LMFDB - Embedded newform 2679.2.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2679,2,Mod(1,2679)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2679, 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("2679.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2679 = 3 \cdot 19 \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2679.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:	$21.3919227015$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 7x^{5} + 16x^{4} + x^{3} - 13x^{2} + 2x + 1 $ x^7 - 2x^6 - 7x^5 + 16x^4 + x^3 - 13x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.56422$ of defining polynomial
Character	$\chi$	$=$	2679.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.56422 q^{2} -1.00000 q^{3} +0.446772 q^{4} +0.791846 q^{5} +1.56422 q^{6} -0.0750818 q^{7} +2.42958 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.56422 q^{2} -1.00000 q^{3} +0.446772 q^{4} +0.791846 q^{5} +1.56422 q^{6} -0.0750818 q^{7} +2.42958 q^{8} +1.00000 q^{9} -1.23862 q^{10} +2.59597 q^{11} -0.446772 q^{12} +2.80412 q^{13} +0.117444 q^{14} -0.791846 q^{15} -4.69394 q^{16} -4.74232 q^{17} -1.56422 q^{18} +1.00000 q^{19} +0.353774 q^{20} +0.0750818 q^{21} -4.06066 q^{22} -2.22663 q^{23} -2.42958 q^{24} -4.37298 q^{25} -4.38626 q^{26} -1.00000 q^{27} -0.0335444 q^{28} -7.42999 q^{29} +1.23862 q^{30} -4.23480 q^{31} +2.48317 q^{32} -2.59597 q^{33} +7.41801 q^{34} -0.0594532 q^{35} +0.446772 q^{36} -2.97148 q^{37} -1.56422 q^{38} -2.80412 q^{39} +1.92386 q^{40} +10.0802 q^{41} -0.117444 q^{42} +7.63595 q^{43} +1.15981 q^{44} +0.791846 q^{45} +3.48293 q^{46} +1.00000 q^{47} +4.69394 q^{48} -6.99436 q^{49} +6.84029 q^{50} +4.74232 q^{51} +1.25280 q^{52} +4.24470 q^{53} +1.56422 q^{54} +2.05561 q^{55} -0.182417 q^{56} -1.00000 q^{57} +11.6221 q^{58} -7.03939 q^{59} -0.353774 q^{60} +7.22754 q^{61} +6.62415 q^{62} -0.0750818 q^{63} +5.50367 q^{64} +2.22043 q^{65} +4.06066 q^{66} -3.35873 q^{67} -2.11873 q^{68} +2.22663 q^{69} +0.0929976 q^{70} +2.75757 q^{71} +2.42958 q^{72} -8.10896 q^{73} +4.64803 q^{74} +4.37298 q^{75} +0.446772 q^{76} -0.194910 q^{77} +4.38626 q^{78} -15.8710 q^{79} -3.71687 q^{80} +1.00000 q^{81} -15.7676 q^{82} -2.95130 q^{83} +0.0335444 q^{84} -3.75518 q^{85} -11.9443 q^{86} +7.42999 q^{87} +6.30713 q^{88} +3.70208 q^{89} -1.23862 q^{90} -0.210539 q^{91} -0.994797 q^{92} +4.23480 q^{93} -1.56422 q^{94} +0.791846 q^{95} -2.48317 q^{96} +4.88638 q^{97} +10.9407 q^{98} +2.59597 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 2 q^{2} - 7 q^{3} + 4 q^{4} + 6 q^{5} + 2 q^{6} - 3 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 2 * q^2 - 7 * q^3 + 4 * q^4 + 6 * q^5 + 2 * q^6 - 3 * q^7 + 6 * q^8 + 7 * q^9	\( 7 q - 2 q^{2} - 7 q^{3} + 4 q^{4} + 6 q^{5} + 2 q^{6} - 3 q^{7} + 6 q^{8} + 7 q^{9} - 10 q^{10} - 9 q^{11} - 4 q^{12} - 8 q^{13} - 9 q^{14} - 6 q^{15} + 14 q^{16} + 7 q^{17} - 2 q^{18} + 7 q^{19} - 4 q^{20} + 3 q^{21} - 7 q^{22} - 7 q^{23} - 6 q^{24} - 9 q^{25} + q^{26} - 7 q^{27} - 12 q^{28} - 12 q^{29} + 10 q^{30} - 13 q^{31} + 15 q^{32} + 9 q^{33} + 2 q^{34} + 4 q^{35} + 4 q^{36} - 10 q^{37} - 2 q^{38} + 8 q^{39} - 26 q^{40} - 8 q^{41} + 9 q^{42} + 12 q^{43} - 14 q^{44} + 6 q^{45} - 7 q^{46} + 7 q^{47} - 14 q^{48} - 16 q^{49} - 12 q^{50} - 7 q^{51} - 6 q^{52} - 17 q^{53} + 2 q^{54} + 7 q^{55} - 38 q^{56} - 7 q^{57} - 12 q^{58} + 12 q^{59} + 4 q^{60} - 23 q^{61} + 23 q^{62} - 3 q^{63} + 12 q^{64} - 13 q^{65} + 7 q^{66} + q^{67} + 15 q^{68} + 7 q^{69} + 8 q^{70} + 6 q^{72} - 29 q^{73} + 5 q^{74} + 9 q^{75} + 4 q^{76} + 4 q^{77} - q^{78} - 3 q^{79} + 15 q^{80} + 7 q^{81} - 7 q^{82} + 19 q^{83} + 12 q^{84} - 5 q^{85} - 23 q^{86} + 12 q^{87} - 33 q^{88} - 14 q^{89} - 10 q^{90} - 3 q^{91} - 5 q^{92} + 13 q^{93} - 2 q^{94} + 6 q^{95} - 15 q^{96} - 17 q^{97} + 38 q^{98} - 9 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 - 7 * q^3 + 4 * q^4 + 6 * q^5 + 2 * q^6 - 3 * q^7 + 6 * q^8 + 7 * q^9 - 10 * q^10 - 9 * q^11 - 4 * q^12 - 8 * q^13 - 9 * q^14 - 6 * q^15 + 14 * q^16 + 7 * q^17 - 2 * q^18 + 7 * q^19 - 4 * q^20 + 3 * q^21 - 7 * q^22 - 7 * q^23 - 6 * q^24 - 9 * q^25 + q^26 - 7 * q^27 - 12 * q^28 - 12 * q^29 + 10 * q^30 - 13 * q^31 + 15 * q^32 + 9 * q^33 + 2 * q^34 + 4 * q^35 + 4 * q^36 - 10 * q^37 - 2 * q^38 + 8 * q^39 - 26 * q^40 - 8 * q^41 + 9 * q^42 + 12 * q^43 - 14 * q^44 + 6 * q^45 - 7 * q^46 + 7 * q^47 - 14 * q^48 - 16 * q^49 - 12 * q^50 - 7 * q^51 - 6 * q^52 - 17 * q^53 + 2 * q^54 + 7 * q^55 - 38 * q^56 - 7 * q^57 - 12 * q^58 + 12 * q^59 + 4 * q^60 - 23 * q^61 + 23 * q^62 - 3 * q^63 + 12 * q^64 - 13 * q^65 + 7 * q^66 + q^67 + 15 * q^68 + 7 * q^69 + 8 * q^70 + 6 * q^72 - 29 * q^73 + 5 * q^74 + 9 * q^75 + 4 * q^76 + 4 * q^77 - q^78 - 3 * q^79 + 15 * q^80 + 7 * q^81 - 7 * q^82 + 19 * q^83 + 12 * q^84 - 5 * q^85 - 23 * q^86 + 12 * q^87 - 33 * q^88 - 14 * q^89 - 10 * q^90 - 3 * q^91 - 5 * q^92 + 13 * q^93 - 2 * q^94 + 6 * q^95 - 15 * q^96 - 17 * q^97 + 38 * q^98 - 9 * 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 $

$2$	−1.56422	−1.10607	−0.553034	−	0.833159i	$-0.686530\pi$
$2$	−1.56422	−1.10607	−0.553034	+	0.833159i	$0.686530\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.446772	0.223386
$5$	0.791846	0.354124	0.177062	−	0.984200i	$-0.443341\pi$
$5$	0.791846	0.354124	0.177062	+	0.984200i	$0.443341\pi$
$6$	1.56422	0.638589
$7$	−0.0750818	−0.0283782	−0.0141891	−	0.999899i	$-0.504517\pi$
$7$	−0.0750818	−0.0283782	−0.0141891	+	0.999899i	$0.504517\pi$
$8$	2.42958	0.858988
$9$	1.00000	0.333333
$10$	−1.23862	−0.391685
$11$	2.59597	0.782714	0.391357	−	0.920239i	$-0.372006\pi$
$11$	2.59597	0.782714	0.391357	+	0.920239i	$0.372006\pi$
$12$	−0.446772	−0.128972
$13$	2.80412	0.777724	0.388862	−	0.921296i	$-0.372868\pi$
$13$	2.80412	0.777724	0.388862	+	0.921296i	$0.372868\pi$
$14$	0.117444	0.0313883
$15$	−0.791846	−0.204454
$16$	−4.69394	−1.17348
$17$	−4.74232	−1.15018	−0.575090	−	0.818090i	$-0.695033\pi$
$17$	−4.74232	−1.15018	−0.575090	+	0.818090i	$0.695033\pi$
$18$	−1.56422	−0.368689
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0.353774	0.0791064
$21$	0.0750818	0.0163842
$22$	−4.06066	−0.865735
$23$	−2.22663	−0.464285	−0.232143	−	0.972682i	$-0.574574\pi$
$23$	−2.22663	−0.464285	−0.232143	+	0.972682i	$0.574574\pi$
$24$	−2.42958	−0.495937
$25$	−4.37298	−0.874596
$26$	−4.38626	−0.860216
$27$	−1.00000	−0.192450
$28$	−0.0335444	−0.00633930
$29$	−7.42999	−1.37972	−0.689858	−	0.723945i	$-0.742327\pi$
$29$	−7.42999	−1.37972	−0.689858	+	0.723945i	$0.742327\pi$
$30$	1.23862	0.226140
$31$	−4.23480	−0.760593	−0.380296	−	0.924865i	$-0.624178\pi$
$31$	−4.23480	−0.760593	−0.380296	+	0.924865i	$0.624178\pi$
$32$	2.48317	0.438966
$33$	−2.59597	−0.451900
$34$	7.41801	1.27218
$35$	−0.0594532	−0.0100494
$36$	0.446772	0.0744620
$37$	−2.97148	−0.488508	−0.244254	−	0.969711i	$-0.578543\pi$
$37$	−2.97148	−0.488508	−0.244254	+	0.969711i	$0.578543\pi$
$38$	−1.56422	−0.253749
$39$	−2.80412	−0.449019
$40$	1.92386	0.304188
$41$	10.0802	1.57426	0.787131	−	0.616786i	$-0.211566\pi$
$41$	10.0802	1.57426	0.787131	+	0.616786i	$0.211566\pi$
$42$	−0.117444	−0.0181220
$43$	7.63595	1.16447	0.582236	−	0.813020i	$-0.302178\pi$
$43$	7.63595	1.16447	0.582236	+	0.813020i	$0.302178\pi$
$44$	1.15981	0.174847
$45$	0.791846	0.118041
$46$	3.48293	0.513531
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	4.69394	0.677512
$49$	−6.99436	−0.999195
$50$	6.84029	0.967363
$51$	4.74232	0.664057
$52$	1.25280	0.173733
$53$	4.24470	0.583054	0.291527	−	0.956563i	$-0.405837\pi$
$53$	4.24470	0.583054	0.291527	+	0.956563i	$0.405837\pi$
$54$	1.56422	0.212863
$55$	2.05561	0.277178
$56$	−0.182417	−0.0243766
$57$	−1.00000	−0.132453
$58$	11.6221	1.52606
$59$	−7.03939	−0.916451	−0.458225	−	0.888836i	$-0.651515\pi$
$59$	−7.03939	−0.916451	−0.458225	+	0.888836i	$0.651515\pi$
$60$	−0.353774	−0.0456721
$61$	7.22754	0.925392	0.462696	−	0.886517i	$-0.346882\pi$
$61$	7.22754	0.925392	0.462696	+	0.886517i	$0.346882\pi$
$62$	6.62415	0.841267
$63$	−0.0750818	−0.00945941
$64$	5.50367	0.687959
$65$	2.22043	0.275411
$66$	4.06066	0.499832
$67$	−3.35873	−0.410334	−0.205167	−	0.978727i	$-0.565774\pi$
$67$	−3.35873	−0.410334	−0.205167	+	0.978727i	$0.565774\pi$
$68$	−2.11873	−0.256934
$69$	2.22663	0.268055
$70$	0.0929976	0.0111153
$71$	2.75757	0.327263	0.163631	−	0.986522i	$-0.447679\pi$
$71$	2.75757	0.327263	0.163631	+	0.986522i	$0.447679\pi$
$72$	2.42958	0.286329
$73$	−8.10896	−0.949082	−0.474541	−	0.880233i	$-0.657386\pi$
$73$	−8.10896	−0.949082	−0.474541	+	0.880233i	$0.657386\pi$
$74$	4.64803	0.540322
$75$	4.37298	0.504948
$76$	0.446772	0.0512483
$77$	−0.194910	−0.0222121
$78$	4.38626	0.496646
$79$	−15.8710	−1.78563	−0.892813	−	0.450428i	$-0.851271\pi$
$79$	−15.8710	−1.78563	−0.892813	+	0.450428i	$0.851271\pi$
$80$	−3.71687	−0.415559
$81$	1.00000	0.111111
$82$	−15.7676	−1.74124
$83$	−2.95130	−0.323947	−0.161973	−	0.986795i	$-0.551786\pi$
$83$	−2.95130	−0.323947	−0.161973	+	0.986795i	$0.551786\pi$
$84$	0.0335444	0.00366000
$85$	−3.75518	−0.407307
$86$	−11.9443	−1.28798
$87$	7.42999	0.796579
$88$	6.30713	0.672342
$89$	3.70208	0.392419	0.196210	−	0.980562i	$-0.437137\pi$
$89$	3.70208	0.392419	0.196210	+	0.980562i	$0.437137\pi$
$90$	−1.23862	−0.130562
$91$	−0.210539	−0.0220704
$92$	−0.994797	−0.103715
$93$	4.23480	0.439129
$94$	−1.56422	−0.161337
$95$	0.791846	0.0812416
$96$	−2.48317	−0.253437
$97$	4.88638	0.496137	0.248068	−	0.968743i	$-0.420204\pi$
$97$	4.88638	0.496137	0.248068	+	0.968743i	$0.420204\pi$
$98$	10.9407	1.10518
$99$	2.59597	0.260905
$100$	−1.95373	−0.195373
$101$	13.8343	1.37657	0.688284	−	0.725442i	$-0.258364\pi$
$101$	13.8343	1.37657	0.688284	+	0.725442i	$0.258364\pi$
$102$	−7.41801	−0.734492
$103$	−4.20257	−0.414092	−0.207046	−	0.978331i	$-0.566385\pi$
$103$	−4.20257	−0.414092	−0.207046	+	0.978331i	$0.566385\pi$
$104$	6.81286	0.668055
$105$	0.0594532	0.00580203
$106$	−6.63962	−0.644897
$107$	−8.42853	−0.814817	−0.407408	−	0.913246i	$-0.633567\pi$
$107$	−8.42853	−0.814817	−0.407408	+	0.913246i	$0.633567\pi$
$108$	−0.446772	−0.0429907
$109$	−13.4505	−1.28833	−0.644163	−	0.764889i	$-0.722794\pi$
$109$	−13.4505	−1.28833	−0.644163	+	0.764889i	$0.722794\pi$
$110$	−3.21541	−0.306578
$111$	2.97148	0.282040
$112$	0.352429	0.0333014
$113$	11.2844	1.06154	0.530771	−	0.847515i	$-0.321902\pi$
$113$	11.2844	1.06154	0.530771	+	0.847515i	$0.321902\pi$
$114$	1.56422	0.146502
$115$	−1.76315	−0.164415
$116$	−3.31951	−0.308209
$117$	2.80412	0.259241
$118$	11.0111	1.01366
$119$	0.356062	0.0326401
$120$	−1.92386	−0.175623
$121$	−4.26094	−0.387358
$122$	−11.3054	−1.02355
$123$	−10.0802	−0.908901
$124$	−1.89199	−0.169906
$125$	−7.42195	−0.663840
$126$	0.117444	0.0104628
$127$	2.62400	0.232842	0.116421	−	0.993200i	$-0.462858\pi$
$127$	2.62400	0.232842	0.116421	+	0.993200i	$0.462858\pi$
$128$	−13.5753	−1.19989
$129$	−7.63595	−0.672308
$130$	−3.47324	−0.304623
$131$	−12.4897	−1.09123	−0.545613	−	0.838037i	$-0.683703\pi$
$131$	−12.4897	−1.09123	−0.545613	+	0.838037i	$0.683703\pi$
$132$	−1.15981	−0.100948
$133$	−0.0750818	−0.00651042
$134$	5.25378	0.453857
$135$	−0.791846	−0.0681512
$136$	−11.5219	−0.987991
$137$	22.1067	1.88870	0.944352	−	0.328936i	$-0.106690\pi$
$137$	22.1067	1.88870	0.944352	+	0.328936i	$0.106690\pi$
$138$	−3.48293	−0.296487
$139$	−10.3335	−0.876476	−0.438238	−	0.898859i	$-0.644397\pi$
$139$	−10.3335	−0.876476	−0.438238	+	0.898859i	$0.644397\pi$
$140$	−0.0265620	−0.00224490
$141$	−1.00000	−0.0842152
$142$	−4.31343	−0.361975
$143$	7.27942	0.608736
$144$	−4.69394	−0.391162
$145$	−5.88341	−0.488590
$146$	12.6842	1.04975
$147$	6.99436	0.576885
$148$	−1.32757	−0.109126
$149$	−11.9980	−0.982913	−0.491456	−	0.870902i	$-0.663535\pi$
$149$	−11.9980	−0.982913	−0.491456	+	0.870902i	$0.663535\pi$
$150$	−6.84029	−0.558507
$151$	13.3367	1.08533	0.542664	−	0.839950i	$-0.317416\pi$
$151$	13.3367	1.08533	0.542664	+	0.839950i	$0.317416\pi$
$152$	2.42958	0.197065
$153$	−4.74232	−0.383394
$154$	0.304881	0.0245680
$155$	−3.35331	−0.269344
$156$	−1.25280	−0.100305
$157$	−9.34960	−0.746179	−0.373090	−	0.927795i	$-0.621702\pi$
$157$	−9.34960	−0.746179	−0.373090	+	0.927795i	$0.621702\pi$
$158$	24.8257	1.97502
$159$	−4.24470	−0.336626
$160$	1.96628	0.155448
$161$	0.167180	0.0131756
$162$	−1.56422	−0.122896
$163$	−7.60243	−0.595469	−0.297734	−	0.954649i	$-0.596231\pi$
$163$	−7.60243	−0.595469	−0.297734	+	0.954649i	$0.596231\pi$
$164$	4.50355	0.351668
$165$	−2.05561	−0.160029
$166$	4.61647	0.358307
$167$	17.7868	1.37639	0.688193	−	0.725528i	$-0.258404\pi$
$167$	17.7868	1.37639	0.688193	+	0.725528i	$0.258404\pi$
$168$	0.182417	0.0140738
$169$	−5.13689	−0.395145
$170$	5.87392	0.450509
$171$	1.00000	0.0764719
$172$	3.41153	0.260127
$173$	−23.6447	−1.79767	−0.898836	−	0.438285i	$-0.855586\pi$
$173$	−23.6447	−1.79767	−0.898836	+	0.438285i	$0.855586\pi$
$174$	−11.6221	−0.881070
$175$	0.328331	0.0248195
$176$	−12.1853	−0.918503
$177$	7.03939	0.529113
$178$	−5.79085	−0.434042
$179$	6.79923	0.508198	0.254099	−	0.967178i	$-0.418221\pi$
$179$	6.79923	0.508198	0.254099	+	0.967178i	$0.418221\pi$
$180$	0.353774	0.0263688
$181$	−15.9378	−1.18464	−0.592322	−	0.805701i	$-0.701789\pi$
$181$	−15.9378	−1.18464	−0.592322	+	0.805701i	$0.701789\pi$
$182$	0.329328	0.0244114
$183$	−7.22754	−0.534275
$184$	−5.40979	−0.398815
$185$	−2.35295	−0.172992
$186$	−6.62415	−0.485706
$187$	−12.3109	−0.900263
$188$	0.446772	0.0325842
$189$	0.0750818	0.00546140
$190$	−1.23862	−0.0898588
$191$	16.7865	1.21463	0.607313	−	0.794463i	$-0.292247\pi$
$191$	16.7865	1.21463	0.607313	+	0.794463i	$0.292247\pi$
$192$	−5.50367	−0.397193
$193$	−4.09764	−0.294954	−0.147477	−	0.989065i	$-0.547115\pi$
$193$	−4.09764	−0.294954	−0.147477	+	0.989065i	$0.547115\pi$
$194$	−7.64335	−0.548761
$195$	−2.22043	−0.159009
$196$	−3.12489	−0.223206
$197$	8.26711	0.589007	0.294504	−	0.955650i	$-0.404846\pi$
$197$	8.26711	0.589007	0.294504	+	0.955650i	$0.404846\pi$
$198$	−4.06066	−0.288578
$199$	−15.5788	−1.10435	−0.552177	−	0.833727i	$-0.686203\pi$
$199$	−15.5788	−1.10435	−0.552177	+	0.833727i	$0.686203\pi$
$200$	−10.6245	−0.751267
$201$	3.35873	0.236906
$202$	−21.6399	−1.52258
$203$	0.557857	0.0391539
$204$	2.11873	0.148341
$205$	7.98196	0.557484
$206$	6.57373	0.458014
$207$	−2.22663	−0.154762
$208$	−13.1624	−0.912647
$209$	2.59597	0.179567
$210$	−0.0929976	−0.00641744
$211$	−7.08669	−0.487868	−0.243934	−	0.969792i	$-0.578438\pi$
$211$	−7.08669	−0.487868	−0.243934	+	0.969792i	$0.578438\pi$
$212$	1.89641	0.130246
$213$	−2.75757	−0.188945
$214$	13.1840	0.901243
$215$	6.04649	0.412367
$216$	−2.42958	−0.165312
$217$	0.317956	0.0215843
$218$	21.0395	1.42497
$219$	8.10896	0.547953
$220$	0.918388	0.0619177
$221$	−13.2980	−0.894523
$222$	−4.64803	−0.311955
$223$	−2.60966	−0.174756	−0.0873779	−	0.996175i	$-0.527849\pi$
$223$	−2.60966	−0.174756	−0.0873779	+	0.996175i	$0.527849\pi$
$224$	−0.186440	−0.0124571
$225$	−4.37298	−0.291532
$226$	−17.6512	−1.17414
$227$	−8.49042	−0.563529	−0.281764	−	0.959484i	$-0.590920\pi$
$227$	−8.49042	−0.563529	−0.281764	+	0.959484i	$0.590920\pi$
$228$	−0.446772	−0.0295882
$229$	2.27526	0.150353	0.0751766	−	0.997170i	$-0.476048\pi$
$229$	2.27526	0.150353	0.0751766	+	0.997170i	$0.476048\pi$
$230$	2.75795	0.181854
$231$	0.194910	0.0128241
$232$	−18.0518	−1.18516
$233$	−18.9961	−1.24448	−0.622238	−	0.782828i	$-0.713776\pi$
$233$	−18.9961	−1.24448	−0.622238	+	0.782828i	$0.713776\pi$
$234$	−4.38626	−0.286739
$235$	0.791846	0.0516543
$236$	−3.14500	−0.204722
$237$	15.8710	1.03093
$238$	−0.556957	−0.0361022
$239$	16.8841	1.09214	0.546070	−	0.837740i	$-0.316123\pi$
$239$	16.8841	1.09214	0.546070	+	0.837740i	$0.316123\pi$
$240$	3.71687	0.239923
$241$	−19.1812	−1.23557	−0.617785	−	0.786347i	$-0.711970\pi$
$241$	−19.1812	−1.23557	−0.617785	+	0.786347i	$0.711970\pi$
$242$	6.66503	0.428445
$243$	−1.00000	−0.0641500
$244$	3.22906	0.206720
$245$	−5.53845	−0.353839
$246$	15.7676	1.00531
$247$	2.80412	0.178422
$248$	−10.2888	−0.653340
$249$	2.95130	0.187031
$250$	11.6095	0.734252
$251$	8.47769	0.535107	0.267554	−	0.963543i	$-0.413785\pi$
$251$	8.47769	0.535107	0.267554	+	0.963543i	$0.413785\pi$
$252$	−0.0335444	−0.00211310
$253$	−5.78027	−0.363403
$254$	−4.10450	−0.257539
$255$	3.75518	0.235159
$256$	10.2273	0.639206
$257$	−4.50102	−0.280766	−0.140383	−	0.990097i	$-0.544833\pi$
$257$	−4.50102	−0.280766	−0.140383	+	0.990097i	$0.544833\pi$
$258$	11.9443	0.743618
$259$	0.223104	0.0138630
$260$	0.992027	0.0615229
$261$	−7.42999	−0.459905
$262$	19.5365	1.20697
$263$	16.1794	0.997664	0.498832	−	0.866699i	$-0.333762\pi$
$263$	16.1794	0.997664	0.498832	+	0.866699i	$0.333762\pi$
$264$	−6.30713	−0.388177
$265$	3.36114	0.206473
$266$	0.117444	0.00720096
$267$	−3.70208	−0.226563
$268$	−1.50059	−0.0916629
$269$	−31.4154	−1.91543	−0.957716	−	0.287717i	$-0.907104\pi$
$269$	−31.4154	−1.91543	−0.957716	+	0.287717i	$0.907104\pi$
$270$	1.23862	0.0753799
$271$	−4.09476	−0.248739	−0.124369	−	0.992236i	$-0.539691\pi$
$271$	−4.09476	−0.248739	−0.124369	+	0.992236i	$0.539691\pi$
$272$	22.2601	1.34972
$273$	0.210539	0.0127424
$274$	−34.5797	−2.08904
$275$	−11.3521	−0.684559
$276$	0.994797	0.0598797
$277$	−6.44779	−0.387410	−0.193705	−	0.981060i	$-0.562051\pi$
$277$	−6.44779	−0.387410	−0.193705	+	0.981060i	$0.562051\pi$
$278$	16.1638	0.969442
$279$	−4.23480	−0.253531
$280$	−0.144446	−0.00863233
$281$	−6.72480	−0.401168	−0.200584	−	0.979677i	$-0.564284\pi$
$281$	−6.72480	−0.401168	−0.200584	+	0.979677i	$0.564284\pi$
$282$	1.56422	0.0931477
$283$	11.9474	0.710198	0.355099	−	0.934829i	$-0.384447\pi$
$283$	11.9474	0.710198	0.355099	+	0.934829i	$0.384447\pi$
$284$	1.23200	0.0731060
$285$	−0.791846	−0.0469049
$286$	−11.3866	−0.673303
$287$	−0.756839	−0.0446748
$288$	2.48317	0.146322
$289$	5.48958	0.322916
$290$	9.20292	0.540414
$291$	−4.88638	−0.286445
$292$	−3.62285	−0.212012
$293$	−18.7850	−1.09743	−0.548716	−	0.836009i	$-0.684883\pi$
$293$	−18.7850	−1.09743	−0.548716	+	0.836009i	$0.684883\pi$
$294$	−10.9407	−0.638074
$295$	−5.57411	−0.324537
$296$	−7.21945	−0.419622
$297$	−2.59597	−0.150633
$298$	18.7674	1.08717
$299$	−6.24375	−0.361086
$300$	1.95373	0.112798
$301$	−0.573320	−0.0330456
$302$	−20.8615	−1.20045
$303$	−13.8343	−0.794762
$304$	−4.69394	−0.269216
$305$	5.72309	0.327703
$306$	7.41801	0.424059
$307$	−4.56173	−0.260351	−0.130176	−	0.991491i	$-0.541554\pi$
$307$	−4.56173	−0.260351	−0.130176	+	0.991491i	$0.541554\pi$
$308$	−0.0870803	−0.00496186
$309$	4.20257	0.239076
$310$	5.24530	0.297913
$311$	22.7977	1.29274	0.646369	−	0.763025i	$-0.276287\pi$
$311$	22.7977	1.29274	0.646369	+	0.763025i	$0.276287\pi$
$312$	−6.81286	−0.385702
$313$	1.22534	0.0692601	0.0346300	−	0.999400i	$-0.488975\pi$
$313$	1.22534	0.0692601	0.0346300	+	0.999400i	$0.488975\pi$
$314$	14.6248	0.825325
$315$	−0.0594532	−0.00334981
$316$	−7.09071	−0.398884
$317$	1.88211	0.105710	0.0528549	−	0.998602i	$-0.483168\pi$
$317$	1.88211	0.105710	0.0528549	+	0.998602i	$0.483168\pi$
$318$	6.63962	0.372332
$319$	−19.2880	−1.07992
$320$	4.35806	0.243623
$321$	8.42853	0.470435
$322$	−0.261505	−0.0145731
$323$	−4.74232	−0.263870
$324$	0.446772	0.0248207
$325$	−12.2624	−0.680194
$326$	11.8919	0.658629
$327$	13.4505	0.743815
$328$	24.4907	1.35227
$329$	−0.0750818	−0.00413939
$330$	3.21541	0.177003
$331$	−6.20759	−0.341200	−0.170600	−	0.985340i	$-0.554571\pi$
$331$	−6.20759	−0.341200	−0.170600	+	0.985340i	$0.554571\pi$
$332$	−1.31856	−0.0723652
$333$	−2.97148	−0.162836
$334$	−27.8224	−1.52238
$335$	−2.65959	−0.145309
$336$	−0.352429	−0.0192266
$337$	−22.7383	−1.23864	−0.619318	−	0.785141i	$-0.712591\pi$
$337$	−22.7383	−1.23864	−0.619318	+	0.785141i	$0.712591\pi$
$338$	8.03520	0.437057
$339$	−11.2844	−0.612882
$340$	−1.67771	−0.0909866
$341$	−10.9934	−0.595327
$342$	−1.56422	−0.0845831
$343$	1.05072	0.0567336
$344$	18.5522	1.00027
$345$	1.76315	0.0949248
$346$	36.9854	1.98835
$347$	−0.694353	−0.0372748	−0.0186374	−	0.999826i	$-0.505933\pi$
$347$	−0.694353	−0.0372748	−0.0186374	+	0.999826i	$0.505933\pi$
$348$	3.31951	0.177945
$349$	−6.99928	−0.374663	−0.187331	−	0.982297i	$-0.559984\pi$
$349$	−6.99928	−0.374663	−0.187331	+	0.982297i	$0.559984\pi$
$350$	−0.513581	−0.0274521
$351$	−2.80412	−0.149673
$352$	6.44622	0.343585
$353$	−28.1471	−1.49812	−0.749060	−	0.662502i	$-0.769495\pi$
$353$	−28.1471	−1.49812	−0.749060	+	0.662502i	$0.769495\pi$
$354$	−11.0111	−0.585235
$355$	2.18357	0.115892
$356$	1.65398	0.0876610
$357$	−0.356062	−0.0188448
$358$	−10.6355	−0.562101
$359$	13.0891	0.690818	0.345409	−	0.938452i	$-0.387740\pi$
$359$	13.0891	0.690818	0.345409	+	0.938452i	$0.387740\pi$
$360$	1.92386	0.101396
$361$	1.00000	0.0526316
$362$	24.9301	1.31030
$363$	4.26094	0.223641
$364$	−0.0940627	−0.00493023
$365$	−6.42104	−0.336093
$366$	11.3054	0.590944
$367$	3.29156	0.171818	0.0859089	−	0.996303i	$-0.472621\pi$
$367$	3.29156	0.171818	0.0859089	+	0.996303i	$0.472621\pi$
$368$	10.4517	0.544831
$369$	10.0802	0.524754
$370$	3.68052	0.191341
$371$	−0.318699	−0.0165460
$372$	1.89199	0.0980952
$373$	−14.9095	−0.771983	−0.385991	−	0.922502i	$-0.626141\pi$
$373$	−14.9095	−0.771983	−0.385991	+	0.922502i	$0.626141\pi$
$374$	19.2569	0.995752
$375$	7.42195	0.383268
$376$	2.42958	0.125296
$377$	−20.8346	−1.07304
$378$	−0.117444	−0.00604067
$379$	−27.1813	−1.39621	−0.698104	−	0.715996i	$-0.745973\pi$
$379$	−27.1813	−1.39621	−0.698104	+	0.715996i	$0.745973\pi$
$380$	0.353774	0.0181482
$381$	−2.62400	−0.134431
$382$	−26.2577	−1.34346
$383$	−13.0270	−0.665649	−0.332824	−	0.942989i	$-0.608002\pi$
$383$	−13.0270	−0.665649	−0.332824	+	0.942989i	$0.608002\pi$
$384$	13.5753	0.692760
$385$	−0.154339	−0.00786582
$386$	6.40959	0.326240
$387$	7.63595	0.388157
$388$	2.18310	0.110830
$389$	−1.52129	−0.0771323	−0.0385662	−	0.999256i	$-0.512279\pi$
$389$	−1.52129	−0.0771323	−0.0385662	+	0.999256i	$0.512279\pi$
$390$	3.47324	0.175874
$391$	10.5594	0.534012
$392$	−16.9934	−0.858296
$393$	12.4897	0.630020
$394$	−12.9315	−0.651482
$395$	−12.5674	−0.632333
$396$	1.15981	0.0582825
$397$	16.0993	0.808001	0.404001	−	0.914759i	$-0.367619\pi$
$397$	16.0993	0.808001	0.404001	+	0.914759i	$0.367619\pi$
$398$	24.3687	1.22149
$399$	0.0750818	0.00375879
$400$	20.5265	1.02633
$401$	−35.9203	−1.79378	−0.896888	−	0.442259i	$-0.854177\pi$
$401$	−35.9203	−1.79378	−0.896888	+	0.442259i	$0.854177\pi$
$402$	−5.25378	−0.262035
$403$	−11.8749	−0.591531
$404$	6.18079	0.307506
$405$	0.791846	0.0393471
$406$	−0.872609	−0.0433069
$407$	−7.71386	−0.382362
$408$	11.5219	0.570417
$409$	−11.3282	−0.560143	−0.280071	−	0.959979i	$-0.590358\pi$
$409$	−11.3282	−0.560143	−0.280071	+	0.959979i	$0.590358\pi$
$410$	−12.4855	−0.616615
$411$	−22.1067	−1.09044
$412$	−1.87759	−0.0925023
$413$	0.528530	0.0260073
$414$	3.48293	0.171177
$415$	−2.33697	−0.114717
$416$	6.96311	0.341394
$417$	10.3335	0.506034
$418$	−4.06066	−0.198613
$419$	2.45815	0.120088	0.0600441	−	0.998196i	$-0.480876\pi$
$419$	2.45815	0.120088	0.0600441	+	0.998196i	$0.480876\pi$
$420$	0.0265620	0.00129609
$421$	14.7828	0.720468	0.360234	−	0.932862i	$-0.382697\pi$
$421$	14.7828	0.720468	0.360234	+	0.932862i	$0.382697\pi$
$422$	11.0851	0.539615
$423$	1.00000	0.0486217
$424$	10.3128	0.500836
$425$	20.7381	1.00594
$426$	4.31343	0.208986
$427$	−0.542656	−0.0262610
$428$	−3.76563	−0.182019
$429$	−7.27942	−0.351454
$430$	−9.45802	−0.456106
$431$	−3.75243	−0.180748	−0.0903741	−	0.995908i	$-0.528806\pi$
$431$	−3.75243	−0.180748	−0.0903741	+	0.995908i	$0.528806\pi$
$432$	4.69394	0.225837
$433$	15.1881	0.729896	0.364948	−	0.931028i	$-0.381087\pi$
$433$	15.1881	0.729896	0.364948	+	0.931028i	$0.381087\pi$
$434$	−0.497353	−0.0238737
$435$	5.88341	0.282088
$436$	−6.00931	−0.287794
$437$	−2.22663	−0.106514
$438$	−12.6842	−0.606073
$439$	−22.0222	−1.05106	−0.525531	−	0.850774i	$-0.676133\pi$
$439$	−22.0222	−1.05106	−0.525531	+	0.850774i	$0.676133\pi$
$440$	4.99427	0.238092
$441$	−6.99436	−0.333065
$442$	20.8010	0.989404
$443$	33.0265	1.56914	0.784569	−	0.620042i	$-0.212884\pi$
$443$	33.0265	1.56914	0.784569	+	0.620042i	$0.212884\pi$
$444$	1.32757	0.0630038
$445$	2.93147	0.138965
$446$	4.08207	0.193292
$447$	11.9980	0.567485
$448$	−0.413225	−0.0195231
$449$	−6.43102	−0.303499	−0.151749	−	0.988419i	$-0.548491\pi$
$449$	−6.43102	−0.303499	−0.151749	+	0.988419i	$0.548491\pi$
$450$	6.84029	0.322454
$451$	26.1679	1.23220
$452$	5.04153	0.237134
$453$	−13.3367	−0.626614
$454$	13.2808	0.623301
$455$	−0.166714	−0.00781567
$456$	−2.42958	−0.113776
$457$	−1.61909	−0.0757378	−0.0378689	−	0.999283i	$-0.512057\pi$
$457$	−1.61909	−0.0757378	−0.0378689	+	0.999283i	$0.512057\pi$
$458$	−3.55899	−0.166301
$459$	4.74232	0.221352
$460$	−0.787726	−0.0367279
$461$	5.18697	0.241581	0.120791	−	0.992678i	$-0.461457\pi$
$461$	5.18697	0.241581	0.120791	+	0.992678i	$0.461457\pi$
$462$	−0.304881	−0.0141844
$463$	34.7421	1.61460	0.807300	−	0.590141i	$-0.200928\pi$
$463$	34.7421	1.61460	0.807300	+	0.590141i	$0.200928\pi$
$464$	34.8759	1.61907
$465$	3.35331	0.155506
$466$	29.7140	1.37647
$467$	41.7548	1.93218	0.966090	−	0.258205i	$-0.0831309\pi$
$467$	41.7548	1.93218	0.966090	+	0.258205i	$0.0831309\pi$
$468$	1.25280	0.0579109
$469$	0.252179	0.0116446
$470$	−1.23862	−0.0571332
$471$	9.34960	0.430807
$472$	−17.1028	−0.787220
$473$	19.8227	0.911448
$474$	−24.8257	−1.14028
$475$	−4.37298	−0.200646
$476$	0.159078	0.00729134
$477$	4.24470	0.194351
$478$	−26.4103	−1.20798
$479$	−32.1847	−1.47056	−0.735278	−	0.677766i	$-0.762948\pi$
$479$	−32.1847	−1.47056	−0.735278	+	0.677766i	$0.762948\pi$
$480$	−1.96628	−0.0897482
$481$	−8.33239	−0.379924
$482$	30.0035	1.36662
$483$	−0.167180	−0.00760693
$484$	−1.90367	−0.0865304
$485$	3.86926	0.175694
$486$	1.56422	0.0709543
$487$	13.6807	0.619930	0.309965	−	0.950748i	$-0.399683\pi$
$487$	13.6807	0.619930	0.309965	+	0.950748i	$0.399683\pi$
$488$	17.5599	0.794900
$489$	7.60243	0.343794
$490$	8.66334	0.391370
$491$	−28.5961	−1.29052	−0.645261	−	0.763962i	$-0.723251\pi$
$491$	−28.5961	−1.29052	−0.645261	+	0.763962i	$0.723251\pi$
$492$	−4.50355	−0.203036
$493$	35.2354	1.58692
$494$	−4.38626	−0.197347
$495$	2.05561	0.0923927
$496$	19.8779	0.892544
$497$	−0.207043	−0.00928715
$498$	−4.61647	−0.206869
$499$	16.4688	0.737246	0.368623	−	0.929579i	$-0.379829\pi$
$499$	16.4688	0.737246	0.368623	+	0.929579i	$0.379829\pi$
$500$	−3.31592	−0.148292
$501$	−17.7868	−0.794657
$502$	−13.2609	−0.591865
$503$	−8.44855	−0.376702	−0.188351	−	0.982102i	$-0.560314\pi$
$503$	−8.44855	−0.376702	−0.188351	+	0.982102i	$0.560314\pi$
$504$	−0.182417	−0.00812552
$505$	10.9547	0.487476
$506$	9.04159	0.401948
$507$	5.13689	0.228137
$508$	1.17233	0.0520137
$509$	−9.77401	−0.433225	−0.216613	−	0.976258i	$-0.569501\pi$
$509$	−9.77401	−0.433225	−0.216613	+	0.976258i	$0.569501\pi$
$510$	−5.87392	−0.260101
$511$	0.608835	0.0269333
$512$	11.1528	0.492889
$513$	−1.00000	−0.0441511
$514$	7.04057	0.310546
$515$	−3.32779	−0.146640
$516$	−3.41153	−0.150184
$517$	2.59597	0.114171
$518$	−0.348982	−0.0153334
$519$	23.6447	1.03789
$520$	5.39473	0.236575
$521$	−10.0261	−0.439250	−0.219625	−	0.975584i	$-0.570483\pi$
$521$	−10.0261	−0.439250	−0.219625	+	0.975584i	$0.570483\pi$
$522$	11.6221	0.508686
$523$	44.6442	1.95215	0.976077	−	0.217425i	$-0.0697656\pi$
$523$	44.6442	1.95215	0.976077	+	0.217425i	$0.0697656\pi$
$524$	−5.58003	−0.243765
$525$	−0.328331	−0.0143295
$526$	−25.3081	−1.10348
$527$	20.0828	0.874819
$528$	12.1853	0.530298
$529$	−18.0421	−0.784439
$530$	−5.25756	−0.228374
$531$	−7.03939	−0.305484
$532$	−0.0335444	−0.00145434
$533$	28.2661	1.22434
$534$	5.79085	0.250595
$535$	−6.67410	−0.288546
$536$	−8.16031	−0.352472
$537$	−6.79923	−0.293408
$538$	49.1405	2.11860
$539$	−18.1572	−0.782084
$540$	−0.353774	−0.0152240
$541$	11.2249	0.482596	0.241298	−	0.970451i	$-0.422427\pi$
$541$	11.2249	0.482596	0.241298	+	0.970451i	$0.422427\pi$
$542$	6.40509	0.275122
$543$	15.9378	0.683955
$544$	−11.7760	−0.504890
$545$	−10.6507	−0.456227
$546$	−0.329328	−0.0140939
$547$	−2.69402	−0.115188	−0.0575940	−	0.998340i	$-0.518343\pi$
$547$	−2.69402	−0.115188	−0.0575940	+	0.998340i	$0.518343\pi$
$548$	9.87666	0.421910
$549$	7.22754	0.308464
$550$	17.7572	0.757169
$551$	−7.42999	−0.316528
$552$	5.40979	0.230256
$553$	1.19162	0.0506729
$554$	10.0857	0.428502
$555$	2.35295	0.0998771
$556$	−4.61672	−0.195792
$557$	−45.6879	−1.93586	−0.967930	−	0.251219i	$-0.919169\pi$
$557$	−45.6879	−1.93586	−0.967930	+	0.251219i	$0.919169\pi$
$558$	6.62415	0.280422
$559$	21.4121	0.905637
$560$	0.279070	0.0117928
$561$	12.3109	0.519767
$562$	10.5190	0.443719
$563$	−6.80216	−0.286677	−0.143338	−	0.989674i	$-0.545784\pi$
$563$	−6.80216	−0.286677	−0.143338	+	0.989674i	$0.545784\pi$
$564$	−0.446772	−0.0188125
$565$	8.93547	0.375918
$566$	−18.6883	−0.785527
$567$	−0.0750818	−0.00315314
$568$	6.69974	0.281115
$569$	1.47894	0.0620002	0.0310001	−	0.999519i	$-0.490131\pi$
$569$	1.47894	0.0620002	0.0310001	+	0.999519i	$0.490131\pi$
$570$	1.23862	0.0518800
$571$	9.50242	0.397664	0.198832	−	0.980034i	$-0.436285\pi$
$571$	9.50242	0.397664	0.198832	+	0.980034i	$0.436285\pi$
$572$	3.25224	0.135983
$573$	−16.7865	−0.701265
$574$	1.18386	0.0494133
$575$	9.73702	0.406062
$576$	5.50367	0.229320
$577$	24.1742	1.00639	0.503193	−	0.864174i	$-0.332158\pi$
$577$	24.1742	1.00639	0.503193	+	0.864174i	$0.332158\pi$
$578$	−8.58688	−0.357167
$579$	4.09764	0.170292
$580$	−2.62854	−0.109144
$581$	0.221589	0.00919304
$582$	7.64335	0.316827
$583$	11.0191	0.456365
$584$	−19.7014	−0.815250
$585$	2.22043	0.0918036
$586$	29.3838	1.21384
$587$	18.1377	0.748621	0.374311	−	0.927303i	$-0.377879\pi$
$587$	18.1377	0.748621	0.374311	+	0.927303i	$0.377879\pi$
$588$	3.12489	0.128868
$589$	−4.23480	−0.174492
$590$	8.71911	0.358960
$591$	−8.26711	−0.340064
$592$	13.9479	0.573256
$593$	−7.65993	−0.314556	−0.157278	−	0.987554i	$-0.550272\pi$
$593$	−7.65993	−0.314556	−0.157278	+	0.987554i	$0.550272\pi$
$594$	4.06066	0.166611
$595$	0.281946	0.0115586
$596$	−5.36036	−0.219569
$597$	15.5788	0.637599
$598$	9.76658	0.399385
$599$	24.2351	0.990220	0.495110	−	0.868830i	$-0.335128\pi$
$599$	24.2351	0.990220	0.495110	+	0.868830i	$0.335128\pi$
$600$	10.6245	0.433744
$601$	−27.2692	−1.11233	−0.556167	−	0.831070i	$-0.687729\pi$
$601$	−27.2692	−1.11233	−0.556167	+	0.831070i	$0.687729\pi$
$602$	0.896797	0.0365507
$603$	−3.35873	−0.136778
$604$	5.95848	0.242447
$605$	−3.37401	−0.137173
$606$	21.6399	0.879060
$607$	−48.2935	−1.96017	−0.980086	−	0.198575i	$-0.936369\pi$
$607$	−48.2935	−1.96017	−0.980086	+	0.198575i	$0.936369\pi$
$608$	2.48317	0.100706
$609$	−0.557857	−0.0226055
$610$	−8.95216	−0.362462
$611$	2.80412	0.113443
$612$	−2.11873	−0.0856448
$613$	−14.3469	−0.579465	−0.289732	−	0.957108i	$-0.593566\pi$
$613$	−14.3469	−0.579465	−0.289732	+	0.957108i	$0.593566\pi$
$614$	7.13552	0.287966
$615$	−7.98196	−0.321864
$616$	−0.473550	−0.0190799
$617$	−42.9975	−1.73101	−0.865507	−	0.500897i	$-0.833004\pi$
$617$	−42.9975	−1.73101	−0.865507	+	0.500897i	$0.833004\pi$
$618$	−6.57373	−0.264434
$619$	12.2538	0.492522	0.246261	−	0.969204i	$-0.420798\pi$
$619$	12.2538	0.492522	0.246261	+	0.969204i	$0.420798\pi$
$620$	−1.49816	−0.0601677
$621$	2.22663	0.0893517
$622$	−35.6605	−1.42986
$623$	−0.277959	−0.0111362
$624$	13.1624	0.526917
$625$	15.9879	0.639515
$626$	−1.91669	−0.0766063
$627$	−2.59597	−0.103673
$628$	−4.17714	−0.166686
$629$	14.0917	0.561872
$630$	0.0929976	0.00370511
$631$	−36.9310	−1.47020	−0.735099	−	0.677960i	$-0.762864\pi$
$631$	−36.9310	−1.47020	−0.735099	+	0.677960i	$0.762864\pi$
$632$	−38.5599	−1.53383
$633$	7.08669	0.281671
$634$	−2.94403	−0.116922
$635$	2.07780	0.0824550
$636$	−1.89641	−0.0751976
$637$	−19.6131	−0.777098
$638$	30.1707	1.19447
$639$	2.75757	0.109088
$640$	−10.7495	−0.424912
$641$	−33.4992	−1.32314	−0.661569	−	0.749884i	$-0.730109\pi$
$641$	−33.4992	−1.32314	−0.661569	+	0.749884i	$0.730109\pi$
$642$	−13.1840	−0.520333
$643$	−21.9291	−0.864801	−0.432400	−	0.901682i	$-0.642333\pi$
$643$	−21.9291	−0.864801	−0.432400	+	0.901682i	$0.642333\pi$
$644$	0.0746911	0.00294324
$645$	−6.04649	−0.238080
$646$	7.41801	0.291858
$647$	14.8445	0.583599	0.291799	−	0.956480i	$-0.405746\pi$
$647$	14.8445	0.583599	0.291799	+	0.956480i	$0.405746\pi$
$648$	2.42958	0.0954431
$649$	−18.2740	−0.717319
$650$	19.1810	0.752341
$651$	−0.317956	−0.0124617
$652$	−3.39655	−0.133019
$653$	13.5290	0.529432	0.264716	−	0.964326i	$-0.414722\pi$
$653$	13.5290	0.529432	0.264716	+	0.964326i	$0.414722\pi$
$654$	−21.0395	−0.822710
$655$	−9.88988	−0.386430
$656$	−47.3158	−1.84737
$657$	−8.10896	−0.316361
$658$	0.117444	0.00457845
$659$	23.4875	0.914945	0.457472	−	0.889224i	$-0.348755\pi$
$659$	23.4875	0.914945	0.457472	+	0.889224i	$0.348755\pi$
$660$	−0.918388	−0.0357482
$661$	−33.6601	−1.30923	−0.654614	−	0.755964i	$-0.727169\pi$
$661$	−33.6601	−1.30923	−0.654614	+	0.755964i	$0.727169\pi$
$662$	9.71000	0.377390
$663$	13.2980	0.516453
$664$	−7.17042	−0.278266
$665$	−0.0594532	−0.00230549
$666$	4.64803	0.180107
$667$	16.5439	0.640581
$668$	7.94666	0.307465
$669$	2.60966	0.100895
$670$	4.16018	0.160722
$671$	18.7625	0.724317
$672$	0.186440	0.00719210
$673$	47.2310	1.82062	0.910310	−	0.413928i	$-0.135843\pi$
$673$	47.2310	1.82062	0.910310	+	0.413928i	$0.135843\pi$
$674$	35.5676	1.37001
$675$	4.37298	0.168316
$676$	−2.29502	−0.0882699
$677$	−11.3970	−0.438023	−0.219012	−	0.975722i	$-0.570283\pi$
$677$	−11.3970	−0.438023	−0.219012	+	0.975722i	$0.570283\pi$
$678$	17.6512	0.677889
$679$	−0.366878	−0.0140795
$680$	−9.12353	−0.349872
$681$	8.49042	0.325354
$682$	17.1961	0.658472
$683$	34.0807	1.30406	0.652030	−	0.758193i	$-0.273918\pi$
$683$	34.0807	1.30406	0.652030	+	0.758193i	$0.273918\pi$
$684$	0.446772	0.0170828
$685$	17.5051	0.668836
$686$	−1.64356	−0.0627512
$687$	−2.27526	−0.0868064
$688$	−35.8427	−1.36649
$689$	11.9027	0.453455
$690$	−2.75795	−0.104993
$691$	14.8220	0.563857	0.281929	−	0.959435i	$-0.409026\pi$
$691$	14.8220	0.563857	0.281929	+	0.959435i	$0.409026\pi$
$692$	−10.5638	−0.401575
$693$	−0.194910	−0.00740402
$694$	1.08612	0.0412285
$695$	−8.18253	−0.310381
$696$	18.0518	0.684252
$697$	−47.8035	−1.81069
$698$	10.9484	0.414402
$699$	18.9961	0.718498
$700$	0.146689	0.00554433
$701$	33.9512	1.28232	0.641160	−	0.767407i	$-0.278453\pi$
$701$	33.9512	1.28232	0.641160	+	0.767407i	$0.278453\pi$
$702$	4.38626	0.165549
$703$	−2.97148	−0.112071
$704$	14.2874	0.538475
$705$	−0.791846	−0.0298226
$706$	44.0282	1.65702
$707$	−1.03871	−0.0390646
$708$	3.14500	0.118196
$709$	19.3006	0.724849	0.362424	−	0.932013i	$-0.381949\pi$
$709$	19.3006	0.724849	0.362424	+	0.932013i	$0.381949\pi$
$710$	−3.41557	−0.128184
$711$	−15.8710	−0.595209
$712$	8.99451	0.337083
$713$	9.42935	0.353132
$714$	0.556957	0.0208436
$715$	5.76418	0.215568
$716$	3.03770	0.113524
$717$	−16.8841	−0.630547
$718$	−20.4742	−0.764092
$719$	−6.35358	−0.236949	−0.118474	−	0.992957i	$-0.537800\pi$
$719$	−6.35358	−0.236949	−0.118474	+	0.992957i	$0.537800\pi$
$720$	−3.71687	−0.138520
$721$	0.315537	0.0117512
$722$	−1.56422	−0.0582141
$723$	19.1812	0.713356
$724$	−7.12054	−0.264633
$725$	32.4912	1.20669
$726$	−6.66503	−0.247363
$727$	16.5900	0.615288	0.307644	−	0.951502i	$-0.400459\pi$
$727$	16.5900	0.615288	0.307644	+	0.951502i	$0.400459\pi$
$728$	−0.511521	−0.0189582
$729$	1.00000	0.0370370
$730$	10.0439	0.371741
$731$	−36.2121	−1.33935
$732$	−3.22906	−0.119350
$733$	8.27651	0.305700	0.152850	−	0.988249i	$-0.451155\pi$
$733$	8.27651	0.305700	0.152850	+	0.988249i	$0.451155\pi$
$734$	−5.14871	−0.190042
$735$	5.53845	0.204289
$736$	−5.52910	−0.203805
$737$	−8.71916	−0.321174
$738$	−15.7676	−0.580413
$739$	−25.2125	−0.927457	−0.463729	−	0.885977i	$-0.653489\pi$
$739$	−25.2125	−0.927457	−0.463729	+	0.885977i	$0.653489\pi$
$740$	−1.05123	−0.0386441
$741$	−2.80412	−0.103012
$742$	0.498515	0.0183010
$743$	−21.0749	−0.773164	−0.386582	−	0.922255i	$-0.626344\pi$
$743$	−21.0749	−0.773164	−0.386582	+	0.922255i	$0.626344\pi$
$744$	10.2888	0.377206
$745$	−9.50054	−0.348073
$746$	23.3216	0.853865
$747$	−2.95130	−0.107982
$748$	−5.50017	−0.201106
$749$	0.632829	0.0231231
$750$	−11.6095	−0.423920
$751$	9.30849	0.339671	0.169836	−	0.985472i	$-0.445676\pi$
$751$	9.30849	0.339671	0.169836	+	0.985472i	$0.445676\pi$
$752$	−4.69394	−0.171170
$753$	−8.47769	−0.308944
$754$	32.5899	1.18685
$755$	10.5606	0.384341
$756$	0.0335444	0.00122000
$757$	20.6103	0.749096	0.374548	−	0.927208i	$-0.377798\pi$
$757$	20.6103	0.749096	0.374548	+	0.927208i	$0.377798\pi$
$758$	42.5174	1.54430
$759$	5.78027	0.209811
$760$	1.92386	0.0697856
$761$	−15.0535	−0.545690	−0.272845	−	0.962058i	$-0.587965\pi$
$761$	−15.0535	−0.545690	−0.272845	+	0.962058i	$0.587965\pi$
$762$	4.10450	0.148690
$763$	1.00989	0.0365604
$764$	7.49972	0.271330
$765$	−3.75518	−0.135769
$766$	20.3770	0.736253
$767$	−19.7393	−0.712746
$768$	−10.2273	−0.369046
$769$	−1.07627	−0.0388112	−0.0194056	−	0.999812i	$-0.506177\pi$
$769$	−1.07627	−0.0388112	−0.0194056	+	0.999812i	$0.506177\pi$
$770$	0.241419	0.00870013
$771$	4.50102	0.162100
$772$	−1.83071	−0.0658887
$773$	15.2175	0.547336	0.273668	−	0.961824i	$-0.411763\pi$
$773$	15.2175	0.547336	0.273668	+	0.961824i	$0.411763\pi$
$774$	−11.9443	−0.429328
$775$	18.5187	0.665212
$776$	11.8719	0.426175
$777$	−0.223104	−0.00800380
$778$	2.37962	0.0853136
$779$	10.0802	0.361160
$780$	−0.992027	−0.0355203
$781$	7.15856	0.256153
$782$	−16.5172	−0.590653
$783$	7.42999	0.265526
$784$	32.8311	1.17254
$785$	−7.40344	−0.264240
$786$	−19.5365	−0.696845
$787$	29.4928	1.05130	0.525652	−	0.850699i	$-0.323821\pi$
$787$	29.4928	1.05130	0.525652	+	0.850699i	$0.323821\pi$
$788$	3.69351	0.131576
$789$	−16.1794	−0.576002
$790$	19.6581	0.699403
$791$	−0.847249	−0.0301247
$792$	6.30713	0.224114
$793$	20.2669	0.719699
$794$	−25.1828	−0.893704
$795$	−3.36114	−0.119207
$796$	−6.96019	−0.246697
$797$	−50.6893	−1.79551	−0.897753	−	0.440498i	$-0.854802\pi$
$797$	−50.6893	−1.79551	−0.897753	+	0.440498i	$0.854802\pi$
$798$	−0.117444	−0.00415748
$799$	−4.74232	−0.167771
$800$	−10.8588	−0.383918
$801$	3.70208	0.130806
$802$	56.1871	1.98404
$803$	−21.0506	−0.742860
$804$	1.50059	0.0529216
$805$	0.132380	0.00466579
$806$	18.5749	0.654274
$807$	31.4154	1.10587
$808$	33.6117	1.18245
$809$	12.2497	0.430676	0.215338	−	0.976540i	$-0.430915\pi$
$809$	12.2497	0.430676	0.215338	+	0.976540i	$0.430915\pi$
$810$	−1.23862	−0.0435206
$811$	−36.1271	−1.26859	−0.634297	−	0.773090i	$-0.718710\pi$
$811$	−36.1271	−1.26859	−0.634297	+	0.773090i	$0.718710\pi$
$812$	0.249235	0.00874643
$813$	4.09476	0.143610
$814$	12.0661	0.422918
$815$	−6.01995	−0.210870
$816$	−22.2601	−0.779261
$817$	7.63595	0.267148
$818$	17.7197	0.619556
$819$	−0.210539	−0.00735681
$820$	3.56611	0.124534
$821$	−1.44772	−0.0505257	−0.0252629	−	0.999681i	$-0.508042\pi$
$821$	−1.44772	−0.0505257	−0.0252629	+	0.999681i	$0.508042\pi$
$822$	34.5797	1.20611
$823$	−46.1434	−1.60846	−0.804229	−	0.594320i	$-0.797421\pi$
$823$	−46.1434	−1.60846	−0.804229	+	0.594320i	$0.797421\pi$
$824$	−10.2105	−0.355700
$825$	11.3521	0.395230
$826$	−0.826735	−0.0287658
$827$	19.5417	0.679531	0.339765	−	0.940510i	$-0.389652\pi$
$827$	19.5417	0.679531	0.339765	+	0.940510i	$0.389652\pi$
$828$	−0.994797	−0.0345716
$829$	−11.9808	−0.416109	−0.208054	−	0.978117i	$-0.566713\pi$
$829$	−11.9808	−0.416109	−0.208054	+	0.978117i	$0.566713\pi$
$830$	3.65553	0.126885
$831$	6.44779	0.223671
$832$	15.4330	0.535042
$833$	33.1695	1.14925
$834$	−16.1638	−0.559707
$835$	14.0844	0.487411
$836$	1.15981	0.0401127
$837$	4.23480	0.146376
$838$	−3.84507	−0.132826
$839$	−18.3871	−0.634792	−0.317396	−	0.948293i	$-0.602808\pi$
$839$	−18.3871	−0.634792	−0.317396	+	0.948293i	$0.602808\pi$
$840$	0.144446	0.00498388
$841$	26.2048	0.903614
$842$	−23.1234	−0.796886
$843$	6.72480	0.231614
$844$	−3.16613	−0.108983
$845$	−4.06762	−0.139930
$846$	−1.56422	−0.0537789
$847$	0.319919	0.0109925
$848$	−19.9243	−0.684205
$849$	−11.9474	−0.410033
$850$	−32.4388	−1.11264
$851$	6.61638	0.226807
$852$	−1.23200	−0.0422077
$853$	43.1717	1.47817	0.739086	−	0.673612i	$-0.235258\pi$
$853$	43.1717	1.47817	0.739086	+	0.673612i	$0.235258\pi$
$854$	0.848832	0.0290464
$855$	0.791846	0.0270805
$856$	−20.4778	−0.699918
$857$	26.1365	0.892807	0.446403	−	0.894832i	$-0.352705\pi$
$857$	26.1365	0.892807	0.446403	+	0.894832i	$0.352705\pi$
$858$	11.3866	0.388732
$859$	0.457971	0.0156258	0.00781288	−	0.999969i	$-0.497513\pi$
$859$	0.457971	0.0156258	0.00781288	+	0.999969i	$0.497513\pi$
$860$	2.70140	0.0921171
$861$	0.756839	0.0257930
$862$	5.86961	0.199920
$863$	−23.1014	−0.786380	−0.393190	−	0.919457i	$-0.628629\pi$
$863$	−23.1014	−0.786380	−0.393190	+	0.919457i	$0.628629\pi$
$864$	−2.48317	−0.0844790
$865$	−18.7229	−0.636599
$866$	−23.7575	−0.807314
$867$	−5.48958	−0.186436
$868$	0.142054	0.00482163
$869$	−41.2006	−1.39763
$870$	−9.20292	−0.312008
$871$	−9.41829	−0.319127
$872$	−32.6791	−1.10666
$873$	4.88638	0.165379
$874$	3.48293	0.117812
$875$	0.557253	0.0188386
$876$	3.62285	0.122405
$877$	−24.3156	−0.821080	−0.410540	−	0.911843i	$-0.634660\pi$
$877$	−24.3156	−0.821080	−0.410540	+	0.911843i	$0.634660\pi$
$878$	34.4475	1.16255
$879$	18.7850	0.633603
$880$	−9.64889	−0.325264
$881$	48.7676	1.64302	0.821511	−	0.570193i	$-0.193132\pi$
$881$	48.7676	1.64302	0.821511	+	0.570193i	$0.193132\pi$
$882$	10.9407	0.368392
$883$	−56.1397	−1.88925	−0.944625	−	0.328152i	$-0.893574\pi$
$883$	−56.1397	−1.88925	−0.944625	+	0.328152i	$0.893574\pi$
$884$	−5.94119	−0.199824
$885$	5.57411	0.187372
$886$	−51.6606	−1.73557
$887$	41.8563	1.40540	0.702699	−	0.711487i	$-0.251978\pi$
$887$	41.8563	1.40540	0.702699	+	0.711487i	$0.251978\pi$
$888$	7.21945	0.242269
$889$	−0.197014	−0.00660765
$890$	−4.58546	−0.153705
$891$	2.59597	0.0869683
$892$	−1.16592	−0.0390380
$893$	1.00000	0.0334637
$894$	−18.7674	−0.627677
$895$	5.38394	0.179965
$896$	1.01925	0.0340509
$897$	6.24375	0.208473
$898$	10.0595	0.335690
$899$	31.4646	1.04940
$900$	−1.95373	−0.0651242
$901$	−20.1297	−0.670617
$902$	−40.9322	−1.36289
$903$	0.573320	0.0190789
$904$	27.4163	0.911852
$905$	−12.6202	−0.419511
$906$	20.8615	0.693078
$907$	29.4776	0.978786	0.489393	−	0.872063i	$-0.337218\pi$
$907$	29.4776	0.978786	0.489393	+	0.872063i	$0.337218\pi$
$908$	−3.79328	−0.125884
$909$	13.8343	0.458856
$910$	0.260777	0.00864467
$911$	35.1673	1.16514	0.582572	−	0.812779i	$-0.302047\pi$
$911$	35.1673	1.16514	0.582572	+	0.812779i	$0.302047\pi$
$912$	4.69394	0.155432
$913$	−7.66148	−0.253558
$914$	2.53260	0.0837711
$915$	−5.72309	−0.189200
$916$	1.01652	0.0335868
$917$	0.937746	0.0309671
$918$	−7.41801	−0.244831
$919$	4.71270	0.155458	0.0777288	−	0.996975i	$-0.475233\pi$
$919$	4.71270	0.155458	0.0777288	+	0.996975i	$0.475233\pi$
$920$	−4.28372	−0.141230
$921$	4.56173	0.150314
$922$	−8.11354	−0.267205
$923$	7.73256	0.254520
$924$	0.0870803	0.00286473
$925$	12.9942	0.427247
$926$	−54.3441	−1.78586
$927$	−4.20257	−0.138031
$928$	−18.4499	−0.605648
$929$	−52.9851	−1.73839	−0.869193	−	0.494473i	$-0.835361\pi$
$929$	−52.9851	−1.73839	−0.869193	+	0.494473i	$0.835361\pi$
$930$	−5.24530	−0.172000
$931$	−6.99436	−0.229231
$932$	−8.48692	−0.277998
$933$	−22.7977	−0.746363
$934$	−65.3135	−2.13712
$935$	−9.74834	−0.318805
$936$	6.81286	0.222685
$937$	29.3048	0.957345	0.478672	−	0.877994i	$-0.341118\pi$
$937$	29.3048	0.957345	0.478672	+	0.877994i	$0.341118\pi$
$938$	−0.394463	−0.0128797
$939$	−1.22534	−0.0399873
$940$	0.353774	0.0115388
$941$	44.8660	1.46259	0.731296	−	0.682061i	$-0.238916\pi$
$941$	44.8660	1.46259	0.731296	+	0.682061i	$0.238916\pi$
$942$	−14.6248	−0.476502
$943$	−22.4449	−0.730906
$944$	33.0425	1.07544
$945$	0.0594532	0.00193401
$946$	−31.0070	−1.00812
$947$	−20.5651	−0.668277	−0.334138	−	0.942524i	$-0.608445\pi$
$947$	−20.5651	−0.668277	−0.334138	+	0.942524i	$0.608445\pi$
$948$	7.09071	0.230296
$949$	−22.7385	−0.738124
$950$	6.84029	0.221928
$951$	−1.88211	−0.0610316
$952$	0.865082	0.0280375
$953$	29.8726	0.967669	0.483834	−	0.875160i	$-0.339244\pi$
$953$	29.8726	0.967669	0.483834	+	0.875160i	$0.339244\pi$
$954$	−6.63962	−0.214966
$955$	13.2923	0.430128
$956$	7.54333	0.243969
$957$	19.2880	0.623494
$958$	50.3438	1.62653
$959$	−1.65981	−0.0535981
$960$	−4.35806	−0.140656
$961$	−13.0665	−0.421498
$962$	13.0337	0.420222
$963$	−8.42853	−0.271606
$964$	−8.56962	−0.276009
$965$	−3.24470	−0.104450
$966$	0.261505	0.00841378
$967$	−35.9826	−1.15712	−0.578561	−	0.815639i	$-0.696386\pi$
$967$	−35.9826	−1.15712	−0.578561	+	0.815639i	$0.696386\pi$
$968$	−10.3523	−0.332736
$969$	4.74232	0.152345
$970$	−6.05235	−0.194329
$971$	35.9583	1.15396	0.576978	−	0.816760i	$-0.304232\pi$
$971$	35.9583	1.15396	0.576978	+	0.816760i	$0.304232\pi$
$972$	−0.446772	−0.0143302
$973$	0.775857	0.0248728
$974$	−21.3995	−0.685684
$975$	12.2624	0.392710
$976$	−33.9256	−1.08593
$977$	−59.7656	−1.91207	−0.956035	−	0.293252i	$-0.905262\pi$
$977$	−59.7656	−1.91207	−0.956035	+	0.293252i	$0.905262\pi$
$978$	−11.8919	−0.380259
$979$	9.61048	0.307152
$980$	−2.47443	−0.0790427
$981$	−13.4505	−0.429442
$982$	44.7304	1.42740
$983$	13.2182	0.421595	0.210798	−	0.977530i	$-0.432394\pi$
$983$	13.2182	0.421595	0.210798	+	0.977530i	$0.432394\pi$
$984$	−24.4907	−0.780734
$985$	6.54627	0.208582
$986$	−55.1158	−1.75524
$987$	0.0750818	0.00238988
$988$	1.25280	0.0398570
$989$	−17.0025	−0.540646
$990$	−3.21541	−0.102193
$991$	−11.0106	−0.349764	−0.174882	−	0.984589i	$-0.555954\pi$
$991$	−11.0106	−0.349764	−0.174882	+	0.984589i	$0.555954\pi$
$992$	−10.5157	−0.333874
$993$	6.20759	0.196992
$994$	0.323860	0.0102722
$995$	−12.3360	−0.391079
$996$	1.31856	0.0417801
$997$	59.6654	1.88962	0.944811	−	0.327616i	$-0.106245\pi$
$997$	59.6654	1.88962	0.944811	+	0.327616i	$0.106245\pi$
$998$	−25.7608	−0.815444
$999$	2.97148	0.0940133

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2679.2.a.k.1.2	✓	7
3.2	odd	2		8037.2.a.j.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2679.2.a.k.1.2	✓	7	1.1	even	1	trivial
8037.2.a.j.1.6		7	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2679 = 3 \cdot 19 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2679.a (trivial)

\(f(q)\)	\(=\)	\(q-1.56422 q^{2} -1.00000 q^{3} +0.446772 q^{4} +0.791846 q^{5} +1.56422 q^{6} -0.0750818 q^{7} +2.42958 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.56422 q^{2} -1.00000 q^{3} +0.446772 q^{4} +0.791846 q^{5} +1.56422 q^{6} -0.0750818 q^{7} +2.42958 q^{8} +1.00000 q^{9} -1.23862 q^{10} +2.59597 q^{11} -0.446772 q^{12} +2.80412 q^{13} +0.117444 q^{14} -0.791846 q^{15} -4.69394 q^{16} -4.74232 q^{17} -1.56422 q^{18} +1.00000 q^{19} +0.353774 q^{20} +0.0750818 q^{21} -4.06066 q^{22} -2.22663 q^{23} -2.42958 q^{24} -4.37298 q^{25} -4.38626 q^{26} -1.00000 q^{27} -0.0335444 q^{28} -7.42999 q^{29} +1.23862 q^{30} -4.23480 q^{31} +2.48317 q^{32} -2.59597 q^{33} +7.41801 q^{34} -0.0594532 q^{35} +0.446772 q^{36} -2.97148 q^{37} -1.56422 q^{38} -2.80412 q^{39} +1.92386 q^{40} +10.0802 q^{41} -0.117444 q^{42} +7.63595 q^{43} +1.15981 q^{44} +0.791846 q^{45} +3.48293 q^{46} +1.00000 q^{47} +4.69394 q^{48} -6.99436 q^{49} +6.84029 q^{50} +4.74232 q^{51} +1.25280 q^{52} +4.24470 q^{53} +1.56422 q^{54} +2.05561 q^{55} -0.182417 q^{56} -1.00000 q^{57} +11.6221 q^{58} -7.03939 q^{59} -0.353774 q^{60} +7.22754 q^{61} +6.62415 q^{62} -0.0750818 q^{63} +5.50367 q^{64} +2.22043 q^{65} +4.06066 q^{66} -3.35873 q^{67} -2.11873 q^{68} +2.22663 q^{69} +0.0929976 q^{70} +2.75757 q^{71} +2.42958 q^{72} -8.10896 q^{73} +4.64803 q^{74} +4.37298 q^{75} +0.446772 q^{76} -0.194910 q^{77} +4.38626 q^{78} -15.8710 q^{79} -3.71687 q^{80} +1.00000 q^{81} -15.7676 q^{82} -2.95130 q^{83} +0.0335444 q^{84} -3.75518 q^{85} -11.9443 q^{86} +7.42999 q^{87} +6.30713 q^{88} +3.70208 q^{89} -1.23862 q^{90} -0.210539 q^{91} -0.994797 q^{92} +4.23480 q^{93} -1.56422 q^{94} +0.791846 q^{95} -2.48317 q^{96} +4.88638 q^{97} +10.9407 q^{98} +2.59597 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 2 q^{2} - 7 q^{3} + 4 q^{4} + 6 q^{5} + 2 q^{6} - 3 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 2 * q^2 - 7 * q^3 + 4 * q^4 + 6 * q^5 + 2 * q^6 - 3 * q^7 + 6 * q^8 + 7 * q^9	\( 7 q - 2 q^{2} - 7 q^{3} + 4 q^{4} + 6 q^{5} + 2 q^{6} - 3 q^{7} + 6 q^{8} + 7 q^{9} - 10 q^{10} - 9 q^{11} - 4 q^{12} - 8 q^{13} - 9 q^{14} - 6 q^{15} + 14 q^{16} + 7 q^{17} - 2 q^{18} + 7 q^{19} - 4 q^{20} + 3 q^{21} - 7 q^{22} - 7 q^{23} - 6 q^{24} - 9 q^{25} + q^{26} - 7 q^{27} - 12 q^{28} - 12 q^{29} + 10 q^{30} - 13 q^{31} + 15 q^{32} + 9 q^{33} + 2 q^{34} + 4 q^{35} + 4 q^{36} - 10 q^{37} - 2 q^{38} + 8 q^{39} - 26 q^{40} - 8 q^{41} + 9 q^{42} + 12 q^{43} - 14 q^{44} + 6 q^{45} - 7 q^{46} + 7 q^{47} - 14 q^{48} - 16 q^{49} - 12 q^{50} - 7 q^{51} - 6 q^{52} - 17 q^{53} + 2 q^{54} + 7 q^{55} - 38 q^{56} - 7 q^{57} - 12 q^{58} + 12 q^{59} + 4 q^{60} - 23 q^{61} + 23 q^{62} - 3 q^{63} + 12 q^{64} - 13 q^{65} + 7 q^{66} + q^{67} + 15 q^{68} + 7 q^{69} + 8 q^{70} + 6 q^{72} - 29 q^{73} + 5 q^{74} + 9 q^{75} + 4 q^{76} + 4 q^{77} - q^{78} - 3 q^{79} + 15 q^{80} + 7 q^{81} - 7 q^{82} + 19 q^{83} + 12 q^{84} - 5 q^{85} - 23 q^{86} + 12 q^{87} - 33 q^{88} - 14 q^{89} - 10 q^{90} - 3 q^{91} - 5 q^{92} + 13 q^{93} - 2 q^{94} + 6 q^{95} - 15 q^{96} - 17 q^{97} + 38 q^{98} - 9 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 - 7 * q^3 + 4 * q^4 + 6 * q^5 + 2 * q^6 - 3 * q^7 + 6 * q^8 + 7 * q^9 - 10 * q^10 - 9 * q^11 - 4 * q^12 - 8 * q^13 - 9 * q^14 - 6 * q^15 + 14 * q^16 + 7 * q^17 - 2 * q^18 + 7 * q^19 - 4 * q^20 + 3 * q^21 - 7 * q^22 - 7 * q^23 - 6 * q^24 - 9 * q^25 + q^26 - 7 * q^27 - 12 * q^28 - 12 * q^29 + 10 * q^30 - 13 * q^31 + 15 * q^32 + 9 * q^33 + 2 * q^34 + 4 * q^35 + 4 * q^36 - 10 * q^37 - 2 * q^38 + 8 * q^39 - 26 * q^40 - 8 * q^41 + 9 * q^42 + 12 * q^43 - 14 * q^44 + 6 * q^45 - 7 * q^46 + 7 * q^47 - 14 * q^48 - 16 * q^49 - 12 * q^50 - 7 * q^51 - 6 * q^52 - 17 * q^53 + 2 * q^54 + 7 * q^55 - 38 * q^56 - 7 * q^57 - 12 * q^58 + 12 * q^59 + 4 * q^60 - 23 * q^61 + 23 * q^62 - 3 * q^63 + 12 * q^64 - 13 * q^65 + 7 * q^66 + q^67 + 15 * q^68 + 7 * q^69 + 8 * q^70 + 6 * q^72 - 29 * q^73 + 5 * q^74 + 9 * q^75 + 4 * q^76 + 4 * q^77 - q^78 - 3 * q^79 + 15 * q^80 + 7 * q^81 - 7 * q^82 + 19 * q^83 + 12 * q^84 - 5 * q^85 - 23 * q^86 + 12 * q^87 - 33 * q^88 - 14 * q^89 - 10 * q^90 - 3 * q^91 - 5 * q^92 + 13 * q^93 - 2 * q^94 + 6 * q^95 - 15 * q^96 - 17 * q^97 + 38 * q^98 - 9 * q^99

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