LMFDB - Embedded newform 5054.2.a.bm.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 24 x^{10} + 68 x^{9} + 213 x^{8} - 555 x^{7} - 814 x^{6} + 1911 x^{5} + 1005 x^{4} + \cdots + 1 $ x^12 - 3x^11 - 24x^10 + 68x^9 + 213x^8 - 555x^7 - 814x^6 + 1911x^5 + 1005x^4 - 2326x^3 + 570x^2 + 105*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$3.20919$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +3.20919 q^{3} +1.00000 q^{4} +2.74348 q^{5} +3.20919 q^{6} +1.00000 q^{7} +1.00000 q^{8} +7.29887 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.20919 q^{3} +1.00000 q^{4} +2.74348 q^{5} +3.20919 q^{6} +1.00000 q^{7} +1.00000 q^{8} +7.29887 q^{9} +2.74348 q^{10} -3.98639 q^{11} +3.20919 q^{12} -4.64202 q^{13} +1.00000 q^{14} +8.80432 q^{15} +1.00000 q^{16} +5.22474 q^{17} +7.29887 q^{18} +2.74348 q^{20} +3.20919 q^{21} -3.98639 q^{22} +0.520464 q^{23} +3.20919 q^{24} +2.52666 q^{25} -4.64202 q^{26} +13.7959 q^{27} +1.00000 q^{28} +5.83623 q^{29} +8.80432 q^{30} -1.38498 q^{31} +1.00000 q^{32} -12.7931 q^{33} +5.22474 q^{34} +2.74348 q^{35} +7.29887 q^{36} -9.44185 q^{37} -14.8971 q^{39} +2.74348 q^{40} -9.40284 q^{41} +3.20919 q^{42} +2.55638 q^{43} -3.98639 q^{44} +20.0243 q^{45} +0.520464 q^{46} +4.77001 q^{47} +3.20919 q^{48} +1.00000 q^{49} +2.52666 q^{50} +16.7672 q^{51} -4.64202 q^{52} +9.11202 q^{53} +13.7959 q^{54} -10.9366 q^{55} +1.00000 q^{56} +5.83623 q^{58} +1.07661 q^{59} +8.80432 q^{60} -1.53726 q^{61} -1.38498 q^{62} +7.29887 q^{63} +1.00000 q^{64} -12.7353 q^{65} -12.7931 q^{66} -12.3091 q^{67} +5.22474 q^{68} +1.67027 q^{69} +2.74348 q^{70} -4.00739 q^{71} +7.29887 q^{72} -0.422816 q^{73} -9.44185 q^{74} +8.10851 q^{75} -3.98639 q^{77} -14.8971 q^{78} -12.7880 q^{79} +2.74348 q^{80} +22.3769 q^{81} -9.40284 q^{82} -1.49938 q^{83} +3.20919 q^{84} +14.3339 q^{85} +2.55638 q^{86} +18.7295 q^{87} -3.98639 q^{88} -8.77859 q^{89} +20.0243 q^{90} -4.64202 q^{91} +0.520464 q^{92} -4.44464 q^{93} +4.77001 q^{94} +3.20919 q^{96} -4.61801 q^{97} +1.00000 q^{98} -29.0962 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} + 12 q^{8} + 21 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 + 12 * q^8 + 21 * q^9	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} + 12 q^{8} + 21 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 6 q^{13} + 12 q^{14} - 6 q^{15} + 12 q^{16} + 3 q^{17} + 21 q^{18} + 3 q^{20} + 3 q^{21} + 3 q^{22} + 12 q^{23} + 3 q^{24} + 33 q^{25} - 6 q^{26} + 21 q^{27} + 12 q^{28} + 6 q^{29} - 6 q^{30} + 3 q^{31} + 12 q^{32} - 6 q^{33} + 3 q^{34} + 3 q^{35} + 21 q^{36} + 27 q^{37} + 27 q^{39} + 3 q^{40} - 27 q^{41} + 3 q^{42} + 30 q^{43} + 3 q^{44} + 30 q^{45} + 12 q^{46} + 21 q^{47} + 3 q^{48} + 12 q^{49} + 33 q^{50} + 3 q^{51} - 6 q^{52} + 6 q^{53} + 21 q^{54} + 48 q^{55} + 12 q^{56} + 6 q^{58} - 27 q^{59} - 6 q^{60} + 18 q^{61} + 3 q^{62} + 21 q^{63} + 12 q^{64} - 9 q^{65} - 6 q^{66} + 9 q^{67} + 3 q^{68} + 18 q^{69} + 3 q^{70} + 27 q^{71} + 21 q^{72} - 9 q^{73} + 27 q^{74} + 33 q^{75} + 3 q^{77} + 27 q^{78} - 12 q^{79} + 3 q^{80} + 24 q^{81} - 27 q^{82} + 9 q^{83} + 3 q^{84} + 78 q^{85} + 30 q^{86} - 45 q^{87} + 3 q^{88} - 24 q^{89} + 30 q^{90} - 6 q^{91} + 12 q^{92} + 3 q^{93} + 21 q^{94} + 3 q^{96} - 18 q^{97} + 12 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 + 12 * q^8 + 21 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 6 * q^13 + 12 * q^14 - 6 * q^15 + 12 * q^16 + 3 * q^17 + 21 * q^18 + 3 * q^20 + 3 * q^21 + 3 * q^22 + 12 * q^23 + 3 * q^24 + 33 * q^25 - 6 * q^26 + 21 * q^27 + 12 * q^28 + 6 * q^29 - 6 * q^30 + 3 * q^31 + 12 * q^32 - 6 * q^33 + 3 * q^34 + 3 * q^35 + 21 * q^36 + 27 * q^37 + 27 * q^39 + 3 * q^40 - 27 * q^41 + 3 * q^42 + 30 * q^43 + 3 * q^44 + 30 * q^45 + 12 * q^46 + 21 * q^47 + 3 * q^48 + 12 * q^49 + 33 * q^50 + 3 * q^51 - 6 * q^52 + 6 * q^53 + 21 * q^54 + 48 * q^55 + 12 * q^56 + 6 * q^58 - 27 * q^59 - 6 * q^60 + 18 * q^61 + 3 * q^62 + 21 * q^63 + 12 * q^64 - 9 * q^65 - 6 * q^66 + 9 * q^67 + 3 * q^68 + 18 * q^69 + 3 * q^70 + 27 * q^71 + 21 * q^72 - 9 * q^73 + 27 * q^74 + 33 * q^75 + 3 * q^77 + 27 * q^78 - 12 * q^79 + 3 * q^80 + 24 * q^81 - 27 * q^82 + 9 * q^83 + 3 * q^84 + 78 * q^85 + 30 * q^86 - 45 * q^87 + 3 * q^88 - 24 * q^89 + 30 * q^90 - 6 * q^91 + 12 * q^92 + 3 * q^93 + 21 * q^94 + 3 * q^96 - 18 * q^97 + 12 * q^98 + 48 * 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
$3$	3.20919	1.85282	0.926412	−	0.376511i	$-0.122876\pi$
$3$	3.20919	1.85282	0.926412	+	0.376511i	$0.122876\pi$
$4$	1.00000	0.500000
$5$	2.74348	1.22692	0.613460	−	0.789726i	$-0.289777\pi$
$5$	2.74348	1.22692	0.613460	+	0.789726i	$0.289777\pi$
$6$	3.20919	1.31014
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	7.29887	2.43296
$10$	2.74348	0.867563
$11$	−3.98639	−1.20194	−0.600971	−	0.799271i	$-0.705219\pi$
$11$	−3.98639	−1.20194	−0.600971	+	0.799271i	$0.705219\pi$
$12$	3.20919	0.926412
$13$	−4.64202	−1.28746	−0.643732	−	0.765251i	$-0.722615\pi$
$13$	−4.64202	−1.28746	−0.643732	+	0.765251i	$0.722615\pi$
$14$	1.00000	0.267261
$15$	8.80432	2.27327
$16$	1.00000	0.250000
$17$	5.22474	1.26719	0.633593	−	0.773667i	$-0.281580\pi$
$17$	5.22474	1.26719	0.633593	+	0.773667i	$0.281580\pi$
$18$	7.29887	1.72036
$19$	0	0
$19$	0	0
$20$	2.74348	0.613460
$21$	3.20919	0.700302
$22$	−3.98639	−0.849901
$23$	0.520464	0.108524	0.0542621	−	0.998527i	$-0.482719\pi$
$23$	0.520464	0.108524	0.0542621	+	0.998527i	$0.482719\pi$
$24$	3.20919	0.655072
$25$	2.52666	0.505331
$26$	−4.64202	−0.910374
$27$	13.7959	2.65502
$28$	1.00000	0.188982
$29$	5.83623	1.08376	0.541880	−	0.840456i	$-0.317713\pi$
$29$	5.83623	1.08376	0.541880	+	0.840456i	$0.317713\pi$
$30$	8.80432	1.60744
$31$	−1.38498	−0.248749	−0.124374	−	0.992235i	$-0.539692\pi$
$31$	−1.38498	−0.248749	−0.124374	+	0.992235i	$0.539692\pi$
$32$	1.00000	0.176777
$33$	−12.7931	−2.22699
$34$	5.22474	0.896035
$35$	2.74348	0.463732
$36$	7.29887	1.21648
$37$	−9.44185	−1.55223	−0.776115	−	0.630591i	$-0.782812\pi$
$37$	−9.44185	−1.55223	−0.776115	+	0.630591i	$0.782812\pi$
$38$	0	0
$39$	−14.8971	−2.38544
$40$	2.74348	0.433781
$41$	−9.40284	−1.46848	−0.734239	−	0.678891i	$-0.762461\pi$
$41$	−9.40284	−1.46848	−0.734239	+	0.678891i	$0.762461\pi$
$42$	3.20919	0.495188
$43$	2.55638	0.389845	0.194922	−	0.980819i	$-0.437555\pi$
$43$	2.55638	0.389845	0.194922	+	0.980819i	$0.437555\pi$
$44$	−3.98639	−0.600971
$45$	20.0243	2.98504
$46$	0.520464	0.0767382
$47$	4.77001	0.695777	0.347889	−	0.937536i	$-0.386899\pi$
$47$	4.77001	0.695777	0.347889	+	0.937536i	$0.386899\pi$
$48$	3.20919	0.463206
$49$	1.00000	0.142857
$50$	2.52666	0.357323
$51$	16.7672	2.34787
$52$	−4.64202	−0.643732
$53$	9.11202	1.25163	0.625816	−	0.779971i	$-0.284766\pi$
$53$	9.11202	1.25163	0.625816	+	0.779971i	$0.284766\pi$
$54$	13.7959	1.87738
$55$	−10.9366	−1.47469
$56$	1.00000	0.133631
$57$	0	0
$58$	5.83623	0.766334
$59$	1.07661	0.140163	0.0700815	−	0.997541i	$-0.477674\pi$
$59$	1.07661	0.140163	0.0700815	+	0.997541i	$0.477674\pi$
$60$	8.80432	1.13663
$61$	−1.53726	−0.196826	−0.0984132	−	0.995146i	$-0.531377\pi$
$61$	−1.53726	−0.196826	−0.0984132	+	0.995146i	$0.531377\pi$
$62$	−1.38498	−0.175892
$63$	7.29887	0.919571
$64$	1.00000	0.125000
$65$	−12.7353	−1.57961
$66$	−12.7931	−1.57472
$67$	−12.3091	−1.50380	−0.751898	−	0.659280i	$-0.770861\pi$
$67$	−12.3091	−1.50380	−0.751898	+	0.659280i	$0.770861\pi$
$68$	5.22474	0.633593
$69$	1.67027	0.201076
$70$	2.74348	0.327908
$71$	−4.00739	−0.475589	−0.237795	−	0.971315i	$-0.576425\pi$
$71$	−4.00739	−0.475589	−0.237795	+	0.971315i	$0.576425\pi$
$72$	7.29887	0.860180
$73$	−0.422816	−0.0494868	−0.0247434	−	0.999694i	$-0.507877\pi$
$73$	−0.422816	−0.0494868	−0.0247434	+	0.999694i	$0.507877\pi$
$74$	−9.44185	−1.09759
$75$	8.10851	0.936290
$76$	0	0
$77$	−3.98639	−0.454291
$78$	−14.8971	−1.68676
$79$	−12.7880	−1.43876	−0.719381	−	0.694616i	$-0.755574\pi$
$79$	−12.7880	−1.43876	−0.719381	+	0.694616i	$0.755574\pi$
$80$	2.74348	0.306730
$81$	22.3769	2.48632
$82$	−9.40284	−1.03837
$83$	−1.49938	−0.164578	−0.0822892	−	0.996608i	$-0.526223\pi$
$83$	−1.49938	−0.164578	−0.0822892	+	0.996608i	$0.526223\pi$
$84$	3.20919	0.350151
$85$	14.3339	1.55473
$86$	2.55638	0.275662
$87$	18.7295	2.00802
$88$	−3.98639	−0.424951
$89$	−8.77859	−0.930529	−0.465265	−	0.885172i	$-0.654041\pi$
$89$	−8.77859	−0.930529	−0.465265	+	0.885172i	$0.654041\pi$
$90$	20.0243	2.11074
$91$	−4.64202	−0.486615
$92$	0.520464	0.0542621
$93$	−4.44464	−0.460888
$94$	4.77001	0.491989
$95$	0	0
$96$	3.20919	0.327536
$97$	−4.61801	−0.468888	−0.234444	−	0.972130i	$-0.575327\pi$
$97$	−4.61801	−0.468888	−0.234444	+	0.972130i	$0.575327\pi$
$98$	1.00000	0.101015
$99$	−29.0962	−2.92427
$100$	2.52666	0.252666
$101$	5.07336	0.504818	0.252409	−	0.967621i	$-0.418777\pi$
$101$	5.07336	0.504818	0.252409	+	0.967621i	$0.418777\pi$
$102$	16.7672	1.66020
$103$	1.40012	0.137958	0.0689790	−	0.997618i	$-0.478026\pi$
$103$	1.40012	0.137958	0.0689790	+	0.997618i	$0.478026\pi$
$104$	−4.64202	−0.455187
$105$	8.80432	0.859214
$106$	9.11202	0.885038
$107$	18.3546	1.77441	0.887205	−	0.461375i	$-0.152644\pi$
$107$	18.3546	1.77441	0.887205	+	0.461375i	$0.152644\pi$
$108$	13.7959	1.32751
$109$	8.49097	0.813287	0.406643	−	0.913587i	$-0.366699\pi$
$109$	8.49097	0.813287	0.406643	+	0.913587i	$0.366699\pi$
$110$	−10.9366	−1.04276
$111$	−30.3006	−2.87601
$112$	1.00000	0.0944911
$113$	8.06367	0.758566	0.379283	−	0.925281i	$-0.376171\pi$
$113$	8.06367	0.758566	0.379283	+	0.925281i	$0.376171\pi$
$114$	0	0
$115$	1.42788	0.133150
$116$	5.83623	0.541880
$117$	−33.8815	−3.13234
$118$	1.07661	0.0991102
$119$	5.22474	0.478951
$120$	8.80432	0.803721
$121$	4.89131	0.444665
$122$	−1.53726	−0.139177
$123$	−30.1755	−2.72083
$124$	−1.38498	−0.124374
$125$	−6.78556	−0.606919
$126$	7.29887	0.650235
$127$	13.1420	1.16617	0.583084	−	0.812412i	$-0.301846\pi$
$127$	13.1420	1.16617	0.583084	+	0.812412i	$0.301846\pi$
$128$	1.00000	0.0883883
$129$	8.20390	0.722313
$130$	−12.7353	−1.11696
$131$	18.3208	1.60069	0.800347	−	0.599537i	$-0.204649\pi$
$131$	18.3208	1.60069	0.800347	+	0.599537i	$0.204649\pi$
$132$	−12.7931	−1.11349
$133$	0	0
$134$	−12.3091	−1.06334
$135$	37.8486	3.25749
$136$	5.22474	0.448018
$137$	−4.18816	−0.357818	−0.178909	−	0.983866i	$-0.557257\pi$
$137$	−4.18816	−0.357818	−0.178909	+	0.983866i	$0.557257\pi$
$138$	1.67027	0.142182
$139$	−14.9473	−1.26781	−0.633905	−	0.773411i	$-0.718549\pi$
$139$	−14.9473	−1.26781	−0.633905	+	0.773411i	$0.718549\pi$
$140$	2.74348	0.231866
$141$	15.3078	1.28915
$142$	−4.00739	−0.336293
$143$	18.5049	1.54746
$144$	7.29887	0.608239
$145$	16.0115	1.32969
$146$	−0.422816	−0.0349925
$147$	3.20919	0.264689
$148$	−9.44185	−0.776115
$149$	−0.0172226	−0.00141093	−0.000705467	−	1.00000i	$-0.500225\pi$
$149$	−0.0172226	−0.00141093	−0.000705467		1.00000i	$0.500225\pi$
$150$	8.10851	0.662057
$151$	−6.94979	−0.565566	−0.282783	−	0.959184i	$-0.591258\pi$
$151$	−6.94979	−0.565566	−0.282783	+	0.959184i	$0.591258\pi$
$152$	0	0
$153$	38.1347	3.08301
$154$	−3.98639	−0.321233
$155$	−3.79964	−0.305195
$156$	−14.8971	−1.19272
$157$	−20.9105	−1.66884	−0.834419	−	0.551130i	$-0.814197\pi$
$157$	−20.9105	−1.66884	−0.834419	+	0.551130i	$0.814197\pi$
$158$	−12.7880	−1.01736
$159$	29.2422	2.31905
$160$	2.74348	0.216891
$161$	0.520464	0.0410183
$162$	22.3769	1.75810
$163$	8.93937	0.700186	0.350093	−	0.936715i	$-0.386150\pi$
$163$	8.93937	0.700186	0.350093	+	0.936715i	$0.386150\pi$
$164$	−9.40284	−0.734239
$165$	−35.0975	−2.73233
$166$	−1.49938	−0.116375
$167$	18.1411	1.40380	0.701901	−	0.712275i	$-0.252335\pi$
$167$	18.1411	1.40380	0.701901	+	0.712275i	$0.252335\pi$
$168$	3.20919	0.247594
$169$	8.54831	0.657562
$170$	14.3339	1.09936
$171$	0	0
$172$	2.55638	0.194922
$173$	−1.97709	−0.150315	−0.0751577	−	0.997172i	$-0.523946\pi$
$173$	−1.97709	−0.150315	−0.0751577	+	0.997172i	$0.523946\pi$
$174$	18.7295	1.41988
$175$	2.52666	0.190997
$176$	−3.98639	−0.300486
$177$	3.45505	0.259697
$178$	−8.77859	−0.657983
$179$	−19.4213	−1.45161	−0.725807	−	0.687899i	$-0.758533\pi$
$179$	−19.4213	−1.45161	−0.725807	+	0.687899i	$0.758533\pi$
$180$	20.0243	1.49252
$181$	−2.54502	−0.189170	−0.0945848	−	0.995517i	$-0.530152\pi$
$181$	−2.54502	−0.189170	−0.0945848	+	0.995517i	$0.530152\pi$
$182$	−4.64202	−0.344089
$183$	−4.93336	−0.364685
$184$	0.520464	0.0383691
$185$	−25.9035	−1.90446
$186$	−4.44464	−0.325897
$187$	−20.8278	−1.52308
$188$	4.77001	0.347889
$189$	13.7959	1.00350
$190$	0	0
$191$	−18.1665	−1.31448	−0.657241	−	0.753681i	$-0.728276\pi$
$191$	−18.1665	−1.31448	−0.657241	+	0.753681i	$0.728276\pi$
$192$	3.20919	0.231603
$193$	−12.5306	−0.901971	−0.450986	−	0.892531i	$-0.648927\pi$
$193$	−12.5306	−0.901971	−0.450986	+	0.892531i	$0.648927\pi$
$194$	−4.61801	−0.331554
$195$	−40.8698	−2.92675
$196$	1.00000	0.0714286
$197$	−11.0525	−0.787456	−0.393728	−	0.919227i	$-0.628815\pi$
$197$	−11.0525	−0.787456	−0.393728	+	0.919227i	$0.628815\pi$
$198$	−29.0962	−2.06777
$199$	−2.42328	−0.171782	−0.0858910	−	0.996305i	$-0.527374\pi$
$199$	−2.42328	−0.171782	−0.0858910	+	0.996305i	$0.527374\pi$
$200$	2.52666	0.178662
$201$	−39.5022	−2.78627
$202$	5.07336	0.356960
$203$	5.83623	0.409623
$204$	16.7672	1.17394
$205$	−25.7965	−1.80170
$206$	1.40012	0.0975510
$207$	3.79880	0.264035
$208$	−4.64202	−0.321866
$209$	0	0
$210$	8.80432	0.607556
$211$	−3.19423	−0.219900	−0.109950	−	0.993937i	$-0.535069\pi$
$211$	−3.19423	−0.219900	−0.109950	+	0.993937i	$0.535069\pi$
$212$	9.11202	0.625816
$213$	−12.8605	−0.881184
$214$	18.3546	1.25470
$215$	7.01337	0.478308
$216$	13.7959	0.938691
$217$	−1.38498	−0.0940182
$218$	8.49097	0.575081
$219$	−1.35689	−0.0916904
$220$	−10.9366	−0.737343
$221$	−24.2533	−1.63145
$222$	−30.3006	−2.03365
$223$	7.11759	0.476629	0.238314	−	0.971188i	$-0.423405\pi$
$223$	7.11759	0.476629	0.238314	+	0.971188i	$0.423405\pi$
$224$	1.00000	0.0668153
$225$	18.4417	1.22945
$226$	8.06367	0.536388
$227$	−15.0860	−1.00130	−0.500648	−	0.865651i	$-0.666905\pi$
$227$	−15.0860	−1.00130	−0.500648	+	0.865651i	$0.666905\pi$
$228$	0	0
$229$	0.806298	0.0532817	0.0266409	−	0.999645i	$-0.491519\pi$
$229$	0.806298	0.0532817	0.0266409	+	0.999645i	$0.491519\pi$
$230$	1.42788	0.0941516
$231$	−12.7931	−0.841722
$232$	5.83623	0.383167
$233$	−9.43769	−0.618284	−0.309142	−	0.951016i	$-0.600042\pi$
$233$	−9.43769	−0.618284	−0.309142	+	0.951016i	$0.600042\pi$
$234$	−33.8815	−2.21490
$235$	13.0864	0.853662
$236$	1.07661	0.0700815
$237$	−41.0390	−2.66577
$238$	5.22474	0.338669
$239$	−1.94285	−0.125672	−0.0628362	−	0.998024i	$-0.520015\pi$
$239$	−1.94285	−0.125672	−0.0628362	+	0.998024i	$0.520015\pi$
$240$	8.80432	0.568316
$241$	−23.4255	−1.50897	−0.754483	−	0.656319i	$-0.772112\pi$
$241$	−23.4255	−1.50897	−0.754483	+	0.656319i	$0.772112\pi$
$242$	4.89131	0.314425
$243$	30.4241	1.95170
$244$	−1.53726	−0.0984132
$245$	2.74348	0.175274
$246$	−30.1755	−1.92392
$247$	0	0
$248$	−1.38498	−0.0879460
$249$	−4.81179	−0.304935
$250$	−6.78556	−0.429156
$251$	1.46460	0.0924449	0.0462224	−	0.998931i	$-0.485282\pi$
$251$	1.46460	0.0924449	0.0462224	+	0.998931i	$0.485282\pi$
$252$	7.29887	0.459786
$253$	−2.07477	−0.130440
$254$	13.1420	0.824605
$255$	46.0003	2.88065
$256$	1.00000	0.0625000
$257$	20.5292	1.28058	0.640289	−	0.768134i	$-0.278815\pi$
$257$	20.5292	1.28058	0.640289	+	0.768134i	$0.278815\pi$
$258$	8.20390	0.510753
$259$	−9.44185	−0.586688
$260$	−12.7353	−0.789807
$261$	42.5979	2.63674
$262$	18.3208	1.13186
$263$	17.3213	1.06808	0.534039	−	0.845460i	$-0.320673\pi$
$263$	17.3213	1.06808	0.534039	+	0.845460i	$0.320673\pi$
$264$	−12.7931	−0.787359
$265$	24.9986	1.53565
$266$	0	0
$267$	−28.1721	−1.72411
$268$	−12.3091	−0.751898
$269$	11.0472	0.673562	0.336781	−	0.941583i	$-0.390662\pi$
$269$	11.0472	0.673562	0.336781	+	0.941583i	$0.390662\pi$
$270$	37.8486	2.30340
$271$	26.8694	1.63220	0.816101	−	0.577910i	$-0.196131\pi$
$271$	26.8694	1.63220	0.816101	+	0.577910i	$0.196131\pi$
$272$	5.22474	0.316796
$273$	−14.8971	−0.901613
$274$	−4.18816	−0.253016
$275$	−10.0722	−0.607379
$276$	1.67027	0.100538
$277$	−17.9579	−1.07899	−0.539493	−	0.841990i	$-0.681384\pi$
$277$	−17.9579	−1.07899	−0.539493	+	0.841990i	$0.681384\pi$
$278$	−14.9473	−0.896478
$279$	−10.1088	−0.605195
$280$	2.74348	0.163954
$281$	−8.35573	−0.498461	−0.249231	−	0.968444i	$-0.580178\pi$
$281$	−8.35573	−0.498461	−0.249231	+	0.968444i	$0.580178\pi$
$282$	15.3078	0.911569
$283$	9.89060	0.587935	0.293968	−	0.955815i	$-0.405024\pi$
$283$	9.89060	0.587935	0.293968	+	0.955815i	$0.405024\pi$
$284$	−4.00739	−0.237795
$285$	0	0
$286$	18.5049	1.09422
$287$	−9.40284	−0.555032
$288$	7.29887	0.430090
$289$	10.2979	0.605758
$290$	16.0115	0.940230
$291$	−14.8201	−0.868767
$292$	−0.422816	−0.0247434
$293$	25.5978	1.49544	0.747719	−	0.664015i	$-0.231149\pi$
$293$	25.5978	1.49544	0.747719	+	0.664015i	$0.231149\pi$
$294$	3.20919	0.187164
$295$	2.95366	0.171969
$296$	−9.44185	−0.548796
$297$	−54.9958	−3.19118
$298$	−0.0172226	−0.000997681 0
$299$	−2.41600	−0.139721
$300$	8.10851	0.468145
$301$	2.55638	0.147347
$302$	−6.94979	−0.399915
$303$	16.2813	0.935339
$304$	0	0
$305$	−4.21744	−0.241490
$306$	38.1347	2.18002
$307$	−9.29373	−0.530421	−0.265211	−	0.964190i	$-0.585442\pi$
$307$	−9.29373	−0.530421	−0.265211	+	0.964190i	$0.585442\pi$
$308$	−3.98639	−0.227146
$309$	4.49324	0.255612
$310$	−3.79964	−0.215805
$311$	−7.03492	−0.398914	−0.199457	−	0.979907i	$-0.563918\pi$
$311$	−7.03492	−0.398914	−0.199457	+	0.979907i	$0.563918\pi$
$312$	−14.8971	−0.843382
$313$	29.7865	1.68363	0.841817	−	0.539762i	$-0.181486\pi$
$313$	29.7865	1.68363	0.841817	+	0.539762i	$0.181486\pi$
$314$	−20.9105	−1.18005
$315$	20.0243	1.12824
$316$	−12.7880	−0.719381
$317$	−18.9853	−1.06632	−0.533160	−	0.846015i	$-0.678995\pi$
$317$	−18.9853	−1.06632	−0.533160	+	0.846015i	$0.678995\pi$
$318$	29.2422	1.63982
$319$	−23.2655	−1.30262
$320$	2.74348	0.153365
$321$	58.9035	3.28767
$322$	0.520464	0.0290043
$323$	0	0
$324$	22.3769	1.24316
$325$	−11.7288	−0.650595
$326$	8.93937	0.495106
$327$	27.2491	1.50688
$328$	−9.40284	−0.519185
$329$	4.77001	0.262979
$330$	−35.0975	−1.93205
$331$	8.68202	0.477207	0.238603	−	0.971117i	$-0.423310\pi$
$331$	8.68202	0.477207	0.238603	+	0.971117i	$0.423310\pi$
$332$	−1.49938	−0.0822892
$333$	−68.9148	−3.77651
$334$	18.1411	0.992637
$335$	−33.7697	−1.84504
$336$	3.20919	0.175075
$337$	−16.7894	−0.914575	−0.457287	−	0.889319i	$-0.651179\pi$
$337$	−16.7894	−0.914575	−0.457287	+	0.889319i	$0.651179\pi$
$338$	8.54831	0.464967
$339$	25.8778	1.40549
$340$	14.3339	0.777367
$341$	5.52105	0.298982
$342$	0	0
$343$	1.00000	0.0539949
$344$	2.55638	0.137831
$345$	4.58233	0.246704
$346$	−1.97709	−0.106289
$347$	13.9880	0.750918	0.375459	−	0.926839i	$-0.377485\pi$
$347$	13.9880	0.750918	0.375459	+	0.926839i	$0.377485\pi$
$348$	18.7295	1.00401
$349$	−17.7151	−0.948269	−0.474134	−	0.880453i	$-0.657239\pi$
$349$	−17.7151	−0.948269	−0.474134	+	0.880453i	$0.657239\pi$
$350$	2.52666	0.135055
$351$	−64.0407	−3.41824
$352$	−3.98639	−0.212475
$353$	−7.84139	−0.417355	−0.208678	−	0.977984i	$-0.566916\pi$
$353$	−7.84139	−0.417355	−0.208678	+	0.977984i	$0.566916\pi$
$354$	3.45505	0.183634
$355$	−10.9942	−0.583510
$356$	−8.77859	−0.465265
$357$	16.7672	0.887412
$358$	−19.4213	−1.02645
$359$	14.7718	0.779625	0.389813	−	0.920894i	$-0.372540\pi$
$359$	14.7718	0.779625	0.389813	+	0.920894i	$0.372540\pi$
$360$	20.0243	1.05537
$361$	0	0
$362$	−2.54502	−0.133763
$363$	15.6971	0.823885
$364$	−4.64202	−0.243308
$365$	−1.15998	−0.0607164
$366$	−4.93336	−0.257871
$367$	5.42648	0.283260	0.141630	−	0.989920i	$-0.454766\pi$
$367$	5.42648	0.283260	0.141630	+	0.989920i	$0.454766\pi$
$368$	0.520464	0.0271311
$369$	−68.6301	−3.57274
$370$	−25.9035	−1.34666
$371$	9.11202	0.473073
$372$	−4.44464	−0.230444
$373$	30.1582	1.56153	0.780767	−	0.624822i	$-0.214828\pi$
$373$	30.1582	1.56153	0.780767	+	0.624822i	$0.214828\pi$
$374$	−20.8278	−1.07698
$375$	−21.7761	−1.12451
$376$	4.77001	0.245994
$377$	−27.0919	−1.39530
$378$	13.7959	0.709583
$379$	−22.1827	−1.13945	−0.569726	−	0.821835i	$-0.692951\pi$
$379$	−22.1827	−1.13945	−0.569726	+	0.821835i	$0.692951\pi$
$380$	0	0
$381$	42.1752	2.16070
$382$	−18.1665	−0.929479
$383$	13.5571	0.692734	0.346367	−	0.938099i	$-0.387415\pi$
$383$	13.5571	0.692734	0.346367	+	0.938099i	$0.387415\pi$
$384$	3.20919	0.163768
$385$	−10.9366	−0.557379
$386$	−12.5306	−0.637790
$387$	18.6587	0.948475
$388$	−4.61801	−0.234444
$389$	30.2938	1.53596	0.767979	−	0.640475i	$-0.221262\pi$
$389$	30.2938	1.53596	0.767979	+	0.640475i	$0.221262\pi$
$390$	−40.8698	−2.06952
$391$	2.71929	0.137520
$392$	1.00000	0.0505076
$393$	58.7948	2.96580
$394$	−11.0525	−0.556816
$395$	−35.0835	−1.76524
$396$	−29.0962	−1.46214
$397$	−21.9430	−1.10129	−0.550644	−	0.834740i	$-0.685618\pi$
$397$	−21.9430	−1.10129	−0.550644	+	0.834740i	$0.685618\pi$
$398$	−2.42328	−0.121468
$399$	0	0
$400$	2.52666	0.126333
$401$	−31.7184	−1.58394	−0.791970	−	0.610560i	$-0.790945\pi$
$401$	−31.7184	−1.58394	−0.791970	+	0.610560i	$0.790945\pi$
$402$	−39.5022	−1.97019
$403$	6.42908	0.320255
$404$	5.07336	0.252409
$405$	61.3905	3.05052
$406$	5.83623	0.289647
$407$	37.6389	1.86569
$408$	16.7672	0.830098
$409$	12.3597	0.611146	0.305573	−	0.952169i	$-0.401152\pi$
$409$	12.3597	0.611146	0.305573	+	0.952169i	$0.401152\pi$
$410$	−25.7965	−1.27400
$411$	−13.4406	−0.662974
$412$	1.40012	0.0689790
$413$	1.07661	0.0529766
$414$	3.79880	0.186701
$415$	−4.11352	−0.201925
$416$	−4.64202	−0.227594
$417$	−47.9686	−2.34903
$418$	0	0
$419$	19.6277	0.958875	0.479438	−	0.877576i	$-0.340841\pi$
$419$	19.6277	0.958875	0.479438	+	0.877576i	$0.340841\pi$
$420$	8.80432	0.429607
$421$	−17.1735	−0.836987	−0.418493	−	0.908220i	$-0.637442\pi$
$421$	−17.1735	−0.836987	−0.418493	+	0.908220i	$0.637442\pi$
$422$	−3.19423	−0.155493
$423$	34.8157	1.69280
$424$	9.11202	0.442519
$425$	13.2011	0.640348
$426$	−12.8605	−0.623091
$427$	−1.53726	−0.0743934
$428$	18.3546	0.887205
$429$	59.3856	2.86716
$430$	7.01337	0.338215
$431$	−32.3852	−1.55994	−0.779969	−	0.625818i	$-0.784765\pi$
$431$	−32.3852	−1.55994	−0.779969	+	0.625818i	$0.784765\pi$
$432$	13.7959	0.663755
$433$	−36.9496	−1.77568	−0.887842	−	0.460148i	$-0.847797\pi$
$433$	−36.9496	−1.77568	−0.887842	+	0.460148i	$0.847797\pi$
$434$	−1.38498	−0.0664809
$435$	51.3840	2.46367
$436$	8.49097	0.406643
$437$	0	0
$438$	−1.35689	−0.0648349
$439$	17.0885	0.815588	0.407794	−	0.913074i	$-0.366298\pi$
$439$	17.0885	0.815588	0.407794	+	0.913074i	$0.366298\pi$
$440$	−10.9366	−0.521380
$441$	7.29887	0.347565
$442$	−24.2533	−1.15361
$443$	12.9797	0.616682	0.308341	−	0.951276i	$-0.400226\pi$
$443$	12.9797	0.616682	0.308341	+	0.951276i	$0.400226\pi$
$444$	−30.3006	−1.43800
$445$	−24.0839	−1.14168
$446$	7.11759	0.337027
$447$	−0.0552706	−0.00261421
$448$	1.00000	0.0472456
$449$	−4.13018	−0.194915	−0.0974575	−	0.995240i	$-0.531071\pi$
$449$	−4.13018	−0.194915	−0.0974575	+	0.995240i	$0.531071\pi$
$450$	18.4417	0.869352
$451$	37.4834	1.76502
$452$	8.06367	0.379283
$453$	−22.3032	−1.04789
$454$	−15.0860	−0.708023
$455$	−12.7353	−0.597038
$456$	0	0
$457$	32.4479	1.51785	0.758925	−	0.651178i	$-0.225725\pi$
$457$	32.4479	1.51785	0.758925	+	0.651178i	$0.225725\pi$
$458$	0.806298	0.0376759
$459$	72.0799	3.36440
$460$	1.42788	0.0665752
$461$	19.0076	0.885272	0.442636	−	0.896701i	$-0.354043\pi$
$461$	19.0076	0.885272	0.442636	+	0.896701i	$0.354043\pi$
$462$	−12.7931	−0.595187
$463$	11.7900	0.547930	0.273965	−	0.961740i	$-0.411665\pi$
$463$	11.7900	0.547930	0.273965	+	0.961740i	$0.411665\pi$
$464$	5.83623	0.270940
$465$	−12.1938	−0.565472
$466$	−9.43769	−0.437193
$467$	−31.0653	−1.43753	−0.718766	−	0.695252i	$-0.755293\pi$
$467$	−31.0653	−1.43753	−0.718766	+	0.695252i	$0.755293\pi$
$468$	−33.8815	−1.56617
$469$	−12.3091	−0.568381
$470$	13.0864	0.603631
$471$	−67.1056	−3.09206
$472$	1.07661	0.0495551
$473$	−10.1907	−0.468571
$474$	−41.0390	−1.88499
$475$	0	0
$476$	5.22474	0.239475
$477$	66.5075	3.04517
$478$	−1.94285	−0.0888638
$479$	−14.0514	−0.642026	−0.321013	−	0.947075i	$-0.604023\pi$
$479$	−14.0514	−0.642026	−0.321013	+	0.947075i	$0.604023\pi$
$480$	8.80432	0.401860
$481$	43.8292	1.99844
$482$	−23.4255	−1.06700
$483$	1.67027	0.0759997
$484$	4.89131	0.222332
$485$	−12.6694	−0.575288
$486$	30.4241	1.38006
$487$	10.4919	0.475431	0.237716	−	0.971335i	$-0.423601\pi$
$487$	10.4919	0.475431	0.237716	+	0.971335i	$0.423601\pi$
$488$	−1.53726	−0.0695886
$489$	28.6881	1.29732
$490$	2.74348	0.123938
$491$	−1.39469	−0.0629415	−0.0314707	−	0.999505i	$-0.510019\pi$
$491$	−1.39469	−0.0629415	−0.0314707	+	0.999505i	$0.510019\pi$
$492$	−30.1755	−1.36042
$493$	30.4928	1.37332
$494$	0	0
$495$	−79.8246	−3.58785
$496$	−1.38498	−0.0621872
$497$	−4.00739	−0.179756
$498$	−4.81179	−0.215622
$499$	20.9626	0.938417	0.469209	−	0.883087i	$-0.344539\pi$
$499$	20.9626	0.938417	0.469209	+	0.883087i	$0.344539\pi$
$500$	−6.78556	−0.303459
$501$	58.2182	2.60100
$502$	1.46460	0.0653684
$503$	24.5284	1.09367	0.546833	−	0.837242i	$-0.315833\pi$
$503$	24.5284	1.09367	0.546833	+	0.837242i	$0.315833\pi$
$504$	7.29887	0.325118
$505$	13.9186	0.619371
$506$	−2.07477	−0.0922349
$507$	27.4331	1.21835
$508$	13.1420	0.583084
$509$	9.65017	0.427736	0.213868	−	0.976863i	$-0.431394\pi$
$509$	9.65017	0.427736	0.213868	+	0.976863i	$0.431394\pi$
$510$	46.0003	2.03693
$511$	−0.422816	−0.0187043
$512$	1.00000	0.0441942
$513$	0	0
$514$	20.5292	0.905505
$515$	3.84119	0.169263
$516$	8.20390	0.361157
$517$	−19.0151	−0.836284
$518$	−9.44185	−0.414851
$519$	−6.34485	−0.278508
$520$	−12.7353	−0.558478
$521$	22.4183	0.982164	0.491082	−	0.871113i	$-0.336602\pi$
$521$	22.4183	0.982164	0.491082	+	0.871113i	$0.336602\pi$
$522$	42.5979	1.86446
$523$	−38.7427	−1.69410	−0.847050	−	0.531514i	$-0.821623\pi$
$523$	−38.7427	−1.69410	−0.847050	+	0.531514i	$0.821623\pi$
$524$	18.3208	0.800347
$525$	8.10851	0.353884
$526$	17.3213	0.755246
$527$	−7.23613	−0.315211
$528$	−12.7931	−0.556747
$529$	−22.7291	−0.988222
$530$	24.9986	1.08587
$531$	7.85806	0.341011
$532$	0	0
$533$	43.6481	1.89061
$534$	−28.1721	−1.21913
$535$	50.3555	2.17706
$536$	−12.3091	−0.531672
$537$	−62.3264	−2.68958
$538$	11.0472	0.476280
$539$	−3.98639	−0.171706
$540$	37.8486	1.62875
$541$	−11.0477	−0.474979	−0.237489	−	0.971390i	$-0.576324\pi$
$541$	−11.0477	−0.474979	−0.237489	+	0.971390i	$0.576324\pi$
$542$	26.8694	1.15414
$543$	−8.16743	−0.350498
$544$	5.22474	0.224009
$545$	23.2948	0.997837
$546$	−14.8971	−0.637537
$547$	32.3458	1.38301	0.691503	−	0.722374i	$-0.256949\pi$
$547$	32.3458	1.38301	0.691503	+	0.722374i	$0.256949\pi$
$548$	−4.18816	−0.178909
$549$	−11.2203	−0.478870
$550$	−10.0722	−0.429482
$551$	0	0
$552$	1.67027	0.0710912
$553$	−12.7880	−0.543801
$554$	−17.9579	−0.762958
$555$	−83.1290	−3.52863
$556$	−14.9473	−0.633905
$557$	−3.95763	−0.167690	−0.0838451	−	0.996479i	$-0.526720\pi$
$557$	−3.95763	−0.167690	−0.0838451	+	0.996479i	$0.526720\pi$
$558$	−10.1088	−0.427938
$559$	−11.8668	−0.501911
$560$	2.74348	0.115933
$561$	−66.8404	−2.82201
$562$	−8.35573	−0.352465
$563$	10.8437	0.457006	0.228503	−	0.973543i	$-0.426617\pi$
$563$	10.8437	0.457006	0.228503	+	0.973543i	$0.426617\pi$
$564$	15.3078	0.644576
$565$	22.1225	0.930700
$566$	9.89060	0.415733
$567$	22.3769	0.939742
$568$	−4.00739	−0.168146
$569$	−35.0709	−1.47025	−0.735123	−	0.677933i	$-0.762876\pi$
$569$	−35.0709	−1.47025	−0.735123	+	0.677933i	$0.762876\pi$
$570$	0	0
$571$	4.49506	0.188112	0.0940561	−	0.995567i	$-0.470017\pi$
$571$	4.49506	0.188112	0.0940561	+	0.995567i	$0.470017\pi$
$572$	18.5049	0.773728
$573$	−58.2996	−2.43550
$574$	−9.40284	−0.392467
$575$	1.31503	0.0548407
$576$	7.29887	0.304120
$577$	−33.3015	−1.38636	−0.693179	−	0.720765i	$-0.743791\pi$
$577$	−33.3015	−1.38636	−0.693179	+	0.720765i	$0.743791\pi$
$578$	10.2979	0.428336
$579$	−40.2130	−1.67119
$580$	16.0115	0.664843
$581$	−1.49938	−0.0622048
$582$	−14.8201	−0.614311
$583$	−36.3241	−1.50439
$584$	−0.422816	−0.0174962
$585$	−92.9530	−3.84313
$586$	25.5978	1.05743
$587$	3.00415	0.123995	0.0619973	−	0.998076i	$-0.480253\pi$
$587$	3.00415	0.123995	0.0619973	+	0.998076i	$0.480253\pi$
$588$	3.20919	0.132345
$589$	0	0
$590$	2.95366	0.121600
$591$	−35.4694	−1.45902
$592$	−9.44185	−0.388057
$593$	12.4444	0.511030	0.255515	−	0.966805i	$-0.417755\pi$
$593$	12.4444	0.511030	0.255515	+	0.966805i	$0.417755\pi$
$594$	−54.9958	−2.25650
$595$	14.3339	0.587634
$596$	−0.0172226	−0.000705467 0
$597$	−7.77677	−0.318282
$598$	−2.41600	−0.0987976
$599$	34.0809	1.39251	0.696255	−	0.717795i	$-0.254848\pi$
$599$	34.0809	1.39251	0.696255	+	0.717795i	$0.254848\pi$
$600$	8.10851	0.331028
$601$	13.3248	0.543529	0.271764	−	0.962364i	$-0.412393\pi$
$601$	13.3248	0.543529	0.271764	+	0.962364i	$0.412393\pi$
$602$	2.55638	0.104190
$603$	−89.8425	−3.65867
$604$	−6.94979	−0.282783
$605$	13.4192	0.545568
$606$	16.2813	0.661385
$607$	42.2842	1.71626	0.858132	−	0.513430i	$-0.171625\pi$
$607$	42.2842	1.71626	0.858132	+	0.513430i	$0.171625\pi$
$608$	0	0
$609$	18.7295	0.758959
$610$	−4.21744	−0.170759
$611$	−22.1425	−0.895788
$612$	38.1347	1.54150
$613$	23.4473	0.947027	0.473513	−	0.880787i	$-0.342986\pi$
$613$	23.4473	0.947027	0.473513	+	0.880787i	$0.342986\pi$
$614$	−9.29373	−0.375065
$615$	−82.7856	−3.33824
$616$	−3.98639	−0.160616
$617$	21.3865	0.860989	0.430495	−	0.902593i	$-0.358339\pi$
$617$	21.3865	0.860989	0.430495	+	0.902593i	$0.358339\pi$
$618$	4.49324	0.180745
$619$	21.3208	0.856954	0.428477	−	0.903553i	$-0.359050\pi$
$619$	21.3208	0.856954	0.428477	+	0.903553i	$0.359050\pi$
$620$	−3.79964	−0.152597
$621$	7.18026	0.288134
$622$	−7.03492	−0.282075
$623$	−8.77859	−0.351707
$624$	−14.8971	−0.596361
$625$	−31.2493	−1.24997
$626$	29.7865	1.19051
$627$	0	0
$628$	−20.9105	−0.834419
$629$	−49.3312	−1.96696
$630$	20.0243	0.797786
$631$	14.5419	0.578903	0.289452	−	0.957193i	$-0.406527\pi$
$631$	14.5419	0.578903	0.289452	+	0.957193i	$0.406527\pi$
$632$	−12.7880	−0.508679
$633$	−10.2509	−0.407436
$634$	−18.9853	−0.754002
$635$	36.0549	1.43079
$636$	29.2422	1.15953
$637$	−4.64202	−0.183923
$638$	−23.2655	−0.921089
$639$	−29.2494	−1.15709
$640$	2.74348	0.108445
$641$	6.21640	0.245533	0.122767	−	0.992436i	$-0.460823\pi$
$641$	6.21640	0.245533	0.122767	+	0.992436i	$0.460823\pi$
$642$	58.9035	2.32473
$643$	38.8654	1.53270	0.766350	−	0.642423i	$-0.222071\pi$
$643$	38.8654	1.53270	0.766350	+	0.642423i	$0.222071\pi$
$644$	0.520464	0.0205091
$645$	22.5072	0.886220
$646$	0	0
$647$	−26.3165	−1.03461	−0.517303	−	0.855802i	$-0.673064\pi$
$647$	−26.3165	−1.03461	−0.517303	+	0.855802i	$0.673064\pi$
$648$	22.3769	0.879048
$649$	−4.29180	−0.168468
$650$	−11.7288	−0.460040
$651$	−4.44464	−0.174199
$652$	8.93937	0.350093
$653$	21.6104	0.845679	0.422840	−	0.906205i	$-0.361033\pi$
$653$	21.6104	0.845679	0.422840	+	0.906205i	$0.361033\pi$
$654$	27.2491	1.06552
$655$	50.2626	1.96392
$656$	−9.40284	−0.367119
$657$	−3.08608	−0.120399
$658$	4.77001	0.185954
$659$	−6.45405	−0.251414	−0.125707	−	0.992067i	$-0.540120\pi$
$659$	−6.45405	−0.251414	−0.125707	+	0.992067i	$0.540120\pi$
$660$	−35.0975	−1.36617
$661$	−6.13106	−0.238470	−0.119235	−	0.992866i	$-0.538044\pi$
$661$	−6.13106	−0.238470	−0.119235	+	0.992866i	$0.538044\pi$
$662$	8.68202	0.337436
$663$	−77.8334	−3.02280
$664$	−1.49938	−0.0581873
$665$	0	0
$666$	−68.9148	−2.67040
$667$	3.03755	0.117614
$668$	18.1411	0.701901
$669$	22.8417	0.883109
$670$	−33.7697	−1.30464
$671$	6.12813	0.236574
$672$	3.20919	0.123797
$673$	−9.63805	−0.371520	−0.185760	−	0.982595i	$-0.559475\pi$
$673$	−9.63805	−0.371520	−0.185760	+	0.982595i	$0.559475\pi$
$674$	−16.7894	−0.646702
$675$	34.8574	1.34166
$676$	8.54831	0.328781
$677$	−1.71964	−0.0660909	−0.0330455	−	0.999454i	$-0.510521\pi$
$677$	−1.71964	−0.0660909	−0.0330455	+	0.999454i	$0.510521\pi$
$678$	25.8778	0.993832
$679$	−4.61801	−0.177223
$680$	14.3339	0.549681
$681$	−48.4139	−1.85523
$682$	5.52105	0.211412
$683$	−9.63395	−0.368633	−0.184317	−	0.982867i	$-0.559007\pi$
$683$	−9.63395	−0.368633	−0.184317	+	0.982867i	$0.559007\pi$
$684$	0	0
$685$	−11.4901	−0.439014
$686$	1.00000	0.0381802
$687$	2.58756	0.0987216
$688$	2.55638	0.0974611
$689$	−42.2981	−1.61143
$690$	4.58233	0.174446
$691$	38.5682	1.46720	0.733602	−	0.679579i	$-0.237838\pi$
$691$	38.5682	1.46720	0.733602	+	0.679579i	$0.237838\pi$
$692$	−1.97709	−0.0751577
$693$	−29.0962	−1.10527
$694$	13.9880	0.530979
$695$	−41.0075	−1.55550
$696$	18.7295	0.709941
$697$	−49.1274	−1.86083
$698$	−17.7151	−0.670527
$699$	−30.2873	−1.14557
$700$	2.52666	0.0954986
$701$	−23.8793	−0.901910	−0.450955	−	0.892547i	$-0.648916\pi$
$701$	−23.8793	−0.901910	−0.450955	+	0.892547i	$0.648916\pi$
$702$	−64.0407	−2.41706
$703$	0	0
$704$	−3.98639	−0.150243
$705$	41.9967	1.58169
$706$	−7.84139	−0.295115
$707$	5.07336	0.190803
$708$	3.45505	0.129849
$709$	−17.7638	−0.667134	−0.333567	−	0.942726i	$-0.608252\pi$
$709$	−17.7638	−0.667134	−0.333567	+	0.942726i	$0.608252\pi$
$710$	−10.9942	−0.412604
$711$	−93.3379	−3.50045
$712$	−8.77859	−0.328992
$713$	−0.720830	−0.0269953
$714$	16.7672	0.627495
$715$	50.7677	1.89860
$716$	−19.4213	−0.725807
$717$	−6.23496	−0.232849
$718$	14.7718	0.551278
$719$	−6.30664	−0.235198	−0.117599	−	0.993061i	$-0.537520\pi$
$719$	−6.30664	−0.235198	−0.117599	+	0.993061i	$0.537520\pi$
$720$	20.0243	0.746261
$721$	1.40012	0.0521432
$722$	0	0
$723$	−75.1767	−2.79585
$724$	−2.54502	−0.0945848
$725$	14.7461	0.547658
$726$	15.6971	0.582575
$727$	−11.7046	−0.434101	−0.217050	−	0.976160i	$-0.569644\pi$
$727$	−11.7046	−0.434101	−0.217050	+	0.976160i	$0.569644\pi$
$728$	−4.64202	−0.172045
$729$	30.5057	1.12984
$730$	−1.15998	−0.0429330
$731$	13.3564	0.494005
$732$	−4.93336	−0.182342
$733$	16.8530	0.622479	0.311239	−	0.950332i	$-0.399256\pi$
$733$	16.8530	0.622479	0.311239	+	0.950332i	$0.399256\pi$
$734$	5.42648	0.200295
$735$	8.80432	0.324752
$736$	0.520464	0.0191846
$737$	49.0689	1.80747
$738$	−68.6301	−2.52631
$739$	33.5157	1.23289	0.616447	−	0.787396i	$-0.288571\pi$
$739$	33.5157	1.23289	0.616447	+	0.787396i	$0.288571\pi$
$740$	−25.9035	−0.952230
$741$	0	0
$742$	9.11202	0.334513
$743$	−21.1455	−0.775754	−0.387877	−	0.921711i	$-0.626792\pi$
$743$	−21.1455	−0.775754	−0.387877	+	0.921711i	$0.626792\pi$
$744$	−4.44464	−0.162948
$745$	−0.0472499	−0.00173110
$746$	30.1582	1.10417
$747$	−10.9438	−0.400412
$748$	−20.8278	−0.761542
$749$	18.3546	0.670664
$750$	−21.7761	−0.795151
$751$	9.61118	0.350717	0.175359	−	0.984505i	$-0.443892\pi$
$751$	9.61118	0.350717	0.175359	+	0.984505i	$0.443892\pi$
$752$	4.77001	0.173944
$753$	4.70018	0.171284
$754$	−27.0919	−0.986627
$755$	−19.0666	−0.693903
$756$	13.7959	0.501751
$757$	33.2945	1.21011	0.605054	−	0.796185i	$-0.293152\pi$
$757$	33.2945	1.21011	0.605054	+	0.796185i	$0.293152\pi$
$758$	−22.1827	−0.805714
$759$	−6.65833	−0.241682
$760$	0	0
$761$	−26.5600	−0.962801	−0.481400	−	0.876501i	$-0.659872\pi$
$761$	−26.5600	−0.962801	−0.481400	+	0.876501i	$0.659872\pi$
$762$	42.1752	1.52785
$763$	8.49097	0.307394
$764$	−18.1665	−0.657241
$765$	104.622	3.78260
$766$	13.5571	0.489837
$767$	−4.99765	−0.180455
$768$	3.20919	0.115802
$769$	6.41593	0.231364	0.115682	−	0.993286i	$-0.463095\pi$
$769$	6.41593	0.231364	0.115682	+	0.993286i	$0.463095\pi$
$770$	−10.9366	−0.394126
$771$	65.8821	2.37268
$772$	−12.5306	−0.450986
$773$	32.9261	1.18427	0.592134	−	0.805839i	$-0.298286\pi$
$773$	32.9261	1.18427	0.592134	+	0.805839i	$0.298286\pi$
$774$	18.6587	0.670673
$775$	−3.49935	−0.125701
$776$	−4.61801	−0.165777
$777$	−30.3006	−1.08703
$778$	30.2938	1.08609
$779$	0	0
$780$	−40.8698	−1.46337
$781$	15.9750	0.571631
$782$	2.71929	0.0972415
$783$	80.5159	2.87740
$784$	1.00000	0.0357143
$785$	−57.3674	−2.04753
$786$	58.7948	2.09714
$787$	−46.7761	−1.66739	−0.833694	−	0.552227i	$-0.813778\pi$
$787$	−46.7761	−1.66739	−0.833694	+	0.552227i	$0.813778\pi$
$788$	−11.0525	−0.393728
$789$	55.5873	1.97896
$790$	−35.0835	−1.24822
$791$	8.06367	0.286711
$792$	−29.0962	−1.03389
$793$	7.13600	0.253407
$794$	−21.9430	−0.778728
$795$	80.2252	2.84529
$796$	−2.42328	−0.0858910
$797$	52.2887	1.85216	0.926080	−	0.377327i	$-0.123157\pi$
$797$	52.2887	1.85216	0.926080	+	0.377327i	$0.123157\pi$
$798$	0	0
$799$	24.9220	0.881678
$800$	2.52666	0.0893308
$801$	−64.0738	−2.26394
$802$	−31.7184	−1.12002
$803$	1.68551	0.0594803
$804$	−39.5022	−1.39313
$805$	1.42788	0.0503261
$806$	6.42908	0.226455
$807$	35.4527	1.24799
$808$	5.07336	0.178480
$809$	42.2566	1.48566	0.742832	−	0.669478i	$-0.233482\pi$
$809$	42.2566	1.48566	0.742832	+	0.669478i	$0.233482\pi$
$810$	61.3905	2.15704
$811$	14.5252	0.510050	0.255025	−	0.966934i	$-0.417916\pi$
$811$	14.5252	0.510050	0.255025	+	0.966934i	$0.417916\pi$
$812$	5.83623	0.204811
$813$	86.2290	3.02418
$814$	37.6389	1.31924
$815$	24.5249	0.859071
$816$	16.7672	0.586968
$817$	0	0
$818$	12.3597	0.432145
$819$	−33.8815	−1.18391
$820$	−25.7965	−0.900852
$821$	24.1732	0.843651	0.421826	−	0.906677i	$-0.361389\pi$
$821$	24.1732	0.843651	0.421826	+	0.906677i	$0.361389\pi$
$822$	−13.4406	−0.468794
$823$	−48.3154	−1.68417	−0.842084	−	0.539346i	$-0.818671\pi$
$823$	−48.3154	−1.68417	−0.842084	+	0.539346i	$0.818671\pi$
$824$	1.40012	0.0487755
$825$	−32.3237	−1.12537
$826$	1.07661	0.0374601
$827$	17.5537	0.610404	0.305202	−	0.952288i	$-0.401276\pi$
$827$	17.5537	0.610404	0.305202	+	0.952288i	$0.401276\pi$
$828$	3.79880	0.132017
$829$	7.73032	0.268485	0.134242	−	0.990949i	$-0.457140\pi$
$829$	7.73032	0.268485	0.134242	+	0.990949i	$0.457140\pi$
$830$	−4.11352	−0.142782
$831$	−57.6303	−1.99917
$832$	−4.64202	−0.160933
$833$	5.22474	0.181026
$834$	−47.9686	−1.66102
$835$	49.7697	1.72235
$836$	0	0
$837$	−19.1069	−0.660433
$838$	19.6277	0.678027
$839$	23.1192	0.798163	0.399081	−	0.916916i	$-0.369329\pi$
$839$	23.1192	0.798163	0.399081	+	0.916916i	$0.369329\pi$
$840$	8.80432	0.303778
$841$	5.06154	0.174536
$842$	−17.1735	−0.591839
$843$	−26.8151	−0.923561
$844$	−3.19423	−0.109950
$845$	23.4521	0.806776
$846$	34.8157	1.19699
$847$	4.89131	0.168067
$848$	9.11202	0.312908
$849$	31.7408	1.08934
$850$	13.2011	0.452794
$851$	−4.91414	−0.168455
$852$	−12.8605	−0.440592
$853$	−27.0971	−0.927787	−0.463894	−	0.885891i	$-0.653548\pi$
$853$	−27.0971	−0.927787	−0.463894	+	0.885891i	$0.653548\pi$
$854$	−1.53726	−0.0526041
$855$	0	0
$856$	18.3546	0.627349
$857$	40.3472	1.37823	0.689117	−	0.724650i	$-0.257999\pi$
$857$	40.3472	1.37823	0.689117	+	0.724650i	$0.257999\pi$
$858$	59.3856	2.02739
$859$	−35.7644	−1.22027	−0.610133	−	0.792299i	$-0.708884\pi$
$859$	−35.7644	−1.22027	−0.610133	+	0.792299i	$0.708884\pi$
$860$	7.01337	0.239154
$861$	−30.1755	−1.02838
$862$	−32.3852	−1.10304
$863$	11.3420	0.386085	0.193042	−	0.981190i	$-0.438165\pi$
$863$	11.3420	0.386085	0.193042	+	0.981190i	$0.438165\pi$
$864$	13.7959	0.469345
$865$	−5.42410	−0.184425
$866$	−36.9496	−1.25560
$867$	33.0478	1.12236
$868$	−1.38498	−0.0470091
$869$	50.9779	1.72931
$870$	51.3840	1.74208
$871$	57.1390	1.93608
$872$	8.49097	0.287540
$873$	−33.7063	−1.14078
$874$	0	0
$875$	−6.78556	−0.229394
$876$	−1.35689	−0.0458452
$877$	21.1454	0.714028	0.357014	−	0.934099i	$-0.383795\pi$
$877$	21.1454	0.714028	0.357014	+	0.934099i	$0.383795\pi$
$878$	17.0885	0.576708
$879$	82.1480	2.77078
$880$	−10.9366	−0.368671
$881$	15.5245	0.523034	0.261517	−	0.965199i	$-0.415777\pi$
$881$	15.5245	0.523034	0.261517	+	0.965199i	$0.415777\pi$
$882$	7.29887	0.245766
$883$	−5.25391	−0.176808	−0.0884040	−	0.996085i	$-0.528177\pi$
$883$	−5.25391	−0.176808	−0.0884040	+	0.996085i	$0.528177\pi$
$884$	−24.2533	−0.815727
$885$	9.47884	0.318628
$886$	12.9797	0.436060
$887$	−25.4039	−0.852979	−0.426489	−	0.904493i	$-0.640250\pi$
$887$	−25.4039	−0.852979	−0.426489	+	0.904493i	$0.640250\pi$
$888$	−30.3006	−1.01682
$889$	13.1420	0.440770
$890$	−24.0839	−0.807293
$891$	−89.2031	−2.98842
$892$	7.11759	0.238314
$893$	0	0
$894$	−0.0552706	−0.00184853
$895$	−53.2818	−1.78101
$896$	1.00000	0.0334077
$897$	−7.75340	−0.258878
$898$	−4.13018	−0.137826
$899$	−8.08303	−0.269584
$900$	18.4417	0.614724
$901$	47.6079	1.58605
$902$	37.4834	1.24806
$903$	8.20390	0.273009
$904$	8.06367	0.268194
$905$	−6.98219	−0.232096
$906$	−22.3032	−0.740973
$907$	9.07682	0.301391	0.150695	−	0.988580i	$-0.451849\pi$
$907$	9.07682	0.301391	0.150695	+	0.988580i	$0.451849\pi$
$908$	−15.0860	−0.500648
$909$	37.0298	1.22820
$910$	−12.7353	−0.422170
$911$	−46.2125	−1.53109	−0.765544	−	0.643383i	$-0.777530\pi$
$911$	−46.2125	−1.53109	−0.765544	+	0.643383i	$0.777530\pi$
$912$	0	0
$913$	5.97712	0.197814
$914$	32.4479	1.07328
$915$	−13.5346	−0.447439
$916$	0.806298	0.0266409
$917$	18.3208	0.605005
$918$	72.0799	2.37899
$919$	12.9003	0.425540	0.212770	−	0.977102i	$-0.431751\pi$
$919$	12.9003	0.425540	0.212770	+	0.977102i	$0.431751\pi$
$920$	1.42788	0.0470758
$921$	−29.8253	−0.982778
$922$	19.0076	0.625982
$923$	18.6024	0.612304
$924$	−12.7931	−0.420861
$925$	−23.8563	−0.784390
$926$	11.7900	0.387445
$927$	10.2193	0.335646
$928$	5.83623	0.191584
$929$	−2.93205	−0.0961975	−0.0480987	−	0.998843i	$-0.515316\pi$
$929$	−2.93205	−0.0961975	−0.0480987	+	0.998843i	$0.515316\pi$
$930$	−12.1938	−0.399849
$931$	0	0
$932$	−9.43769	−0.309142
$933$	−22.5764	−0.739117
$934$	−31.0653	−1.01649
$935$	−57.1407	−1.86870
$936$	−33.8815	−1.10745
$937$	38.6251	1.26183	0.630914	−	0.775853i	$-0.282680\pi$
$937$	38.6251	1.26183	0.630914	+	0.775853i	$0.282680\pi$
$938$	−12.3091	−0.401906
$939$	95.5905	3.11948
$940$	13.0864	0.426831
$941$	23.1348	0.754172	0.377086	−	0.926178i	$-0.376926\pi$
$941$	23.1348	0.754172	0.377086	+	0.926178i	$0.376926\pi$
$942$	−67.1056	−2.18642
$943$	−4.89384	−0.159365
$944$	1.07661	0.0350408
$945$	37.8486	1.23122
$946$	−10.1907	−0.331329
$947$	−43.9090	−1.42685	−0.713425	−	0.700732i	$-0.752857\pi$
$947$	−43.9090	−1.42685	−0.713425	+	0.700732i	$0.752857\pi$
$948$	−41.0390	−1.33289
$949$	1.96272	0.0637125
$950$	0	0
$951$	−60.9273	−1.97570
$952$	5.22474	0.169335
$953$	59.8811	1.93974	0.969869	−	0.243625i	$-0.0783366\pi$
$953$	59.8811	1.93974	0.969869	+	0.243625i	$0.0783366\pi$
$954$	66.5075	2.15326
$955$	−49.8393	−1.61276
$956$	−1.94285	−0.0628362
$957$	−74.6632	−2.41352
$958$	−14.0514	−0.453981
$959$	−4.18816	−0.135243
$960$	8.80432	0.284158
$961$	−29.0818	−0.938124
$962$	43.8292	1.41311
$963$	133.968	4.31706
$964$	−23.4255	−0.754483
$965$	−34.3773	−1.10665
$966$	1.67027	0.0537399
$967$	2.27299	0.0730943	0.0365472	−	0.999332i	$-0.488364\pi$
$967$	2.27299	0.0730943	0.0365472	+	0.999332i	$0.488364\pi$
$968$	4.89131	0.157213
$969$	0	0
$970$	−12.6694	−0.406790
$971$	−37.9775	−1.21876	−0.609378	−	0.792880i	$-0.708581\pi$
$971$	−37.9775	−1.21876	−0.609378	+	0.792880i	$0.708581\pi$
$972$	30.4241	0.975852
$973$	−14.9473	−0.479187
$974$	10.4919	0.336181
$975$	−37.6398	−1.20544
$976$	−1.53726	−0.0492066
$977$	−7.14080	−0.228455	−0.114227	−	0.993455i	$-0.536439\pi$
$977$	−7.14080	−0.228455	−0.114227	+	0.993455i	$0.536439\pi$
$978$	28.6881	0.917345
$979$	34.9949	1.11844
$980$	2.74348	0.0876371
$981$	61.9745	1.97869
$982$	−1.39469	−0.0445064
$983$	−0.297396	−0.00948547	−0.00474273	−	0.999989i	$-0.501510\pi$
$983$	−0.297396	−0.00948547	−0.00474273	+	0.999989i	$0.501510\pi$
$984$	−30.1755	−0.961959
$985$	−30.3222	−0.966145
$986$	30.4928	0.971087
$987$	15.3078	0.487254
$988$	0	0
$989$	1.33050	0.0423076
$990$	−79.8246	−2.53699
$991$	−24.7749	−0.786999	−0.393500	−	0.919325i	$-0.628736\pi$
$991$	−24.7749	−0.786999	−0.393500	+	0.919325i	$0.628736\pi$
$992$	−1.38498	−0.0439730
$993$	27.8622	0.884180
$994$	−4.00739	−0.127107
$995$	−6.64822	−0.210763
$996$	−4.81179	−0.152467
$997$	−29.9031	−0.947040	−0.473520	−	0.880783i	$-0.657017\pi$
$997$	−29.9031	−0.947040	−0.473520	+	0.880783i	$0.657017\pi$
$998$	20.9626	0.663561
$999$	−130.259	−4.12120

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.bm.1.12		12
19.2	odd	18		266.2.u.d.99.1	yes	24
19.10	odd	18		266.2.u.d.43.1	✓	24
19.18	odd	2		5054.2.a.bl.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.u.d.43.1	✓	24	19.10	odd	18
266.2.u.d.99.1	yes	24	19.2	odd	18
5054.2.a.bl.1.1		12	19.18	odd	2
5054.2.a.bm.1.12		12	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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.20919 q^{3} +1.00000 q^{4} +2.74348 q^{5} +3.20919 q^{6} +1.00000 q^{7} +1.00000 q^{8} +7.29887 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.20919 q^{3} +1.00000 q^{4} +2.74348 q^{5} +3.20919 q^{6} +1.00000 q^{7} +1.00000 q^{8} +7.29887 q^{9} +2.74348 q^{10} -3.98639 q^{11} +3.20919 q^{12} -4.64202 q^{13} +1.00000 q^{14} +8.80432 q^{15} +1.00000 q^{16} +5.22474 q^{17} +7.29887 q^{18} +2.74348 q^{20} +3.20919 q^{21} -3.98639 q^{22} +0.520464 q^{23} +3.20919 q^{24} +2.52666 q^{25} -4.64202 q^{26} +13.7959 q^{27} +1.00000 q^{28} +5.83623 q^{29} +8.80432 q^{30} -1.38498 q^{31} +1.00000 q^{32} -12.7931 q^{33} +5.22474 q^{34} +2.74348 q^{35} +7.29887 q^{36} -9.44185 q^{37} -14.8971 q^{39} +2.74348 q^{40} -9.40284 q^{41} +3.20919 q^{42} +2.55638 q^{43} -3.98639 q^{44} +20.0243 q^{45} +0.520464 q^{46} +4.77001 q^{47} +3.20919 q^{48} +1.00000 q^{49} +2.52666 q^{50} +16.7672 q^{51} -4.64202 q^{52} +9.11202 q^{53} +13.7959 q^{54} -10.9366 q^{55} +1.00000 q^{56} +5.83623 q^{58} +1.07661 q^{59} +8.80432 q^{60} -1.53726 q^{61} -1.38498 q^{62} +7.29887 q^{63} +1.00000 q^{64} -12.7353 q^{65} -12.7931 q^{66} -12.3091 q^{67} +5.22474 q^{68} +1.67027 q^{69} +2.74348 q^{70} -4.00739 q^{71} +7.29887 q^{72} -0.422816 q^{73} -9.44185 q^{74} +8.10851 q^{75} -3.98639 q^{77} -14.8971 q^{78} -12.7880 q^{79} +2.74348 q^{80} +22.3769 q^{81} -9.40284 q^{82} -1.49938 q^{83} +3.20919 q^{84} +14.3339 q^{85} +2.55638 q^{86} +18.7295 q^{87} -3.98639 q^{88} -8.77859 q^{89} +20.0243 q^{90} -4.64202 q^{91} +0.520464 q^{92} -4.44464 q^{93} +4.77001 q^{94} +3.20919 q^{96} -4.61801 q^{97} +1.00000 q^{98} -29.0962 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} + 12 q^{8} + 21 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 + 12 * q^8 + 21 * q^9	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} + 12 q^{8} + 21 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 6 q^{13} + 12 q^{14} - 6 q^{15} + 12 q^{16} + 3 q^{17} + 21 q^{18} + 3 q^{20} + 3 q^{21} + 3 q^{22} + 12 q^{23} + 3 q^{24} + 33 q^{25} - 6 q^{26} + 21 q^{27} + 12 q^{28} + 6 q^{29} - 6 q^{30} + 3 q^{31} + 12 q^{32} - 6 q^{33} + 3 q^{34} + 3 q^{35} + 21 q^{36} + 27 q^{37} + 27 q^{39} + 3 q^{40} - 27 q^{41} + 3 q^{42} + 30 q^{43} + 3 q^{44} + 30 q^{45} + 12 q^{46} + 21 q^{47} + 3 q^{48} + 12 q^{49} + 33 q^{50} + 3 q^{51} - 6 q^{52} + 6 q^{53} + 21 q^{54} + 48 q^{55} + 12 q^{56} + 6 q^{58} - 27 q^{59} - 6 q^{60} + 18 q^{61} + 3 q^{62} + 21 q^{63} + 12 q^{64} - 9 q^{65} - 6 q^{66} + 9 q^{67} + 3 q^{68} + 18 q^{69} + 3 q^{70} + 27 q^{71} + 21 q^{72} - 9 q^{73} + 27 q^{74} + 33 q^{75} + 3 q^{77} + 27 q^{78} - 12 q^{79} + 3 q^{80} + 24 q^{81} - 27 q^{82} + 9 q^{83} + 3 q^{84} + 78 q^{85} + 30 q^{86} - 45 q^{87} + 3 q^{88} - 24 q^{89} + 30 q^{90} - 6 q^{91} + 12 q^{92} + 3 q^{93} + 21 q^{94} + 3 q^{96} - 18 q^{97} + 12 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 + 12 * q^8 + 21 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 6 * q^13 + 12 * q^14 - 6 * q^15 + 12 * q^16 + 3 * q^17 + 21 * q^18 + 3 * q^20 + 3 * q^21 + 3 * q^22 + 12 * q^23 + 3 * q^24 + 33 * q^25 - 6 * q^26 + 21 * q^27 + 12 * q^28 + 6 * q^29 - 6 * q^30 + 3 * q^31 + 12 * q^32 - 6 * q^33 + 3 * q^34 + 3 * q^35 + 21 * q^36 + 27 * q^37 + 27 * q^39 + 3 * q^40 - 27 * q^41 + 3 * q^42 + 30 * q^43 + 3 * q^44 + 30 * q^45 + 12 * q^46 + 21 * q^47 + 3 * q^48 + 12 * q^49 + 33 * q^50 + 3 * q^51 - 6 * q^52 + 6 * q^53 + 21 * q^54 + 48 * q^55 + 12 * q^56 + 6 * q^58 - 27 * q^59 - 6 * q^60 + 18 * q^61 + 3 * q^62 + 21 * q^63 + 12 * q^64 - 9 * q^65 - 6 * q^66 + 9 * q^67 + 3 * q^68 + 18 * q^69 + 3 * q^70 + 27 * q^71 + 21 * q^72 - 9 * q^73 + 27 * q^74 + 33 * q^75 + 3 * q^77 + 27 * q^78 - 12 * q^79 + 3 * q^80 + 24 * q^81 - 27 * q^82 + 9 * q^83 + 3 * q^84 + 78 * q^85 + 30 * q^86 - 45 * q^87 + 3 * q^88 - 24 * q^89 + 30 * q^90 - 6 * q^91 + 12 * q^92 + 3 * q^93 + 21 * q^94 + 3 * q^96 - 18 * q^97 + 12 * q^98 + 48 * q^99

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