	0.126087
$478$	−47.6129	−2.17776
$479$	−23.1452	−1.05753	−0.528766	−	0.848768i	$-0.677345\pi$
$479$	−23.1452	−1.05753	−0.528766	+	0.848768i	$0.677345\pi$
$480$	6.50629	0.296970
$481$	8.47826	0.386575
$482$	−9.67015	−0.440463
$483$	−27.2228	−1.23868
$484$	37.2562	1.69347
$485$	−2.00000	−0.0908153
$486$	−2.24750	−0.101948
$487$	38.3075	1.73588	0.867939	−	0.496671i	$-0.165445\pi$
$487$	38.3075	1.73588	0.867939	+	0.496671i	$0.165445\pi$
$488$	12.0692	0.546349
$489$	−10.6234	−0.480408
$490$	−6.80086	−0.307232
$491$	23.7745	1.07293	0.536464	−	0.843923i	$-0.319760\pi$
$491$	23.7745	1.07293	0.536464	+	0.843923i	$0.319760\pi$
$492$	7.61280	0.343211
$493$	−42.7330	−1.92460
$494$	0	0
$495$	4.81770	0.216539
$496$	−4.04340	−0.181554
$497$	13.6873	0.613961
$498$	20.1917	0.904811
$499$	0.421635	0.0188750	0.00943749	−	0.999955i	$-0.496996\pi$
$499$	0.421635	0.0188750	0.00943749	+	0.999955i	$0.496996\pi$
$500$	3.05123	0.136455
$501$	−14.6195	−0.653150
$502$	30.4378	1.35851
$503$	27.4655	1.22463	0.612313	−	0.790615i	$-0.290239\pi$
$503$	27.4655	1.22463	0.612313	+	0.790615i	$0.290239\pi$
$504$	−7.48103	−0.333232
$505$	10.9202	0.485941
$506$	93.0912	4.13841
$507$	−11.6396	−0.516931
$508$	−0.312653	−0.0138718
$509$	−7.83777	−0.347403	−0.173702	−	0.984798i	$-0.555573\pi$
$509$	−7.83777	−0.347403	−0.173702	+	0.984798i	$0.555573\pi$
$510$	−13.1336	−0.581567
$511$	11.5049	0.508947
$512$	−8.90034	−0.393343
$513$	0	0
$514$	−49.2655	−2.17301
$515$	5.72113	0.252103
$516$	3.55890	0.156672
$517$	45.1736	1.98673
$518$	51.7282	2.27281
$519$	0.657216	0.0288486
$520$	2.75574	0.120847
$521$	4.93772	0.216325	0.108163	−	0.994133i	$-0.465503\pi$
$521$	4.93772	0.216325	0.108163	+	0.994133i	$0.465503\pi$
$522$	16.4352	0.719351
$523$	17.1198	0.748595	0.374297	−	0.927309i	$-0.377884\pi$
$523$	17.1198	0.748595	0.374297	+	0.927309i	$0.377884\pi$
$524$	41.3971	1.80844
$525$	3.16638	0.138192
$526$	43.0910	1.87886
$527$	29.8172	1.29886
$528$	−3.81773	−0.166146
$529$	50.9163	2.21375
$530$	−6.18912	−0.268838
$531$	10.1125	0.438846
$532$	0	0
$533$	−2.91011	−0.126051
$534$	9.37718	0.405790
$535$	2.98408	0.129013
$536$	2.45373	0.105985
$537$	23.2647	1.00395
$538$	45.8604	1.97718
$539$	14.5782	0.627929
$540$	3.05123	0.131304
$541$	−6.09893	−0.262213	−0.131107	−	0.991368i	$-0.541853\pi$
$541$	−6.09893	−0.262213	−0.131107	+	0.991368i	$0.541853\pi$
$542$	−36.6839	−1.57571
$543$	−1.45115	−0.0622749
$544$	38.0206	1.63012
$545$	−12.8663	−0.551132
$546$	8.30047	0.355227
$547$	22.9763	0.982396	0.491198	−	0.871048i	$-0.336559\pi$
$547$	22.9763	0.982396	0.491198	+	0.871048i	$0.336559\pi$
$548$	48.3428	2.06510
$549$	−5.10837	−0.218020
$550$	−10.8278	−0.461697
$551$	0	0
$552$	20.3127	0.864567
$553$	47.7380	2.03003
$554$	−15.9137	−0.676109
$555$	−7.26885	−0.308545
$556$	−13.1590	−0.558067
$557$	−6.98998	−0.296175	−0.148087	−	0.988974i	$-0.547312\pi$
$557$	−6.98998	−0.296175	−0.148087	+	0.988974i	$0.547312\pi$
$558$	−11.4678	−0.485469
$559$	−1.36045	−0.0575408
$560$	−2.50917	−0.106032
$561$	28.1531	1.18862
$562$	−22.7504	−0.959670
$563$	12.7111	0.535708	0.267854	−	0.963460i	$-0.413686\pi$
$563$	12.7111	0.535708	0.267854	+	0.963460i	$0.413686\pi$
$564$	28.6102	1.20471
$565$	16.7739	0.705683
$566$	−32.6136	−1.37085
$567$	3.16638	0.132976
$568$	−10.2130	−0.428529
$569$	28.0036	1.17397	0.586986	−	0.809597i	$-0.300315\pi$
$569$	28.0036	1.17397	0.586986	+	0.809597i	$0.300315\pi$
$570$	0	0
$571$	39.0506	1.63422	0.817108	−	0.576484i	$-0.195576\pi$
$571$	39.0506	1.63422	0.817108	+	0.576484i	$0.195576\pi$
$572$	−17.1457	−0.716899
$573$	19.0598	0.796234
$574$	−17.7554	−0.741097
$575$	−8.59746	−0.358539
$576$	−13.0380	−0.543249
$577$	18.5294	0.771389	0.385694	−	0.922627i	$-0.373962\pi$
$577$	18.5294	0.771389	0.385694	+	0.922627i	$0.373962\pi$
$578$	−38.5412	−1.60310
$579$	−15.6958	−0.652294
$580$	−22.3127	−0.926485
$581$	−28.4470	−1.18018
$582$	4.49499	0.186323
$583$	13.2669	0.549459
$584$	−8.58455	−0.355231
$585$	−1.16638	−0.0482240
$586$	13.7285	0.567120
$587$	19.2292	0.793673	0.396836	−	0.917889i	$-0.370108\pi$
$587$	19.2292	0.793673	0.396836	+	0.917889i	$0.370108\pi$
$588$	9.23296	0.380761
$589$	0	0
$590$	−22.7278	−0.935691
$591$	8.23620	0.338792
$592$	5.76012	0.236740
$593$	−31.0587	−1.27543	−0.637714	−	0.770273i	$-0.720120\pi$
$593$	−31.0587	−1.27543	−0.637714	+	0.770273i	$0.720120\pi$
$594$	−10.8278	−0.444268
$595$	18.5033	0.758561
$596$	29.2228	1.19701
$597$	17.3892	0.711692
$598$	−22.5377	−0.921635
$599$	9.69382	0.396079	0.198039	−	0.980194i	$-0.436543\pi$
$599$	9.69382	0.396079	0.198039	+	0.980194i	$0.436543\pi$
$600$	−2.36264	−0.0964545
$601$	−9.02069	−0.367962	−0.183981	−	0.982930i	$-0.558898\pi$
$601$	−9.02069	−0.367962	−0.183981	+	0.982930i	$0.558898\pi$
$602$	−8.30047	−0.338302
$603$	−1.03855	−0.0422932
$604$	−5.80249	−0.236100
$605$	12.2102	0.496416
$606$	−24.5430	−0.996992
$607$	38.5916	1.56638	0.783192	−	0.621780i	$-0.213590\pi$
$607$	38.5916	1.56638	0.783192	+	0.621780i	$0.213590\pi$
$608$	0	0
$609$	−23.1548	−0.938278
$610$	11.4810	0.464853
$611$	−10.9367	−0.442452
$612$	17.8304	0.720752
$613$	−20.7414	−0.837738	−0.418869	−	0.908047i	$-0.637573\pi$
$613$	−20.7414	−0.837738	−0.418869	+	0.908047i	$0.637573\pi$
$614$	28.1902	1.13766
$615$	2.49499	0.100608
$616$	−36.0413	−1.45215
$617$	−30.4010	−1.22390	−0.611949	−	0.790897i	$-0.709614\pi$
$617$	−30.4010	−1.22390	−0.611949	+	0.790897i	$0.709614\pi$
$618$	−12.8582	−0.517233
$619$	−9.69562	−0.389700	−0.194850	−	0.980833i	$-0.562422\pi$
$619$	−9.69562	−0.389700	−0.194850	+	0.980833i	$0.562422\pi$
$620$	15.5688	0.625259
$621$	−8.59746	−0.345004
$622$	40.3834	1.61922
$623$	−13.2110	−0.529289
$624$	0.924287	0.0370011
$625$	1.00000	0.0400000
$626$	−16.9567	−0.677728
$627$	0	0
$628$	−56.1020	−2.23871
$629$	−42.4768	−1.69366
$630$	−7.11643	−0.283525
$631$	−3.70262	−0.147399	−0.0736994	−	0.997281i	$-0.523481\pi$
$631$	−3.70262	−0.147399	−0.0736994	+	0.997281i	$0.523481\pi$
$632$	−35.6205	−1.41691
$633$	−21.0824	−0.837951
$634$	10.1520	0.403186
$635$	−0.102468	−0.00406631
$636$	8.40244	0.333178
$637$	−3.52944	−0.139842
$638$	79.1800	3.13477
$639$	4.32271	0.171004
$640$	16.2902	0.643927
$641$	−19.7959	−0.781890	−0.390945	−	0.920414i	$-0.627852\pi$
$641$	−19.7959	−0.781890	−0.390945	+	0.920414i	$0.627852\pi$
$642$	−6.70671	−0.264693
$643$	−5.26885	−0.207783	−0.103892	−	0.994589i	$-0.533129\pi$
$643$	−5.26885	−0.207783	−0.103892	+	0.994589i	$0.533129\pi$
$644$	−83.0632	−3.27315
$645$	1.16638	0.0459262
$646$	0	0
$647$	25.3370	0.996098	0.498049	−	0.867149i	$-0.334050\pi$
$647$	25.3370	0.996098	0.498049	+	0.867149i	$0.334050\pi$
$648$	−2.36264	−0.0928134
$649$	48.7191	1.91239
$650$	2.62144	0.102821
$651$	16.1564	0.633218
$652$	−32.4146	−1.26945
$653$	12.3697	0.484065	0.242032	−	0.970268i	$-0.422186\pi$
$653$	12.3697	0.484065	0.242032	+	0.970268i	$0.422186\pi$
$654$	28.9170	1.13074
$655$	13.5673	0.530119
$656$	−1.97713	−0.0771939
$657$	3.63345	0.141754
$658$	−66.7279	−2.60133
$659$	22.9101	0.892451	0.446226	−	0.894920i	$-0.352768\pi$
$659$	22.9101	0.892451	0.446226	+	0.894920i	$0.352768\pi$
$660$	14.6999	0.572194
$661$	−3.28163	−0.127641	−0.0638203	−	0.997961i	$-0.520328\pi$
$661$	−3.28163	−0.127641	−0.0638203	+	0.997961i	$0.520328\pi$
$662$	37.6846	1.46465
$663$	−6.81595	−0.264710
$664$	21.2262	0.823735
$665$	0	0
$666$	16.3367	0.633034
$667$	62.8705	2.43436
$668$	−44.6074	−1.72591
$669$	−0.929608	−0.0359407
$670$	2.33414	0.0901759
$671$	−24.6106	−0.950081
$672$	20.6014	0.794716
$673$	−29.2183	−1.12628	−0.563142	−	0.826360i	$-0.690408\pi$
$673$	−29.2183	−1.12628	−0.563142	+	0.826360i	$0.690408\pi$
$674$	−39.1820	−1.50923
$675$	1.00000	0.0384900
$676$	−35.5150	−1.36596
$677$	36.0085	1.38392	0.691960	−	0.721936i	$-0.256747\pi$
$677$	36.0085	1.38392	0.691960	+	0.721936i	$0.256747\pi$
$678$	−37.6992	−1.44783
$679$	−6.33276	−0.243029
$680$	−13.8065	−0.529456
$681$	−2.53770	−0.0972449
$682$	−55.2483	−2.11557
$683$	−32.7395	−1.25274	−0.626371	−	0.779525i	$-0.715460\pi$
$683$	−32.7395	−1.25274	−0.626371	+	0.779525i	$0.715460\pi$
$684$	0	0
$685$	15.8437	0.605356
$686$	28.2809	1.07977
$687$	−0.912322	−0.0348073
$688$	−0.924287	−0.0352381
$689$	−3.21196	−0.122366
$690$	19.3227	0.735604
$691$	−17.3452	−0.659842	−0.329921	−	0.944009i	$-0.607022\pi$
$691$	−17.3452	−0.659842	−0.329921	+	0.944009i	$0.607022\pi$
$692$	2.00532	0.0762308
$693$	15.2547	0.579477
$694$	69.8726	2.65233
$695$	−4.31269	−0.163590
$696$	17.2773	0.654893
$697$	14.5799	0.552253
$698$	−1.99460	−0.0754967
$699$	−22.9788	−0.869139
$700$	9.66137	0.365166
$701$	2.42436	0.0915668	0.0457834	−	0.998951i	$-0.485422\pi$
$701$	2.42436	0.0915668	0.0457834	+	0.998951i	$0.485422\pi$
$702$	2.62144	0.0989398
$703$	0	0
$704$	−62.8130	−2.36736
$705$	9.37660	0.353143
$706$	11.8461	0.445833
$707$	34.5774	1.30042
$708$	30.8557	1.15963
$709$	10.5076	0.394620	0.197310	−	0.980341i	$-0.436779\pi$
$709$	10.5076	0.394620	0.197310	+	0.980341i	$0.436779\pi$
$710$	−9.71527	−0.364607
$711$	15.0765	0.565414
$712$	9.85761	0.369430
$713$	−43.8683	−1.64288
$714$	−41.5861	−1.55632
$715$	−5.61928	−0.210149
$716$	70.9861	2.65288
$717$	21.1849	0.791163
$718$	61.2734	2.28670
$719$	−15.4832	−0.577427	−0.288713	−	0.957416i	$-0.593227\pi$
$719$	−15.4832	−0.577427	−0.288713	+	0.957416i	$0.593227\pi$
$720$	−0.792439	−0.0295325
$721$	18.1153	0.674648
$722$	0	0
$723$	4.30263	0.160017
$724$	−4.42780	−0.164558
$725$	−7.31269	−0.271586
$726$	−27.4424	−1.01848
$727$	18.0738	0.670320	0.335160	−	0.942161i	$-0.391210\pi$
$727$	18.0738	0.670320	0.335160	+	0.942161i	$0.391210\pi$
$728$	8.72574	0.323397
$729$	1.00000	0.0370370
$730$	−8.16617	−0.302243
$731$	6.81595	0.252097
$732$	−15.5868	−0.576106
$733$	−32.5312	−1.20157	−0.600784	−	0.799411i	$-0.705145\pi$
$733$	−32.5312	−1.20157	−0.600784	+	0.799411i	$0.705145\pi$
$734$	−3.08203	−0.113760
$735$	3.02597	0.111615
$736$	−55.9376	−2.06189
$737$	−5.00344	−0.184304
$738$	−5.60748	−0.206414
$739$	47.9647	1.76441	0.882205	−	0.470866i	$-0.156058\pi$
$739$	47.9647	1.76441	0.882205	+	0.470866i	$0.156058\pi$
$740$	−22.1790	−0.815315
$741$	0	0
$742$	−19.5971	−0.719433
$743$	25.7106	0.943230	0.471615	−	0.881804i	$-0.343671\pi$
$743$	25.7106	0.943230	0.471615	+	0.881804i	$0.343671\pi$
$744$	−12.0553	−0.441969
$745$	9.57738	0.350888
$746$	74.5722	2.73028
$747$	−8.98408	−0.328710
$748$	85.9016	3.14087
$749$	9.44874	0.345249
$750$	−2.24750	−0.0820669
$751$	9.11427	0.332584	0.166292	−	0.986077i	$-0.446821\pi$
$751$	9.11427	0.332584	0.166292	+	0.986077i	$0.446821\pi$
$752$	−7.43039	−0.270958
$753$	−13.5430	−0.493534
$754$	−19.1698	−0.698121
$755$	−1.90169	−0.0692095
$756$	9.66137	0.351381
$757$	−39.1916	−1.42444	−0.712222	−	0.701955i	$-0.752311\pi$
$757$	−39.1916	−1.42444	−0.712222	+	0.701955i	$0.752311\pi$
$758$	−70.0414	−2.54402
$759$	−41.4200	−1.50345
$760$	0	0
$761$	52.4574	1.90158	0.950790	−	0.309837i	$-0.100275\pi$
$761$	52.4574	1.90158	0.950790	+	0.309837i	$0.100275\pi$
$762$	0.230296	0.00834274
$763$	−40.7396	−1.47487
$764$	58.1559	2.10401
$765$	5.84367	0.211278
$766$	66.6639	2.40866
$767$	−11.7951	−0.425895
$768$	−10.5362	−0.380193
$769$	23.6572	0.853101	0.426551	−	0.904464i	$-0.359729\pi$
$769$	23.6572	0.853101	0.426551	+	0.904464i	$0.359729\pi$
$770$	−34.2848	−1.23554
$771$	21.9202	0.789437
$772$	−47.8915	−1.72365
$773$	5.35110	0.192466	0.0962328	−	0.995359i	$-0.469321\pi$
$773$	5.35110	0.192466	0.0962328	+	0.995359i	$0.469321\pi$
$774$	−2.62144	−0.0942256
$775$	5.10247	0.183286
$776$	4.72529	0.169628
$777$	−23.0160	−0.825693
$778$	45.0352	1.61459
$779$	0	0
$780$	−3.55890	−0.127429
$781$	20.8255	0.745195
$782$	112.916	4.03786
$783$	−7.31269	−0.261334
$784$	−2.39790	−0.0856393
$785$	−18.3867	−0.656248
$786$	−30.4925	−1.08763
$787$	−26.2322	−0.935078	−0.467539	−	0.883972i	$-0.654859\pi$
$787$	−26.2322	−0.935078	−0.467539	+	0.883972i	$0.654859\pi$
$788$	25.1306	0.895239
$789$	−19.1729	−0.682573
$790$	−33.8844	−1.20555
$791$	53.1126	1.88847
$792$	−11.3825	−0.404460
$793$	5.95831	0.211586
$794$	43.7605	1.55300
$795$	2.75378	0.0976667
$796$	53.0585	1.88061
$797$	−4.25354	−0.150668	−0.0753341	−	0.997158i	$-0.524002\pi$
$797$	−4.25354	−0.150668	−0.0753341	+	0.997158i	$0.524002\pi$
$798$	0	0
$799$	54.7938	1.93847
$800$	6.50629	0.230032
$801$	−4.17228	−0.147420
$802$	−82.6252	−2.91760
$803$	17.5049	0.617734
$804$	−3.16887	−0.111757
$805$	−27.2228	−0.959479
$806$	13.3758	0.471143
$807$	−20.4051	−0.718295
$808$	−25.8005	−0.907657
$809$	−12.2708	−0.431419	−0.215710	−	0.976458i	$-0.569206\pi$
$809$	−12.2708	−0.431419	−0.215710	+	0.976458i	$0.569206\pi$
$810$	−2.24750	−0.0789689
$811$	10.4512	0.366991	0.183495	−	0.983021i	$-0.441259\pi$
$811$	10.4512	0.366991	0.183495	+	0.983021i	$0.441259\pi$
$812$	−70.6506	−2.47935
$813$	16.3221	0.572442
$814$	78.7053	2.75862
$815$	−10.6234	−0.372123
$816$	−4.63076	−0.162109
$817$	0	0
$818$	−28.2393	−0.987365
$819$	−3.69321	−0.129051
$820$	7.61280	0.265850
$821$	10.0671	0.351343	0.175671	−	0.984449i	$-0.443790\pi$
$821$	10.0671	0.351343	0.175671	+	0.984449i	$0.443790\pi$
$822$	−35.6086	−1.24199
$823$	43.3948	1.51265	0.756324	−	0.654197i	$-0.226993\pi$
$823$	43.3948	1.51265	0.756324	+	0.654197i	$0.226993\pi$
$824$	−13.5170	−0.470887
$825$	4.81770	0.167731
$826$	−71.9650	−2.50398
$827$	14.7390	0.512525	0.256263	−	0.966607i	$-0.417509\pi$
$827$	14.7390	0.512525	0.256263	+	0.966607i	$0.417509\pi$
$828$	−26.2329	−0.911655
$829$	−54.5313	−1.89395	−0.946974	−	0.321309i	$-0.895877\pi$
$829$	−54.5313	−1.89395	−0.946974	+	0.321309i	$0.895877\pi$
$830$	20.1917	0.700863
$831$	7.08065	0.245625
$832$	15.2073	0.527217
$833$	17.6828	0.612673
$834$	9.69275	0.335632
$835$	−14.6195	−0.505928
$836$	0	0
$837$	5.10247	0.176367
$838$	−53.6419	−1.85303
$839$	−37.5263	−1.29555	−0.647777	−	0.761830i	$-0.724301\pi$
$839$	−37.5263	−1.29555	−0.647777	+	0.761830i	$0.724301\pi$
$840$	−7.48103	−0.258120
$841$	24.4754	0.843980
$842$	−14.8561	−0.511975
$843$	10.1226	0.348640
$844$	−64.3274	−2.21424
$845$	−11.6396	−0.400413
$846$	−21.0739	−0.724535
$847$	38.6622	1.32845
$848$	−2.18221	−0.0749373
$849$	14.5111	0.498020
$850$	−13.1336	−0.450480
$851$	62.4936	2.14225
$852$	13.1896	0.451868
$853$	1.75297	0.0600205	0.0300103	−	0.999550i	$-0.490446\pi$
$853$	1.75297	0.0600205	0.0300103	+	0.999550i	$0.490446\pi$
$854$	36.3533	1.24399
$855$	0	0
$856$	−7.05032	−0.240975
$857$	−30.5260	−1.04275	−0.521375	−	0.853328i	$-0.674581\pi$
$857$	−30.5260	−1.04275	−0.521375	+	0.853328i	$0.674581\pi$
$858$	12.6293	0.431157
$859$	7.26725	0.247955	0.123978	−	0.992285i	$-0.460435\pi$
$859$	7.26725	0.247955	0.123978	+	0.992285i	$0.460435\pi$
$860$	3.55890	0.121358
$861$	7.90009	0.269234
$862$	−16.7733	−0.571301
$863$	30.4383	1.03613	0.518066	−	0.855341i	$-0.326652\pi$
$863$	30.4383	1.03613	0.518066	+	0.855341i	$0.326652\pi$
$864$	6.50629	0.221348
$865$	0.657216	0.0223460
$866$	48.5350	1.64929
$867$	17.1485	0.582394
$868$	49.2968	1.67324
$869$	72.6342	2.46395
$870$	16.4352	0.557207
$871$	1.21135	0.0410450
$872$	30.3985	1.02942
$873$	−2.00000	−0.0676897
$874$	0	0
$875$	3.16638	0.107043
$876$	11.0865	0.374579
$877$	−46.6637	−1.57572	−0.787860	−	0.615855i	$-0.788811\pi$
$877$	−46.6637	−1.57572	−0.787860	+	0.615855i	$0.788811\pi$
$878$	−75.8484	−2.55976
$879$	−6.10837	−0.206030
$880$	−3.81773	−0.128696
$881$	−31.2809	−1.05388	−0.526939	−	0.849903i	$-0.676660\pi$
$881$	−31.2809	−1.05388	−0.526939	+	0.849903i	$0.676660\pi$
$882$	−6.80086	−0.228997
$883$	7.74117	0.260511	0.130256	−	0.991480i	$-0.458420\pi$
$883$	7.74117	0.260511	0.130256	+	0.991480i	$0.458420\pi$
$884$	−20.7971	−0.699481
$885$	10.1125	0.339929
$886$	17.3081	0.581476
$887$	4.99189	0.167611	0.0838056	−	0.996482i	$-0.473293\pi$
$887$	4.99189	0.167611	0.0838056	+	0.996482i	$0.473293\pi$
$888$	17.1737	0.576312
$889$	−0.324452	−0.0108818
$890$	9.37718	0.314324
$891$	4.81770	0.161399
$892$	−2.83645	−0.0949714
$893$	0	0
$894$	−21.5251	−0.719908
$895$	23.2647	0.777654
$896$	51.5810	1.72320
$897$	10.0279	0.334822
$898$	10.8848	0.363229
$899$	−37.3128	−1.24445
$900$	3.05123	0.101708
$901$	16.0922	0.536110
$902$	−27.0151	−0.899506
$903$	3.69321	0.122902
$904$	−39.6307	−1.31810
$905$	−1.45115	−0.0482379
$906$	4.27403	0.141995
$907$	−53.3987	−1.77307	−0.886537	−	0.462657i	$-0.846896\pi$
$907$	−53.3987	−1.77307	−0.886537	+	0.462657i	$0.846896\pi$
$908$	−7.74312	−0.256964
$909$	10.9202	0.362199
$910$	8.30047	0.275158
$911$	−22.8765	−0.757933	−0.378967	−	0.925410i	$-0.623720\pi$
$911$	−22.8765	−0.757933	−0.378967	+	0.925410i	$0.623720\pi$
$912$	0	0
$913$	−43.2826	−1.43244
$914$	40.9769	1.35539
$915$	−5.10837	−0.168877
$916$	−2.78371	−0.0919763
$917$	42.9593	1.41864
$918$	−13.1336	−0.433474
$919$	−3.88045	−0.128004	−0.0640021	−	0.997950i	$-0.520386\pi$
$919$	−3.88045	−0.128004	−0.0640021	+	0.997950i	$0.520386\pi$
$920$	20.3127	0.669691
$921$	−12.5429	−0.413304
$922$	73.1686	2.40968
$923$	−5.04193	−0.165957
$924$	46.5456	1.53124
$925$	−7.26885	−0.238998
$926$	69.5972	2.28711
$927$	5.72113	0.187907
$928$	−47.5785	−1.56184
$929$	51.7641	1.69833	0.849163	−	0.528131i	$-0.177107\pi$
$929$	51.7641	1.69833	0.849163	+	0.528131i	$0.177107\pi$
$930$	−11.4678	−0.376043
$931$	0	0
$932$	−70.1138	−2.29665
$933$	−17.9682	−0.588251
$934$	59.5488	1.94850
$935$	28.1531	0.920703
$936$	2.75574	0.0900743
$937$	−4.22187	−0.137923	−0.0689613	−	0.997619i	$-0.521968\pi$
$937$	−4.22187	−0.137923	−0.0689613	+	0.997619i	$0.521968\pi$
$938$	7.39079	0.241318
$939$	7.54473	0.246213
$940$	28.6102	0.933162
$941$	17.7653	0.579131	0.289566	−	0.957158i	$-0.406489\pi$
$941$	17.7653	0.579131	0.289566	+	0.957158i	$0.406489\pi$
$942$	41.3239	1.34641
$943$	−21.4506	−0.698527
$944$	−8.01356	−0.260819
$945$	3.16638	0.103002
$946$	−12.6293	−0.410614
$947$	13.4679	0.437649	0.218824	−	0.975764i	$-0.429778\pi$
$947$	13.4679	0.437649	0.218824	+	0.975764i	$0.429778\pi$
$948$	46.0020	1.49408
$949$	−4.23799	−0.137571
$950$	0	0
$951$	−4.51701	−0.146474
$952$	−43.7167	−1.41687
$953$	26.6779	0.864182	0.432091	−	0.901830i	$-0.357776\pi$
$953$	26.6779	0.864182	0.432091	+	0.901830i	$0.357776\pi$
$954$	−6.18912	−0.200380
$955$	19.0598	0.616760
$956$	64.6400	2.09061
$957$	−35.2303	−1.13883
$958$	52.0188	1.68065
$959$	50.1671	1.61998
$960$	−13.0380	−0.420799
$961$	−4.96482	−0.160156
$962$	−19.0548	−0.614353
$963$	2.98408	0.0961607
$964$	13.1283	0.422835
$965$	−15.6958	−0.505265
$966$	61.1832	1.96854
$967$	−14.2069	−0.456862	−0.228431	−	0.973560i	$-0.573360\pi$
$967$	−14.2069	−0.456862	−0.228431	+	0.973560i	$0.573360\pi$
$968$	−28.8484	−0.927222
$969$	0	0
$970$	4.49499	0.144325
$971$	−18.4124	−0.590883	−0.295442	−	0.955361i	$-0.595467\pi$
$971$	−18.4124	−0.590883	−0.295442	+	0.955361i	$0.595467\pi$
$972$	3.05123	0.0978684
$973$	−13.6556	−0.437779
$974$	−86.0959	−2.75869
$975$	−1.16638	−0.0373541
$976$	4.04807	0.129576
$977$	3.75672	0.120188	0.0600941	−	0.998193i	$-0.480860\pi$
$977$	3.75672	0.120188	0.0600941	+	0.998193i	$0.480860\pi$
$978$	23.8761	0.763474
$979$	−20.1008	−0.642424
$980$	9.23296	0.294936
$981$	−12.8663	−0.410790
$982$	−53.4331	−1.70512
$983$	11.4615	0.365566	0.182783	−	0.983153i	$-0.441489\pi$
$983$	11.4615	0.365566	0.182783	+	0.983153i	$0.441489\pi$
$984$	−5.89477	−0.187918
$985$	8.23620	0.262427
$986$	96.0421	3.05860
$987$	29.6899	0.945040
$988$	0	0
$989$	−10.0279	−0.318869
$990$	−10.8278	−0.344129
$991$	9.09896	0.289038	0.144519	−	0.989502i	$-0.453837\pi$
$991$	9.09896	0.289038	0.144519	+	0.989502i	$0.453837\pi$
$992$	33.1981	1.05404
$993$	−16.7674	−0.532097
$994$	−30.7622	−0.975719
$995$	17.3892	0.551274
$996$	−27.4125	−0.868599
$997$	24.6926	0.782023	0.391012	−	0.920386i	$-0.372125\pi$
$997$	24.6926	0.782023	0.391012	+	0.920386i	$0.372125\pi$
$998$	−0.947623	−0.0299965
$999$	−7.26885	−0.229976

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5415.2.a.z.1.1		5
19.8	odd	6		285.2.i.f.121.1	yes	10
19.12	odd	6		285.2.i.f.106.1	✓	10
19.18	odd	2		5415.2.a.y.1.5		5
57.8	even	6		855.2.k.i.406.5		10
57.50	even	6		855.2.k.i.676.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.i.f.106.1	✓	10	19.12	odd	6
285.2.i.f.121.1	yes	10	19.8	odd	6
855.2.k.i.406.5		10	57.8	even	6
855.2.k.i.676.5		10	57.50	even	6
5415.2.a.y.1.5		5	19.18	odd	2
5415.2.a.z.1.1		5	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 5415 = 3 \cdot 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5415.a (trivial)

\(f(q)\)	\(=\)	\(q-2.24750 q^{2} +1.00000 q^{3} +3.05123 q^{4} +1.00000 q^{5} -2.24750 q^{6} +3.16638 q^{7} -2.36264 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.24750 q^{2} +1.00000 q^{3} +3.05123 q^{4} +1.00000 q^{5} -2.24750 q^{6} +3.16638 q^{7} -2.36264 q^{8} +1.00000 q^{9} -2.24750 q^{10} +4.81770 q^{11} +3.05123 q^{12} -1.16638 q^{13} -7.11643 q^{14} +1.00000 q^{15} -0.792439 q^{16} +5.84367 q^{17} -2.24750 q^{18} +3.05123 q^{20} +3.16638 q^{21} -10.8278 q^{22} -8.59746 q^{23} -2.36264 q^{24} +1.00000 q^{25} +2.62144 q^{26} +1.00000 q^{27} +9.66137 q^{28} -7.31269 q^{29} -2.24750 q^{30} +5.10247 q^{31} +6.50629 q^{32} +4.81770 q^{33} -13.1336 q^{34} +3.16638 q^{35} +3.05123 q^{36} -7.26885 q^{37} -1.16638 q^{39} -2.36264 q^{40} +2.49499 q^{41} -7.11643 q^{42} +1.16638 q^{43} +14.6999 q^{44} +1.00000 q^{45} +19.3227 q^{46} +9.37660 q^{47} -0.792439 q^{48} +3.02597 q^{49} -2.24750 q^{50} +5.84367 q^{51} -3.55890 q^{52} +2.75378 q^{53} -2.24750 q^{54} +4.81770 q^{55} -7.48103 q^{56} +16.4352 q^{58} +10.1125 q^{59} +3.05123 q^{60} -5.10837 q^{61} -11.4678 q^{62} +3.16638 q^{63} -13.0380 q^{64} -1.16638 q^{65} -10.8278 q^{66} -1.03855 q^{67} +17.8304 q^{68} -8.59746 q^{69} -7.11643 q^{70} +4.32271 q^{71} -2.36264 q^{72} +3.63345 q^{73} +16.3367 q^{74} +1.00000 q^{75} +15.2547 q^{77} +2.62144 q^{78} +15.0765 q^{79} -0.792439 q^{80} +1.00000 q^{81} -5.60748 q^{82} -8.98408 q^{83} +9.66137 q^{84} +5.84367 q^{85} -2.62144 q^{86} -7.31269 q^{87} -11.3825 q^{88} -4.17228 q^{89} -2.24750 q^{90} -3.69321 q^{91} -26.2329 q^{92} +5.10247 q^{93} -21.0739 q^{94} +6.50629 q^{96} -2.00000 q^{97} -6.80086 q^{98} +4.81770 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 5 q^{3} + 7 q^{4} + 5 q^{5} + q^{6} + 2 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + q^2 + 5 * q^3 + 7 * q^4 + 5 * q^5 + q^6 + 2 * q^7 + 6 * q^8 + 5 * q^9	\( 5 q + q^{2} + 5 q^{3} + 7 q^{4} + 5 q^{5} + q^{6} + 2 q^{7} + 6 q^{8} + 5 q^{9} + q^{10} + 5 q^{11} + 7 q^{12} + 8 q^{13} + 4 q^{14} + 5 q^{15} + 7 q^{16} + 10 q^{17} + q^{18} + 7 q^{20} + 2 q^{21} - 2 q^{22} - 2 q^{23} + 6 q^{24} + 5 q^{25} - 2 q^{26} + 5 q^{27} + 10 q^{28} + 7 q^{29} + q^{30} + 9 q^{31} + 23 q^{32} + 5 q^{33} - 25 q^{34} + 2 q^{35} + 7 q^{36} - 6 q^{37} + 8 q^{39} + 6 q^{40} - 12 q^{41} + 4 q^{42} - 8 q^{43} + 16 q^{44} + 5 q^{45} + 20 q^{46} + 6 q^{47} + 7 q^{48} + 15 q^{49} + q^{50} + 10 q^{51} + 4 q^{52} - 8 q^{53} + q^{54} + 5 q^{55} - 36 q^{56} + 38 q^{58} + q^{59} + 7 q^{60} + 7 q^{61} + 15 q^{62} + 2 q^{63} + 14 q^{64} + 8 q^{65} - 2 q^{66} + 14 q^{67} - q^{68} - 2 q^{69} + 4 q^{70} + 27 q^{71} + 6 q^{72} + 26 q^{73} - 18 q^{74} + 5 q^{75} + 14 q^{77} - 2 q^{78} - 23 q^{79} + 7 q^{80} + 5 q^{81} - 36 q^{82} - 12 q^{83} + 10 q^{84} + 10 q^{85} + 2 q^{86} + 7 q^{87} + 9 q^{89} + q^{90} - 46 q^{91} - 52 q^{92} + 9 q^{93} - 45 q^{94} + 23 q^{96} - 10 q^{97} - 21 q^{98} + 5 q^{99}+O(q^{100}) \) 5 * q + q^2 + 5 * q^3 + 7 * q^4 + 5 * q^5 + q^6 + 2 * q^7 + 6 * q^8 + 5 * q^9 + q^10 + 5 * q^11 + 7 * q^12 + 8 * q^13 + 4 * q^14 + 5 * q^15 + 7 * q^16 + 10 * q^17 + q^18 + 7 * q^20 + 2 * q^21 - 2 * q^22 - 2 * q^23 + 6 * q^24 + 5 * q^25 - 2 * q^26 + 5 * q^27 + 10 * q^28 + 7 * q^29 + q^30 + 9 * q^31 + 23 * q^32 + 5 * q^33 - 25 * q^34 + 2 * q^35 + 7 * q^36 - 6 * q^37 + 8 * q^39 + 6 * q^40 - 12 * q^41 + 4 * q^42 - 8 * q^43 + 16 * q^44 + 5 * q^45 + 20 * q^46 + 6 * q^47 + 7 * q^48 + 15 * q^49 + q^50 + 10 * q^51 + 4 * q^52 - 8 * q^53 + q^54 + 5 * q^55 - 36 * q^56 + 38 * q^58 + q^59 + 7 * q^60 + 7 * q^61 + 15 * q^62 + 2 * q^63 + 14 * q^64 + 8 * q^65 - 2 * q^66 + 14 * q^67 - q^68 - 2 * q^69 + 4 * q^70 + 27 * q^71 + 6 * q^72 + 26 * q^73 - 18 * q^74 + 5 * q^75 + 14 * q^77 - 2 * q^78 - 23 * q^79 + 7 * q^80 + 5 * q^81 - 36 * q^82 - 12 * q^83 + 10 * q^84 + 10 * q^85 + 2 * q^86 + 7 * q^87 + 9 * q^89 + q^90 - 46 * q^91 - 52 * q^92 + 9 * q^93 - 45 * q^94 + 23 * q^96 - 10 * q^97 - 21 * q^98 + 5 * q^99

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