LMFDB - Embedded newform 667.2.a.d.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,2,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, 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("667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	667.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:	$5.32602181482$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} - 22 x^{14} + 68 x^{13} + 187 x^{12} - 597 x^{11} - 795 x^{10} + 2592 x^{9} + \cdots + 64 $ x^16 - 3x^15 - 22x^14 + 68x^13 + 187x^12 - 597x^11 - 795x^10 + 2592x^9 + 1860x^8 - 5877x^7 - 2496x^6 + 6612x^5 + 1842x^4 - 3011x^3 - 505x^2 + 336*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$2.14844$ of defining polynomial
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.14844 q^{2} -1.74064 q^{3} +2.61580 q^{4} -1.42439 q^{5} -3.73966 q^{6} +3.61731 q^{7} +1.32302 q^{8} +0.0298167 q^{9} +O(q^{10})$	\(q+2.14844 q^{2} -1.74064 q^{3} +2.61580 q^{4} -1.42439 q^{5} -3.73966 q^{6} +3.61731 q^{7} +1.32302 q^{8} +0.0298167 q^{9} -3.06021 q^{10} +4.28818 q^{11} -4.55317 q^{12} +0.939230 q^{13} +7.77158 q^{14} +2.47934 q^{15} -2.38917 q^{16} +7.48700 q^{17} +0.0640594 q^{18} +4.97904 q^{19} -3.72592 q^{20} -6.29642 q^{21} +9.21291 q^{22} +1.00000 q^{23} -2.30290 q^{24} -2.97112 q^{25} +2.01788 q^{26} +5.17001 q^{27} +9.46218 q^{28} -1.00000 q^{29} +5.32672 q^{30} -2.22916 q^{31} -7.77905 q^{32} -7.46416 q^{33} +16.0854 q^{34} -5.15245 q^{35} +0.0779946 q^{36} -0.191258 q^{37} +10.6972 q^{38} -1.63486 q^{39} -1.88449 q^{40} -5.36788 q^{41} -13.5275 q^{42} -6.26248 q^{43} +11.2170 q^{44} -0.0424705 q^{45} +2.14844 q^{46} +0.471038 q^{47} +4.15869 q^{48} +6.08494 q^{49} -6.38329 q^{50} -13.0321 q^{51} +2.45684 q^{52} -6.09535 q^{53} +11.1075 q^{54} -6.10802 q^{55} +4.78578 q^{56} -8.66670 q^{57} -2.14844 q^{58} +7.35600 q^{59} +6.48547 q^{60} +9.04719 q^{61} -4.78922 q^{62} +0.107856 q^{63} -11.9345 q^{64} -1.33783 q^{65} -16.0363 q^{66} +8.32218 q^{67} +19.5845 q^{68} -1.74064 q^{69} -11.0697 q^{70} +4.71689 q^{71} +0.0394481 q^{72} -10.9752 q^{73} -0.410907 q^{74} +5.17165 q^{75} +13.0242 q^{76} +15.5117 q^{77} -3.51240 q^{78} -7.80891 q^{79} +3.40311 q^{80} -9.08856 q^{81} -11.5326 q^{82} -16.6667 q^{83} -16.4702 q^{84} -10.6644 q^{85} -13.4546 q^{86} +1.74064 q^{87} +5.67335 q^{88} +2.37020 q^{89} -0.0912454 q^{90} +3.39749 q^{91} +2.61580 q^{92} +3.88016 q^{93} +1.01200 q^{94} -7.09207 q^{95} +13.5405 q^{96} -11.3963 q^{97} +13.0731 q^{98} +0.127859 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) $ 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9} - 14 q^{10} + 4 q^{11} + 3 q^{12} + 15 q^{13} + 8 q^{14} + 8 q^{15} + 23 q^{16} + 20 q^{17} + 2 q^{18} - 4 q^{19} + 25 q^{20} + 5 q^{21} + 13 q^{22} + 16 q^{23} - 24 q^{24} + 30 q^{25} + 25 q^{26} + 8 q^{27} - 13 q^{28} - 16 q^{29} - 45 q^{30} - 19 q^{32} + q^{33} - 23 q^{34} + 5 q^{35} + 37 q^{36} + 5 q^{37} + 38 q^{38} - 10 q^{39} - 20 q^{40} + 7 q^{41} + 14 q^{42} - 17 q^{43} - 21 q^{44} + 48 q^{45} + 3 q^{46} + 29 q^{47} + 35 q^{48} + 31 q^{49} - 44 q^{50} - 14 q^{51} + 20 q^{52} + 63 q^{53} - 13 q^{54} + q^{55} - 19 q^{56} - 22 q^{57} - 3 q^{58} + 11 q^{59} - 3 q^{60} + 33 q^{62} - 33 q^{63} + 29 q^{64} + 53 q^{65} - 43 q^{66} - 13 q^{67} + 63 q^{68} + 5 q^{69} - 46 q^{70} - 23 q^{71} + 46 q^{72} - 38 q^{73} - 47 q^{74} + 37 q^{75} - 56 q^{76} + 97 q^{77} - 24 q^{78} - 27 q^{79} + 8 q^{80} + 40 q^{81} + 9 q^{82} + 36 q^{83} + 22 q^{84} + 6 q^{85} - 11 q^{86} - 5 q^{87} - 24 q^{88} - 16 q^{89} - 95 q^{90} - 47 q^{91} + 21 q^{92} + 62 q^{93} + 37 q^{94} - 12 q^{95} - 74 q^{96} - 30 q^{97} - 27 q^{98} - 42 q^{99}+O(q^{100}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9 - 14 * q^10 + 4 * q^11 + 3 * q^12 + 15 * q^13 + 8 * q^14 + 8 * q^15 + 23 * q^16 + 20 * q^17 + 2 * q^18 - 4 * q^19 + 25 * q^20 + 5 * q^21 + 13 * q^22 + 16 * q^23 - 24 * q^24 + 30 * q^25 + 25 * q^26 + 8 * q^27 - 13 * q^28 - 16 * q^29 - 45 * q^30 - 19 * q^32 + q^33 - 23 * q^34 + 5 * q^35 + 37 * q^36 + 5 * q^37 + 38 * q^38 - 10 * q^39 - 20 * q^40 + 7 * q^41 + 14 * q^42 - 17 * q^43 - 21 * q^44 + 48 * q^45 + 3 * q^46 + 29 * q^47 + 35 * q^48 + 31 * q^49 - 44 * q^50 - 14 * q^51 + 20 * q^52 + 63 * q^53 - 13 * q^54 + q^55 - 19 * q^56 - 22 * q^57 - 3 * q^58 + 11 * q^59 - 3 * q^60 + 33 * q^62 - 33 * q^63 + 29 * q^64 + 53 * q^65 - 43 * q^66 - 13 * q^67 + 63 * q^68 + 5 * q^69 - 46 * q^70 - 23 * q^71 + 46 * q^72 - 38 * q^73 - 47 * q^74 + 37 * q^75 - 56 * q^76 + 97 * q^77 - 24 * q^78 - 27 * q^79 + 8 * q^80 + 40 * q^81 + 9 * q^82 + 36 * q^83 + 22 * q^84 + 6 * q^85 - 11 * q^86 - 5 * q^87 - 24 * q^88 - 16 * q^89 - 95 * q^90 - 47 * q^91 + 21 * q^92 + 62 * q^93 + 37 * q^94 - 12 * q^95 - 74 * q^96 - 30 * q^97 - 27 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.14844	1.51918	0.759589	−	0.650403i	$-0.225400\pi$
$2$	2.14844	1.51918	0.759589	+	0.650403i	$0.225400\pi$
$3$	−1.74064	−1.00496	−0.502479	−	0.864590i	$-0.667578\pi$
$3$	−1.74064	−1.00496	−0.502479	+	0.864590i	$0.667578\pi$
$4$	2.61580	1.30790
$5$	−1.42439	−0.637005	−0.318502	−	0.947922i	$-0.603180\pi$
$5$	−1.42439	−0.637005	−0.318502	+	0.947922i	$0.603180\pi$
$6$	−3.73966	−1.52671
$7$	3.61731	1.36721	0.683607	−	0.729850i	$-0.260410\pi$
$7$	3.61731	1.36721	0.683607	+	0.729850i	$0.260410\pi$
$8$	1.32302	0.467759
$9$	0.0298167	0.00993890
$10$	−3.06021	−0.967724
$11$	4.28818	1.29293	0.646467	−	0.762942i	$-0.276246\pi$
$11$	4.28818	1.29293	0.646467	+	0.762942i	$0.276246\pi$
$12$	−4.55317	−1.31439
$13$	0.939230	0.260496	0.130248	−	0.991481i	$-0.458423\pi$
$13$	0.939230	0.260496	0.130248	+	0.991481i	$0.458423\pi$
$14$	7.77158	2.07704
$15$	2.47934	0.640163
$16$	−2.38917	−0.597294
$17$	7.48700	1.81586	0.907932	−	0.419119i	$-0.137661\pi$
$17$	7.48700	1.81586	0.907932	+	0.419119i	$0.137661\pi$
$18$	0.0640594	0.0150990
$19$	4.97904	1.14227	0.571135	−	0.820856i	$-0.306503\pi$
$19$	4.97904	1.14227	0.571135	+	0.820856i	$0.306503\pi$
$20$	−3.72592	−0.833140
$21$	−6.29642	−1.37399
$22$	9.21291	1.96420
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.30290	−0.470077
$25$	−2.97112	−0.594225
$26$	2.01788	0.395739
$27$	5.17001	0.994969
$28$	9.46218	1.78818
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	5.32672	0.972521
$31$	−2.22916	−0.400369	−0.200185	−	0.979758i	$-0.564154\pi$
$31$	−2.22916	−0.400369	−0.200185	+	0.979758i	$0.564154\pi$
$32$	−7.77905	−1.37515
$33$	−7.46416	−1.29934
$34$	16.0854	2.75862
$35$	−5.15245	−0.870923
$36$	0.0779946	0.0129991
$37$	−0.191258	−0.0314426	−0.0157213	−	0.999876i	$-0.505004\pi$
$37$	−0.191258	−0.0314426	−0.0157213	+	0.999876i	$0.505004\pi$
$38$	10.6972	1.73531
$39$	−1.63486	−0.261787
$40$	−1.88449	−0.297965
$41$	−5.36788	−0.838322	−0.419161	−	0.907912i	$-0.637676\pi$
$41$	−5.36788	−0.838322	−0.419161	+	0.907912i	$0.637676\pi$
$42$	−13.5275	−2.08734
$43$	−6.26248	−0.955019	−0.477510	−	0.878627i	$-0.658460\pi$
$43$	−6.26248	−0.955019	−0.477510	+	0.878627i	$0.658460\pi$
$44$	11.2170	1.69103
$45$	−0.0424705	−0.00633113
$46$	2.14844	0.316771
$47$	0.471038	0.0687080	0.0343540	−	0.999410i	$-0.489063\pi$
$47$	0.471038	0.0687080	0.0343540	+	0.999410i	$0.489063\pi$
$48$	4.15869	0.600255
$49$	6.08494	0.869277
$50$	−6.38329	−0.902733
$51$	−13.0321	−1.82486
$52$	2.45684	0.340703
$53$	−6.09535	−0.837261	−0.418631	−	0.908157i	$-0.637490\pi$
$53$	−6.09535	−0.837261	−0.418631	+	0.908157i	$0.637490\pi$
$54$	11.1075	1.51154
$55$	−6.10802	−0.823606
$56$	4.78578	0.639527
$57$	−8.66670	−1.14793
$58$	−2.14844	−0.282104
$59$	7.35600	0.957670	0.478835	−	0.877905i	$-0.341059\pi$
$59$	7.35600	0.957670	0.478835	+	0.877905i	$0.341059\pi$
$60$	6.48547	0.837270
$61$	9.04719	1.15837	0.579187	−	0.815195i	$-0.303370\pi$
$61$	9.04719	1.15837	0.579187	+	0.815195i	$0.303370\pi$
$62$	−4.78922	−0.608232
$63$	0.107856	0.0135886
$64$	−11.9345	−1.49181
$65$	−1.33783	−0.165937
$66$	−16.0363	−1.97393
$67$	8.32218	1.01672	0.508358	−	0.861146i	$-0.330253\pi$
$67$	8.32218	1.01672	0.508358	+	0.861146i	$0.330253\pi$
$68$	19.5845	2.37497
$69$	−1.74064	−0.209548
$70$	−11.0697	−1.32309
$71$	4.71689	0.559792	0.279896	−	0.960030i	$-0.409700\pi$
$71$	4.71689	0.559792	0.279896	+	0.960030i	$0.409700\pi$
$72$	0.0394481	0.00464900
$73$	−10.9752	−1.28455	−0.642274	−	0.766475i	$-0.722009\pi$
$73$	−10.9752	−1.28455	−0.642274	+	0.766475i	$0.722009\pi$
$74$	−0.410907	−0.0477670
$75$	5.17165	0.597170
$76$	13.0242	1.49398
$77$	15.5117	1.76772
$78$	−3.51240	−0.397701
$79$	−7.80891	−0.878571	−0.439286	−	0.898347i	$-0.644768\pi$
$79$	−7.80891	−0.878571	−0.439286	+	0.898347i	$0.644768\pi$
$80$	3.40311	0.380479
$81$	−9.08856	−1.00984
$82$	−11.5326	−1.27356
$83$	−16.6667	−1.82941	−0.914707	−	0.404118i	$-0.867578\pi$
$83$	−16.6667	−1.82941	−0.914707	+	0.404118i	$0.867578\pi$
$84$	−16.4702	−1.79705
$85$	−10.6644	−1.15671
$86$	−13.4546	−1.45084
$87$	1.74064	0.186616
$88$	5.67335	0.604781
$89$	2.37020	0.251241	0.125621	−	0.992078i	$-0.459908\pi$
$89$	2.37020	0.251241	0.125621	+	0.992078i	$0.459908\pi$
$90$	−0.0912454	−0.00961811
$91$	3.39749	0.356153
$92$	2.61580	0.272717
$93$	3.88016	0.402354
$94$	1.01200	0.104380
$95$	−7.09207	−0.727631
$96$	13.5405	1.38197
$97$	−11.3963	−1.15712	−0.578560	−	0.815640i	$-0.696385\pi$
$97$	−11.3963	−1.15712	−0.578560	+	0.815640i	$0.696385\pi$
$98$	13.0731	1.32059
$99$	0.127859	0.0128503
$100$	−7.77188	−0.777188
$101$	15.9434	1.58643	0.793216	−	0.608940i	$-0.208405\pi$
$101$	15.9434	1.58643	0.793216	+	0.608940i	$0.208405\pi$
$102$	−27.9988	−2.77229
$103$	−8.88555	−0.875519	−0.437760	−	0.899092i	$-0.644228\pi$
$103$	−8.88555	−0.875519	−0.437760	+	0.899092i	$0.644228\pi$
$104$	1.24262	0.121849
$105$	8.96854	0.875240
$106$	−13.0955	−1.27195
$107$	−3.21047	−0.310368	−0.155184	−	0.987886i	$-0.549597\pi$
$107$	−3.21047	−0.310368	−0.155184	+	0.987886i	$0.549597\pi$
$108$	13.5237	1.30132
$109$	−0.712956	−0.0682888	−0.0341444	−	0.999417i	$-0.510871\pi$
$109$	−0.712956	−0.0682888	−0.0341444	+	0.999417i	$0.510871\pi$
$110$	−13.1227	−1.25120
$111$	0.332911	0.0315985
$112$	−8.64239	−0.816629
$113$	6.57373	0.618405	0.309202	−	0.950996i	$-0.399938\pi$
$113$	6.57373	0.618405	0.309202	+	0.950996i	$0.399938\pi$
$114$	−18.6199	−1.74391
$115$	−1.42439	−0.132825
$116$	−2.61580	−0.242871
$117$	0.0280047	0.00258904
$118$	15.8039	1.45487
$119$	27.0828	2.48268
$120$	3.28022	0.299442
$121$	7.38848	0.671680
$122$	19.4374	1.75978
$123$	9.34353	0.842478
$124$	−5.83105	−0.523644
$125$	11.3540	1.01553
$126$	0.231723	0.0206435
$127$	−20.9025	−1.85480	−0.927401	−	0.374070i	$-0.877962\pi$
$127$	−20.9025	−1.85480	−0.927401	+	0.374070i	$0.877962\pi$
$128$	−10.0825	−0.891172
$129$	10.9007	0.959753
$130$	−2.87424	−0.252088
$131$	−5.49993	−0.480531	−0.240266	−	0.970707i	$-0.577235\pi$
$131$	−5.49993	−0.480531	−0.240266	+	0.970707i	$0.577235\pi$
$132$	−19.5248	−1.69942
$133$	18.0107	1.56173
$134$	17.8797	1.54457
$135$	−7.36409	−0.633800
$136$	9.90545	0.849386
$137$	2.30717	0.197115	0.0985573	−	0.995131i	$-0.468577\pi$
$137$	2.30717	0.197115	0.0985573	+	0.995131i	$0.468577\pi$
$138$	−3.73966	−0.318341
$139$	−9.74965	−0.826954	−0.413477	−	0.910514i	$-0.635686\pi$
$139$	−9.74965	−0.826954	−0.413477	+	0.910514i	$0.635686\pi$
$140$	−13.4778	−1.13908
$141$	−0.819907	−0.0690486
$142$	10.1340	0.850424
$143$	4.02759	0.336804
$144$	−0.0712373	−0.00593644
$145$	1.42439	0.118289
$146$	−23.5795	−1.95146
$147$	−10.5917	−0.873586
$148$	−0.500294	−0.0411239
$149$	−20.0433	−1.64201	−0.821004	−	0.570923i	$-0.806585\pi$
$149$	−20.0433	−1.64201	−0.821004	+	0.570923i	$0.806585\pi$
$150$	11.1110	0.907208
$151$	−22.1151	−1.79970	−0.899849	−	0.436202i	$-0.856323\pi$
$151$	−22.1151	−1.79970	−0.899849	+	0.436202i	$0.856323\pi$
$152$	6.58737	0.534306
$153$	0.223237	0.0180477
$154$	33.3259	2.68548
$155$	3.17519	0.255037
$156$	−4.27647	−0.342392
$157$	17.2042	1.37304	0.686522	−	0.727109i	$-0.259137\pi$
$157$	17.2042	1.37304	0.686522	+	0.727109i	$0.259137\pi$
$158$	−16.7770	−1.33471
$159$	10.6098	0.841412
$160$	11.0804	0.875980
$161$	3.61731	0.285084
$162$	−19.5262	−1.53413
$163$	18.2181	1.42695	0.713475	−	0.700680i	$-0.247120\pi$
$163$	18.2181	1.42695	0.713475	+	0.700680i	$0.247120\pi$
$164$	−14.0413	−1.09644
$165$	10.6319	0.827688
$166$	−35.8076	−2.77920
$167$	19.0888	1.47714	0.738569	−	0.674177i	$-0.235502\pi$
$167$	19.0888	1.47714	0.738569	+	0.674177i	$0.235502\pi$
$168$	−8.33030	−0.642697
$169$	−12.1178	−0.932142
$170$	−22.9118	−1.75725
$171$	0.148458	0.0113529
$172$	−16.3814	−1.24907
$173$	4.81592	0.366147	0.183074	−	0.983099i	$-0.441395\pi$
$173$	4.81592	0.366147	0.183074	+	0.983099i	$0.441395\pi$
$174$	3.73966	0.283503
$175$	−10.7475	−0.812433
$176$	−10.2452	−0.772262
$177$	−12.8041	−0.962417
$178$	5.09225	0.381680
$179$	−7.48859	−0.559723	−0.279862	−	0.960040i	$-0.590289\pi$
$179$	−7.48859	−0.559723	−0.279862	+	0.960040i	$0.590289\pi$
$180$	−0.111094	−0.00828049
$181$	9.18783	0.682926	0.341463	−	0.939895i	$-0.389078\pi$
$181$	9.18783	0.682926	0.341463	+	0.939895i	$0.389078\pi$
$182$	7.29930	0.541060
$183$	−15.7479	−1.16412
$184$	1.32302	0.0975344
$185$	0.272425	0.0200291
$186$	8.33630	0.611247
$187$	32.1056	2.34779
$188$	1.23214	0.0898634
$189$	18.7015	1.36034
$190$	−15.2369	−1.10540
$191$	11.7239	0.848311	0.424155	−	0.905589i	$-0.360571\pi$
$191$	11.7239	0.848311	0.424155	+	0.905589i	$0.360571\pi$
$192$	20.7736	1.49921
$193$	−5.79568	−0.417182	−0.208591	−	0.978003i	$-0.566888\pi$
$193$	−5.79568	−0.417182	−0.208591	+	0.978003i	$0.566888\pi$
$194$	−24.4843	−1.75787
$195$	2.32867	0.166759
$196$	15.9170	1.13693
$197$	19.8932	1.41733	0.708665	−	0.705545i	$-0.249298\pi$
$197$	19.8932	1.41733	0.708665	+	0.705545i	$0.249298\pi$
$198$	0.274698	0.0195220
$199$	6.73338	0.477317	0.238658	−	0.971104i	$-0.423292\pi$
$199$	6.73338	0.477317	0.238658	+	0.971104i	$0.423292\pi$
$200$	−3.93086	−0.277954
$201$	−14.4859	−1.02176
$202$	34.2536	2.41007
$203$	−3.61731	−0.253885
$204$	−34.0895	−2.38674
$205$	7.64594	0.534015
$206$	−19.0901	−1.33007
$207$	0.0298167	0.00207240
$208$	−2.24398	−0.155592
$209$	21.3510	1.47688
$210$	19.2684	1.32965
$211$	−12.5526	−0.864159	−0.432080	−	0.901835i	$-0.642220\pi$
$211$	−12.5526	−0.864159	−0.432080	+	0.901835i	$0.642220\pi$
$212$	−15.9443	−1.09506
$213$	−8.21039	−0.562567
$214$	−6.89751	−0.471504
$215$	8.92019	0.608352
$216$	6.84003	0.465405
$217$	−8.06357	−0.547391
$218$	−1.53174	−0.103743
$219$	19.1038	1.29092
$220$	−15.9774	−1.07720
$221$	7.03201	0.473024
$222$	0.715240	0.0480037
$223$	25.5659	1.71202	0.856010	−	0.516959i	$-0.172936\pi$
$223$	25.5659	1.71202	0.856010	+	0.516959i	$0.172936\pi$
$224$	−28.1392	−1.88013
$225$	−0.0885891	−0.00590594
$226$	14.1233	0.939467
$227$	−20.8928	−1.38670	−0.693351	−	0.720600i	$-0.743867\pi$
$227$	−20.8928	−1.38670	−0.693351	+	0.720600i	$0.743867\pi$
$228$	−22.6704	−1.50138
$229$	18.1024	1.19624	0.598120	−	0.801406i	$-0.295915\pi$
$229$	18.1024	1.19624	0.598120	+	0.801406i	$0.295915\pi$
$230$	−3.06021	−0.201784
$231$	−27.0002	−1.77648
$232$	−1.32302	−0.0868606
$233$	6.86606	0.449810	0.224905	−	0.974381i	$-0.427793\pi$
$233$	6.86606	0.449810	0.224905	+	0.974381i	$0.427793\pi$
$234$	0.0601665	0.00393321
$235$	−0.670941	−0.0437673
$236$	19.2419	1.25254
$237$	13.5925	0.882927
$238$	58.1858	3.77163
$239$	8.00068	0.517521	0.258760	−	0.965942i	$-0.416686\pi$
$239$	8.00068	0.517521	0.258760	+	0.965942i	$0.416686\pi$
$240$	−5.92358	−0.382365
$241$	−10.7624	−0.693267	−0.346634	−	0.938001i	$-0.612675\pi$
$241$	−10.7624	−0.693267	−0.346634	+	0.938001i	$0.612675\pi$
$242$	15.8737	1.02040
$243$	0.309853	0.0198771
$244$	23.6657	1.51504
$245$	−8.66730	−0.553734
$246$	20.0740	1.27987
$247$	4.67646	0.297556
$248$	−2.94923	−0.187276
$249$	29.0108	1.83848
$250$	24.3933	1.54277
$251$	18.6479	1.17705	0.588523	−	0.808481i	$-0.299710\pi$
$251$	18.6479	1.17705	0.588523	+	0.808481i	$0.299710\pi$
$252$	0.282131	0.0177726
$253$	4.28818	0.269596
$254$	−44.9079	−2.81777
$255$	18.5628	1.16245
$256$	2.20739	0.137962
$257$	6.50023	0.405473	0.202737	−	0.979233i	$-0.435017\pi$
$257$	6.50023	0.405473	0.202737	+	0.979233i	$0.435017\pi$
$258$	23.4195	1.45804
$259$	−0.691840	−0.0429888
$260$	−3.49949	−0.217029
$261$	−0.0298167	−0.00184561
$262$	−11.8163	−0.730012
$263$	−5.94459	−0.366559	−0.183280	−	0.983061i	$-0.558671\pi$
$263$	−5.94459	−0.366559	−0.183280	+	0.983061i	$0.558671\pi$
$264$	−9.87524	−0.607779
$265$	8.68214	0.533340
$266$	38.6950	2.37254
$267$	−4.12567	−0.252487
$268$	21.7692	1.32977
$269$	−17.3345	−1.05691	−0.528453	−	0.848963i	$-0.677228\pi$
$269$	−17.3345	−1.05691	−0.528453	+	0.848963i	$0.677228\pi$
$270$	−15.8213	−0.962855
$271$	−24.0282	−1.45961	−0.729805	−	0.683656i	$-0.760389\pi$
$271$	−24.0282	−1.45961	−0.729805	+	0.683656i	$0.760389\pi$
$272$	−17.8877	−1.08460
$273$	−5.91379	−0.357919
$274$	4.95682	0.299452
$275$	−12.7407	−0.768294
$276$	−4.55317	−0.274068
$277$	−8.60153	−0.516816	−0.258408	−	0.966036i	$-0.583198\pi$
$277$	−8.60153	−0.516816	−0.258408	+	0.966036i	$0.583198\pi$
$278$	−20.9466	−1.25629
$279$	−0.0664662	−0.00397923
$280$	−6.81680	−0.407382
$281$	−7.79943	−0.465275	−0.232638	−	0.972564i	$-0.574736\pi$
$281$	−7.79943	−0.465275	−0.232638	+	0.972564i	$0.574736\pi$
$282$	−1.76152	−0.104897
$283$	16.4894	0.980191	0.490096	−	0.871669i	$-0.336962\pi$
$283$	16.4894	0.980191	0.490096	+	0.871669i	$0.336962\pi$
$284$	12.3385	0.732153
$285$	12.3447	0.731238
$286$	8.65304	0.511665
$287$	−19.4173	−1.14617
$288$	−0.231945	−0.0136675
$289$	39.0551	2.29736
$290$	3.06021	0.179702
$291$	19.8369	1.16286
$292$	−28.7089	−1.68006
$293$	24.2731	1.41805	0.709023	−	0.705185i	$-0.249136\pi$
$293$	24.2731	1.41805	0.709023	+	0.705185i	$0.249136\pi$
$294$	−22.7556	−1.32713
$295$	−10.4778	−0.610041
$296$	−0.253038	−0.0147076
$297$	22.1699	1.28643
$298$	−43.0618	−2.49450
$299$	0.939230	0.0543171
$300$	13.5280	0.781041
$301$	−22.6533	−1.30572
$302$	−47.5129	−2.73406
$303$	−27.7517	−1.59430
$304$	−11.8958	−0.682270
$305$	−12.8867	−0.737890
$306$	0.479613	0.0274176
$307$	−30.4031	−1.73520	−0.867598	−	0.497266i	$-0.834337\pi$
$307$	−30.4031	−1.73520	−0.867598	+	0.497266i	$0.834337\pi$
$308$	40.5755	2.31200
$309$	15.4665	0.879859
$310$	6.82170	0.387447
$311$	−18.8544	−1.06914	−0.534568	−	0.845126i	$-0.679526\pi$
$311$	−18.8544	−1.06914	−0.534568	+	0.845126i	$0.679526\pi$
$312$	−2.16295	−0.122453
$313$	−23.4073	−1.32306	−0.661531	−	0.749918i	$-0.730093\pi$
$313$	−23.4073	−1.32306	−0.661531	+	0.749918i	$0.730093\pi$
$314$	36.9622	2.08590
$315$	−0.153629	−0.00865601
$316$	−20.4266	−1.14909
$317$	−2.08214	−0.116944	−0.0584722	−	0.998289i	$-0.518623\pi$
$317$	−2.08214	−0.116944	−0.0584722	+	0.998289i	$0.518623\pi$
$318$	22.7945	1.27825
$319$	−4.28818	−0.240092
$320$	16.9993	0.950291
$321$	5.58826	0.311907
$322$	7.77158	0.433093
$323$	37.2780	2.07421
$324$	−23.7739	−1.32077
$325$	−2.79057	−0.154793
$326$	39.1405	2.16779
$327$	1.24100	0.0686273
$328$	−7.10182	−0.392132
$329$	1.70389	0.0939386
$330$	22.8419	1.25741
$331$	−14.9198	−0.820067	−0.410034	−	0.912070i	$-0.634483\pi$
$331$	−14.9198	−0.820067	−0.410034	+	0.912070i	$0.634483\pi$
$332$	−43.5970	−2.39269
$333$	−0.00570268	−0.000312505 0
$334$	41.0113	2.24404
$335$	−11.8540	−0.647653
$336$	15.0433	0.820677
$337$	13.2112	0.719660	0.359830	−	0.933018i	$-0.382835\pi$
$337$	13.2112	0.719660	0.359830	+	0.933018i	$0.382835\pi$
$338$	−26.0345	−1.41609
$339$	−11.4425	−0.621470
$340$	−27.8959	−1.51287
$341$	−9.55904	−0.517651
$342$	0.318954	0.0172471
$343$	−3.31007	−0.178727
$344$	−8.28539	−0.446718
$345$	2.47934	0.133483
$346$	10.3467	0.556243
$347$	−25.0711	−1.34589	−0.672943	−	0.739695i	$-0.734970\pi$
$347$	−25.0711	−1.34589	−0.672943	+	0.739695i	$0.734970\pi$
$348$	4.55317	0.244075
$349$	−15.3540	−0.821880	−0.410940	−	0.911662i	$-0.634799\pi$
$349$	−15.3540	−0.821880	−0.410940	+	0.911662i	$0.634799\pi$
$350$	−23.0903	−1.23423
$351$	4.85583	0.259185
$352$	−33.3579	−1.77798
$353$	7.44772	0.396402	0.198201	−	0.980161i	$-0.436490\pi$
$353$	7.44772	0.396402	0.198201	+	0.980161i	$0.436490\pi$
$354$	−27.5089	−1.46208
$355$	−6.71868	−0.356590
$356$	6.19999	0.328599
$357$	−47.1413	−2.49498
$358$	−16.0888	−0.850320
$359$	−29.2314	−1.54277	−0.771386	−	0.636367i	$-0.780436\pi$
$359$	−29.2314	−1.54277	−0.771386	+	0.636367i	$0.780436\pi$
$360$	−0.0561893	−0.00296144
$361$	5.79082	0.304780
$362$	19.7395	1.03749
$363$	−12.8607	−0.675010
$364$	8.88716	0.465814
$365$	15.6329	0.818263
$366$	−33.8334	−1.76850
$367$	−34.3083	−1.79088	−0.895438	−	0.445186i	$-0.853138\pi$
$367$	−34.3083	−1.79088	−0.895438	+	0.445186i	$0.853138\pi$
$368$	−2.38917	−0.124544
$369$	−0.160052	−0.00833200
$370$	0.585290	0.0304278
$371$	−22.0488	−1.14472
$372$	10.1497	0.526239
$373$	21.0318	1.08899	0.544494	−	0.838765i	$-0.316722\pi$
$373$	21.0318	1.08899	0.544494	+	0.838765i	$0.316722\pi$
$374$	68.9770	3.56671
$375$	−19.7631	−1.02056
$376$	0.623194	0.0321388
$377$	−0.939230	−0.0483728
$378$	40.1792	2.06659
$379$	−27.7769	−1.42681	−0.713403	−	0.700754i	$-0.752847\pi$
$379$	−27.7769	−1.42681	−0.713403	+	0.700754i	$0.752847\pi$
$380$	−18.5515	−0.951671
$381$	36.3837	1.86400
$382$	25.1881	1.28874
$383$	−11.7934	−0.602617	−0.301308	−	0.953527i	$-0.597423\pi$
$383$	−11.7934	−0.602617	−0.301308	+	0.953527i	$0.597423\pi$
$384$	17.5499	0.895590
$385$	−22.0946	−1.12605
$386$	−12.4517	−0.633774
$387$	−0.186726	−0.00949184
$388$	−29.8105	−1.51340
$389$	−14.3127	−0.725683	−0.362842	−	0.931851i	$-0.618193\pi$
$389$	−14.3127	−0.725683	−0.362842	+	0.931851i	$0.618193\pi$
$390$	5.00301	0.253337
$391$	7.48700	0.378634
$392$	8.05050	0.406612
$393$	9.57338	0.482913
$394$	42.7393	2.15318
$395$	11.1229	0.559654
$396$	0.334455	0.0168070
$397$	−5.90410	−0.296318	−0.148159	−	0.988964i	$-0.547335\pi$
$397$	−5.90410	−0.296318	−0.148159	+	0.988964i	$0.547335\pi$
$398$	14.4663	0.725129
$399$	−31.3501	−1.56947
$400$	7.09853	0.354927
$401$	20.6738	1.03240	0.516200	−	0.856468i	$-0.327346\pi$
$401$	20.6738	1.03240	0.516200	+	0.856468i	$0.327346\pi$
$402$	−31.1221	−1.55223
$403$	−2.09369	−0.104294
$404$	41.7049	2.07490
$405$	12.9456	0.643273
$406$	−7.77158	−0.385697
$407$	−0.820149	−0.0406533
$408$	−17.2418	−0.853596
$409$	2.66079	0.131568	0.0657839	−	0.997834i	$-0.479045\pi$
$409$	2.66079	0.131568	0.0657839	+	0.997834i	$0.479045\pi$
$410$	16.4269	0.811265
$411$	−4.01594	−0.198092
$412$	−23.2429	−1.14509
$413$	26.6090	1.30934
$414$	0.0640594	0.00314835
$415$	23.7399	1.16535
$416$	−7.30631	−0.358221
$417$	16.9706	0.831054
$418$	45.8714	2.24364
$419$	18.2654	0.892325	0.446163	−	0.894952i	$-0.352790\pi$
$419$	18.2654	0.892325	0.446163	+	0.894952i	$0.352790\pi$
$420$	23.4600	1.14473
$421$	−8.51137	−0.414819	−0.207409	−	0.978254i	$-0.566503\pi$
$421$	−8.51137	−0.414819	−0.207409	+	0.978254i	$0.566503\pi$
$422$	−26.9686	−1.31281
$423$	0.0140448	0.000682882 0
$424$	−8.06428	−0.391636
$425$	−22.2448	−1.07903
$426$	−17.6396	−0.854639
$427$	32.7265	1.58375
$428$	−8.39797	−0.405931
$429$	−7.01056	−0.338473
$430$	19.1645	0.924195
$431$	29.9998	1.44504	0.722520	−	0.691349i	$-0.242983\pi$
$431$	29.9998	1.44504	0.722520	+	0.691349i	$0.242983\pi$
$432$	−12.3521	−0.594289
$433$	5.23836	0.251739	0.125870	−	0.992047i	$-0.459828\pi$
$433$	5.23836	0.251739	0.125870	+	0.992047i	$0.459828\pi$
$434$	−17.3241	−0.831584
$435$	−2.47934	−0.118875
$436$	−1.86495	−0.0893151
$437$	4.97904	0.238180
$438$	41.0434	1.96113
$439$	4.15170	0.198150	0.0990750	−	0.995080i	$-0.468412\pi$
$439$	4.15170	0.198150	0.0990750	+	0.995080i	$0.468412\pi$
$440$	−8.08104	−0.385249
$441$	0.181433	0.00863965
$442$	15.1079	0.718608
$443$	−0.571163	−0.0271368	−0.0135684	−	0.999908i	$-0.504319\pi$
$443$	−0.571163	−0.0271368	−0.0135684	+	0.999908i	$0.504319\pi$
$444$	0.870830	0.0413278
$445$	−3.37609	−0.160042
$446$	54.9269	2.60086
$447$	34.8880	1.65015
$448$	−43.1707	−2.03963
$449$	1.55742	0.0734992	0.0367496	−	0.999325i	$-0.488300\pi$
$449$	1.55742	0.0734992	0.0367496	+	0.999325i	$0.488300\pi$
$450$	−0.190329	−0.00897217
$451$	−23.0184	−1.08390
$452$	17.1956	0.808813
$453$	38.4943	1.80862
$454$	−44.8869	−2.10665
$455$	−4.83933	−0.226871
$456$	−11.4662	−0.536955
$457$	17.4868	0.817999	0.408999	−	0.912535i	$-0.365878\pi$
$457$	17.4868	0.817999	0.408999	+	0.912535i	$0.365878\pi$
$458$	38.8920	1.81730
$459$	38.7078	1.80673
$460$	−3.72592	−0.173722
$461$	−12.3367	−0.574578	−0.287289	−	0.957844i	$-0.592754\pi$
$461$	−12.3367	−0.574578	−0.287289	+	0.957844i	$0.592754\pi$
$462$	−58.0084	−2.69879
$463$	36.6206	1.70191	0.850953	−	0.525242i	$-0.176025\pi$
$463$	36.6206	1.70191	0.850953	+	0.525242i	$0.176025\pi$
$464$	2.38917	0.110915
$465$	−5.52685	−0.256301
$466$	14.7513	0.683342
$467$	32.9192	1.52332	0.761659	−	0.647978i	$-0.224385\pi$
$467$	32.9192	1.52332	0.761659	+	0.647978i	$0.224385\pi$
$468$	0.0732549	0.00338621
$469$	30.1039	1.39007
$470$	−1.44148	−0.0664904
$471$	−29.9462	−1.37985
$472$	9.73215	0.447958
$473$	−26.8546	−1.23478
$474$	29.2027	1.34132
$475$	−14.7933	−0.678765
$476$	70.8433	3.24710
$477$	−0.181743	−0.00832145
$478$	17.1890	0.786206
$479$	−32.8624	−1.50152	−0.750761	−	0.660573i	$-0.770313\pi$
$479$	−32.8624	−1.50152	−0.750761	+	0.660573i	$0.770313\pi$
$480$	−19.2869	−0.880322
$481$	−0.179635	−0.00819066
$482$	−23.1224	−1.05320
$483$	−6.29642	−0.286497
$484$	19.3268	0.878492
$485$	16.2328	0.737092
$486$	0.665701	0.0301968
$487$	−14.1334	−0.640445	−0.320223	−	0.947342i	$-0.603758\pi$
$487$	−14.1334	−0.640445	−0.320223	+	0.947342i	$0.603758\pi$
$488$	11.9696	0.541839
$489$	−31.7111	−1.43402
$490$	−18.6212	−0.841220
$491$	34.7675	1.56904	0.784519	−	0.620105i	$-0.212910\pi$
$491$	34.7675	1.56904	0.784519	+	0.620105i	$0.212910\pi$
$492$	24.4409	1.10188
$493$	−7.48700	−0.337197
$494$	10.0471	0.452041
$495$	−0.182121	−0.00818573
$496$	5.32585	0.239138
$497$	17.0625	0.765356
$498$	62.3279	2.79298
$499$	−5.83942	−0.261408	−0.130704	−	0.991421i	$-0.541724\pi$
$499$	−5.83942	−0.261408	−0.130704	+	0.991421i	$0.541724\pi$
$500$	29.6997	1.32821
$501$	−33.2267	−1.48446
$502$	40.0639	1.78814
$503$	−7.00546	−0.312358	−0.156179	−	0.987729i	$-0.549918\pi$
$503$	−7.00546	−0.312358	−0.156179	+	0.987729i	$0.549918\pi$
$504$	0.142696	0.00635619
$505$	−22.7096	−1.01056
$506$	9.21291	0.409564
$507$	21.0928	0.936763
$508$	−54.6770	−2.42590
$509$	19.2678	0.854032	0.427016	−	0.904244i	$-0.359565\pi$
$509$	19.2678	0.854032	0.427016	+	0.904244i	$0.359565\pi$
$510$	39.8811	1.76597
$511$	−39.7006	−1.75625
$512$	24.9074	1.10076
$513$	25.7417	1.13652
$514$	13.9654	0.615986
$515$	12.6565	0.557710
$516$	28.5141	1.25526
$517$	2.01990	0.0888350
$518$	−1.48638	−0.0653077
$519$	−8.38276	−0.367962
$520$	−1.76997	−0.0776184
$521$	−24.3594	−1.06720	−0.533602	−	0.845736i	$-0.679162\pi$
$521$	−24.3594	−1.06720	−0.533602	+	0.845736i	$0.679162\pi$
$522$	−0.0640594	−0.00280381
$523$	16.2475	0.710454	0.355227	−	0.934780i	$-0.384404\pi$
$523$	16.2475	0.710454	0.355227	+	0.934780i	$0.384404\pi$
$524$	−14.3867	−0.628488
$525$	18.7075	0.816460
$526$	−12.7716	−0.556869
$527$	−16.6897	−0.727015
$528$	17.8332	0.776090
$529$	1.00000	0.0434783
$530$	18.6531	0.810238
$531$	0.219332	0.00951818
$532$	47.1125	2.04259
$533$	−5.04167	−0.218379
$534$	−8.86376	−0.383572
$535$	4.57295	0.197706
$536$	11.0104	0.475578
$537$	13.0349	0.562498
$538$	−37.2423	−1.60563
$539$	26.0933	1.12392
$540$	−19.2630	−0.828949
$541$	−9.28757	−0.399304	−0.199652	−	0.979867i	$-0.563981\pi$
$541$	−9.28757	−0.399304	−0.199652	+	0.979867i	$0.563981\pi$
$542$	−51.6232	−2.21741
$543$	−15.9927	−0.686311
$544$	−58.2417	−2.49709
$545$	1.01552	0.0435003
$546$	−12.7054	−0.543743
$547$	−13.4050	−0.573157	−0.286579	−	0.958057i	$-0.592518\pi$
$547$	−13.4050	−0.573157	−0.286579	+	0.958057i	$0.592518\pi$
$548$	6.03510	0.257807
$549$	0.269757	0.0115130
$550$	−27.3727	−1.16718
$551$	−4.97904	−0.212114
$552$	−2.30290	−0.0980179
$553$	−28.2473	−1.20120
$554$	−18.4799	−0.785135
$555$	−0.474194	−0.0201284
$556$	−25.5032	−1.08158
$557$	26.1238	1.10690	0.553450	−	0.832883i	$-0.313311\pi$
$557$	26.1238	1.10690	0.553450	+	0.832883i	$0.313311\pi$
$558$	−0.142799	−0.00604515
$559$	−5.88191	−0.248778
$560$	12.3101	0.520197
$561$	−55.8841	−2.35943
$562$	−16.7566	−0.706836
$563$	29.3871	1.23852	0.619260	−	0.785186i	$-0.287433\pi$
$563$	29.3871	1.23852	0.619260	+	0.785186i	$0.287433\pi$
$564$	−2.14472	−0.0903088
$565$	−9.36353	−0.393927
$566$	35.4265	1.48909
$567$	−32.8762	−1.38067
$568$	6.24055	0.261848
$569$	16.9654	0.711228	0.355614	−	0.934633i	$-0.384272\pi$
$569$	16.9654	0.711228	0.355614	+	0.934633i	$0.384272\pi$
$570$	26.5219	1.11088
$571$	−16.3163	−0.682818	−0.341409	−	0.939915i	$-0.610904\pi$
$571$	−16.3163	−0.682818	−0.341409	+	0.939915i	$0.610904\pi$
$572$	10.5354	0.440506
$573$	−20.4070	−0.852516
$574$	−41.7169	−1.74123
$575$	−2.97112	−0.123904
$576$	−0.355847	−0.0148270
$577$	−11.6604	−0.485427	−0.242714	−	0.970098i	$-0.578038\pi$
$577$	−11.6604	−0.485427	−0.242714	+	0.970098i	$0.578038\pi$
$578$	83.9076	3.49010
$579$	10.0882	0.419250
$580$	3.72592	0.154710
$581$	−60.2888	−2.50120
$582$	42.6183	1.76659
$583$	−26.1380	−1.08252
$584$	−14.5204	−0.600858
$585$	−0.0398895	−0.00164923
$586$	52.1493	2.15427
$587$	−4.57966	−0.189023	−0.0945114	−	0.995524i	$-0.530129\pi$
$587$	−4.57966	−0.189023	−0.0945114	+	0.995524i	$0.530129\pi$
$588$	−27.7057	−1.14257
$589$	−11.0991	−0.457329
$590$	−22.5109	−0.926760
$591$	−34.6268	−1.42436
$592$	0.456949	0.0187805
$593$	−27.8865	−1.14516	−0.572581	−	0.819848i	$-0.694058\pi$
$593$	−27.8865	−1.14516	−0.572581	+	0.819848i	$0.694058\pi$
$594$	47.6308	1.95432
$595$	−38.5764	−1.58148
$596$	−52.4292	−2.14759
$597$	−11.7204	−0.479683
$598$	2.01788	0.0825173
$599$	−10.3105	−0.421277	−0.210639	−	0.977564i	$-0.567554\pi$
$599$	−10.3105	−0.421277	−0.210639	+	0.977564i	$0.567554\pi$
$600$	6.84220	0.279332
$601$	4.82829	0.196950	0.0984751	−	0.995140i	$-0.468604\pi$
$601$	4.82829	0.196950	0.0984751	+	0.995140i	$0.468604\pi$
$602$	−48.6694	−1.98362
$603$	0.248140	0.0101050
$604$	−57.8487	−2.35383
$605$	−10.5240	−0.427863
$606$	−59.6230	−2.42202
$607$	18.8619	0.765581	0.382790	−	0.923835i	$-0.374963\pi$
$607$	18.8619	0.765581	0.382790	+	0.923835i	$0.374963\pi$
$608$	−38.7322	−1.57080
$609$	6.29642	0.255144
$610$	−27.6863	−1.12099
$611$	0.442413	0.0178981
$612$	0.583945	0.0236046
$613$	4.42684	0.178798	0.0893991	−	0.995996i	$-0.471505\pi$
$613$	4.42684	0.178798	0.0893991	+	0.995996i	$0.471505\pi$
$614$	−65.3193	−2.63607
$615$	−13.3088	−0.536663
$616$	20.5223	0.826866
$617$	17.2207	0.693280	0.346640	−	0.937998i	$-0.387323\pi$
$617$	17.2207	0.693280	0.346640	+	0.937998i	$0.387323\pi$
$618$	33.2289	1.33666
$619$	−39.0725	−1.57046	−0.785228	−	0.619207i	$-0.787454\pi$
$619$	−39.0725	−1.57046	−0.785228	+	0.619207i	$0.787454\pi$
$620$	8.30567	0.333564
$621$	5.17001	0.207465
$622$	−40.5076	−1.62421
$623$	8.57377	0.343501
$624$	3.90596	0.156364
$625$	−1.31681	−0.0526723
$626$	−50.2893	−2.00997
$627$	−37.1643	−1.48420
$628$	45.0028	1.79581
$629$	−1.43195	−0.0570955
$630$	−0.330063	−0.0131500
$631$	31.4897	1.25359	0.626793	−	0.779186i	$-0.284367\pi$
$631$	31.4897	1.25359	0.626793	+	0.779186i	$0.284367\pi$
$632$	−10.3314	−0.410959
$633$	21.8496	0.868443
$634$	−4.47335	−0.177659
$635$	29.7733	1.18152
$636$	27.7532	1.10048
$637$	5.71516	0.226443
$638$	−9.21291	−0.364742
$639$	0.140642	0.00556371
$640$	14.3613	0.567681
$641$	−22.9920	−0.908130	−0.454065	−	0.890969i	$-0.650027\pi$
$641$	−22.9920	−0.908130	−0.454065	+	0.890969i	$0.650027\pi$
$642$	12.0061	0.473842
$643$	10.1036	0.398446	0.199223	−	0.979954i	$-0.436158\pi$
$643$	10.1036	0.398446	0.199223	+	0.979954i	$0.436158\pi$
$644$	9.46218	0.372862
$645$	−15.5268	−0.611368
$646$	80.0897	3.15109
$647$	27.7945	1.09271	0.546357	−	0.837553i	$-0.316014\pi$
$647$	27.7945	1.09271	0.546357	+	0.837553i	$0.316014\pi$
$648$	−12.0244	−0.472361
$649$	31.5439	1.23820
$650$	−5.99537	−0.235158
$651$	14.0357	0.550104
$652$	47.6550	1.86631
$653$	24.8044	0.970670	0.485335	−	0.874328i	$-0.338698\pi$
$653$	24.8044	0.970670	0.485335	+	0.874328i	$0.338698\pi$
$654$	2.66621	0.104257
$655$	7.83402	0.306101
$656$	12.8248	0.500725
$657$	−0.327244	−0.0127670
$658$	3.66071	0.142710
$659$	−14.3327	−0.558322	−0.279161	−	0.960244i	$-0.590056\pi$
$659$	−14.3327	−0.558322	−0.279161	+	0.960244i	$0.590056\pi$
$660$	27.8108	1.08254
$661$	31.8919	1.24045	0.620226	−	0.784423i	$-0.287041\pi$
$661$	31.8919	1.24045	0.620226	+	0.784423i	$0.287041\pi$
$662$	−32.0544	−1.24583
$663$	−12.2402	−0.475369
$664$	−22.0505	−0.855724
$665$	−25.6542	−0.994828
$666$	−0.0122519	−0.000474751 0
$667$	−1.00000	−0.0387202
$668$	49.9327	1.93195
$669$	−44.5010	−1.72051
$670$	−25.4676	−0.983901
$671$	38.7960	1.49770
$672$	48.9802	1.88945
$673$	−16.2702	−0.627172	−0.313586	−	0.949560i	$-0.601530\pi$
$673$	−16.2702	−0.627172	−0.313586	+	0.949560i	$0.601530\pi$
$674$	28.3835	1.09329
$675$	−15.3607	−0.591235
$676$	−31.6979	−1.21915
$677$	−42.9053	−1.64898	−0.824492	−	0.565874i	$-0.808539\pi$
$677$	−42.9053	−1.64898	−0.824492	+	0.565874i	$0.808539\pi$
$678$	−24.5835	−0.944124
$679$	−41.2240	−1.58203
$680$	−14.1092	−0.541063
$681$	36.3667	1.39358
$682$	−20.5370	−0.786404
$683$	25.5812	0.978838	0.489419	−	0.872049i	$-0.337209\pi$
$683$	25.5812	0.978838	0.489419	+	0.872049i	$0.337209\pi$
$684$	0.388338	0.0148485
$685$	−3.28630	−0.125563
$686$	−7.11148	−0.271518
$687$	−31.5097	−1.20217
$688$	14.9622	0.570427
$689$	−5.72494	−0.218103
$690$	5.32672	0.202785
$691$	37.5806	1.42963	0.714816	−	0.699312i	$-0.246510\pi$
$691$	37.5806	1.42963	0.714816	+	0.699312i	$0.246510\pi$
$692$	12.5975	0.478885
$693$	0.462507	0.0175692
$694$	−53.8637	−2.04464
$695$	13.8873	0.526774
$696$	2.30290	0.0872912
$697$	−40.1893	−1.52228
$698$	−32.9872	−1.24858
$699$	−11.9513	−0.452040
$700$	−28.1133	−1.06258
$701$	−5.02646	−0.189847	−0.0949234	−	0.995485i	$-0.530261\pi$
$701$	−5.02646	−0.189847	−0.0949234	+	0.995485i	$0.530261\pi$
$702$	10.4325	0.393748
$703$	−0.952281	−0.0359160
$704$	−51.1772	−1.92881
$705$	1.16786	0.0439843
$706$	16.0010	0.602205
$707$	57.6724	2.16899
$708$	−33.4931	−1.25875
$709$	5.13423	0.192820	0.0964101	−	0.995342i	$-0.469264\pi$
$709$	5.13423	0.192820	0.0964101	+	0.995342i	$0.469264\pi$
$710$	−14.4347	−0.541724
$711$	−0.232836	−0.00873203
$712$	3.13583	0.117520
$713$	−2.22916	−0.0834827
$714$	−101.280	−3.79032
$715$	−5.73684	−0.214546
$716$	−19.5887	−0.732064
$717$	−13.9263	−0.520086
$718$	−62.8019	−2.34375
$719$	3.09716	0.115505	0.0577523	−	0.998331i	$-0.481607\pi$
$719$	3.09716	0.115505	0.0577523	+	0.998331i	$0.481607\pi$
$720$	0.101469	0.00378154
$721$	−32.1418	−1.19702
$722$	12.4412	0.463015
$723$	18.7334	0.696704
$724$	24.0336	0.893201
$725$	2.97112	0.110345
$726$	−27.6304	−1.02546
$727$	51.8440	1.92279	0.961393	−	0.275177i	$-0.0887366\pi$
$727$	51.8440	1.92279	0.961393	+	0.275177i	$0.0887366\pi$
$728$	4.49495	0.166594
$729$	26.7263	0.989865
$730$	33.5864	1.24309
$731$	−46.8872	−1.73418
$732$	−41.1934	−1.52255
$733$	−47.7628	−1.76416	−0.882080	−	0.471099i	$-0.843858\pi$
$733$	−47.7628	−1.76416	−0.882080	+	0.471099i	$0.843858\pi$
$734$	−73.7093	−2.72066
$735$	15.0866	0.556479
$736$	−7.77905	−0.286739
$737$	35.6870	1.31455
$738$	−0.343863	−0.0126578
$739$	10.8623	0.399576	0.199788	−	0.979839i	$-0.435975\pi$
$739$	10.8623	0.399576	0.199788	+	0.979839i	$0.435975\pi$
$740$	0.712612	0.0261961
$741$	−8.14002	−0.299031
$742$	−47.3706	−1.73903
$743$	−26.6848	−0.978970	−0.489485	−	0.872012i	$-0.662815\pi$
$743$	−26.6848	−0.978970	−0.489485	+	0.872012i	$0.662815\pi$
$744$	5.13353	0.188204
$745$	28.5493	1.04597
$746$	45.1857	1.65437
$747$	−0.496947	−0.0181824
$748$	83.9819	3.07068
$749$	−11.6133	−0.424340
$750$	−42.4599	−1.55042
$751$	−23.0568	−0.841354	−0.420677	−	0.907210i	$-0.638207\pi$
$751$	−23.0568	−0.841354	−0.420677	+	0.907210i	$0.638207\pi$
$752$	−1.12539	−0.0410389
$753$	−32.4592	−1.18288
$754$	−2.01788	−0.0734869
$755$	31.5004	1.14642
$756$	48.9196	1.77919
$757$	−7.36545	−0.267702	−0.133851	−	0.991001i	$-0.542734\pi$
$757$	−7.36545	−0.267702	−0.133851	+	0.991001i	$0.542734\pi$
$758$	−59.6771	−2.16757
$759$	−7.46416	−0.270932
$760$	−9.38296	−0.340356
$761$	29.2835	1.06153	0.530764	−	0.847520i	$-0.321905\pi$
$761$	29.2835	1.06153	0.530764	+	0.847520i	$0.321905\pi$
$762$	78.1684	2.83174
$763$	−2.57898	−0.0933655
$764$	30.6674	1.10951
$765$	−0.317976	−0.0114965
$766$	−25.3375	−0.915482
$767$	6.90898	0.249469
$768$	−3.84226	−0.138646
$769$	−33.3173	−1.20145	−0.600727	−	0.799454i	$-0.705122\pi$
$769$	−33.3173	−1.20145	−0.600727	+	0.799454i	$0.705122\pi$
$770$	−47.4690	−1.71066
$771$	−11.3145	−0.407483
$772$	−15.1604	−0.545634
$773$	8.75575	0.314922	0.157461	−	0.987525i	$-0.449669\pi$
$773$	8.75575	0.314922	0.157461	+	0.987525i	$0.449669\pi$
$774$	−0.401171	−0.0144198
$775$	6.62311	0.237909
$776$	−15.0776	−0.541253
$777$	1.20424	0.0432019
$778$	−30.7500	−1.10244
$779$	−26.7269	−0.957590
$780$	6.09135	0.218105
$781$	20.2269	0.723774
$782$	16.0854	0.575212
$783$	−5.17001	−0.184761
$784$	−14.5380	−0.519214
$785$	−24.5054	−0.874635
$786$	20.5679	0.733631
$787$	8.42865	0.300449	0.150224	−	0.988652i	$-0.452000\pi$
$787$	8.42865	0.300449	0.150224	+	0.988652i	$0.452000\pi$
$788$	52.0366	1.85373
$789$	10.3474	0.368376
$790$	23.8969	0.850215
$791$	23.7792	0.845492
$792$	0.169161	0.00601086
$793$	8.49739	0.301751
$794$	−12.6846	−0.450160
$795$	−15.1125	−0.535983
$796$	17.6132	0.624284
$797$	49.8884	1.76714	0.883568	−	0.468303i	$-0.155134\pi$
$797$	49.8884	1.76714	0.883568	+	0.468303i	$0.155134\pi$
$798$	−67.3540	−2.38430
$799$	3.52666	0.124764
$800$	23.1125	0.817151
$801$	0.0706717	0.00249706
$802$	44.4164	1.56840
$803$	−47.0635	−1.66084
$804$	−37.8923	−1.33636
$805$	−5.15245	−0.181600
$806$	−4.49818	−0.158442
$807$	30.1731	1.06214
$808$	21.0935	0.742067
$809$	−14.5866	−0.512839	−0.256420	−	0.966566i	$-0.582543\pi$
$809$	−14.5866	−0.512839	−0.256420	+	0.966566i	$0.582543\pi$
$810$	27.8129	0.977247
$811$	−24.9937	−0.877646	−0.438823	−	0.898574i	$-0.644604\pi$
$811$	−24.9937	−0.877646	−0.438823	+	0.898574i	$0.644604\pi$
$812$	−9.46218	−0.332057
$813$	41.8244	1.46685
$814$	−1.76204	−0.0617596
$815$	−25.9496	−0.908975
$816$	31.1361	1.08998
$817$	−31.1811	−1.09089
$818$	5.71656	0.199875
$819$	0.101302	0.00353977
$820$	20.0003	0.698440
$821$	−1.14274	−0.0398818	−0.0199409	−	0.999801i	$-0.506348\pi$
$821$	−1.14274	−0.0398818	−0.0199409	+	0.999801i	$0.506348\pi$
$822$	−8.62802	−0.300937
$823$	45.5226	1.58682	0.793409	−	0.608688i	$-0.208304\pi$
$823$	45.5226	1.58682	0.793409	+	0.608688i	$0.208304\pi$
$824$	−11.7558	−0.409532
$825$	22.1769	0.772102
$826$	57.1678	1.98912
$827$	53.4312	1.85799	0.928993	−	0.370097i	$-0.120676\pi$
$827$	53.4312	1.85799	0.928993	+	0.370097i	$0.120676\pi$
$828$	0.0779946	0.00271050
$829$	−17.8514	−0.620004	−0.310002	−	0.950736i	$-0.600330\pi$
$829$	−17.8514	−0.620004	−0.310002	+	0.950736i	$0.600330\pi$
$830$	51.0038	1.77037
$831$	14.9721	0.519378
$832$	−11.2092	−0.388610
$833$	45.5579	1.57849
$834$	36.4604	1.26252
$835$	−27.1899	−0.940945
$836$	55.8501	1.93161
$837$	−11.5248	−0.398355
$838$	39.2423	1.35560
$839$	−18.4282	−0.636210	−0.318105	−	0.948055i	$-0.603047\pi$
$839$	−18.4282	−0.636210	−0.318105	+	0.948055i	$0.603047\pi$
$840$	11.8656	0.409401
$841$	1.00000	0.0344828
$842$	−18.2862	−0.630184
$843$	13.5760	0.467581
$844$	−32.8353	−1.13024
$845$	17.2605	0.593779
$846$	0.0301745	0.00103742
$847$	26.7264	0.918331
$848$	14.5629	0.500091
$849$	−28.7020	−0.985050
$850$	−47.7916	−1.63924
$851$	−0.191258	−0.00655624
$852$	−21.4768	−0.735783
$853$	−30.0943	−1.03041	−0.515205	−	0.857067i	$-0.672284\pi$
$853$	−30.0943	−1.03041	−0.515205	+	0.857067i	$0.672284\pi$
$854$	70.3110	2.40599
$855$	−0.211462	−0.00723185
$856$	−4.24752	−0.145177
$857$	−24.9732	−0.853070	−0.426535	−	0.904471i	$-0.640266\pi$
$857$	−24.9732	−0.853070	−0.426535	+	0.904471i	$0.640266\pi$
$858$	−15.0618	−0.514201
$859$	22.8073	0.778175	0.389087	−	0.921201i	$-0.372790\pi$
$859$	22.8073	0.778175	0.389087	+	0.921201i	$0.372790\pi$
$860$	23.3335	0.795665
$861$	33.7985	1.15185
$862$	64.4529	2.19527
$863$	26.3898	0.898319	0.449159	−	0.893452i	$-0.351724\pi$
$863$	26.3898	0.898319	0.449159	+	0.893452i	$0.351724\pi$
$864$	−40.2178	−1.36824
$865$	−6.85973	−0.233238
$866$	11.2543	0.382437
$867$	−67.9807	−2.30875
$868$	−21.0927	−0.715933
$869$	−33.4860	−1.13594
$870$	−5.32672	−0.180593
$871$	7.81644	0.264850
$872$	−0.943256	−0.0319427
$873$	−0.339800	−0.0115005
$874$	10.6972	0.361837
$875$	41.0708	1.38845
$876$	49.9718	1.68839
$877$	17.9650	0.606636	0.303318	−	0.952889i	$-0.401906\pi$
$877$	17.9650	0.606636	0.303318	+	0.952889i	$0.401906\pi$
$878$	8.91970	0.301025
$879$	−42.2506	−1.42508
$880$	14.5931	0.491935
$881$	34.8937	1.17560	0.587799	−	0.809007i	$-0.299995\pi$
$881$	34.8937	1.17560	0.587799	+	0.809007i	$0.299995\pi$
$882$	0.389798	0.0131252
$883$	24.3100	0.818095	0.409048	−	0.912513i	$-0.365861\pi$
$883$	24.3100	0.818095	0.409048	+	0.912513i	$0.365861\pi$
$884$	18.3944	0.618669
$885$	18.2380	0.613065
$886$	−1.22711	−0.0412256
$887$	−15.3916	−0.516799	−0.258400	−	0.966038i	$-0.583195\pi$
$887$	−15.3916	−0.516799	−0.258400	+	0.966038i	$0.583195\pi$
$888$	0.440448	0.0147805
$889$	−75.6110	−2.53591
$890$	−7.25333	−0.243132
$891$	−38.9734	−1.30566
$892$	66.8755	2.23916
$893$	2.34532	0.0784831
$894$	74.9549	2.50687
$895$	10.6666	0.356547
$896$	−36.4714	−1.21842
$897$	−1.63486	−0.0545863
$898$	3.34603	0.111658
$899$	2.22916	0.0743467
$900$	−0.231732	−0.00772439
$901$	−45.6359	−1.52035
$902$	−49.4538	−1.64663
$903$	39.4312	1.31219
$904$	8.69718	0.289264
$905$	−13.0870	−0.435027
$906$	82.7028	2.74761
$907$	−48.0004	−1.59383	−0.796913	−	0.604094i	$-0.793535\pi$
$907$	−48.0004	−1.59383	−0.796913	+	0.604094i	$0.793535\pi$
$908$	−54.6514	−1.81367
$909$	0.475381	0.0157674
$910$	−10.3970	−0.344658
$911$	−45.0598	−1.49290	−0.746448	−	0.665444i	$-0.768242\pi$
$911$	−45.0598	−1.49290	−0.746448	+	0.665444i	$0.768242\pi$
$912$	20.7063	0.685653
$913$	−71.4700	−2.36531
$914$	37.5694	1.24269
$915$	22.4311	0.741548
$916$	47.3523	1.56457
$917$	−19.8950	−0.656989
$918$	83.1616	2.74474
$919$	−27.3705	−0.902870	−0.451435	−	0.892304i	$-0.649088\pi$
$919$	−27.3705	−0.902870	−0.451435	+	0.892304i	$0.649088\pi$
$920$	−1.88449	−0.0621299
$921$	52.9208	1.74380
$922$	−26.5047	−0.872886
$923$	4.43025	0.145823
$924$	−70.6272	−2.32347
$925$	0.568251	0.0186840
$926$	78.6774	2.58550
$927$	−0.264938	−0.00870170
$928$	7.77905	0.255360
$929$	23.4108	0.768084	0.384042	−	0.923316i	$-0.374532\pi$
$929$	23.4108	0.768084	0.384042	+	0.923316i	$0.374532\pi$
$930$	−11.8741	−0.389367
$931$	30.2971	0.992948
$932$	17.9603	0.588308
$933$	32.8187	1.07444
$934$	70.7249	2.31419
$935$	−45.7307	−1.49556
$936$	0.0370508	0.00121104
$937$	−16.8103	−0.549168	−0.274584	−	0.961563i	$-0.588540\pi$
$937$	−16.8103	−0.549168	−0.274584	+	0.961563i	$0.588540\pi$
$938$	64.6765	2.11176
$939$	40.7437	1.32962
$940$	−1.75505	−0.0572434
$941$	42.4050	1.38236	0.691181	−	0.722682i	$-0.257091\pi$
$941$	42.4050	1.38236	0.691181	+	0.722682i	$0.257091\pi$
$942$	−64.3378	−2.09624
$943$	−5.36788	−0.174802
$944$	−17.5748	−0.572010
$945$	−26.6382	−0.866541
$946$	−57.6956	−1.87585
$947$	37.7128	1.22550	0.612751	−	0.790276i	$-0.290063\pi$
$947$	37.7128	1.22550	0.612751	+	0.790276i	$0.290063\pi$
$948$	35.5553	1.15478
$949$	−10.3082	−0.334619
$950$	−31.7826	−1.03116
$951$	3.62424	0.117524
$952$	35.8311	1.16129
$953$	47.6248	1.54272	0.771360	−	0.636399i	$-0.219577\pi$
$953$	47.6248	1.54272	0.771360	+	0.636399i	$0.219577\pi$
$954$	−0.390465	−0.0126418
$955$	−16.6993	−0.540378
$956$	20.9282	0.676866
$957$	7.46416	0.241282
$958$	−70.6030	−2.28108
$959$	8.34574	0.269498
$960$	−29.5896	−0.955001
$961$	−26.0308	−0.839705
$962$	−0.385936	−0.0124431
$963$	−0.0957256	−0.00308472
$964$	−28.1523	−0.906726
$965$	8.25529	0.265747
$966$	−13.5275	−0.435240
$967$	4.85286	0.156057	0.0780287	−	0.996951i	$-0.475137\pi$
$967$	4.85286	0.156057	0.0780287	+	0.996951i	$0.475137\pi$
$968$	9.77511	0.314184
$969$	−64.8875	−2.08449
$970$	34.8751	1.11977
$971$	−31.9786	−1.02624	−0.513122	−	0.858316i	$-0.671511\pi$
$971$	−31.9786	−1.02624	−0.513122	+	0.858316i	$0.671511\pi$
$972$	0.810514	0.0259973
$973$	−35.2675	−1.13062
$974$	−30.3648	−0.972950
$975$	4.85737	0.155560
$976$	−21.6153	−0.691889
$977$	24.3468	0.778925	0.389462	−	0.921042i	$-0.372661\pi$
$977$	24.3468	0.778925	0.389462	+	0.921042i	$0.372661\pi$
$978$	−68.1294	−2.17854
$979$	10.1639	0.324838
$980$	−22.6720	−0.724230
$981$	−0.0212580	−0.000678715 0
$982$	74.6961	2.38365
$983$	1.54152	0.0491667	0.0245834	−	0.999698i	$-0.492174\pi$
$983$	1.54152	0.0491667	0.0245834	+	0.999698i	$0.492174\pi$
$984$	12.3617	0.394076
$985$	−28.3356	−0.902846
$986$	−16.0854	−0.512263
$987$	−2.96586	−0.0944043
$988$	12.2327	0.389174
$989$	−6.26248	−0.199135
$990$	−0.391277	−0.0124356
$991$	8.91405	0.283164	0.141582	−	0.989927i	$-0.454781\pi$
$991$	8.91405	0.283164	0.141582	+	0.989927i	$0.454781\pi$
$992$	17.3407	0.550569
$993$	25.9700	0.824132
$994$	36.6577	1.16271
$995$	−9.59094	−0.304053
$996$	75.8865	2.40456
$997$	43.7974	1.38708	0.693538	−	0.720420i	$-0.256051\pi$
$997$	43.7974	1.38708	0.693538	+	0.720420i	$0.256051\pi$
$998$	−12.5456	−0.397126
$999$	−0.988806	−0.0312844

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.d.1.14	✓	16
3.2	odd	2		6003.2.a.q.1.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.d.1.14	✓	16	1.1	even	1	trivial
6003.2.a.q.1.3		16	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:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q+2.14844 q^{2} -1.74064 q^{3} +2.61580 q^{4} -1.42439 q^{5} -3.73966 q^{6} +3.61731 q^{7} +1.32302 q^{8} +0.0298167 q^{9} +O(q^{10})\)	\(q+2.14844 q^{2} -1.74064 q^{3} +2.61580 q^{4} -1.42439 q^{5} -3.73966 q^{6} +3.61731 q^{7} +1.32302 q^{8} +0.0298167 q^{9} -3.06021 q^{10} +4.28818 q^{11} -4.55317 q^{12} +0.939230 q^{13} +7.77158 q^{14} +2.47934 q^{15} -2.38917 q^{16} +7.48700 q^{17} +0.0640594 q^{18} +4.97904 q^{19} -3.72592 q^{20} -6.29642 q^{21} +9.21291 q^{22} +1.00000 q^{23} -2.30290 q^{24} -2.97112 q^{25} +2.01788 q^{26} +5.17001 q^{27} +9.46218 q^{28} -1.00000 q^{29} +5.32672 q^{30} -2.22916 q^{31} -7.77905 q^{32} -7.46416 q^{33} +16.0854 q^{34} -5.15245 q^{35} +0.0779946 q^{36} -0.191258 q^{37} +10.6972 q^{38} -1.63486 q^{39} -1.88449 q^{40} -5.36788 q^{41} -13.5275 q^{42} -6.26248 q^{43} +11.2170 q^{44} -0.0424705 q^{45} +2.14844 q^{46} +0.471038 q^{47} +4.15869 q^{48} +6.08494 q^{49} -6.38329 q^{50} -13.0321 q^{51} +2.45684 q^{52} -6.09535 q^{53} +11.1075 q^{54} -6.10802 q^{55} +4.78578 q^{56} -8.66670 q^{57} -2.14844 q^{58} +7.35600 q^{59} +6.48547 q^{60} +9.04719 q^{61} -4.78922 q^{62} +0.107856 q^{63} -11.9345 q^{64} -1.33783 q^{65} -16.0363 q^{66} +8.32218 q^{67} +19.5845 q^{68} -1.74064 q^{69} -11.0697 q^{70} +4.71689 q^{71} +0.0394481 q^{72} -10.9752 q^{73} -0.410907 q^{74} +5.17165 q^{75} +13.0242 q^{76} +15.5117 q^{77} -3.51240 q^{78} -7.80891 q^{79} +3.40311 q^{80} -9.08856 q^{81} -11.5326 q^{82} -16.6667 q^{83} -16.4702 q^{84} -10.6644 q^{85} -13.4546 q^{86} +1.74064 q^{87} +5.67335 q^{88} +2.37020 q^{89} -0.0912454 q^{90} +3.39749 q^{91} +2.61580 q^{92} +3.88016 q^{93} +1.01200 q^{94} -7.09207 q^{95} +13.5405 q^{96} -11.3963 q^{97} +13.0731 q^{98} +0.127859 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9} - 14 q^{10} + 4 q^{11} + 3 q^{12} + 15 q^{13} + 8 q^{14} + 8 q^{15} + 23 q^{16} + 20 q^{17} + 2 q^{18} - 4 q^{19} + 25 q^{20} + 5 q^{21} + 13 q^{22} + 16 q^{23} - 24 q^{24} + 30 q^{25} + 25 q^{26} + 8 q^{27} - 13 q^{28} - 16 q^{29} - 45 q^{30} - 19 q^{32} + q^{33} - 23 q^{34} + 5 q^{35} + 37 q^{36} + 5 q^{37} + 38 q^{38} - 10 q^{39} - 20 q^{40} + 7 q^{41} + 14 q^{42} - 17 q^{43} - 21 q^{44} + 48 q^{45} + 3 q^{46} + 29 q^{47} + 35 q^{48} + 31 q^{49} - 44 q^{50} - 14 q^{51} + 20 q^{52} + 63 q^{53} - 13 q^{54} + q^{55} - 19 q^{56} - 22 q^{57} - 3 q^{58} + 11 q^{59} - 3 q^{60} + 33 q^{62} - 33 q^{63} + 29 q^{64} + 53 q^{65} - 43 q^{66} - 13 q^{67} + 63 q^{68} + 5 q^{69} - 46 q^{70} - 23 q^{71} + 46 q^{72} - 38 q^{73} - 47 q^{74} + 37 q^{75} - 56 q^{76} + 97 q^{77} - 24 q^{78} - 27 q^{79} + 8 q^{80} + 40 q^{81} + 9 q^{82} + 36 q^{83} + 22 q^{84} + 6 q^{85} - 11 q^{86} - 5 q^{87} - 24 q^{88} - 16 q^{89} - 95 q^{90} - 47 q^{91} + 21 q^{92} + 62 q^{93} + 37 q^{94} - 12 q^{95} - 74 q^{96} - 30 q^{97} - 27 q^{98} - 42 q^{99}+O(q^{100}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9 - 14 * q^10 + 4 * q^11 + 3 * q^12 + 15 * q^13 + 8 * q^14 + 8 * q^15 + 23 * q^16 + 20 * q^17 + 2 * q^18 - 4 * q^19 + 25 * q^20 + 5 * q^21 + 13 * q^22 + 16 * q^23 - 24 * q^24 + 30 * q^25 + 25 * q^26 + 8 * q^27 - 13 * q^28 - 16 * q^29 - 45 * q^30 - 19 * q^32 + q^33 - 23 * q^34 + 5 * q^35 + 37 * q^36 + 5 * q^37 + 38 * q^38 - 10 * q^39 - 20 * q^40 + 7 * q^41 + 14 * q^42 - 17 * q^43 - 21 * q^44 + 48 * q^45 + 3 * q^46 + 29 * q^47 + 35 * q^48 + 31 * q^49 - 44 * q^50 - 14 * q^51 + 20 * q^52 + 63 * q^53 - 13 * q^54 + q^55 - 19 * q^56 - 22 * q^57 - 3 * q^58 + 11 * q^59 - 3 * q^60 + 33 * q^62 - 33 * q^63 + 29 * q^64 + 53 * q^65 - 43 * q^66 - 13 * q^67 + 63 * q^68 + 5 * q^69 - 46 * q^70 - 23 * q^71 + 46 * q^72 - 38 * q^73 - 47 * q^74 + 37 * q^75 - 56 * q^76 + 97 * q^77 - 24 * q^78 - 27 * q^79 + 8 * q^80 + 40 * q^81 + 9 * q^82 + 36 * q^83 + 22 * q^84 + 6 * q^85 - 11 * q^86 - 5 * q^87 - 24 * q^88 - 16 * q^89 - 95 * q^90 - 47 * q^91 + 21 * q^92 + 62 * q^93 + 37 * q^94 - 12 * q^95 - 74 * q^96 - 30 * q^97 - 27 * q^98 - 42 * q^99

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