LMFDB - Embedded newform 4030.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4030,2,Mod(1,4030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4030, 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("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.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:	$32.1797120146$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 6x^{5} + 20x^{4} + 9x^{3} - 37x^{2} - 3x + 20 $ x^7 - 3x^6 - 6x^5 + 20x^4 + 9x^3 - 37x^2 - 3x + 20
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.937425$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.21109 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.21109 q^{6} +3.80132 q^{7} +1.00000 q^{8} +7.31111 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.21109 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.21109 q^{6} +3.80132 q^{7} +1.00000 q^{8} +7.31111 q^{9} -1.00000 q^{10} -3.35276 q^{11} -3.21109 q^{12} -1.00000 q^{13} +3.80132 q^{14} +3.21109 q^{15} +1.00000 q^{16} +4.57817 q^{17} +7.31111 q^{18} -6.20083 q^{19} -1.00000 q^{20} -12.2064 q^{21} -3.35276 q^{22} -7.34764 q^{23} -3.21109 q^{24} +1.00000 q^{25} -1.00000 q^{26} -13.8434 q^{27} +3.80132 q^{28} +2.26156 q^{29} +3.21109 q^{30} +1.00000 q^{31} +1.00000 q^{32} +10.7660 q^{33} +4.57817 q^{34} -3.80132 q^{35} +7.31111 q^{36} -7.91619 q^{37} -6.20083 q^{38} +3.21109 q^{39} -1.00000 q^{40} +3.61802 q^{41} -12.2064 q^{42} +6.65090 q^{43} -3.35276 q^{44} -7.31111 q^{45} -7.34764 q^{46} -4.33505 q^{47} -3.21109 q^{48} +7.45001 q^{49} +1.00000 q^{50} -14.7009 q^{51} -1.00000 q^{52} -0.573444 q^{53} -13.8434 q^{54} +3.35276 q^{55} +3.80132 q^{56} +19.9114 q^{57} +2.26156 q^{58} +9.60208 q^{59} +3.21109 q^{60} +6.28723 q^{61} +1.00000 q^{62} +27.7918 q^{63} +1.00000 q^{64} +1.00000 q^{65} +10.7660 q^{66} -7.09433 q^{67} +4.57817 q^{68} +23.5940 q^{69} -3.80132 q^{70} -12.6559 q^{71} +7.31111 q^{72} +4.48787 q^{73} -7.91619 q^{74} -3.21109 q^{75} -6.20083 q^{76} -12.7449 q^{77} +3.21109 q^{78} -3.50654 q^{79} -1.00000 q^{80} +22.5190 q^{81} +3.61802 q^{82} +1.95170 q^{83} -12.2064 q^{84} -4.57817 q^{85} +6.65090 q^{86} -7.26206 q^{87} -3.35276 q^{88} -15.7041 q^{89} -7.31111 q^{90} -3.80132 q^{91} -7.34764 q^{92} -3.21109 q^{93} -4.33505 q^{94} +6.20083 q^{95} -3.21109 q^{96} +7.92445 q^{97} +7.45001 q^{98} -24.5124 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} - 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 4 q^{7} + 7 q^{8} + 4 q^{9}+O(q^{10}) $ 7 * q + 7 * q^2 - 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 4 * q^7 + 7 * q^8 + 4 * q^9	\( 7 q + 7 q^{2} - 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 4 q^{7} + 7 q^{8} + 4 q^{9} - 7 q^{10} - 10 q^{11} - 3 q^{12} - 7 q^{13} + 4 q^{14} + 3 q^{15} + 7 q^{16} - 6 q^{17} + 4 q^{18} - 5 q^{19} - 7 q^{20} - 15 q^{21} - 10 q^{22} - 11 q^{23} - 3 q^{24} + 7 q^{25} - 7 q^{26} - 21 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 7 q^{31} + 7 q^{32} + 4 q^{33} - 6 q^{34} - 4 q^{35} + 4 q^{36} - 8 q^{37} - 5 q^{38} + 3 q^{39} - 7 q^{40} - 12 q^{41} - 15 q^{42} - 5 q^{43} - 10 q^{44} - 4 q^{45} - 11 q^{46} - 10 q^{47} - 3 q^{48} + 7 q^{49} + 7 q^{50} - 29 q^{51} - 7 q^{52} - 18 q^{53} - 21 q^{54} + 10 q^{55} + 4 q^{56} + 13 q^{57} - 18 q^{58} - 11 q^{59} + 3 q^{60} - 25 q^{61} + 7 q^{62} + 17 q^{63} + 7 q^{64} + 7 q^{65} + 4 q^{66} - 22 q^{67} - 6 q^{68} - 18 q^{69} - 4 q^{70} - 22 q^{71} + 4 q^{72} + 19 q^{73} - 8 q^{74} - 3 q^{75} - 5 q^{76} - 47 q^{77} + 3 q^{78} - 20 q^{79} - 7 q^{80} + 7 q^{81} - 12 q^{82} - 8 q^{83} - 15 q^{84} + 6 q^{85} - 5 q^{86} + 29 q^{87} - 10 q^{88} - 4 q^{89} - 4 q^{90} - 4 q^{91} - 11 q^{92} - 3 q^{93} - 10 q^{94} + 5 q^{95} - 3 q^{96} + 13 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 - 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 4 * q^7 + 7 * q^8 + 4 * q^9 - 7 * q^10 - 10 * q^11 - 3 * q^12 - 7 * q^13 + 4 * q^14 + 3 * q^15 + 7 * q^16 - 6 * q^17 + 4 * q^18 - 5 * q^19 - 7 * q^20 - 15 * q^21 - 10 * q^22 - 11 * q^23 - 3 * q^24 + 7 * q^25 - 7 * q^26 - 21 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 7 * q^31 + 7 * q^32 + 4 * q^33 - 6 * q^34 - 4 * q^35 + 4 * q^36 - 8 * q^37 - 5 * q^38 + 3 * q^39 - 7 * q^40 - 12 * q^41 - 15 * q^42 - 5 * q^43 - 10 * q^44 - 4 * q^45 - 11 * q^46 - 10 * q^47 - 3 * q^48 + 7 * q^49 + 7 * q^50 - 29 * q^51 - 7 * q^52 - 18 * q^53 - 21 * q^54 + 10 * q^55 + 4 * q^56 + 13 * q^57 - 18 * q^58 - 11 * q^59 + 3 * q^60 - 25 * q^61 + 7 * q^62 + 17 * q^63 + 7 * q^64 + 7 * q^65 + 4 * q^66 - 22 * q^67 - 6 * q^68 - 18 * q^69 - 4 * q^70 - 22 * q^71 + 4 * q^72 + 19 * q^73 - 8 * q^74 - 3 * q^75 - 5 * q^76 - 47 * q^77 + 3 * q^78 - 20 * q^79 - 7 * q^80 + 7 * q^81 - 12 * q^82 - 8 * q^83 - 15 * q^84 + 6 * q^85 - 5 * q^86 + 29 * q^87 - 10 * q^88 - 4 * q^89 - 4 * q^90 - 4 * q^91 - 11 * q^92 - 3 * q^93 - 10 * q^94 + 5 * q^95 - 3 * q^96 + 13 * q^97 + 7 * q^98 - 27 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.21109	−1.85392	−0.926962	−	0.375155i	$-0.877590\pi$
$3$	−3.21109	−1.85392	−0.926962	+	0.375155i	$0.877590\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.21109	−1.31092
$7$	3.80132	1.43676	0.718381	−	0.695650i	$-0.244883\pi$
$7$	3.80132	1.43676	0.718381	+	0.695650i	$0.244883\pi$
$8$	1.00000	0.353553
$9$	7.31111	2.43704
$10$	−1.00000	−0.316228
$11$	−3.35276	−1.01089	−0.505447	−	0.862858i	$-0.668672\pi$
$11$	−3.35276	−1.01089	−0.505447	+	0.862858i	$0.668672\pi$
$12$	−3.21109	−0.926962
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	3.80132	1.01594
$15$	3.21109	0.829100
$16$	1.00000	0.250000
$17$	4.57817	1.11037	0.555184	−	0.831727i	$-0.312648\pi$
$17$	4.57817	1.11037	0.555184	+	0.831727i	$0.312648\pi$
$18$	7.31111	1.72324
$19$	−6.20083	−1.42257	−0.711284	−	0.702904i	$-0.751886\pi$
$19$	−6.20083	−1.42257	−0.711284	+	0.702904i	$0.751886\pi$
$20$	−1.00000	−0.223607
$21$	−12.2064	−2.66365
$22$	−3.35276	−0.714810
$23$	−7.34764	−1.53209	−0.766045	−	0.642787i	$-0.777778\pi$
$23$	−7.34764	−1.53209	−0.766045	+	0.642787i	$0.777778\pi$
$24$	−3.21109	−0.655461
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	−13.8434	−2.66416
$28$	3.80132	0.718381
$29$	2.26156	0.419960	0.209980	−	0.977706i	$-0.432660\pi$
$29$	2.26156	0.419960	0.209980	+	0.977706i	$0.432660\pi$
$30$	3.21109	0.586262
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	10.7660	1.87412
$34$	4.57817	0.785149
$35$	−3.80132	−0.642540
$36$	7.31111	1.21852
$37$	−7.91619	−1.30141	−0.650707	−	0.759329i	$-0.725527\pi$
$37$	−7.91619	−1.30141	−0.650707	+	0.759329i	$0.725527\pi$
$38$	−6.20083	−1.00591
$39$	3.21109	0.514186
$40$	−1.00000	−0.158114
$41$	3.61802	0.565039	0.282520	−	0.959262i	$-0.408830\pi$
$41$	3.61802	0.565039	0.282520	+	0.959262i	$0.408830\pi$
$42$	−12.2064	−1.88348
$43$	6.65090	1.01425	0.507126	−	0.861872i	$-0.330708\pi$
$43$	6.65090	1.01425	0.507126	+	0.861872i	$0.330708\pi$
$44$	−3.35276	−0.505447
$45$	−7.31111	−1.08988
$46$	−7.34764	−1.08335
$47$	−4.33505	−0.632331	−0.316166	−	0.948704i	$-0.602396\pi$
$47$	−4.33505	−0.632331	−0.316166	+	0.948704i	$0.602396\pi$
$48$	−3.21109	−0.463481
$49$	7.45001	1.06429
$50$	1.00000	0.141421
$51$	−14.7009	−2.05854
$52$	−1.00000	−0.138675
$53$	−0.573444	−0.0787685	−0.0393843	−	0.999224i	$-0.512540\pi$
$53$	−0.573444	−0.0787685	−0.0393843	+	0.999224i	$0.512540\pi$
$54$	−13.8434	−1.88384
$55$	3.35276	0.452086
$56$	3.80132	0.507972
$57$	19.9114	2.63733
$58$	2.26156	0.296957
$59$	9.60208	1.25008	0.625042	−	0.780591i	$-0.285082\pi$
$59$	9.60208	1.25008	0.625042	+	0.780591i	$0.285082\pi$
$60$	3.21109	0.414550
$61$	6.28723	0.804997	0.402499	−	0.915421i	$-0.368142\pi$
$61$	6.28723	0.804997	0.402499	+	0.915421i	$0.368142\pi$
$62$	1.00000	0.127000
$63$	27.7918	3.50144
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	10.7660	1.32520
$67$	−7.09433	−0.866710	−0.433355	−	0.901223i	$-0.642670\pi$
$67$	−7.09433	−0.866710	−0.433355	+	0.901223i	$0.642670\pi$
$68$	4.57817	0.555184
$69$	23.5940	2.84038
$70$	−3.80132	−0.454344
$71$	−12.6559	−1.50198	−0.750990	−	0.660313i	$-0.770424\pi$
$71$	−12.6559	−1.50198	−0.750990	+	0.660313i	$0.770424\pi$
$72$	7.31111	0.861622
$73$	4.48787	0.525266	0.262633	−	0.964896i	$-0.415409\pi$
$73$	4.48787	0.525266	0.262633	+	0.964896i	$0.415409\pi$
$74$	−7.91619	−0.920239
$75$	−3.21109	−0.370785
$76$	−6.20083	−0.711284
$77$	−12.7449	−1.45242
$78$	3.21109	0.363584
$79$	−3.50654	−0.394517	−0.197258	−	0.980352i	$-0.563204\pi$
$79$	−3.50654	−0.394517	−0.197258	+	0.980352i	$0.563204\pi$
$80$	−1.00000	−0.111803
$81$	22.5190	2.50211
$82$	3.61802	0.399543
$83$	1.95170	0.214227	0.107113	−	0.994247i	$-0.465839\pi$
$83$	1.95170	0.214227	0.107113	+	0.994247i	$0.465839\pi$
$84$	−12.2064	−1.33182
$85$	−4.57817	−0.496572
$86$	6.65090	0.717185
$87$	−7.26206	−0.778575
$88$	−3.35276	−0.357405
$89$	−15.7041	−1.66464	−0.832318	−	0.554299i	$-0.812986\pi$
$89$	−15.7041	−1.66464	−0.832318	+	0.554299i	$0.812986\pi$
$90$	−7.31111	−0.770658
$91$	−3.80132	−0.398486
$92$	−7.34764	−0.766045
$93$	−3.21109	−0.332975
$94$	−4.33505	−0.447126
$95$	6.20083	0.636192
$96$	−3.21109	−0.327731
$97$	7.92445	0.804606	0.402303	−	0.915507i	$-0.368210\pi$
$97$	7.92445	0.804606	0.402303	+	0.915507i	$0.368210\pi$
$98$	7.45001	0.752564
$99$	−24.5124	−2.46359
$100$	1.00000	0.100000
$101$	−5.47279	−0.544563	−0.272282	−	0.962218i	$-0.587778\pi$
$101$	−5.47279	−0.544563	−0.272282	+	0.962218i	$0.587778\pi$
$102$	−14.7009	−1.45561
$103$	7.63730	0.752525	0.376263	−	0.926513i	$-0.377209\pi$
$103$	7.63730	0.752525	0.376263	+	0.926513i	$0.377209\pi$
$104$	−1.00000	−0.0980581
$105$	12.2064	1.19122
$106$	−0.573444	−0.0556978
$107$	−0.485529	−0.0469379	−0.0234689	−	0.999725i	$-0.507471\pi$
$107$	−0.485529	−0.0469379	−0.0234689	+	0.999725i	$0.507471\pi$
$108$	−13.8434	−1.33208
$109$	−7.37017	−0.705935	−0.352967	−	0.935636i	$-0.614827\pi$
$109$	−7.37017	−0.705935	−0.352967	+	0.935636i	$0.614827\pi$
$110$	3.35276	0.319673
$111$	25.4196	2.41272
$112$	3.80132	0.359191
$113$	6.43988	0.605813	0.302906	−	0.953020i	$-0.402043\pi$
$113$	6.43988	0.605813	0.302906	+	0.953020i	$0.402043\pi$
$114$	19.9114	1.86488
$115$	7.34764	0.685171
$116$	2.26156	0.209980
$117$	−7.31111	−0.675912
$118$	9.60208	0.883943
$119$	17.4031	1.59534
$120$	3.21109	0.293131
$121$	0.240981	0.0219073
$122$	6.28723	0.569219
$123$	−11.6178	−1.04754
$124$	1.00000	0.0898027
$125$	−1.00000	−0.0894427
$126$	27.7918	2.47589
$127$	−19.8662	−1.76284	−0.881420	−	0.472334i	$-0.843412\pi$
$127$	−19.8662	−1.76284	−0.881420	+	0.472334i	$0.843412\pi$
$128$	1.00000	0.0883883
$129$	−21.3566	−1.88035
$130$	1.00000	0.0877058
$131$	−6.22313	−0.543717	−0.271859	−	0.962337i	$-0.587638\pi$
$131$	−6.22313	−0.543717	−0.271859	+	0.962337i	$0.587638\pi$
$132$	10.7660	0.937061
$133$	−23.5713	−2.04389
$134$	−7.09433	−0.612857
$135$	13.8434	1.19145
$136$	4.57817	0.392574
$137$	−2.60702	−0.222733	−0.111367	−	0.993779i	$-0.535523\pi$
$137$	−2.60702	−0.222733	−0.111367	+	0.993779i	$0.535523\pi$
$138$	23.5940	2.00845
$139$	0.517571	0.0438998	0.0219499	−	0.999759i	$-0.493013\pi$
$139$	0.517571	0.0438998	0.0219499	+	0.999759i	$0.493013\pi$
$140$	−3.80132	−0.321270
$141$	13.9202	1.17229
$142$	−12.6559	−1.06206
$143$	3.35276	0.280372
$144$	7.31111	0.609259
$145$	−2.26156	−0.187812
$146$	4.48787	0.371419
$147$	−23.9227	−1.97311
$148$	−7.91619	−0.650707
$149$	−18.5359	−1.51852	−0.759261	−	0.650786i	$-0.774440\pi$
$149$	−18.5359	−1.51852	−0.759261	+	0.650786i	$0.774440\pi$
$150$	−3.21109	−0.262185
$151$	−5.39472	−0.439016	−0.219508	−	0.975611i	$-0.570445\pi$
$151$	−5.39472	−0.439016	−0.219508	+	0.975611i	$0.570445\pi$
$152$	−6.20083	−0.502954
$153$	33.4715	2.70601
$154$	−12.7449	−1.02701
$155$	−1.00000	−0.0803219
$156$	3.21109	0.257093
$157$	−6.47010	−0.516370	−0.258185	−	0.966096i	$-0.583124\pi$
$157$	−6.47010	−0.516370	−0.258185	+	0.966096i	$0.583124\pi$
$158$	−3.50654	−0.278965
$159$	1.84138	0.146031
$160$	−1.00000	−0.0790569
$161$	−27.9307	−2.20125
$162$	22.5190	1.76926
$163$	−0.441829	−0.0346067	−0.0173034	−	0.999850i	$-0.505508\pi$
$163$	−0.441829	−0.0346067	−0.0173034	+	0.999850i	$0.505508\pi$
$164$	3.61802	0.282520
$165$	−10.7660	−0.838133
$166$	1.95170	0.151481
$167$	−11.9570	−0.925261	−0.462630	−	0.886551i	$-0.653094\pi$
$167$	−11.9570	−0.925261	−0.462630	+	0.886551i	$0.653094\pi$
$168$	−12.2064	−0.941742
$169$	1.00000	0.0769231
$170$	−4.57817	−0.351129
$171$	−45.3350	−3.46685
$172$	6.65090	0.507126
$173$	15.2902	1.16250	0.581248	−	0.813727i	$-0.302565\pi$
$173$	15.2902	1.16250	0.581248	+	0.813727i	$0.302565\pi$
$174$	−7.26206	−0.550536
$175$	3.80132	0.287353
$176$	−3.35276	−0.252724
$177$	−30.8331	−2.31756
$178$	−15.7041	−1.17707
$179$	−10.3670	−0.774862	−0.387431	−	0.921899i	$-0.626638\pi$
$179$	−10.3670	−0.774862	−0.387431	+	0.921899i	$0.626638\pi$
$180$	−7.31111	−0.544938
$181$	−24.8794	−1.84927	−0.924634	−	0.380857i	$-0.875629\pi$
$181$	−24.8794	−1.84927	−0.924634	+	0.380857i	$0.875629\pi$
$182$	−3.80132	−0.281772
$183$	−20.1889	−1.49240
$184$	−7.34764	−0.541675
$185$	7.91619	0.582010
$186$	−3.21109	−0.235449
$187$	−15.3495	−1.12246
$188$	−4.33505	−0.316166
$189$	−52.6230	−3.82776
$190$	6.20083	0.449856
$191$	−18.5114	−1.33944	−0.669719	−	0.742615i	$-0.733585\pi$
$191$	−18.5114	−1.33944	−0.669719	+	0.742615i	$0.733585\pi$
$192$	−3.21109	−0.231741
$193$	11.7174	0.843433	0.421717	−	0.906728i	$-0.361428\pi$
$193$	11.7174	0.843433	0.421717	+	0.906728i	$0.361428\pi$
$194$	7.92445	0.568942
$195$	−3.21109	−0.229951
$196$	7.45001	0.532143
$197$	−25.0089	−1.78181	−0.890904	−	0.454191i	$-0.849928\pi$
$197$	−25.0089	−1.78181	−0.890904	+	0.454191i	$0.849928\pi$
$198$	−24.5124	−1.74202
$199$	7.49385	0.531225	0.265613	−	0.964080i	$-0.414426\pi$
$199$	7.49385	0.531225	0.265613	+	0.964080i	$0.414426\pi$
$200$	1.00000	0.0707107
$201$	22.7805	1.60682
$202$	−5.47279	−0.385064
$203$	8.59689	0.603383
$204$	−14.7009	−1.02927
$205$	−3.61802	−0.252693
$206$	7.63730	0.532116
$207$	−53.7194	−3.73376
$208$	−1.00000	−0.0693375
$209$	20.7899	1.43807
$210$	12.2064	0.842320
$211$	25.6076	1.76290	0.881450	−	0.472277i	$-0.156568\pi$
$211$	25.6076	1.76290	0.881450	+	0.472277i	$0.156568\pi$
$212$	−0.573444	−0.0393843
$213$	40.6393	2.78456
$214$	−0.485529	−0.0331901
$215$	−6.65090	−0.453588
$216$	−13.8434	−0.941921
$217$	3.80132	0.258050
$218$	−7.37017	−0.499171
$219$	−14.4110	−0.973803
$220$	3.35276	0.226043
$221$	−4.57817	−0.307961
$222$	25.4196	1.70605
$223$	13.3329	0.892834	0.446417	−	0.894825i	$-0.352700\pi$
$223$	13.3329	0.892834	0.446417	+	0.894825i	$0.352700\pi$
$224$	3.80132	0.253986
$225$	7.31111	0.487407
$226$	6.43988	0.428374
$227$	13.7897	0.915253	0.457626	−	0.889145i	$-0.348700\pi$
$227$	13.7897	0.915253	0.457626	+	0.889145i	$0.348700\pi$
$228$	19.9114	1.31867
$229$	−14.0902	−0.931108	−0.465554	−	0.885020i	$-0.654145\pi$
$229$	−14.0902	−0.931108	−0.465554	+	0.885020i	$0.654145\pi$
$230$	7.34764	0.484489
$231$	40.9250	2.69267
$232$	2.26156	0.148478
$233$	−0.796574	−0.0521853	−0.0260927	−	0.999660i	$-0.508306\pi$
$233$	−0.796574	−0.0521853	−0.0260927	+	0.999660i	$0.508306\pi$
$234$	−7.31111	−0.477942
$235$	4.33505	0.282787
$236$	9.60208	0.625042
$237$	11.2598	0.731404
$238$	17.4031	1.12807
$239$	−25.0303	−1.61908	−0.809539	−	0.587066i	$-0.800283\pi$
$239$	−25.0303	−1.61908	−0.809539	+	0.587066i	$0.800283\pi$
$240$	3.21109	0.207275
$241$	1.30466	0.0840405	0.0420203	−	0.999117i	$-0.486621\pi$
$241$	1.30466	0.0840405	0.0420203	+	0.999117i	$0.486621\pi$
$242$	0.240981	0.0154908
$243$	−30.7804	−1.97456
$244$	6.28723	0.402499
$245$	−7.45001	−0.475964
$246$	−11.6178	−0.740723
$247$	6.20083	0.394550
$248$	1.00000	0.0635001
$249$	−6.26709	−0.397161
$250$	−1.00000	−0.0632456
$251$	−5.29370	−0.334136	−0.167068	−	0.985945i	$-0.553430\pi$
$251$	−5.29370	−0.334136	−0.167068	+	0.985945i	$0.553430\pi$
$252$	27.7918	1.75072
$253$	24.6349	1.54878
$254$	−19.8662	−1.24652
$255$	14.7009	0.920607
$256$	1.00000	0.0625000
$257$	27.4350	1.71135	0.855675	−	0.517514i	$-0.173143\pi$
$257$	27.4350	1.71135	0.855675	+	0.517514i	$0.173143\pi$
$258$	−21.3566	−1.32961
$259$	−30.0920	−1.86982
$260$	1.00000	0.0620174
$261$	16.5345	1.02346
$262$	−6.22313	−0.384466
$263$	−4.59303	−0.283218	−0.141609	−	0.989923i	$-0.545228\pi$
$263$	−4.59303	−0.283218	−0.141609	+	0.989923i	$0.545228\pi$
$264$	10.7660	0.662602
$265$	0.573444	0.0352264
$266$	−23.5713	−1.44525
$267$	50.4274	3.08611
$268$	−7.09433	−0.433355
$269$	12.4368	0.758287	0.379144	−	0.925338i	$-0.376219\pi$
$269$	12.4368	0.758287	0.379144	+	0.925338i	$0.376219\pi$
$270$	13.8434	0.842480
$271$	−31.2859	−1.90049	−0.950243	−	0.311511i	$-0.899165\pi$
$271$	−31.2859	−1.90049	−0.950243	+	0.311511i	$0.899165\pi$
$272$	4.57817	0.277592
$273$	12.2064	0.738763
$274$	−2.60702	−0.157496
$275$	−3.35276	−0.202179
$276$	23.5940	1.42019
$277$	−30.0861	−1.80770	−0.903849	−	0.427851i	$-0.859271\pi$
$277$	−30.0861	−1.80770	−0.903849	+	0.427851i	$0.859271\pi$
$278$	0.517571	0.0310418
$279$	7.31111	0.437705
$280$	−3.80132	−0.227172
$281$	−30.9881	−1.84860	−0.924298	−	0.381672i	$-0.875348\pi$
$281$	−30.9881	−1.84860	−0.924298	+	0.381672i	$0.875348\pi$
$282$	13.9202	0.828937
$283$	32.2322	1.91601	0.958003	−	0.286760i	$-0.0925781\pi$
$283$	32.2322	1.91601	0.958003	+	0.286760i	$0.0925781\pi$
$284$	−12.6559	−0.750990
$285$	−19.9114	−1.17945
$286$	3.35276	0.198253
$287$	13.7532	0.811827
$288$	7.31111	0.430811
$289$	3.95960	0.232918
$290$	−2.26156	−0.132803
$291$	−25.4461	−1.49168
$292$	4.48787	0.262633
$293$	−15.0144	−0.877151	−0.438575	−	0.898694i	$-0.644517\pi$
$293$	−15.0144	−0.877151	−0.438575	+	0.898694i	$0.644517\pi$
$294$	−23.9227	−1.39520
$295$	−9.60208	−0.559054
$296$	−7.91619	−0.460119
$297$	46.4134	2.69318
$298$	−18.5359	−1.07376
$299$	7.34764	0.424925
$300$	−3.21109	−0.185392
$301$	25.2822	1.45724
$302$	−5.39472	−0.310431
$303$	17.5736	1.00958
$304$	−6.20083	−0.355642
$305$	−6.28723	−0.360006
$306$	33.4715	1.91344
$307$	−6.74937	−0.385207	−0.192603	−	0.981277i	$-0.561693\pi$
$307$	−6.74937	−0.385207	−0.192603	+	0.981277i	$0.561693\pi$
$308$	−12.7449	−0.726208
$309$	−24.5241	−1.39513
$310$	−1.00000	−0.0567962
$311$	−25.7221	−1.45857	−0.729283	−	0.684212i	$-0.760146\pi$
$311$	−25.7221	−1.45857	−0.729283	+	0.684212i	$0.760146\pi$
$312$	3.21109	0.181792
$313$	12.2854	0.694409	0.347205	−	0.937789i	$-0.387131\pi$
$313$	12.2854	0.694409	0.347205	+	0.937789i	$0.387131\pi$
$314$	−6.47010	−0.365129
$315$	−27.7918	−1.56589
$316$	−3.50654	−0.197258
$317$	31.2113	1.75300	0.876501	−	0.481400i	$-0.159872\pi$
$317$	31.2113	1.75300	0.876501	+	0.481400i	$0.159872\pi$
$318$	1.84138	0.103259
$319$	−7.58245	−0.424536
$320$	−1.00000	−0.0559017
$321$	1.55908	0.0870193
$322$	−27.9307	−1.55652
$323$	−28.3884	−1.57958
$324$	22.5190	1.25105
$325$	−1.00000	−0.0554700
$326$	−0.441829	−0.0244707
$327$	23.6663	1.30875
$328$	3.61802	0.199772
$329$	−16.4789	−0.908510
$330$	−10.7660	−0.592649
$331$	−3.32314	−0.182656	−0.0913281	−	0.995821i	$-0.529111\pi$
$331$	−3.32314	−0.182656	−0.0913281	+	0.995821i	$0.529111\pi$
$332$	1.95170	0.107113
$333$	−57.8761	−3.17159
$334$	−11.9570	−0.654258
$335$	7.09433	0.387605
$336$	−12.2064	−0.665912
$337$	14.2543	0.776483	0.388242	−	0.921558i	$-0.373083\pi$
$337$	14.2543	0.776483	0.388242	+	0.921558i	$0.373083\pi$
$338$	1.00000	0.0543928
$339$	−20.6790	−1.12313
$340$	−4.57817	−0.248286
$341$	−3.35276	−0.181562
$342$	−45.3350	−2.45143
$343$	1.71062	0.0923649
$344$	6.65090	0.358592
$345$	−23.5940	−1.27026
$346$	15.2902	0.822008
$347$	−23.5257	−1.26293	−0.631463	−	0.775406i	$-0.717545\pi$
$347$	−23.5257	−1.26293	−0.631463	+	0.775406i	$0.717545\pi$
$348$	−7.26206	−0.389287
$349$	−15.5791	−0.833928	−0.416964	−	0.908923i	$-0.636906\pi$
$349$	−15.5791	−0.833928	−0.416964	+	0.908923i	$0.636906\pi$
$350$	3.80132	0.203189
$351$	13.8434	0.738904
$352$	−3.35276	−0.178703
$353$	−1.10871	−0.0590104	−0.0295052	−	0.999565i	$-0.509393\pi$
$353$	−1.10871	−0.0590104	−0.0295052	+	0.999565i	$0.509393\pi$
$354$	−30.8331	−1.63876
$355$	12.6559	0.671706
$356$	−15.7041	−0.832318
$357$	−55.8828	−2.95763
$358$	−10.3670	−0.547910
$359$	4.62514	0.244106	0.122053	−	0.992524i	$-0.461052\pi$
$359$	4.62514	0.244106	0.122053	+	0.992524i	$0.461052\pi$
$360$	−7.31111	−0.385329
$361$	19.4503	1.02370
$362$	−24.8794	−1.30763
$363$	−0.773810	−0.0406145
$364$	−3.80132	−0.199243
$365$	−4.48787	−0.234906
$366$	−20.1889	−1.05529
$367$	30.0074	1.56637	0.783187	−	0.621786i	$-0.213593\pi$
$367$	30.0074	1.56637	0.783187	+	0.621786i	$0.213593\pi$
$368$	−7.34764	−0.383022
$369$	26.4517	1.37702
$370$	7.91619	0.411543
$371$	−2.17984	−0.113172
$372$	−3.21109	−0.166487
$373$	20.5383	1.06343	0.531717	−	0.846922i	$-0.321547\pi$
$373$	20.5383	1.06343	0.531717	+	0.846922i	$0.321547\pi$
$374$	−15.3495	−0.793703
$375$	3.21109	0.165820
$376$	−4.33505	−0.223563
$377$	−2.26156	−0.116476
$378$	−52.6230	−2.70663
$379$	13.0618	0.670939	0.335470	−	0.942051i	$-0.391105\pi$
$379$	13.0618	0.670939	0.335470	+	0.942051i	$0.391105\pi$
$380$	6.20083	0.318096
$381$	63.7922	3.26817
$382$	−18.5114	−0.947126
$383$	−25.5566	−1.30588	−0.652941	−	0.757409i	$-0.726465\pi$
$383$	−25.5566	−1.30588	−0.652941	+	0.757409i	$0.726465\pi$
$384$	−3.21109	−0.163865
$385$	12.7449	0.649540
$386$	11.7174	0.596397
$387$	48.6254	2.47177
$388$	7.92445	0.402303
$389$	18.8535	0.955911	0.477956	−	0.878384i	$-0.341378\pi$
$389$	18.8535	0.955911	0.477956	+	0.878384i	$0.341378\pi$
$390$	−3.21109	−0.162600
$391$	−33.6387	−1.70118
$392$	7.45001	0.376282
$393$	19.9830	1.00801
$394$	−25.0089	−1.25993
$395$	3.50654	0.176433
$396$	−24.5124	−1.23179
$397$	−37.0400	−1.85898	−0.929492	−	0.368842i	$-0.879754\pi$
$397$	−37.0400	−1.85898	−0.929492	+	0.368842i	$0.879754\pi$
$398$	7.49385	0.375633
$399$	75.6897	3.78922
$400$	1.00000	0.0500000
$401$	−13.4976	−0.674036	−0.337018	−	0.941498i	$-0.609418\pi$
$401$	−13.4976	−0.674036	−0.337018	+	0.941498i	$0.609418\pi$
$402$	22.7805	1.13619
$403$	−1.00000	−0.0498135
$404$	−5.47279	−0.272282
$405$	−22.5190	−1.11898
$406$	8.59689	0.426657
$407$	26.5411	1.31559
$408$	−14.7009	−0.727803
$409$	−9.90694	−0.489867	−0.244933	−	0.969540i	$-0.578766\pi$
$409$	−9.90694	−0.489867	−0.244933	+	0.969540i	$0.578766\pi$
$410$	−3.61802	−0.178681
$411$	8.37139	0.412930
$412$	7.63730	0.376263
$413$	36.5005	1.79607
$414$	−53.7194	−2.64016
$415$	−1.95170	−0.0958052
$416$	−1.00000	−0.0490290
$417$	−1.66197	−0.0813869
$418$	20.7899	1.01687
$419$	−9.36172	−0.457350	−0.228675	−	0.973503i	$-0.573439\pi$
$419$	−9.36172	−0.457350	−0.228675	+	0.973503i	$0.573439\pi$
$420$	12.2064	0.595610
$421$	−14.3979	−0.701712	−0.350856	−	0.936429i	$-0.614109\pi$
$421$	−14.3979	−0.701712	−0.350856	+	0.936429i	$0.614109\pi$
$422$	25.6076	1.24656
$423$	−31.6940	−1.54101
$424$	−0.573444	−0.0278489
$425$	4.57817	0.222074
$426$	40.6393	1.96898
$427$	23.8998	1.15659
$428$	−0.485529	−0.0234689
$429$	−10.7660	−0.519788
$430$	−6.65090	−0.320735
$431$	−3.77007	−0.181598	−0.0907989	−	0.995869i	$-0.528942\pi$
$431$	−3.77007	−0.181598	−0.0907989	+	0.995869i	$0.528942\pi$
$432$	−13.8434	−0.666039
$433$	11.8921	0.571500	0.285750	−	0.958304i	$-0.407757\pi$
$433$	11.8921	0.571500	0.285750	+	0.958304i	$0.407757\pi$
$434$	3.80132	0.182469
$435$	7.26206	0.348189
$436$	−7.37017	−0.352967
$437$	45.5615	2.17950
$438$	−14.4110	−0.688583
$439$	25.8824	1.23530	0.617649	−	0.786454i	$-0.288085\pi$
$439$	25.8824	1.23530	0.617649	+	0.786454i	$0.288085\pi$
$440$	3.35276	0.159836
$441$	54.4678	2.59371
$442$	−4.57817	−0.217761
$443$	−33.0213	−1.56889	−0.784444	−	0.620200i	$-0.787052\pi$
$443$	−33.0213	−1.56889	−0.784444	+	0.620200i	$0.787052\pi$
$444$	25.4196	1.20636
$445$	15.7041	0.744447
$446$	13.3329	0.631329
$447$	59.5206	2.81523
$448$	3.80132	0.179595
$449$	14.2635	0.673138	0.336569	−	0.941659i	$-0.390733\pi$
$449$	14.2635	0.673138	0.336569	+	0.941659i	$0.390733\pi$
$450$	7.31111	0.344649
$451$	−12.1303	−0.571195
$452$	6.43988	0.302906
$453$	17.3229	0.813903
$454$	13.7897	0.647182
$455$	3.80132	0.178208
$456$	19.9114	0.932439
$457$	−1.55627	−0.0727991	−0.0363995	−	0.999337i	$-0.511589\pi$
$457$	−1.55627	−0.0727991	−0.0363995	+	0.999337i	$0.511589\pi$
$458$	−14.0902	−0.658392
$459$	−63.3772	−2.95819
$460$	7.34764	0.342586
$461$	−11.5844	−0.539541	−0.269770	−	0.962925i	$-0.586948\pi$
$461$	−11.5844	−0.539541	−0.269770	+	0.962925i	$0.586948\pi$
$462$	40.9250	1.90400
$463$	0.527973	0.0245370	0.0122685	−	0.999925i	$-0.496095\pi$
$463$	0.527973	0.0245370	0.0122685	+	0.999925i	$0.496095\pi$
$464$	2.26156	0.104990
$465$	3.21109	0.148911
$466$	−0.796574	−0.0369006
$467$	−22.2279	−1.02858	−0.514292	−	0.857615i	$-0.671945\pi$
$467$	−22.2279	−1.02858	−0.514292	+	0.857615i	$0.671945\pi$
$468$	−7.31111	−0.337956
$469$	−26.9678	−1.24526
$470$	4.33505	0.199961
$471$	20.7761	0.957311
$472$	9.60208	0.441971
$473$	−22.2988	−1.02530
$474$	11.2598	0.517181
$475$	−6.20083	−0.284514
$476$	17.4031	0.797668
$477$	−4.19251	−0.191962
$478$	−25.0303	−1.14486
$479$	−39.0594	−1.78467	−0.892334	−	0.451375i	$-0.850934\pi$
$479$	−39.0594	−1.78467	−0.892334	+	0.451375i	$0.850934\pi$
$480$	3.21109	0.146566
$481$	7.91619	0.360947
$482$	1.30466	0.0594256
$483$	89.6881	4.08095
$484$	0.240981	0.0109537
$485$	−7.92445	−0.359831
$486$	−30.7804	−1.39623
$487$	37.1258	1.68233	0.841166	−	0.540776i	$-0.181869\pi$
$487$	37.1258	1.68233	0.841166	+	0.540776i	$0.181869\pi$
$488$	6.28723	0.284610
$489$	1.41875	0.0641583
$490$	−7.45001	−0.336557
$491$	−3.88429	−0.175296	−0.0876479	−	0.996152i	$-0.527935\pi$
$491$	−3.88429	−0.175296	−0.0876479	+	0.996152i	$0.527935\pi$
$492$	−11.6178	−0.523770
$493$	10.3538	0.466311
$494$	6.20083	0.278989
$495$	24.5124	1.10175
$496$	1.00000	0.0449013
$497$	−48.1091	−2.15799
$498$	−6.26709	−0.280835
$499$	22.2268	0.995007	0.497503	−	0.867462i	$-0.334250\pi$
$499$	22.2268	0.995007	0.497503	+	0.867462i	$0.334250\pi$
$500$	−1.00000	−0.0447214
$501$	38.3950	1.71536
$502$	−5.29370	−0.236269
$503$	−13.4658	−0.600412	−0.300206	−	0.953874i	$-0.597055\pi$
$503$	−13.4658	−0.600412	−0.300206	+	0.953874i	$0.597055\pi$
$504$	27.7918	1.23795
$505$	5.47279	0.243536
$506$	24.6349	1.09515
$507$	−3.21109	−0.142610
$508$	−19.8662	−0.881420
$509$	14.3905	0.637848	0.318924	−	0.947780i	$-0.396678\pi$
$509$	14.3905	0.637848	0.318924	+	0.947780i	$0.396678\pi$
$510$	14.7009	0.650967
$511$	17.0598	0.754682
$512$	1.00000	0.0441942
$513$	85.8404	3.78994
$514$	27.4350	1.21011
$515$	−7.63730	−0.336540
$516$	−21.3566	−0.940174
$517$	14.5344	0.639220
$518$	−30.0920	−1.32216
$519$	−49.0984	−2.15518
$520$	1.00000	0.0438529
$521$	−3.93606	−0.172442	−0.0862210	−	0.996276i	$-0.527479\pi$
$521$	−3.93606	−0.172442	−0.0862210	+	0.996276i	$0.527479\pi$
$522$	16.5345	0.723695
$523$	−25.6936	−1.12350	−0.561752	−	0.827306i	$-0.689872\pi$
$523$	−25.6936	−1.12350	−0.561752	+	0.827306i	$0.689872\pi$
$524$	−6.22313	−0.271859
$525$	−12.2064	−0.532730
$526$	−4.59303	−0.200266
$527$	4.57817	0.199428
$528$	10.7660	0.468530
$529$	30.9879	1.34730
$530$	0.573444	0.0249088
$531$	70.2018	3.04650
$532$	−23.5713	−1.02195
$533$	−3.61802	−0.156714
$534$	50.4274	2.18221
$535$	0.485529	0.0209913
$536$	−7.09433	−0.306428
$537$	33.2892	1.43654
$538$	12.4368	0.536190
$539$	−24.9781	−1.07588
$540$	13.8434	0.595723
$541$	28.2881	1.21620	0.608101	−	0.793860i	$-0.291932\pi$
$541$	28.2881	1.21620	0.608101	+	0.793860i	$0.291932\pi$
$542$	−31.2859	−1.34385
$543$	79.8899	3.42840
$544$	4.57817	0.196287
$545$	7.37017	0.315704
$546$	12.2064	0.522385
$547$	2.67604	0.114419	0.0572097	−	0.998362i	$-0.481780\pi$
$547$	2.67604	0.114419	0.0572097	+	0.998362i	$0.481780\pi$
$548$	−2.60702	−0.111367
$549$	45.9666	1.96181
$550$	−3.35276	−0.142962
$551$	−14.0235	−0.597423
$552$	23.5940	1.00423
$553$	−13.3295	−0.566827
$554$	−30.0861	−1.27824
$555$	−25.4196	−1.07900
$556$	0.517571	0.0219499
$557$	−43.2722	−1.83350	−0.916750	−	0.399462i	$-0.869197\pi$
$557$	−43.2722	−1.83350	−0.916750	+	0.399462i	$0.869197\pi$
$558$	7.31111	0.309504
$559$	−6.65090	−0.281303
$560$	−3.80132	−0.160635
$561$	49.2886	2.08097
$562$	−30.9881	−1.30715
$563$	−13.7638	−0.580075	−0.290038	−	0.957015i	$-0.593668\pi$
$563$	−13.7638	−0.580075	−0.290038	+	0.957015i	$0.593668\pi$
$564$	13.9202	0.586147
$565$	−6.43988	−0.270928
$566$	32.2322	1.35482
$567$	85.6017	3.59493
$568$	−12.6559	−0.531030
$569$	45.6090	1.91203	0.956014	−	0.293323i	$-0.0947610\pi$
$569$	45.6090	1.91203	0.956014	+	0.293323i	$0.0947610\pi$
$570$	−19.9114	−0.833999
$571$	1.64552	0.0688630	0.0344315	−	0.999407i	$-0.489038\pi$
$571$	1.64552	0.0688630	0.0344315	+	0.999407i	$0.489038\pi$
$572$	3.35276	0.140186
$573$	59.4418	2.48322
$574$	13.7532	0.574049
$575$	−7.34764	−0.306418
$576$	7.31111	0.304629
$577$	32.4073	1.34914	0.674568	−	0.738213i	$-0.264330\pi$
$577$	32.4073	1.34914	0.674568	+	0.738213i	$0.264330\pi$
$578$	3.95960	0.164698
$579$	−37.6255	−1.56366
$580$	−2.26156	−0.0939060
$581$	7.41903	0.307793
$582$	−25.4461	−1.05478
$583$	1.92262	0.0796267
$584$	4.48787	0.185709
$585$	7.31111	0.302277
$586$	−15.0144	−0.620239
$587$	−16.1204	−0.665360	−0.332680	−	0.943040i	$-0.607953\pi$
$587$	−16.1204	−0.665360	−0.332680	+	0.943040i	$0.607953\pi$
$588$	−23.9227	−0.986554
$589$	−6.20083	−0.255501
$590$	−9.60208	−0.395311
$591$	80.3058	3.30334
$592$	−7.91619	−0.325353
$593$	44.9420	1.84555	0.922773	−	0.385344i	$-0.125917\pi$
$593$	44.9420	1.84555	0.922773	+	0.385344i	$0.125917\pi$
$594$	46.4134	1.90437
$595$	−17.4031	−0.713456
$596$	−18.5359	−0.759261
$597$	−24.0634	−0.984851
$598$	7.34764	0.300467
$599$	−22.1484	−0.904957	−0.452479	−	0.891775i	$-0.649460\pi$
$599$	−22.1484	−0.904957	−0.452479	+	0.891775i	$0.649460\pi$
$600$	−3.21109	−0.131092
$601$	−24.6562	−1.00575	−0.502873	−	0.864360i	$-0.667724\pi$
$601$	−24.6562	−1.00575	−0.502873	+	0.864360i	$0.667724\pi$
$602$	25.2822	1.03042
$603$	−51.8674	−2.11220
$604$	−5.39472	−0.219508
$605$	−0.240981	−0.00979725
$606$	17.5736	0.713880
$607$	33.0447	1.34124	0.670622	−	0.741799i	$-0.266027\pi$
$607$	33.0447	1.34124	0.670622	+	0.741799i	$0.266027\pi$
$608$	−6.20083	−0.251477
$609$	−27.6054	−1.11863
$610$	−6.28723	−0.254563
$611$	4.33505	0.175377
$612$	33.4715	1.35300
$613$	33.7783	1.36429	0.682146	−	0.731216i	$-0.261047\pi$
$613$	33.7783	1.36429	0.682146	+	0.731216i	$0.261047\pi$
$614$	−6.74937	−0.272382
$615$	11.6178	0.468474
$616$	−12.7449	−0.513506
$617$	6.00427	0.241723	0.120861	−	0.992669i	$-0.461434\pi$
$617$	6.00427	0.241723	0.120861	+	0.992669i	$0.461434\pi$
$618$	−24.5241	−0.986502
$619$	30.7954	1.23777	0.618885	−	0.785481i	$-0.287585\pi$
$619$	30.7954	1.23777	0.618885	+	0.785481i	$0.287585\pi$
$620$	−1.00000	−0.0401610
$621$	101.716	4.08172
$622$	−25.7221	−1.03136
$623$	−59.6964	−2.39169
$624$	3.21109	0.128547
$625$	1.00000	0.0400000
$626$	12.2854	0.491021
$627$	−66.7582	−2.66607
$628$	−6.47010	−0.258185
$629$	−36.2416	−1.44505
$630$	−27.7918	−1.10725
$631$	4.34625	0.173022	0.0865108	−	0.996251i	$-0.472428\pi$
$631$	4.34625	0.173022	0.0865108	+	0.996251i	$0.472428\pi$
$632$	−3.50654	−0.139483
$633$	−82.2284	−3.26828
$634$	31.2113	1.23956
$635$	19.8662	0.788366
$636$	1.84138	0.0730155
$637$	−7.45001	−0.295180
$638$	−7.58245	−0.300192
$639$	−92.5287	−3.66038
$640$	−1.00000	−0.0395285
$641$	29.6421	1.17079	0.585396	−	0.810747i	$-0.300939\pi$
$641$	29.6421	1.17079	0.585396	+	0.810747i	$0.300939\pi$
$642$	1.55908	0.0615319
$643$	−26.3001	−1.03718	−0.518588	−	0.855024i	$-0.673542\pi$
$643$	−26.3001	−1.03718	−0.518588	+	0.855024i	$0.673542\pi$
$644$	−27.9307	−1.10062
$645$	21.3566	0.840917
$646$	−28.3884	−1.11693
$647$	13.7887	0.542092	0.271046	−	0.962566i	$-0.412630\pi$
$647$	13.7887	0.542092	0.271046	+	0.962566i	$0.412630\pi$
$648$	22.5190	0.884629
$649$	−32.1934	−1.26370
$650$	−1.00000	−0.0392232
$651$	−12.2064	−0.478406
$652$	−0.441829	−0.0173034
$653$	−2.47856	−0.0969937	−0.0484969	−	0.998823i	$-0.515443\pi$
$653$	−2.47856	−0.0969937	−0.0484969	+	0.998823i	$0.515443\pi$
$654$	23.6663	0.925426
$655$	6.22313	0.243158
$656$	3.61802	0.141260
$657$	32.8113	1.28009
$658$	−16.4789	−0.642414
$659$	41.1481	1.60290	0.801450	−	0.598061i	$-0.204062\pi$
$659$	41.1481	1.60290	0.801450	+	0.598061i	$0.204062\pi$
$660$	−10.7660	−0.419066
$661$	−5.99133	−0.233036	−0.116518	−	0.993189i	$-0.537173\pi$
$661$	−5.99133	−0.233036	−0.116518	+	0.993189i	$0.537173\pi$
$662$	−3.32314	−0.129157
$663$	14.7009	0.570936
$664$	1.95170	0.0757407
$665$	23.5713	0.914057
$666$	−57.8761	−2.24265
$667$	−16.6171	−0.643417
$668$	−11.9570	−0.462630
$669$	−42.8130	−1.65525
$670$	7.09433	0.274078
$671$	−21.0796	−0.813767
$672$	−12.2064	−0.470871
$673$	4.04605	0.155964	0.0779819	−	0.996955i	$-0.475152\pi$
$673$	4.04605	0.155964	0.0779819	+	0.996955i	$0.475152\pi$
$674$	14.2543	0.549057
$675$	−13.8434	−0.532831
$676$	1.00000	0.0384615
$677$	−8.20637	−0.315397	−0.157698	−	0.987487i	$-0.550407\pi$
$677$	−8.20637	−0.315397	−0.157698	+	0.987487i	$0.550407\pi$
$678$	−20.6790	−0.794174
$679$	30.1233	1.15603
$680$	−4.57817	−0.175565
$681$	−44.2799	−1.69681
$682$	−3.35276	−0.128384
$683$	−18.6519	−0.713696	−0.356848	−	0.934162i	$-0.616149\pi$
$683$	−18.6519	−0.713696	−0.356848	+	0.934162i	$0.616149\pi$
$684$	−45.3350	−1.73343
$685$	2.60702	0.0996092
$686$	1.71062	0.0653119
$687$	45.2450	1.72620
$688$	6.65090	0.253563
$689$	0.573444	0.0218465
$690$	−23.5940	−0.898206
$691$	−14.0369	−0.533991	−0.266995	−	0.963698i	$-0.586031\pi$
$691$	−14.0369	−0.533991	−0.266995	+	0.963698i	$0.586031\pi$
$692$	15.2902	0.581248
$693$	−93.1793	−3.53959
$694$	−23.5257	−0.893024
$695$	−0.517571	−0.0196326
$696$	−7.26206	−0.275268
$697$	16.5639	0.627402
$698$	−15.5791	−0.589676
$699$	2.55787	0.0967476
$700$	3.80132	0.143676
$701$	−31.8267	−1.20208	−0.601038	−	0.799220i	$-0.705246\pi$
$701$	−31.8267	−1.20208	−0.601038	+	0.799220i	$0.705246\pi$
$702$	13.8434	0.522484
$703$	49.0870	1.85135
$704$	−3.35276	−0.126362
$705$	−13.9202	−0.524266
$706$	−1.10871	−0.0417267
$707$	−20.8038	−0.782408
$708$	−30.8331	−1.15878
$709$	20.5912	0.773318	0.386659	−	0.922223i	$-0.373629\pi$
$709$	20.5912	0.773318	0.386659	+	0.922223i	$0.373629\pi$
$710$	12.6559	0.474968
$711$	−25.6367	−0.961451
$712$	−15.7041	−0.588537
$713$	−7.34764	−0.275171
$714$	−55.8828	−2.09136
$715$	−3.35276	−0.125386
$716$	−10.3670	−0.387431
$717$	80.3747	3.00165
$718$	4.62514	0.172609
$719$	−20.2063	−0.753566	−0.376783	−	0.926302i	$-0.622970\pi$
$719$	−20.2063	−0.753566	−0.376783	+	0.926302i	$0.622970\pi$
$720$	−7.31111	−0.272469
$721$	29.0318	1.08120
$722$	19.4503	0.723866
$723$	−4.18938	−0.155805
$724$	−24.8794	−0.924634
$725$	2.26156	0.0839921
$726$	−0.773810	−0.0287188
$727$	26.5899	0.986164	0.493082	−	0.869983i	$-0.335870\pi$
$727$	26.5899	0.986164	0.493082	+	0.869983i	$0.335870\pi$
$728$	−3.80132	−0.140886
$729$	31.2817	1.15858
$730$	−4.48787	−0.166104
$731$	30.4489	1.12619
$732$	−20.1889	−0.746202
$733$	45.4172	1.67752	0.838761	−	0.544500i	$-0.183280\pi$
$733$	45.4172	1.67752	0.838761	+	0.544500i	$0.183280\pi$
$734$	30.0074	1.10759
$735$	23.9227	0.882400
$736$	−7.34764	−0.270838
$737$	23.7856	0.876153
$738$	26.4517	0.973701
$739$	29.0138	1.06729	0.533645	−	0.845709i	$-0.320822\pi$
$739$	29.0138	1.06729	0.533645	+	0.845709i	$0.320822\pi$
$740$	7.91619	0.291005
$741$	−19.9114	−0.731465
$742$	−2.17984	−0.0800245
$743$	−9.54161	−0.350048	−0.175024	−	0.984564i	$-0.556000\pi$
$743$	−9.54161	−0.350048	−0.175024	+	0.984564i	$0.556000\pi$
$744$	−3.21109	−0.117724
$745$	18.5359	0.679104
$746$	20.5383	0.751962
$747$	14.2691	0.522079
$748$	−15.3495	−0.561232
$749$	−1.84565	−0.0674386
$750$	3.21109	0.117252
$751$	−52.8767	−1.92950	−0.964750	−	0.263169i	$-0.915232\pi$
$751$	−52.8767	−1.92950	−0.964750	+	0.263169i	$0.915232\pi$
$752$	−4.33505	−0.158083
$753$	16.9986	0.619462
$754$	−2.26156	−0.0823610
$755$	5.39472	0.196334
$756$	−52.6230	−1.91388
$757$	−17.1938	−0.624920	−0.312460	−	0.949931i	$-0.601153\pi$
$757$	−17.1938	−0.624920	−0.312460	+	0.949931i	$0.601153\pi$
$758$	13.0618	0.474426
$759$	−79.1048	−2.87132
$760$	6.20083	0.224928
$761$	−10.6808	−0.387180	−0.193590	−	0.981082i	$-0.562013\pi$
$761$	−10.6808	−0.387180	−0.193590	+	0.981082i	$0.562013\pi$
$762$	63.7922	2.31095
$763$	−28.0164	−1.01426
$764$	−18.5114	−0.669719
$765$	−33.4715	−1.21016
$766$	−25.5566	−0.923398
$767$	−9.60208	−0.346711
$768$	−3.21109	−0.115870
$769$	−33.0025	−1.19010	−0.595050	−	0.803689i	$-0.702868\pi$
$769$	−33.0025	−1.19010	−0.595050	+	0.803689i	$0.702868\pi$
$770$	12.7449	0.459294
$771$	−88.0963	−3.17271
$772$	11.7174	0.421717
$773$	3.88473	0.139724	0.0698620	−	0.997557i	$-0.477744\pi$
$773$	3.88473	0.139724	0.0698620	+	0.997557i	$0.477744\pi$
$774$	48.6254	1.74781
$775$	1.00000	0.0359211
$776$	7.92445	0.284471
$777$	96.6280	3.46651
$778$	18.8535	0.675931
$779$	−22.4347	−0.803807
$780$	−3.21109	−0.114976
$781$	42.4322	1.51834
$782$	−33.6387	−1.20292
$783$	−31.3075	−1.11884
$784$	7.45001	0.266072
$785$	6.47010	0.230928
$786$	19.9830	0.712771
$787$	34.3732	1.22527	0.612636	−	0.790365i	$-0.290109\pi$
$787$	34.3732	1.22527	0.612636	+	0.790365i	$0.290109\pi$
$788$	−25.0089	−0.890904
$789$	14.7486	0.525065
$790$	3.50654	0.124757
$791$	24.4800	0.870409
$792$	−24.5124	−0.871009
$793$	−6.28723	−0.223266
$794$	−37.0400	−1.31450
$795$	−1.84138	−0.0653070
$796$	7.49385	0.265613
$797$	33.5365	1.18793	0.593963	−	0.804493i	$-0.297563\pi$
$797$	33.5365	1.18793	0.593963	+	0.804493i	$0.297563\pi$
$798$	75.6897	2.67939
$799$	−19.8466	−0.702121
$800$	1.00000	0.0353553
$801$	−114.815	−4.05678
$802$	−13.4976	−0.476615
$803$	−15.0467	−0.530988
$804$	22.7805	0.803408
$805$	27.9307	0.984428
$806$	−1.00000	−0.0352235
$807$	−39.9358	−1.40581
$808$	−5.47279	−0.192532
$809$	8.27795	0.291037	0.145519	−	0.989356i	$-0.453515\pi$
$809$	8.27795	0.291037	0.145519	+	0.989356i	$0.453515\pi$
$810$	−22.5190	−0.791236
$811$	−1.29426	−0.0454475	−0.0227238	−	0.999742i	$-0.507234\pi$
$811$	−1.29426	−0.0454475	−0.0227238	+	0.999742i	$0.507234\pi$
$812$	8.59689	0.301692
$813$	100.462	3.52336
$814$	26.5411	0.930264
$815$	0.441829	0.0154766
$816$	−14.7009	−0.514635
$817$	−41.2411	−1.44284
$818$	−9.90694	−0.346388
$819$	−27.7918	−0.971125
$820$	−3.61802	−0.126347
$821$	−46.6346	−1.62756	−0.813779	−	0.581174i	$-0.802594\pi$
$821$	−46.6346	−1.62756	−0.813779	+	0.581174i	$0.802594\pi$
$822$	8.37139	0.291986
$823$	15.1239	0.527186	0.263593	−	0.964634i	$-0.415092\pi$
$823$	15.1239	0.527186	0.263593	+	0.964634i	$0.415092\pi$
$824$	7.63730	0.266058
$825$	10.7660	0.374824
$826$	36.5005	1.27002
$827$	43.7621	1.52176	0.760879	−	0.648894i	$-0.224768\pi$
$827$	43.7621	1.52176	0.760879	+	0.648894i	$0.224768\pi$
$828$	−53.7194	−1.86688
$829$	−46.2703	−1.60703	−0.803517	−	0.595281i	$-0.797041\pi$
$829$	−46.2703	−1.60703	−0.803517	+	0.595281i	$0.797041\pi$
$830$	−1.95170	−0.0677445
$831$	96.6092	3.35134
$832$	−1.00000	−0.0346688
$833$	34.1074	1.18175
$834$	−1.66197	−0.0575492
$835$	11.9570	0.413789
$836$	20.7899	0.719033
$837$	−13.8434	−0.478496
$838$	−9.36172	−0.323395
$839$	10.7113	0.369794	0.184897	−	0.982758i	$-0.440805\pi$
$839$	10.7113	0.369794	0.184897	+	0.982758i	$0.440805\pi$
$840$	12.2064	0.421160
$841$	−23.8854	−0.823633
$842$	−14.3979	−0.496185
$843$	99.5056	3.42716
$844$	25.6076	0.881450
$845$	−1.00000	−0.0344010
$846$	−31.6940	−1.08966
$847$	0.916043	0.0314756
$848$	−0.573444	−0.0196921
$849$	−103.501	−3.55213
$850$	4.57817	0.157030
$851$	58.1654	1.99388
$852$	40.6393	1.39228
$853$	−54.7761	−1.87550	−0.937750	−	0.347312i	$-0.887094\pi$
$853$	−54.7761	−1.87550	−0.937750	+	0.347312i	$0.887094\pi$
$854$	23.8998	0.817833
$855$	45.3350	1.55042
$856$	−0.485529	−0.0165950
$857$	51.2051	1.74913	0.874566	−	0.484906i	$-0.161146\pi$
$857$	51.2051	1.74913	0.874566	+	0.484906i	$0.161146\pi$
$858$	−10.7660	−0.367545
$859$	27.7277	0.946056	0.473028	−	0.881047i	$-0.343161\pi$
$859$	27.7277	0.946056	0.473028	+	0.881047i	$0.343161\pi$
$860$	−6.65090	−0.226794
$861$	−44.1629	−1.50507
$862$	−3.77007	−0.128409
$863$	−36.7370	−1.25054	−0.625271	−	0.780408i	$-0.715012\pi$
$863$	−36.7370	−1.25054	−0.625271	+	0.780408i	$0.715012\pi$
$864$	−13.8434	−0.470961
$865$	−15.2902	−0.519884
$866$	11.8921	0.404112
$867$	−12.7146	−0.431812
$868$	3.80132	0.129025
$869$	11.7566	0.398815
$870$	7.26206	0.246207
$871$	7.09433	0.240382
$872$	−7.37017	−0.249586
$873$	57.9365	1.96085
$874$	45.5615	1.54114
$875$	−3.80132	−0.128508
$876$	−14.4110	−0.486901
$877$	8.11120	0.273896	0.136948	−	0.990578i	$-0.456271\pi$
$877$	8.11120	0.273896	0.136948	+	0.990578i	$0.456271\pi$
$878$	25.8824	0.873487
$879$	48.2126	1.62617
$880$	3.35276	0.113021
$881$	18.5859	0.626176	0.313088	−	0.949724i	$-0.398637\pi$
$881$	18.5859	0.626176	0.313088	+	0.949724i	$0.398637\pi$
$882$	54.4678	1.83403
$883$	10.7614	0.362149	0.181074	−	0.983469i	$-0.442043\pi$
$883$	10.7614	0.362149	0.181074	+	0.983469i	$0.442043\pi$
$884$	−4.57817	−0.153980
$885$	30.8331	1.03644
$886$	−33.0213	−1.10937
$887$	−47.8243	−1.60578	−0.802891	−	0.596126i	$-0.796706\pi$
$887$	−47.8243	−1.60578	−0.802891	+	0.596126i	$0.796706\pi$
$888$	25.4196	0.853026
$889$	−75.5177	−2.53278
$890$	15.7041	0.526404
$891$	−75.5006	−2.52937
$892$	13.3329	0.446417
$893$	26.8809	0.899535
$894$	59.5206	1.99067
$895$	10.3670	0.346529
$896$	3.80132	0.126993
$897$	−23.5940	−0.787779
$898$	14.2635	0.475981
$899$	2.26156	0.0754271
$900$	7.31111	0.243704
$901$	−2.62532	−0.0874621
$902$	−12.1303	−0.403896
$903$	−81.1834	−2.70161
$904$	6.43988	0.214187
$905$	24.8794	0.827018
$906$	17.3229	0.575516
$907$	−50.5576	−1.67874	−0.839370	−	0.543561i	$-0.817076\pi$
$907$	−50.5576	−1.67874	−0.839370	+	0.543561i	$0.817076\pi$
$908$	13.7897	0.457626
$909$	−40.0122	−1.32712
$910$	3.80132	0.126012
$911$	−14.4713	−0.479456	−0.239728	−	0.970840i	$-0.577058\pi$
$911$	−14.4713	−0.479456	−0.239728	+	0.970840i	$0.577058\pi$
$912$	19.9114	0.659334
$913$	−6.54358	−0.216561
$914$	−1.55627	−0.0514767
$915$	20.1889	0.667424
$916$	−14.0902	−0.465554
$917$	−23.6561	−0.781193
$918$	−63.3772	−2.09176
$919$	35.5352	1.17220	0.586100	−	0.810239i	$-0.300663\pi$
$919$	35.5352	1.17220	0.586100	+	0.810239i	$0.300663\pi$
$920$	7.34764	0.242245
$921$	21.6728	0.714144
$922$	−11.5844	−0.381513
$923$	12.6559	0.416574
$924$	40.9250	1.34633
$925$	−7.91619	−0.260283
$926$	0.527973	0.0173503
$927$	55.8371	1.83393
$928$	2.26156	0.0742392
$929$	27.8765	0.914600	0.457300	−	0.889313i	$-0.348817\pi$
$929$	27.8765	0.914600	0.457300	+	0.889313i	$0.348817\pi$
$930$	3.21109	0.105296
$931$	−46.1963	−1.51402
$932$	−0.796574	−0.0260927
$933$	82.5960	2.70407
$934$	−22.2279	−0.727319
$935$	15.3495	0.501982
$936$	−7.31111	−0.238971
$937$	−59.3362	−1.93843	−0.969215	−	0.246216i	$-0.920813\pi$
$937$	−59.3362	−1.93843	−0.969215	+	0.246216i	$0.920813\pi$
$938$	−26.9678	−0.880530
$939$	−39.4494	−1.28738
$940$	4.33505	0.141394
$941$	52.8741	1.72365	0.861823	−	0.507209i	$-0.169323\pi$
$941$	52.8741	1.72365	0.861823	+	0.507209i	$0.169323\pi$
$942$	20.7761	0.676921
$943$	−26.5839	−0.865691
$944$	9.60208	0.312521
$945$	52.6230	1.71183
$946$	−22.2988	−0.724998
$947$	−8.00210	−0.260033	−0.130017	−	0.991512i	$-0.541503\pi$
$947$	−8.00210	−0.260033	−0.130017	+	0.991512i	$0.541503\pi$
$948$	11.2598	0.365702
$949$	−4.48787	−0.145682
$950$	−6.20083	−0.201182
$951$	−100.222	−3.24993
$952$	17.4031	0.564036
$953$	−0.531677	−0.0172227	−0.00861136	−	0.999963i	$-0.502741\pi$
$953$	−0.531677	−0.0172227	−0.00861136	+	0.999963i	$0.502741\pi$
$954$	−4.19251	−0.135737
$955$	18.5114	0.599015
$956$	−25.0303	−0.809539
$957$	24.3479	0.787057
$958$	−39.0594	−1.26195
$959$	−9.91012	−0.320014
$960$	3.21109	0.103638
$961$	1.00000	0.0322581
$962$	7.91619	0.255228
$963$	−3.54976	−0.114389
$964$	1.30466	0.0420203
$965$	−11.7174	−0.377195
$966$	89.6881	2.88567
$967$	24.6046	0.791230	0.395615	−	0.918416i	$-0.370532\pi$
$967$	24.6046	0.791230	0.395615	+	0.918416i	$0.370532\pi$
$968$	0.240981	0.00774541
$969$	91.1579	2.92841
$970$	−7.92445	−0.254439
$971$	34.4347	1.10506	0.552531	−	0.833492i	$-0.313662\pi$
$971$	34.4347	1.10506	0.552531	+	0.833492i	$0.313662\pi$
$972$	−30.7804	−0.987281
$973$	1.96745	0.0630736
$974$	37.1258	1.18959
$975$	3.21109	0.102837
$976$	6.28723	0.201249
$977$	−21.5053	−0.688015	−0.344007	−	0.938967i	$-0.611785\pi$
$977$	−21.5053	−0.688015	−0.344007	+	0.938967i	$0.611785\pi$
$978$	1.41875	0.0453668
$979$	52.6522	1.68277
$980$	−7.45001	−0.237982
$981$	−53.8841	−1.72039
$982$	−3.88429	−0.123953
$983$	−30.7065	−0.979384	−0.489692	−	0.871895i	$-0.662891\pi$
$983$	−30.7065	−0.979384	−0.489692	+	0.871895i	$0.662891\pi$
$984$	−11.6178	−0.370361
$985$	25.0089	0.796849
$986$	10.3538	0.329732
$987$	52.9152	1.68431
$988$	6.20083	0.197275
$989$	−48.8684	−1.55393
$990$	24.5124	0.779054
$991$	14.9694	0.475517	0.237759	−	0.971324i	$-0.423587\pi$
$991$	14.9694	0.475517	0.237759	+	0.971324i	$0.423587\pi$
$992$	1.00000	0.0317500
$993$	10.6709	0.338631
$994$	−48.1091	−1.52593
$995$	−7.49385	−0.237571
$996$	−6.26709	−0.198580
$997$	39.9494	1.26521	0.632606	−	0.774474i	$-0.281985\pi$
$997$	39.9494	1.26521	0.632606	+	0.774474i	$0.281985\pi$
$998$	22.2268	0.703576
$999$	109.587	3.46717

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.j.1.1	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.j.1.1	✓	7	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:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.21109 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.21109 q^{6} +3.80132 q^{7} +1.00000 q^{8} +7.31111 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.21109 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.21109 q^{6} +3.80132 q^{7} +1.00000 q^{8} +7.31111 q^{9} -1.00000 q^{10} -3.35276 q^{11} -3.21109 q^{12} -1.00000 q^{13} +3.80132 q^{14} +3.21109 q^{15} +1.00000 q^{16} +4.57817 q^{17} +7.31111 q^{18} -6.20083 q^{19} -1.00000 q^{20} -12.2064 q^{21} -3.35276 q^{22} -7.34764 q^{23} -3.21109 q^{24} +1.00000 q^{25} -1.00000 q^{26} -13.8434 q^{27} +3.80132 q^{28} +2.26156 q^{29} +3.21109 q^{30} +1.00000 q^{31} +1.00000 q^{32} +10.7660 q^{33} +4.57817 q^{34} -3.80132 q^{35} +7.31111 q^{36} -7.91619 q^{37} -6.20083 q^{38} +3.21109 q^{39} -1.00000 q^{40} +3.61802 q^{41} -12.2064 q^{42} +6.65090 q^{43} -3.35276 q^{44} -7.31111 q^{45} -7.34764 q^{46} -4.33505 q^{47} -3.21109 q^{48} +7.45001 q^{49} +1.00000 q^{50} -14.7009 q^{51} -1.00000 q^{52} -0.573444 q^{53} -13.8434 q^{54} +3.35276 q^{55} +3.80132 q^{56} +19.9114 q^{57} +2.26156 q^{58} +9.60208 q^{59} +3.21109 q^{60} +6.28723 q^{61} +1.00000 q^{62} +27.7918 q^{63} +1.00000 q^{64} +1.00000 q^{65} +10.7660 q^{66} -7.09433 q^{67} +4.57817 q^{68} +23.5940 q^{69} -3.80132 q^{70} -12.6559 q^{71} +7.31111 q^{72} +4.48787 q^{73} -7.91619 q^{74} -3.21109 q^{75} -6.20083 q^{76} -12.7449 q^{77} +3.21109 q^{78} -3.50654 q^{79} -1.00000 q^{80} +22.5190 q^{81} +3.61802 q^{82} +1.95170 q^{83} -12.2064 q^{84} -4.57817 q^{85} +6.65090 q^{86} -7.26206 q^{87} -3.35276 q^{88} -15.7041 q^{89} -7.31111 q^{90} -3.80132 q^{91} -7.34764 q^{92} -3.21109 q^{93} -4.33505 q^{94} +6.20083 q^{95} -3.21109 q^{96} +7.92445 q^{97} +7.45001 q^{98} -24.5124 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} - 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 4 q^{7} + 7 q^{8} + 4 q^{9}+O(q^{10}) \) 7 * q + 7 * q^2 - 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 4 * q^7 + 7 * q^8 + 4 * q^9	\( 7 q + 7 q^{2} - 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 4 q^{7} + 7 q^{8} + 4 q^{9} - 7 q^{10} - 10 q^{11} - 3 q^{12} - 7 q^{13} + 4 q^{14} + 3 q^{15} + 7 q^{16} - 6 q^{17} + 4 q^{18} - 5 q^{19} - 7 q^{20} - 15 q^{21} - 10 q^{22} - 11 q^{23} - 3 q^{24} + 7 q^{25} - 7 q^{26} - 21 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 7 q^{31} + 7 q^{32} + 4 q^{33} - 6 q^{34} - 4 q^{35} + 4 q^{36} - 8 q^{37} - 5 q^{38} + 3 q^{39} - 7 q^{40} - 12 q^{41} - 15 q^{42} - 5 q^{43} - 10 q^{44} - 4 q^{45} - 11 q^{46} - 10 q^{47} - 3 q^{48} + 7 q^{49} + 7 q^{50} - 29 q^{51} - 7 q^{52} - 18 q^{53} - 21 q^{54} + 10 q^{55} + 4 q^{56} + 13 q^{57} - 18 q^{58} - 11 q^{59} + 3 q^{60} - 25 q^{61} + 7 q^{62} + 17 q^{63} + 7 q^{64} + 7 q^{65} + 4 q^{66} - 22 q^{67} - 6 q^{68} - 18 q^{69} - 4 q^{70} - 22 q^{71} + 4 q^{72} + 19 q^{73} - 8 q^{74} - 3 q^{75} - 5 q^{76} - 47 q^{77} + 3 q^{78} - 20 q^{79} - 7 q^{80} + 7 q^{81} - 12 q^{82} - 8 q^{83} - 15 q^{84} + 6 q^{85} - 5 q^{86} + 29 q^{87} - 10 q^{88} - 4 q^{89} - 4 q^{90} - 4 q^{91} - 11 q^{92} - 3 q^{93} - 10 q^{94} + 5 q^{95} - 3 q^{96} + 13 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 - 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 4 * q^7 + 7 * q^8 + 4 * q^9 - 7 * q^10 - 10 * q^11 - 3 * q^12 - 7 * q^13 + 4 * q^14 + 3 * q^15 + 7 * q^16 - 6 * q^17 + 4 * q^18 - 5 * q^19 - 7 * q^20 - 15 * q^21 - 10 * q^22 - 11 * q^23 - 3 * q^24 + 7 * q^25 - 7 * q^26 - 21 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 7 * q^31 + 7 * q^32 + 4 * q^33 - 6 * q^34 - 4 * q^35 + 4 * q^36 - 8 * q^37 - 5 * q^38 + 3 * q^39 - 7 * q^40 - 12 * q^41 - 15 * q^42 - 5 * q^43 - 10 * q^44 - 4 * q^45 - 11 * q^46 - 10 * q^47 - 3 * q^48 + 7 * q^49 + 7 * q^50 - 29 * q^51 - 7 * q^52 - 18 * q^53 - 21 * q^54 + 10 * q^55 + 4 * q^56 + 13 * q^57 - 18 * q^58 - 11 * q^59 + 3 * q^60 - 25 * q^61 + 7 * q^62 + 17 * q^63 + 7 * q^64 + 7 * q^65 + 4 * q^66 - 22 * q^67 - 6 * q^68 - 18 * q^69 - 4 * q^70 - 22 * q^71 + 4 * q^72 + 19 * q^73 - 8 * q^74 - 3 * q^75 - 5 * q^76 - 47 * q^77 + 3 * q^78 - 20 * q^79 - 7 * q^80 + 7 * q^81 - 12 * q^82 - 8 * q^83 - 15 * q^84 + 6 * q^85 - 5 * q^86 + 29 * q^87 - 10 * q^88 - 4 * q^89 - 4 * q^90 - 4 * q^91 - 11 * q^92 - 3 * q^93 - 10 * q^94 + 5 * q^95 - 3 * q^96 + 13 * q^97 + 7 * q^98 - 27 * q^99

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