LMFDB - Embedded newform 6015.2.a.f.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.98597 q^{2} -1.00000 q^{3} +1.94407 q^{4} -1.00000 q^{5} +1.98597 q^{6} -2.98220 q^{7} +0.111071 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.98597 q^{2} -1.00000 q^{3} +1.94407 q^{4} -1.00000 q^{5} +1.98597 q^{6} -2.98220 q^{7} +0.111071 q^{8} +1.00000 q^{9} +1.98597 q^{10} +5.57216 q^{11} -1.94407 q^{12} -2.87753 q^{13} +5.92256 q^{14} +1.00000 q^{15} -4.10873 q^{16} +6.23654 q^{17} -1.98597 q^{18} -3.43293 q^{19} -1.94407 q^{20} +2.98220 q^{21} -11.0661 q^{22} -5.27032 q^{23} -0.111071 q^{24} +1.00000 q^{25} +5.71468 q^{26} -1.00000 q^{27} -5.79762 q^{28} +3.21211 q^{29} -1.98597 q^{30} -0.153360 q^{31} +7.93766 q^{32} -5.57216 q^{33} -12.3856 q^{34} +2.98220 q^{35} +1.94407 q^{36} +2.03909 q^{37} +6.81768 q^{38} +2.87753 q^{39} -0.111071 q^{40} -7.80435 q^{41} -5.92256 q^{42} +6.57129 q^{43} +10.8327 q^{44} -1.00000 q^{45} +10.4667 q^{46} -3.40569 q^{47} +4.10873 q^{48} +1.89354 q^{49} -1.98597 q^{50} -6.23654 q^{51} -5.59412 q^{52} -7.15490 q^{53} +1.98597 q^{54} -5.57216 q^{55} -0.331238 q^{56} +3.43293 q^{57} -6.37915 q^{58} -4.60389 q^{59} +1.94407 q^{60} +0.941816 q^{61} +0.304567 q^{62} -2.98220 q^{63} -7.54649 q^{64} +2.87753 q^{65} +11.0661 q^{66} -12.7330 q^{67} +12.1243 q^{68} +5.27032 q^{69} -5.92256 q^{70} +14.6053 q^{71} +0.111071 q^{72} +0.369202 q^{73} -4.04956 q^{74} -1.00000 q^{75} -6.67385 q^{76} -16.6173 q^{77} -5.71468 q^{78} +16.4442 q^{79} +4.10873 q^{80} +1.00000 q^{81} +15.4992 q^{82} -2.96649 q^{83} +5.79762 q^{84} -6.23654 q^{85} -13.0504 q^{86} -3.21211 q^{87} +0.618907 q^{88} -3.19517 q^{89} +1.98597 q^{90} +8.58137 q^{91} -10.2459 q^{92} +0.153360 q^{93} +6.76359 q^{94} +3.43293 q^{95} -7.93766 q^{96} -11.0343 q^{97} -3.76051 q^{98} +5.57216 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) $ 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9} + 7 q^{10} - q^{11} - 45 q^{12} - 8 q^{13} - 4 q^{14} + 36 q^{15} + 63 q^{16} - 50 q^{17} - 7 q^{18} + 15 q^{19} - 45 q^{20} - 2 q^{21} + 7 q^{22} - 32 q^{23} + 24 q^{24} + 36 q^{25} - 12 q^{26} - 36 q^{27} - 10 q^{28} + 7 q^{29} - 7 q^{30} + 7 q^{31} - 50 q^{32} + q^{33} + 8 q^{34} - 2 q^{35} + 45 q^{36} - 10 q^{37} - 48 q^{38} + 8 q^{39} + 24 q^{40} - 31 q^{41} + 4 q^{42} + 27 q^{43} - 9 q^{44} - 36 q^{45} + 23 q^{46} - 46 q^{47} - 63 q^{48} + 48 q^{49} - 7 q^{50} + 50 q^{51} - 14 q^{52} - 39 q^{53} + 7 q^{54} + q^{55} - 29 q^{56} - 15 q^{57} - 26 q^{58} - 9 q^{59} + 45 q^{60} + 5 q^{61} - 65 q^{62} + 2 q^{63} + 90 q^{64} + 8 q^{65} - 7 q^{66} + 18 q^{67} - 128 q^{68} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 24 q^{72} - 45 q^{73} - 22 q^{74} - 36 q^{75} + 26 q^{76} - 38 q^{77} + 12 q^{78} + 25 q^{79} - 63 q^{80} + 36 q^{81} - 5 q^{82} - 71 q^{83} + 10 q^{84} + 50 q^{85} + 3 q^{86} - 7 q^{87} - 9 q^{88} - 39 q^{89} + 7 q^{90} + 19 q^{91} - 95 q^{92} - 7 q^{93} + 16 q^{94} - 15 q^{95} + 50 q^{96} - 61 q^{97} - 76 q^{98} - q^{99}+O(q^{100}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9 + 7 * q^10 - q^11 - 45 * q^12 - 8 * q^13 - 4 * q^14 + 36 * q^15 + 63 * q^16 - 50 * q^17 - 7 * q^18 + 15 * q^19 - 45 * q^20 - 2 * q^21 + 7 * q^22 - 32 * q^23 + 24 * q^24 + 36 * q^25 - 12 * q^26 - 36 * q^27 - 10 * q^28 + 7 * q^29 - 7 * q^30 + 7 * q^31 - 50 * q^32 + q^33 + 8 * q^34 - 2 * q^35 + 45 * q^36 - 10 * q^37 - 48 * q^38 + 8 * q^39 + 24 * q^40 - 31 * q^41 + 4 * q^42 + 27 * q^43 - 9 * q^44 - 36 * q^45 + 23 * q^46 - 46 * q^47 - 63 * q^48 + 48 * q^49 - 7 * q^50 + 50 * q^51 - 14 * q^52 - 39 * q^53 + 7 * q^54 + q^55 - 29 * q^56 - 15 * q^57 - 26 * q^58 - 9 * q^59 + 45 * q^60 + 5 * q^61 - 65 * q^62 + 2 * q^63 + 90 * q^64 + 8 * q^65 - 7 * q^66 + 18 * q^67 - 128 * q^68 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 24 * q^72 - 45 * q^73 - 22 * q^74 - 36 * q^75 + 26 * q^76 - 38 * q^77 + 12 * q^78 + 25 * q^79 - 63 * q^80 + 36 * q^81 - 5 * q^82 - 71 * q^83 + 10 * q^84 + 50 * q^85 + 3 * q^86 - 7 * q^87 - 9 * q^88 - 39 * q^89 + 7 * q^90 + 19 * q^91 - 95 * q^92 - 7 * q^93 + 16 * q^94 - 15 * q^95 + 50 * q^96 - 61 * q^97 - 76 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.98597	−1.40429	−0.702146	−	0.712033i	$-0.747775\pi$
$2$	−1.98597	−1.40429	−0.702146	+	0.712033i	$0.747775\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.94407	0.972036
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.98597	0.810768
$7$	−2.98220	−1.12717	−0.563583	−	0.826059i	$-0.690578\pi$
$7$	−2.98220	−1.12717	−0.563583	+	0.826059i	$0.690578\pi$
$8$	0.111071	0.0392697
$9$	1.00000	0.333333
$10$	1.98597	0.628018
$11$	5.57216	1.68007	0.840034	−	0.542533i	$-0.182535\pi$
$11$	5.57216	1.68007	0.840034	+	0.542533i	$0.182535\pi$
$12$	−1.94407	−0.561205
$13$	−2.87753	−0.798082	−0.399041	−	0.916933i	$-0.630657\pi$
$13$	−2.87753	−0.798082	−0.399041	+	0.916933i	$0.630657\pi$
$14$	5.92256	1.58287
$15$	1.00000	0.258199
$16$	−4.10873	−1.02718
$17$	6.23654	1.51258	0.756292	−	0.654235i	$-0.227009\pi$
$17$	6.23654	1.51258	0.756292	+	0.654235i	$0.227009\pi$
$18$	−1.98597	−0.468097
$19$	−3.43293	−0.787567	−0.393784	−	0.919203i	$-0.628834\pi$
$19$	−3.43293	−0.787567	−0.393784	+	0.919203i	$0.628834\pi$
$20$	−1.94407	−0.434708
$21$	2.98220	0.650770
$22$	−11.0661	−2.35931
$23$	−5.27032	−1.09894	−0.549469	−	0.835514i	$-0.685170\pi$
$23$	−5.27032	−1.09894	−0.549469	+	0.835514i	$0.685170\pi$
$24$	−0.111071	−0.0226724
$25$	1.00000	0.200000
$26$	5.71468	1.12074
$27$	−1.00000	−0.192450
$28$	−5.79762	−1.09565
$29$	3.21211	0.596474	0.298237	−	0.954492i	$-0.403601\pi$
$29$	3.21211	0.596474	0.298237	+	0.954492i	$0.403601\pi$
$30$	−1.98597	−0.362587
$31$	−0.153360	−0.0275442	−0.0137721	−	0.999905i	$-0.504384\pi$
$31$	−0.153360	−0.0275442	−0.0137721	+	0.999905i	$0.504384\pi$
$32$	7.93766	1.40319
$33$	−5.57216	−0.969988
$34$	−12.3856	−2.12411
$35$	2.98220	0.504084
$36$	1.94407	0.324012
$37$	2.03909	0.335224	0.167612	−	0.985853i	$-0.446394\pi$
$37$	2.03909	0.335224	0.167612	+	0.985853i	$0.446394\pi$
$38$	6.81768	1.10597
$39$	2.87753	0.460773
$40$	−0.111071	−0.0175619
$41$	−7.80435	−1.21884	−0.609418	−	0.792849i	$-0.708597\pi$
$41$	−7.80435	−1.21884	−0.609418	+	0.792849i	$0.708597\pi$
$42$	−5.92256	−0.913871
$43$	6.57129	1.00211	0.501056	−	0.865415i	$-0.332945\pi$
$43$	6.57129	1.00211	0.501056	+	0.865415i	$0.332945\pi$
$44$	10.8327	1.63309
$45$	−1.00000	−0.149071
$46$	10.4667	1.54323
$47$	−3.40569	−0.496771	−0.248385	−	0.968661i	$-0.579900\pi$
$47$	−3.40569	−0.496771	−0.248385	+	0.968661i	$0.579900\pi$
$48$	4.10873	0.593044
$49$	1.89354	0.270505
$50$	−1.98597	−0.280858
$51$	−6.23654	−0.873290
$52$	−5.59412	−0.775765
$53$	−7.15490	−0.982802	−0.491401	−	0.870934i	$-0.663515\pi$
$53$	−7.15490	−0.982802	−0.491401	+	0.870934i	$0.663515\pi$
$54$	1.98597	0.270256
$55$	−5.57216	−0.751349
$56$	−0.331238	−0.0442635
$57$	3.43293	0.454702
$58$	−6.37915	−0.837623
$59$	−4.60389	−0.599375	−0.299688	−	0.954037i	$-0.596882\pi$
$59$	−4.60389	−0.599375	−0.299688	+	0.954037i	$0.596882\pi$
$60$	1.94407	0.250979
$61$	0.941816	0.120587	0.0602936	−	0.998181i	$-0.480796\pi$
$61$	0.941816	0.120587	0.0602936	+	0.998181i	$0.480796\pi$
$62$	0.304567	0.0386801
$63$	−2.98220	−0.375722
$64$	−7.54649	−0.943312
$65$	2.87753	0.356913
$66$	11.0661	1.36215
$67$	−12.7330	−1.55559	−0.777793	−	0.628520i	$-0.783661\pi$
$67$	−12.7330	−1.55559	−0.777793	+	0.628520i	$0.783661\pi$
$68$	12.1243	1.47029
$69$	5.27032	0.634473
$70$	−5.92256	−0.707882
$71$	14.6053	1.73333	0.866666	−	0.498889i	$-0.166258\pi$
$71$	14.6053	1.73333	0.866666	+	0.498889i	$0.166258\pi$
$72$	0.111071	0.0130899
$73$	0.369202	0.0432118	0.0216059	−	0.999767i	$-0.493122\pi$
$73$	0.369202	0.0432118	0.0216059	+	0.999767i	$0.493122\pi$
$74$	−4.04956	−0.470752
$75$	−1.00000	−0.115470
$76$	−6.67385	−0.765543
$77$	−16.6173	−1.89372
$78$	−5.71468	−0.647060
$79$	16.4442	1.85012	0.925059	−	0.379822i	$-0.124015\pi$
$79$	16.4442	1.85012	0.925059	+	0.379822i	$0.124015\pi$
$80$	4.10873	0.459370
$81$	1.00000	0.111111
$82$	15.4992	1.71160
$83$	−2.96649	−0.325615	−0.162808	−	0.986658i	$-0.552055\pi$
$83$	−2.96649	−0.325615	−0.162808	+	0.986658i	$0.552055\pi$
$84$	5.79762	0.632572
$85$	−6.23654	−0.676448
$86$	−13.0504	−1.40726
$87$	−3.21211	−0.344374
$88$	0.618907	0.0659757
$89$	−3.19517	−0.338688	−0.169344	−	0.985557i	$-0.554165\pi$
$89$	−3.19517	−0.338688	−0.169344	+	0.985557i	$0.554165\pi$
$90$	1.98597	0.209339
$91$	8.58137	0.899572
$92$	−10.2459	−1.06821
$93$	0.153360	0.0159027
$94$	6.76359	0.697611
$95$	3.43293	0.352211
$96$	−7.93766	−0.810134
$97$	−11.0343	−1.12037	−0.560184	−	0.828368i	$-0.689270\pi$
$97$	−11.0343	−1.12037	−0.560184	+	0.828368i	$0.689270\pi$
$98$	−3.76051	−0.379869
$99$	5.57216	0.560023
$100$	1.94407	0.194407
$101$	2.56127	0.254856	0.127428	−	0.991848i	$-0.459328\pi$
$101$	2.56127	0.254856	0.127428	+	0.991848i	$0.459328\pi$
$102$	12.3856	1.22635
$103$	5.03759	0.496369	0.248184	−	0.968713i	$-0.420166\pi$
$103$	5.03759	0.496369	0.248184	+	0.968713i	$0.420166\pi$
$104$	−0.319611	−0.0313404
$105$	−2.98220	−0.291033
$106$	14.2094	1.38014
$107$	−3.02744	−0.292674	−0.146337	−	0.989235i	$-0.546748\pi$
$107$	−3.02744	−0.292674	−0.146337	+	0.989235i	$0.546748\pi$
$108$	−1.94407	−0.187068
$109$	16.6283	1.59270	0.796350	−	0.604836i	$-0.206761\pi$
$109$	16.6283	1.59270	0.796350	+	0.604836i	$0.206761\pi$
$110$	11.0661	1.05511
$111$	−2.03909	−0.193541
$112$	12.2531	1.15781
$113$	−14.8933	−1.40104	−0.700521	−	0.713632i	$-0.747049\pi$
$113$	−14.8933	−1.40104	−0.700521	+	0.713632i	$0.747049\pi$
$114$	−6.81768	−0.638534
$115$	5.27032	0.491460
$116$	6.24457	0.579794
$117$	−2.87753	−0.266027
$118$	9.14318	0.841698
$119$	−18.5986	−1.70493
$120$	0.111071	0.0101394
$121$	20.0489	1.82263
$122$	−1.87042	−0.169340
$123$	7.80435	0.703695
$124$	−0.298142	−0.0267740
$125$	−1.00000	−0.0894427
$126$	5.92256	0.527624
$127$	13.5738	1.20448	0.602238	−	0.798317i	$-0.294276\pi$
$127$	13.5738	1.20448	0.602238	+	0.798317i	$0.294276\pi$
$128$	−0.888224	−0.0785086
$129$	−6.57129	−0.578570
$130$	−5.71468	−0.501210
$131$	11.8531	1.03561	0.517804	−	0.855499i	$-0.326749\pi$
$131$	11.8531	1.03561	0.517804	+	0.855499i	$0.326749\pi$
$132$	−10.8327	−0.942863
$133$	10.2377	0.887720
$134$	25.2874	2.18450
$135$	1.00000	0.0860663
$136$	0.692701	0.0593987
$137$	0.118439	0.0101189	0.00505947	−	0.999987i	$-0.498390\pi$
$137$	0.118439	0.0101189	0.00505947	+	0.999987i	$0.498390\pi$
$138$	−10.4667	−0.890985
$139$	6.83023	0.579333	0.289666	−	0.957128i	$-0.406456\pi$
$139$	6.83023	0.579333	0.289666	+	0.957128i	$0.406456\pi$
$140$	5.79762	0.489988
$141$	3.40569	0.286811
$142$	−29.0057	−2.43410
$143$	−16.0340	−1.34083
$144$	−4.10873	−0.342394
$145$	−3.21211	−0.266751
$146$	−0.733224	−0.0606820
$147$	−1.89354	−0.156176
$148$	3.96413	0.325849
$149$	21.6654	1.77490	0.887451	−	0.460902i	$-0.152474\pi$
$149$	21.6654	1.77490	0.887451	+	0.460902i	$0.152474\pi$
$150$	1.98597	0.162154
$151$	6.19473	0.504120	0.252060	−	0.967712i	$-0.418892\pi$
$151$	6.19473	0.504120	0.252060	+	0.967712i	$0.418892\pi$
$152$	−0.381300	−0.0309275
$153$	6.23654	0.504194
$154$	33.0014	2.65933
$155$	0.153360	0.0123181
$156$	5.59412	0.447888
$157$	−15.4179	−1.23048	−0.615241	−	0.788339i	$-0.710941\pi$
$157$	−15.4179	−1.23048	−0.615241	+	0.788339i	$0.710941\pi$
$158$	−32.6577	−2.59811
$159$	7.15490	0.567421
$160$	−7.93766	−0.627527
$161$	15.7172	1.23869
$162$	−1.98597	−0.156032
$163$	−6.97966	−0.546689	−0.273345	−	0.961916i	$-0.588130\pi$
$163$	−6.97966	−0.546689	−0.273345	+	0.961916i	$0.588130\pi$
$164$	−15.1722	−1.18475
$165$	5.57216	0.433792
$166$	5.89137	0.457259
$167$	12.2437	0.947448	0.473724	−	0.880673i	$-0.342909\pi$
$167$	12.2437	0.947448	0.473724	+	0.880673i	$0.342909\pi$
$168$	0.331238	0.0255555
$169$	−4.71984	−0.363064
$170$	12.3856	0.949930
$171$	−3.43293	−0.262522
$172$	12.7751	0.974089
$173$	−5.13203	−0.390181	−0.195090	−	0.980785i	$-0.562500\pi$
$173$	−5.13203	−0.390181	−0.195090	+	0.980785i	$0.562500\pi$
$174$	6.37915	0.483602
$175$	−2.98220	−0.225433
$176$	−22.8945	−1.72574
$177$	4.60389	0.346050
$178$	6.34552	0.475617
$179$	−10.5405	−0.787834	−0.393917	−	0.919146i	$-0.628880\pi$
$179$	−10.5405	−0.787834	−0.393917	+	0.919146i	$0.628880\pi$
$180$	−1.94407	−0.144903
$181$	3.28855	0.244436	0.122218	−	0.992503i	$-0.460999\pi$
$181$	3.28855	0.244436	0.122218	+	0.992503i	$0.460999\pi$
$182$	−17.0423	−1.26326
$183$	−0.941816	−0.0696210
$184$	−0.585382	−0.0431550
$185$	−2.03909	−0.149917
$186$	−0.304567	−0.0223320
$187$	34.7510	2.54124
$188$	−6.62090	−0.482879
$189$	2.98220	0.216923
$190$	−6.81768	−0.494607
$191$	4.48790	0.324733	0.162366	−	0.986731i	$-0.448087\pi$
$191$	4.48790	0.324733	0.162366	+	0.986731i	$0.448087\pi$
$192$	7.54649	0.544621
$193$	−9.06891	−0.652795	−0.326397	−	0.945233i	$-0.605835\pi$
$193$	−9.06891	−0.652795	−0.326397	+	0.945233i	$0.605835\pi$
$194$	21.9139	1.57332
$195$	−2.87753	−0.206064
$196$	3.68117	0.262941
$197$	18.3813	1.30962	0.654808	−	0.755795i	$-0.272750\pi$
$197$	18.3813	1.30962	0.654808	+	0.755795i	$0.272750\pi$
$198$	−11.0661	−0.786436
$199$	−25.8989	−1.83593	−0.917963	−	0.396667i	$-0.870167\pi$
$199$	−25.8989	−1.83593	−0.917963	+	0.396667i	$0.870167\pi$
$200$	0.111071	0.00785394
$201$	12.7330	0.898118
$202$	−5.08660	−0.357892
$203$	−9.57917	−0.672326
$204$	−12.1243	−0.848870
$205$	7.80435	0.545080
$206$	−10.0045	−0.697047
$207$	−5.27032	−0.366313
$208$	11.8230	0.819776
$209$	−19.1288	−1.32317
$210$	5.92256	0.408696
$211$	2.16925	0.149337	0.0746686	−	0.997208i	$-0.476210\pi$
$211$	2.16925	0.149337	0.0746686	+	0.997208i	$0.476210\pi$
$212$	−13.9096	−0.955318
$213$	−14.6053	−1.00074
$214$	6.01240	0.410999
$215$	−6.57129	−0.448158
$216$	−0.111071	−0.00755745
$217$	0.457350	0.0310469
$218$	−33.0232	−2.23662
$219$	−0.369202	−0.0249484
$220$	−10.8327	−0.730339
$221$	−17.9458	−1.20717
$222$	4.04956	0.271789
$223$	5.76491	0.386047	0.193023	−	0.981194i	$-0.438171\pi$
$223$	5.76491	0.386047	0.193023	+	0.981194i	$0.438171\pi$
$224$	−23.6717	−1.58163
$225$	1.00000	0.0666667
$226$	29.5776	1.96747
$227$	12.3171	0.817518	0.408759	−	0.912642i	$-0.365962\pi$
$227$	12.3171	0.817518	0.408759	+	0.912642i	$0.365962\pi$
$228$	6.67385	0.441987
$229$	7.12839	0.471057	0.235529	−	0.971867i	$-0.424318\pi$
$229$	7.12839	0.471057	0.235529	+	0.971867i	$0.424318\pi$
$230$	−10.4667	−0.690154
$231$	16.6173	1.09334
$232$	0.356774	0.0234233
$233$	0.816584	0.0534962	0.0267481	−	0.999642i	$-0.491485\pi$
$233$	0.816584	0.0534962	0.0267481	+	0.999642i	$0.491485\pi$
$234$	5.71468	0.373580
$235$	3.40569	0.222163
$236$	−8.95029	−0.582614
$237$	−16.4442	−1.06817
$238$	36.9363	2.39423
$239$	1.98669	0.128508	0.0642542	−	0.997934i	$-0.479533\pi$
$239$	1.98669	0.128508	0.0642542	+	0.997934i	$0.479533\pi$
$240$	−4.10873	−0.265217
$241$	−12.9999	−0.837397	−0.418698	−	0.908125i	$-0.637514\pi$
$241$	−12.9999	−0.837397	−0.418698	+	0.908125i	$0.637514\pi$
$242$	−39.8165	−2.55950
$243$	−1.00000	−0.0641500
$244$	1.83096	0.117215
$245$	−1.89354	−0.120974
$246$	−15.4992	−0.988193
$247$	9.87833	0.628543
$248$	−0.0170339	−0.00108165
$249$	2.96649	0.187994
$250$	1.98597	0.125604
$251$	−27.4909	−1.73521	−0.867604	−	0.497256i	$-0.834341\pi$
$251$	−27.4909	−1.73521	−0.867604	+	0.497256i	$0.834341\pi$
$252$	−5.79762	−0.365216
$253$	−29.3671	−1.84629
$254$	−26.9570	−1.69144
$255$	6.23654	0.390547
$256$	16.8570	1.05356
$257$	5.78164	0.360649	0.180324	−	0.983607i	$-0.442285\pi$
$257$	5.78164	0.360649	0.180324	+	0.983607i	$0.442285\pi$
$258$	13.0504	0.812481
$259$	−6.08097	−0.377853
$260$	5.59412	0.346933
$261$	3.21211	0.198825
$262$	−23.5399	−1.45430
$263$	−8.36595	−0.515866	−0.257933	−	0.966163i	$-0.583041\pi$
$263$	−8.36595	−0.515866	−0.257933	+	0.966163i	$0.583041\pi$
$264$	−0.618907	−0.0380911
$265$	7.15490	0.439522
$266$	−20.3317	−1.24662
$267$	3.19517	0.195542
$268$	−24.7539	−1.51209
$269$	−25.1734	−1.53485	−0.767425	−	0.641139i	$-0.778462\pi$
$269$	−25.1734	−1.53485	−0.767425	+	0.641139i	$0.778462\pi$
$270$	−1.98597	−0.120862
$271$	19.0220	1.15551	0.577753	−	0.816212i	$-0.303930\pi$
$271$	19.0220	1.15551	0.577753	+	0.816212i	$0.303930\pi$
$272$	−25.6243	−1.55370
$273$	−8.58137	−0.519368
$274$	−0.235216	−0.0142099
$275$	5.57216	0.336014
$276$	10.2459	0.616730
$277$	16.2788	0.978098	0.489049	−	0.872256i	$-0.337344\pi$
$277$	16.2788	0.978098	0.489049	+	0.872256i	$0.337344\pi$
$278$	−13.5646	−0.813552
$279$	−0.153360	−0.00918140
$280$	0.331238	0.0197952
$281$	−12.3278	−0.735416	−0.367708	−	0.929941i	$-0.619857\pi$
$281$	−12.3278	−0.735416	−0.367708	+	0.929941i	$0.619857\pi$
$282$	−6.76359	−0.402766
$283$	−5.09935	−0.303125	−0.151562	−	0.988448i	$-0.548430\pi$
$283$	−5.09935	−0.303125	−0.151562	+	0.988448i	$0.548430\pi$
$284$	28.3938	1.68486
$285$	−3.43293	−0.203349
$286$	31.8431	1.88292
$287$	23.2742	1.37383
$288$	7.93766	0.467731
$289$	21.8944	1.28791
$290$	6.37915	0.374597
$291$	11.0343	0.646845
$292$	0.717755	0.0420035
$293$	−15.3340	−0.895823	−0.447911	−	0.894078i	$-0.647832\pi$
$293$	−15.3340	−0.895823	−0.447911	+	0.894078i	$0.647832\pi$
$294$	3.76051	0.219317
$295$	4.60389	0.268049
$296$	0.226484	0.0131641
$297$	−5.57216	−0.323329
$298$	−43.0269	−2.49248
$299$	15.1655	0.877044
$300$	−1.94407	−0.112241
$301$	−19.5969	−1.12955
$302$	−12.3025	−0.707931
$303$	−2.56127	−0.147141
$304$	14.1050	0.808975
$305$	−0.941816	−0.0539282
$306$	−12.3856	−0.708036
$307$	12.5279	0.715004	0.357502	−	0.933912i	$-0.383628\pi$
$307$	12.5279	0.715004	0.357502	+	0.933912i	$0.383628\pi$
$308$	−32.3052	−1.84076
$309$	−5.03759	−0.286579
$310$	−0.304567	−0.0172983
$311$	−4.87098	−0.276208	−0.138104	−	0.990418i	$-0.544101\pi$
$311$	−4.87098	−0.276208	−0.138104	+	0.990418i	$0.544101\pi$
$312$	0.319611	0.0180944
$313$	3.79318	0.214403	0.107202	−	0.994237i	$-0.465811\pi$
$313$	3.79318	0.214403	0.107202	+	0.994237i	$0.465811\pi$
$314$	30.6194	1.72795
$315$	2.98220	0.168028
$316$	31.9687	1.79838
$317$	33.4890	1.88093	0.940466	−	0.339888i	$-0.110389\pi$
$317$	33.4890	1.88093	0.940466	+	0.339888i	$0.110389\pi$
$318$	−14.2094	−0.796824
$319$	17.8984	1.00212
$320$	7.54649	0.421862
$321$	3.02744	0.168975
$322$	−31.2138	−1.73948
$323$	−21.4096	−1.19126
$324$	1.94407	0.108004
$325$	−2.87753	−0.159616
$326$	13.8614	0.767711
$327$	−16.6283	−0.919546
$328$	−0.866841	−0.0478633
$329$	10.1565	0.559943
$330$	−11.0661	−0.609170
$331$	34.7645	1.91083	0.955414	−	0.295269i	$-0.0954093\pi$
$331$	34.7645	1.91083	0.955414	+	0.295269i	$0.0954093\pi$
$332$	−5.76708	−0.316510
$333$	2.03909	0.111741
$334$	−24.3157	−1.33049
$335$	12.7330	0.695680
$336$	−12.2531	−0.668459
$337$	−1.20469	−0.0656235	−0.0328118	−	0.999462i	$-0.510446\pi$
$337$	−1.20469	−0.0656235	−0.0328118	+	0.999462i	$0.510446\pi$
$338$	9.37345	0.509849
$339$	14.8933	0.808892
$340$	−12.1243	−0.657532
$341$	−0.854544	−0.0462762
$342$	6.81768	0.368658
$343$	15.2285	0.822262
$344$	0.729883	0.0393526
$345$	−5.27032	−0.283745
$346$	10.1920	0.547928
$347$	−15.7017	−0.842913	−0.421457	−	0.906849i	$-0.638481\pi$
$347$	−15.7017	−0.842913	−0.421457	+	0.906849i	$0.638481\pi$
$348$	−6.24457	−0.334744
$349$	−32.3826	−1.73340	−0.866700	−	0.498829i	$-0.833763\pi$
$349$	−32.3826	−1.73340	−0.866700	+	0.498829i	$0.833763\pi$
$350$	5.92256	0.316574
$351$	2.87753	0.153591
$352$	44.2299	2.35746
$353$	3.57065	0.190047	0.0950234	−	0.995475i	$-0.469707\pi$
$353$	3.57065	0.190047	0.0950234	+	0.995475i	$0.469707\pi$
$354$	−9.14318	−0.485955
$355$	−14.6053	−0.775170
$356$	−6.21165	−0.329217
$357$	18.5986	0.984344
$358$	20.9331	1.10635
$359$	−13.8128	−0.729013	−0.364507	−	0.931201i	$-0.618762\pi$
$359$	−13.8128	−0.729013	−0.364507	+	0.931201i	$0.618762\pi$
$360$	−0.111071	−0.00585398
$361$	−7.21503	−0.379738
$362$	−6.53095	−0.343259
$363$	−20.0489	−1.05230
$364$	16.6828	0.874416
$365$	−0.369202	−0.0193249
$366$	1.87042	0.0977682
$367$	26.9654	1.40758	0.703791	−	0.710407i	$-0.251489\pi$
$367$	26.9654	1.40758	0.703791	+	0.710407i	$0.251489\pi$
$368$	21.6543	1.12881
$369$	−7.80435	−0.406278
$370$	4.04956	0.210527
$371$	21.3374	1.10778
$372$	0.298142	0.0154580
$373$	−21.2851	−1.10210	−0.551050	−	0.834472i	$-0.685773\pi$
$373$	−21.2851	−1.10210	−0.551050	+	0.834472i	$0.685773\pi$
$374$	−69.0144	−3.56865
$375$	1.00000	0.0516398
$376$	−0.378275	−0.0195080
$377$	−9.24293	−0.476035
$378$	−5.92256	−0.304624
$379$	−16.0959	−0.826790	−0.413395	−	0.910552i	$-0.635657\pi$
$379$	−16.0959	−0.826790	−0.413395	+	0.910552i	$0.635657\pi$
$380$	6.67385	0.342361
$381$	−13.5738	−0.695404
$382$	−8.91283	−0.456020
$383$	17.3143	0.884721	0.442360	−	0.896837i	$-0.354141\pi$
$383$	17.3143	0.884721	0.442360	+	0.896837i	$0.354141\pi$
$384$	0.888224	0.0453270
$385$	16.6173	0.846896
$386$	18.0106	0.916714
$387$	6.57129	0.334038
$388$	−21.4516	−1.08904
$389$	−8.77863	−0.445094	−0.222547	−	0.974922i	$-0.571437\pi$
$389$	−8.77863	−0.445094	−0.222547	+	0.974922i	$0.571437\pi$
$390$	5.71468	0.289374
$391$	−32.8686	−1.66224
$392$	0.210318	0.0106227
$393$	−11.8531	−0.597909
$394$	−36.5048	−1.83908
$395$	−16.4442	−0.827398
$396$	10.8327	0.544362
$397$	11.3788	0.571088	0.285544	−	0.958366i	$-0.407826\pi$
$397$	11.3788	0.571088	0.285544	+	0.958366i	$0.407826\pi$
$398$	51.4344	2.57818
$399$	−10.2377	−0.512525
$400$	−4.10873	−0.205436
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−25.2874	−1.26122
$403$	0.441297	0.0219825
$404$	4.97929	0.247729
$405$	−1.00000	−0.0496904
$406$	19.0239	0.944142
$407$	11.3621	0.563199
$408$	−0.692701	−0.0342938
$409$	−15.4087	−0.761913	−0.380957	−	0.924593i	$-0.624405\pi$
$409$	−15.4087	−0.761913	−0.380957	+	0.924593i	$0.624405\pi$
$410$	−15.4992	−0.765451
$411$	−0.118439	−0.00584217
$412$	9.79344	0.482488
$413$	13.7297	0.675596
$414$	10.4667	0.514410
$415$	2.96649	0.145620
$416$	−22.8408	−1.11986
$417$	−6.83023	−0.334478
$418$	37.9892	1.85811
$419$	−10.1897	−0.497802	−0.248901	−	0.968529i	$-0.580069\pi$
$419$	−10.1897	−0.497802	−0.248901	+	0.968529i	$0.580069\pi$
$420$	−5.79762	−0.282895
$421$	−17.0965	−0.833232	−0.416616	−	0.909083i	$-0.636784\pi$
$421$	−17.0965	−0.833232	−0.416616	+	0.909083i	$0.636784\pi$
$422$	−4.30806	−0.209713
$423$	−3.40569	−0.165590
$424$	−0.794705	−0.0385943
$425$	6.23654	0.302517
$426$	29.0057	1.40533
$427$	−2.80869	−0.135922
$428$	−5.88556	−0.284489
$429$	16.0340	0.774130
$430$	13.0504	0.629345
$431$	2.40297	0.115747	0.0578736	−	0.998324i	$-0.481568\pi$
$431$	2.40297	0.115747	0.0578736	+	0.998324i	$0.481568\pi$
$432$	4.10873	0.197681
$433$	−37.8449	−1.81871	−0.909354	−	0.416024i	$-0.863423\pi$
$433$	−37.8449	−1.81871	−0.909354	+	0.416024i	$0.863423\pi$
$434$	−0.908282	−0.0435989
$435$	3.21211	0.154009
$436$	32.3266	1.54816
$437$	18.0926	0.865488
$438$	0.733224	0.0350348
$439$	−18.2518	−0.871110	−0.435555	−	0.900162i	$-0.643448\pi$
$439$	−18.2518	−0.871110	−0.435555	+	0.900162i	$0.643448\pi$
$440$	−0.618907	−0.0295053
$441$	1.89354	0.0901685
$442$	35.6398	1.69521
$443$	−14.1017	−0.669990	−0.334995	−	0.942220i	$-0.608735\pi$
$443$	−14.1017	−0.669990	−0.334995	+	0.942220i	$0.608735\pi$
$444$	−3.96413	−0.188129
$445$	3.19517	0.151466
$446$	−11.4489	−0.542122
$447$	−21.6654	−1.02474
$448$	22.5052	1.06327
$449$	21.9543	1.03609	0.518044	−	0.855354i	$-0.326660\pi$
$449$	21.9543	1.03609	0.518044	+	0.855354i	$0.326660\pi$
$450$	−1.98597	−0.0936195
$451$	−43.4871	−2.04773
$452$	−28.9536	−1.36186
$453$	−6.19473	−0.291054
$454$	−24.4615	−1.14803
$455$	−8.58137	−0.402301
$456$	0.381300	0.0178560
$457$	−23.4535	−1.09711	−0.548554	−	0.836115i	$-0.684822\pi$
$457$	−23.4535	−1.09711	−0.548554	+	0.836115i	$0.684822\pi$
$458$	−14.1568	−0.661502
$459$	−6.23654	−0.291097
$460$	10.2459	0.477717
$461$	−21.6373	−1.00775	−0.503875	−	0.863776i	$-0.668093\pi$
$461$	−21.6373	−1.00775	−0.503875	+	0.863776i	$0.668093\pi$
$462$	−33.0014	−1.53537
$463$	−27.3661	−1.27181	−0.635905	−	0.771767i	$-0.719373\pi$
$463$	−27.3661	−1.27181	−0.635905	+	0.771767i	$0.719373\pi$
$464$	−13.1977	−0.612687
$465$	−0.153360	−0.00711188
$466$	−1.62171	−0.0751242
$467$	−0.325462	−0.0150606	−0.00753029	−	0.999972i	$-0.502397\pi$
$467$	−0.325462	−0.0150606	−0.00753029	+	0.999972i	$0.502397\pi$
$468$	−5.59412	−0.258588
$469$	37.9725	1.75341
$470$	−6.76359	−0.311981
$471$	15.4179	0.710419
$472$	−0.511361	−0.0235373
$473$	36.6163	1.68362
$474$	32.6577	1.50002
$475$	−3.43293	−0.157513
$476$	−36.1571	−1.65726
$477$	−7.15490	−0.327601
$478$	−3.94551	−0.180463
$479$	40.4500	1.84821	0.924104	−	0.382140i	$-0.124813\pi$
$479$	40.4500	1.84821	0.924104	+	0.382140i	$0.124813\pi$
$480$	7.93766	0.362303
$481$	−5.86752	−0.267536
$482$	25.8174	1.17595
$483$	−15.7172	−0.715156
$484$	38.9766	1.77166
$485$	11.0343	0.501044
$486$	1.98597	0.0900854
$487$	−11.4303	−0.517957	−0.258978	−	0.965883i	$-0.583386\pi$
$487$	−11.4303	−0.517957	−0.258978	+	0.965883i	$0.583386\pi$
$488$	0.104609	0.00473542
$489$	6.97966	0.315631
$490$	3.76051	0.169882
$491$	13.0493	0.588907	0.294454	−	0.955666i	$-0.404862\pi$
$491$	13.0493	0.588907	0.294454	+	0.955666i	$0.404862\pi$
$492$	15.1722	0.684017
$493$	20.0325	0.902216
$494$	−19.6181	−0.882658
$495$	−5.57216	−0.250450
$496$	0.630113	0.0282929
$497$	−43.5560	−1.95375
$498$	−5.89137	−0.263998
$499$	18.7175	0.837910	0.418955	−	0.908007i	$-0.362396\pi$
$499$	18.7175	0.837910	0.418955	+	0.908007i	$0.362396\pi$
$500$	−1.94407	−0.0869415
$501$	−12.2437	−0.547010
$502$	54.5960	2.43674
$503$	−32.0179	−1.42761	−0.713803	−	0.700347i	$-0.753029\pi$
$503$	−32.0179	−1.42761	−0.713803	+	0.700347i	$0.753029\pi$
$504$	−0.331238	−0.0147545
$505$	−2.56127	−0.113975
$506$	58.3221	2.59273
$507$	4.71984	0.209615
$508$	26.3884	1.17079
$509$	−4.12805	−0.182973	−0.0914864	−	0.995806i	$-0.529162\pi$
$509$	−4.12805	−0.182973	−0.0914864	+	0.995806i	$0.529162\pi$
$510$	−12.3856	−0.548442
$511$	−1.10104	−0.0487069
$512$	−31.7010	−1.40100
$513$	3.43293	0.151567
$514$	−11.4821	−0.506456
$515$	−5.03759	−0.221983
$516$	−12.7751	−0.562391
$517$	−18.9770	−0.834609
$518$	12.0766	0.530616
$519$	5.13203	0.225271
$520$	0.319611	0.0140159
$521$	1.06490	0.0466541	0.0233271	−	0.999728i	$-0.492574\pi$
$521$	1.06490	0.0466541	0.0233271	+	0.999728i	$0.492574\pi$
$522$	−6.37915	−0.279208
$523$	−10.6554	−0.465927	−0.232963	−	0.972486i	$-0.574842\pi$
$523$	−10.6554	−0.465927	−0.232963	+	0.972486i	$0.574842\pi$
$524$	23.0433	1.00665
$525$	2.98220	0.130154
$526$	16.6145	0.724427
$527$	−0.956434	−0.0416629
$528$	22.8945	0.996354
$529$	4.77632	0.207666
$530$	−14.2094	−0.617218
$531$	−4.60389	−0.199792
$532$	19.9028	0.862895
$533$	22.4572	0.972731
$534$	−6.34552	−0.274597
$535$	3.02744	0.130888
$536$	−1.41428	−0.0610874
$537$	10.5405	0.454856
$538$	49.9936	2.15538
$539$	10.5511	0.454468
$540$	1.94407	0.0836595
$541$	−4.44849	−0.191255	−0.0956277	−	0.995417i	$-0.530486\pi$
$541$	−4.44849	−0.191255	−0.0956277	+	0.995417i	$0.530486\pi$
$542$	−37.7772	−1.62267
$543$	−3.28855	−0.141125
$544$	49.5036	2.12245
$545$	−16.6283	−0.712277
$546$	17.0423	0.729345
$547$	−16.9817	−0.726084	−0.363042	−	0.931773i	$-0.618262\pi$
$547$	−16.9817	−0.726084	−0.363042	+	0.931773i	$0.618262\pi$
$548$	0.230254	0.00983597
$549$	0.941816	0.0401957
$550$	−11.0661	−0.471861
$551$	−11.0269	−0.469763
$552$	0.585382	0.0249155
$553$	−49.0400	−2.08539
$554$	−32.3292	−1.37353
$555$	2.03909	0.0865544
$556$	13.2785	0.563132
$557$	−24.7515	−1.04875	−0.524377	−	0.851486i	$-0.675702\pi$
$557$	−24.7515	−1.04875	−0.524377	+	0.851486i	$0.675702\pi$
$558$	0.304567	0.0128934
$559$	−18.9091	−0.799768
$560$	−12.2531	−0.517786
$561$	−34.7510	−1.46719
$562$	24.4827	1.03274
$563$	−6.19304	−0.261005	−0.130503	−	0.991448i	$-0.541659\pi$
$563$	−6.19304	−0.261005	−0.130503	+	0.991448i	$0.541659\pi$
$564$	6.62090	0.278790
$565$	14.8933	0.626565
$566$	10.1272	0.425676
$567$	−2.98220	−0.125241
$568$	1.62223	0.0680674
$569$	−35.2754	−1.47882	−0.739412	−	0.673254i	$-0.764896\pi$
$569$	−35.2754	−1.47882	−0.739412	+	0.673254i	$0.764896\pi$
$570$	6.81768	0.285561
$571$	3.15673	0.132105	0.0660525	−	0.997816i	$-0.478960\pi$
$571$	3.15673	0.132105	0.0660525	+	0.997816i	$0.478960\pi$
$572$	−31.1713	−1.30334
$573$	−4.48790	−0.187485
$574$	−46.2218	−1.92926
$575$	−5.27032	−0.219788
$576$	−7.54649	−0.314437
$577$	26.1879	1.09021	0.545107	−	0.838366i	$-0.316489\pi$
$577$	26.1879	1.09021	0.545107	+	0.838366i	$0.316489\pi$
$578$	−43.4817	−1.80860
$579$	9.06891	0.376891
$580$	−6.24457	−0.259292
$581$	8.84669	0.367023
$582$	−21.9139	−0.908359
$583$	−39.8682	−1.65117
$584$	0.0410078	0.00169691
$585$	2.87753	0.118971
$586$	30.4529	1.25800
$587$	9.11778	0.376331	0.188166	−	0.982137i	$-0.439746\pi$
$587$	9.11778	0.376331	0.188166	+	0.982137i	$0.439746\pi$
$588$	−3.68117	−0.151809
$589$	0.526472	0.0216929
$590$	−9.14318	−0.376419
$591$	−18.3813	−0.756107
$592$	−8.37805	−0.344336
$593$	11.2031	0.460058	0.230029	−	0.973184i	$-0.426118\pi$
$593$	11.2031	0.460058	0.230029	+	0.973184i	$0.426118\pi$
$594$	11.0661	0.454049
$595$	18.5986	0.762470
$596$	42.1192	1.72527
$597$	25.8989	1.05997
$598$	−30.1182	−1.23163
$599$	−44.1896	−1.80554	−0.902770	−	0.430125i	$-0.858470\pi$
$599$	−44.1896	−1.80554	−0.902770	+	0.430125i	$0.858470\pi$
$600$	−0.111071	−0.00453447
$601$	−16.7879	−0.684795	−0.342397	−	0.939555i	$-0.611239\pi$
$601$	−16.7879	−0.684795	−0.342397	+	0.939555i	$0.611239\pi$
$602$	38.9189	1.58622
$603$	−12.7330	−0.518529
$604$	12.0430	0.490022
$605$	−20.0489	−0.815105
$606$	5.08660	0.206629
$607$	0.327912	0.0133095	0.00665477	−	0.999978i	$-0.497882\pi$
$607$	0.327912	0.0133095	0.00665477	+	0.999978i	$0.497882\pi$
$608$	−27.2494	−1.10511
$609$	9.57917	0.388167
$610$	1.87042	0.0757309
$611$	9.79996	0.396464
$612$	12.1243	0.490095
$613$	17.8661	0.721605	0.360803	−	0.932642i	$-0.382503\pi$
$613$	17.8661	0.721605	0.360803	+	0.932642i	$0.382503\pi$
$614$	−24.8800	−1.00407
$615$	−7.80435	−0.314702
$616$	−1.84571	−0.0743657
$617$	−3.51388	−0.141464	−0.0707318	−	0.997495i	$-0.522533\pi$
$617$	−3.51388	−0.141464	−0.0707318	+	0.997495i	$0.522533\pi$
$618$	10.0045	0.402440
$619$	12.1694	0.489129	0.244564	−	0.969633i	$-0.421355\pi$
$619$	12.1694	0.489129	0.244564	+	0.969633i	$0.421355\pi$
$620$	0.298142	0.0119737
$621$	5.27032	0.211491
$622$	9.67361	0.387876
$623$	9.52866	0.381758
$624$	−11.8230	−0.473298
$625$	1.00000	0.0400000
$626$	−7.53314	−0.301085
$627$	19.1288	0.763931
$628$	−29.9735	−1.19607
$629$	12.7168	0.507054
$630$	−5.92256	−0.235961
$631$	4.25669	0.169456	0.0847281	−	0.996404i	$-0.472998\pi$
$631$	4.25669	0.169456	0.0847281	+	0.996404i	$0.472998\pi$
$632$	1.82648	0.0726536
$633$	−2.16925	−0.0862199
$634$	−66.5082	−2.64138
$635$	−13.5738	−0.538658
$636$	13.9096	0.551553
$637$	−5.44871	−0.215886
$638$	−35.5456	−1.40726
$639$	14.6053	0.577777
$640$	0.888224	0.0351101
$641$	28.2921	1.11747	0.558735	−	0.829346i	$-0.311287\pi$
$641$	28.2921	1.11747	0.558735	+	0.829346i	$0.311287\pi$
$642$	−6.01240	−0.237290
$643$	−47.4596	−1.87162	−0.935812	−	0.352500i	$-0.885332\pi$
$643$	−47.4596	−1.87162	−0.935812	+	0.352500i	$0.885332\pi$
$644$	30.5553	1.20405
$645$	6.57129	0.258744
$646$	42.5188	1.67288
$647$	−44.8914	−1.76486	−0.882431	−	0.470443i	$-0.844094\pi$
$647$	−44.8914	−1.76486	−0.882431	+	0.470443i	$0.844094\pi$
$648$	0.111071	0.00436330
$649$	−25.6536	−1.00699
$650$	5.71468	0.224148
$651$	−0.457350	−0.0179249
$652$	−13.5690	−0.531402
$653$	22.5419	0.882134	0.441067	−	0.897474i	$-0.354600\pi$
$653$	22.5419	0.882134	0.441067	+	0.897474i	$0.354600\pi$
$654$	33.0232	1.29131
$655$	−11.8531	−0.463138
$656$	32.0660	1.25197
$657$	0.369202	0.0144039
$658$	−20.1704	−0.786324
$659$	−45.0671	−1.75557	−0.877783	−	0.479058i	$-0.840978\pi$
$659$	−45.0671	−1.75557	−0.877783	+	0.479058i	$0.840978\pi$
$660$	10.8327	0.421661
$661$	−42.3427	−1.64694	−0.823469	−	0.567361i	$-0.807965\pi$
$661$	−42.3427	−1.64694	−0.823469	+	0.567361i	$0.807965\pi$
$662$	−69.0412	−2.68336
$663$	17.9458	0.696958
$664$	−0.329493	−0.0127868
$665$	−10.2377	−0.397000
$666$	−4.04956	−0.156917
$667$	−16.9289	−0.655488
$668$	23.8027	0.920954
$669$	−5.76491	−0.222884
$670$	−25.2874	−0.976937
$671$	5.24794	0.202595
$672$	23.6717	0.913157
$673$	6.37914	0.245898	0.122949	−	0.992413i	$-0.460765\pi$
$673$	6.37914	0.245898	0.122949	+	0.992413i	$0.460765\pi$
$674$	2.39247	0.0921546
$675$	−1.00000	−0.0384900
$676$	−9.17571	−0.352912
$677$	−47.8174	−1.83777	−0.918887	−	0.394521i	$-0.870911\pi$
$677$	−47.8174	−1.83777	−0.918887	+	0.394521i	$0.870911\pi$
$678$	−29.5776	−1.13592
$679$	32.9067	1.26284
$680$	−0.692701	−0.0265639
$681$	−12.3171	−0.471994
$682$	1.69710	0.0649852
$683$	−13.3756	−0.511804	−0.255902	−	0.966703i	$-0.582372\pi$
$683$	−13.3756	−0.511804	−0.255902	+	0.966703i	$0.582372\pi$
$684$	−6.67385	−0.255181
$685$	−0.118439	−0.00452532
$686$	−30.2433	−1.15470
$687$	−7.12839	−0.271965
$688$	−26.9996	−1.02935
$689$	20.5884	0.784357
$690$	10.4667	0.398460
$691$	15.8631	0.603462	0.301731	−	0.953393i	$-0.402436\pi$
$691$	15.8631	0.603462	0.301731	+	0.953393i	$0.402436\pi$
$692$	−9.97703	−0.379270
$693$	−16.6173	−0.631239
$694$	31.1831	1.18370
$695$	−6.83023	−0.259085
$696$	−0.356774	−0.0135235
$697$	−48.6722	−1.84359
$698$	64.3108	2.43420
$699$	−0.816584	−0.0308860
$700$	−5.79762	−0.219129
$701$	−0.142529	−0.00538326	−0.00269163	−	0.999996i	$-0.500857\pi$
$701$	−0.142529	−0.00538326	−0.00269163	+	0.999996i	$0.500857\pi$
$702$	−5.71468	−0.215687
$703$	−7.00003	−0.264011
$704$	−42.0502	−1.58483
$705$	−3.40569	−0.128266
$706$	−7.09121	−0.266881
$707$	−7.63822	−0.287265
$708$	8.95029	0.336373
$709$	−12.2376	−0.459594	−0.229797	−	0.973239i	$-0.573806\pi$
$709$	−12.2376	−0.459594	−0.229797	+	0.973239i	$0.573806\pi$
$710$	29.0057	1.08856
$711$	16.4442	0.616706
$712$	−0.354893	−0.0133002
$713$	0.808255	0.0302694
$714$	−36.9363	−1.38231
$715$	16.0340	0.599639
$716$	−20.4915	−0.765803
$717$	−1.98669	−0.0741944
$718$	27.4319	1.02375
$719$	4.92890	0.183817	0.0919085	−	0.995767i	$-0.470703\pi$
$719$	4.92890	0.183817	0.0919085	+	0.995767i	$0.470703\pi$
$720$	4.10873	0.153123
$721$	−15.0231	−0.559491
$722$	14.3288	0.533263
$723$	12.9999	0.483471
$724$	6.39317	0.237600
$725$	3.21211	0.119295
$726$	39.8165	1.47773
$727$	−7.95268	−0.294948	−0.147474	−	0.989066i	$-0.547114\pi$
$727$	−7.95268	−0.294948	−0.147474	+	0.989066i	$0.547114\pi$
$728$	0.953145	0.0353259
$729$	1.00000	0.0370370
$730$	0.733224	0.0271378
$731$	40.9821	1.51578
$732$	−1.83096	−0.0676741
$733$	−31.5300	−1.16459	−0.582293	−	0.812979i	$-0.697844\pi$
$733$	−31.5300	−1.16459	−0.582293	+	0.812979i	$0.697844\pi$
$734$	−53.5524	−1.97666
$735$	1.89354	0.0698442
$736$	−41.8341	−1.54202
$737$	−70.9504	−2.61349
$738$	15.4992	0.570534
$739$	−24.0272	−0.883855	−0.441927	−	0.897051i	$-0.645705\pi$
$739$	−24.0272	−0.883855	−0.441927	+	0.897051i	$0.645705\pi$
$740$	−3.96413	−0.145724
$741$	−9.87833	−0.362890
$742$	−42.3754	−1.55565
$743$	−45.5559	−1.67128	−0.835641	−	0.549276i	$-0.814904\pi$
$743$	−45.5559	−1.67128	−0.835641	+	0.549276i	$0.814904\pi$
$744$	0.0170339	0.000624492 0
$745$	−21.6654	−0.793760
$746$	42.2715	1.54767
$747$	−2.96649	−0.108538
$748$	67.5584	2.47018
$749$	9.02844	0.329892
$750$	−1.98597	−0.0725173
$751$	36.4863	1.33140	0.665702	−	0.746218i	$-0.268132\pi$
$751$	36.4863	1.33140	0.665702	+	0.746218i	$0.268132\pi$
$752$	13.9930	0.510274
$753$	27.4909	1.00182
$754$	18.3562	0.668493
$755$	−6.19473	−0.225449
$756$	5.79762	0.210857
$757$	20.9901	0.762899	0.381449	−	0.924390i	$-0.375425\pi$
$757$	20.9901	0.762899	0.381449	+	0.924390i	$0.375425\pi$
$758$	31.9659	1.16106
$759$	29.3671	1.06596
$760$	0.381300	0.0138312
$761$	−1.83412	−0.0664868	−0.0332434	−	0.999447i	$-0.510584\pi$
$761$	−1.83412	−0.0664868	−0.0332434	+	0.999447i	$0.510584\pi$
$762$	26.9570	0.976551
$763$	−49.5889	−1.79524
$764$	8.72480	0.315652
$765$	−6.23654	−0.225483
$766$	−34.3857	−1.24241
$767$	13.2478	0.478351
$768$	−16.8570	−0.608274
$769$	12.0606	0.434918	0.217459	−	0.976069i	$-0.430223\pi$
$769$	12.0606	0.434918	0.217459	+	0.976069i	$0.430223\pi$
$770$	−33.0014	−1.18929
$771$	−5.78164	−0.208221
$772$	−17.6306	−0.634540
$773$	−7.19184	−0.258672	−0.129336	−	0.991601i	$-0.541285\pi$
$773$	−7.19184	−0.258672	−0.129336	+	0.991601i	$0.541285\pi$
$774$	−13.0504	−0.469086
$775$	−0.153360	−0.00550884
$776$	−1.22560	−0.0439965
$777$	6.08097	0.218154
$778$	17.4341	0.625042
$779$	26.7918	0.959914
$780$	−5.59412	−0.200302
$781$	81.3831	2.91212
$782$	65.2760	2.33427
$783$	−3.21211	−0.114791
$784$	−7.78003	−0.277858
$785$	15.4179	0.550288
$786$	23.5399	0.839639
$787$	−6.20829	−0.221302	−0.110651	−	0.993859i	$-0.535294\pi$
$787$	−6.20829	−0.221302	−0.110651	+	0.993859i	$0.535294\pi$
$788$	35.7346	1.27299
$789$	8.36595	0.297836
$790$	32.6577	1.16191
$791$	44.4148	1.57921
$792$	0.618907	0.0219919
$793$	−2.71010	−0.0962385
$794$	−22.5980	−0.801974
$795$	−7.15490	−0.253758
$796$	−50.3493	−1.78459
$797$	13.1851	0.467039	0.233520	−	0.972352i	$-0.424976\pi$
$797$	13.1851	0.467039	0.233520	+	0.972352i	$0.424976\pi$
$798$	20.3317	0.719735
$799$	−21.2397	−0.751407
$800$	7.93766	0.280639
$801$	−3.19517	−0.112896
$802$	1.98597	0.0701270
$803$	2.05725	0.0725988
$804$	24.7539	0.873003
$805$	−15.7172	−0.553958
$806$	−0.876401	−0.0308699
$807$	25.1734	0.886146
$808$	0.284484	0.0100081
$809$	−32.0777	−1.12779	−0.563895	−	0.825846i	$-0.690698\pi$
$809$	−32.0777	−1.12779	−0.563895	+	0.825846i	$0.690698\pi$
$810$	1.98597	0.0697798
$811$	−23.8675	−0.838101	−0.419051	−	0.907963i	$-0.637637\pi$
$811$	−23.8675	−0.838101	−0.419051	+	0.907963i	$0.637637\pi$
$812$	−18.6226	−0.653525
$813$	−19.0220	−0.667132
$814$	−22.5648	−0.790895
$815$	6.97966	0.244487
$816$	25.6243	0.897028
$817$	−22.5588	−0.789231
$818$	30.6013	1.06995
$819$	8.58137	0.299857
$820$	15.1722	0.529837
$821$	−55.8009	−1.94746	−0.973732	−	0.227697i	$-0.926881\pi$
$821$	−55.8009	−1.94746	−0.973732	+	0.227697i	$0.926881\pi$
$822$	0.235216	0.00820411
$823$	7.69449	0.268213	0.134107	−	0.990967i	$-0.457184\pi$
$823$	7.69449	0.268213	0.134107	+	0.990967i	$0.457184\pi$
$824$	0.559533	0.0194922
$825$	−5.57216	−0.193998
$826$	−27.2668	−0.948734
$827$	−6.97993	−0.242716	−0.121358	−	0.992609i	$-0.538725\pi$
$827$	−6.97993	−0.242716	−0.121358	+	0.992609i	$0.538725\pi$
$828$	−10.2459	−0.356069
$829$	10.8011	0.375137	0.187569	−	0.982251i	$-0.439939\pi$
$829$	10.8011	0.375137	0.187569	+	0.982251i	$0.439939\pi$
$830$	−5.89137	−0.204492
$831$	−16.2788	−0.564705
$832$	21.7152	0.752841
$833$	11.8091	0.409162
$834$	13.5646	0.469705
$835$	−12.2437	−0.423712
$836$	−37.1878	−1.28617
$837$	0.153360	0.00530089
$838$	20.2365	0.699059
$839$	−27.4832	−0.948825	−0.474412	−	0.880303i	$-0.657339\pi$
$839$	−27.4832	−0.948825	−0.474412	+	0.880303i	$0.657339\pi$
$840$	−0.331238	−0.0114288
$841$	−18.6823	−0.644219
$842$	33.9531	1.17010
$843$	12.3278	0.424593
$844$	4.21718	0.145161
$845$	4.71984	0.162367
$846$	6.76359	0.232537
$847$	−59.7900	−2.05441
$848$	29.3976	1.00952
$849$	5.09935	0.175009
$850$	−12.3856	−0.424822
$851$	−10.7466	−0.368390
$852$	−28.3938	−0.972755
$853$	34.4087	1.17813	0.589066	−	0.808085i	$-0.299496\pi$
$853$	34.4087	1.17813	0.589066	+	0.808085i	$0.299496\pi$
$854$	5.57796	0.190874
$855$	3.43293	0.117404
$856$	−0.336262	−0.0114932
$857$	−3.16490	−0.108111	−0.0540554	−	0.998538i	$-0.517215\pi$
$857$	−3.16490	−0.108111	−0.0540554	+	0.998538i	$0.517215\pi$
$858$	−31.8431	−1.08711
$859$	−32.6714	−1.11473	−0.557367	−	0.830266i	$-0.688188\pi$
$859$	−32.6714	−1.11473	−0.557367	+	0.830266i	$0.688188\pi$
$860$	−12.7751	−0.435626
$861$	−23.2742	−0.793182
$862$	−4.77223	−0.162543
$863$	−41.1875	−1.40204	−0.701020	−	0.713142i	$-0.747272\pi$
$863$	−41.1875	−1.40204	−0.701020	+	0.713142i	$0.747272\pi$
$864$	−7.93766	−0.270045
$865$	5.13203	0.174494
$866$	75.1587	2.55400
$867$	−21.8944	−0.743574
$868$	0.889121	0.0301787
$869$	91.6298	3.10833
$870$	−6.37915	−0.216273
$871$	36.6396	1.24149
$872$	1.84693	0.0625448
$873$	−11.0343	−0.373456
$874$	−35.9314	−1.21540
$875$	2.98220	0.100817
$876$	−0.717755	−0.0242507
$877$	38.4231	1.29745	0.648727	−	0.761021i	$-0.275302\pi$
$877$	38.4231	1.29745	0.648727	+	0.761021i	$0.275302\pi$
$878$	36.2475	1.22329
$879$	15.3340	0.517203
$880$	22.8945	0.771773
$881$	−54.6696	−1.84187	−0.920933	−	0.389722i	$-0.872571\pi$
$881$	−54.6696	−1.84187	−0.920933	+	0.389722i	$0.872571\pi$
$882$	−3.76051	−0.126623
$883$	0.634080	0.0213385	0.0106692	−	0.999943i	$-0.496604\pi$
$883$	0.634080	0.0213385	0.0106692	+	0.999943i	$0.496604\pi$
$884$	−34.8880	−1.17341
$885$	−4.60389	−0.154758
$886$	28.0055	0.940862
$887$	16.8864	0.566990	0.283495	−	0.958974i	$-0.408506\pi$
$887$	16.8864	0.566990	0.283495	+	0.958974i	$0.408506\pi$
$888$	−0.226484	−0.00760031
$889$	−40.4797	−1.35765
$890$	−6.34552	−0.212702
$891$	5.57216	0.186674
$892$	11.2074	0.375251
$893$	11.6915	0.391240
$894$	43.0269	1.43903
$895$	10.5405	0.352330
$896$	2.64886	0.0884924
$897$	−15.1655	−0.506361
$898$	−43.6006	−1.45497
$899$	−0.492608	−0.0164294
$900$	1.94407	0.0648024
$901$	−44.6218	−1.48657
$902$	86.3640	2.87561
$903$	19.5969	0.652145
$904$	−1.65422	−0.0550185
$905$	−3.28855	−0.109315
$906$	12.3025	0.408724
$907$	17.2191	0.571751	0.285876	−	0.958267i	$-0.407716\pi$
$907$	17.2191	0.571751	0.285876	+	0.958267i	$0.407716\pi$
$908$	23.9454	0.794657
$909$	2.56127	0.0849519
$910$	17.0423	0.564948
$911$	39.5362	1.30989	0.654946	−	0.755676i	$-0.272691\pi$
$911$	39.5362	1.30989	0.654946	+	0.755676i	$0.272691\pi$
$912$	−14.1050	−0.467062
$913$	−16.5298	−0.547056
$914$	46.5779	1.54066
$915$	0.941816	0.0311355
$916$	13.8581	0.457885
$917$	−35.3483	−1.16730
$918$	12.3856	0.408785
$919$	45.5646	1.50304	0.751519	−	0.659711i	$-0.229321\pi$
$919$	45.5646	1.50304	0.751519	+	0.659711i	$0.229321\pi$
$920$	0.585382	0.0192995
$921$	−12.5279	−0.412808
$922$	42.9711	1.41518
$923$	−42.0272	−1.38334
$924$	32.3052	1.06276
$925$	2.03909	0.0670447
$926$	54.3482	1.78599
$927$	5.03759	0.165456
$928$	25.4966	0.836968
$929$	40.6003	1.33205	0.666026	−	0.745929i	$-0.267994\pi$
$929$	40.6003	1.33205	0.666026	+	0.745929i	$0.267994\pi$
$930$	0.304567	0.00998716
$931$	−6.50037	−0.213041
$932$	1.58750	0.0520002
$933$	4.87098	0.159469
$934$	0.646357	0.0211494
$935$	−34.7510	−1.13648
$936$	−0.319611	−0.0104468
$937$	4.26729	0.139406	0.0697032	−	0.997568i	$-0.477795\pi$
$937$	4.26729	0.139406	0.0697032	+	0.997568i	$0.477795\pi$
$938$	−75.4122	−2.46229
$939$	−3.79318	−0.123786
$940$	6.62090	0.215950
$941$	−47.4411	−1.54654	−0.773268	−	0.634079i	$-0.781379\pi$
$941$	−47.4411	−1.54654	−0.773268	+	0.634079i	$0.781379\pi$
$942$	−30.6194	−0.997635
$943$	41.1315	1.33943
$944$	18.9161	0.615668
$945$	−2.98220	−0.0970111
$946$	−72.7188	−2.36429
$947$	57.5847	1.87125	0.935625	−	0.352995i	$-0.114837\pi$
$947$	57.5847	1.87125	0.935625	+	0.352995i	$0.114837\pi$
$948$	−31.9687	−1.03830
$949$	−1.06239	−0.0344866
$950$	6.81768	0.221195
$951$	−33.4890	−1.08596
$952$	−2.06578	−0.0669522
$953$	−19.1477	−0.620256	−0.310128	−	0.950695i	$-0.600372\pi$
$953$	−19.1477	−0.620256	−0.310128	+	0.950695i	$0.600372\pi$
$954$	14.2094	0.460047
$955$	−4.48790	−0.145225
$956$	3.86227	0.124915
$957$	−17.8984	−0.578572
$958$	−80.3325	−2.59542
$959$	−0.353209	−0.0114057
$960$	−7.54649	−0.243562
$961$	−30.9765	−0.999241
$962$	11.6527	0.375699
$963$	−3.02744	−0.0975578
$964$	−25.2727	−0.813980
$965$	9.06891	0.291939
$966$	31.2138	1.00429
$967$	43.5345	1.39997	0.699987	−	0.714155i	$-0.253189\pi$
$967$	43.5345	1.39997	0.699987	+	0.714155i	$0.253189\pi$
$968$	2.22686	0.0715741
$969$	21.4096	0.687775
$970$	−21.9139	−0.703612
$971$	21.5317	0.690986	0.345493	−	0.938421i	$-0.387712\pi$
$971$	21.5317	0.690986	0.345493	+	0.938421i	$0.387712\pi$
$972$	−1.94407	−0.0623561
$973$	−20.3691	−0.653005
$974$	22.7002	0.727363
$975$	2.87753	0.0921546
$976$	−3.86966	−0.123865
$977$	10.4284	0.333634	0.166817	−	0.985988i	$-0.446651\pi$
$977$	10.4284	0.333634	0.166817	+	0.985988i	$0.446651\pi$
$978$	−13.8614	−0.443238
$979$	−17.8040	−0.569019
$980$	−3.68117	−0.117591
$981$	16.6283	0.530900
$982$	−25.9155	−0.826998
$983$	−26.1498	−0.834049	−0.417025	−	0.908895i	$-0.636927\pi$
$983$	−26.1498	−0.834049	−0.417025	+	0.908895i	$0.636927\pi$
$984$	0.866841	0.0276339
$985$	−18.3813	−0.585678
$986$	−39.7838	−1.26698
$987$	−10.1565	−0.323283
$988$	19.2042	0.610967
$989$	−34.6328	−1.10126
$990$	11.0661	0.351705
$991$	−50.8246	−1.61450	−0.807249	−	0.590211i	$-0.799044\pi$
$991$	−50.8246	−1.61450	−0.807249	+	0.590211i	$0.799044\pi$
$992$	−1.21732	−0.0386499
$993$	−34.7645	−1.10322
$994$	86.5009	2.74364
$995$	25.8989	0.821051
$996$	5.76708	0.182737
$997$	46.5468	1.47415	0.737075	−	0.675810i	$-0.236206\pi$
$997$	46.5468	1.47415	0.737075	+	0.675810i	$0.236206\pi$
$998$	−37.1724	−1.17667
$999$	−2.03909	−0.0645138

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.f.1.9	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.f.1.9	✓	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.98597 q^{2} -1.00000 q^{3} +1.94407 q^{4} -1.00000 q^{5} +1.98597 q^{6} -2.98220 q^{7} +0.111071 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.98597 q^{2} -1.00000 q^{3} +1.94407 q^{4} -1.00000 q^{5} +1.98597 q^{6} -2.98220 q^{7} +0.111071 q^{8} +1.00000 q^{9} +1.98597 q^{10} +5.57216 q^{11} -1.94407 q^{12} -2.87753 q^{13} +5.92256 q^{14} +1.00000 q^{15} -4.10873 q^{16} +6.23654 q^{17} -1.98597 q^{18} -3.43293 q^{19} -1.94407 q^{20} +2.98220 q^{21} -11.0661 q^{22} -5.27032 q^{23} -0.111071 q^{24} +1.00000 q^{25} +5.71468 q^{26} -1.00000 q^{27} -5.79762 q^{28} +3.21211 q^{29} -1.98597 q^{30} -0.153360 q^{31} +7.93766 q^{32} -5.57216 q^{33} -12.3856 q^{34} +2.98220 q^{35} +1.94407 q^{36} +2.03909 q^{37} +6.81768 q^{38} +2.87753 q^{39} -0.111071 q^{40} -7.80435 q^{41} -5.92256 q^{42} +6.57129 q^{43} +10.8327 q^{44} -1.00000 q^{45} +10.4667 q^{46} -3.40569 q^{47} +4.10873 q^{48} +1.89354 q^{49} -1.98597 q^{50} -6.23654 q^{51} -5.59412 q^{52} -7.15490 q^{53} +1.98597 q^{54} -5.57216 q^{55} -0.331238 q^{56} +3.43293 q^{57} -6.37915 q^{58} -4.60389 q^{59} +1.94407 q^{60} +0.941816 q^{61} +0.304567 q^{62} -2.98220 q^{63} -7.54649 q^{64} +2.87753 q^{65} +11.0661 q^{66} -12.7330 q^{67} +12.1243 q^{68} +5.27032 q^{69} -5.92256 q^{70} +14.6053 q^{71} +0.111071 q^{72} +0.369202 q^{73} -4.04956 q^{74} -1.00000 q^{75} -6.67385 q^{76} -16.6173 q^{77} -5.71468 q^{78} +16.4442 q^{79} +4.10873 q^{80} +1.00000 q^{81} +15.4992 q^{82} -2.96649 q^{83} +5.79762 q^{84} -6.23654 q^{85} -13.0504 q^{86} -3.21211 q^{87} +0.618907 q^{88} -3.19517 q^{89} +1.98597 q^{90} +8.58137 q^{91} -10.2459 q^{92} +0.153360 q^{93} +6.76359 q^{94} +3.43293 q^{95} -7.93766 q^{96} -11.0343 q^{97} -3.76051 q^{98} +5.57216 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9} + 7 q^{10} - q^{11} - 45 q^{12} - 8 q^{13} - 4 q^{14} + 36 q^{15} + 63 q^{16} - 50 q^{17} - 7 q^{18} + 15 q^{19} - 45 q^{20} - 2 q^{21} + 7 q^{22} - 32 q^{23} + 24 q^{24} + 36 q^{25} - 12 q^{26} - 36 q^{27} - 10 q^{28} + 7 q^{29} - 7 q^{30} + 7 q^{31} - 50 q^{32} + q^{33} + 8 q^{34} - 2 q^{35} + 45 q^{36} - 10 q^{37} - 48 q^{38} + 8 q^{39} + 24 q^{40} - 31 q^{41} + 4 q^{42} + 27 q^{43} - 9 q^{44} - 36 q^{45} + 23 q^{46} - 46 q^{47} - 63 q^{48} + 48 q^{49} - 7 q^{50} + 50 q^{51} - 14 q^{52} - 39 q^{53} + 7 q^{54} + q^{55} - 29 q^{56} - 15 q^{57} - 26 q^{58} - 9 q^{59} + 45 q^{60} + 5 q^{61} - 65 q^{62} + 2 q^{63} + 90 q^{64} + 8 q^{65} - 7 q^{66} + 18 q^{67} - 128 q^{68} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 24 q^{72} - 45 q^{73} - 22 q^{74} - 36 q^{75} + 26 q^{76} - 38 q^{77} + 12 q^{78} + 25 q^{79} - 63 q^{80} + 36 q^{81} - 5 q^{82} - 71 q^{83} + 10 q^{84} + 50 q^{85} + 3 q^{86} - 7 q^{87} - 9 q^{88} - 39 q^{89} + 7 q^{90} + 19 q^{91} - 95 q^{92} - 7 q^{93} + 16 q^{94} - 15 q^{95} + 50 q^{96} - 61 q^{97} - 76 q^{98} - q^{99}+O(q^{100}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9 + 7 * q^10 - q^11 - 45 * q^12 - 8 * q^13 - 4 * q^14 + 36 * q^15 + 63 * q^16 - 50 * q^17 - 7 * q^18 + 15 * q^19 - 45 * q^20 - 2 * q^21 + 7 * q^22 - 32 * q^23 + 24 * q^24 + 36 * q^25 - 12 * q^26 - 36 * q^27 - 10 * q^28 + 7 * q^29 - 7 * q^30 + 7 * q^31 - 50 * q^32 + q^33 + 8 * q^34 - 2 * q^35 + 45 * q^36 - 10 * q^37 - 48 * q^38 + 8 * q^39 + 24 * q^40 - 31 * q^41 + 4 * q^42 + 27 * q^43 - 9 * q^44 - 36 * q^45 + 23 * q^46 - 46 * q^47 - 63 * q^48 + 48 * q^49 - 7 * q^50 + 50 * q^51 - 14 * q^52 - 39 * q^53 + 7 * q^54 + q^55 - 29 * q^56 - 15 * q^57 - 26 * q^58 - 9 * q^59 + 45 * q^60 + 5 * q^61 - 65 * q^62 + 2 * q^63 + 90 * q^64 + 8 * q^65 - 7 * q^66 + 18 * q^67 - 128 * q^68 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 24 * q^72 - 45 * q^73 - 22 * q^74 - 36 * q^75 + 26 * q^76 - 38 * q^77 + 12 * q^78 + 25 * q^79 - 63 * q^80 + 36 * q^81 - 5 * q^82 - 71 * q^83 + 10 * q^84 + 50 * q^85 + 3 * q^86 - 7 * q^87 - 9 * q^88 - 39 * q^89 + 7 * q^90 + 19 * q^91 - 95 * q^92 - 7 * q^93 + 16 * q^94 - 15 * q^95 + 50 * q^96 - 61 * q^97 - 76 * q^98 - q^99

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