LMFDB - Embedded newform 2415.2.a.q.1.6

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			1.6
Root			$2.27955$ 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)

$f(q)$	$=$	$q+2.72718 q^{2} -1.00000 q^{3} +5.43751 q^{4} -1.00000 q^{5} -2.72718 q^{6} +1.00000 q^{7} +9.37471 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.72718 q^{2} -1.00000 q^{3} +5.43751 q^{4} -1.00000 q^{5} -2.72718 q^{6} +1.00000 q^{7} +9.37471 q^{8} +1.00000 q^{9} -2.72718 q^{10} +2.45553 q^{11} -5.43751 q^{12} -0.635562 q^{13} +2.72718 q^{14} +1.00000 q^{15} +14.6915 q^{16} -0.765589 q^{17} +2.72718 q^{18} +4.19990 q^{19} -5.43751 q^{20} -1.00000 q^{21} +6.69668 q^{22} -1.00000 q^{23} -9.37471 q^{24} +1.00000 q^{25} -1.73329 q^{26} -1.00000 q^{27} +5.43751 q^{28} +1.83362 q^{29} +2.72718 q^{30} -5.20108 q^{31} +21.3169 q^{32} -2.45553 q^{33} -2.08790 q^{34} -1.00000 q^{35} +5.43751 q^{36} -6.88688 q^{37} +11.4539 q^{38} +0.635562 q^{39} -9.37471 q^{40} -1.85668 q^{41} -2.72718 q^{42} +3.23657 q^{43} +13.3520 q^{44} -1.00000 q^{45} -2.72718 q^{46} +5.66386 q^{47} -14.6915 q^{48} +1.00000 q^{49} +2.72718 q^{50} +0.765589 q^{51} -3.45588 q^{52} +13.1556 q^{53} -2.72718 q^{54} -2.45553 q^{55} +9.37471 q^{56} -4.19990 q^{57} +5.00062 q^{58} -4.02676 q^{59} +5.43751 q^{60} +5.03838 q^{61} -14.1843 q^{62} +1.00000 q^{63} +28.7522 q^{64} +0.635562 q^{65} -6.69668 q^{66} +8.70100 q^{67} -4.16290 q^{68} +1.00000 q^{69} -2.72718 q^{70} -9.37188 q^{71} +9.37471 q^{72} +1.39390 q^{73} -18.7818 q^{74} -1.00000 q^{75} +22.8370 q^{76} +2.45553 q^{77} +1.73329 q^{78} -7.59381 q^{79} -14.6915 q^{80} +1.00000 q^{81} -5.06351 q^{82} +17.5182 q^{83} -5.43751 q^{84} +0.765589 q^{85} +8.82670 q^{86} -1.83362 q^{87} +23.0199 q^{88} -7.80397 q^{89} -2.72718 q^{90} -0.635562 q^{91} -5.43751 q^{92} +5.20108 q^{93} +15.4464 q^{94} -4.19990 q^{95} -21.3169 q^{96} +6.17860 q^{97} +2.72718 q^{98} +2.45553 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.72718	1.92841	0.964204	−	0.265163i	$-0.0854256\pi$
$2$	2.72718	1.92841	0.964204	+	0.265163i	$0.0854256\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.43751	2.71876
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.72718	−1.11337
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	9.37471	3.31446
$9$	1.00000	0.333333
$10$	−2.72718	−0.862410
$11$	2.45553	0.740371	0.370185	−	0.928958i	$-0.379294\pi$
$11$	2.45553	0.740371	0.370185	+	0.928958i	$0.379294\pi$
$12$	−5.43751	−1.56967
$13$	−0.635562	−0.176273	−0.0881366	−	0.996108i	$-0.528091\pi$
$13$	−0.635562	−0.176273	−0.0881366	+	0.996108i	$0.528091\pi$
$14$	2.72718	0.728870
$15$	1.00000	0.258199
$16$	14.6915	3.67288
$17$	−0.765589	−0.185683	−0.0928413	−	0.995681i	$-0.529595\pi$
$17$	−0.765589	−0.185683	−0.0928413	+	0.995681i	$0.529595\pi$
$18$	2.72718	0.642802
$19$	4.19990	0.963524	0.481762	−	0.876302i	$-0.339997\pi$
$19$	4.19990	0.963524	0.481762	+	0.876302i	$0.339997\pi$
$20$	−5.43751	−1.21586
$21$	−1.00000	−0.218218
$22$	6.69668	1.42774
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−9.37471	−1.91360
$25$	1.00000	0.200000
$26$	−1.73329	−0.339927
$27$	−1.00000	−0.192450
$28$	5.43751	1.02759
$29$	1.83362	0.340495	0.170248	−	0.985401i	$-0.445543\pi$
$29$	1.83362	0.340495	0.170248	+	0.985401i	$0.445543\pi$
$30$	2.72718	0.497913
$31$	−5.20108	−0.934141	−0.467070	−	0.884220i	$-0.654691\pi$
$31$	−5.20108	−0.934141	−0.467070	+	0.884220i	$0.654691\pi$
$32$	21.3169	3.76834
$33$	−2.45553	−0.427453
$34$	−2.08790	−0.358072
$35$	−1.00000	−0.169031
$36$	5.43751	0.906252
$37$	−6.88688	−1.13220	−0.566098	−	0.824338i	$-0.691548\pi$
$37$	−6.88688	−1.13220	−0.566098	+	0.824338i	$0.691548\pi$
$38$	11.4539	1.85807
$39$	0.635562	0.101771
$40$	−9.37471	−1.48227
$41$	−1.85668	−0.289965	−0.144983	−	0.989434i	$-0.546313\pi$
$41$	−1.85668	−0.289965	−0.144983	+	0.989434i	$0.546313\pi$
$42$	−2.72718	−0.420813
$43$	3.23657	0.493572	0.246786	−	0.969070i	$-0.420626\pi$
$43$	3.23657	0.493572	0.246786	+	0.969070i	$0.420626\pi$
$44$	13.3520	2.01289
$45$	−1.00000	−0.149071
$46$	−2.72718	−0.402101
$47$	5.66386	0.826158	0.413079	−	0.910695i	$-0.364453\pi$
$47$	5.66386	0.826158	0.413079	+	0.910695i	$0.364453\pi$
$48$	−14.6915	−2.12054
$49$	1.00000	0.142857
$50$	2.72718	0.385681
$51$	0.765589	0.107204
$52$	−3.45588	−0.479244
$53$	13.1556	1.80706	0.903531	−	0.428522i	$-0.140966\pi$
$53$	13.1556	1.80706	0.903531	+	0.428522i	$0.140966\pi$
$54$	−2.72718	−0.371122
$55$	−2.45553	−0.331104
$56$	9.37471	1.25275
$57$	−4.19990	−0.556291
$58$	5.00062	0.656614
$59$	−4.02676	−0.524239	−0.262120	−	0.965035i	$-0.584422\pi$
$59$	−4.02676	−0.524239	−0.262120	+	0.965035i	$0.584422\pi$
$60$	5.43751	0.701980
$61$	5.03838	0.645099	0.322549	−	0.946553i	$-0.395460\pi$
$61$	5.03838	0.645099	0.322549	+	0.946553i	$0.395460\pi$
$62$	−14.1843	−1.80140
$63$	1.00000	0.125988
$64$	28.7522	3.59402
$65$	0.635562	0.0788318
$66$	−6.69668	−0.824304
$67$	8.70100	1.06300	0.531498	−	0.847060i	$-0.321629\pi$
$67$	8.70100	1.06300	0.531498	+	0.847060i	$0.321629\pi$
$68$	−4.16290	−0.504825
$69$	1.00000	0.120386
$70$	−2.72718	−0.325960
$71$	−9.37188	−1.11224	−0.556119	−	0.831103i	$-0.687710\pi$
$71$	−9.37188	−1.11224	−0.556119	+	0.831103i	$0.687710\pi$
$72$	9.37471	1.10482
$73$	1.39390	0.163144	0.0815720	−	0.996667i	$-0.474006\pi$
$73$	1.39390	0.163144	0.0815720	+	0.996667i	$0.474006\pi$
$74$	−18.7818	−2.18334
$75$	−1.00000	−0.115470
$76$	22.8370	2.61959
$77$	2.45553	0.279834
$78$	1.73329	0.196257
$79$	−7.59381	−0.854370	−0.427185	−	0.904164i	$-0.640495\pi$
$79$	−7.59381	−0.854370	−0.427185	+	0.904164i	$0.640495\pi$
$80$	−14.6915	−1.64256
$81$	1.00000	0.111111
$82$	−5.06351	−0.559171
$83$	17.5182	1.92287	0.961436	−	0.275029i	$-0.0886876\pi$
$83$	17.5182	1.92287	0.961436	+	0.275029i	$0.0886876\pi$
$84$	−5.43751	−0.593281
$85$	0.765589	0.0830398
$86$	8.82670	0.951808
$87$	−1.83362	−0.196585
$88$	23.0199	2.45393
$89$	−7.80397	−0.827219	−0.413610	−	0.910454i	$-0.635732\pi$
$89$	−7.80397	−0.827219	−0.413610	+	0.910454i	$0.635732\pi$
$90$	−2.72718	−0.287470
$91$	−0.635562	−0.0666250
$92$	−5.43751	−0.566900
$93$	5.20108	0.539326
$94$	15.4464	1.59317
$95$	−4.19990	−0.430901
$96$	−21.3169	−2.17565
$97$	6.17860	0.627342	0.313671	−	0.949532i	$-0.398441\pi$
$97$	6.17860	0.627342	0.313671	+	0.949532i	$0.398441\pi$
$98$	2.72718	0.275487
$99$	2.45553	0.246790
$100$	5.43751	0.543751
$101$	−8.94951	−0.890510	−0.445255	−	0.895404i	$-0.646887\pi$
$101$	−8.94951	−0.890510	−0.445255	+	0.895404i	$0.646887\pi$
$102$	2.08790	0.206733
$103$	−1.68174	−0.165707	−0.0828535	−	0.996562i	$-0.526403\pi$
$103$	−1.68174	−0.165707	−0.0828535	+	0.996562i	$0.526403\pi$
$104$	−5.95821	−0.584251
$105$	1.00000	0.0975900
$106$	35.8777	3.48475
$107$	4.18558	0.404635	0.202318	−	0.979320i	$-0.435153\pi$
$107$	4.18558	0.404635	0.202318	+	0.979320i	$0.435153\pi$
$108$	−5.43751	−0.523225
$109$	−17.4772	−1.67402	−0.837008	−	0.547190i	$-0.815697\pi$
$109$	−17.4772	−1.67402	−0.837008	+	0.547190i	$0.815697\pi$
$110$	−6.69668	−0.638503
$111$	6.88688	0.653674
$112$	14.6915	1.38822
$113$	−5.80735	−0.546310	−0.273155	−	0.961970i	$-0.588067\pi$
$113$	−5.80735	−0.546310	−0.273155	+	0.961970i	$0.588067\pi$
$114$	−11.4539	−1.07276
$115$	1.00000	0.0932505
$116$	9.97035	0.925724
$117$	−0.635562	−0.0587577
$118$	−10.9817	−1.01095
$119$	−0.765589	−0.0701814
$120$	9.37471	0.855790
$121$	−4.97036	−0.451851
$122$	13.7406	1.24401
$123$	1.85668	0.167411
$124$	−28.2809	−2.53970
$125$	−1.00000	−0.0894427
$126$	2.72718	0.242957
$127$	−14.6453	−1.29956	−0.649780	−	0.760122i	$-0.725139\pi$
$127$	−14.6453	−1.29956	−0.649780	+	0.760122i	$0.725139\pi$
$128$	35.7784	3.16239
$129$	−3.23657	−0.284964
$130$	1.73329	0.152020
$131$	0.546003	0.0477045	0.0238523	−	0.999715i	$-0.492407\pi$
$131$	0.546003	0.0477045	0.0238523	+	0.999715i	$0.492407\pi$
$132$	−13.3520	−1.16214
$133$	4.19990	0.364178
$134$	23.7292	2.04989
$135$	1.00000	0.0860663
$136$	−7.17717	−0.615438
$137$	−2.12488	−0.181541	−0.0907704	−	0.995872i	$-0.528933\pi$
$137$	−2.12488	−0.181541	−0.0907704	+	0.995872i	$0.528933\pi$
$138$	2.72718	0.232153
$139$	−19.0027	−1.61179	−0.805894	−	0.592060i	$-0.798315\pi$
$139$	−19.0027	−1.61179	−0.805894	+	0.592060i	$0.798315\pi$
$140$	−5.43751	−0.459554
$141$	−5.66386	−0.476983
$142$	−25.5588	−2.14485
$143$	−1.56064	−0.130507
$144$	14.6915	1.22429
$145$	−1.83362	−0.152274
$146$	3.80142	0.314608
$147$	−1.00000	−0.0824786
$148$	−37.4475	−3.07817
$149$	−10.1158	−0.828721	−0.414360	−	0.910113i	$-0.635995\pi$
$149$	−10.1158	−0.828721	−0.414360	+	0.910113i	$0.635995\pi$
$150$	−2.72718	−0.222673
$151$	12.9627	1.05489	0.527444	−	0.849590i	$-0.323151\pi$
$151$	12.9627	1.05489	0.527444	+	0.849590i	$0.323151\pi$
$152$	39.3729	3.19356
$153$	−0.765589	−0.0618942
$154$	6.69668	0.539634
$155$	5.20108	0.417760
$156$	3.45588	0.276691
$157$	−15.1600	−1.20990	−0.604951	−	0.796262i	$-0.706807\pi$
$157$	−15.1600	−1.20990	−0.604951	+	0.796262i	$0.706807\pi$
$158$	−20.7097	−1.64757
$159$	−13.1556	−1.04331
$160$	−21.3169	−1.68525
$161$	−1.00000	−0.0788110
$162$	2.72718	0.214267
$163$	−11.9576	−0.936592	−0.468296	−	0.883572i	$-0.655132\pi$
$163$	−11.9576	−0.936592	−0.468296	+	0.883572i	$0.655132\pi$
$164$	−10.0957	−0.788344
$165$	2.45553	0.191163
$166$	47.7753	3.70808
$167$	−11.1590	−0.863509	−0.431754	−	0.901991i	$-0.642105\pi$
$167$	−11.1590	−0.863509	−0.431754	+	0.901991i	$0.642105\pi$
$168$	−9.37471	−0.723275
$169$	−12.5961	−0.968928
$170$	2.08790	0.160134
$171$	4.19990	0.321175
$172$	17.5989	1.34190
$173$	−12.1720	−0.925424	−0.462712	−	0.886509i	$-0.653124\pi$
$173$	−12.1720	−0.925424	−0.462712	+	0.886509i	$0.653124\pi$
$174$	−5.00062	−0.379096
$175$	1.00000	0.0755929
$176$	36.0754	2.71929
$177$	4.02676	0.302670
$178$	−21.2828	−1.59522
$179$	−3.30712	−0.247185	−0.123593	−	0.992333i	$-0.539442\pi$
$179$	−3.30712	−0.247185	−0.123593	+	0.992333i	$0.539442\pi$
$180$	−5.43751	−0.405288
$181$	−11.6111	−0.863050	−0.431525	−	0.902101i	$-0.642024\pi$
$181$	−11.6111	−0.863050	−0.431525	+	0.902101i	$0.642024\pi$
$182$	−1.73329	−0.128480
$183$	−5.03838	−0.372448
$184$	−9.37471	−0.691113
$185$	6.88688	0.506334
$186$	14.1843	1.04004
$187$	−1.87993	−0.137474
$188$	30.7973	2.24612
$189$	−1.00000	−0.0727393
$190$	−11.4539	−0.830953
$191$	16.3547	1.18339	0.591693	−	0.806164i	$-0.298460\pi$
$191$	16.3547	1.18339	0.591693	+	0.806164i	$0.298460\pi$
$192$	−28.7522	−2.07501
$193$	−7.63245	−0.549396	−0.274698	−	0.961531i	$-0.588578\pi$
$193$	−7.63245	−0.549396	−0.274698	+	0.961531i	$0.588578\pi$
$194$	16.8502	1.20977
$195$	−0.635562	−0.0455135
$196$	5.43751	0.388394
$197$	19.9868	1.42400	0.712002	−	0.702178i	$-0.247789\pi$
$197$	19.9868	1.42400	0.712002	+	0.702178i	$0.247789\pi$
$198$	6.69668	0.475912
$199$	14.8081	1.04972	0.524859	−	0.851189i	$-0.324118\pi$
$199$	14.8081	1.04972	0.524859	+	0.851189i	$0.324118\pi$
$200$	9.37471	0.662892
$201$	−8.70100	−0.613721
$202$	−24.4069	−1.71727
$203$	1.83362	0.128695
$204$	4.16290	0.291461
$205$	1.85668	0.129676
$206$	−4.58642	−0.319551
$207$	−1.00000	−0.0695048
$208$	−9.33736	−0.647429
$209$	10.3130	0.713365
$210$	2.72718	0.188193
$211$	17.8527	1.22903	0.614515	−	0.788905i	$-0.289352\pi$
$211$	17.8527	1.22903	0.614515	+	0.788905i	$0.289352\pi$
$212$	71.5338	4.91296
$213$	9.37188	0.642151
$214$	11.4148	0.780302
$215$	−3.23657	−0.220732
$216$	−9.37471	−0.637868
$217$	−5.20108	−0.353072
$218$	−47.6636	−3.22819
$219$	−1.39390	−0.0941912
$220$	−13.3520	−0.900190
$221$	0.486579	0.0327309
$222$	18.7818	1.26055
$223$	−13.9252	−0.932498	−0.466249	−	0.884653i	$-0.654395\pi$
$223$	−13.9252	−0.932498	−0.466249	+	0.884653i	$0.654395\pi$
$224$	21.3169	1.42430
$225$	1.00000	0.0666667
$226$	−15.8377	−1.05351
$227$	1.69381	0.112422	0.0562112	−	0.998419i	$-0.482098\pi$
$227$	1.69381	0.112422	0.0562112	+	0.998419i	$0.482098\pi$
$228$	−22.8370	−1.51242
$229$	1.52735	0.100930	0.0504650	−	0.998726i	$-0.483930\pi$
$229$	1.52735	0.100930	0.0504650	+	0.998726i	$0.483930\pi$
$230$	2.72718	0.179825
$231$	−2.45553	−0.161562
$232$	17.1897	1.12856
$233$	13.0685	0.856148	0.428074	−	0.903744i	$-0.359192\pi$
$233$	13.0685	0.856148	0.428074	+	0.903744i	$0.359192\pi$
$234$	−1.73329	−0.113309
$235$	−5.66386	−0.369469
$236$	−21.8955	−1.42528
$237$	7.59381	0.493271
$238$	−2.08790	−0.135338
$239$	−9.50860	−0.615060	−0.307530	−	0.951538i	$-0.599503\pi$
$239$	−9.50860	−0.615060	−0.307530	+	0.951538i	$0.599503\pi$
$240$	14.6915	0.948332
$241$	10.9990	0.708509	0.354255	−	0.935149i	$-0.384735\pi$
$241$	10.9990	0.708509	0.354255	+	0.935149i	$0.384735\pi$
$242$	−13.5551	−0.871353
$243$	−1.00000	−0.0641500
$244$	27.3963	1.75387
$245$	−1.00000	−0.0638877
$246$	5.06351	0.322837
$247$	−2.66930	−0.169843
$248$	−48.7586	−3.09617
$249$	−17.5182	−1.11017
$250$	−2.72718	−0.172482
$251$	−5.69448	−0.359433	−0.179716	−	0.983718i	$-0.557518\pi$
$251$	−5.69448	−0.359433	−0.179716	+	0.983718i	$0.557518\pi$
$252$	5.43751	0.342531
$253$	−2.45553	−0.154378
$254$	−39.9404	−2.50608
$255$	−0.765589	−0.0479430
$256$	40.0698	2.50436
$257$	21.6631	1.35131	0.675655	−	0.737218i	$-0.263861\pi$
$257$	21.6631	1.35131	0.675655	+	0.737218i	$0.263861\pi$
$258$	−8.82670	−0.549527
$259$	−6.88688	−0.427930
$260$	3.45588	0.214324
$261$	1.83362	0.113498
$262$	1.48905	0.0919938
$263$	−24.8192	−1.53042	−0.765209	−	0.643782i	$-0.777364\pi$
$263$	−24.8192	−1.53042	−0.765209	+	0.643782i	$0.777364\pi$
$264$	−23.0199	−1.41678
$265$	−13.1556	−0.808143
$266$	11.4539	0.702283
$267$	7.80397	0.477595
$268$	47.3118	2.89003
$269$	−0.384435	−0.0234394	−0.0117197	−	0.999931i	$-0.503731\pi$
$269$	−0.384435	−0.0234394	−0.0117197	+	0.999931i	$0.503731\pi$
$270$	2.72718	0.165971
$271$	13.7033	0.832414	0.416207	−	0.909270i	$-0.363359\pi$
$271$	13.7033	0.832414	0.416207	+	0.909270i	$0.363359\pi$
$272$	−11.2476	−0.681989
$273$	0.635562	0.0384660
$274$	−5.79493	−0.350085
$275$	2.45553	0.148074
$276$	5.43751	0.327300
$277$	−4.48404	−0.269420	−0.134710	−	0.990885i	$-0.543010\pi$
$277$	−4.48404	−0.269420	−0.134710	+	0.990885i	$0.543010\pi$
$278$	−51.8238	−3.10818
$279$	−5.20108	−0.311380
$280$	−9.37471	−0.560246
$281$	−7.39467	−0.441129	−0.220565	−	0.975372i	$-0.570790\pi$
$281$	−7.39467	−0.441129	−0.220565	+	0.975372i	$0.570790\pi$
$282$	−15.4464	−0.919817
$283$	−26.0392	−1.54787	−0.773934	−	0.633267i	$-0.781714\pi$
$283$	−26.0392	−1.54787	−0.773934	+	0.633267i	$0.781714\pi$
$284$	−50.9597	−3.02390
$285$	4.19990	0.248781
$286$	−4.25615	−0.251672
$287$	−1.85668	−0.109596
$288$	21.3169	1.25611
$289$	−16.4139	−0.965522
$290$	−5.00062	−0.293647
$291$	−6.17860	−0.362196
$292$	7.57936	0.443549
$293$	16.1046	0.940841	0.470421	−	0.882442i	$-0.344102\pi$
$293$	16.1046	0.940841	0.470421	+	0.882442i	$0.344102\pi$
$294$	−2.72718	−0.159052
$295$	4.02676	0.234447
$296$	−64.5625	−3.75262
$297$	−2.45553	−0.142484
$298$	−27.5877	−1.59811
$299$	0.635562	0.0367555
$300$	−5.43751	−0.313935
$301$	3.23657	0.186553
$302$	35.3515	2.03425
$303$	8.94951	0.514136
$304$	61.7029	3.53890
$305$	−5.03838	−0.288497
$306$	−2.08790	−0.119357
$307$	−27.3377	−1.56025	−0.780124	−	0.625625i	$-0.784844\pi$
$307$	−27.3377	−1.56025	−0.780124	+	0.625625i	$0.784844\pi$
$308$	13.3520	0.760800
$309$	1.68174	0.0956710
$310$	14.1843	0.805612
$311$	−4.39877	−0.249432	−0.124716	−	0.992193i	$-0.539802\pi$
$311$	−4.39877	−0.249432	−0.124716	+	0.992193i	$0.539802\pi$
$312$	5.95821	0.337317
$313$	23.1120	1.30637	0.653185	−	0.757198i	$-0.273432\pi$
$313$	23.1120	1.30637	0.653185	+	0.757198i	$0.273432\pi$
$314$	−41.3442	−2.33319
$315$	−1.00000	−0.0563436
$316$	−41.2914	−2.32282
$317$	−17.0735	−0.958943	−0.479472	−	0.877557i	$-0.659172\pi$
$317$	−17.0735	−0.958943	−0.479472	+	0.877557i	$0.659172\pi$
$318$	−35.8777	−2.01192
$319$	4.50252	0.252093
$320$	−28.7522	−1.60729
$321$	−4.18558	−0.233616
$322$	−2.72718	−0.151980
$323$	−3.21540	−0.178910
$324$	5.43751	0.302084
$325$	−0.635562	−0.0352546
$326$	−32.6105	−1.80613
$327$	17.4772	0.966494
$328$	−17.4059	−0.961078
$329$	5.66386	0.312258
$330$	6.69668	0.368640
$331$	−22.1135	−1.21547	−0.607733	−	0.794141i	$-0.707921\pi$
$331$	−22.1135	−1.21547	−0.607733	+	0.794141i	$0.707921\pi$
$332$	95.2554	5.22782
$333$	−6.88688	−0.377399
$334$	−30.4326	−1.66520
$335$	−8.70100	−0.475386
$336$	−14.6915	−0.801487
$337$	−22.5318	−1.22738	−0.613691	−	0.789546i	$-0.710316\pi$
$337$	−22.5318	−1.22738	−0.613691	+	0.789546i	$0.710316\pi$
$338$	−34.3517	−1.86849
$339$	5.80735	0.315412
$340$	4.16290	0.225765
$341$	−12.7714	−0.691610
$342$	11.4539	0.619356
$343$	1.00000	0.0539949
$344$	30.3419	1.63592
$345$	−1.00000	−0.0538382
$346$	−33.1954	−1.78459
$347$	28.7034	1.54088	0.770439	−	0.637513i	$-0.220037\pi$
$347$	28.7034	1.54088	0.770439	+	0.637513i	$0.220037\pi$
$348$	−9.97035	−0.534467
$349$	16.9985	0.909911	0.454956	−	0.890514i	$-0.349655\pi$
$349$	16.9985	0.909911	0.454956	+	0.890514i	$0.349655\pi$
$350$	2.72718	0.145774
$351$	0.635562	0.0339238
$352$	52.3444	2.78997
$353$	13.6520	0.726622	0.363311	−	0.931668i	$-0.381646\pi$
$353$	13.6520	0.726622	0.363311	+	0.931668i	$0.381646\pi$
$354$	10.9817	0.583671
$355$	9.37188	0.497408
$356$	−42.4342	−2.24901
$357$	0.765589	0.0405193
$358$	−9.01910	−0.476674
$359$	−24.3856	−1.28702	−0.643512	−	0.765436i	$-0.722523\pi$
$359$	−24.3856	−1.28702	−0.643512	+	0.765436i	$0.722523\pi$
$360$	−9.37471	−0.494091
$361$	−1.36080	−0.0716212
$362$	−31.6657	−1.66431
$363$	4.97036	0.260876
$364$	−3.45588	−0.181137
$365$	−1.39390	−0.0729602
$366$	−13.7406	−0.718232
$367$	28.3320	1.47892	0.739460	−	0.673200i	$-0.235081\pi$
$367$	28.3320	1.47892	0.739460	+	0.673200i	$0.235081\pi$
$368$	−14.6915	−0.765847
$369$	−1.85668	−0.0966550
$370$	18.7818	0.976418
$371$	13.1556	0.683005
$372$	28.2809	1.46630
$373$	21.8013	1.12883	0.564414	−	0.825492i	$-0.309102\pi$
$373$	21.8013	1.12883	0.564414	+	0.825492i	$0.309102\pi$
$374$	−5.12690	−0.265106
$375$	1.00000	0.0516398
$376$	53.0970	2.73827
$377$	−1.16538	−0.0600202
$378$	−2.72718	−0.140271
$379$	−21.5664	−1.10779	−0.553896	−	0.832586i	$-0.686860\pi$
$379$	−21.5664	−1.10779	−0.553896	+	0.832586i	$0.686860\pi$
$380$	−22.8370	−1.17151
$381$	14.6453	0.750301
$382$	44.6022	2.28205
$383$	8.82125	0.450745	0.225373	−	0.974273i	$-0.427640\pi$
$383$	8.82125	0.450745	0.225373	+	0.974273i	$0.427640\pi$
$384$	−35.7784	−1.82581
$385$	−2.45553	−0.125145
$386$	−20.8151	−1.05946
$387$	3.23657	0.164524
$388$	33.5962	1.70559
$389$	−11.4178	−0.578908	−0.289454	−	0.957192i	$-0.593474\pi$
$389$	−11.4178	−0.578908	−0.289454	+	0.957192i	$0.593474\pi$
$390$	−1.73329	−0.0877686
$391$	0.765589	0.0387175
$392$	9.37471	0.473494
$393$	−0.546003	−0.0275422
$394$	54.5077	2.74606
$395$	7.59381	0.382086
$396$	13.3520	0.670962
$397$	3.54519	0.177928	0.0889641	−	0.996035i	$-0.471644\pi$
$397$	3.54519	0.177928	0.0889641	+	0.996035i	$0.471644\pi$
$398$	40.3843	2.02428
$399$	−4.19990	−0.210258
$400$	14.6915	0.734575
$401$	27.5527	1.37592	0.687958	−	0.725750i	$-0.258507\pi$
$401$	27.5527	1.37592	0.687958	+	0.725750i	$0.258507\pi$
$402$	−23.7292	−1.18350
$403$	3.30561	0.164664
$404$	−48.6631	−2.42108
$405$	−1.00000	−0.0496904
$406$	5.00062	0.248177
$407$	−16.9110	−0.838245
$408$	7.17717	0.355323
$409$	20.6762	1.02237	0.511186	−	0.859470i	$-0.329206\pi$
$409$	20.6762	1.02237	0.511186	+	0.859470i	$0.329206\pi$
$410$	5.06351	0.250069
$411$	2.12488	0.104813
$412$	−9.14450	−0.450517
$413$	−4.02676	−0.198144
$414$	−2.72718	−0.134034
$415$	−17.5182	−0.859934
$416$	−13.5482	−0.664257
$417$	19.0027	0.930566
$418$	28.1254	1.37566
$419$	−8.71853	−0.425928	−0.212964	−	0.977060i	$-0.568312\pi$
$419$	−8.71853	−0.425928	−0.212964	+	0.977060i	$0.568312\pi$
$420$	5.43751	0.265323
$421$	−1.62005	−0.0789564	−0.0394782	−	0.999220i	$-0.512570\pi$
$421$	−1.62005	−0.0789564	−0.0394782	+	0.999220i	$0.512570\pi$
$422$	48.6875	2.37007
$423$	5.66386	0.275386
$424$	123.330	5.98944
$425$	−0.765589	−0.0371365
$426$	25.5588	1.23833
$427$	5.03838	0.243824
$428$	22.7591	1.10010
$429$	1.56064	0.0753485
$430$	−8.82670	−0.425661
$431$	14.1371	0.680960	0.340480	−	0.940252i	$-0.389411\pi$
$431$	14.1371	0.680960	0.340480	+	0.940252i	$0.389411\pi$
$432$	−14.6915	−0.706845
$433$	3.33423	0.160233	0.0801164	−	0.996786i	$-0.474471\pi$
$433$	3.33423	0.160233	0.0801164	+	0.996786i	$0.474471\pi$
$434$	−14.1843	−0.680867
$435$	1.83362	0.0879155
$436$	−95.0327	−4.55124
$437$	−4.19990	−0.200909
$438$	−3.80142	−0.181639
$439$	−38.1645	−1.82149	−0.910745	−	0.412969i	$-0.864492\pi$
$439$	−38.1645	−1.82149	−0.910745	+	0.412969i	$0.864492\pi$
$440$	−23.0199	−1.09743
$441$	1.00000	0.0476190
$442$	1.32699	0.0631184
$443$	−3.72025	−0.176754	−0.0883771	−	0.996087i	$-0.528168\pi$
$443$	−3.72025	−0.176754	−0.0883771	+	0.996087i	$0.528168\pi$
$444$	37.4475	1.77718
$445$	7.80397	0.369944
$446$	−37.9764	−1.79824
$447$	10.1158	0.478462
$448$	28.7522	1.35841
$449$	37.3801	1.76408	0.882038	−	0.471178i	$-0.156171\pi$
$449$	37.3801	1.76408	0.882038	+	0.471178i	$0.156171\pi$
$450$	2.72718	0.128560
$451$	−4.55914	−0.214682
$452$	−31.5775	−1.48528
$453$	−12.9627	−0.609040
$454$	4.61933	0.216796
$455$	0.635562	0.0297956
$456$	−39.3729	−1.84380
$457$	27.1660	1.27077	0.635386	−	0.772195i	$-0.280841\pi$
$457$	27.1660	1.27077	0.635386	+	0.772195i	$0.280841\pi$
$458$	4.16535	0.194634
$459$	0.765589	0.0357346
$460$	5.43751	0.253525
$461$	−16.7650	−0.780823	−0.390412	−	0.920640i	$-0.627667\pi$
$461$	−16.7650	−0.780823	−0.390412	+	0.920640i	$0.627667\pi$
$462$	−6.69668	−0.311558
$463$	−1.72877	−0.0803428	−0.0401714	−	0.999193i	$-0.512790\pi$
$463$	−1.72877	−0.0803428	−0.0401714	+	0.999193i	$0.512790\pi$
$464$	26.9387	1.25060
$465$	−5.20108	−0.241194
$466$	35.6402	1.65100
$467$	−24.4835	−1.13296	−0.566481	−	0.824075i	$-0.691695\pi$
$467$	−24.4835	−1.13296	−0.566481	+	0.824075i	$0.691695\pi$
$468$	−3.45588	−0.159748
$469$	8.70100	0.401775
$470$	−15.4464	−0.712487
$471$	15.1600	0.698538
$472$	−37.7497	−1.73757
$473$	7.94749	0.365426
$474$	20.7097	0.951227
$475$	4.19990	0.192705
$476$	−4.16290	−0.190806
$477$	13.1556	0.602354
$478$	−25.9317	−1.18609
$479$	29.3628	1.34162	0.670811	−	0.741628i	$-0.265946\pi$
$479$	29.3628	1.34162	0.670811	+	0.741628i	$0.265946\pi$
$480$	21.3169	0.972981
$481$	4.37704	0.199576
$482$	29.9963	1.36629
$483$	1.00000	0.0455016
$484$	−27.0264	−1.22847
$485$	−6.17860	−0.280556
$486$	−2.72718	−0.123707
$487$	24.3753	1.10455	0.552275	−	0.833662i	$-0.313760\pi$
$487$	24.3753	1.10455	0.552275	+	0.833662i	$0.313760\pi$
$488$	47.2334	2.13815
$489$	11.9576	0.540742
$490$	−2.72718	−0.123201
$491$	−20.8420	−0.940589	−0.470294	−	0.882510i	$-0.655852\pi$
$491$	−20.8420	−0.940589	−0.470294	+	0.882510i	$0.655852\pi$
$492$	10.0957	0.455151
$493$	−1.40380	−0.0632241
$494$	−7.27966	−0.327527
$495$	−2.45553	−0.110368
$496$	−76.4116	−3.43098
$497$	−9.37188	−0.420386
$498$	−47.7753	−2.14086
$499$	−14.3910	−0.644231	−0.322116	−	0.946700i	$-0.604394\pi$
$499$	−14.3910	−0.644231	−0.322116	+	0.946700i	$0.604394\pi$
$500$	−5.43751	−0.243173
$501$	11.1590	0.498547
$502$	−15.5299	−0.693133
$503$	23.9875	1.06955	0.534774	−	0.844995i	$-0.320397\pi$
$503$	23.9875	1.06955	0.534774	+	0.844995i	$0.320397\pi$
$504$	9.37471	0.417583
$505$	8.94951	0.398248
$506$	−6.69668	−0.297704
$507$	12.5961	0.559411
$508$	−79.6340	−3.53319
$509$	−41.4911	−1.83906	−0.919531	−	0.393017i	$-0.871431\pi$
$509$	−41.4911	−1.83906	−0.919531	+	0.393017i	$0.871431\pi$
$510$	−2.08790	−0.0924537
$511$	1.39390	0.0616626
$512$	37.7208	1.66704
$513$	−4.19990	−0.185430
$514$	59.0793	2.60587
$515$	1.68174	0.0741065
$516$	−17.5989	−0.774747
$517$	13.9078	0.611663
$518$	−18.7818	−0.825223
$519$	12.1720	0.534294
$520$	5.95821	0.261285
$521$	44.2152	1.93710	0.968551	−	0.248815i	$-0.0800412\pi$
$521$	44.2152	1.93710	0.968551	+	0.248815i	$0.0800412\pi$
$522$	5.00062	0.218871
$523$	−1.76274	−0.0770791	−0.0385395	−	0.999257i	$-0.512271\pi$
$523$	−1.76274	−0.0770791	−0.0385395	+	0.999257i	$0.512271\pi$
$524$	2.96890	0.129697
$525$	−1.00000	−0.0436436
$526$	−67.6865	−2.95127
$527$	3.98189	0.173454
$528$	−36.0754	−1.56998
$529$	1.00000	0.0434783
$530$	−35.8777	−1.55843
$531$	−4.02676	−0.174746
$532$	22.8370	0.990111
$533$	1.18004	0.0511131
$534$	21.2828	0.920998
$535$	−4.18558	−0.180958
$536$	81.5693	3.52326
$537$	3.30712	0.142713
$538$	−1.04842	−0.0452007
$539$	2.45553	0.105767
$540$	5.43751	0.233993
$541$	−16.1813	−0.695687	−0.347843	−	0.937553i	$-0.613086\pi$
$541$	−16.1813	−0.695687	−0.347843	+	0.937553i	$0.613086\pi$
$542$	37.3712	1.60523
$543$	11.6111	0.498282
$544$	−16.3200	−0.699715
$545$	17.4772	0.748643
$546$	1.73329	0.0741780
$547$	−29.0265	−1.24108	−0.620542	−	0.784173i	$-0.713088\pi$
$547$	−29.0265	−1.24108	−0.620542	+	0.784173i	$0.713088\pi$
$548$	−11.5541	−0.493565
$549$	5.03838	0.215033
$550$	6.69668	0.285547
$551$	7.70104	0.328076
$552$	9.37471	0.399014
$553$	−7.59381	−0.322922
$554$	−12.2288	−0.519552
$555$	−6.88688	−0.292332
$556$	−103.327	−4.38206
$557$	−35.8286	−1.51811	−0.759053	−	0.651028i	$-0.774338\pi$
$557$	−35.8286	−1.51811	−0.759053	+	0.651028i	$0.774338\pi$
$558$	−14.1843	−0.600468
$559$	−2.05704	−0.0870035
$560$	−14.6915	−0.620829
$561$	1.87993	0.0793706
$562$	−20.1666	−0.850677
$563$	31.1392	1.31236	0.656181	−	0.754604i	$-0.272171\pi$
$563$	31.1392	1.31236	0.656181	+	0.754604i	$0.272171\pi$
$564$	−30.7973	−1.29680
$565$	5.80735	0.244317
$566$	−71.0135	−2.98492
$567$	1.00000	0.0419961
$568$	−87.8586	−3.68647
$569$	−21.2983	−0.892873	−0.446437	−	0.894815i	$-0.647307\pi$
$569$	−21.2983	−0.892873	−0.446437	+	0.894815i	$0.647307\pi$
$570$	11.4539	0.479751
$571$	9.98015	0.417656	0.208828	−	0.977952i	$-0.433035\pi$
$571$	9.98015	0.417656	0.208828	+	0.977952i	$0.433035\pi$
$572$	−8.48601	−0.354818
$573$	−16.3547	−0.683228
$574$	−5.06351	−0.211347
$575$	−1.00000	−0.0417029
$576$	28.7522	1.19801
$577$	33.9427	1.41305	0.706526	−	0.707687i	$-0.250261\pi$
$577$	33.9427	1.41305	0.706526	+	0.707687i	$0.250261\pi$
$578$	−44.7636	−1.86192
$579$	7.63245	0.317194
$580$	−9.97035	−0.413996
$581$	17.5182	0.726777
$582$	−16.8502	−0.698461
$583$	32.3040	1.33790
$584$	13.0674	0.540734
$585$	0.635562	0.0262773
$586$	43.9202	1.81433
$587$	34.6642	1.43075	0.715373	−	0.698743i	$-0.246257\pi$
$587$	34.6642	1.43075	0.715373	+	0.698743i	$0.246257\pi$
$588$	−5.43751	−0.224239
$589$	−21.8440	−0.900067
$590$	10.9817	0.452109
$591$	−19.9868	−0.822149
$592$	−101.179	−4.15842
$593$	−39.7819	−1.63365	−0.816824	−	0.576887i	$-0.804267\pi$
$593$	−39.7819	−1.63365	−0.816824	+	0.576887i	$0.804267\pi$
$594$	−6.69668	−0.274768
$595$	0.765589	0.0313861
$596$	−55.0049	−2.25309
$597$	−14.8081	−0.606055
$598$	1.73329	0.0708796
$599$	3.25863	0.133144	0.0665721	−	0.997782i	$-0.478794\pi$
$599$	3.25863	0.133144	0.0665721	+	0.997782i	$0.478794\pi$
$600$	−9.37471	−0.382721
$601$	46.8001	1.90901	0.954507	−	0.298187i	$-0.0963819\pi$
$601$	46.8001	1.90901	0.954507	+	0.298187i	$0.0963819\pi$
$602$	8.82670	0.359750
$603$	8.70100	0.354332
$604$	70.4847	2.86798
$605$	4.97036	0.202074
$606$	24.4069	0.991464
$607$	−27.0582	−1.09826	−0.549130	−	0.835737i	$-0.685041\pi$
$607$	−27.0582	−1.09826	−0.549130	+	0.835737i	$0.685041\pi$
$608$	89.5291	3.63089
$609$	−1.83362	−0.0743022
$610$	−13.7406	−0.556340
$611$	−3.59973	−0.145630
$612$	−4.16290	−0.168275
$613$	40.3576	1.63003	0.815013	−	0.579443i	$-0.196730\pi$
$613$	40.3576	1.63003	0.815013	+	0.579443i	$0.196730\pi$
$614$	−74.5549	−3.00879
$615$	−1.85668	−0.0748687
$616$	23.0199	0.927498
$617$	19.0465	0.766784	0.383392	−	0.923586i	$-0.374756\pi$
$617$	19.0465	0.766784	0.383392	+	0.923586i	$0.374756\pi$
$618$	4.58642	0.184493
$619$	6.22178	0.250075	0.125037	−	0.992152i	$-0.460095\pi$
$619$	6.22178	0.250075	0.125037	+	0.992152i	$0.460095\pi$
$620$	28.2809	1.13579
$621$	1.00000	0.0401286
$622$	−11.9962	−0.481006
$623$	−7.80397	−0.312660
$624$	9.33736	0.373794
$625$	1.00000	0.0400000
$626$	63.0307	2.51921
$627$	−10.3130	−0.411861
$628$	−82.4329	−3.28943
$629$	5.27252	0.210229
$630$	−2.72718	−0.108653
$631$	−39.4176	−1.56919	−0.784595	−	0.620008i	$-0.787129\pi$
$631$	−39.4176	−1.56919	−0.784595	+	0.620008i	$0.787129\pi$
$632$	−71.1897	−2.83178
$633$	−17.8527	−0.709580
$634$	−46.5625	−1.84923
$635$	14.6453	0.581181
$636$	−71.5338	−2.83650
$637$	−0.635562	−0.0251819
$638$	12.2792	0.486138
$639$	−9.37188	−0.370746
$640$	−35.7784	−1.41427
$641$	39.9669	1.57860	0.789300	−	0.614008i	$-0.210444\pi$
$641$	39.9669	1.57860	0.789300	+	0.614008i	$0.210444\pi$
$642$	−11.4148	−0.450507
$643$	−21.2321	−0.837313	−0.418657	−	0.908145i	$-0.637499\pi$
$643$	−21.2321	−0.837313	−0.418657	+	0.908145i	$0.637499\pi$
$644$	−5.43751	−0.214268
$645$	3.23657	0.127440
$646$	−8.76897	−0.345011
$647$	4.77763	0.187828	0.0939139	−	0.995580i	$-0.470062\pi$
$647$	4.77763	0.187828	0.0939139	+	0.995580i	$0.470062\pi$
$648$	9.37471	0.368273
$649$	−9.88783	−0.388131
$650$	−1.73329	−0.0679853
$651$	5.20108	0.203846
$652$	−65.0196	−2.54636
$653$	47.7229	1.86754	0.933770	−	0.357872i	$-0.116498\pi$
$653$	47.7229	1.86754	0.933770	+	0.357872i	$0.116498\pi$
$654$	47.6636	1.86379
$655$	−0.546003	−0.0213341
$656$	−27.2775	−1.06501
$657$	1.39390	0.0543813
$658$	15.4464	0.602162
$659$	18.0110	0.701610	0.350805	−	0.936448i	$-0.385908\pi$
$659$	18.0110	0.701610	0.350805	+	0.936448i	$0.385908\pi$
$660$	13.3520	0.519725
$661$	−31.1235	−1.21056	−0.605282	−	0.796011i	$-0.706940\pi$
$661$	−31.1235	−1.21056	−0.605282	+	0.796011i	$0.706940\pi$
$662$	−60.3074	−2.34392
$663$	−0.486579	−0.0188972
$664$	164.228	6.37328
$665$	−4.19990	−0.162865
$666$	−18.7818	−0.727779
$667$	−1.83362	−0.0709982
$668$	−60.6771	−2.34767
$669$	13.9252	0.538378
$670$	−23.7292	−0.916738
$671$	12.3719	0.477612
$672$	−21.3169	−0.822319
$673$	2.38868	0.0920770	0.0460385	−	0.998940i	$-0.485340\pi$
$673$	2.38868	0.0920770	0.0460385	+	0.998940i	$0.485340\pi$
$674$	−61.4481	−2.36689
$675$	−1.00000	−0.0384900
$676$	−68.4912	−2.63428
$677$	−20.6564	−0.793888	−0.396944	−	0.917843i	$-0.629929\pi$
$677$	−20.6564	−0.793888	−0.396944	+	0.917843i	$0.629929\pi$
$678$	15.8377	0.608243
$679$	6.17860	0.237113
$680$	7.17717	0.275232
$681$	−1.69381	−0.0649071
$682$	−34.8299	−1.33371
$683$	−8.20881	−0.314102	−0.157051	−	0.987591i	$-0.550199\pi$
$683$	−8.20881	−0.314102	−0.157051	+	0.987591i	$0.550199\pi$
$684$	22.8370	0.873195
$685$	2.12488	0.0811875
$686$	2.72718	0.104124
$687$	−1.52735	−0.0582720
$688$	47.5500	1.81283
$689$	−8.36121	−0.318537
$690$	−2.72718	−0.103822
$691$	−7.31775	−0.278380	−0.139190	−	0.990266i	$-0.544450\pi$
$691$	−7.31775	−0.278380	−0.139190	+	0.990266i	$0.544450\pi$
$692$	−66.1856	−2.51600
$693$	2.45553	0.0932779
$694$	78.2793	2.97144
$695$	19.0027	0.720814
$696$	−17.1897	−0.651574
$697$	1.42146	0.0538415
$698$	46.3581	1.75468
$699$	−13.0685	−0.494297
$700$	5.43751	0.205519
$701$	49.5428	1.87121	0.935604	−	0.353052i	$-0.114856\pi$
$701$	49.5428	1.87121	0.935604	+	0.353052i	$0.114856\pi$
$702$	1.73329	0.0654189
$703$	−28.9242	−1.09090
$704$	70.6018	2.66091
$705$	5.66386	0.213313
$706$	37.2314	1.40122
$707$	−8.94951	−0.336581
$708$	21.8955	0.822885
$709$	−7.93296	−0.297929	−0.148964	−	0.988843i	$-0.547594\pi$
$709$	−7.93296	−0.297929	−0.148964	+	0.988843i	$0.547594\pi$
$710$	25.5588	0.959205
$711$	−7.59381	−0.284790
$712$	−73.1600	−2.74179
$713$	5.20108	0.194782
$714$	2.08790	0.0781376
$715$	1.56064	0.0583647
$716$	−17.9825	−0.672037
$717$	9.50860	0.355105
$718$	−66.5039	−2.48190
$719$	−12.7732	−0.476360	−0.238180	−	0.971221i	$-0.576551\pi$
$719$	−12.7732	−0.476360	−0.238180	+	0.971221i	$0.576551\pi$
$720$	−14.6915	−0.547520
$721$	−1.68174	−0.0626314
$722$	−3.71116	−0.138115
$723$	−10.9990	−0.409058
$724$	−63.1357	−2.34642
$725$	1.83362	0.0680991
$726$	13.5551	0.503076
$727$	36.1188	1.33957	0.669786	−	0.742554i	$-0.266386\pi$
$727$	36.1188	1.33957	0.669786	+	0.742554i	$0.266386\pi$
$728$	−5.95821	−0.220826
$729$	1.00000	0.0370370
$730$	−3.80142	−0.140697
$731$	−2.47788	−0.0916477
$732$	−27.3963	−1.01260
$733$	20.5934	0.760634	0.380317	−	0.924856i	$-0.375815\pi$
$733$	20.5934	0.760634	0.380317	+	0.924856i	$0.375815\pi$
$734$	77.2666	2.85196
$735$	1.00000	0.0368856
$736$	−21.3169	−0.785753
$737$	21.3656	0.787011
$738$	−5.06351	−0.186390
$739$	44.2396	1.62738	0.813690	−	0.581300i	$-0.197456\pi$
$739$	44.2396	1.62738	0.813690	+	0.581300i	$0.197456\pi$
$740$	37.4475	1.37660
$741$	2.66930	0.0980592
$742$	35.8777	1.31711
$743$	−4.35232	−0.159671	−0.0798356	−	0.996808i	$-0.525440\pi$
$743$	−4.35232	−0.159671	−0.0798356	+	0.996808i	$0.525440\pi$
$744$	48.7586	1.78758
$745$	10.1158	0.370615
$746$	59.4560	2.17684
$747$	17.5182	0.640957
$748$	−10.2221	−0.373758
$749$	4.18558	0.152938
$750$	2.72718	0.0995825
$751$	−9.65089	−0.352166	−0.176083	−	0.984375i	$-0.556343\pi$
$751$	−9.65089	−0.352166	−0.176083	+	0.984375i	$0.556343\pi$
$752$	83.2105	3.03438
$753$	5.69448	0.207519
$754$	−3.17821	−0.115743
$755$	−12.9627	−0.471760
$756$	−5.43751	−0.197760
$757$	−17.2899	−0.628412	−0.314206	−	0.949355i	$-0.601738\pi$
$757$	−17.2899	−0.628412	−0.314206	+	0.949355i	$0.601738\pi$
$758$	−58.8155	−2.13628
$759$	2.45553	0.0891302
$760$	−39.3729	−1.42820
$761$	20.9155	0.758185	0.379093	−	0.925359i	$-0.376236\pi$
$761$	20.9155	0.758185	0.379093	+	0.925359i	$0.376236\pi$
$762$	39.9404	1.44689
$763$	−17.4772	−0.632719
$764$	88.9289	3.21734
$765$	0.765589	0.0276799
$766$	24.0571	0.869220
$767$	2.55925	0.0924093
$768$	−40.0698	−1.44590
$769$	24.9989	0.901484	0.450742	−	0.892654i	$-0.351159\pi$
$769$	24.9989	0.901484	0.450742	+	0.892654i	$0.351159\pi$
$770$	−6.69668	−0.241331
$771$	−21.6631	−0.780179
$772$	−41.5015	−1.49367
$773$	−21.3187	−0.766780	−0.383390	−	0.923587i	$-0.625243\pi$
$773$	−21.3187	−0.766780	−0.383390	+	0.923587i	$0.625243\pi$
$774$	8.82670	0.317269
$775$	−5.20108	−0.186828
$776$	57.9226	2.07930
$777$	6.88688	0.247066
$778$	−31.1385	−1.11637
$779$	−7.79789	−0.279388
$780$	−3.45588	−0.123740
$781$	−23.0129	−0.823468
$782$	2.08790	0.0746631
$783$	−1.83362	−0.0655284
$784$	14.6915	0.524696
$785$	15.1600	0.541085
$786$	−1.48905	−0.0531126
$787$	−30.5769	−1.08995	−0.544974	−	0.838453i	$-0.683460\pi$
$787$	−30.5769	−1.08995	−0.544974	+	0.838453i	$0.683460\pi$
$788$	108.679	3.87152
$789$	24.8192	0.883587
$790$	20.7097	0.736817
$791$	−5.80735	−0.206486
$792$	23.0199	0.817976
$793$	−3.20221	−0.113714
$794$	9.66838	0.343118
$795$	13.1556	0.466582
$796$	80.5191	2.85392
$797$	37.7321	1.33654	0.668270	−	0.743919i	$-0.267035\pi$
$797$	37.7321	1.33654	0.668270	+	0.743919i	$0.267035\pi$
$798$	−11.4539	−0.405463
$799$	−4.33618	−0.153403
$800$	21.3169	0.753668
$801$	−7.80397	−0.275740
$802$	75.1412	2.65333
$803$	3.42277	0.120787
$804$	−47.3118	−1.66856
$805$	1.00000	0.0352454
$806$	9.01498	0.317539
$807$	0.384435	0.0135327
$808$	−83.8991	−2.95156
$809$	17.8474	0.627480	0.313740	−	0.949509i	$-0.398418\pi$
$809$	17.8474	0.627480	0.313740	+	0.949509i	$0.398418\pi$
$810$	−2.72718	−0.0958233
$811$	−27.4782	−0.964891	−0.482445	−	0.875926i	$-0.660251\pi$
$811$	−27.4782	−0.964891	−0.482445	+	0.875926i	$0.660251\pi$
$812$	9.97035	0.349891
$813$	−13.7033	−0.480594
$814$	−46.1192	−1.61648
$815$	11.9576	0.418857
$816$	11.2476	0.393746
$817$	13.5933	0.475569
$818$	56.3877	1.97155
$819$	−0.635562	−0.0222083
$820$	10.0957	0.352558
$821$	−17.6318	−0.615355	−0.307677	−	0.951491i	$-0.599552\pi$
$821$	−17.6318	−0.615355	−0.307677	+	0.951491i	$0.599552\pi$
$822$	5.79493	0.202121
$823$	−9.18291	−0.320096	−0.160048	−	0.987109i	$-0.551165\pi$
$823$	−9.18291	−0.320096	−0.160048	+	0.987109i	$0.551165\pi$
$824$	−15.7659	−0.549230
$825$	−2.45553	−0.0854906
$826$	−10.9817	−0.382102
$827$	16.6638	0.579456	0.289728	−	0.957109i	$-0.406435\pi$
$827$	16.6638	0.579456	0.289728	+	0.957109i	$0.406435\pi$
$828$	−5.43751	−0.188967
$829$	39.2279	1.36244	0.681220	−	0.732078i	$-0.261450\pi$
$829$	39.2279	1.36244	0.681220	+	0.732078i	$0.261450\pi$
$830$	−47.7753	−1.65830
$831$	4.48404	0.155550
$832$	−18.2738	−0.633529
$833$	−0.765589	−0.0265261
$834$	51.8238	1.79451
$835$	11.1590	0.386173
$836$	56.0770	1.93946
$837$	5.20108	0.179775
$838$	−23.7770	−0.821362
$839$	−51.4613	−1.77664	−0.888320	−	0.459224i	$-0.848127\pi$
$839$	−51.4613	−1.77664	−0.888320	+	0.459224i	$0.848127\pi$
$840$	9.37471	0.323458
$841$	−25.6378	−0.884063
$842$	−4.41817	−0.152260
$843$	7.39467	0.254686
$844$	97.0742	3.34143
$845$	12.5961	0.433318
$846$	15.4464	0.531057
$847$	−4.97036	−0.170784
$848$	193.276	6.63712
$849$	26.0392	0.893662
$850$	−2.08790	−0.0716143
$851$	6.88688	0.236079
$852$	50.9597	1.74585
$853$	17.3558	0.594252	0.297126	−	0.954838i	$-0.403972\pi$
$853$	17.3558	0.594252	0.297126	+	0.954838i	$0.403972\pi$
$854$	13.7406	0.470193
$855$	−4.19990	−0.143634
$856$	39.2386	1.34115
$857$	32.2667	1.10221	0.551105	−	0.834436i	$-0.314206\pi$
$857$	32.2667	1.10221	0.551105	+	0.834436i	$0.314206\pi$
$858$	4.25615	0.145303
$859$	13.4199	0.457882	0.228941	−	0.973440i	$-0.426474\pi$
$859$	13.4199	0.457882	0.228941	+	0.973440i	$0.426474\pi$
$860$	−17.5989	−0.600117
$861$	1.85668	0.0632756
$862$	38.5544	1.31317
$863$	26.4965	0.901952	0.450976	−	0.892536i	$-0.351076\pi$
$863$	26.4965	0.901952	0.450976	+	0.892536i	$0.351076\pi$
$864$	−21.3169	−0.725217
$865$	12.1720	0.413862
$866$	9.09304	0.308994
$867$	16.4139	0.557444
$868$	−28.2809	−0.959917
$869$	−18.6468	−0.632551
$870$	5.00062	0.169537
$871$	−5.53002	−0.187378
$872$	−163.844	−5.54846
$873$	6.17860	0.209114
$874$	−11.4539	−0.387434
$875$	−1.00000	−0.0338062
$876$	−7.57936	−0.256083
$877$	4.66482	0.157520	0.0787599	−	0.996894i	$-0.474904\pi$
$877$	4.66482	0.157520	0.0787599	+	0.996894i	$0.474904\pi$
$878$	−104.081	−3.51258
$879$	−16.1046	−0.543195
$880$	−36.0754	−1.21610
$881$	26.5292	0.893792	0.446896	−	0.894586i	$-0.352529\pi$
$881$	26.5292	0.893792	0.446896	+	0.894586i	$0.352529\pi$
$882$	2.72718	0.0918289
$883$	−4.08252	−0.137388	−0.0686939	−	0.997638i	$-0.521883\pi$
$883$	−4.08252	−0.137388	−0.0686939	+	0.997638i	$0.521883\pi$
$884$	2.64578	0.0889872
$885$	−4.02676	−0.135358
$886$	−10.1458	−0.340854
$887$	−6.48560	−0.217765	−0.108883	−	0.994055i	$-0.534727\pi$
$887$	−6.48560	−0.217765	−0.108883	+	0.994055i	$0.534727\pi$
$888$	64.5625	2.16658
$889$	−14.6453	−0.491187
$890$	21.2828	0.713402
$891$	2.45553	0.0822634
$892$	−75.7183	−2.53523
$893$	23.7877	0.796023
$894$	27.5877	0.922670
$895$	3.30712	0.110545
$896$	35.7784	1.19527
$897$	−0.635562	−0.0212208
$898$	101.942	3.40186
$899$	−9.53682	−0.318071
$900$	5.43751	0.181250
$901$	−10.0718	−0.335540
$902$	−12.4336	−0.413994
$903$	−3.23657	−0.107706
$904$	−54.4422	−1.81072
$905$	11.6111	0.385968
$906$	−35.3515	−1.17448
$907$	−21.0120	−0.697693	−0.348846	−	0.937180i	$-0.613426\pi$
$907$	−21.0120	−0.697693	−0.348846	+	0.937180i	$0.613426\pi$
$908$	9.21013	0.305649
$909$	−8.94951	−0.296837
$910$	1.73329	0.0574581
$911$	24.9307	0.825992	0.412996	−	0.910733i	$-0.364482\pi$
$911$	24.9307	0.825992	0.412996	+	0.910733i	$0.364482\pi$
$912$	−61.7029	−2.04319
$913$	43.0165	1.42364
$914$	74.0866	2.45057
$915$	5.03838	0.166564
$916$	8.30497	0.274404
$917$	0.546003	0.0180306
$918$	2.08790	0.0689109
$919$	−25.1777	−0.830537	−0.415269	−	0.909699i	$-0.636312\pi$
$919$	−25.1777	−0.830537	−0.415269	+	0.909699i	$0.636312\pi$
$920$	9.37471	0.309075
$921$	27.3377	0.900809
$922$	−45.7211	−1.50574
$923$	5.95641	0.196058
$924$	−13.3520	−0.439248
$925$	−6.88688	−0.226439
$926$	−4.71467	−0.154934
$927$	−1.68174	−0.0552357
$928$	39.0873	1.28310
$929$	−8.20845	−0.269311	−0.134655	−	0.990893i	$-0.542993\pi$
$929$	−8.20845	−0.269311	−0.134655	+	0.990893i	$0.542993\pi$
$930$	−14.1843	−0.465121
$931$	4.19990	0.137646
$932$	71.0603	2.32766
$933$	4.39877	0.144009
$934$	−66.7709	−2.18481
$935$	1.87993	0.0614802
$936$	−5.95821	−0.194750
$937$	−48.1782	−1.57391	−0.786957	−	0.617008i	$-0.788344\pi$
$937$	−48.1782	−1.57391	−0.786957	+	0.617008i	$0.788344\pi$
$938$	23.7292	0.774785
$939$	−23.1120	−0.754233
$940$	−30.7973	−1.00450
$941$	47.8352	1.55938	0.779692	−	0.626163i	$-0.215376\pi$
$941$	47.8352	1.55938	0.779692	+	0.626163i	$0.215376\pi$
$942$	41.3442	1.34707
$943$	1.85668	0.0604619
$944$	−59.1591	−1.92547
$945$	1.00000	0.0325300
$946$	21.6742	0.704691
$947$	−37.0246	−1.20314	−0.601569	−	0.798821i	$-0.705458\pi$
$947$	−37.0246	−1.20314	−0.601569	+	0.798821i	$0.705458\pi$
$948$	41.2914	1.34108
$949$	−0.885912	−0.0287579
$950$	11.4539	0.371613
$951$	17.0735	0.553646
$952$	−7.17717	−0.232614
$953$	−3.31523	−0.107391	−0.0536955	−	0.998557i	$-0.517100\pi$
$953$	−3.31523	−0.107391	−0.0536955	+	0.998557i	$0.517100\pi$
$954$	35.8777	1.16158
$955$	−16.3547	−0.529226
$956$	−51.7031	−1.67220
$957$	−4.50252	−0.145546
$958$	80.0778	2.58719
$959$	−2.12488	−0.0686160
$960$	28.7522	0.927972
$961$	−3.94881	−0.127381
$962$	11.9370	0.384864
$963$	4.18558	0.134878
$964$	59.8073	1.92626
$965$	7.63245	0.245697
$966$	2.72718	0.0877456
$967$	7.87953	0.253389	0.126694	−	0.991942i	$-0.459563\pi$
$967$	7.87953	0.253389	0.126694	+	0.991942i	$0.459563\pi$
$968$	−46.5957	−1.49764
$969$	3.21540	0.103294
$970$	−16.8502	−0.541026
$971$	18.9213	0.607212	0.303606	−	0.952798i	$-0.401809\pi$
$971$	18.9213	0.607212	0.303606	+	0.952798i	$0.401809\pi$
$972$	−5.43751	−0.174408
$973$	−19.0027	−0.609199
$974$	66.4758	2.13002
$975$	0.635562	0.0203543
$976$	74.0214	2.36937
$977$	1.53350	0.0490609	0.0245304	−	0.999699i	$-0.492191\pi$
$977$	1.53350	0.0490609	0.0245304	+	0.999699i	$0.492191\pi$
$978$	32.6105	1.04277
$979$	−19.1629	−0.612449
$980$	−5.43751	−0.173695
$981$	−17.4772	−0.558006
$982$	−56.8400	−1.81384
$983$	11.8696	0.378582	0.189291	−	0.981921i	$-0.439381\pi$
$983$	11.8696	0.378582	0.189291	+	0.981921i	$0.439381\pi$
$984$	17.4059	0.554879
$985$	−19.9868	−0.636834
$986$	−3.82842	−0.121922
$987$	−5.66386	−0.180283
$988$	−14.5143	−0.461763
$989$	−3.23657	−0.102917
$990$	−6.69668	−0.212834
$991$	−8.32373	−0.264412	−0.132206	−	0.991222i	$-0.542206\pi$
$991$	−8.32373	−0.264412	−0.132206	+	0.991222i	$0.542206\pi$
$992$	−110.871	−3.52016
$993$	22.1135	0.701750
$994$	−25.5588	−0.810676
$995$	−14.8081	−0.469448
$996$	−95.2554	−3.01828
$997$	45.1605	1.43025	0.715124	−	0.698997i	$-0.246370\pi$
$997$	45.1605	1.43025	0.715124	+	0.698997i	$0.246370\pi$
$998$	−39.2469	−1.24234
$999$	6.88688	0.217891

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2415.2.a.q.1.6	✓	6
3.2	odd	2		7245.2.a.bj.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2415.2.a.q.1.6	✓	6	1.1	even	1	trivial
7245.2.a.bj.1.1		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)

\(f(q)\)	\(=\)	\(q+2.72718 q^{2} -1.00000 q^{3} +5.43751 q^{4} -1.00000 q^{5} -2.72718 q^{6} +1.00000 q^{7} +9.37471 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.72718 q^{2} -1.00000 q^{3} +5.43751 q^{4} -1.00000 q^{5} -2.72718 q^{6} +1.00000 q^{7} +9.37471 q^{8} +1.00000 q^{9} -2.72718 q^{10} +2.45553 q^{11} -5.43751 q^{12} -0.635562 q^{13} +2.72718 q^{14} +1.00000 q^{15} +14.6915 q^{16} -0.765589 q^{17} +2.72718 q^{18} +4.19990 q^{19} -5.43751 q^{20} -1.00000 q^{21} +6.69668 q^{22} -1.00000 q^{23} -9.37471 q^{24} +1.00000 q^{25} -1.73329 q^{26} -1.00000 q^{27} +5.43751 q^{28} +1.83362 q^{29} +2.72718 q^{30} -5.20108 q^{31} +21.3169 q^{32} -2.45553 q^{33} -2.08790 q^{34} -1.00000 q^{35} +5.43751 q^{36} -6.88688 q^{37} +11.4539 q^{38} +0.635562 q^{39} -9.37471 q^{40} -1.85668 q^{41} -2.72718 q^{42} +3.23657 q^{43} +13.3520 q^{44} -1.00000 q^{45} -2.72718 q^{46} +5.66386 q^{47} -14.6915 q^{48} +1.00000 q^{49} +2.72718 q^{50} +0.765589 q^{51} -3.45588 q^{52} +13.1556 q^{53} -2.72718 q^{54} -2.45553 q^{55} +9.37471 q^{56} -4.19990 q^{57} +5.00062 q^{58} -4.02676 q^{59} +5.43751 q^{60} +5.03838 q^{61} -14.1843 q^{62} +1.00000 q^{63} +28.7522 q^{64} +0.635562 q^{65} -6.69668 q^{66} +8.70100 q^{67} -4.16290 q^{68} +1.00000 q^{69} -2.72718 q^{70} -9.37188 q^{71} +9.37471 q^{72} +1.39390 q^{73} -18.7818 q^{74} -1.00000 q^{75} +22.8370 q^{76} +2.45553 q^{77} +1.73329 q^{78} -7.59381 q^{79} -14.6915 q^{80} +1.00000 q^{81} -5.06351 q^{82} +17.5182 q^{83} -5.43751 q^{84} +0.765589 q^{85} +8.82670 q^{86} -1.83362 q^{87} +23.0199 q^{88} -7.80397 q^{89} -2.72718 q^{90} -0.635562 q^{91} -5.43751 q^{92} +5.20108 q^{93} +15.4464 q^{94} -4.19990 q^{95} -21.3169 q^{96} +6.17860 q^{97} +2.72718 q^{98} +2.45553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 6 q^{3} + 5 q^{4} - 6 q^{5} - 3 q^{6} + 6 q^{7} + 9 q^{8} + 6 q^{9}+O(q^{10}) \) 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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