LMFDB - Embedded newform 8022.2.a.z.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8022,2,Mod(1,8022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8022, 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("8022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8022 = 2 \cdot 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8022.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:	$64.0559925015$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 53 x^{13} - x^{12} + 1068 x^{11} + 45 x^{10} - 10139 x^{9} - 615 x^{8} + 45390 x^{7} + \cdots + 4704 $ x^15 - 53x^13 - x^12 + 1068x^11 + 45x^10 - 10139x^9 - 615x^8 + 45390x^7 + 2130x^6 - 84842x^5 + 7822x^4 + 62828x^3 - 16144x^2 - 13616x + 4704
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$-4.12898$ of defining polynomial
Character	$\chi$	$=$	8022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.12898 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.12898 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.12898 q^{10} -0.209559 q^{11} +1.00000 q^{12} +2.02818 q^{13} -1.00000 q^{14} +4.12898 q^{15} +1.00000 q^{16} -6.22636 q^{17} -1.00000 q^{18} +7.05387 q^{19} +4.12898 q^{20} +1.00000 q^{21} +0.209559 q^{22} +4.78157 q^{23} -1.00000 q^{24} +12.0485 q^{25} -2.02818 q^{26} +1.00000 q^{27} +1.00000 q^{28} -6.72132 q^{29} -4.12898 q^{30} +3.59681 q^{31} -1.00000 q^{32} -0.209559 q^{33} +6.22636 q^{34} +4.12898 q^{35} +1.00000 q^{36} -4.94388 q^{37} -7.05387 q^{38} +2.02818 q^{39} -4.12898 q^{40} +3.48339 q^{41} -1.00000 q^{42} +10.4873 q^{43} -0.209559 q^{44} +4.12898 q^{45} -4.78157 q^{46} +2.83496 q^{47} +1.00000 q^{48} +1.00000 q^{49} -12.0485 q^{50} -6.22636 q^{51} +2.02818 q^{52} +0.180654 q^{53} -1.00000 q^{54} -0.865264 q^{55} -1.00000 q^{56} +7.05387 q^{57} +6.72132 q^{58} -1.70932 q^{59} +4.12898 q^{60} -5.32771 q^{61} -3.59681 q^{62} +1.00000 q^{63} +1.00000 q^{64} +8.37430 q^{65} +0.209559 q^{66} -2.99419 q^{67} -6.22636 q^{68} +4.78157 q^{69} -4.12898 q^{70} -5.25692 q^{71} -1.00000 q^{72} -1.40462 q^{73} +4.94388 q^{74} +12.0485 q^{75} +7.05387 q^{76} -0.209559 q^{77} -2.02818 q^{78} +10.0851 q^{79} +4.12898 q^{80} +1.00000 q^{81} -3.48339 q^{82} -2.56494 q^{83} +1.00000 q^{84} -25.7085 q^{85} -10.4873 q^{86} -6.72132 q^{87} +0.209559 q^{88} -10.5427 q^{89} -4.12898 q^{90} +2.02818 q^{91} +4.78157 q^{92} +3.59681 q^{93} -2.83496 q^{94} +29.1253 q^{95} -1.00000 q^{96} +13.1808 q^{97} -1.00000 q^{98} -0.209559 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} + 15 q^{3} + 15 q^{4} - 15 q^{6} + 15 q^{7} - 15 q^{8} + 15 q^{9}+O(q^{10}) $ 15 * q - 15 * q^2 + 15 * q^3 + 15 * q^4 - 15 * q^6 + 15 * q^7 - 15 * q^8 + 15 * q^9	$ 15 q - 15 q^{2} + 15 q^{3} + 15 q^{4} - 15 q^{6} + 15 q^{7} - 15 q^{8} + 15 q^{9} - 7 q^{11} + 15 q^{12} + 10 q^{13} - 15 q^{14} + 15 q^{16} - 3 q^{17} - 15 q^{18} + 12 q^{19} + 15 q^{21} + 7 q^{22} - q^{23} - 15 q^{24} + 31 q^{25} - 10 q^{26} + 15 q^{27} + 15 q^{28} - 3 q^{29} + 19 q^{31} - 15 q^{32} - 7 q^{33} + 3 q^{34} + 15 q^{36} + 25 q^{37} - 12 q^{38} + 10 q^{39} + 8 q^{41} - 15 q^{42} + 25 q^{43} - 7 q^{44} + q^{46} + 11 q^{47} + 15 q^{48} + 15 q^{49} - 31 q^{50} - 3 q^{51} + 10 q^{52} - 4 q^{53} - 15 q^{54} + 9 q^{55} - 15 q^{56} + 12 q^{57} + 3 q^{58} + 27 q^{61} - 19 q^{62} + 15 q^{63} + 15 q^{64} - 2 q^{65} + 7 q^{66} + 31 q^{67} - 3 q^{68} - q^{69} - 16 q^{71} - 15 q^{72} + 26 q^{73} - 25 q^{74} + 31 q^{75} + 12 q^{76} - 7 q^{77} - 10 q^{78} + 32 q^{79} + 15 q^{81} - 8 q^{82} + 7 q^{83} + 15 q^{84} + 26 q^{85} - 25 q^{86} - 3 q^{87} + 7 q^{88} - 11 q^{89} + 10 q^{91} - q^{92} + 19 q^{93} - 11 q^{94} - 8 q^{95} - 15 q^{96} + 30 q^{97} - 15 q^{98} - 7 q^{99}+O(q^{100}) $ 15 * q - 15 * q^2 + 15 * q^3 + 15 * q^4 - 15 * q^6 + 15 * q^7 - 15 * q^8 + 15 * q^9 - 7 * q^11 + 15 * q^12 + 10 * q^13 - 15 * q^14 + 15 * q^16 - 3 * q^17 - 15 * q^18 + 12 * q^19 + 15 * q^21 + 7 * q^22 - q^23 - 15 * q^24 + 31 * q^25 - 10 * q^26 + 15 * q^27 + 15 * q^28 - 3 * q^29 + 19 * q^31 - 15 * q^32 - 7 * q^33 + 3 * q^34 + 15 * q^36 + 25 * q^37 - 12 * q^38 + 10 * q^39 + 8 * q^41 - 15 * q^42 + 25 * q^43 - 7 * q^44 + q^46 + 11 * q^47 + 15 * q^48 + 15 * q^49 - 31 * q^50 - 3 * q^51 + 10 * q^52 - 4 * q^53 - 15 * q^54 + 9 * q^55 - 15 * q^56 + 12 * q^57 + 3 * q^58 + 27 * q^61 - 19 * q^62 + 15 * q^63 + 15 * q^64 - 2 * q^65 + 7 * q^66 + 31 * q^67 - 3 * q^68 - q^69 - 16 * q^71 - 15 * q^72 + 26 * q^73 - 25 * q^74 + 31 * q^75 + 12 * q^76 - 7 * q^77 - 10 * q^78 + 32 * q^79 + 15 * q^81 - 8 * q^82 + 7 * q^83 + 15 * q^84 + 26 * q^85 - 25 * q^86 - 3 * q^87 + 7 * q^88 - 11 * q^89 + 10 * q^91 - q^92 + 19 * q^93 - 11 * q^94 - 8 * q^95 - 15 * q^96 + 30 * q^97 - 15 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	4.12898	1.84654	0.923268	−	0.384157i	$-0.125508\pi$
$5$	4.12898	1.84654	0.923268	+	0.384157i	$0.125508\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−4.12898	−1.30570
$11$	−0.209559	−0.0631844	−0.0315922	−	0.999501i	$-0.510058\pi$
$11$	−0.209559	−0.0631844	−0.0315922	+	0.999501i	$0.510058\pi$
$12$	1.00000	0.288675
$13$	2.02818	0.562515	0.281258	−	0.959632i	$-0.409248\pi$
$13$	2.02818	0.562515	0.281258	+	0.959632i	$0.409248\pi$
$14$	−1.00000	−0.267261
$15$	4.12898	1.06610
$16$	1.00000	0.250000
$17$	−6.22636	−1.51011	−0.755057	−	0.655660i	$-0.772391\pi$
$17$	−6.22636	−1.51011	−0.755057	+	0.655660i	$0.772391\pi$
$18$	−1.00000	−0.235702
$19$	7.05387	1.61827	0.809134	−	0.587624i	$-0.199937\pi$
$19$	7.05387	1.61827	0.809134	+	0.587624i	$0.199937\pi$
$20$	4.12898	0.923268
$21$	1.00000	0.218218
$22$	0.209559	0.0446781
$23$	4.78157	0.997027	0.498514	−	0.866882i	$-0.333879\pi$
$23$	4.78157	0.997027	0.498514	+	0.866882i	$0.333879\pi$
$24$	−1.00000	−0.204124
$25$	12.0485	2.40970
$26$	−2.02818	−0.397758
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	−6.72132	−1.24812	−0.624059	−	0.781377i	$-0.714518\pi$
$29$	−6.72132	−1.24812	−0.624059	+	0.781377i	$0.714518\pi$
$30$	−4.12898	−0.753845
$31$	3.59681	0.646006	0.323003	−	0.946398i	$-0.395308\pi$
$31$	3.59681	0.646006	0.323003	+	0.946398i	$0.395308\pi$
$32$	−1.00000	−0.176777
$33$	−0.209559	−0.0364795
$34$	6.22636	1.06781
$35$	4.12898	0.697925
$36$	1.00000	0.166667
$37$	−4.94388	−0.812768	−0.406384	−	0.913702i	$-0.633210\pi$
$37$	−4.94388	−0.812768	−0.406384	+	0.913702i	$0.633210\pi$
$38$	−7.05387	−1.14429
$39$	2.02818	0.324768
$40$	−4.12898	−0.652849
$41$	3.48339	0.544015	0.272007	−	0.962295i	$-0.412312\pi$
$41$	3.48339	0.544015	0.272007	+	0.962295i	$0.412312\pi$
$42$	−1.00000	−0.154303
$43$	10.4873	1.59930	0.799648	−	0.600469i	$-0.205019\pi$
$43$	10.4873	1.59930	0.799648	+	0.600469i	$0.205019\pi$
$44$	−0.209559	−0.0315922
$45$	4.12898	0.615512
$46$	−4.78157	−0.705005
$47$	2.83496	0.413521	0.206761	−	0.978392i	$-0.433708\pi$
$47$	2.83496	0.413521	0.206761	+	0.978392i	$0.433708\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−12.0485	−1.70391
$51$	−6.22636	−0.871864
$52$	2.02818	0.281258
$53$	0.180654	0.0248148	0.0124074	−	0.999923i	$-0.496051\pi$
$53$	0.180654	0.0248148	0.0124074	+	0.999923i	$0.496051\pi$
$54$	−1.00000	−0.136083
$55$	−0.865264	−0.116672
$56$	−1.00000	−0.133631
$57$	7.05387	0.934308
$58$	6.72132	0.882553
$59$	−1.70932	−0.222535	−0.111267	−	0.993791i	$-0.535491\pi$
$59$	−1.70932	−0.222535	−0.111267	+	0.993791i	$0.535491\pi$
$60$	4.12898	0.533049
$61$	−5.32771	−0.682144	−0.341072	−	0.940037i	$-0.610790\pi$
$61$	−5.32771	−0.682144	−0.341072	+	0.940037i	$0.610790\pi$
$62$	−3.59681	−0.456795
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	8.37430	1.03870
$66$	0.209559	0.0257949
$67$	−2.99419	−0.365799	−0.182899	−	0.983132i	$-0.558548\pi$
$67$	−2.99419	−0.365799	−0.182899	+	0.983132i	$0.558548\pi$
$68$	−6.22636	−0.755057
$69$	4.78157	0.575634
$70$	−4.12898	−0.493507
$71$	−5.25692	−0.623881	−0.311941	−	0.950102i	$-0.600979\pi$
$71$	−5.25692	−0.623881	−0.311941	+	0.950102i	$0.600979\pi$
$72$	−1.00000	−0.117851
$73$	−1.40462	−0.164398	−0.0821992	−	0.996616i	$-0.526194\pi$
$73$	−1.40462	−0.164398	−0.0821992	+	0.996616i	$0.526194\pi$
$74$	4.94388	0.574714
$75$	12.0485	1.39124
$76$	7.05387	0.809134
$77$	−0.209559	−0.0238814
$78$	−2.02818	−0.229646
$79$	10.0851	1.13466	0.567332	−	0.823489i	$-0.307976\pi$
$79$	10.0851	1.13466	0.567332	+	0.823489i	$0.307976\pi$
$80$	4.12898	0.461634
$81$	1.00000	0.111111
$82$	−3.48339	−0.384677
$83$	−2.56494	−0.281539	−0.140769	−	0.990042i	$-0.544958\pi$
$83$	−2.56494	−0.281539	−0.140769	+	0.990042i	$0.544958\pi$
$84$	1.00000	0.109109
$85$	−25.7085	−2.78848
$86$	−10.4873	−1.13087
$87$	−6.72132	−0.720601
$88$	0.209559	0.0223391
$89$	−10.5427	−1.11753	−0.558764	−	0.829326i	$-0.688724\pi$
$89$	−10.5427	−1.11753	−0.558764	+	0.829326i	$0.688724\pi$
$90$	−4.12898	−0.435233
$91$	2.02818	0.212611
$92$	4.78157	0.498514
$93$	3.59681	0.372971
$94$	−2.83496	−0.292404
$95$	29.1253	2.98819
$96$	−1.00000	−0.102062
$97$	13.1808	1.33830	0.669152	−	0.743125i	$-0.266657\pi$
$97$	13.1808	1.33830	0.669152	+	0.743125i	$0.266657\pi$
$98$	−1.00000	−0.101015
$99$	−0.209559	−0.0210615
$100$	12.0485	1.20485
$101$	9.89625	0.984713	0.492357	−	0.870394i	$-0.336136\pi$
$101$	9.89625	0.984713	0.492357	+	0.870394i	$0.336136\pi$
$102$	6.22636	0.616501
$103$	−15.4322	−1.52058	−0.760290	−	0.649584i	$-0.774943\pi$
$103$	−15.4322	−1.52058	−0.760290	+	0.649584i	$0.774943\pi$
$104$	−2.02818	−0.198879
$105$	4.12898	0.402947
$106$	−0.180654	−0.0175467
$107$	−11.0914	−1.07225	−0.536124	−	0.844139i	$-0.680112\pi$
$107$	−11.0914	−1.07225	−0.536124	+	0.844139i	$0.680112\pi$
$108$	1.00000	0.0962250
$109$	−9.63485	−0.922851	−0.461426	−	0.887179i	$-0.652662\pi$
$109$	−9.63485	−0.922851	−0.461426	+	0.887179i	$0.652662\pi$
$110$	0.865264	0.0824997
$111$	−4.94388	−0.469252
$112$	1.00000	0.0944911
$113$	−0.918217	−0.0863786	−0.0431893	−	0.999067i	$-0.513752\pi$
$113$	−0.918217	−0.0863786	−0.0431893	+	0.999067i	$0.513752\pi$
$114$	−7.05387	−0.660655
$115$	19.7430	1.84105
$116$	−6.72132	−0.624059
$117$	2.02818	0.187505
$118$	1.70932	0.157356
$119$	−6.22636	−0.570769
$120$	−4.12898	−0.376923
$121$	−10.9561	−0.996008
$122$	5.32771	0.482349
$123$	3.48339	0.314087
$124$	3.59681	0.323003
$125$	29.1030	2.60305
$126$	−1.00000	−0.0890871
$127$	−2.34957	−0.208491	−0.104245	−	0.994552i	$-0.533243\pi$
$127$	−2.34957	−0.208491	−0.104245	+	0.994552i	$0.533243\pi$
$128$	−1.00000	−0.0883883
$129$	10.4873	0.923354
$130$	−8.37430	−0.734475
$131$	−19.6153	−1.71379	−0.856897	−	0.515488i	$-0.827611\pi$
$131$	−19.6153	−1.71379	−0.856897	+	0.515488i	$0.827611\pi$
$132$	−0.209559	−0.0182398
$133$	7.05387	0.611648
$134$	2.99419	0.258659
$135$	4.12898	0.355366
$136$	6.22636	0.533906
$137$	−0.842858	−0.0720102	−0.0360051	−	0.999352i	$-0.511463\pi$
$137$	−0.842858	−0.0720102	−0.0360051	+	0.999352i	$0.511463\pi$
$138$	−4.78157	−0.407035
$139$	20.0606	1.70152	0.850760	−	0.525554i	$-0.176142\pi$
$139$	20.0606	1.70152	0.850760	+	0.525554i	$0.176142\pi$
$140$	4.12898	0.348962
$141$	2.83496	0.238746
$142$	5.25692	0.441151
$143$	−0.425023	−0.0355422
$144$	1.00000	0.0833333
$145$	−27.7522	−2.30470
$146$	1.40462	0.116247
$147$	1.00000	0.0824786
$148$	−4.94388	−0.406384
$149$	16.7046	1.36849	0.684246	−	0.729252i	$-0.260132\pi$
$149$	16.7046	1.36849	0.684246	+	0.729252i	$0.260132\pi$
$150$	−12.0485	−0.983754
$151$	17.3820	1.41452	0.707262	−	0.706952i	$-0.249930\pi$
$151$	17.3820	1.41452	0.707262	+	0.706952i	$0.249930\pi$
$152$	−7.05387	−0.572144
$153$	−6.22636	−0.503371
$154$	0.209559	0.0168867
$155$	14.8511	1.19287
$156$	2.02818	0.162384
$157$	15.0449	1.20072	0.600359	−	0.799731i	$-0.295025\pi$
$157$	15.0449	1.20072	0.600359	+	0.799731i	$0.295025\pi$
$158$	−10.0851	−0.802329
$159$	0.180654	0.0143268
$160$	−4.12898	−0.326425
$161$	4.78157	0.376841
$162$	−1.00000	−0.0785674
$163$	−18.7826	−1.47117	−0.735583	−	0.677434i	$-0.763092\pi$
$163$	−18.7826	−1.47117	−0.735583	+	0.677434i	$0.763092\pi$
$164$	3.48339	0.272007
$165$	−0.865264	−0.0673607
$166$	2.56494	0.199078
$167$	23.9736	1.85513	0.927566	−	0.373659i	$-0.121897\pi$
$167$	23.9736	1.85513	0.927566	+	0.373659i	$0.121897\pi$
$168$	−1.00000	−0.0771517
$169$	−8.88650	−0.683577
$170$	25.7085	1.97175
$171$	7.05387	0.539423
$172$	10.4873	0.799648
$173$	12.3775	0.941040	0.470520	−	0.882389i	$-0.344066\pi$
$173$	12.3775	0.941040	0.470520	+	0.882389i	$0.344066\pi$
$174$	6.72132	0.509542
$175$	12.0485	0.910779
$176$	−0.209559	−0.0157961
$177$	−1.70932	−0.128481
$178$	10.5427	0.790212
$179$	5.57573	0.416750	0.208375	−	0.978049i	$-0.433183\pi$
$179$	5.57573	0.416750	0.208375	+	0.978049i	$0.433183\pi$
$180$	4.12898	0.307756
$181$	−5.45735	−0.405642	−0.202821	−	0.979216i	$-0.565011\pi$
$181$	−5.45735	−0.405642	−0.202821	+	0.979216i	$0.565011\pi$
$182$	−2.02818	−0.150339
$183$	−5.32771	−0.393836
$184$	−4.78157	−0.352502
$185$	−20.4132	−1.50081
$186$	−3.59681	−0.263731
$187$	1.30479	0.0954156
$188$	2.83496	0.206761
$189$	1.00000	0.0727393
$190$	−29.1253	−2.11297
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	1.00000	0.0721688
$193$	18.3976	1.32429	0.662143	−	0.749377i	$-0.269647\pi$
$193$	18.3976	1.32429	0.662143	+	0.749377i	$0.269647\pi$
$194$	−13.1808	−0.946324
$195$	8.37430	0.599696
$196$	1.00000	0.0714286
$197$	14.6727	1.04538	0.522692	−	0.852522i	$-0.324928\pi$
$197$	14.6727	1.04538	0.522692	+	0.852522i	$0.324928\pi$
$198$	0.209559	0.0148927
$199$	−24.0144	−1.70234	−0.851168	−	0.524894i	$-0.824105\pi$
$199$	−24.0144	−1.70234	−0.851168	+	0.524894i	$0.824105\pi$
$200$	−12.0485	−0.851956
$201$	−2.99419	−0.211194
$202$	−9.89625	−0.696297
$203$	−6.72132	−0.471744
$204$	−6.22636	−0.435932
$205$	14.3829	1.00454
$206$	15.4322	1.07521
$207$	4.78157	0.332342
$208$	2.02818	0.140629
$209$	−1.47820	−0.102249
$210$	−4.12898	−0.284927
$211$	20.9610	1.44302	0.721508	−	0.692406i	$-0.243449\pi$
$211$	20.9610	1.44302	0.721508	+	0.692406i	$0.243449\pi$
$212$	0.180654	0.0124074
$213$	−5.25692	−0.360198
$214$	11.0914	0.758193
$215$	43.3018	2.95316
$216$	−1.00000	−0.0680414
$217$	3.59681	0.244167
$218$	9.63485	0.652554
$219$	−1.40462	−0.0949155
$220$	−0.865264	−0.0583361
$221$	−12.6282	−0.849462
$222$	4.94388	0.331811
$223$	−13.5926	−0.910230	−0.455115	−	0.890433i	$-0.650402\pi$
$223$	−13.5926	−0.910230	−0.455115	+	0.890433i	$0.650402\pi$
$224$	−1.00000	−0.0668153
$225$	12.0485	0.803232
$226$	0.918217	0.0610789
$227$	−2.57729	−0.171061	−0.0855304	−	0.996336i	$-0.527258\pi$
$227$	−2.57729	−0.171061	−0.0855304	+	0.996336i	$0.527258\pi$
$228$	7.05387	0.467154
$229$	−9.48792	−0.626979	−0.313490	−	0.949592i	$-0.601498\pi$
$229$	−9.48792	−0.626979	−0.313490	+	0.949592i	$0.601498\pi$
$230$	−19.7430	−1.30182
$231$	−0.209559	−0.0137880
$232$	6.72132	0.441276
$233$	−22.7794	−1.49233	−0.746164	−	0.665762i	$-0.768107\pi$
$233$	−22.7794	−1.49233	−0.746164	+	0.665762i	$0.768107\pi$
$234$	−2.02818	−0.132586
$235$	11.7055	0.763581
$236$	−1.70932	−0.111267
$237$	10.0851	0.655099
$238$	6.22636	0.403595
$239$	0.387214	0.0250468	0.0125234	−	0.999922i	$-0.496014\pi$
$239$	0.387214	0.0250468	0.0125234	+	0.999922i	$0.496014\pi$
$240$	4.12898	0.266525
$241$	8.46439	0.545239	0.272620	−	0.962122i	$-0.412110\pi$
$241$	8.46439	0.545239	0.272620	+	0.962122i	$0.412110\pi$
$242$	10.9561	0.704284
$243$	1.00000	0.0641500
$244$	−5.32771	−0.341072
$245$	4.12898	0.263791
$246$	−3.48339	−0.222093
$247$	14.3065	0.910300
$248$	−3.59681	−0.228397
$249$	−2.56494	−0.162546
$250$	−29.1030	−1.84064
$251$	16.4880	1.04071	0.520356	−	0.853949i	$-0.325799\pi$
$251$	16.4880	1.04071	0.520356	+	0.853949i	$0.325799\pi$
$252$	1.00000	0.0629941
$253$	−1.00202	−0.0629965
$254$	2.34957	0.147425
$255$	−25.7085	−1.60993
$256$	1.00000	0.0625000
$257$	10.8753	0.678384	0.339192	−	0.940717i	$-0.389846\pi$
$257$	10.8753	0.678384	0.339192	+	0.940717i	$0.389846\pi$
$258$	−10.4873	−0.652910
$259$	−4.94388	−0.307197
$260$	8.37430	0.519352
$261$	−6.72132	−0.416039
$262$	19.6153	1.21184
$263$	−10.6537	−0.656933	−0.328466	−	0.944516i	$-0.606532\pi$
$263$	−10.6537	−0.656933	−0.328466	+	0.944516i	$0.606532\pi$
$264$	0.209559	0.0128975
$265$	0.745918	0.0458214
$266$	−7.05387	−0.432500
$267$	−10.5427	−0.645206
$268$	−2.99419	−0.182899
$269$	6.16061	0.375619	0.187810	−	0.982205i	$-0.439861\pi$
$269$	6.16061	0.375619	0.187810	+	0.982205i	$0.439861\pi$
$270$	−4.12898	−0.251282
$271$	−30.4720	−1.85104	−0.925522	−	0.378694i	$-0.876373\pi$
$271$	−30.4720	−1.85104	−0.925522	+	0.378694i	$0.876373\pi$
$272$	−6.22636	−0.377528
$273$	2.02818	0.122751
$274$	0.842858	0.0509189
$275$	−2.52486	−0.152255
$276$	4.78157	0.287817
$277$	−1.25569	−0.0754471	−0.0377236	−	0.999288i	$-0.512011\pi$
$277$	−1.25569	−0.0754471	−0.0377236	+	0.999288i	$0.512011\pi$
$278$	−20.0606	−1.20316
$279$	3.59681	0.215335
$280$	−4.12898	−0.246754
$281$	−6.90189	−0.411732	−0.205866	−	0.978580i	$-0.566001\pi$
$281$	−6.90189	−0.411732	−0.205866	+	0.978580i	$0.566001\pi$
$282$	−2.83496	−0.168819
$283$	−16.6816	−0.991620	−0.495810	−	0.868431i	$-0.665129\pi$
$283$	−16.6816	−0.991620	−0.495810	+	0.868431i	$0.665129\pi$
$284$	−5.25692	−0.311941
$285$	29.1253	1.72523
$286$	0.425023	0.0251321
$287$	3.48339	0.205618
$288$	−1.00000	−0.0589256
$289$	21.7675	1.28044
$290$	27.7522	1.62967
$291$	13.1808	0.772670
$292$	−1.40462	−0.0821992
$293$	3.60894	0.210837	0.105418	−	0.994428i	$-0.466382\pi$
$293$	3.60894	0.210837	0.105418	+	0.994428i	$0.466382\pi$
$294$	−1.00000	−0.0583212
$295$	−7.05776	−0.410919
$296$	4.94388	0.287357
$297$	−0.209559	−0.0121598
$298$	−16.7046	−0.967669
$299$	9.69788	0.560843
$300$	12.0485	0.695619
$301$	10.4873	0.604477
$302$	−17.3820	−1.00022
$303$	9.89625	0.568524
$304$	7.05387	0.404567
$305$	−21.9980	−1.25960
$306$	6.22636	0.355937
$307$	11.4665	0.654428	0.327214	−	0.944950i	$-0.393890\pi$
$307$	11.4665	0.654428	0.327214	+	0.944950i	$0.393890\pi$
$308$	−0.209559	−0.0119407
$309$	−15.4322	−0.877908
$310$	−14.8511	−0.843488
$311$	−23.1601	−1.31329	−0.656644	−	0.754201i	$-0.728024\pi$
$311$	−23.1601	−1.31329	−0.656644	+	0.754201i	$0.728024\pi$
$312$	−2.02818	−0.114823
$313$	−12.5111	−0.707169	−0.353584	−	0.935403i	$-0.615037\pi$
$313$	−12.5111	−0.707169	−0.353584	+	0.935403i	$0.615037\pi$
$314$	−15.0449	−0.849035
$315$	4.12898	0.232642
$316$	10.0851	0.567332
$317$	−19.9376	−1.11981	−0.559904	−	0.828557i	$-0.689162\pi$
$317$	−19.9376	−1.11981	−0.559904	+	0.828557i	$0.689162\pi$
$318$	−0.180654	−0.0101306
$319$	1.40851	0.0788616
$320$	4.12898	0.230817
$321$	−11.0914	−0.619062
$322$	−4.78157	−0.266467
$323$	−43.9199	−2.44377
$324$	1.00000	0.0555556
$325$	24.4364	1.35549
$326$	18.7826	1.04027
$327$	−9.63485	−0.532809
$328$	−3.48339	−0.192338
$329$	2.83496	0.156296
$330$	0.865264	0.0476312
$331$	−21.1247	−1.16112	−0.580560	−	0.814218i	$-0.697166\pi$
$331$	−21.1247	−1.16112	−0.580560	+	0.814218i	$0.697166\pi$
$332$	−2.56494	−0.140769
$333$	−4.94388	−0.270923
$334$	−23.9736	−1.31178
$335$	−12.3630	−0.675461
$336$	1.00000	0.0545545
$337$	19.9919	1.08903	0.544514	−	0.838752i	$-0.316714\pi$
$337$	19.9919	1.08903	0.544514	+	0.838752i	$0.316714\pi$
$338$	8.88650	0.483362
$339$	−0.918217	−0.0498707
$340$	−25.7085	−1.39424
$341$	−0.753743	−0.0408175
$342$	−7.05387	−0.381429
$343$	1.00000	0.0539949
$344$	−10.4873	−0.565437
$345$	19.7430	1.06293
$346$	−12.3775	−0.665416
$347$	−9.43676	−0.506592	−0.253296	−	0.967389i	$-0.581515\pi$
$347$	−9.43676	−0.506592	−0.253296	+	0.967389i	$0.581515\pi$
$348$	−6.72132	−0.360301
$349$	25.0965	1.34339	0.671693	−	0.740829i	$-0.265567\pi$
$349$	25.0965	1.34339	0.671693	+	0.740829i	$0.265567\pi$
$350$	−12.0485	−0.644018
$351$	2.02818	0.108256
$352$	0.209559	0.0111695
$353$	21.1716	1.12685	0.563425	−	0.826167i	$-0.309483\pi$
$353$	21.1716	1.12685	0.563425	+	0.826167i	$0.309483\pi$
$354$	1.70932	0.0908495
$355$	−21.7057	−1.15202
$356$	−10.5427	−0.558764
$357$	−6.22636	−0.329534
$358$	−5.57573	−0.294687
$359$	3.27751	0.172980	0.0864902	−	0.996253i	$-0.472435\pi$
$359$	3.27751	0.172980	0.0864902	+	0.996253i	$0.472435\pi$
$360$	−4.12898	−0.217616
$361$	30.7570	1.61879
$362$	5.45735	0.286832
$363$	−10.9561	−0.575045
$364$	2.02818	0.106305
$365$	−5.79965	−0.303568
$366$	5.32771	0.278484
$367$	3.47820	0.181560	0.0907802	−	0.995871i	$-0.471064\pi$
$367$	3.47820	0.181560	0.0907802	+	0.995871i	$0.471064\pi$
$368$	4.78157	0.249257
$369$	3.48339	0.181338
$370$	20.4132	1.06123
$371$	0.180654	0.00937910
$372$	3.59681	0.186486
$373$	32.7940	1.69801	0.849005	−	0.528384i	$-0.177202\pi$
$373$	32.7940	1.69801	0.849005	+	0.528384i	$0.177202\pi$
$374$	−1.30479	−0.0674690
$375$	29.1030	1.50287
$376$	−2.83496	−0.146202
$377$	−13.6320	−0.702086
$378$	−1.00000	−0.0514344
$379$	−20.6446	−1.06044	−0.530220	−	0.847860i	$-0.677891\pi$
$379$	−20.6446	−1.06044	−0.530220	+	0.847860i	$0.677891\pi$
$380$	29.1253	1.49410
$381$	−2.34957	−0.120372
$382$	−1.00000	−0.0511645
$383$	14.8895	0.760818	0.380409	−	0.924818i	$-0.375783\pi$
$383$	14.8895	0.760818	0.380409	+	0.924818i	$0.375783\pi$
$384$	−1.00000	−0.0510310
$385$	−0.865264	−0.0440980
$386$	−18.3976	−0.936412
$387$	10.4873	0.533099
$388$	13.1808	0.669152
$389$	−19.7364	−1.00068	−0.500338	−	0.865830i	$-0.666791\pi$
$389$	−19.7364	−1.00068	−0.500338	+	0.865830i	$0.666791\pi$
$390$	−8.37430	−0.424049
$391$	−29.7718	−1.50562
$392$	−1.00000	−0.0505076
$393$	−19.6153	−0.989459
$394$	−14.6727	−0.739198
$395$	41.6413	2.09520
$396$	−0.209559	−0.0105307
$397$	−19.5452	−0.980945	−0.490473	−	0.871457i	$-0.663176\pi$
$397$	−19.5452	−0.980945	−0.490473	+	0.871457i	$0.663176\pi$
$398$	24.0144	1.20373
$399$	7.05387	0.353135
$400$	12.0485	0.602424
$401$	−35.5126	−1.77341	−0.886707	−	0.462331i	$-0.847013\pi$
$401$	−35.5126	−1.77341	−0.886707	+	0.462331i	$0.847013\pi$
$402$	2.99419	0.149337
$403$	7.29496	0.363388
$404$	9.89625	0.492357
$405$	4.12898	0.205171
$406$	6.72132	0.333574
$407$	1.03603	0.0513542
$408$	6.22636	0.308251
$409$	8.32702	0.411745	0.205872	−	0.978579i	$-0.433997\pi$
$409$	8.32702	0.411745	0.205872	+	0.978579i	$0.433997\pi$
$410$	−14.3829	−0.710319
$411$	−0.842858	−0.0415751
$412$	−15.4322	−0.760290
$413$	−1.70932	−0.0841103
$414$	−4.78157	−0.235002
$415$	−10.5906	−0.519871
$416$	−2.02818	−0.0994396
$417$	20.0606	0.982373
$418$	1.47820	0.0723011
$419$	−27.0567	−1.32180	−0.660902	−	0.750472i	$-0.729826\pi$
$419$	−27.0567	−1.32180	−0.660902	+	0.750472i	$0.729826\pi$
$420$	4.12898	0.201474
$421$	13.8867	0.676796	0.338398	−	0.941003i	$-0.390115\pi$
$421$	13.8867	0.676796	0.338398	+	0.941003i	$0.390115\pi$
$422$	−20.9610	−1.02037
$423$	2.83496	0.137840
$424$	−0.180654	−0.00877335
$425$	−75.0181	−3.63891
$426$	5.25692	0.254698
$427$	−5.32771	−0.257826
$428$	−11.0914	−0.536124
$429$	−0.425023	−0.0205203
$430$	−43.3018	−2.08820
$431$	−12.1610	−0.585774	−0.292887	−	0.956147i	$-0.594616\pi$
$431$	−12.1610	−0.585774	−0.292887	+	0.956147i	$0.594616\pi$
$432$	1.00000	0.0481125
$433$	−18.6182	−0.894736	−0.447368	−	0.894350i	$-0.647639\pi$
$433$	−18.6182	−0.894736	−0.447368	+	0.894350i	$0.647639\pi$
$434$	−3.59681	−0.172652
$435$	−27.7522	−1.33062
$436$	−9.63485	−0.461426
$437$	33.7286	1.61346
$438$	1.40462	0.0671154
$439$	3.26934	0.156037	0.0780186	−	0.996952i	$-0.475141\pi$
$439$	3.26934	0.156037	0.0780186	+	0.996952i	$0.475141\pi$
$440$	0.865264	0.0412499
$441$	1.00000	0.0476190
$442$	12.6282	0.600660
$443$	17.2478	0.819466	0.409733	−	0.912206i	$-0.365622\pi$
$443$	17.2478	0.819466	0.409733	+	0.912206i	$0.365622\pi$
$444$	−4.94388	−0.234626
$445$	−43.5308	−2.06356
$446$	13.5926	0.643630
$447$	16.7046	0.790099
$448$	1.00000	0.0472456
$449$	7.40157	0.349302	0.174651	−	0.984630i	$-0.444120\pi$
$449$	7.40157	0.349302	0.174651	+	0.984630i	$0.444120\pi$
$450$	−12.0485	−0.567971
$451$	−0.729976	−0.0343732
$452$	−0.918217	−0.0431893
$453$	17.3820	0.816676
$454$	2.57729	0.120958
$455$	8.37430	0.392593
$456$	−7.05387	−0.330328
$457$	−4.79271	−0.224193	−0.112097	−	0.993697i	$-0.535757\pi$
$457$	−4.79271	−0.224193	−0.112097	+	0.993697i	$0.535757\pi$
$458$	9.48792	0.443341
$459$	−6.22636	−0.290621
$460$	19.7430	0.920523
$461$	−22.3166	−1.03939	−0.519694	−	0.854353i	$-0.673954\pi$
$461$	−22.3166	−1.03939	−0.519694	+	0.854353i	$0.673954\pi$
$462$	0.209559	0.00974956
$463$	−30.6046	−1.42232	−0.711159	−	0.703031i	$-0.751829\pi$
$463$	−30.6046	−1.42232	−0.711159	+	0.703031i	$0.751829\pi$
$464$	−6.72132	−0.312030
$465$	14.8511	0.688705
$466$	22.7794	1.05524
$467$	5.03627	0.233051	0.116525	−	0.993188i	$-0.462824\pi$
$467$	5.03627	0.233051	0.116525	+	0.993188i	$0.462824\pi$
$468$	2.02818	0.0937525
$469$	−2.99419	−0.138259
$470$	−11.7055	−0.539934
$471$	15.0449	0.693234
$472$	1.70932	0.0786779
$473$	−2.19770	−0.101051
$474$	−10.0851	−0.463225
$475$	84.9883	3.89953
$476$	−6.22636	−0.285385
$477$	0.180654	0.00827159
$478$	−0.387214	−0.0177107
$479$	2.54880	0.116458	0.0582289	−	0.998303i	$-0.481455\pi$
$479$	2.54880	0.116458	0.0582289	+	0.998303i	$0.481455\pi$
$480$	−4.12898	−0.188461
$481$	−10.0271	−0.457194
$482$	−8.46439	−0.385542
$483$	4.78157	0.217569
$484$	−10.9561	−0.498004
$485$	54.4231	2.47123
$486$	−1.00000	−0.0453609
$487$	25.2682	1.14501	0.572507	−	0.819900i	$-0.305971\pi$
$487$	25.2682	1.14501	0.572507	+	0.819900i	$0.305971\pi$
$488$	5.32771	0.241174
$489$	−18.7826	−0.849378
$490$	−4.12898	−0.186528
$491$	−16.4132	−0.740717	−0.370359	−	0.928889i	$-0.620765\pi$
$491$	−16.4132	−0.740717	−0.370359	+	0.928889i	$0.620765\pi$
$492$	3.48339	0.157044
$493$	41.8493	1.88480
$494$	−14.3065	−0.643680
$495$	−0.865264	−0.0388907
$496$	3.59681	0.161501
$497$	−5.25692	−0.235805
$498$	2.56494	0.114938
$499$	−24.2488	−1.08553	−0.542763	−	0.839886i	$-0.682622\pi$
$499$	−24.2488	−1.08553	−0.542763	+	0.839886i	$0.682622\pi$
$500$	29.1030	1.30153
$501$	23.9736	1.07106
$502$	−16.4880	−0.735894
$503$	−41.7783	−1.86280	−0.931401	−	0.363994i	$-0.881413\pi$
$503$	−41.7783	−1.86280	−0.931401	+	0.363994i	$0.881413\pi$
$504$	−1.00000	−0.0445435
$505$	40.8614	1.81831
$506$	1.00202	0.0445453
$507$	−8.88650	−0.394663
$508$	−2.34957	−0.104245
$509$	−6.92957	−0.307148	−0.153574	−	0.988137i	$-0.549078\pi$
$509$	−6.92957	−0.307148	−0.153574	+	0.988137i	$0.549078\pi$
$510$	25.7085	1.13839
$511$	−1.40462	−0.0621368
$512$	−1.00000	−0.0441942
$513$	7.05387	0.311436
$514$	−10.8753	−0.479690
$515$	−63.7193	−2.80781
$516$	10.4873	0.461677
$517$	−0.594090	−0.0261281
$518$	4.94388	0.217221
$519$	12.3775	0.543310
$520$	−8.37430	−0.367238
$521$	−27.4284	−1.20166	−0.600829	−	0.799377i	$-0.705163\pi$
$521$	−27.4284	−1.20166	−0.600829	+	0.799377i	$0.705163\pi$
$522$	6.72132	0.294184
$523$	10.1868	0.445440	0.222720	−	0.974883i	$-0.428507\pi$
$523$	10.1868	0.445440	0.222720	+	0.974883i	$0.428507\pi$
$524$	−19.6153	−0.856897
$525$	12.0485	0.525839
$526$	10.6537	0.464521
$527$	−22.3950	−0.975541
$528$	−0.209559	−0.00911988
$529$	−0.136543	−0.00593664
$530$	−0.745918	−0.0324006
$531$	−1.70932	−0.0741783
$532$	7.05387	0.305824
$533$	7.06494	0.306017
$534$	10.5427	0.456229
$535$	−45.7962	−1.97994
$536$	2.99419	0.129329
$537$	5.57573	0.240611
$538$	−6.16061	−0.265603
$539$	−0.209559	−0.00902634
$540$	4.12898	0.177683
$541$	30.7526	1.32216	0.661080	−	0.750316i	$-0.270099\pi$
$541$	30.7526	1.32216	0.661080	+	0.750316i	$0.270099\pi$
$542$	30.4720	1.30889
$543$	−5.45735	−0.234197
$544$	6.22636	0.266953
$545$	−39.7821	−1.70408
$546$	−2.02818	−0.0867980
$547$	41.6810	1.78215	0.891075	−	0.453855i	$-0.149952\pi$
$547$	41.6810	1.78215	0.891075	+	0.453855i	$0.149952\pi$
$548$	−0.842858	−0.0360051
$549$	−5.32771	−0.227381
$550$	2.52486	0.107661
$551$	−47.4113	−2.01979
$552$	−4.78157	−0.203517
$553$	10.0851	0.428863
$554$	1.25569	0.0533492
$555$	−20.4132	−0.866490
$556$	20.0606	0.850760
$557$	16.4358	0.696406	0.348203	−	0.937419i	$-0.386792\pi$
$557$	16.4358	0.696406	0.348203	+	0.937419i	$0.386792\pi$
$558$	−3.59681	−0.152265
$559$	21.2701	0.899628
$560$	4.12898	0.174481
$561$	1.30479	0.0550882
$562$	6.90189	0.291139
$563$	18.9007	0.796569	0.398284	−	0.917262i	$-0.369606\pi$
$563$	18.9007	0.796569	0.398284	+	0.917262i	$0.369606\pi$
$564$	2.83496	0.119373
$565$	−3.79130	−0.159501
$566$	16.6816	0.701182
$567$	1.00000	0.0419961
$568$	5.25692	0.220575
$569$	17.4316	0.730771	0.365386	−	0.930856i	$-0.380937\pi$
$569$	17.4316	0.730771	0.365386	+	0.930856i	$0.380937\pi$
$570$	−29.1253	−1.21992
$571$	34.1497	1.42912	0.714559	−	0.699575i	$-0.246627\pi$
$571$	34.1497	1.42912	0.714559	+	0.699575i	$0.246627\pi$
$572$	−0.425023	−0.0177711
$573$	1.00000	0.0417756
$574$	−3.48339	−0.145394
$575$	57.6107	2.40253
$576$	1.00000	0.0416667
$577$	19.3645	0.806156	0.403078	−	0.915166i	$-0.367940\pi$
$577$	19.3645	0.806156	0.403078	+	0.915166i	$0.367940\pi$
$578$	−21.7675	−0.905409
$579$	18.3976	0.764577
$580$	−27.7522	−1.15235
$581$	−2.56494	−0.106412
$582$	−13.1808	−0.546360
$583$	−0.0378577	−0.00156791
$584$	1.40462	0.0581236
$585$	8.37430	0.346235
$586$	−3.60894	−0.149084
$587$	−46.9897	−1.93947	−0.969737	−	0.244152i	$-0.921490\pi$
$587$	−46.9897	−1.93947	−0.969737	+	0.244152i	$0.921490\pi$
$588$	1.00000	0.0412393
$589$	25.3714	1.04541
$590$	7.05776	0.290563
$591$	14.6727	0.603552
$592$	−4.94388	−0.203192
$593$	24.8919	1.02219	0.511094	−	0.859525i	$-0.329240\pi$
$593$	24.8919	1.02219	0.511094	+	0.859525i	$0.329240\pi$
$594$	0.209559	0.00859830
$595$	−25.7085	−1.05395
$596$	16.7046	0.684246
$597$	−24.0144	−0.982844
$598$	−9.69788	−0.396576
$599$	−1.72732	−0.0705763	−0.0352881	−	0.999377i	$-0.511235\pi$
$599$	−1.72732	−0.0705763	−0.0352881	+	0.999377i	$0.511235\pi$
$600$	−12.0485	−0.491877
$601$	13.7591	0.561244	0.280622	−	0.959818i	$-0.409459\pi$
$601$	13.7591	0.561244	0.280622	+	0.959818i	$0.409459\pi$
$602$	−10.4873	−0.427430
$603$	−2.99419	−0.121933
$604$	17.3820	0.707262
$605$	−45.2375	−1.83916
$606$	−9.89625	−0.402008
$607$	9.69679	0.393581	0.196790	−	0.980446i	$-0.436948\pi$
$607$	9.69679	0.393581	0.196790	+	0.980446i	$0.436948\pi$
$608$	−7.05387	−0.286072
$609$	−6.72132	−0.272362
$610$	21.9980	0.890674
$611$	5.74980	0.232612
$612$	−6.22636	−0.251686
$613$	−15.1943	−0.613691	−0.306846	−	0.951759i	$-0.599274\pi$
$613$	−15.1943	−0.613691	−0.306846	+	0.951759i	$0.599274\pi$
$614$	−11.4665	−0.462751
$615$	14.3829	0.579973
$616$	0.209559	0.00844337
$617$	37.7308	1.51898	0.759492	−	0.650516i	$-0.225448\pi$
$617$	37.7308	1.51898	0.759492	+	0.650516i	$0.225448\pi$
$618$	15.4322	0.620774
$619$	6.13396	0.246545	0.123272	−	0.992373i	$-0.460661\pi$
$619$	6.13396	0.246545	0.123272	+	0.992373i	$0.460661\pi$
$620$	14.8511	0.596436
$621$	4.78157	0.191878
$622$	23.1601	0.928635
$623$	−10.5427	−0.422386
$624$	2.02818	0.0811921
$625$	59.9234	2.39694
$626$	12.5111	0.500044
$627$	−1.47820	−0.0590336
$628$	15.0449	0.600359
$629$	30.7823	1.22737
$630$	−4.12898	−0.164502
$631$	44.7159	1.78011	0.890056	−	0.455852i	$-0.150665\pi$
$631$	44.7159	1.78011	0.890056	+	0.455852i	$0.150665\pi$
$632$	−10.0851	−0.401165
$633$	20.9610	0.833126
$634$	19.9376	0.791824
$635$	−9.70133	−0.384985
$636$	0.180654	0.00716341
$637$	2.02818	0.0803593
$638$	−1.40851	−0.0557636
$639$	−5.25692	−0.207960
$640$	−4.12898	−0.163212
$641$	−2.02034	−0.0797987	−0.0398994	−	0.999204i	$-0.512704\pi$
$641$	−2.02034	−0.0797987	−0.0398994	+	0.999204i	$0.512704\pi$
$642$	11.0914	0.437743
$643$	13.6876	0.539785	0.269893	−	0.962890i	$-0.413012\pi$
$643$	13.6876	0.539785	0.269893	+	0.962890i	$0.413012\pi$
$644$	4.78157	0.188420
$645$	43.3018	1.70501
$646$	43.9199	1.72800
$647$	−40.6446	−1.59790	−0.798952	−	0.601394i	$-0.794612\pi$
$647$	−40.6446	−1.59790	−0.798952	+	0.601394i	$0.794612\pi$
$648$	−1.00000	−0.0392837
$649$	0.358204	0.0140607
$650$	−24.4364	−0.958476
$651$	3.59681	0.140970
$652$	−18.7826	−0.735583
$653$	−6.26129	−0.245023	−0.122512	−	0.992467i	$-0.539095\pi$
$653$	−6.26129	−0.245023	−0.122512	+	0.992467i	$0.539095\pi$
$654$	9.63485	0.376753
$655$	−80.9910	−3.16458
$656$	3.48339	0.136004
$657$	−1.40462	−0.0547995
$658$	−2.83496	−0.110518
$659$	−31.0525	−1.20963	−0.604817	−	0.796365i	$-0.706754\pi$
$659$	−31.0525	−1.20963	−0.604817	+	0.796365i	$0.706754\pi$
$660$	−0.865264	−0.0336804
$661$	−17.4954	−0.680491	−0.340245	−	0.940337i	$-0.610510\pi$
$661$	−17.4954	−0.680491	−0.340245	+	0.940337i	$0.610510\pi$
$662$	21.1247	0.821036
$663$	−12.6282	−0.490437
$664$	2.56494	0.0995389
$665$	29.1253	1.12943
$666$	4.94388	0.191571
$667$	−32.1385	−1.24441
$668$	23.9736	0.927566
$669$	−13.5926	−0.525522
$670$	12.3630	0.477623
$671$	1.11647	0.0431008
$672$	−1.00000	−0.0385758
$673$	21.0846	0.812752	0.406376	−	0.913706i	$-0.366792\pi$
$673$	21.0846	0.812752	0.406376	+	0.913706i	$0.366792\pi$
$674$	−19.9919	−0.770059
$675$	12.0485	0.463746
$676$	−8.88650	−0.341788
$677$	9.16837	0.352369	0.176184	−	0.984357i	$-0.443624\pi$
$677$	9.16837	0.352369	0.176184	+	0.984357i	$0.443624\pi$
$678$	0.918217	0.0352639
$679$	13.1808	0.505832
$680$	25.7085	0.985876
$681$	−2.57729	−0.0987620
$682$	0.753743	0.0288623
$683$	−41.5313	−1.58915	−0.794575	−	0.607166i	$-0.792306\pi$
$683$	−41.5313	−1.58915	−0.794575	+	0.607166i	$0.792306\pi$
$684$	7.05387	0.269711
$685$	−3.48014	−0.132969
$686$	−1.00000	−0.0381802
$687$	−9.48792	−0.361987
$688$	10.4873	0.399824
$689$	0.366399	0.0139587
$690$	−19.7430	−0.751604
$691$	−20.5244	−0.780785	−0.390392	−	0.920649i	$-0.627661\pi$
$691$	−20.5244	−0.780785	−0.390392	+	0.920649i	$0.627661\pi$
$692$	12.3775	0.470520
$693$	−0.209559	−0.00796048
$694$	9.43676	0.358214
$695$	82.8299	3.14192
$696$	6.72132	0.254771
$697$	−21.6889	−0.821524
$698$	−25.0965	−0.949918
$699$	−22.7794	−0.861596
$700$	12.0485	0.455390
$701$	−3.48849	−0.131758	−0.0658792	−	0.997828i	$-0.520985\pi$
$701$	−3.48849	−0.131758	−0.0658792	+	0.997828i	$0.520985\pi$
$702$	−2.02818	−0.0765486
$703$	−34.8734	−1.31528
$704$	−0.209559	−0.00789805
$705$	11.7055	0.440854
$706$	−21.1716	−0.796803
$707$	9.89625	0.372187
$708$	−1.70932	−0.0642403
$709$	22.0203	0.826991	0.413496	−	0.910506i	$-0.364308\pi$
$709$	22.0203	0.826991	0.413496	+	0.910506i	$0.364308\pi$
$710$	21.7057	0.814601
$711$	10.0851	0.378222
$712$	10.5427	0.395106
$713$	17.1984	0.644085
$714$	6.22636	0.233015
$715$	−1.75491	−0.0656299
$716$	5.57573	0.208375
$717$	0.387214	0.0144608
$718$	−3.27751	−0.122316
$719$	−48.5894	−1.81208	−0.906040	−	0.423191i	$-0.860910\pi$
$719$	−48.5894	−1.81208	−0.906040	+	0.423191i	$0.860910\pi$
$720$	4.12898	0.153878
$721$	−15.4322	−0.574725
$722$	−30.7570	−1.14466
$723$	8.46439	0.314794
$724$	−5.45735	−0.202821
$725$	−80.9817	−3.00758
$726$	10.9561	0.406618
$727$	15.5701	0.577464	0.288732	−	0.957410i	$-0.406766\pi$
$727$	15.5701	0.577464	0.288732	+	0.957410i	$0.406766\pi$
$728$	−2.02818	−0.0751693
$729$	1.00000	0.0370370
$730$	5.79965	0.214655
$731$	−65.2976	−2.41512
$732$	−5.32771	−0.196918
$733$	−48.2666	−1.78277	−0.891385	−	0.453248i	$-0.850265\pi$
$733$	−48.2666	−1.78277	−0.891385	+	0.453248i	$0.850265\pi$
$734$	−3.47820	−0.128383
$735$	4.12898	0.152300
$736$	−4.78157	−0.176251
$737$	0.627460	0.0231128
$738$	−3.48339	−0.128226
$739$	1.11081	0.0408620	0.0204310	−	0.999791i	$-0.493496\pi$
$739$	1.11081	0.0408620	0.0204310	+	0.999791i	$0.493496\pi$
$740$	−20.4132	−0.750403
$741$	14.3065	0.525562
$742$	−0.180654	−0.00663203
$743$	−29.7708	−1.09218	−0.546092	−	0.837725i	$-0.683885\pi$
$743$	−29.7708	−1.09218	−0.546092	+	0.837725i	$0.683885\pi$
$744$	−3.59681	−0.131865
$745$	68.9728	2.52697
$746$	−32.7940	−1.20068
$747$	−2.56494	−0.0938462
$748$	1.30479	0.0477078
$749$	−11.0914	−0.405271
$750$	−29.1030	−1.06269
$751$	33.3874	1.21832	0.609162	−	0.793046i	$-0.291506\pi$
$751$	33.3874	1.21832	0.609162	+	0.793046i	$0.291506\pi$
$752$	2.83496	0.103380
$753$	16.4880	0.600855
$754$	13.6320	0.496449
$755$	71.7698	2.61197
$756$	1.00000	0.0363696
$757$	−7.73763	−0.281229	−0.140614	−	0.990064i	$-0.544908\pi$
$757$	−7.73763	−0.281229	−0.140614	+	0.990064i	$0.544908\pi$
$758$	20.6446	0.749844
$759$	−1.00202	−0.0363711
$760$	−29.1253	−1.05648
$761$	3.26551	0.118375	0.0591874	−	0.998247i	$-0.481149\pi$
$761$	3.26551	0.118375	0.0591874	+	0.998247i	$0.481149\pi$
$762$	2.34957	0.0851159
$763$	−9.63485	−0.348805
$764$	1.00000	0.0361787
$765$	−25.7085	−0.929493
$766$	−14.8895	−0.537980
$767$	−3.46681	−0.125179
$768$	1.00000	0.0360844
$769$	−12.2150	−0.440485	−0.220243	−	0.975445i	$-0.570685\pi$
$769$	−12.2150	−0.440485	−0.220243	+	0.975445i	$0.570685\pi$
$770$	0.865264	0.0311820
$771$	10.8753	0.391665
$772$	18.3976	0.662143
$773$	1.80905	0.0650671	0.0325335	−	0.999471i	$-0.489642\pi$
$773$	1.80905	0.0650671	0.0325335	+	0.999471i	$0.489642\pi$
$774$	−10.4873	−0.376958
$775$	43.3360	1.55668
$776$	−13.1808	−0.473162
$777$	−4.94388	−0.177361
$778$	19.7364	0.707585
$779$	24.5714	0.880362
$780$	8.37430	0.299848
$781$	1.10163	0.0394195
$782$	29.7718	1.06464
$783$	−6.72132	−0.240200
$784$	1.00000	0.0357143
$785$	62.1203	2.21717
$786$	19.6153	0.699653
$787$	13.6398	0.486208	0.243104	−	0.970000i	$-0.421834\pi$
$787$	13.6398	0.486208	0.243104	+	0.970000i	$0.421834\pi$
$788$	14.6727	0.522692
$789$	−10.6537	−0.379280
$790$	−41.6413	−1.48153
$791$	−0.918217	−0.0326480
$792$	0.209559	0.00744635
$793$	−10.8055	−0.383716
$794$	19.5452	0.693633
$795$	0.745918	0.0264550
$796$	−24.0144	−0.851168
$797$	−6.59396	−0.233570	−0.116785	−	0.993157i	$-0.537259\pi$
$797$	−6.59396	−0.233570	−0.116785	+	0.993157i	$0.537259\pi$
$798$	−7.05387	−0.249704
$799$	−17.6515	−0.624464
$800$	−12.0485	−0.425978
$801$	−10.5427	−0.372510
$802$	35.5126	1.25399
$803$	0.294351	0.0103874
$804$	−2.99419	−0.105597
$805$	19.7430	0.695850
$806$	−7.29496	−0.256954
$807$	6.16061	0.216864
$808$	−9.89625	−0.348149
$809$	47.0295	1.65347	0.826734	−	0.562593i	$-0.190196\pi$
$809$	47.0295	1.65347	0.826734	+	0.562593i	$0.190196\pi$
$810$	−4.12898	−0.145078
$811$	−46.0404	−1.61670	−0.808348	−	0.588705i	$-0.799638\pi$
$811$	−46.0404	−1.61670	−0.808348	+	0.588705i	$0.799638\pi$
$812$	−6.72132	−0.235872
$813$	−30.4720	−1.06870
$814$	−1.03603	−0.0363129
$815$	−77.5530	−2.71656
$816$	−6.22636	−0.217966
$817$	73.9759	2.58809
$818$	−8.32702	−0.291148
$819$	2.02818	0.0708703
$820$	14.3829	0.502271
$821$	6.11960	0.213576	0.106788	−	0.994282i	$-0.465943\pi$
$821$	6.11960	0.213576	0.106788	+	0.994282i	$0.465943\pi$
$822$	0.842858	0.0293980
$823$	−20.9431	−0.730029	−0.365014	−	0.931002i	$-0.618936\pi$
$823$	−20.9431	−0.730029	−0.365014	+	0.931002i	$0.618936\pi$
$824$	15.4322	0.537606
$825$	−2.52486	−0.0879045
$826$	1.70932	0.0594749
$827$	−18.0133	−0.626385	−0.313192	−	0.949690i	$-0.601398\pi$
$827$	−18.0133	−0.626385	−0.313192	+	0.949690i	$0.601398\pi$
$828$	4.78157	0.166171
$829$	6.35650	0.220770	0.110385	−	0.993889i	$-0.464792\pi$
$829$	6.35650	0.220770	0.110385	+	0.993889i	$0.464792\pi$
$830$	10.5906	0.367604
$831$	−1.25569	−0.0435594
$832$	2.02818	0.0703144
$833$	−6.22636	−0.215730
$834$	−20.0606	−0.694643
$835$	98.9865	3.42557
$836$	−1.47820	−0.0511246
$837$	3.59681	0.124324
$838$	27.0567	0.934657
$839$	54.0168	1.86487	0.932433	−	0.361343i	$-0.117682\pi$
$839$	54.0168	1.86487	0.932433	+	0.361343i	$0.117682\pi$
$840$	−4.12898	−0.142463
$841$	16.1762	0.557800
$842$	−13.8867	−0.478567
$843$	−6.90189	−0.237714
$844$	20.9610	0.721508
$845$	−36.6922	−1.26225
$846$	−2.83496	−0.0974678
$847$	−10.9561	−0.376456
$848$	0.180654	0.00620369
$849$	−16.6816	−0.572512
$850$	75.0181	2.57310
$851$	−23.6395	−0.810352
$852$	−5.25692	−0.180099
$853$	−6.20941	−0.212606	−0.106303	−	0.994334i	$-0.533901\pi$
$853$	−6.20941	−0.212606	−0.106303	+	0.994334i	$0.533901\pi$
$854$	5.32771	0.182311
$855$	29.1253	0.996063
$856$	11.0914	0.379097
$857$	9.62067	0.328636	0.164318	−	0.986407i	$-0.447458\pi$
$857$	9.62067	0.328636	0.164318	+	0.986407i	$0.447458\pi$
$858$	0.425023	0.0145100
$859$	−16.7560	−0.571706	−0.285853	−	0.958274i	$-0.592277\pi$
$859$	−16.7560	−0.571706	−0.285853	+	0.958274i	$0.592277\pi$
$860$	43.3018	1.47658
$861$	3.48339	0.118714
$862$	12.1610	0.414205
$863$	25.8718	0.880686	0.440343	−	0.897830i	$-0.354857\pi$
$863$	25.8718	0.880686	0.440343	+	0.897830i	$0.354857\pi$
$864$	−1.00000	−0.0340207
$865$	51.1063	1.73766
$866$	18.6182	0.632674
$867$	21.7675	0.739263
$868$	3.59681	0.122084
$869$	−2.11343	−0.0716931
$870$	27.7522	0.940888
$871$	−6.07276	−0.205767
$872$	9.63485	0.326277
$873$	13.1808	0.446101
$874$	−33.7286	−1.14089
$875$	29.1030	0.983861
$876$	−1.40462	−0.0474577
$877$	55.2544	1.86581	0.932905	−	0.360122i	$-0.117265\pi$
$877$	55.2544	1.86581	0.932905	+	0.360122i	$0.117265\pi$
$878$	−3.26934	−0.110335
$879$	3.60894	0.121727
$880$	−0.865264	−0.0291681
$881$	39.9008	1.34429	0.672146	−	0.740418i	$-0.265373\pi$
$881$	39.9008	1.34429	0.672146	+	0.740418i	$0.265373\pi$
$882$	−1.00000	−0.0336718
$883$	18.5278	0.623509	0.311754	−	0.950163i	$-0.399083\pi$
$883$	18.5278	0.623509	0.311754	+	0.950163i	$0.399083\pi$
$884$	−12.6282	−0.424731
$885$	−7.05776	−0.237244
$886$	−17.2478	−0.579450
$887$	−13.1384	−0.441144	−0.220572	−	0.975371i	$-0.570792\pi$
$887$	−13.1384	−0.441144	−0.220572	+	0.975371i	$0.570792\pi$
$888$	4.94388	0.165906
$889$	−2.34957	−0.0788020
$890$	43.5308	1.45916
$891$	−0.209559	−0.00702049
$892$	−13.5926	−0.455115
$893$	19.9974	0.669188
$894$	−16.7046	−0.558684
$895$	23.0221	0.769544
$896$	−1.00000	−0.0334077
$897$	9.69788	0.323803
$898$	−7.40157	−0.246994
$899$	−24.1753	−0.806291
$900$	12.0485	0.401616
$901$	−1.12482	−0.0374731
$902$	0.729976	0.0243055
$903$	10.4873	0.348995
$904$	0.918217	0.0305394
$905$	−22.5333	−0.749032
$906$	−17.3820	−0.577477
$907$	10.3695	0.344312	0.172156	−	0.985070i	$-0.444927\pi$
$907$	10.3695	0.344312	0.172156	+	0.985070i	$0.444927\pi$
$908$	−2.57729	−0.0855304
$909$	9.89625	0.328238
$910$	−8.37430	−0.277605
$911$	−40.3119	−1.33559	−0.667797	−	0.744343i	$-0.732763\pi$
$911$	−40.3119	−1.33559	−0.667797	+	0.744343i	$0.732763\pi$
$912$	7.05387	0.233577
$913$	0.537506	0.0177888
$914$	4.79271	0.158529
$915$	−21.9980	−0.727232
$916$	−9.48792	−0.313490
$917$	−19.6153	−0.647753
$918$	6.22636	0.205500
$919$	−28.5440	−0.941580	−0.470790	−	0.882245i	$-0.656031\pi$
$919$	−28.5440	−0.941580	−0.470790	+	0.882245i	$0.656031\pi$
$920$	−19.7430	−0.650908
$921$	11.4665	0.377834
$922$	22.3166	0.734958
$923$	−10.6620	−0.350943
$924$	−0.209559	−0.00689398
$925$	−59.5662	−1.95852
$926$	30.6046	1.00573
$927$	−15.4322	−0.506860
$928$	6.72132	0.220638
$929$	26.8482	0.880859	0.440430	−	0.897787i	$-0.354826\pi$
$929$	26.8482	0.880859	0.440430	+	0.897787i	$0.354826\pi$
$930$	−14.8511	−0.486988
$931$	7.05387	0.231181
$932$	−22.7794	−0.746164
$933$	−23.1601	−0.758227
$934$	−5.03627	−0.164792
$935$	5.38744	0.176188
$936$	−2.02818	−0.0662931
$937$	−30.1435	−0.984747	−0.492373	−	0.870384i	$-0.663871\pi$
$937$	−30.1435	−0.984747	−0.492373	+	0.870384i	$0.663871\pi$
$938$	2.99419	0.0977639
$939$	−12.5111	−0.408284
$940$	11.7055	0.381791
$941$	−44.5904	−1.45360	−0.726802	−	0.686847i	$-0.758994\pi$
$941$	−44.5904	−1.45360	−0.726802	+	0.686847i	$0.758994\pi$
$942$	−15.0449	−0.490191
$943$	16.6561	0.542398
$944$	−1.70932	−0.0556337
$945$	4.12898	0.134316
$946$	2.19770	0.0714535
$947$	45.8429	1.48969	0.744847	−	0.667236i	$-0.232523\pi$
$947$	45.8429	1.48969	0.744847	+	0.667236i	$0.232523\pi$
$948$	10.0851	0.327549
$949$	−2.84882	−0.0924766
$950$	−84.9883	−2.75739
$951$	−19.9376	−0.646522
$952$	6.22636	0.201797
$953$	27.0965	0.877742	0.438871	−	0.898550i	$-0.355379\pi$
$953$	27.0965	0.877742	0.438871	+	0.898550i	$0.355379\pi$
$954$	−0.180654	−0.00584890
$955$	4.12898	0.133611
$956$	0.387214	0.0125234
$957$	1.40851	0.0455308
$958$	−2.54880	−0.0823481
$959$	−0.842858	−0.0272173
$960$	4.12898	0.133262
$961$	−18.0630	−0.582677
$962$	10.0271	0.323285
$963$	−11.0914	−0.357416
$964$	8.46439	0.272620
$965$	75.9632	2.44534
$966$	−4.78157	−0.153845
$967$	−35.3526	−1.13686	−0.568432	−	0.822730i	$-0.692450\pi$
$967$	−35.3526	−1.13686	−0.568432	+	0.822730i	$0.692450\pi$
$968$	10.9561	0.352142
$969$	−43.9199	−1.41091
$970$	−54.4231	−1.74742
$971$	15.4232	0.494955	0.247477	−	0.968894i	$-0.420398\pi$
$971$	15.4232	0.494955	0.247477	+	0.968894i	$0.420398\pi$
$972$	1.00000	0.0320750
$973$	20.0606	0.643114
$974$	−25.2682	−0.809646
$975$	24.4364	0.782593
$976$	−5.32771	−0.170536
$977$	43.7582	1.39995	0.699974	−	0.714168i	$-0.253195\pi$
$977$	43.7582	1.39995	0.699974	+	0.714168i	$0.253195\pi$
$978$	18.7826	0.600601
$979$	2.20933	0.0706104
$980$	4.12898	0.131895
$981$	−9.63485	−0.307617
$982$	16.4132	0.523766
$983$	13.8091	0.440442	0.220221	−	0.975450i	$-0.429322\pi$
$983$	13.8091	0.440442	0.220221	+	0.975450i	$0.429322\pi$
$984$	−3.48339	−0.111047
$985$	60.5831	1.93034
$986$	−41.8493	−1.33275
$987$	2.83496	0.0902377
$988$	14.3065	0.455150
$989$	50.1457	1.59454
$990$	0.865264	0.0274999
$991$	41.0410	1.30371	0.651855	−	0.758344i	$-0.273991\pi$
$991$	41.0410	1.30371	0.651855	+	0.758344i	$0.273991\pi$
$992$	−3.59681	−0.114199
$993$	−21.1247	−0.670373
$994$	5.25692	0.166739
$995$	−99.1550	−3.14342
$996$	−2.56494	−0.0812732
$997$	−17.2625	−0.546709	−0.273354	−	0.961913i	$-0.588133\pi$
$997$	−17.2625	−0.546709	−0.273354	+	0.961913i	$0.588133\pi$
$998$	24.2488	0.767583
$999$	−4.94388	−0.156417

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.z.1.15	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.z.1.15	✓	15	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:	\( N \)	\(=\)	\( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.12898 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.12898 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.12898 q^{10} -0.209559 q^{11} +1.00000 q^{12} +2.02818 q^{13} -1.00000 q^{14} +4.12898 q^{15} +1.00000 q^{16} -6.22636 q^{17} -1.00000 q^{18} +7.05387 q^{19} +4.12898 q^{20} +1.00000 q^{21} +0.209559 q^{22} +4.78157 q^{23} -1.00000 q^{24} +12.0485 q^{25} -2.02818 q^{26} +1.00000 q^{27} +1.00000 q^{28} -6.72132 q^{29} -4.12898 q^{30} +3.59681 q^{31} -1.00000 q^{32} -0.209559 q^{33} +6.22636 q^{34} +4.12898 q^{35} +1.00000 q^{36} -4.94388 q^{37} -7.05387 q^{38} +2.02818 q^{39} -4.12898 q^{40} +3.48339 q^{41} -1.00000 q^{42} +10.4873 q^{43} -0.209559 q^{44} +4.12898 q^{45} -4.78157 q^{46} +2.83496 q^{47} +1.00000 q^{48} +1.00000 q^{49} -12.0485 q^{50} -6.22636 q^{51} +2.02818 q^{52} +0.180654 q^{53} -1.00000 q^{54} -0.865264 q^{55} -1.00000 q^{56} +7.05387 q^{57} +6.72132 q^{58} -1.70932 q^{59} +4.12898 q^{60} -5.32771 q^{61} -3.59681 q^{62} +1.00000 q^{63} +1.00000 q^{64} +8.37430 q^{65} +0.209559 q^{66} -2.99419 q^{67} -6.22636 q^{68} +4.78157 q^{69} -4.12898 q^{70} -5.25692 q^{71} -1.00000 q^{72} -1.40462 q^{73} +4.94388 q^{74} +12.0485 q^{75} +7.05387 q^{76} -0.209559 q^{77} -2.02818 q^{78} +10.0851 q^{79} +4.12898 q^{80} +1.00000 q^{81} -3.48339 q^{82} -2.56494 q^{83} +1.00000 q^{84} -25.7085 q^{85} -10.4873 q^{86} -6.72132 q^{87} +0.209559 q^{88} -10.5427 q^{89} -4.12898 q^{90} +2.02818 q^{91} +4.78157 q^{92} +3.59681 q^{93} -2.83496 q^{94} +29.1253 q^{95} -1.00000 q^{96} +13.1808 q^{97} -1.00000 q^{98} -0.209559 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} + 15 q^{3} + 15 q^{4} - 15 q^{6} + 15 q^{7} - 15 q^{8} + 15 q^{9}+O(q^{10}) \) 15 * q - 15 * q^2 + 15 * q^3 + 15 * q^4 - 15 * q^6 + 15 * q^7 - 15 * q^8 + 15 * q^9	\( 15 q - 15 q^{2} + 15 q^{3} + 15 q^{4} - 15 q^{6} + 15 q^{7} - 15 q^{8} + 15 q^{9} - 7 q^{11} + 15 q^{12} + 10 q^{13} - 15 q^{14} + 15 q^{16} - 3 q^{17} - 15 q^{18} + 12 q^{19} + 15 q^{21} + 7 q^{22} - q^{23} - 15 q^{24} + 31 q^{25} - 10 q^{26} + 15 q^{27} + 15 q^{28} - 3 q^{29} + 19 q^{31} - 15 q^{32} - 7 q^{33} + 3 q^{34} + 15 q^{36} + 25 q^{37} - 12 q^{38} + 10 q^{39} + 8 q^{41} - 15 q^{42} + 25 q^{43} - 7 q^{44} + q^{46} + 11 q^{47} + 15 q^{48} + 15 q^{49} - 31 q^{50} - 3 q^{51} + 10 q^{52} - 4 q^{53} - 15 q^{54} + 9 q^{55} - 15 q^{56} + 12 q^{57} + 3 q^{58} + 27 q^{61} - 19 q^{62} + 15 q^{63} + 15 q^{64} - 2 q^{65} + 7 q^{66} + 31 q^{67} - 3 q^{68} - q^{69} - 16 q^{71} - 15 q^{72} + 26 q^{73} - 25 q^{74} + 31 q^{75} + 12 q^{76} - 7 q^{77} - 10 q^{78} + 32 q^{79} + 15 q^{81} - 8 q^{82} + 7 q^{83} + 15 q^{84} + 26 q^{85} - 25 q^{86} - 3 q^{87} + 7 q^{88} - 11 q^{89} + 10 q^{91} - q^{92} + 19 q^{93} - 11 q^{94} - 8 q^{95} - 15 q^{96} + 30 q^{97} - 15 q^{98} - 7 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 + 15 * q^3 + 15 * q^4 - 15 * q^6 + 15 * q^7 - 15 * q^8 + 15 * q^9 - 7 * q^11 + 15 * q^12 + 10 * q^13 - 15 * q^14 + 15 * q^16 - 3 * q^17 - 15 * q^18 + 12 * q^19 + 15 * q^21 + 7 * q^22 - q^23 - 15 * q^24 + 31 * q^25 - 10 * q^26 + 15 * q^27 + 15 * q^28 - 3 * q^29 + 19 * q^31 - 15 * q^32 - 7 * q^33 + 3 * q^34 + 15 * q^36 + 25 * q^37 - 12 * q^38 + 10 * q^39 + 8 * q^41 - 15 * q^42 + 25 * q^43 - 7 * q^44 + q^46 + 11 * q^47 + 15 * q^48 + 15 * q^49 - 31 * q^50 - 3 * q^51 + 10 * q^52 - 4 * q^53 - 15 * q^54 + 9 * q^55 - 15 * q^56 + 12 * q^57 + 3 * q^58 + 27 * q^61 - 19 * q^62 + 15 * q^63 + 15 * q^64 - 2 * q^65 + 7 * q^66 + 31 * q^67 - 3 * q^68 - q^69 - 16 * q^71 - 15 * q^72 + 26 * q^73 - 25 * q^74 + 31 * q^75 + 12 * q^76 - 7 * q^77 - 10 * q^78 + 32 * q^79 + 15 * q^81 - 8 * q^82 + 7 * q^83 + 15 * q^84 + 26 * q^85 - 25 * q^86 - 3 * q^87 + 7 * q^88 - 11 * q^89 + 10 * q^91 - q^92 + 19 * q^93 - 11 * q^94 - 8 * q^95 - 15 * q^96 + 30 * q^97 - 15 * q^98 - 7 * q^99

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