LMFDB - Embedded newform 9282.2.a.ce.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9282,2,Mod(1,9282)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9282, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9282.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9282.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:	$74.1171431562$
Analytic rank:	$0$
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} - 23x^{5} + 70x^{4} + 115x^{3} - 422x^{2} + 118x + 208 $ x^7 - 3x^6 - 23x^5 + 70x^4 + 115x^3 - 422x^2 + 118x + 208
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$4.16178$ of defining polynomial
Character	$\chi$	$=$	9282.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.16178 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.16178 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.16178 q^{10} +1.08980 q^{11} +1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{14} +4.16178 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +1.17983 q^{19} +4.16178 q^{20} -1.00000 q^{21} +1.08980 q^{22} -1.29674 q^{23} +1.00000 q^{24} +12.3204 q^{25} -1.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} +4.27277 q^{29} +4.16178 q^{30} +5.14373 q^{31} +1.00000 q^{32} +1.08980 q^{33} +1.00000 q^{34} -4.16178 q^{35} +1.00000 q^{36} +9.36559 q^{37} +1.17983 q^{38} -1.00000 q^{39} +4.16178 q^{40} -10.3024 q^{41} -1.00000 q^{42} +4.11691 q^{43} +1.08980 q^{44} +4.16178 q^{45} -1.29674 q^{46} -4.73838 q^{47} +1.00000 q^{48} +1.00000 q^{49} +12.3204 q^{50} +1.00000 q^{51} -1.00000 q^{52} +3.93731 q^{53} +1.00000 q^{54} +4.53551 q^{55} -1.00000 q^{56} +1.17983 q^{57} +4.27277 q^{58} -10.2397 q^{59} +4.16178 q^{60} +1.41766 q^{61} +5.14373 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.16178 q^{65} +1.08980 q^{66} -12.9657 q^{67} +1.00000 q^{68} -1.29674 q^{69} -4.16178 q^{70} -12.5483 q^{71} +1.00000 q^{72} -12.1755 q^{73} +9.36559 q^{74} +12.3204 q^{75} +1.17983 q^{76} -1.08980 q^{77} -1.00000 q^{78} +13.1278 q^{79} +4.16178 q^{80} +1.00000 q^{81} -10.3024 q^{82} -9.59319 q^{83} -1.00000 q^{84} +4.16178 q^{85} +4.11691 q^{86} +4.27277 q^{87} +1.08980 q^{88} +5.80704 q^{89} +4.16178 q^{90} +1.00000 q^{91} -1.29674 q^{92} +5.14373 q^{93} -4.73838 q^{94} +4.91020 q^{95} +1.00000 q^{96} -16.8638 q^{97} +1.00000 q^{98} +1.08980 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 3 q^{5} + 7 q^{6} - 7 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + 3 * q^5 + 7 * q^6 - 7 * q^7 + 7 * q^8 + 7 * q^9	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 3 q^{5} + 7 q^{6} - 7 q^{7} + 7 q^{8} + 7 q^{9} + 3 q^{10} + 7 q^{11} + 7 q^{12} - 7 q^{13} - 7 q^{14} + 3 q^{15} + 7 q^{16} + 7 q^{17} + 7 q^{18} - 2 q^{19} + 3 q^{20} - 7 q^{21} + 7 q^{22} + 12 q^{23} + 7 q^{24} + 20 q^{25} - 7 q^{26} + 7 q^{27} - 7 q^{28} + 18 q^{29} + 3 q^{30} - 6 q^{31} + 7 q^{32} + 7 q^{33} + 7 q^{34} - 3 q^{35} + 7 q^{36} + 5 q^{37} - 2 q^{38} - 7 q^{39} + 3 q^{40} + 10 q^{41} - 7 q^{42} + 18 q^{43} + 7 q^{44} + 3 q^{45} + 12 q^{46} + 3 q^{47} + 7 q^{48} + 7 q^{49} + 20 q^{50} + 7 q^{51} - 7 q^{52} + 18 q^{53} + 7 q^{54} + 4 q^{55} - 7 q^{56} - 2 q^{57} + 18 q^{58} + 20 q^{59} + 3 q^{60} + 19 q^{61} - 6 q^{62} - 7 q^{63} + 7 q^{64} - 3 q^{65} + 7 q^{66} - 16 q^{67} + 7 q^{68} + 12 q^{69} - 3 q^{70} + 5 q^{71} + 7 q^{72} + 2 q^{73} + 5 q^{74} + 20 q^{75} - 2 q^{76} - 7 q^{77} - 7 q^{78} + 12 q^{79} + 3 q^{80} + 7 q^{81} + 10 q^{82} + 11 q^{83} - 7 q^{84} + 3 q^{85} + 18 q^{86} + 18 q^{87} + 7 q^{88} + 6 q^{89} + 3 q^{90} + 7 q^{91} + 12 q^{92} - 6 q^{93} + 3 q^{94} + 35 q^{95} + 7 q^{96} - 3 q^{97} + 7 q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + 3 * q^5 + 7 * q^6 - 7 * q^7 + 7 * q^8 + 7 * q^9 + 3 * q^10 + 7 * q^11 + 7 * q^12 - 7 * q^13 - 7 * q^14 + 3 * q^15 + 7 * q^16 + 7 * q^17 + 7 * q^18 - 2 * q^19 + 3 * q^20 - 7 * q^21 + 7 * q^22 + 12 * q^23 + 7 * q^24 + 20 * q^25 - 7 * q^26 + 7 * q^27 - 7 * q^28 + 18 * q^29 + 3 * q^30 - 6 * q^31 + 7 * q^32 + 7 * q^33 + 7 * q^34 - 3 * q^35 + 7 * q^36 + 5 * q^37 - 2 * q^38 - 7 * q^39 + 3 * q^40 + 10 * q^41 - 7 * q^42 + 18 * q^43 + 7 * q^44 + 3 * q^45 + 12 * q^46 + 3 * q^47 + 7 * q^48 + 7 * q^49 + 20 * q^50 + 7 * q^51 - 7 * q^52 + 18 * q^53 + 7 * q^54 + 4 * q^55 - 7 * q^56 - 2 * q^57 + 18 * q^58 + 20 * q^59 + 3 * q^60 + 19 * q^61 - 6 * q^62 - 7 * q^63 + 7 * q^64 - 3 * q^65 + 7 * q^66 - 16 * q^67 + 7 * q^68 + 12 * q^69 - 3 * q^70 + 5 * q^71 + 7 * q^72 + 2 * q^73 + 5 * q^74 + 20 * q^75 - 2 * q^76 - 7 * q^77 - 7 * q^78 + 12 * q^79 + 3 * q^80 + 7 * q^81 + 10 * q^82 + 11 * q^83 - 7 * q^84 + 3 * q^85 + 18 * q^86 + 18 * q^87 + 7 * q^88 + 6 * q^89 + 3 * q^90 + 7 * q^91 + 12 * q^92 - 6 * q^93 + 3 * q^94 + 35 * q^95 + 7 * q^96 - 3 * q^97 + 7 * q^98 + 7 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	4.16178	1.86121	0.930603	−	0.366031i	$-0.119284\pi$
$5$	4.16178	1.86121	0.930603	+	0.366031i	$0.119284\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	4.16178	1.31607
$11$	1.08980	0.328587	0.164294	−	0.986411i	$-0.447466\pi$
$11$	1.08980	0.328587	0.164294	+	0.986411i	$0.447466\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.00000	−0.267261
$15$	4.16178	1.07457
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	1.17983	0.270672	0.135336	−	0.990800i	$-0.456789\pi$
$19$	1.17983	0.270672	0.135336	+	0.990800i	$0.456789\pi$
$20$	4.16178	0.930603
$21$	−1.00000	−0.218218
$22$	1.08980	0.232346
$23$	−1.29674	−0.270390	−0.135195	−	0.990819i	$-0.543166\pi$
$23$	−1.29674	−0.270390	−0.135195	+	0.990819i	$0.543166\pi$
$24$	1.00000	0.204124
$25$	12.3204	2.46409
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	4.27277	0.793433	0.396716	−	0.917941i	$-0.370150\pi$
$29$	4.27277	0.793433	0.396716	+	0.917941i	$0.370150\pi$
$30$	4.16178	0.759834
$31$	5.14373	0.923842	0.461921	−	0.886921i	$-0.347160\pi$
$31$	5.14373	0.923842	0.461921	+	0.886921i	$0.347160\pi$
$32$	1.00000	0.176777
$33$	1.08980	0.189710
$34$	1.00000	0.171499
$35$	−4.16178	−0.703470
$36$	1.00000	0.166667
$37$	9.36559	1.53969	0.769847	−	0.638229i	$-0.220333\pi$
$37$	9.36559	1.53969	0.769847	+	0.638229i	$0.220333\pi$
$38$	1.17983	0.191394
$39$	−1.00000	−0.160128
$40$	4.16178	0.658035
$41$	−10.3024	−1.60896	−0.804481	−	0.593979i	$-0.797556\pi$
$41$	−10.3024	−1.60896	−0.804481	+	0.593979i	$0.797556\pi$
$42$	−1.00000	−0.154303
$43$	4.11691	0.627823	0.313912	−	0.949452i	$-0.398360\pi$
$43$	4.11691	0.627823	0.313912	+	0.949452i	$0.398360\pi$
$44$	1.08980	0.164294
$45$	4.16178	0.620402
$46$	−1.29674	−0.191194
$47$	−4.73838	−0.691163	−0.345582	−	0.938389i	$-0.612318\pi$
$47$	−4.73838	−0.691163	−0.345582	+	0.938389i	$0.612318\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	12.3204	1.74237
$51$	1.00000	0.140028
$52$	−1.00000	−0.138675
$53$	3.93731	0.540831	0.270416	−	0.962744i	$-0.412839\pi$
$53$	3.93731	0.540831	0.270416	+	0.962744i	$0.412839\pi$
$54$	1.00000	0.136083
$55$	4.53551	0.611569
$56$	−1.00000	−0.133631
$57$	1.17983	0.156272
$58$	4.27277	0.561042
$59$	−10.2397	−1.33309	−0.666547	−	0.745463i	$-0.732228\pi$
$59$	−10.2397	−1.33309	−0.666547	+	0.745463i	$0.732228\pi$
$60$	4.16178	0.537284
$61$	1.41766	0.181512	0.0907562	−	0.995873i	$-0.471072\pi$
$61$	1.41766	0.181512	0.0907562	+	0.995873i	$0.471072\pi$
$62$	5.14373	0.653255
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	−4.16178	−0.516206
$66$	1.08980	0.134145
$67$	−12.9657	−1.58401	−0.792006	−	0.610514i	$-0.790963\pi$
$67$	−12.9657	−1.58401	−0.792006	+	0.610514i	$0.790963\pi$
$68$	1.00000	0.121268
$69$	−1.29674	−0.156110
$70$	−4.16178	−0.497428
$71$	−12.5483	−1.48920	−0.744602	−	0.667508i	$-0.767361\pi$
$71$	−12.5483	−1.48920	−0.744602	+	0.667508i	$0.767361\pi$
$72$	1.00000	0.117851
$73$	−12.1755	−1.42504	−0.712519	−	0.701652i	$-0.752446\pi$
$73$	−12.1755	−1.42504	−0.712519	+	0.701652i	$0.752446\pi$
$74$	9.36559	1.08873
$75$	12.3204	1.42264
$76$	1.17983	0.135336
$77$	−1.08980	−0.124194
$78$	−1.00000	−0.113228
$79$	13.1278	1.47699	0.738494	−	0.674260i	$-0.235537\pi$
$79$	13.1278	1.47699	0.738494	+	0.674260i	$0.235537\pi$
$80$	4.16178	0.465301
$81$	1.00000	0.111111
$82$	−10.3024	−1.13771
$83$	−9.59319	−1.05299	−0.526495	−	0.850178i	$-0.676494\pi$
$83$	−9.59319	−1.05299	−0.526495	+	0.850178i	$0.676494\pi$
$84$	−1.00000	−0.109109
$85$	4.16178	0.451409
$86$	4.11691	0.443938
$87$	4.27277	0.458088
$88$	1.08980	0.116173
$89$	5.80704	0.615545	0.307773	−	0.951460i	$-0.400416\pi$
$89$	5.80704	0.615545	0.307773	+	0.951460i	$0.400416\pi$
$90$	4.16178	0.438690
$91$	1.00000	0.104828
$92$	−1.29674	−0.135195
$93$	5.14373	0.533380
$94$	−4.73838	−0.488726
$95$	4.91020	0.503776
$96$	1.00000	0.102062
$97$	−16.8638	−1.71226	−0.856128	−	0.516764i	$-0.827137\pi$
$97$	−16.8638	−1.71226	−0.856128	+	0.516764i	$0.827137\pi$
$98$	1.00000	0.101015
$99$	1.08980	0.109529
$100$	12.3204	1.23204
$101$	10.3478	1.02965	0.514824	−	0.857296i	$-0.327857\pi$
$101$	10.3478	1.02965	0.514824	+	0.857296i	$0.327857\pi$
$102$	1.00000	0.0990148
$103$	5.38654	0.530752	0.265376	−	0.964145i	$-0.414504\pi$
$103$	5.38654	0.530752	0.265376	+	0.964145i	$0.414504\pi$
$104$	−1.00000	−0.0980581
$105$	−4.16178	−0.406148
$106$	3.93731	0.382425
$107$	5.21949	0.504587	0.252293	−	0.967651i	$-0.418815\pi$
$107$	5.21949	0.504587	0.252293	+	0.967651i	$0.418815\pi$
$108$	1.00000	0.0962250
$109$	3.10600	0.297501	0.148750	−	0.988875i	$-0.452475\pi$
$109$	3.10600	0.297501	0.148750	+	0.988875i	$0.452475\pi$
$110$	4.53551	0.432444
$111$	9.36559	0.888942
$112$	−1.00000	−0.0944911
$113$	7.76217	0.730204	0.365102	−	0.930968i	$-0.381034\pi$
$113$	7.76217	0.730204	0.365102	+	0.930968i	$0.381034\pi$
$114$	1.17983	0.110501
$115$	−5.39676	−0.503251
$116$	4.27277	0.396716
$117$	−1.00000	−0.0924500
$118$	−10.2397	−0.942640
$119$	−1.00000	−0.0916698
$120$	4.16178	0.379917
$121$	−9.81233	−0.892030
$122$	1.41766	0.128349
$123$	−10.3024	−0.928934
$124$	5.14373	0.461921
$125$	30.4660	2.72496
$126$	−1.00000	−0.0890871
$127$	14.4582	1.28296	0.641480	−	0.767140i	$-0.278321\pi$
$127$	14.4582	1.28296	0.641480	+	0.767140i	$0.278321\pi$
$128$	1.00000	0.0883883
$129$	4.11691	0.362474
$130$	−4.16178	−0.365012
$131$	−11.4181	−0.997600	−0.498800	−	0.866717i	$-0.666226\pi$
$131$	−11.4181	−0.997600	−0.498800	+	0.866717i	$0.666226\pi$
$132$	1.08980	0.0948550
$133$	−1.17983	−0.102304
$134$	−12.9657	−1.12006
$135$	4.16178	0.358189
$136$	1.00000	0.0857493
$137$	2.26399	0.193426	0.0967130	−	0.995312i	$-0.469167\pi$
$137$	2.26399	0.193426	0.0967130	+	0.995312i	$0.469167\pi$
$138$	−1.29674	−0.110386
$139$	7.03180	0.596430	0.298215	−	0.954499i	$-0.403609\pi$
$139$	7.03180	0.596430	0.298215	+	0.954499i	$0.403609\pi$
$140$	−4.16178	−0.351735
$141$	−4.73838	−0.399043
$142$	−12.5483	−1.05303
$143$	−1.08980	−0.0911337
$144$	1.00000	0.0833333
$145$	17.7823	1.47674
$146$	−12.1755	−1.00765
$147$	1.00000	0.0824786
$148$	9.36559	0.769847
$149$	12.6378	1.03533	0.517666	−	0.855583i	$-0.326801\pi$
$149$	12.6378	1.03533	0.517666	+	0.855583i	$0.326801\pi$
$150$	12.3204	1.00596
$151$	−15.2605	−1.24188	−0.620942	−	0.783856i	$-0.713250\pi$
$151$	−15.2605	−1.24188	−0.620942	+	0.783856i	$0.713250\pi$
$152$	1.17983	0.0956969
$153$	1.00000	0.0808452
$154$	−1.08980	−0.0878187
$155$	21.4071	1.71946
$156$	−1.00000	−0.0800641
$157$	16.0190	1.27845	0.639226	−	0.769019i	$-0.279255\pi$
$157$	16.0190	1.27845	0.639226	+	0.769019i	$0.279255\pi$
$158$	13.1278	1.04439
$159$	3.93731	0.312249
$160$	4.16178	0.329018
$161$	1.29674	0.102198
$162$	1.00000	0.0785674
$163$	−10.2815	−0.805312	−0.402656	−	0.915351i	$-0.631913\pi$
$163$	−10.2815	−0.805312	−0.402656	+	0.915351i	$0.631913\pi$
$164$	−10.3024	−0.804481
$165$	4.53551	0.353089
$166$	−9.59319	−0.744576
$167$	19.3710	1.49897	0.749486	−	0.662020i	$-0.230301\pi$
$167$	19.3710	1.49897	0.749486	+	0.662020i	$0.230301\pi$
$168$	−1.00000	−0.0771517
$169$	1.00000	0.0769231
$170$	4.16178	0.319194
$171$	1.17983	0.0902239
$172$	4.11691	0.313912
$173$	2.33830	0.177777	0.0888887	−	0.996042i	$-0.471668\pi$
$173$	2.33830	0.177777	0.0888887	+	0.996042i	$0.471668\pi$
$174$	4.27277	0.323917
$175$	−12.3204	−0.931337
$176$	1.08980	0.0821468
$177$	−10.2397	−0.769662
$178$	5.80704	0.435256
$179$	−21.8961	−1.63659	−0.818296	−	0.574798i	$-0.805081\pi$
$179$	−21.8961	−1.63659	−0.818296	+	0.574798i	$0.805081\pi$
$180$	4.16178	0.310201
$181$	1.42736	0.106095	0.0530473	−	0.998592i	$-0.483107\pi$
$181$	1.42736	0.106095	0.0530473	+	0.998592i	$0.483107\pi$
$182$	1.00000	0.0741249
$183$	1.41766	0.104796
$184$	−1.29674	−0.0955972
$185$	38.9775	2.86569
$186$	5.14373	0.377157
$187$	1.08980	0.0796941
$188$	−4.73838	−0.345582
$189$	−1.00000	−0.0727393
$190$	4.91020	0.356223
$191$	12.5851	0.910624	0.455312	−	0.890332i	$-0.349528\pi$
$191$	12.5851	0.910624	0.455312	+	0.890332i	$0.349528\pi$
$192$	1.00000	0.0721688
$193$	−18.9948	−1.36727	−0.683637	−	0.729822i	$-0.739603\pi$
$193$	−18.9948	−1.36727	−0.683637	+	0.729822i	$0.739603\pi$
$194$	−16.8638	−1.21075
$195$	−4.16178	−0.298031
$196$	1.00000	0.0714286
$197$	12.7352	0.907349	0.453674	−	0.891168i	$-0.350113\pi$
$197$	12.7352	0.907349	0.453674	+	0.891168i	$0.350113\pi$
$198$	1.08980	0.0774488
$199$	−14.5129	−1.02879	−0.514395	−	0.857553i	$-0.671983\pi$
$199$	−14.5129	−1.02879	−0.514395	+	0.857553i	$0.671983\pi$
$200$	12.3204	0.871186
$201$	−12.9657	−0.914529
$202$	10.3478	0.728071
$203$	−4.27277	−0.299889
$204$	1.00000	0.0700140
$205$	−42.8763	−2.99461
$206$	5.38654	0.375298
$207$	−1.29674	−0.0901299
$208$	−1.00000	−0.0693375
$209$	1.28578	0.0889393
$210$	−4.16178	−0.287190
$211$	6.67551	0.459561	0.229780	−	0.973243i	$-0.426199\pi$
$211$	6.67551	0.459561	0.229780	+	0.973243i	$0.426199\pi$
$212$	3.93731	0.270416
$213$	−12.5483	−0.859793
$214$	5.21949	0.356797
$215$	17.1337	1.16851
$216$	1.00000	0.0680414
$217$	−5.14373	−0.349179
$218$	3.10600	0.210365
$219$	−12.1755	−0.822746
$220$	4.53551	0.305784
$221$	−1.00000	−0.0672673
$222$	9.36559	0.628577
$223$	−1.89524	−0.126915	−0.0634573	−	0.997985i	$-0.520213\pi$
$223$	−1.89524	−0.126915	−0.0634573	+	0.997985i	$0.520213\pi$
$224$	−1.00000	−0.0668153
$225$	12.3204	0.821362
$226$	7.76217	0.516332
$227$	−15.0019	−0.995713	−0.497856	−	0.867259i	$-0.665879\pi$
$227$	−15.0019	−0.995713	−0.497856	+	0.867259i	$0.665879\pi$
$228$	1.17983	0.0781362
$229$	−2.56615	−0.169576	−0.0847879	−	0.996399i	$-0.527021\pi$
$229$	−2.56615	−0.169576	−0.0847879	+	0.996399i	$0.527021\pi$
$230$	−5.39676	−0.355852
$231$	−1.08980	−0.0717036
$232$	4.27277	0.280521
$233$	0.588564	0.0385581	0.0192791	−	0.999814i	$-0.493863\pi$
$233$	0.588564	0.0385581	0.0192791	+	0.999814i	$0.493863\pi$
$234$	−1.00000	−0.0653720
$235$	−19.7201	−1.28640
$236$	−10.2397	−0.666547
$237$	13.1278	0.852740
$238$	−1.00000	−0.0648204
$239$	22.3881	1.44817	0.724083	−	0.689712i	$-0.242263\pi$
$239$	22.3881	1.44817	0.724083	+	0.689712i	$0.242263\pi$
$240$	4.16178	0.268642
$241$	9.91684	0.638800	0.319400	−	0.947620i	$-0.396519\pi$
$241$	9.91684	0.638800	0.319400	+	0.947620i	$0.396519\pi$
$242$	−9.81233	−0.630761
$243$	1.00000	0.0641500
$244$	1.41766	0.0907562
$245$	4.16178	0.265886
$246$	−10.3024	−0.656856
$247$	−1.17983	−0.0750708
$248$	5.14373	0.326627
$249$	−9.59319	−0.607944
$250$	30.4660	1.92684
$251$	−8.50834	−0.537042	−0.268521	−	0.963274i	$-0.586535\pi$
$251$	−8.50834	−0.537042	−0.268521	+	0.963274i	$0.586535\pi$
$252$	−1.00000	−0.0629941
$253$	−1.41319	−0.0888466
$254$	14.4582	0.907190
$255$	4.16178	0.260621
$256$	1.00000	0.0625000
$257$	7.38556	0.460699	0.230349	−	0.973108i	$-0.426013\pi$
$257$	7.38556	0.460699	0.230349	+	0.973108i	$0.426013\pi$
$258$	4.11691	0.256308
$259$	−9.36559	−0.581949
$260$	−4.16178	−0.258103
$261$	4.27277	0.264478
$262$	−11.4181	−0.705410
$263$	−1.19888	−0.0739263	−0.0369632	−	0.999317i	$-0.511768\pi$
$263$	−1.19888	−0.0739263	−0.0369632	+	0.999317i	$0.511768\pi$
$264$	1.08980	0.0670726
$265$	16.3862	1.00660
$266$	−1.17983	−0.0723401
$267$	5.80704	0.355385
$268$	−12.9657	−0.792006
$269$	−19.6161	−1.19601	−0.598007	−	0.801491i	$-0.704040\pi$
$269$	−19.6161	−1.19601	−0.598007	+	0.801491i	$0.704040\pi$
$270$	4.16178	0.253278
$271$	14.9251	0.906634	0.453317	−	0.891349i	$-0.350241\pi$
$271$	14.9251	0.906634	0.453317	+	0.891349i	$0.350241\pi$
$272$	1.00000	0.0606339
$273$	1.00000	0.0605228
$274$	2.26399	0.136773
$275$	13.4268	0.809667
$276$	−1.29674	−0.0780548
$277$	27.2993	1.64025	0.820127	−	0.572182i	$-0.193903\pi$
$277$	27.2993	1.64025	0.820127	+	0.572182i	$0.193903\pi$
$278$	7.03180	0.421740
$279$	5.14373	0.307947
$280$	−4.16178	−0.248714
$281$	−20.4085	−1.21747	−0.608736	−	0.793373i	$-0.708323\pi$
$281$	−20.4085	−1.21747	−0.608736	+	0.793373i	$0.708323\pi$
$282$	−4.73838	−0.282166
$283$	17.5240	1.04169	0.520847	−	0.853650i	$-0.325616\pi$
$283$	17.5240	1.04169	0.520847	+	0.853650i	$0.325616\pi$
$284$	−12.5483	−0.744602
$285$	4.91020	0.290855
$286$	−1.08980	−0.0644413
$287$	10.3024	0.608130
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	17.7823	1.04421
$291$	−16.8638	−0.988572
$292$	−12.1755	−0.712519
$293$	−11.0420	−0.645078	−0.322539	−	0.946556i	$-0.604536\pi$
$293$	−11.0420	−0.645078	−0.322539	+	0.946556i	$0.604536\pi$
$294$	1.00000	0.0583212
$295$	−42.6154	−2.48116
$296$	9.36559	0.544364
$297$	1.08980	0.0632367
$298$	12.6378	0.732090
$299$	1.29674	0.0749926
$300$	12.3204	0.711320
$301$	−4.11691	−0.237295
$302$	−15.2605	−0.878145
$303$	10.3478	0.594467
$304$	1.17983	0.0676679
$305$	5.89998	0.337832
$306$	1.00000	0.0571662
$307$	−17.6735	−1.00868	−0.504340	−	0.863505i	$-0.668264\pi$
$307$	−17.6735	−1.00868	−0.504340	+	0.863505i	$0.668264\pi$
$308$	−1.08980	−0.0620972
$309$	5.38654	0.306430
$310$	21.4071	1.21584
$311$	−13.2464	−0.751133	−0.375566	−	0.926796i	$-0.622552\pi$
$311$	−13.2464	−0.751133	−0.375566	+	0.926796i	$0.622552\pi$
$312$	−1.00000	−0.0566139
$313$	17.0456	0.963475	0.481737	−	0.876316i	$-0.340006\pi$
$313$	17.0456	0.963475	0.481737	+	0.876316i	$0.340006\pi$
$314$	16.0190	0.904003
$315$	−4.16178	−0.234490
$316$	13.1278	0.738494
$317$	−12.3439	−0.693302	−0.346651	−	0.937994i	$-0.612681\pi$
$317$	−12.3439	−0.693302	−0.346651	+	0.937994i	$0.612681\pi$
$318$	3.93731	0.220793
$319$	4.65646	0.260712
$320$	4.16178	0.232651
$321$	5.21949	0.291323
$322$	1.29674	0.0722647
$323$	1.17983	0.0656476
$324$	1.00000	0.0555556
$325$	−12.3204	−0.683414
$326$	−10.2815	−0.569442
$327$	3.10600	0.171762
$328$	−10.3024	−0.568854
$329$	4.73838	0.261235
$330$	4.53551	0.249672
$331$	5.80722	0.319194	0.159597	−	0.987182i	$-0.448981\pi$
$331$	5.80722	0.319194	0.159597	+	0.987182i	$0.448981\pi$
$332$	−9.59319	−0.526495
$333$	9.36559	0.513231
$334$	19.3710	1.05993
$335$	−53.9604	−2.94817
$336$	−1.00000	−0.0545545
$337$	−10.7140	−0.583631	−0.291816	−	0.956475i	$-0.594259\pi$
$337$	−10.7140	−0.583631	−0.291816	+	0.956475i	$0.594259\pi$
$338$	1.00000	0.0543928
$339$	7.76217	0.421583
$340$	4.16178	0.225704
$341$	5.60564	0.303563
$342$	1.17983	0.0637980
$343$	−1.00000	−0.0539949
$344$	4.11691	0.221969
$345$	−5.39676	−0.290552
$346$	2.33830	0.125708
$347$	0.148004	0.00794526	0.00397263	−	0.999992i	$-0.498735\pi$
$347$	0.148004	0.00794526	0.00397263	+	0.999992i	$0.498735\pi$
$348$	4.27277	0.229044
$349$	−26.5625	−1.42186	−0.710930	−	0.703263i	$-0.751726\pi$
$349$	−26.5625	−1.42186	−0.710930	+	0.703263i	$0.751726\pi$
$350$	−12.3204	−0.658555
$351$	−1.00000	−0.0533761
$352$	1.08980	0.0580866
$353$	5.70530	0.303663	0.151831	−	0.988406i	$-0.451483\pi$
$353$	5.70530	0.303663	0.151831	+	0.988406i	$0.451483\pi$
$354$	−10.2397	−0.544233
$355$	−52.2231	−2.77172
$356$	5.80704	0.307773
$357$	−1.00000	−0.0529256
$358$	−21.8961	−1.15724
$359$	9.13369	0.482058	0.241029	−	0.970518i	$-0.422515\pi$
$359$	9.13369	0.482058	0.241029	+	0.970518i	$0.422515\pi$
$360$	4.16178	0.219345
$361$	−17.6080	−0.926737
$362$	1.42736	0.0750202
$363$	−9.81233	−0.515014
$364$	1.00000	0.0524142
$365$	−50.6719	−2.65229
$366$	1.41766	0.0741021
$367$	−2.44262	−0.127504	−0.0637519	−	0.997966i	$-0.520307\pi$
$367$	−2.44262	−0.127504	−0.0637519	+	0.997966i	$0.520307\pi$
$368$	−1.29674	−0.0675974
$369$	−10.3024	−0.536320
$370$	38.9775	2.02635
$371$	−3.93731	−0.204415
$372$	5.14373	0.266690
$373$	2.96338	0.153438	0.0767190	−	0.997053i	$-0.475556\pi$
$373$	2.96338	0.153438	0.0767190	+	0.997053i	$0.475556\pi$
$374$	1.08980	0.0563523
$375$	30.4660	1.57326
$376$	−4.73838	−0.244363
$377$	−4.27277	−0.220059
$378$	−1.00000	−0.0514344
$379$	11.5342	0.592473	0.296236	−	0.955115i	$-0.404268\pi$
$379$	11.5342	0.592473	0.296236	+	0.955115i	$0.404268\pi$
$380$	4.91020	0.251888
$381$	14.4582	0.740718
$382$	12.5851	0.643908
$383$	2.78040	0.142072	0.0710360	−	0.997474i	$-0.477369\pi$
$383$	2.78040	0.142072	0.0710360	+	0.997474i	$0.477369\pi$
$384$	1.00000	0.0510310
$385$	−4.53551	−0.231151
$386$	−18.9948	−0.966809
$387$	4.11691	0.209274
$388$	−16.8638	−0.856128
$389$	−28.8416	−1.46233	−0.731163	−	0.682203i	$-0.761022\pi$
$389$	−28.8416	−1.46233	−0.731163	+	0.682203i	$0.761022\pi$
$390$	−4.16178	−0.210740
$391$	−1.29674	−0.0655791
$392$	1.00000	0.0505076
$393$	−11.4181	−0.575965
$394$	12.7352	0.641592
$395$	54.6349	2.74898
$396$	1.08980	0.0547646
$397$	−4.86912	−0.244374	−0.122187	−	0.992507i	$-0.538991\pi$
$397$	−4.86912	−0.244374	−0.122187	+	0.992507i	$0.538991\pi$
$398$	−14.5129	−0.727464
$399$	−1.17983	−0.0590654
$400$	12.3204	0.616021
$401$	29.8641	1.49134	0.745670	−	0.666316i	$-0.232130\pi$
$401$	29.8641	1.49134	0.745670	+	0.666316i	$0.232130\pi$
$402$	−12.9657	−0.646670
$403$	−5.14373	−0.256228
$404$	10.3478	0.514824
$405$	4.16178	0.206801
$406$	−4.27277	−0.212054
$407$	10.2066	0.505924
$408$	1.00000	0.0495074
$409$	24.4849	1.21070	0.605351	−	0.795959i	$-0.293033\pi$
$409$	24.4849	1.21070	0.605351	+	0.795959i	$0.293033\pi$
$410$	−42.8763	−2.11751
$411$	2.26399	0.111675
$412$	5.38654	0.265376
$413$	10.2397	0.503862
$414$	−1.29674	−0.0637315
$415$	−39.9248	−1.95983
$416$	−1.00000	−0.0490290
$417$	7.03180	0.344349
$418$	1.28578	0.0628896
$419$	1.37727	0.0672839	0.0336419	−	0.999434i	$-0.489289\pi$
$419$	1.37727	0.0672839	0.0336419	+	0.999434i	$0.489289\pi$
$420$	−4.16178	−0.203074
$421$	7.80876	0.380576	0.190288	−	0.981728i	$-0.439058\pi$
$421$	7.80876	0.380576	0.190288	+	0.981728i	$0.439058\pi$
$422$	6.67551	0.324959
$423$	−4.73838	−0.230388
$424$	3.93731	0.191213
$425$	12.3204	0.597629
$426$	−12.5483	−0.607965
$427$	−1.41766	−0.0686052
$428$	5.21949	0.252293
$429$	−1.08980	−0.0526161
$430$	17.1337	0.826260
$431$	−14.2627	−0.687008	−0.343504	−	0.939151i	$-0.611614\pi$
$431$	−14.2627	−0.687008	−0.343504	+	0.939151i	$0.611614\pi$
$432$	1.00000	0.0481125
$433$	−24.8433	−1.19389	−0.596947	−	0.802281i	$-0.703620\pi$
$433$	−24.8433	−1.19389	−0.596947	+	0.802281i	$0.703620\pi$
$434$	−5.14373	−0.246907
$435$	17.7823	0.852597
$436$	3.10600	0.148750
$437$	−1.52994	−0.0731869
$438$	−12.1755	−0.581770
$439$	−10.7010	−0.510729	−0.255364	−	0.966845i	$-0.582195\pi$
$439$	−10.7010	−0.510729	−0.255364	+	0.966845i	$0.582195\pi$
$440$	4.53551	0.216222
$441$	1.00000	0.0476190
$442$	−1.00000	−0.0475651
$443$	12.6936	0.603093	0.301546	−	0.953451i	$-0.402497\pi$
$443$	12.6936	0.603093	0.301546	+	0.953451i	$0.402497\pi$
$444$	9.36559	0.444471
$445$	24.1676	1.14566
$446$	−1.89524	−0.0897421
$447$	12.6378	0.597749
$448$	−1.00000	−0.0472456
$449$	−0.519180	−0.0245016	−0.0122508	−	0.999925i	$-0.503900\pi$
$449$	−0.519180	−0.0245016	−0.0122508	+	0.999925i	$0.503900\pi$
$450$	12.3204	0.580791
$451$	−11.2275	−0.528684
$452$	7.76217	0.365102
$453$	−15.2605	−0.717002
$454$	−15.0019	−0.704075
$455$	4.16178	0.195107
$456$	1.17983	0.0552506
$457$	−32.5851	−1.52427	−0.762133	−	0.647420i	$-0.775848\pi$
$457$	−32.5851	−1.52427	−0.762133	+	0.647420i	$0.775848\pi$
$458$	−2.56615	−0.119908
$459$	1.00000	0.0466760
$460$	−5.39676	−0.251625
$461$	17.1352	0.798064	0.399032	−	0.916937i	$-0.369346\pi$
$461$	17.1352	0.798064	0.399032	+	0.916937i	$0.369346\pi$
$462$	−1.08980	−0.0507021
$463$	4.55193	0.211546	0.105773	−	0.994390i	$-0.466268\pi$
$463$	4.55193	0.211546	0.105773	+	0.994390i	$0.466268\pi$
$464$	4.27277	0.198358
$465$	21.4071	0.992730
$466$	0.588564	0.0272647
$467$	10.5907	0.490077	0.245039	−	0.969513i	$-0.421199\pi$
$467$	10.5907	0.490077	0.245039	+	0.969513i	$0.421199\pi$
$468$	−1.00000	−0.0462250
$469$	12.9657	0.598700
$470$	−19.7201	−0.909620
$471$	16.0190	0.738115
$472$	−10.2397	−0.471320
$473$	4.48662	0.206295
$474$	13.1278	0.602978
$475$	14.5360	0.666958
$476$	−1.00000	−0.0458349
$477$	3.93731	0.180277
$478$	22.3881	1.02401
$479$	−33.1507	−1.51469	−0.757347	−	0.653013i	$-0.773505\pi$
$479$	−33.1507	−1.51469	−0.757347	+	0.653013i	$0.773505\pi$
$480$	4.16178	0.189958
$481$	−9.36559	−0.427034
$482$	9.91684	0.451700
$483$	1.29674	0.0590039
$484$	−9.81233	−0.446015
$485$	−70.1833	−3.18686
$486$	1.00000	0.0453609
$487$	14.8405	0.672487	0.336243	−	0.941775i	$-0.390844\pi$
$487$	14.8405	0.672487	0.336243	+	0.941775i	$0.390844\pi$
$488$	1.41766	0.0641743
$489$	−10.2815	−0.464947
$490$	4.16178	0.188010
$491$	−9.79544	−0.442062	−0.221031	−	0.975267i	$-0.570942\pi$
$491$	−9.79544	−0.442062	−0.221031	+	0.975267i	$0.570942\pi$
$492$	−10.3024	−0.464467
$493$	4.27277	0.192436
$494$	−1.17983	−0.0530831
$495$	4.53551	0.203856
$496$	5.14373	0.230960
$497$	12.5483	0.562866
$498$	−9.59319	−0.429881
$499$	−17.6399	−0.789668	−0.394834	−	0.918752i	$-0.629198\pi$
$499$	−17.6399	−0.789668	−0.394834	+	0.918752i	$0.629198\pi$
$500$	30.4660	1.36248
$501$	19.3710	0.865432
$502$	−8.50834	−0.379746
$503$	−23.8619	−1.06395	−0.531974	−	0.846761i	$-0.678550\pi$
$503$	−23.8619	−1.06395	−0.531974	+	0.846761i	$0.678550\pi$
$504$	−1.00000	−0.0445435
$505$	43.0654	1.91639
$506$	−1.41319	−0.0628241
$507$	1.00000	0.0444116
$508$	14.4582	0.641480
$509$	29.7874	1.32030	0.660152	−	0.751132i	$-0.270492\pi$
$509$	29.7874	1.32030	0.660152	+	0.751132i	$0.270492\pi$
$510$	4.16178	0.184287
$511$	12.1755	0.538614
$512$	1.00000	0.0441942
$513$	1.17983	0.0520908
$514$	7.38556	0.325763
$515$	22.4176	0.987838
$516$	4.11691	0.181237
$517$	−5.16389	−0.227108
$518$	−9.36559	−0.411500
$519$	2.33830	0.102640
$520$	−4.16178	−0.182506
$521$	−33.3510	−1.46114	−0.730568	−	0.682840i	$-0.760745\pi$
$521$	−33.3510	−1.46114	−0.730568	+	0.682840i	$0.760745\pi$
$522$	4.27277	0.187014
$523$	28.2161	1.23380	0.616901	−	0.787041i	$-0.288388\pi$
$523$	28.2161	1.23380	0.616901	+	0.787041i	$0.288388\pi$
$524$	−11.4181	−0.498800
$525$	−12.3204	−0.537708
$526$	−1.19888	−0.0522738
$527$	5.14373	0.224065
$528$	1.08980	0.0474275
$529$	−21.3185	−0.926889
$530$	16.3862	0.711772
$531$	−10.2397	−0.444365
$532$	−1.17983	−0.0511522
$533$	10.3024	0.446246
$534$	5.80704	0.251295
$535$	21.7224	0.939139
$536$	−12.9657	−0.560032
$537$	−21.8961	−0.944886
$538$	−19.6161	−0.845709
$539$	1.08980	0.0469410
$540$	4.16178	0.179095
$541$	3.18995	0.137147	0.0685734	−	0.997646i	$-0.478155\pi$
$541$	3.18995	0.137147	0.0685734	+	0.997646i	$0.478155\pi$
$542$	14.9251	0.641087
$543$	1.42736	0.0612537
$544$	1.00000	0.0428746
$545$	12.9265	0.553710
$546$	1.00000	0.0427960
$547$	−18.6461	−0.797249	−0.398625	−	0.917114i	$-0.630512\pi$
$547$	−18.6461	−0.797249	−0.398625	+	0.917114i	$0.630512\pi$
$548$	2.26399	0.0967130
$549$	1.41766	0.0605041
$550$	13.4268	0.572521
$551$	5.04114	0.214760
$552$	−1.29674	−0.0551931
$553$	−13.1278	−0.558249
$554$	27.2993	1.15983
$555$	38.9775	1.65450
$556$	7.03180	0.298215
$557$	−33.0570	−1.40067	−0.700335	−	0.713814i	$-0.746966\pi$
$557$	−33.0570	−1.40067	−0.700335	+	0.713814i	$0.746966\pi$
$558$	5.14373	0.217752
$559$	−4.11691	−0.174127
$560$	−4.16178	−0.175867
$561$	1.08980	0.0460114
$562$	−20.4085	−0.860882
$563$	−2.91657	−0.122919	−0.0614593	−	0.998110i	$-0.519575\pi$
$563$	−2.91657	−0.122919	−0.0614593	+	0.998110i	$0.519575\pi$
$564$	−4.73838	−0.199522
$565$	32.3045	1.35906
$566$	17.5240	0.736589
$567$	−1.00000	−0.0419961
$568$	−12.5483	−0.526513
$569$	9.91491	0.415655	0.207827	−	0.978166i	$-0.433361\pi$
$569$	9.91491	0.415655	0.207827	+	0.978166i	$0.433361\pi$
$570$	4.91020	0.205666
$571$	18.8091	0.787138	0.393569	−	0.919295i	$-0.371240\pi$
$571$	18.8091	0.787138	0.393569	+	0.919295i	$0.371240\pi$
$572$	−1.08980	−0.0455669
$573$	12.5851	0.525749
$574$	10.3024	0.430013
$575$	−15.9764	−0.666263
$576$	1.00000	0.0416667
$577$	3.64218	0.151626	0.0758129	−	0.997122i	$-0.475845\pi$
$577$	3.64218	0.151626	0.0758129	+	0.997122i	$0.475845\pi$
$578$	1.00000	0.0415945
$579$	−18.9948	−0.789396
$580$	17.7823	0.738370
$581$	9.59319	0.397993
$582$	−16.8638	−0.699026
$583$	4.29088	0.177710
$584$	−12.1755	−0.503827
$585$	−4.16178	−0.172069
$586$	−11.0420	−0.456139
$587$	−31.9328	−1.31801	−0.659004	−	0.752139i	$-0.729022\pi$
$587$	−31.9328	−1.31801	−0.659004	+	0.752139i	$0.729022\pi$
$588$	1.00000	0.0412393
$589$	6.06874	0.250058
$590$	−42.6154	−1.75445
$591$	12.7352	0.523858
$592$	9.36559	0.384923
$593$	3.44486	0.141464	0.0707318	−	0.997495i	$-0.477467\pi$
$593$	3.44486	0.141464	0.0707318	+	0.997495i	$0.477467\pi$
$594$	1.08980	0.0447151
$595$	−4.16178	−0.170616
$596$	12.6378	0.517666
$597$	−14.5129	−0.593972
$598$	1.29674	0.0530278
$599$	−2.97101	−0.121392	−0.0606962	−	0.998156i	$-0.519332\pi$
$599$	−2.97101	−0.121392	−0.0606962	+	0.998156i	$0.519332\pi$
$600$	12.3204	0.502979
$601$	43.5130	1.77493	0.887467	−	0.460872i	$-0.152463\pi$
$601$	43.5130	1.77493	0.887467	+	0.460872i	$0.152463\pi$
$602$	−4.11691	−0.167793
$603$	−12.9657	−0.528004
$604$	−15.2605	−0.620942
$605$	−40.8368	−1.66025
$606$	10.3478	0.420352
$607$	−39.3271	−1.59624	−0.798119	−	0.602500i	$-0.794171\pi$
$607$	−39.3271	−1.59624	−0.798119	+	0.602500i	$0.794171\pi$
$608$	1.17983	0.0478485
$609$	−4.27277	−0.173141
$610$	5.89998	0.238883
$611$	4.73838	0.191694
$612$	1.00000	0.0404226
$613$	−30.6987	−1.23991	−0.619954	−	0.784638i	$-0.712849\pi$
$613$	−30.6987	−1.23991	−0.619954	+	0.784638i	$0.712849\pi$
$614$	−17.6735	−0.713244
$615$	−42.8763	−1.72894
$616$	−1.08980	−0.0439093
$617$	−26.1435	−1.05250	−0.526249	−	0.850331i	$-0.676402\pi$
$617$	−26.1435	−1.05250	−0.526249	+	0.850331i	$0.676402\pi$
$618$	5.38654	0.216678
$619$	34.7144	1.39529	0.697644	−	0.716444i	$-0.254232\pi$
$619$	34.7144	1.39529	0.697644	+	0.716444i	$0.254232\pi$
$620$	21.4071	0.859730
$621$	−1.29674	−0.0520365
$622$	−13.2464	−0.531131
$623$	−5.80704	−0.232654
$624$	−1.00000	−0.0400320
$625$	65.1908	2.60763
$626$	17.0456	0.681279
$627$	1.28578	0.0513491
$628$	16.0190	0.639226
$629$	9.36559	0.373430
$630$	−4.16178	−0.165809
$631$	−28.2744	−1.12559	−0.562793	−	0.826598i	$-0.690273\pi$
$631$	−28.2744	−1.12559	−0.562793	+	0.826598i	$0.690273\pi$
$632$	13.1278	0.522194
$633$	6.67551	0.265328
$634$	−12.3439	−0.490238
$635$	60.1720	2.38785
$636$	3.93731	0.156125
$637$	−1.00000	−0.0396214
$638$	4.65646	0.184351
$639$	−12.5483	−0.496402
$640$	4.16178	0.164509
$641$	−4.92139	−0.194383	−0.0971917	−	0.995266i	$-0.530986\pi$
$641$	−4.92139	−0.194383	−0.0971917	+	0.995266i	$0.530986\pi$
$642$	5.21949	0.205997
$643$	7.55710	0.298023	0.149011	−	0.988835i	$-0.452391\pi$
$643$	7.55710	0.298023	0.149011	+	0.988835i	$0.452391\pi$
$644$	1.29674	0.0510989
$645$	17.1337	0.674638
$646$	1.17983	0.0464198
$647$	−15.4751	−0.608390	−0.304195	−	0.952610i	$-0.598387\pi$
$647$	−15.4751	−0.608390	−0.304195	+	0.952610i	$0.598387\pi$
$648$	1.00000	0.0392837
$649$	−11.1592	−0.438038
$650$	−12.3204	−0.483247
$651$	−5.14373	−0.201599
$652$	−10.2815	−0.402656
$653$	20.8017	0.814033	0.407017	−	0.913421i	$-0.366569\pi$
$653$	20.8017	0.814033	0.407017	+	0.913421i	$0.366569\pi$
$654$	3.10600	0.121454
$655$	−47.5195	−1.85674
$656$	−10.3024	−0.402240
$657$	−12.1755	−0.475013
$658$	4.73838	0.184721
$659$	13.5672	0.528503	0.264252	−	0.964454i	$-0.414875\pi$
$659$	13.5672	0.528503	0.264252	+	0.964454i	$0.414875\pi$
$660$	4.53551	0.176545
$661$	11.7906	0.458602	0.229301	−	0.973356i	$-0.426356\pi$
$661$	11.7906	0.458602	0.229301	+	0.973356i	$0.426356\pi$
$662$	5.80722	0.225704
$663$	−1.00000	−0.0388368
$664$	−9.59319	−0.372288
$665$	−4.91020	−0.190409
$666$	9.36559	0.362909
$667$	−5.54068	−0.214536
$668$	19.3710	0.749486
$669$	−1.89524	−0.0732741
$670$	−53.9604	−2.08467
$671$	1.54496	0.0596427
$672$	−1.00000	−0.0385758
$673$	−0.590538	−0.0227636	−0.0113818	−	0.999935i	$-0.503623\pi$
$673$	−0.590538	−0.0227636	−0.0113818	+	0.999935i	$0.503623\pi$
$674$	−10.7140	−0.412690
$675$	12.3204	0.474213
$676$	1.00000	0.0384615
$677$	26.5973	1.02222	0.511109	−	0.859516i	$-0.329235\pi$
$677$	26.5973	1.02222	0.511109	+	0.859516i	$0.329235\pi$
$678$	7.76217	0.298104
$679$	16.8638	0.647172
$680$	4.16178	0.159597
$681$	−15.0019	−0.574875
$682$	5.60564	0.214651
$683$	−45.9386	−1.75779	−0.878896	−	0.477014i	$-0.841719\pi$
$683$	−45.9386	−1.75779	−0.878896	+	0.477014i	$0.841719\pi$
$684$	1.17983	0.0451120
$685$	9.42225	0.360006
$686$	−1.00000	−0.0381802
$687$	−2.56615	−0.0979046
$688$	4.11691	0.156956
$689$	−3.93731	−0.150000
$690$	−5.39676	−0.205451
$691$	−46.2924	−1.76105	−0.880523	−	0.474004i	$-0.842808\pi$
$691$	−46.2924	−1.76105	−0.880523	+	0.474004i	$0.842808\pi$
$692$	2.33830	0.0888887
$693$	−1.08980	−0.0413981
$694$	0.148004	0.00561815
$695$	29.2648	1.11008
$696$	4.27277	0.161959
$697$	−10.3024	−0.390230
$698$	−26.5625	−1.00541
$699$	0.588564	0.0222615
$700$	−12.3204	−0.465668
$701$	−22.5163	−0.850427	−0.425214	−	0.905093i	$-0.639801\pi$
$701$	−22.5163	−0.850427	−0.425214	+	0.905093i	$0.639801\pi$
$702$	−1.00000	−0.0377426
$703$	11.0498	0.416752
$704$	1.08980	0.0410734
$705$	−19.7201	−0.742702
$706$	5.70530	0.214722
$707$	−10.3478	−0.389170
$708$	−10.2397	−0.384831
$709$	−39.8461	−1.49645	−0.748226	−	0.663444i	$-0.769094\pi$
$709$	−39.8461	−1.49645	−0.748226	+	0.663444i	$0.769094\pi$
$710$	−52.2231	−1.95990
$711$	13.1278	0.492330
$712$	5.80704	0.217628
$713$	−6.67010	−0.249797
$714$	−1.00000	−0.0374241
$715$	−4.53551	−0.169619
$716$	−21.8961	−0.818296
$717$	22.3881	0.836100
$718$	9.13369	0.340866
$719$	−17.4258	−0.649872	−0.324936	−	0.945736i	$-0.605343\pi$
$719$	−17.4258	−0.649872	−0.324936	+	0.945736i	$0.605343\pi$
$720$	4.16178	0.155100
$721$	−5.38654	−0.200605
$722$	−17.6080	−0.655302
$723$	9.91684	0.368811
$724$	1.42736	0.0530473
$725$	52.6423	1.95509
$726$	−9.81233	−0.364170
$727$	−45.3102	−1.68046	−0.840231	−	0.542228i	$-0.817581\pi$
$727$	−45.3102	−1.68046	−0.840231	+	0.542228i	$0.817581\pi$
$728$	1.00000	0.0370625
$729$	1.00000	0.0370370
$730$	−50.6719	−1.87545
$731$	4.11691	0.152270
$732$	1.41766	0.0523981
$733$	32.9523	1.21712	0.608560	−	0.793508i	$-0.291748\pi$
$733$	32.9523	1.21712	0.608560	+	0.793508i	$0.291748\pi$
$734$	−2.44262	−0.0901588
$735$	4.16178	0.153510
$736$	−1.29674	−0.0477986
$737$	−14.1300	−0.520486
$738$	−10.3024	−0.379236
$739$	29.3081	1.07811	0.539057	−	0.842269i	$-0.318781\pi$
$739$	29.3081	1.07811	0.539057	+	0.842269i	$0.318781\pi$
$740$	38.9775	1.43284
$741$	−1.17983	−0.0433422
$742$	−3.93731	−0.144543
$743$	11.0197	0.404274	0.202137	−	0.979357i	$-0.435211\pi$
$743$	11.0197	0.404274	0.202137	+	0.979357i	$0.435211\pi$
$744$	5.14373	0.188578
$745$	52.5959	1.92696
$746$	2.96338	0.108497
$747$	−9.59319	−0.350997
$748$	1.08980	0.0398471
$749$	−5.21949	−0.190716
$750$	30.4660	1.11246
$751$	−51.2537	−1.87028	−0.935138	−	0.354284i	$-0.884725\pi$
$751$	−51.2537	−1.87028	−0.935138	+	0.354284i	$0.884725\pi$
$752$	−4.73838	−0.172791
$753$	−8.50834	−0.310061
$754$	−4.27277	−0.155605
$755$	−63.5110	−2.31140
$756$	−1.00000	−0.0363696
$757$	−0.832320	−0.0302512	−0.0151256	−	0.999886i	$-0.504815\pi$
$757$	−0.832320	−0.0302512	−0.0151256	+	0.999886i	$0.504815\pi$
$758$	11.5342	0.418941
$759$	−1.41319	−0.0512956
$760$	4.91020	0.178112
$761$	44.2231	1.60309	0.801543	−	0.597938i	$-0.204013\pi$
$761$	44.2231	1.60309	0.801543	+	0.597938i	$0.204013\pi$
$762$	14.4582	0.523766
$763$	−3.10600	−0.112445
$764$	12.5851	0.455312
$765$	4.16178	0.150470
$766$	2.78040	0.100460
$767$	10.2397	0.369734
$768$	1.00000	0.0360844
$769$	−41.8931	−1.51070	−0.755352	−	0.655320i	$-0.772534\pi$
$769$	−41.8931	−1.51070	−0.755352	+	0.655320i	$0.772534\pi$
$770$	−4.53551	−0.163449
$771$	7.38556	0.265984
$772$	−18.9948	−0.683637
$773$	13.7093	0.493090	0.246545	−	0.969131i	$-0.420705\pi$
$773$	13.7093	0.493090	0.246545	+	0.969131i	$0.420705\pi$
$774$	4.11691	0.147979
$775$	63.3730	2.27642
$776$	−16.8638	−0.605374
$777$	−9.36559	−0.335989
$778$	−28.8416	−1.03402
$779$	−12.1551	−0.435500
$780$	−4.16178	−0.149016
$781$	−13.6751	−0.489334
$782$	−1.29674	−0.0463715
$783$	4.27277	0.152696
$784$	1.00000	0.0357143
$785$	66.6675	2.37946
$786$	−11.4181	−0.407269
$787$	−20.6274	−0.735288	−0.367644	−	0.929967i	$-0.619835\pi$
$787$	−20.6274	−0.735288	−0.367644	+	0.929967i	$0.619835\pi$
$788$	12.7352	0.453674
$789$	−1.19888	−0.0426814
$790$	54.6349	1.94382
$791$	−7.76217	−0.275991
$792$	1.08980	0.0387244
$793$	−1.41766	−0.0503425
$794$	−4.86912	−0.172799
$795$	16.3862	0.581160
$796$	−14.5129	−0.514395
$797$	−7.63275	−0.270366	−0.135183	−	0.990821i	$-0.543162\pi$
$797$	−7.63275	−0.270366	−0.135183	+	0.990821i	$0.543162\pi$
$798$	−1.17983	−0.0417656
$799$	−4.73838	−0.167632
$800$	12.3204	0.435593
$801$	5.80704	0.205182
$802$	29.8641	1.05454
$803$	−13.2689	−0.468250
$804$	−12.9657	−0.457265
$805$	5.39676	0.190211
$806$	−5.14373	−0.181180
$807$	−19.6161	−0.690519
$808$	10.3478	0.364035
$809$	43.0295	1.51284	0.756419	−	0.654087i	$-0.226947\pi$
$809$	43.0295	1.51284	0.756419	+	0.654087i	$0.226947\pi$
$810$	4.16178	0.146230
$811$	17.2846	0.606944	0.303472	−	0.952840i	$-0.401854\pi$
$811$	17.2846	0.606944	0.303472	+	0.952840i	$0.401854\pi$
$812$	−4.27277	−0.149945
$813$	14.9251	0.523445
$814$	10.2066	0.357742
$815$	−42.7895	−1.49885
$816$	1.00000	0.0350070
$817$	4.85726	0.169934
$818$	24.4849	0.856096
$819$	1.00000	0.0349428
$820$	−42.8763	−1.49730
$821$	−37.5694	−1.31118	−0.655591	−	0.755116i	$-0.727581\pi$
$821$	−37.5694	−1.31118	−0.655591	+	0.755116i	$0.727581\pi$
$822$	2.26399	0.0789659
$823$	4.40876	0.153680	0.0768398	−	0.997043i	$-0.475517\pi$
$823$	4.40876	0.153680	0.0768398	+	0.997043i	$0.475517\pi$
$824$	5.38654	0.187649
$825$	13.4268	0.467462
$826$	10.2397	0.356284
$827$	−39.5437	−1.37507	−0.687534	−	0.726152i	$-0.741307\pi$
$827$	−39.5437	−1.37507	−0.687534	+	0.726152i	$0.741307\pi$
$828$	−1.29674	−0.0450650
$829$	45.6325	1.58488	0.792441	−	0.609948i	$-0.208810\pi$
$829$	45.6325	1.58488	0.792441	+	0.609948i	$0.208810\pi$
$830$	−39.9248	−1.38581
$831$	27.2993	0.947001
$832$	−1.00000	−0.0346688
$833$	1.00000	0.0346479
$834$	7.03180	0.243491
$835$	80.6179	2.78990
$836$	1.28578	0.0444697
$837$	5.14373	0.177793
$838$	1.37727	0.0475769
$839$	−30.0243	−1.03655	−0.518277	−	0.855213i	$-0.673426\pi$
$839$	−30.0243	−1.03655	−0.518277	+	0.855213i	$0.673426\pi$
$840$	−4.16178	−0.143595
$841$	−10.7435	−0.370465
$842$	7.80876	0.269108
$843$	−20.4085	−0.702907
$844$	6.67551	0.229780
$845$	4.16178	0.143170
$846$	−4.73838	−0.162909
$847$	9.81233	0.337156
$848$	3.93731	0.135208
$849$	17.5240	0.601422
$850$	12.3204	0.422587
$851$	−12.1448	−0.416317
$852$	−12.5483	−0.429896
$853$	−36.8659	−1.26227	−0.631133	−	0.775675i	$-0.717410\pi$
$853$	−36.8659	−1.26227	−0.631133	+	0.775675i	$0.717410\pi$
$854$	−1.41766	−0.0485112
$855$	4.91020	0.167925
$856$	5.21949	0.178398
$857$	47.1675	1.61121	0.805606	−	0.592451i	$-0.201840\pi$
$857$	47.1675	1.61121	0.805606	+	0.592451i	$0.201840\pi$
$858$	−1.08980	−0.0372052
$859$	2.33299	0.0796006	0.0398003	−	0.999208i	$-0.487328\pi$
$859$	2.33299	0.0796006	0.0398003	+	0.999208i	$0.487328\pi$
$860$	17.1337	0.584254
$861$	10.3024	0.351104
$862$	−14.2627	−0.485788
$863$	55.4542	1.88768	0.943841	−	0.330400i	$-0.107184\pi$
$863$	55.4542	1.88768	0.943841	+	0.330400i	$0.107184\pi$
$864$	1.00000	0.0340207
$865$	9.73148	0.330880
$866$	−24.8433	−0.844211
$867$	1.00000	0.0339618
$868$	−5.14373	−0.174590
$869$	14.3066	0.485320
$870$	17.7823	0.602877
$871$	12.9657	0.439326
$872$	3.10600	0.105182
$873$	−16.8638	−0.570752
$874$	−1.52994	−0.0517509
$875$	−30.4660	−1.02994
$876$	−12.1755	−0.411373
$877$	6.94701	0.234584	0.117292	−	0.993097i	$-0.462579\pi$
$877$	6.94701	0.234584	0.117292	+	0.993097i	$0.462579\pi$
$878$	−10.7010	−0.361140
$879$	−11.0420	−0.372436
$880$	4.53551	0.152892
$881$	27.4761	0.925694	0.462847	−	0.886438i	$-0.346828\pi$
$881$	27.4761	0.925694	0.462847	+	0.886438i	$0.346828\pi$
$882$	1.00000	0.0336718
$883$	50.5838	1.70228	0.851140	−	0.524938i	$-0.175912\pi$
$883$	50.5838	1.70228	0.851140	+	0.524938i	$0.175912\pi$
$884$	−1.00000	−0.0336336
$885$	−42.6154	−1.43250
$886$	12.6936	0.426451
$887$	−22.9917	−0.771987	−0.385993	−	0.922502i	$-0.626141\pi$
$887$	−22.9917	−0.771987	−0.385993	+	0.922502i	$0.626141\pi$
$888$	9.36559	0.314289
$889$	−14.4582	−0.484914
$890$	24.1676	0.810101
$891$	1.08980	0.0365097
$892$	−1.89524	−0.0634573
$893$	−5.59048	−0.187078
$894$	12.6378	0.422672
$895$	−91.1268	−3.04603
$896$	−1.00000	−0.0334077
$897$	1.29674	0.0432970
$898$	−0.519180	−0.0173253
$899$	21.9780	0.733006
$900$	12.3204	0.410681
$901$	3.93731	0.131171
$902$	−11.2275	−0.373836
$903$	−4.11691	−0.137002
$904$	7.76217	0.258166
$905$	5.94034	0.197464
$906$	−15.2605	−0.506997
$907$	−38.5111	−1.27874	−0.639370	−	0.768899i	$-0.720805\pi$
$907$	−38.5111	−1.27874	−0.639370	+	0.768899i	$0.720805\pi$
$908$	−15.0019	−0.497856
$909$	10.3478	0.343216
$910$	4.16178	0.137962
$911$	21.5701	0.714650	0.357325	−	0.933980i	$-0.383689\pi$
$911$	21.5701	0.714650	0.357325	+	0.933980i	$0.383689\pi$
$912$	1.17983	0.0390681
$913$	−10.4547	−0.345999
$914$	−32.5851	−1.07782
$915$	5.89998	0.195047
$916$	−2.56615	−0.0847879
$917$	11.4181	0.377057
$918$	1.00000	0.0330049
$919$	−0.677952	−0.0223636	−0.0111818	−	0.999937i	$-0.503559\pi$
$919$	−0.677952	−0.0223636	−0.0111818	+	0.999937i	$0.503559\pi$
$920$	−5.39676	−0.177926
$921$	−17.6735	−0.582361
$922$	17.1352	0.564317
$923$	12.5483	0.413031
$924$	−1.08980	−0.0358518
$925$	115.388	3.79394
$926$	4.55193	0.149586
$927$	5.38654	0.176917
$928$	4.27277	0.140260
$929$	−19.5710	−0.642103	−0.321052	−	0.947062i	$-0.604036\pi$
$929$	−19.5710	−0.642103	−0.321052	+	0.947062i	$0.604036\pi$
$930$	21.4071	0.701966
$931$	1.17983	0.0386674
$932$	0.588564	0.0192791
$933$	−13.2464	−0.433667
$934$	10.5907	0.346537
$935$	4.53551	0.148327
$936$	−1.00000	−0.0326860
$937$	27.4217	0.895829	0.447915	−	0.894076i	$-0.352167\pi$
$937$	27.4217	0.895829	0.447915	+	0.894076i	$0.352167\pi$
$938$	12.9657	0.423345
$939$	17.0456	0.556262
$940$	−19.7201	−0.643198
$941$	−31.2045	−1.01724	−0.508618	−	0.860992i	$-0.669844\pi$
$941$	−31.2045	−1.01724	−0.508618	+	0.860992i	$0.669844\pi$
$942$	16.0190	0.521926
$943$	13.3595	0.435047
$944$	−10.2397	−0.333274
$945$	−4.16178	−0.135383
$946$	4.48662	0.145872
$947$	18.5251	0.601983	0.300992	−	0.953627i	$-0.402682\pi$
$947$	18.5251	0.601983	0.300992	+	0.953627i	$0.402682\pi$
$948$	13.1278	0.426370
$949$	12.1755	0.395235
$950$	14.5360	0.471611
$951$	−12.3439	−0.400278
$952$	−1.00000	−0.0324102
$953$	−24.5464	−0.795136	−0.397568	−	0.917573i	$-0.630146\pi$
$953$	−24.5464	−0.795136	−0.397568	+	0.917573i	$0.630146\pi$
$954$	3.93731	0.127475
$955$	52.3763	1.69486
$956$	22.3881	0.724083
$957$	4.65646	0.150522
$958$	−33.1507	−1.07105
$959$	−2.26399	−0.0731082
$960$	4.16178	0.134321
$961$	−4.54201	−0.146517
$962$	−9.36559	−0.301959
$963$	5.21949	0.168196
$964$	9.91684	0.319400
$965$	−79.0521	−2.54478
$966$	1.29674	0.0417220
$967$	−17.0857	−0.549438	−0.274719	−	0.961525i	$-0.588585\pi$
$967$	−17.0857	−0.549438	−0.274719	+	0.961525i	$0.588585\pi$
$968$	−9.81233	−0.315380
$969$	1.17983	0.0379016
$970$	−70.1833	−2.25345
$971$	−28.9920	−0.930396	−0.465198	−	0.885207i	$-0.654017\pi$
$971$	−28.9920	−0.930396	−0.465198	+	0.885207i	$0.654017\pi$
$972$	1.00000	0.0320750
$973$	−7.03180	−0.225429
$974$	14.8405	0.475520
$975$	−12.3204	−0.394569
$976$	1.41766	0.0453781
$977$	59.6170	1.90732	0.953658	−	0.300893i	$-0.0972847\pi$
$977$	59.6170	1.90732	0.953658	+	0.300893i	$0.0972847\pi$
$978$	−10.2815	−0.328767
$979$	6.32852	0.202260
$980$	4.16178	0.132943
$981$	3.10600	0.0991669
$982$	−9.79544	−0.312585
$983$	−54.8771	−1.75031	−0.875154	−	0.483844i	$-0.839240\pi$
$983$	−54.8771	−1.75031	−0.875154	+	0.483844i	$0.839240\pi$
$984$	−10.3024	−0.328428
$985$	53.0013	1.68876
$986$	4.27277	0.136073
$987$	4.73838	0.150824
$988$	−1.17983	−0.0375354
$989$	−5.33858	−0.169757
$990$	4.53551	0.144148
$991$	15.0562	0.478275	0.239137	−	0.970986i	$-0.423135\pi$
$991$	15.0562	0.478275	0.239137	+	0.970986i	$0.423135\pi$
$992$	5.14373	0.163314
$993$	5.80722	0.184287
$994$	12.5483	0.398007
$995$	−60.3994	−1.91479
$996$	−9.59319	−0.303972
$997$	−3.28467	−0.104027	−0.0520133	−	0.998646i	$-0.516564\pi$
$997$	−3.28467	−0.104027	−0.0520133	+	0.998646i	$0.516564\pi$
$998$	−17.6399	−0.558380
$999$	9.36559	0.296314

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9282.2.a.ce.1.7	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9282.2.a.ce.1.7	✓	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:	\( N \)	\(=\)	\( 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9282.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.16178 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.16178 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.16178 q^{10} +1.08980 q^{11} +1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{14} +4.16178 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +1.17983 q^{19} +4.16178 q^{20} -1.00000 q^{21} +1.08980 q^{22} -1.29674 q^{23} +1.00000 q^{24} +12.3204 q^{25} -1.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} +4.27277 q^{29} +4.16178 q^{30} +5.14373 q^{31} +1.00000 q^{32} +1.08980 q^{33} +1.00000 q^{34} -4.16178 q^{35} +1.00000 q^{36} +9.36559 q^{37} +1.17983 q^{38} -1.00000 q^{39} +4.16178 q^{40} -10.3024 q^{41} -1.00000 q^{42} +4.11691 q^{43} +1.08980 q^{44} +4.16178 q^{45} -1.29674 q^{46} -4.73838 q^{47} +1.00000 q^{48} +1.00000 q^{49} +12.3204 q^{50} +1.00000 q^{51} -1.00000 q^{52} +3.93731 q^{53} +1.00000 q^{54} +4.53551 q^{55} -1.00000 q^{56} +1.17983 q^{57} +4.27277 q^{58} -10.2397 q^{59} +4.16178 q^{60} +1.41766 q^{61} +5.14373 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.16178 q^{65} +1.08980 q^{66} -12.9657 q^{67} +1.00000 q^{68} -1.29674 q^{69} -4.16178 q^{70} -12.5483 q^{71} +1.00000 q^{72} -12.1755 q^{73} +9.36559 q^{74} +12.3204 q^{75} +1.17983 q^{76} -1.08980 q^{77} -1.00000 q^{78} +13.1278 q^{79} +4.16178 q^{80} +1.00000 q^{81} -10.3024 q^{82} -9.59319 q^{83} -1.00000 q^{84} +4.16178 q^{85} +4.11691 q^{86} +4.27277 q^{87} +1.08980 q^{88} +5.80704 q^{89} +4.16178 q^{90} +1.00000 q^{91} -1.29674 q^{92} +5.14373 q^{93} -4.73838 q^{94} +4.91020 q^{95} +1.00000 q^{96} -16.8638 q^{97} +1.00000 q^{98} +1.08980 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 3 q^{5} + 7 q^{6} - 7 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + 3 * q^5 + 7 * q^6 - 7 * q^7 + 7 * q^8 + 7 * q^9	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 3 q^{5} + 7 q^{6} - 7 q^{7} + 7 q^{8} + 7 q^{9} + 3 q^{10} + 7 q^{11} + 7 q^{12} - 7 q^{13} - 7 q^{14} + 3 q^{15} + 7 q^{16} + 7 q^{17} + 7 q^{18} - 2 q^{19} + 3 q^{20} - 7 q^{21} + 7 q^{22} + 12 q^{23} + 7 q^{24} + 20 q^{25} - 7 q^{26} + 7 q^{27} - 7 q^{28} + 18 q^{29} + 3 q^{30} - 6 q^{31} + 7 q^{32} + 7 q^{33} + 7 q^{34} - 3 q^{35} + 7 q^{36} + 5 q^{37} - 2 q^{38} - 7 q^{39} + 3 q^{40} + 10 q^{41} - 7 q^{42} + 18 q^{43} + 7 q^{44} + 3 q^{45} + 12 q^{46} + 3 q^{47} + 7 q^{48} + 7 q^{49} + 20 q^{50} + 7 q^{51} - 7 q^{52} + 18 q^{53} + 7 q^{54} + 4 q^{55} - 7 q^{56} - 2 q^{57} + 18 q^{58} + 20 q^{59} + 3 q^{60} + 19 q^{61} - 6 q^{62} - 7 q^{63} + 7 q^{64} - 3 q^{65} + 7 q^{66} - 16 q^{67} + 7 q^{68} + 12 q^{69} - 3 q^{70} + 5 q^{71} + 7 q^{72} + 2 q^{73} + 5 q^{74} + 20 q^{75} - 2 q^{76} - 7 q^{77} - 7 q^{78} + 12 q^{79} + 3 q^{80} + 7 q^{81} + 10 q^{82} + 11 q^{83} - 7 q^{84} + 3 q^{85} + 18 q^{86} + 18 q^{87} + 7 q^{88} + 6 q^{89} + 3 q^{90} + 7 q^{91} + 12 q^{92} - 6 q^{93} + 3 q^{94} + 35 q^{95} + 7 q^{96} - 3 q^{97} + 7 q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + 3 * q^5 + 7 * q^6 - 7 * q^7 + 7 * q^8 + 7 * q^9 + 3 * q^10 + 7 * q^11 + 7 * q^12 - 7 * q^13 - 7 * q^14 + 3 * q^15 + 7 * q^16 + 7 * q^17 + 7 * q^18 - 2 * q^19 + 3 * q^20 - 7 * q^21 + 7 * q^22 + 12 * q^23 + 7 * q^24 + 20 * q^25 - 7 * q^26 + 7 * q^27 - 7 * q^28 + 18 * q^29 + 3 * q^30 - 6 * q^31 + 7 * q^32 + 7 * q^33 + 7 * q^34 - 3 * q^35 + 7 * q^36 + 5 * q^37 - 2 * q^38 - 7 * q^39 + 3 * q^40 + 10 * q^41 - 7 * q^42 + 18 * q^43 + 7 * q^44 + 3 * q^45 + 12 * q^46 + 3 * q^47 + 7 * q^48 + 7 * q^49 + 20 * q^50 + 7 * q^51 - 7 * q^52 + 18 * q^53 + 7 * q^54 + 4 * q^55 - 7 * q^56 - 2 * q^57 + 18 * q^58 + 20 * q^59 + 3 * q^60 + 19 * q^61 - 6 * q^62 - 7 * q^63 + 7 * q^64 - 3 * q^65 + 7 * q^66 - 16 * q^67 + 7 * q^68 + 12 * q^69 - 3 * q^70 + 5 * q^71 + 7 * q^72 + 2 * q^73 + 5 * q^74 + 20 * q^75 - 2 * q^76 - 7 * q^77 - 7 * q^78 + 12 * q^79 + 3 * q^80 + 7 * q^81 + 10 * q^82 + 11 * q^83 - 7 * q^84 + 3 * q^85 + 18 * q^86 + 18 * q^87 + 7 * q^88 + 6 * q^89 + 3 * q^90 + 7 * q^91 + 12 * q^92 - 6 * q^93 + 3 * q^94 + 35 * q^95 + 7 * q^96 - 3 * q^97 + 7 * q^98 + 7 * q^99

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