LMFDB - Embedded newform 2415.2.a.q.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2415,2,Mod(1,2415)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2415, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2415.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2415 = 3 \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2415.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:	$19.2838720881$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.15751800.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 6x^{3} + 16x^{2} - 7x - 1 $ x^6 - x^5 - 8x^4 + 6x^3 + 16x^2 - 7x - 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			1.3
Root			$-0.114413$ of defining polynomial
Character	$\chi$	$=$	2415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.456154 q^{2} -1.00000 q^{3} -1.79192 q^{4} -1.00000 q^{5} -0.456154 q^{6} +1.00000 q^{7} -1.72970 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.456154 q^{2} -1.00000 q^{3} -1.79192 q^{4} -1.00000 q^{5} -0.456154 q^{6} +1.00000 q^{7} -1.72970 q^{8} +1.00000 q^{9} -0.456154 q^{10} -4.03604 q^{11} +1.79192 q^{12} -3.30193 q^{13} +0.456154 q^{14} +1.00000 q^{15} +2.79484 q^{16} +1.85325 q^{17} +0.456154 q^{18} -4.75642 q^{19} +1.79192 q^{20} -1.00000 q^{21} -1.84106 q^{22} -1.00000 q^{23} +1.72970 q^{24} +1.00000 q^{25} -1.50619 q^{26} -1.00000 q^{27} -1.79192 q^{28} -3.74499 q^{29} +0.456154 q^{30} +5.70477 q^{31} +4.73428 q^{32} +4.03604 q^{33} +0.845365 q^{34} -1.00000 q^{35} -1.79192 q^{36} -4.66577 q^{37} -2.16966 q^{38} +3.30193 q^{39} +1.72970 q^{40} +4.58736 q^{41} -0.456154 q^{42} -10.9530 q^{43} +7.23228 q^{44} -1.00000 q^{45} -0.456154 q^{46} +0.630041 q^{47} -2.79484 q^{48} +1.00000 q^{49} +0.456154 q^{50} -1.85325 q^{51} +5.91681 q^{52} +12.2192 q^{53} -0.456154 q^{54} +4.03604 q^{55} -1.72970 q^{56} +4.75642 q^{57} -1.70829 q^{58} -6.42601 q^{59} -1.79192 q^{60} -1.18101 q^{61} +2.60225 q^{62} +1.00000 q^{63} -3.43012 q^{64} +3.30193 q^{65} +1.84106 q^{66} +10.8656 q^{67} -3.32087 q^{68} +1.00000 q^{69} -0.456154 q^{70} +8.99051 q^{71} -1.72970 q^{72} -10.9222 q^{73} -2.12831 q^{74} -1.00000 q^{75} +8.52314 q^{76} -4.03604 q^{77} +1.50619 q^{78} +13.6786 q^{79} -2.79484 q^{80} +1.00000 q^{81} +2.09254 q^{82} +9.93938 q^{83} +1.79192 q^{84} -1.85325 q^{85} -4.99623 q^{86} +3.74499 q^{87} +6.98115 q^{88} +1.03425 q^{89} -0.456154 q^{90} -3.30193 q^{91} +1.79192 q^{92} -5.70477 q^{93} +0.287396 q^{94} +4.75642 q^{95} -4.73428 q^{96} +15.8451 q^{97} +0.456154 q^{98} -4.03604 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 6 q^{3} + 5 q^{4} - 6 q^{5} - 3 q^{6} + 6 q^{7} + 9 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 6 * q^3 + 5 * q^4 - 6 * q^5 - 3 * q^6 + 6 * q^7 + 9 * q^8 + 6 * q^9	\( 6 q + 3 q^{2} - 6 q^{3} + 5 q^{4} - 6 q^{5} - 3 q^{6} + 6 q^{7} + 9 q^{8} + 6 q^{9} - 3 q^{10} + 6 q^{11} - 5 q^{12} - 6 q^{13} + 3 q^{14} + 6 q^{15} + 11 q^{16} + 8 q^{17} + 3 q^{18} - 8 q^{19} - 5 q^{20} - 6 q^{21} + 18 q^{22} - 6 q^{23} - 9 q^{24} + 6 q^{25} + 13 q^{26} - 6 q^{27} + 5 q^{28} + 8 q^{29} + 3 q^{30} - 16 q^{31} + 26 q^{32} - 6 q^{33} - 13 q^{34} - 6 q^{35} + 5 q^{36} + 8 q^{37} - 14 q^{38} + 6 q^{39} - 9 q^{40} + 8 q^{41} - 3 q^{42} + 8 q^{43} + 15 q^{44} - 6 q^{45} - 3 q^{46} + 10 q^{47} - 11 q^{48} + 6 q^{49} + 3 q^{50} - 8 q^{51} + 28 q^{53} - 3 q^{54} - 6 q^{55} + 9 q^{56} + 8 q^{57} + 14 q^{58} - 6 q^{59} + 5 q^{60} - 12 q^{61} + 18 q^{62} + 6 q^{63} + 15 q^{64} + 6 q^{65} - 18 q^{66} + 18 q^{67} + 18 q^{68} + 6 q^{69} - 3 q^{70} + 10 q^{71} + 9 q^{72} - 2 q^{73} + q^{74} - 6 q^{75} + 25 q^{76} + 6 q^{77} - 13 q^{78} - 2 q^{79} - 11 q^{80} + 6 q^{81} - 12 q^{82} + 26 q^{83} - 5 q^{84} - 8 q^{85} + 16 q^{86} - 8 q^{87} + 21 q^{88} + 8 q^{89} - 3 q^{90} - 6 q^{91} - 5 q^{92} + 16 q^{93} - 8 q^{94} + 8 q^{95} - 26 q^{96} + 20 q^{97} + 3 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 6 * q^3 + 5 * q^4 - 6 * q^5 - 3 * q^6 + 6 * q^7 + 9 * q^8 + 6 * q^9 - 3 * q^10 + 6 * q^11 - 5 * q^12 - 6 * q^13 + 3 * q^14 + 6 * q^15 + 11 * q^16 + 8 * q^17 + 3 * q^18 - 8 * q^19 - 5 * q^20 - 6 * q^21 + 18 * q^22 - 6 * q^23 - 9 * q^24 + 6 * q^25 + 13 * q^26 - 6 * q^27 + 5 * q^28 + 8 * q^29 + 3 * q^30 - 16 * q^31 + 26 * q^32 - 6 * q^33 - 13 * q^34 - 6 * q^35 + 5 * q^36 + 8 * q^37 - 14 * q^38 + 6 * q^39 - 9 * q^40 + 8 * q^41 - 3 * q^42 + 8 * q^43 + 15 * q^44 - 6 * q^45 - 3 * q^46 + 10 * q^47 - 11 * q^48 + 6 * q^49 + 3 * q^50 - 8 * q^51 + 28 * q^53 - 3 * q^54 - 6 * q^55 + 9 * q^56 + 8 * q^57 + 14 * q^58 - 6 * q^59 + 5 * q^60 - 12 * q^61 + 18 * q^62 + 6 * q^63 + 15 * q^64 + 6 * q^65 - 18 * q^66 + 18 * q^67 + 18 * q^68 + 6 * q^69 - 3 * q^70 + 10 * q^71 + 9 * q^72 - 2 * q^73 + q^74 - 6 * q^75 + 25 * q^76 + 6 * q^77 - 13 * q^78 - 2 * q^79 - 11 * q^80 + 6 * q^81 - 12 * q^82 + 26 * q^83 - 5 * q^84 - 8 * q^85 + 16 * q^86 - 8 * q^87 + 21 * q^88 + 8 * q^89 - 3 * q^90 - 6 * q^91 - 5 * q^92 + 16 * q^93 - 8 * q^94 + 8 * q^95 - 26 * q^96 + 20 * q^97 + 3 * q^98 + 6 * 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 $

$2$	0.456154	0.322549	0.161275	−	0.986910i	$-0.448439\pi$
$2$	0.456154	0.322549	0.161275	+	0.986910i	$0.448439\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.79192	−0.895962
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.456154	−0.186224
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.72970	−0.611542
$9$	1.00000	0.333333
$10$	−0.456154	−0.144249
$11$	−4.03604	−1.21691	−0.608456	−	0.793587i	$-0.708211\pi$
$11$	−4.03604	−1.21691	−0.608456	+	0.793587i	$0.708211\pi$
$12$	1.79192	0.517284
$13$	−3.30193	−0.915791	−0.457895	−	0.889006i	$-0.651397\pi$
$13$	−3.30193	−0.915791	−0.457895	+	0.889006i	$0.651397\pi$
$14$	0.456154	0.121912
$15$	1.00000	0.258199
$16$	2.79484	0.698709
$17$	1.85325	0.449478	0.224739	−	0.974419i	$-0.427847\pi$
$17$	1.85325	0.449478	0.224739	+	0.974419i	$0.427847\pi$
$18$	0.456154	0.107516
$19$	−4.75642	−1.09120	−0.545599	−	0.838046i	$-0.683698\pi$
$19$	−4.75642	−1.09120	−0.545599	+	0.838046i	$0.683698\pi$
$20$	1.79192	0.400686
$21$	−1.00000	−0.218218
$22$	−1.84106	−0.392515
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.72970	0.353074
$25$	1.00000	0.200000
$26$	−1.50619	−0.295388
$27$	−1.00000	−0.192450
$28$	−1.79192	−0.338642
$29$	−3.74499	−0.695428	−0.347714	−	0.937601i	$-0.613042\pi$
$29$	−3.74499	−0.695428	−0.347714	+	0.937601i	$0.613042\pi$
$30$	0.456154	0.0832819
$31$	5.70477	1.02461	0.512304	−	0.858804i	$-0.328792\pi$
$31$	5.70477	1.02461	0.512304	+	0.858804i	$0.328792\pi$
$32$	4.73428	0.836910
$33$	4.03604	0.702585
$34$	0.845365	0.144979
$35$	−1.00000	−0.169031
$36$	−1.79192	−0.298654
$37$	−4.66577	−0.767049	−0.383524	−	0.923531i	$-0.625290\pi$
$37$	−4.66577	−0.767049	−0.383524	+	0.923531i	$0.625290\pi$
$38$	−2.16966	−0.351965
$39$	3.30193	0.528732
$40$	1.72970	0.273490
$41$	4.58736	0.716425	0.358212	−	0.933640i	$-0.383386\pi$
$41$	4.58736	0.716425	0.358212	+	0.933640i	$0.383386\pi$
$42$	−0.456154	−0.0703861
$43$	−10.9530	−1.67031	−0.835155	−	0.550015i	$-0.814622\pi$
$43$	−10.9530	−1.67031	−0.835155	+	0.550015i	$0.814622\pi$
$44$	7.23228	1.09031
$45$	−1.00000	−0.149071
$46$	−0.456154	−0.0672562
$47$	0.630041	0.0919009	0.0459504	−	0.998944i	$-0.485368\pi$
$47$	0.630041	0.0919009	0.0459504	+	0.998944i	$0.485368\pi$
$48$	−2.79484	−0.403400
$49$	1.00000	0.142857
$50$	0.456154	0.0645099
$51$	−1.85325	−0.259506
$52$	5.91681	0.820513
$53$	12.2192	1.67843	0.839217	−	0.543796i	$-0.183014\pi$
$53$	12.2192	1.67843	0.839217	+	0.543796i	$0.183014\pi$
$54$	−0.456154	−0.0620747
$55$	4.03604	0.544220
$56$	−1.72970	−0.231141
$57$	4.75642	0.630003
$58$	−1.70829	−0.224310
$59$	−6.42601	−0.836596	−0.418298	−	0.908310i	$-0.637373\pi$
$59$	−6.42601	−0.836596	−0.418298	+	0.908310i	$0.637373\pi$
$60$	−1.79192	−0.231336
$61$	−1.18101	−0.151212	−0.0756062	−	0.997138i	$-0.524089\pi$
$61$	−1.18101	−0.151212	−0.0756062	+	0.997138i	$0.524089\pi$
$62$	2.60225	0.330487
$63$	1.00000	0.125988
$64$	−3.43012	−0.428765
$65$	3.30193	0.409554
$66$	1.84106	0.226618
$67$	10.8656	1.32745	0.663723	−	0.747978i	$-0.268975\pi$
$67$	10.8656	1.32745	0.663723	+	0.747978i	$0.268975\pi$
$68$	−3.32087	−0.402715
$69$	1.00000	0.120386
$70$	−0.456154	−0.0545208
$71$	8.99051	1.06698	0.533488	−	0.845807i	$-0.320881\pi$
$71$	8.99051	1.06698	0.533488	+	0.845807i	$0.320881\pi$
$72$	−1.72970	−0.203847
$73$	−10.9222	−1.27834	−0.639172	−	0.769064i	$-0.720723\pi$
$73$	−10.9222	−1.27834	−0.639172	+	0.769064i	$0.720723\pi$
$74$	−2.12831	−0.247411
$75$	−1.00000	−0.115470
$76$	8.52314	0.977672
$77$	−4.03604	−0.459950
$78$	1.50619	0.170542
$79$	13.6786	1.53896	0.769481	−	0.638670i	$-0.220515\pi$
$79$	13.6786	1.53896	0.769481	+	0.638670i	$0.220515\pi$
$80$	−2.79484	−0.312472
$81$	1.00000	0.111111
$82$	2.09254	0.231082
$83$	9.93938	1.09099	0.545495	−	0.838114i	$-0.316342\pi$
$83$	9.93938	1.09099	0.545495	+	0.838114i	$0.316342\pi$
$84$	1.79192	0.195515
$85$	−1.85325	−0.201013
$86$	−4.99623	−0.538757
$87$	3.74499	0.401505
$88$	6.98115	0.744193
$89$	1.03425	0.109630	0.0548152	−	0.998497i	$-0.482543\pi$
$89$	1.03425	0.109630	0.0548152	+	0.998497i	$0.482543\pi$
$90$	−0.456154	−0.0480828
$91$	−3.30193	−0.346136
$92$	1.79192	0.186821
$93$	−5.70477	−0.591557
$94$	0.287396	0.0296426
$95$	4.75642	0.487999
$96$	−4.73428	−0.483190
$97$	15.8451	1.60882	0.804411	−	0.594073i	$-0.202481\pi$
$97$	15.8451	1.60882	0.804411	+	0.594073i	$0.202481\pi$
$98$	0.456154	0.0460785
$99$	−4.03604	−0.405638
$100$	−1.79192	−0.179192
$101$	9.30633	0.926014	0.463007	−	0.886355i	$-0.346770\pi$
$101$	9.30633	0.926014	0.463007	+	0.886355i	$0.346770\pi$
$102$	−0.845365	−0.0837036
$103$	−15.2517	−1.50280	−0.751398	−	0.659849i	$-0.770620\pi$
$103$	−15.2517	−1.50280	−0.751398	+	0.659849i	$0.770620\pi$
$104$	5.71135	0.560044
$105$	1.00000	0.0975900
$106$	5.57383	0.541378
$107$	−9.58825	−0.926931	−0.463466	−	0.886115i	$-0.653394\pi$
$107$	−9.58825	−0.926931	−0.463466	+	0.886115i	$0.653394\pi$
$108$	1.79192	0.172428
$109$	7.83993	0.750929	0.375465	−	0.926837i	$-0.377483\pi$
$109$	7.83993	0.750929	0.375465	+	0.926837i	$0.377483\pi$
$110$	1.84106	0.175538
$111$	4.66577	0.442856
$112$	2.79484	0.264087
$113$	13.8417	1.30211	0.651057	−	0.759029i	$-0.274326\pi$
$113$	13.8417	1.30211	0.651057	+	0.759029i	$0.274326\pi$
$114$	2.16966	0.203207
$115$	1.00000	0.0932505
$116$	6.71074	0.623077
$117$	−3.30193	−0.305264
$118$	−2.93125	−0.269844
$119$	1.85325	0.169887
$120$	−1.72970	−0.157899
$121$	5.28964	0.480876
$122$	−0.538720	−0.0487735
$123$	−4.58736	−0.413628
$124$	−10.2225	−0.918009
$125$	−1.00000	−0.0894427
$126$	0.456154	0.0406374
$127$	14.0266	1.24466	0.622328	−	0.782757i	$-0.286187\pi$
$127$	14.0266	1.24466	0.622328	+	0.782757i	$0.286187\pi$
$128$	−11.0332	−0.975208
$129$	10.9530	0.964354
$130$	1.50619	0.132101
$131$	−3.06186	−0.267516	−0.133758	−	0.991014i	$-0.542704\pi$
$131$	−3.06186	−0.267516	−0.133758	+	0.991014i	$0.542704\pi$
$132$	−7.23228	−0.629489
$133$	−4.75642	−0.412434
$134$	4.95640	0.428167
$135$	1.00000	0.0860663
$136$	−3.20556	−0.274874
$137$	14.7943	1.26396	0.631980	−	0.774985i	$-0.282243\pi$
$137$	14.7943	1.26396	0.631980	+	0.774985i	$0.282243\pi$
$138$	0.456154	0.0388304
$139$	−3.15768	−0.267831	−0.133915	−	0.990993i	$-0.542755\pi$
$139$	−3.15768	−0.267831	−0.133915	+	0.990993i	$0.542755\pi$
$140$	1.79192	0.151445
$141$	−0.630041	−0.0530590
$142$	4.10105	0.344153
$143$	13.3267	1.11444
$144$	2.79484	0.232903
$145$	3.74499	0.311005
$146$	−4.98219	−0.412329
$147$	−1.00000	−0.0824786
$148$	8.36071	0.687246
$149$	3.50810	0.287395	0.143697	−	0.989622i	$-0.454101\pi$
$149$	3.50810	0.287395	0.143697	+	0.989622i	$0.454101\pi$
$150$	−0.456154	−0.0372448
$151$	−7.14508	−0.581458	−0.290729	−	0.956805i	$-0.593898\pi$
$151$	−7.14508	−0.581458	−0.290729	+	0.956805i	$0.593898\pi$
$152$	8.22718	0.667313
$153$	1.85325	0.149826
$154$	−1.84106	−0.148357
$155$	−5.70477	−0.458218
$156$	−5.91681	−0.473724
$157$	−1.18846	−0.0948495	−0.0474247	−	0.998875i	$-0.515101\pi$
$157$	−1.18846	−0.0948495	−0.0474247	+	0.998875i	$0.515101\pi$
$158$	6.23954	0.496391
$159$	−12.2192	−0.969045
$160$	−4.73428	−0.374277
$161$	−1.00000	−0.0788110
$162$	0.456154	0.0358388
$163$	−1.72815	−0.135359	−0.0676797	−	0.997707i	$-0.521560\pi$
$163$	−1.72815	−0.135359	−0.0676797	+	0.997707i	$0.521560\pi$
$164$	−8.22019	−0.641889
$165$	−4.03604	−0.314205
$166$	4.53389	0.351898
$167$	0.588212	0.0455172	0.0227586	−	0.999741i	$-0.492755\pi$
$167$	0.588212	0.0455172	0.0227586	+	0.999741i	$0.492755\pi$
$168$	1.72970	0.133449
$169$	−2.09726	−0.161328
$170$	−0.845365	−0.0648365
$171$	−4.75642	−0.363733
$172$	19.6269	1.49653
$173$	8.70232	0.661625	0.330813	−	0.943696i	$-0.392677\pi$
$173$	8.70232	0.661625	0.330813	+	0.943696i	$0.392677\pi$
$174$	1.70829	0.129505
$175$	1.00000	0.0755929
$176$	−11.2801	−0.850268
$177$	6.42601	0.483009
$178$	0.471778	0.0353612
$179$	1.62759	0.121652	0.0608259	−	0.998148i	$-0.480627\pi$
$179$	1.62759	0.121652	0.0608259	+	0.998148i	$0.480627\pi$
$180$	1.79192	0.133562
$181$	−4.18315	−0.310931	−0.155465	−	0.987841i	$-0.549688\pi$
$181$	−4.18315	−0.310931	−0.155465	+	0.987841i	$0.549688\pi$
$182$	−1.50619	−0.111646
$183$	1.18101	0.0873025
$184$	1.72970	0.127515
$185$	4.66577	0.343035
$186$	−2.60225	−0.190806
$187$	−7.47978	−0.546975
$188$	−1.12898	−0.0823397
$189$	−1.00000	−0.0727393
$190$	2.16966	0.157404
$191$	0.261565	0.0189262	0.00946308	−	0.999955i	$-0.496988\pi$
$191$	0.261565	0.0189262	0.00946308	+	0.999955i	$0.496988\pi$
$192$	3.43012	0.247547
$193$	18.4183	1.32578	0.662890	−	0.748716i	$-0.269330\pi$
$193$	18.4183	1.32578	0.662890	+	0.748716i	$0.269330\pi$
$194$	7.22779	0.518925
$195$	−3.30193	−0.236456
$196$	−1.79192	−0.127995
$197$	−2.26400	−0.161304	−0.0806518	−	0.996742i	$-0.525700\pi$
$197$	−2.26400	−0.161304	−0.0806518	+	0.996742i	$0.525700\pi$
$198$	−1.84106	−0.130838
$199$	9.03172	0.640242	0.320121	−	0.947377i	$-0.396276\pi$
$199$	9.03172	0.640242	0.320121	+	0.947377i	$0.396276\pi$
$200$	−1.72970	−0.122308
$201$	−10.8656	−0.766402
$202$	4.24512	0.298685
$203$	−3.74499	−0.262847
$204$	3.32087	0.232508
$205$	−4.58736	−0.320395
$206$	−6.95713	−0.484726
$207$	−1.00000	−0.0695048
$208$	−9.22836	−0.639872
$209$	19.1971	1.32789
$210$	0.456154	0.0314776
$211$	13.4445	0.925559	0.462779	−	0.886474i	$-0.346852\pi$
$211$	13.4445	0.925559	0.462779	+	0.886474i	$0.346852\pi$
$212$	−21.8959	−1.50381
$213$	−8.99051	−0.616019
$214$	−4.37372	−0.298981
$215$	10.9530	0.746985
$216$	1.72970	0.117691
$217$	5.70477	0.387265
$218$	3.57622	0.242212
$219$	10.9222	0.738052
$220$	−7.23228	−0.487600
$221$	−6.11929	−0.411628
$222$	2.12831	0.142843
$223$	22.0973	1.47974	0.739872	−	0.672748i	$-0.234886\pi$
$223$	22.0973	1.47974	0.739872	+	0.672748i	$0.234886\pi$
$224$	4.73428	0.316322
$225$	1.00000	0.0666667
$226$	6.31392	0.419996
$227$	20.9955	1.39352	0.696759	−	0.717306i	$-0.254625\pi$
$227$	20.9955	1.39352	0.696759	+	0.717306i	$0.254625\pi$
$228$	−8.52314	−0.564459
$229$	18.2353	1.20502	0.602510	−	0.798111i	$-0.294167\pi$
$229$	18.2353	1.20502	0.602510	+	0.798111i	$0.294167\pi$
$230$	0.456154	0.0300779
$231$	4.03604	0.265552
$232$	6.47772	0.425283
$233$	−8.56277	−0.560966	−0.280483	−	0.959859i	$-0.590495\pi$
$233$	−8.56277	−0.560966	−0.280483	+	0.959859i	$0.590495\pi$
$234$	−1.50619	−0.0984626
$235$	−0.630041	−0.0410993
$236$	11.5149	0.749558
$237$	−13.6786	−0.888520
$238$	0.845365	0.0547969
$239$	6.53477	0.422699	0.211350	−	0.977411i	$-0.432214\pi$
$239$	6.53477	0.422699	0.211350	+	0.977411i	$0.432214\pi$
$240$	2.79484	0.180406
$241$	−15.1111	−0.973390	−0.486695	−	0.873572i	$-0.661798\pi$
$241$	−15.1111	−0.973390	−0.486695	+	0.873572i	$0.661798\pi$
$242$	2.41289	0.155106
$243$	−1.00000	−0.0641500
$244$	2.11627	0.135480
$245$	−1.00000	−0.0638877
$246$	−2.09254	−0.133416
$247$	15.7054	0.999309
$248$	−9.86755	−0.626590
$249$	−9.93938	−0.629883
$250$	−0.456154	−0.0288497
$251$	−26.2343	−1.65590	−0.827948	−	0.560806i	$-0.810492\pi$
$251$	−26.2343	−1.65590	−0.827948	+	0.560806i	$0.810492\pi$
$252$	−1.79192	−0.112881
$253$	4.03604	0.253744
$254$	6.39827	0.401463
$255$	1.85325	0.116055
$256$	1.82739	0.114212
$257$	−8.03978	−0.501508	−0.250754	−	0.968051i	$-0.580678\pi$
$257$	−8.03978	−0.501508	−0.250754	+	0.968051i	$0.580678\pi$
$258$	4.99623	0.311052
$259$	−4.66577	−0.289917
$260$	−5.91681	−0.366945
$261$	−3.74499	−0.231809
$262$	−1.39668	−0.0862872
$263$	−13.6119	−0.839346	−0.419673	−	0.907675i	$-0.637855\pi$
$263$	−13.6119	−0.839346	−0.419673	+	0.907675i	$0.637855\pi$
$264$	−6.98115	−0.429660
$265$	−12.2192	−0.750619
$266$	−2.16966	−0.133030
$267$	−1.03425	−0.0632951
$268$	−19.4704	−1.18934
$269$	20.1213	1.22682	0.613410	−	0.789765i	$-0.289797\pi$
$269$	20.1213	1.22682	0.613410	+	0.789765i	$0.289797\pi$
$270$	0.456154	0.0277606
$271$	−26.4096	−1.60427	−0.802134	−	0.597145i	$-0.796302\pi$
$271$	−26.4096	−1.60427	−0.802134	+	0.597145i	$0.796302\pi$
$272$	5.17952	0.314054
$273$	3.30193	0.199842
$274$	6.74846	0.407690
$275$	−4.03604	−0.243383
$276$	−1.79192	−0.107861
$277$	−18.1491	−1.09047	−0.545237	−	0.838282i	$-0.683560\pi$
$277$	−18.1491	−1.09047	−0.545237	+	0.838282i	$0.683560\pi$
$278$	−1.44039	−0.0863887
$279$	5.70477	0.341536
$280$	1.72970	0.103369
$281$	−23.8987	−1.42568	−0.712839	−	0.701327i	$-0.752591\pi$
$281$	−23.8987	−1.42568	−0.712839	+	0.701327i	$0.752591\pi$
$282$	−0.287396	−0.0171142
$283$	−11.4670	−0.681644	−0.340822	−	0.940128i	$-0.610705\pi$
$283$	−11.4670	−0.681644	−0.340822	+	0.940128i	$0.610705\pi$
$284$	−16.1103	−0.955971
$285$	−4.75642	−0.281746
$286$	6.07904	0.359461
$287$	4.58736	0.270783
$288$	4.73428	0.278970
$289$	−13.5655	−0.797970
$290$	1.70829	0.100314
$291$	−15.8451	−0.928854
$292$	19.5717	1.14535
$293$	10.8965	0.636581	0.318291	−	0.947993i	$-0.396891\pi$
$293$	10.8965	0.636581	0.318291	+	0.947993i	$0.396891\pi$
$294$	−0.456154	−0.0266034
$295$	6.42601	0.374137
$296$	8.07039	0.469082
$297$	4.03604	0.234195
$298$	1.60023	0.0926990
$299$	3.30193	0.190956
$300$	1.79192	0.103457
$301$	−10.9530	−0.631318
$302$	−3.25925	−0.187549
$303$	−9.30633	−0.534634
$304$	−13.2934	−0.762430
$305$	1.18101	0.0676242
$306$	0.845365	0.0483263
$307$	−19.4228	−1.10852	−0.554258	−	0.832345i	$-0.686998\pi$
$307$	−19.4228	−1.10852	−0.554258	+	0.832345i	$0.686998\pi$
$308$	7.23228	0.412097
$309$	15.2517	0.867640
$310$	−2.60225	−0.147798
$311$	6.60214	0.374373	0.187187	−	0.982324i	$-0.440063\pi$
$311$	6.60214	0.374373	0.187187	+	0.982324i	$0.440063\pi$
$312$	−5.71135	−0.323342
$313$	−32.1550	−1.81751	−0.908753	−	0.417334i	$-0.862965\pi$
$313$	−32.1550	−1.81751	−0.908753	+	0.417334i	$0.862965\pi$
$314$	−0.542121	−0.0305936
$315$	−1.00000	−0.0563436
$316$	−24.5110	−1.37885
$317$	5.83318	0.327624	0.163812	−	0.986492i	$-0.447621\pi$
$317$	5.83318	0.327624	0.163812	+	0.986492i	$0.447621\pi$
$318$	−5.57383	−0.312565
$319$	15.1150	0.846275
$320$	3.43012	0.191749
$321$	9.58825	0.535164
$322$	−0.456154	−0.0254205
$323$	−8.81481	−0.490469
$324$	−1.79192	−0.0995513
$325$	−3.30193	−0.183158
$326$	−0.788304	−0.0436601
$327$	−7.83993	−0.433549
$328$	−7.93476	−0.438124
$329$	0.630041	0.0347353
$330$	−1.84106	−0.101347
$331$	−12.3886	−0.680939	−0.340470	−	0.940256i	$-0.610586\pi$
$331$	−12.3886	−0.680939	−0.340470	+	0.940256i	$0.610586\pi$
$332$	−17.8106	−0.977485
$333$	−4.66577	−0.255683
$334$	0.268315	0.0146816
$335$	−10.8656	−0.593652
$336$	−2.79484	−0.152471
$337$	12.8458	0.699753	0.349876	−	0.936796i	$-0.386224\pi$
$337$	12.8458	0.699753	0.349876	+	0.936796i	$0.386224\pi$
$338$	−0.956672	−0.0520361
$339$	−13.8417	−0.751775
$340$	3.32087	0.180100
$341$	−23.0247	−1.24686
$342$	−2.16966	−0.117322
$343$	1.00000	0.0539949
$344$	18.9453	1.02146
$345$	−1.00000	−0.0538382
$346$	3.96960	0.213407
$347$	31.1200	1.67061	0.835305	−	0.549788i	$-0.185291\pi$
$347$	31.1200	1.67061	0.835305	+	0.549788i	$0.185291\pi$
$348$	−6.71074	−0.359734
$349$	−21.5432	−1.15318	−0.576590	−	0.817033i	$-0.695617\pi$
$349$	−21.5432	−1.15318	−0.576590	+	0.817033i	$0.695617\pi$
$350$	0.456154	0.0243824
$351$	3.30193	0.176244
$352$	−19.1077	−1.01845
$353$	3.38080	0.179942	0.0899709	−	0.995944i	$-0.471323\pi$
$353$	3.38080	0.179942	0.0899709	+	0.995944i	$0.471323\pi$
$354$	2.93125	0.155794
$355$	−8.99051	−0.477167
$356$	−1.85330	−0.0982246
$357$	−1.85325	−0.0980841
$358$	0.742432	0.0392388
$359$	1.86576	0.0984713	0.0492356	−	0.998787i	$-0.484321\pi$
$359$	1.86576	0.0984713	0.0492356	+	0.998787i	$0.484321\pi$
$360$	1.72970	0.0911632
$361$	3.62354	0.190713
$362$	−1.90816	−0.100291
$363$	−5.28964	−0.277634
$364$	5.91681	0.310125
$365$	10.9222	0.571692
$366$	0.538720	0.0281594
$367$	−26.1488	−1.36495	−0.682477	−	0.730907i	$-0.739097\pi$
$367$	−26.1488	−1.36495	−0.682477	+	0.730907i	$0.739097\pi$
$368$	−2.79484	−0.145691
$369$	4.58736	0.238808
$370$	2.12831	0.110646
$371$	12.2192	0.634389
$372$	10.2225	0.530013
$373$	18.0116	0.932606	0.466303	−	0.884625i	$-0.345586\pi$
$373$	18.0116	0.932606	0.466303	+	0.884625i	$0.345586\pi$
$374$	−3.41193	−0.176427
$375$	1.00000	0.0516398
$376$	−1.08978	−0.0562012
$377$	12.3657	0.636866
$378$	−0.456154	−0.0234620
$379$	−17.6738	−0.907842	−0.453921	−	0.891042i	$-0.649975\pi$
$379$	−17.6738	−0.907842	−0.453921	+	0.891042i	$0.649975\pi$
$380$	−8.52314	−0.437228
$381$	−14.0266	−0.718602
$382$	0.119314	0.00610462
$383$	18.2953	0.934848	0.467424	−	0.884033i	$-0.345182\pi$
$383$	18.2953	0.934848	0.467424	+	0.884033i	$0.345182\pi$
$384$	11.0332	0.563036
$385$	4.03604	0.205696
$386$	8.40160	0.427630
$387$	−10.9530	−0.556770
$388$	−28.3931	−1.44144
$389$	7.03157	0.356515	0.178257	−	0.983984i	$-0.442954\pi$
$389$	7.03157	0.356515	0.178257	+	0.983984i	$0.442954\pi$
$390$	−1.50619	−0.0762688
$391$	−1.85325	−0.0937226
$392$	−1.72970	−0.0873631
$393$	3.06186	0.154450
$394$	−1.03273	−0.0520284
$395$	−13.6786	−0.688245
$396$	7.23228	0.363436
$397$	−6.26306	−0.314334	−0.157167	−	0.987572i	$-0.550236\pi$
$397$	−6.26306	−0.314334	−0.157167	+	0.987572i	$0.550236\pi$
$398$	4.11985	0.206510
$399$	4.75642	0.238119
$400$	2.79484	0.139742
$401$	27.7530	1.38592	0.692959	−	0.720977i	$-0.256307\pi$
$401$	27.7530	1.38592	0.692959	+	0.720977i	$0.256307\pi$
$402$	−4.95640	−0.247203
$403$	−18.8368	−0.938326
$404$	−16.6762	−0.829673
$405$	−1.00000	−0.0496904
$406$	−1.70829	−0.0847812
$407$	18.8313	0.933431
$408$	3.20556	0.158699
$409$	−18.1539	−0.897652	−0.448826	−	0.893619i	$-0.648158\pi$
$409$	−18.1539	−0.897652	−0.448826	+	0.893619i	$0.648158\pi$
$410$	−2.09254	−0.103343
$411$	−14.7943	−0.729747
$412$	27.3299	1.34645
$413$	−6.42601	−0.316204
$414$	−0.456154	−0.0224187
$415$	−9.93938	−0.487905
$416$	−15.6323	−0.766434
$417$	3.15768	0.154632
$418$	8.75684	0.428311
$419$	3.33207	0.162782	0.0813912	−	0.996682i	$-0.474064\pi$
$419$	3.33207	0.162782	0.0813912	+	0.996682i	$0.474064\pi$
$420$	−1.79192	−0.0874369
$421$	−8.41883	−0.410309	−0.205154	−	0.978730i	$-0.565770\pi$
$421$	−8.41883	−0.410309	−0.205154	+	0.978730i	$0.565770\pi$
$422$	6.13277	0.298538
$423$	0.630041	0.0306336
$424$	−21.1355	−1.02643
$425$	1.85325	0.0898956
$426$	−4.10105	−0.198697
$427$	−1.18101	−0.0571529
$428$	17.1814	0.830495
$429$	−13.3267	−0.643421
$430$	4.99623	0.240940
$431$	8.30618	0.400095	0.200047	−	0.979786i	$-0.435890\pi$
$431$	8.30618	0.400095	0.200047	+	0.979786i	$0.435890\pi$
$432$	−2.79484	−0.134467
$433$	16.7516	0.805032	0.402516	−	0.915413i	$-0.368136\pi$
$433$	16.7516	0.805032	0.402516	+	0.915413i	$0.368136\pi$
$434$	2.60225	0.124912
$435$	−3.74499	−0.179559
$436$	−14.0486	−0.672804
$437$	4.75642	0.227530
$438$	4.98219	0.238058
$439$	−36.6428	−1.74887	−0.874434	−	0.485145i	$-0.838767\pi$
$439$	−36.6428	−1.74887	−0.874434	+	0.485145i	$0.838767\pi$
$440$	−6.98115	−0.332813
$441$	1.00000	0.0476190
$442$	−2.79134	−0.132770
$443$	5.52048	0.262286	0.131143	−	0.991363i	$-0.458135\pi$
$443$	5.52048	0.262286	0.131143	+	0.991363i	$0.458135\pi$
$444$	−8.36071	−0.396782
$445$	−1.03425	−0.0490282
$446$	10.0798	0.477290
$447$	−3.50810	−0.165927
$448$	−3.43012	−0.162058
$449$	25.1414	1.18650	0.593249	−	0.805019i	$-0.297845\pi$
$449$	25.1414	1.18650	0.593249	+	0.805019i	$0.297845\pi$
$450$	0.456154	0.0215033
$451$	−18.5148	−0.871826
$452$	−24.8032	−1.16664
$453$	7.14508	0.335705
$454$	9.57716	0.449478
$455$	3.30193	0.154797
$456$	−8.22718	−0.385273
$457$	37.0985	1.73539	0.867697	−	0.497094i	$-0.165600\pi$
$457$	37.0985	1.73539	0.867697	+	0.497094i	$0.165600\pi$
$458$	8.31808	0.388679
$459$	−1.85325	−0.0865021
$460$	−1.79192	−0.0835489
$461$	−10.0586	−0.468476	−0.234238	−	0.972179i	$-0.575259\pi$
$461$	−10.0586	−0.468476	−0.234238	+	0.972179i	$0.575259\pi$
$462$	1.84106	0.0856537
$463$	−5.98695	−0.278237	−0.139119	−	0.990276i	$-0.544427\pi$
$463$	−5.98695	−0.278237	−0.139119	+	0.990276i	$0.544427\pi$
$464$	−10.4666	−0.485902
$465$	5.70477	0.264552
$466$	−3.90594	−0.180939
$467$	7.57978	0.350750	0.175375	−	0.984502i	$-0.443886\pi$
$467$	7.57978	0.350750	0.175375	+	0.984502i	$0.443886\pi$
$468$	5.91681	0.273504
$469$	10.8656	0.501728
$470$	−0.287396	−0.0132566
$471$	1.18846	0.0547614
$472$	11.1151	0.511613
$473$	44.2066	2.03262
$474$	−6.23954	−0.286592
$475$	−4.75642	−0.218240
$476$	−3.32087	−0.152212
$477$	12.2192	0.559478
$478$	2.98086	0.136341
$479$	−33.6736	−1.53859	−0.769294	−	0.638895i	$-0.779392\pi$
$479$	−33.6736	−1.53859	−0.769294	+	0.638895i	$0.779392\pi$
$480$	4.73428	0.216089
$481$	15.4061	0.702456
$482$	−6.89298	−0.313967
$483$	1.00000	0.0455016
$484$	−9.47863	−0.430847
$485$	−15.8451	−0.719487
$486$	−0.456154	−0.0206916
$487$	14.8370	0.672328	0.336164	−	0.941803i	$-0.390870\pi$
$487$	14.8370	0.672328	0.336164	+	0.941803i	$0.390870\pi$
$488$	2.04279	0.0924726
$489$	1.72815	0.0781498
$490$	−0.456154	−0.0206069
$491$	15.2914	0.690092	0.345046	−	0.938586i	$-0.387863\pi$
$491$	15.2914	0.690092	0.345046	+	0.938586i	$0.387863\pi$
$492$	8.22019	0.370595
$493$	−6.94039	−0.312579
$494$	7.16407	0.322327
$495$	4.03604	0.181407
$496$	15.9439	0.715903
$497$	8.99051	0.403279
$498$	−4.53389	−0.203168
$499$	31.2709	1.39988	0.699939	−	0.714203i	$-0.253211\pi$
$499$	31.2709	1.39988	0.699939	+	0.714203i	$0.253211\pi$
$500$	1.79192	0.0801373
$501$	−0.588212	−0.0262794
$502$	−11.9669	−0.534108
$503$	−30.4574	−1.35803	−0.679014	−	0.734125i	$-0.737593\pi$
$503$	−30.4574	−1.35803	−0.679014	+	0.734125i	$0.737593\pi$
$504$	−1.72970	−0.0770470
$505$	−9.30633	−0.414126
$506$	1.84106	0.0818449
$507$	2.09726	0.0931425
$508$	−25.1345	−1.11516
$509$	−7.53245	−0.333870	−0.166935	−	0.985968i	$-0.553387\pi$
$509$	−7.53245	−0.333870	−0.166935	+	0.985968i	$0.553387\pi$
$510$	0.845365	0.0374334
$511$	−10.9222	−0.483168
$512$	22.9000	1.01205
$513$	4.75642	0.210001
$514$	−3.66738	−0.161761
$515$	15.2517	0.672071
$516$	−19.6269	−0.864024
$517$	−2.54287	−0.111835
$518$	−2.12831	−0.0935126
$519$	−8.70232	−0.381990
$520$	−5.71135	−0.250459
$521$	−23.6985	−1.03825	−0.519125	−	0.854698i	$-0.673742\pi$
$521$	−23.6985	−1.03825	−0.519125	+	0.854698i	$0.673742\pi$
$522$	−1.70829	−0.0747700
$523$	24.3362	1.06415	0.532073	−	0.846698i	$-0.321413\pi$
$523$	24.3362	1.06415	0.532073	+	0.846698i	$0.321413\pi$
$524$	5.48662	0.239684
$525$	−1.00000	−0.0436436
$526$	−6.20912	−0.270731
$527$	10.5723	0.460538
$528$	11.2801	0.490903
$529$	1.00000	0.0434783
$530$	−5.57383	−0.242112
$531$	−6.42601	−0.278865
$532$	8.52314	0.369525
$533$	−15.1471	−0.656095
$534$	−0.471778	−0.0204158
$535$	9.58825	0.414536
$536$	−18.7943	−0.811789
$537$	−1.62759	−0.0702358
$538$	9.17843	0.395710
$539$	−4.03604	−0.173845
$540$	−1.79192	−0.0771121
$541$	−18.9218	−0.813510	−0.406755	−	0.913537i	$-0.633340\pi$
$541$	−18.9218	−0.813510	−0.406755	+	0.913537i	$0.633340\pi$
$542$	−12.0468	−0.517456
$543$	4.18315	0.179516
$544$	8.77378	0.376173
$545$	−7.83993	−0.335826
$546$	1.50619	0.0644589
$547$	30.3996	1.29979	0.649896	−	0.760024i	$-0.274813\pi$
$547$	30.3996	1.29979	0.649896	+	0.760024i	$0.274813\pi$
$548$	−26.5102	−1.13246
$549$	−1.18101	−0.0504041
$550$	−1.84106	−0.0785029
$551$	17.8128	0.758849
$552$	−1.72970	−0.0736209
$553$	13.6786	0.581673
$554$	−8.27878	−0.351732
$555$	−4.66577	−0.198051
$556$	5.65832	0.239966
$557$	42.7403	1.81096	0.905482	−	0.424385i	$-0.139510\pi$
$557$	42.7403	1.81096	0.905482	+	0.424385i	$0.139510\pi$
$558$	2.60225	0.110162
$559$	36.1659	1.52965
$560$	−2.79484	−0.118103
$561$	7.47978	0.315796
$562$	−10.9015	−0.459852
$563$	24.1193	1.01651	0.508254	−	0.861207i	$-0.330291\pi$
$563$	24.1193	1.01651	0.508254	+	0.861207i	$0.330291\pi$
$564$	1.12898	0.0475388
$565$	−13.8417	−0.582323
$566$	−5.23073	−0.219864
$567$	1.00000	0.0419961
$568$	−15.5509	−0.652501
$569$	−7.49344	−0.314141	−0.157071	−	0.987587i	$-0.550205\pi$
$569$	−7.49344	−0.314141	−0.157071	+	0.987587i	$0.550205\pi$
$570$	−2.16966	−0.0908771
$571$	−19.8749	−0.831739	−0.415870	−	0.909424i	$-0.636523\pi$
$571$	−19.8749	−0.831739	−0.415870	+	0.909424i	$0.636523\pi$
$572$	−23.8805	−0.998493
$573$	−0.261565	−0.0109270
$574$	2.09254	0.0873410
$575$	−1.00000	−0.0417029
$576$	−3.43012	−0.142922
$577$	10.1208	0.421334	0.210667	−	0.977558i	$-0.432436\pi$
$577$	10.1208	0.421334	0.210667	+	0.977558i	$0.432436\pi$
$578$	−6.18795	−0.257385
$579$	−18.4183	−0.765440
$580$	−6.71074	−0.278648
$581$	9.93938	0.412355
$582$	−7.22779	−0.299601
$583$	−49.3172	−2.04251
$584$	18.8921	0.781760
$585$	3.30193	0.136518
$586$	4.97049	0.205329
$587$	−23.2845	−0.961055	−0.480527	−	0.876980i	$-0.659555\pi$
$587$	−23.2845	−0.961055	−0.480527	+	0.876980i	$0.659555\pi$
$588$	1.79192	0.0738977
$589$	−27.1343	−1.11805
$590$	2.93125	0.120678
$591$	2.26400	0.0931287
$592$	−13.0401	−0.535944
$593$	17.9489	0.737075	0.368537	−	0.929613i	$-0.379859\pi$
$593$	17.9489	0.737075	0.368537	+	0.929613i	$0.379859\pi$
$594$	1.84106	0.0755395
$595$	−1.85325	−0.0759756
$596$	−6.28624	−0.257495
$597$	−9.03172	−0.369644
$598$	1.50619	0.0615926
$599$	40.2354	1.64397	0.821987	−	0.569507i	$-0.192866\pi$
$599$	40.2354	1.64397	0.821987	+	0.569507i	$0.192866\pi$
$600$	1.72970	0.0706147
$601$	30.4068	1.24032	0.620160	−	0.784476i	$-0.287068\pi$
$601$	30.4068	1.24032	0.620160	+	0.784476i	$0.287068\pi$
$602$	−4.99623	−0.203631
$603$	10.8656	0.442482
$604$	12.8034	0.520964
$605$	−5.28964	−0.215054
$606$	−4.24512	−0.172446
$607$	−46.0065	−1.86735	−0.933674	−	0.358125i	$-0.883416\pi$
$607$	−46.0065	−1.86735	−0.933674	+	0.358125i	$0.883416\pi$
$608$	−22.5182	−0.913234
$609$	3.74499	0.151755
$610$	0.538720	0.0218122
$611$	−2.08035	−0.0841620
$612$	−3.32087	−0.134238
$613$	1.69384	0.0684135	0.0342068	−	0.999415i	$-0.489110\pi$
$613$	1.69384	0.0684135	0.0342068	+	0.999415i	$0.489110\pi$
$614$	−8.85976	−0.357551
$615$	4.58736	0.184980
$616$	6.98115	0.281278
$617$	17.1129	0.688938	0.344469	−	0.938798i	$-0.388059\pi$
$617$	17.1129	0.688938	0.344469	+	0.938798i	$0.388059\pi$
$618$	6.95713	0.279857
$619$	−36.0133	−1.44750	−0.723749	−	0.690063i	$-0.757583\pi$
$619$	−36.0133	−1.44750	−0.723749	+	0.690063i	$0.757583\pi$
$620$	10.2225	0.410546
$621$	1.00000	0.0401286
$622$	3.01159	0.120754
$623$	1.03425	0.0414364
$624$	9.22836	0.369430
$625$	1.00000	0.0400000
$626$	−14.6676	−0.586236
$627$	−19.1971	−0.766659
$628$	2.12963	0.0849815
$629$	−8.64682	−0.344771
$630$	−0.456154	−0.0181736
$631$	27.5508	1.09678	0.548391	−	0.836222i	$-0.315241\pi$
$631$	27.5508	1.09678	0.548391	+	0.836222i	$0.315241\pi$
$632$	−23.6599	−0.941139
$633$	−13.4445	−0.534371
$634$	2.66083	0.105675
$635$	−14.0266	−0.556627
$636$	21.8959	0.868227
$637$	−3.30193	−0.130827
$638$	6.89474	0.272966
$639$	8.99051	0.355659
$640$	11.0332	0.436126
$641$	49.8312	1.96821	0.984106	−	0.177582i	$-0.0568274\pi$
$641$	49.8312	1.96821	0.984106	+	0.177582i	$0.0568274\pi$
$642$	4.37372	0.172617
$643$	−10.2120	−0.402721	−0.201361	−	0.979517i	$-0.564536\pi$
$643$	−10.2120	−0.402721	−0.201361	+	0.979517i	$0.564536\pi$
$644$	1.79192	0.0706117
$645$	−10.9530	−0.431272
$646$	−4.02091	−0.158201
$647$	21.8913	0.860634	0.430317	−	0.902678i	$-0.358402\pi$
$647$	21.8913	0.860634	0.430317	+	0.902678i	$0.358402\pi$
$648$	−1.72970	−0.0679491
$649$	25.9357	1.01806
$650$	−1.50619	−0.0590776
$651$	−5.70477	−0.223588
$652$	3.09672	0.121277
$653$	10.0027	0.391435	0.195718	−	0.980660i	$-0.437296\pi$
$653$	10.0027	0.391435	0.195718	+	0.980660i	$0.437296\pi$
$654$	−3.57622	−0.139841
$655$	3.06186	0.119637
$656$	12.8209	0.500573
$657$	−10.9222	−0.426114
$658$	0.287396	0.0112038
$659$	−44.2830	−1.72502	−0.862511	−	0.506038i	$-0.831110\pi$
$659$	−44.2830	−1.72502	−0.862511	+	0.506038i	$0.831110\pi$
$660$	7.23228	0.281516
$661$	−3.24459	−0.126200	−0.0630999	−	0.998007i	$-0.520099\pi$
$661$	−3.24459	−0.126200	−0.0630999	+	0.998007i	$0.520099\pi$
$662$	−5.65111	−0.219637
$663$	6.11929	0.237653
$664$	−17.1922	−0.667185
$665$	4.75642	0.184446
$666$	−2.12831	−0.0824704
$667$	3.74499	0.145007
$668$	−1.05403	−0.0407817
$669$	−22.0973	−0.854330
$670$	−4.95640	−0.191482
$671$	4.76659	0.184012
$672$	−4.73428	−0.182629
$673$	−10.0930	−0.389058	−0.194529	−	0.980897i	$-0.562318\pi$
$673$	−10.0930	−0.389058	−0.194529	+	0.980897i	$0.562318\pi$
$674$	5.85964	0.225705
$675$	−1.00000	−0.0384900
$676$	3.75813	0.144543
$677$	10.5971	0.407279	0.203639	−	0.979046i	$-0.434723\pi$
$677$	10.5971	0.407279	0.203639	+	0.979046i	$0.434723\pi$
$678$	−6.31392	−0.242485
$679$	15.8451	0.608078
$680$	3.20556	0.122928
$681$	−20.9955	−0.804548
$682$	−10.5028	−0.402173
$683$	43.3679	1.65942	0.829712	−	0.558191i	$-0.188504\pi$
$683$	43.3679	1.65942	0.829712	+	0.558191i	$0.188504\pi$
$684$	8.52314	0.325891
$685$	−14.7943	−0.565260
$686$	0.456154	0.0174160
$687$	−18.2353	−0.695719
$688$	−30.6117	−1.16706
$689$	−40.3469	−1.53709
$690$	−0.456154	−0.0173655
$691$	−21.0382	−0.800332	−0.400166	−	0.916443i	$-0.631048\pi$
$691$	−21.0382	−0.800332	−0.400166	+	0.916443i	$0.631048\pi$
$692$	−15.5939	−0.592791
$693$	−4.03604	−0.153317
$694$	14.1955	0.538854
$695$	3.15768	0.119778
$696$	−6.47772	−0.245537
$697$	8.50150	0.322017
$698$	−9.82701	−0.371958
$699$	8.56277	0.323874
$700$	−1.79192	−0.0677283
$701$	48.4565	1.83018	0.915088	−	0.403253i	$-0.132121\pi$
$701$	48.4565	1.83018	0.915088	+	0.403253i	$0.132121\pi$
$702$	1.50619	0.0568474
$703$	22.1924	0.837002
$704$	13.8441	0.521769
$705$	0.630041	0.0237287
$706$	1.54216	0.0580401
$707$	9.30633	0.350000
$708$	−11.5149	−0.432757
$709$	−0.721275	−0.0270881	−0.0135440	−	0.999908i	$-0.504311\pi$
$709$	−0.721275	−0.0270881	−0.0135440	+	0.999908i	$0.504311\pi$
$710$	−4.10105	−0.153910
$711$	13.6786	0.512987
$712$	−1.78894	−0.0670435
$713$	−5.70477	−0.213645
$714$	−0.845365	−0.0316370
$715$	−13.3267	−0.498391
$716$	−2.91652	−0.108995
$717$	−6.53477	−0.244045
$718$	0.851076	0.0317619
$719$	−14.3681	−0.535838	−0.267919	−	0.963441i	$-0.586336\pi$
$719$	−14.3681	−0.535838	−0.267919	+	0.963441i	$0.586336\pi$
$720$	−2.79484	−0.104157
$721$	−15.2517	−0.568004
$722$	1.65289	0.0615143
$723$	15.1111	0.561987
$724$	7.49588	0.278582
$725$	−3.74499	−0.139086
$726$	−2.41289	−0.0895507
$727$	8.09084	0.300073	0.150036	−	0.988680i	$-0.452061\pi$
$727$	8.09084	0.300073	0.150036	+	0.988680i	$0.452061\pi$
$728$	5.71135	0.211677
$729$	1.00000	0.0370370
$730$	4.98219	0.184399
$731$	−20.2985	−0.750767
$732$	−2.11627	−0.0782197
$733$	−0.476183	−0.0175882	−0.00879411	−	0.999961i	$-0.502799\pi$
$733$	−0.476183	−0.0175882	−0.00879411	+	0.999961i	$0.502799\pi$
$734$	−11.9279	−0.440265
$735$	1.00000	0.0368856
$736$	−4.73428	−0.174508
$737$	−43.8541	−1.61539
$738$	2.09254	0.0770275
$739$	23.5931	0.867887	0.433944	−	0.900940i	$-0.357122\pi$
$739$	23.5931	0.867887	0.433944	+	0.900940i	$0.357122\pi$
$740$	−8.36071	−0.307346
$741$	−15.7054	−0.576951
$742$	5.57383	0.204622
$743$	23.6806	0.868756	0.434378	−	0.900731i	$-0.356968\pi$
$743$	23.6806	0.868756	0.434378	+	0.900731i	$0.356968\pi$
$744$	9.86755	0.361762
$745$	−3.50810	−0.128527
$746$	8.21607	0.300812
$747$	9.93938	0.363663
$748$	13.4032	0.490069
$749$	−9.58825	−0.350347
$750$	0.456154	0.0166564
$751$	21.5906	0.787854	0.393927	−	0.919142i	$-0.371116\pi$
$751$	21.5906	0.787854	0.393927	+	0.919142i	$0.371116\pi$
$752$	1.76086	0.0642120
$753$	26.2343	0.956031
$754$	5.64067	0.205421
$755$	7.14508	0.260036
$756$	1.79192	0.0651716
$757$	21.8766	0.795118	0.397559	−	0.917577i	$-0.369857\pi$
$757$	21.8766	0.795118	0.397559	+	0.917577i	$0.369857\pi$
$758$	−8.06197	−0.292824
$759$	−4.03604	−0.146499
$760$	−8.22718	−0.298431
$761$	−9.79019	−0.354894	−0.177447	−	0.984130i	$-0.556784\pi$
$761$	−9.79019	−0.354894	−0.177447	+	0.984130i	$0.556784\pi$
$762$	−6.39827	−0.231785
$763$	7.83993	0.283825
$764$	−0.468704	−0.0169571
$765$	−1.85325	−0.0670042
$766$	8.34549	0.301535
$767$	21.2183	0.766147
$768$	−1.82739	−0.0659402
$769$	−17.0054	−0.613229	−0.306615	−	0.951834i	$-0.599196\pi$
$769$	−17.0054	−0.613229	−0.306615	+	0.951834i	$0.599196\pi$
$770$	1.84106	0.0663471
$771$	8.03978	0.289546
$772$	−33.0043	−1.18785
$773$	40.4234	1.45393	0.726965	−	0.686674i	$-0.240930\pi$
$773$	40.4234	1.45393	0.726965	+	0.686674i	$0.240930\pi$
$774$	−4.99623	−0.179586
$775$	5.70477	0.204921
$776$	−27.4072	−0.983862
$777$	4.66577	0.167384
$778$	3.20748	0.114994
$779$	−21.8194	−0.781761
$780$	5.91681	0.211856
$781$	−36.2861	−1.29842
$782$	−0.845365	−0.0302302
$783$	3.74499	0.133835
$784$	2.79484	0.0998156
$785$	1.18846	0.0424180
$786$	1.39668	0.0498179
$787$	42.9017	1.52928	0.764640	−	0.644457i	$-0.222917\pi$
$787$	42.9017	1.52928	0.764640	+	0.644457i	$0.222917\pi$
$788$	4.05692	0.144522
$789$	13.6119	0.484597
$790$	−6.23954	−0.221993
$791$	13.8417	0.492153
$792$	6.98115	0.248064
$793$	3.89960	0.138479
$794$	−2.85692	−0.101388
$795$	12.2192	0.433370
$796$	−16.1842	−0.573632
$797$	50.0032	1.77120	0.885602	−	0.464445i	$-0.153746\pi$
$797$	50.0032	1.77120	0.885602	+	0.464445i	$0.153746\pi$
$798$	2.16966	0.0768051
$799$	1.16762	0.0413074
$800$	4.73428	0.167382
$801$	1.03425	0.0365435
$802$	12.6596	0.447027
$803$	44.0823	1.55563
$804$	19.4704	0.686667
$805$	1.00000	0.0352454
$806$	−8.59246	−0.302656
$807$	−20.1213	−0.708305
$808$	−16.0972	−0.566296
$809$	−32.7931	−1.15294	−0.576472	−	0.817117i	$-0.695571\pi$
$809$	−32.7931	−1.15294	−0.576472	+	0.817117i	$0.695571\pi$
$810$	−0.456154	−0.0160276
$811$	34.6457	1.21657	0.608287	−	0.793717i	$-0.291857\pi$
$811$	34.6457	1.21657	0.608287	+	0.793717i	$0.291857\pi$
$812$	6.71074	0.235501
$813$	26.4096	0.926224
$814$	8.58995	0.301078
$815$	1.72815	0.0605346
$816$	−5.17952	−0.181319
$817$	52.0969	1.82264
$818$	−8.28097	−0.289537
$819$	−3.30193	−0.115379
$820$	8.22019	0.287062
$821$	−23.7751	−0.829755	−0.414878	−	0.909877i	$-0.636176\pi$
$821$	−23.7751	−0.829755	−0.414878	+	0.909877i	$0.636176\pi$
$822$	−6.74846	−0.235380
$823$	32.2641	1.12465	0.562327	−	0.826915i	$-0.309906\pi$
$823$	32.2641	1.12465	0.562327	+	0.826915i	$0.309906\pi$
$824$	26.3809	0.919023
$825$	4.03604	0.140517
$826$	−2.93125	−0.101991
$827$	−15.0607	−0.523712	−0.261856	−	0.965107i	$-0.584335\pi$
$827$	−15.0607	−0.523712	−0.261856	+	0.965107i	$0.584335\pi$
$828$	1.79192	0.0622737
$829$	−36.6634	−1.27337	−0.636687	−	0.771122i	$-0.719696\pi$
$829$	−36.6634	−1.27337	−0.636687	+	0.771122i	$0.719696\pi$
$830$	−4.53389	−0.157374
$831$	18.1491	0.629585
$832$	11.3260	0.392659
$833$	1.85325	0.0642111
$834$	1.44039	0.0498765
$835$	−0.588212	−0.0203559
$836$	−34.3998	−1.18974
$837$	−5.70477	−0.197186
$838$	1.51994	0.0525054
$839$	33.9205	1.17107	0.585533	−	0.810648i	$-0.300885\pi$
$839$	33.9205	1.17107	0.585533	+	0.810648i	$0.300885\pi$
$840$	−1.72970	−0.0596803
$841$	−14.9750	−0.516380
$842$	−3.84028	−0.132345
$843$	23.8987	0.823116
$844$	−24.0915	−0.829265
$845$	2.09726	0.0721479
$846$	0.287396	0.00988086
$847$	5.28964	0.181754
$848$	34.1507	1.17274
$849$	11.4670	0.393548
$850$	0.845365	0.0289958
$851$	4.66577	0.159941
$852$	16.1103	0.551930
$853$	6.98538	0.239175	0.119587	−	0.992824i	$-0.461843\pi$
$853$	6.98538	0.239175	0.119587	+	0.992824i	$0.461843\pi$
$854$	−0.538720	−0.0184346
$855$	4.75642	0.162666
$856$	16.5848	0.566857
$857$	3.55659	0.121491	0.0607453	−	0.998153i	$-0.480652\pi$
$857$	3.55659	0.121491	0.0607453	+	0.998153i	$0.480652\pi$
$858$	−6.07904	−0.207535
$859$	−21.1660	−0.722174	−0.361087	−	0.932532i	$-0.617594\pi$
$859$	−21.1660	−0.722174	−0.361087	+	0.932532i	$0.617594\pi$
$860$	−19.6269	−0.669270
$861$	−4.58736	−0.156337
$862$	3.78890	0.129050
$863$	−46.5076	−1.58314	−0.791568	−	0.611081i	$-0.790735\pi$
$863$	−46.5076	−1.58314	−0.791568	+	0.611081i	$0.790735\pi$
$864$	−4.73428	−0.161063
$865$	−8.70232	−0.295888
$866$	7.64132	0.259663
$867$	13.5655	0.460708
$868$	−10.2225	−0.346975
$869$	−55.2074	−1.87278
$870$	−1.70829	−0.0579166
$871$	−35.8775	−1.21566
$872$	−13.5607	−0.459225
$873$	15.8451	0.536274
$874$	2.16966	0.0733898
$875$	−1.00000	−0.0338062
$876$	−19.5717	−0.661266
$877$	32.7415	1.10560	0.552801	−	0.833313i	$-0.313559\pi$
$877$	32.7415	1.10560	0.552801	+	0.833313i	$0.313559\pi$
$878$	−16.7148	−0.564096
$879$	−10.8965	−0.367530
$880$	11.2801	0.380252
$881$	−48.4254	−1.63149	−0.815746	−	0.578410i	$-0.803674\pi$
$881$	−48.4254	−1.63149	−0.815746	+	0.578410i	$0.803674\pi$
$882$	0.456154	0.0153595
$883$	−7.36524	−0.247860	−0.123930	−	0.992291i	$-0.539550\pi$
$883$	−7.36524	−0.247860	−0.123930	+	0.992291i	$0.539550\pi$
$884$	10.9653	0.368803
$885$	−6.42601	−0.216008
$886$	2.51819	0.0846002
$887$	−49.1015	−1.64867	−0.824333	−	0.566105i	$-0.808450\pi$
$887$	−49.1015	−1.64867	−0.824333	+	0.566105i	$0.808450\pi$
$888$	−8.07039	−0.270825
$889$	14.0266	0.470436
$890$	−0.471778	−0.0158140
$891$	−4.03604	−0.135213
$892$	−39.5966	−1.32579
$893$	−2.99674	−0.100282
$894$	−1.60023	−0.0535198
$895$	−1.62759	−0.0544044
$896$	−11.0332	−0.368594
$897$	−3.30193	−0.110248
$898$	11.4684	0.382704
$899$	−21.3643	−0.712540
$900$	−1.79192	−0.0597308
$901$	22.6452	0.754419
$902$	−8.44558	−0.281207
$903$	10.9530	0.364491
$904$	−23.9419	−0.796296
$905$	4.18315	0.139053
$906$	3.25925	0.108281
$907$	−44.6761	−1.48344	−0.741722	−	0.670707i	$-0.765991\pi$
$907$	−44.6761	−1.48344	−0.741722	+	0.670707i	$0.765991\pi$
$908$	−37.6223	−1.24854
$909$	9.30633	0.308671
$910$	1.50619	0.0499297
$911$	−23.7633	−0.787315	−0.393657	−	0.919257i	$-0.628790\pi$
$911$	−23.7633	−0.787315	−0.393657	+	0.919257i	$0.628790\pi$
$912$	13.2934	0.440189
$913$	−40.1158	−1.32764
$914$	16.9226	0.559750
$915$	−1.18101	−0.0390429
$916$	−32.6762	−1.07965
$917$	−3.06186	−0.101112
$918$	−0.845365	−0.0279012
$919$	−33.7668	−1.11386	−0.556932	−	0.830558i	$-0.688022\pi$
$919$	−33.7668	−1.11386	−0.556932	+	0.830558i	$0.688022\pi$
$920$	−1.72970	−0.0570265
$921$	19.4228	0.640001
$922$	−4.58827	−0.151107
$923$	−29.6860	−0.977127
$924$	−7.23228	−0.237925
$925$	−4.66577	−0.153410
$926$	−2.73097	−0.0897453
$927$	−15.2517	−0.500932
$928$	−17.7298	−0.582010
$929$	19.3401	0.634529	0.317264	−	0.948337i	$-0.397236\pi$
$929$	19.3401	0.634529	0.317264	+	0.948337i	$0.397236\pi$
$930$	2.60225	0.0853313
$931$	−4.75642	−0.155885
$932$	15.3438	0.502604
$933$	−6.60214	−0.216144
$934$	3.45755	0.113134
$935$	7.47978	0.244615
$936$	5.71135	0.186681
$937$	39.3742	1.28630	0.643150	−	0.765740i	$-0.277627\pi$
$937$	39.3742	1.28630	0.643150	+	0.765740i	$0.277627\pi$
$938$	4.95640	0.161832
$939$	32.1550	1.04934
$940$	1.12898	0.0368234
$941$	1.40898	0.0459313	0.0229656	−	0.999736i	$-0.492689\pi$
$941$	1.40898	0.0459313	0.0229656	+	0.999736i	$0.492689\pi$
$942$	0.542121	0.0176633
$943$	−4.58736	−0.149385
$944$	−17.9597	−0.584537
$945$	1.00000	0.0325300
$946$	20.1650	0.655621
$947$	34.3246	1.11540	0.557699	−	0.830043i	$-0.311684\pi$
$947$	34.3246	1.11540	0.557699	+	0.830043i	$0.311684\pi$
$948$	24.5110	0.796080
$949$	36.0642	1.17069
$950$	−2.16966	−0.0703931
$951$	−5.83318	−0.189154
$952$	−3.20556	−0.103893
$953$	−29.5790	−0.958157	−0.479079	−	0.877772i	$-0.659029\pi$
$953$	−29.5790	−0.958157	−0.479079	+	0.877772i	$0.659029\pi$
$954$	5.57383	0.180459
$955$	−0.261565	−0.00846403
$956$	−11.7098	−0.378722
$957$	−15.1150	−0.488597
$958$	−15.3604	−0.496271
$959$	14.7943	0.477732
$960$	−3.43012	−0.110707
$961$	1.54442	0.0498199
$962$	7.02754	0.226577
$963$	−9.58825	−0.308977
$964$	27.0779	0.872121
$965$	−18.4183	−0.592907
$966$	0.456154	0.0146765
$967$	−13.9804	−0.449581	−0.224790	−	0.974407i	$-0.572170\pi$
$967$	−13.9804	−0.449581	−0.224790	+	0.974407i	$0.572170\pi$
$968$	−9.14949	−0.294076
$969$	8.81481	0.283173
$970$	−7.22779	−0.232070
$971$	28.0005	0.898578	0.449289	−	0.893387i	$-0.351677\pi$
$971$	28.0005	0.898578	0.449289	+	0.893387i	$0.351677\pi$
$972$	1.79192	0.0574760
$973$	−3.15768	−0.101231
$974$	6.76795	0.216859
$975$	3.30193	0.105746
$976$	−3.30072	−0.105653
$977$	7.62176	0.243842	0.121921	−	0.992540i	$-0.461095\pi$
$977$	7.62176	0.243842	0.121921	+	0.992540i	$0.461095\pi$
$978$	0.788304	0.0252072
$979$	−4.17428	−0.133411
$980$	1.79192	0.0572409
$981$	7.83993	0.250310
$982$	6.97524	0.222589
$983$	−3.97645	−0.126829	−0.0634145	−	0.997987i	$-0.520199\pi$
$983$	−3.97645	−0.126829	−0.0634145	+	0.997987i	$0.520199\pi$
$984$	7.93476	0.252951
$985$	2.26400	0.0721372
$986$	−3.16589	−0.100822
$987$	−0.630041	−0.0200544
$988$	−28.1428	−0.895343
$989$	10.9530	0.348284
$990$	1.84106	0.0585126
$991$	32.1935	1.02266	0.511331	−	0.859384i	$-0.329153\pi$
$991$	32.1935	1.02266	0.511331	+	0.859384i	$0.329153\pi$
$992$	27.0080	0.857504
$993$	12.3886	0.393140
$994$	4.10105	0.130078
$995$	−9.03172	−0.286325
$996$	17.8106	0.564351
$997$	50.0847	1.58620	0.793098	−	0.609093i	$-0.208467\pi$
$997$	50.0847	1.58620	0.793098	+	0.609093i	$0.208467\pi$
$998$	14.2643	0.451530
$999$	4.66577	0.147619

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2415.2.a.q.1.3	✓	6
3.2	odd	2		7245.2.a.bj.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2415.2.a.q.1.3	✓	6	1.1	even	1	trivial
7245.2.a.bj.1.4		6	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:	\( N \)	\(=\)	\( 2415 = 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2415.a (trivial)

\(f(q)\)	\(=\)	\(q+0.456154 q^{2} -1.00000 q^{3} -1.79192 q^{4} -1.00000 q^{5} -0.456154 q^{6} +1.00000 q^{7} -1.72970 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.456154 q^{2} -1.00000 q^{3} -1.79192 q^{4} -1.00000 q^{5} -0.456154 q^{6} +1.00000 q^{7} -1.72970 q^{8} +1.00000 q^{9} -0.456154 q^{10} -4.03604 q^{11} +1.79192 q^{12} -3.30193 q^{13} +0.456154 q^{14} +1.00000 q^{15} +2.79484 q^{16} +1.85325 q^{17} +0.456154 q^{18} -4.75642 q^{19} +1.79192 q^{20} -1.00000 q^{21} -1.84106 q^{22} -1.00000 q^{23} +1.72970 q^{24} +1.00000 q^{25} -1.50619 q^{26} -1.00000 q^{27} -1.79192 q^{28} -3.74499 q^{29} +0.456154 q^{30} +5.70477 q^{31} +4.73428 q^{32} +4.03604 q^{33} +0.845365 q^{34} -1.00000 q^{35} -1.79192 q^{36} -4.66577 q^{37} -2.16966 q^{38} +3.30193 q^{39} +1.72970 q^{40} +4.58736 q^{41} -0.456154 q^{42} -10.9530 q^{43} +7.23228 q^{44} -1.00000 q^{45} -0.456154 q^{46} +0.630041 q^{47} -2.79484 q^{48} +1.00000 q^{49} +0.456154 q^{50} -1.85325 q^{51} +5.91681 q^{52} +12.2192 q^{53} -0.456154 q^{54} +4.03604 q^{55} -1.72970 q^{56} +4.75642 q^{57} -1.70829 q^{58} -6.42601 q^{59} -1.79192 q^{60} -1.18101 q^{61} +2.60225 q^{62} +1.00000 q^{63} -3.43012 q^{64} +3.30193 q^{65} +1.84106 q^{66} +10.8656 q^{67} -3.32087 q^{68} +1.00000 q^{69} -0.456154 q^{70} +8.99051 q^{71} -1.72970 q^{72} -10.9222 q^{73} -2.12831 q^{74} -1.00000 q^{75} +8.52314 q^{76} -4.03604 q^{77} +1.50619 q^{78} +13.6786 q^{79} -2.79484 q^{80} +1.00000 q^{81} +2.09254 q^{82} +9.93938 q^{83} +1.79192 q^{84} -1.85325 q^{85} -4.99623 q^{86} +3.74499 q^{87} +6.98115 q^{88} +1.03425 q^{89} -0.456154 q^{90} -3.30193 q^{91} +1.79192 q^{92} -5.70477 q^{93} +0.287396 q^{94} +4.75642 q^{95} -4.73428 q^{96} +15.8451 q^{97} +0.456154 q^{98} -4.03604 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 6 q^{3} + 5 q^{4} - 6 q^{5} - 3 q^{6} + 6 q^{7} + 9 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 6 * q^3 + 5 * q^4 - 6 * q^5 - 3 * q^6 + 6 * q^7 + 9 * q^8 + 6 * q^9	\( 6 q + 3 q^{2} - 6 q^{3} + 5 q^{4} - 6 q^{5} - 3 q^{6} + 6 q^{7} + 9 q^{8} + 6 q^{9} - 3 q^{10} + 6 q^{11} - 5 q^{12} - 6 q^{13} + 3 q^{14} + 6 q^{15} + 11 q^{16} + 8 q^{17} + 3 q^{18} - 8 q^{19} - 5 q^{20} - 6 q^{21} + 18 q^{22} - 6 q^{23} - 9 q^{24} + 6 q^{25} + 13 q^{26} - 6 q^{27} + 5 q^{28} + 8 q^{29} + 3 q^{30} - 16 q^{31} + 26 q^{32} - 6 q^{33} - 13 q^{34} - 6 q^{35} + 5 q^{36} + 8 q^{37} - 14 q^{38} + 6 q^{39} - 9 q^{40} + 8 q^{41} - 3 q^{42} + 8 q^{43} + 15 q^{44} - 6 q^{45} - 3 q^{46} + 10 q^{47} - 11 q^{48} + 6 q^{49} + 3 q^{50} - 8 q^{51} + 28 q^{53} - 3 q^{54} - 6 q^{55} + 9 q^{56} + 8 q^{57} + 14 q^{58} - 6 q^{59} + 5 q^{60} - 12 q^{61} + 18 q^{62} + 6 q^{63} + 15 q^{64} + 6 q^{65} - 18 q^{66} + 18 q^{67} + 18 q^{68} + 6 q^{69} - 3 q^{70} + 10 q^{71} + 9 q^{72} - 2 q^{73} + q^{74} - 6 q^{75} + 25 q^{76} + 6 q^{77} - 13 q^{78} - 2 q^{79} - 11 q^{80} + 6 q^{81} - 12 q^{82} + 26 q^{83} - 5 q^{84} - 8 q^{85} + 16 q^{86} - 8 q^{87} + 21 q^{88} + 8 q^{89} - 3 q^{90} - 6 q^{91} - 5 q^{92} + 16 q^{93} - 8 q^{94} + 8 q^{95} - 26 q^{96} + 20 q^{97} + 3 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 6 * q^3 + 5 * q^4 - 6 * q^5 - 3 * q^6 + 6 * q^7 + 9 * q^8 + 6 * q^9 - 3 * q^10 + 6 * q^11 - 5 * q^12 - 6 * q^13 + 3 * q^14 + 6 * q^15 + 11 * q^16 + 8 * q^17 + 3 * q^18 - 8 * q^19 - 5 * q^20 - 6 * q^21 + 18 * q^22 - 6 * q^23 - 9 * q^24 + 6 * q^25 + 13 * q^26 - 6 * q^27 + 5 * q^28 + 8 * q^29 + 3 * q^30 - 16 * q^31 + 26 * q^32 - 6 * q^33 - 13 * q^34 - 6 * q^35 + 5 * q^36 + 8 * q^37 - 14 * q^38 + 6 * q^39 - 9 * q^40 + 8 * q^41 - 3 * q^42 + 8 * q^43 + 15 * q^44 - 6 * q^45 - 3 * q^46 + 10 * q^47 - 11 * q^48 + 6 * q^49 + 3 * q^50 - 8 * q^51 + 28 * q^53 - 3 * q^54 - 6 * q^55 + 9 * q^56 + 8 * q^57 + 14 * q^58 - 6 * q^59 + 5 * q^60 - 12 * q^61 + 18 * q^62 + 6 * q^63 + 15 * q^64 + 6 * q^65 - 18 * q^66 + 18 * q^67 + 18 * q^68 + 6 * q^69 - 3 * q^70 + 10 * q^71 + 9 * q^72 - 2 * q^73 + q^74 - 6 * q^75 + 25 * q^76 + 6 * q^77 - 13 * q^78 - 2 * q^79 - 11 * q^80 + 6 * q^81 - 12 * q^82 + 26 * q^83 - 5 * q^84 - 8 * q^85 + 16 * q^86 - 8 * q^87 + 21 * q^88 + 8 * q^89 - 3 * q^90 - 6 * q^91 - 5 * q^92 + 16 * q^93 - 8 * q^94 + 8 * q^95 - 26 * q^96 + 20 * q^97 + 3 * q^98 + 6 * q^99

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